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Worked example: Calculating E° using standard reduction potentials | https://www.youtube.com/watch?v=PNolxY6rOKk | vtt | https://www.youtube.com/api/timedtext?v=PNolxY6rOKk&ei=ylWUZby-INOKp-oPl8SXmAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=73FE0066445C24E6090F48DFC035500D1515E4B3.4676EB1B352D0B1039D8445D22BCD6B46888976F&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:02.210
- [Instructor] Let's do a worked example
00:00:02.210 --> 00:00:04.910
where we calculate the standard potential
00:00:04.910 --> 00:00:09.640
at 25 degrees Celsius for this reaction.
00:00:09.640 --> 00:00:11.020
In this redox reaction,
00:00:11.020 --> 00:00:14.950
silver cations are reduced
to form solid silver
00:00:14.950 --> 00:00:19.950
and solid chromium is
oxidized to form the Cr3+ ion.
00:00:20.160 --> 00:00:22.980
The first step is to write
down the half reactions
00:00:22.980 --> 00:00:26.060
that make up the overall redox reaction.
00:00:26.060 --> 00:00:29.360
So we said that silver
cations are reduced,
00:00:29.360 --> 00:00:31.100
therefore we need to gain the electron
00:00:31.100 --> 00:00:34.270
to turn into solid
silver and solid chromium
00:00:34.270 --> 00:00:38.610
to turn into chromium 3+ ions
must lose three electrons.
00:00:38.610 --> 00:00:41.900
Next, we need to find
the standard voltages
00:00:41.900 --> 00:00:43.800
for our two half reactions.
00:00:43.800 --> 00:00:44.633
And to do that,
00:00:44.633 --> 00:00:48.210
we could consult a standard
reduction potential table,
00:00:48.210 --> 00:00:50.790
and here's our table that
shows standard reduction
00:00:50.790 --> 00:00:53.450
potentials for some
reduction half reactions
00:00:53.450 --> 00:00:55.920
at 25 degrees Celsius.
00:00:55.920 --> 00:00:57.840
The standard reduction potentials
00:00:57.840 --> 00:01:00.500
or standard reduction voltages
for these half reactions
00:01:00.500 --> 00:01:05.064
are all compared to the
reduction of H+ ion.
00:01:05.064 --> 00:01:08.740
So two H+ plus two electrons
forming hydrogen gas
00:01:08.740 --> 00:01:12.840
has a standard reduction
potential of exactly zero volts.
00:01:12.840 --> 00:01:15.270
For our particular redox reaction,
00:01:15.270 --> 00:01:17.330
we need to know the reduction potential
00:01:17.330 --> 00:01:21.150
for the reduction of silver
cations to form solid silver.
00:01:21.150 --> 00:01:24.010
The standard reduction
potential for this half reaction
00:01:24.010 --> 00:01:27.330
is equal to positive 0.80 volts.
00:01:27.330 --> 00:01:30.180
The other half reaction that
we need to know about involves
00:01:30.180 --> 00:01:34.380
the oxidation of solid chromium
to chromium 3+ cations.
00:01:34.380 --> 00:01:37.410
But since this is a standard
reduction potential table,
00:01:37.410 --> 00:01:41.760
the half reaction is written
as a reduction half reaction.
00:01:41.760 --> 00:01:44.580
The standard reduction
potential for this half reaction
00:01:44.580 --> 00:01:48.000
is negative 0.74 volts.
00:01:48.000 --> 00:01:50.100
But since we need this
half reaction written
00:01:50.100 --> 00:01:52.300
as an oxidation half reaction,
00:01:52.300 --> 00:01:56.190
if we were to reverse this half
reaction, how it's written,
00:01:56.190 --> 00:01:59.190
we would need to change
the sign of the voltage.
00:01:59.190 --> 00:02:02.160
So the standard oxidation potential
00:02:02.160 --> 00:02:05.740
would be positive 0.74 volts.
00:02:05.740 --> 00:02:08.410
So I've gone ahead and
written in the voltages
00:02:08.410 --> 00:02:10.200
for our half reactions.
00:02:10.200 --> 00:02:13.030
The standard reduction
potential for our half reaction
00:02:13.030 --> 00:02:15.170
was positive 0.80 volts,
00:02:15.170 --> 00:02:18.450
and the standard oxidation
potential for our half reaction
00:02:18.450 --> 00:02:21.370
is positive 0.74 volts.
00:02:21.370 --> 00:02:24.620
Our next step is to make the
number of electrons equal
00:02:24.620 --> 00:02:27.930
for our two half reactions
and add them together.
00:02:27.930 --> 00:02:30.470
For our oxidation half reaction,
00:02:30.470 --> 00:02:32.210
we're losing three electrons,
00:02:32.210 --> 00:02:34.330
but for our reduction half reaction,
00:02:34.330 --> 00:02:36.420
we're only gaining one electron.
00:02:36.420 --> 00:02:39.060
Therefore we need to
multiply everything through
00:02:39.060 --> 00:02:42.550
in our reduction half reaction by three,
00:02:42.550 --> 00:02:47.550
that gives us 3Ag+ plus
three electrons goes to 3Ag.
00:02:48.020 --> 00:02:50.600
Notice that even though
we multiplied everything
00:02:50.600 --> 00:02:54.010
through in our reduction half
reaction by a factor of three,
00:02:54.010 --> 00:02:57.100
we did not multiply the
standard reduction potential
00:02:57.100 --> 00:02:58.660
by a factor of three.
00:02:58.660 --> 00:03:02.560
And that's because voltage
is an intensive property
00:03:02.560 --> 00:03:06.220
and doesn't depend on
the amount of substance.
00:03:06.220 --> 00:03:08.820
So it doesn't matter if we're
talking about the reduction
00:03:08.820 --> 00:03:10.320
of one mole of silver cations,
00:03:10.320 --> 00:03:13.660
or three moles of silver cations.
00:03:13.660 --> 00:03:16.380
The standard reduction
potential is the same
00:03:16.380 --> 00:03:19.240
for both half reactions.
00:03:19.240 --> 00:03:22.100
And when we add our two
half reactions together,
00:03:22.100 --> 00:03:24.040
so here are all of the reactants
00:03:24.040 --> 00:03:27.410
and then over here would
be all of the products.
00:03:27.410 --> 00:03:30.540
The three electrons would
cancel out on both sides
00:03:30.540 --> 00:03:33.680
and give us 3Ag+ plus solid chromium
00:03:33.680 --> 00:03:37.440
goes to 3Ag plus Cr3+,
00:03:37.440 --> 00:03:41.390
which gives us back our
original redox reaction.
00:03:41.390 --> 00:03:43.960
And since we were able to
add our two half reactions
00:03:43.960 --> 00:03:47.380
together and get our
overall redox reaction,
00:03:47.380 --> 00:03:51.420
to find the standard
voltage for this reaction,
00:03:51.420 --> 00:03:54.250
we should be able to add
together the voltages
00:03:54.250 --> 00:03:56.760
for the two half reactions.
00:03:56.760 --> 00:04:01.760
So positive 0.8 plus 0.74 is
equal to positive 1.54 volts.
00:04:05.450 --> 00:04:08.700
So the standard potential
for this redox reaction
00:04:08.700 --> 00:04:13.623
at 25 degrees Celsius is
equal to positive 1.54 volts.
00:04:14.580 --> 00:04:17.470
There's another way to
calculate the standard potential
00:04:17.470 --> 00:04:19.250
for this redox reaction,
00:04:19.250 --> 00:04:23.200
and this way only uses
standard reduction potentials.
00:04:23.200 --> 00:04:26.050
So to calculate the standard potential
00:04:26.050 --> 00:04:27.890
for the redox reaction,
00:04:27.890 --> 00:04:30.290
we take the standard reduction potential
00:04:30.290 --> 00:04:32.170
for the reduction process
00:04:32.170 --> 00:04:35.920
and from that we subtract the
standard reduction potential
00:04:35.920 --> 00:04:38.550
for the oxidation process.
00:04:38.550 --> 00:04:40.850
So for our reduction half reaction
00:04:40.850 --> 00:04:42.970
the standard reduction potential
00:04:42.970 --> 00:04:45.860
is equal to positive 0.80 volts.
00:04:45.860 --> 00:04:48.260
So we'd plug that into our equation
00:04:48.260 --> 00:04:50.210
for the reduction process.
00:04:50.210 --> 00:04:53.330
And for our oxidation half reaction,
00:04:53.330 --> 00:04:55.530
the standard reduction potential,
00:04:55.530 --> 00:04:58.830
if you remember from the standard
reduction potential table
00:04:58.830 --> 00:05:01.900
is equal to negative 0.74 volts.
00:05:01.900 --> 00:05:04.440
So that would get
plugged into our equation
00:05:04.440 --> 00:05:06.900
for the oxidation process.
00:05:06.900 --> 00:05:08.920
And when we plug in our voltages,
00:05:08.920 --> 00:05:11.620
we get the same answer that we got before.
00:05:11.620 --> 00:05:14.480
So the standard potential for our reaction
00:05:14.480 --> 00:05:19.480
is equal to positive 1.54
volts at 25 degrees Celsius.
|
Standard cell potential | https://www.youtube.com/watch?v=nBZ4PDBhSrY | vtt | https://www.youtube.com/api/timedtext?v=nBZ4PDBhSrY&ei=ylWUZaX8IYOCp-oP1N-aiA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0F63ADF8F04989C9FC3F79D7BC0EFB609413F4C1.3E09F5D307120E3252B7CB3FE8B673A4748FF6B4&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.330 --> 00:00:02.280
- [Instructor] Standard Cell Potential,
00:00:03.557 --> 00:00:04.883
which is also called
Standard Cell Voltage,
00:00:05.793 --> 00:00:07.890
refers to the voltage of
an electrochemical cell
00:00:08.992 --> 00:00:11.013
when reactants and products
are in their standard states,
00:00:12.051 --> 00:00:12.884
at a particular temperature.
00:00:14.043 --> 00:00:15.033
For a zinc copper galvanic cell,
00:00:16.236 --> 00:00:18.663
solid zinc reacts with
copper two plus ions,
00:00:20.104 --> 00:00:22.793
to form solid copper,
and zinc two plus ions.
00:00:24.777 --> 00:00:27.227
Standard Cell Potential
is symbolized by E naught
00:00:28.660 --> 00:00:30.710
of the cell, where the superscript naught
00:00:32.276 --> 00:00:34.611
refers to the fact that
reactants and products
00:00:34.611 --> 00:00:35.663
are in their standard states.
00:00:36.819 --> 00:00:39.060
For a solid, standard state
refers to the pure solid
00:00:40.096 --> 00:00:41.333
under a pressure of one atmosphere.
00:00:42.435 --> 00:00:43.383
So we're talking about pure solid zinc,
00:00:44.397 --> 00:00:45.230
and pure solid copper.
00:00:46.194 --> 00:00:47.547
And for a solution,
00:00:47.547 --> 00:00:50.063
standard state refers to
a one molar concentration.
00:00:51.213 --> 00:00:52.140
So our concentration of copper two
00:00:53.121 --> 00:00:54.323
plus ions in solution is one molar,
00:00:55.531 --> 00:00:58.073
and so is our concentration
of zinc two plus ions.
00:01:00.163 --> 00:01:02.593
And for this zinc copper
cell, at 25 degrees Celsius,
00:01:03.579 --> 00:01:06.843
the Standard Cell Potential is
equal to positive 1.10 volts.
00:01:08.819 --> 00:01:10.320
Now that we've talked about
the Standard Cell Potential
00:01:11.227 --> 00:01:12.213
for a zinc copper cell,
00:01:13.241 --> 00:01:15.353
let's look at a diagram
of this galvanic cell.
00:01:16.858 --> 00:01:18.510
For this cell, the anode
compartment contains
00:01:19.639 --> 00:01:22.150
solid zinc metal, and
one molar concentration
00:01:23.643 --> 00:01:25.633
of zinc two plus ions,
in aqueous solution.
00:01:27.158 --> 00:01:29.063
The anode is where oxidation takes place.
00:01:30.122 --> 00:01:31.123
So at the zinc electrode,
00:01:32.074 --> 00:01:34.674
the solid zinc is converted
into zinc two plus ions,
00:01:35.732 --> 00:01:36.893
and two electrons are lost.
00:01:38.475 --> 00:01:40.883
So this is the oxidation
half reaction for this cell.
00:01:42.092 --> 00:01:45.029
The electrons that are lost
in the oxidation half reaction
00:01:45.029 --> 00:01:46.183
travel through the wire.
00:01:47.598 --> 00:01:50.398
So there's a flow of electrons,
from the zinc electrode,
00:01:51.763 --> 00:01:52.663
toward the copper electrode.
00:01:54.221 --> 00:01:55.054
The cathode compartment
00:01:55.980 --> 00:01:58.580
contains the solid copper
electrode and in solution,
00:01:59.861 --> 00:02:02.153
one molar concentration
of copper two plus ions.
00:02:03.530 --> 00:02:05.273
And the cathode is where
reduction takes place.
00:02:06.424 --> 00:02:07.933
So at the surface of the copper electrode,
00:02:09.077 --> 00:02:10.540
the copper two plus ions in solution
00:02:11.483 --> 00:02:13.883
gain two electrons and
turn into solid copper.
00:02:15.709 --> 00:02:18.253
So this is the reduction
half reaction for this cell.
00:02:19.845 --> 00:02:22.463
If we were to attach a volt
meter to our two electrodes,
00:02:23.511 --> 00:02:25.773
the volt meter would read 1.10 volts.
00:02:27.708 --> 00:02:30.108
And this voltage is the
Standard Cell Potential.
00:02:31.039 --> 00:02:32.189
So E naught of the cell
00:02:33.690 --> 00:02:36.473
is equal to positive 1.10 volts.
00:02:38.709 --> 00:02:40.940
And the Standard Cell Potential
depends on the potentials
00:02:42.113 --> 00:02:44.563
for the two half reactions
that make up the cell.
00:02:46.165 --> 00:02:48.173
So if we know the potentials
for the half reactions
00:02:48.173 --> 00:02:49.469
that make up the cell,
00:02:49.469 --> 00:02:50.920
we can calculate the standard potential
00:02:51.848 --> 00:02:52.681
of any galvanic cell.
00:02:54.020 --> 00:02:55.813
And let's see how we could do
that for this particular cell.
00:02:57.840 --> 00:02:58.673
To calculate these standard cell potential
00:02:59.722 --> 00:03:00.555
for our zinc copper cell,
00:03:01.591 --> 00:03:03.176
we're going to use what are called
00:03:03.176 --> 00:03:04.676
Standard Reduction Potentials.
00:03:06.468 --> 00:03:08.360
Standard Reduction
Potentials are symbolized by
00:03:09.251 --> 00:03:10.351
E naught of reduction.
00:03:11.982 --> 00:03:13.689
And these refer to the voltages
00:03:13.689 --> 00:03:14.522
for half reactions that are
00:03:15.457 --> 00:03:17.003
written as reduction half reactions.
00:03:18.136 --> 00:03:21.086
For example, if copper two plus
is reduced by two electrons
00:03:22.405 --> 00:03:23.238
to form solid copper,
00:03:24.306 --> 00:03:25.703
the voltage for this half reaction,
00:03:26.548 --> 00:03:28.228
or the Standard Reduction Potential,
00:03:28.228 --> 00:03:30.063
is equal to positive 0.34 volts.
00:03:32.047 --> 00:03:33.650
And for the reduction
of zinc two plus ions
00:03:34.831 --> 00:03:36.383
by two electrons to form solid zinc,
00:03:37.317 --> 00:03:38.150
the Standard Reduction Potential
00:03:38.150 --> 00:03:41.263
is equal to negative 0.76 volts.
00:03:43.271 --> 00:03:45.003
We just saw from our
zinc copper cell diagram,
00:03:45.861 --> 00:03:47.711
that copper two plus ions are reduced
00:03:48.818 --> 00:03:49.651
to form solid copper.
00:03:50.597 --> 00:03:52.373
So, we're going to leave this
half reaction as it's written.
00:03:53.767 --> 00:03:56.051
However, in our diagram
for our zinc copper cell,
00:03:56.051 --> 00:03:59.688
we saw that solid zinc was
actually being oxidized to form
00:03:59.688 --> 00:04:00.638
zinc two plus ions.
00:04:02.167 --> 00:04:04.050
So we need to rewrite
the second half reaction
00:04:05.011 --> 00:04:06.463
as an oxidation half reaction.
00:04:07.583 --> 00:04:08.873
And that just means reversing everything.
00:04:10.048 --> 00:04:11.353
And if we're reversing our half reaction,
00:04:12.438 --> 00:04:14.393
we have to change the sign on the voltage.
00:04:15.738 --> 00:04:17.838
So if the potential is negative 0.76 volts
00:04:18.958 --> 00:04:20.013
for the reduction half reaction,
00:04:20.972 --> 00:04:22.522
it would be positive 0.76 volts
00:04:23.540 --> 00:04:24.923
for the oxidation half reaction.
00:04:26.518 --> 00:04:28.553
So now I've changed it to show
the oxidation half reaction,
00:04:29.595 --> 00:04:31.923
solid zinc turning into zinc
two plus ions in solution,
00:04:33.122 --> 00:04:33.955
and the loss of two electrons.
00:04:34.854 --> 00:04:37.604
The Standard Oxidation
Potential for this half reaction
00:04:38.906 --> 00:04:40.163
is positive 0.76 volts.
00:04:42.349 --> 00:04:44.683
The next step is to add the
two half reactions together.
00:04:45.611 --> 00:04:47.163
So here are all of our reactants,
00:04:48.397 --> 00:04:50.047
and here are all of the products.
00:04:51.749 --> 00:04:53.273
Notice how two electrons would cancel out,
00:04:54.295 --> 00:04:57.670
and that gives us copper two
plus ions in aqueous solution,
00:04:57.670 --> 00:05:00.403
plus solid zinc forms solid copper,
00:05:01.806 --> 00:05:03.556
and zinc two plus ions in solution.
00:05:05.484 --> 00:05:06.960
Since we were able to
get the overall equation
00:05:07.899 --> 00:05:09.623
by adding the two half reactions together,
00:05:10.701 --> 00:05:13.480
we should be able to get the
overall Standard Cell Potential
00:05:14.705 --> 00:05:16.330
E naught of the cell,
by adding together the
00:05:17.184 --> 00:05:19.534
standard potentials for
our two half reactions.
00:05:21.154 --> 00:05:22.050
So E naught of the cell is equal to
00:05:23.055 --> 00:05:24.493
E naught of the reduction half reaction,
00:05:25.514 --> 00:05:27.463
plus E naught of the
oxidation half reaction,
00:05:28.561 --> 00:05:31.893
which is equal to 0.34 plus 0.76,
00:05:33.400 --> 00:05:35.023
or positive 1.10 volts.
00:05:36.550 --> 00:05:38.780
So, the Standard Cell Potential
of our zinc copper cell
00:05:39.930 --> 00:05:43.313
is equal to positive 1.10
volts at 25 degrees Celsius.
00:05:45.022 --> 00:05:46.380
We can also calculate
Standard Cell Potential
00:05:47.215 --> 00:05:48.060
using a slightly different form
00:05:48.984 --> 00:05:49.963
of the equation that we just learned.
00:05:51.431 --> 00:05:52.264
Remember that we flipped the sign
00:05:53.198 --> 00:05:54.390
of the Standard Reduction Potential
00:05:55.465 --> 00:05:57.033
to get the Standard Oxidation Potential,
00:05:58.113 --> 00:05:59.863
which we plugged into this equation,
00:06:00.783 --> 00:06:02.348
and were able to calculate
00:06:02.348 --> 00:06:04.098
the standard potential of the cell.
00:06:05.755 --> 00:06:06.593
Instead of flipping the sign ourselves,
00:06:07.633 --> 00:06:08.793
and getting a Standard
Oxidation Potential,
00:06:09.719 --> 00:06:11.850
we could use this new equation to just use
00:06:13.182 --> 00:06:15.347
reduction potentials to calculate
00:06:15.347 --> 00:06:16.953
the standard potential of the cell.
00:06:18.282 --> 00:06:20.390
Notice that this new
equation has a negative sign
00:06:21.299 --> 00:06:22.990
that essentially flips the sign of the
00:06:23.981 --> 00:06:26.353
Standard Reduction Potential
for the oxidation process.
00:06:27.402 --> 00:06:29.470
So, it accomplishes the same
thing that we did ourselves
00:06:30.341 --> 00:06:31.174
in the first equation.
00:06:32.402 --> 00:06:33.623
So to find the standard
potential of the cell,
00:06:34.506 --> 00:06:36.599
we take the Standard Reduction Potential
00:06:36.599 --> 00:06:37.899
for the reduction process,
00:06:38.915 --> 00:06:41.160
and from that, we subtract the
Standard Reduction Potential
00:06:42.164 --> 00:06:43.123
for the oxidation process.
00:06:44.239 --> 00:06:45.333
So, this equation is a bit of a shortcut.
00:06:46.819 --> 00:06:48.090
So when we plug in our
Standard Reduction Potentials
00:06:49.054 --> 00:06:52.123
of positive 0.34 volts
and negative 0.76 volts,
00:06:53.333 --> 00:06:55.330
the negative sign means we
end up with the same answer
00:06:56.264 --> 00:06:58.553
we got before, a positive 1.10 volts.
|
Electrolytic cells | https://www.youtube.com/watch?v=patZ8zoemVo | vtt | https://www.youtube.com/api/timedtext?v=patZ8zoemVo&ei=ylWUZZfdLIeop-oP3uCdKA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6A1AFBE576980BE72707940B7C7A385C0857848A.692170AD61228B03AEE88FC1438B810BBBCBD85E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.420 --> 00:00:01.370
- [Instructor] Electrolytic cells
00:00:01.370 --> 00:00:03.200
use an electric current to drive
00:00:03.200 --> 00:00:06.320
a thermodynamically unfavorable reaction.
00:00:06.320 --> 00:00:09.190
Before we look at a diagram
of electrolytic cell,
00:00:09.190 --> 00:00:10.930
let's look at the half reactions
00:00:10.930 --> 00:00:13.060
that will occur in the cell.
00:00:13.060 --> 00:00:16.550
In one half reaction, liquid sodium ions
00:00:16.550 --> 00:00:20.980
react with an electron to
form liquid sodium metal.
00:00:20.980 --> 00:00:24.530
Because the liquid sodium
ion is gaining an electron,
00:00:24.530 --> 00:00:28.180
this represents the
reduction half reaction.
00:00:28.180 --> 00:00:30.210
The other way to tell
that this is a reduction
00:00:30.210 --> 00:00:33.460
half reaction is to
assign oxidation numbers.
00:00:33.460 --> 00:00:36.980
Liquid sodium ions have
an oxidation number
00:00:36.980 --> 00:00:41.060
of plus one and liquid sodium metal
00:00:41.060 --> 00:00:43.510
has an oxidation number of zero.
00:00:43.510 --> 00:00:45.520
So going from plus one to zero
00:00:45.520 --> 00:00:49.610
is a decrease or a reduction
in the oxidation number.
00:00:49.610 --> 00:00:53.020
Therefore, liquid sodium ions are reduced
00:00:53.020 --> 00:00:56.720
to form liquid sodium metal
in this half reaction.
00:00:56.720 --> 00:00:59.410
In our next unbalanced half reaction,
00:00:59.410 --> 00:01:03.940
liquid chloride anions
turn into chlorine gas.
00:01:03.940 --> 00:01:06.260
If we assign oxidation numbers,
00:01:06.260 --> 00:01:10.540
liquid chloride anions have a
oxidation number of minus one,
00:01:10.540 --> 00:01:13.710
and chlorine gas has an
oxidation number of zero.
00:01:13.710 --> 00:01:15.490
So going from minus one to zero
00:01:15.490 --> 00:01:18.270
is an increase in the oxidation number.
00:01:18.270 --> 00:01:20.100
Therefore, the liquid chloride anions
00:01:20.100 --> 00:01:22.670
are oxidized to chlorine gas.
00:01:22.670 --> 00:01:25.830
So this is the oxidation half reaction,
00:01:25.830 --> 00:01:27.190
and we need to balance it.
00:01:27.190 --> 00:01:29.804
Since we have two chlorines on the right,
00:01:29.804 --> 00:01:32.038
we need to put two as a coefficient
00:01:32.038 --> 00:01:34.810
in front of the chloride
anions on the left.
00:01:34.810 --> 00:01:37.120
Loss of electrons is oxidation.
00:01:37.120 --> 00:01:40.530
And since we're oxidizing
two chloride anions,
00:01:40.530 --> 00:01:43.993
we're going to lose two electrons.
00:01:44.850 --> 00:01:45.850
As a quick reminder,
00:01:45.850 --> 00:01:46.970
one way to remember that
00:01:46.970 --> 00:01:49.850
loss of electrons is oxidation
00:01:49.850 --> 00:01:53.220
and gain of electrons is reduction
00:01:53.220 --> 00:01:56.520
is to think about LEO the lion goes GER.
00:01:56.520 --> 00:01:59.810
So loss of electrons is oxidation
00:01:59.810 --> 00:02:03.320
and gain of electrons is reduction.
00:02:03.320 --> 00:02:05.870
Next let's add our two
half reactions together
00:02:05.870 --> 00:02:08.520
to get the overall redox reaction.
00:02:08.520 --> 00:02:09.620
And before we do that,
00:02:09.620 --> 00:02:11.640
we have to make sure
the number of electrons
00:02:11.640 --> 00:02:14.090
are equal in both half reactions.
00:02:14.090 --> 00:02:15.670
Since we have two electrons
00:02:15.670 --> 00:02:17.380
in the oxidation half reaction
00:02:17.380 --> 00:02:20.710
and only one electron in
the reduction half reaction,
00:02:20.710 --> 00:02:22.320
we need to multiply everything
00:02:22.320 --> 00:02:25.430
in our reduction half
reaction through by two.
00:02:25.430 --> 00:02:28.470
So that'd be two liquid sodium ions,
00:02:28.470 --> 00:02:32.970
two electrons, and two liquid sodiums.
00:02:32.970 --> 00:02:35.100
When we add the two
half reactions together,
00:02:35.100 --> 00:02:37.420
the two electrons cancel out
00:02:37.420 --> 00:02:41.350
and we get two liquid sodium cations
00:02:41.350 --> 00:02:44.630
plus two liquid chloride anions
00:02:44.630 --> 00:02:48.780
goes to two liquid
sodiums and chlorine gas.
00:02:48.780 --> 00:02:51.560
So if we had some molten sodium chloride,
00:02:51.560 --> 00:02:55.460
we could form sodium and chlorine gas.
00:02:55.460 --> 00:02:57.970
However, delta G naught for this reaction
00:02:57.970 --> 00:02:59.750
is greater than zero,
00:02:59.750 --> 00:03:01.200
which means this reaction
00:03:01.200 --> 00:03:04.220
is thermodynamically unfavorable.
00:03:04.220 --> 00:03:06.460
So in order for this reaction to occur,
00:03:06.460 --> 00:03:08.200
we need some sort of a power source
00:03:08.200 --> 00:03:10.770
to provide an electric current,
00:03:10.770 --> 00:03:15.300
to drive this thermodynamically
unfavorable reaction.
00:03:15.300 --> 00:03:18.310
Here's a diagram showing
our electrolytic cell
00:03:18.310 --> 00:03:22.320
for the electrolysis of
molten sodium chloride,
00:03:22.320 --> 00:03:24.390
and let's start with the power source.
00:03:24.390 --> 00:03:26.910
So the negative terminal
of the power source
00:03:26.910 --> 00:03:28.660
is where the electrons come from.
00:03:28.660 --> 00:03:32.460
So imagine we have electrons
moving in this wire
00:03:32.460 --> 00:03:35.460
toward the inert electrode on the right.
00:03:35.460 --> 00:03:36.860
Inert means the electrodes
00:03:36.860 --> 00:03:39.970
aren't going to participate
in this reaction.
00:03:39.970 --> 00:03:41.360
For example, the electrode
00:03:41.360 --> 00:03:43.150
could be a piece of platinum metal,
00:03:43.150 --> 00:03:44.990
which is very unreactive.
00:03:44.990 --> 00:03:47.470
At the surface of the electrode,
00:03:47.470 --> 00:03:51.400
the electrons reduce
the liquid sodium ions
00:03:51.400 --> 00:03:53.680
into liquid sodium.
00:03:53.680 --> 00:03:58.060
Therefore, liquid sodium
will form at this electrode.
00:03:58.060 --> 00:04:00.350
The melting point of sodium chloride
00:04:00.350 --> 00:04:04.110
is higher than the
melting point of sodium.
00:04:04.110 --> 00:04:06.210
Therefore, at this high temperature
00:04:06.210 --> 00:04:08.900
sodium will remain a liquid.
00:04:08.900 --> 00:04:11.760
Eventually when the
liquid sodium cools down,
00:04:11.760 --> 00:04:14.350
you would have some solid sodium metal
00:04:14.350 --> 00:04:16.130
because reduction is occurring
00:04:16.130 --> 00:04:18.090
at the electrode on the right,
00:04:18.090 --> 00:04:21.200
the electrode on the
right must be the cathode.
00:04:21.200 --> 00:04:22.720
Next, let's think about the other
00:04:22.720 --> 00:04:24.940
inert electrode on the left.
00:04:24.940 --> 00:04:27.780
At this electrode,
oxidation is taking place
00:04:27.780 --> 00:04:29.780
because liquid chloride anions
00:04:29.780 --> 00:04:32.240
are turning into chlorine gas.
00:04:32.240 --> 00:04:33.860
So we would see bubbles
00:04:33.860 --> 00:04:37.560
of chlorine gas at this electrode.
00:04:37.560 --> 00:04:41.200
And as the liquid chloride
anions are oxidized,
00:04:41.200 --> 00:04:42.920
that's loss of electrons.
00:04:42.920 --> 00:04:46.770
So the electrons would
flow through this wire
00:04:46.770 --> 00:04:51.110
back toward the positive
terminal of the power source.
00:04:51.110 --> 00:04:52.910
Since oxidation is occurring
00:04:52.910 --> 00:04:55.730
at the inert electrode on the left,
00:04:55.730 --> 00:04:58.660
this electrode must be the anode.
00:04:58.660 --> 00:05:00.950
As a quick review,
remember that a good way
00:05:00.950 --> 00:05:04.500
to remember this is to
think about an ox and a cat.
00:05:04.500 --> 00:05:06.470
So oxidation occurs at the anode.
00:05:06.470 --> 00:05:08.110
That's an ox.
00:05:08.110 --> 00:05:10.770
And reduction occurs at the cathode.
00:05:10.770 --> 00:05:12.960
That's a red cat.
00:05:12.960 --> 00:05:14.280
And as a quick summary,
00:05:14.280 --> 00:05:17.540
this diagram shows the electrolytic cell
00:05:17.540 --> 00:05:20.790
for the electrolysis of
molten sodium chloride
00:05:20.790 --> 00:05:24.550
to form liquid sodium and chlorine gas.
00:05:24.550 --> 00:05:28.170
Let's look at another example
of an electrolytic cell.
00:05:28.170 --> 00:05:29.850
This electrolytic cell shows
00:05:29.850 --> 00:05:32.540
the process of electroplating.
00:05:32.540 --> 00:05:34.670
So let's say you have
a pendant made of steel
00:05:34.670 --> 00:05:36.960
and you do some engraving on it.
00:05:36.960 --> 00:05:38.280
I do a lot of engraving.
00:05:38.280 --> 00:05:39.890
And so I drew a little picture
00:05:39.890 --> 00:05:43.040
of some flowers on this steel pendant,
00:05:43.040 --> 00:05:45.180
however, steel rusts pretty easily.
00:05:45.180 --> 00:05:47.340
So if we want to protect the engraving,
00:05:47.340 --> 00:05:48.680
we could electroplate it
00:05:48.680 --> 00:05:52.120
and put a thin layer of
nickel on top of the steel.
00:05:52.120 --> 00:05:54.790
So electroplating uses electrolysis
00:05:54.790 --> 00:05:58.180
to plate one metal onto another metal,
00:05:58.180 --> 00:06:01.130
either to protect against
rust or corrosion,
00:06:01.130 --> 00:06:03.290
or if you want to plate silver or gold
00:06:03.290 --> 00:06:05.870
onto another metal to
make it more beautiful.
00:06:05.870 --> 00:06:07.560
So for this electrolytic cell,
00:06:07.560 --> 00:06:09.640
we have a steel electrode on the right
00:06:09.640 --> 00:06:12.050
and a nickel electrode on the left.
00:06:12.050 --> 00:06:16.210
And we have an aqueous
solution of nickel sulfate.
00:06:16.210 --> 00:06:17.760
We know that electrons come
00:06:17.760 --> 00:06:20.250
from the negative terminal
of the power source.
00:06:20.250 --> 00:06:23.540
So imagine that electrons move in the wire
00:06:23.540 --> 00:06:26.720
toward the steel electrode on the right.
00:06:26.720 --> 00:06:29.070
When the nickel two
plus ion is in solution
00:06:29.070 --> 00:06:31.180
come in contact with the electrons
00:06:31.180 --> 00:06:33.320
at the surface of the steel electrode,
00:06:33.320 --> 00:06:35.630
reduction takes place.
00:06:35.630 --> 00:06:38.570
So reduction takes place at the cathode
00:06:38.570 --> 00:06:40.000
and for the half reaction,
00:06:40.000 --> 00:06:42.640
it'd be nickel two
plus, plus two electrons
00:06:42.640 --> 00:06:44.620
turns into solid nickel.
00:06:44.620 --> 00:06:47.040
So a thin layer of nickel is now
00:06:47.040 --> 00:06:49.610
plated on the steel object.
00:06:49.610 --> 00:06:53.020
The electrode on the left
is a piece of solid nickel.
00:06:53.020 --> 00:06:55.370
And when solid nickel is oxidized,
00:06:55.370 --> 00:06:58.540
it turns into nickel two plus ions.
00:06:58.540 --> 00:06:59.880
When solid nickel turns
00:06:59.880 --> 00:07:03.000
into nickel two plus ions in solution,
00:07:03.000 --> 00:07:04.990
two electrons are lost.
00:07:04.990 --> 00:07:07.020
And so we can think about electrons
00:07:07.020 --> 00:07:08.760
moving in this wire back toward
00:07:08.760 --> 00:07:11.930
the positive terminal of the power source.
00:07:11.930 --> 00:07:14.010
So for the oxidation half reaction,
00:07:14.010 --> 00:07:17.700
solid nickel turns into
nickel two plus ions,
00:07:17.700 --> 00:07:19.920
and two electrons are lost.
00:07:19.920 --> 00:07:22.510
And because oxidation occurs at the anode,
00:07:22.510 --> 00:07:25.630
the nickel electrode is the anode
00:07:25.630 --> 00:07:27.520
for this electrolytic cell.
00:07:27.520 --> 00:07:30.810
Let's look at a quick summary
for an electrolytic cell.
00:07:30.810 --> 00:07:32.330
In an electrolytic cell,
00:07:32.330 --> 00:07:36.720
the redox reaction is
thermodynamically unfavorable.
00:07:36.720 --> 00:07:38.170
Because the redox reaction
00:07:38.170 --> 00:07:40.430
is thermodynamically unfavorable,
00:07:40.430 --> 00:07:42.330
an electrolytic cell requires
00:07:42.330 --> 00:07:45.550
a power source to supply a current
00:07:45.550 --> 00:07:48.560
to drive the unfavorable redox reaction.
00:07:48.560 --> 00:07:50.440
Oxidation occurs at the anode
00:07:50.440 --> 00:07:53.210
and reduction occurs at the cathode.
00:07:53.210 --> 00:07:54.790
And finally, an electrolytic cell
00:07:54.790 --> 00:07:56.410
is used for electroplating
00:07:56.410 --> 00:07:58.510
where a thin layer of one metal
00:07:58.510 --> 00:08:00.713
is plated onto another metal.
|
Galvanic (voltaic) cells | https://www.youtube.com/watch?v=inXgVjz1BDQ | vtt | https://www.youtube.com/api/timedtext?v=inXgVjz1BDQ&ei=ylWUZZ_lKp3Hp-oP54OMgA0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=4773B39A75177CF14B913D4AE6C7D72C53F57AC8.8855CB2F875DC6131EB5B124B5963F1BA7A4A080&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.210 --> 00:00:01.300
- [Instructor] Galvanic cells,
00:00:01.300 --> 00:00:03.010
which are also called voltaic cells,
00:00:03.010 --> 00:00:05.480
use a thermodynamically favorable reaction
00:00:05.480 --> 00:00:08.040
to generate an electric current.
00:00:08.040 --> 00:00:09.440
Before we look at a diagram
00:00:09.440 --> 00:00:11.570
of a galvanic or voltaic cell,
00:00:11.570 --> 00:00:13.970
let's first look at the half reactions
00:00:13.970 --> 00:00:16.620
that are going to be used in the cell.
00:00:16.620 --> 00:00:18.090
In the first half reaction,
00:00:18.090 --> 00:00:20.520
zinc metal loses two electrons
00:00:20.520 --> 00:00:23.560
to turn into the zinc 2+ cation.
00:00:23.560 --> 00:00:25.760
Loss of electrons is oxidation.
00:00:25.760 --> 00:00:29.740
Therefore, this is the
oxidation half reaction.
00:00:29.740 --> 00:00:31.660
As a quick review, the other way to tell
00:00:31.660 --> 00:00:34.030
that this is the oxidation half reaction
00:00:34.030 --> 00:00:35.960
is we go from an oxidation number
00:00:35.960 --> 00:00:38.020
for solid zinc of zero
00:00:38.020 --> 00:00:40.973
to an oxidation number
for zinc 2+ of plus two
00:00:42.372 --> 00:00:46.160
and increase in the oxidation
number is oxidation.
00:00:46.160 --> 00:00:49.100
Therefore, zinc metal is oxidized.
00:00:49.100 --> 00:00:50.900
And here is the other half reaction
00:00:50.900 --> 00:00:54.190
that we're going to see in
our galvanic cell diagram.
00:00:54.190 --> 00:00:55.300
In this half reaction,
00:00:55.300 --> 00:00:58.550
the copper 2+ cation gains two electrons
00:00:58.550 --> 00:01:00.820
to turn into solid copper.
00:01:00.820 --> 00:01:03.200
Gain of electrons is reduction.
00:01:03.200 --> 00:01:06.370
Therefore, this is the
reduction half reaction.
00:01:06.370 --> 00:01:08.460
The other way to tell
that this is the reduction
00:01:08.460 --> 00:01:11.770
half reaction is to look
at the oxidation numbers.
00:01:11.770 --> 00:01:14.840
So the copper 2+ cation has an oxidation
00:01:14.840 --> 00:01:18.090
number of plus two and solid copper
00:01:18.090 --> 00:01:20.510
has an oxidation number of zero.
00:01:20.510 --> 00:01:23.320
Since there's a decrease or a reduction
00:01:23.320 --> 00:01:26.610
in the oxidation number
from plus two to zero,
00:01:26.610 --> 00:01:29.670
this is the reduction half reaction.
00:01:29.670 --> 00:01:32.620
A good way to remember
which half reaction is which
00:01:32.620 --> 00:01:35.930
is to think about LEO the lion goes GER.
00:01:35.930 --> 00:01:39.470
So loss of electrons is oxidation
00:01:39.470 --> 00:01:43.160
and gain of electrons is reduction.
00:01:43.160 --> 00:01:46.000
When we add the two
half reactions together,
00:01:46.000 --> 00:01:48.240
we have two electrons on the reactant side
00:01:48.240 --> 00:01:50.200
and two electrons on the product side.
00:01:50.200 --> 00:01:53.500
So those cancel out and
that gives us a solid zinc
00:01:53.500 --> 00:01:58.030
plus copper 2+ ions
goes to zinc 2+ cations
00:01:58.030 --> 00:01:59.860
and solid copper.
00:01:59.860 --> 00:02:01.530
In this redox reaction,
00:02:01.530 --> 00:02:05.210
zinc metal is oxidized to zinc 2+ cations
00:02:05.210 --> 00:02:09.700
and copper 2+ cations are
reduced to solid copper.
00:02:09.700 --> 00:02:11.390
Delta G naught for this reaction
00:02:11.390 --> 00:02:14.110
at 25 degrees Celsius or room temperature
00:02:14.110 --> 00:02:15.680
is less than zero,
00:02:15.680 --> 00:02:17.290
which means this reaction
00:02:17.290 --> 00:02:19.760
is thermodynamically favorable.
00:02:19.760 --> 00:02:23.140
Therefore, if we were to
put a piece of solid zinc
00:02:23.140 --> 00:02:26.490
in an aqueous solution of copper 2+ ions,
00:02:26.490 --> 00:02:28.370
we would see copper metal
00:02:28.370 --> 00:02:32.300
form on the zinc metal and zinc 2+ ions
00:02:32.300 --> 00:02:33.780
would form in solution.
00:02:33.780 --> 00:02:35.020
So that's what would happen
00:02:35.020 --> 00:02:36.380
if we did this reaction
00:02:36.380 --> 00:02:38.410
in only a single compartment.
00:02:38.410 --> 00:02:41.520
However, in a galvanic or voltaic cell,
00:02:41.520 --> 00:02:44.800
each half reaction gets
its own compartment.
00:02:44.800 --> 00:02:48.660
And the two compartments
are connected with a wire.
00:02:48.660 --> 00:02:51.130
Therefore, a thermodynamically favorable
00:02:51.130 --> 00:02:54.490
redox reaction is used to generate
00:02:54.490 --> 00:02:57.110
an electric current in the wire.
00:02:57.110 --> 00:02:58.500
And by electric current,
00:02:58.500 --> 00:03:01.320
we're talking the flow of electrons.
00:03:01.320 --> 00:03:03.560
Now that we've gone
over the half reactions
00:03:03.560 --> 00:03:07.350
in detail for this zinc-copper
galvanic or voltaic cell,
00:03:07.350 --> 00:03:09.390
let's look at a diagram of this cell
00:03:09.390 --> 00:03:11.410
and see how things actually work.
00:03:11.410 --> 00:03:14.170
Let's start by looking at
the compartment on the left,
00:03:14.170 --> 00:03:16.580
which is a beaker that contains
00:03:16.580 --> 00:03:20.290
a one molar aqueous
solution of zinc sulfate.
00:03:20.290 --> 00:03:23.040
Therefore, there are zinc 2+ ions
00:03:23.040 --> 00:03:27.080
and sulfate anions in aqueous
solution in the beaker.
00:03:27.080 --> 00:03:29.690
We saw from the oxidation half reaction
00:03:29.690 --> 00:03:31.870
that solid zinc is oxidized
00:03:31.870 --> 00:03:35.400
and turns into zinc 2+ cations.
00:03:35.400 --> 00:03:37.460
When zinc turns into zinc 2+,
00:03:37.460 --> 00:03:39.320
two electrons are lost.
00:03:39.320 --> 00:03:41.660
So those electrons will move
00:03:41.660 --> 00:03:44.880
in this wire that connects
the two compartments.
00:03:44.880 --> 00:03:47.530
So imagine we have movement of electrons
00:03:47.530 --> 00:03:49.150
going from the compartment on the left
00:03:49.150 --> 00:03:51.760
towards the compartment on the right.
00:03:51.760 --> 00:03:55.060
This piece of solid zinc
is called an electrode.
00:03:55.060 --> 00:03:57.690
The electrode at which
oxidation takes place
00:03:57.690 --> 00:03:59.520
is called the anode.
00:03:59.520 --> 00:04:02.450
So let me go ahead and
write anode in here.
00:04:02.450 --> 00:04:04.790
Next, let's look at the
compartment on the right,
00:04:04.790 --> 00:04:06.510
which is a beaker that contains
00:04:06.510 --> 00:04:09.760
a one molar solution of copper sulfate.
00:04:09.760 --> 00:04:12.630
So in this beaker,
there are copper 2+ ions
00:04:12.630 --> 00:04:15.600
and sulfate anions in aqueous solution.
00:04:15.600 --> 00:04:18.030
We know that electrons
are moving in this wire
00:04:18.030 --> 00:04:20.460
that connects the two compartments.
00:04:20.460 --> 00:04:23.350
At the surface of this copper electrode,
00:04:23.350 --> 00:04:26.430
the copper 2+ ions come in contact
00:04:26.430 --> 00:04:30.760
with two electrons and are
reduced to form solid copper.
00:04:30.760 --> 00:04:33.380
The electrode where reduction takes place
00:04:33.380 --> 00:04:35.540
is called the cathode.
00:04:35.540 --> 00:04:40.540
So the copper electrode is
the cathode for this cell.
00:04:40.710 --> 00:04:43.080
I went ahead and rewrote
each half reaction
00:04:43.080 --> 00:04:45.560
to remind us of what's going
on in each compartment.
00:04:45.560 --> 00:04:47.280
So we can think about what's gonna happen
00:04:47.280 --> 00:04:49.330
to our cell over time.
00:04:49.330 --> 00:04:51.940
The anode is where oxidation takes place.
00:04:51.940 --> 00:04:55.240
So solid zinc turns into zinc 2+ cations.
00:04:55.240 --> 00:04:58.870
So as time goes on,
the amount of the solid
00:04:58.870 --> 00:05:01.720
zinc electrode will decrease.
00:05:01.720 --> 00:05:04.340
And the amount of zinc 2+ cations
00:05:04.340 --> 00:05:07.330
in solution will increase.
00:05:07.330 --> 00:05:10.830
And the cathode is where
reduction takes place.
00:05:10.830 --> 00:05:13.330
So as copper 2+ cations gained
00:05:13.330 --> 00:05:16.100
two electrons to turn into solid copper,
00:05:16.100 --> 00:05:18.480
over time, the amount of copper,
00:05:18.480 --> 00:05:21.160
solid copper electrode will increase.
00:05:21.160 --> 00:05:23.930
And the concentration of copper 2+ ions
00:05:23.930 --> 00:05:26.830
in solution will decrease.
00:05:26.830 --> 00:05:28.590
A good way to remember that oxidation
00:05:28.590 --> 00:05:32.070
occurs at the anode and
reduction occurs at the cathode
00:05:32.070 --> 00:05:36.750
is to think about two
animals, an ox and a cat.
00:05:36.750 --> 00:05:39.510
So thinking about an ox reminds us
00:05:39.510 --> 00:05:42.430
that oxidation occurs at the anode
00:05:42.430 --> 00:05:44.950
and thinking about a red cat
00:05:44.950 --> 00:05:49.340
reminds us that reduction
occurs at the cathode.
00:05:49.340 --> 00:05:50.420
The next part of the cell
00:05:50.420 --> 00:05:52.020
that we have to think about
00:05:52.020 --> 00:05:55.090
is the salt bridge that connects
00:05:55.090 --> 00:05:56.870
these two compartments.
00:05:56.870 --> 00:05:58.150
Inside the salt bridge,
00:05:58.150 --> 00:06:02.460
there's an electrolyte solution
such as sodium nitrate.
00:06:02.460 --> 00:06:04.270
The electrolyte is often in a gel
00:06:04.270 --> 00:06:06.960
or paste form to prevent early mixing
00:06:06.960 --> 00:06:08.880
with the other compartments.
00:06:08.880 --> 00:06:11.210
These solutions in each compartment
00:06:11.210 --> 00:06:14.790
also called a half cell must
remain electrically neutral.
00:06:14.790 --> 00:06:16.430
And the purpose of the salt bridge
00:06:16.430 --> 00:06:18.410
is to balance the charges.
00:06:18.410 --> 00:06:20.530
Let's start by thinking
about the compartment
00:06:20.530 --> 00:06:22.750
or the half cell on the left.
00:06:22.750 --> 00:06:25.240
When we started, we had
equal concentrations
00:06:25.240 --> 00:06:27.840
of zinc 2+ and sulfate anion,
00:06:27.840 --> 00:06:29.630
so the charges were balanced.
00:06:29.630 --> 00:06:31.910
However, over time, the concentration
00:06:31.910 --> 00:06:35.250
of zinc 2+ ions increases.
00:06:35.250 --> 00:06:38.220
To balance out the
increased positive charge,
00:06:38.220 --> 00:06:40.300
the negatively charged anion,
00:06:40.300 --> 00:06:42.360
and in this case, the nitrate anion,
00:06:42.360 --> 00:06:43.640
moves from the salt bridge
00:06:43.640 --> 00:06:46.490
into the half cell on the left.
00:06:46.490 --> 00:06:48.280
Next, let's think about the compartment
00:06:48.280 --> 00:06:50.610
or the half cell on the right.
00:06:50.610 --> 00:06:52.700
We started off with equal concentrations
00:06:52.700 --> 00:06:56.170
of copper 2+ cation and sulfate anion.
00:06:56.170 --> 00:07:01.170
However, over time, there's a
decrease in copper 2+ cation.
00:07:01.340 --> 00:07:03.810
Therefore, there's too
much negative charge
00:07:03.810 --> 00:07:05.320
in this half cell.
00:07:05.320 --> 00:07:08.400
To balance out the negatively
charged sulfate anions,
00:07:08.400 --> 00:07:11.070
the positively charged
ion and the salt bridge,
00:07:11.070 --> 00:07:13.070
in this case, the sodium cation,
00:07:13.070 --> 00:07:14.490
moves from the salt bridge
00:07:14.490 --> 00:07:16.860
into the half cell on the right.
00:07:16.860 --> 00:07:18.590
A good way to remember which direction
00:07:18.590 --> 00:07:20.630
the ions go in the salt bridge
00:07:20.630 --> 00:07:23.730
is to think about anions
going toward the anode
00:07:23.730 --> 00:07:26.850
and cations going toward the cathode.
00:07:26.850 --> 00:07:28.460
The salt bridge is necessary
00:07:28.460 --> 00:07:30.320
for the galvanic cell to work.
00:07:30.320 --> 00:07:32.380
If the salt bridge were removed,
00:07:32.380 --> 00:07:35.200
the electrons would
stop moving in the wire,
00:07:35.200 --> 00:07:36.970
And that brings us to the last component
00:07:36.970 --> 00:07:40.390
of our galvanic cell, which
is this volt meter here.
00:07:40.390 --> 00:07:42.570
For this particular galvanic cell
00:07:42.570 --> 00:07:45.040
with one molar concentration
of zinc sulfate,
00:07:45.040 --> 00:07:47.610
one more concentration of copper sulfate
00:07:47.610 --> 00:07:49.790
at 25 degrees Celsius,
00:07:49.790 --> 00:07:53.590
the initial voltage would be 1.10 volts.
00:07:53.590 --> 00:07:56.300
So that's what would show
up on the volt meter.
00:07:56.300 --> 00:07:58.070
The volt meter measures the difference
00:07:58.070 --> 00:08:00.480
in electric potential between two points.
00:08:00.480 --> 00:08:01.810
And as long as there's a difference
00:08:01.810 --> 00:08:03.180
in electric potential,
00:08:03.180 --> 00:08:05.610
electrons will flow in the wire.
00:08:05.610 --> 00:08:07.570
However, this thermodynamically favorable
00:08:07.570 --> 00:08:10.190
redox reaction doesn't last forever.
00:08:10.190 --> 00:08:13.200
Eventually, the reaction
reaches equilibrium.
00:08:13.200 --> 00:08:17.080
And at that point, the
voltage is equal to zero.
00:08:17.080 --> 00:08:18.880
And when the voltage goes to zero,
00:08:18.880 --> 00:08:21.170
the current also goes to zero,
00:08:21.170 --> 00:08:22.650
which means the electrons
00:08:22.650 --> 00:08:25.210
are no longer moving in the wire.
00:08:25.210 --> 00:08:29.220
You could also call a galvanic
or voltaic cell a battery.
00:08:29.220 --> 00:08:31.930
So at that point, the battery is dead.
00:08:31.930 --> 00:08:35.470
Let's do a quick summary of
galvanic or voltaic cells.
00:08:35.470 --> 00:08:37.650
These cells use a thermodynamically
00:08:37.650 --> 00:08:40.210
favored redox reaction.
00:08:40.210 --> 00:08:42.040
This redox reaction generates
00:08:42.040 --> 00:08:44.180
an electric current that flows
00:08:44.180 --> 00:08:47.260
in the wire between the two electrodes.
00:08:47.260 --> 00:08:49.720
The electrode where oxidation takes place
00:08:49.720 --> 00:08:50.990
is called the anode,
00:08:50.990 --> 00:08:53.340
and the electrode where
reduction takes place
00:08:53.340 --> 00:08:55.000
is called the cathode.
00:08:55.000 --> 00:08:57.750
A salt bridge is used
to balance the charges
00:08:57.750 --> 00:08:59.550
in the two compartments.
00:08:59.550 --> 00:09:02.120
Eventually, the reaction
reaches equilibrium
00:09:02.120 --> 00:09:05.310
and at equilibrium, the
voltage is equal to zero,
00:09:05.310 --> 00:09:07.430
which means there's no more current.
00:09:07.430 --> 00:09:10.853
And the galvanic or
voltaic cell stops working.
|
Coupled reactions | https://www.youtube.com/watch?v=NnSJsYa1IK0 | vtt | https://www.youtube.com/api/timedtext?v=NnSJsYa1IK0&ei=ylWUZe2QK5uMp-oPtOCu4Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0BD5DD6FCB7B7EB4B48726949B2CC0758CC6E7E6.9EBC0DCB04D8204E0B7B8ACF15B8D163409DD42E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.420 --> 00:00:01.470
- [Instructor] Coupled reactions
00:00:01.470 --> 00:00:03.880
use a thermodynamically favorable reaction
00:00:03.880 --> 00:00:07.910
to drive a thermodynamically
unfavorable reaction.
00:00:07.910 --> 00:00:10.960
For example, let's look
at a hypothetical reaction
00:00:10.960 --> 00:00:15.960
where reactants A and B combine
to form products C and i.
00:00:16.550 --> 00:00:20.370
The standard change in free
energy for this reaction,
00:00:20.370 --> 00:00:23.970
delta G naught, let's
say, is greater than zero.
00:00:23.970 --> 00:00:26.360
And when delta G naught
is greater than zero,
00:00:26.360 --> 00:00:30.050
that's a thermodynamically
unfavorable reaction.
00:00:30.050 --> 00:00:31.770
And at equilibrium,
00:00:31.770 --> 00:00:35.150
the equilibrium constant,
K, is less than one.
00:00:35.150 --> 00:00:36.710
When K is less than one,
00:00:36.710 --> 00:00:39.140
that means there are more
reactants than products
00:00:39.140 --> 00:00:40.420
at equilibrium.
00:00:40.420 --> 00:00:44.560
And if our goal is to make
a lot of the product C,
00:00:44.560 --> 00:00:46.820
that won't happen as long as this reaction
00:00:46.820 --> 00:00:49.370
is thermodynamically unfavorable.
00:00:49.370 --> 00:00:52.120
Next, let's look at another
hypothetical reaction
00:00:52.120 --> 00:00:56.990
where i reacts with D to
form E and F as the products.
00:00:56.990 --> 00:00:58.590
For this hypothetical reaction,
00:00:58.590 --> 00:01:01.740
the standard change in free
energy, delta G naught,
00:01:01.740 --> 00:01:04.820
is much less than zero.
00:01:04.820 --> 00:01:07.850
Since delta G naught for the
second hypothetical reaction
00:01:07.850 --> 00:01:09.350
is less than zero,
00:01:09.350 --> 00:01:12.800
reaction two is
thermodynamically favorable.
00:01:12.800 --> 00:01:14.280
And at equilibrium,
00:01:14.280 --> 00:01:18.220
the equilibrium constant,
K, is much greater than one.
00:01:18.220 --> 00:01:20.200
If K is much greater than one,
00:01:20.200 --> 00:01:22.960
then we can assume that the
second reaction essentially goes
00:01:22.960 --> 00:01:23.890
to completion.
00:01:23.890 --> 00:01:27.460
So all the i and the D will
react together to form E and F.
00:01:27.460 --> 00:01:28.700
And at equilibrium,
00:01:28.700 --> 00:01:32.210
there are way more products
than there are reactants.
00:01:32.210 --> 00:01:36.640
Remember that our goal was to
make a lot of the product C,
00:01:36.640 --> 00:01:39.460
but we can't get that by just
running the first reaction
00:01:39.460 --> 00:01:40.720
by itself.
00:01:40.720 --> 00:01:43.410
However, by coupling the first reaction,
00:01:43.410 --> 00:01:45.730
which is thermodynamically unfavorable,
00:01:45.730 --> 00:01:47.110
to the second reaction,
00:01:47.110 --> 00:01:49.300
which is thermodynamically favorable,
00:01:49.300 --> 00:01:52.760
we can make a significant
amount of product C.
00:01:52.760 --> 00:01:55.950
These two hypothetical reactions
can be coupled together
00:01:55.950 --> 00:01:59.320
because they share a
common intermediate, i.
00:01:59.320 --> 00:02:02.910
Even though reaction one is
thermodynamically unfavorable,
00:02:02.910 --> 00:02:05.740
even if it forms only a small amount of i,
00:02:05.740 --> 00:02:08.620
since reaction two is
thermodynamically favorable,
00:02:08.620 --> 00:02:12.350
the i from reaction one will
be used up in reaction two
00:02:12.350 --> 00:02:15.030
to form the products for reaction two.
00:02:15.030 --> 00:02:18.860
Removing the product i
causes the equilibrium
00:02:18.860 --> 00:02:21.390
to shift to the right
in the first reaction,
00:02:21.390 --> 00:02:25.390
therefore producing more
of our desired product C.
00:02:25.390 --> 00:02:27.930
So the thermodynamically
favorable reaction
00:02:27.930 --> 00:02:31.260
is driving the thermodynamically
unfavorable reaction
00:02:31.260 --> 00:02:32.580
to the right.
00:02:32.580 --> 00:02:35.540
Since we are coupling these
two reactions together,
00:02:35.540 --> 00:02:38.340
if we add reaction one to reaction two,
00:02:38.340 --> 00:02:40.510
the intermediate would cancel out.
00:02:40.510 --> 00:02:41.910
And for the reactants,
00:02:41.910 --> 00:02:44.350
we would get A plus B plus D;
00:02:44.350 --> 00:02:48.910
and for the products, we
would get C plus E plus F.
00:02:48.910 --> 00:02:51.850
To find delta G naught
for this overall equation,
00:02:51.850 --> 00:02:54.200
we would need to add
together delta G naught
00:02:54.200 --> 00:02:58.460
for reaction one and delta
G naught for reaction two.
00:02:58.460 --> 00:03:01.080
So delta G naught for
this overall equation
00:03:01.080 --> 00:03:02.850
would be less than zero,
00:03:02.850 --> 00:03:05.310
which tells us this overall equation
00:03:05.310 --> 00:03:07.740
is thermodynamically favorable.
00:03:07.740 --> 00:03:11.230
And the equilibrium constant
is greater than one,
00:03:11.230 --> 00:03:14.380
which means at equilibrium,
we'll have a decent amount
00:03:14.380 --> 00:03:16.940
of our desired product C.
00:03:16.940 --> 00:03:19.110
Next, let's look at a practical example
00:03:19.110 --> 00:03:20.920
of coupled reactions.
00:03:20.920 --> 00:03:24.150
Let's say that our goal
is to extract solid copper
00:03:24.150 --> 00:03:26.370
from copper(I) sulfide.
00:03:26.370 --> 00:03:29.390
The other product of
this reaction is sulfur.
00:03:29.390 --> 00:03:31.820
However, delta G naught for this reaction
00:03:31.820 --> 00:03:36.390
is equal to positive 86.1
kilojoules per mole of reaction.
00:03:36.390 --> 00:03:38.300
Since delta G naught is positive,
00:03:38.300 --> 00:03:41.200
this reaction is
thermodynamically unfavorable.
00:03:41.200 --> 00:03:44.900
And at equilibrium, there'd
be very little of our product,
00:03:44.900 --> 00:03:47.380
so we wouldn't get very much copper.
00:03:47.380 --> 00:03:49.990
The solution is to couple
this first reaction
00:03:49.990 --> 00:03:52.950
to a thermodynamically favorable reaction.
00:03:52.950 --> 00:03:57.150
And that's the conversion of
sulfur into sulfur dioxide.
00:03:57.150 --> 00:04:00.830
So solid sulfur plus oxygen
gas give sulfur dioxide,
00:04:00.830 --> 00:04:02.760
and delta G naught for this reaction
00:04:02.760 --> 00:04:07.760
is equal to negative 300.4
kilojoules per mole of reaction.
00:04:07.780 --> 00:04:09.880
So adding our two reactions together,
00:04:09.880 --> 00:04:12.820
the common intermediate,
sulfur, cancels out,
00:04:12.820 --> 00:04:16.340
and that gives us copper(I)
sulfide plus oxygen
00:04:16.340 --> 00:04:21.340
for the reactants goes to
solid copper and sulfur dioxide
00:04:22.150 --> 00:04:23.550
for the products.
00:04:23.550 --> 00:04:26.810
And if we add the two delta
G naught values together,
00:04:26.810 --> 00:04:30.990
positive 86.1 plus negative 300.4
00:04:30.990 --> 00:04:34.290
gives a delta G naught
for this overall equation
00:04:34.290 --> 00:04:39.290
equal to negative 214.3
kilojoules per mole of reaction.
00:04:39.570 --> 00:04:42.280
Since delta G naught is negative,
00:04:42.280 --> 00:04:45.910
now, this overall reaction is
thermodynamically favorable
00:04:45.910 --> 00:04:49.130
with an equilibrium
constant greater than one.
00:04:49.130 --> 00:04:52.500
Therefore, we will now
produce a lot of copper.
00:04:52.500 --> 00:04:56.210
So burning copper(I) sulfide
in air gives us a feasible way
00:04:56.210 --> 00:05:00.100
of extracting copper
from copper(I) sulfide.
00:05:00.100 --> 00:05:04.010
Coupled reactions are also
very important in biochemistry.
00:05:04.010 --> 00:05:08.250
For example, two amino acids
are alanine and glycine.
00:05:08.250 --> 00:05:10.970
And if these two amino
acids come together,
00:05:10.970 --> 00:05:13.670
they form what's called a dipeptide.
00:05:13.670 --> 00:05:15.010
It's very important for the body
00:05:15.010 --> 00:05:16.840
to be able to make dipeptides
00:05:16.840 --> 00:05:20.010
because if we were to add
on some more amino acids,
00:05:20.010 --> 00:05:22.550
we would form what's called a polypeptide,
00:05:22.550 --> 00:05:25.750
which eventually leads to
the formation of a protein.
00:05:25.750 --> 00:05:28.030
However, the formation of dipeptides
00:05:28.030 --> 00:05:30.670
is thermodynamically unfavorable.
00:05:30.670 --> 00:05:32.250
Therefore, the body needs a way
00:05:32.250 --> 00:05:35.350
of making this reaction
thermodynamically favorable
00:05:35.350 --> 00:05:37.400
so the body can make proteins.
00:05:37.400 --> 00:05:39.940
To do this, the body uses ATP,
00:05:39.940 --> 00:05:42.343
which stands for adenosine triphosphate.
00:05:43.720 --> 00:05:47.900
And here's the dot structure
for ATP in the ionized form.
00:05:47.900 --> 00:05:51.100
ATP is often called a
high energy compound,
00:05:51.100 --> 00:05:53.370
and the hydrolysis of ATP
00:05:53.370 --> 00:05:56.890
is used to drive protein synthesis.
00:05:56.890 --> 00:05:59.530
Next, let's look at the
equation showing the hydrolysis
00:05:59.530 --> 00:06:02.040
of ATP to ADP,
00:06:02.040 --> 00:06:06.410
which is adenosine diphosphate
and inorganic phosphate.
00:06:06.410 --> 00:06:10.450
The standard change in free
energy for the hydrolysis of ATP
00:06:10.450 --> 00:06:14.340
is equal to negative 31
kilojoules per mole of reaction.
00:06:14.340 --> 00:06:16.420
Since delta G naught is negative,
00:06:16.420 --> 00:06:20.580
the hydrolysis of ATP is
thermodynamically favorable.
00:06:20.580 --> 00:06:22.550
Alanine and glycine combine
00:06:22.550 --> 00:06:26.150
to form the dipeptide
alanylglycine and water.
00:06:26.150 --> 00:06:28.650
Delta G naught for the
formation of this dipeptide
00:06:28.650 --> 00:06:32.450
is equal to positive 29
kilojoules per mole of reaction.
00:06:32.450 --> 00:06:34.650
Since delta G naught is positive,
00:06:34.650 --> 00:06:38.290
this reaction is
thermodynamically unfavorable.
00:06:38.290 --> 00:06:39.700
With the help of an enzyme,
00:06:39.700 --> 00:06:42.330
the unfavorable reaction is coupled
00:06:42.330 --> 00:06:44.500
to the favorable reaction.
00:06:44.500 --> 00:06:46.460
And if we add the two reactions together,
00:06:46.460 --> 00:06:50.140
water would cancel out and
give us alanine plus glycine
00:06:50.140 --> 00:06:52.900
plus ATP for the reactants,
00:06:52.900 --> 00:06:57.190
and alanylglycine and ADP
and inorganic phosphate
00:06:57.190 --> 00:06:58.690
for the products.
00:06:58.690 --> 00:07:01.680
Adding the two values of
delta G naught together,
00:07:01.680 --> 00:07:02.740
we get delta G naught
00:07:02.740 --> 00:07:06.750
is equal to negative two
kilojoules per mole of reaction.
00:07:06.750 --> 00:07:08.800
And since delta G naught is negative,
00:07:08.800 --> 00:07:10.490
it's now favorable for the body
00:07:10.490 --> 00:07:12.853
to synthesize this dipeptide.
|
Free energy and equilibrium | https://www.youtube.com/watch?v=4ZcTEiJru84 | vtt | https://www.youtube.com/api/timedtext?v=4ZcTEiJru84&ei=ylWUZeLbKsqep-oP2J2I2AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=214725CB2E886834608A6F23AEF44F82E224B8CD.8A7906445F62A4339677FB2426E72DE1186BAD94&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.360 --> 00:00:02.330
- [Instructor] Let's say
we have a generic reaction
00:00:02.330 --> 00:00:04.470
where reactants turn into products.
00:00:04.470 --> 00:00:07.380
And our goal is to think
about the relationship
00:00:07.380 --> 00:00:10.240
between free energy and this reaction
00:00:10.240 --> 00:00:12.650
when it comes to equilibrium.
00:00:12.650 --> 00:00:15.100
First, we need to consider the equation
00:00:15.100 --> 00:00:17.780
that allows us to calculate
non-standard changes
00:00:17.780 --> 00:00:19.720
in free energy delta G.
00:00:19.720 --> 00:00:21.180
We can think about delta G
00:00:21.180 --> 00:00:24.010
as the instantaneous
difference in free energy
00:00:24.010 --> 00:00:26.770
between reactants and products.
00:00:26.770 --> 00:00:29.130
And from the equation we see that delta G
00:00:29.130 --> 00:00:34.090
is equal to delta naught plus RT ln of Q.
00:00:34.090 --> 00:00:37.540
Delta G naught is the
standard change in free energy
00:00:37.540 --> 00:00:40.030
between reactants and products.
00:00:40.030 --> 00:00:42.930
This value refers to the
difference in free energy
00:00:42.930 --> 00:00:46.020
between reactants and products
in their standard states
00:00:46.020 --> 00:00:48.150
at a specified temperature.
00:00:48.150 --> 00:00:50.510
R is the ideal gas constant,
00:00:50.510 --> 00:00:52.870
T is the absolute temperature in Kelvin,
00:00:52.870 --> 00:00:55.920
and Q is the reaction quotient.
00:00:55.920 --> 00:00:59.280
At equilibrium, the instantaneous
difference in free energy
00:00:59.280 --> 00:01:02.000
between reactants and products is zero,
00:01:02.000 --> 00:01:05.780
which means there's no more
driving force for the reaction.
00:01:05.780 --> 00:01:09.430
And at equilibrium,
the reaction quotient Q
00:01:09.430 --> 00:01:13.420
is equal to the equilibrium constant K.
00:01:13.420 --> 00:01:17.140
So we can plug in zero for
delta G in our equation.
00:01:17.140 --> 00:01:19.890
And we can plug in K for Q,
00:01:19.890 --> 00:01:22.530
that gives us zero is
equal to delta G naught
00:01:22.530 --> 00:01:25.590
plus RT ln of K.
00:01:25.590 --> 00:01:29.000
If we subtract RT ln of K from both sides,
00:01:29.000 --> 00:01:30.250
we get delta G naught
00:01:30.250 --> 00:01:34.160
is equal to negative RT ln of K.
00:01:34.160 --> 00:01:36.590
This equation is extremely useful
00:01:36.590 --> 00:01:38.770
because now we have a relationship
00:01:38.770 --> 00:01:41.840
between free energy and equilibrium.
00:01:41.840 --> 00:01:44.250
If we know the standard
change in free energy
00:01:44.250 --> 00:01:47.640
for a particular reaction
at a particular temperature,
00:01:47.640 --> 00:01:52.640
we can calculate the equilibrium
constant for that reaction.
00:01:52.640 --> 00:01:54.480
Next, let's go ahead
and go through the math
00:01:54.480 --> 00:01:57.360
to solve for the equilibrium constant K.
00:01:57.360 --> 00:01:58.530
To solve for K,
00:01:58.530 --> 00:02:02.763
we need to first divide
both sides by negative RT.
00:02:04.050 --> 00:02:05.300
So on the right side,
00:02:05.300 --> 00:02:08.060
negative RT would cancel out.
00:02:08.060 --> 00:02:10.420
We could then rewrite it as ln of K
00:02:10.420 --> 00:02:15.070
is equal to negative delta
G naught divided by RT.
00:02:15.070 --> 00:02:16.770
And to get rid of the ln,
00:02:16.770 --> 00:02:21.370
we need to take e to both sides,
00:02:21.370 --> 00:02:23.140
which gives us the following equation.
00:02:23.140 --> 00:02:25.160
The equilibrium constant K
00:02:25.160 --> 00:02:30.160
is equal to e to the negative
delta G naught divided by RT.
00:02:30.430 --> 00:02:32.520
So if we know the value for delta G naught
00:02:32.520 --> 00:02:34.290
for a particular reaction,
00:02:34.290 --> 00:02:35.550
and we know that temperature,
00:02:35.550 --> 00:02:39.010
we can calculate the equilibrium
constant for that reaction
00:02:39.010 --> 00:02:41.370
at that particular temperature.
00:02:41.370 --> 00:02:43.850
Let's calculate the equilibrium constant K
00:02:43.850 --> 00:02:47.820
for the synthesis of ammonia
from nitrogen and hydrogen.
00:02:47.820 --> 00:02:51.290
And let's do this for three
different temperatures.
00:02:51.290 --> 00:02:53.540
Well, let's start with
a temperature of 298K.
00:02:54.830 --> 00:02:56.203
delta G naught at this temperature
00:02:56.203 --> 00:03:01.203
is equal to - 33.0 kilojoules
per mole of reaction.
00:03:01.570 --> 00:03:04.500
So to solve for the
equilibrium constant K,
00:03:04.500 --> 00:03:08.430
we need to plug in the
value for delta G naught.
00:03:08.430 --> 00:03:11.040
We also need to plug in
the temperature in Kelvin
00:03:11.040 --> 00:03:13.760
and the ideal gas constant R.
00:03:13.760 --> 00:03:15.160
The ideal gas constant
00:03:15.160 --> 00:03:19.720
is equal to 8.314 joules
per mole of reaction Kelvin.
00:03:19.720 --> 00:03:21.790
And since we're using joules in the units,
00:03:21.790 --> 00:03:25.470
we need to make sure to convert
the units for delta G naught
00:03:25.470 --> 00:03:27.530
into joules per mole of reaction.
00:03:27.530 --> 00:03:31.590
So - 33.0 kilojoules per mole of reaction
00:03:31.590 --> 00:03:35.610
is equal to - 33,000
joules per mole of reaction
00:03:35.610 --> 00:03:38.130
still with three significant digits.
00:03:38.130 --> 00:03:41.770
And once we plug in our
temperature of 298 Kelvin,
00:03:41.770 --> 00:03:44.140
notice how Kelvin cancels out
00:03:44.140 --> 00:03:47.940
and also joules per mole
of reaction cancels out.
00:03:47.940 --> 00:03:48.850
When don't we do the math,
00:03:48.850 --> 00:03:51.130
we find that the equilibrium constant K
00:03:51.130 --> 00:03:54.380
is equal to e to the 13.3 power,
00:03:54.380 --> 00:03:57.310
which is equal to 6 times 10 to the fifth.
00:03:57.310 --> 00:04:01.370
Notice how equilibrium
constants don't have units.
00:04:01.370 --> 00:04:03.370
When e is raised to a power,
00:04:03.370 --> 00:04:06.670
the result has the same
number of significant figures
00:04:06.670 --> 00:04:09.400
as there are decimal places in the power.
00:04:09.400 --> 00:04:12.300
Since we have only one
decimal place in this power,
00:04:12.300 --> 00:04:16.130
we have one significant
figure for our final answer.
00:04:16.130 --> 00:04:19.990
Since the value for K for
this reaction at 298 Kelvin
00:04:19.990 --> 00:04:21.750
is much greater than one,
00:04:21.750 --> 00:04:25.360
that tells us at equilibrium
there are more products
00:04:25.360 --> 00:04:27.050
than there are reactants.
00:04:27.050 --> 00:04:28.980
So there's a lot more ammonia
00:04:28.980 --> 00:04:31.430
than there is nitrogen or hydrogen,
00:04:31.430 --> 00:04:36.430
when this reaction reaches
equilibrium at 298 Kelvin.
00:04:36.530 --> 00:04:39.340
So whenever delta G naught is negative,
00:04:39.340 --> 00:04:42.170
or you could say delta G
naught is less than zero.
00:04:42.170 --> 00:04:44.770
The equilibrium constant
is greater than one,
00:04:44.770 --> 00:04:49.360
and products are favored over
reactants at equilibrium.
00:04:49.360 --> 00:04:52.220
For the same reaction for
the synthesis of ammonia,
00:04:52.220 --> 00:04:54.540
let's calculate the equilibrium constant K
00:04:54.540 --> 00:04:55.750
at a different temperature,
00:04:55.750 --> 00:04:57.950
this time it's 1000 Kelvin.
00:04:57.950 --> 00:05:01.160
And that 1000 Kelvin delta
G naught for this reaction
00:05:01.160 --> 00:05:06.160
is equal to + 106.5 kilojoules
per mole of reaction.
00:05:06.450 --> 00:05:07.820
Just like the previous example,
00:05:07.820 --> 00:05:09.990
we're gonna plug everything
into our equation
00:05:09.990 --> 00:05:11.570
to calculate K.
00:05:11.570 --> 00:05:13.780
So we need to plug in delta G naught,
00:05:13.780 --> 00:05:16.730
the temperature which
is 1000 Kelvin this time
00:05:16.730 --> 00:05:19.030
and the ideal gas constant.
00:05:19.030 --> 00:05:21.130
So we plug in the ideal gas constant,
00:05:21.130 --> 00:05:23.960
the temperature and delta G naught.
00:05:23.960 --> 00:05:25.490
Once again, we had to convert
00:05:25.490 --> 00:05:27.480
from kilojoules per mole reaction
00:05:27.480 --> 00:05:30.490
into joules per mole of reaction.
00:05:30.490 --> 00:05:32.850
So joules per mole of reaction cancels out
00:05:32.850 --> 00:05:35.390
and Kelvin cancels out.
00:05:35.390 --> 00:05:40.390
That gives us K is equal
to e to the - 12.81 power,
00:05:40.670 --> 00:05:44.670
which is equal to 2.7 times 10 to the - 6.
00:05:44.670 --> 00:05:47.630
Because we have two decimal
places in the power.
00:05:47.630 --> 00:05:51.450
The final answer is to
two significant figures.
00:05:51.450 --> 00:05:54.810
For this example, K is much less than one
00:05:54.810 --> 00:05:57.060
which tells us at equilibrium,
00:05:57.060 --> 00:06:00.540
there are far more reactants
than there are products.
00:06:00.540 --> 00:06:02.350
So at 1000 Kelvin,
00:06:02.350 --> 00:06:04.260
if this reaction at equilibrium
00:06:04.260 --> 00:06:06.140
we'd have a lot more of our reactants,
00:06:06.140 --> 00:06:07.460
nitrogen and hydrogen,
00:06:07.460 --> 00:06:11.210
and only a small amount
of our product ammonia.
00:06:11.210 --> 00:06:14.080
So whenever delta G naught is positive,
00:06:14.080 --> 00:06:17.230
or you could say delta G
naught is greater than zero.
00:06:17.230 --> 00:06:20.600
The equilibrium constant
K is less than one,
00:06:20.600 --> 00:06:22.180
which means that equilibrium,
00:06:22.180 --> 00:06:26.210
there are a lot more reactants
than there are products.
00:06:26.210 --> 00:06:27.330
And for our last example,
00:06:27.330 --> 00:06:29.690
let's calculate the equilibrium constant K
00:06:29.690 --> 00:06:31.340
for the same reaction.
00:06:31.340 --> 00:06:33.970
This time at 464 Kelvin,
00:06:33.970 --> 00:06:36.010
at that temperature delta G naught
00:06:36.010 --> 00:06:38.560
for this reaction is equal to zero.
00:06:38.560 --> 00:06:41.160
Calculating K is a lot
easier for this example,
00:06:41.160 --> 00:06:44.320
because if we plug in
zero for delta G naught,
00:06:44.320 --> 00:06:48.360
K is equal to each of the zero
power which is equal to one.
00:06:48.360 --> 00:06:51.150
And when the equilibrium
constant is equal to one,
00:06:51.150 --> 00:06:53.630
that means that equilibrium
there's significant
00:06:53.630 --> 00:06:56.410
amounts of both reactants and products.
00:06:56.410 --> 00:07:01.360
So if this reaction were to
reach equilibrium at 464 Kelvin,
00:07:01.360 --> 00:07:04.500
there'll be a significant
amount of both our reactants,
00:07:04.500 --> 00:07:06.270
which are nitrogen and hydrogen,
00:07:06.270 --> 00:07:08.600
and our product which is ammonia.
00:07:08.600 --> 00:07:10.850
Let's summarize what we've
learned about the relationship
00:07:10.850 --> 00:07:13.810
between free energy and equilibrium.
00:07:13.810 --> 00:07:16.070
The standard at change in free energy
00:07:16.070 --> 00:07:18.110
for a reaction delta G naught
00:07:18.110 --> 00:07:22.800
is related to the equilibrium
constant K by this equation.
00:07:22.800 --> 00:07:24.560
And if we are using this equation,
00:07:24.560 --> 00:07:27.310
we know the reaction is at equilibrium
00:07:27.310 --> 00:07:29.140
because we found that equation
00:07:29.140 --> 00:07:31.940
by setting the instantaneous
change in free energy
00:07:31.940 --> 00:07:35.690
delta G equal to zero.
00:07:35.690 --> 00:07:38.080
It's very easy to think that delta G
00:07:38.080 --> 00:07:39.830
without the superscript naught,
00:07:39.830 --> 00:07:42.630
and delta G naught are the same thing.
00:07:42.630 --> 00:07:45.760
However, they are very
different quantities.
00:07:45.760 --> 00:07:49.330
For all three of the situations
that we talked about,
00:07:49.330 --> 00:07:53.070
delta G without the
superscript was equal to zero,
00:07:53.070 --> 00:07:56.370
because the reaction was at equilibrium.
00:07:56.370 --> 00:07:57.980
However, because delta G naught
00:07:57.980 --> 00:07:59.470
is the difference in free energy
00:07:59.470 --> 00:08:02.240
between reactants and products
and their standard states,
00:08:02.240 --> 00:08:04.910
delta G naught does not
have to be equal to zero
00:08:04.910 --> 00:08:06.270
at equilibrium.
00:08:06.270 --> 00:08:09.740
delta G naught is a constant
at a particular temperature,
00:08:09.740 --> 00:08:12.340
just like the equilibrium constant K.
00:08:12.340 --> 00:08:15.660
And if delta G naught is less than zero,
00:08:15.660 --> 00:08:17.310
K is greater than one,
00:08:17.310 --> 00:08:19.040
which means at equilibrium,
00:08:19.040 --> 00:08:21.850
there are more products than reactants.
00:08:21.850 --> 00:08:24.060
If delta G naught at a
particular temperature
00:08:24.060 --> 00:08:25.570
is greater than zero.
00:08:25.570 --> 00:08:28.650
That means the equilibrium
constant is less than one,
00:08:28.650 --> 00:08:30.120
which means that equilibrium
00:08:30.120 --> 00:08:32.470
there are more reactants than products.
00:08:32.470 --> 00:08:36.220
And when delta G naught is
equal to zero K is equal to one,
00:08:36.220 --> 00:08:38.970
which means significant
amounts of both reactants
00:08:38.970 --> 00:08:40.753
and products at equilibrium.
|
Nonstandard free energy changes | https://www.youtube.com/watch?v=P6dcloxLv2Q | vtt | https://www.youtube.com/api/timedtext?v=P6dcloxLv2Q&ei=ylWUZaHNJqWWhcIPisOF8A4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2CA35EDADC55623508D2D1D91BC6732585B853DE.B7F250438871E0CADA054B81A7DD872A4ED12A53&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.360 --> 00:00:01.690
- [Instructor] Understanding the concept
00:00:01.690 --> 00:00:04.250
of nonstandard free energy changes
00:00:04.250 --> 00:00:07.380
is really important when it
comes to a chemical reaction.
00:00:07.380 --> 00:00:09.140
For this generic chemical reaction,
00:00:09.140 --> 00:00:11.760
the reactants turn into the products.
00:00:11.760 --> 00:00:16.450
And nonstandard free energy
change is symbolized by delta G.
00:00:16.450 --> 00:00:18.000
And notice, this delta G
00:00:18.000 --> 00:00:20.830
doesn't have the naught superscript,
00:00:20.830 --> 00:00:24.970
and therefore, it's nonstandard
change in free energy.
00:00:24.970 --> 00:00:26.930
The reason why this
concept is so important
00:00:26.930 --> 00:00:29.510
for a chemical reaction is by calculating
00:00:29.510 --> 00:00:31.770
the nonstandard change in free energy,
00:00:31.770 --> 00:00:34.210
we can figure out which direction
00:00:34.210 --> 00:00:36.520
the net reaction will proceed.
00:00:36.520 --> 00:00:38.710
When delta G is less than zero,
00:00:38.710 --> 00:00:40.540
so when delta G is negative,
00:00:40.540 --> 00:00:44.680
the forward reaction is
thermodynamically favored.
00:00:44.680 --> 00:00:48.050
Therefore, the reactants
will turn into the products.
00:00:48.050 --> 00:00:50.080
And the amount of products will increase,
00:00:50.080 --> 00:00:52.750
and the amount of reactants will decrease.
00:00:52.750 --> 00:00:54.790
When delta G is greater than zero,
00:00:54.790 --> 00:00:56.860
so when delta G is positive,
00:00:56.860 --> 00:01:01.340
the forward reaction is not
thermodynamically favored,
00:01:01.340 --> 00:01:04.210
which means the reverse
reaction is favored.
00:01:04.210 --> 00:01:07.020
So the net reaction goes
to the left to increase
00:01:07.020 --> 00:01:10.500
the amount of reactants and
decrease the amount of products.
00:01:10.500 --> 00:01:12.530
As long as there's a
difference in free energy
00:01:12.530 --> 00:01:14.530
between the reactants and the products,
00:01:14.530 --> 00:01:16.720
the net reaction will
proceed either to the left
00:01:16.720 --> 00:01:17.780
or to the right.
00:01:17.780 --> 00:01:20.260
However, when there's no
difference in free energy
00:01:20.260 --> 00:01:22.220
between the reactants and the products,
00:01:22.220 --> 00:01:24.580
or delta G is equal to zero,
00:01:24.580 --> 00:01:27.160
the reaction is at equilibrium.
00:01:27.160 --> 00:01:29.040
And when the reaction is at equilibrium,
00:01:29.040 --> 00:01:30.870
the concentrations of reactants
00:01:30.870 --> 00:01:33.450
and products remain constant.
00:01:33.450 --> 00:01:36.040
So it's useful to think
about nonstandard change
00:01:36.040 --> 00:01:38.410
in free energy as the driving force
00:01:38.410 --> 00:01:39.970
for a chemical reaction.
00:01:39.970 --> 00:01:42.150
As long as there's a
difference in free energy
00:01:42.150 --> 00:01:43.840
between reactants and products,
00:01:43.840 --> 00:01:46.510
the net reaction will move
one direction or the other
00:01:46.510 --> 00:01:48.140
to the left or to the right.
00:01:48.140 --> 00:01:50.620
However, when there's no
difference in free energy
00:01:50.620 --> 00:01:51.960
between reactants and products,
00:01:51.960 --> 00:01:53.510
there's no more driving force
00:01:53.510 --> 00:01:56.120
and the reaction is at equilibrium.
00:01:56.120 --> 00:01:57.580
Next, let's look at the equation
00:01:57.580 --> 00:02:01.540
that relates nonstandard
change in free energy, delta G,
00:02:01.540 --> 00:02:04.840
to standard change in free
energy, delta G naught.
00:02:04.840 --> 00:02:07.100
Remember, the superscript naught refers
00:02:07.100 --> 00:02:10.340
to the substances being
in their standard states
00:02:10.340 --> 00:02:12.660
under a pressure of one atmosphere.
00:02:12.660 --> 00:02:16.180
So delta G, or the nonstandard
change in free energy,
00:02:16.180 --> 00:02:18.550
refers to the instantaneous difference
00:02:18.550 --> 00:02:21.760
in free energy between the
reactants and the products.
00:02:21.760 --> 00:02:24.610
So when that reaction moves
to the left or to the right,
00:02:24.610 --> 00:02:26.550
this value is always changing.
00:02:26.550 --> 00:02:29.530
It's the driving force for the reaction.
00:02:29.530 --> 00:02:32.800
Delta G naught is a different situation.
00:02:32.800 --> 00:02:36.440
Delta G naught is a constant
at a certain temperature.
00:02:36.440 --> 00:02:39.140
And that's because it's
referring to the difference
00:02:39.140 --> 00:02:41.570
in free energy between
reactants and products
00:02:41.570 --> 00:02:43.320
in their standard states.
00:02:43.320 --> 00:02:46.130
And so this value will remain the same
00:02:46.130 --> 00:02:49.760
as the net reaction moves
to the left or to the right.
00:02:49.760 --> 00:02:51.580
To calculate the nonstandard change
00:02:51.580 --> 00:02:53.530
in free energy, delta G,
00:02:53.530 --> 00:02:55.500
it's equal to the standard change
00:02:55.500 --> 00:03:00.270
in free energy, delta G naught,
plus RT natural log of Q,
00:03:00.270 --> 00:03:02.930
where R is the ideal gas constant,
00:03:02.930 --> 00:03:05.000
T is the temperature in Kelvin,
00:03:05.000 --> 00:03:08.250
and Q is the reaction quotient.
00:03:08.250 --> 00:03:11.660
Next, let's calculate delta
G for a chemical reaction.
00:03:11.660 --> 00:03:14.940
And this is the reaction for
the synthesis of ammonia gas
00:03:14.940 --> 00:03:18.170
from nitrogen gas and hydrogen gas.
00:03:18.170 --> 00:03:22.540
Our goal is to calculate
delta G at 25 degrees Celsius
00:03:22.540 --> 00:03:24.720
at the moment in time
when the partial pressures
00:03:24.720 --> 00:03:27.440
of all three gases are one atmosphere.
00:03:27.440 --> 00:03:29.910
So one atmosphere for
nitrogen, for hydrogen,
00:03:29.910 --> 00:03:31.920
and for ammonia.
00:03:31.920 --> 00:03:36.030
At 25 degrees Celsius, delta
G naught for this reaction
00:03:36.030 --> 00:03:41.030
is equal to negative 33.0
kilojoules per mole of reaction.
00:03:41.170 --> 00:03:43.140
So our goal is to calculate delta G.
00:03:43.140 --> 00:03:45.240
And we know delta G naught,
00:03:45.240 --> 00:03:48.640
but we need to figure out what
Q is at this moment in time,
00:03:48.640 --> 00:03:50.610
when the partial
pressures of all the gases
00:03:50.610 --> 00:03:52.430
are one atmosphere.
00:03:52.430 --> 00:03:55.240
We can get the expression
for the reaction quotient Q
00:03:55.240 --> 00:03:57.230
from the balanced equation.
00:03:57.230 --> 00:03:59.430
So it would be the partial
pressure of ammonia.
00:03:59.430 --> 00:04:02.000
And since there's a two,
it'd be the partial pressure
00:04:02.000 --> 00:04:04.600
of ammonia raised to the second power
00:04:04.600 --> 00:04:07.510
divided by the partial
pressure of nitrogen.
00:04:07.510 --> 00:04:09.400
And since there's a one as a coefficient
00:04:09.400 --> 00:04:10.460
in the balanced equation,
00:04:10.460 --> 00:04:12.310
it's the partial pressure
of nitrogen raised
00:04:12.310 --> 00:04:13.470
to the first power,
00:04:13.470 --> 00:04:15.710
times the partial pressure of hydrogen.
00:04:15.710 --> 00:04:17.040
And since we have a three here,
00:04:17.040 --> 00:04:19.210
it'd be the partial
pressure of hydrogen raised
00:04:19.210 --> 00:04:20.910
to the third power.
00:04:20.910 --> 00:04:23.210
Since all three gases
have a partial pressure
00:04:23.210 --> 00:04:26.980
of one atmosphere, when
we plug in one atmosphere,
00:04:26.980 --> 00:04:30.400
we find that Q is equal to one.
00:04:30.400 --> 00:04:34.400
And the natural log of
one is equal to zero.
00:04:34.400 --> 00:04:38.290
So this second term here in
our equation goes to zero.
00:04:38.290 --> 00:04:40.240
And at this moment in time,
00:04:40.240 --> 00:04:44.410
delta G is equal to delta G naught.
00:04:44.410 --> 00:04:46.000
And since delta G naught is equal
00:04:46.000 --> 00:04:50.680
to negative 33.0 kilojoules
per mole of reaction,
00:04:50.680 --> 00:04:53.945
since delta G is negative
at this moment in time,
00:04:53.945 --> 00:04:57.320
the reaction is thermodynamically favored
00:04:57.320 --> 00:04:59.600
in the forward direction.
00:04:59.600 --> 00:05:02.840
So the reactants will
react together to form
00:05:02.840 --> 00:05:04.260
more of the products.
00:05:04.260 --> 00:05:07.080
The reason why delta G is
equal to delta G naught
00:05:07.080 --> 00:05:10.520
at this moment in time is because
our reactants and products
00:05:10.520 --> 00:05:13.300
are all in their standard states.
00:05:13.300 --> 00:05:14.830
By convention for a gas,
00:05:14.830 --> 00:05:17.750
standard state refers to
the pure gas at a pressure
00:05:17.750 --> 00:05:19.700
of one atmosphere.
00:05:19.700 --> 00:05:21.870
And since all of the
partial pressures are equal
00:05:21.870 --> 00:05:25.940
to one atmosphere, that
gave us Q is equal to one,
00:05:25.940 --> 00:05:27.950
which made the second term equal to zero.
00:05:27.950 --> 00:05:31.700
So only when the substances
are in their standard states
00:05:31.700 --> 00:05:34.970
is delta G equal to delta G naught.
00:05:34.970 --> 00:05:37.700
So if we had a different
set of partial pressures,
00:05:37.700 --> 00:05:41.640
delta G wouldn't be
equal to delta G naught.
00:05:41.640 --> 00:05:44.680
Let's calculate delta
G for the same reaction
00:05:44.680 --> 00:05:46.730
at 25 degrees Celsius.
00:05:46.730 --> 00:05:49.180
However, this time, instead
of having partial pressures
00:05:49.180 --> 00:05:52.850
of one atmosphere, all three
gasses at this moment in time
00:05:52.850 --> 00:05:55.990
have a partial pressure
of two atmospheres.
00:05:55.990 --> 00:05:59.480
Let's start by calculating
the reaction quotient Q.
00:05:59.480 --> 00:06:01.460
So when we plug in two atmospheres
00:06:01.460 --> 00:06:03.560
for the partial pressures of our gasses,
00:06:03.560 --> 00:06:07.220
we find that Q is equal to .25.
00:06:07.220 --> 00:06:09.492
Next, to calculate delta G,
we need to plug everything
00:06:09.492 --> 00:06:11.530
into our equation.
00:06:11.530 --> 00:06:16.530
So delta G naught is still equal
to negative 33.0 kilojoules
00:06:16.540 --> 00:06:17.880
per mole of reaction.
00:06:17.880 --> 00:06:20.040
So we can see, we plugged that in here.
00:06:20.040 --> 00:06:24.390
The ideal gas constant R is 8.314 joules
00:06:24.390 --> 00:06:26.640
per Kelvin mole of reaction.
00:06:26.640 --> 00:06:29.080
But to keep our units
the same in kilojoules,
00:06:29.080 --> 00:06:31.910
you can see I've converted
the ideal gas constant
00:06:31.910 --> 00:06:34.460
into kilojoules per
Kelvin mole of reaction.
00:06:34.460 --> 00:06:35.293
So it's .008314.
00:06:38.420 --> 00:06:41.280
We said the temperature
was 25 degrees Celsius.
00:06:41.280 --> 00:06:46.280
So 25 plus 273 is equal to 298 Kelvin.
00:06:46.370 --> 00:06:49.880
And the reaction quotient
Q is equal to .25.
00:06:49.880 --> 00:06:53.200
So be the it'd natural log of .25.
00:06:53.200 --> 00:06:55.740
So Kelvin will cancel out.
00:06:55.740 --> 00:06:57.360
And when we do the calculation,
00:06:57.360 --> 00:06:59.210
we find that delta G is equal
00:06:59.210 --> 00:07:03.860
to negative 36.4 kilojoules
per mole of reaction.
00:07:03.860 --> 00:07:07.120
Since delta G is negative
at this moment in time,
00:07:07.120 --> 00:07:09.790
the reaction is
thermodynamically favorable
00:07:09.790 --> 00:07:12.010
in the forward direction.
00:07:12.010 --> 00:07:14.370
So the net reaction will move to the right
00:07:14.370 --> 00:07:15.820
to make more products,
00:07:15.820 --> 00:07:18.890
and to decrease the amount of reactants.
00:07:18.890 --> 00:07:21.690
An increase in the amount
of ammonia means an increase
00:07:21.690 --> 00:07:23.490
in the partial pressure of ammonia.
00:07:23.490 --> 00:07:25.740
And a decrease in the amount of reactants
00:07:25.740 --> 00:07:28.030
means a decrease in the partial pressures
00:07:28.030 --> 00:07:29.340
of the reactants.
00:07:29.340 --> 00:07:32.140
Therefore, when the net
reaction goes to the right,
00:07:32.140 --> 00:07:35.910
the reaction quotient Q increases.
00:07:35.910 --> 00:07:40.510
So we started with a relatively
small value for Q of .25.
00:07:40.510 --> 00:07:43.480
And we know that Q is going to increase.
00:07:43.480 --> 00:07:45.120
Let's just jump ahead to a point,
00:07:45.120 --> 00:07:49.640
and let's say that Q is equal
to 1.0 times 10 to the third,
00:07:49.640 --> 00:07:51.970
and let's plug that into our equation
00:07:51.970 --> 00:07:54.510
and see what happens to delta G.
00:07:54.510 --> 00:07:56.730
So delta G naught stays the same
00:07:56.730 --> 00:08:00.770
at negative 33.0 kilojoules
per mole of reaction.
00:08:00.770 --> 00:08:02.730
The ideal gas constant's the same.
00:08:02.730 --> 00:08:03.920
The temperature's the same.
00:08:03.920 --> 00:08:06.810
So all we've done is increase Q.
00:08:06.810 --> 00:08:08.790
Once again, Kelvin cancels out,
00:08:08.790 --> 00:08:10.870
and we find that delta G,
00:08:10.870 --> 00:08:13.470
the instantaneous
difference in free energy,
00:08:13.470 --> 00:08:17.440
is equal to negative 15.9
kilojoules per mole of reaction
00:08:17.440 --> 00:08:19.180
at this moment in time.
00:08:19.180 --> 00:08:21.800
Since delta G is negative, once again,
00:08:21.800 --> 00:08:24.360
the forward reaction is favored.
00:08:24.360 --> 00:08:27.380
So the reaction moves to the
right to increase products
00:08:27.380 --> 00:08:29.530
and to decrease reactants.
00:08:29.530 --> 00:08:33.690
So again, Q will continue to increase.
00:08:33.690 --> 00:08:35.950
And think about what's
happening to delta G.
00:08:35.950 --> 00:08:40.660
It was negative 36.4, and
now it's negative 15.9.
00:08:40.660 --> 00:08:44.950
And as Q keeps increasing,
delta G keeps getting closer
00:08:44.950 --> 00:08:47.320
and closer to zero.
00:08:47.320 --> 00:08:52.320
Q will keep increasing until
delta G is equal to zero
00:08:53.030 --> 00:08:56.140
and the reaction is at equilibrium.
00:08:56.140 --> 00:08:59.890
So as long as Q is not equal
to the equilibrium constant K
00:08:59.890 --> 00:09:04.040
for this reaction, the
reaction is not at equilibrium.
00:09:04.040 --> 00:09:06.500
But eventually, Q will be equal
00:09:06.500 --> 00:09:08.440
to the equilibrium constant K.
00:09:08.440 --> 00:09:12.030
And if we were to plug that
value into our equation,
00:09:12.030 --> 00:09:15.480
we would find that delta
G is equal to zero.
00:09:15.480 --> 00:09:19.020
And therefore, the
reaction is at equilibrium.
00:09:19.020 --> 00:09:21.060
Let's summarize the difference between
00:09:21.060 --> 00:09:24.180
the nonstandard change
in free energy, delta G,
00:09:24.180 --> 00:09:27.890
and the standard change in
free energy, delta G naught.
00:09:27.890 --> 00:09:30.310
Delta G naught is talking
about the difference
00:09:30.310 --> 00:09:32.900
in free energy between
reactants and products
00:09:32.900 --> 00:09:35.950
when reactants and products
are in their standard states.
00:09:35.950 --> 00:09:39.040
And since that value is a constant,
00:09:39.040 --> 00:09:40.910
if the temperature is constant,
00:09:40.910 --> 00:09:42.820
notice for all of our calculations,
00:09:42.820 --> 00:09:43.990
delta G naught was equal
00:09:43.990 --> 00:09:48.220
to negative 33.0 kilojoules
per mole of reaction.
00:09:48.220 --> 00:09:51.690
Delta G is talking about
the instantaneous difference
00:09:51.690 --> 00:09:54.750
in free energy between
reactants and products.
00:09:54.750 --> 00:09:58.020
And as long as there's a
difference in free energy,
00:09:58.020 --> 00:10:00.120
there's a driving force
for the net reaction
00:10:00.120 --> 00:10:02.420
to go to the left or to the right.
00:10:02.420 --> 00:10:05.420
And eventually, when
delta G is equal to zero,
00:10:05.420 --> 00:10:07.760
the reaction is at equilibrium.
00:10:07.760 --> 00:10:10.900
Delta G is only equal to delta G naught
00:10:10.900 --> 00:10:12.500
when the reactants and products
00:10:12.500 --> 00:10:14.723
are in their standard states.
|
Thermodynamics vs. kinetics | https://www.youtube.com/watch?v=ur7GBAQgiB0 | vtt | https://www.youtube.com/api/timedtext?v=ur7GBAQgiB0&ei=ylWUZZvKKOy_mLAPk9e9mAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A7ADEF3CB951DD43E3AF4724116F8BD26ADD1870.9212819D588E5867BF8540526E21AFA119F7E6CE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:01.313
- [Tutor] In chemistry,
00:00:01.313 --> 00:00:02.370
it's important to distinguish
00:00:02.370 --> 00:00:05.270
between thermodynamics and kinetics.
00:00:05.270 --> 00:00:06.103
For example,
00:00:06.103 --> 00:00:08.370
if we think about the conversion of carbon
00:00:08.370 --> 00:00:10.430
as a solid in the diamond form
00:00:10.430 --> 00:00:13.290
to carbon as a solid in the graphite form,
00:00:13.290 --> 00:00:15.970
thermodynamics tells us what will happen.
00:00:15.970 --> 00:00:19.370
Will this conversion happen
at a specific temperature?
00:00:19.370 --> 00:00:23.410
Whereas kinetics tells us when
the conversion could happen.
00:00:23.410 --> 00:00:25.040
Let's start with thermodynamics.
00:00:25.040 --> 00:00:27.480
We can calculate if this
conversion will happen
00:00:27.480 --> 00:00:30.210
at room temperature of 25 degrees Celsius
00:00:30.210 --> 00:00:33.130
by calculating the standard
change in free energy
00:00:33.130 --> 00:00:36.130
for this reaction at that temperature.
00:00:36.130 --> 00:00:37.950
To calculate the standard change
00:00:37.950 --> 00:00:40.200
in free energy for this reaction
00:00:40.200 --> 00:00:42.870
we need to know the standard change
00:00:42.870 --> 00:00:45.660
in free energy of
formation of the products.
00:00:45.660 --> 00:00:48.720
And from that we subtract
the standard change
00:00:48.720 --> 00:00:52.120
in free energy of
formation of the reactants.
00:00:52.120 --> 00:00:53.130
For this conversion
00:00:53.130 --> 00:00:56.430
our product is carbon
in the graphite form.
00:00:56.430 --> 00:00:58.360
And because carbon in the graphite form
00:00:58.360 --> 00:01:01.800
is the most stable
elemental form of carbon
00:01:01.800 --> 00:01:03.820
at a pressure of one atmosphere,
00:01:03.820 --> 00:01:07.540
the standard change in
free energy of formation
00:01:07.540 --> 00:01:10.800
of carbon in the graphite
form is equal to zero.
00:01:10.800 --> 00:01:12.860
Next, we think about our reactant,
00:01:12.860 --> 00:01:15.740
which is carbon in the form of diamond.
00:01:15.740 --> 00:01:18.600
The standard change in free
energy of formation of carbon
00:01:18.600 --> 00:01:22.580
in the diamond form is
2.84 kilojoules per mole.
00:01:22.580 --> 00:01:25.010
Looking at our balanced
equation for this conversion,
00:01:25.010 --> 00:01:26.880
we're converting one mole of diamond
00:01:26.880 --> 00:01:28.870
into one mole of graphite.
00:01:28.870 --> 00:01:32.250
Since there's a one as a
coefficient in front of diamond,
00:01:32.250 --> 00:01:34.920
we multiply the standard
change in free energy
00:01:34.920 --> 00:01:38.550
of formation of diamond
by one mole of diamond.
00:01:38.550 --> 00:01:42.600
Moles cancel, and we get
negative 2.84 kilojoules
00:01:42.600 --> 00:01:46.030
as the standard change in
free energy for this reaction.
00:01:46.030 --> 00:01:47.130
Instead of kilojoules,
00:01:47.130 --> 00:01:48.500
the units could've been written
00:01:48.500 --> 00:01:51.340
as kilojoules per mole of reaction.
00:01:51.340 --> 00:01:53.870
Because there's one mole of
carbon in the diamond form
00:01:53.870 --> 00:01:55.950
for how the balanced equation is written,
00:01:55.950 --> 00:01:58.470
we could write a conversion
factor of one mole
00:01:58.470 --> 00:02:02.570
of carbon in the diamond
form per mole of reaction.
00:02:02.570 --> 00:02:04.770
And because the standard
change in free energy
00:02:04.770 --> 00:02:06.070
of formation of diamond
00:02:06.070 --> 00:02:10.010
is equal to 2.84 kilojoules
per mole of diamond,
00:02:10.010 --> 00:02:12.100
moles of diamond would cancel out
00:02:12.100 --> 00:02:16.930
and give kilojoules per mole
of reaction as the units.
00:02:16.930 --> 00:02:18.190
Because the standard change
00:02:18.190 --> 00:02:21.760
in free energy for this
reaction is negative.
00:02:21.760 --> 00:02:25.310
We know that the conversion
of diamond into graphite
00:02:25.310 --> 00:02:30.310
at 25 degrees Celsius is
thermodynamically favorable.
00:02:30.590 --> 00:02:34.040
Next, let's think about the
kinetics of this reaction.
00:02:34.040 --> 00:02:35.850
If we look at the structure of diamond,
00:02:35.850 --> 00:02:40.400
each carbon atom is covalently
bonded to four other carbons.
00:02:40.400 --> 00:02:41.233
For example,
00:02:41.233 --> 00:02:45.060
this carbon right here is bonded
to four other carbon atoms
00:02:45.060 --> 00:02:50.060
and the tetrahedral geometry
around the central carbon atom.
00:02:50.060 --> 00:02:52.160
Graphite has a very different structure.
00:02:52.160 --> 00:02:52.993
In graphite,
00:02:52.993 --> 00:02:57.000
carbon atoms form covalently
bonded layers or sheets.
00:02:57.000 --> 00:02:58.770
And these layers or sheets
00:02:58.770 --> 00:03:02.200
are held together by
London dispersion forces.
00:03:02.200 --> 00:03:05.680
So in order to convert
diamond into graphite
00:03:05.680 --> 00:03:09.280
we would have to break a
lot of carbon-carbon bonds.
00:03:09.280 --> 00:03:11.590
And that would take a lot of energy.
00:03:11.590 --> 00:03:12.980
Since it takes a lot of energy
00:03:12.980 --> 00:03:15.610
to break the carbon-carbon
bonds in diamond,
00:03:15.610 --> 00:03:18.600
if we look at the energy
profile for this reaction,
00:03:18.600 --> 00:03:21.860
this reaction would have a
very high activation energy,
00:03:21.860 --> 00:03:24.360
symbolized by EA.
00:03:24.360 --> 00:03:27.820
And the higher the activation
energy for the reaction
00:03:27.820 --> 00:03:31.720
the slower the rate of the reaction.
00:03:31.720 --> 00:03:32.750
At room temperature,
00:03:32.750 --> 00:03:36.100
it's estimated this reaction
could take billions of years.
00:03:36.100 --> 00:03:38.010
Therefore we would say this reaction
00:03:38.010 --> 00:03:40.990
is kinetically unfavorable.
00:03:40.990 --> 00:03:42.710
Finally, let's summarize
what we've learned
00:03:42.710 --> 00:03:46.410
about the conversion of
diamond into graphite.
00:03:46.410 --> 00:03:50.480
Thermodynamics answers the
question, will the reaction go?
00:03:50.480 --> 00:03:52.630
And the answer to that question is yes.
00:03:52.630 --> 00:03:54.060
At room temperature,
00:03:54.060 --> 00:03:56.910
diamond will convert into graphite
00:03:56.910 --> 00:04:00.340
because delta G naught for
the reaction was negative.
00:04:00.340 --> 00:04:03.970
Kinetics answers the question,
how long will it take?
00:04:03.970 --> 00:04:05.160
And the answer to that question
00:04:05.160 --> 00:04:07.740
is it would take billions
of years for diamond
00:04:07.740 --> 00:04:10.640
to turn into graphite at room temperature.
00:04:10.640 --> 00:04:12.710
The reason why the reaction is so slow
00:04:12.710 --> 00:04:15.910
is because of the extremely
high activation energy.
00:04:15.910 --> 00:04:18.940
So even though the reaction
is thermodynamically favorable
00:04:18.940 --> 00:04:22.830
at room temperature, because
the reaction is so slow,
00:04:22.830 --> 00:04:25.260
the reaction is kinetically unfavored.
00:04:25.260 --> 00:04:28.893
And for all practical purposes,
the reaction doesn't happen.
|
Free energy of dissolution | https://www.youtube.com/watch?v=UJ_etGNuIOg | vtt | https://www.youtube.com/api/timedtext?v=UJ_etGNuIOg&ei=ylWUZYSpJuSnp-oPwIyYmAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6226D8FF7B5D7CC9A9EB081F3F0C61CA7FD41BAD.0D6A8B33893BFF6E1C40FB98C0F0B3ACE3AE5062&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.220 --> 00:00:02.420
- [Instructor] The term
dissolution refers to
00:00:02.420 --> 00:00:06.100
the dissolving of one
substance in a solvent.
00:00:06.100 --> 00:00:09.160
The dissolve substance
is now called a salute
00:00:09.160 --> 00:00:13.270
and the solute plus the
solvent form a solution.
00:00:13.270 --> 00:00:15.930
If the standard change in
free energy, delta G naught
00:00:15.930 --> 00:00:17.450
is less than zero,
00:00:17.450 --> 00:00:21.010
the dissolution is
thermodynamically favorable.
00:00:21.010 --> 00:00:23.000
So, if we were to put this substance
00:00:23.000 --> 00:00:25.030
in a solvent like water,
00:00:25.030 --> 00:00:28.440
the substance would dissolve
and it would form a solution.
00:00:28.440 --> 00:00:30.850
However, if delta G naught
is greater than zero,
00:00:30.850 --> 00:00:34.690
the dissolution is
thermodynamically unfavorable.
00:00:34.690 --> 00:00:37.940
So, if we try to dissolve
the substance in water,
00:00:37.940 --> 00:00:39.050
it wouldn't dissolve
00:00:39.050 --> 00:00:40.750
and therefore we would just see it
00:00:40.750 --> 00:00:43.360
on the bottom of the beaker.
00:00:43.360 --> 00:00:46.240
Since we're talking about
potentially making a solution,
00:00:46.240 --> 00:00:49.870
sometimes you see a
subscript soln written next
00:00:49.870 --> 00:00:51.140
to delta G naught.
00:00:51.140 --> 00:00:54.240
So, this would be delta
G naught of solution.
00:00:54.240 --> 00:00:57.710
We could also call this the
free energy of dissolution.
00:00:57.710 --> 00:01:00.650
We can calculate delta
G naught of solution
00:01:00.650 --> 00:01:04.270
by taking the standard change
and enthalpy of the solution
00:01:04.270 --> 00:01:07.100
and from that subtracting
the absolute temperature,
00:01:07.100 --> 00:01:11.200
times the standard change
in entropy of the solution.
00:01:11.200 --> 00:01:13.390
So, let's look in more
detail at what determines
00:01:13.390 --> 00:01:17.350
the signs for delta H
naught and delta S naught.
00:01:17.350 --> 00:01:19.700
We can think about the
disillusion of a solid
00:01:19.700 --> 00:01:21.970
in three hypothetical steps.
00:01:21.970 --> 00:01:25.110
The first step involves
breaking up the solid.
00:01:25.110 --> 00:01:27.570
Let's think about the change in enthalpy,
00:01:27.570 --> 00:01:31.520
delta H one, for this first step.
00:01:31.520 --> 00:01:34.120
Solids are held together
by attractive forces.
00:01:34.120 --> 00:01:37.010
For example, if we had an ionic solid,
00:01:37.010 --> 00:01:38.500
it would be ionic bonds
00:01:38.500 --> 00:01:41.160
or electrostatic
interactions holding together
00:01:41.160 --> 00:01:42.920
the opposite charges.
00:01:42.920 --> 00:01:46.320
So, if our goal is to pull
apart or break apart the solid,
00:01:46.320 --> 00:01:49.790
it would take energy to overcome
these attractive forces.
00:01:49.790 --> 00:01:53.440
Therefore, delta H one would be positive.
00:01:53.440 --> 00:01:55.550
Next, let's think about
the change in entropy.
00:01:55.550 --> 00:01:58.090
Delta S one for the first step.
00:01:58.090 --> 00:01:59.570
When the solid is broken up,
00:01:59.570 --> 00:02:03.000
the particles have a greater
number of possible positions
00:02:03.000 --> 00:02:05.400
and an increased number of
possible positions means
00:02:05.400 --> 00:02:08.640
an increase in number
of possible microstates.
00:02:08.640 --> 00:02:10.660
An increase in the number of microstates
00:02:10.660 --> 00:02:13.050
means an increase in entropy.
00:02:13.050 --> 00:02:14.880
Therefore, breaking up the solid
00:02:14.880 --> 00:02:17.180
means an increase in entropy
00:02:17.180 --> 00:02:20.360
and delta S one will be positive.
00:02:20.360 --> 00:02:22.810
Step two is the preparation of the solvent
00:02:22.810 --> 00:02:25.260
to receive the salute.
00:02:25.260 --> 00:02:28.180
And let's think about
the change in enthalpy
00:02:28.180 --> 00:02:30.870
for this second step.
00:02:30.870 --> 00:02:33.380
The solvent particles are held together
00:02:33.380 --> 00:02:36.240
by intermolecular forces.
00:02:36.240 --> 00:02:37.370
For water molecules,
00:02:37.370 --> 00:02:41.610
the most important intermolecular
force is hydrogen bonding.
00:02:41.610 --> 00:02:43.710
The goal of this theoretical second step
00:02:43.710 --> 00:02:45.920
is to break apart the solvent particles
00:02:45.920 --> 00:02:48.250
and to move them far apart from each other
00:02:48.250 --> 00:02:51.390
so there's enough room to
fit in a solute particle.
00:02:51.390 --> 00:02:53.350
Since it takes energy to overcome
00:02:53.350 --> 00:02:55.280
the intermolecular forces holding
00:02:55.280 --> 00:02:57.180
the solvent particles together,
00:02:57.180 --> 00:03:00.000
delta H two is positive.
00:03:00.000 --> 00:03:02.010
Next, let's think about
the change in entropy,
00:03:02.010 --> 00:03:04.960
delta S two for this second step.
00:03:04.960 --> 00:03:07.370
When the water molecules are pulled apart,
00:03:07.370 --> 00:03:10.050
there's an increase in the
number of possible positions
00:03:10.050 --> 00:03:11.650
of the water molecules.
00:03:11.650 --> 00:03:14.040
And like the first step,
an increase in the number
00:03:14.040 --> 00:03:16.090
of possible positions means an increase
00:03:16.090 --> 00:03:17.550
in the number of microstates,
00:03:17.550 --> 00:03:20.110
which means an increase in entropy.
00:03:20.110 --> 00:03:23.690
Therefore, delta S two is positive.
00:03:23.690 --> 00:03:26.060
The third step is called solvation,
00:03:26.060 --> 00:03:28.140
which refers to the interaction
00:03:28.140 --> 00:03:30.200
of the solute and the solvent.
00:03:30.200 --> 00:03:33.520
So, imagine there's an attractive force
00:03:33.520 --> 00:03:36.480
between this white solute particle
00:03:36.480 --> 00:03:39.790
and these four blue solvent particles.
00:03:39.790 --> 00:03:43.700
If the solvent is water, this
process is called hydration.
00:03:43.700 --> 00:03:46.140
And if we think about,
say a positive cation,
00:03:46.140 --> 00:03:47.610
interacting with water,
00:03:47.610 --> 00:03:49.520
since opposite charges attract,
00:03:49.520 --> 00:03:53.510
the positive cation is
attracted to the negative end
00:03:53.510 --> 00:03:55.990
of the water molecule.
00:03:55.990 --> 00:03:58.970
Since we have a positively
charged ion interacting
00:03:58.970 --> 00:04:02.730
with water, which is a polar
molecule with a dipole moment,
00:04:02.730 --> 00:04:03.750
this type of interaction
00:04:03.750 --> 00:04:06.990
is called an ion dipole interaction.
00:04:06.990 --> 00:04:09.850
And let's think about
the change in enthalpy
00:04:09.850 --> 00:04:12.210
for this third step.
00:04:12.210 --> 00:04:14.720
When the solute comes
together with the solvent,
00:04:14.720 --> 00:04:16.110
energy is released,
00:04:16.110 --> 00:04:19.680
therefore delta H three is negative.
00:04:19.680 --> 00:04:21.610
One way to think about
why this is negative
00:04:21.610 --> 00:04:25.710
is to consider the ion dipole
interactions on the right.
00:04:25.710 --> 00:04:27.130
Since it would take energy
00:04:27.130 --> 00:04:29.950
to break these ion dipole interactions,
00:04:29.950 --> 00:04:32.470
when those ion dipole interactions form,
00:04:32.470 --> 00:04:34.730
energy must be given off.
00:04:34.730 --> 00:04:36.740
Next, let's think about
the change in entropy.
00:04:36.740 --> 00:04:39.430
Delta S three for the third step.
00:04:39.430 --> 00:04:42.210
Because the water molecules are attracted
00:04:42.210 --> 00:04:44.690
to the ions in solution,
00:04:44.690 --> 00:04:47.890
the water molecules have a
decreased freedom of movement
00:04:47.890 --> 00:04:50.620
and therefore there are
fewer positions possible
00:04:50.620 --> 00:04:52.360
for the water molecules.
00:04:52.360 --> 00:04:55.070
A decrease in the number
of possible positions
00:04:55.070 --> 00:04:58.300
means a decrease in the
number of microstates,
00:04:58.300 --> 00:05:00.760
which means a decrease in entropy.
00:05:00.760 --> 00:05:05.760
Therefore, for the third step,
delta S three is negative.
00:05:05.790 --> 00:05:07.100
Now that we've talked about the signs
00:05:07.100 --> 00:05:10.500
for delta H and delta S for
each of the three steps,
00:05:10.500 --> 00:05:13.510
let's think about how they
influence the overall changes
00:05:13.510 --> 00:05:15.500
in delta H naught of solution
00:05:15.500 --> 00:05:18.220
and delta S naught of solution.
00:05:18.220 --> 00:05:21.010
And let's start with delta
H naught of solution,
00:05:21.010 --> 00:05:23.490
which is equal to the sum of the changes
00:05:23.490 --> 00:05:26.130
in enthalpy for the three steps.
00:05:26.130 --> 00:05:30.530
So, delta H one, plus delta
H two, plus delta H three.
00:05:30.530 --> 00:05:33.710
We've already seen that
delta H one is positive,
00:05:33.710 --> 00:05:38.610
delta H two is positive, and
delta H three is negative.
00:05:38.610 --> 00:05:41.790
So, adding delta H one
and delta H two together,
00:05:41.790 --> 00:05:43.870
it gives us a positive value.
00:05:43.870 --> 00:05:46.600
And since we're adding a
negative in delta H three,
00:05:46.600 --> 00:05:48.930
it's the magnitude of delta H three
00:05:48.930 --> 00:05:52.480
that determines if the overall
delta H naught of solution
00:05:52.480 --> 00:05:54.780
is positive or negative.
00:05:54.780 --> 00:05:57.840
If the magnitude of delta
H one, plus delta H two
00:05:57.840 --> 00:06:00.900
is greater than the
magnitude of delta H three,
00:06:00.900 --> 00:06:04.380
delta H naught of
solution will be positive.
00:06:04.380 --> 00:06:06.930
However, if the magnitude of delta H three
00:06:06.930 --> 00:06:08.460
is greater than the magnitude
00:06:08.460 --> 00:06:11.050
of delta H one plus delta H two,
00:06:11.050 --> 00:06:14.200
delta H naught of
solution will be negative.
00:06:14.200 --> 00:06:17.290
Therefore, it's possible for
delta H naught of solution
00:06:17.290 --> 00:06:19.160
to be positive or negative,
00:06:19.160 --> 00:06:21.740
depending on the
substance being dissolved.
00:06:21.740 --> 00:06:24.640
An example of a substance
that has a positive value
00:06:24.640 --> 00:06:28.370
for delta H naught of
solution is sodium chloride.
00:06:28.370 --> 00:06:29.870
At 25 degrees Celsius,
00:06:29.870 --> 00:06:32.560
delta H naught of solution
for sodium chloride
00:06:32.560 --> 00:06:37.130
is positive 3.9 kilojoules
per mole of reaction.
00:06:37.130 --> 00:06:39.750
An example of a substance
that has a negative value
00:06:39.750 --> 00:06:43.520
for delta H naught of solution
is magnesium chloride.
00:06:43.520 --> 00:06:45.040
At 25 degrees Celsius,
00:06:45.040 --> 00:06:47.900
delta H naught of solution
for magnesium chloride
00:06:47.900 --> 00:06:52.900
is equal to negative 160.0
kilojoules per mole of reaction.
00:06:53.350 --> 00:06:55.470
The main reason why these two substances
00:06:55.470 --> 00:06:58.110
have such different enthalpies of solution
00:06:58.110 --> 00:07:00.430
has to do with the third step.
00:07:00.430 --> 00:07:03.290
So, the value of delta H three.
00:07:03.290 --> 00:07:05.320
So, let's take a look
at some diagrams showing
00:07:05.320 --> 00:07:08.480
the ion dipole interaction of the cation
00:07:08.480 --> 00:07:11.220
of both of these substances
in aqueous solution,
00:07:11.220 --> 00:07:13.580
interacting with water molecules.
00:07:13.580 --> 00:07:16.770
For sodium chloride, we
would have a sodium cation
00:07:16.770 --> 00:07:19.930
in solution with a one plus charge.
00:07:19.930 --> 00:07:21.790
And for magnesium chloride,
00:07:21.790 --> 00:07:25.090
it would be an Mg two
plus cation interacting
00:07:25.090 --> 00:07:27.120
with the water molecules.
00:07:27.120 --> 00:07:30.730
Because the Mg two plus
cation has a higher charge
00:07:30.730 --> 00:07:33.920
than the sodium cation
and because it's smaller,
00:07:33.920 --> 00:07:37.750
the Mg two plus cation exerts
a greater electric force
00:07:37.750 --> 00:07:39.700
on the water molecules,
00:07:39.700 --> 00:07:42.660
and because the magnesium
two plus cation exerts
00:07:42.660 --> 00:07:45.730
a greater electric force
on the water molecules,
00:07:45.730 --> 00:07:49.840
more energy is released when
the magnesium two plus cation
00:07:49.840 --> 00:07:52.210
is hydrated compared to
00:07:52.210 --> 00:07:56.600
when the sodium one
plus cation is hydrated.
00:07:56.600 --> 00:08:00.240
And since more energy is
given off in the third step
00:08:00.240 --> 00:08:04.310
for the hydration of the
magnesium two plus cation,
00:08:04.310 --> 00:08:05.240
that's enough to turn
00:08:05.240 --> 00:08:09.490
the overall delta H naught
of solution negative.
00:08:09.490 --> 00:08:12.310
Therefore, the dissolution
of magnesium chloride
00:08:12.310 --> 00:08:14.970
is an exothermic process.
00:08:14.970 --> 00:08:18.110
For sodium chloride, when the
sodium cation is hydrated,
00:08:18.110 --> 00:08:20.710
not as much energy is released.
00:08:20.710 --> 00:08:25.050
Therefore, the overall delta
H of solution is positive
00:08:25.050 --> 00:08:27.410
and the dissolution of sodium chloride
00:08:27.410 --> 00:08:30.030
is an endothermic process.
00:08:30.030 --> 00:08:33.410
Next, let's think about
delta S naught of solution.
00:08:33.410 --> 00:08:34.900
Delta S naught of solution
00:08:34.900 --> 00:08:37.640
is equal to delta S one, plus delta S two,
00:08:37.640 --> 00:08:39.580
plus delta S three.
00:08:39.580 --> 00:08:41.610
Delta S one, the change in entropy
00:08:41.610 --> 00:08:44.460
for the first step, we saw was positive.
00:08:44.460 --> 00:08:46.830
Delta S two was also positive,
00:08:46.830 --> 00:08:49.610
but delta S3 was negative.
00:08:49.610 --> 00:08:52.300
Therefore, just like we
saw for delta H naught,
00:08:52.300 --> 00:08:55.360
the sign for delta S naught
depends on the magnitude
00:08:55.360 --> 00:08:59.970
of delta S one, plus delta S
two, compared to delta S three.
00:08:59.970 --> 00:09:01.960
If delta S one, plus delta S two
00:09:01.960 --> 00:09:04.650
is greater in magnitude
than delta S three,
00:09:04.650 --> 00:09:07.970
delta S naught of
solution will be positive.
00:09:07.970 --> 00:09:10.260
However, if the magnitude of delta S three
00:09:10.260 --> 00:09:12.510
is greater than the
magnitude of delta S one,
00:09:12.510 --> 00:09:14.250
plus delta S two,
00:09:14.250 --> 00:09:17.300
delta S naught of
solution will be negative.
00:09:17.300 --> 00:09:19.950
An example of a substance
that has a positive value
00:09:19.950 --> 00:09:22.970
for delta S naught of
solution is sodium chloride.
00:09:22.970 --> 00:09:24.500
At 25 degrees Celsius,
00:09:24.500 --> 00:09:26.780
delta S naught of solution is equal
00:09:26.780 --> 00:09:31.780
to positive 43.4 joules per
Kelvin mole of reaction.
00:09:32.360 --> 00:09:34.920
An example of a substance
that has a negative value
00:09:34.920 --> 00:09:38.350
for delta S naught of solution
is magnesium chloride.
00:09:38.350 --> 00:09:39.860
At 25 degrees Celsius,
00:09:39.860 --> 00:09:41.840
delta S naught of solution is equal
00:09:41.840 --> 00:09:46.840
to negative 114.7 joules
per Kelvin mole of reaction.
00:09:47.250 --> 00:09:49.530
The main reason for the
difference in entropies
00:09:49.530 --> 00:09:53.090
for these two substances has
to do with the third step.
00:09:53.090 --> 00:09:56.000
So, the magnitude of delta S three.
00:09:56.000 --> 00:09:57.310
So, once again, let's take a look
00:09:57.310 --> 00:09:59.630
at the diagrams showing the hydration
00:09:59.630 --> 00:10:02.110
of the cations in aqueous solution.
00:10:02.110 --> 00:10:04.240
We've already talked about
the fact that the smaller
00:10:04.240 --> 00:10:06.700
and more positive
magnesium two-plus cation
00:10:06.700 --> 00:10:08.360
has a greater electric force
00:10:08.360 --> 00:10:10.460
on its surrounding water molecules
00:10:10.460 --> 00:10:13.560
than the sodium one plus cation does
00:10:13.560 --> 00:10:15.980
on its surrounding water molecules.
00:10:15.980 --> 00:10:19.300
The stronger electric force
means a decreased freedom
00:10:19.300 --> 00:10:21.340
of movement of water molecules
00:10:21.340 --> 00:10:24.330
around the magnesium two plus cation,
00:10:24.330 --> 00:10:26.690
and a decreased freedom of movement means
00:10:26.690 --> 00:10:29.540
a decreased number of
possible microstates,
00:10:29.540 --> 00:10:33.620
which means a greater decrease in entropy.
00:10:33.620 --> 00:10:36.940
So, the hydration of the
magnesium two plus cation leads
00:10:36.940 --> 00:10:41.140
to a greater decrease in
entropy for step three,
00:10:41.140 --> 00:10:44.930
which outweighs the positive
values for steps one and two.
00:10:44.930 --> 00:10:47.430
And that gives an overall negative value
00:10:47.430 --> 00:10:49.610
for delta S naught of solution,
00:10:49.610 --> 00:10:51.740
therefore dissolving magnesium chloride
00:10:51.740 --> 00:10:55.560
in water results in a decrease in entropy.
00:10:55.560 --> 00:10:57.010
Since the sodium cation
00:10:57.010 --> 00:11:00.870
has a weaker electrostatic
attraction for water molecules,
00:11:00.870 --> 00:11:03.480
the decrease in entropy is not as much.
00:11:03.480 --> 00:11:05.990
And therefore, the
magnitude of the third term
00:11:05.990 --> 00:11:09.440
does not overcome the magnitude
of the first two terms,
00:11:09.440 --> 00:11:12.550
which means the overall
delta S naught of solution
00:11:12.550 --> 00:11:15.530
is positive and dissolving sodium chloride
00:11:15.530 --> 00:11:19.910
in water results in an
increase in entropy.
00:11:19.910 --> 00:11:22.390
We've just looked at
delta H naught of solution
00:11:22.390 --> 00:11:25.290
and delta S naught of
solution for two salts,
00:11:25.290 --> 00:11:28.170
sodium chloride and magnesium chloride.
00:11:28.170 --> 00:11:30.720
Let's calculate delta G naught of solution
00:11:30.720 --> 00:11:34.700
for both salts at 25 degrees Celsius.
00:11:34.700 --> 00:11:36.090
Let's start with the dissolution
00:11:36.090 --> 00:11:38.070
of solid sodium chloride and water
00:11:38.070 --> 00:11:41.310
to form sodium cations
and chloride anions.
00:11:41.310 --> 00:11:44.860
25 degrees Celsius is 298 Kelvin
00:11:44.860 --> 00:11:47.200
so we can plug that into our equation.
00:11:47.200 --> 00:11:49.830
And we can also plug in the
values for delta H naught
00:11:49.830 --> 00:11:51.640
and delta S naught.
00:11:51.640 --> 00:11:54.360
So, both of them were positive values
00:11:54.360 --> 00:11:57.250
for the dissolution of sodium chloride.
00:11:57.250 --> 00:12:00.880
Kelvin cancels out and gives
us delta G naught of solution
00:12:00.880 --> 00:12:05.260
is equal to negative 9.0
kilojoules per mole of reaction.
00:12:05.260 --> 00:12:07.750
Since delta G naught is negative,
00:12:07.750 --> 00:12:10.550
the dissolution of solid sodium chloride
00:12:10.550 --> 00:12:13.500
is a thermodynamically favorable process,
00:12:13.500 --> 00:12:15.630
which means at 25 degrees Celsius,
00:12:15.630 --> 00:12:18.380
sodium chloride is soluble in water.
00:12:18.380 --> 00:12:19.810
Notice how in this case,
00:12:19.810 --> 00:12:23.890
the favorable positive
entropy term outweighs
00:12:23.890 --> 00:12:26.790
the unfavorable positive enthalpy term
00:12:26.790 --> 00:12:29.960
to give a negative value
for delta G naught.
00:12:29.960 --> 00:12:32.410
Therefore, for the dissolution
of sodium chloride,
00:12:32.410 --> 00:12:36.420
the increase in entropy
drives the dissolution.
00:12:36.420 --> 00:12:38.390
Next, let's do the same calculation
00:12:38.390 --> 00:12:41.600
for the dissolution of solid
magnesium chloride and water
00:12:41.600 --> 00:12:43.760
to form the magnesium two plus cation
00:12:43.760 --> 00:12:45.710
and two chloride anions.
00:12:45.710 --> 00:12:48.300
We've already seen how the
increased positive charge
00:12:48.300 --> 00:12:50.920
of the Mg two plus cation in solution
00:12:50.920 --> 00:12:53.540
gave us a negative
value for delta H naught
00:12:53.540 --> 00:12:56.060
and a negative value for delta S naught.
00:12:56.060 --> 00:12:57.610
So, plugging in all our numbers
00:12:57.610 --> 00:12:59.940
and a temperature of 298 Kelvin,
00:12:59.940 --> 00:13:03.030
Kelvin cancels out and gives
us delta G naught of solution
00:13:03.030 --> 00:13:08.030
is equal to negative 125.8
kilojoules per mole of reaction.
00:13:08.120 --> 00:13:10.980
Since, delta G naught
of solution is negative,
00:13:10.980 --> 00:13:13.860
the dissolution of magnesium chloride
00:13:13.860 --> 00:13:17.190
is a thermodynamically favorable process.
00:13:17.190 --> 00:13:20.320
So, at room temperature
of 25 degrees Celsius,
00:13:20.320 --> 00:13:23.060
magnesium chloride is soluble in water.
00:13:23.060 --> 00:13:26.280
However, this time it's the
favorable negative value
00:13:26.280 --> 00:13:28.500
for the enthalpy term that outweighs
00:13:28.500 --> 00:13:30.520
the unfavorable negative value
00:13:30.520 --> 00:13:34.490
for the entropy term to give
a negative value overall
00:13:34.490 --> 00:13:36.590
for delta G naught of solution.
00:13:36.590 --> 00:13:39.650
So, this time it's the
decrease in enthalpy
00:13:39.650 --> 00:13:41.870
that drives the dissolution.
00:13:41.870 --> 00:13:45.130
Delta G naught has been negative
for both sodium chloride
00:13:45.130 --> 00:13:47.020
and for magnesium chloride.
00:13:47.020 --> 00:13:48.810
However, those are just the two examples
00:13:48.810 --> 00:13:49.970
that I chose for this video,
00:13:49.970 --> 00:13:52.150
it's certainly possible
to get a positive value
00:13:52.150 --> 00:13:54.040
for delta G naught of solution,
00:13:54.040 --> 00:13:56.630
which would mean an insoluble salt,
00:13:56.630 --> 00:13:59.350
and because it can be very
difficult to predict the signs
00:13:59.350 --> 00:14:01.710
for delta H naught and for delta S naught
00:14:01.710 --> 00:14:03.400
for a particular salt,
00:14:03.400 --> 00:14:06.160
it's even more difficult to
predict if delta G naught
00:14:06.160 --> 00:14:09.440
is positive or negative
for that particular salt.
00:14:09.440 --> 00:14:12.340
Therefore, it's often
necessary to do a calculation
00:14:12.340 --> 00:14:14.953
to see if delta G naught
is positive or negative.
|
Free energy of formation | https://www.youtube.com/watch?v=9igPBrHMnCc | vtt | https://www.youtube.com/api/timedtext?v=9igPBrHMnCc&ei=ylWUZZG-Muycp-oPzJ6_0AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=551B8A8A2D8808A77B08649EE0A561844DEF50A9.5798BF85E274B72606B06CF042D6C5D5D4309FAA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.310 --> 00:00:02.960
- [Instructor] Free
energy is symbolized by G.
00:00:02.960 --> 00:00:05.620
And the change in free energy is delta G.
00:00:05.620 --> 00:00:07.160
When there's a subscript of F,
00:00:07.160 --> 00:00:08.570
this is talking about the change
00:00:08.570 --> 00:00:11.010
in the free energy of formation.
00:00:11.010 --> 00:00:13.360
Which refers to the
change in the free energy
00:00:13.360 --> 00:00:16.300
for the formation of
one mole of a substance
00:00:16.300 --> 00:00:19.440
from its elements in
their standard states.
00:00:19.440 --> 00:00:21.770
These superscript naught
refers to the fact
00:00:21.770 --> 00:00:25.260
that the substances are
in their standard states.
00:00:25.260 --> 00:00:27.410
By convention, the standard change
00:00:27.410 --> 00:00:29.920
in free energy of formation for an element
00:00:29.920 --> 00:00:32.910
and its standard state is equal to zero.
00:00:32.910 --> 00:00:36.900
Therefore, if we think about
forming one mole of oxygen gas,
00:00:36.900 --> 00:00:39.900
we would be making it
from elemental oxygen
00:00:39.900 --> 00:00:42.350
which is also oxygen gas.
00:00:42.350 --> 00:00:44.930
So forming one mole of
oxygen gas from one mole
00:00:44.930 --> 00:00:47.480
of oxygen gas means
there will be no change
00:00:47.480 --> 00:00:49.710
and therefore the standard change
00:00:49.710 --> 00:00:54.150
in free energy of
formation is equal to zero.
00:00:54.150 --> 00:00:57.220
Textbooks often tabulate
data for standard change
00:00:57.220 --> 00:00:59.430
in free energy of formation of substances
00:00:59.430 --> 00:01:01.110
at 25 degrees Celsius.
00:01:01.110 --> 00:01:03.760
However, it doesn't have
to be that temperature.
00:01:03.760 --> 00:01:06.730
The units are in kilojoules per mole.
00:01:06.730 --> 00:01:08.580
We've already seen that
the standard change
00:01:08.580 --> 00:01:11.670
in free energy of formation for an element
00:01:11.670 --> 00:01:13.690
is equal to zero.
00:01:13.690 --> 00:01:17.900
Therefore for elemental
oxygen, O2 delta G naught
00:01:17.900 --> 00:01:19.440
is equal to zero.
00:01:19.440 --> 00:01:23.550
And for carbon in the solid
state in the form of graphite,
00:01:23.550 --> 00:01:26.360
delta G naught is also equal to zero.
00:01:26.360 --> 00:01:29.670
The value for carbon monoxide
is naught equal to zero.
00:01:29.670 --> 00:01:30.920
Delta G naught is equal
00:01:30.920 --> 00:01:35.190
to negative 137.2 kilojoules per mole.
00:01:35.190 --> 00:01:38.670
So if we think about forming
one mole of carbon monoxide
00:01:38.670 --> 00:01:39.890
from its elements,
00:01:39.890 --> 00:01:43.360
carbon monoxide is composed
of carbon and oxygen.
00:01:43.360 --> 00:01:46.260
And the elemental form of oxygen is O2 gas
00:01:46.260 --> 00:01:48.070
and the elements of form of carbon
00:01:48.070 --> 00:01:50.690
is the solid form in graphite.
00:01:50.690 --> 00:01:52.960
So this value for the standard change
00:01:52.960 --> 00:01:57.050
in free energy of formation
of carbon monoxide is talking
00:01:57.050 --> 00:02:00.220
about the change in free
energy for the formation
00:02:00.220 --> 00:02:03.830
of one mole of carbon
monoxide from its elements
00:02:03.830 --> 00:02:05.860
in their standard states.
00:02:05.860 --> 00:02:09.210
Standard changes in free energy
of formation of substances
00:02:09.210 --> 00:02:12.100
are useful because they
can be used to calculate
00:02:12.100 --> 00:02:15.940
the standard change in free
energy for a chemical reaction.
00:02:15.940 --> 00:02:18.920
The standard change in free
energy of a chemical reaction
00:02:18.920 --> 00:02:22.440
is equal to the sum of the standard change
00:02:22.440 --> 00:02:25.440
in free energy of formation
of the products and from that
00:02:25.440 --> 00:02:27.670
you subtract the sum
of the standard change
00:02:27.670 --> 00:02:30.950
in free energy of
formation of the reactants.
00:02:30.950 --> 00:02:32.300
For our reaction,
00:02:32.300 --> 00:02:34.770
let's look at these
synthesis of ammonia gas
00:02:34.770 --> 00:02:37.500
from nitrogen gas and hydrogen gas.
00:02:37.500 --> 00:02:40.560
Our goal is to calculate the
standard change in free energy
00:02:40.560 --> 00:02:44.540
for this reaction at 25 degrees Celsius.
00:02:44.540 --> 00:02:46.580
First, we need to think
about our products.
00:02:46.580 --> 00:02:47.740
For this reaction,
00:02:47.740 --> 00:02:50.270
we have only one product
and that's ammonia.
00:02:50.270 --> 00:02:52.410
Notice how there's a two as a coefficient
00:02:52.410 --> 00:02:55.220
in front of ammonia and
the balanced equation.
00:02:55.220 --> 00:02:57.460
So we would need to look
up the standard change
00:02:57.460 --> 00:03:00.270
in free energy of formation of ammonia
00:03:00.270 --> 00:03:02.170
at 25 degrees Celsius.
00:03:02.170 --> 00:03:04.880
And because this value
is per mole of ammonia,
00:03:04.880 --> 00:03:06.970
we would need to multiply it by two
00:03:06.970 --> 00:03:10.260
because we have two moles
in our balanced equation.
00:03:10.260 --> 00:03:12.140
Next, we think about our reactants.
00:03:12.140 --> 00:03:15.220
And we have two reactants,
nitrogen and hydrogen.
00:03:15.220 --> 00:03:18.110
And we need the sum of
their standard changes
00:03:18.110 --> 00:03:20.320
in free energy of formation.
00:03:20.320 --> 00:03:22.030
So we would write the standard change
00:03:22.030 --> 00:03:24.240
in free energy of formation of nitrogen.
00:03:24.240 --> 00:03:26.460
And because there's a one
in our balanced equation,
00:03:26.460 --> 00:03:29.760
we multiply that value by
one and two that we add
00:03:29.760 --> 00:03:31.930
the standard change in
free energy of formation
00:03:31.930 --> 00:03:33.090
of hydrogen gas.
00:03:33.090 --> 00:03:35.150
And since we have a three
in our balanced equation,
00:03:35.150 --> 00:03:37.200
we would multiply that by three.
00:03:37.200 --> 00:03:38.730
So going back to ammonia,
00:03:38.730 --> 00:03:40.970
the standard change in
free energy of formation
00:03:40.970 --> 00:03:44.520
is equal to negative
16.5 kilojoules per mole,
00:03:44.520 --> 00:03:48.340
multiply that by two moles
and the moles will cancel out.
00:03:48.340 --> 00:03:50.080
For nitrogen and hydrogen,
00:03:50.080 --> 00:03:52.800
those are both elements
in their standard states
00:03:52.800 --> 00:03:55.900
and therefore their standard
free energy of formations
00:03:55.900 --> 00:03:57.180
are equal to zero.
00:03:57.180 --> 00:03:59.820
So this is just zero plus zero.
00:03:59.820 --> 00:04:03.450
So the standard change in
free energy for this reaction
00:04:03.450 --> 00:04:08.450
is equal to negative 33.0
kilojoules at 25 degrees Celsius.
00:04:08.980 --> 00:04:12.150
Standard state for a gas
refers to the pure gas
00:04:12.150 --> 00:04:14.250
at a pressure of one atmosphere.
00:04:14.250 --> 00:04:16.890
So we think about all three of our gases
00:04:16.890 --> 00:04:18.960
at a partial pressure of one atmosphere
00:04:18.960 --> 00:04:22.260
at a temperature of 25 degrees Celsius.
00:04:22.260 --> 00:04:25.260
The standard change and free
energy for this reaction
00:04:25.260 --> 00:04:28.190
is negative 33.0 kilojoules.
00:04:28.190 --> 00:04:32.140
Since the change in
free energy is negative,
00:04:32.140 --> 00:04:35.400
that tells us the reaction as
thermodynamically favorable
00:04:35.400 --> 00:04:37.760
in the forward direction.
00:04:37.760 --> 00:04:40.750
So nitrogen and hydrogen
will react together
00:04:40.750 --> 00:04:43.110
to form more ammonia.
00:04:43.110 --> 00:04:45.370
Textbooks often give
the units as kilojoules
00:04:45.370 --> 00:04:46.970
for the standard change and free energy
00:04:46.970 --> 00:04:48.480
of a chemical reaction.
00:04:48.480 --> 00:04:49.590
However, sometimes you
00:04:49.590 --> 00:04:53.530
also see kilojoules per mole of reaction.
00:04:53.530 --> 00:04:55.440
Per mole of reaction simply refers
00:04:55.440 --> 00:04:57.550
to how the balanced equation is written.
00:04:57.550 --> 00:05:00.880
And here we have the formation
of two moles of ammonia.
00:05:00.880 --> 00:05:03.660
So we can write a conversion
factor of two moles
00:05:03.660 --> 00:05:07.300
of ammonia per one mole of reaction.
00:05:07.300 --> 00:05:09.880
For standard free energies of formation,
00:05:09.880 --> 00:05:12.700
the units are kilojoules
per mole of the substance.
00:05:12.700 --> 00:05:13.533
So in this case,
00:05:13.533 --> 00:05:17.280
it's negative 16.5 kilojoules
per mole of ammonia.
00:05:17.280 --> 00:05:19.840
So moles of ammonia would cancel out,
00:05:19.840 --> 00:05:24.423
which gives kilojoules per
mole of reaction for the units.
|
Worked example: Determining the effect of temperature on thermodynamic favorability | https://www.youtube.com/watch?v=_pRo2jlA-9I | vtt | https://www.youtube.com/api/timedtext?v=_pRo2jlA-9I&ei=ylWUZf_3HvKjp-oP5umJ6A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D548D1BD8AB7FAB6A59941D4829C42C4F07033CC.5ECE4D53363650FDB0734E497A6C4D1BB4ED4399&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.240 --> 00:00:01.530
- [Lecturer] Let's do a work example
00:00:01.530 --> 00:00:03.240
where we calculate the standard change
00:00:03.240 --> 00:00:06.690
in free energy, delta G naught,
for a chemical reaction.
00:00:06.690 --> 00:00:07.830
And for our reaction,
00:00:07.830 --> 00:00:10.620
let's look at the synthesis of ammonia gas
00:00:10.620 --> 00:00:13.560
from nitrogen gas and hydrogen gas.
00:00:13.560 --> 00:00:15.180
At 25 degrees Celsius,
00:00:15.180 --> 00:00:17.370
delta H naught for this reaction is equal
00:00:17.370 --> 00:00:21.870
to negative 92.2 kilojoules
per mole of reaction.
00:00:21.870 --> 00:00:23.560
Since delta H naught is negative,
00:00:23.560 --> 00:00:25.850
this reaction is exothermic
00:00:25.850 --> 00:00:27.640
and at 25 degrees Celsius,
00:00:27.640 --> 00:00:29.620
delta S naught for this reaction is equal
00:00:29.620 --> 00:00:34.330
to negative 198.7 joules
per kelvin mole of reaction.
00:00:34.330 --> 00:00:36.580
Our goal is to calculate delta G naught
00:00:36.580 --> 00:00:39.530
for this reaction at 25 degrees Celsius.
00:00:39.530 --> 00:00:41.480
Remember if delta G naught is negative,
00:00:41.480 --> 00:00:44.500
the forward reaction is
thermodynamically favorable,
00:00:44.500 --> 00:00:46.500
but if delta G naught is positive,
00:00:46.500 --> 00:00:50.550
the forward reaction is
thermodynamically unfavorable.
00:00:50.550 --> 00:00:52.640
Since the change in enthalpy is negative,
00:00:52.640 --> 00:00:54.810
and the change in entropy is negative,
00:00:54.810 --> 00:00:56.790
whether or not delta G naught is negative
00:00:56.790 --> 00:00:58.810
depends on the temperature.
00:00:58.810 --> 00:01:00.790
To calculate the value for delta G naught,
00:01:00.790 --> 00:01:02.970
we're going to use the following equation.
00:01:02.970 --> 00:01:05.720
Delta G naught is equal to delta H naught
00:01:05.720 --> 00:01:07.710
minus T delta S naught,
00:01:07.710 --> 00:01:10.320
where T is the temperature in kelvin.
00:01:10.320 --> 00:01:12.760
Next, we need to plug
everything into our equation.
00:01:12.760 --> 00:01:14.690
So delta H nought is equal
00:01:14.690 --> 00:01:19.690
to negative 92.2 kilojoules
per mole of reaction.
00:01:20.020 --> 00:01:22.800
The temperature is 25 degrees Celsius.
00:01:22.800 --> 00:01:27.800
So 25 plus 273 is equal to 298 kelvin.
00:01:28.630 --> 00:01:32.290
So we're gonna plug 298
kelvin into our equation.
00:01:32.290 --> 00:01:35.280
And for delta S naught,
notice we have this in joules,
00:01:35.280 --> 00:01:38.230
whereas for delta H naught,
it was in kilojoules.
00:01:38.230 --> 00:01:40.140
So we need to convert delta S naught
00:01:40.140 --> 00:01:43.130
into kilojoules per
kelvin mole of reaction.
00:01:43.130 --> 00:01:44.750
One way to do that is just to move
00:01:44.750 --> 00:01:47.180
the decimal place three to the left,
00:01:47.180 --> 00:01:51.350
which gives us negative 0.1987 kilojoules
00:01:51.350 --> 00:01:53.520
per kelvin mole of reaction.
00:01:53.520 --> 00:01:57.033
So we're gonna plug all of
this in for delta S naught.
00:01:57.960 --> 00:02:00.460
Here's our equation with
everything plugged in.
00:02:00.460 --> 00:02:03.110
Notice that kelvin will cancel out,
00:02:03.110 --> 00:02:06.960
which gives us kilojoules per
mole of reaction as our units.
00:02:06.960 --> 00:02:08.010
And when we do the math,
00:02:08.010 --> 00:02:09.970
we find that delta G naught is equal
00:02:09.970 --> 00:02:14.940
to negative 33.0 kilojoules
per mole of reaction.
00:02:14.940 --> 00:02:16.770
Because delta G naught is negative,
00:02:16.770 --> 00:02:19.850
that means the reaction is
thermodynamically favorable
00:02:19.850 --> 00:02:22.110
in the forward direction.
00:02:22.110 --> 00:02:25.440
And the superscript naught
means that both the reactants
00:02:25.440 --> 00:02:28.070
and products are in their standard states.
00:02:28.070 --> 00:02:31.750
So what our calculation tells
us is if we had a mixture
00:02:31.750 --> 00:02:35.070
of nitrogen, hydrogen, and ammonia gas
00:02:35.070 --> 00:02:37.340
at 25 degrees Celsius,
00:02:37.340 --> 00:02:40.040
and all three gases had a partial pressure
00:02:40.040 --> 00:02:41.940
of one atmosphere,
00:02:41.940 --> 00:02:44.400
the reaction is
thermodynamically favorable
00:02:44.400 --> 00:02:45.790
in the forward direction,
00:02:45.790 --> 00:02:49.830
meaning nitrogen gas and
hydrogen gas would come together
00:02:49.830 --> 00:02:53.150
to synthesize or make more ammonia.
00:02:53.150 --> 00:02:56.130
So at 298 kelvin, delta G naught
00:02:56.130 --> 00:02:58.870
for this reaction is negative.
00:02:58.870 --> 00:03:02.470
Let's do another calculation
for the same reaction
00:03:02.470 --> 00:03:03.880
at a different temperature,
00:03:03.880 --> 00:03:06.360
a temperature of 1,000 kelvin.
00:03:06.360 --> 00:03:08.880
Also, even though the
value for delta G naught
00:03:08.880 --> 00:03:10.940
is highly dependent on temperature,
00:03:10.940 --> 00:03:14.320
the values for delta H
naught and delta S naught
00:03:14.320 --> 00:03:17.400
are not as dependent on the temperature.
00:03:17.400 --> 00:03:19.690
Therefore, we're gonna
assume that these values
00:03:19.690 --> 00:03:23.190
for delta H naught and
delta S naught don't change,
00:03:23.190 --> 00:03:24.880
and we're gonna use the same ones
00:03:24.880 --> 00:03:28.140
at the higher temperature of 1,000 kelvin.
00:03:28.140 --> 00:03:30.330
Here's the equation with
everything plugged in
00:03:30.330 --> 00:03:32.300
for the calculation of delta G naught
00:03:32.300 --> 00:03:35.360
at the higher temperature of 1,000 kelvin.
00:03:35.360 --> 00:03:38.260
And notice that the values
we're using for delta H naught
00:03:38.260 --> 00:03:40.970
and delta S naught are
the same as the ones
00:03:40.970 --> 00:03:45.540
that we used at the lower
temperature of 298 kelvin.
00:03:45.540 --> 00:03:47.640
Once again, kelvin cancels out
00:03:47.640 --> 00:03:50.190
and gives us kilojoules
per mole of reaction
00:03:50.190 --> 00:03:52.810
as our units for our final answer.
00:03:52.810 --> 00:03:53.810
And after we do the math,
00:03:53.810 --> 00:03:55.700
we find that delta G naught is equal
00:03:55.700 --> 00:04:00.350
to positive 106.5 kilojoules
per mole of reaction.
00:04:00.350 --> 00:04:02.530
Since delta G naught is positive,
00:04:02.530 --> 00:04:04.460
that means the forward reaction
00:04:04.460 --> 00:04:06.810
is thermodynamically unfavorable,
00:04:06.810 --> 00:04:08.970
which means the reverse reaction
00:04:08.970 --> 00:04:11.000
is thermodynamically favorable.
00:04:11.000 --> 00:04:14.310
So if we had a mixture of
nitrogen gas, hydrogen gas,
00:04:14.310 --> 00:04:17.780
and ammonia gas at a
temperature of 1,000 kelvin,
00:04:17.780 --> 00:04:20.460
and all three gases had a partial pressure
00:04:20.460 --> 00:04:22.140
of one atmosphere,
00:04:22.140 --> 00:04:25.470
the ammonia gas would
turn into nitrogen gas
00:04:25.470 --> 00:04:26.950
and hydrogen gas.
00:04:26.950 --> 00:04:29.560
And while we have both
calculations on the screen,
00:04:29.560 --> 00:04:32.830
let's analyze why one calculation
gives a negative value
00:04:32.830 --> 00:04:33.860
for delta G naught,
00:04:33.860 --> 00:04:36.670
and the other one gives a positive value.
00:04:36.670 --> 00:04:40.010
For the calculation at 298 kelvin,
00:04:40.010 --> 00:04:42.460
the temperature was low enough
00:04:42.460 --> 00:04:45.570
that the entropy term didn't overwhelm
00:04:45.570 --> 00:04:47.970
the negative value for the enthalpy term,
00:04:47.970 --> 00:04:50.700
and we ended up with a
negative overall value
00:04:50.700 --> 00:04:52.600
for delta G naught.
00:04:52.600 --> 00:04:55.720
However, for the
calculation at 1,000 kelvin,
00:04:55.720 --> 00:04:58.230
this time the temperature was high enough
00:04:58.230 --> 00:05:01.290
where the entropy term outweighed
00:05:01.290 --> 00:05:04.050
the negative value for the enthalpy term,
00:05:04.050 --> 00:05:06.060
and therefore the overall value
00:05:06.060 --> 00:05:09.640
for delta G naught
ended up being positive.
00:05:09.640 --> 00:05:12.490
We've just seen that for
the synthesis of ammonia
00:05:12.490 --> 00:05:15.060
from nitrogen gas and hydrogen gas
00:05:15.060 --> 00:05:19.470
at relatively low
temperatures like 298 kelvin,
00:05:19.470 --> 00:05:22.260
delta G naught is less than zero,
00:05:22.260 --> 00:05:26.040
and at relatively high
temperatures like 1,000 kelvin,
00:05:26.040 --> 00:05:28.800
delta G naught is greater than zero.
00:05:28.800 --> 00:05:30.580
So there must be some temperature
00:05:30.580 --> 00:05:34.410
between 298 kelvin and 1,000 kelvin
00:05:34.410 --> 00:05:36.380
where the forward reaction goes
00:05:36.380 --> 00:05:38.760
from being thermodynamically favorable
00:05:38.760 --> 00:05:41.500
to thermodynamically unfavorable.
00:05:41.500 --> 00:05:45.385
And this crossover point
occurs when the enthalpy term
00:05:45.385 --> 00:05:49.220
and the entropy term
are perfectly balanced.
00:05:49.220 --> 00:05:52.700
Therefore, delta G naught is equal to zero
00:05:52.700 --> 00:05:54.870
at this crossover point.
00:05:54.870 --> 00:05:57.490
So we plug in zero for delta G naught
00:05:57.490 --> 00:06:00.890
and we solve for the temperature
at the crossover point.
00:06:00.890 --> 00:06:02.160
After some algebra,
00:06:02.160 --> 00:06:04.060
we find that the temperature is equal
00:06:04.060 --> 00:06:07.330
to delta H naught divided
by delta S naught,
00:06:07.330 --> 00:06:10.660
which is equal to negative 92.2 kilojoules
00:06:10.660 --> 00:06:15.660
per mole of reaction divided
by negative 0.1987 kilojoules
00:06:15.960 --> 00:06:18.380
per kelvin mole of reaction.
00:06:18.380 --> 00:06:21.230
Kilojoules per mole of
reaction cancels out
00:06:21.230 --> 00:06:26.230
and gives us 464 kelvin for
the crossover temperature.
00:06:26.690 --> 00:06:28.400
So for this particular reaction,
00:06:28.400 --> 00:06:32.890
delta G naught is equal
to zero at 464 kelvin.
00:06:32.890 --> 00:06:35.490
At temperatures less than 464 kelvin,
00:06:35.490 --> 00:06:39.020
the forward reaction is
thermodynamically favorable.
00:06:39.020 --> 00:06:42.620
However, at temperatures
higher than 464 kelvin,
00:06:42.620 --> 00:06:46.153
the forward reaction is
thermodynamically unfavorable.
|
Thermodynamic favorability and temperature | https://www.youtube.com/watch?v=eejDYxFKGNs | vtt | https://www.youtube.com/api/timedtext?v=eejDYxFKGNs&ei=ylWUZdGAJLqfp-oP4MqeKA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=081A01E89D0695B66B97FF9017FCA759DDF8597F.89072812BCC4EED8A65CEDAD248F6D96A49349AE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.230 --> 00:00:02.360
- [Instructor] The
thermodynamic favorability
00:00:02.360 --> 00:00:03.590
of a chemical reaction
00:00:03.590 --> 00:00:05.690
can be affected by the temperature.
00:00:05.690 --> 00:00:07.580
Let's say we have a generic reaction
00:00:07.580 --> 00:00:09.910
where the reactants
turn into the products.
00:00:09.910 --> 00:00:13.060
As a quick review, when the
standard change in free energy,
00:00:13.060 --> 00:00:14.070
delta G naught,
00:00:14.070 --> 00:00:15.690
is less than zero,
00:00:15.690 --> 00:00:19.740
the forward reaction is
thermodynamically favorable.
00:00:19.740 --> 00:00:22.090
Therefore, the net
reaction goes to the right
00:00:22.090 --> 00:00:24.110
to make more of the products.
00:00:24.110 --> 00:00:26.440
And when delta G naught
is greater than zero,
00:00:26.440 --> 00:00:30.230
the forward reaction is
thermodynamically unfavorable.
00:00:30.230 --> 00:00:32.930
That means that the reverse
reaction is favorable
00:00:32.930 --> 00:00:34.830
and the net reaction would go to the left
00:00:34.830 --> 00:00:37.150
to make more of the reactants.
00:00:37.150 --> 00:00:38.990
One way to calculate delta G naught
00:00:38.990 --> 00:00:40.890
is to use the following equation.
00:00:40.890 --> 00:00:43.410
Delta G naught is equal to delta H naught
00:00:43.410 --> 00:00:47.590
minus the absolute temperature
times delta S naught.
00:00:47.590 --> 00:00:48.870
And since delta H naught
00:00:48.870 --> 00:00:51.870
is talking about the
standard change enthalpy,
00:00:51.870 --> 00:00:53.050
for this equation
00:00:53.050 --> 00:00:56.240
delta H naught will be
called the enthalpy term.
00:00:56.240 --> 00:00:57.580
And because delta S naught
00:00:57.580 --> 00:01:00.340
is talking about the
standard change in entropy,
00:01:00.340 --> 00:01:02.780
the absolute temperature
times delta S naught
00:01:02.780 --> 00:01:06.590
will be referred to as the entropy term.
00:01:06.590 --> 00:01:08.050
So when we're trying to figure out
00:01:08.050 --> 00:01:09.610
if delta G naught is negative
00:01:09.610 --> 00:01:11.730
or if delta G naught is positive,
00:01:11.730 --> 00:01:15.210
we need to consider the
sign for delta H naught,
00:01:15.210 --> 00:01:17.750
the sign for delta S naught,
00:01:17.750 --> 00:01:20.020
and sometimes we also need to consider
00:01:20.020 --> 00:01:22.020
what the temperature is.
00:01:22.020 --> 00:01:24.770
There are four possible
combinations of signs
00:01:24.770 --> 00:01:27.190
for delta H naught and delta S naught
00:01:27.190 --> 00:01:28.970
as we can see in this table.
00:01:28.970 --> 00:01:30.750
For each of these four combinations,
00:01:30.750 --> 00:01:32.260
we're gonna think about the temperatures
00:01:32.260 --> 00:01:34.930
at which delta G naught is less than zero
00:01:34.930 --> 00:01:37.930
and we're gonna finish
filling out this table.
00:01:37.930 --> 00:01:40.180
To start with, we're gonna
think about the situation
00:01:40.180 --> 00:01:42.270
where delta H naught is negative
00:01:42.270 --> 00:01:45.060
and delta S naught is positive.
00:01:45.060 --> 00:01:47.710
So for this first possible combination,
00:01:47.710 --> 00:01:50.180
when delta H naught is negative,
00:01:50.180 --> 00:01:52.750
we say that's an exothermic reaction.
00:01:52.750 --> 00:01:55.620
And when delta S naught is positive,
00:01:55.620 --> 00:01:57.780
that's saying there's
an increase in entropy
00:01:57.780 --> 00:02:00.310
as reactants turn into products.
00:02:00.310 --> 00:02:02.660
So let's think about the
sign for delta G naught
00:02:02.660 --> 00:02:05.380
if we plug in some numbers
for delta H naught,
00:02:05.380 --> 00:02:08.070
temperature, and delta S naught.
00:02:08.070 --> 00:02:09.460
And when I plug in some numbers,
00:02:09.460 --> 00:02:11.940
I'm not really concerned
about a particular reaction.
00:02:11.940 --> 00:02:13.540
I'm not concerned about units.
00:02:13.540 --> 00:02:15.920
I'm not concerned about
significant figures.
00:02:15.920 --> 00:02:17.930
I'm just interested in
looking at the numbers
00:02:17.930 --> 00:02:22.210
and seeing how the math affects
the sign for delta G naught.
00:02:22.210 --> 00:02:24.760
So for delta H naught,
I'm saying that's -100.
00:02:26.508 --> 00:02:30.050
For T, I'm saying that's 100,
00:02:30.050 --> 00:02:32.423
and for delta S naught,
I'm saying that's +0.1.
00:02:36.039 --> 00:02:37.307
So this would be equal to -100 - 10,
00:02:40.996 --> 00:02:43.550
which is equal to -110.
00:02:43.550 --> 00:02:45.930
So delta G naught is negative.
00:02:45.930 --> 00:02:48.940
Notice how a negative entropy term
00:02:48.940 --> 00:02:53.180
favors getting a negative
value for delta G naught.
00:02:53.180 --> 00:02:55.910
And notice how a positive entropy term,
00:02:55.910 --> 00:02:59.080
since we're subtracting
that in our equation
00:02:59.080 --> 00:03:02.070
is also favorable for
getting a negative value
00:03:02.070 --> 00:03:03.770
for delta G naught.
00:03:03.770 --> 00:03:06.670
Also notice, no matter what
we put in for the temperature
00:03:06.670 --> 00:03:09.400
since delta S naught is positive,
00:03:09.400 --> 00:03:12.180
the entropy term will always be positive.
00:03:12.180 --> 00:03:15.010
And since we're subtracting
it in our equation,
00:03:15.010 --> 00:03:18.990
we would always get a negative
value for delta G naught.
00:03:18.990 --> 00:03:22.492
So whenever delta H naught is negative
00:03:22.492 --> 00:03:25.200
and when delta S naught is positive,
00:03:25.200 --> 00:03:26.750
delta G naught will be negative
00:03:26.750 --> 00:03:29.040
no matter what the temperature.
00:03:29.040 --> 00:03:30.630
So if we go back to our chart
00:03:30.630 --> 00:03:32.800
for our first possible combination,
00:03:32.800 --> 00:03:35.690
when delta H naught is
negative, that's favorable.
00:03:35.690 --> 00:03:39.510
And when delta S naught as
positive, that's also favorable.
00:03:39.510 --> 00:03:44.090
Therefore delta G naught is
less than 0 at all temperatures.
00:03:44.090 --> 00:03:45.367
So I'm gonna go ahead and write in here,
00:03:45.367 --> 00:03:47.930
'at all temperatures' in our chart.
00:03:47.930 --> 00:03:49.000
As an example of this,
00:03:49.000 --> 00:03:53.710
let's consider the conversion
of ozone gas into oxygen gas.
00:03:53.710 --> 00:03:55.360
Since energy is released,
00:03:55.360 --> 00:03:57.780
this is an exothermic reaction,
00:03:57.780 --> 00:04:00.470
and delta H naught is negative.
00:04:00.470 --> 00:04:02.600
And since we're going from 2 moles of gas
00:04:02.600 --> 00:04:03.700
on the reactant side
00:04:03.700 --> 00:04:06.450
to 3 moles of gas on the product side,
00:04:06.450 --> 00:04:08.460
that's an increase in entropy.
00:04:08.460 --> 00:04:10.830
So delta S naught is positive.
00:04:10.830 --> 00:04:12.640
Since delta H naught is negative
00:04:12.640 --> 00:04:14.720
and delta S naught is positive,
00:04:14.720 --> 00:04:16.320
delta G naught for this reaction
00:04:16.320 --> 00:04:19.080
is less than zero at all temperatures.
00:04:19.080 --> 00:04:21.580
That means the forward reaction
00:04:21.580 --> 00:04:24.150
is thermodynamically favorable,
00:04:24.150 --> 00:04:28.170
and ozone gas would turn into oxygen gas,
00:04:28.170 --> 00:04:31.160
and this reaction would
occur at all temperatures.
00:04:31.160 --> 00:04:34.030
The second possible
combination for the signs
00:04:34.030 --> 00:04:36.710
is when delta H naught is positive
00:04:36.710 --> 00:04:39.380
and when delta S naught is negative.
00:04:39.380 --> 00:04:41.240
When delta H naught is positive,
00:04:41.240 --> 00:04:43.470
that's an endothermic reaction.
00:04:43.470 --> 00:04:45.450
And when delta S naught is negative,
00:04:45.450 --> 00:04:47.210
there's a decrease in entropy
00:04:47.210 --> 00:04:49.610
going from reactants to products.
00:04:49.610 --> 00:04:51.710
Once again we're gonna
plug in some numbers
00:04:51.710 --> 00:04:53.780
and solve for delta G naught.
00:04:53.780 --> 00:04:55.290
So for delta H naught,
00:04:55.290 --> 00:04:58.070
let's say that's +100,
00:04:58.070 --> 00:05:01.760
for the temperature term,
let's say that's 100,
00:05:01.760 --> 00:05:05.133
and delta S naught, let's say that's -0.1.
00:05:06.638 --> 00:05:07.733
When we do the math,
00:05:10.162 --> 00:05:11.862
we get positive 100 - negative 10,
00:05:15.345 --> 00:05:18.030
which is equal to +110.
00:05:18.030 --> 00:05:20.520
So delta G naught is positive.
00:05:20.520 --> 00:05:23.370
Notice when the entropy term is positive,
00:05:23.370 --> 00:05:26.120
that's not favorable for
getting a negative value
00:05:26.120 --> 00:05:27.780
for delta G naught.
00:05:27.780 --> 00:05:31.000
And when the entropy term is negative,
00:05:31.000 --> 00:05:34.060
since we're subtracting this negative,
00:05:34.060 --> 00:05:37.110
we would actually be
adding the entropy term.
00:05:37.110 --> 00:05:38.990
And that would not favor
00:05:38.990 --> 00:05:41.840
a negative value for delta G naught.
00:05:41.840 --> 00:05:42.673
Also notice,
00:05:42.673 --> 00:05:45.030
no matter what you put in
for the temperature here,
00:05:45.030 --> 00:05:46.900
you're always gonna get a negative value
00:05:46.900 --> 00:05:48.640
for the entropy term.
00:05:48.640 --> 00:05:51.040
And if the enthalpy term is positive,
00:05:51.040 --> 00:05:54.260
since we would mathematically
be adding the entropy term,
00:05:54.260 --> 00:05:57.880
we would always get a positive
value for delta G naught.
00:05:57.880 --> 00:06:00.040
So whenever delta H naught is positive
00:06:00.040 --> 00:06:02.660
and delta S naught is negative,
00:06:02.660 --> 00:06:05.240
delta G naught will be positive
00:06:05.240 --> 00:06:07.330
no matter what the temperature.
00:06:07.330 --> 00:06:10.930
So going back to our charge
when delta H naught is positive,
00:06:10.930 --> 00:06:12.430
that was not favorable,
00:06:12.430 --> 00:06:14.820
and when delta S naught was negative,
00:06:14.820 --> 00:06:16.940
that was also not favorable.
00:06:16.940 --> 00:06:18.700
So it doesn't matter
what the temperature is.
00:06:18.700 --> 00:06:21.440
Delta G naught will not be less than zero.
00:06:21.440 --> 00:06:24.610
Therefore, on our chart
here we can write in,
00:06:24.610 --> 00:06:28.730
at no temperature will delta
G naught be less than zero.
00:06:28.730 --> 00:06:29.810
As an example of this,
00:06:29.810 --> 00:06:32.530
let's look at the reverse
of the reaction we saw
00:06:32.530 --> 00:06:34.820
for the first possible combination.
00:06:34.820 --> 00:06:37.700
Before we had ozone
turning into oxygen gas,
00:06:37.700 --> 00:06:41.170
and now we have oxygen
gas turning into ozone.
00:06:41.170 --> 00:06:43.010
Because heat is on the reactant side,
00:06:43.010 --> 00:06:44.980
we know this reaction is endothermic
00:06:44.980 --> 00:06:47.240
and delta H naught is positive.
00:06:47.240 --> 00:06:49.360
And since we're going from 3 moles of gas
00:06:49.360 --> 00:06:50.440
on the reactant side
00:06:50.440 --> 00:06:53.120
to 2 moles of gas on the product side,
00:06:53.120 --> 00:06:55.270
that's a decrease in entropy,
00:06:55.270 --> 00:06:58.190
and delta S naught is negative.
00:06:58.190 --> 00:07:00.180
Since delta H naught is positive
00:07:00.180 --> 00:07:02.640
and delta S naught is negative,
00:07:02.640 --> 00:07:05.150
delta G naught will
never be less than zero.
00:07:05.150 --> 00:07:07.470
It doesn't matter what the temperature is.
00:07:07.470 --> 00:07:09.150
And so the forward reaction
00:07:09.150 --> 00:07:12.770
is always thermodynamically unfavorable.
00:07:12.770 --> 00:07:14.880
The third possible combination of signs
00:07:14.880 --> 00:07:17.930
has both delta H naught and delta S naught
00:07:17.930 --> 00:07:19.430
as being negative.
00:07:19.430 --> 00:07:22.080
Once again we're gonna plug
some numbers into the equation
00:07:22.080 --> 00:07:24.750
and see what happens to
the sign of delta G naught.
00:07:24.750 --> 00:07:27.890
So let's say delta H naught is -100.
00:07:27.890 --> 00:07:31.810
The temperature is 100 and
delta S naught is -0.1.
00:07:32.870 --> 00:07:36.630
Doing the math, we get
negative 100 minus negative 10.
00:07:36.630 --> 00:07:38.640
So that's -100 + 10,
00:07:38.640 --> 00:07:40.127
which is equal to -90.
00:07:40.970 --> 00:07:43.260
Let's think about why
we got a negative value
00:07:43.260 --> 00:07:44.920
for delta G naught.
00:07:44.920 --> 00:07:46.720
The enthalpy term is negative,
00:07:46.720 --> 00:07:50.060
which favors a negative
value for delta G naught.
00:07:50.060 --> 00:07:52.590
The entropy term is also negative,
00:07:52.590 --> 00:07:54.870
but since we're subtracting
the entropy term,
00:07:54.870 --> 00:07:56.210
it actually gets added
00:07:56.210 --> 00:07:59.000
for the overall delta
G naught calculation.
00:07:59.000 --> 00:08:01.850
So the entropy term is not favorable.
00:08:01.850 --> 00:08:03.260
However, in this case,
00:08:03.260 --> 00:08:05.460
the favorable entropy term
00:08:05.460 --> 00:08:08.900
outweighs the unfavorable entropy term.
00:08:08.900 --> 00:08:12.050
And that's the reason why
we get a negative value
00:08:12.050 --> 00:08:15.300
for delta G naught at this temperature.
00:08:15.300 --> 00:08:18.110
Let's compare the
calculation that we just did
00:08:18.110 --> 00:08:19.900
at a temperature of 100,
00:08:19.900 --> 00:08:22.720
which gave us a negative
value for delta G naught,
00:08:22.720 --> 00:08:24.280
to a similar calculation,
00:08:24.280 --> 00:08:26.620
except this time we have
a much higher temperature.
00:08:26.620 --> 00:08:28.450
This time it's 2000.
00:08:28.450 --> 00:08:30.870
But notice how the
values for delta H naught
00:08:30.870 --> 00:08:33.960
and delta S naught are the same as before.
00:08:33.960 --> 00:08:35.950
The reason why we can use the same values
00:08:35.950 --> 00:08:37.340
at a different temperature
00:08:37.340 --> 00:08:39.620
is because delta H and delta S naught
00:08:39.620 --> 00:08:42.100
don't change much with temperature.
00:08:42.100 --> 00:08:45.610
However, delta G naught does
change a lot with temperature.
00:08:45.610 --> 00:08:48.470
Because at this higher
temperature, when we do the math,
00:08:48.470 --> 00:08:52.940
we see that now we get delta
G naught is equal to +100.
00:08:52.940 --> 00:08:54.540
So at this higher temperature,
00:08:54.540 --> 00:08:57.670
even though the enthalpy
term is favorable,
00:08:57.670 --> 00:09:00.470
now the unfavorable entropy term
00:09:00.470 --> 00:09:03.550
outweighs the favorable enthalpy term
00:09:03.550 --> 00:09:07.410
and gives us a positive
value for delta G naught.
00:09:07.410 --> 00:09:09.960
Therefore, at a relatively
lower temperature,
00:09:09.960 --> 00:09:12.190
delta G naught is negative.
00:09:12.190 --> 00:09:14.180
However, at a higher temperature,
00:09:14.180 --> 00:09:16.900
delta G naught is positive.
00:09:16.900 --> 00:09:20.200
So when delta H naught is
negative, that's favorable,
00:09:20.200 --> 00:09:24.010
but when delta S naught is
negative, that's not favorable.
00:09:24.010 --> 00:09:25.800
And we just saw from the calculations
00:09:25.800 --> 00:09:29.730
that delta G naught will be
negative at low temperatures.
00:09:29.730 --> 00:09:32.850
So let's write that in here in our chart.
00:09:32.850 --> 00:09:35.130
So far we've been talking
about delta G naught
00:09:35.130 --> 00:09:37.840
relative to a chemical process.
00:09:37.840 --> 00:09:42.120
However, delta G naught also
applies to a physical process.
00:09:42.120 --> 00:09:42.953
In this case
00:09:42.953 --> 00:09:46.070
we're looking at liquid water
turning into solid water.
00:09:46.070 --> 00:09:48.740
So this is the process of freezing.
00:09:48.740 --> 00:09:51.320
The process of freezing gives off energy.
00:09:51.320 --> 00:09:53.320
So this process is exothermic,
00:09:53.320 --> 00:09:55.670
and delta H naught will be negative.
00:09:55.670 --> 00:09:59.780
Going from a liquid to a solid
is a decrease in entropy,
00:09:59.780 --> 00:10:02.500
therefore, delta S naught is negative.
00:10:02.500 --> 00:10:06.800
For this combination of signs,
delta G naught is negative
00:10:06.800 --> 00:10:09.500
only at relatively low temperatures.
00:10:09.500 --> 00:10:12.860
Therefore, the forward process of freezing
00:10:12.860 --> 00:10:16.340
is thermodynamically
favorable at low temperatures.
00:10:16.340 --> 00:10:18.790
And this matches with what
we already know about water,
00:10:18.790 --> 00:10:22.200
water freezes at a
relatively low temperature.
00:10:22.200 --> 00:10:25.320
Finally, let's look at our
fourth combination of signs,
00:10:25.320 --> 00:10:27.530
and that's when both delta H naught
00:10:27.530 --> 00:10:30.010
and delta S naught are positive.
00:10:30.010 --> 00:10:33.360
So let's say delta H
naught is equal to +100,
00:10:33.360 --> 00:10:35.990
delta S naught is equal able to +0.1,
00:10:35.990 --> 00:10:39.800
and first we'll look at the
lower temperature of 100.
00:10:39.800 --> 00:10:42.600
Doing the math, we get positive 100 - 10,
00:10:42.600 --> 00:10:46.080
which gives us a positive
value for delta G naught.
00:10:46.080 --> 00:10:47.400
And if we do the calculation
00:10:47.400 --> 00:10:49.580
at a higher temperature of 2000,
00:10:49.580 --> 00:10:52.180
notice that delta H naught is still +100
00:10:52.180 --> 00:10:54.043
and delta S not is still +0.1.
00:10:55.340 --> 00:10:58.680
This time we get -100 for delta G naught.
00:10:58.680 --> 00:11:01.640
Notice how for this example
at the higher temperature,
00:11:01.640 --> 00:11:03.710
the entropy term is unfavorable
00:11:03.710 --> 00:11:06.540
for giving a negative
value for delta G naught.
00:11:06.540 --> 00:11:09.600
However, the entropy term is favorable.
00:11:09.600 --> 00:11:11.810
A positive value for delta S naught
00:11:11.810 --> 00:11:14.460
gives a positive value
for the entropy term.
00:11:14.460 --> 00:11:16.500
And since we are subtracting it,
00:11:16.500 --> 00:11:20.040
the entropy term outweighs
the enthalpy term,
00:11:20.040 --> 00:11:23.020
giving a negative value
for delta G naught.
00:11:23.020 --> 00:11:26.080
However, for the first example
at the lower temperature,
00:11:26.080 --> 00:11:27.780
since the temperature is lower,
00:11:27.780 --> 00:11:30.450
the entropy term is a smaller value,
00:11:30.450 --> 00:11:35.450
and is unable to overcome the
unfavorable enthalpy term.
00:11:35.890 --> 00:11:37.800
And that's the reason why delta G naught
00:11:37.800 --> 00:11:41.110
ends up being positive
at the lower temperature.
00:11:41.110 --> 00:11:43.020
So for this combination of signs,
00:11:43.020 --> 00:11:46.560
delta G naught is negative
at higher temperatures.
00:11:46.560 --> 00:11:48.400
So for our fourth combination,
00:11:48.400 --> 00:11:50.560
when delta H naught is positive,
00:11:50.560 --> 00:11:52.250
that is unfavorable.
00:11:52.250 --> 00:11:56.460
However, when delta S naught
is positive, that is favorable.
00:11:56.460 --> 00:12:00.840
And we just saw that delta
G naught is less than zero
00:12:00.840 --> 00:12:02.170
at high temperatures.
00:12:02.170 --> 00:12:05.217
So I'll go ahead and write
in on our table here,
00:12:05.217 --> 00:12:07.420
'at high temperatures.'
00:12:07.420 --> 00:12:08.570
As an example of this,
00:12:08.570 --> 00:12:12.490
let's consider solid water
turning into liquid water.
00:12:12.490 --> 00:12:16.280
So the forward process is
the process of melting.
00:12:16.280 --> 00:12:17.170
It takes energy
00:12:17.170 --> 00:12:20.030
to disrupt the intermolecular
forces of the solid,
00:12:20.030 --> 00:12:22.140
therefore, heat is on the reactant side
00:12:22.140 --> 00:12:24.830
and delta H naught is positive.
00:12:24.830 --> 00:12:27.820
Melting is an endothermic process.
00:12:27.820 --> 00:12:32.250
Going from a solid to a liquid
is an increase in entropy.
00:12:32.250 --> 00:12:35.300
Therefore, delta S naught is positive.
00:12:35.300 --> 00:12:37.130
And when both signs are positive,
00:12:37.130 --> 00:12:38.930
our calculations showed us
00:12:38.930 --> 00:12:43.630
that delta G naught is less
than zero at high temperatures.
00:12:43.630 --> 00:12:46.870
Therefore, the forward process of melting
00:12:46.870 --> 00:12:49.100
is thermodynamically favorable
00:12:49.100 --> 00:12:51.380
at relatively high temperatures.
00:12:51.380 --> 00:12:53.780
And this matches what we
already know from experience.
00:12:53.780 --> 00:12:57.050
At relatively low temperatures
ice does not melt.
00:12:57.050 --> 00:13:00.940
However, at relatively high
temperatures ice does melt.
00:13:00.940 --> 00:13:02.490
Now that we have our chart filled out,
00:13:02.490 --> 00:13:04.070
let's summarize what we've learned
00:13:04.070 --> 00:13:06.490
about these four possible combinations.
00:13:06.490 --> 00:13:10.350
When delta H naught and delta
S naught are both favorable,
00:13:10.350 --> 00:13:13.660
the forward process is
thermodynamically favorable
00:13:13.660 --> 00:13:15.450
at all temperatures.
00:13:15.450 --> 00:13:19.670
When delta H naught and delta
S naught are both unfavorable,
00:13:19.670 --> 00:13:23.170
the forward process is
thermodynamically favorable
00:13:23.170 --> 00:13:24.760
at no temperatures,
00:13:24.760 --> 00:13:26.750
or you could say the forward process
00:13:26.750 --> 00:13:30.690
is thermodynamically
unfavorable at all temperatures.
00:13:30.690 --> 00:13:32.980
When delta H naught is favorable
00:13:32.980 --> 00:13:35.920
and delta S naught is unfavorable,
00:13:35.920 --> 00:13:39.970
the forward process is only
thermodynamically favorable
00:13:39.970 --> 00:13:42.500
at low temperatures.
00:13:42.500 --> 00:13:45.540
And finally, if delta H
naught is unfavorable,
00:13:45.540 --> 00:13:47.930
but delta S naught is favorable,
00:13:47.930 --> 00:13:51.370
the forward process is
thermodynamically favorable
00:13:51.370 --> 00:13:53.553
only at high temperatures.
|
Introduction to Gibbs free energy | https://www.youtube.com/watch?v=_ikwCBn8wLE | vtt | https://www.youtube.com/api/timedtext?v=_ikwCBn8wLE&ei=ylWUZZOlMoCjp-oPn863yAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E2413CFFCABF962B67ABF001F507478B4AE0F8DC.50BF1F5AED8DE010DCBBD867FD424AB6333DF8D9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.510 --> 00:00:03.340
- [Instructor] Gibbs Free
Energy is symbolized by G
00:00:03.340 --> 00:00:08.020
and change in Gibbs Free Energy
is symbolized by delta G.
00:00:08.020 --> 00:00:09.970
And the change in free energy, delta G,
00:00:09.970 --> 00:00:12.450
is equal to the change
in enthalpy, delta H,
00:00:12.450 --> 00:00:14.470
minus the temperature in Kelvin,
00:00:14.470 --> 00:00:18.120
times the change in entropy, delta S.
00:00:18.120 --> 00:00:20.140
When delta G is less than zero,
00:00:20.140 --> 00:00:22.880
a chemical or physical process is favored
00:00:22.880 --> 00:00:24.780
in the forward direction.
00:00:24.780 --> 00:00:27.520
Therefore, we say that the forward process
00:00:27.520 --> 00:00:30.390
is thermodynamically favored.
00:00:30.390 --> 00:00:32.740
As an example, if we look at a reaction
00:00:32.740 --> 00:00:34.940
where reactants turn into products,
00:00:34.940 --> 00:00:37.270
if delta G is less than zero,
00:00:37.270 --> 00:00:40.600
the forward reaction as
thermodynamically favored,
00:00:40.600 --> 00:00:42.960
meaning the reaction will go to the right
00:00:42.960 --> 00:00:44.780
to make more products.
00:00:44.780 --> 00:00:47.250
Textbooks will often use
the word spontaneous.
00:00:47.250 --> 00:00:50.170
So, when delta G is less than zero,
00:00:50.170 --> 00:00:54.220
the reaction would be spontaneous
in the forward direction.
00:00:54.220 --> 00:00:56.620
When delta G is greater than zero,
00:00:56.620 --> 00:00:58.550
the chemical or physical process
00:00:58.550 --> 00:01:01.130
is favored in the reverse direction.
00:01:01.130 --> 00:01:03.410
Therefore, the forward process
00:01:03.410 --> 00:01:06.490
is not thermodynamically favored.
00:01:06.490 --> 00:01:09.460
Going back to our reaction, as an example,
00:01:09.460 --> 00:01:12.390
if delta G is greater than zero,
00:01:12.390 --> 00:01:15.500
that means the reverse
reaction is favored,
00:01:15.500 --> 00:01:18.880
which favors the formation
of the reactants.
00:01:18.880 --> 00:01:19.760
For this example,
00:01:19.760 --> 00:01:22.210
textbooks will often say that the reaction
00:01:22.210 --> 00:01:25.430
is non-spontaneous in
the forward direction,
00:01:25.430 --> 00:01:27.470
which means the reaction is spontaneous
00:01:27.470 --> 00:01:29.620
in the reverse direction.
00:01:29.620 --> 00:01:31.520
And when delta G is equal to zero,
00:01:31.520 --> 00:01:35.400
the chemical or physical
process is at equilibrium.
00:01:35.400 --> 00:01:39.370
So, for our chemical reaction,
if delta G is equal to zero,
00:01:39.370 --> 00:01:42.150
the reaction is at equilibrium
and the concentration
00:01:42.150 --> 00:01:45.660
of reactants and products
will remain constant.
00:01:45.660 --> 00:01:48.210
When we see delta G with
a superscript naught,
00:01:48.210 --> 00:01:51.650
we're talking about the
change in Gibbs Free Energy
00:01:51.650 --> 00:01:54.770
when substances are in
their standard states.
00:01:54.770 --> 00:01:58.630
By convention, the standard
state of a solid or liquid
00:01:58.630 --> 00:02:01.960
is referring to the pure
solid or the pure liquid
00:02:01.960 --> 00:02:04.810
under a pressure of one atmosphere.
00:02:04.810 --> 00:02:08.010
The standard state of a gas
is referring to the pure gas
00:02:08.010 --> 00:02:10.000
at a pressure of one atmosphere.
00:02:10.000 --> 00:02:11.920
And the standard state of a solution
00:02:11.920 --> 00:02:14.990
is talking about a one
Mueller concentration.
00:02:14.990 --> 00:02:17.010
If our substances are
in the standard state,
00:02:17.010 --> 00:02:20.970
we can add a superscript to the
equation that we saw before.
00:02:20.970 --> 00:02:23.140
So, we could calculate delta G naught,
00:02:23.140 --> 00:02:25.360
the standard change in free energy
00:02:25.360 --> 00:02:28.830
by getting the standard change
in enthalpy and from that,
00:02:28.830 --> 00:02:31.980
subtracting the absolute
temperature in Kelvin,
00:02:31.980 --> 00:02:35.270
times the standard change in entropy.
00:02:35.270 --> 00:02:38.270
When the substances are
in their standard states,
00:02:38.270 --> 00:02:41.830
delta G naught is equal to delta G.
00:02:41.830 --> 00:02:44.720
Therefore, we can say
that if delta G naught
00:02:44.720 --> 00:02:46.340
is less than zero,
00:02:46.340 --> 00:02:47.910
if we're talking about a reaction,
00:02:47.910 --> 00:02:50.140
the reaction is thermodynamically favored
00:02:50.140 --> 00:02:52.330
in the forward direction.
00:02:52.330 --> 00:02:55.100
And if delta G naught
is greater than zero,
00:02:55.100 --> 00:02:58.580
we could say the reaction is
not thermodynamically favored
00:02:58.580 --> 00:03:00.450
in the forward direction.
00:03:00.450 --> 00:03:02.540
Next, let's calculate delta G naught
00:03:02.540 --> 00:03:04.260
for a chemical reaction.
00:03:04.260 --> 00:03:05.410
And for our reaction,
00:03:05.410 --> 00:03:08.300
let's look at the synthesis
of hydrogen fluoride gas
00:03:08.300 --> 00:03:11.480
from hydrogen gas and fluorine gas.
00:03:11.480 --> 00:03:13.730
Our goal is to calculate delta G naught
00:03:13.730 --> 00:03:17.170
for this reaction at 25 degrees Celsius.
00:03:17.170 --> 00:03:20.640
Delta H naught for this
reaction at 25 degrees Celsius
00:03:20.640 --> 00:03:25.640
is equal to negative 537.2
kilojoules per mole of reaction.
00:03:26.470 --> 00:03:30.000
And delta S naught for this
reaction at 25 degrees Celsius
00:03:30.000 --> 00:03:34.680
is equal to 13.7 joules per
Kelvin mole of reaction.
00:03:34.680 --> 00:03:37.430
The next step is to plug
everything into our equation.
00:03:37.430 --> 00:03:40.020
So, to calculate delta
G naught of reaction,
00:03:40.020 --> 00:03:42.610
we need to plug in delta
H naught of reaction,
00:03:42.610 --> 00:03:44.180
delta S naught of reaction,
00:03:44.180 --> 00:03:46.940
and also the temperature in Kelvin.
00:03:46.940 --> 00:03:49.900
So, we can plug in delta
H naught of reaction
00:03:49.900 --> 00:03:51.410
into our equations.
00:03:51.410 --> 00:03:56.230
That's negative 537.2
kilojoules per mole of reaction.
00:03:56.230 --> 00:03:58.670
Next, we think about the temperature.
00:03:58.670 --> 00:04:01.340
The temperature is 25 degrees Celsius
00:04:01.340 --> 00:04:03.640
and we need to convert that into Kelvin.
00:04:03.640 --> 00:04:08.640
So, 25 plus 273 is equal to 298 Kelvin.
00:04:08.670 --> 00:04:10.870
Next we think about delta S naught,
00:04:10.870 --> 00:04:12.820
and here we have to be careful with units
00:04:12.820 --> 00:04:15.360
because delta H naught was in kilojoules
00:04:15.360 --> 00:04:18.860
and delta S naught was
given to us in joules.
00:04:18.860 --> 00:04:19.900
So, one approach is
00:04:19.900 --> 00:04:23.020
to convert delta S naught into kilojoules
00:04:23.020 --> 00:04:25.010
per Kelvin mole of reaction.
00:04:25.010 --> 00:04:27.260
So, we could divide this number by 1,000,
00:04:27.260 --> 00:04:31.450
or we could move the decimal
place three to the left.
00:04:31.450 --> 00:04:35.300
So, 13.7 joules per
Kelvin mole of reaction
00:04:35.300 --> 00:04:40.300
is equal to 0.0137 kilojoules
per Kelvin mole of reaction.
00:04:41.770 --> 00:04:44.660
Looking at our units,
Kelvin will cancel out
00:04:44.660 --> 00:04:47.950
and that gives us kilojoules
per mole of reaction.
00:04:47.950 --> 00:04:50.850
So, when we do the math, delta
G naught for this reaction
00:04:50.850 --> 00:04:55.850
is equal to negative 541.3
kilojoules per mole of reaction.
00:04:57.350 --> 00:04:59.970
Since delta G naught for
this reaction is negative,
00:04:59.970 --> 00:05:01.830
that means the forward reaction
00:05:01.830 --> 00:05:03.760
is thermodynamically favored.
00:05:03.760 --> 00:05:06.550
So, we can think about the
reactants coming together
00:05:06.550 --> 00:05:08.340
to make the products.
00:05:08.340 --> 00:05:10.860
And since we calculated delta G naught,
00:05:10.860 --> 00:05:14.170
the reactants and products
are in their standard states.
00:05:14.170 --> 00:05:17.690
So, what our calculation
means is if we had a mixture
00:05:17.690 --> 00:05:21.830
of hydrogen gas, fluorine gas,
and hydrogen fluoride gas,
00:05:21.830 --> 00:05:24.960
and we're at a temperature
of 25 degrees Celsius,
00:05:24.960 --> 00:05:29.000
and each gas had a partial
pressure of one atmosphere,
00:05:29.000 --> 00:05:32.380
the forward reaction is
thermodynamically favored,
00:05:32.380 --> 00:05:35.460
which means the hydrogen
gas and fluorine gas
00:05:35.460 --> 00:05:38.663
would come together to make
more hydrogen fluoride.
|
Absolute entropy and entropy change | https://www.youtube.com/watch?v=ObridY7EHyk | vtt | https://www.youtube.com/api/timedtext?v=ObridY7EHyk&ei=ylWUZYjAKaufxN8Pv_SakA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=128A8DE8C627A497FB56F7F1C225F09B0079641E.92454C9020CCF146DD077EE097E0DCA86AA233FD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.400 --> 00:00:02.810
- [Instructor] Entropy can be
measured on an absolute scale,
00:00:02.810 --> 00:00:06.020
which means there is a
point of zero entropy.
00:00:06.020 --> 00:00:09.110
And that point is reached for
a pure crystalline substance
00:00:09.110 --> 00:00:11.760
when the temperature
is equal to zero kelvin
00:00:11.760 --> 00:00:13.350
or absolute zero.
00:00:13.350 --> 00:00:14.500
At zero kelvin,
00:00:14.500 --> 00:00:17.880
the entropy of the pure
crystalline substance, S,
00:00:17.880 --> 00:00:19.960
is equal to zero.
00:00:19.960 --> 00:00:22.450
We can think about why the
entropy is equal to zero
00:00:22.450 --> 00:00:25.160
by looking at the equation
developed by Boltzmann,
00:00:25.160 --> 00:00:29.620
that relates entropy, S, to
number of microstates, W.
00:00:29.620 --> 00:00:32.790
A microstate refers to a
microscopic arrangement
00:00:32.790 --> 00:00:35.470
of all of the positions and energies
00:00:35.470 --> 00:00:37.170
of all of the particles.
00:00:37.170 --> 00:00:41.000
For our pure crystalline
substance at absolute zero,
00:00:41.000 --> 00:00:44.010
all of the particles are perfectly ordered
00:00:44.010 --> 00:00:46.000
in their lattice states.
00:00:46.000 --> 00:00:48.910
And at zero kelvin
there's no thermal motion.
00:00:48.910 --> 00:00:50.430
So all of the particles
00:00:50.430 --> 00:00:52.770
are perfectly ordered
in their lattice states
00:00:52.770 --> 00:00:54.250
with no thermal motion.
00:00:54.250 --> 00:00:57.310
That means there's only
one possible arrangement
00:00:57.310 --> 00:00:59.050
for these particles.
00:00:59.050 --> 00:01:02.040
And that means there's
only one microstate.
00:01:02.040 --> 00:01:03.820
So when we think about our equation,
00:01:03.820 --> 00:01:07.550
if we plug in the number of
microstates is equal to one,
00:01:07.550 --> 00:01:10.900
the natural log of one is equal to zero,
00:01:10.900 --> 00:01:15.130
which means that the entropy
is equal to zero at zero kelvin
00:01:15.130 --> 00:01:17.670
for this pure crystalline substance.
00:01:17.670 --> 00:01:20.900
This is called the third
law of thermodynamics.
00:01:20.900 --> 00:01:22.560
Next, let's think about what happens
00:01:22.560 --> 00:01:24.950
to our hypothetically perfect crystal
00:01:24.950 --> 00:01:27.050
if we increase the temperature.
00:01:27.050 --> 00:01:30.570
The increased temperature
means the particles gain energy
00:01:30.570 --> 00:01:33.380
and have motion around
their lattice states.
00:01:33.380 --> 00:01:34.213
Therefore,
00:01:34.213 --> 00:01:37.800
there's an increase in the
number of possible microstates.
00:01:37.800 --> 00:01:40.930
And if there's an increase
in the number of microstates,
00:01:40.930 --> 00:01:43.410
according to the equation
developed by Boltzmann,
00:01:43.410 --> 00:01:46.790
that also means an increase in entropy.
00:01:46.790 --> 00:01:50.240
Since we started with zero
entropy at zero kelvin,
00:01:50.240 --> 00:01:52.490
and the entropy increases,
00:01:52.490 --> 00:01:55.670
at all temperatures that are
greater than zero kelvin,
00:01:55.670 --> 00:01:58.380
the entropy must be greater than zero,
00:01:58.380 --> 00:02:01.030
or you can say the entropy is positive.
00:02:01.030 --> 00:02:02.780
We can get the units for entropy
00:02:02.780 --> 00:02:04.910
from the Boltzmann constant, K.
00:02:04.910 --> 00:02:07.000
K is equal to 1.38
00:02:07.000 --> 00:02:11.040
times 10 to the negative
23rd joules per kelvin.
00:02:11.040 --> 00:02:13.970
So we will use these units for entropy.
00:02:13.970 --> 00:02:16.680
Now that we understand the
concept of zero entropy,
00:02:16.680 --> 00:02:19.110
let's look at the entropy of a substance.
00:02:19.110 --> 00:02:22.510
And let's say that we
have one mole of carbon
00:02:22.510 --> 00:02:24.430
in the form of graphite.
00:02:24.430 --> 00:02:25.740
Standard entropy
00:02:25.740 --> 00:02:29.260
refers to the absolute
entropy of a substance
00:02:29.260 --> 00:02:31.620
at a pressure of one atmosphere
00:02:31.620 --> 00:02:33.750
and a specified temperature.
00:02:33.750 --> 00:02:37.690
Often that temperature
is 25 degrees Celsius.
00:02:37.690 --> 00:02:42.010
The standard entropy of
graphite at 25 degrees Celsius
00:02:42.010 --> 00:02:44.920
is equal to 5.7 joules per kelvin.
00:02:44.920 --> 00:02:47.920
And since we're dealing
with one mole of graphite,
00:02:47.920 --> 00:02:51.680
we could write the units
as joules per kelvin mole.
00:02:51.680 --> 00:02:55.510
And often this is called
standard molar entropy.
00:02:55.510 --> 00:02:59.150
The standard molar entropy
of graphite is positive
00:02:59.150 --> 00:03:00.550
because it's being compared
00:03:00.550 --> 00:03:03.330
to a hypothetically
perfect crystal of graphite
00:03:03.330 --> 00:03:04.960
at zero kelvin.
00:03:04.960 --> 00:03:07.093
So really it's a change in entropy
00:03:07.093 --> 00:03:10.270
and therefore it would be 5.7 minus zero
00:03:10.270 --> 00:03:13.910
with zero being the entropy
of a hypothetical crystal
00:03:13.910 --> 00:03:15.420
at zero kelvin.
00:03:15.420 --> 00:03:16.253
However,
00:03:16.253 --> 00:03:17.720
when we write standard molar entropies,
00:03:17.720 --> 00:03:19.700
we don't include the delta sign
00:03:19.700 --> 00:03:22.810
and we reserve the
delta sign for processes
00:03:22.810 --> 00:03:26.930
such as phase changes or
also chemical reactions.
00:03:26.930 --> 00:03:28.290
The superscript, not,
00:03:28.290 --> 00:03:32.110
refers to the standard
state of the substance.
00:03:32.110 --> 00:03:33.080
By convention,
00:03:33.080 --> 00:03:35.350
the standard state of a solid or liquid
00:03:35.350 --> 00:03:38.380
is referring to the pure
solid or pure liquid
00:03:38.380 --> 00:03:41.010
under a pressure of one atmosphere.
00:03:41.010 --> 00:03:44.330
For gases, standard state
is referring to the pure gas
00:03:44.330 --> 00:03:46.670
at a pressure of one atmosphere.
00:03:46.670 --> 00:03:49.860
And for solutions, we're
talking about a solution
00:03:49.860 --> 00:03:52.390
with a concentration of one molar.
00:03:52.390 --> 00:03:54.850
In our case, we're talking
about one mole of carbon
00:03:54.850 --> 00:03:57.720
in the form of graphite
in the solid state.
00:03:57.720 --> 00:03:58.553
Therefore,
00:03:58.553 --> 00:04:01.450
the standard molar entropy of graphite
00:04:01.450 --> 00:04:04.030
is referring to the entropy value
00:04:04.030 --> 00:04:07.020
for one mole of a pure solid
00:04:07.020 --> 00:04:09.950
under a pressure of one atmosphere.
00:04:09.950 --> 00:04:11.170
Next let's look at a table
00:04:11.170 --> 00:04:14.330
showing standard molar entropies
of different substances
00:04:14.330 --> 00:04:16.750
at 25 degrees Celsius.
00:04:16.750 --> 00:04:20.070
We just saw that the standard
molar entropy of carbon
00:04:20.070 --> 00:04:21.270
in the form of graphite
00:04:21.270 --> 00:04:25.130
is equal to 5.7 joules per kelvin mole.
00:04:25.130 --> 00:04:26.920
Let's compare that solid
00:04:26.920 --> 00:04:29.820
to two other standard molar entropies.
00:04:29.820 --> 00:04:30.653
For example,
00:04:30.653 --> 00:04:34.740
liquid water has a standard
molar entropy of 69.9,
00:04:34.740 --> 00:04:39.490
and methane gas has a standard
molar entropy of 186.3.
00:04:39.490 --> 00:04:41.200
Looking at these numbers, in general,
00:04:41.200 --> 00:04:45.300
gasses have higher standard
molar entropies than liquids,
00:04:45.300 --> 00:04:47.410
as we can see comparing the values,
00:04:47.410 --> 00:04:49.160
and liquids, in general,
00:04:49.160 --> 00:04:52.480
have higher standard molar
entropies than solids.
00:04:52.480 --> 00:04:54.430
The reason why this is generally true
00:04:54.430 --> 00:04:57.120
has to do with the number
of microstates available
00:04:57.120 --> 00:04:59.610
to solids, liquids, and gasses.
00:04:59.610 --> 00:05:02.420
Solids are held together
by either chemical bonds
00:05:02.420 --> 00:05:04.830
or by intermolecular forces.
00:05:04.830 --> 00:05:08.320
Liquids are held together
by intermolecular forces.
00:05:08.320 --> 00:05:10.920
And gases, if we assume ideal gases,
00:05:10.920 --> 00:05:14.920
there are no intermolecular
forces between the particles.
00:05:14.920 --> 00:05:19.170
So in general, as we go from
a solid to a liquid to a gas,
00:05:19.170 --> 00:05:20.150
there's an increase
00:05:20.150 --> 00:05:23.340
in the number of possible
arrangements of particles.
00:05:23.340 --> 00:05:25.640
There's an increased freedom of movement.
00:05:25.640 --> 00:05:28.770
And therefore going from
solid to liquid to gas means
00:05:28.770 --> 00:05:32.470
an increase in the number
of possible microstates.
00:05:32.470 --> 00:05:35.620
And an increase in the number
of possible microstates means
00:05:35.620 --> 00:05:38.660
an increase in entropy.
00:05:38.660 --> 00:05:39.493
Next,
00:05:39.493 --> 00:05:42.070
let's compare the standard
molar entropies of two gases.
00:05:42.070 --> 00:05:46.553
Methane is 186.3, whereas ethane is 229.6.
00:05:48.230 --> 00:05:49.510
Looking at their dots structures,
00:05:49.510 --> 00:05:52.820
methane is on the left and
ethane is on the right.
00:05:52.820 --> 00:05:55.110
They're both composed
of carbon and hydrogen.
00:05:55.110 --> 00:05:58.900
However, ethane has more
carbons and more hydrogens.
00:05:58.900 --> 00:06:01.210
Single bonds allow free rotation.
00:06:01.210 --> 00:06:03.830
And since ethane has
more bonds than methane,
00:06:03.830 --> 00:06:07.470
there's more ways for the
ethane molecule to rotate.
00:06:07.470 --> 00:06:10.600
Bonds can also stretch and
compress like a spring.
00:06:10.600 --> 00:06:13.330
So we could imagine
this carbon-carbon bond
00:06:13.330 --> 00:06:15.600
having some vibrational motion.
00:06:15.600 --> 00:06:18.830
And since ethane has
more bonds than methane,
00:06:18.830 --> 00:06:22.680
ethane has more ways to
vibrate than methane does.
00:06:22.680 --> 00:06:26.170
More ways to rotate and
more ways to vibrate mean
00:06:26.170 --> 00:06:27.810
that there are more possible ways
00:06:27.810 --> 00:06:31.350
to distribute the energy
in ethane than in methane.
00:06:31.350 --> 00:06:34.270
And an increased number of ways
of distributing energy means
00:06:34.270 --> 00:06:37.140
an increase in the number
of available microstates,
00:06:37.140 --> 00:06:39.970
which means an increase in the entropy.
00:06:39.970 --> 00:06:40.840
So in general,
00:06:40.840 --> 00:06:43.310
as there's an increase
in the number of atoms,
00:06:43.310 --> 00:06:45.200
or an increase in the molar mass,
00:06:45.200 --> 00:06:47.800
from say methane to ethane,
00:06:47.800 --> 00:06:50.840
there's also an increase in entropy.
00:06:50.840 --> 00:06:53.810
Next, let's calculate the
standard change in entropy
00:06:53.810 --> 00:06:55.740
for a chemical reaction.
00:06:55.740 --> 00:06:56.680
For our reaction,
00:06:56.680 --> 00:06:58.030
let's look at the decomposition
00:06:58.030 --> 00:07:00.370
of one mole of calcium carbonate
00:07:00.370 --> 00:07:02.850
turning into one mole of calcium oxide
00:07:02.850 --> 00:07:05.640
and one mole of carbon dioxide gas.
00:07:05.640 --> 00:07:08.520
To calculate the standard
change in entropy
00:07:08.520 --> 00:07:10.300
for this chemical reaction,
00:07:10.300 --> 00:07:13.460
we need to sum up the
standard molar entropies
00:07:13.460 --> 00:07:14.330
of the products.
00:07:14.330 --> 00:07:15.163
And from that,
00:07:15.163 --> 00:07:18.400
we subtract the sum of the
standard molar entropies
00:07:18.400 --> 00:07:19.870
of the reactants.
00:07:19.870 --> 00:07:22.600
So first we think about our products,
00:07:22.600 --> 00:07:26.670
which are calcium oxide
and carbon dioxide.
00:07:26.670 --> 00:07:29.430
So we need to sum the
standard molar entropies
00:07:29.430 --> 00:07:31.630
of these two substances.
00:07:31.630 --> 00:07:33.610
Next, we think about our reactants.
00:07:33.610 --> 00:07:37.010
And for this reaction, we
have only calcium carbonate.
00:07:37.010 --> 00:07:37.843
So therefore,
00:07:37.843 --> 00:07:40.500
we're gonna plug in the
standard molar entropy
00:07:40.500 --> 00:07:42.120
of calcium carbonate.
00:07:42.120 --> 00:07:45.530
Before we plug in our values
for standard molar entropies,
00:07:45.530 --> 00:07:48.930
let's predict the sign for
the standard entropy change
00:07:48.930 --> 00:07:50.290
for this reaction.
00:07:50.290 --> 00:07:51.130
In our reaction,
00:07:51.130 --> 00:07:52.714
we go from one mole of a solid,
00:07:52.714 --> 00:07:57.260
to one mole of another
solid and one mole of a gas.
00:07:57.260 --> 00:07:58.910
We already know that in general
00:07:58.910 --> 00:08:02.010
gases have higher values
for entropy than solids.
00:08:02.010 --> 00:08:05.430
And since we have zero moles
of gas on the reactant side,
00:08:05.430 --> 00:08:08.590
and one mole of gas on the product side,
00:08:08.590 --> 00:08:09.530
we would predict
00:08:09.530 --> 00:08:12.980
that the sum of the standard
molar entropies of the products
00:08:12.980 --> 00:08:16.520
would be greater than the sum
of the standard molar entropy
00:08:16.520 --> 00:08:17.460
of the reactants.
00:08:17.460 --> 00:08:19.370
In this case, only one reactant.
00:08:19.370 --> 00:08:21.970
And since we'd be
subtracting a smaller number
00:08:21.970 --> 00:08:23.740
from a larger number,
00:08:23.740 --> 00:08:27.850
we would predict that the
standard change in entropy
00:08:27.850 --> 00:08:32.610
for this reaction would be positive.
00:08:32.610 --> 00:08:33.990
Now that we've made our prediction,
00:08:33.990 --> 00:08:36.810
let's plug in our
standard molar entropies,
00:08:36.810 --> 00:08:39.110
and these are for a 25 degrees Celsius.
00:08:39.110 --> 00:08:41.550
And see if our prediction was correct.
00:08:41.550 --> 00:08:45.030
The standard molar
entropy of calcium oxide
00:08:45.030 --> 00:08:48.640
is equal to 39.8 joules per kelvin mole.
00:08:48.640 --> 00:08:49.870
In our balanced equation,
00:08:49.870 --> 00:08:52.980
we have one mole of calcium oxide.
00:08:52.980 --> 00:08:55.840
So we're gonna multiply
one mole of calcium oxide
00:08:55.840 --> 00:08:59.120
by the standard molar entropy
and moles will cancel.
00:08:59.120 --> 00:08:59.953
Next,
00:08:59.953 --> 00:09:03.280
we look up the standard molar
entropy of carbon dioxide,
00:09:03.280 --> 00:09:07.120
which is equal to 213.6
joules per kelvin mole
00:09:07.120 --> 00:09:09.170
and our balanced equation, once again,
00:09:09.170 --> 00:09:12.170
there's a one in front of carbon dioxide.
00:09:12.170 --> 00:09:14.280
So we're gonna multiply
the standard molar entropy
00:09:14.280 --> 00:09:16.930
by one mole and moles will cancel.
00:09:16.930 --> 00:09:19.200
So we're gonna add those two together.
00:09:19.200 --> 00:09:20.033
And from that,
00:09:20.033 --> 00:09:23.130
we're going to subtract
the standard molar entropy
00:09:23.130 --> 00:09:26.980
of our reactants, which
is calcium carbonate.
00:09:26.980 --> 00:09:29.280
So the standard molar
entropy of calcium carbonate
00:09:29.280 --> 00:09:31.970
is 92.9 joules per kelvin mole.
00:09:31.970 --> 00:09:33.560
And in our balanced equation,
00:09:33.560 --> 00:09:35.420
there's a one as a coefficient
00:09:35.420 --> 00:09:37.470
in front of calcium carbonate.
00:09:37.470 --> 00:09:38.990
So multiply that by one mole.
00:09:38.990 --> 00:09:41.500
And once again, the moles will cancel out.
00:09:41.500 --> 00:09:43.990
For this particular reaction,
in the balanced equation,
00:09:43.990 --> 00:09:46.430
all of the coefficients happen to be one.
00:09:46.430 --> 00:09:47.263
However,
00:09:47.263 --> 00:09:49.790
if one of our reactants or
products in a different reaction
00:09:49.790 --> 00:09:51.750
happened to have a coefficient of two,
00:09:51.750 --> 00:09:56.298
we would multiply the standard
molar entropy by two moles.
00:09:56.298 --> 00:09:57.910
After we do the math we find
00:09:57.910 --> 00:10:00.800
that the standard change in
entropy for this reaction
00:10:00.800 --> 00:10:05.260
is equal to positive
160.5 joules per kelvin.
00:10:05.260 --> 00:10:07.880
Therefore one mole of calcium carbonate
00:10:07.880 --> 00:10:10.750
decomposing to form one
mole of calcium oxide
00:10:10.750 --> 00:10:12.700
and one mole of carbon dioxide
00:10:12.700 --> 00:10:15.220
involves an increase in entropy
00:10:15.220 --> 00:10:18.370
just as we had predicted earlier on.
00:10:18.370 --> 00:10:20.740
Sometimes you'll see the
units as joules per kelvin,
00:10:20.740 --> 00:10:21.573
and sometimes,
00:10:21.573 --> 00:10:24.990
you might see joules per
kelvin mole of reaction.
00:10:24.990 --> 00:10:26.680
To understand how to get those units,
00:10:26.680 --> 00:10:27.513
let's just consider
00:10:27.513 --> 00:10:30.950
the standard molar
entropy of carbon dioxide.
00:10:30.950 --> 00:10:35.640
And that value is 213.6 joules per kelvin
00:10:35.640 --> 00:10:39.090
per one mole of carbon dioxide.
00:10:39.090 --> 00:10:41.650
And looking at the balanced equation,
00:10:41.650 --> 00:10:46.030
there's a one as a coefficient
in front of carbon dioxide.
00:10:46.030 --> 00:10:50.010
Therefore, there's one
mole of carbon dioxide
00:10:50.010 --> 00:10:52.760
per one mole of reaction.
00:10:52.760 --> 00:10:54.770
So molar reaction is just talking about,
00:10:54.770 --> 00:10:57.260
how the balanced equation is written.
00:10:57.260 --> 00:11:01.170
So the one mole of carbon
dioxide, it cancels out,
00:11:01.170 --> 00:11:06.170
and that leaves us with joules
per kelvin mole of reaction.
00:11:06.840 --> 00:11:08.990
So using these units is simply saying,
00:11:08.990 --> 00:11:12.950
for the decomposition of one
mole of calcium carbonate,
00:11:12.950 --> 00:11:14.410
there'll be a change in entropy
00:11:14.410 --> 00:11:18.490
of positive 160.5 joules per kelvin.
00:11:18.490 --> 00:11:19.323
Therefore,
00:11:19.323 --> 00:11:20.740
if we were talking about the decomposition
00:11:20.740 --> 00:11:22.950
of two moles of calcium carbonate,
00:11:22.950 --> 00:11:25.760
the change in entropy
would be twice this value
00:11:25.760 --> 00:11:27.353
that we already calculated.
|
Introduction to entropy | https://www.youtube.com/watch?v=0Z2bIv4DXts | vtt | https://www.youtube.com/api/timedtext?v=0Z2bIv4DXts&ei=ylWUZZm4MqCIhcIP6Iex0AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=161D35218216BEDB5A33FF388475233897F75FAB.34CD9D30375B21CB30D6AFE0C6E0A80E588B6B75&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.600 --> 00:00:02.830
- [Instructor] The concept
of entropy is related
00:00:02.830 --> 00:00:05.620
to the idea of microstates.
00:00:05.620 --> 00:00:06.990
And to think about microstates,
00:00:06.990 --> 00:00:09.740
let's consider one mole of an ideal gas.
00:00:09.740 --> 00:00:13.940
So remember, n represents
moles at a specific pressure,
00:00:13.940 --> 00:00:16.710
volume, and temperature.
00:00:16.710 --> 00:00:19.990
If the system of gas
particles is at equilibrium,
00:00:19.990 --> 00:00:21.550
then the pressure, the volume,
00:00:21.550 --> 00:00:23.150
the number of moles, and the temperature
00:00:23.150 --> 00:00:24.500
all remain the same.
00:00:24.500 --> 00:00:27.050
So from a macroscopic point of view,
00:00:27.050 --> 00:00:29.350
nothing seems to be changing.
00:00:29.350 --> 00:00:31.530
However, from a microscopic point of view,
00:00:31.530 --> 00:00:33.370
things are changing all of the time.
00:00:33.370 --> 00:00:36.300
So looking at our gas particles
here in the first box,
00:00:36.300 --> 00:00:38.610
imagine these gas particles
slamming into the sides
00:00:38.610 --> 00:00:41.110
of the container and maybe
slamming into each other
00:00:41.110 --> 00:00:44.540
and transferring energy from
one particle to another.
00:00:44.540 --> 00:00:47.370
So if we think about the
particles in our system
00:00:47.370 --> 00:00:49.720
at one moment in time, in box 1,
00:00:49.720 --> 00:00:51.620
if we think about them at
a different moment in time,
00:00:51.620 --> 00:00:52.540
in box 2,
00:00:52.540 --> 00:00:55.490
the particles might be in
slightly different positions
00:00:55.490 --> 00:00:59.320
and the velocities might have changed.
00:00:59.320 --> 00:01:01.240
Remember that the speed
of a particle tells us
00:01:01.240 --> 00:01:03.040
how fast the particle is traveling.
00:01:03.040 --> 00:01:05.340
However, when we put an
arrow on each particle,
00:01:05.340 --> 00:01:07.340
that also gives us the direction.
00:01:07.340 --> 00:01:10.370
And the magnitude and the
direction give a velocity.
00:01:10.370 --> 00:01:14.060
So these arrows on these
particles are meant to represent
00:01:14.060 --> 00:01:16.640
the velocities of the particles.
00:01:16.640 --> 00:01:19.550
And the kinetic energy
of each particle is equal
00:01:19.550 --> 00:01:22.810
to 1/2 mv squared,
00:01:22.810 --> 00:01:27.480
where m is the mass of each
particle and v is the velocity.
00:01:27.480 --> 00:01:30.870
A microstate refers to a
microscopic arrangement
00:01:30.870 --> 00:01:34.900
of all of the positions and
energies of the gas particles.
00:01:34.900 --> 00:01:37.520
Since we're dealing
with an ideal gas here,
00:01:37.520 --> 00:01:40.420
by energies, we're referring
to the kinetic energies
00:01:40.420 --> 00:01:42.030
of the particles.
00:01:42.030 --> 00:01:46.280
So going back to our boxes,
box 1, box 2 and box 3,
00:01:46.280 --> 00:01:49.930
each box shows a different
microscopic arrangement
00:01:49.930 --> 00:01:53.710
of positions and energies
of the gas particles.
00:01:53.710 --> 00:01:57.640
Therefore, each box
represents one microstate.
00:01:57.640 --> 00:01:59.540
A good way to think about
a microstate would be
00:01:59.540 --> 00:02:03.220
like taking a picture of
our system of gas particles.
00:02:03.220 --> 00:02:05.130
So from a macroscopic point of view,
00:02:05.130 --> 00:02:06.690
nothing seems to change.
00:02:06.690 --> 00:02:10.140
But taking a picture at
the microscopic level,
00:02:10.140 --> 00:02:12.980
we see that the system is
moving from one microstate
00:02:12.980 --> 00:02:15.890
into another, into another, into another.
00:02:15.890 --> 00:02:19.340
So the number of microstates
available to this system
00:02:19.340 --> 00:02:22.710
of one mole of gas particles
is a number that's too high
00:02:22.710 --> 00:02:25.210
for us to even comprehend.
00:02:25.210 --> 00:02:27.560
Now that we understand the
concept of microstates,
00:02:27.560 --> 00:02:29.970
let's look at an equation
developed by Boltzmann
00:02:29.970 --> 00:02:33.530
that relates entropy to
the number of microstates.
00:02:33.530 --> 00:02:34.960
According to this equation,
00:02:34.960 --> 00:02:36.860
entropy, symbolized by S,
00:02:36.860 --> 00:02:39.510
is equal to Boltzmann's constant, k,
00:02:39.510 --> 00:02:42.050
times the natural log of W,
00:02:42.050 --> 00:02:45.960
and W represents the number
of microstates in a system.
00:02:45.960 --> 00:02:49.870
So if the number of microstates
of a system increases,
00:02:49.870 --> 00:02:53.220
that represents an increase in entropy,
00:02:53.220 --> 00:02:56.260
and if the number of
microstates decreases,
00:02:56.260 --> 00:03:00.650
that represents a decrease
in the entropy of the system.
00:03:00.650 --> 00:03:03.360
Sometimes, instead of
using the word microstates,
00:03:03.360 --> 00:03:05.930
people will describe
an increase in entropy
00:03:05.930 --> 00:03:08.160
as an increase in disorder
00:03:08.160 --> 00:03:13.160
or an increase in the dispersal
of either matter or energy.
00:03:13.560 --> 00:03:16.810
Sometimes, using these terms
helps us think about entropy.
00:03:16.810 --> 00:03:17.643
However,
00:03:17.643 --> 00:03:19.980
when we're using the equation
developed by Boltzmann,
00:03:19.980 --> 00:03:22.430
we should think about these
terms as meaning an increase
00:03:22.430 --> 00:03:23.860
in the number of microstates
00:03:23.860 --> 00:03:27.750
and therefore an increase in
the entropy of the system.
00:03:27.750 --> 00:03:30.460
And if we think about a
decrease in the disorder
00:03:30.460 --> 00:03:33.090
of the system or an increase in the order,
00:03:33.090 --> 00:03:37.610
or a decrease in the dispersal
of either matter or energy,
00:03:37.610 --> 00:03:39.380
that really relates to a decrease
00:03:39.380 --> 00:03:41.550
in the number of available microstates,
00:03:41.550 --> 00:03:44.970
which means a decrease in
the entropy of the system.
00:03:44.970 --> 00:03:47.200
Next, let's think about
the change in entropy
00:03:47.200 --> 00:03:49.720
for a number of different situations.
00:03:49.720 --> 00:03:50.840
In our first situation,
00:03:50.840 --> 00:03:53.310
we're starting off with
one mole of an ideal gas,
00:03:53.310 --> 00:03:56.520
so here are the gas
particles, in a container,
00:03:56.520 --> 00:03:59.970
and the container has a removable divider
00:03:59.970 --> 00:04:02.970
separating the container
into two compartments.
00:04:02.970 --> 00:04:05.230
Let's say we go ahead
and remove the divider.
00:04:05.230 --> 00:04:08.340
And now our gas particles
are free to travel around
00:04:08.340 --> 00:04:09.960
in a larger volume.
00:04:09.960 --> 00:04:12.150
So if the initial volume is V1,
00:04:12.150 --> 00:04:15.460
let's say we have twice the
volume for the final volume,
00:04:15.460 --> 00:04:17.360
therefore, V2, or the final volume,
00:04:17.360 --> 00:04:19.720
is equal to 2 times V1.
00:04:19.720 --> 00:04:21.190
The number of moles remains the same.
00:04:21.190 --> 00:04:24.360
So n1 is equal to one
mole of our ideal gas
00:04:24.360 --> 00:04:26.920
and n2 is also equal to one mole.
00:04:26.920 --> 00:04:29.170
So n2 is equal to n1.
00:04:29.170 --> 00:04:30.930
During the expansion of the gas,
00:04:30.930 --> 00:04:32.670
the temperature is kept constant.
00:04:32.670 --> 00:04:34.980
Therefore, the initial temperature, T1,
00:04:34.980 --> 00:04:37.670
is equal to the final temperature, T2.
00:04:37.670 --> 00:04:39.040
Next, let's think about what happens
00:04:39.040 --> 00:04:41.160
to the number of available microstates
00:04:41.160 --> 00:04:42.890
when the volume is doubled.
00:04:42.890 --> 00:04:43.900
When the volume is doubled,
00:04:43.900 --> 00:04:46.900
that increases the number
of possible positions
00:04:46.900 --> 00:04:48.420
for the gas particles.
00:04:48.420 --> 00:04:52.040
Therefore, the number of
microstates increases.
00:04:52.040 --> 00:04:53.530
And looking at our equation,
00:04:53.530 --> 00:04:56.560
if the number of microstates increases,
00:04:56.560 --> 00:04:59.220
then so does the entropy.
00:04:59.220 --> 00:05:04.220
Therefore, we can say that
S2 is greater than S1.
00:05:04.860 --> 00:05:08.530
And thinking about the change
in the entropy, delta S,
00:05:08.530 --> 00:05:11.130
if S2 is greater than S1,
00:05:11.130 --> 00:05:15.000
then S2 minus S1 would
be a positive value.
00:05:15.000 --> 00:05:15.833
Therefore,
00:05:15.833 --> 00:05:19.650
the change in entropy for
the free expansion of a gas
00:05:19.650 --> 00:05:23.110
when the temperature is
constant is positive.
00:05:23.110 --> 00:05:24.300
For our next situation,
00:05:24.300 --> 00:05:27.590
we're starting once again
with one mole of an ideal gas.
00:05:27.590 --> 00:05:30.300
However, this time the
volume will be held constant
00:05:30.300 --> 00:05:32.710
and the temperature will be increased.
00:05:32.710 --> 00:05:35.210
So we start with one mole of our ideal gas
00:05:35.210 --> 00:05:37.970
at a certain volume, so n1 and V1,
00:05:37.970 --> 00:05:39.890
and we are increasing the temperature,
00:05:39.890 --> 00:05:42.750
but we're not changing the
number of moles or the volume.
00:05:42.750 --> 00:05:44.770
Therefore, the final number of moles, n2,
00:05:44.770 --> 00:05:47.550
is equal to the initial
number, n1, which is one mole.
00:05:47.550 --> 00:05:49.110
And the final volume, V2,
00:05:49.110 --> 00:05:51.720
is equal to the initial volume, V1.
00:05:51.720 --> 00:05:53.530
Since we are increasing the temperature,
00:05:53.530 --> 00:05:55.210
the final temperature, T2,
00:05:55.210 --> 00:05:58.380
is greater than the
initial temperature, T1.
00:05:58.380 --> 00:06:02.040
Next, let's use a Maxwell-Boltzmann
distribution over here
00:06:02.040 --> 00:06:04.770
on the right to explain what we see
00:06:04.770 --> 00:06:07.910
in our particulate diagrams on the left.
00:06:07.910 --> 00:06:09.610
In the particulate diagram on the left,
00:06:09.610 --> 00:06:11.780
we can see that the particles are moving
00:06:11.780 --> 00:06:15.450
with different velocities or
different magnitudes or speeds.
00:06:15.450 --> 00:06:18.600
And we can see that by the
length of the arrows in the box.
00:06:18.600 --> 00:06:20.700
And that's what the
Maxwell-Boltzmann distribution
00:06:20.700 --> 00:06:21.533
tells us here.
00:06:21.533 --> 00:06:23.370
So for the one in blue,
00:06:23.370 --> 00:06:26.080
we know that there are a
range of speeds available
00:06:26.080 --> 00:06:26.980
to the particles.
00:06:26.980 --> 00:06:30.030
So the area under the curve
represents all of the particles
00:06:30.030 --> 00:06:31.400
in the gas sample.
00:06:31.400 --> 00:06:34.140
So some are moving at a slower speed.
00:06:34.140 --> 00:06:35.820
Some are moving at a higher speed,
00:06:35.820 --> 00:06:37.320
but most of them are moving at a speed
00:06:37.320 --> 00:06:39.830
close to the center of this peak.
00:06:39.830 --> 00:06:42.900
Increasing the temperature
means that, on average,
00:06:42.900 --> 00:06:45.240
the particles are moving faster.
00:06:45.240 --> 00:06:46.690
So we can see that, on average,
00:06:46.690 --> 00:06:49.410
the length of these arrows is longer
00:06:49.410 --> 00:06:51.920
than the length of the arrows
in the particulate diagram
00:06:51.920 --> 00:06:53.270
on the left.
00:06:53.270 --> 00:06:54.103
But it also means,
00:06:54.103 --> 00:06:55.990
if we look at the
Maxwell-Boltzmann distribution,
00:06:55.990 --> 00:06:58.670
there are greater range
of speeds available
00:06:58.670 --> 00:07:00.300
to the particles.
00:07:00.300 --> 00:07:02.020
And if there's a greater range of speeds
00:07:02.020 --> 00:07:03.520
or greater range of velocities,
00:07:03.520 --> 00:07:06.600
that means there's a greater
range of kinetic energies,
00:07:06.600 --> 00:07:09.770
which means there are more
possible microstates available
00:07:09.770 --> 00:07:11.980
to the system of gas particles.
00:07:11.980 --> 00:07:15.330
Therefore, increasing the
temperature causes an increase
00:07:15.330 --> 00:07:18.290
in the number of possible microstates.
00:07:18.290 --> 00:07:21.310
And an increase in the
number of microstates means
00:07:21.310 --> 00:07:23.920
an increase in the entropy.
00:07:23.920 --> 00:07:26.360
Therefore, the final entropy, S2,
00:07:26.360 --> 00:07:30.200
is greater than the initial entropy, S1.
00:07:30.200 --> 00:07:32.240
So when we think about
the change in entropy,
00:07:32.240 --> 00:07:35.470
delta S for the system,
if S2 is greater than S1,
00:07:35.470 --> 00:07:38.390
the change in entropy is positive.
00:07:38.390 --> 00:07:40.260
So for a system of gas particles
00:07:40.260 --> 00:07:42.910
with constant volume and
constant number of moles,
00:07:42.910 --> 00:07:44.570
if we increased the temperature,
00:07:44.570 --> 00:07:47.610
there's an increase in the entropy.
00:07:47.610 --> 00:07:48.690
For our next situation,
00:07:48.690 --> 00:07:51.980
we're once again starting
with one mole of an ideal gas
00:07:51.980 --> 00:07:56.450
at a certain temperature,
T1, and a certain volume, V1.
00:07:56.450 --> 00:07:57.283
This time,
00:07:57.283 --> 00:07:58.980
we're going to increase
the number of moles
00:07:58.980 --> 00:08:02.500
from one mole of an ideal gas
to two moles of an ideal gas.
00:08:02.500 --> 00:08:05.180
So if we had four particles on the left,
00:08:05.180 --> 00:08:07.140
now we have eight particles
00:08:08.583 --> 00:08:11.050
in the particulate diagram on the right.
00:08:11.050 --> 00:08:12.930
So the final number of moles, n2,
00:08:12.930 --> 00:08:15.930
is greater than the initial number, n1.
00:08:15.930 --> 00:08:17.600
But we're gonna keep the
temperature the same.
00:08:17.600 --> 00:08:18.980
So the final temperature is equal
00:08:18.980 --> 00:08:20.130
to the initial temperature,
00:08:20.130 --> 00:08:22.190
and we're gonna keep
the volume constant too.
00:08:22.190 --> 00:08:24.000
So V2, or the final volume,
00:08:24.000 --> 00:08:26.670
is equal to the initial volume, V1.
00:08:26.670 --> 00:08:29.030
Because we have increased
the number of particles,
00:08:29.030 --> 00:08:31.690
there are more possible
arrangements of particles
00:08:31.690 --> 00:08:34.600
and also more ways to
distribute the energy.
00:08:34.600 --> 00:08:37.010
Therefore, when we increase
the number of moles,
00:08:37.010 --> 00:08:40.100
there's an increase in the
number of possible microstates
00:08:41.620 --> 00:08:44.200
and increasing the number
of microstates in a system
00:08:44.200 --> 00:08:46.460
increases the entropy.
00:08:46.460 --> 00:08:48.630
Therefore, the final entropy, S2,
00:08:48.630 --> 00:08:52.030
is greater than the initial entropy, S1.
00:08:52.030 --> 00:08:54.410
And once again, the change in entropy,
00:08:54.410 --> 00:08:57.200
if S2 greater than S1, would be positive.
00:08:57.200 --> 00:09:01.080
So increasing the number
of moles of gas particles
00:09:01.080 --> 00:09:03.910
increases the entropy of the system.
00:09:03.910 --> 00:09:04.990
For our next situation,
00:09:04.990 --> 00:09:07.920
let's consider the
evaporation of liquid water
00:09:07.920 --> 00:09:09.620
into gaseous water.
00:09:09.620 --> 00:09:11.950
Water molecules in the liquid
state are held together
00:09:11.950 --> 00:09:14.590
by intermolecular forces,
00:09:14.590 --> 00:09:16.870
with hydrogen bonding
being the most important
00:09:16.870 --> 00:09:19.960
intermolecular force holding
the particles together.
00:09:19.960 --> 00:09:22.870
Water molecules in the liquid
state are still free to move.
00:09:22.870 --> 00:09:25.740
However, when water
molecules in the liquid state
00:09:25.740 --> 00:09:28.430
get converted into water
molecules in the gaseous state,
00:09:28.430 --> 00:09:31.390
we assume there are no
more intermolecular forces
00:09:31.390 --> 00:09:33.720
between the gas particles.
00:09:33.720 --> 00:09:35.810
So we're assuming this is an ideal gas.
00:09:35.810 --> 00:09:38.100
And if there are no intermolecular forces
00:09:38.100 --> 00:09:39.750
between the gas particles,
00:09:39.750 --> 00:09:41.710
we've increased the freedom of movement
00:09:41.710 --> 00:09:42.870
of the water molecules.
00:09:42.870 --> 00:09:45.600
We've increased the number
of possible positions,
00:09:45.600 --> 00:09:46.490
and, therefore,
00:09:46.490 --> 00:09:50.380
we've increased the number
of microstates available.
00:09:50.380 --> 00:09:52.210
And if we increase the
number of microstates,
00:09:52.210 --> 00:09:54.500
we increase the entropy.
00:09:54.500 --> 00:09:57.450
Therefore, thinking
about the entropy change,
00:09:57.450 --> 00:09:59.560
this would be the final entropy, S2,
00:09:59.560 --> 00:10:02.070
minus the initial entropy, S1.
00:10:02.070 --> 00:10:04.050
And since the entropy increased,
00:10:04.050 --> 00:10:06.680
going from liquid water to gaseous water,
00:10:06.680 --> 00:10:09.870
the change in entropy would be positive.
00:10:09.870 --> 00:10:12.480
This is also one example
where thinking about entropy
00:10:12.480 --> 00:10:14.900
in terms of disorder can be helpful
00:10:14.900 --> 00:10:17.850
because gasses are more
disordered than liquids,
00:10:17.850 --> 00:10:19.460
you could say, and, therefore,
00:10:19.460 --> 00:10:21.990
going from a liquid to a
gas increases the amount
00:10:21.990 --> 00:10:24.630
of disorder, which increases the entropy.
00:10:24.630 --> 00:10:25.520
But remember, really,
00:10:25.520 --> 00:10:27.630
disorder is really just a way to describe
00:10:27.630 --> 00:10:30.420
an increased number of
available microstates.
00:10:30.420 --> 00:10:31.790
And for our final situation,
00:10:31.790 --> 00:10:35.270
let's look at a reaction
that involves only gases.
00:10:35.270 --> 00:10:36.240
On the left side,
00:10:36.240 --> 00:10:39.770
we can see there's two moles
of SO2 and one mole of O2.
00:10:39.770 --> 00:10:43.600
So there are three moles of
gas on the reactant side.
00:10:43.600 --> 00:10:48.500
And on the product side,
there are two moles of gas.
00:10:48.500 --> 00:10:50.450
Next, let's think about
the change in entropy
00:10:50.450 --> 00:10:52.730
for this reaction, delta S.
00:10:52.730 --> 00:10:53.563
That'd be equal
00:10:53.563 --> 00:10:57.190
to the final entropy
minus the initial entropy.
00:10:57.190 --> 00:10:59.810
So thinking about the initial entropy, S1,
00:10:59.810 --> 00:11:02.130
and the final entropy, S2,
00:11:02.130 --> 00:11:05.500
we went from three moles
of gas to two moles of gas.
00:11:05.500 --> 00:11:08.590
Remember that a decrease in
the number of moles of gas
00:11:08.590 --> 00:11:12.350
means a decrease in the number
of possible microstates.
00:11:12.350 --> 00:11:15.050
That means a decrease in the entropy.
00:11:15.050 --> 00:11:18.810
Therefore, S2 is less than S1,
00:11:18.810 --> 00:11:22.710
or we could say that
S1 is greater than S2.
00:11:22.710 --> 00:11:25.020
Therefore, for the change in the entropy,
00:11:25.020 --> 00:11:27.720
if S1 is greater than S2,
00:11:27.720 --> 00:11:30.870
we're subtracting a larger
number from a smaller number,
00:11:30.870 --> 00:11:33.400
which means the change in
entropy for this reaction,
00:11:33.400 --> 00:11:35.840
delta S, will be negative.
00:11:35.840 --> 00:11:36.870
So as a quick summary,
00:11:36.870 --> 00:11:40.080
when trying to figure out
the change in entropy,
00:11:40.080 --> 00:11:43.020
we need to consider the number
of available microstates.
00:11:43.020 --> 00:11:45.670
If the number of available
microstates increases,
00:11:45.670 --> 00:11:47.840
then the change in entropy is positive.
00:11:47.840 --> 00:11:50.520
If the number of available
microstates decreases,
00:11:50.520 --> 00:11:52.943
then the change in entropy is negative.
|
Solving unit price problem | https://www.youtube.com/watch?v=rpGGMSFO6Ks | vtt | https://www.youtube.com/api/timedtext?v=rpGGMSFO6Ks&ei=ylWUZZKFJLvLp-oPnomH8Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=337998E76D7E18A2C204EAEDD7A45B7EF9FEDA9C.E166F0B358C79D5FD30B92FC4BAB806C259089C1&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.210 --> 00:00:02.930
- [Instructor] We're told
that Nierria earns $75
00:00:02.930 --> 00:00:04.960
for 4 hours of tutoring.
00:00:04.960 --> 00:00:08.540
How much does Nierria earn
for 1 hour of tutoring?
00:00:08.540 --> 00:00:11.190
Pause this video, and see
if you can figure that out.
00:00:12.420 --> 00:00:16.810
Well, the key here is $75
for 4 hours of tutoring.
00:00:16.810 --> 00:00:18.480
And there's a couple of
ways you can think about it.
00:00:18.480 --> 00:00:22.600
The ratio here is $75 for every 4 hours.
00:00:22.600 --> 00:00:25.110
So if you wanted one hour of tutoring,
00:00:25.110 --> 00:00:28.220
well, it's just going
to be 1/4 of the $75,
00:00:28.220 --> 00:00:30.960
or you could just take 75 and divide by 4.
00:00:30.960 --> 00:00:32.320
Another way you could think about it,
00:00:32.320 --> 00:00:37.270
you could say Nierria gets $75
00:00:37.270 --> 00:00:40.563
for every 4 hours,
00:00:41.430 --> 00:00:43.640
which is another way of saying
00:00:43.640 --> 00:00:45.810
that Nierria is going to earn
00:00:45.810 --> 00:00:50.810
75 divided by 4 dollars per hour.
00:00:51.920 --> 00:00:53.200
So really we just have to figure out
00:00:53.200 --> 00:00:55.260
what 75 divided by 4 is.
00:00:55.260 --> 00:00:58.800
So let's do a little bit of long division.
00:00:58.800 --> 00:01:03.660
So 4 goes into 7 one time, 1 times 4 is 4.
00:01:03.660 --> 00:01:06.940
We're going to subtract. 7 minus 4 is 3.
00:01:06.940 --> 00:01:08.540
Bring down that 5.
00:01:08.540 --> 00:01:11.290
4 goes into 35 eight times.
00:01:11.290 --> 00:01:13.680
8 times 4 is 32.
00:01:13.680 --> 00:01:16.710
I will subtract again. I get a 3.
00:01:16.710 --> 00:01:18.930
Well now I'm going to
get some decimals here,
00:01:18.930 --> 00:01:22.620
so let me bring down a zero.
00:01:22.620 --> 00:01:25.270
4 goes into 30 seven times.
00:01:25.270 --> 00:01:27.580
7 times 4 is 28.
00:01:27.580 --> 00:01:32.080
Subtract, and then I get a
2. Bring down another zero.
00:01:32.080 --> 00:01:35.190
4 goes into 20 five times.
00:01:35.190 --> 00:01:38.260
5 times 4 is 20, and I am done,
00:01:38.260 --> 00:01:40.060
no more remainder here.
00:01:40.060 --> 00:01:44.770
So we get that Nierria
earns 18.75 dollars,
00:01:47.140 --> 00:01:50.480
dollars per hour,
00:01:50.480 --> 00:01:55.053
or you can just say that
she makes $18.75 per hour.
|
Sine equation algebraic solution set | https://www.youtube.com/watch?v=ES15mSuqHM8 | vtt | https://www.youtube.com/api/timedtext?v=ES15mSuqHM8&ei=ylWUZZ2xMumNmLAP2421CA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A81E38E3D93BC931338DFE67A891B0E2D45E8376.77CCA9FA42110AF212D0F2CC6BAE5D17A6DAD917&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.120 --> 00:00:01.260
- [Instructor] The goal of this video
00:00:01.260 --> 00:00:05.230
is to find the solution set
for the following equation.
00:00:05.230 --> 00:00:07.940
So all of the X values, and we're dealing
00:00:07.940 --> 00:00:12.090
with radians, that will
satisfy this equation.
00:00:12.090 --> 00:00:14.820
So I encourage you, like
always, pause this video
00:00:14.820 --> 00:00:16.480
and see if you can work
through this on your own
00:00:16.480 --> 00:00:18.930
before we worked through it together.
00:00:18.930 --> 00:00:21.240
All right, now let's
work through it together.
00:00:21.240 --> 00:00:23.700
Now your intuition, which
would be correct, might be,
00:00:23.700 --> 00:00:25.590
let's see if we can isolate the sin
00:00:25.590 --> 00:00:27.970
of X over four algebraically.
00:00:27.970 --> 00:00:30.420
And the first step I
would do is subtract 11
00:00:30.420 --> 00:00:31.290
from both sides.
00:00:31.290 --> 00:00:36.060
And if you do that, you
would get eight sin of X
00:00:36.060 --> 00:00:40.950
over four is equal to three,
just subtracted 11, both sides.
00:00:40.950 --> 00:00:44.850
Now to isolate the sin, I would
divide both sides by eight
00:00:44.850 --> 00:00:49.850
and I would get sin of X
over four is equal to 3/8.
00:00:51.790 --> 00:00:54.760
Now, before I go further,
let's think about
00:00:54.760 --> 00:00:57.700
whether this is the most
general solution here
00:00:57.700 --> 00:01:01.220
or whether we're going to find
all of the solution set here.
00:01:01.220 --> 00:01:02.700
Well, we have to remind ourselves,
00:01:02.700 --> 00:01:06.510
let me actually draw a little
bit of a unit circle here.
00:01:06.510 --> 00:01:08.800
So that's my X axis.
00:01:08.800 --> 00:01:10.373
That's my Y axis.
00:01:12.018 --> 00:01:13.350
Then a circle.
00:01:13.350 --> 00:01:18.350
And if we have some angle
theta right over here.
00:01:18.910 --> 00:01:21.920
So that's theta, we know that
the sin of theta is equal
00:01:21.920 --> 00:01:23.350
to the Y coordinate
00:01:23.350 --> 00:01:26.760
of where this radius
intersects the unit circle.
00:01:26.760 --> 00:01:27.750
And we also know
00:01:27.750 --> 00:01:30.720
that if we add an arbitrary
number of two pies here
00:01:30.720 --> 00:01:32.830
or if we subtract an
arbitrary number of two pis,
00:01:32.830 --> 00:01:34.240
we go all the way around the unit circle,
00:01:34.240 --> 00:01:35.420
back to where we began
00:01:35.420 --> 00:01:37.100
and so the sin of theta would be the same.
00:01:37.100 --> 00:01:42.100
So we know that sin of theta
plus any integer multiple
00:01:42.500 --> 00:01:47.487
of two pi, that's going to
be equal to the sin of theta.
00:01:49.150 --> 00:01:51.290
And so we can generalize
this a little bit.
00:01:51.290 --> 00:01:53.530
We can instead of just
saying, sin of X over four
00:01:53.530 --> 00:01:58.530
is equal to 3/8, we could
write that sin of X over four
00:01:58.570 --> 00:02:02.530
plus any integer multiple of
two pi is going to be equal
00:02:02.530 --> 00:02:05.300
to 3/8 where N is any integer.
00:02:05.300 --> 00:02:06.980
It could even be a negative
one, a negative two
00:02:06.980 --> 00:02:09.440
or of course it could be
zero, one, two, three,
00:02:09.440 --> 00:02:11.560
so on and so forth.
00:02:11.560 --> 00:02:15.420
So is this, if we solve now for X,
00:02:15.420 --> 00:02:19.410
is this going to give us the
most general solution set?
00:02:19.410 --> 00:02:24.190
Well, we can also remind ourselves
that if I have theta here
00:02:24.190 --> 00:02:25.830
and sin if theta gets there.
00:02:25.830 --> 00:02:27.660
There's one other point on the unit circle
00:02:27.660 --> 00:02:29.800
where I get the same sin.
00:02:29.800 --> 00:02:31.520
It would be right over here.
00:02:31.520 --> 00:02:33.810
The Y coordinate would be the same.
00:02:33.810 --> 00:02:35.940
And one way to think about it is
00:02:35.940 --> 00:02:38.810
if we start at pi radians,
which would be right over there
00:02:38.810 --> 00:02:41.210
and we were to subtract theta,
00:02:41.210 --> 00:02:43.030
we're going to get the same thing.
00:02:43.030 --> 00:02:45.160
So this angle right over here,
00:02:45.160 --> 00:02:49.000
you could view as pi minus theta.
00:02:49.000 --> 00:02:51.360
And you could keep trying
it out for any theta,
00:02:51.360 --> 00:02:53.300
even the theta that put
you in the second quadrant,
00:02:53.300 --> 00:02:56.840
third quadrant or fourth quadrant,
if you do pi minus theta,
00:02:56.840 --> 00:02:58.190
sin of pi minus theta,
00:02:58.190 --> 00:03:00.320
you're going to get the same sin value.
00:03:00.320 --> 00:03:04.990
So we also know that sin of pi minus theta
00:03:04.990 --> 00:03:08.920
is equal to sin of theta.
00:03:08.920 --> 00:03:12.670
And so let me write another
expression over here.
00:03:12.670 --> 00:03:14.560
So it's not just sin of X over four
00:03:14.560 --> 00:03:15.720
is equal to 3/8.
00:03:15.720 --> 00:03:20.560
We could also write that
sin of pi minus X over four,
00:03:20.560 --> 00:03:22.680
'cause X over four is the theta here.
00:03:22.680 --> 00:03:27.680
Sin of pi minus X over
four is equal to 3/8.
00:03:28.680 --> 00:03:30.460
And of course we can also
use the other principle
00:03:30.460 --> 00:03:33.570
that we can add 2 pi or
subtract two pi from this,
00:03:33.570 --> 00:03:34.910
an arbitrary number of times
00:03:34.910 --> 00:03:37.540
and the sin of that will
still be equal to 3/8.
00:03:37.540 --> 00:03:39.300
So I could write it like this.
00:03:39.300 --> 00:03:44.300
Sin of pi minus X over four
plus an integer multiple
00:03:45.530 --> 00:03:49.890
of two pi, that is going
to be equal to 3/8.
00:03:49.890 --> 00:03:52.140
And if I solve both of these,
00:03:52.140 --> 00:03:54.980
the combination of them, the union of them
00:03:54.980 --> 00:03:56.990
would give me the broadest solution set.
00:03:56.990 --> 00:03:58.420
So let's do that.
00:03:58.420 --> 00:04:01.450
So over here, let me take the
inverse sin of both sides.
00:04:01.450 --> 00:04:06.450
I get X over four plus two pi N is equal
00:04:06.470 --> 00:04:11.050
to the inverse sign of 3/8.
00:04:11.050 --> 00:04:13.960
Now I could subtract two
pi N from both sides.
00:04:13.960 --> 00:04:16.530
I get X over four is equal
00:04:16.530 --> 00:04:21.530
to the inverse sin of 3/8, minus two pi N.
00:04:22.840 --> 00:04:25.330
And if you think about it,
because N can be any integer,
00:04:25.330 --> 00:04:27.050
this sin here in front of the two,
00:04:27.050 --> 00:04:28.420
this negative really doesn't matter.
00:04:28.420 --> 00:04:29.650
It could even be a positive.
00:04:29.650 --> 00:04:32.100
And now let's multiply both sides by four.
00:04:32.100 --> 00:04:36.720
We get X is equal to four
times the inverse sin
00:04:36.720 --> 00:04:41.720
of 3/8 minus eight pi N.
00:04:42.410 --> 00:04:45.430
And then if I work on this
blue part right over here,
00:04:45.430 --> 00:04:47.910
same idea, take the
inverse side of both sides.
00:04:47.910 --> 00:04:52.910
We get pi minus X over
four plus two pi N is equal
00:04:53.370 --> 00:04:57.093
to the inverse sin of 3/8.
00:04:58.100 --> 00:05:00.510
And then let's see, I can
subtract pi from both sides
00:05:00.510 --> 00:05:02.360
and subtract two pi N from both sides.
00:05:02.360 --> 00:05:06.150
And so I get negative X over four is equal
00:05:06.150 --> 00:05:11.150
to the inverse sin of 3/8
minus pi minus two pi N.
00:05:14.470 --> 00:05:16.910
And I multiply both
sides by negative four.
00:05:16.910 --> 00:05:21.910
I get X is equal to negative
four times the inverse sin
00:05:22.220 --> 00:05:27.220
of 3/8 plus four pi plus eight pi N.
00:05:29.040 --> 00:05:31.810
And as I mentioned, the
union of both of these
00:05:31.810 --> 00:05:33.700
give us the entire solution set
00:05:33.700 --> 00:05:35.570
to our original equation here.
|
Using matrices to transform a 4D vector | https://www.youtube.com/watch?v=Foy8cAMqnAo | vtt | https://www.youtube.com/api/timedtext?v=Foy8cAMqnAo&ei=ylWUZaSUK_TWxN8PmdyyuAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2ADD752CDEB96AB38C22130990E3D4955BA955A5.2AA2531FBB2A4ACDEAA01DE70A728F60C5700415&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.470 --> 00:00:01.590
- [Trainer] We've already
thought a lot about
00:00:01.590 --> 00:00:05.890
two by two transformation
matrices as being able to map
00:00:05.890 --> 00:00:08.720
any point in the coordinate
plane to any other point
00:00:08.720 --> 00:00:10.420
or any two-dimensional vector
00:00:10.420 --> 00:00:12.690
to any other two-dimensional vector.
00:00:12.690 --> 00:00:16.160
What we're going to do in
this video is generalize a bit
00:00:16.160 --> 00:00:18.450
and realize that the same principles
00:00:18.450 --> 00:00:22.230
can be used for n dimensional spaces.
00:00:22.230 --> 00:00:24.430
Now I know that sounds a little bit fancy
00:00:24.430 --> 00:00:26.470
and it really is on some level,
00:00:26.470 --> 00:00:28.830
but it's really the same ideas.
00:00:28.830 --> 00:00:31.420
So for example, let's extend what we know
00:00:31.420 --> 00:00:32.590
about two dimensions,
00:00:32.590 --> 00:00:35.660
let's extend it to say four dimensions.
00:00:35.660 --> 00:00:39.340
So let's write a
four-dimensional vector here
00:00:39.340 --> 00:00:41.700
and it is hard to visualize
in four dimensions,
00:00:41.700 --> 00:00:44.170
so don't be hard on yourself
if you have trouble.
00:00:44.170 --> 00:00:47.520
Two dimensions not too hard,
three dimensions not too hard,
00:00:47.520 --> 00:00:49.560
four dimensions a little bit hard for us.
00:00:49.560 --> 00:00:52.380
Maybe we have to think about
time as the fourth dimension
00:00:52.380 --> 00:00:54.690
but in matrix world or in vector world,
00:00:54.690 --> 00:00:56.250
it's pretty easy to represent them
00:00:56.250 --> 00:00:58.250
as hard a it is to visualize.
00:00:58.250 --> 00:01:01.050
So a four-dimensional vector,
we'll just have four numbers.
00:01:01.050 --> 00:01:03.450
Negative one, let's see, negative three,
00:01:03.450 --> 00:01:06.920
I'm just making these up
randomly, negative five and one.
00:01:06.920 --> 00:01:09.070
This is a four-dimensional vector,
00:01:09.070 --> 00:01:13.140
and we could view it
as being a weighted sum
00:01:13.140 --> 00:01:16.610
of the unit vectors in
the different dimensions
00:01:16.610 --> 00:01:18.600
of four-dimensional space.
00:01:18.600 --> 00:01:19.920
I guess you could say it.
00:01:19.920 --> 00:01:21.980
You could say that this
is the same thing as,
00:01:21.980 --> 00:01:23.770
actually let me color code a little bit.
00:01:23.770 --> 00:01:27.370
This would be equal to
negative one times the one,
00:01:27.370 --> 00:01:32.370
zero, zero, zero vector
plus negative three,
00:01:33.100 --> 00:01:38.100
plus negative three times the
zero, one, zero, zero vector
00:01:39.820 --> 00:01:44.820
plus negative five, plus
negative five times the zero,
00:01:46.170 --> 00:01:48.290
zero, one, zero vector.
00:01:48.290 --> 00:01:49.990
I think you see where this is going.
00:01:49.990 --> 00:01:51.860
And then last but not least,
00:01:51.860 --> 00:01:56.860
plus one times the zero,
zero, zero, one vector.
00:01:59.210 --> 00:02:00.560
Now when I write it this way,
00:02:00.560 --> 00:02:02.067
you might immediately start realizing,
00:02:02.067 --> 00:02:05.330
"Oh I think I know how to
do transformations here."
00:02:05.330 --> 00:02:09.610
For example, if I were to give
you the transformation matrix
00:02:09.610 --> 00:02:11.160
and this would be a transformation matrix
00:02:11.160 --> 00:02:12.653
for four dimensions.
00:02:13.580 --> 00:02:16.010
This is gonna be a four-by-four matrix.
00:02:16.010 --> 00:02:17.830
So I'm gonna write some
random numbers here.
00:02:17.830 --> 00:02:22.270
One, zero, negative three,
negative one, two, zero,
00:02:22.270 --> 00:02:27.270
negative three, one, three,
two, zero, two, three,
00:02:28.770 --> 00:02:31.960
negative one, zero and three.
00:02:31.960 --> 00:02:35.230
So my question to you is,
what would be the mapping
00:02:35.230 --> 00:02:38.370
of this four-dimensional
vector if we were to apply
00:02:38.370 --> 00:02:43.050
this transformation to
four-dimensional space?
00:02:43.050 --> 00:02:44.520
What would be the result?
00:02:44.520 --> 00:02:46.320
Pause this video and think about it.
00:02:47.360 --> 00:02:49.620
Well, it's completely
analogous to what we did
00:02:49.620 --> 00:02:53.250
in the two-by-two world
in two-dimensional space.
00:02:53.250 --> 00:02:55.500
We thought about, all
right, instead of the one,
00:02:55.500 --> 00:03:00.023
zero, zero, zero vector, we're
now going to use this vector.
00:03:00.920 --> 00:03:04.250
Instead of the zero,
one, zero, zero vector,
00:03:04.250 --> 00:03:07.290
we're now going to use this vector.
00:03:07.290 --> 00:03:09.960
Instead of this one in
that blue-green color,
00:03:09.960 --> 00:03:12.260
we're now going to use this one.
00:03:12.260 --> 00:03:14.260
And last but not least instead of that,
00:03:14.260 --> 00:03:16.450
I guess we could say
same in colored vector,
00:03:16.450 --> 00:03:19.130
we're now going to be using this one.
00:03:19.130 --> 00:03:21.770
So another way to think about it is,
00:03:21.770 --> 00:03:24.600
the mapping of this vector,
let me write it this way.
00:03:24.600 --> 00:03:26.400
Let me make a little line here
00:03:26.400 --> 00:03:28.550
so we can separate things a little bit
00:03:28.550 --> 00:03:30.910
but we could write, all
right, a little bit smaller,
00:03:30.910 --> 00:03:32.300
hopefully you can see this.
00:03:32.300 --> 00:03:35.860
So this is our original
vector, negative five, one,
00:03:35.860 --> 00:03:37.100
but we wanna do the prime.
00:03:37.100 --> 00:03:39.990
What does it get mapped to
under this transformation?
00:03:39.990 --> 00:03:42.100
Well, this is going to be negative one,
00:03:42.100 --> 00:03:44.050
instead of this unit
vector right over here,
00:03:44.050 --> 00:03:45.990
it's gonna be negative one
of this one right over here.
00:03:45.990 --> 00:03:49.980
So it's negative one times
all of this business,
00:03:49.980 --> 00:03:53.453
one, two, three, and three.
00:03:54.360 --> 00:03:57.670
And then we could have just
instead of plus negative three
00:03:57.670 --> 00:04:02.260
I can just write in minus three
times all of this business,
00:04:02.260 --> 00:04:07.080
zero, zero, two, negative one.
00:04:07.080 --> 00:04:12.080
And then we have minus five
times all of this business,
00:04:13.690 --> 00:04:16.270
negative three, negative three
00:04:16.270 --> 00:04:20.350
and then we get zero, zero, and then,
00:04:20.350 --> 00:04:23.130
that definitely gets a little
bit more work involved,
00:04:23.130 --> 00:04:27.440
the more dimensions we have,
plus one times this business.
00:04:27.440 --> 00:04:32.440
So plus one times negative
one, one, two, three.
00:04:37.430 --> 00:04:40.440
And so what's this going to be equal to?
00:04:40.440 --> 00:04:42.970
So actually this could be a
good time to pause the video too
00:04:42.970 --> 00:04:44.003
and have a go at it.
00:04:45.450 --> 00:04:48.450
All right, so this is
going to be this first one,
00:04:48.450 --> 00:04:49.640
I just make all of these negatives.
00:04:49.640 --> 00:04:53.110
So negative one, negative
two, negative three,
00:04:53.110 --> 00:04:56.900
negative three, and to
that, I'm going to add,
00:04:56.900 --> 00:04:59.850
let's see if I multiply all
of those times negative three,
00:04:59.850 --> 00:05:04.400
I'm going to get zero, zero, negative six
00:05:04.400 --> 00:05:07.010
and positive three.
00:05:07.010 --> 00:05:10.860
And then if I multiply all
of these times negative five,
00:05:10.860 --> 00:05:15.860
I am going to get 15, 15, zero and zero.
00:05:17.610 --> 00:05:20.510
And then if I multiply
all of these times one,
00:05:20.510 --> 00:05:22.680
well, I just get those things again.
00:05:22.680 --> 00:05:27.360
So that's going to be negative
one, one, two, and three
00:05:27.360 --> 00:05:29.610
and we are in the home stretch.
00:05:29.610 --> 00:05:32.230
So now we can just add everything together
00:05:32.230 --> 00:05:34.000
the corresponding terms.
00:05:34.000 --> 00:05:37.390
And so this is going to
be negative one plus zero,
00:05:37.390 --> 00:05:39.010
plus 15, plus negative one.
00:05:39.010 --> 00:05:42.370
So that's gonna be the
same thing as 15 minus two
00:05:42.370 --> 00:05:44.570
which is going to be 13,
00:05:44.570 --> 00:05:47.880
then negative two plus
zero, plus 15, plus one,
00:05:47.880 --> 00:05:52.100
so that's gonna be 16
minus two which is 14,
00:05:52.100 --> 00:05:53.900
then we have negative
three plus negative six
00:05:53.900 --> 00:05:57.450
which is negative nine and
then we add two to that,
00:05:57.450 --> 00:05:59.710
so that is negative seven.
00:05:59.710 --> 00:06:03.130
And then negative three
plus three is zero,
00:06:03.130 --> 00:06:07.840
plus zero is zero, plus three
is three, and we are done.
00:06:07.840 --> 00:06:12.600
We have found the mapping of
this four-dimensional vector
00:06:12.600 --> 00:06:17.060
based on a four-by-four
transformation matrix.
00:06:17.060 --> 00:06:17.993
Very cool.
|
Using matrices to transform the plane: Composing matrices | https://www.youtube.com/watch?v=OzoEqs1f1S8 | vtt | https://www.youtube.com/api/timedtext?v=OzoEqs1f1S8&ei=ylWUZdK2McmQvdIP9bO7oAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B71F2F336F09FFAB35E946A61A49696258204944.4EC6FC662778165982AEB4F4AB96B3EA1BEC55E8&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.340 --> 00:00:01.220
- [Instructor] So what I have here
00:00:01.220 --> 00:00:03.060
is two different transformation matrices,
00:00:03.060 --> 00:00:04.880
and what we're going to
think about in this video
00:00:04.880 --> 00:00:07.530
is can we construct a new matrix
00:00:07.530 --> 00:00:10.550
that's based on the composition
of these transformations?
00:00:10.550 --> 00:00:12.380
Or a simpler way of saying that,
00:00:12.380 --> 00:00:14.720
a new transformation
that's based on applying
00:00:14.720 --> 00:00:16.640
one of these transformations first,
00:00:16.640 --> 00:00:19.490
and then the other one right after that.
00:00:19.490 --> 00:00:22.070
So first, let's just
review what's going on.
00:00:22.070 --> 00:00:27.020
If we have some random vector here, a, b,
00:00:27.020 --> 00:00:28.910
we know that we could view this
00:00:28.910 --> 00:00:32.990
as a times the one, zero vector,
00:00:32.990 --> 00:00:35.460
the unit vector in the x direction,
00:00:35.460 --> 00:00:38.819
plus b times the zero, one vector,
00:00:38.819 --> 00:00:42.190
the unit vector that goes
in the vertical direction.
00:00:42.190 --> 00:00:44.760
Now, if you were to apply
this transformational
00:00:44.760 --> 00:00:46.180
capital A here,
00:00:46.180 --> 00:00:48.790
it tells you instead of using
one, zero and zero, one,
00:00:48.790 --> 00:00:51.310
use these two columns instead.
00:00:51.310 --> 00:00:54.230
So if you were to apply
the transformation here,
00:00:54.230 --> 00:00:59.230
I guess we could call it a,
b prime, that is going to be,
00:00:59.240 --> 00:01:02.200
if you apply capital A
transformation matrix,
00:01:02.200 --> 00:01:04.630
it's going to be a times, not one, zero,
00:01:04.630 --> 00:01:07.620
you use zero, five instead.
00:01:07.620 --> 00:01:10.200
And then plus b times not zero, one,
00:01:10.200 --> 00:01:13.370
you use two, negative one instead.
00:01:13.370 --> 00:01:15.500
So that's just a little bit of review.
00:01:15.500 --> 00:01:17.350
But what we're gonna think
about in this video is,
00:01:17.350 --> 00:01:21.000
what would be the transformation
matrix for the composition?
00:01:21.000 --> 00:01:26.000
And I could write that as
B of A right over here.
00:01:26.090 --> 00:01:29.260
And you might recognize
this from function notation,
00:01:29.260 --> 00:01:30.350
where essentially it's saying
00:01:30.350 --> 00:01:32.510
you would apply the function A first,
00:01:32.510 --> 00:01:34.320
and then whatever the output of that is,
00:01:34.320 --> 00:01:35.930
you would then input that into B
00:01:35.930 --> 00:01:37.890
and you'd get the output of that.
00:01:37.890 --> 00:01:38.870
And that makes sense,
00:01:38.870 --> 00:01:40.950
because you can view
transformation matrices
00:01:40.950 --> 00:01:43.150
really as functions, functions
00:01:43.150 --> 00:01:46.590
that map points on the coordinate plane.
00:01:46.590 --> 00:01:48.370
So, in this situation,
00:01:48.370 --> 00:01:50.790
what would be the transformation matrix
00:01:50.790 --> 00:01:52.780
that is a composition of these two?
00:01:52.780 --> 00:01:54.680
Pause this video and think about that.
00:01:56.070 --> 00:01:58.210
All right, well, what would happen is,
00:01:58.210 --> 00:02:02.180
we would first transform any
point using these two vectors,
00:02:02.180 --> 00:02:03.870
the zero, five, the two, negative one,
00:02:03.870 --> 00:02:06.180
because that's the first
transformation we do.
00:02:06.180 --> 00:02:09.400
And then we would apply
this transformation
00:02:09.400 --> 00:02:12.090
to whatever the resulting vector is.
00:02:12.090 --> 00:02:13.630
Now, that seems pretty involved
00:02:13.630 --> 00:02:15.990
and we don't wanna write
it in terms of A or B's,
00:02:15.990 --> 00:02:18.890
we just wanna write it in terms
of a transformation matrix.
00:02:18.890 --> 00:02:20.800
So one way to think about it is,
00:02:20.800 --> 00:02:24.570
we can transform each of these vectors
00:02:24.570 --> 00:02:27.120
that you have in matrix A.
00:02:27.120 --> 00:02:29.260
Because remember, that
says, what do you turn
00:02:29.260 --> 00:02:32.140
the vectors one, zero and zero, one into?
00:02:32.140 --> 00:02:36.990
So if we transform zero,
five using the matrix B,
00:02:36.990 --> 00:02:41.220
and if we transform two,
negative one using the matrix B
00:02:41.220 --> 00:02:43.350
and we put them in their
respective columns,
00:02:43.350 --> 00:02:46.030
we should have the composition of this.
00:02:46.030 --> 00:02:48.720
So let me write it this way,
create a little bit of space.
00:02:48.720 --> 00:02:53.720
So let's say that the
composition B of A is equal to,
00:02:53.753 --> 00:02:57.060
I'll write a big two-by-two
matrix right over here.
00:02:57.060 --> 00:03:01.170
The first thing we can do is
apply transformation matrix B
00:03:01.170 --> 00:03:03.860
to the purple column right over here.
00:03:03.860 --> 00:03:05.640
And what is that going to tell us?
00:03:05.640 --> 00:03:09.470
Well, that's gonna be zero
times negative three, one.
00:03:09.470 --> 00:03:10.700
So let me write it that way.
00:03:10.700 --> 00:03:15.700
It's going to be zero
times negative three, one
00:03:17.440 --> 00:03:22.440
plus five times zero, four, zero, four.
00:03:23.320 --> 00:03:24.670
And this is going to give us
00:03:24.670 --> 00:03:27.320
a two by one vector right over here.
00:03:27.320 --> 00:03:28.680
So that you can view
00:03:28.680 --> 00:03:32.710
as filling up the first
column of this transformation,
00:03:32.710 --> 00:03:34.670
this composition, I guess you could say.
00:03:34.670 --> 00:03:37.560
And then let's think
about this second vector
00:03:37.560 --> 00:03:39.250
right over here, two, negative one.
00:03:39.250 --> 00:03:42.510
If you transform that using
B, what are you going to get?
00:03:42.510 --> 00:03:45.320
You're going to get two
times negative three, one.
00:03:45.320 --> 00:03:50.320
So right here, two times
negative three, one,
00:03:50.490 --> 00:03:53.390
plus negative one, or maybe
I just write it this way,
00:03:53.390 --> 00:03:58.390
minus one times zero, four.
00:04:00.030 --> 00:04:03.290
And this doesn't look
like a matrix just yet,
00:04:03.290 --> 00:04:05.870
but if you work through it,
it will become a matrix.
00:04:05.870 --> 00:04:08.260
For example, if I multiply,
00:04:08.260 --> 00:04:10.630
well, zero times all of
this is going to be zero,
00:04:10.630 --> 00:04:13.730
and then five times zero is going to be,
00:04:13.730 --> 00:04:15.080
let me just write it this way.
00:04:15.080 --> 00:04:17.470
This would turn into
five times zero is zero,
00:04:17.470 --> 00:04:20.320
five times four is 20.
00:04:20.320 --> 00:04:22.880
And then this matrix right over here
00:04:22.880 --> 00:04:26.060
is going to be two times
negative three, one,
00:04:26.060 --> 00:04:30.170
is going to be negative six, two,
00:04:30.170 --> 00:04:35.170
and then we have minus zero, four.
00:04:35.470 --> 00:04:37.090
And now if we wanted to write this clearly
00:04:37.090 --> 00:04:39.980
as a two-by-two matrix,
this would be equal to,
00:04:39.980 --> 00:04:42.140
and we get a little bit
of a drum roll here,
00:04:42.140 --> 00:04:45.040
the first column is zero, 20.
00:04:45.040 --> 00:04:47.910
And then the second column
is going to be, let's see,
00:04:47.910 --> 00:04:51.240
negative six minus zero
is still negative six
00:04:51.240 --> 00:04:54.720
and two minus four is negative two.
00:04:54.720 --> 00:04:55.720
And we're done.
00:04:55.720 --> 00:04:58.980
We have just created a
new transformation matrix.
00:04:58.980 --> 00:05:01.970
It's based on the composition B of A.
00:05:01.970 --> 00:05:05.630
So if you apply transformation
A first to any vector
00:05:05.630 --> 00:05:09.870
and then apply transformation
B to whatever you get there,
00:05:09.870 --> 00:05:13.140
that is equivalent to
just applying this one
00:05:13.140 --> 00:05:16.233
two-by-two transformation matrix, B of A.
|
Using matrices to transform the plane: Mapping a vector | https://www.youtube.com/watch?v=TuDYc-8L2Bw | vtt | https://www.youtube.com/api/timedtext?v=TuDYc-8L2Bw&ei=ylWUZYOoJty4vdIP3OaPkAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B8120DB5F28DD040DA8C4299A2D659C59C8F5078.99C55D39D2132B5C81E4515A1D524B06C69C1B3D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.240 --> 00:00:04.040
- [Instructor] Let's say that
we have the vector three, two.
00:00:04.040 --> 00:00:07.190
We know that we can express
this as a weighted sum
00:00:07.190 --> 00:00:09.530
of the unit vectors in two dimensions
00:00:09.530 --> 00:00:12.040
or we can view it as a linear combination.
00:00:12.040 --> 00:00:14.600
And you could view this as three times
00:00:14.600 --> 00:00:16.650
the unit vector in the X direction
00:00:16.650 --> 00:00:21.390
which is one zero plus
two times the unit vector
00:00:21.390 --> 00:00:24.350
in the Y direction, which is zero, one.
00:00:24.350 --> 00:00:27.370
And we can graph three,
two by saying okay,
00:00:27.370 --> 00:00:30.210
we have three unit vectors
in the X direction.
00:00:30.210 --> 00:00:33.100
This would be one right over there.
00:00:33.100 --> 00:00:37.250
That would be two and
then that would be three.
00:00:37.250 --> 00:00:40.610
And then we have plus two unit
vectors in the Y direction.
00:00:40.610 --> 00:00:45.610
So one and then two, and then
we know where our vector is
00:00:46.790 --> 00:00:47.740
or what it would look like.
00:00:47.740 --> 00:00:51.070
The vector three, two
would look like this.
00:00:53.700 --> 00:00:58.160
Now let's apply a
transformation to this vector.
00:00:58.160 --> 00:01:01.670
And so let's say we have
the transformation matrix.
00:01:01.670 --> 00:01:02.820
I'll write it this way.
00:01:03.750 --> 00:01:07.040
Two, one, two, three.
00:01:07.040 --> 00:01:08.620
Now we've thought about this before.
00:01:08.620 --> 00:01:11.540
One way of thinking about
a transformation matrix is
00:01:11.540 --> 00:01:15.110
it gives you the image
of the unit vectors.
00:01:15.110 --> 00:01:17.650
And so instead of being
this linear combination
00:01:17.650 --> 00:01:19.090
of the unit vectors,
00:01:19.090 --> 00:01:21.010
it's going to be this linear combination
00:01:21.010 --> 00:01:22.990
of the images of the unit vectors
00:01:22.990 --> 00:01:24.670
when we take the transformation.
00:01:24.670 --> 00:01:25.900
What do I mean?
00:01:25.900 --> 00:01:28.460
Well, instead of having three one, zeros,
00:01:28.460 --> 00:01:32.010
we are now going to have three two, ones.
00:01:32.010 --> 00:01:33.870
Instead of having two zero, ones,
00:01:33.870 --> 00:01:37.210
we're now going to have two two, threes.
00:01:37.210 --> 00:01:39.490
So I could write it this way.
00:01:39.490 --> 00:01:43.960
Let me write it this way, the
image of our original vector.
00:01:43.960 --> 00:01:46.720
I'll put a prime here to say
we're talking about its image
00:01:46.720 --> 00:01:50.000
is going to be three times
instead of one, zero,
00:01:50.000 --> 00:01:53.840
it's going to be times two, one vectors.
00:01:53.840 --> 00:01:56.880
That's the image of the
one, zero unit vector
00:01:56.880 --> 00:01:58.950
under this transformation.
00:01:58.950 --> 00:02:03.390
And then we're gonna say plus
two instead of zero, one,
00:02:03.390 --> 00:02:04.860
we're gonna look at the image
00:02:04.860 --> 00:02:07.460
under the transformation
of the zero, one vector,
00:02:07.460 --> 00:02:09.580
which the transformation matrix gives us
00:02:09.580 --> 00:02:11.483
and that is the two, three, vector.
00:02:12.450 --> 00:02:16.130
Two, three, and we can graph this.
00:02:16.130 --> 00:02:19.350
If we have three two,
ones and two two, threes,
00:02:19.350 --> 00:02:23.910
what I could do is overlay
this extra grid to help us.
00:02:23.910 --> 00:02:27.630
So this is two, one, that's one to one,
00:02:27.630 --> 00:02:30.480
that is two two, ones going here.
00:02:30.480 --> 00:02:33.620
And then we have three
two, ones right over here.
00:02:33.620 --> 00:02:35.600
So there's three two, ones.
00:02:35.600 --> 00:02:37.790
Let me do this in this color.
00:02:37.790 --> 00:02:41.930
This part right over here
is going to be this vector.
00:02:41.930 --> 00:02:46.710
The three two, ones is
going to look like that.
00:02:46.710 --> 00:02:50.200
And then to that, we add two two, threes.
00:02:50.200 --> 00:02:51.520
So this is going to...
00:02:51.520 --> 00:02:52.910
Let's see, two and then three
00:02:52.910 --> 00:02:55.730
so this is going to be one two, three,
00:02:55.730 --> 00:02:58.280
and then we have two two, threes.
00:02:58.280 --> 00:03:01.800
So we end up right over there.
00:03:01.800 --> 00:03:04.110
And so let me actually
get rid of this grid
00:03:04.110 --> 00:03:07.510
so we can see things a
little bit more clearly.
00:03:07.510 --> 00:03:09.480
And so we have here in purple,
00:03:09.480 --> 00:03:11.720
we have our original three, two vector
00:03:11.720 --> 00:03:14.840
and now the image is going
to be three two, ones
00:03:14.840 --> 00:03:19.500
plus two two, threes so the
image of our three, two vector
00:03:19.500 --> 00:03:23.130
under this transformation
is going to be this vector
00:03:23.130 --> 00:03:25.150
that I'm drawing right here.
00:03:25.150 --> 00:03:27.420
And it looks when I eyeball it,
00:03:27.420 --> 00:03:31.120
it looks like it is the 10, nine vector
00:03:31.120 --> 00:03:33.940
and we can verify that by
doing the math right over here.
00:03:33.940 --> 00:03:34.773
So let's do that.
00:03:34.773 --> 00:03:39.490
This is going to be equal
to three times two is six,
00:03:39.490 --> 00:03:41.580
three times one is three.
00:03:41.580 --> 00:03:45.700
And we're going to add that
to two times two is four,
00:03:45.700 --> 00:03:48.320
two times three is six.
00:03:48.320 --> 00:03:51.110
And indeed you add the
corresponding entry,
00:03:51.110 --> 00:03:55.490
six plus four is 10 and
three plus six is nine.
00:03:55.490 --> 00:03:56.640
And we're done.
00:03:56.640 --> 00:03:58.010
The important takeaway here
00:03:58.010 --> 00:03:59.750
is that any vector can be represented
00:03:59.750 --> 00:04:02.760
as a linear combination
of the unit vectors.
00:04:02.760 --> 00:04:04.730
Now when we take the transformation,
00:04:04.730 --> 00:04:06.650
it's now going to be a linear combination
00:04:06.650 --> 00:04:08.010
not of the unit vectors,
00:04:08.010 --> 00:04:10.750
but of the images of the unit factors.
00:04:10.750 --> 00:04:12.040
And we saw that visually
00:04:12.040 --> 00:04:14.223
and we verified that mathematically.
|
Working with matrices as transformations of the plane | https://www.youtube.com/watch?v=vCkvVAvmJwY | vtt | https://www.youtube.com/api/timedtext?v=vCkvVAvmJwY&ei=ylWUZcTzIuz_mLAPoIyimAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B4E54C33CC63495E1D725A84927930A72CF5D19C.2284C32B74322A65B8E822524050522C49191D19&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:01.360
- [Instructor] In a previous video,
00:00:01.360 --> 00:00:04.330
I talked about how a
two-by-two matrix can be used
00:00:04.330 --> 00:00:08.290
to define a transformation for
the entire coordinate plane.
00:00:08.290 --> 00:00:09.500
What we're going to do in this video,
00:00:09.500 --> 00:00:10.860
is experiment with that little bit
00:00:10.860 --> 00:00:13.450
and see if we can think
about how to engineer
00:00:13.450 --> 00:00:16.580
two-by-two matrices to do
some of the transformations
00:00:16.580 --> 00:00:17.900
that you might be familiar with,
00:00:17.900 --> 00:00:22.100
like rotations, or
dilations, or reflections.
00:00:22.100 --> 00:00:26.360
So this is a website run
by the University of Texas,
00:00:26.360 --> 00:00:28.900
web.ma.utexas.edu.
00:00:28.900 --> 00:00:30.730
And you have the URL here,
I encourage you to go there
00:00:30.730 --> 00:00:32.490
and play around with it yourself.
00:00:32.490 --> 00:00:37.480
And what I have here is,
I have our two vectors,
00:00:37.480 --> 00:00:40.570
which any point on our
coordinate access can be defined
00:00:40.570 --> 00:00:44.120
by some combination of these two vectors.
00:00:44.120 --> 00:00:46.570
This in red here is the vector one, zero.
00:00:46.570 --> 00:00:50.150
It goes one in the x-direction,
zero in the y-direction,
00:00:50.150 --> 00:00:52.780
and you can see that is this
first column right over here
00:00:52.780 --> 00:00:54.270
in this identity matrix.
00:00:54.270 --> 00:00:56.270
And this blue vector right over here,
00:00:56.270 --> 00:00:58.040
this is the vector zero, one,
00:00:58.040 --> 00:01:00.500
which is the second column
in this identity matrix.
00:01:00.500 --> 00:01:02.350
It goes zero in the x-direction,
00:01:02.350 --> 00:01:05.760
and then one in the y-direction.
00:01:05.760 --> 00:01:09.940
Now, the way to engineer a
transformation is to say, well,
00:01:09.940 --> 00:01:12.690
what would that transformation
do to these two vectors,
00:01:12.690 --> 00:01:15.490
and then change the numbers accordingly.
00:01:15.490 --> 00:01:18.480
So, for example, let's say that we wanted
00:01:18.480 --> 00:01:23.210
to have a reflection about the x-axis.
00:01:23.210 --> 00:01:25.730
So if you did a reflection
about the x-axis,
00:01:25.730 --> 00:01:27.950
this red vector would not change.
00:01:27.950 --> 00:01:29.690
It would stay one, zero.
00:01:29.690 --> 00:01:31.520
But what would happen to this blue vector?
00:01:31.520 --> 00:01:33.260
Instead of being zero, one,
00:01:33.260 --> 00:01:35.610
it would be zero, negative one.
00:01:35.610 --> 00:01:38.040
So in the transformation matrix,
00:01:38.040 --> 00:01:39.810
if I go from the identity matrix here,
00:01:39.810 --> 00:01:41.840
but instead of zero, one, I now,
00:01:41.840 --> 00:01:43.390
it will no longer be the identity matrix
00:01:43.390 --> 00:01:44.930
if I put a negative one here.
00:01:44.930 --> 00:01:46.290
And when I press Enter,
00:01:46.290 --> 00:01:50.730
this should flip this blue
vector over the x-axis
00:01:50.730 --> 00:01:52.570
and essentially flip
everything else with it.
00:01:52.570 --> 00:01:53.403
So let's try that out.
00:01:53.403 --> 00:01:55.720
I'm gonna press Enter,
and there you have it.
00:01:55.720 --> 00:02:00.720
That cute little golden
retriever is now flipped over.
00:02:00.920 --> 00:02:02.880
So that met our intuition.
00:02:02.880 --> 00:02:04.670
So let's go back back to
what we were doing before.
00:02:04.670 --> 00:02:05.640
So that's a reflection,
00:02:05.640 --> 00:02:07.190
and you could think
about what would you do
00:02:07.190 --> 00:02:10.400
if you wanted to flip the
other way across the y-axis.
00:02:10.400 --> 00:02:12.880
Now, what about a dilation?
00:02:12.880 --> 00:02:17.080
What if we wanted to shrink
everything by a factor of two?
00:02:17.080 --> 00:02:19.610
How do you think we would
modify this matrix to do that?
00:02:19.610 --> 00:02:21.510
Pause this video and think about that?
00:02:22.870 --> 00:02:25.450
Well, if we want to scale everything down,
00:02:25.450 --> 00:02:27.230
what we would want is,
each of these vectors,
00:02:27.230 --> 00:02:28.920
and especially if it's by a factor of two,
00:02:28.920 --> 00:02:31.460
we'd want each of these
vectors to be half as long.
00:02:31.460 --> 00:02:33.440
So instead of one, zero and zero, one,
00:02:33.440 --> 00:02:38.440
we would do 0.5, zero and 0.5.
00:02:38.950 --> 00:02:40.360
Let me press Enter and see what happens.
00:02:40.360 --> 00:02:41.280
There you go.
00:02:41.280 --> 00:02:42.690
It indeed worked.
00:02:42.690 --> 00:02:44.920
And really this should
have showed this red vector
00:02:44.920 --> 00:02:47.110
gets smaller and this
blue vector gets smaller.
00:02:47.110 --> 00:02:48.950
But hopefully you get the idea.
00:02:48.950 --> 00:02:50.430
And so let me go.
00:02:50.430 --> 00:02:52.600
Or maybe this one that always show
00:02:52.600 --> 00:02:54.960
what we could kind of
call it, unit vectors.
00:02:54.960 --> 00:02:56.710
But let's go back to the original.
00:02:56.710 --> 00:02:58.280
And now let's think about our rotation.
00:02:58.280 --> 00:02:59.610
This is an interesting one.
00:02:59.610 --> 00:03:01.500
Pause this video and think
about how you would rotate it
00:03:01.500 --> 00:03:05.363
if you wanted to rotate this
clockwise by 90 degrees.
00:03:07.040 --> 00:03:07.873
All right.
00:03:07.873 --> 00:03:09.400
If you rotate clockwise by 90 degrees
00:03:09.400 --> 00:03:12.163
this red vector is no longer one, zero.
00:03:14.032 --> 00:03:16.550
It would become zero, negative one.
00:03:16.550 --> 00:03:17.550
So let me write that down.
00:03:17.550 --> 00:03:20.350
Zero, negative one.
00:03:20.350 --> 00:03:22.050
And the blue vector would then go
00:03:22.050 --> 00:03:24.870
to where this red vector is
and it would become one, zero.
00:03:24.870 --> 00:03:29.540
So let's see if we did it the right way.
00:03:29.540 --> 00:03:30.950
I'm gonna click Enter.
00:03:30.950 --> 00:03:31.900
And there you go.
00:03:31.900 --> 00:03:34.170
We got our 90 degree rotation.
00:03:34.170 --> 00:03:36.730
And so I just gave you some examples
00:03:36.730 --> 00:03:39.420
of how you can do a pure rotation,
00:03:39.420 --> 00:03:41.600
a pure dilation, or a pure reflection.
00:03:41.600 --> 00:03:44.410
But you can imagine you can
also do combinations of them,
00:03:44.410 --> 00:03:47.030
by manipulating this matrix accordingly.
00:03:47.030 --> 00:03:48.320
And I encourage you to play around.
00:03:48.320 --> 00:03:51.100
You can do some exotic
transformations if you want.
00:03:51.100 --> 00:03:53.220
Let's see what happens
if I make this a one.
00:03:53.220 --> 00:03:54.053
Press Enter.
00:03:54.053 --> 00:03:55.110
Oh, that's interesting.
00:03:55.110 --> 00:03:58.400
What happens if I then make this a two?
00:03:58.400 --> 00:03:59.510
Oh, that's interesting.
00:03:59.510 --> 00:04:00.830
So notice, you can do all sorts
00:04:00.830 --> 00:04:02.750
of really interesting
linear transformation.
00:04:02.750 --> 00:04:04.760
And just as a reminder,
linear transformation
00:04:04.760 --> 00:04:07.300
is one where the origin
always maps to itself,
00:04:07.300 --> 00:04:10.110
and any lines are mapped to other lines.
00:04:10.110 --> 00:04:11.470
Not necessarily the same line,
00:04:11.470 --> 00:04:14.120
but whatever it gets mapped
to will still be aligned.
|
Matrices as transformations of the plane | https://www.youtube.com/watch?v=PtjdhADnJi4 | vtt | https://www.youtube.com/api/timedtext?v=PtjdhADnJi4&ei=ylWUZcCyOrO-mLAP7cWu6Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245307&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0CBC221D0BA7D2394D19842A249EF4AAFAE95B49.60473DEDB72E9D52971BAAAD454ED26B8BFE1AE5&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.210 --> 00:00:01.950
- [Instructor] In this
video, we're going to explore
00:00:01.950 --> 00:00:05.520
how a two by two matrix can be interpreted
00:00:05.520 --> 00:00:10.520
as representing a transformation
on the coordinate plane.
00:00:10.750 --> 00:00:13.410
So let's just start with some examples
00:00:13.410 --> 00:00:15.870
or some conceptual ideas.
00:00:15.870 --> 00:00:19.010
So the first conceptual idea is that
00:00:19.010 --> 00:00:21.680
any point on our coordinate plane here
00:00:21.680 --> 00:00:26.680
and this of course is our X
axis and this is our Y axis,
00:00:27.150 --> 00:00:31.610
can be represented by a
combination of two vectors.
00:00:31.610 --> 00:00:34.340
You could have this
vector right over here.
00:00:34.340 --> 00:00:38.080
That goes exactly one unit
in the horizontal direction.
00:00:38.080 --> 00:00:43.080
We can represent that as a
vector like this, one, zero,
00:00:43.490 --> 00:00:45.300
when you write a vector
vertically like this
00:00:45.300 --> 00:00:47.730
the convention is that the top number here
00:00:47.730 --> 00:00:49.440
is what we're doing in the X direction.
00:00:49.440 --> 00:00:51.200
And then the bottom number,
00:00:51.200 --> 00:00:53.350
the zero is what we're doing
in the vertical direction
00:00:53.350 --> 00:00:56.650
or the Y direction, so this
is the one, zero vector.
00:00:56.650 --> 00:01:00.953
And then this right over
here, what would we call that?
00:01:01.870 --> 00:01:05.110
Well that we would call
the zero, one vector
00:01:05.110 --> 00:01:08.030
because it doesn't go at
all in the X direction.
00:01:08.030 --> 00:01:11.460
And it only goes up
one in the Y direction.
00:01:11.460 --> 00:01:14.740
Now just to feel good that any
point on the coordinate plane
00:01:14.740 --> 00:01:18.560
can be represented as a
weighted sum of these.
00:01:18.560 --> 00:01:21.170
Let's just pick a point at random.
00:01:21.170 --> 00:01:23.960
Let's say this point, all right over here,
00:01:23.960 --> 00:01:26.160
let's call it point A.
00:01:26.160 --> 00:01:28.670
And you could represent that as a vector
00:01:28.670 --> 00:01:30.120
that looks something like this,
00:01:30.120 --> 00:01:31.890
I'll do it as a dotted line,
00:01:31.890 --> 00:01:33.300
but this could be represented
00:01:33.300 --> 00:01:36.150
as a positional vector like that.
00:01:36.150 --> 00:01:38.100
And of course, if we're
thinking about it in coordinates
00:01:38.100 --> 00:01:41.710
we would just say this is at
the coordinate three comma one.
00:01:41.710 --> 00:01:44.460
The X coordinate is a three,
the Y coordinate is one.
00:01:44.460 --> 00:01:47.240
But if we wanted to express
it in terms of a vector,
00:01:47.240 --> 00:01:51.850
we could write it out as three, one,
00:01:51.850 --> 00:01:55.040
the X direction we're moving
three from the origin,
00:01:55.040 --> 00:01:56.710
positive three and the Y direction
00:01:56.710 --> 00:01:58.190
we're moving one to get there.
00:01:58.190 --> 00:02:01.280
And you could see that
we can represent this
00:02:01.280 --> 00:02:03.820
as a weighted sum of these two vectors.
00:02:03.820 --> 00:02:08.820
We can write this as, this is
the same thing as three times
00:02:08.920 --> 00:02:13.920
our one, zero vector, one, zero
00:02:14.290 --> 00:02:19.290
plus one times our zero
one, vector zero one vector.
00:02:20.820 --> 00:02:22.530
And you can see it visually,
00:02:22.530 --> 00:02:27.210
this yellow vector that points
to point a right over there.
00:02:27.210 --> 00:02:32.210
You can have three of this
vector, one, two, and then three.
00:02:32.810 --> 00:02:35.963
And then one of the orange vector.
00:02:36.870 --> 00:02:41.870
Now I said that I would
explain how two by two matrices
00:02:41.930 --> 00:02:44.460
can represent a transformation.
00:02:44.460 --> 00:02:46.950
And the way that you
could think about it is
00:02:46.950 --> 00:02:51.940
if I have a two by two
matrix that looks like this,
00:02:51.940 --> 00:02:53.960
so let me just draw the matrix,
00:02:53.960 --> 00:02:56.990
where the first column is one, zero
00:02:56.990 --> 00:03:00.070
and then the second column is zero, one.
00:03:00.070 --> 00:03:03.850
This just tells you what to
do with these two vectors.
00:03:03.850 --> 00:03:06.170
I know this might be a little
bit confusing at first,
00:03:06.170 --> 00:03:08.390
but let's just walk through it together.
00:03:08.390 --> 00:03:09.640
So the way I've represented it,
00:03:09.640 --> 00:03:12.750
this first column says
what is the transformation
00:03:12.750 --> 00:03:15.220
you want to apply to
this one, zero vector,
00:03:15.220 --> 00:03:16.800
this first blue vector?
00:03:16.800 --> 00:03:18.640
Well, we're just keeping it one zero.
00:03:18.640 --> 00:03:20.560
So we're not changing it, it's the same.
00:03:20.560 --> 00:03:23.350
One, zero vector here
one, zero vector here.
00:03:23.350 --> 00:03:28.030
Likewise, zero, one vector
here, zero, one vector here.
00:03:28.030 --> 00:03:32.160
So this two by two matrix
actually represents
00:03:32.160 --> 00:03:34.800
what's sometimes known as
the identity transformation.
00:03:34.800 --> 00:03:38.220
It maps any point on the
coordinate plane back to itself.
00:03:38.220 --> 00:03:40.050
It doesn't change the points,
00:03:40.050 --> 00:03:42.210
but I'm showing this because
now I'm going to show
00:03:42.210 --> 00:03:43.940
a two by two matrix that represents
00:03:43.940 --> 00:03:46.370
a non identity transformation.
00:03:46.370 --> 00:03:48.943
For example, let me draw the matrix again.
00:03:50.050 --> 00:03:53.910
So let's say I have the matrix,
00:03:53.910 --> 00:03:56.850
instead of one, zero here I'm
going to write a two, one here
00:03:56.850 --> 00:04:00.613
instead of a zero, one here
let me write a one, two.
00:04:01.540 --> 00:04:04.510
So in this transformation,
what we're doing is
00:04:04.510 --> 00:04:08.300
we're turning this one, zero
vector into a two, one vector.
00:04:08.300 --> 00:04:10.680
You're going to see what I'm
talking about in a second.
00:04:10.680 --> 00:04:13.020
So what does a two, one vector look like?
00:04:13.020 --> 00:04:14.403
Let me do it in that color.
00:04:15.510 --> 00:04:18.450
Well, we go two in the X
direction one in the Y direction.
00:04:18.450 --> 00:04:20.700
So it's going to look like this,
00:04:20.700 --> 00:04:24.530
it's going to look like that.
00:04:24.530 --> 00:04:28.250
And then what does a one,
two vector look like?
00:04:28.250 --> 00:04:30.170
Well, it goes one in the X direction
00:04:30.170 --> 00:04:34.240
and then two in the Y direction,
so it looks like this.
00:04:34.240 --> 00:04:36.400
And the way that this
represents a transformation
00:04:36.400 --> 00:04:38.890
is that anything that was a weighted sum
00:04:38.890 --> 00:04:42.030
of the one, zero and the
zero, one vectors originally,
00:04:42.030 --> 00:04:44.510
you can now view as a
weighted sum of the two, one
00:04:44.510 --> 00:04:46.140
and the one, two vectors.
00:04:46.140 --> 00:04:50.040
And so we can now think
of another point A prime,
00:04:50.040 --> 00:04:52.530
that's not going to be
three of the ones zeros
00:04:52.530 --> 00:04:54.290
and one of the zero ones.
00:04:54.290 --> 00:04:57.270
We can think of it as,
let me write it over here,
00:04:57.270 --> 00:05:01.010
as three of the two, ones
00:05:03.340 --> 00:05:08.340
plus one of the one twos,
one of these one, two.
00:05:13.330 --> 00:05:15.180
So where would that put that now?
00:05:15.180 --> 00:05:17.400
What we're going to go,
go three of the two, ones.
00:05:17.400 --> 00:05:22.400
So this is one of them,
this is two of them
00:05:22.410 --> 00:05:25.520
and then this is three of them.
00:05:25.520 --> 00:05:28.810
And then I'm going to have
one of the one, two vectors,
00:05:28.810 --> 00:05:30.650
this orange vector right over here.
00:05:30.650 --> 00:05:33.850
And so I'm going to have one of those.
00:05:33.850 --> 00:05:37.300
And so that will take me to A prime.
00:05:37.300 --> 00:05:41.330
This is my new point
after the transformation,
00:05:41.330 --> 00:05:42.620
I go to A prime.
00:05:42.620 --> 00:05:46.190
So I've gone from this
point A to this A prime.
00:05:46.190 --> 00:05:51.190
And this two by two matrix is
telling us how to transform.
00:05:51.290 --> 00:05:53.990
Now we can do that with multiple points.
00:05:53.990 --> 00:05:56.810
Now, if I talk about a
point here at the origin
00:05:56.810 --> 00:05:59.040
that was originally at the origin point B,
00:05:59.040 --> 00:06:00.710
well that's zero of the orange vector,
00:06:00.710 --> 00:06:02.230
zero of the blue vectors.
00:06:02.230 --> 00:06:03.740
So even after the transformation,
00:06:03.740 --> 00:06:05.307
it's going to be zero
of the two, one vector
00:06:05.307 --> 00:06:06.890
and zero of the one, two vectors.
00:06:06.890 --> 00:06:08.400
So it's just going to stay in place.
00:06:08.400 --> 00:06:09.730
It's just going to map to itself.
00:06:09.730 --> 00:06:12.060
So B is equal to B prime,
00:06:12.060 --> 00:06:14.620
and we could also imagine another point.
00:06:14.620 --> 00:06:19.620
Let's say right over here,
let's call that point C.
00:06:20.050 --> 00:06:23.430
Well point C is originally
two of the blue vectors
00:06:23.430 --> 00:06:25.610
and none of the orange vectors.
00:06:25.610 --> 00:06:28.810
So after the mapping, it'll
be two of the two, one vectors
00:06:28.810 --> 00:06:31.140
and none of the one, two vectors.
00:06:31.140 --> 00:06:32.330
So two of the two ones.
00:06:32.330 --> 00:06:36.910
So if you go one, two, and
then none of the one, twos
00:06:36.910 --> 00:06:39.710
you're going to get C
prime right over there.
00:06:39.710 --> 00:06:43.260
And so notice, if originally
you had a triangle
00:06:43.260 --> 00:06:45.990
between A, B and C, let
me draw it like this.
00:06:45.990 --> 00:06:50.950
So originally you had
this triangle A, B, C
00:06:50.950 --> 00:06:54.180
what is it now gotten mapped,
what is it now mapped to?
00:06:54.180 --> 00:06:56.870
Well, it's now mapped to big triangle.
00:06:56.870 --> 00:07:00.470
I'll do my best to draw
it relatively straight
00:07:00.470 --> 00:07:01.590
so we land on target.
00:07:01.590 --> 00:07:03.250
So that's that side.
00:07:03.250 --> 00:07:08.250
And then we have this side
going from B prime to C prime
00:07:08.350 --> 00:07:13.170
and then we wanna connect that
side from C prime to A prime.
00:07:13.170 --> 00:07:14.003
Now you might be saying,
00:07:14.003 --> 00:07:16.850
so how do you know that the
lines map onto other lines?
00:07:16.850 --> 00:07:18.050
How do you know this transformation
00:07:18.050 --> 00:07:20.970
didn't all of a sudden make
this line squiggly or zigzag?
00:07:20.970 --> 00:07:22.570
And that's one of the
interesting properties
00:07:22.570 --> 00:07:24.560
of the type of transformation
we're talking about.
00:07:24.560 --> 00:07:29.330
A two by two matrix will
represent a linear transformation.
00:07:29.330 --> 00:07:31.560
And there's two ways to think
about it in this context,
00:07:31.560 --> 00:07:34.480
a linear transformation
will always map the origin
00:07:34.480 --> 00:07:38.850
onto itself and it will always
map a line onto another line,
00:07:38.850 --> 00:07:40.510
it won't turn that line into a curve,
00:07:40.510 --> 00:07:43.030
or it won't make it zigzag somehow.
00:07:43.030 --> 00:07:44.790
Now the last thing you
might be wondering is,
00:07:44.790 --> 00:07:46.210
Hey what about all these transformations
00:07:46.210 --> 00:07:49.130
we had from geometry, these
similarity transformations,
00:07:49.130 --> 00:07:52.230
things like rotations
reflections, dilations,
00:07:52.230 --> 00:07:53.950
can you do those with matrices?
00:07:53.950 --> 00:07:55.630
And the simple answer is yes,
00:07:55.630 --> 00:07:59.520
you can do them as long as
you keep the origin in place.
00:07:59.520 --> 00:08:02.400
And you can actually
using a two by two matrix
00:08:02.400 --> 00:08:05.490
come up with a whole series of
other linear transformations
00:08:05.490 --> 00:08:07.970
that are much more, let's call it exotic,
00:08:07.970 --> 00:08:10.523
than just the rotations,
reflections and dilations.
|
Using the tangent angle addition identity | https://www.youtube.com/watch?v=4nPMCRuts9o | vtt | https://www.youtube.com/api/timedtext?v=4nPMCRuts9o&ei=ylWUZauWM_S2mLAP_LOFqAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=879A6CF900299BD574DD75A05544537E27FFFDF7.861EEAA4E3D2BF0D93D64F66C508D5FF83DBACE0&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.090 --> 00:00:03.580
- [Instructor] In this video,
we're going to try to compute
00:00:03.580 --> 00:00:08.580
what tangent of 13 pi over 12
is without using a calculator.
00:00:11.120 --> 00:00:13.260
But I will give you a few hints.
00:00:13.260 --> 00:00:16.900
First of all, you can rewrite
tangent of 13 pi over 12
00:00:16.900 --> 00:00:19.500
as tangent of,
00:00:19.500 --> 00:00:21.840
instead of 13 pi over
12, we can express that
00:00:21.840 --> 00:00:24.090
in terms of angles where we
might be able to figure out
00:00:24.090 --> 00:00:26.350
the tangents just based
on other things we know
00:00:26.350 --> 00:00:27.720
about the unit circle.
00:00:27.720 --> 00:00:31.817
13 pi over 12 is the same
thing as 15 pi over 12
00:00:33.900 --> 00:00:37.350
minus two pi over 12,
00:00:37.350 --> 00:00:41.680
which is the same thing as the tangent
00:00:41.680 --> 00:00:46.680
of five pi over four
00:00:47.320 --> 00:00:50.540
minus pi over six,
00:00:50.540 --> 00:00:54.660
or we could even view it as
plus negative pi over six.
00:00:54.660 --> 00:00:56.660
So that's my hint right over there.
00:00:56.660 --> 00:00:59.650
So pause this video and
see if you can keep going
00:00:59.650 --> 00:01:01.380
with this train of reasoning
00:01:01.380 --> 00:01:04.070
to evaluate what tangent
of 13 pi over 12 is
00:01:04.070 --> 00:01:05.733
without using a calculator.
00:01:07.390 --> 00:01:11.220
All right, now let's
keep on going together.
00:01:11.220 --> 00:01:13.270
Well, we already know what the tangent
00:01:13.270 --> 00:01:15.240
of the sum of two angles are.
00:01:15.240 --> 00:01:17.600
We've proven that in another video.
00:01:17.600 --> 00:01:19.390
We know that this is going to be equal
00:01:19.390 --> 00:01:24.390
to the tangent of the
first of these angles,
00:01:24.440 --> 00:01:27.740
five pi over four,
00:01:27.740 --> 00:01:30.120
plus the tangent of the second angle,
00:01:30.120 --> 00:01:34.830
tangent of negative pi over six,
00:01:34.830 --> 00:01:36.800
all of that is going to be over
00:01:38.300 --> 00:01:42.050
one minus tangent of the first angle,
00:01:42.050 --> 00:01:45.520
five pi over four,
00:01:45.520 --> 00:01:48.920
times the tangent of the second angle,
00:01:48.920 --> 00:01:51.370
negative pi over six.
00:01:51.370 --> 00:01:53.910
And so now we can break
out our unit circles
00:01:53.910 --> 00:01:56.490
to figure out what these things are.
00:01:56.490 --> 00:02:00.370
So I have pre-put some unit circles here.
00:02:00.370 --> 00:02:02.350
And so let's first think about
00:02:02.350 --> 00:02:04.700
what five pi over four looks like.
00:02:04.700 --> 00:02:05.780
Pi over four,
00:02:05.780 --> 00:02:07.990
you might already associate
it with 45 degrees.
00:02:07.990 --> 00:02:10.840
That's pi over four right over there.
00:02:10.840 --> 00:02:13.550
Two pi over four would get you here.
00:02:13.550 --> 00:02:15.590
Three pi over fours would get you there.
00:02:15.590 --> 00:02:17.520
Four pi over four, which
the same thing as pi,
00:02:17.520 --> 00:02:18.353
gets us over there.
00:02:18.353 --> 00:02:23.023
Five pi over four would
get us right about there.
00:02:23.930 --> 00:02:27.800
Now, you might already recognize
the tangent of an angle
00:02:27.800 --> 00:02:30.030
as the slope of the radius,
00:02:30.030 --> 00:02:32.420
and so you might already be able to intuit
00:02:32.420 --> 00:02:34.610
that the tangent here is going to be one,
00:02:34.610 --> 00:02:38.120
but we can also break out
our knowledge of triangles
00:02:38.120 --> 00:02:39.810
in the unit circle to figure this out
00:02:39.810 --> 00:02:41.530
if you didn't realize that.
00:02:41.530 --> 00:02:43.520
So what we need to do is
figure out the coordinates
00:02:43.520 --> 00:02:45.480
of that point right over there,
00:02:45.480 --> 00:02:46.880
and to help us do that,
00:02:46.880 --> 00:02:49.623
we can set up a little
bit of a right triangle,
00:02:50.660 --> 00:02:52.800
which you might immediately recognize
00:02:52.800 --> 00:02:55.550
is a 45-45-90 triangle.
00:02:55.550 --> 00:02:56.670
How do I know that?
00:02:56.670 --> 00:02:58.280
Well five pi over four,
00:02:58.280 --> 00:03:00.120
remember we go four pi
over four to get here,
00:03:00.120 --> 00:03:03.080
then we have one more pi
over four to go down here.
00:03:03.080 --> 00:03:05.120
So this angle right over
here is pi over four
00:03:05.120 --> 00:03:07.300
or you could view it as 45 degrees.
00:03:07.300 --> 00:03:09.520
And of course, if that's
45 degrees and that's 90,
00:03:09.520 --> 00:03:11.200
then this has to be 45 degrees
00:03:11.200 --> 00:03:14.300
'cause they all add up to 180 degrees.
00:03:14.300 --> 00:03:17.630
And we know a triangle like
this by the Pythagorean theorem,
00:03:17.630 --> 00:03:19.380
if our hypothesis is one,
00:03:19.380 --> 00:03:20.710
each of the other two sides
00:03:20.710 --> 00:03:23.440
is square root of two over
two times the hypotenuse.
00:03:23.440 --> 00:03:25.020
So this is square root of two over two
00:03:25.020 --> 00:03:27.740
and then this is square
root of two over two.
00:03:27.740 --> 00:03:29.630
Now, if we think about the coordinates,
00:03:29.630 --> 00:03:31.970
our X coordinate is square
root of two over two
00:03:31.970 --> 00:03:33.290
in the negative direction.
00:03:33.290 --> 00:03:37.260
So our X coordinate is negative
square root of two over two
00:03:37.260 --> 00:03:38.220
and our Y coordinate
00:03:38.220 --> 00:03:40.550
is square root of two over two going down,
00:03:40.550 --> 00:03:44.380
so that's also negative
square root of two over two.
00:03:44.380 --> 00:03:46.240
And the tangent is just
00:03:46.240 --> 00:03:50.360
the Y coordinate over
the X coordinate here.
00:03:50.360 --> 00:03:52.180
So the tangent is just going to be
00:03:52.180 --> 00:03:53.520
negative square root of two over two
00:03:53.520 --> 00:03:55.100
over negative square root of two over two,
00:03:55.100 --> 00:03:58.090
which is once again, one,
which was our intuition.
00:03:58.090 --> 00:04:03.090
So we can write the tangent
of five pi over four
00:04:03.590 --> 00:04:05.470
is equal to one.
00:04:05.470 --> 00:04:08.180
And then what about negative pi over six?
00:04:08.180 --> 00:04:09.340
Well, negative pi over six,
00:04:09.340 --> 00:04:12.130
you might recognize pi over
six as being a 30 degree angle.
00:04:12.130 --> 00:04:15.330
Pi is 180 degrees, so
divided by six is 30 degrees,
00:04:15.330 --> 00:04:17.120
and negative pi over six
00:04:17.120 --> 00:04:20.350
would be going 30 degrees
below the positive x-axis.
00:04:20.350 --> 00:04:22.640
So it would look just like that.
00:04:22.640 --> 00:04:25.970
And as we said, this angle
right over here is pi over six,
00:04:25.970 --> 00:04:29.290
which you can also view
as a 30 degree angle.
00:04:29.290 --> 00:04:32.420
If we were to drop a
perpendicular right over here,
00:04:32.420 --> 00:04:33.940
you might immediately recognize this
00:04:33.940 --> 00:04:37.970
as a 30-60-90 triangle.
00:04:37.970 --> 00:04:41.140
We know if the hypotenuse
is of length one,
00:04:41.140 --> 00:04:43.050
the side opposite the 30 degree side
00:04:43.050 --> 00:04:45.520
is 1/2 the hypotenuse,
00:04:45.520 --> 00:04:47.900
and then the longer non-hypotenuse side
00:04:47.900 --> 00:04:50.070
is going to be square root of
three times the shorter side,
00:04:50.070 --> 00:04:53.170
so square root of three over two.
00:04:53.170 --> 00:04:55.360
And so our coordinate's right over here,
00:04:55.360 --> 00:04:57.230
we are moving square
root of three over two
00:04:57.230 --> 00:04:58.580
in the positive X direction,
00:04:58.580 --> 00:05:00.400
square root of three over two,
00:05:00.400 --> 00:05:04.240
and then we're going negative
1/2 in the Y direction,
00:05:04.240 --> 00:05:07.780
so we put negative 1/2 right over there.
00:05:07.780 --> 00:05:12.780
And so now we know that the
tangent of negative pi over six
00:05:14.230 --> 00:05:16.800
is going to be equal to negative 1/2
00:05:18.120 --> 00:05:21.030
over square root of three over two,
00:05:21.030 --> 00:05:25.280
which is the same thing
as negative 1/2 times,
00:05:25.280 --> 00:05:26.610
let me write it this way, negative 1/2
00:05:26.610 --> 00:05:29.870
times two over the square root of three,
00:05:29.870 --> 00:05:32.170
which is equal to negative one
00:05:32.170 --> 00:05:34.340
over the square root of three.
00:05:34.340 --> 00:05:36.220
This right over here is one.
00:05:36.220 --> 00:05:37.250
We saw that there.
00:05:37.250 --> 00:05:39.420
This right over here is one.
00:05:39.420 --> 00:05:41.460
And then this right over here
00:05:41.460 --> 00:05:45.380
is negative one over the
square root of three.
00:05:45.380 --> 00:05:47.970
And then this is negative one
over the square root of three.
00:05:47.970 --> 00:05:51.420
And so I can rewrite this
entire expression as being equal
00:05:51.420 --> 00:05:56.420
to one minus one over the square to three,
00:05:56.990 --> 00:05:59.840
all of that over one,
00:05:59.840 --> 00:06:01.420
and then I have a negative
here and a negative here,
00:06:01.420 --> 00:06:03.030
so then that becomes, a
negative times a negative,
00:06:03.030 --> 00:06:07.330
so positive one plus one over
the square root of three.
00:06:07.330 --> 00:06:09.680
And if we multiply both the
numerator and the denominator
00:06:09.680 --> 00:06:12.450
by square root of three,
00:06:12.450 --> 00:06:14.000
what we're going to get in the numerator
00:06:14.000 --> 00:06:16.990
is square root of three minus one
00:06:16.990 --> 00:06:18.820
and then our denominator is going to be
00:06:18.820 --> 00:06:21.730
square root of three plus one.
00:06:21.730 --> 00:06:24.210
And we are done.
00:06:24.210 --> 00:06:28.353
That's tangent of 13 pi over
12 without using a calculator.
|
Interpreting solutions of trigonometric equations | https://www.youtube.com/watch?v=c-VkOXIGTqU | vtt | https://www.youtube.com/api/timedtext?v=c-VkOXIGTqU&ei=ylWUZcq3KMG-mLAP65eU4Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=04D5F379CA12FF5F66A6E7EFB93ED30B07F2F7A2.1515E86C299C79D7A5EF9D286A67E1A18E9D7896&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.090 --> 00:00:02.040
- [Instructor] Alvaro presses the treadle
00:00:02.040 --> 00:00:04.720
of a spinning wheel with his foot.
00:00:04.720 --> 00:00:08.030
It moves a bar up and down
making the wheels spin.
00:00:08.030 --> 00:00:09.950
So just to be clear what a treadle is
00:00:09.950 --> 00:00:11.670
this is an old spinning wheel
00:00:11.670 --> 00:00:14.080
and this little pedal that is a treadle.
00:00:14.080 --> 00:00:17.400
And as this goes up and down,
00:00:17.400 --> 00:00:19.320
it's gonna pull on this bar,
00:00:19.320 --> 00:00:21.650
which is then going to spin this wheel
00:00:21.650 --> 00:00:24.993
which can then be used to
essentially power the machine.
00:00:26.020 --> 00:00:27.920
So it says the function B of t
00:00:27.920 --> 00:00:32.060
models the height in centimeters
of the top of the bar
00:00:32.060 --> 00:00:36.010
when Alvaro has pressed
the treadle for t seconds.
00:00:36.010 --> 00:00:37.900
So it's telling us the height of,
00:00:37.900 --> 00:00:40.160
I can barely see where
the top of the bar is
00:00:40.160 --> 00:00:41.230
someplace over here.
00:00:41.230 --> 00:00:42.720
And this isn't exactly
00:00:42.720 --> 00:00:45.510
what they're probably talking
about in this exercise here.
00:00:45.510 --> 00:00:47.680
But this is just to
give you a visualization
00:00:47.680 --> 00:00:49.910
of what a treadle is and what the bar is
00:00:49.910 --> 00:00:53.300
and then, what the spinning wheel is.
00:00:53.300 --> 00:00:56.330
Alvaro has pressed those
treadle for t seconds.
00:00:56.330 --> 00:00:58.460
So they give us B of t right over here
00:00:58.460 --> 00:01:00.753
and 90 minus 12 times sine of 5t.
00:01:01.670 --> 00:01:02.640
The first question is,
00:01:02.640 --> 00:01:05.280
what does the solution set to y is equal
00:01:05.280 --> 00:01:10.280
to 90 minus 12 times sine of
five times six, represent?
00:01:11.710 --> 00:01:14.083
Pause this video and see if
you can think about that.
00:01:14.950 --> 00:01:15.783
All right.
00:01:15.783 --> 00:01:17.830
So, it looks like right over here,
00:01:17.830 --> 00:01:20.470
so we have the 90, 90, 12, 12
00:01:20.470 --> 00:01:25.470
and we're subtracting 12 sine
of five times t, five times t.
00:01:25.610 --> 00:01:27.853
So this right over here is t.
00:01:29.090 --> 00:01:32.960
The solution set right over here tells us
00:01:32.960 --> 00:01:36.010
what is the height, because
that's what B of t is.
00:01:36.010 --> 00:01:38.070
So B of t is equal to y.
00:01:38.070 --> 00:01:40.930
What is the height when t is equal to six?
00:01:40.930 --> 00:01:43.530
And remember, t is in seconds.
00:01:43.530 --> 00:01:44.883
So, this is height,
00:01:46.510 --> 00:01:50.060
height of top of bar,
00:01:50.060 --> 00:01:55.060
top of bar at six seconds.
00:01:56.460 --> 00:01:59.300
All right, now we have
more questions here.
00:01:59.300 --> 00:02:01.493
The next question asks us,
00:02:02.370 --> 00:02:04.970
what does the solution set to 95
00:02:04.970 --> 00:02:09.130
equals 90 minus 12 sign of 5t represent?
00:02:09.130 --> 00:02:11.363
Pause the video and think about that.
00:02:13.100 --> 00:02:13.933
All right.
00:02:13.933 --> 00:02:18.153
So here, they're saying
that B of t is equal to 95.
00:02:19.480 --> 00:02:22.541
And so, the solution set,
you're really solving for t.
00:02:22.541 --> 00:02:25.950
So you're really solving
for all of the times
00:02:25.950 --> 00:02:30.940
when our height is going
to be 95 centimeters.
00:02:30.940 --> 00:02:35.940
So all times t
00:02:35.960 --> 00:02:40.960
when height of top of bar,
00:02:41.770 --> 00:02:44.770
of top of bar
00:02:45.720 --> 00:02:48.710
at 95 centimeters.
00:02:48.710 --> 00:02:50.490
And that's going to keep happening
00:02:50.490 --> 00:02:54.930
over and over and over again
as t goes forward in time.
00:02:54.930 --> 00:02:56.840
So you're going to have a very large,
00:02:56.840 --> 00:02:58.810
you're gonna have an infinite
solution set over here.
00:02:58.810 --> 00:03:01.020
You're gonna have an
infinite number of t's
00:03:01.020 --> 00:03:04.580
at which your solution at
which the top of the bar
00:03:04.580 --> 00:03:06.423
is at 95 centimeters.
00:03:07.270 --> 00:03:08.980
Now we have another question.
00:03:08.980 --> 00:03:12.070
This one is asking us,
what does the solution set
00:03:12.070 --> 00:03:16.170
to y is equal to 90 minus 12 sine
00:03:16.170 --> 00:03:19.310
of pi over two represent?
00:03:19.310 --> 00:03:21.383
So pause the video and think about that.
00:03:22.840 --> 00:03:24.640
All right, now this is pretty interesting.
00:03:24.640 --> 00:03:29.000
We can actually evaluate
what sine of pi over two is.
00:03:29.000 --> 00:03:33.030
So sign of pi over two
radians or sign of 90 degrees
00:03:33.030 --> 00:03:35.703
that is going to be equal to one.
00:03:36.840 --> 00:03:38.450
And so, that's the maximum value
00:03:38.450 --> 00:03:41.100
that this sign over here can take on.
00:03:41.100 --> 00:03:43.950
Now, we're going to
subtract 12 times that.
00:03:43.950 --> 00:03:46.600
So this is taking on a max.
00:03:46.600 --> 00:03:49.190
Then when you subtract 12 times that
00:03:49.190 --> 00:03:52.020
this is actually the minimum
value that you can take on.
00:03:52.020 --> 00:03:55.230
You're gonna have, you can't
get any lower than this.
00:03:55.230 --> 00:04:00.103
And so, this is going to be
the lowest, the lowest height
00:04:01.910 --> 00:04:06.910
for the top of the bar.
00:04:07.730 --> 00:04:08.563
And we're done.
|
Using specific values to test for inverses | https://www.youtube.com/watch?v=EYv2EoEFRbo | vtt | https://www.youtube.com/api/timedtext?v=EYv2EoEFRbo&ei=ylWUZe7cOaG4vdIPrOu0eA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=590477C002E3FAF727DEA386F377C4D1EEFC4965.706058041CA5431D172A74EE595B2C3ED4973ABC&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.160 --> 00:00:01.450
- [Instructor] In this video,
we're gonna think about
00:00:01.450 --> 00:00:03.590
function inverses a little bit more,
00:00:03.590 --> 00:00:06.240
or whether functions are
inverses of each other,
00:00:06.240 --> 00:00:08.140
and specifically we're gonna think about
00:00:08.140 --> 00:00:10.440
can we tell that by essentially looking at
00:00:10.440 --> 00:00:14.030
a few inputs for the
functions and a few outputs?
00:00:14.030 --> 00:00:17.390
So for example, let's say we have f of x
00:00:17.390 --> 00:00:22.140
is equal to x squared plus three,
00:00:22.140 --> 00:00:27.140
and let's say that g of x
is equal to the square root,
00:00:29.410 --> 00:00:32.940
the principal root of x minus three.
00:00:32.940 --> 00:00:34.050
Pause this video and think about
00:00:34.050 --> 00:00:37.223
whether f and g are
inverses of each other.
00:00:38.870 --> 00:00:43.460
All right, now one approach
is to try out some values.
00:00:43.460 --> 00:00:47.410
So for example, let me make
a little table here for f,
00:00:47.410 --> 00:00:50.660
so this is x and then
this would be f of x.
00:00:50.660 --> 00:00:52.490
And then let me do the same thing for g.
00:00:52.490 --> 00:00:57.490
So we have x and then we have g of x.
00:00:58.020 --> 00:00:59.860
Now, first let's try a simple value.
00:00:59.860 --> 00:01:02.440
If we try out the value
one, what is f of one?
00:01:02.440 --> 00:01:04.010
Well, it's gonna be
one squared plus three.
00:01:04.010 --> 00:01:06.470
That's one plus three, that is four.
00:01:06.470 --> 00:01:11.470
So if g is an inverse of f,
then if I input four here,
00:01:12.360 --> 00:01:13.280
I should get one.
00:01:13.280 --> 00:01:15.110
Now, that wouldn't prove
that their inverses,
00:01:15.110 --> 00:01:16.660
but if it is an inverse,
we should at least
00:01:16.660 --> 00:01:17.493
be able to get that.
00:01:17.493 --> 00:01:19.290
So let's see if that's true.
00:01:19.290 --> 00:01:22.400
If we take four here,
four minus three is one.
00:01:22.400 --> 00:01:24.740
The principal root of that is one,
00:01:24.740 --> 00:01:26.090
so that's looking pretty good.
00:01:26.090 --> 00:01:27.900
Let's try one more value here.
00:01:27.900 --> 00:01:29.900
Let's try two.
00:01:29.900 --> 00:01:33.490
Two squared plus three is seven.
00:01:33.490 --> 00:01:36.033
Now let's try out seven here.
00:01:36.950 --> 00:01:39.330
Seven minus three is four.
00:01:39.330 --> 00:01:41.790
The principal root of that is two.
00:01:41.790 --> 00:01:44.650
So, so far it is looking pretty good.
00:01:44.650 --> 00:01:46.640
But then what happens if
we try a negative value?
00:01:46.640 --> 00:01:48.490
Pause the video and think about that.
00:01:49.430 --> 00:01:50.810
Let's do that.
00:01:50.810 --> 00:01:55.810
Let me put a negative two right over here.
00:01:57.340 --> 00:02:00.700
Now, if I have negative two
squared, that's positive four,
00:02:00.700 --> 00:02:03.920
plus three is seven, so I have seven here.
00:02:03.920 --> 00:02:07.430
But we already know that
when we input seven into g,
00:02:07.430 --> 00:02:09.820
we don't get negative two, we get two.
00:02:09.820 --> 00:02:12.580
In fact, there's no
way to get negative two
00:02:12.580 --> 00:02:15.100
out of this function right over here.
00:02:15.100 --> 00:02:16.860
So we have just found a case,
00:02:16.860 --> 00:02:19.340
and frankly any negative
number that you try to use
00:02:19.340 --> 00:02:21.450
would be a case where you could show
00:02:21.450 --> 00:02:24.570
that these are not inverses of each other.
00:02:24.570 --> 00:02:27.030
Not inverses.
00:02:27.030 --> 00:02:30.510
So you actually can use
specific points to determine
00:02:30.510 --> 00:02:33.110
that two functions like
this, especially functions
00:02:33.110 --> 00:02:36.240
that are defined over really
an infinite number of values,
00:02:36.240 --> 00:02:40.170
these are continuous functions,
that using specific points,
00:02:40.170 --> 00:02:43.270
you can show examples where
they are not inverses,
00:02:43.270 --> 00:02:45.260
but you actually can't use specific points
00:02:45.260 --> 00:02:46.880
to prove that they are inverses
00:02:46.880 --> 00:02:50.030
because there's an
infinite number of values
00:02:50.030 --> 00:02:51.360
that you could input into these functions,
00:02:51.360 --> 00:02:52.520
and there's no way that
you're going to be able
00:02:52.520 --> 00:02:54.070
to try out every value.
00:02:54.070 --> 00:02:58.490
For example, if I were
to tell you that h of x,
00:02:58.490 --> 00:03:01.680
really simple functions,
h of x is equal to four x,
00:03:01.680 --> 00:03:06.680
and let's say that j of x
is equal to x over four.
00:03:07.070 --> 00:03:09.350
We know that these are
inverse of each other.
00:03:09.350 --> 00:03:12.360
We'll prove it in other
ways in future videos,
00:03:12.360 --> 00:03:16.054
but you can't try every single input here
00:03:16.054 --> 00:03:19.560
and look at every single output,
and every single input here
00:03:19.560 --> 00:03:20.930
and every single output.
00:03:20.930 --> 00:03:23.620
So we need some other technique
other than just looking
00:03:23.620 --> 00:03:26.910
at specific values to
prove that two functions
00:03:26.910 --> 00:03:28.190
are inverses of each other.
00:03:28.190 --> 00:03:30.300
Although you can use
specific values to prove
00:03:30.300 --> 00:03:32.350
that they are not inverses of each other.
|
Verifying inverse functions from tables | https://www.youtube.com/watch?v=UTUuyCXFAs4 | vtt | https://www.youtube.com/api/timedtext?v=UTUuyCXFAs4&ei=ylWUZc33KuGwp-oPgviqUA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1F5A2563305551AB995234A53B226ABF9E43009C.BDFA14AD9EF19DC67F24B571DBBB4DE73C5C16B2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.190 --> 00:00:01.800
- [Instructor] We're told
the following tables,
00:00:01.800 --> 00:00:04.270
give all of the input output pairs
00:00:04.270 --> 00:00:06.030
for the functions S and T.
00:00:06.030 --> 00:00:09.180
So we see this first table
here, we have some Xs
00:00:09.180 --> 00:00:12.020
and then they tell us what
the corresponding S of X is.
00:00:12.020 --> 00:00:14.460
And then in this table
that we have some Xs
00:00:14.460 --> 00:00:17.170
and they tell us the corresponding T of X.
00:00:17.170 --> 00:00:20.400
It says complete the table
for the composite function,
00:00:20.400 --> 00:00:25.310
S of T of X, we wanna fill
in these five entries here.
00:00:25.310 --> 00:00:28.700
And then they ask us our S and T inverses.
00:00:28.700 --> 00:00:31.430
So pause this video and see
if you can figure this out
00:00:31.430 --> 00:00:33.780
on your own before we
work through it together.
00:00:34.900 --> 00:00:37.500
All right, now let's work
through this together.
00:00:37.500 --> 00:00:38.780
So let's just remind ourselves
00:00:38.780 --> 00:00:41.510
what's going on with a
composite function like this.
00:00:41.510 --> 00:00:44.190
So you're going to take some X value
00:00:44.190 --> 00:00:46.230
and it looks like we're
first going to put it
00:00:46.230 --> 00:00:51.230
into the function T, that
is going to output T of X.
00:00:53.200 --> 00:00:55.630
And then we're gonna take
that output, take that T of X,
00:00:55.630 --> 00:00:59.020
and then it will be the input into S.
00:00:59.020 --> 00:01:01.600
So then we're gonna input that into S
00:01:01.600 --> 00:01:05.140
and then that would output
S of what we inputted
00:01:05.140 --> 00:01:08.170
which in this case is T of X.
00:01:08.170 --> 00:01:09.410
So let's go on that journey.
00:01:09.410 --> 00:01:11.820
So what we're gonna do is
first take these numbers,
00:01:11.820 --> 00:01:16.170
put them into the function,
T figure out what it outputs
00:01:16.170 --> 00:01:17.100
and then take that output
00:01:17.100 --> 00:01:19.480
and then put it into the function S,
00:01:19.480 --> 00:01:21.400
it's going to be a fun little ride.
00:01:21.400 --> 00:01:23.830
All right, so when X is equal to 12,
00:01:23.830 --> 00:01:26.830
we're gonna put it into
our function T first.
00:01:26.830 --> 00:01:29.660
So when X is an input into T
00:01:29.660 --> 00:01:32.710
the output is equal to negative one.
00:01:32.710 --> 00:01:35.850
So that's our T of X, and there
we're take this negative one
00:01:35.850 --> 00:01:39.460
and input it into S, so negative one here.
00:01:39.460 --> 00:01:44.010
And when you input that into
S you get as the output,
00:01:44.010 --> 00:01:48.320
S of negative one is 12,
so S of T of X is 12.
00:01:48.320 --> 00:01:52.070
So interestingly, this is 12.
00:01:52.070 --> 00:01:54.580
Now let's do the next one.
00:01:54.580 --> 00:01:59.580
So when we input 18 into
T, so the 18 is the input.
00:01:59.810 --> 00:02:03.000
The T of X, T of 18 is two.
00:02:03.000 --> 00:02:06.780
And then if we wanna do, if
we wanna input that into S,
00:02:06.780 --> 00:02:11.580
so this is gonna be the input
into S, the output is 18.
00:02:11.580 --> 00:02:16.180
Very interesting,
alright, let's keep going.
00:02:16.180 --> 00:02:21.180
So when we input 61 into
T, the output is eight.
00:02:21.890 --> 00:02:26.210
Then when we take eight
and we input it into S of X
00:02:26.210 --> 00:02:29.670
or S of eight I should
say, is going to be 61.
00:02:29.670 --> 00:02:33.060
All right, things are looking good so far
00:02:33.060 --> 00:02:35.370
and I'm running out of
colors, I'll do green.
00:02:35.370 --> 00:02:39.000
So when we take 70 and we input it into T,
00:02:39.000 --> 00:02:44.000
T of 7O is seven, when you
take seven and input it into S
00:02:45.740 --> 00:02:49.030
you get 70, all right.
00:02:49.030 --> 00:02:53.270
And then one last one I
will do in this blue color.
00:02:53.270 --> 00:02:58.270
When you take 100, input it
into T it outputs negative five
00:02:59.100 --> 00:03:04.100
you take negative five
input into S you get 100.
00:03:04.750 --> 00:03:08.500
So in every situation
that we have looked at
00:03:08.500 --> 00:03:11.420
right over here, in all
of these situations,
00:03:11.420 --> 00:03:16.420
we see that S of T of X is equal to X,
00:03:19.610 --> 00:03:22.320
which inclines us to believe
that they are inverses.
00:03:22.320 --> 00:03:24.360
Remember if these two are
inverses of each other,
00:03:24.360 --> 00:03:28.580
this would be true and also T of S of X
00:03:28.580 --> 00:03:30.760
is going to be equal to X.
00:03:30.760 --> 00:03:33.560
But we don't really know 100%
00:03:33.560 --> 00:03:36.750
unless we know that we have
looked at every combination
00:03:36.750 --> 00:03:39.440
in the domains for each of them.
00:03:39.440 --> 00:03:42.030
Now, when you look at these,
the two tables up here
00:03:42.030 --> 00:03:44.010
and I could have done this,
this is the one we looked at
00:03:44.010 --> 00:03:46.090
on our journey to get to
this 12 right over here.
00:03:46.090 --> 00:03:49.760
The following table gives
all of the input output pairs
00:03:49.760 --> 00:03:51.470
for the function S and T.
00:03:51.470 --> 00:03:55.890
So this right over here is
the domain for the function S
00:03:55.890 --> 00:04:00.320
and this right over here is
the domain for the function T.
00:04:00.320 --> 00:04:04.160
So because for every
member of the function S,
00:04:04.160 --> 00:04:06.470
every member of the
domain of the function S,
00:04:06.470 --> 00:04:09.440
the corresponding output right over there
00:04:09.440 --> 00:04:12.790
is the domain for the function T
00:04:12.790 --> 00:04:14.750
and it takes us back to where we began.
00:04:14.750 --> 00:04:16.750
And then the opposite is true as well,
00:04:16.750 --> 00:04:21.430
for every member of the
domain of T, what it outputs,
00:04:21.430 --> 00:04:24.470
that is the all of the
possible inputs for X
00:04:24.470 --> 00:04:26.890
and they all take us
back to where we began.
00:04:26.890 --> 00:04:30.043
So yes, the functions are inverses.
|
Reading inverse values from a table | https://www.youtube.com/watch?v=ygVpyyASavk | vtt | https://www.youtube.com/api/timedtext?v=ygVpyyASavk&ei=ylWUZYz6MqnKp-oPlZW_2A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0144957055D35E7ED8587A0B35A0CF88EE7307B3.7C323A2467BD90DB759B4EF85A978A50370581C6&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.220 --> 00:00:01.500
- [Instructor] We're
told the following table
00:00:01.500 --> 00:00:05.110
shows a few inputs and outputs
of function G, all right.
00:00:05.110 --> 00:00:07.550
We have some possible inputs here for X
00:00:07.550 --> 00:00:10.530
and then the corresponding
outputs here, G of X.
00:00:10.530 --> 00:00:13.783
What is the value of G inverse of 54?
00:00:14.870 --> 00:00:16.800
So pause this video and see
if you can figure that out
00:00:16.800 --> 00:00:19.330
before we work through it together.
00:00:19.330 --> 00:00:20.163
All right.
00:00:20.163 --> 00:00:21.130
Let's just remind ourselves
00:00:21.130 --> 00:00:23.710
what an inverse function even does.
00:00:23.710 --> 00:00:26.910
So if you have some
value, X and you input it
00:00:26.910 --> 00:00:29.560
into some function, G,
00:00:29.560 --> 00:00:32.860
that function is going to output G of X.
00:00:32.860 --> 00:00:35.730
And an inverse function
takes us the other way.
00:00:35.730 --> 00:00:37.050
We could take this
00:00:37.050 --> 00:00:39.790
what was the output of G, G of X.
00:00:39.790 --> 00:00:43.140
We can input that into
an inverse function.
00:00:43.140 --> 00:00:44.750
The inverse function of G
00:00:44.750 --> 00:00:48.290
and that is actually going to give us X.
00:00:48.290 --> 00:00:50.610
It's going to get us back
to our original input
00:00:50.610 --> 00:00:51.930
right over here.
00:00:51.930 --> 00:00:55.860
So what we're focused on right
over here is G inverse of 54.
00:00:55.860 --> 00:00:57.584
So we can think about this part
00:00:57.584 --> 00:01:00.400
of this little chain that we set up.
00:01:00.400 --> 00:01:05.400
So what we're inputting into
this inverse function is 54.
00:01:05.540 --> 00:01:08.150
So what we want to say is, all right,
00:01:08.150 --> 00:01:11.800
when G of X is equal to 54, what is X?
00:01:11.800 --> 00:01:13.010
And we can see that right over here.
00:01:13.010 --> 00:01:17.530
When G of X is 54, the
corresponding input, original input,
00:01:17.530 --> 00:01:19.900
one way to think about it, is 62.
00:01:19.900 --> 00:01:21.940
So this will be equal to 62.
00:01:21.940 --> 00:01:24.450
Now some of you might have been
tempted to say, okay, look.
00:01:24.450 --> 00:01:27.420
It looks like I'm inputting
a 54 into a function.
00:01:27.420 --> 00:01:29.270
So I'll say, okay, X is the input.
00:01:29.270 --> 00:01:33.130
Let me just go to 54 right
over there as the input.
00:01:33.130 --> 00:01:38.130
But remember, this 54 isn't an
input into the inverse of G.
00:01:38.250 --> 00:01:40.550
This is an input into G of X.
00:01:40.550 --> 00:01:43.030
So if you wanted to evaluate this,
00:01:43.030 --> 00:01:46.753
if you wanted to evaluate G of 54,
00:01:47.660 --> 00:01:49.830
then you would look at the
54 up here and say, okay,
00:01:49.830 --> 00:01:52.140
that's going to be equal to 65.
00:01:52.140 --> 00:01:54.850
But we're looking at the inverse of G.
00:01:54.850 --> 00:01:59.700
So one way to think about it
is when 54 is the output in G,
00:02:00.540 --> 00:02:02.360
what is going to be the input?
00:02:02.360 --> 00:02:04.473
And we see that that is 62.
|
Meaningfully composing functions | https://www.youtube.com/watch?v=q9JGGVXdl9I | vtt | https://www.youtube.com/api/timedtext?v=q9JGGVXdl9I&ei=ylWUZfLAIrqAp-oPnpSosAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8FD6475345366303FFC07D2C56455882C39883A6.6AB19FD87888DB8A68DCF268168C4AF6CEDA58D7&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.240 --> 00:00:02.040
- [Instructor] We're
told that Jaylen modeled
00:00:02.040 --> 00:00:05.040
the following relationships
about their bus ride.
00:00:05.040 --> 00:00:06.510
So there's three functions here.
00:00:06.510 --> 00:00:08.520
We have their inputs, and
we have their outputs.
00:00:08.520 --> 00:00:12.350
So function P, the input is
the time the bus arrives,
00:00:12.350 --> 00:00:14.000
given as lowercase b,
00:00:14.000 --> 00:00:16.460
and the output is the
probability that Jaylen
00:00:16.460 --> 00:00:18.210
gets to work on time.
00:00:18.210 --> 00:00:20.440
So P of b, all right.
00:00:20.440 --> 00:00:24.160
Function N, the input is
the time the bus arrives,
00:00:24.160 --> 00:00:25.330
given as k,
00:00:25.330 --> 00:00:28.350
and the output is the number
of people at the bus stop
00:00:28.350 --> 00:00:29.580
when the bus arrives.
00:00:29.580 --> 00:00:31.110
So it's the number of
people at the bus stop
00:00:31.110 --> 00:00:34.450
as a function of the time the bus arrives.
00:00:34.450 --> 00:00:37.430
And then T, centimeters of precipitation,
00:00:37.430 --> 00:00:41.910
the input is centimeters of
precipitation per hour, x.
00:00:41.910 --> 00:00:44.560
And this gives us the time the bus arrives
00:00:44.560 --> 00:00:46.570
as a function of that precipitation.
00:00:46.570 --> 00:00:47.860
Interesting.
00:00:47.860 --> 00:00:50.580
Now, they ask us which of the
following composed functions
00:00:50.580 --> 00:00:52.360
makes sense in this context?
00:00:52.360 --> 00:00:53.670
And we have to pick two.
00:00:53.670 --> 00:00:56.510
So pause this video and see
if you can have a go at it
00:00:56.510 --> 00:00:58.260
before we work through it together.
00:00:59.110 --> 00:01:00.360
All right, now let's look
00:01:00.360 --> 00:01:03.020
at this first composite function here.
00:01:03.020 --> 00:01:04.180
So let's see what's going on.
00:01:04.180 --> 00:01:07.570
One way to think about
this is we're taking x,
00:01:07.570 --> 00:01:11.310
we are inputting that
into our function, T,
00:01:11.310 --> 00:01:14.400
that will then output T of x,
00:01:14.400 --> 00:01:16.080
and then we're trying to input that
00:01:16.080 --> 00:01:19.030
into our function P,
00:01:19.030 --> 00:01:21.880
which would then output P of the input,
00:01:21.880 --> 00:01:24.250
which is T of x.
00:01:24.250 --> 00:01:25.690
Now, does this make sense?
00:01:25.690 --> 00:01:29.860
X is the centimeters of
precipitation per hour.
00:01:29.860 --> 00:01:34.140
T of x is a time the bus
arrives as a function of that.
00:01:34.140 --> 00:01:35.960
So we're gonna take the
time the bus arrives,
00:01:35.960 --> 00:01:38.980
is that a reasonable input into P?
00:01:38.980 --> 00:01:39.990
Well, let's see, function P,
00:01:39.990 --> 00:01:42.370
the input is the time the bus arrives.
00:01:42.370 --> 00:01:43.800
So this makes a lot of sense.
00:01:43.800 --> 00:01:46.230
We're taking this, which
is a time the bus arrives,
00:01:46.230 --> 00:01:48.100
and we're using that as an input into P,
00:01:48.100 --> 00:01:51.220
which is exactly what we
want to be the input into P.
00:01:51.220 --> 00:01:54.170
And so we have P as a function
of the time the bus arrives,
00:01:54.170 --> 00:01:55.450
which is then a function
00:01:55.450 --> 00:01:58.950
of the centimeters of
precipitation per hour.
00:01:58.950 --> 00:02:02.270
So I like this choice right over there.
00:02:02.270 --> 00:02:03.810
Now let's look at the next choice.
00:02:03.810 --> 00:02:07.780
P as a function of N of k.
00:02:07.780 --> 00:02:10.420
Let's see, so we're taking k,
00:02:10.420 --> 00:02:13.320
which is the time the bus arrives,
00:02:13.320 --> 00:02:17.320
we're inputting it into the function N,
00:02:17.320 --> 00:02:19.900
which then outputs N of k.
00:02:19.900 --> 00:02:21.430
Now the output here, N of k,
00:02:21.430 --> 00:02:23.530
is the number of people at the bus stop
00:02:23.530 --> 00:02:25.260
when the bus arrives.
00:02:25.260 --> 00:02:30.200
And then we're trying to put
that into our function P.
00:02:30.200 --> 00:02:32.940
Now, does that make sense
to take the number of people
00:02:32.940 --> 00:02:34.830
at the bus stop when the bus arrives
00:02:34.830 --> 00:02:37.960
and input it into a function
that expects as the input
00:02:37.960 --> 00:02:40.510
the time the bus arrives?
00:02:40.510 --> 00:02:42.570
That does not make sense.
00:02:42.570 --> 00:02:45.420
P wants as an input time the bus arrives,
00:02:45.420 --> 00:02:48.290
but we're giving it the number
of people at the bus stop.
00:02:48.290 --> 00:02:50.910
So I do not like this choice.
00:02:50.910 --> 00:02:54.190
Now let's look at choice C.
00:02:54.190 --> 00:02:56.500
So T of x, right over here,
00:02:56.500 --> 00:03:00.410
we already know that outputs
the time the bus arrives,
00:03:00.410 --> 00:03:04.000
which we know is a legitimate
input into function N.
00:03:04.000 --> 00:03:05.970
Function N takes the time the bus arrives
00:03:05.970 --> 00:03:08.180
and as a function, and
based on that input,
00:03:08.180 --> 00:03:10.190
it gives you the number
of people at the bus stop.
00:03:10.190 --> 00:03:11.350
So this makes sense.
00:03:11.350 --> 00:03:13.230
So I like this choice as well.
00:03:13.230 --> 00:03:15.290
So I'm guessing I won't like choice D,
00:03:15.290 --> 00:03:16.870
but let me validate that.
00:03:16.870 --> 00:03:18.690
So P of b.
00:03:18.690 --> 00:03:21.690
So this is going to
give us the probability
00:03:21.690 --> 00:03:23.490
that Jaylen gets to work on time,
00:03:23.490 --> 00:03:26.530
and then we're inputting
that into this function, T,
00:03:26.530 --> 00:03:29.410
that's expecting centimeters
of precipitation per hour.
00:03:29.410 --> 00:03:30.930
Well, that's not going to work out.
00:03:30.930 --> 00:03:32.460
You're trying to take a probability
00:03:32.460 --> 00:03:34.370
and you're inputting it into a function
00:03:34.370 --> 00:03:36.980
that expects centimeters
of precipitation per hour,
00:03:36.980 --> 00:03:38.870
so I would rule that one out as well.
00:03:38.870 --> 00:03:39.770
So I like A and C.
|
Finding the whole with a tape diagram | https://www.youtube.com/watch?v=M0vf7idRTLA | vtt | https://www.youtube.com/api/timedtext?v=M0vf7idRTLA&ei=ylWUZbuNM-mMp-oP7oekIA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=482DECA7D6EB29FAE82103C44A19EB0684736538.7B1F4012B966D157C4E0BCD4699C4A0D12C03277&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.370 --> 00:00:01.450
- [Instructor] We are told that Keisha
00:00:01.450 --> 00:00:03.920
can run 170 meters in one minute.
00:00:03.920 --> 00:00:07.060
This is 125% of the distance
00:00:07.060 --> 00:00:10.260
that she could run in one
minute three years ago.
00:00:10.260 --> 00:00:13.860
How far could Keisha run in
one minute three years ago?
00:00:13.860 --> 00:00:16.703
Pause this video, and see
if you can figure this out.
00:00:18.110 --> 00:00:19.650
All right, now let's do it together.
00:00:19.650 --> 00:00:22.450
And my brain wants to make
sure I know the difference
00:00:22.450 --> 00:00:27.450
between three years ago and today.
00:00:29.170 --> 00:00:34.170
So today, she can run
170 meters in one minute.
00:00:35.590 --> 00:00:36.540
And what we want to figure out
00:00:36.540 --> 00:00:40.790
is how much could she run in
one minute three years ago?
00:00:40.790 --> 00:00:45.790
Well, we know this 170 meters
is 125% of the distance
00:00:46.080 --> 00:00:47.690
that she could do three years ago.
00:00:47.690 --> 00:00:49.440
And the distance she
could do three years ago,
00:00:49.440 --> 00:00:51.840
of course, is 100% of the distance
00:00:51.840 --> 00:00:52.920
that she could do three years ago,
00:00:52.920 --> 00:00:55.750
because it's the exact same distance.
00:00:55.750 --> 00:00:58.290
But I like to think in terms of fractions.
00:00:58.290 --> 00:01:03.290
So 125%, I could rewrite
that as 125 over 100.
00:01:04.350 --> 00:01:07.860
If I divide both the numerator
and the denominator by 25,
00:01:07.860 --> 00:01:10.810
this is equivalent to five over four.
00:01:10.810 --> 00:01:12.740
So that 170 meters,
00:01:12.740 --> 00:01:15.433
that is five-fourths of what
she could do three years ago.
00:01:15.433 --> 00:01:17.080
And what you could do three years ago
00:01:17.080 --> 00:01:19.532
would be four-fourths of what
she could do three years ago,
00:01:19.532 --> 00:01:21.830
because that's 100%.
00:01:21.830 --> 00:01:25.100
And so to figure out if
five-fourths is 170 meters,
00:01:25.100 --> 00:01:26.760
what is four-fourths?
00:01:26.760 --> 00:01:30.463
Let us set up a tape
diagram right over here.
00:01:31.370 --> 00:01:34.640
And I'm going to try to hand
draw it as best as I can.
00:01:34.640 --> 00:01:37.550
I want to make five equal sections.
00:01:37.550 --> 00:01:38.700
And I know it's not exactly,
00:01:38.700 --> 00:01:40.840
but let's say for the sake
of argument for this video,
00:01:40.840 --> 00:01:42.400
this is five equal sections.
00:01:42.400 --> 00:01:44.720
And so if we imagine that
each of these are a fourth,
00:01:44.720 --> 00:01:46.120
this is five-fourths.
00:01:46.120 --> 00:01:48.340
And then this distance right over here
00:01:48.340 --> 00:01:50.720
is going to be 170 meters.
00:01:50.720 --> 00:01:52.220
That's what she could run today.
00:01:52.220 --> 00:01:54.830
And what we want to do is
figure out what is four-fourths?
00:01:54.830 --> 00:01:57.610
That's the distance that
she could run in one minute
00:01:57.610 --> 00:01:58.960
three years ago.
00:01:58.960 --> 00:02:01.090
So this is our question mark.
00:02:01.090 --> 00:02:01.923
Well to do that,
00:02:01.923 --> 00:02:05.340
we just have to figure out how
big is each of these fourths?
00:02:05.340 --> 00:02:08.070
And if five of them is 170 meters,
00:02:08.070 --> 00:02:12.550
well, I just have to divide five into 170.
00:02:12.550 --> 00:02:15.010
Five goes into 17 three times.
00:02:15.010 --> 00:02:17.180
Three times five is 15.
00:02:17.180 --> 00:02:21.710
Subtract, I get a two
here, bring down the zero.
00:02:21.710 --> 00:02:23.760
Five goes into 20 four times.
00:02:23.760 --> 00:02:27.640
Four times five is 20, and
it works out perfectly.
00:02:27.640 --> 00:02:32.220
So each of these
five-fourths are 34 meters.
00:02:32.220 --> 00:02:37.220
34 meters, 34 meters, 34 meters,
34 meters, and 34 meters.
00:02:38.400 --> 00:02:40.900
And so the distance that she
could run three years ago
00:02:40.900 --> 00:02:42.660
is going to be four of these fourths,
00:02:42.660 --> 00:02:45.020
or four of these 34 meters.
00:02:45.020 --> 00:02:50.020
So 34 times four, four times four is 16,
00:02:50.720 --> 00:02:54.350
three times four is 12, plus one is 13.
00:02:54.350 --> 00:02:56.640
So the mystery distance that
she could run in one minute
00:02:56.640 --> 00:03:01.090
three years ago is 136 meters.
00:03:01.090 --> 00:03:02.823
And we are done.
|
Finding percentages with a double number line | https://www.youtube.com/watch?v=bVNnQX5nEFg | vtt | https://www.youtube.com/api/timedtext?v=bVNnQX5nEFg&ei=ylWUZbX_MoXKp-oP98SnkAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8E98547EC7686DFD96945C575723322F3E88F7A7.9EBE0600D7A28A5E4A76EA4BAD96CF8B3C8D4AE8&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.250 --> 00:00:01.790
- [Instructor] We're
told that Omar's class
00:00:01.790 --> 00:00:03.580
has 28 students in it.
00:00:03.580 --> 00:00:06.530
21 of them take the bus to school.
00:00:06.530 --> 00:00:09.620
What percentage of the
students in Omar's class
00:00:09.620 --> 00:00:11.550
take the bus to school?
00:00:11.550 --> 00:00:14.403
Pause this video, and see
if you can figure that out.
00:00:15.750 --> 00:00:18.540
All right, well, I'm going
to try to visualize this
00:00:18.540 --> 00:00:22.830
with what we call a double number line.
00:00:22.830 --> 00:00:24.960
So let's say that is zero,
00:00:24.960 --> 00:00:28.540
and 28 is the total number of students
00:00:28.540 --> 00:00:30.840
in this classroom right over here.
00:00:30.840 --> 00:00:32.060
As a double number line,
00:00:32.060 --> 00:00:33.630
because I'm going to
make another number line
00:00:33.630 --> 00:00:34.920
right below it.
00:00:34.920 --> 00:00:38.570
But I'm going to write these
points in terms of percentages.
00:00:38.570 --> 00:00:41.090
So zero students would be 0%
00:00:41.090 --> 00:00:43.610
of the students in Omar's class,
00:00:43.610 --> 00:00:48.530
and 28 students would be 100%
00:00:48.530 --> 00:00:51.100
of the students in Omar's class.
00:00:51.100 --> 00:00:53.990
And so what we really need to do now is,
00:00:53.990 --> 00:00:56.910
we know that 21 of them take the bus.
00:00:56.910 --> 00:01:00.830
21 is going to be roughly around here.
00:01:00.830 --> 00:01:02.200
So that's 21.
00:01:02.200 --> 00:01:04.010
So we really just need to figure out,
00:01:04.010 --> 00:01:06.970
is what percentage is this going to be?
00:01:06.970 --> 00:01:11.310
One way to think about it is
what fraction is 21 of 28?
00:01:11.310 --> 00:01:13.683
Well, if I write 21 over 28,
00:01:14.860 --> 00:01:16.660
we know that we can
divide both the numerator
00:01:16.660 --> 00:01:18.720
and the denominator by seven,
00:01:18.720 --> 00:01:20.080
they're both divisible by seven,
00:01:20.080 --> 00:01:23.400
21 divided by seven is three,
00:01:23.400 --> 00:01:27.070
and 28 divided by seven is four.
00:01:27.070 --> 00:01:31.350
So 21 is three-fourths of 28.
00:01:31.350 --> 00:01:33.190
So let's divide this number line
00:01:33.190 --> 00:01:35.500
from zero to 28 into fourths.
00:01:35.500 --> 00:01:37.310
So that would be halfway,
00:01:37.310 --> 00:01:40.220
and now we have it divided into fourths,
00:01:40.220 --> 00:01:45.100
and we can see that 21 is one,
two, three of these fourths.
00:01:45.100 --> 00:01:48.010
Well, if 21 is three-fourths
of the way to 28,
00:01:48.010 --> 00:01:50.070
then whatever percentage this is here,
00:01:50.070 --> 00:01:52.630
that would be three-fourths
of the way to 100.
00:01:52.630 --> 00:01:55.740
So let's divide this into fourths as well.
00:01:55.740 --> 00:01:59.560
Now we know that one-fourth of 100 is 25%.
00:01:59.560 --> 00:02:02.220
Two-fourths of 100 is 50%.
00:02:02.220 --> 00:02:05.910
Three-fourths of 100 is 75%.
00:02:05.910 --> 00:02:07.860
So what percentage of the
students in Omar's class
00:02:07.860 --> 00:02:09.300
take the bus to school?
00:02:09.300 --> 00:02:11.213
75%.
|
Ways to rewrite a percentage | https://www.youtube.com/watch?v=MD5JUwAeg6c | vtt | https://www.youtube.com/api/timedtext?v=MD5JUwAeg6c&ei=ylWUZdT_Mqmhp-oPtaO8uAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A1756C9134AD5DDA786DD43BCC9D0BD593E56B17.5CD62F279417A0CE321E871616FC85391B2D3A52&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.420 --> 00:00:02.390
- [Instructor] We're asked
which of the following options
00:00:02.390 --> 00:00:07.050
have the same value as 2% of 90?
00:00:07.050 --> 00:00:09.130
Pause this video, and see
if you can figure it out.
00:00:09.130 --> 00:00:13.720
And as a reminder, they
say, pick two answers.
00:00:13.720 --> 00:00:16.320
All right, now let's work
through this together.
00:00:16.320 --> 00:00:18.110
So before I even look at the choices,
00:00:18.110 --> 00:00:20.160
I'm just going to try to
think of all of the ways
00:00:20.160 --> 00:00:23.810
that I can write 2% of 90.
00:00:23.810 --> 00:00:25.860
2%, this right over here,
00:00:25.860 --> 00:00:28.540
this literally means two per 100.
00:00:28.540 --> 00:00:32.530
So I could view it as the
same thing as two over 100,
00:00:32.530 --> 00:00:36.610
times 90, that's one
way to write 2% of 90.
00:00:36.610 --> 00:00:37.560
Two over a 100,
00:00:37.560 --> 00:00:41.400
I can divide both the numerator
and the denominator by two.
00:00:41.400 --> 00:00:43.700
And so two over a 100
is also the same thing
00:00:43.700 --> 00:00:45.320
as one over 50.
00:00:45.320 --> 00:00:50.320
And so it could also be
one over 50, times 90.
00:00:50.440 --> 00:00:52.880
Now let's see what other
choices they have here.
00:00:52.880 --> 00:00:54.910
Well, I could also write 2% as a decimal.
00:00:54.910 --> 00:00:58.300
Two-hundredths should
be written like this.
00:00:58.300 --> 00:01:00.900
Zero point, this is the tenths place.
00:01:00.900 --> 00:01:03.730
I have no tenths, but
I have two-hundredths.
00:01:03.730 --> 00:01:06.100
So I'm multiplying that by 90.
00:01:06.100 --> 00:01:07.570
All of these right over here
00:01:07.570 --> 00:01:11.630
are equivalent to the 2%, 2% of 90.
00:01:11.630 --> 00:01:13.470
All right, now let's look at the choices.
00:01:13.470 --> 00:01:16.260
This is 0.2 times 90.
00:01:16.260 --> 00:01:17.550
This is not 2%.
00:01:17.550 --> 00:01:20.790
This actually would be two-tenths, or 20%.
00:01:20.790 --> 00:01:22.793
So let me rule that one out.
00:01:23.650 --> 00:01:24.490
This one right over here.
00:01:24.490 --> 00:01:27.260
This is two-hundredths times 90.
00:01:27.260 --> 00:01:28.380
We already wrote that down.
00:01:28.380 --> 00:01:29.773
I like this choice.
00:01:30.950 --> 00:01:33.330
200 times 90.
00:01:33.330 --> 00:01:36.520
No, that would be far larger
than what we are looking for.
00:01:36.520 --> 00:01:38.470
We are looking for two-hundredths,
00:01:38.470 --> 00:01:40.930
not two hundreds times 90,
00:01:40.930 --> 00:01:43.210
so definitely rule that one out.
00:01:43.210 --> 00:01:45.020
Two times 90.
00:01:45.020 --> 00:01:49.640
Well, no, we're looking for
2% of 90, not two times 90.
00:01:49.640 --> 00:01:51.560
Once again, this is too large.
00:01:51.560 --> 00:01:54.640
And then we have two-hundredths times 90,
00:01:54.640 --> 00:01:56.430
which is the first thing that we wrote.
00:01:56.430 --> 00:01:59.033
And so I like this choice as well.
|
Khan Academy Ed Talks with Judy Heumann | https://www.youtube.com/watch?v=X07839HOgV4 | vtt | https://www.youtube.com/api/timedtext?v=X07839HOgV4&ei=ylWUZYTQILC6vdIPz9G8iAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A8087D973BB5556E665DA3CA9FFB0076D3A2E97A.F06D973FB75EB19ABECBD8D9AAA0D0097C48F30D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.270 --> 00:00:04.940
- Hello, and welcome to Ed
Talks with Khan Academy.
00:00:04.940 --> 00:00:07.450
I'm Kristen DiCerbo, the
chief learning officer
00:00:07.450 --> 00:00:08.440
here at Khan Academy.
00:00:08.440 --> 00:00:12.540
And today I am excited
to welcome Judy Heumann,
00:00:12.540 --> 00:00:16.110
who is an international
disability rights activists.
00:00:16.110 --> 00:00:18.169
And look forward to talking
to her about her work
00:00:18.169 --> 00:00:21.610
and how we can help
learners with disabilities
00:00:21.610 --> 00:00:24.560
succeed in the education space.
00:00:24.560 --> 00:00:25.930
Before we get started,
00:00:25.930 --> 00:00:30.250
I wanna remind you that
Khan Academy is a non-profit
00:00:30.250 --> 00:00:32.620
and we are able to continue to do our work
00:00:32.620 --> 00:00:35.170
thanks to donations from folks like you.
00:00:35.170 --> 00:00:39.440
If you are able to, we
appreciate every dollar
00:00:39.440 --> 00:00:40.890
that you are able to give.
00:00:40.890 --> 00:00:43.360
If you go to khanacademy.org/donate,
00:00:43.360 --> 00:00:47.380
you will find an easy ways
to make those donations.
00:00:47.380 --> 00:00:50.770
In addition, we want
to thank some companies
00:00:50.770 --> 00:00:53.950
who helped us during the COVID-19 crisis
00:00:53.950 --> 00:00:57.330
to continue to maintain the
quality content that we offer.
00:00:57.330 --> 00:01:01.730
And those include Bank of
America, AT&T, Google.org,
00:01:01.730 --> 00:01:05.663
Novartis, Fastly, and
General Motors. Thank you.
00:01:07.244 --> 00:01:11.970
Next if you want to listen
to other guests we've had,
00:01:11.970 --> 00:01:15.400
or to relisten to this
episode in an audio version,
00:01:15.400 --> 00:01:20.040
you can find a podcast
version of our Ed Talks
00:01:20.040 --> 00:01:23.920
in homeroom chats under Homeroom
with Sal the, the podcast.
00:01:23.920 --> 00:01:27.203
So take a look for that
wherever you get your podcasts.
00:01:28.711 --> 00:01:33.600
As I said today, I am excited
to welcome Judy Heumann.
00:01:33.600 --> 00:01:36.720
She is an international
disability rights activist.
00:01:36.720 --> 00:01:41.180
She's also an author, she's
written more than one book,
00:01:41.180 --> 00:01:44.700
but her latest is "Rolling
Warrior: The Incredible,
00:01:44.700 --> 00:01:48.370
Sometimes Awkward, True Story
of a Rebel Girl on Wheels
00:01:48.370 --> 00:01:50.740
Who Helped Spark a Revolution."
00:01:50.740 --> 00:01:54.620
And this is a book even for
kids who are about 10 years old.
00:01:54.620 --> 00:01:55.590
So that's a good space.
00:01:55.590 --> 00:01:58.797
If you have kids on your holiday lists,
00:01:58.797 --> 00:02:03.110
take a look for this option. Welcome Judy.
00:02:03.110 --> 00:02:05.163
- Hi, so happy to be with you.
00:02:06.150 --> 00:02:09.713
- Thanks for joining us. (indistinct)
00:02:10.580 --> 00:02:14.950
- Yeah. I was gonna say,
in addition to that book,
00:02:14.950 --> 00:02:18.457
the original book, which came out in 2020
00:02:20.750 --> 00:02:23.460
is for adults and it's called,
00:02:23.460 --> 00:02:25.750
it's not that there's
anything pornographic in it,
00:02:25.750 --> 00:02:29.919
it's just the writing is more for adults.
00:02:29.919 --> 00:02:34.320
So it's called "Being
Heumann: An Unrepentant Memoir
00:02:34.320 --> 00:02:36.450
of a Disability Rights Activist."
00:02:36.450 --> 00:02:40.470
And one of the differences
between this book
00:02:40.470 --> 00:02:42.450
and the "Rolling Warrior"
00:02:42.450 --> 00:02:47.030
is we had a group of
young people work with us
00:02:47.030 --> 00:02:51.300
on the transition from the
adult book to the youth book.
00:02:51.300 --> 00:02:53.100
And so you'll see,
00:02:53.100 --> 00:02:56.260
not only is the cover different,
the title is different,
00:02:56.260 --> 00:02:59.300
the layout is different, the
chapter names are different.
00:02:59.300 --> 00:03:01.850
The story is essentially the same,
00:03:01.850 --> 00:03:04.230
but it's for a younger reading audience.
00:03:04.230 --> 00:03:08.853
And then for all of you
who are Japanese readers,
00:03:10.100 --> 00:03:12.380
the Japanese have come out
00:03:12.380 --> 00:03:16.330
with a translation of "Being Heumann".
00:03:16.330 --> 00:03:18.120
And here it is.
00:03:18.120 --> 00:03:22.883
So if any of you are in Japan
or know people in Japan,
00:03:23.850 --> 00:03:27.280
same book in Japanese.
00:03:27.280 --> 00:03:31.560
I was very happy that
people that I knew in Japan
00:03:31.560 --> 00:03:36.390
from the disability community
wanted to translate the book.
00:03:36.390 --> 00:03:40.553
And you can get the book
also in Great Britain.
00:03:44.438 --> 00:03:46.700
This is their version, same book,
00:03:46.700 --> 00:03:49.120
sorry, guys, a little more boring cover,
00:03:49.120 --> 00:03:51.430
but same (indistinct)
00:03:51.430 --> 00:03:56.430
And if I could also say
I'm one of the people
00:03:56.550 --> 00:04:01.550
in an academy nominated
film called "Crip Camp".
00:04:02.810 --> 00:04:07.810
And I think "Crip Camp is
a really important film
00:04:07.990 --> 00:04:12.160
and it's probably for 10 or 11 year olds
00:04:12.160 --> 00:04:17.160
and up and it's R-rated.
00:04:18.120 --> 00:04:21.630
So some schools have
not been able to show it
00:04:21.630 --> 00:04:25.140
because of that until the
upper grades of high school,
00:04:25.140 --> 00:04:28.490
but certainly all of you
should be watching it.
00:04:28.490 --> 00:04:30.320
It's a great documentary.
00:04:30.320 --> 00:04:33.390
It's won the Peabody
Award and many others.
00:04:33.390 --> 00:04:35.610
And it is, as I said, a documentary.
00:04:35.610 --> 00:04:38.220
And I think from an
educational perspective,
00:04:38.220 --> 00:04:41.270
while it's not talking about pedagogy,
00:04:41.270 --> 00:04:44.160
it has a number of people like myself.
00:04:44.160 --> 00:04:46.890
We had our disabilities
when we were younger.
00:04:46.890 --> 00:04:50.460
And I think it allows you to, in part,
00:04:50.460 --> 00:04:53.940
see some of the differences that existed
00:04:53.940 --> 00:04:57.430
in the '40s, '50s, '60s, and early '70s,
00:04:57.430 --> 00:05:00.930
before there was any
legislation in the United States
00:05:00.930 --> 00:05:04.350
that was meaningful and
made it a requirement
00:05:04.350 --> 00:05:06.150
that disabled children go to school.
00:05:08.040 --> 00:05:08.873
- Excellent.
00:05:08.873 --> 00:05:13.120
Well, you just took a whole
lot of my recommendations.
00:05:13.120 --> 00:05:15.690
I recommend all those things,
00:05:15.690 --> 00:05:18.960
but particularly I found "Crip Camp"
00:05:18.960 --> 00:05:22.710
to be an excellent piece of
work and I also recommend it.
00:05:22.710 --> 00:05:26.770
So speaking of your
story, let's start there.
00:05:26.770 --> 00:05:31.770
Tell us a little bit about how
your experiences growing up
00:05:31.800 --> 00:05:33.803
influenced who you are today.
00:05:34.895 --> 00:05:39.895
- Well, I was 18 months
old when I had polio
00:05:42.360 --> 00:05:45.280
and I learned when I was 36
00:05:46.440 --> 00:05:50.640
that a doctor had told my
parents that he recommended
00:05:50.640 --> 00:05:54.330
they put me in an
institution when I was two.
00:05:54.330 --> 00:05:57.040
And the reason I tell you
I didn't learn about this
00:05:57.040 --> 00:05:58.900
till I was way an adult,
00:05:58.900 --> 00:06:01.960
was my parents never
wanted me to know this,
00:06:01.960 --> 00:06:05.603
which I think was a very
good thing actually,
00:06:06.980 --> 00:06:11.500
but they were, they passed away
00:06:11.500 --> 00:06:14.320
German-Jewish refugees.
00:06:14.320 --> 00:06:19.320
And so for any of you who know the history
00:06:21.450 --> 00:06:24.340
under Hitler in the Holocaust,
00:06:24.340 --> 00:06:26.370
the first group of people
that they were killing
00:06:26.370 --> 00:06:28.240
were disabled people.
00:06:28.240 --> 00:06:33.030
And so my parents obviously,
00:06:33.030 --> 00:06:35.470
'cause they also lost all their families,
00:06:35.470 --> 00:06:40.150
were reconstructing and
starting a new family.
00:06:40.150 --> 00:06:45.150
So we were on the road to,
from my parents perspective,
00:06:45.450 --> 00:06:48.050
raising me like they intended to raise me
00:06:48.050 --> 00:06:50.010
if I didn't have a disability.
00:06:50.010 --> 00:06:54.329
But they began to realize that
that wasn't really the case.
00:06:54.329 --> 00:06:56.673
I mean, accessibility in the '40s, '50s,
00:06:59.190 --> 00:07:02.900
'60s started changing in
Brooklyn, in New York city,
00:07:02.900 --> 00:07:05.190
but still not significantly.
00:07:05.190 --> 00:07:07.300
I started using a wheelchair.
00:07:07.300 --> 00:07:09.480
I use braces and crutches,
00:07:09.480 --> 00:07:12.383
but I wasn't really able
to walk independently.
00:07:13.736 --> 00:07:16.590
On polio quadriplegic, my
arms are not very strong.
00:07:16.590 --> 00:07:20.220
So I wasn't using a motorized wheelchair
00:07:20.220 --> 00:07:22.490
'cause they didn't even exist then.
00:07:22.490 --> 00:07:25.450
They started slowly coming in in the '60s
00:07:25.450 --> 00:07:26.407
and then more in the '70s.
00:07:26.407 --> 00:07:29.880
And I did get a motorized
wheelchair in the late '60s
00:07:29.880 --> 00:07:32.010
and I've used one ever since.
00:07:32.010 --> 00:07:33.630
And we could go back to that,
00:07:33.630 --> 00:07:36.750
but for those of you
who work with children
00:07:36.750 --> 00:07:39.290
who have physical disabilities,
00:07:39.290 --> 00:07:42.860
mobility is something
which is very important.
00:07:42.860 --> 00:07:43.693
And
00:07:47.180 --> 00:07:52.180
sometimes people look at
using a motorized wheelchair
00:07:52.360 --> 00:07:55.343
as something which is not
gonna advance your strength.
00:07:56.660 --> 00:08:00.240
But I think the reality
is that we really need
00:08:00.240 --> 00:08:02.820
to look at what children need.
00:08:02.820 --> 00:08:06.360
And one of the things children
need is to be able to be
00:08:06.360 --> 00:08:10.790
as independent as possible
with their friends.
00:08:10.790 --> 00:08:14.760
And also, I didn't get
a motorized wheelchair
00:08:14.760 --> 00:08:17.120
till my late teens, 2021.
00:08:17.120 --> 00:08:21.340
So I had never gone across
the street by myself.
00:08:21.340 --> 00:08:23.570
I had never just gone out
00:08:23.570 --> 00:08:25.120
and walked around the neighborhood.
00:08:25.120 --> 00:08:27.840
I couldn't take a bus,
I couldn't take a chain,
00:08:27.840 --> 00:08:29.630
they weren't accessible.
00:08:29.630 --> 00:08:33.290
All of those things, from
an educational perspective,
00:08:33.290 --> 00:08:35.760
kids beginning as they're getting older
00:08:35.760 --> 00:08:37.660
to go across the street
and visit a neighbor.
00:08:37.660 --> 00:08:39.450
And as they're getting even older,
00:08:39.450 --> 00:08:42.220
taking a bus to go someplace,
00:08:42.220 --> 00:08:44.660
being able to go to the
store by themselves.
00:08:44.660 --> 00:08:48.090
Those are things I couldn't do by myself.
00:08:48.090 --> 00:08:49.840
Now, of course I can.
00:08:49.840 --> 00:08:53.350
But I really think when
we think about education,
00:08:53.350 --> 00:08:54.980
there's the classroom,
00:08:54.980 --> 00:08:58.950
but there is life and
life also does impact.
00:08:58.950 --> 00:09:02.950
So when my mother took me to school,
00:09:02.950 --> 00:09:06.010
the principal denied me
the right to go to school
00:09:06.010 --> 00:09:08.830
because he said I would be a fire hazard.
00:09:08.830 --> 00:09:12.890
So this again was before we had
any of these laws in the US.
00:09:12.890 --> 00:09:16.020
And so I was home.
00:09:16.020 --> 00:09:18.370
I wasn't homeschooled
00:09:18.370 --> 00:09:21.890
'cause there wasn't anything
like that at that time.
00:09:21.890 --> 00:09:24.070
My mother was teaching me.
00:09:24.070 --> 00:09:25.520
And then in the first grade,
00:09:25.520 --> 00:09:28.720
the teachers started coming
to the house twice a week,
00:09:28.720 --> 00:09:31.130
once for an hour, once
for an hour and a half.
00:09:31.130 --> 00:09:33.600
So until the middle of the fourth grade,
00:09:33.600 --> 00:09:35.440
I was getting two and a half hours a week
00:09:35.440 --> 00:09:37.300
of educational training.
00:09:37.300 --> 00:09:41.360
Then I went to segregated
education, special ed classes.
00:09:41.360 --> 00:09:45.130
And quite frankly, they
were not comparable
00:09:45.130 --> 00:09:49.130
to the same classes for
non-disabled children.
00:09:49.130 --> 00:09:53.423
And then I went to college
and wanted to be a teacher,
00:09:54.720 --> 00:09:57.360
was denied my teaching license
00:09:57.360 --> 00:10:00.520
because in writing, they
said I couldn't walk.
00:10:00.520 --> 00:10:03.970
So then I sued the board of education
00:10:03.970 --> 00:10:08.010
and the judge remanded the
case back to the board of ed,
00:10:08.010 --> 00:10:11.380
who did grant me another medical
00:10:11.380 --> 00:10:13.010
and I did get my teaching license
00:10:13.010 --> 00:10:15.630
and I taught in New York for three years.
00:10:15.630 --> 00:10:20.630
But during all that time, I was learning.
00:10:22.100 --> 00:10:25.010
And when you look at "Crip
Camp" and read the book,
00:10:25.010 --> 00:10:27.640
you'll get a chance to understand
00:10:28.750 --> 00:10:32.430
what many of us were going
through and still go through.
00:10:32.430 --> 00:10:36.420
And that is discrimination
that we experience
00:10:37.330 --> 00:10:41.010
and what both our families
00:10:41.010 --> 00:10:45.960
and we as individuals,
as we're growing older,
00:10:45.960 --> 00:10:49.690
what responsibilities we
need to take for ourselves
00:10:49.690 --> 00:10:54.360
and how we individually
and more collectively
00:10:55.560 --> 00:11:00.560
have been working together,
not only to improve the system,
00:11:02.520 --> 00:11:07.520
but also to give ourselves
stability and confidence,
00:11:07.950 --> 00:11:10.003
because one of the issues that,
00:11:10.003 --> 00:11:14.420
this is not just disability
issue, but race or religion,
00:11:14.420 --> 00:11:19.043
which is different or sexual
orientation, whatever,
00:11:20.340 --> 00:11:24.030
and disabled people come
from all of those categories.
00:11:24.030 --> 00:11:28.310
Black, Asian, indigenous, Latino,
00:11:28.310 --> 00:11:31.340
gay, straight, Muslim, whatever.
00:11:31.340 --> 00:11:36.340
So I think what's important about where,
00:11:36.880 --> 00:11:39.850
for those of you who are
doing anything in education
00:11:39.850 --> 00:11:44.230
is really to understand
some of the very important
00:11:44.230 --> 00:11:49.230
additional issues that are beneficial
00:11:50.550 --> 00:11:54.290
for families and disabled kids,
00:11:54.290 --> 00:11:59.200
to be able to get the
kind of support they need.
00:11:59.200 --> 00:12:03.010
So that assuming they're
getting a decent education,
00:12:03.010 --> 00:12:07.720
they are not fearful of
going out into the world,
00:12:07.720 --> 00:12:09.823
getting a job and being competitive.
00:12:10.800 --> 00:12:11.633
- Yeah.
00:12:11.633 --> 00:12:14.340
That issue of establishing
your own independence
00:12:14.340 --> 00:12:17.650
is such a key, both psychological issue
00:12:17.650 --> 00:12:20.530
and issue that we all
go through growing up,
00:12:20.530 --> 00:12:24.150
but it has different
elements as we're thinking
00:12:24.150 --> 00:12:26.140
about learners with disabilities.
00:12:26.140 --> 00:12:28.920
When you think about students (indistinct)
00:12:28.920 --> 00:12:32.490
Yeah, yeah. Right, right, right.
00:12:32.490 --> 00:12:33.780
Yeah.
00:12:33.780 --> 00:12:37.360
Thinking about schools
as many of the folks
00:12:37.360 --> 00:12:41.510
who are joining us today are
related to either schools
00:12:41.510 --> 00:12:44.180
or teaching and elements,
00:12:44.180 --> 00:12:47.240
just broadly, how do you think about the,
00:12:47.240 --> 00:12:51.200
what are the needs of learners
with disabilities in schools?
00:12:51.200 --> 00:12:53.880
What should folks that are
in schools be thinking about
00:12:53.880 --> 00:12:56.270
in order to ensure that those students
00:12:56.270 --> 00:12:59.023
get that education that they need?
00:13:00.180 --> 00:13:03.083
- Well, the word disability is so broad.
00:13:03.980 --> 00:13:08.980
And so there isn't one
approach for all kids.
00:13:10.340 --> 00:13:13.800
Now, that's also true for
non-disabled children.
00:13:13.800 --> 00:13:18.370
So I think what we
really need to understand
00:13:18.370 --> 00:13:21.540
is every child is different
00:13:22.550 --> 00:13:27.070
and whether or not you have any kids
00:13:27.070 --> 00:13:31.360
that are defined as having a
disability, as I was saying,
00:13:31.360 --> 00:13:34.270
not all kids learn the same way.
00:13:34.270 --> 00:13:38.843
And part of what we're
needing to do is to enable
00:13:40.700 --> 00:13:45.470
the teacher to have
knowledge and confidence
00:13:45.470 --> 00:13:49.070
that they can look at what
the needs of the child are.
00:13:49.070 --> 00:13:54.070
And I do believe we need to
be getting our universities
00:13:55.470 --> 00:13:59.310
to be doing a better
job of teaching teachers
00:13:59.310 --> 00:14:04.310
and administrators about how
to have effective classes
00:14:04.410 --> 00:14:08.340
and for teachers to
have some more knowledge
00:14:08.340 --> 00:14:10.550
about the types of needs
00:14:10.550 --> 00:14:15.550
that some students identified
with disabilities or not.
00:14:15.890 --> 00:14:17.163
I mean, when I taught,
00:14:22.527 --> 00:14:25.040
there were no children who were identified
00:14:25.040 --> 00:14:27.960
in my three years of teaching
who had disabilities.
00:14:27.960 --> 00:14:32.253
On the other hand categorically,
quite a number of them did.
00:14:33.560 --> 00:14:37.580
They had things like learning
disabilities or dyslexia
00:14:37.580 --> 00:14:39.360
at a time when those words
00:14:39.360 --> 00:14:41.063
weren't even known in this system?
00:14:42.250 --> 00:14:46.310
I think it's teachers
knowing how to teach reading
00:14:46.310 --> 00:14:51.310
'cause that's a very big
issue in younger grades
00:14:51.410 --> 00:14:55.950
that I think phonetically
learning is very important
00:14:55.950 --> 00:15:00.910
and it's been shown to really
help children learn to read
00:15:00.910 --> 00:15:04.083
and also in some cases,
00:15:05.030 --> 00:15:08.520
not result in the child
needing additional services,
00:15:08.520 --> 00:15:11.290
but if they do at least you know
00:15:11.290 --> 00:15:13.910
that you've clearly been
working with the child
00:15:13.910 --> 00:15:18.910
and the family to help them
get the kind of supports
00:15:19.470 --> 00:15:20.423
that they need.
00:15:21.420 --> 00:15:26.420
I think having an
assistant in a classroom,
00:15:28.630 --> 00:15:31.890
which may happen if you
have a disabled student,
00:15:31.890 --> 00:15:36.370
can be very helpful and trying
to have that assistance,
00:15:36.370 --> 00:15:39.050
not just work with the disabled kids,
00:15:39.050 --> 00:15:41.550
sometimes it needs to be that way.
00:15:41.550 --> 00:15:44.890
But I would say by large,
00:15:44.890 --> 00:15:47.250
you want the child to be in the classroom
00:15:47.250 --> 00:15:52.100
and be as integrated and
as included as possible.
00:15:52.100 --> 00:15:54.600
And I think it's not being afraid,
00:15:54.600 --> 00:15:58.410
I think it's really not only
learning about the child,
00:15:58.410 --> 00:16:02.960
but learning about the disability
that the child may have
00:16:02.960 --> 00:16:06.980
and really be there because you believe
00:16:06.980 --> 00:16:08.950
that the child can learn
00:16:08.950 --> 00:16:11.050
like the other children in your classroom.
00:16:11.910 --> 00:16:15.390
So I think those are all
very important points
00:16:15.390 --> 00:16:20.310
and it may mean that you
need to get some literature,
00:16:20.310 --> 00:16:23.530
look at some of the
organizations that are out there
00:16:23.530 --> 00:16:25.643
that could provide you with assistance.
00:16:26.780 --> 00:16:30.910
But I think the most important thing
00:16:30.910 --> 00:16:35.910
is that the classrooms of
today, meaning now 2021,
00:16:37.660 --> 00:16:39.950
continue to change every year
00:16:39.950 --> 00:16:42.460
with the diversity in our schools.
00:16:42.460 --> 00:16:47.460
Cultural diversity, language
diversity, food diversity.
00:16:47.530 --> 00:16:49.173
I mean, I'll tell you a story.
00:16:50.470 --> 00:16:52.780
The second year I was teaching,
00:16:52.780 --> 00:16:57.780
the first year I taught special
ed and I was an itinerant,
00:16:58.110 --> 00:17:01.670
which meant the teacher
didn't wanna teach a class,
00:17:01.670 --> 00:17:03.270
they asked me.
00:17:03.270 --> 00:17:08.240
And so I was teaching a myriad of classes.
00:17:08.240 --> 00:17:11.300
The second year I had a second grade class
00:17:11.300 --> 00:17:16.300
and one day, one of my students
who was a very good student,
00:17:17.710 --> 00:17:19.123
I really liked her,
00:17:20.100 --> 00:17:23.100
she was having a little rough day.
00:17:23.100 --> 00:17:27.390
And her mother would bring
her to school and pick her up.
00:17:27.390 --> 00:17:30.737
And so when she came to pick
her up this day, I said,
00:17:30.737 --> 00:17:33.280
"Could you please speak to Diana
00:17:33.280 --> 00:17:38.280
and just tell her that she
had a little rambunctious day
00:17:39.030 --> 00:17:42.060
and just talk to her
about it. No big deal."
00:17:42.060 --> 00:17:45.517
The next morning, her mother said to me,
00:17:45.517 --> 00:17:47.900
"She will not do that again,
00:17:47.900 --> 00:17:52.900
I had her kneel rice for three
hours saying some prayers."
00:17:57.200 --> 00:18:02.200
I felt terrible because I had no idea
00:18:04.780 --> 00:18:09.780
that, really, I was not
hard with the mother.
00:18:09.940 --> 00:18:10.773
It was just like,
00:18:10.773 --> 00:18:13.470
I knew mother came here
to (indistinct) school.
00:18:13.470 --> 00:18:15.040
Everyday she was really engaged,
00:18:15.040 --> 00:18:18.083
so I never said another word.
00:18:19.730 --> 00:18:23.960
Those kinds of things
where we need to know more
00:18:23.960 --> 00:18:26.730
about the cultures of the families--
00:18:26.730 --> 00:18:28.333
- Of the family, yeah.
00:18:31.049 --> 00:18:32.830
Yeah, that makes sense.
00:18:32.830 --> 00:18:36.983
What are some things that
we can do to, you mentioned,
00:18:37.827 --> 00:18:39.815
when the students in the classroom,
00:18:39.815 --> 00:18:43.095
we want them to integrate with their peers
00:18:43.095 --> 00:18:46.325
and have those interactions
that are so important.
00:18:46.325 --> 00:18:49.450
What are things we can
do to work with students
00:18:49.450 --> 00:18:51.340
or that students themselves can do
00:18:51.340 --> 00:18:53.933
to help make sure that that's happening?
00:18:55.975 --> 00:18:56.808
- I mean, first of all,
00:18:56.808 --> 00:18:59.983
I think the teacher sets the example.
00:19:01.160 --> 00:19:05.440
And if you are setting an example
00:19:05.440 --> 00:19:08.973
that this child is not
being distinguished,
00:19:10.056 --> 00:19:12.210
they may be getting some assistance,
00:19:12.210 --> 00:19:16.320
they may be sitting in a
different place in the classroom,
00:19:16.320 --> 00:19:21.320
but it's to allow for the students
00:19:21.740 --> 00:19:25.900
to really learn and respect different ways
00:19:25.900 --> 00:19:27.920
that children learn.
00:19:27.920 --> 00:19:32.920
And I think depending on the age,
00:19:34.740 --> 00:19:36.300
younger children really
00:19:36.300 --> 00:19:40.010
are pretty into accepting each other.
00:19:40.010 --> 00:19:45.010
And if there is any bullying going on,
00:19:45.580 --> 00:19:47.830
I think that's something which really
00:19:47.830 --> 00:19:50.830
needs to be addressed right away.
00:19:50.830 --> 00:19:53.490
And that shouldn't be just because,
00:19:53.490 --> 00:19:55.830
typically if somebody is bullying,
00:19:55.830 --> 00:19:58.710
they're not just gonna be
bullying the disabled kid.
00:19:58.710 --> 00:20:01.790
And I think, we're hearing that
00:20:03.200 --> 00:20:07.370
one of the effects of
the COVID period is that
00:20:07.370 --> 00:20:10.430
kids are exhibiting more angry behavior
00:20:10.430 --> 00:20:12.910
in classrooms than before.
00:20:12.910 --> 00:20:17.230
So I think it's just a
mix of what's going on.
00:20:17.230 --> 00:20:20.390
Some of the universities in your area
00:20:20.390 --> 00:20:23.450
also have teachers who are knowledgeable
00:20:23.450 --> 00:20:25.283
about inclusive education.
00:20:26.180 --> 00:20:29.310
That's something that you
also may wanna call on.
00:20:29.310 --> 00:20:34.310
And I hope that you were
receiving some education in school
00:20:34.330 --> 00:20:37.000
about working with students
who have disabilities.
00:20:37.000 --> 00:20:40.460
But by large, I think
it's you treat the student
00:20:40.460 --> 00:20:42.623
like you treat any other student,
00:20:43.820 --> 00:20:46.820
and that sets an example for the class
00:20:46.820 --> 00:20:50.093
about what you're expecting
through your leadership.
00:20:51.700 --> 00:20:52.670
- Right. Right.
00:20:52.670 --> 00:20:53.603
That makes sense.
00:20:55.190 --> 00:20:59.643
We have a comment that
came in from Facebook,
00:21:00.900 --> 00:21:03.187
from (indistinct), who says,
00:21:03.187 --> 00:21:06.850
"I feel we have youth with
invisible disabilities,
00:21:06.850 --> 00:21:10.520
things such as anxiety, panic
attacks, social anxiety."
00:21:10.520 --> 00:21:11.760
This reminded me of your comments,
00:21:11.760 --> 00:21:15.177
especially now it seems like
some of those are there.
00:21:15.177 --> 00:21:19.380
"And those can, can go under
the radar in our system.
00:21:19.380 --> 00:21:23.700
How do we ensure that we're making sure
00:21:23.700 --> 00:21:26.347
we're serving all students
who may need help?"
00:21:27.330 --> 00:21:30.260
- I wish I had an answer or a magic wand.
00:21:30.260 --> 00:21:34.970
I think your point is very well taken.
00:21:34.970 --> 00:21:39.170
And those children have always been there.
00:21:39.170 --> 00:21:44.170
But I do think we are seeing
it in a much more extreme way,
00:21:45.530 --> 00:21:47.470
there are more students.
00:21:47.470 --> 00:21:52.470
And it really is a district
issue, a principal issue,
00:21:54.200 --> 00:21:58.640
meaning really looking at social workers
00:21:58.640 --> 00:22:02.520
and school psychologists and
others who need to be there.
00:22:02.520 --> 00:22:04.500
So that as a teacher,
00:22:04.500 --> 00:22:07.320
you can be given some basic skills
00:22:07.320 --> 00:22:10.260
on how to be working
with students like this,
00:22:10.260 --> 00:22:13.668
who may not be identified
as having a disability.
00:22:13.668 --> 00:22:16.610
They may need to be identified
00:22:16.610 --> 00:22:19.790
in order to be able to
get appropriate supports,
00:22:19.790 --> 00:22:24.090
but not to pull them out of a classroom,
00:22:24.090 --> 00:22:26.830
but rather to make sure that they can get
00:22:26.830 --> 00:22:29.570
some accommodations that could be helpful.
00:22:29.570 --> 00:22:34.570
So, they could be anything
from extended school,
00:22:34.780 --> 00:22:37.590
I'm sorry, extended time for testing.
00:22:37.590 --> 00:22:42.590
Or I really think some of
the flaws in our system
00:22:43.520 --> 00:22:46.050
are now really becoming more apparent,
00:22:46.050 --> 00:22:48.950
like not having enough
school social workers
00:22:48.950 --> 00:22:51.110
or a school psychologist.
00:22:51.110 --> 00:22:54.770
And, if you have time,
00:22:54.770 --> 00:22:59.770
it's also getting other teachers
who can really be working
00:23:00.050 --> 00:23:03.640
with families and trying to
address some of these issues
00:23:03.640 --> 00:23:06.570
from a fiscal perspective
with school boards
00:23:06.570 --> 00:23:09.090
and city governments and state government.
00:23:09.090 --> 00:23:09.923
So it's--
00:23:09.923 --> 00:23:11.732
- So that leads into my next question.
00:23:11.732 --> 00:23:13.320
(laughs)
00:23:13.320 --> 00:23:16.973
Your history of activism is so impressive.
00:23:18.210 --> 00:23:22.460
How do you advise folks
to maybe start getting
00:23:22.460 --> 00:23:24.220
into a little bit of advocacy
00:23:24.220 --> 00:23:27.190
or activism in their communities?
00:23:27.190 --> 00:23:30.653
- First of all, anybody in
education is an activist,
00:23:31.553 --> 00:23:34.410
that's the way I feel about it.
00:23:34.410 --> 00:23:39.410
You have a commitment to
working in a classroom,
00:23:40.890 --> 00:23:45.640
knowing that there's
all kinds of diversity,
00:23:45.640 --> 00:23:49.360
families with different income
levels, different needs.
00:23:49.360 --> 00:23:51.300
And in some way,
00:23:51.300 --> 00:23:55.740
teachers are also a little
social workers, right?
00:23:55.740 --> 00:23:58.090
We have lots of responsibilities.
00:23:58.090 --> 00:23:59.370
- Yes.
00:23:59.370 --> 00:24:04.370
- I think some people will
get active in a union,
00:24:04.410 --> 00:24:07.980
will get active in teacher associations.
00:24:07.980 --> 00:24:11.810
So for me, the work that
I've done in advocacy
00:24:11.810 --> 00:24:16.810
has typically not been, I mean,
I advocate on my own behalf,
00:24:17.480 --> 00:24:20.870
but the majority of
the work that I've done
00:24:20.870 --> 00:24:23.680
has been collaborating with others
00:24:23.680 --> 00:24:27.780
who have similar views and objectives.
00:24:27.780 --> 00:24:30.483
And I think that's really
what we're talking about.
00:24:31.330 --> 00:24:35.330
Is what do we need to do to ensure
00:24:35.330 --> 00:24:37.620
that children in our classrooms
00:24:37.620 --> 00:24:39.660
are getting the right education?
00:24:39.660 --> 00:24:42.790
And in part, that means
what are we getting?
00:24:42.790 --> 00:24:45.010
What do we need as teachers
00:24:45.010 --> 00:24:47.930
to be able to be as effective as possible?
00:24:47.930 --> 00:24:50.910
And at the end of the day
for disabled children,
00:24:50.910 --> 00:24:55.910
my belief is children need to
be in integrated classrooms.
00:24:56.200 --> 00:24:58.130
They need to be getting the support
00:24:58.130 --> 00:25:02.760
so that they are living
in the world of today.
00:25:02.760 --> 00:25:05.390
And that the other students also
00:25:05.390 --> 00:25:09.190
see them as valuable
members of the community.
00:25:09.190 --> 00:25:11.320
And we have a range of people
00:25:11.320 --> 00:25:13.900
with various forms of disabilities.
00:25:13.900 --> 00:25:16.850
Some people don't have
a good day every day
00:25:16.850 --> 00:25:18.800
and it may be because of their disability
00:25:18.800 --> 00:25:20.610
and it may be because of COVID
00:25:20.610 --> 00:25:23.093
and they're having more acting out.
00:25:25.150 --> 00:25:30.150
I very much respect the
amount of work that goes on
00:25:30.910 --> 00:25:32.430
for a teacher,
00:25:32.430 --> 00:25:36.223
but really, I think from
an advocacy perspective,
00:25:38.270 --> 00:25:40.760
allowing people to have
more of an understanding
00:25:40.760 --> 00:25:43.320
of what we believe can be done
00:25:43.320 --> 00:25:45.610
and what we need in order to achieve that.
00:25:47.370 --> 00:25:48.630
- Fantastic.
00:25:48.630 --> 00:25:51.950
So if you did have a magic wand
00:25:51.950 --> 00:25:54.050
and we'll get back to that magic wand,
00:25:54.050 --> 00:25:56.480
what are one or two things
that you would like to see
00:25:56.480 --> 00:26:00.440
changed about either schools
or legislation about schools
00:26:00.440 --> 00:26:03.643
or things to improve
on where we are today?
00:26:04.820 --> 00:26:09.530
- Well, one is that all
educators, school board members,
00:26:09.530 --> 00:26:12.500
administrators, principals, teachers,
00:26:12.500 --> 00:26:15.370
believe that all disabled children
00:26:15.370 --> 00:26:18.250
can learn and have the right to learn.
00:26:18.250 --> 00:26:23.250
And that the education system
has responsibility to teach.
00:26:23.790 --> 00:26:27.420
That universities are doing a better job
00:26:27.420 --> 00:26:29.970
of training teachers.
00:26:29.970 --> 00:26:32.350
Those teachers are equipped
00:26:32.350 --> 00:26:36.130
to effectively work in a classroom,
00:26:36.130 --> 00:26:39.600
and if they have a child or
two children or three children,
00:26:39.600 --> 00:26:41.890
whatever it may be with disabilities,
00:26:41.890 --> 00:26:44.750
that they feel confident
00:26:44.750 --> 00:26:47.430
and that they get the
support that they need.
00:26:47.430 --> 00:26:50.660
But I think still too many universities
00:26:50.660 --> 00:26:55.660
are not training general ed
teachers in basic education
00:26:57.470 --> 00:27:00.090
to work with children
who have disabilities.
00:27:00.090 --> 00:27:03.690
And some universities
are doing better jobs
00:27:03.690 --> 00:27:06.090
where they're offering dual degrees
00:27:06.090 --> 00:27:09.010
or late childhood and primary education,
00:27:09.010 --> 00:27:11.510
but there's still not
enough of that going on.
00:27:11.510 --> 00:27:14.820
So in waving my magic wand,
00:27:14.820 --> 00:27:18.460
it will be that academics
that are teaching
00:27:18.460 --> 00:27:22.520
for training of teachers
really have more knowledge
00:27:22.520 --> 00:27:26.080
about effective ways
of inclusive education,
00:27:26.080 --> 00:27:31.010
which I also believe really
address issues around race,
00:27:31.010 --> 00:27:33.820
because I think what we
were seeing and have seen
00:27:33.820 --> 00:27:38.820
for many years now is that the
biases that teachers may have
00:27:39.980 --> 00:27:42.760
towards certain populations of kids
00:27:42.760 --> 00:27:45.140
may also be resulting
00:27:45.140 --> 00:27:48.113
in higher rates of
suspensions and expulsions.
00:27:49.150 --> 00:27:54.150
So cultural competency I
think is really difficult.
00:27:56.530 --> 00:28:01.530
Honestly, I also think that
salaries need to be raised
00:28:01.710 --> 00:28:04.680
so that people like in Finland
00:28:04.680 --> 00:28:07.120
and Japan and other countries,
00:28:07.120 --> 00:28:10.050
that teachers are earning and respected
00:28:10.050 --> 00:28:12.430
for the work that you're all doing.
00:28:12.430 --> 00:28:17.430
And I think that's something
that is not as strong
00:28:18.850 --> 00:28:20.850
as it needs to be
00:28:20.850 --> 00:28:24.450
and I'm really appreciative of the work
00:28:24.450 --> 00:28:26.193
that most of you are doing.
00:28:28.200 --> 00:28:29.570
- Well.
00:28:29.570 --> 00:28:31.020
That is the end of our 30 minutes.
00:28:31.020 --> 00:28:32.660
I really appreciated all those thoughts.
00:28:32.660 --> 00:28:34.250
Particularly I think
that's an interesting point
00:28:34.250 --> 00:28:37.900
about bias, being biased across groups
00:28:37.900 --> 00:28:39.550
and thinking about where that is.
00:28:40.480 --> 00:28:42.230
Thank you so much for joining us today,
00:28:42.230 --> 00:28:45.740
but thank you more for all
of the work you've been doing
00:28:45.740 --> 00:28:48.810
in activism for learners
with disabilities.
00:28:48.810 --> 00:28:51.450
Look forward to seeing what you do next
00:28:51.450 --> 00:28:54.770
and to picking up your most recent book.
00:28:54.770 --> 00:28:56.080
Thank you.
00:28:56.080 --> 00:28:57.293
- Thank you very much.
00:28:59.430 --> 00:29:01.250
Thank you, interpreter.
|
Effects of different wavelengths of radiation | https://www.youtube.com/watch?v=zH7ZT2tdqQ0 | vtt | https://www.youtube.com/api/timedtext?v=zH7ZT2tdqQ0&ei=ylWUZc7zMvP3xN8PupKrgAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=18EEA10A1E661AE53C0169C5F874F7B6D022ACA2.C54A9F6B64E6F355996B02EC96808F58DD1FBDBE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.300 --> 00:00:02.210
- We've talked about this in other videos.
00:00:02.210 --> 00:00:03.690
But just as a review,
00:00:03.690 --> 00:00:05.721
things like visible light,
00:00:05.721 --> 00:00:10.300
or the x-rays used when you
go to the doctor's office
00:00:10.300 --> 00:00:12.390
to see what's going on with your bones,
00:00:12.390 --> 00:00:15.480
or the microwaves used to heat your food,
00:00:15.480 --> 00:00:18.980
or the radio waves used for communication.
00:00:18.980 --> 00:00:22.140
That these are all really
the same phenomenon,
00:00:22.140 --> 00:00:23.780
which is that they are all
00:00:23.780 --> 00:00:26.880
different types of electromagnetic waves.
00:00:26.880 --> 00:00:28.960
And the main difference between them
00:00:28.960 --> 00:00:31.750
is their wavelength or their frequencies.
00:00:31.750 --> 00:00:33.570
We know that the longer the wavelength,
00:00:33.570 --> 00:00:35.200
the lower the frequency,
00:00:35.200 --> 00:00:39.340
and the shorter the wavelength,
the higher the frequency.
00:00:39.340 --> 00:00:41.830
Now, what's also interesting
about electromagnetic waves
00:00:41.830 --> 00:00:44.010
is that everything in the universe
00:00:44.010 --> 00:00:45.910
that has any temperature at all,
00:00:45.910 --> 00:00:47.880
which is most things in the universe,
00:00:47.880 --> 00:00:50.040
will emit electromagnetic waves.
00:00:50.040 --> 00:00:51.640
You might look at yourself
right now and say,
00:00:51.640 --> 00:00:53.731
wait, am I emitting electromagnetic waves?
00:00:53.731 --> 00:00:57.410
Well, you're probably not
emitting visible waves.
00:00:57.410 --> 00:00:58.760
You're reflecting visible waves,
00:00:58.760 --> 00:01:00.480
that's why you can see your hand.
00:01:00.480 --> 00:01:04.111
But your body is emitting infrared waves.
00:01:04.111 --> 00:01:07.190
Now, just as almost
everything can emit ways,
00:01:07.190 --> 00:01:09.470
waves can also be absorbed,
00:01:09.470 --> 00:01:11.220
depending on the material,
00:01:11.220 --> 00:01:13.970
depending on the size of the object.
00:01:13.970 --> 00:01:15.210
Now, generally speaking,
00:01:15.210 --> 00:01:19.460
when electromagnetic waves are
absorbed by some substance,
00:01:19.460 --> 00:01:21.520
it's turned into thermal energy.
00:01:21.520 --> 00:01:22.620
You can experience that,
00:01:22.620 --> 00:01:26.260
go outside on a sunny
day, wear a black shirt,
00:01:26.260 --> 00:01:30.410
and a black shirt is not
reflecting much visible light.
00:01:30.410 --> 00:01:31.740
And so it's all being absorbed,
00:01:31.740 --> 00:01:33.310
or most of it is being absorbed,
00:01:33.310 --> 00:01:34.730
and it gets converted to heat.
00:01:34.730 --> 00:01:36.770
You will get much hotter than a friend
00:01:36.770 --> 00:01:39.720
who is wearing a white t-shirt.
00:01:39.720 --> 00:01:41.160
Now, we have to be pretty careful
00:01:41.160 --> 00:01:43.880
as we get to higher
frequencies in visible light.
00:01:43.880 --> 00:01:46.770
Ultraviolet light, that's
what's causing sunburn.
00:01:46.770 --> 00:01:48.220
And the risks only increase
00:01:48.220 --> 00:01:49.790
as you get to higher frequencies,
00:01:49.790 --> 00:01:52.340
like x-rays, and gamma rays.
00:01:52.340 --> 00:01:53.880
What these really high frequency
00:01:53.880 --> 00:01:55.800
electromagnetic waves can do
00:01:55.800 --> 00:01:59.130
is knock out electrons from atoms,
00:01:59.130 --> 00:02:00.310
which would ionize them,
00:02:00.310 --> 00:02:02.300
which would change their
chemical properties.
00:02:02.300 --> 00:02:05.200
That could affect DNA. It
could affect other cell tissue.
00:02:05.200 --> 00:02:06.720
And so that's why it could cause cancer
00:02:06.720 --> 00:02:10.653
or just even kill cells
if they get strong enough.
|
Waves and Technology | https://www.youtube.com/watch?v=FSyKEseXgWI | vtt | https://www.youtube.com/api/timedtext?v=FSyKEseXgWI&ei=ylWUZavRKrC6vdIPz9G8iAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D66FED95ADAF2436A76B73F46064FF1E8FEF4075.16D6DDB6F0A7DC56BE3E0E70D0BA25C51BAE0CD7&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.490 --> 00:00:02.290
- [Narrator] We've already
learned a lot about waves
00:00:02.290 --> 00:00:04.740
and now we're going to connected
to the bit to technology,
00:00:04.740 --> 00:00:06.640
especially the technology that most of us
00:00:06.640 --> 00:00:09.630
use most frequently and
that's our cell phone.
00:00:09.630 --> 00:00:12.730
So pause this video and
think if you can list
00:00:12.730 --> 00:00:15.160
all of the waves that your cell phone
00:00:15.160 --> 00:00:19.453
has to utilize or deal
with or generate waves.
00:00:21.690 --> 00:00:25.040
All right, so the first
thing that some of you
00:00:25.040 --> 00:00:27.890
might have realized is
that your cell phone
00:00:27.890 --> 00:00:30.930
has to deal with sound waves.
00:00:30.930 --> 00:00:34.250
So you have sound
traveling through the air.
00:00:34.250 --> 00:00:37.720
Your phone has to detect that sound.
00:00:37.720 --> 00:00:41.370
And then in most cases, it
needs to digitize that sound.
00:00:41.370 --> 00:00:43.860
And we did other videos
where we talked about
00:00:43.860 --> 00:00:46.360
sampling sound waves so
that you can store it
00:00:46.360 --> 00:00:48.240
as digital information.
00:00:48.240 --> 00:00:49.820
And then depending what's happening,
00:00:49.820 --> 00:00:52.400
that detection is going to
happen with your microphone.
00:00:52.400 --> 00:00:54.260
And if you were recording something,
00:00:54.260 --> 00:00:57.180
say recording a video or
recording an audio file
00:00:57.180 --> 00:01:00.100
that digitize sound wave
would then be stored.
00:01:00.100 --> 00:01:01.970
And then if you wanted to play it back,
00:01:01.970 --> 00:01:04.780
it would have to be turned
back into a sound wave,
00:01:04.780 --> 00:01:08.080
which could then be
emitted by your microphone.
00:01:08.080 --> 00:01:10.130
Now, it could also be that you're on,
00:01:10.130 --> 00:01:12.740
let's say a video call or you are having
00:01:12.740 --> 00:01:15.830
an actual phone call, the
original purpose of phones.
00:01:15.830 --> 00:01:18.450
And so then that digitized information
00:01:18.450 --> 00:01:23.200
is going to be transmitted to a cell tower
00:01:23.200 --> 00:01:25.560
that could be tens of miles away.
00:01:25.560 --> 00:01:28.130
And I always find that
amazing because the cell phone
00:01:28.130 --> 00:01:31.350
really has, it doesn't transmit
in a particular direction,
00:01:31.350 --> 00:01:33.810
it kind of transmits in every direction.
00:01:33.810 --> 00:01:36.670
So it's got to be pretty powerful
to get to that cell tower
00:01:36.670 --> 00:01:40.230
that might be around five or
10 or even more miles away.
00:01:40.230 --> 00:01:42.620
And then of course, if
you're having a conversation,
00:01:42.620 --> 00:01:45.880
that cell tower is transmitting
electromagnetic waves
00:01:45.880 --> 00:01:47.470
in a bunch of different directions.
00:01:47.470 --> 00:01:48.767
And then this cell phone says,
00:01:48.767 --> 00:01:50.680
"Hey, that's the signal for me."
00:01:50.680 --> 00:01:52.950
And it can take that digital information.
00:01:52.950 --> 00:01:56.610
And then it could use that
to generate a wave pattern,
00:01:56.610 --> 00:01:58.600
which is then emitted
by the microphone again,
00:01:58.600 --> 00:02:00.410
which you'd then hear.
00:02:00.410 --> 00:02:04.390
So sound waves is clearly a
big part of what's going on
00:02:04.390 --> 00:02:07.010
with a lot of technology, not
just cell phones, obviously.
00:02:07.010 --> 00:02:09.160
If you have a stereo system,
if you have a television,
00:02:09.160 --> 00:02:11.650
sound waves are heavily utilized,
00:02:11.650 --> 00:02:13.590
or at least you have to deal with them.
00:02:13.590 --> 00:02:15.890
Now, what other type of wave?
00:02:15.890 --> 00:02:17.990
Well, you might be saying light waves,
00:02:17.990 --> 00:02:19.590
which would be correct,
00:02:19.590 --> 00:02:21.770
but I'm gonna generalize
a little bit more and say,
00:02:21.770 --> 00:02:26.370
electromagnetic waves of which light waves
00:02:26.370 --> 00:02:28.950
are a type of electromagnetic waves.
00:02:28.950 --> 00:02:31.400
How do you use light waves?
00:02:31.400 --> 00:02:34.910
Well, a modern smartphone or
cell phone will have a camera.
00:02:34.910 --> 00:02:39.730
And so it needs a way
to detect light waves.
00:02:39.730 --> 00:02:43.300
So it will detect them and
once again, it will digitize,
00:02:43.300 --> 00:02:45.560
it will store and then of course,
00:02:45.560 --> 00:02:47.810
it has this nice big screen here.
00:02:47.810 --> 00:02:50.430
So it needs a way to take
that digitized information
00:02:50.430 --> 00:02:52.550
and then generate light waves.
00:02:52.550 --> 00:02:56.210
Every pixel on the screen can
generate different frequencies
00:02:56.210 --> 00:02:58.650
of light waves or at least
give the appearance altogether
00:02:58.650 --> 00:03:02.320
of generating different
frequencies of light waves.
00:03:02.320 --> 00:03:04.300
Now, light waves are not the only type
00:03:04.300 --> 00:03:05.940
of electromagnetic wave.
00:03:05.940 --> 00:03:09.230
We've talked about having to
communicate with a cell tower
00:03:09.230 --> 00:03:13.320
that could be 5, 10, 15,
even further miles away.
00:03:13.320 --> 00:03:15.480
Well, those waves it's using to connect
00:03:15.480 --> 00:03:18.940
with your cell tower,
those are radio waves,
00:03:18.940 --> 00:03:21.980
which are another type
of electromagnetic waves.
00:03:21.980 --> 00:03:23.650
Now, are we done?
00:03:23.650 --> 00:03:25.870
Well just to make sure we can
look at this little key here
00:03:25.870 --> 00:03:27.520
that you see at the top of a cell phone,
00:03:27.520 --> 00:03:30.060
and you could see that
cell signal that tells you
00:03:30.060 --> 00:03:32.870
how good of a radio signal it is getting
00:03:32.870 --> 00:03:35.200
from the cell tower,
00:03:35.200 --> 00:03:38.070
but you can also see
this Wi-Fi signal here.
00:03:38.070 --> 00:03:42.140
So Wi-Fi uses different
frequencies of radio waves
00:03:42.140 --> 00:03:45.990
to communicate with the local
network wherever you are.
00:03:45.990 --> 00:03:49.160
But once again, that is more radio waves.
00:03:49.160 --> 00:03:50.460
So I will let you go.
00:03:50.460 --> 00:03:53.010
I encourage you as you
learn anything in any topic.
00:03:53.010 --> 00:03:54.410
Always look at the world around you
00:03:54.410 --> 00:03:57.260
and see how these concepts
that you're learning in school
00:03:57.260 --> 00:03:59.620
or that you're learning
in, say a Physics class
00:03:59.620 --> 00:04:02.553
are connected to things you
do every moment of your life.
|
Specific Heat Capacity | https://www.youtube.com/watch?v=9_gvwicIbHg | vtt | https://www.youtube.com/api/timedtext?v=9_gvwicIbHg&ei=ylWUZf3_Ieqrp-oPgLqBuAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=319E10C984FB5162D46F6007001E7215FE0E0B36.65FF3B72804F444E39EBD9F1BE807F32B485E235&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.170 --> 00:00:01.230
- [Instructor] Hello everyones.
00:00:01.230 --> 00:00:03.610
Today we are going to be
talking about heat capacity,
00:00:03.610 --> 00:00:05.490
also known as thermal capacity.
00:00:05.490 --> 00:00:07.570
Now this is just the
amount of heat required
00:00:07.570 --> 00:00:10.240
to change the temperature of a material.
00:00:10.240 --> 00:00:11.560
So given this definition,
00:00:11.560 --> 00:00:15.020
what units would you expect
heat capacity to have?
00:00:15.020 --> 00:00:16.690
Heat is a form of energy
00:00:16.690 --> 00:00:18.730
and we're describing how
much of that is needed
00:00:18.730 --> 00:00:19.820
to change the temperature,
00:00:19.820 --> 00:00:23.160
so the units for heat capacity
are energy per temperature,
00:00:23.160 --> 00:00:26.030
in SI would be Joules per Kelvin.
00:00:26.030 --> 00:00:28.660
Now, remember, in SI we
use Kelvin for temperature,
00:00:28.660 --> 00:00:30.810
which is the same in magnitude as Celsius.
00:00:30.810 --> 00:00:32.610
So a difference of 1 degree Celsius
00:00:32.610 --> 00:00:34.780
is equal to a difference of 1 Kelvin,
00:00:34.780 --> 00:00:37.040
however, Kelvin does not
have any negative numbers,
00:00:37.040 --> 00:00:40.240
and so 0 Kelvin is as low as you can get.
00:00:40.240 --> 00:00:43.060
Now, you probably already have
an intuitive understanding
00:00:43.060 --> 00:00:43.893
of heat capacity
00:00:43.893 --> 00:00:45.330
even if you haven't heard it phrased
00:00:45.330 --> 00:00:46.943
exactly like this before.
00:00:47.870 --> 00:00:50.440
Imagine you have two pots of
water over the same burner,
00:00:50.440 --> 00:00:51.857
but one of the pots is full of water
00:00:51.857 --> 00:00:54.600
and the other is only about half full.
00:00:54.600 --> 00:00:57.130
You would probably expect
the one with less water in it
00:00:57.130 --> 00:00:58.690
to boil faster,
00:00:58.690 --> 00:01:01.440
and this is actually because
of the heat capacity.
00:01:01.440 --> 00:01:02.820
The pot with the less water in it
00:01:02.820 --> 00:01:04.160
has a lower heat capacity.
00:01:04.160 --> 00:01:05.510
And this is because one of the things
00:01:05.510 --> 00:01:07.000
that heat capacity depends on
00:01:07.000 --> 00:01:09.540
is the mass of the object or system.
00:01:09.540 --> 00:01:12.850
Less water is less mass
xis a lower heat capacity.
00:01:12.850 --> 00:01:14.900
The other thing that the
heat capacity depends on
00:01:14.900 --> 00:01:16.360
is the material.
00:01:16.360 --> 00:01:18.670
This is also something
you are probably already
00:01:18.670 --> 00:01:20.530
intuitively familiar with.
00:01:20.530 --> 00:01:22.630
Imagine you go to a barbecue on a hot day
00:01:22.630 --> 00:01:23.920
and there are two folding chairs
00:01:23.920 --> 00:01:26.120
left open for you to choose between.
00:01:26.120 --> 00:01:28.100
One is made of metal,
the other of plastic,
00:01:28.100 --> 00:01:30.770
and they've both been
sitting out in the sun.
00:01:30.770 --> 00:01:32.490
You'd probably choose the plastic one
00:01:32.490 --> 00:01:34.160
to save yourself some discomfort.
00:01:34.160 --> 00:01:36.280
The reason that the metal
chair would be hotter
00:01:36.280 --> 00:01:39.170
despite both chairs having
been sitting out in the sun
00:01:39.170 --> 00:01:42.420
is because metal and plastic
are different materials
00:01:42.420 --> 00:01:44.690
and have different heat capacities.
00:01:44.690 --> 00:01:47.300
So we know that the heat
capacity of an object or system
00:01:47.300 --> 00:01:51.480
depends on both the mass and
the material it is made of.
00:01:51.480 --> 00:01:53.040
We can actually combine these then
00:01:53.040 --> 00:01:55.930
into something called
specific heat capacity.
00:01:55.930 --> 00:01:57.620
Now the specific heat capacity
00:01:57.620 --> 00:02:00.800
is just the heat capacity per mass.
00:02:00.800 --> 00:02:02.910
This means that the specific heat capacity
00:02:02.910 --> 00:02:05.070
is independent of the mass of the system
00:02:05.070 --> 00:02:07.380
because we're measuring it per mass.
00:02:07.380 --> 00:02:10.810
Therefore, this is constant
for a given material.
00:02:10.810 --> 00:02:12.730
This means it will take
the same amount of energy
00:02:12.730 --> 00:02:14.840
to raise the temperature of 1 kilogram
00:02:14.840 --> 00:02:16.420
of any given material,
00:02:16.420 --> 00:02:18.140
but then for a different material,
00:02:18.140 --> 00:02:20.580
it will take a different amount of energy.
00:02:20.580 --> 00:02:22.740
Given this, what do you expect the units
00:02:22.740 --> 00:02:25.390
of specific heat capacity to be?
00:02:25.390 --> 00:02:26.560
Well, just like heat capacity,
00:02:26.560 --> 00:02:28.250
we have an energy per temperature,
00:02:28.250 --> 00:02:30.410
but now we also have a per mass.
00:02:30.410 --> 00:02:34.800
In SI this is going to be
Joules per Kelvin per kilogram.
00:02:34.800 --> 00:02:36.860
This means that the heat capacity
00:02:36.860 --> 00:02:40.793
and the specific heat
capacity are related by mass.
00:02:41.897 --> 00:02:45.290
so, if you have a specific heat capacity
00:02:45.290 --> 00:02:47.890
and you want to get
the total heat capacity
00:02:47.890 --> 00:02:49.800
for the object or system,
00:02:49.800 --> 00:02:54.170
then you need to multiply by
the object or system's mass.
00:02:54.170 --> 00:02:57.480
Conversely, if you have the
heat capacity and the mass
00:02:57.480 --> 00:02:58.500
and you want to figure out
00:02:58.500 --> 00:03:01.820
what the heat capacity of a material is,
00:03:01.820 --> 00:03:05.080
you can divide the heat
capacity by the mass.
00:03:05.080 --> 00:03:07.040
However, because specific heat capacity
00:03:07.040 --> 00:03:09.570
is a constant property
of a given material,
00:03:09.570 --> 00:03:12.620
we can usually just go ahead
and look up what that value is
00:03:12.620 --> 00:03:14.300
because scientists have already measured
00:03:14.300 --> 00:03:17.300
the specific heat capacities
of lots of materials.
00:03:17.300 --> 00:03:20.090
Let's consider the water in
those pots we talked about.
00:03:20.090 --> 00:03:22.570
Pure liquid water has a
specific heat capacity
00:03:22.570 --> 00:03:27.450
of 4,184 Joules per Kelvin per kilogram,
00:03:27.450 --> 00:03:28.700
but different materials
00:03:28.700 --> 00:03:30.860
have different specific heat capacities.
00:03:30.860 --> 00:03:34.260
So let's think back to our
chairs at a barbecue example
00:03:34.260 --> 00:03:37.720
and how the metal chair is
hotter than the plastic chair.
00:03:37.720 --> 00:03:40.810
Now metal folding chairs are
typically made of aluminum,
00:03:40.810 --> 00:03:42.620
which has a specific heat capacity
00:03:43.606 --> 00:03:47.250
of 897 Joules per Kelvin per kilogram.
00:03:47.250 --> 00:03:48.540
Solid plastic, however,
00:03:48.540 --> 00:03:49.940
has a specific heat capacity
00:03:51.320 --> 00:03:55.060
of 1,670 Joules per Kelvin per kilogram.
00:03:55.060 --> 00:03:57.320
So you can see from the
specific heat capacities
00:03:57.320 --> 00:04:00.190
that since the sun is providing
the same amount of energy
00:04:00.190 --> 00:04:01.500
to both chairs,
00:04:01.500 --> 00:04:03.020
the temperature of the metal chair
00:04:03.020 --> 00:04:04.980
is getting much more increased
00:04:04.980 --> 00:04:08.640
because it needs less energy
to increase its temperature
00:04:08.640 --> 00:04:12.030
because it has a lower
specific heat capacity.
00:04:12.030 --> 00:04:14.840
Now that we see how the material
changes the heat capacity,
00:04:14.840 --> 00:04:17.100
let's talk a bit more about the mass
00:04:17.100 --> 00:04:19.560
and go back to our example of the pots.
00:04:19.560 --> 00:04:21.890
So in these pots, we
have pure liquid water,
00:04:21.890 --> 00:04:24.720
which we know now has a
specific heat capacity
00:04:24.720 --> 00:04:29.050
of 4,184 Joules per Kelvin per kilogram.
00:04:29.050 --> 00:04:31.300
Now the pots themselves
also have a heat capacity,
00:04:31.300 --> 00:04:33.700
but we're going to ignore
that to simplify the problem.
00:04:33.700 --> 00:04:36.570
If this pot has 2
kilograms of water in it,
00:04:36.570 --> 00:04:38.770
we can calculate how
much energy it will take
00:04:38.770 --> 00:04:41.550
to change the temperature of this water.
00:04:41.550 --> 00:04:43.470
Let's say that the initial
temperature of the water
00:04:43.470 --> 00:04:44.950
is about 300 Kelvin,
00:04:44.950 --> 00:04:47.260
which is approximately room temperature.
00:04:47.260 --> 00:04:48.860
And suppose we want to use this water
00:04:48.860 --> 00:04:49.910
to make some white tea,
00:04:49.910 --> 00:04:54.190
which has made best with water
that's at about 355 Kelvin.
00:04:54.190 --> 00:04:56.610
Based off our understanding
of heat capacity now,
00:04:56.610 --> 00:04:59.630
we can figure out how many
joules it is going to take
00:04:59.630 --> 00:05:04.610
to raise the water from
300 Kelvin to 355 Kelvin.
00:05:04.610 --> 00:05:07.420
We have the specific
heat capacity and a mass,
00:05:07.420 --> 00:05:08.980
and we know we can multiply those
00:05:08.980 --> 00:05:11.340
to get a total heat capacity.
00:05:11.340 --> 00:05:13.020
And we know that by definition,
00:05:13.020 --> 00:05:16.390
heat capacity is the energy
required per temperature,
00:05:16.390 --> 00:05:18.780
which means that if we
multiply the heat capacity
00:05:18.780 --> 00:05:20.210
by the change in temperature,
00:05:20.210 --> 00:05:23.170
we'll find out what
the energy required is.
00:05:23.170 --> 00:05:24.380
In fact, this relationship
00:05:24.380 --> 00:05:27.120
is an important thermodynamic equation.
00:05:27.120 --> 00:05:29.980
Lower case c is commonly used
for specific heat capacity
00:05:29.980 --> 00:05:31.700
and Q for heat.
00:05:31.700 --> 00:05:34.220
So this is exactly what
we've just worked out.
00:05:34.220 --> 00:05:35.640
The heat or energy required
00:05:35.640 --> 00:05:38.470
equals the specific heat
capacity times the mass,
00:05:38.470 --> 00:05:40.290
times the change in temperature.
00:05:40.290 --> 00:05:42.830
Let's go ahead and put our values in here.
00:05:42.830 --> 00:05:43.683
The mass,
00:05:44.700 --> 00:05:46.183
specific heat capacity,
00:05:47.510 --> 00:05:49.010
and the change in temperature.
00:05:50.000 --> 00:05:52.250
As always, we can use
our units to guide us.
00:05:52.250 --> 00:05:53.340
Specific heat capacity
00:05:53.340 --> 00:05:56.430
has a unit of Joules
per Kelvin per kilogram,
00:05:56.430 --> 00:05:59.160
we're multiplying mass that
has a unit of kilograms,
00:05:59.160 --> 00:06:01.520
so those kilograms will cancel out.
00:06:01.520 --> 00:06:03.620
We're also multiplying by
a change in temperature,
00:06:03.620 --> 00:06:05.160
which is measured Kelvin.
00:06:05.160 --> 00:06:06.770
And so that will also cancel out,
00:06:06.770 --> 00:06:09.710
leaving us just with
joules which is an energy,
00:06:09.710 --> 00:06:10.930
just like we want.
00:06:10.930 --> 00:06:12.900
In this case, if we
multiply this together,
00:06:12.900 --> 00:06:14.500
we would find that the energy required
00:06:14.500 --> 00:06:18.000
would be 460.24 kilojoules.
00:06:18.000 --> 00:06:20.350
Now, let's consider the other pot.
00:06:20.350 --> 00:06:22.930
If this pot has 1 kilogram of water,
00:06:22.930 --> 00:06:24.970
how would that change our calculation?
00:06:24.970 --> 00:06:25.803
Pause the video
00:06:25.803 --> 00:06:28.480
and think about what its
heat capacity would be.
00:06:28.480 --> 00:06:30.440
So because we still have the same material
00:06:30.440 --> 00:06:32.690
and therefore the same
specific heat capacity,
00:06:32.690 --> 00:06:35.720
the total heat capacity is
going to decrease by half
00:06:35.720 --> 00:06:38.100
because of the mass is half.
00:06:38.100 --> 00:06:40.650
And since we still want to
raise the water's temperature,
00:06:40.650 --> 00:06:41.640
the same amount,
00:06:41.640 --> 00:06:43.210
this means that the energy required
00:06:43.210 --> 00:06:45.970
is going to decrease by half as well,
00:06:45.970 --> 00:06:50.200
now requiring 230.12 kilojoules.
00:06:50.200 --> 00:06:51.480
So now we can see how the mass,
00:06:51.480 --> 00:06:53.983
as well as the material
affect heat capacity.
00:06:55.010 --> 00:06:57.290
Today we talked about heat capacity.
00:06:57.290 --> 00:06:59.370
We learned that it is the
amount of heat required
00:06:59.370 --> 00:07:01.160
to change the temperature of a material
00:07:01.160 --> 00:07:03.970
and that it is measured
in Joules per Kelvin,
00:07:03.970 --> 00:07:06.540
and that it depends on
both the mass of the system
00:07:06.540 --> 00:07:09.170
and the materials that
the system is made up.
00:07:09.170 --> 00:07:10.470
We did a couple of examples
00:07:10.470 --> 00:07:13.630
to help us quantify this
intuitive understanding we have
00:07:13.630 --> 00:07:15.530
of the world around us.
00:07:15.530 --> 00:07:16.450
And I encourage you
00:07:16.450 --> 00:07:18.670
to think about the ways
he capacity pops up
00:07:18.670 --> 00:07:20.400
in your everyday life.
00:07:20.400 --> 00:07:23.140
For example, why are some
things drier than other things
00:07:23.140 --> 00:07:26.290
when you unload the dishwasher?
Have a think about that.
00:07:26.290 --> 00:07:27.470
Thank you so much for joining us.
00:07:27.470 --> 00:07:29.240
I hope you learned a
little bit of something,
00:07:29.240 --> 00:07:31.190
and we'll see you again next time. Bye.
|
Titrations of polyprotic acids | https://www.youtube.com/watch?v=AXKqh3za1Fg | vtt | https://www.youtube.com/api/timedtext?v=AXKqh3za1Fg&ei=y1WUZbPfBPToxN8Pja2skAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245307&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5C75055A089FD6BE3F4C4AB9C83242C7AFE3F56A.27906F8307109358CF4E7726BF493A1B56072057&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.190 --> 00:00:02.210
- [Instructor] A
polyprotic acid is an acid
00:00:02.210 --> 00:00:06.000
with more than one proton that
it can donate in solution.
00:00:06.000 --> 00:00:09.610
An example of a polyprotic
acid is the protonated form
00:00:09.610 --> 00:00:12.120
of the amino acid alanine.
00:00:12.120 --> 00:00:14.730
Here's a dot structure
showing the protonated form
00:00:14.730 --> 00:00:16.440
of the amino acid alanine,
00:00:16.440 --> 00:00:19.780
and we can represent this as H2A plus.
00:00:19.780 --> 00:00:21.770
Let's say we're doing a titration
00:00:21.770 --> 00:00:23.820
with the protonated form of alanine,
00:00:23.820 --> 00:00:26.250
and we're adding sodium hydroxide
00:00:26.250 --> 00:00:29.450
to an aqueous solution
of the protonated form.
00:00:29.450 --> 00:00:33.340
The protonated form of alanine
has two acidic protons.
00:00:33.340 --> 00:00:36.290
So one acidic proton is on the oxygen,
00:00:36.290 --> 00:00:38.460
and the other acidic proton is one
00:00:38.460 --> 00:00:40.920
of the protons bonded to the nitrogen.
00:00:40.920 --> 00:00:42.680
The proton bonded to the oxygen
00:00:42.680 --> 00:00:44.820
is the more acidic of the two.
00:00:44.820 --> 00:00:47.420
Therefore, when we add
some hydroxide anions
00:00:47.420 --> 00:00:48.370
to the solution,
00:00:48.370 --> 00:00:52.380
the hydroxide anions will pick
up this proton and form water
00:00:52.380 --> 00:00:55.290
and convert the protonated form of alanine
00:00:55.290 --> 00:00:59.180
into the overall neutral
form of alanine, HA.
00:00:59.180 --> 00:01:01.620
Let's say that we start
out in our titration
00:01:01.620 --> 00:01:05.130
with one mole of the
protonated form of alanine,
00:01:05.130 --> 00:01:08.500
and then we add in our hydroxide anions.
00:01:08.500 --> 00:01:11.990
After we've added in one
mole of hydroxide anions,
00:01:11.990 --> 00:01:15.680
we've completely neutralized
the protonated form of alanine,
00:01:15.680 --> 00:01:19.807
and H2A plus is converted into HA.
00:01:19.807 --> 00:01:22.050
So one mole of H2A plus reacts
00:01:22.050 --> 00:01:24.380
with one mole of hydroxide anions
00:01:24.380 --> 00:01:27.183
to form one mole of HA.
00:01:28.740 --> 00:01:32.680
So now we have one mole of HA in solution.
00:01:32.680 --> 00:01:35.750
And if we continue to
add hydroxide anions,
00:01:35.750 --> 00:01:38.980
hydroxide anions react with HA
00:01:38.980 --> 00:01:41.970
and take one of the acidic
protons on the nitrogen
00:01:41.970 --> 00:01:43.920
to form A minus.
00:01:43.920 --> 00:01:47.040
A minus is the conjugate base to HA.
00:01:47.040 --> 00:01:50.250
It would take another
mole of hydroxide anions
00:01:50.250 --> 00:01:55.250
to completely neutralize the
HA and to turn it into A minus.
00:01:55.340 --> 00:02:00.020
So one mole of HA reacts with
one mole of hydroxide anions
00:02:00.020 --> 00:02:04.780
to form one mole of A minus.
00:02:04.780 --> 00:02:06.830
So going back to the protonated form
00:02:06.830 --> 00:02:08.820
of the amino acid alanine,
00:02:08.820 --> 00:02:12.110
since the protonated form
has two acidic protons,
00:02:12.110 --> 00:02:15.250
we call this a diprotic acid.
00:02:15.250 --> 00:02:17.700
So let me go ahead and
write in here diprotic.
00:02:17.700 --> 00:02:20.600
And because there are two acidic protons
00:02:20.600 --> 00:02:23.510
on the protonated form of alanine,
00:02:23.510 --> 00:02:25.870
there will be two pKa values,
00:02:25.870 --> 00:02:29.210
which we can figure out
from the titration curve.
00:02:29.210 --> 00:02:31.800
Next, let's look at the
titration curve for the titration
00:02:31.800 --> 00:02:34.940
of our diprotic acid
with sodium hydroxide.
00:02:34.940 --> 00:02:36.810
On the y-axis is pH,
00:02:36.810 --> 00:02:40.870
and on the x-axis is moles
of hydroxide anions added.
00:02:40.870 --> 00:02:43.350
Before we've added any hydroxide anion,
00:02:43.350 --> 00:02:46.770
so this point right here
on our titration curve,
00:02:46.770 --> 00:02:49.130
we have our diprotic acid present,
00:02:49.130 --> 00:02:52.860
so H2A plus.
00:02:52.860 --> 00:02:57.380
And since we started with
one mole of H2A plus,
00:02:57.380 --> 00:03:00.020
it would take one mole of hydroxide anions
00:03:00.020 --> 00:03:03.630
to completely neutralize the H2A plus.
00:03:03.630 --> 00:03:07.120
So after one mole of hydroxide
anions has been added,
00:03:07.120 --> 00:03:10.300
that brings us to equivalence point one.
00:03:10.300 --> 00:03:14.130
So we go to one mole of
hydroxide anions on the x-axis,
00:03:14.130 --> 00:03:17.570
and we'd go up to where that
intersects our titration curve.
00:03:17.570 --> 00:03:20.150
And this point on our titration curve
00:03:20.150 --> 00:03:22.530
is equivalence point one.
00:03:22.530 --> 00:03:23.880
At equivalence point one,
00:03:23.880 --> 00:03:28.193
all of the H2A plus has
been converted into HA.
00:03:28.193 --> 00:03:32.450
So now we have one mole of HA present.
00:03:32.450 --> 00:03:34.760
Next, let's think about adding 0.5 moles
00:03:34.760 --> 00:03:36.670
of hydroxide anions.
00:03:36.670 --> 00:03:38.430
So that would only neutralize half
00:03:38.430 --> 00:03:41.740
of the H2A plus that
was initially present.
00:03:41.740 --> 00:03:44.610
Therefore, if we go to 0.5
moles of hydroxide anions
00:03:44.610 --> 00:03:47.770
and we'd go up to where that
intersects our titration curve,
00:03:47.770 --> 00:03:51.110
this point represents the
half equivalence point
00:03:51.110 --> 00:03:54.700
or half equivalence point
one for this titration.
00:03:54.700 --> 00:03:56.950
Next, let's look at half
equivalence point one
00:03:56.950 --> 00:03:58.210
in more detail.
00:03:58.210 --> 00:04:00.470
So here is half equivalence point one
00:04:00.470 --> 00:04:02.280
on the titration curve.
00:04:02.280 --> 00:04:05.230
So if we started out
with one mole of H2A plus
00:04:05.230 --> 00:04:07.920
and we've added 0.5 moles
of hydroxide anions,
00:04:07.920 --> 00:04:12.760
we've neutralized half, or
0.5 moles, of the H2A plus.
00:04:12.760 --> 00:04:14.880
Therefore, at the half equivalence point,
00:04:14.880 --> 00:04:18.750
we have half a mole of H2A
plus and half a mole of HA,
00:04:18.750 --> 00:04:22.190
which means the concentration
of H2A plus is equal
00:04:22.190 --> 00:04:24.600
to the concentration of HA.
00:04:24.600 --> 00:04:27.380
And because at this point
we have significant amounts
00:04:27.380 --> 00:04:30.560
of both the weak acid
and its conjugate base,
00:04:30.560 --> 00:04:32.460
we've formed a buffer.
00:04:32.460 --> 00:04:35.890
So notice how the pH changes very slowly
00:04:35.890 --> 00:04:39.720
in this region around the
half equivalence point one.
00:04:39.720 --> 00:04:43.670
So this is called buffer
region one right in here.
00:04:43.670 --> 00:04:45.610
And since we've formed a buffer,
00:04:45.610 --> 00:04:47.900
the Henderson-Hasselbalch
equation tells us
00:04:47.900 --> 00:04:50.330
when the concentration
of the weak acid is equal
00:04:50.330 --> 00:04:53.320
to the concentration
of the conjugate base,
00:04:53.320 --> 00:04:58.210
the pH of the solution is equal
to the pKa of the weak acid.
00:04:58.210 --> 00:05:00.820
In this case, we're
talking about the pKa value
00:05:00.820 --> 00:05:02.580
of the more acidic proton,
00:05:02.580 --> 00:05:06.940
so the proton that's on
the oxygen, NH2A plus.
00:05:06.940 --> 00:05:08.930
So if we find the half equivalence point
00:05:08.930 --> 00:05:13.350
and we go over to where this
intersects with the y-axis,
00:05:13.350 --> 00:05:17.410
the pH at this point should
be equal to the pKa value
00:05:17.410 --> 00:05:19.810
for the more acidic proton.
00:05:19.810 --> 00:05:21.620
So looking at the y-axis here,
00:05:21.620 --> 00:05:24.170
it looks like it's a little bit over two.
00:05:24.170 --> 00:05:25.370
And in reality,
00:05:25.370 --> 00:05:29.343
the value of pKa one is equal to 2.34.
00:05:31.640 --> 00:05:34.010
Next, let's go back to the
first equivalence point,
00:05:34.010 --> 00:05:37.720
which occurred after we added
one mole of hydroxide anions.
00:05:37.720 --> 00:05:40.070
So at this point, we have HA.
00:05:40.070 --> 00:05:43.280
If we think about adding another
mole of hydroxide anions,
00:05:43.280 --> 00:05:46.850
so going from one mole
total to two moles total,
00:05:46.850 --> 00:05:49.480
the extra mole of hydroxide anions
00:05:49.480 --> 00:05:54.480
will completely neutralize the
HA and turn it into A minus.
00:05:54.610 --> 00:05:57.250
So one mole of HA reacts
00:05:57.250 --> 00:05:59.910
with one mole of hydroxide anions
00:05:59.910 --> 00:06:03.793
to form one mole of A minus.
00:06:04.860 --> 00:06:07.400
And since the extra
mole of hydroxide anions
00:06:07.400 --> 00:06:11.100
completely neutralize the
HA and turn it into A minus,
00:06:11.100 --> 00:06:14.860
after we've added a total of
two moles of hydroxide anions,
00:06:14.860 --> 00:06:17.700
we go up to where that
intersects our titration curve,
00:06:17.700 --> 00:06:21.600
and this point represents
equivalence point two.
00:06:21.600 --> 00:06:23.560
So the equivalence point one occurs
00:06:23.560 --> 00:06:25.580
after adding one mole of hydroxide anions,
00:06:25.580 --> 00:06:28.780
and we can see the pH by
going over to the y-axis.
00:06:28.780 --> 00:06:31.990
And equivalence point two
occurs after we've added a total
00:06:31.990 --> 00:06:35.080
of two moles of hydroxide anions.
00:06:35.080 --> 00:06:37.520
Let's go back to our
first equivalence point
00:06:37.520 --> 00:06:40.280
where we had one mole of HA.
00:06:40.280 --> 00:06:41.113
And at that point,
00:06:41.113 --> 00:06:43.460
we've already added one
mole of hydroxide anions.
00:06:43.460 --> 00:06:46.880
And so if we add another 0.5
moles of hydroxide anions
00:06:46.880 --> 00:06:49.310
to give a total of 1.5 moles,
00:06:49.310 --> 00:06:52.300
we would neutralize half of the HA
00:06:52.300 --> 00:06:55.360
and turn half of it into A minus.
00:06:55.360 --> 00:06:58.280
Therefore, we have another
half equivalence point
00:06:58.280 --> 00:07:02.710
after 1.5 moles of hydroxide
anions have been added.
00:07:02.710 --> 00:07:05.930
Let's look in more detail at
half equivalence point two,
00:07:05.930 --> 00:07:08.700
which is right here on our titration curve
00:07:08.700 --> 00:07:12.610
after we've added 1.5
moles of hydroxide anions.
00:07:12.610 --> 00:07:15.020
Since we've neutralized half of the HA
00:07:15.020 --> 00:07:18.030
that was present at equivalence point one,
00:07:18.030 --> 00:07:20.460
now the concentration of HA is equal
00:07:20.460 --> 00:07:23.470
to the concentration of A minus.
00:07:23.470 --> 00:07:25.610
And since we have significant amounts
00:07:25.610 --> 00:07:28.170
of both the weak acid
and its conjugate base,
00:07:28.170 --> 00:07:31.040
we have a buffer present in the region
00:07:31.040 --> 00:07:34.120
around half equivalence point two.
00:07:34.120 --> 00:07:37.580
So we can see the pH is changing
very slowly in this region
00:07:37.580 --> 00:07:39.070
around the half equivalence point
00:07:39.070 --> 00:07:41.420
as hydroxide anions are added.
00:07:41.420 --> 00:07:44.450
And so this represents buffer region two.
00:07:44.450 --> 00:07:46.730
And because the concentration
of weak acid is equal
00:07:46.730 --> 00:07:49.230
to the concentration
of its conjugate base,
00:07:49.230 --> 00:07:52.280
the Henderson-Hasselbalch
equation tells us the pH
00:07:52.280 --> 00:07:55.760
at this point is equal to the pKa value.
00:07:55.760 --> 00:07:58.010
In this case, it would be pKa two,
00:07:58.010 --> 00:08:01.150
so one of the acidic
protons on the nitrogen.
00:08:01.150 --> 00:08:03.490
So we can find the value for pKa two
00:08:03.490 --> 00:08:06.250
by locating half equivalence point two
00:08:06.250 --> 00:08:11.250
and going over to see where
that intersects with our y-axis.
00:08:11.920 --> 00:08:14.130
It looks to be a little bit under 10,
00:08:14.130 --> 00:08:17.700
which matches with the
actual pKa two value,
00:08:17.700 --> 00:08:20.113
which turns out to be 9.87.
00:08:22.300 --> 00:08:25.250
Finally, let's go back to
the two equivalence points
00:08:25.250 --> 00:08:26.900
for our titration curve.
00:08:26.900 --> 00:08:29.560
The number of equivalence
points in a titration curve
00:08:29.560 --> 00:08:31.720
for a polyprotic acid is equal
00:08:31.720 --> 00:08:34.570
to the number of acidic
protons in the acid.
00:08:34.570 --> 00:08:37.850
Therefore, since we
titrated a diprotic acid
00:08:37.850 --> 00:08:39.690
with two acidic protons,
00:08:39.690 --> 00:08:43.303
the titration curve has
two equivalence points.
|
All in for Education: Keep Khan Academy Free | https://www.youtube.com/watch?v=I8XdUy-wyyM | vtt | https://www.youtube.com/api/timedtext?v=I8XdUy-wyyM&ei=y1WUZa2fAvSJp-oP-LOqqAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245307&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1EBD04C84899155A5E61C56D6BF77D9D04DE9512.DE9977A01E28B17EC208CA87E5E887BFB4B3A541&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.240 --> 00:00:02.160
- Hi, everyone! Sal Khan here.
00:00:02.160 --> 00:00:04.270
Just to remind everyone that Khan Academy
00:00:04.270 --> 00:00:06.180
is a not-for-profit organization.
00:00:06.180 --> 00:00:07.860
That means I don't own Khan Academy,
00:00:07.860 --> 00:00:10.470
no one owns Khan Academy,
we are a public charity.
00:00:10.470 --> 00:00:12.290
And we can only do the work we do
00:00:12.290 --> 00:00:15.070
through donations from
folks like yourself.
00:00:15.070 --> 00:00:16.520
So if you're in a position to do so,
00:00:16.520 --> 00:00:19.310
please think about making a donation.
00:00:19.310 --> 00:00:20.143
As a reminder,
00:00:20.143 --> 00:00:23.460
Khan Academy is about the
budget of a large high school,
00:00:23.460 --> 00:00:26.960
but we try to reach all of humanity.
00:00:26.960 --> 00:00:27.793
And last year,
00:00:27.793 --> 00:00:30.510
we had 13 billion learning
minutes on the platform.
00:00:30.510 --> 00:00:34.100
Half of that are students and
families all over the world,
00:00:34.100 --> 00:00:37.440
oftentimes telling us that
this is a learning resource,
00:00:37.440 --> 00:00:39.450
the tutor, the help that their family
00:00:39.450 --> 00:00:41.390
could not otherwise afford.
00:00:41.390 --> 00:00:43.230
The other half is hundreds of thousands
00:00:43.230 --> 00:00:45.260
of teachers using Khan
Academy in the classroom
00:00:45.260 --> 00:00:47.810
to personalize learning,
to make it more engaging,
00:00:47.810 --> 00:00:49.030
for them to have better information
00:00:49.030 --> 00:00:50.380
about where their kids are,
00:00:50.380 --> 00:00:53.790
so that they can do more focus
interventions with students.
00:00:53.790 --> 00:00:56.520
There's some calculations
around social return.
00:00:56.520 --> 00:00:57.690
In the for-profit sector,
00:00:57.690 --> 00:01:00.510
if you've got even a 20 or
30% return on investment,
00:01:00.510 --> 00:01:02.870
that's considered a
very, very good return.
00:01:02.870 --> 00:01:04.280
In the not-for-profit sector,
00:01:04.280 --> 00:01:09.090
if you get even a 2X or
3X benefit to cost ratio
00:01:09.090 --> 00:01:12.820
for a not-for-profit,
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00:01:12.820 --> 00:01:16.690
Even conservative estimates
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to a thousand to one benefit.
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Because we're at a special time in history
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where something like education,
00:01:22.530 --> 00:01:23.780
which has always been scarce
00:01:23.780 --> 00:01:26.970
and frankly always been expensive,
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at least aspects of it,
very important aspects of it
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can now be delivered to tens of millions,
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in ways that we could not have imagined
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And as I tell everyone,
00:01:40.440 --> 00:01:41.860
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over the last 10 or 12 years,
00:01:43.490 --> 00:01:45.650
and as much as we've done this past year,
00:01:45.650 --> 00:01:47.210
especially during the pandemic,
00:01:47.210 --> 00:01:48.620
we're just getting started.
00:01:48.620 --> 00:01:51.390
We really wanna cover all of
the core academic subjects
00:01:51.390 --> 00:01:53.870
from pre-K through the core of college.
00:01:53.870 --> 00:01:55.960
We wanna meet students where they are,
00:01:55.960 --> 00:01:58.470
and we wanna think about how
do we connect that learning
00:01:58.470 --> 00:02:00.810
to real opportunity, whether
it's getting into college,
00:02:00.810 --> 00:02:02.950
getting a job, or getting
credit in some way.
00:02:02.950 --> 00:02:04.690
And we wanna do it one day
00:02:04.690 --> 00:02:06.930
for billions of people around the world.
00:02:06.930 --> 00:02:08.670
So if you're in a position to do so,
00:02:08.670 --> 00:02:10.280
please think about making a contribution
00:02:10.280 --> 00:02:12.580
of any size to Khan Academy.
00:02:12.580 --> 00:02:14.593
It will go a long, long way.
|
Part to whole ratio word problem using tables | https://www.youtube.com/watch?v=ZJ6y8OVJRw8 | vtt | https://www.youtube.com/api/timedtext?v=ZJ6y8OVJRw8&ei=ylWUZeHQMrS1vdIPoLuoUA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=46934B5C984AB4D36C778AD99FEAC3D9533175F4.7CFF4859E3EC9860060823CAF595E3BAE150994A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.250 --> 00:00:01.500
- [Instructor] We're told that one month,
00:00:01.500 --> 00:00:04.810
the ratio of indoor to outdoor play times
00:00:04.810 --> 00:00:08.170
for Yousef's class was two to three.
00:00:08.170 --> 00:00:11.370
They had 30 total play times.
00:00:11.370 --> 00:00:14.240
How many of the play times were indoors?
00:00:14.240 --> 00:00:16.350
How many were outdoors?
00:00:16.350 --> 00:00:18.950
Pause this video and see
if you can figure that out.
00:00:19.810 --> 00:00:21.650
Alright, now let's work
through this together.
00:00:21.650 --> 00:00:23.220
And I'm going to figure this out
00:00:23.220 --> 00:00:25.570
by setting up a little bit of a table.
00:00:25.570 --> 00:00:30.570
So we have our indoor, indoor play times.
00:00:31.690 --> 00:00:32.550
I'll write it out.
00:00:32.550 --> 00:00:34.990
Play times.
00:00:34.990 --> 00:00:37.770
We have our outdoor play times.
00:00:37.770 --> 00:00:41.593
Outdoor play times.
00:00:42.470 --> 00:00:44.970
Then we have our total play times.
00:00:44.970 --> 00:00:48.223
Total play times.
00:00:49.070 --> 00:00:52.750
And then, let me set up
a table here as promised,
00:00:52.750 --> 00:00:55.780
and then, I'm going to
set up two columns here.
00:00:55.780 --> 00:00:57.250
So the first column
00:00:57.250 --> 00:00:59.840
is going to concern
itself with the ratios.
00:00:59.840 --> 00:01:01.463
So this is the original,
00:01:02.830 --> 00:01:04.853
original ratio,
00:01:05.870 --> 00:01:08.523
and here, we're going to
put the actual counts.
00:01:09.500 --> 00:01:11.610
Actual counts.
00:01:11.610 --> 00:01:13.840
So what information do we know?
00:01:13.840 --> 00:01:18.840
We know that the ratio of indoor
to outdoor is two to three.
00:01:19.110 --> 00:01:23.580
So the ratio of indoor to
outdoor is two to three.
00:01:23.580 --> 00:01:24.800
And then we could also think about
00:01:24.800 --> 00:01:26.420
what would be the ratio of either of these
00:01:26.420 --> 00:01:28.240
to total play times?
00:01:28.240 --> 00:01:31.010
Well, for every two indoor play times,
00:01:31.010 --> 00:01:33.280
there are three outdoor play times.
00:01:33.280 --> 00:01:35.940
That means for every
two indoor play times,
00:01:35.940 --> 00:01:38.670
there are five total play times,
00:01:38.670 --> 00:01:40.750
or for every three outdoor play times,
00:01:40.750 --> 00:01:43.240
there are five total play times.
00:01:43.240 --> 00:01:44.300
And now, let's think about
00:01:44.300 --> 00:01:46.560
what we know about the actual counts.
00:01:46.560 --> 00:01:51.300
They tell us that there was
a 30 total actual play times.
00:01:51.300 --> 00:01:53.980
So this is the actual number is 30.
00:01:53.980 --> 00:01:56.050
Now this is useful because
now we can think about
00:01:56.050 --> 00:01:59.090
how do we go from the original
ratios to the actual counts?
00:01:59.090 --> 00:02:00.540
If we take the total,
00:02:00.540 --> 00:02:03.820
we notice that we are multiplying by six.
00:02:03.820 --> 00:02:05.070
So to maintain the ratios,
00:02:05.070 --> 00:02:07.350
we would want to multiply
everything by six.
00:02:07.350 --> 00:02:09.370
So if you multiply this by six,
00:02:09.370 --> 00:02:12.820
you're going to have 12
actual indoor play times.
00:02:12.820 --> 00:02:15.030
And if you multiply this by six,
00:02:15.030 --> 00:02:18.760
you're going to have 18
actual outdoor play times.
00:02:18.760 --> 00:02:21.350
And notice, the ratio still holds up.
00:02:21.350 --> 00:02:24.500
Two is to three as 12 is to 18
00:02:24.500 --> 00:02:28.460
or two is to five as 12 is to 30.
00:02:28.460 --> 00:02:29.980
And so, there we have it.
00:02:29.980 --> 00:02:32.930
We know how many of the
play times were indoors, 12,
00:02:32.930 --> 00:02:34.973
and how many were outdoors, 18.
|
Announcing Khan Academy India talent search 2021 | https://www.youtube.com/watch?v=1s3CniZ2OLI | vtt | https://www.youtube.com/api/timedtext?v=1s3CniZ2OLI&ei=ylWUZYjNMue4mLAPpuqSyAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E2D543997F18CDBFAF928933C6CB1B289EE52182.EAD8F3433224AC5FE1B0A48E693155923C557D0C&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:01.153
- Hi.
00:00:01.153 --> 00:00:02.170
Mohish here from Khan India team.
00:00:02.170 --> 00:00:05.860
And we are excited to announce
our India talent search 2021.
00:00:05.860 --> 00:00:08.560
We're looking to connect with
passionate science teachers
00:00:08.560 --> 00:00:10.400
and explore ways of working together.
00:00:10.400 --> 00:00:13.420
So if you are an Indian
citizen based out of India
00:00:13.420 --> 00:00:15.410
and are interested joining us,
00:00:15.410 --> 00:00:17.800
then please click on the link
in the description below.
00:00:17.800 --> 00:00:18.860
There are more details there,
00:00:18.860 --> 00:00:21.200
including a message from Sal himself.
00:00:21.200 --> 00:00:22.033
See you there.
|
National SAT Practice Test Day 2021 | https://www.youtube.com/watch?v=_lyyvZFiAjQ | vtt | https://www.youtube.com/api/timedtext?v=_lyyvZFiAjQ&ei=y1WUZYGrCdKOvdIPv_i3iAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245307&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=12DA0071D352ABAD1E4088E0AECDF4474D2D9730.E6FD881D55E19C4955601008B890228280DDD7D6&key=yt8&lang=en&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:06.200 --> 00:00:07.033
- Hi, everyone.
00:00:07.033 --> 00:00:08.720
Sal Khan here from Khan Academy.
00:00:08.720 --> 00:00:09.960
I just wanted to welcome you
00:00:09.960 --> 00:00:13.940
to National SAT Practice Test Day.
00:00:13.940 --> 00:00:16.160
Now, a lot of you probably are putting
00:00:16.160 --> 00:00:17.690
a lot of weight into the Sat.
00:00:17.690 --> 00:00:21.560
It is an input into the
college admissions process,
00:00:21.560 --> 00:00:24.270
but the one thing I wanna
emphasize is more important
00:00:24.270 --> 00:00:28.400
than the SAT or your score is your ability
00:00:28.400 --> 00:00:30.840
to practice, your ability
to develop yourself
00:00:30.840 --> 00:00:33.200
and how college ready you can be.
00:00:33.200 --> 00:00:36.050
And one thing that I've seen
in my life over and over again,
00:00:36.050 --> 00:00:38.050
and I've seen in many other people's lives
00:00:38.050 --> 00:00:40.610
is the more that you focus on the process
00:00:40.610 --> 00:00:42.230
versus the outcome.
00:00:42.230 --> 00:00:44.380
One, the more enjoyable it will be,
00:00:44.380 --> 00:00:46.800
but also you'll probably
get a better outcome.
00:00:46.800 --> 00:00:50.400
So as you go into National
SAT Practice Test Day,
00:00:50.400 --> 00:00:52.440
and eventually as you
go into the real SAT,
00:00:52.440 --> 00:00:54.560
or really if you go into
anything in your life
00:00:54.560 --> 00:00:58.580
that might feel important,
focus on the process
00:00:58.580 --> 00:01:01.400
and when you do so you'll
get into kind of a Zen Mode
00:01:01.400 --> 00:01:04.120
and it's really starts
to get a little bit fun.
00:01:04.120 --> 00:01:06.460
So take that mindset into the SAT,
00:01:06.460 --> 00:01:09.250
put your best effort, get into the flow,
00:01:09.250 --> 00:01:14.250
get into that zone if you
will, and do the best you can,
00:01:14.420 --> 00:01:17.260
but don't get fixated
on what the outcome is.
00:01:17.260 --> 00:01:20.320
So with that said, let's get started.
00:01:20.320 --> 00:01:21.340
- Thanks Sal.
00:01:21.340 --> 00:01:22.173
Hi, everyone.
00:01:22.173 --> 00:01:23.630
I'm Lauren from Khan Academy.
00:01:23.630 --> 00:01:25.260
Before we get to the practice test,
00:01:25.260 --> 00:01:27.330
I want us to note that we're
giving away some prizes
00:01:27.330 --> 00:01:29.000
for our live attendees today.
00:01:29.000 --> 00:01:30.730
So be sure to check
out the notes on screen
00:01:30.730 --> 00:01:32.710
and follow the instructions to enter.
00:01:32.710 --> 00:01:35.810
We're giving away five, one
hour SATs tutoring sessions
00:01:35.810 --> 00:01:38.410
with our SAT practice content expert.
00:01:38.410 --> 00:01:42.720
And we're also giving your
way 10 $25 Amazon gift cards.
00:01:42.720 --> 00:01:44.390
Okay everyone, let's get started
00:01:44.390 --> 00:01:46.320
on your full full-length practice test.
00:01:46.320 --> 00:01:48.630
The first step is to
log into your official
00:01:48.630 --> 00:01:50.970
SAT practice account on Khan Academy.
00:01:50.970 --> 00:01:55.970
So go to khanacademy.org/sat
and sign into your account.
00:01:56.060 --> 00:01:58.560
If you don't have an account,
you can create one for free
00:01:58.560 --> 00:02:00.268
in just a couple of minutes.
00:02:00.268 --> 00:02:01.780
I'm already signed in.
00:02:01.780 --> 00:02:04.100
So I'm going to click, let's go.
00:02:04.100 --> 00:02:05.530
And once you're logged in,
00:02:05.530 --> 00:02:09.300
you can go ahead and click on
Full Tests at the top here.
00:02:09.300 --> 00:02:10.260
Today we're recommending
00:02:10.260 --> 00:02:12.730
that you take practice test number 10,
00:02:12.730 --> 00:02:14.180
which is the first test you'll see
00:02:14.180 --> 00:02:15.920
after you click on Full Tests.
00:02:15.920 --> 00:02:18.360
Practice tests number 10
is a newest practice test
00:02:18.360 --> 00:02:19.330
on our site.
00:02:19.330 --> 00:02:21.430
And like most of our practice tests,
00:02:21.430 --> 00:02:24.630
it was previously given
as a real SAT exam.
00:02:24.630 --> 00:02:26.770
So it'll give you a great
idea of what to expect
00:02:26.770 --> 00:02:28.850
when you take the SAT in a few weeks.
00:02:28.850 --> 00:02:31.330
If you've already taken
practice tests number 10,
00:02:31.330 --> 00:02:33.280
you can choose one of
these other practice tests
00:02:33.280 --> 00:02:35.700
to take that you haven't taken before.
00:02:35.700 --> 00:02:37.500
Before we start the practice tests,
00:02:37.500 --> 00:02:38.560
I want you to take a minute
00:02:38.560 --> 00:02:40.460
and make sure you have
everything you need.
00:02:40.460 --> 00:02:43.050
So you should have a
pen or a pencil nearby
00:02:43.050 --> 00:02:44.690
along with some scratch paper,
00:02:44.690 --> 00:02:45.523
so you can make notes
00:02:45.523 --> 00:02:47.330
as you work through your math problems.
00:02:47.330 --> 00:02:49.450
You also wanna have an approved calculator
00:02:49.450 --> 00:02:51.090
for the final math sections,
00:02:51.090 --> 00:02:53.820
and you can go to
collegeboard.com to learn about
00:02:53.820 --> 00:02:56.740
what calculators are
approved for the test.
00:02:56.740 --> 00:02:58.500
Generally, most graphing calculators,
00:02:58.500 --> 00:03:00.220
all scientific calculators
00:03:00.220 --> 00:03:02.610
and all four-function
calculators are approved.
00:03:02.610 --> 00:03:04.550
So whatever calculator you have today,
00:03:04.550 --> 00:03:07.090
that will be just fine
for the practice test.
00:03:07.090 --> 00:03:08.680
Another thing important thing to do
00:03:08.680 --> 00:03:11.350
is eliminate as many
distractions as possible.
00:03:11.350 --> 00:03:15.120
So make sure your phone is
off or set to Do Not Disturb
00:03:15.120 --> 00:03:17.030
and make sure you're in a
quiet, comfortable space
00:03:17.030 --> 00:03:19.460
where you can really focus
on your practice tests.
00:03:19.460 --> 00:03:22.250
Also, if you're using a laptop,
make sure it's plugged in
00:03:22.250 --> 00:03:24.900
so that you don't have to
worry about the battery dying.
00:03:24.900 --> 00:03:26.900
Next, let's take a minute to get over
00:03:26.900 --> 00:03:28.260
the structure of the test.
00:03:28.260 --> 00:03:30.190
So you know what to expect.
00:03:30.190 --> 00:03:33.950
The first section is reading
and it is 65 minutes long.
00:03:33.950 --> 00:03:36.150
Then we'll take a 10-minute break.
00:03:36.150 --> 00:03:38.420
The next section is writing and language
00:03:38.420 --> 00:03:40.540
and it is 35 minutes long.
00:03:40.540 --> 00:03:42.900
Right after that section,
we'll move into the math,
00:03:42.900 --> 00:03:46.540
no calculator section,
which is 25 minutes long.
00:03:46.540 --> 00:03:48.830
Then we'll take a five-minute break.
00:03:48.830 --> 00:03:50.870
Then you'll return for the final section,
00:03:50.870 --> 00:03:52.970
which is the math with calculator section,
00:03:52.970 --> 00:03:54.453
which is 55 minutes long.
00:03:55.470 --> 00:03:58.520
We won't be adding in the
optional essay section today,
00:03:58.520 --> 00:04:00.480
but you can practice the
essay on Khan Academy
00:04:00.480 --> 00:04:03.290
after the practice test, if you'd like to.
00:04:03.290 --> 00:04:06.080
So we'll have a timer running
on the screen for each section
00:04:06.080 --> 00:04:07.440
that you can refer to.
00:04:07.440 --> 00:04:09.530
And just like when you take the real SAT,
00:04:09.530 --> 00:04:11.650
you'll hear me announce when
we reached the halfway point
00:04:11.650 --> 00:04:14.630
of each section, and when you
have five minutes remaining.
00:04:14.630 --> 00:04:16.860
I know it's a big commitment
to take a three-hour test
00:04:16.860 --> 00:04:19.270
on a Saturday, but going
through the full test
00:04:19.270 --> 00:04:21.450
in one sitting is really
a great way to prepare
00:04:21.450 --> 00:04:22.910
for the test experience.
00:04:22.910 --> 00:04:25.090
So I applaud all of you
for being here today
00:04:25.090 --> 00:04:26.460
and taking the time.
00:04:26.460 --> 00:04:28.810
So as you're getting
ready to start the test,
00:04:28.810 --> 00:04:30.360
stop (indistinct) a minute and think about
00:04:30.360 --> 00:04:33.290
what your goal is on
the practice test today.
00:04:33.290 --> 00:04:36.220
Maybe you wanna improve your
pacing in a certain section,
00:04:36.220 --> 00:04:38.320
or maybe there's a certain benchmark score
00:04:38.320 --> 00:04:39.680
you're hoping to improve,
00:04:39.680 --> 00:04:41.080
or maybe you just wanna get a sense
00:04:41.080 --> 00:04:42.730
of what the full test is like.
00:04:42.730 --> 00:04:45.020
Whatever your goal is
just take a quick minute
00:04:45.020 --> 00:04:46.920
and write it down on your scratch paper
00:04:46.920 --> 00:04:49.290
and we'll revisit it at the end.
00:04:49.290 --> 00:04:51.210
All right, so we're ready.
00:04:51.210 --> 00:04:53.330
So let's everyone take a deep breath,
00:04:53.330 --> 00:04:55.410
relax and let's get started.
00:04:55.410 --> 00:04:56.260
Please begin now.
00:24:59.607 --> 00:25:02.430
You have 35 minutes
remaining in this section.
00:35:00.340 --> 00:35:02.870
You have 25 minutes
remaining in this section.
00:49:59.740 --> 00:50:02.040
You have 20 minutes
remaining in this section.
00:54:58.730 --> 00:55:01.683
You have 15 minutes
remaining in this section.
01:04:59.547 --> 01:05:02.113
You have five minutes
remaining in this section.
01:09:59.117 --> 01:10:00.863
Stop work on this section.
01:10:06.660 --> 01:10:09.200
Congratulations on completing
the reading section.
01:10:09.200 --> 01:10:11.180
Now it's time for your 10 minute break.
01:10:11.180 --> 01:10:13.030
So grab a snack, use the restroom,
01:10:13.030 --> 01:10:14.420
get up and stretch for a bit.
01:10:14.420 --> 01:10:16.120
And we'll see you back here in 10.
01:20:25.450 --> 01:20:27.450
All right, everyone break is over.
01:20:27.450 --> 01:20:29.670
So it's time to get back to your computers
01:20:29.670 --> 01:20:31.410
and get ready for section two.
01:20:31.410 --> 01:20:32.310
Let's get started.
01:20:33.330 --> 01:20:35.847
Please begin the writing
and language section now.
01:40:33.330 --> 01:40:36.687
You have 15 minutes
remaining in this section.
01:50:33.550 --> 01:50:35.950
You have five minutes
remaining in this section.
01:55:34.373 --> 01:55:35.983
Stop work on this section.
01:55:51.930 --> 01:55:55.017
Please begin the math, no
calculator section now.
02:05:51.257 --> 02:05:54.160
You have 15 minutes
remaining in this section.
02:15:42.030 --> 02:15:44.550
You have five minutes
remaining in this section.
02:20:52.120 --> 02:20:53.853
Stop work on this section.
02:20:59.040 --> 02:20:59.950
Great job.
02:20:59.950 --> 02:21:02.540
You've completed three
out of four sections.
02:21:02.540 --> 02:21:04.980
Now it's time for your five minute break.
02:21:04.980 --> 02:21:06.900
Be sure to stand up and walk around
02:21:06.900 --> 02:21:08.190
and get a drink of water.
02:21:08.190 --> 02:21:09.540
You're in the home stretch.
02:21:09.540 --> 02:21:11.540
We'll see you back here in five minutes.
02:26:19.297 --> 02:26:20.620
All right, everyone,
02:26:20.620 --> 02:26:23.500
time to get back to your
computers for the final section,
02:26:23.500 --> 02:26:26.320
get your calculator ready
and let's get started.
02:26:26.320 --> 02:26:28.853
Please begin the math
calculator section now.
02:46:31.347 --> 02:46:34.180
You have 35 minutes
remaining in this section.
02:56:32.090 --> 02:56:34.620
You have 25 minutes
remaining in this section.
03:01:32.177 --> 03:01:34.850
You have 20 minutes
remaining in this section.
03:06:32.750 --> 03:06:35.440
You have 15 minutes
remaining in this section.
03:16:33.167 --> 03:16:35.900
You have five minutes
remaining in this section.
03:21:34.293 --> 03:21:35.993
Stop work on this section.
03:21:39.270 --> 03:21:40.740
Congratulations, everyone.
03:21:40.740 --> 03:21:43.350
You just completed a
full-length practice test.
03:21:43.350 --> 03:21:45.530
Now I know you're
probably tired right now.
03:21:45.530 --> 03:21:48.060
So after you've had some
time to rest and relax,
03:21:48.060 --> 03:21:49.660
I highly encourage you
to come visit the test
03:21:49.660 --> 03:21:50.690
that you just took
03:21:50.690 --> 03:21:52.140
so that you can go over
what you've got right,
03:21:52.140 --> 03:21:55.300
and what you missed, and you
can see what you need to study.
03:21:55.300 --> 03:21:58.010
And as we wrap up this Practice Test Day
03:21:58.010 --> 03:21:59.940
I want you to think back
to that goal you wrote down
03:21:59.940 --> 03:22:01.220
when we first started.
03:22:01.220 --> 03:22:03.010
Do you think you achieved that goal?
03:22:03.010 --> 03:22:04.500
Why or why not?
03:22:04.500 --> 03:22:06.890
Just take a few quick
moments to reflect on that
03:22:06.890 --> 03:22:09.250
and consider how this might
affect your future plans
03:22:09.250 --> 03:22:10.500
as you study for the SAT.
03:22:14.440 --> 03:22:17.000
Thanks again for participating
in the event today.
03:22:17.000 --> 03:22:19.460
And before you go, don't
forget to enter our raffle
03:22:19.460 --> 03:22:21.030
where you can have a chance to win one
03:22:21.030 --> 03:22:23.320
of our free one hour tutoring sessions
03:22:23.320 --> 03:22:25.800
or $25 Amazon gift cards.
03:22:25.800 --> 03:22:27.582
Have a great day, take care.
03:22:27.582 --> 03:22:28.943
And bye for now.
|
Acid–base indicators | https://www.youtube.com/watch?v=ZDgYWaeuwbw | vtt | https://www.youtube.com/api/timedtext?v=ZDgYWaeuwbw&ei=0lWUZeykEOD7vdIPgJKjgAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=18E979188E78298A7ED95BC246D8DCFD95E6E182.20B08F1C91FABDD5257D683C28C1FE0970C12809&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:03.000
- [Instructor] Acid-base
indicators are used in titrations
00:00:03.000 --> 00:00:06.060
to determine when the
equivalence point is reached.
00:00:06.060 --> 00:00:08.650
Let's look at a hypothetical indicator.
00:00:08.650 --> 00:00:13.456
In the protonated form, the
indicator has the formula HIn.
00:00:13.456 --> 00:00:18.010
So this would be the acidic
proton on this protonated form.
00:00:18.010 --> 00:00:20.210
When base is added, the protonated form
00:00:20.210 --> 00:00:23.490
is converted into the deprotonated form.
00:00:23.490 --> 00:00:26.040
So we lose an H and we
lose a positive charge.
00:00:26.040 --> 00:00:28.580
So the deprotonated form is represented by
00:00:28.580 --> 00:00:30.860
In with a negative charge.
00:00:30.860 --> 00:00:34.240
And if we add an H plus
to the deprotonated form,
00:00:34.240 --> 00:00:36.110
we would make the protonated form
00:00:36.110 --> 00:00:37.990
of the acid-base indicator.
00:00:37.990 --> 00:00:40.280
For this hypothetical acid-base indicator,
00:00:40.280 --> 00:00:42.390
the protonated form is red
00:00:42.390 --> 00:00:45.730
and the deprotonated form is yellow.
00:00:45.730 --> 00:00:47.740
Next, let's think about
the color of a solution
00:00:47.740 --> 00:00:51.750
containing this acid-base
indicator at different pH values.
00:00:51.750 --> 00:00:55.160
Let's say that the pKa
value for the acidic proton
00:00:55.160 --> 00:00:58.400
on the protonated form is equal to three
00:00:58.400 --> 00:01:00.800
at 25 degrees Celsius.
00:01:00.800 --> 00:01:05.500
And let's say the pH of the
solution is equal to two.
00:01:05.500 --> 00:01:07.300
In that case, the pH of the solution
00:01:07.300 --> 00:01:12.090
is less than the pKa value
for our acidic proton.
00:01:12.090 --> 00:01:15.870
So if you think about the
protonated form being a weak acid
00:01:15.870 --> 00:01:19.610
and the deprotonated form
being the conjugate base,
00:01:19.610 --> 00:01:22.350
when the pH is less than the pKa value
00:01:22.350 --> 00:01:24.680
for a conjugate acid-base pair,
00:01:24.680 --> 00:01:27.760
the concentration of the
weak acid is greater than
00:01:27.760 --> 00:01:30.660
the concentration of the conjugate base.
00:01:30.660 --> 00:01:33.610
At a pH of two, we have a lot
more of the protonated form
00:01:33.610 --> 00:01:36.830
which is red than the
deprotonated form which is yellow.
00:01:36.830 --> 00:01:40.220
Therefore, the color of the
solution that a pH of two
00:01:40.220 --> 00:01:42.530
would appear to be red.
00:01:42.530 --> 00:01:44.930
Next, let's think about
the color of the solution
00:01:44.930 --> 00:01:48.480
if the pH of the solution
is equal to four.
00:01:48.480 --> 00:01:50.710
Since the pKa value is equal to three,
00:01:50.710 --> 00:01:52.660
if the pH is equal to four,
00:01:52.660 --> 00:01:56.690
the pH is greater than the pKa value.
00:01:56.690 --> 00:01:58.640
And for a conjugate acid-base pair,
00:01:58.640 --> 00:02:02.230
when the pH of the solution
is greater than the pKa value,
00:02:02.230 --> 00:02:04.030
the concentration of the conjugate base
00:02:04.030 --> 00:02:07.160
is greater than the
concentration of the weak acid.
00:02:07.160 --> 00:02:08.580
Or as I have written here,
00:02:08.580 --> 00:02:10.980
the concentration of the
weak acid is less than
00:02:10.980 --> 00:02:13.460
the concentration of the conjugate base.
00:02:13.460 --> 00:02:15.490
So at a pH of four, we have a lot more
00:02:15.490 --> 00:02:18.000
of the deprotonated form which is yellow
00:02:18.000 --> 00:02:20.010
than the protonated form which is red.
00:02:20.010 --> 00:02:22.240
And since we have more yellow than red,
00:02:22.240 --> 00:02:24.480
the solution would be yellow.
00:02:24.480 --> 00:02:26.380
Finally, let's think about the situation
00:02:26.380 --> 00:02:29.700
where the pH is equal to three.
00:02:29.700 --> 00:02:32.980
Since the pKa value is
also equal to three,
00:02:32.980 --> 00:02:36.270
the pH is equal to the pKa value.
00:02:36.270 --> 00:02:38.210
And for a conjugate acid-base pair,
00:02:38.210 --> 00:02:40.560
when the pH is equal to the pKa,
00:02:40.560 --> 00:02:42.900
the concentration of the weak acid
00:02:42.900 --> 00:02:46.740
is equal to the concentration
of the conjugate base.
00:02:46.740 --> 00:02:49.120
And if we have equal amounts
of the protonated form
00:02:49.120 --> 00:02:51.790
and the deprotonated form,
we have equal amounts
00:02:51.790 --> 00:02:55.500
of red and yellow,
therefore at a pH of three,
00:02:55.500 --> 00:02:58.310
the solution would be orange.
00:02:58.310 --> 00:03:01.400
Next let's think the pH
range of the color change
00:03:01.400 --> 00:03:03.630
for this hypothetical indicator.
00:03:03.630 --> 00:03:06.560
The approximate pH range
over which an indicator
00:03:06.560 --> 00:03:11.560
changes color is equal to the
pKa value plus or minus one.
00:03:12.160 --> 00:03:14.990
The pKa value for our
hypothetical indicator
00:03:14.990 --> 00:03:18.080
was equal to three,
therefore three plus one
00:03:18.080 --> 00:03:21.150
is equal to four and three
minus one is equal to two,
00:03:21.150 --> 00:03:24.700
and two to four is the
approximate pH range
00:03:24.700 --> 00:03:27.410
over which our indicator changes color.
00:03:27.410 --> 00:03:28.910
And we already know our solution
00:03:28.910 --> 00:03:33.400
with the acid-base indicator
in it at a pH of two is red
00:03:33.400 --> 00:03:35.870
and at a pH of three
the solution is orange
00:03:35.870 --> 00:03:38.580
and at a pH of four
the solution is yellow.
00:03:38.580 --> 00:03:42.410
Therefore, if we were to
change the pH from two to four,
00:03:42.410 --> 00:03:45.130
we would see the color of the solution go
00:03:45.130 --> 00:03:48.010
from red to orange to yellow.
00:03:48.010 --> 00:03:50.820
Now let's see how to choose
the right acid-base indicator
00:03:50.820 --> 00:03:52.210
for a titration.
00:03:52.210 --> 00:03:55.450
Our goal is to choose an indicator
whose color change occurs
00:03:55.450 --> 00:03:59.720
as close as possible to the
pH of the equivalence point.
00:03:59.720 --> 00:04:02.400
For a weak acid strong based titration,
00:04:02.400 --> 00:04:06.250
the equivalence point occurs
at a pH greater than seven.
00:04:06.250 --> 00:04:09.460
First, let's look at the
acid-base indicator methyl red.
00:04:09.460 --> 00:04:13.950
Methyl red has a pH range of
approximately four to six.
00:04:13.950 --> 00:04:17.090
So a little bit over four
methyl red starts to change
00:04:17.090 --> 00:04:20.290
from red to orange, and
then eventually to yellow
00:04:20.290 --> 00:04:22.900
by the time you hit a pH of about six.
00:04:22.900 --> 00:04:25.750
However, the pH at the equivalence
point for this titration
00:04:25.750 --> 00:04:28.680
looks to be somewhere
between eight and 10.
00:04:28.680 --> 00:04:31.480
Therefore, if we used
methyl red and we stopped
00:04:31.480 --> 00:04:33.930
the titration when the color changed,
00:04:33.930 --> 00:04:36.130
we'd be stopping the titration too early.
00:04:36.130 --> 00:04:38.220
So we might be stopping
it somewhere in here
00:04:38.220 --> 00:04:40.840
before we reach the equivalence point.
00:04:40.840 --> 00:04:43.340
So methyl red would not be a good choice
00:04:43.340 --> 00:04:46.490
as an acid-base indicator
for this titration.
00:04:46.490 --> 00:04:49.440
Another way to think about
this is with pKa values.
00:04:49.440 --> 00:04:53.150
For methyl red, the pKa
value is approximately five.
00:04:53.150 --> 00:04:55.180
And the goal is to match the pKa value
00:04:55.180 --> 00:04:58.490
as closely as possible to the
pH at the equivalence point.
00:04:58.490 --> 00:05:00.490
But since the pH at the equivalence point
00:05:00.490 --> 00:05:04.390
is between eight and 10,
that's too far away from five.
00:05:04.390 --> 00:05:07.390
So by looking at the pKa
value, we know that methyl red
00:05:07.390 --> 00:05:09.863
is not a good fit for this titration.
00:05:10.750 --> 00:05:12.650
Phenolphthalein is an example of another
00:05:12.650 --> 00:05:16.090
acid-base indicator, and it
has a different pH range.
00:05:16.090 --> 00:05:18.840
At a pH of about eight,
phenolphthalein is colorless.
00:05:18.840 --> 00:05:22.160
However, as the pH
changes from eight to 10,
00:05:22.160 --> 00:05:25.020
phenolphthalein goes
from colorless to pink.
00:05:25.020 --> 00:05:27.930
Because the color of the indicator
changes in the same range
00:05:27.930 --> 00:05:29.730
where we would find the equivalence point,
00:05:29.730 --> 00:05:33.090
phenolphthalein is a good
choice as an acid-base indicator
00:05:33.090 --> 00:05:34.600
for this titration.
00:05:34.600 --> 00:05:37.320
And thinking about the pKa
value for phenolphthalein
00:05:37.320 --> 00:05:40.330
which is approximately nine,
that falls in the range
00:05:40.330 --> 00:05:43.020
of eight to 10 where we
find our equivalence point.
00:05:43.020 --> 00:05:45.860
So we could think about it
either in terms of the pH range
00:05:45.860 --> 00:05:47.683
or the pKa value.
00:05:48.570 --> 00:05:49.890
Next let's choose an indicator
00:05:49.890 --> 00:05:52.870
for a weak based strong acid titration.
00:05:52.870 --> 00:05:54.810
For a weak based strong acid titration,
00:05:54.810 --> 00:05:58.950
the equivalence point occurs
at a pH less than seven.
00:05:58.950 --> 00:06:01.600
If we try to use phenolphthalein
for this titration,
00:06:01.600 --> 00:06:04.710
remember phenolphthalein
changes from eight to 10,
00:06:04.710 --> 00:06:07.410
or in this case, it'd be
changing from 10 to eight.
00:06:07.410 --> 00:06:10.130
So we'd start at this
relatively high pH here,
00:06:10.130 --> 00:06:11.880
and if we tried to use phenolphthalein
00:06:11.880 --> 00:06:13.700
and we stopped at when
the color change occurred,
00:06:13.700 --> 00:06:15.920
we'd be stopping the titration too early.
00:06:15.920 --> 00:06:19.020
So we might be stopping the
titration somewhere in here.
00:06:19.020 --> 00:06:21.380
So phenolphthalein is not a good choice
00:06:21.380 --> 00:06:25.620
as an acid-base indicator for
this particular titration.
00:06:25.620 --> 00:06:27.670
Thinking about using pKa values,
00:06:27.670 --> 00:06:30.570
the pKa value for phenolphthalein
is approximately nine,
00:06:30.570 --> 00:06:33.330
which is not a good fit for
the pH at the equivalence point
00:06:33.330 --> 00:06:37.510
which appears to be between four and six.
00:06:37.510 --> 00:06:40.110
Methyl red has a pH range
of about four to six
00:06:40.110 --> 00:06:41.360
over which it changes color
00:06:41.360 --> 00:06:43.820
and a pKa value of approximately five.
00:06:43.820 --> 00:06:46.160
And since the equivalence point,
00:06:46.160 --> 00:06:48.950
the pH of the equivalence
point is between four and six,
00:06:48.950 --> 00:06:51.100
methyl red would be a good choice
00:06:51.100 --> 00:06:54.520
as an acid-based indicator
for this titration.
00:06:54.520 --> 00:06:57.190
So to summarize, when choosing
an acid-base indicator
00:06:57.190 --> 00:06:59.360
for a titration, choose an indicator
00:06:59.360 --> 00:07:02.330
whose color change occurs
as closely as possible
00:07:02.330 --> 00:07:04.453
to the pH at the equivalence point.
|
Weak base–strong acid titrations | https://www.youtube.com/watch?v=IZ7NEYnuovI | vtt | https://www.youtube.com/api/timedtext?v=IZ7NEYnuovI&ei=0lWUZYP9EOW2vdIPl4GMoAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9E3F94E3798A64E9E3F4AC786D940F81C896FC08.0B6F5E5592657C9ACDF4759256577DDEC8DE23CA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.400 --> 00:00:03.100
- [Instructor] Ammonia is
an example of a weak base
00:00:03.100 --> 00:00:06.730
and hydrochloric acid is an
example of a strong acid.
00:00:06.730 --> 00:00:10.700
And if we're doing a weak
base-strong acid titration,
00:00:10.700 --> 00:00:12.950
that means that ammonia is the analyte,
00:00:12.950 --> 00:00:14.600
the substance we're analyzing,
00:00:14.600 --> 00:00:17.800
and we're titrating ammonia
with hydrochloric acid
00:00:17.800 --> 00:00:20.840
and therefore hydrochloric
acid is the titrant.
00:00:20.840 --> 00:00:24.650
And when ammonia reacts
with hydrochloric acid,
00:00:24.650 --> 00:00:28.700
the product is an aqueous
solution of ammonium chloride.
00:00:28.700 --> 00:00:32.020
For our complete or
overall ionic equation,
00:00:32.020 --> 00:00:33.920
since ammonia is a weak base,
00:00:33.920 --> 00:00:38.050
we show it as NH3 in our
complete ionic equation.
00:00:38.050 --> 00:00:40.830
However, since hydrochloric
acid is a strong acid
00:00:40.830 --> 00:00:42.530
that ionizes 100%,
00:00:42.530 --> 00:00:44.690
we show it as breaking up into its ion,
00:00:44.690 --> 00:00:45.523
so H+ and CL-.
00:00:47.270 --> 00:00:50.480
Ammonium chloride is a soluble salt,
00:00:50.480 --> 00:00:52.750
therefore we would show ammonium chloride
00:00:52.750 --> 00:00:55.070
in aqueous solution as ammonium cations
00:00:55.070 --> 00:00:57.000
and chloride anions.
00:00:57.000 --> 00:00:58.560
To write the net ionic equation,
00:00:58.560 --> 00:01:00.390
we leave out spectator ions.
00:01:00.390 --> 00:01:02.840
And since we have chloride
anions on the left side
00:01:02.840 --> 00:01:04.200
and on the right side,
00:01:04.200 --> 00:01:06.250
chloride anions are the spectator ions.
00:01:06.250 --> 00:01:08.930
And leaving those out, we
get the net ionic equation,
00:01:08.930 --> 00:01:13.930
which is ammonia NH3 plus H+ goes to NH4+.
00:01:14.000 --> 00:01:17.130
So this is one way to write
to the net ionic equation
00:01:17.130 --> 00:01:20.370
for this weak base-strong acid titration.
00:01:20.370 --> 00:01:22.280
Next, let's look at the titration curve
00:01:22.280 --> 00:01:25.220
for our weak base-strong acid titration.
00:01:25.220 --> 00:01:29.360
pH is on the y-axis and milliliters
of acid is on the x-axis
00:01:29.360 --> 00:01:33.750
because we're adding our strong
acid to our aqueous solution
00:01:33.750 --> 00:01:35.390
of our weak base.
00:01:35.390 --> 00:01:37.900
Looking at the first point
on our titration curve,
00:01:37.900 --> 00:01:40.030
the pH is relatively basic.
00:01:40.030 --> 00:01:43.410
So this is before any
strong acid has been added.
00:01:43.410 --> 00:01:45.900
The reason why the pH is
basic is because we have
00:01:45.900 --> 00:01:48.290
an aqueous solution of
our weak base, ammonia,
00:01:48.290 --> 00:01:51.240
which reacts with water to
produce ammonium cations
00:01:51.240 --> 00:01:52.820
and hydroxide anions.
00:01:52.820 --> 00:01:55.610
And it's these hydroxide
anions that cause the pH
00:01:55.610 --> 00:01:57.390
to be relatively high.
00:01:57.390 --> 00:02:00.210
However, the equilibrium
favors the reactants
00:02:00.210 --> 00:02:01.330
for this reaction.
00:02:01.330 --> 00:02:04.960
So we have mostly ammonia
and very little ammonium
00:02:04.960 --> 00:02:07.370
at this point in the titration curve.
00:02:07.370 --> 00:02:09.760
Next, we think about adding some acid
00:02:09.760 --> 00:02:12.740
to our aqueous solution of ammonia.
00:02:12.740 --> 00:02:15.060
And from our net ionic equation,
00:02:15.060 --> 00:02:16.530
when ammonia reacts with H+,
00:02:16.530 --> 00:02:20.490
that forms the ammonium cation, NH4+.
00:02:20.490 --> 00:02:21.910
Looking at the titration curve,
00:02:21.910 --> 00:02:23.760
as we add more and more acid,
00:02:23.760 --> 00:02:26.070
the pH starts to decrease.
00:02:26.070 --> 00:02:30.410
However, in this range, there's
a slow decrease in the pH.
00:02:30.410 --> 00:02:31.860
As more acid is added,
00:02:31.860 --> 00:02:35.310
more ammonia is turned
into the ammonium cation.
00:02:35.310 --> 00:02:36.900
Eventually, we reach a point
00:02:36.900 --> 00:02:39.530
where all of the initial
ammonia has been neutralized
00:02:39.530 --> 00:02:41.400
by the addition of the acid.
00:02:41.400 --> 00:02:44.690
This point is called
the equivalence point.
00:02:44.690 --> 00:02:46.260
And the way to find the equivalence point
00:02:46.260 --> 00:02:47.620
on our titration curve
00:02:47.620 --> 00:02:51.600
is to first look for this
sharp decrease in the pH.
00:02:51.600 --> 00:02:54.400
And then we can draw a straight line here.
00:02:54.400 --> 00:02:57.380
And approximately halfway
down that straight line
00:02:57.380 --> 00:03:00.170
is a good estimate of
the equivalence point
00:03:00.170 --> 00:03:02.030
for this titration.
00:03:02.030 --> 00:03:04.500
To find the pH of the solution
at the equivalence point,
00:03:04.500 --> 00:03:07.470
we simply go over to where
the equivalence point is
00:03:07.470 --> 00:03:09.170
on the y-axis.
00:03:09.170 --> 00:03:10.520
And so for this pH,
00:03:10.520 --> 00:03:12.850
we can see the pH at the equivalence point
00:03:12.850 --> 00:03:14.210
is less than seven.
00:03:14.210 --> 00:03:15.640
So let me go ahead and
write that down here.
00:03:15.640 --> 00:03:17.840
The pH is less than seven
00:03:17.840 --> 00:03:21.120
for a weak base-strong acid titration.
00:03:21.120 --> 00:03:23.240
The reason why the pH is less than seven
00:03:23.240 --> 00:03:24.420
at the equivalence point
00:03:24.420 --> 00:03:26.730
is because all the ammonia
that we started with
00:03:26.730 --> 00:03:28.540
has been completely neutralized
00:03:28.540 --> 00:03:32.160
and turned into the ammonium cation, NH4+.
00:03:32.160 --> 00:03:34.500
The ammonium cation is a weak acid
00:03:34.500 --> 00:03:38.970
and reacts with water to
form hydronium ions, H3O+,
00:03:38.970 --> 00:03:41.220
and ammonia, an aqueous solution.
00:03:41.220 --> 00:03:45.380
At 25 degrees Celsius,
water has a pH of seven.
00:03:45.380 --> 00:03:48.940
However, since the ammonium
cation is a weak acid
00:03:48.940 --> 00:03:52.950
and we're increasing the
concentration of hydronium ions
00:03:52.950 --> 00:03:56.400
in solution, that decreases the pH,
00:03:56.400 --> 00:03:58.780
therefore the pH is less than seven
00:03:58.780 --> 00:04:00.420
at the equivalence point.
00:04:00.420 --> 00:04:02.340
In addition to ammonium ions,
00:04:02.340 --> 00:04:04.820
there are also chloride
anions in solution.
00:04:04.820 --> 00:04:07.740
However, chloride anions
do not react with water
00:04:07.740 --> 00:04:10.660
and therefore do not affect the pH.
00:04:10.660 --> 00:04:13.590
Going back to the equivalence
point on our titration curve,
00:04:13.590 --> 00:04:16.170
if we dropped down here to the x-axis,
00:04:16.170 --> 00:04:19.900
we can see the equivalence point
occurs after 50 milliliters
00:04:19.900 --> 00:04:22.180
of acid has been added.
00:04:22.180 --> 00:04:24.710
Therefore, if it took
50 milliliters of acid
00:04:24.710 --> 00:04:28.170
to neutralize all of the ammonia
that was initially present,
00:04:28.170 --> 00:04:32.320
it would take half that volume
or 25 milliliters of acid
00:04:32.320 --> 00:04:34.740
to neutralize half of the ammonia.
00:04:34.740 --> 00:04:37.890
So if we go back up here
and we draw a dashed line
00:04:37.890 --> 00:04:39.640
to our titration curve,
00:04:39.640 --> 00:04:42.340
this point on our
titration curve represents
00:04:42.340 --> 00:04:44.920
the half equivalence point.
00:04:44.920 --> 00:04:47.600
So this point represents
the half equivalence point
00:04:47.600 --> 00:04:48.960
on our titration curve.
00:04:48.960 --> 00:04:52.030
And since we've neutralized
half of the ammonia
00:04:52.030 --> 00:04:53.820
that was initially present,
00:04:53.820 --> 00:04:57.030
that means there are equal
concentrations of ammonia
00:04:57.030 --> 00:04:59.860
and the ammonium cation at this point.
00:04:59.860 --> 00:05:01.810
Let's go back to our equivalence points
00:05:01.810 --> 00:05:04.050
where all the ammonia that we started with
00:05:04.050 --> 00:05:05.710
has been neutralized.
00:05:05.710 --> 00:05:09.500
Therefore, if we add some
more acid to the solution,
00:05:09.500 --> 00:05:12.000
there's no more ammonia
for it to react with.
00:05:12.000 --> 00:05:15.640
And therefore we see the pH drop.
00:05:15.640 --> 00:05:18.050
So this portion of the titration curve
00:05:18.050 --> 00:05:21.150
is the region of excess acid.
00:05:21.150 --> 00:05:24.100
Let's go back to the
half equivalence point
00:05:24.100 --> 00:05:25.970
on our titration curve.
00:05:25.970 --> 00:05:27.160
Remember at that point,
00:05:27.160 --> 00:05:29.240
the concentration of ammonium cation
00:05:29.240 --> 00:05:31.860
is equal to the concentration of ammonia.
00:05:31.860 --> 00:05:33.930
The ammonium cation and ammonia
00:05:33.930 --> 00:05:36.140
are a conjugate acid-base pair.
00:05:36.140 --> 00:05:38.220
And when there are significant amounts
00:05:38.220 --> 00:05:41.430
of a weak conjugate acid-base pair,
00:05:41.430 --> 00:05:43.380
there's a buffer solution.
00:05:43.380 --> 00:05:45.680
Therefore, at the half equivalence point,
00:05:45.680 --> 00:05:47.090
we have a buffer solution,
00:05:47.090 --> 00:05:50.000
and we can calculate the pH at that point
00:05:50.000 --> 00:05:53.100
by using the
Henderson-Hasselbalch equation.
00:05:53.100 --> 00:05:56.330
So pH is equal to the
pKa of the weak acid,
00:05:56.330 --> 00:05:59.790
plus the log of the concentration
of the conjugate base,
00:05:59.790 --> 00:06:02.780
divided by the concentration
of the weak acid.
00:06:02.780 --> 00:06:06.100
For this example, the
base is ammonia, NH3,
00:06:06.100 --> 00:06:09.830
and the conjugate acid is
the ammonium cation. NH4+.
00:06:09.830 --> 00:06:11.540
Therefore, this pKa value
00:06:11.540 --> 00:06:13.170
in the Henderson-Hasselbalch equation
00:06:13.170 --> 00:06:16.570
is referring to the pKa value of ammonium.
00:06:16.570 --> 00:06:19.650
And because the concentrations
of ammonium and ammonia
00:06:19.650 --> 00:06:21.990
are equal at the half equivalence point,
00:06:21.990 --> 00:06:25.390
the ratio of their
concentrations is equal to one
00:06:25.390 --> 00:06:28.600
and the log of one is equal to zero.
00:06:28.600 --> 00:06:30.620
Therefore, at the half equivalence point,
00:06:30.620 --> 00:06:35.620
the pH is equal to the pKa
value of the weak acid.
00:06:35.730 --> 00:06:37.770
So if we wanted to find the pKa value
00:06:37.770 --> 00:06:38.990
for the ammonium cation,
00:06:38.990 --> 00:06:40.990
we would find the half equivalence point
00:06:40.990 --> 00:06:43.420
and we'd draw our dotted line over to
00:06:43.420 --> 00:06:45.660
where the intersects on our y-axis
00:06:45.660 --> 00:06:47.520
and whatever pH that is,
00:06:47.520 --> 00:06:50.040
that's the pKa value of ammonium.
00:06:50.040 --> 00:06:52.800
So in this case, it looks
to be a little bit over nine
00:06:52.800 --> 00:06:55.300
as a good estimate for the pKa value
00:06:55.300 --> 00:06:57.120
of the ammonium cation.
00:06:57.120 --> 00:07:00.290
Next, let's think about how
our titration curve can tell us
00:07:00.290 --> 00:07:02.200
about the relative concentrations
00:07:02.200 --> 00:07:05.010
of our weak conjugate acid-base pair.
00:07:05.010 --> 00:07:07.030
We know that at the
half equivalence points
00:07:07.030 --> 00:07:09.320
where the pH is equal to the pKa value,
00:07:09.320 --> 00:07:11.950
the concentration of ammonium cations
00:07:11.950 --> 00:07:14.500
is equal to the concentration of ammonia.
00:07:14.500 --> 00:07:16.950
So let's think about a
point just to the left
00:07:16.950 --> 00:07:18.570
of our half equivalence point,
00:07:18.570 --> 00:07:21.070
which I'm gonna call point P.
00:07:21.070 --> 00:07:24.210
At point P, the pH is greater
00:07:24.210 --> 00:07:26.220
than the pKa value.
00:07:26.220 --> 00:07:28.840
And we know the initial
point on our titration curve
00:07:28.840 --> 00:07:32.380
was almost all weak base, almost all NH3.
00:07:32.380 --> 00:07:35.410
Because point P is in
between the initial point
00:07:35.410 --> 00:07:38.040
where there was almost all NH3,
00:07:38.040 --> 00:07:40.690
and the half equivalence point
where there was equal amounts
00:07:40.690 --> 00:07:42.980
of NH3 and NH4+,
00:07:42.980 --> 00:07:46.140
at point P, there must be more NH3
00:07:46.140 --> 00:07:48.480
than NH4+.
00:07:48.480 --> 00:07:50.630
Therefore, when the pH of
the solution is greater
00:07:50.630 --> 00:07:52.430
than the pKa value,
00:07:52.430 --> 00:07:55.080
we know the concentration
of ammonia is greater than
00:07:55.080 --> 00:07:57.550
the concentration of the ammonium cation.
00:07:57.550 --> 00:07:59.810
Or you could say the
concentration of ammonium
00:07:59.810 --> 00:08:02.360
is less than the concentration of ammonia.
00:08:02.360 --> 00:08:03.940
We could have also figured this out using
00:08:03.940 --> 00:08:05.780
the Henderson-Hasselbalch equation.
00:08:05.780 --> 00:08:08.350
However, it's often
easier just to think about
00:08:08.350 --> 00:08:10.470
the shape of the titration curve
00:08:10.470 --> 00:08:12.430
and where the point in question is
00:08:12.430 --> 00:08:14.080
in relation to important points.
00:08:14.080 --> 00:08:15.250
For example, in this case,
00:08:15.250 --> 00:08:18.230
the initial point and the
half equivalence point.
00:08:18.230 --> 00:08:20.680
Next, let's think about
a point just to the right
00:08:20.680 --> 00:08:22.330
of the half equivalence point.
00:08:22.330 --> 00:08:24.970
And I'm gonna call this point Q.
00:08:24.970 --> 00:08:29.970
At point Q, the pH of the
solution is less than the pKa.
00:08:30.850 --> 00:08:34.960
Point Q is in between the
half equivalence point
00:08:34.960 --> 00:08:36.800
and the equivalence point,
00:08:36.800 --> 00:08:39.920
which is approximately here
on the titration curve.
00:08:39.920 --> 00:08:41.760
Remember at the equivalence point,
00:08:41.760 --> 00:08:43.360
all the ammonia that we started with
00:08:43.360 --> 00:08:46.810
has been converted into ammonium, NH4+.
00:08:46.810 --> 00:08:50.560
And because point Q is in between
the half equivalence point
00:08:50.560 --> 00:08:55.080
where the amount of NH3 is
equal to the amount of NH4+,
00:08:55.080 --> 00:08:57.900
and the equivalence
point where all the NH3
00:08:57.900 --> 00:09:00.210
has been converted into NH4+,
00:09:00.210 --> 00:09:02.140
all of the initial NH3.
00:09:02.140 --> 00:09:07.007
That means that at Q, there
must be more NH4+ than NH3.
00:09:08.020 --> 00:09:12.100
Therefore, when the pH is
less than the pKa value,
00:09:12.100 --> 00:09:15.490
we can say the concentration
of ammonium, NH4+,
00:09:15.490 --> 00:09:19.260
is greater than the
concentration of ammonia, NH3.
00:09:19.260 --> 00:09:23.300
The half equivalence
point, point P and point Q
00:09:23.300 --> 00:09:28.300
are all a part of the buffer
region on the titration curve.
00:09:28.710 --> 00:09:32.280
Remember that buffers
resist large changes in pH,
00:09:32.280 --> 00:09:35.760
and that's why we see
a slow decrease in pH
00:09:35.760 --> 00:09:39.760
as acid is added at this
part of the titration curve.
00:09:39.760 --> 00:09:41.320
At the very beginning of the titration,
00:09:41.320 --> 00:09:45.070
we had almost all ammonia
and therefore we did not have
00:09:45.070 --> 00:09:46.490
a buffer solution.
00:09:46.490 --> 00:09:50.040
However, as acid was added
and the ammonia was converted
00:09:50.040 --> 00:09:52.590
into the ammonium cation, NH4+,
00:09:53.460 --> 00:09:55.960
when significant amounts
of both are present,
00:09:55.960 --> 00:09:58.050
we do have a buffer solution.
00:09:58.050 --> 00:10:00.740
And that represents the buffer region
00:10:00.740 --> 00:10:03.490
on our titration curve, so in here.
00:10:03.490 --> 00:10:05.920
However, as more and more acid is added,
00:10:05.920 --> 00:10:08.960
we can see a sharp change in pH start
00:10:08.960 --> 00:10:10.220
to occur right about here,
00:10:10.220 --> 00:10:12.670
so we're no longer in the buffer region
00:10:12.670 --> 00:10:15.150
as we approach the equivalence point.
00:10:15.150 --> 00:10:17.410
So when we think about the titration curve
00:10:17.410 --> 00:10:20.390
of a weak base-strong acid titration,
00:10:20.390 --> 00:10:22.430
and we think about the
half equivalence point
00:10:22.430 --> 00:10:26.510
where the pH is equal to the
pKa value of the weak acid,
00:10:26.510 --> 00:10:29.290
it's important to remember
that there's a buffer region
00:10:29.290 --> 00:10:33.373
or a buffer zone around
that half equivalence point.
|
Weak acid–strong base titrations | https://www.youtube.com/watch?v=sZW1qoQl3ng | vtt | https://www.youtube.com/api/timedtext?v=sZW1qoQl3ng&ei=0lWUZe-ZEK_oxN8PkpOn4A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=11CCD117FBA72DAA454636741117089E6CFAD797.7F944D617CE4C2226BC8323461376E336A40766E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:03.560
- [Instructor] Acetic acid
is an example of a weak acid
00:00:03.560 --> 00:00:07.750
and sodium hydroxide is an
example of a strong base.
00:00:07.750 --> 00:00:09.410
If we are titrating a sample
00:00:09.410 --> 00:00:12.260
of acetic acid with sodium hydroxide,
00:00:12.260 --> 00:00:14.190
acetic acid would be the analyte,
00:00:14.190 --> 00:00:15.920
the substance that we are analyzing,
00:00:15.920 --> 00:00:18.890
and sodium hydroxide would be the titrant.
00:00:18.890 --> 00:00:21.540
When acetic acid reacts
with sodium hydroxide,
00:00:21.540 --> 00:00:23.350
the products are an aqueous solution
00:00:23.350 --> 00:00:26.050
of sodium acetate and water.
00:00:26.050 --> 00:00:29.710
Next, let's look at the complete
or overall ionic equation
00:00:29.710 --> 00:00:30.930
for this reaction.
00:00:30.930 --> 00:00:33.190
Because the acetic acid is a weak acid,
00:00:33.190 --> 00:00:36.460
it does not ionize completely
in aqueous solution.
00:00:36.460 --> 00:00:39.010
Therefore, for our
complete ionic equation,
00:00:39.010 --> 00:00:40.680
we simply write a acetic acid.
00:00:40.680 --> 00:00:43.280
We don't show it as being ionized.
00:00:43.280 --> 00:00:46.065
However, sodium hydroxide is a strong base
00:00:46.065 --> 00:00:49.680
that associates 100% in aqueous solution.
00:00:49.680 --> 00:00:52.150
Therefore, we would show it as its ions,
00:00:52.150 --> 00:00:52.983
Na+ and OH-.
00:00:54.460 --> 00:00:58.370
Since sodium acetate is a
soluble salt in aqueous solution,
00:00:58.370 --> 00:01:01.973
it would consist of sodium
cations and the acetate anion.
00:01:01.973 --> 00:01:04.980
And we would also include
water in our overall
00:01:04.980 --> 00:01:07.100
or complete ionic equation.
00:01:07.100 --> 00:01:08.730
For our net ionic equation,
00:01:08.730 --> 00:01:10.530
we leave out spectator ions.
00:01:10.530 --> 00:01:13.370
Since sodium cations are on
the left and the right side,
00:01:13.370 --> 00:01:14.440
when we take those out,
00:01:14.440 --> 00:01:16.610
we're left with the net ionic equation
00:01:16.610 --> 00:01:19.200
for this weak acid-strong base titration.
00:01:19.200 --> 00:01:22.320
So acetic acid reacts
with hydroxide anions
00:01:22.320 --> 00:01:25.020
to form the acetate anion and water.
00:01:25.020 --> 00:01:27.050
Next, let's look at the titration curve
00:01:27.050 --> 00:01:29.840
for our weak acid-strong base titration,
00:01:29.840 --> 00:01:33.280
pH is on the y-axis and since
we're adding our strong base
00:01:33.280 --> 00:01:34.970
to our solution of weak acid,
00:01:34.970 --> 00:01:38.330
milliliters of base
added is on the x-axis.
00:01:38.330 --> 00:01:40.760
Let's use particulate
diagrams to help us figure out
00:01:40.760 --> 00:01:43.130
what's going on in this titration.
00:01:43.130 --> 00:01:45.100
Keep in mind that these
particulate diagrams
00:01:45.100 --> 00:01:47.310
are only meant to
represent what's going on
00:01:47.310 --> 00:01:49.260
in the solution during the titration
00:01:49.260 --> 00:01:52.800
and water molecules will
be left out for clarity.
00:01:52.800 --> 00:01:55.010
Looking at our first particulate diagram,
00:01:55.010 --> 00:01:57.850
there's only acetic acid present,
00:01:57.850 --> 00:02:00.660
only two particles of acetic acid present.
00:02:00.660 --> 00:02:03.720
Therefore, this is before
any base has been added.
00:02:03.720 --> 00:02:05.540
So on our titration curve,
00:02:05.540 --> 00:02:08.830
we're right here at zero
milliliters of base added.
00:02:08.830 --> 00:02:10.820
Next, let's add some sodium hydroxide
00:02:10.820 --> 00:02:13.811
to our initial solution of acetic acid.
00:02:13.811 --> 00:02:15.820
So for sodium hydroxide,
00:02:15.820 --> 00:02:18.150
the pink sphere represents
the sodium cation.
00:02:18.150 --> 00:02:20.650
So we think about adding
in the sodium cation
00:02:20.650 --> 00:02:23.043
and also a hydroxide anion.
00:02:23.900 --> 00:02:25.957
Remember from our net ionic equation,
00:02:25.957 --> 00:02:29.890
hydroxide anion reacts with acetic acid
00:02:29.890 --> 00:02:33.360
to form the acetate anion and water.
00:02:33.360 --> 00:02:36.310
Since water is left out of
our particulate diagrams,
00:02:36.310 --> 00:02:39.265
we don't see it here in this
second particulate diagram.
00:02:39.265 --> 00:02:43.372
However, we do see the
acetate anion that formed
00:02:43.372 --> 00:02:46.220
when the hydroxide anion reacted
00:02:46.220 --> 00:02:48.770
with the acetic acid particle.
00:02:48.770 --> 00:02:50.560
In the second particulate diagram,
00:02:50.560 --> 00:02:53.508
we also see the sodium
cation that was added
00:02:53.508 --> 00:02:56.407
and also the particle of acetic acid
00:02:56.407 --> 00:02:58.910
that was present initially.
00:02:58.910 --> 00:03:02.040
Because we started with two
particles of acetic acid
00:03:02.040 --> 00:03:05.740
and we have only one left in
the second particulate diagram,
00:03:05.740 --> 00:03:07.960
that means that half of the initial acid
00:03:07.960 --> 00:03:09.680
has been neutralized.
00:03:09.680 --> 00:03:13.250
So this second particulate
diagram is meant to represent
00:03:13.250 --> 00:03:16.730
the half equivalence
point in the titration.
00:03:16.730 --> 00:03:19.110
Next, let's add enough sodium hydroxide
00:03:19.110 --> 00:03:21.480
to neutralize the other half of acid
00:03:21.480 --> 00:03:24.300
that was initially present in solution.
00:03:24.300 --> 00:03:27.833
The acetic acid particle
reacts with the hydroxide anion
00:03:27.833 --> 00:03:31.800
to form water and the acetate anion.
00:03:31.800 --> 00:03:34.180
Since water is left out of
our particulate diagram,
00:03:34.180 --> 00:03:37.030
we don't see water in this
third particulate diagram.
00:03:37.030 --> 00:03:40.780
However, we do see the
acetate anion that was formed.
00:03:40.780 --> 00:03:43.710
We also see these sodium
cation that was added.
00:03:43.710 --> 00:03:45.330
And at the half equivalence point,
00:03:45.330 --> 00:03:49.410
we already had a sodium
cation and an acetate anion,
00:03:49.410 --> 00:03:50.360
so we can see those
00:03:50.360 --> 00:03:52.970
in our third particulate diagram as well.
00:03:52.970 --> 00:03:55.430
If we compare the third
particulate diagram
00:03:55.430 --> 00:03:57.560
to the first particulate diagram,
00:03:57.560 --> 00:03:59.825
all of the acid that was initially present
00:03:59.825 --> 00:04:01.516
has been neutralized.
00:04:01.516 --> 00:04:04.740
Therefore, the third particulate diagram
00:04:04.740 --> 00:04:08.290
represents the equivalence
point of the titration.
00:04:08.290 --> 00:04:11.230
We can estimate the equivalence
point on our titration curve
00:04:11.230 --> 00:04:14.750
by looking for the area where
we see a sharp increase in pH.
00:04:14.750 --> 00:04:15.940
So right about in here.
00:04:15.940 --> 00:04:17.410
And if we draw a little line,
00:04:17.410 --> 00:04:19.847
about halfway up that line approximately,
00:04:19.847 --> 00:04:23.280
is a good place to mark
the equivalence point.
00:04:23.280 --> 00:04:25.990
So this is a good estimate
of our equivalence point.
00:04:25.990 --> 00:04:29.020
And if we go over to where
that intersects in the y-axis,
00:04:29.020 --> 00:04:30.480
we can estimate the pH
00:04:30.480 --> 00:04:33.320
for this weak acid-strong base titration.
00:04:33.320 --> 00:04:35.320
It looks to be a little bit over eight,
00:04:35.320 --> 00:04:37.610
so between eight and nine somewhere.
00:04:37.610 --> 00:04:40.470
So the pH of the solution
at the equivalence point
00:04:40.470 --> 00:04:42.480
is greater than seven.
00:04:42.480 --> 00:04:44.575
The reason why the pH
is greater than seven
00:04:44.575 --> 00:04:47.050
is because at the equivalence point,
00:04:47.050 --> 00:04:51.130
there are acetate anions in
solution and acetate anion
00:04:51.130 --> 00:04:55.540
react with water to form
hydroxide anions and acetic acid.
00:04:55.540 --> 00:04:59.080
The pH of water at 25
degrees Celsius is seven,
00:04:59.080 --> 00:05:01.590
but because we've
increased the concentration
00:05:01.590 --> 00:05:04.910
of hydroxide anions in solution,
00:05:04.910 --> 00:05:08.391
the pH will be greater than
seven at the equivalence point.
00:05:08.391 --> 00:05:11.030
This is called anion hydrolysis
00:05:11.030 --> 00:05:13.600
and is the reason why the
pH is greater than seven
00:05:13.600 --> 00:05:14.700
at the equivalence point
00:05:14.700 --> 00:05:17.670
for a weak acid-strong base titration.
00:05:17.670 --> 00:05:20.640
Going back to our titration
curve to the equivalence point,
00:05:20.640 --> 00:05:23.290
if we drop down to the x-axis,
00:05:23.290 --> 00:05:25.890
we can see that the equivalence
point has been reached
00:05:25.890 --> 00:05:29.110
after 50 milliliters of
base have been added.
00:05:29.110 --> 00:05:31.390
So if it takes 50 milliliters of base
00:05:31.390 --> 00:05:33.230
to reach the equivalence point,
00:05:33.230 --> 00:05:35.100
it should take half that volume
00:05:35.100 --> 00:05:37.220
to reach the half equivalence point.
00:05:37.220 --> 00:05:39.500
Therefore, the half
equivalence point is reached
00:05:39.500 --> 00:05:42.630
after 25 milliliters
of base has been added.
00:05:42.630 --> 00:05:45.400
So if we go up here to
our titration curve,
00:05:45.400 --> 00:05:49.620
we can mark the location
or the approximate location
00:05:49.620 --> 00:05:52.010
of the half equivalence point.
00:05:52.010 --> 00:05:55.400
So let me draw a line here
from half equivalence point
00:05:55.400 --> 00:05:57.570
to the point on our titration curve.
00:05:57.570 --> 00:06:00.150
Let's go back to our
third particulate diagram
00:06:00.150 --> 00:06:01.990
which represents the equivalence point
00:06:01.990 --> 00:06:06.543
and let's add some more sodium
hydroxide into the solution.
00:06:06.543 --> 00:06:08.900
Because there's no more acid present
00:06:08.900 --> 00:06:11.320
to react with the sodium hydroxide
00:06:11.320 --> 00:06:13.130
in our fourth particulate diagram,
00:06:13.130 --> 00:06:15.380
we can see the sodium cation
00:06:15.380 --> 00:06:18.230
and the hydroxide anion that we added.
00:06:18.230 --> 00:06:19.200
At the equivalence point,
00:06:19.200 --> 00:06:20.610
we also had two sodium cations.
00:06:20.610 --> 00:06:23.670
So here they are on the
fourth particulate diagram
00:06:23.670 --> 00:06:27.350
and two acetate anions
which are also present.
00:06:27.350 --> 00:06:28.927
So the fourth particulate diagram
00:06:28.927 --> 00:06:33.240
represents excess base
past the equivalence point.
00:06:33.240 --> 00:06:35.360
As a quick summary of our titration curve,
00:06:35.360 --> 00:06:37.690
we started out with only weak acid
00:06:37.690 --> 00:06:39.930
so the pH was relatively low.
00:06:39.930 --> 00:06:43.840
As we add base, the pH increases slowly,
00:06:43.840 --> 00:06:46.430
and we get to the half equivalence point
00:06:46.430 --> 00:06:49.160
where half of the weak acid
that was initially present
00:06:49.160 --> 00:06:50.690
has been neutralized.
00:06:50.690 --> 00:06:53.040
Notice how the pH is changing very slowly
00:06:53.040 --> 00:06:55.700
in this region of the titration curve.
00:06:55.700 --> 00:06:57.690
As we continue to add more and more base,
00:06:57.690 --> 00:07:00.650
the pH keeps on increasing.
00:07:00.650 --> 00:07:02.250
And around the equivalence point,
00:07:02.250 --> 00:07:05.703
we see a dramatic increase in the pH.
00:07:05.703 --> 00:07:08.410
Once we go past the equivalence point,
00:07:08.410 --> 00:07:10.580
we're in the region of excess base
00:07:10.580 --> 00:07:12.220
and the pH keeps increasing
00:07:12.220 --> 00:07:15.087
as we add more and more hydroxide anions.
00:07:15.930 --> 00:07:18.970
During the titration of a
weak acid with a strong base,
00:07:18.970 --> 00:07:21.027
a buffer solution is actually formed.
00:07:21.027 --> 00:07:23.910
So let's look at more
detail at the buffer region
00:07:23.910 --> 00:07:26.900
or the buffer zone on our titration curve.
00:07:26.900 --> 00:07:30.250
The buffer region occurs around
the half equivalence point.
00:07:30.250 --> 00:07:32.480
And we can see on our titration curve,
00:07:32.480 --> 00:07:34.700
there are very small changes in pH
00:07:34.700 --> 00:07:38.250
as we add hydroxide anions in this region.
00:07:38.250 --> 00:07:41.680
That's because the weak acid
that's present in solution
00:07:41.680 --> 00:07:43.880
is neutralizing the added base
00:07:43.880 --> 00:07:47.520
and protecting against
a dramatic change in pH.
00:07:47.520 --> 00:07:50.750
We can calculate the pH at
the half equivalence point
00:07:50.750 --> 00:07:52.880
because we know at the
half equivalence point,
00:07:52.880 --> 00:07:55.340
half of the initial acid that was present
00:07:55.340 --> 00:07:58.960
has been neutralized and
turned into the conjugate base.
00:07:58.960 --> 00:08:00.800
Therefore, at the half equivalence point,
00:08:00.800 --> 00:08:02.413
the concentration of weak acid
00:08:02.413 --> 00:08:06.380
is equal to the concentration
of the conjugate base.
00:08:06.380 --> 00:08:08.470
We can use the
Henderson-Hasselbalch equation
00:08:08.470 --> 00:08:09.910
to find the pH.
00:08:09.910 --> 00:08:11.460
If the concentration of weak acid
00:08:11.460 --> 00:08:13.876
is equal to the concentration
of the conjugate base,
00:08:13.876 --> 00:08:17.740
then the ratio of their
concentrations is equal to one.
00:08:17.740 --> 00:08:20.850
And the log of one is equal to zero.
00:08:20.850 --> 00:08:24.800
Therefore, the pH is
equal to the pKa value
00:08:24.800 --> 00:08:26.390
of the weak acid
00:08:26.390 --> 00:08:28.900
at the half equivalence point.
00:08:28.900 --> 00:08:31.500
So if we wanted to find the pKa value
00:08:31.500 --> 00:08:33.960
of a weak acid from our titration curve,
00:08:33.960 --> 00:08:36.570
we would simply find the
half equivalence point
00:08:36.570 --> 00:08:39.610
and go over to the y-axis
00:08:39.610 --> 00:08:42.290
to estimate the pKa value.
00:08:42.290 --> 00:08:45.180
Because at this point,
the pH of the solution
00:08:45.180 --> 00:08:48.950
is equal to the pKa
value of the weak acid.
00:08:48.950 --> 00:08:51.560
Next, let's think about
how the titration curve
00:08:51.560 --> 00:08:54.070
can tell us about the
relative concentrations
00:08:54.070 --> 00:08:56.472
of weak acid and conjugate base.
00:08:56.472 --> 00:08:59.920
We know that the pH is
equal to the pKa value
00:08:59.920 --> 00:09:01.330
at the half equivalence point
00:09:01.330 --> 00:09:03.340
right here on our titration curve.
00:09:03.340 --> 00:09:05.270
And we know at the half equivalence point,
00:09:05.270 --> 00:09:06.680
the concentration of weak acid
00:09:06.680 --> 00:09:10.080
is equal to the concentration
of conjugate base.
00:09:10.080 --> 00:09:12.110
Therefore, if we think about a point
00:09:12.110 --> 00:09:14.640
just to the left of the
half equivalence point,
00:09:14.640 --> 00:09:17.430
so right here on our titration curve,
00:09:17.430 --> 00:09:19.397
I'll call this point P,
00:09:19.397 --> 00:09:23.430
we know that the pH at that point is less
00:09:23.430 --> 00:09:27.250
than the pKa value of the weak acid.
00:09:27.250 --> 00:09:30.697
And we know that the initial
point on our titration curve
00:09:30.697 --> 00:09:33.382
was almost all weak acid.
00:09:33.382 --> 00:09:38.382
Therefore, since point P is
in between the initial point
00:09:38.520 --> 00:09:40.130
where we have almost all acid
00:09:40.130 --> 00:09:41.610
and the half equivalence point
00:09:41.610 --> 00:09:44.831
where we have equal amounts of
weak acid and conjugate base,
00:09:44.831 --> 00:09:49.831
point P must have more weak
acid than conjugate base.
00:09:50.230 --> 00:09:52.380
Therefore, we can say when the pH
00:09:52.380 --> 00:09:54.770
is less than the pKa value.
00:09:54.770 --> 00:09:56.450
The concentration of weak acid
00:09:56.450 --> 00:09:59.980
is greater than the
concentration of conjugate base.
00:09:59.980 --> 00:10:01.380
We could have also figured this out
00:10:01.380 --> 00:10:03.680
using the Henderson-Hasselbalch equation.
00:10:03.680 --> 00:10:05.310
However, it's often simpler
00:10:05.310 --> 00:10:08.180
just to think about the
shape of the titration curve.
00:10:08.180 --> 00:10:09.530
Next, let's think about a point
00:10:09.530 --> 00:10:12.380
just to the right of the
half equivalence point.
00:10:12.380 --> 00:10:15.460
So I'm gonna call this point, point Q.
00:10:15.460 --> 00:10:17.700
At point Q, the pH of the solution
00:10:17.700 --> 00:10:21.440
is greater than the pKa
value of the weak acid.
00:10:21.440 --> 00:10:24.170
So for trying to determine
the relative concentrations
00:10:24.170 --> 00:10:27.280
of weak acid and
conjugate base at point Q,
00:10:27.280 --> 00:10:30.780
remember that point Q is in between
00:10:30.780 --> 00:10:34.010
the half equivalence point
and the equivalence point,
00:10:34.010 --> 00:10:36.930
which is right about here
on our titration curve.
00:10:36.930 --> 00:10:38.370
And at the equivalence point,
00:10:38.370 --> 00:10:40.420
there's no more weak acid present.
00:10:40.420 --> 00:10:42.550
All of the weak acid has been neutralized
00:10:42.550 --> 00:10:46.350
and only the conjugate base, A-, remains.
00:10:46.350 --> 00:10:49.380
Since point Q is in between
the half equivalence point
00:10:49.380 --> 00:10:50.440
where there are equal amounts
00:10:50.440 --> 00:10:52.500
of weak acid and conjugate base,
00:10:52.500 --> 00:10:55.750
and the equivalence point where
there's only conjugate base,
00:10:55.750 --> 00:10:59.330
at point Q, there must
be more conjugate base
00:10:59.330 --> 00:11:01.150
than weak acid.
00:11:01.150 --> 00:11:04.100
Therefore, we can say when
the pH of the solution
00:11:04.100 --> 00:11:07.220
is greater than the pKa
value of the weak acid,
00:11:07.220 --> 00:11:09.010
the concentration of weak acid
00:11:09.010 --> 00:11:12.350
is less than the concentration
of the conjugate base.
00:11:12.350 --> 00:11:14.950
Or we could say the
concentration of conjugate base
00:11:14.950 --> 00:11:18.110
is greater than the
concentration of weak acid.
00:11:18.110 --> 00:11:20.950
Finally, let's talk
about why a buffer forms
00:11:20.950 --> 00:11:22.730
on this titration curve.
00:11:22.730 --> 00:11:23.790
When we first start off,
00:11:23.790 --> 00:11:25.680
we have almost all weak acid,
00:11:25.680 --> 00:11:27.950
and therefore we do not have a buffer.
00:11:27.950 --> 00:11:30.630
However, as base is added to the solution,
00:11:30.630 --> 00:11:33.520
the weak acid is converted
into its conjugate base.
00:11:33.520 --> 00:11:35.330
And when there are significant amounts
00:11:35.330 --> 00:11:37.620
of the weak acid and its conjugate base,
00:11:37.620 --> 00:11:39.350
we have a buffer solution.
00:11:39.350 --> 00:11:41.707
So that's right about here
on our titration curve.
00:11:41.707 --> 00:11:44.660
And we can see the buffer is resisting
00:11:44.660 --> 00:11:47.610
large changes to pH in this region.
00:11:47.610 --> 00:11:49.734
However, as we continue to add base,
00:11:49.734 --> 00:11:53.840
the concentrations of weak
acid and conjugate base change.
00:11:53.840 --> 00:11:56.490
And eventually, we no longer
have a buffer solution.
00:11:56.490 --> 00:11:59.840
So the pH changes more
dramatically at this point.
00:11:59.840 --> 00:12:02.210
So the buffer region or the buffer zone
00:12:03.300 --> 00:12:06.200
is only right around the
half equivalence point
00:12:06.200 --> 00:12:07.953
on our titration curve.
|
Strong acid–strong base titrations | https://www.youtube.com/watch?v=qkh0SMozSBQ | vtt | https://www.youtube.com/api/timedtext?v=qkh0SMozSBQ&ei=0lWUZaDdD6C5vdIPxuKG4As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=AD81342B37529BD2410E8209CF9E74AA450A3152.EAC68C4B030845C738908F89AE5CF4F7768FBA71&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.520 --> 00:00:02.600
- [Instructor] Hydrochloric
acid is an example
00:00:02.600 --> 00:00:05.420
of a strong acid and sodium hydroxide
00:00:05.420 --> 00:00:08.290
is an example of a strong base.
00:00:08.290 --> 00:00:09.570
Let's say we are titrating
00:00:09.570 --> 00:00:12.106
an unknown concentration
of hydrochloric acid
00:00:12.106 --> 00:00:15.530
with a known concentration
of sodium hydroxide.
00:00:15.530 --> 00:00:17.820
Let's say it's .20 molar.
00:00:17.820 --> 00:00:20.640
Because we know the concentration
of sodium hydroxide,
00:00:20.640 --> 00:00:22.290
we call that the titrant.
00:00:22.290 --> 00:00:23.510
And because we don't know
00:00:23.510 --> 00:00:25.349
the concentration of hydrochloric acid,
00:00:25.349 --> 00:00:27.940
we call that the analyte.
00:00:27.940 --> 00:00:30.480
And when our strong
acid, hydrochloric acid,
00:00:30.480 --> 00:00:33.870
reacts with our strong
base, sodium hydroxide,
00:00:33.870 --> 00:00:36.270
the products are an aqueous solution
00:00:36.270 --> 00:00:38.720
of sodium chloride and water.
00:00:38.720 --> 00:00:40.965
As a quick review of
how to write the overall
00:00:40.965 --> 00:00:43.320
or the complete ionic equation
00:00:43.320 --> 00:00:45.800
for a strong acid-strong base reaction,
00:00:45.800 --> 00:00:48.640
remember that sodium
hydroxide being a strong base
00:00:48.640 --> 00:00:50.960
dissociates completely in aqueous solution
00:00:50.960 --> 00:00:54.380
to form sodium cations
and hydroxide anions.
00:00:54.380 --> 00:00:56.560
Hydrochloric acid being a strong acid
00:00:56.560 --> 00:00:58.820
will ionize completely in aqueous solution
00:00:58.820 --> 00:01:02.025
to form H+ ions and chloride anions.
00:01:02.025 --> 00:01:04.900
Sodium chloride is a soluble salt,
00:01:04.900 --> 00:01:06.530
so an aqueous solution.
00:01:06.530 --> 00:01:09.330
We would have sodium
cations and chloride anions.
00:01:09.330 --> 00:01:11.760
And of course, we would also have water.
00:01:11.760 --> 00:01:13.620
When writing the net ionic equation,
00:01:13.620 --> 00:01:15.650
we cross out these spectator ions.
00:01:15.650 --> 00:01:18.600
So since we have sodium cations
in left and on the right,
00:01:18.600 --> 00:01:20.054
we can cross out the sodium cations
00:01:20.054 --> 00:01:20.953
and the same with the chloride anions.
00:01:22.320 --> 00:01:24.970
So both of those are the spectator ions.
00:01:24.970 --> 00:01:27.319
What we're left with is
our net ionic equation.
00:01:27.319 --> 00:01:30.200
So one way to write the net ionic equation
00:01:30.200 --> 00:01:32.176
for a strong acid-strong base reaction
00:01:32.176 --> 00:01:37.130
is hydroxide anions plus
H+ cations form water.
00:01:37.130 --> 00:01:40.350
And our goal for the strong
acids-strong based titration
00:01:40.350 --> 00:01:43.480
is to find the concentration
of hydrochloric acid
00:01:43.480 --> 00:01:45.630
using a titration curve.
00:01:45.630 --> 00:01:47.320
Let's say we do our titration
00:01:47.320 --> 00:01:49.800
and we come up with this
as a titration curve.
00:01:49.800 --> 00:01:50.870
For titration curves,
00:01:50.870 --> 00:01:55.350
you put the pH on the y-axis
and the titrant on the x-axis.
00:01:55.350 --> 00:01:56.183
So in this case,
00:01:56.183 --> 00:01:59.990
we're adding base to our
solution of hydrochloric acid.
00:01:59.990 --> 00:02:01.840
And before we use our titration curve
00:02:01.840 --> 00:02:04.100
to find the concentration
of hydrochloric acid,
00:02:04.100 --> 00:02:05.890
let's go through the titration curve
00:02:05.890 --> 00:02:08.380
and look at some particulate diagrams.
00:02:08.380 --> 00:02:10.190
And as we look at particulate diagrams,
00:02:10.190 --> 00:02:12.310
keep in mind they're just
to help us understand
00:02:12.310 --> 00:02:14.360
what's going on in the actual solution,
00:02:14.360 --> 00:02:16.190
so they're are just a representation.
00:02:16.190 --> 00:02:20.190
And we're also gonna
leave out water molecules
00:02:20.190 --> 00:02:21.610
for clarity purposes.
00:02:21.610 --> 00:02:24.500
So let's think about this
point on our titration curve.
00:02:24.500 --> 00:02:27.290
So that's zero milliliters of base added,
00:02:27.290 --> 00:02:30.440
meaning we're starting only
with hydrochloric acid.
00:02:30.440 --> 00:02:33.300
So there are two H+ particles,
00:02:33.300 --> 00:02:37.660
and there are two
chloride anion particles.
00:02:37.660 --> 00:02:39.860
Next, we add in some sodium hydroxide.
00:02:39.860 --> 00:02:42.820
So the sodium cation is this
purple sphere right here,
00:02:42.820 --> 00:02:45.540
and the hydroxide anion
is over here as well.
00:02:45.540 --> 00:02:47.570
So we add in some sodium hydroxide
00:02:47.570 --> 00:02:49.926
to our solution of hydrochloric acid
00:02:49.926 --> 00:02:52.860
and for the hydroxide
anion that's neutralized
00:02:52.860 --> 00:02:55.830
by one of the H+ ions that's present.
00:02:55.830 --> 00:02:59.800
So the OH- and the H+ react to form H2O.
00:02:59.800 --> 00:03:02.920
And since we're leaving H2O out
of our particulate diagrams,
00:03:02.920 --> 00:03:06.210
we don't see it in this
second particulate diagram.
00:03:06.210 --> 00:03:09.120
What we do see in this
second particulate diagram
00:03:09.120 --> 00:03:11.850
are the chloride anions
that were initially present.
00:03:11.850 --> 00:03:12.980
So here they are.
00:03:12.980 --> 00:03:16.520
And the other H+ ion that
was initially present
00:03:16.520 --> 00:03:19.000
and the added sodium cation.
00:03:19.000 --> 00:03:22.020
And since there's still an
H+ cation left in solution,
00:03:22.020 --> 00:03:24.150
we haven't neutralized all of the acid
00:03:24.150 --> 00:03:26.010
that was initially present.
00:03:26.010 --> 00:03:28.460
So next, we add some
more sodium hydroxide.
00:03:28.460 --> 00:03:30.350
So here we're adding a sodium cation,
00:03:30.350 --> 00:03:32.990
and we're also gonna
add this hydroxide anion
00:03:32.990 --> 00:03:34.150
to our solution.
00:03:34.150 --> 00:03:36.860
The added hydroxide
anion will be neutralized
00:03:36.860 --> 00:03:39.480
by the H+ ion that's already present.
00:03:39.480 --> 00:03:40.640
They will form water.
00:03:40.640 --> 00:03:41.930
And since we're leaving water
00:03:41.930 --> 00:03:43.502
out of the particulate diagrams,
00:03:43.502 --> 00:03:47.320
we don't see water in this
third particulate diagram.
00:03:47.320 --> 00:03:50.030
What we do see in our third
particulate diagram here
00:03:50.030 --> 00:03:52.940
are the two chloride anions
that have always been with us
00:03:52.940 --> 00:03:53.778
in the titration.
00:03:53.778 --> 00:03:56.440
We had one sodium cation already present,
00:03:56.440 --> 00:03:59.210
and then we added one more sodium cation.
00:03:59.210 --> 00:04:01.570
So this third particulate
diagram represents
00:04:01.570 --> 00:04:03.970
the equivalence point of our titration.
00:04:03.970 --> 00:04:06.710
All of the acid that we
initially had present
00:04:06.710 --> 00:04:09.190
has been neutralized by the added base
00:04:09.190 --> 00:04:13.090
and we're left with an aqueous
solution of sodium chloride.
00:04:13.090 --> 00:04:14.690
So there are only sodium cations
00:04:14.690 --> 00:04:16.940
and chloride anions in solution.
00:04:16.940 --> 00:04:18.540
At 25 degrees Celsius,
00:04:18.540 --> 00:04:21.720
the pH of water is equal to seven.
00:04:21.720 --> 00:04:24.440
And since neither the sodium cation
00:04:24.440 --> 00:04:25.890
nor the chloride anion
00:04:25.890 --> 00:04:28.803
will react with water to change the pH,
00:04:28.803 --> 00:04:30.860
the pH at the equivalence point
00:04:30.860 --> 00:04:34.900
of a strong acid-strong
base titration is seven.
00:04:34.900 --> 00:04:37.980
And we can find the equivalence
point on our titration curve
00:04:37.980 --> 00:04:41.070
by going over to a pH of about seven here.
00:04:41.070 --> 00:04:43.570
And if we draw a little dash line,
00:04:43.570 --> 00:04:46.090
wherever that dash line
hits our titration curve,
00:04:46.090 --> 00:04:48.158
represents the equivalence point.
00:04:48.158 --> 00:04:50.230
So the first particulate diagram
00:04:50.230 --> 00:04:51.890
was before any base was added.
00:04:51.890 --> 00:04:54.790
So that's this point
on our titration curve.
00:04:54.790 --> 00:04:57.489
The third particulate
diagram is meant to represent
00:04:57.489 --> 00:04:59.410
the equivalence point,
00:04:59.410 --> 00:05:01.630
so this point on our titration curve.
00:05:01.630 --> 00:05:03.752
And our second particulate diagram
00:05:03.752 --> 00:05:06.220
was when we haven't neutralized
00:05:06.220 --> 00:05:07.710
all of the acid that's present.
00:05:07.710 --> 00:05:09.840
So that's in between those two points
00:05:09.840 --> 00:05:11.456
on the titration curve.
00:05:11.456 --> 00:05:13.620
Also notice how steep
00:05:13.620 --> 00:05:18.340
the graph is around the equivalence
point of this titration.
00:05:18.340 --> 00:05:20.200
Therefore, adding very small amounts
00:05:20.200 --> 00:05:22.240
of base around the equivalence point
00:05:22.240 --> 00:05:25.920
causes large changes in
the pH of the solution.
00:05:25.920 --> 00:05:28.330
Let's go back to our particulate diagram
00:05:28.330 --> 00:05:29.690
at the equivalence point,
00:05:29.690 --> 00:05:32.450
and let's add some more sodium hydroxide.
00:05:32.450 --> 00:05:34.380
So we add one more sodium cation
00:05:34.380 --> 00:05:37.120
and one more hydroxide anion.
00:05:37.120 --> 00:05:39.150
This time, since there's no more acid
00:05:39.150 --> 00:05:42.140
to neutralize the added hydroxide anion,
00:05:42.140 --> 00:05:43.870
in our fourth particulate diagram,
00:05:43.870 --> 00:05:46.100
here's our hydroxide anion.
00:05:46.100 --> 00:05:47.720
And one of these sodium cations
00:05:47.720 --> 00:05:49.720
is the one that we just added.
00:05:49.720 --> 00:05:53.330
And we still have the chloride
anions and the sodium cations
00:05:53.330 --> 00:05:56.110
that were present at
the equivalence point.
00:05:56.110 --> 00:06:00.719
So this fourth particulate
diagram represents the titration
00:06:00.719 --> 00:06:04.670
after the equivalence point
when we're adding excess base.
00:06:04.670 --> 00:06:06.550
And we can see on our titration curve,
00:06:06.550 --> 00:06:10.571
as we continue to add excess
base, the pH keeps increasing.
00:06:10.571 --> 00:06:13.610
Now that we've gone through
the particulate diagrams
00:06:13.610 --> 00:06:15.750
for our strong acid-strong base titration,
00:06:15.750 --> 00:06:18.080
let's get back to our original problem
00:06:18.080 --> 00:06:21.010
which was to find the
initial concentration
00:06:21.010 --> 00:06:22.710
of hydrochloric acid.
00:06:22.710 --> 00:06:24.740
And we can do that by figuring out
00:06:24.740 --> 00:06:27.180
how many milliliters of base were added
00:06:27.180 --> 00:06:29.830
to get to the equivalence point.
00:06:29.830 --> 00:06:32.810
So if we just drop down
here on our titration curve,
00:06:32.810 --> 00:06:35.660
we can see that after
50 milliliters of base
00:06:35.660 --> 00:06:36.670
have been added,
00:06:36.670 --> 00:06:39.040
the equivalence point has been reached.
00:06:39.040 --> 00:06:41.270
Therefore, it took 50 milliliters
00:06:41.270 --> 00:06:44.760
of our .20 molar solution
of sodium hydroxide
00:06:44.760 --> 00:06:46.600
to completely neutralize
00:06:46.600 --> 00:06:49.740
the hydrochloric acid that
was originally present.
00:06:49.740 --> 00:06:51.810
And if we know the initial volume
00:06:51.810 --> 00:06:53.330
of the hydrochloric acid solution,
00:06:53.330 --> 00:06:55.460
let's say it was 100 milliliters.
00:06:55.460 --> 00:06:57.730
We can calculate the concentration
00:06:57.730 --> 00:07:01.490
using the MV is equal to MV equation.
00:07:01.490 --> 00:07:02.520
So for our equation,
00:07:02.520 --> 00:07:04.670
let's think about acid
being on the left side.
00:07:04.670 --> 00:07:07.410
So we don't know the
concentration, the molarities,
00:07:07.410 --> 00:07:08.503
we make that x.
00:07:08.503 --> 00:07:10.470
And for the volume of the acid,
00:07:10.470 --> 00:07:11.890
it's 100 milliliters.
00:07:11.890 --> 00:07:14.010
So we plugged that into our equation.
00:07:14.010 --> 00:07:14.860
On the right side,
00:07:14.860 --> 00:07:16.580
let's think about this being the base.
00:07:16.580 --> 00:07:18.280
So we know the molarity of the base,
00:07:18.280 --> 00:07:19.820
it's .20 molar.
00:07:19.820 --> 00:07:22.010
And we also know the volume of base
00:07:22.010 --> 00:07:24.400
that was necessary to
reach the equivalence point
00:07:24.400 --> 00:07:26.050
which is 50 milliliters.
00:07:26.050 --> 00:07:30.570
Solving for x, we find that
x is equal to .10 molar.
00:07:30.570 --> 00:07:33.490
So that was the initial concentration
00:07:33.490 --> 00:07:35.920
of our hydrochloric acid solution.
00:07:35.920 --> 00:07:37.930
And notice on our titration curve,
00:07:37.930 --> 00:07:40.090
remember we started with
only hydrochloric acid.
00:07:40.090 --> 00:07:42.130
So we start with a very low pH
00:07:42.130 --> 00:07:45.300
if we're titrating a strong
acid with a strong base.
00:07:45.300 --> 00:07:47.420
As we add more and more
of the strong base,
00:07:47.420 --> 00:07:49.500
the pH increases.
00:07:49.500 --> 00:07:51.670
We've just looked at the titration curve
00:07:51.670 --> 00:07:54.060
of a strong acid with a strong base.
00:07:54.060 --> 00:07:56.940
Let's compare that
titration curve to this one
00:07:56.940 --> 00:08:01.410
which is the titration of a
strong base with a strong acid.
00:08:01.410 --> 00:08:03.090
Since we're starting with a strong base,
00:08:03.090 --> 00:08:06.010
notice how the initial pH is very high.
00:08:06.010 --> 00:08:09.630
And since we're adding acid
notice down here on the x-axis,
00:08:09.630 --> 00:08:12.930
it now says milliliters of acid added.
00:08:12.930 --> 00:08:14.140
As acid is added,
00:08:14.140 --> 00:08:16.120
we can see the pH dropping slowly.
00:08:16.120 --> 00:08:18.270
And as we approach the equivalence point,
00:08:18.270 --> 00:08:22.600
we see a large drop in pH
with small additions of acid.
00:08:22.600 --> 00:08:24.660
However, the pH at the equivalence point
00:08:24.660 --> 00:08:26.110
is still equal to seven.
00:08:26.110 --> 00:08:28.800
So if we find a pH of seven on the y-axis
00:08:28.800 --> 00:08:31.190
and go over to our titration curve,
00:08:31.190 --> 00:08:33.570
this point represents
the equivalence point.
00:08:33.570 --> 00:08:35.810
And we can drop down to the x-axis
00:08:35.810 --> 00:08:39.010
and we would see it took
20 milliliters of acid
00:08:39.010 --> 00:08:42.180
to neutralize the base
that was initially present.
00:08:42.180 --> 00:08:44.330
Finally, once we go past
the equivalence point,
00:08:44.330 --> 00:08:46.160
we can see as we add more and more acid,
00:08:46.160 --> 00:08:48.420
the pH keeps getting lower.
00:08:48.420 --> 00:08:51.615
So this titration curve of a
strong base with a strong acid
00:08:51.615 --> 00:08:53.210
is essentially the reverse
00:08:53.210 --> 00:08:55.190
of the first titration curve that we saw
00:08:55.190 --> 00:08:58.933
which was the titration of a
strong acid with a strong base.
|
Opportunities for high school and college tutors | https://www.youtube.com/watch?v=5CdSLyACbUE | vtt | https://www.youtube.com/api/timedtext?v=5CdSLyACbUE&ei=0lWUZYeYEK_6vdIPmd2K2Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A58BCAEB4F3D5666FE00910054DC1C190A254C1A.CAF26463F8958FA069B028F47EF339D1A1130B27&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.850 --> 00:00:03.110
- Hi everyone, Sal Khan
here from Khan Academy,
00:00:03.110 --> 00:00:05.110
and many of you all know
about another project,
00:00:05.110 --> 00:00:06.940
another not-for-profit that
I've been involved with
00:00:06.940 --> 00:00:08.700
known as Schoolhouse.world,
00:00:08.700 --> 00:00:10.930
which is all about giving
folks free tutoring,
00:00:10.930 --> 00:00:14.520
and we do that by finding
amazing volunteer tutors.
00:00:14.520 --> 00:00:16.280
Now, the tutors we've been finding,
00:00:16.280 --> 00:00:17.650
they found a lot of reward
00:00:17.650 --> 00:00:19.520
just being able to tutor other folks,
00:00:19.520 --> 00:00:22.510
but we wanna make sure that
they also get other rewards,
00:00:22.510 --> 00:00:24.030
because if you can tutor something,
00:00:24.030 --> 00:00:26.300
not only does that mean
that you know the material,
00:00:26.300 --> 00:00:28.080
but it also means that
you can communicate,
00:00:28.080 --> 00:00:28.913
you have empathy,
00:00:28.913 --> 00:00:31.310
you wanna spend your time
doing good for others.
00:00:31.310 --> 00:00:33.940
So we were excited last year
when University of Chicago
00:00:33.940 --> 00:00:36.820
said that they were gonna use
someone's tutor reputation
00:00:36.820 --> 00:00:39.370
as a way to evaluate students applying
00:00:39.370 --> 00:00:40.790
for University of Chicago.
00:00:40.790 --> 00:00:43.890
And just a few weeks
ago, MIT also announced
00:00:43.890 --> 00:00:47.060
that they were putting
Schoolhouse.world profiles
00:00:47.060 --> 00:00:49.820
as an optional thing that
students could submit,
00:00:49.820 --> 00:00:51.470
and the school will look at them.
00:00:51.470 --> 00:00:54.210
To get a sense of the
amazing tutors we're finding,
00:00:54.210 --> 00:00:55.170
this right over here
00:00:55.170 --> 00:00:58.100
is the tutor profile and
the transcript for Karen Ji,
00:00:58.100 --> 00:00:59.480
who's a high school student,
00:00:59.480 --> 00:01:02.540
and you can see that she's
hosted a ton of sessions,
00:01:02.540 --> 00:01:06.570
543 learners impacted,
33 countries reached,
00:01:06.570 --> 00:01:09.350
864 positive ratings,
00:01:09.350 --> 00:01:11.387
and you can see what people
are saying about her,
00:01:11.387 --> 00:01:13.570
"My friend and I have been trying to go
00:01:13.570 --> 00:01:16.050
to every single one of your
sessions for the past few weeks,
00:01:16.050 --> 00:01:17.190
and we literally love you."
00:01:17.190 --> 00:01:20.390
And we can go after page after page
00:01:20.390 --> 00:01:22.970
of what everyone is saying about her,
00:01:22.970 --> 00:01:25.580
and then what also
fellow tutors are saying.
00:01:25.580 --> 00:01:26.740
So she's getting feedback
00:01:26.740 --> 00:01:28.430
to become a better and better tutor,
00:01:28.430 --> 00:01:30.470
and we also have the
certification mechanism,
00:01:30.470 --> 00:01:33.270
which is qualifying her
to tutor in specific units
00:01:33.270 --> 00:01:36.200
to show all of the things that
she has gotten mastery in.
00:01:36.200 --> 00:01:40.200
This right over here is the
tutor profile for Kate Pearce.
00:01:40.200 --> 00:01:41.140
So once again,
00:01:41.140 --> 00:01:44.270
another incredibly amazing
high school student,
00:01:44.270 --> 00:01:48.090
326 sessions hosted, over a
thousand positive ratings,
00:01:48.090 --> 00:01:51.337
and what people are saying
about Kate right over here,
00:01:51.337 --> 00:01:54.840
"She was very reassuring
and checks in with us
00:01:54.840 --> 00:01:57.280
whenever we needed help
or got a question wrong.
00:01:57.280 --> 00:02:00.170
Very helpful and patient
and broke things down."
00:02:00.170 --> 00:02:01.600
These are things that you can't get
00:02:01.600 --> 00:02:03.600
just through traditional transcripts,
00:02:03.600 --> 00:02:05.180
the ability of someone like Kate
00:02:05.180 --> 00:02:07.790
to communicate and
empathize with other folks.
00:02:07.790 --> 00:02:10.440
So if you're a university or an employer,
00:02:10.440 --> 00:02:12.930
who's really interested in
these types of students,
00:02:12.930 --> 00:02:14.620
I encourage you to click on that form
00:02:14.620 --> 00:02:18.120
in the link on this post,
and we can reach out to you,
00:02:18.120 --> 00:02:20.340
and figure out how we
can build a relationship,
00:02:20.340 --> 00:02:22.920
so that you can discover amazing talent
00:02:22.920 --> 00:02:25.180
from the tutors at Schoolhouse.world.
00:02:25.180 --> 00:02:26.510
So any young folks out there,
00:02:26.510 --> 00:02:28.330
especially high school
students or college students,
00:02:28.330 --> 00:02:29.650
who are interested in tutoring,
00:02:29.650 --> 00:02:32.030
I encourage you to check
out Schoolhouse.world,
00:02:32.030 --> 00:02:35.110
and I am going to work
with you and work for you
00:02:35.110 --> 00:02:36.850
to ensure that the rest of the world,
00:02:36.850 --> 00:02:38.290
college admissions officers,
00:02:38.290 --> 00:02:41.210
and eventually internships
and employers and scholarships
00:02:41.210 --> 00:02:43.070
recognize that one of the best ways
00:02:43.070 --> 00:02:45.580
to prove what you know
and give back to others
00:02:45.580 --> 00:02:47.683
is to tutor on Schoolhouse.world.
|
Second "Ask Sal anything" session focused on life advice | https://www.youtube.com/watch?v=UhCXlgyZXMk | vtt | https://www.youtube.com/api/timedtext?v=UhCXlgyZXMk&ei=0lWUZd-jELHXxN8Pz4SZ0As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=507F2FF252CFFE1FAE1F78A4287EFD82A5521325.C9C2E636EC1E7E71949F530A7871ED7842F734EB&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.140 --> 00:00:02.040
- Let's start with Christine.
00:00:02.040 --> 00:00:03.300
I believe Christine, you had your hand
00:00:03.300 --> 00:00:04.750
very patiently raised last time.
00:00:04.750 --> 00:00:06.486
So let's start with you.
00:00:06.486 --> 00:00:07.490
And a reminder we-
- Yeah.
00:00:07.490 --> 00:00:09.150
- We are recording this session
00:00:09.150 --> 00:00:11.020
as I put the last one on LinkedIn.
00:00:11.020 --> 00:00:12.930
So, (chuckles) it's gonna happen again.
00:00:12.930 --> 00:00:14.350
So by participating, you know,
00:00:14.350 --> 00:00:17.190
that that might happen not
you know, just kind of our,
00:00:17.190 --> 00:00:18.590
our release form, implicitly.
00:00:18.590 --> 00:00:20.580
All right, Christine, go ahead.
00:00:20.580 --> 00:00:22.730
- Sounds good, thanks for the great memory
00:00:22.730 --> 00:00:24.810
and of course like everyone here, big fan.
00:00:24.810 --> 00:00:26.960
I've been a user for quite some time.
00:00:26.960 --> 00:00:29.130
My question for you is,
00:00:29.130 --> 00:00:30.990
in times where you're
trying to make a decision
00:00:30.990 --> 00:00:32.730
where the answer isn't super clear,
00:00:32.730 --> 00:00:33.890
it's a really tough choice.
00:00:33.890 --> 00:00:35.330
Whether this is deciding
00:00:35.330 --> 00:00:37.470
what major you wanna have in college?
00:00:37.470 --> 00:00:40.810
When you wanna stay in
a job or leave a job?
00:00:40.810 --> 00:00:42.870
What are values or a piece of advice
00:00:42.870 --> 00:00:45.470
that you turn to in making
these types of decisions?
00:00:46.330 --> 00:00:47.930
- Yeah that's a good,
that's a good question.
00:00:47.930 --> 00:00:51.770
I do feel like you know,
this decision-making
00:00:51.770 --> 00:00:52.770
is one of these things that no one
00:00:52.770 --> 00:00:55.340
really explicitly in any way teaches you
00:00:55.340 --> 00:00:57.460
or gives you even frames of reference.
00:00:57.460 --> 00:00:59.510
I heard a quote recently
which I really liked,
00:00:59.510 --> 00:01:02.300
and I do think this is
part of my life philosophy,
00:01:02.300 --> 00:01:03.550
I'd like to believe.
00:01:03.550 --> 00:01:04.383
Which is,
00:01:06.357 --> 00:01:08.040
"There's oftentimes no right decision
00:01:08.040 --> 00:01:10.050
but you can make the decision right."
00:01:10.050 --> 00:01:13.540
So once you've committed to a decision,
00:01:13.540 --> 00:01:15.780
I do think that it is and,
00:01:15.780 --> 00:01:18.670
my mind does tend to work this way.
00:01:18.670 --> 00:01:20.300
I tend to convince myself
00:01:20.300 --> 00:01:22.580
that I made the best possible decision
00:01:22.580 --> 00:01:24.650
and then I do what I can
00:01:24.650 --> 00:01:27.230
to make the decision right.
00:01:27.230 --> 00:01:28.920
You know, first of all,
00:01:28.920 --> 00:01:30.310
if you're always second
guessing the decision
00:01:30.310 --> 00:01:32.340
by definition, whatever decision you made
00:01:32.340 --> 00:01:34.230
will almost, you're making it wrong
00:01:34.230 --> 00:01:35.350
cause you're always looking at
00:01:35.350 --> 00:01:37.570
what the alternative path could have been.
00:01:37.570 --> 00:01:40.430
So that's my first advice is always
00:01:40.430 --> 00:01:43.150
have an attitude of
making the decision right.
00:01:43.150 --> 00:01:44.610
No matter what you're doing,
00:01:44.610 --> 00:01:47.020
whether it's a job or a major,
00:01:47.020 --> 00:01:48.820
or choosing a partner.
00:01:48.820 --> 00:01:50.930
Just think day in, day out,
00:01:50.930 --> 00:01:53.570
what can I do today to make
this, make things better,
00:01:53.570 --> 00:01:55.330
to make a positive dent in the universe,
00:01:55.330 --> 00:01:58.130
to learn more, to get excited about it.
00:01:58.130 --> 00:02:00.963
When you're at the point
of making a decision,
00:02:01.870 --> 00:02:05.470
I tend to you know, do my best to just
00:02:09.370 --> 00:02:12.123
do a fairly rational
decision tree, if I can.
00:02:13.030 --> 00:02:16.680
Now I will say and I do, I do do that.
00:02:16.680 --> 00:02:19.580
You know, I've often
joked that people know me
00:02:19.580 --> 00:02:22.310
for my math videos and science
videos and other videos,
00:02:22.310 --> 00:02:23.410
but I've also wanted to make like,
00:02:23.410 --> 00:02:24.760
things like a dating video.
00:02:25.600 --> 00:02:29.710
I've met friends who might be with someone
00:02:29.710 --> 00:02:32.170
and I'm like, well, are you
going to marry that person?
00:02:32.170 --> 00:02:33.277
And they're like, well no, probably not.
00:02:33.277 --> 00:02:35.700
And I was like, then why are you?
00:02:35.700 --> 00:02:37.430
Like every day that you delay this,
00:02:37.430 --> 00:02:39.680
you're just making the pain larger
00:02:39.680 --> 00:02:41.890
in some future state.
00:02:41.890 --> 00:02:43.270
And if you do the decision tree,
00:02:43.270 --> 00:02:44.390
it's not a complicated one.
00:02:44.390 --> 00:02:47.930
You're like less pain
now versus ignoring it
00:02:47.930 --> 00:02:50.150
and making more pain in the future.
00:02:50.150 --> 00:02:54.350
So I do recommend taking a lens of that.
00:02:54.350 --> 00:02:55.563
I also think,
00:02:56.900 --> 00:02:58.380
making decisions that are not just
00:02:58.380 --> 00:03:02.300
in your best interest but
making decisions that are,
00:03:02.300 --> 00:03:04.220
that you're truly trying to make it
00:03:04.220 --> 00:03:06.630
an interest of anyone, everyone involved
00:03:06.630 --> 00:03:08.400
in the system, you know.
00:03:08.400 --> 00:03:09.890
I try not to judge people,
00:03:09.890 --> 00:03:11.643
but when I do judge (chuckles) people,
00:03:13.046 --> 00:03:15.890
I judge them on the decisions they make
00:03:15.890 --> 00:03:19.220
that the consequences for them,
00:03:19.220 --> 00:03:21.150
were they looking at the
consequences of the system,
00:03:21.150 --> 00:03:23.200
not just the consequences for themselves?
00:03:24.560 --> 00:03:25.770
I mean going back to the whole,
00:03:25.770 --> 00:03:28.143
the whole dating example,
I've seen people.
00:03:29.240 --> 00:03:31.110
I'd say not to judge but sometimes
00:03:31.110 --> 00:03:33.290
selfishly stay in something that lowers
00:03:33.290 --> 00:03:36.340
the other person's option value over time.
00:03:36.340 --> 00:03:38.520
Which I think is actually
very, very selfish
00:03:38.520 --> 00:03:41.270
that's the times I've most
harshly judged people.
00:03:41.270 --> 00:03:43.170
Although I try not to judge, you know,
00:03:44.872 --> 00:03:46.570
we all have our flaws.
00:03:46.570 --> 00:03:51.290
I do think that intuition,
intuition sometimes,
00:03:51.290 --> 00:03:52.750
we don't take it that seriously
00:03:52.750 --> 00:03:53.610
because it's kind of like, oh,
00:03:53.610 --> 00:03:55.100
you're just going off of gut.
00:03:55.100 --> 00:03:56.900
I do remind folks that your gut actually
00:03:56.900 --> 00:03:58.120
does have a lot of neurons.
00:03:58.120 --> 00:04:00.120
So your gut is kind of a mini brain.
00:04:00.120 --> 00:04:01.360
Your gut actually has more neurons
00:04:01.360 --> 00:04:04.120
than some animals have in their brains
00:04:04.120 --> 00:04:05.333
but on top of that.
00:04:06.630 --> 00:04:07.890
You know, in our actual brains
00:04:07.890 --> 00:04:09.520
not just even our gut brains,
00:04:09.520 --> 00:04:11.220
we have a hundred billion neurons.
00:04:13.329 --> 00:04:15.320
One of the critiques of machine learning
00:04:15.320 --> 00:04:16.800
is that it can come up with insights
00:04:16.800 --> 00:04:19.670
but you can't explain why that neural net
00:04:19.670 --> 00:04:21.920
is coming, is saying that that is a dog
00:04:21.920 --> 00:04:23.550
and that is not a dog.
00:04:23.550 --> 00:04:25.450
I think our human brains are similar
00:04:25.450 --> 00:04:30.420
is that it can, it is a
big neural net and it can.
00:04:30.420 --> 00:04:34.210
What intuition really is,
is it's your neural net
00:04:34.210 --> 00:04:37.650
telling you this is a
dog and that's not a dog
00:04:37.650 --> 00:04:38.970
but you can't exactly explain why.
00:04:38.970 --> 00:04:39.980
Of course I can explain why
00:04:39.980 --> 00:04:42.310
something might be a dog or not.
00:04:42.310 --> 00:04:43.860
But why this is the right major?
00:04:43.860 --> 00:04:45.070
Why this is the right career?
00:04:45.070 --> 00:04:46.870
Why this might be the right partner?
00:04:47.720 --> 00:04:50.393
Sometimes I do think, is a gut thing.
00:04:51.470 --> 00:04:54.430
I've got to say, last time I talked
00:04:54.430 --> 00:04:55.830
about solving hard problems
00:04:55.830 --> 00:04:56.663
and sometimes you just have
00:04:56.663 --> 00:04:57.520
to look at the problem
00:04:57.520 --> 00:04:58.630
and engage with the problem
00:04:58.630 --> 00:04:59.910
and then sleep on it.
00:04:59.910 --> 00:05:02.500
And then the next day all of a sudden,
00:05:02.500 --> 00:05:04.470
you've delegated to your subconscious mind
00:05:04.470 --> 00:05:05.840
and it's been churning on that problem
00:05:05.840 --> 00:05:07.020
while you're sleeping.
00:05:07.020 --> 00:05:09.000
And then when you wake up, I found this,
00:05:09.000 --> 00:05:11.890
sometimes you can solve the
problem, almost magically.
00:05:11.890 --> 00:05:14.070
I found the same thing
with major decisions.
00:05:14.070 --> 00:05:15.803
I don't fret too much about them.
00:05:16.690 --> 00:05:18.240
I will, I will think about them.
00:05:18.240 --> 00:05:20.880
I will do the whole decision tree thing.
00:05:20.880 --> 00:05:23.470
I'll oftentimes meditate
to try to clear my mind
00:05:23.470 --> 00:05:25.620
so I'm not thinking about the decision
00:05:25.620 --> 00:05:27.440
And it's interesting,
sometimes I'm meditating,
00:05:27.440 --> 00:05:29.540
I'm meditating and the
answer just comes to me.
00:05:29.540 --> 00:05:30.373
It's just like, you've gotta do this.
00:05:30.373 --> 00:05:32.110
I was like oh, of course, it's obvious.
00:05:32.110 --> 00:05:34.380
Or you sleep on it for a night or two
00:05:34.380 --> 00:05:35.340
and then you just wake up in the morning
00:05:35.340 --> 00:05:36.870
and was like, of course,
I've got to do this.
00:05:36.870 --> 00:05:37.860
This is the right thing.
00:05:37.860 --> 00:05:39.000
Everything tells me that this,
00:05:39.000 --> 00:05:40.520
the stars are aligned here.
00:05:40.520 --> 00:05:42.930
So there's no perfect
formula for decision-making.
00:05:42.930 --> 00:05:44.990
It's a great question but that's my,
00:05:44.990 --> 00:05:46.880
the best wisdom that I have
00:05:46.880 --> 00:05:48.700
and you know, the more in life
00:05:49.740 --> 00:05:52.360
you can perceive the grass on your side
00:05:52.360 --> 00:05:53.840
of the fence to be greener,
00:05:53.840 --> 00:05:55.750
the more happy you're
going to be as a person.
00:05:55.750 --> 00:05:58.660
And I'm the king of that,
for better for worse,
00:05:58.660 --> 00:06:02.680
almost to a fault but
I'm happy. (chuckles)
00:06:02.680 --> 00:06:04.663
All right, let's see Ahmed?
00:06:07.390 --> 00:06:08.223
Ahmed A.
00:06:09.130 --> 00:06:10.920
- Hello, As-salamu alaykum everyone
00:06:10.920 --> 00:06:13.523
and thank you so much
Sal for hosting this.
00:06:14.570 --> 00:06:16.150
I'm delighted to be here and it's an honor
00:06:16.150 --> 00:06:18.620
to be here with all of
you aspiring learners.
00:06:18.620 --> 00:06:21.809
My question is about being content.
00:06:21.809 --> 00:06:24.550
I've struggled with this contest or,
00:06:24.550 --> 00:06:26.820
I've struggled with this concept a lot.
00:06:26.820 --> 00:06:30.610
I think that people that aim to accomplish
00:06:30.610 --> 00:06:33.730
shouldn't be content because being content
00:06:33.730 --> 00:06:37.030
like, limits them to a certain extent.
00:06:37.030 --> 00:06:37.899
What do you think about this?
00:06:37.899 --> 00:06:39.530
Do you think that being content
00:06:39.530 --> 00:06:41.080
is just being happy where you're at
00:06:41.080 --> 00:06:43.040
or is it being happy along with
00:06:44.390 --> 00:06:47.163
being or aspiring to be
more than where you're at?
00:06:48.620 --> 00:06:50.870
- Another very good,
very deep question that,
00:06:52.090 --> 00:06:53.560
you know, my life journey
00:06:53.560 --> 00:06:56.200
I've had different frames of it.
00:06:56.200 --> 00:06:57.500
I think early,
00:06:57.500 --> 00:07:00.060
early on in my life
00:07:00.060 --> 00:07:01.380
of when I was a lot of y'all's age,
00:07:01.380 --> 00:07:04.080
I was very not content. (chuckles)
00:07:04.080 --> 00:07:06.773
I had that proverbial fire in my belly.
00:07:07.970 --> 00:07:10.550
I was constantly thinking, you know,
00:07:10.550 --> 00:07:11.590
to Christine's last question,
00:07:11.590 --> 00:07:12.690
how do I make the right decision?
00:07:12.690 --> 00:07:13.523
Pick the right major?
00:07:13.523 --> 00:07:15.340
Find the right job?
00:07:15.340 --> 00:07:18.290
I was afraid if I'm
honest, about well what if,
00:07:18.290 --> 00:07:19.500
what if I don't succeed?
00:07:19.500 --> 00:07:24.000
What if I can't be in a a
solid financial position?
00:07:24.000 --> 00:07:26.153
Many of y'all know my family, we didn't,
00:07:27.110 --> 00:07:28.450
I was raised by a single mother.
00:07:28.450 --> 00:07:31.110
We didn't, she worked a
lot of minimum wage jobs,
00:07:31.110 --> 00:07:33.670
cashiers, different places,
eventually scrounged up
00:07:33.670 --> 00:07:35.570
enough, you know, pennies to open up
00:07:35.570 --> 00:07:38.040
a not so impressive convenience store.
00:07:38.040 --> 00:07:40.480
So when I was a lot of
y'all's age I was just like,
00:07:40.480 --> 00:07:42.440
and the good thing is we had a lot
00:07:42.440 --> 00:07:44.380
of family friends who were professionals,
00:07:44.380 --> 00:07:46.430
who were doctors, who were engineers.
00:07:46.430 --> 00:07:49.220
And I saw how much
better your life could be
00:07:49.220 --> 00:07:51.720
even materially but put aside what you do
00:07:51.720 --> 00:07:53.160
in the hours of your work,
00:07:53.160 --> 00:07:54.970
but even materially, you know,
00:07:54.970 --> 00:07:57.060
my friends whose parents were engineers,
00:07:57.060 --> 00:07:59.130
had nice houses in better neighborhoods.
00:07:59.130 --> 00:08:01.020
They had health insurance.
00:08:01.020 --> 00:08:02.740
Their path was easier.
00:08:02.740 --> 00:08:05.130
And so I had a lot when I
was a lot of y'all's age
00:08:05.130 --> 00:08:07.520
of angst, I could only
describe it as angst.
00:08:07.520 --> 00:08:11.260
So like, I can't, I
need to get out of this.
00:08:11.260 --> 00:08:12.350
I need to get some.
00:08:12.350 --> 00:08:14.730
So that was always a bit
of a burning motivation
00:08:14.730 --> 00:08:16.050
and I wasn't content.
00:08:16.050 --> 00:08:18.700
And when you're not
content, it can sometimes,
00:08:18.700 --> 00:08:22.120
I wasn't overly angsty,
I think I was a pretty.
00:08:22.120 --> 00:08:23.230
If people knew me they would say,
00:08:23.230 --> 00:08:25.230
oh, he's a pretty,
happy-go-lucky laid back guy
00:08:25.230 --> 00:08:26.240
but there was a piece of me
00:08:26.240 --> 00:08:27.270
that I would sometimes wake up
00:08:27.270 --> 00:08:28.350
in the middle of the night it's like,
00:08:28.350 --> 00:08:29.210
I can't, I can't,
00:08:29.210 --> 00:08:30.760
I can't mess this up, you know.
00:08:32.400 --> 00:08:34.260
To quote Eminem, "You only
got one shot," you know,
00:08:34.260 --> 00:08:35.810
don't, I forgot what he said in 8 Mile
00:08:35.810 --> 00:08:37.600
but (chuckles) it's always
00:08:40.430 --> 00:08:41.680
there was some of that.
00:08:41.680 --> 00:08:45.070
I think, as I've grown older,
00:08:45.070 --> 00:08:47.700
especially I think in my thirties,
00:08:47.700 --> 00:08:50.880
I'm now 44 going on 45.
00:08:50.880 --> 00:08:53.100
But in my thirties I
started to realize that
00:08:53.100 --> 00:08:55.450
that angstiness and that a little bit
00:08:55.450 --> 00:08:57.890
of a chip on your shoulder, it's not
00:08:57.890 --> 00:09:00.540
maybe as useful as you think it is.
00:09:00.540 --> 00:09:03.040
It can continue to make you, once again,
00:09:03.040 --> 00:09:06.700
you're not enjoying the
ride as much as you should
00:09:08.114 --> 00:09:10.340
and once again, I did enjoy my ride a lot.
00:09:10.340 --> 00:09:12.500
I had a lot of really great memories
00:09:12.500 --> 00:09:14.440
from my journey but I think it's,
00:09:14.440 --> 00:09:15.273
I've started to appreciate more
00:09:15.273 --> 00:09:17.040
that I should appreciate it in the moment
00:09:17.040 --> 00:09:19.430
while it's happening and be present
00:09:22.411 --> 00:09:24.660
In Vedic philosophy,
00:09:24.660 --> 00:09:27.480
there's three aspects to
everything in the universe.
00:09:27.480 --> 00:09:32.290
The one is Sattvic, which
means truthful, you know.
00:09:32.290 --> 00:09:34.710
Maybe you speak Urdu,
such, you know, truth
00:09:38.090 --> 00:09:41.210
and even in actions there
can be truthful action.
00:09:41.210 --> 00:09:43.080
The second aspect is Rajasic for those
00:09:43.080 --> 00:09:45.190
who are familiar with the, you know,
00:09:45.190 --> 00:09:46.580
languages from the Indian sub-continent.
00:09:46.580 --> 00:09:48.390
You can think of Raja like a king
00:09:48.390 --> 00:09:51.410
and Rajasic is when you're very,
00:09:51.410 --> 00:09:53.420
it's considered a form of energy.
00:09:53.420 --> 00:09:55.797
It's when you're very focused on,
00:09:55.797 --> 00:09:57.350
and Rajasic action is when you're
00:09:57.350 --> 00:09:59.510
very focused on the outcomes,
00:09:59.510 --> 00:10:00.533
and then there's Tamasic.
00:10:00.533 --> 00:10:03.600
Tamasic can kind of like,
you're not really in control.
00:10:03.600 --> 00:10:04.890
It's a little bit chaotic
00:10:04.890 --> 00:10:06.510
and you're doing something
cause you're forced.
00:10:06.510 --> 00:10:07.740
So Sattvic action,
00:10:07.740 --> 00:10:09.670
you're doing something because it's right
00:10:09.670 --> 00:10:11.140
but you accept the outcome,
00:10:11.140 --> 00:10:12.230
whatever the outcome is,
00:10:12.230 --> 00:10:13.210
it is what it is.
00:10:13.210 --> 00:10:15.230
You get new data points and then you make
00:10:15.230 --> 00:10:17.420
a new set of decisions
and do what's right.
00:10:17.420 --> 00:10:21.623
Rajasic action or Rajasic
decision-making is to say,
00:10:22.800 --> 00:10:25.170
you know I'm gonna do
this because if I do this,
00:10:25.170 --> 00:10:26.490
I'm gonna become rich and famous
00:10:26.490 --> 00:10:27.840
and if I don't become rich and famous,
00:10:27.840 --> 00:10:29.230
I'm gonna be really miserable.
00:10:29.230 --> 00:10:31.570
Or I'm gonna do this
because if I don't do this,
00:10:31.570 --> 00:10:32.870
something really bad's going to have.
00:10:32.870 --> 00:10:33.810
We're not going to have enough money.
00:10:33.810 --> 00:10:34.960
We're not gonna have food on the table.
00:10:34.960 --> 00:10:36.360
We're not gonna do all that.
00:10:37.320 --> 00:10:38.953
And then the Tamasic is
like I'm forced to do it.
00:10:38.953 --> 00:10:40.690
I don't really feel like doing it
00:10:40.690 --> 00:10:42.410
but someone's, you know, whatever.
00:10:42.410 --> 00:10:43.800
I think we all agree that Tamasic
00:10:43.800 --> 00:10:45.340
is not a good place to be for most,
00:10:45.340 --> 00:10:46.790
most things in your life.
00:10:46.790 --> 00:10:49.770
Rajasic is where most of
us are most of the time.
00:10:49.770 --> 00:10:53.120
Most of us are saying hey, if I do this
00:10:53.120 --> 00:10:54.250
I'm gonna get a promotion.
00:10:54.250 --> 00:10:55.520
I'm gonna get a better job.
00:10:55.520 --> 00:10:56.513
I'm gonna do this.
00:10:58.070 --> 00:11:01.140
It can be very motivating
and it can give you
00:11:01.140 --> 00:11:05.290
the external appearances of success
00:11:05.290 --> 00:11:07.580
but, it can also make you miserable
00:11:07.580 --> 00:11:10.480
and non-content your entire life
00:11:10.480 --> 00:11:12.960
because no matter what,
there's going to be outcomes
00:11:12.960 --> 00:11:15.370
that when you're in a
Rajasic frame of mind,
00:11:15.370 --> 00:11:16.990
you have trouble accepting.
00:11:16.990 --> 00:11:19.050
I've found that the more that I can move
00:11:19.050 --> 00:11:21.810
to a kind of Sattvic form of action,
00:11:21.810 --> 00:11:23.180
where I just do what is,
00:11:23.180 --> 00:11:24.980
what I think is right at any moment.
00:11:27.002 --> 00:11:28.480
And then whatever the outcome is,
00:11:28.480 --> 00:11:30.930
I can just accept it and
sometimes even enjoy it
00:11:30.930 --> 00:11:32.690
or savor it and learn from it
00:11:32.690 --> 00:11:34.680
and then take the next set of actions.
00:11:34.680 --> 00:11:37.150
I found that in no way does it,
00:11:37.150 --> 00:11:39.600
does it quelch my ability to do things
00:11:39.600 --> 00:11:41.970
or in no way, does it suppress my ability
00:11:41.970 --> 00:11:44.840
to take action or to be ambitious
00:11:44.840 --> 00:11:46.330
or try to do big things
00:11:46.330 --> 00:11:48.490
but it makes me a lot more content
00:11:48.490 --> 00:11:50.260
and a lot, frankly, a lot more pleasant
00:11:50.260 --> 00:11:53.180
to be around (chuckles)
if I'm just accepting,
00:11:53.180 --> 00:11:54.410
if I'm just accepting things.
00:11:54.410 --> 00:11:56.490
And I'll say a lot of times,
00:11:56.490 --> 00:11:58.210
I actually think you'll be more productive
00:11:58.210 --> 00:12:00.570
if you take that Sattvic aspect
00:12:00.570 --> 00:12:03.780
because a lot of times the Rajasic aspect,
00:12:03.780 --> 00:12:06.330
your ego gets involved very, very heavily.
00:12:06.330 --> 00:12:09.270
And so, you know a lot of
times I think we procrastinate
00:12:09.270 --> 00:12:11.590
because our ego doesn't wanna realize
00:12:11.590 --> 00:12:12.960
that it can't do the thing.
00:12:12.960 --> 00:12:15.600
And so it's like, well oh,
maybe let me go get a snack
00:12:15.600 --> 00:12:17.100
because your ego is
like protecting itself.
00:12:17.100 --> 00:12:18.220
Like what if you start to study it
00:12:18.220 --> 00:12:19.230
and you have trouble doing it,
00:12:19.230 --> 00:12:21.250
or what if you start to write that paper
00:12:21.250 --> 00:12:22.760
and you have writer's block.
00:12:22.760 --> 00:12:24.470
When you have a Sattvic point of mind,
00:12:24.470 --> 00:12:25.340
you're like, you know what,
00:12:25.340 --> 00:12:27.630
the right thing to do
right now is just to start.
00:12:27.630 --> 00:12:29.650
The chips will fall where they do
00:12:29.650 --> 00:12:32.674
and so I find myself
procrastinating a lot less
00:12:32.674 --> 00:12:35.310
when I've gotten less
caught up with the outcome
00:12:35.310 --> 00:12:37.450
and I just wanna start,
start taking action
00:12:37.450 --> 00:12:39.000
and then I just accept the outcome
00:12:39.000 --> 00:12:40.340
wherever it is.
00:12:40.340 --> 00:12:42.200
A lot of the stress at work
00:12:42.200 --> 00:12:43.410
has gone down dramatically.
00:12:43.410 --> 00:12:45.030
I used to you know, sometimes I have
00:12:45.030 --> 00:12:46.370
some big decisions to make
00:12:46.370 --> 00:12:48.250
that could affect a lot of people
00:12:48.250 --> 00:12:50.730
and when I take the Rajasic mindset,
00:12:50.730 --> 00:12:52.290
I'm like wow, this is the wrong decision.
00:12:52.290 --> 00:12:55.010
It could affect these 10
people's lives, you know.
00:12:55.010 --> 00:12:56.470
It can really stress you out.
00:12:56.470 --> 00:12:57.930
It's not gonna help you
make a better decision.
00:12:57.930 --> 00:12:59.130
You take a Sattvic point of view,
00:12:59.130 --> 00:13:00.620
let me look at the data.
00:13:00.620 --> 00:13:01.800
Let me meditate on it.
00:13:01.800 --> 00:13:03.600
Let me take the best
possible decision I can
00:13:03.600 --> 00:13:05.620
and look, I just have
to accept the outcome
00:13:05.620 --> 00:13:07.880
and then let me make another
decision based on that.
00:13:07.880 --> 00:13:09.790
But anyway, I gave you
a long-winded answer.
00:13:09.790 --> 00:13:12.863
My apologies but
hopefully that was useful.
00:13:12.863 --> 00:13:14.878
- All right, thank you so much.
00:13:14.878 --> 00:13:16.520
- Great.
00:13:16.520 --> 00:13:17.689
Let's see.
00:13:17.689 --> 00:13:19.040
Sharvari, I don't know if,
00:13:19.040 --> 00:13:21.490
I'm pronouncing your name correctly?
00:13:21.490 --> 00:13:23.394
- Yeah, you are.
- Oh good.
00:13:23.394 --> 00:13:25.150
- First of all. (chuckles)
00:13:25.150 --> 00:13:26.510
Hi from India.
00:13:26.510 --> 00:13:29.890
It's actually 12:45 am.
00:13:29.890 --> 00:13:31.360
- Thank you for staying up. (laughs)
00:13:31.360 --> 00:13:32.470
- Yeah. (chuckles)
00:13:32.470 --> 00:13:35.240
I'm a huge fan and I just wanted to ask
00:13:35.240 --> 00:13:36.900
that, you know we've always.
00:13:36.900 --> 00:13:38.760
I'm a college student currently
00:13:38.760 --> 00:13:41.860
and we've always been having so many like,
00:13:41.860 --> 00:13:44.350
we've been getting so many tips about
00:13:44.350 --> 00:13:47.160
how to do smart work and hard work
00:13:47.160 --> 00:13:49.050
and how there's a difference.
00:13:49.050 --> 00:13:51.820
And I've been using Khan
Academy for a long time
00:13:52.670 --> 00:13:54.700
and I just wanted to know how you
00:13:54.700 --> 00:13:56.770
would differentiate between those two?
00:13:56.770 --> 00:14:00.690
And if you would have any
particular great tips for us
00:14:00.690 --> 00:14:03.560
as we're making our way through college
00:14:03.560 --> 00:14:07.340
and building a resume and, you know?
00:14:07.340 --> 00:14:08.370
- Yeah well, I think the difference
00:14:08.370 --> 00:14:09.700
between hard work and smart work.
00:14:09.700 --> 00:14:12.110
I do think I was fortunate
00:14:12.110 --> 00:14:13.790
throughout my entire academic career
00:14:13.790 --> 00:14:15.820
that I kind of fell into what would now
00:14:15.820 --> 00:14:18.570
be described as smart
work versus hard work
00:14:18.570 --> 00:14:22.690
because when I was young,
I was the student that
00:14:22.690 --> 00:14:23.890
actually in my early years,
00:14:23.890 --> 00:14:25.860
I wasn't particularly grade motivated.
00:14:25.860 --> 00:14:28.420
I guess I was less Rajasic
than I realized. (chuckles)
00:14:28.420 --> 00:14:31.150
I was actually more motivated by,
00:14:31.150 --> 00:14:32.520
hey, this is interesting,
00:14:32.520 --> 00:14:33.740
let me connect the dots.
00:14:33.740 --> 00:14:35.500
Okay, they're teaching me this formula
00:14:35.500 --> 00:14:37.010
in this class but wait,
00:14:37.010 --> 00:14:38.220
that's kind of the same formula
00:14:38.220 --> 00:14:39.360
that we learned in the other class.
00:14:39.360 --> 00:14:40.850
If we just changed the variables or,
00:14:40.850 --> 00:14:44.250
if you just format the algebra
a little bit differently
00:14:44.250 --> 00:14:47.790
and when you approach
any knowledge that way,
00:14:47.790 --> 00:14:49.860
it naturally is going to connect more.
00:14:49.860 --> 00:14:51.610
It's naturally going to stick more.
00:14:54.960 --> 00:14:57.000
Some of the things I really enjoy
00:14:57.000 --> 00:14:58.530
when I get a cover in Khan Academy
00:14:58.530 --> 00:15:00.710
or when other people are
covering it in Khan Academy,
00:15:00.710 --> 00:15:02.610
try to connect the dots
between different things
00:15:02.610 --> 00:15:05.320
so they don't just feel
like things to memorize.
00:15:05.320 --> 00:15:06.560
One, you're gonna learn it better
00:15:06.560 --> 00:15:08.430
and life is just gonna become,
00:15:08.430 --> 00:15:11.150
it's going to become a
lot more interesting.
00:15:11.150 --> 00:15:13.270
In the US a lot of times they
00:15:13.270 --> 00:15:14.440
teach the Louisiana Purchase.
00:15:14.440 --> 00:15:15.630
Some of y'all might know about this.
00:15:15.630 --> 00:15:17.840
You know, in 1803 Thomas Jefferson
00:15:17.840 --> 00:15:20.330
is able to buy Louisiana from,
00:15:20.330 --> 00:15:22.700
at the time Napoléon controlled France,
00:15:22.700 --> 00:15:23.750
for like $3 million.
00:15:23.750 --> 00:15:26.570
And Louisiana was not just
the State of Louisiana,
00:15:26.570 --> 00:15:28.640
it was like a third of
what we now consider
00:15:28.640 --> 00:15:30.800
to be the United States.
00:15:30.800 --> 00:15:33.750
And the way they teach it
when I first learned that
00:15:33.750 --> 00:15:35.440
I think in fifth or sixth grade,
00:15:35.440 --> 00:15:37.597
it was kind of like they got a good deal.
00:15:37.597 --> 00:15:39.770
Like (chuckles) you know,
that's how it's taught.
00:15:39.770 --> 00:15:41.690
Like just memorize the fact 1803,
00:15:41.690 --> 00:15:44.410
they bought Louisiana
and they got a good deal.
00:15:44.410 --> 00:15:45.860
Later I learned, well the reason
00:15:45.860 --> 00:15:48.450
why they got a good deal is that Napoléon,
00:15:48.450 --> 00:15:50.440
who was trying to take over Europe,
00:15:50.440 --> 00:15:55.140
had his Navy defeated at
Trafalgar by the British.
00:15:55.140 --> 00:15:56.610
And so he really did not have
00:15:56.610 --> 00:15:58.360
much of a Navy to speak of
00:15:58.360 --> 00:15:59.550
and so there's no way that he
00:15:59.550 --> 00:16:00.690
could protect this territory
00:16:00.690 --> 00:16:02.540
that's on the other side of the planet.
00:16:02.540 --> 00:16:05.400
And so in some ways
Napoléon got $3 million
00:16:05.400 --> 00:16:07.720
that probably the Americans
could have just taken it
00:16:07.720 --> 00:16:09.890
and Napoléon could have
done nothing about it
00:16:09.890 --> 00:16:13.650
and at least he got $3 million
(chuckles) more for it.
00:16:13.650 --> 00:16:15.580
So you know, that's just an example of
00:16:15.580 --> 00:16:16.890
it's fun to connect
these and then when you,
00:16:16.890 --> 00:16:18.440
when you connect it you realize,
00:16:18.440 --> 00:16:19.710
wow, that's so interesting, right?
00:16:19.710 --> 00:16:22.110
Like these decisions
that people are making,
00:16:22.110 --> 00:16:26.210
very human decisions, as
opposed to just random,
00:16:26.210 --> 00:16:28.110
random facts in history.
00:16:28.110 --> 00:16:29.560
You know there's things that,
00:16:30.920 --> 00:16:33.520
there's things in history or whatever,
00:16:33.520 --> 00:16:35.990
you know, in math that
will give you goosebumps.
00:16:35.990 --> 00:16:37.930
If you just look at them the right way.
00:16:37.930 --> 00:16:39.580
So I try to remind everyone sometimes,
00:16:39.580 --> 00:16:41.810
you'll hear me say this
in Khan Academy videos.
00:16:41.810 --> 00:16:43.010
You know your biology textbook
00:16:43.010 --> 00:16:44.870
might seem a little bit dry sometimes
00:16:44.870 --> 00:16:47.230
or hard to read, or your stats textbook.
00:16:47.230 --> 00:16:50.000
But that biology textbook,
like every chapter
00:16:50.000 --> 00:16:52.470
is the culmination of probably
00:16:52.470 --> 00:16:54.470
a few hundred people's life work.
00:16:54.470 --> 00:16:57.060
Like you know, those
people would have done.
00:16:57.060 --> 00:16:59.440
You know what Isaac
Newton would have done to
00:17:00.660 --> 00:17:03.050
get his hands on your
calculus physics book
00:17:05.384 --> 00:17:06.929
You know.
00:17:06.929 --> 00:17:10.000
name them, Pasteur or
Curie would have done
00:17:10.000 --> 00:17:12.290
to get their hands on
your chemistry textbook,
00:17:12.290 --> 00:17:14.730
or to get their hands
on your biology textbook
00:17:14.730 --> 00:17:16.130
And they really are
explaining the universe.
00:17:16.130 --> 00:17:17.040
Sometimes they're not doing it
00:17:17.040 --> 00:17:20.010
in the most wondrous wonder provoking way
00:17:20.010 --> 00:17:21.540
but they are fascinating things.
00:17:21.540 --> 00:17:23.550
So that's my you know, when you study,
00:17:23.550 --> 00:17:24.383
when you learn things,
00:17:24.383 --> 00:17:26.930
just try to have that air of wonder.
00:17:26.930 --> 00:17:31.610
And when you watch a movie
like Harry Potter or something,
00:17:31.610 --> 00:17:33.710
we all get excited because we're like,
00:17:33.710 --> 00:17:35.190
wow, they're finding out different spells,
00:17:35.190 --> 00:17:36.810
and they're looking at
these ancient ruins,
00:17:36.810 --> 00:17:38.810
and they're figuring out
things about the universe
00:17:38.810 --> 00:17:40.580
and then they're able to do magic.
00:17:40.580 --> 00:17:42.210
And I've used learning as the same thing.
00:17:42.210 --> 00:17:43.810
Yes, the books that you're looking at
00:17:43.810 --> 00:17:46.200
are sometimes not the
most interesting thing
00:17:46.200 --> 00:17:47.680
but if you really engage in it,
00:17:47.680 --> 00:17:50.500
the way that Hermione
Granger would engage with it.
00:17:50.500 --> 00:17:51.430
You're going to see that you're
00:17:51.430 --> 00:17:52.560
gonna be able to do magic.
00:17:52.560 --> 00:17:54.110
You're going to be able
to understand things
00:17:54.110 --> 00:17:55.210
about the universe that frankly,
00:17:55.210 --> 00:17:58.860
would have seemed like
magic even 500 years ago.
00:17:58.860 --> 00:18:01.490
And so when you view yourself
as you're this person.
00:18:01.490 --> 00:18:03.160
You're going on this quest.
00:18:03.160 --> 00:18:05.520
There's things for you to explore.
00:18:05.520 --> 00:18:07.300
Dots to connect.
00:18:07.300 --> 00:18:10.690
It just becomes a much more
exciting, frankly experience
00:18:10.690 --> 00:18:12.960
and then when you're
doing that the whole time.
00:18:12.960 --> 00:18:16.180
Yes I've sometimes found
myself cramming and having to,
00:18:16.180 --> 00:18:18.830
but even then when you're cramming,
00:18:18.830 --> 00:18:21.780
but the knowledge is being
connected with other things,
00:18:21.780 --> 00:18:23.000
you're more likely to learn it.
00:18:23.000 --> 00:18:25.403
You're more likely to, retain that.
00:18:27.170 --> 00:18:31.230
My Hermione Granger analogy
reminds me of an answer
00:18:31.230 --> 00:18:34.610
to Christine's question
about decision-making.
00:18:34.610 --> 00:18:37.660
Sometimes I do, and this
might be mildly delusional.
00:18:37.660 --> 00:18:40.290
I say look, you can view yourself
00:18:40.290 --> 00:18:41.740
as just kind of living a mundane life
00:18:41.740 --> 00:18:43.400
or you could view
yourself as a protagonist
00:18:43.400 --> 00:18:44.870
in an epic movie.
00:18:44.870 --> 00:18:47.180
And whenever you're faced
with a hard decision,
00:18:47.180 --> 00:18:49.090
you're like, well what
would the protagonist?
00:18:49.090 --> 00:18:51.010
What would Bilbo Baggins
do, in the Hobbit?
00:18:51.010 --> 00:18:54.350
What would Hermoine or
Harry do, in Harry Potter?
00:18:54.350 --> 00:18:58.860
What would Hari Seldon do
in the Foundation Series?
00:18:58.860 --> 00:19:00.620
And I find that when you do that,
00:19:00.620 --> 00:19:03.090
first of all, life becomes a
little bit more fun to live
00:19:03.090 --> 00:19:05.150
but you'll actually do
the more Sattvic thing.
00:19:05.150 --> 00:19:06.600
You'll do the more like,
00:19:06.600 --> 00:19:08.858
what would the protagonist
to do, in the story?
00:19:08.858 --> 00:19:10.220
What would happen here to make
00:19:10.220 --> 00:19:11.790
this a more interesting story?
00:19:11.790 --> 00:19:13.500
And it also reminds myself the other way
00:19:13.500 --> 00:19:15.703
that no great story is not without,
00:19:16.990 --> 00:19:18.190
some significant stress.
00:19:18.190 --> 00:19:19.760
You wouldn't wanna read any of these books
00:19:19.760 --> 00:19:21.180
or watch any of these movies,
00:19:21.180 --> 00:19:23.330
if they did not have significant stress,
00:19:23.330 --> 00:19:25.780
and moments of tension, and
moments where you're not sure
00:19:25.780 --> 00:19:27.270
how things are going to turn out.
00:19:27.270 --> 00:19:29.170
So when you have those
significant stresses
00:19:29.170 --> 00:19:31.690
or moments of tension
or times that you are
00:19:31.690 --> 00:19:33.330
unsure of yourself, you're like oh, well,
00:19:33.330 --> 00:19:34.963
I got a good movie that I'm living in.
00:19:34.963 --> 00:19:37.292
Like (chuckles) my movie is interesting.
00:19:37.292 --> 00:19:40.910
That's my best advice, stay curious.
00:19:40.910 --> 00:19:42.630
My advice on making decisions also,
00:19:42.630 --> 00:19:44.840
especially if you're thinking
about careers and majors.
00:19:44.840 --> 00:19:48.160
Ask a ton of questions,
people like giving advice,
00:19:48.160 --> 00:19:51.150
as you see, I'm enjoying
giving advice to you right now.
00:19:51.150 --> 00:19:53.810
People, even in, I try to fundraise a lot
00:19:53.810 --> 00:19:55.420
and someone told me this piece of advice,
00:19:55.420 --> 00:19:58.030
which actually turned out really true.
00:19:58.030 --> 00:20:00.890
If you ask for money,
people will give you advice.
00:20:00.890 --> 00:20:05.100
If you ask for advice, people
give you money. (chuckles)
00:20:05.100 --> 00:20:06.720
And it is somewhat true, but the simple,
00:20:06.720 --> 00:20:09.240
but oftentimes the advice
is the most useful thing.
00:20:09.240 --> 00:20:12.050
So don't be afraid to
ask as many questions.
00:20:12.050 --> 00:20:13.560
People who are a little
bit older than you,
00:20:13.560 --> 00:20:16.420
who've gone through this
decision making process.
00:20:16.420 --> 00:20:18.700
You know get em one-on-one
and ask em some,
00:20:18.700 --> 00:20:21.245
pry you know, what stresses you out?
00:20:21.245 --> 00:20:24.010
If they're close to
you and it's not tacky,
00:20:24.010 --> 00:20:25.360
ask em how much money they're making?
00:20:25.360 --> 00:20:26.780
Ask em if they made the right decision?
00:20:26.780 --> 00:20:28.830
Ask em how it's affecting other impacts
00:20:28.830 --> 00:20:30.570
of their life, their life-work balance?
00:20:30.570 --> 00:20:32.570
And I think that's
really going to help you
00:20:32.570 --> 00:20:34.300
make good decisions.
00:20:34.300 --> 00:20:37.660
I was the kid when I was in
college, I would somewhat,
00:20:37.660 --> 00:20:39.650
I've never had a really strict filter.
00:20:39.650 --> 00:20:41.800
I've always said what I've thought
00:20:41.800 --> 00:20:42.710
and when I talked to people,
00:20:42.710 --> 00:20:45.980
I've always been willing to
ask them pretty open questions.
00:20:45.980 --> 00:20:47.770
And I think if they
realize that you're coming
00:20:47.770 --> 00:20:50.080
from a place of vulnerability yourself
00:20:50.080 --> 00:20:51.560
and authenticity yourself?
00:20:51.560 --> 00:20:53.360
People will also be
vulnerable and authentic
00:20:53.360 --> 00:20:55.070
with you and they'll give you a lot
00:20:55.070 --> 00:20:56.970
of really good information and advice.
00:20:58.880 --> 00:21:00.170
- That is such a great outlook.
00:21:00.170 --> 00:21:01.470
Thank you so much.
00:21:01.470 --> 00:21:03.110
- Thank you.
00:21:03.110 --> 00:21:06.240
All right, let's go to,
00:21:06.240 --> 00:21:07.073
Vinay.
00:21:09.274 --> 00:21:11.050
- Hi Sal.
- Hello.
00:21:11.050 --> 00:21:13.960
- I'm in Grade 10 and
first, thank you so, so much
00:21:13.960 --> 00:21:15.790
like for both Khan
Academy and Schoolhouse.
00:21:15.790 --> 00:21:18.640
Like especially for India, I'm from India
00:21:18.640 --> 00:21:21.870
so we have the CBSE Grade 10 Board Exam.
00:21:21.870 --> 00:21:23.800
So thank you so much like Khan Academy
00:21:23.800 --> 00:21:26.300
really helped me a lot,
especially in these exams.
00:21:27.800 --> 00:21:29.420
Like I'll just ask one question.
00:21:29.420 --> 00:21:32.160
If you were 18 right now
or if you were at my age,
00:21:32.160 --> 00:21:33.100
what would you work on and why?
00:21:33.100 --> 00:21:35.010
Like what would you think lies ahead
00:21:35.010 --> 00:21:36.423
in the future for the youth?
00:21:37.830 --> 00:21:39.500
- Well I think it's gonna
be a different answer
00:21:39.500 --> 00:21:40.990
depending on what you're interested in,
00:21:40.990 --> 00:21:44.210
what you like, but I do think.
- The most trending thing
00:21:44.210 --> 00:21:45.500
is that Artificial Intelligence
00:21:45.500 --> 00:21:47.150
and the most trending part,
Artificial Intelligence,
00:21:47.150 --> 00:21:50.780
Computer Engineering and all these things.
00:21:50.780 --> 00:21:52.880
- If you're interested in that.
00:21:52.880 --> 00:21:54.470
I don't think you can go wrong with it,
00:21:54.470 --> 00:21:55.800
If you're interested in it.
00:21:55.800 --> 00:21:59.430
I will say, you know I've
often joked, like I can meet.
00:21:59.430 --> 00:22:01.710
I was a Computer Science,
Electrical Engineering,
00:22:01.710 --> 00:22:03.080
Math major when I was in college.
00:22:03.080 --> 00:22:04.680
So I was doing the equivalent of
00:22:04.680 --> 00:22:07.090
what you're thinking about going forward
00:22:07.090 --> 00:22:08.727
but that's because I was
really interested in it.
00:22:08.727 --> 00:22:10.300
And when I went to college,
00:22:10.300 --> 00:22:12.200
I thought I wanted to be
a Theoretical Physicist.
00:22:12.200 --> 00:22:14.330
I was fascinated by theoretical physics.
00:22:14.330 --> 00:22:16.950
So like, I wanna explain
the nature of reality
00:22:16.950 --> 00:22:18.360
and that's what physics is after.
00:22:18.360 --> 00:22:20.930
I was, you know I would
read Feynman's books
00:22:20.930 --> 00:22:21.980
and look at his lectures,
00:22:21.980 --> 00:22:23.920
and I was really inspired by that.
00:22:23.920 --> 00:22:25.440
Then I go to college and I'm like,
00:22:25.440 --> 00:22:27.560
even better than studying reality
00:22:27.560 --> 00:22:29.100
is creating your own realities.
00:22:29.100 --> 00:22:31.580
And that's what I found was interesting
00:22:31.580 --> 00:22:34.100
about computing is that software,
00:22:34.100 --> 00:22:36.390
especially if you thought
about virtual reality
00:22:36.390 --> 00:22:38.930
and things like that, you
can actually create realities
00:22:38.930 --> 00:22:40.740
and so that's what drew me to that.
00:22:40.740 --> 00:22:41.940
So if you have a passion for that?
00:22:41.940 --> 00:22:44.160
You have an interest for that, absolutely.
00:22:44.160 --> 00:22:45.960
What I do recommend for everyone here,
00:22:45.960 --> 00:22:48.480
who's roughly 18 or so years old,
00:22:48.480 --> 00:22:50.100
is those subjects that you're learning
00:22:50.100 --> 00:22:51.480
in your end of high school,
00:22:51.480 --> 00:22:54.010
early college, really master them.
00:22:54.010 --> 00:22:56.270
Master them as well as you can master them
00:22:56.270 --> 00:23:00.310
because if you truly
master your high school,
00:23:00.310 --> 00:23:02.930
early college level calculus,
00:23:02.930 --> 00:23:05.970
statistics, biology, chemistry, physics,
00:23:05.970 --> 00:23:07.110
maybe a little bit of econ.
00:23:07.110 --> 00:23:09.920
If you truly master it,
you're going to be unstoppable
00:23:09.920 --> 00:23:12.600
in pretty much any
field that you wanna go.
00:23:12.600 --> 00:23:14.300
Your reading and your
writing of course, as well.
00:23:14.300 --> 00:23:16.530
If you can write well at that level,
00:23:16.530 --> 00:23:17.820
you're going to be unstoppable
00:23:17.820 --> 00:23:19.430
pretty much in any field you can go in.
00:23:19.430 --> 00:23:21.640
I'll add communications
because I think a lot
00:23:21.640 --> 00:23:23.620
of the schoolhouse.world tutors,
00:23:23.620 --> 00:23:25.340
they're building a muscle of communication
00:23:25.340 --> 00:23:26.730
which is gonna be invaluable.
00:23:26.730 --> 00:23:28.410
No one has grades on communication.
00:23:28.410 --> 00:23:30.800
There's no standardized
test scores on communication
00:23:30.800 --> 00:23:33.450
but the reason why schools
like MIT and UChicago
00:23:33.450 --> 00:23:35.800
are interested in
schoolhouse.world tutors.
00:23:35.800 --> 00:23:37.350
Is one, it shows they know the material
00:23:37.350 --> 00:23:38.410
but it also shows that they know
00:23:38.410 --> 00:23:41.980
how to communicate fairly,
fairly complex things.
00:23:41.980 --> 00:23:43.210
So that's my best advice
00:23:43.210 --> 00:23:44.760
and you'd be surprised even today,
00:23:44.760 --> 00:23:46.920
I meet a friend who has a PhD in Biology.
00:23:46.920 --> 00:23:48.200
They're working at a biotech farm
00:23:48.200 --> 00:23:50.140
and they start explaining their research
00:23:50.140 --> 00:23:52.250
and I can go surprisingly far with them.
00:23:52.250 --> 00:23:53.940
I'm like, oh you're talking
about the Krebs cycle.
00:23:53.940 --> 00:23:55.670
Oh, that's affecting ATP production
00:23:55.670 --> 00:23:57.530
and they're like, how do you know this?
00:23:57.530 --> 00:23:59.900
And I'm like, it's senior level biology
00:23:59.900 --> 00:24:02.290
or freshmen biology in college.
00:24:02.290 --> 00:24:05.410
And everyone learns,
everyone takes those classes
00:24:05.410 --> 00:24:09.010
but most people cram, take the
test and then forget it all.
00:24:09.010 --> 00:24:10.770
But I will tell you that those classes,
00:24:10.770 --> 00:24:13.330
if you really master it,
you're going to be unstoppable
00:24:13.330 --> 00:24:14.790
and then of course you can layer it on.
00:24:14.790 --> 00:24:16.610
If you go into computer science
00:24:16.610 --> 00:24:19.510
or artificial intelligence
or whatever else.
00:24:19.510 --> 00:24:21.080
You know if I were to think about
00:24:21.080 --> 00:24:22.750
what industries are really interesting?
00:24:22.750 --> 00:24:26.210
Obviously artificial intelligence
is really interesting.
00:24:26.210 --> 00:24:27.250
I think biotech is going
00:24:27.250 --> 00:24:28.620
to be really interesting with Christopher.
00:24:28.620 --> 00:24:30.220
I think you're going to
start seeing the intersection
00:24:30.220 --> 00:24:33.120
of the two, where genetic engineering?
00:24:33.120 --> 00:24:34.880
There's gonna be a lot of
ethical questions around it
00:24:34.880 --> 00:24:36.450
but there's gonna be a lot of interesting,
00:24:36.450 --> 00:24:37.780
positive things that can happen
00:24:37.780 --> 00:24:39.920
for humanity there as well.
00:24:39.920 --> 00:24:42.000
But even if you're not interested
in either of those two,
00:24:42.000 --> 00:24:44.130
if you can speak well,
if you can write well,
00:24:44.130 --> 00:24:46.650
if you have a solid dose
of analytical skills,
00:24:46.650 --> 00:24:50.280
you will, you will be very relevant.
00:24:50.280 --> 00:24:52.330
And if you take, and generally be,
00:24:52.330 --> 00:24:56.320
if you're positive and you're authentic
00:24:56.320 --> 00:24:57.460
and you're trying to do right
00:24:57.460 --> 00:24:58.910
by the people around you?
00:24:58.910 --> 00:25:00.890
And you surround yourself
with good people,
00:25:00.890 --> 00:25:02.883
you're going to do just fine.
00:25:04.580 --> 00:25:05.413
- Thank you so much Sal.
00:25:05.413 --> 00:25:07.760
Hope to meet you in person on one day.
00:25:07.760 --> 00:25:09.260
- Yeah, one day maybe.
- Yes.
00:25:09.260 --> 00:25:12.463
It's disappointing, but yeah. (chuckles)
00:25:15.100 --> 00:25:16.000
All right, let's see.
00:25:16.000 --> 00:25:18.550
Okay we have, I could go
a little bit longer today.
00:25:20.190 --> 00:25:21.913
I will, let's see Matthew.
00:25:24.010 --> 00:25:24.843
- Thanks Sal.
00:25:26.035 --> 00:25:27.800
This is Matt, I'm no longer a student.
00:25:27.800 --> 00:25:30.380
Well, I am a continuous
student and I love to learn
00:25:30.380 --> 00:25:34.480
but I actually came to ask
about schoolhouse.world.
00:25:34.480 --> 00:25:37.560
I was wondering what you
need to reach more people
00:25:37.560 --> 00:25:40.550
and what your like, pain
points and blockers are
00:25:40.550 --> 00:25:42.973
for growing the business?
00:25:44.800 --> 00:25:46.173
- Yeah, I think.
00:25:47.010 --> 00:25:51.630
You know, schoolhouse.world is
00:25:51.630 --> 00:25:53.113
as you know, the way that we,
00:25:54.210 --> 00:25:55.720
the dream here, the vision here is
00:25:55.720 --> 00:25:58.100
that we eventually are
able to make a world
00:25:58.100 --> 00:25:59.330
where millions of people are able
00:25:59.330 --> 00:26:03.110
to get free tutoring for everyone.
00:26:03.110 --> 00:26:05.920
And the, I don't know it
keeps spotlighting my video.
00:26:05.920 --> 00:26:09.000
I actually like seeing
everybody else but anyway.
00:26:09.000 --> 00:26:12.650
The goal here is to give free tutoring,
00:26:12.650 --> 00:26:13.810
make it for everyone.
00:26:13.810 --> 00:26:15.610
Right now, we're at a reasonable scale.
00:26:15.610 --> 00:26:18.590
We have several thousand
people using schoolhouse.world.
00:26:18.590 --> 00:26:21.570
We have many hundreds of amazing tutors.
00:26:21.570 --> 00:26:24.230
I know many of y'all are some of them
00:26:24.230 --> 00:26:25.560
and I thank you for that.
00:26:25.560 --> 00:26:27.460
But our hope at the schoolhouse.world team
00:26:27.460 --> 00:26:28.870
is to just continue to scale it
00:26:28.870 --> 00:26:30.390
because I think once we get to a scale,
00:26:30.390 --> 00:26:32.160
that's maybe 10 times bigger
00:26:32.160 --> 00:26:34.840
than where schoolhouse.world is right now.
00:26:34.840 --> 00:26:36.900
Then I think the flywheel is there.
00:26:36.900 --> 00:26:38.190
Then I think schoolhouse.world
00:26:38.190 --> 00:26:40.040
will only grow and grow and grow.
00:26:40.040 --> 00:26:42.560
And as y'all might appreciate,
the more tutors there are,
00:26:42.560 --> 00:26:45.160
if we have 500 tutors now, if
we can get to 5,000 tutors.
00:26:45.160 --> 00:26:47.050
If we have 500 sessions a week now,
00:26:47.050 --> 00:26:49.250
if we go to 5,000 sessions a week.
00:26:49.250 --> 00:26:51.030
Then pretty much anyone who shows up
00:26:51.030 --> 00:26:52.480
there's probably going to be a session
00:26:52.480 --> 00:26:54.690
on what they care about within minutes
00:26:54.690 --> 00:26:56.570
or there might be a series, a group,
00:26:56.570 --> 00:26:58.580
that they could join for multiple weeks
00:26:58.580 --> 00:27:00.900
that's available very soon
00:27:00.900 --> 00:27:03.110
and so then you have high liquidity.
00:27:03.110 --> 00:27:04.670
I'm also hoping that,
00:27:04.670 --> 00:27:06.220
and I've talked about this last time,
00:27:06.220 --> 00:27:08.010
that your ability to become a tutor
00:27:08.010 --> 00:27:09.820
and be a highly reputed tutor
00:27:09.820 --> 00:27:11.900
actually is gonna, one, it'll feel good.
00:27:11.900 --> 00:27:13.330
I think many of y'all enjoy doing that
00:27:13.330 --> 00:27:14.210
but above and beyond that,
00:27:14.210 --> 00:27:16.210
it has some cache in the broader world
00:27:16.210 --> 00:27:17.720
that it can connect you with opportunity.
00:27:17.720 --> 00:27:18.930
It can get you into colleges.
00:27:18.930 --> 00:27:20.700
It can get you a job.
00:27:20.700 --> 00:27:22.150
It can get you a scholarship.
00:27:22.150 --> 00:27:24.320
I've talked to a major scholarship group
00:27:24.320 --> 00:27:26.720
just day before yesterday
about exactly this.
00:27:26.720 --> 00:27:28.340
About, and they are interested.
00:27:28.340 --> 00:27:29.680
They are very interested if you
00:27:29.680 --> 00:27:31.940
are a schoolhouse.world tutor,
00:27:31.940 --> 00:27:33.230
wow, these are exactly the types
00:27:33.230 --> 00:27:35.220
of young people that we
wanna give the scholarship to
00:27:35.220 --> 00:27:36.740
and it's a significant scholarship
00:27:36.740 --> 00:27:39.110
worth hundreds of thousands of dollars.
00:27:39.110 --> 00:27:42.120
And I showed them and not
to set people's expectations
00:27:42.120 --> 00:27:43.100
too high, I showed them some of
00:27:43.100 --> 00:27:45.310
our highly ranked tutors who
are high school students.
00:27:45.310 --> 00:27:47.440
And they said, wow, this is amazing.
00:27:47.440 --> 00:27:48.770
These are exactly the type of people
00:27:48.770 --> 00:27:50.623
that we wanna, we wanna work with.
00:27:53.034 --> 00:27:56.410
You know my hope is, if we
go five years in the future,
00:27:56.410 --> 00:27:58.860
we have millions of people on schoolhouse.
00:27:58.860 --> 00:28:00.040
The quality is high.
00:28:00.040 --> 00:28:01.900
The amazing people who are giving tutors,
00:28:01.900 --> 00:28:03.190
many of whom who might've started
00:28:03.190 --> 00:28:04.980
as a student trying to get tutoring,
00:28:04.980 --> 00:28:06.830
are able to get opportunities
00:28:06.830 --> 00:28:08.820
because they clearly
know the subject matter.
00:28:08.820 --> 00:28:11.890
They can, they're trying
to do good for others.
00:28:11.890 --> 00:28:13.500
And they're clearly articulate
00:28:13.500 --> 00:28:16.230
and can explain things quite well.
00:28:16.230 --> 00:28:18.630
So unfortunately, I
have people calling me.
00:28:18.630 --> 00:28:22.230
I realized I did have
12:30 Pacific time booked
00:28:22.230 --> 00:28:24.280
but I have really enjoyed this.
00:28:24.280 --> 00:28:26.140
Sorry for the long-winded answers.
00:28:26.140 --> 00:28:28.710
I hope they can be
vaguely useful for y'all
00:28:28.710 --> 00:28:32.570
and I see that I'm leaving
about 30 hands raised.
00:28:32.570 --> 00:28:34.200
My apologies for that.
00:28:34.200 --> 00:28:37.010
What I will do, is see if we
can schedule more of these
00:28:37.010 --> 00:28:38.620
cause I enjoyed these as well.
00:28:38.620 --> 00:28:40.860
So don't fret if this is,
00:28:40.860 --> 00:28:41.810
if you're enjoying this,
00:28:41.810 --> 00:28:44.200
we will get a chance to do this again.
00:28:44.200 --> 00:28:45.650
So I will see you all then.
00:28:45.650 --> 00:28:47.070
Talk to y'all later, thanks for joining.
00:28:47.070 --> 00:28:49.350
And thanks for being part of
the schoolhouse community.
00:28:49.350 --> 00:28:50.373
- Thanks Sal.
- Have a nice day.
00:28:50.373 --> 00:28:51.398
- Thanks Sal.
- Thank you so much Sal.
00:28:51.398 --> 00:28:52.715
- Thank you.
- Thanks Sal.
00:28:52.715 --> 00:28:53.832
- Thank you so much.
- Yeah.
00:28:53.832 --> 00:28:54.911
- Thanks Sal.
- Thank you Sal.
00:28:54.911 --> 00:28:55.744
- All right.
- Thank you.
00:28:55.744 --> 00:28:56.744
- Bye.
- Bye.
00:28:59.677 --> 00:29:01.234
- Bye.
- Bye Sal.
00:29:01.234 --> 00:29:03.317
- Thanks.
- Thank you Sal.
|
Buffer capacity | https://www.youtube.com/watch?v=XcSZ5jeG5mA | vtt | https://www.youtube.com/api/timedtext?v=XcSZ5jeG5mA&ei=0lWUZY-_ILaIp-oPupS2OA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7880FFFC29A1812E8061DF1F671F95195670C03D.05C87CEAE4498428758B76B60D84C7C7332B5C09&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.400 --> 00:00:03.300
- [Instructor] Buffer capacity
refers to the amount of acid
00:00:03.300 --> 00:00:06.620
or base a buffer can neutralize
before the pH changes
00:00:06.620 --> 00:00:08.210
by a large amount.
00:00:08.210 --> 00:00:09.890
An increased buffer capacity
00:00:09.890 --> 00:00:12.750
means an increased amount
of acid or base neutralized
00:00:12.750 --> 00:00:15.560
before the pH changes dramatically.
00:00:15.560 --> 00:00:17.020
Let's compare two buffers;
00:00:17.020 --> 00:00:20.210
buffer solution one and
buffer solution two,
00:00:20.210 --> 00:00:23.580
and see which one has the
higher buffer capacity.
00:00:23.580 --> 00:00:25.700
Buffer solution one has a concentration
00:00:25.700 --> 00:00:28.710
of acidic acid of 0.250 molar
00:00:28.710 --> 00:00:33.710
and a concentration of acetate
anion also 0.250 molar.
00:00:33.910 --> 00:00:36.910
Buffer solution two also
consists of acidic acid
00:00:36.910 --> 00:00:38.420
and the acetate anion.
00:00:38.420 --> 00:00:39.500
However, in this case,
00:00:39.500 --> 00:00:43.830
both concentrations are 0.0250 molar.
00:00:43.830 --> 00:00:46.677
So buffer solution one
has a higher concentration
00:00:46.677 --> 00:00:50.170
of both acidic acid and the acetate anion.
00:00:50.170 --> 00:00:53.110
Let's calculate the initial
pH of both buffer solutions
00:00:53.110 --> 00:00:55.500
using the Henderson-Hasselbalch equation.
00:00:55.500 --> 00:00:57.190
In the Henderson-Hasselbalch equation,
00:00:57.190 --> 00:01:01.360
the pH of the solution is equal
to the pka of the weak acid,
00:01:01.360 --> 00:01:04.830
which for both buffers is a acidic acid
00:01:04.830 --> 00:01:08.510
plus the log of the concentration
of the conjugate base
00:01:08.510 --> 00:01:11.970
divided by the concentration
of the weak acid.
00:01:11.970 --> 00:01:15.080
In this case, the conjugate
base is the acetate anion,
00:01:15.080 --> 00:01:17.290
so the concentration of the acetate anion
00:01:17.290 --> 00:01:20.130
divided by the concentration
of acidic acid.
00:01:20.130 --> 00:01:21.640
For buffer solution number one,
00:01:21.640 --> 00:01:24.030
the concentration of the acetate anion
00:01:24.030 --> 00:01:27.270
is equal to the
concentration of acidic acid.
00:01:27.270 --> 00:01:29.660
Therefore, the ratio
of their concentrations
00:01:29.660 --> 00:01:31.320
is equal to one.
00:01:31.320 --> 00:01:33.850
And it's the same idea for
buffer solution number two,
00:01:33.850 --> 00:01:36.020
the concentration of the acetate anion
00:01:36.020 --> 00:01:38.680
is equal to the
concentration of acidic acid.
00:01:38.680 --> 00:01:40.958
Therefore, the ratio
of their concentrations
00:01:40.958 --> 00:01:44.210
is also equal to one for buffer two.
00:01:44.210 --> 00:01:47.790
Since the ratio of the
concentrations is equal to one,
00:01:47.790 --> 00:01:52.010
the log of one is equal to zero,
00:01:52.010 --> 00:01:56.640
and the pka value of acidic
acid at 25 degrees Celsius
00:01:58.001 --> 00:01:59.990
is equal to 4.74.
00:01:59.990 --> 00:02:04.240
So the pH of both buffer
solutions is equal to 4.74
00:02:04.240 --> 00:02:08.490
plus zero, or just 4.74.
00:02:08.490 --> 00:02:10.700
So we're starting with
two buffer solutions,
00:02:10.700 --> 00:02:14.900
each at a pH of 4.74, and
to those buffer solutions,
00:02:14.900 --> 00:02:19.900
we're gonna add 0.0200
moles of hydroxide anions.
00:02:20.930 --> 00:02:23.050
And by calculating the pH change
00:02:23.050 --> 00:02:25.350
after adding the hydroxide anions,
00:02:25.350 --> 00:02:26.250
we'll be able to see
00:02:26.250 --> 00:02:29.340
which buffer has the
higher buffer capacity.
00:02:29.340 --> 00:02:32.100
The added hydroxide
anions will be neutralized
00:02:32.100 --> 00:02:35.270
by the weak acid that's
present in the buffer system.
00:02:35.270 --> 00:02:37.110
So that's acidic acid.
00:02:37.110 --> 00:02:41.080
So acidic acid is going to
react with the hydroxide anions.
00:02:41.080 --> 00:02:42.500
And to make the math easier,
00:02:42.500 --> 00:02:44.310
we're gonna assume that the total volume
00:02:44.310 --> 00:02:47.030
of the buffer solutions
is equal to one that liter
00:02:47.030 --> 00:02:50.620
both before and after
the addition of the base.
00:02:50.620 --> 00:02:53.340
So if the total volume of
the solution is one liter
00:02:53.340 --> 00:02:55.230
and the concentration of acidic acid
00:02:55.230 --> 00:02:58.670
is equal to 0.250 molar in buffer one,
00:02:58.670 --> 00:03:03.640
that means there's 0.250 moles
of acidic acid in the buffer.
00:03:03.640 --> 00:03:06.870
So 0.250 moles of a acidic acid will react
00:03:06.870 --> 00:03:10.800
with the 0.0200 moles of hydroxide anions
00:03:10.800 --> 00:03:13.083
that we're adding to buffer solution one.
00:03:13.960 --> 00:03:16.661
Let's calculate the pH
of buffer solution one
00:03:16.661 --> 00:03:20.300
after the addition of
the hydroxide anions.
00:03:20.300 --> 00:03:23.250
The hydroxide anions
react with a acidic acid
00:03:23.250 --> 00:03:26.630
to form water and the acetate anion.
00:03:26.630 --> 00:03:28.890
In buffer solution one, the initial moles
00:03:28.890 --> 00:03:33.890
of both acidic acid and the
acetate anion are both 0.250.
00:03:34.080 --> 00:03:36.180
And to that buffer solution we're adding
00:03:36.180 --> 00:03:40.450
0.0200 moles of hydroxide anions.
00:03:40.450 --> 00:03:43.490
To help us find the final
moles of acidic acid
00:03:43.490 --> 00:03:46.470
and the acetate anion, we're
gonna use an ICF table,
00:03:46.470 --> 00:03:48.660
where I is the initial amount of moles,
00:03:48.660 --> 00:03:52.960
C is the change in moles and F
as the final amount of moles.
00:03:52.960 --> 00:03:55.070
For this reaction, hydroxide anions
00:03:55.070 --> 00:03:56.812
are the limiting reactant.
00:03:56.812 --> 00:03:58.110
So we're gonna use up
00:03:58.110 --> 00:04:01.940
all of the 0.0200 moles
of hydroxide anions,
00:04:01.940 --> 00:04:03.630
and we're left with nothing.
00:04:03.630 --> 00:04:08.630
Since the mole ratio of
hydroxide anions to acidic acid
00:04:08.730 --> 00:04:11.360
is a one-to-one mole ratio,
00:04:11.360 --> 00:04:16.230
we're also gonna use up 0.0200 moles
00:04:16.230 --> 00:04:17.800
of acidic acid,
00:04:17.800 --> 00:04:22.270
which leaves us with 0.230
moles of acidic acid.
00:04:22.270 --> 00:04:25.340
And for the acetate anion,
there's also a coefficient of one
00:04:25.340 --> 00:04:26.870
in the balanced equation.
00:04:26.870 --> 00:04:30.780
So for losing 0.0200
moles for the reactants,
00:04:30.780 --> 00:04:35.780
we're gaining 0.0200 moles
for the acetate anion,
00:04:36.090 --> 00:04:38.530
which gives us a final amount of moles
00:04:38.530 --> 00:04:42.440
of the acetate anion of 0.270.
00:04:42.440 --> 00:04:43.860
Now that we have our final moles,
00:04:43.860 --> 00:04:46.760
we're ready to calculate the
pH of the buffer solution.
00:04:46.760 --> 00:04:49.280
So the pH is equal to the pka value,
00:04:49.280 --> 00:04:52.020
which for a acidic acid is 4.74,
00:04:52.020 --> 00:04:56.100
plus the log of the ratio
of the concentrations.
00:04:56.100 --> 00:04:58.000
And we could put in the concentrations,
00:04:58.000 --> 00:05:00.050
but since concentration or molarity
00:05:00.050 --> 00:05:02.280
is equal to moles divided by liters,
00:05:02.280 --> 00:05:04.750
a ratio of the concentrations
00:05:04.750 --> 00:05:07.540
would just have the volume
cancel out because it's the same
00:05:07.540 --> 00:05:11.100
for both our conjugate
base and our weak acid.
00:05:11.100 --> 00:05:13.730
So a ratio of the moles is the same thing
00:05:13.730 --> 00:05:15.620
as a ratio of the concentrations
00:05:15.620 --> 00:05:17.960
in the Henderson-Hasselbalch equation.
00:05:17.960 --> 00:05:21.290
And we can get our moles
directly from our ICF table.
00:05:21.290 --> 00:05:26.260
So the moles of the acetate
anion are equal to 0.270,
00:05:26.260 --> 00:05:31.260
and the moles of a acidic
acid is equal to 0.230.
00:05:31.410 --> 00:05:33.010
And when we solve for the pH,
00:05:33.010 --> 00:05:37.573
we find the pH of the
solution is equal to 4.81.
00:05:38.880 --> 00:05:42.210
So buffer one started at a pH of 4.74,
00:05:42.210 --> 00:05:44.819
and after the addition
of the hydroxide anions,
00:05:44.819 --> 00:05:48.210
the pH rose a little bit to 4.81,
00:05:48.210 --> 00:05:51.840
however, that's a relatively
small change in the pH.
00:05:51.840 --> 00:05:53.800
So buffer one did a pretty good job
00:05:53.800 --> 00:05:57.410
of resisting a large change in pH.
00:05:57.410 --> 00:05:59.740
Next, let's calculate the pH of buffer two
00:05:59.740 --> 00:06:03.040
after the addition of
the hydroxide anions.
00:06:03.040 --> 00:06:06.030
So the initial moles of a
acidic acid in buffer two
00:06:06.030 --> 00:06:08.970
is equal to 0.0250 moles,
00:06:08.970 --> 00:06:12.100
which is the same number of
moles as the acetate anion,
00:06:12.100 --> 00:06:14.400
so 0.0250,
00:06:14.400 --> 00:06:16.920
and the hydroxide anions that we add
00:06:16.920 --> 00:06:20.490
is equal to 0.0200 moles.
00:06:20.490 --> 00:06:23.470
Once again, hydroxide anions
are the limiting reactant,
00:06:23.470 --> 00:06:26.200
so all of the hydroxide anions are used up
00:06:26.200 --> 00:06:28.340
and we're left with zero moles.
00:06:28.340 --> 00:06:32.040
Since the mole ratio of
hydroxide anions to acidic acid
00:06:32.040 --> 00:06:36.830
is one to one, we use up the
same amount of acidic acid,
00:06:36.830 --> 00:06:38.880
0.0200 moles,
00:06:38.880 --> 00:06:42.750
and we're left with 0.0050
moles of a acidic acid
00:06:42.750 --> 00:06:44.700
after the neutralization.
00:06:44.700 --> 00:06:46.660
And since there's a one as a coefficient
00:06:46.660 --> 00:06:48.700
in front of the acetate anion,
00:06:48.700 --> 00:06:52.700
the acetate anion is
going to gain 0.0200 moles
00:06:52.700 --> 00:06:57.110
for a final moles of 0.0450.
00:06:57.110 --> 00:06:59.260
Next, we can calculate
the pH of the solution
00:06:59.260 --> 00:07:01.370
using the Henderson-Hasselbalch equation.
00:07:01.370 --> 00:07:06.290
So the pH is equal to the pka
value of acidic acid of 4.74,
00:07:06.290 --> 00:07:10.450
plus the log of the concentration
of the conjugate base
00:07:10.450 --> 00:07:13.600
divided by the concentration
of the weak acid.
00:07:13.600 --> 00:07:15.690
And since we can
substitute moles for that,
00:07:15.690 --> 00:07:18.620
we can grab those from
our ICF table and plug in
00:07:18.620 --> 00:07:23.620
the moles of acetate anion
and the moles of acidic acid,
00:07:23.620 --> 00:07:25.800
and then solve for the pH.
00:07:25.800 --> 00:07:27.150
When we solve for the pH,
00:07:27.150 --> 00:07:31.933
we find that the pH of buffer
solution two is equal to 5.69.
00:07:34.360 --> 00:07:38.050
So buffer solution two
started at pH of 4.74,
00:07:38.050 --> 00:07:40.650
and after the addition
of the hydroxide anions,
00:07:40.650 --> 00:07:43.730
the pH rose to 5.69.
00:07:43.730 --> 00:07:46.010
That's a relatively large increase
00:07:46.010 --> 00:07:48.300
in the pH of the solution.
00:07:48.300 --> 00:07:50.260
So going back to buffer solution one,
00:07:50.260 --> 00:07:52.157
the initial pH was 4.74,
00:07:52.157 --> 00:07:56.680
and the pH rose to 4.81 upon
the addition of the base.
00:07:56.680 --> 00:07:59.347
For buffer solution
two, we started at 4.74
00:07:59.347 --> 00:08:02.750
and the pH rose to 5.69.
00:08:02.750 --> 00:08:06.370
Therefore buffer solution
one had a higher capacity
00:08:06.370 --> 00:08:08.900
to neutralize the added base.
00:08:08.900 --> 00:08:11.410
And so we say that buffer solution one
00:08:11.410 --> 00:08:14.760
has the higher buffer capacity.
00:08:14.760 --> 00:08:16.700
And since buffer solution two
00:08:16.700 --> 00:08:18.710
had the more dramatic change in pH
00:08:18.710 --> 00:08:21.250
upon the addition of
the same amount of base,
00:08:21.250 --> 00:08:24.800
buffer two has a decreased
capacity to neutralize the base
00:08:24.800 --> 00:08:26.360
compared to buffer one.
00:08:26.360 --> 00:08:30.420
So we say that buffer two has
a decreased buffer capacity.
00:08:30.420 --> 00:08:32.970
Remember that the only difference
between these two buffers
00:08:32.970 --> 00:08:35.282
was that buffer one had
a higher concentration
00:08:35.282 --> 00:08:38.770
of acidic acid and the acetate anion.
00:08:38.770 --> 00:08:41.570
Therefore the higher the
concentration of the weak acid
00:08:41.570 --> 00:08:45.003
and the conjugate base, the
higher the buffer capacity.
00:08:46.000 --> 00:08:48.050
We just looked at two buffer solutions
00:08:48.050 --> 00:08:50.150
in which the concentrations of weak acid
00:08:50.150 --> 00:08:52.090
and conjugate base were equal.
00:08:52.090 --> 00:08:54.900
However, a buffer solution
doesn't have to start
00:08:54.900 --> 00:08:57.440
with equal concentrations of the weak acid
00:08:57.440 --> 00:08:59.620
and its conjugate base.
00:08:59.620 --> 00:09:02.240
For example, when the
concentration of weak acid
00:09:02.240 --> 00:09:05.240
is greater than the
concentration of conjugate base,
00:09:05.240 --> 00:09:07.330
the buffer has a higher capacity
00:09:07.330 --> 00:09:10.220
for added base than added acid.
00:09:10.220 --> 00:09:12.330
And when the concentration
of conjugate base
00:09:12.330 --> 00:09:15.090
is greater than the
concentration of weak acid,
00:09:15.090 --> 00:09:18.300
the buffer has a higher
capacity for added acid
00:09:18.300 --> 00:09:20.300
than added base.
00:09:20.300 --> 00:09:22.180
As an example, let's think about blood,
00:09:22.180 --> 00:09:23.343
which has a pH of 7.4.
00:09:24.670 --> 00:09:28.260
The major buffer system used
to control the pH of blood
00:09:28.260 --> 00:09:32.420
is the carbonic acid
bicarbonate buffer system.
00:09:32.420 --> 00:09:35.010
In blood, the concentration of bicarbonate
00:09:35.010 --> 00:09:38.890
is greater than the
concentration of carbonic acid.
00:09:38.890 --> 00:09:41.580
And since bicarbonate
is the conjugate base
00:09:41.580 --> 00:09:45.930
to carbonic acid, the
concentration of the conjugate base
00:09:45.930 --> 00:09:49.370
is greater than the
concentration of the weak acid.
00:09:49.370 --> 00:09:52.810
And therefore the buffer
system has a higher capacity
00:09:52.810 --> 00:09:56.040
for added acid than added base.
00:09:56.040 --> 00:09:57.530
The reason why the buffer system
00:09:57.530 --> 00:10:00.540
needs to have a higher
capacity for added acid
00:10:00.540 --> 00:10:02.770
is because the products of metabolism
00:10:02.770 --> 00:10:05.570
that enter the bloodstream
are mostly acidic
00:10:05.570 --> 00:10:08.220
and therefore the bicarbonate anion
00:10:08.220 --> 00:10:11.940
can react with those acidic
products and neutralize them.
00:10:11.940 --> 00:10:15.580
Therefore, the buffer system
is able to resist large changes
00:10:15.580 --> 00:10:17.053
to the pH of blood.
|
Sal answers questions from attendees at his Schoolhouse.world series | https://www.youtube.com/watch?v=wMm0UFU3hPg | vtt | https://www.youtube.com/api/timedtext?v=wMm0UFU3hPg&ei=0lWUZcaDI_u4vdIPus-juAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EB72C5BA363E4E42C26362764E7576E9D1FBDED2.C9B8D1BCE94004C27FD16C715F6AA475194F82A2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.270 --> 00:00:02.450
- I'd love to answer any questions
00:00:02.450 --> 00:00:04.253
y'all have about anything.
00:00:06.400 --> 00:00:07.530
Raise your hands.
00:00:07.530 --> 00:00:12.530
Or probably raising your hand
is the best way to do it.
00:00:13.890 --> 00:00:15.543
Yes, Kai, ask your question.
00:00:18.637 --> 00:00:19.470
- All right, thanks.
00:00:19.470 --> 00:00:21.190
Thanks again, Sal, for taking your time
00:00:21.190 --> 00:00:22.700
and answering questions.
00:00:22.700 --> 00:00:23.793
Super appreciate it.
00:00:24.760 --> 00:00:28.110
My question revolves around a lot of like
00:00:28.110 --> 00:00:29.470
things that my colleagues have brought up,
00:00:29.470 --> 00:00:31.380
which is like dealing with burnout,
00:00:31.380 --> 00:00:33.820
especially with like obviously last year
00:00:33.820 --> 00:00:36.720
with the coronavirus and
even now with Delta variant
00:00:36.720 --> 00:00:39.410
and like some quarantine and
some measures coming back in.
00:00:39.410 --> 00:00:41.350
I think a lot of people, you know,
00:00:41.350 --> 00:00:43.140
they're dealing with multiple
things outside of work,
00:00:43.140 --> 00:00:46.110
but it affects their work
and their state of mind.
00:00:46.110 --> 00:00:50.180
So what are some tips that you have
00:00:50.180 --> 00:00:51.480
like dealing with burnout?
00:00:52.640 --> 00:00:54.670
- Good question and excellent question.
00:00:54.670 --> 00:00:56.020
Maybe the most important question.
00:00:56.020 --> 00:00:57.620
And I think burnout is
one of these things.
00:00:57.620 --> 00:00:58.660
I don't know how many,
00:00:58.660 --> 00:01:00.440
I'm sure everyone here has experienced it
00:01:00.440 --> 00:01:01.810
in some way, shape, or form.
00:01:01.810 --> 00:01:03.420
But it creeps up on you.
00:01:03.420 --> 00:01:04.370
You think you can handle it.
00:01:04.370 --> 00:01:05.230
You think you can handle it.
00:01:05.230 --> 00:01:06.140
You think you can handle it
00:01:06.140 --> 00:01:07.830
until you can't handle it anymore.
00:01:07.830 --> 00:01:11.230
And then it's usually
too late to address it.
00:01:11.230 --> 00:01:14.100
There's a couple of things
that I have done preventatively
00:01:14.100 --> 00:01:17.540
that I have found have been
like life-changing for me.
00:01:17.540 --> 00:01:19.130
I meditate regularly.
00:01:19.130 --> 00:01:20.980
I remember when I was younger.
00:01:20.980 --> 00:01:23.090
I was intrigued by this
idea of meditation.
00:01:23.090 --> 00:01:26.400
It seemed very mystical and very powerful.
00:01:26.400 --> 00:01:29.260
But I remember when I tried
it when I was a teenager.
00:01:29.260 --> 00:01:33.300
I was like, you just sit
quietly for 10 minutes,
00:01:33.300 --> 00:01:34.710
20 minutes, 30 minutes.
00:01:34.710 --> 00:01:35.840
How does that work?
00:01:35.840 --> 00:01:39.850
And in hindsight, I think I
just had an overactive mind
00:01:39.850 --> 00:01:42.150
and I couldn't even imagine what it meant
00:01:42.150 --> 00:01:43.523
to have a still mind.
00:01:44.520 --> 00:01:47.740
Fast forward until about five years ago,
00:01:47.740 --> 00:01:50.770
I'm in my late 30s at this point,
00:01:50.770 --> 00:01:54.360
and I realized that I
was approaching a burnout
00:01:54.360 --> 00:01:55.470
on a lot of levels.
00:01:55.470 --> 00:01:56.720
I'd kind of spread myself too thin.
00:01:56.720 --> 00:01:58.890
I was having to do a
lot of travel for work.
00:01:58.890 --> 00:02:00.140
I never enjoyed planes
00:02:00.140 --> 00:02:01.906
and I'm starting to get
claustrophobic on the planes.
00:02:01.906 --> 00:02:03.540
I was like, okay, something's going.
00:02:03.540 --> 00:02:06.400
And that's when I rediscovered meditation.
00:02:06.400 --> 00:02:07.990
And I think it's one of those things
00:02:07.990 --> 00:02:11.350
and if possible, folks can
mute their microphones.
00:02:11.350 --> 00:02:13.143
I hear some background noise.
00:02:13.990 --> 00:02:18.690
Is that it's a very subtle
but very powerful thing.
00:02:18.690 --> 00:02:22.400
I read a lot of these gurus
who speak about meditation,
00:02:22.400 --> 00:02:23.820
instilling the mind.
00:02:23.820 --> 00:02:26.020
And our minds naturally gravitate
00:02:26.020 --> 00:02:27.630
to the very obvious things.
00:02:27.630 --> 00:02:30.010
The things that really
hit our senses hard,
00:02:30.010 --> 00:02:32.230
but our emotional state
and our mental state
00:02:32.230 --> 00:02:33.740
is a very subtle thing.
00:02:33.740 --> 00:02:36.140
But what I can guarantee
to almost everyone here
00:02:36.140 --> 00:02:39.610
is if you do sit down for
that even five or 10 minutes,
00:02:39.610 --> 00:02:42.330
but I find it really starts to kick in
00:02:42.330 --> 00:02:43.733
at around 30 or 40 minutes.
00:02:44.590 --> 00:02:47.863
And you just have faith that
it's going to be good for you,
00:02:48.930 --> 00:02:49.940
that it will be.
00:02:49.940 --> 00:02:51.660
And there's even going to be those days
00:02:51.660 --> 00:02:54.730
where your mind is wandering
and there's noise outside.
00:02:54.730 --> 00:02:56.030
And you're like, oh, this
isn't a good meditation.
00:02:56.030 --> 00:02:59.420
Even that, I find after 20 or 30 minutes
00:02:59.420 --> 00:03:01.290
makes a big, big difference.
00:03:01.290 --> 00:03:03.640
Also, the perspective that you take to it,
00:03:03.640 --> 00:03:06.340
I think some of us, myself,
00:03:06.340 --> 00:03:07.920
when I first tried to do this, I was like,
00:03:07.920 --> 00:03:09.270
I wanted to be the perfect meditator
00:03:09.270 --> 00:03:11.470
and I wanted perfect conditions
and I'd want silence.
00:03:11.470 --> 00:03:13.860
And I found myself getting
stressed about the meditation.
00:03:13.860 --> 00:03:16.560
I would like yell at my kids,
"Be quiet, I'm meditating!"
00:03:16.560 --> 00:03:17.480
And I realized at some point
00:03:17.480 --> 00:03:20.250
that's completely the
wrong way to approach it.
00:03:20.250 --> 00:03:23.640
The way to approach it
is to accept everything
00:03:23.640 --> 00:03:27.020
and to observe everything
and to just try to be still
00:03:27.020 --> 00:03:30.340
and to be curious and have
a sense of humor about it.
00:03:30.340 --> 00:03:31.880
And then when you do it that way,
00:03:31.880 --> 00:03:33.340
I find it very energetic.
00:03:33.340 --> 00:03:35.323
So that's my biggest life hack.
00:03:36.260 --> 00:03:38.180
Outside of that, just really make sure
00:03:38.180 --> 00:03:41.130
that you have time for
yourself and your family.
00:03:41.130 --> 00:03:42.240
I just talked about meditation.
00:03:42.240 --> 00:03:44.570
For some people, it might be exercise,
00:03:44.570 --> 00:03:45.770
it might be socializing.
00:03:45.770 --> 00:03:48.230
But you can't under invest in that.
00:03:48.230 --> 00:03:50.840
That's something that I've
learned over the years.
00:03:50.840 --> 00:03:53.910
That we have a culture that idolizes work,
00:03:53.910 --> 00:03:57.410
and that has certain
positive aspects of it.
00:03:57.410 --> 00:04:00.060
But we're here to live our lives as well.
00:04:00.060 --> 00:04:02.060
So that's my best advice.
00:04:02.060 --> 00:04:04.930
Stay socially connected, meditate,
00:04:04.930 --> 00:04:07.380
and make sure you have time
and space for yourself.
00:04:07.380 --> 00:04:08.743
It's not going to be.
00:04:11.400 --> 00:04:12.717
Someone told me the saying,
00:04:12.717 --> 00:04:15.240
"If you don't have the time
to meditate for an hour,
00:04:15.240 --> 00:04:18.167
you should meditate for two." (laughs)
00:04:19.800 --> 00:04:23.420
And I also found the other
way that when I meditate,
00:04:23.420 --> 00:04:24.930
it's always a good use of time.
00:04:24.930 --> 00:04:27.080
Like part of my brain says,
oh, I don't have 10 minutes.
00:04:27.080 --> 00:04:28.110
Really, you don't have 10 minutes?
00:04:28.110 --> 00:04:29.150
Then that's a problem, Sal.
00:04:29.150 --> 00:04:32.240
If you don't have 10 minutes,
you need to slow down.
00:04:32.240 --> 00:04:33.073
Let's see, so many questions.
00:04:33.073 --> 00:04:34.790
I know I'm giving these super long.
00:04:34.790 --> 00:04:36.483
I think Selena was next.
00:04:39.210 --> 00:04:40.043
- Hi, Sal.
00:04:41.645 --> 00:04:43.395
Thank you so much for this session.
00:04:44.320 --> 00:04:46.260
I'm a high school junior at this moment,
00:04:46.260 --> 00:04:50.820
and I'm in a situation
where it's very hard for me
00:04:50.820 --> 00:04:53.343
to attend junior year in person.
00:04:54.200 --> 00:04:59.010
And as I live in NYC, there
is no remote option as of now.
00:04:59.010 --> 00:05:01.890
So I'm not really sure how
I should proceed with this.
00:05:01.890 --> 00:05:04.680
And since I'm in a small Ivy school,
00:05:04.680 --> 00:05:06.600
the courses in 11th grade and 12th grade
00:05:06.600 --> 00:05:08.070
are two year courses.
00:05:08.070 --> 00:05:11.050
So if I miss junior year, that
would be really problematic
00:05:11.050 --> 00:05:15.650
because 12th grade curriculum is based on
00:05:15.650 --> 00:05:17.800
what I learned in 11th grade.
00:05:17.800 --> 00:05:20.270
And I feel that even in the scenario
00:05:20.270 --> 00:05:23.230
where my teachers do provide
some guidance from home,
00:05:23.230 --> 00:05:26.090
it would be really difficult
for me to perform well
00:05:26.090 --> 00:05:27.920
or even effectively learn the content
00:05:27.920 --> 00:05:30.760
as I'm having a different experience
00:05:30.760 --> 00:05:32.930
from all my other classmates.
00:05:32.930 --> 00:05:34.990
And I would really, really like to hear
00:05:34.990 --> 00:05:37.150
your insight and advice on this.
00:05:37.150 --> 00:05:38.520
Thank you.
00:05:38.520 --> 00:05:39.353
- Yeah, first of all, thanks
00:05:39.353 --> 00:05:41.302
for asking the questions, Selena.
00:05:41.302 --> 00:05:43.152
It does sound like a tough situation.
00:05:44.330 --> 00:05:46.630
My best advice, as you know, junior year,
00:05:46.630 --> 00:05:49.360
it can be very important
year, especially now
00:05:49.360 --> 00:05:52.360
as you're trying to think about
college and all of the rest.
00:05:53.810 --> 00:05:57.110
I don't fully know all
of what you might have
00:05:57.110 --> 00:05:58.900
or not have access to.
00:05:58.900 --> 00:06:02.900
I do think the good news
is there are avenues
00:06:02.900 --> 00:06:06.820
outside of the traditional that could,
00:06:06.820 --> 00:06:08.490
you could still learn
a lot of the material
00:06:08.490 --> 00:06:10.620
or most of the material
and prove what you know,
00:06:10.620 --> 00:06:12.953
so that colleges and other folks
00:06:12.953 --> 00:06:15.900
can take a serious look at it.
00:06:15.900 --> 00:06:18.400
Many of y'all know that we've been talking
00:06:18.400 --> 00:06:21.320
to universities about Schoolhouse.
00:06:21.320 --> 00:06:23.670
University of Chicago
famously last year said,
00:06:23.670 --> 00:06:26.640
hey, if you can certify your
knowledge on Schoolhouse
00:06:26.640 --> 00:06:29.610
and then even better go on to
become a tutor on Schoolhouse,
00:06:29.610 --> 00:06:31.340
we, Universe of Chicago,
are gonna take that
00:06:31.340 --> 00:06:33.750
very seriously in the
college admissions process.
00:06:33.750 --> 00:06:36.250
And they actually, I don't
know if this is public,
00:06:36.250 --> 00:06:38.910
they had a very high admissions
rate for the 40 or so kids
00:06:38.910 --> 00:06:40.670
who actually use Schoolhouse.world
00:06:40.670 --> 00:06:43.493
as one of the main signals that they use.
00:06:44.880 --> 00:06:47.340
Y'all will hear shortly about MIT,
00:06:47.340 --> 00:06:51.410
is also doing something similar.
00:06:51.410 --> 00:06:52.870
And we're talking, just yesterday,
00:06:52.870 --> 00:06:54.210
I've talked to 30 admissions officers
00:06:54.210 --> 00:06:55.600
at a bunch of universities
saying, hey, look,
00:06:55.600 --> 00:06:56.680
there's an interesting signal here.
00:06:56.680 --> 00:06:58.520
You don't wanna force everyone to do it,
00:06:58.520 --> 00:07:01.260
but here's a mechanism where
at least in the subjects
00:07:01.260 --> 00:07:04.120
that Schoolhouse has, we
can certify your knowledge
00:07:04.120 --> 00:07:06.090
and then you can go on to become tutor.
00:07:06.090 --> 00:07:09.520
I think that can be a very
powerful potential route,
00:07:09.520 --> 00:07:12.120
especially because you can
leverage Schoolhouse.world
00:07:12.120 --> 00:07:14.530
and Khan Academy to learn the material
00:07:14.530 --> 00:07:16.860
and then certify yourself
00:07:16.860 --> 00:07:19.340
and then hopefully even
become a tutor yourself.
00:07:19.340 --> 00:07:21.370
I think that will speak very favorably
00:07:21.370 --> 00:07:23.610
of how you are leveraging your junior year
00:07:23.610 --> 00:07:26.380
above and beyond the things, you know,
00:07:26.380 --> 00:07:29.250
all of your maths subjects that
I imagine you'd be covering.
00:07:29.250 --> 00:07:33.860
Your science subjects,
including, you know,
00:07:33.860 --> 00:07:35.300
we just lost Environmental Science
00:07:35.300 --> 00:07:37.850
and we've always had things
like Econ on Khan Academy.
00:07:37.850 --> 00:07:38.960
Between Khan Academy and Schoolhouse,
00:07:38.960 --> 00:07:40.640
I think you can do a lot.
00:07:40.640 --> 00:07:42.143
I think in your Humanities,
00:07:43.450 --> 00:07:46.650
we wanna explore eventually
doing that in Schoolhouse.world.
00:07:46.650 --> 00:07:47.483
We're not quite there.
00:07:47.483 --> 00:07:48.530
There's some enrichment courses
00:07:48.530 --> 00:07:50.410
where people are starting
to dabble in that.
00:07:50.410 --> 00:07:51.520
But I would recommend, you know,
00:07:51.520 --> 00:07:53.030
take a look at some of the MOOCs.
00:07:53.030 --> 00:07:54.870
I think if you're able to
go into some of those MOOCs
00:07:54.870 --> 00:07:59.130
and do well in them, especially
if you could leverage
00:07:59.130 --> 00:08:02.170
Khan Academy for your STEM
and Schoolhouse for your STEM
00:08:02.170 --> 00:08:04.220
and then use MOOCs for
some of the other courses,
00:08:04.220 --> 00:08:05.950
whether it's the History
course or your English course,
00:08:05.950 --> 00:08:07.070
whatever else.
00:08:07.070 --> 00:08:09.727
And then also use the time to do well
00:08:10.610 --> 00:08:13.778
on standardized tests,
on your SATs, whatever.
00:08:13.778 --> 00:08:16.740
I think you're gonna have
a good junior year then.
00:08:16.740 --> 00:08:18.650
And I gotta believe that when you go
00:08:18.650 --> 00:08:19.760
next year into your senior year,
00:08:19.760 --> 00:08:21.910
if next year you're going
to apply to college,
00:08:21.910 --> 00:08:23.530
those colleges are going to take
00:08:23.530 --> 00:08:26.420
your circumstances very seriously.
00:08:26.420 --> 00:08:28.790
They definitely look at people who had
00:08:28.790 --> 00:08:30.160
hard circumstances to deal with.
00:08:30.160 --> 00:08:33.040
And they say, what did you do
with those hard circumstances?
00:08:33.040 --> 00:08:35.220
And if you're able to surprise them
00:08:35.220 --> 00:08:37.550
with what you're able to do
with those hard circumstances,
00:08:37.550 --> 00:08:39.810
I think you're going to
be fully in the game.
00:08:39.810 --> 00:08:42.020
And I think in some strange way,
00:08:42.020 --> 00:08:44.590
having this time might end
up being a gift in some ways,
00:08:44.590 --> 00:08:45.893
because you're going to explore things
00:08:45.893 --> 00:08:48.833
that you might not have
otherwise had time for.
00:08:50.020 --> 00:08:50.977
That's my best advice,
00:08:50.977 --> 00:08:53.610
not fully knowing all
of your circumstances.
00:08:53.610 --> 00:08:56.300
And I'll add what I had just said.
00:08:56.300 --> 00:08:59.440
Also make sure you don't burn
out, take care of yourself,
00:08:59.440 --> 00:09:03.150
make sure you don't lose that
piece of the puzzle as well.
00:09:03.150 --> 00:09:03.983
- Okay.
00:09:04.877 --> 00:09:06.560
Sal, sorry about this.
00:09:06.560 --> 00:09:08.010
Thank you for all the advice.
00:09:08.940 --> 00:09:11.340
I wanted to ask another
question related to this,
00:09:11.340 --> 00:09:14.220
because my parents are
actually considering
00:09:14.220 --> 00:09:15.890
virtual high school as an option instead,
00:09:15.890 --> 00:09:19.020
because I'm not really
sure if I can end up
00:09:19.020 --> 00:09:22.640
either retaking junior
year or delaying it.
00:09:22.640 --> 00:09:25.850
So I wanted to know if an
online high school diploma
00:09:25.850 --> 00:09:27.980
would end up putting me at a disadvantage
00:09:27.980 --> 00:09:29.773
in college admissions.
00:09:31.754 --> 00:09:33.380
- I'm not an expert here.
00:09:33.380 --> 00:09:35.910
I suspect and I think there's
different online high schools.
00:09:35.910 --> 00:09:37.860
I'm familiar with a few of them.
00:09:37.860 --> 00:09:39.230
There's Stanford Online High School,
00:09:39.230 --> 00:09:40.810
which is very highly reputed.
00:09:40.810 --> 00:09:43.160
And I'm sure there's others like that.
00:09:43.160 --> 00:09:45.020
I don't think you're at
a disadvantage at all
00:09:45.020 --> 00:09:46.720
if you go to some of
these online high schools.
00:09:46.720 --> 00:09:47.710
And on top of that,
00:09:47.710 --> 00:09:49.610
if you're able to do
other interesting things,
00:09:49.610 --> 00:09:51.230
I think you're going to
be very much in the game.
00:09:51.230 --> 00:09:53.530
So yeah, I wouldn't worry
too much about that.
00:09:55.670 --> 00:09:56.850
Thanks, Selena.
00:09:56.850 --> 00:09:58.320
Let's see, I'm gonna go, let's see.
00:09:58.320 --> 00:10:01.260
I think Zoom does it so
that whoever's furthest
00:10:01.260 --> 00:10:02.600
to the right was the next person.
00:10:02.600 --> 00:10:06.710
So Shivam, your question.
00:10:06.710 --> 00:10:08.430
- Hi, Sal.
00:10:08.430 --> 00:10:10.500
It's really a dream come true.
00:10:10.500 --> 00:10:12.550
I am meeting you after so long.
00:10:12.550 --> 00:10:13.800
- You need better dreams.
00:10:15.990 --> 00:10:18.360
- Actually, just a little intro.
00:10:18.360 --> 00:10:21.900
Like I have been using Khan
Academy since like grade six
00:10:21.900 --> 00:10:26.330
and I have over one
million points on Khan.
00:10:26.330 --> 00:10:27.820
- That's an achievement.
00:10:27.820 --> 00:10:28.653
- Yeah.
00:10:31.090 --> 00:10:36.066
Just award, like I have
perfected my maths through you.
00:10:36.066 --> 00:10:38.450
I admire you so much.
00:10:38.450 --> 00:10:41.710
So the thing is I want to ask
00:10:41.710 --> 00:10:45.420
is I belong to a very small town
00:10:45.420 --> 00:10:50.420
where there are not many good facilities.
00:10:51.001 --> 00:10:55.660
So how do you think would I be able to,
00:10:55.660 --> 00:10:58.280
do you think is it okay to dream big?
00:10:58.280 --> 00:11:03.050
Like am I suitable for big universities?
00:11:03.050 --> 00:11:06.710
Like students at the U.S. have like,
00:11:06.710 --> 00:11:09.010
they do summer programs and all like that.
00:11:09.010 --> 00:11:14.010
And I am from India and I don't
have that much facilities.
00:11:16.960 --> 00:11:19.310
But yeah, I am a tutor at Schoolhouse,
00:11:19.310 --> 00:11:22.900
and I really enjoy
that, tutoring students.
00:11:22.900 --> 00:11:27.034
But yeah, the thing is
I sometimes feel that
00:11:27.034 --> 00:11:29.970
am I really disadvantaged
with the students
00:11:29.970 --> 00:11:32.610
who do such kind of programs,
00:11:32.610 --> 00:11:36.660
who have done internships and all kinds,
00:11:36.660 --> 00:11:38.043
all things like that?
00:11:39.260 --> 00:11:41.060
- Yeah, so it's a great question.
00:11:41.060 --> 00:11:44.120
And the way I think about
it and I have, you're right,
00:11:44.120 --> 00:11:45.510
I'm sure you're in a circumstance
00:11:45.510 --> 00:11:47.110
where you don't have all of the resources
00:11:47.110 --> 00:11:49.030
that you would ideally have.
00:11:49.030 --> 00:11:51.540
But one of the dreams of Schoolhouse.world
00:11:51.540 --> 00:11:54.420
is that we can hopefully
reward folks like yourself
00:11:54.420 --> 00:11:57.820
who are tutors and who are
doing really good at it
00:11:57.820 --> 00:12:00.140
to connect them with opportunities
00:12:00.140 --> 00:12:02.090
that might not otherwise have been there.
00:12:02.090 --> 00:12:04.580
So I kind of view myself
as the guidance counselor
00:12:04.580 --> 00:12:06.820
for all of the tutor community here
00:12:06.820 --> 00:12:08.750
and say, like, how can I help
00:12:08.750 --> 00:12:10.250
all of these people get opportunity?
00:12:10.250 --> 00:12:12.940
Because if you really think about it,
00:12:12.940 --> 00:12:14.810
for college or for jobs,
00:12:14.810 --> 00:12:16.880
there are these huge complex processes
00:12:16.880 --> 00:12:17.770
that you have to usually,
00:12:17.770 --> 00:12:19.580
all these hoops you have to jump through.
00:12:19.580 --> 00:12:20.960
But if you boil down to it,
00:12:20.960 --> 00:12:22.930
and I've talked to other
people who hire people
00:12:22.930 --> 00:12:25.350
as like, you show me someone who can,
00:12:25.350 --> 00:12:26.760
who's a highly rated tutor
00:12:26.760 --> 00:12:28.440
on Schoolhouse.world in Statistics.
00:12:28.440 --> 00:12:31.230
I'm just picking Statistics,
could be other subjects.
00:12:31.230 --> 00:12:32.840
Why wouldn't you hire that person?
00:12:32.840 --> 00:12:34.990
That person clearly has analytical skills.
00:12:34.990 --> 00:12:36.510
That person clearly can communicate.
00:12:36.510 --> 00:12:38.183
That person clearly has empathy.
00:12:40.590 --> 00:12:41.423
Here's a little secret.
00:12:41.423 --> 00:12:44.940
In most jobs in the world,
if you have those things,
00:12:44.940 --> 00:12:46.500
you're going to do very, very well.
00:12:46.500 --> 00:12:48.000
Everything else you can learn.
00:12:49.120 --> 00:12:52.193
And so my hope is that I can,
00:12:53.070 --> 00:12:54.700
we collectively, not just myself,
00:12:54.700 --> 00:12:57.200
can figure out ways to
connect you to opportunity.
00:12:58.920 --> 00:13:00.800
What grade are you in right now?
00:13:00.800 --> 00:13:02.431
What class are you in?
00:13:02.431 --> 00:13:03.410
- 12th grade.
00:13:03.410 --> 00:13:04.820
- You're in 12th?
00:13:04.820 --> 00:13:05.653
- Yeah.
00:13:05.653 --> 00:13:06.520
- Okay.
- Applying.
00:13:07.460 --> 00:13:10.007
Looking to apply for U.S. colleges.
00:13:10.870 --> 00:13:14.250
- Yeah, well, I think I just listed a few,
00:13:14.250 --> 00:13:15.560
and obviously, none of these colleges
00:13:15.560 --> 00:13:17.773
are "easy to get into," so to speak.
00:13:19.333 --> 00:13:21.460
But expect to hear a few more.
00:13:21.460 --> 00:13:23.350
And I think even the
colleges that aren't part
00:13:23.350 --> 00:13:26.130
of our initial consortium, so to speak,
00:13:26.130 --> 00:13:29.850
I think if you are a very active,
00:13:29.850 --> 00:13:32.123
highly reputed tutor on Schoolhouse.world,
00:13:33.771 --> 00:13:36.460
through the tutor community,
we wanna be able to help you.
00:13:36.460 --> 00:13:39.080
Like, even if there's a college
00:13:39.080 --> 00:13:41.570
that doesn't know about Schoolhouse.world,
00:13:41.570 --> 00:13:43.460
if we can leverage what we know,
00:13:43.460 --> 00:13:45.700
our notoriety to let them know, hey,
00:13:45.700 --> 00:13:48.840
this is not a joke to become
a highly reputed tutor.
00:13:48.840 --> 00:13:50.290
I would take this very seriously.
00:13:50.290 --> 00:13:52.050
So then I think you would have,
00:13:52.050 --> 00:13:53.300
I think you would have a fighting chance.
00:13:53.300 --> 00:13:55.820
And I will say, even if it does,
00:13:55.820 --> 00:13:57.240
if it does work out, awesome.
00:13:57.240 --> 00:13:58.700
If it doesn't work out,
00:13:58.700 --> 00:14:01.460
I think you're gonna have
multiple shots at gold.
00:14:01.460 --> 00:14:04.740
So wherever you go to
college, there's always,
00:14:04.740 --> 00:14:07.770
you can transfer or even
post-college graduate school
00:14:07.770 --> 00:14:10.110
or your job, I hope over the
next three or four years,
00:14:10.110 --> 00:14:12.680
Schoolhouse.world, being a
highly reputed tutor on it
00:14:12.680 --> 00:14:14.420
becomes a major thing that a lot of people
00:14:14.420 --> 00:14:16.300
are going to index on.
00:14:16.300 --> 00:14:19.703
So that's my best advice.
00:14:21.120 --> 00:14:22.140
- Okay, thank you.
00:14:22.140 --> 00:14:23.260
Thanks a lot.
00:14:23.260 --> 00:14:24.093
- No, thank you.
00:14:24.093 --> 00:14:24.973
Thank you for being a tutor.
00:14:27.000 --> 00:14:27.833
Let's see.
00:14:27.833 --> 00:14:29.040
I'm not sure if this
is showing up in order.
00:14:29.040 --> 00:14:31.480
I'm gonna go somewhat random-
00:14:31.480 --> 00:14:35.280
- Hey, Sal, just a followup
on Shivam's question.
00:14:35.280 --> 00:14:36.920
I have a four sisters in Afghanistan
00:14:36.920 --> 00:14:38.930
who is there right now,
and then a lot of girls,
00:14:38.930 --> 00:14:40.940
the situation being really dire.
00:14:40.940 --> 00:14:43.750
I, myself, am working in
Facebook here, project's here.
00:14:43.750 --> 00:14:46.920
So I've been really fortunate
to have your Khan Academy,
00:14:46.920 --> 00:14:50.190
learning things from you
and then also your platform.
00:14:50.190 --> 00:14:53.670
I was wondering how can
we expand that further
00:14:53.670 --> 00:14:55.670
and then give the chance for the,
00:14:55.670 --> 00:14:58.120
like a fighting chance for
the girls in Afghanistan
00:14:58.120 --> 00:15:00.960
or other like countries where there's war,
00:15:00.960 --> 00:15:02.610
or they don't have
facilities like in India
00:15:02.610 --> 00:15:03.960
or elsewhere too.
00:15:03.960 --> 00:15:04.930
How can they do that?
00:15:04.930 --> 00:15:08.340
And how can they take
advantage of the situation,
00:15:08.340 --> 00:15:09.710
especially when the schools,
00:15:09.710 --> 00:15:11.610
when the system do not
allow you to go to schools
00:15:11.610 --> 00:15:13.380
and that past sixth grade,
00:15:13.380 --> 00:15:15.400
you cannot even attend if you're a woman.
00:15:15.400 --> 00:15:18.220
So how can we use your platform
and then have those girls
00:15:18.220 --> 00:15:19.490
like a fighting chance?
00:15:19.490 --> 00:15:20.860
If you could maybe kindly answer to that.
00:15:20.860 --> 00:15:22.890
- Yeah, wonderful question.
00:15:22.890 --> 00:15:24.070
So, yeah, it's a big,
00:15:24.070 --> 00:15:26.440
especially given what's going on now.
00:15:26.440 --> 00:15:28.600
Some of y'all, I've
told this story before.
00:15:28.600 --> 00:15:30.350
The case in point is very clear.
00:15:30.350 --> 00:15:32.070
There's actually a young
girl named Sultana.
00:15:32.070 --> 00:15:34.650
You could do a Google search for her.
00:15:34.650 --> 00:15:36.607
Nicholas Kristof wrote an op-ed about her:
00:15:36.607 --> 00:15:38.350
"Meet Sultana, the Taliban's Worst Fear."
00:15:38.350 --> 00:15:40.820
He wrote this three or four years ago.
00:15:40.820 --> 00:15:42.410
But it's exactly what you described
00:15:42.410 --> 00:15:45.090
even before the current
circumstances in Afghanistan,
00:15:45.090 --> 00:15:46.530
where when she entered sixth grade,
00:15:46.530 --> 00:15:47.680
she wasn't allowed to go to school.
00:15:47.680 --> 00:15:48.960
Her brothers were.
00:15:48.960 --> 00:15:52.300
And then she luckily did
have an internet connection
00:15:52.300 --> 00:15:56.040
and she was able to essentially
self-teach herself English.
00:15:56.040 --> 00:15:57.600
She found out about Khan Academy.
00:15:57.600 --> 00:15:59.160
That became her lifeline.
00:15:59.160 --> 00:16:00.330
By the time she gets into high school,
00:16:00.330 --> 00:16:02.740
she decides that she wants
to be a physics researcher,
00:16:02.740 --> 00:16:04.003
a theoretical physicist.
00:16:04.840 --> 00:16:08.480
She lies to her parents to go
to Pakistan to take the SAT.
00:16:08.480 --> 00:16:10.150
She does unusually well.
00:16:10.150 --> 00:16:15.150
Anyway, long story short,
Sultana was eventually able
00:16:15.170 --> 00:16:19.040
to make it to the U.S. and is now doing
00:16:19.040 --> 00:16:21.370
quantum computing research
at Tufts University.
00:16:21.370 --> 00:16:23.390
And what I always remind folks is
00:16:23.390 --> 00:16:26.260
for every Sultana we know
about who's able to do it,
00:16:26.260 --> 00:16:28.990
how many more tens or hundreds
00:16:28.990 --> 00:16:30.660
of thousands or millions might there be?
00:16:30.660 --> 00:16:33.560
And what she had to do
to get there, none of us,
00:16:33.560 --> 00:16:35.150
I don't think I would
have been able to do that
00:16:35.150 --> 00:16:36.970
if I was given the same set of obstacles.
00:16:36.970 --> 00:16:41.683
So she had unusual determination,
unusual resilience.
00:16:42.770 --> 00:16:47.730
My hope is that Khan
Academy, Schoolhouse.world
00:16:47.730 --> 00:16:48.990
can be that lifeline.
00:16:48.990 --> 00:16:51.290
Now, it is predicated on internet access.
00:16:51.290 --> 00:16:53.740
My understanding of what's
going on in the ground
00:16:53.740 --> 00:16:56.320
in places like Afghanistan is that,
00:16:56.320 --> 00:16:59.190
fingers crossed, they haven't
shut down internet access.
00:16:59.190 --> 00:17:02.780
So if that's what we can depend on
00:17:02.780 --> 00:17:04.253
that we can provide layers on top of that
00:17:04.253 --> 00:17:06.570
that can at least give someone a lifeline.
00:17:06.570 --> 00:17:09.240
And I could imagine,
Sultana went on her journey
00:17:09.240 --> 00:17:12.220
before Schoolhouse.world existed.
00:17:12.220 --> 00:17:14.090
But if Schoolhouse.world existed,
00:17:14.090 --> 00:17:17.030
she is someone who I
very easily could imagine
00:17:17.030 --> 00:17:19.440
would have been very
active in this community.
00:17:19.440 --> 00:17:21.400
She would have certified her knowledge.
00:17:21.400 --> 00:17:22.820
She would have used
the community to learn,
00:17:22.820 --> 00:17:24.410
frankly, not just to
learn the subject matter,
00:17:24.410 --> 00:17:27.450
but frankly, to learn the
language, to learn English.
00:17:27.450 --> 00:17:30.470
And then she would have
gone on to become a tutor.
00:17:30.470 --> 00:17:33.320
And just like Shivam's question,
00:17:33.320 --> 00:17:34.770
I think she could have then used that
00:17:34.770 --> 00:17:37.290
as a signal to people to say, look,
00:17:37.290 --> 00:17:38.580
this is someone interesting
00:17:38.580 --> 00:17:41.170
that we need to make
sure has opportunities.
00:17:41.170 --> 00:17:43.440
So that's my best answer.
00:17:43.440 --> 00:17:47.410
I wish there were things that we could do
00:17:47.410 --> 00:17:48.430
more on the ground.
00:17:48.430 --> 00:17:50.670
And I don't know, I don't know.
00:17:50.670 --> 00:17:54.453
But our collective avenue here is,
00:17:55.350 --> 00:17:57.040
the Khan Academy can make more resources,
00:17:57.040 --> 00:17:58.230
but I think Schoolhouse.world can actually
00:17:58.230 --> 00:18:02.020
be a very, very powerful
resource for these young girls.
00:18:02.020 --> 00:18:04.650
If they just have an internet connection,
00:18:04.650 --> 00:18:06.440
they can become part of this community.
00:18:06.440 --> 00:18:08.510
And I'm hoping, my dream
for Schoolhouse.world
00:18:08.510 --> 00:18:10.710
is between it and Khan
Academy can almost turn
00:18:10.710 --> 00:18:14.040
into a safety net education
system for the world.
00:18:14.040 --> 00:18:17.730
So that if you are going to
school with resources, awesome.
00:18:17.730 --> 00:18:20.860
You use Khan Academy to
personalize and get even better
00:18:20.860 --> 00:18:22.890
and use Schoolhouse for
supplemental tutoring
00:18:22.890 --> 00:18:24.320
so you don't fall through the cracks.
00:18:24.320 --> 00:18:25.440
But if you don't have a great school,
00:18:25.440 --> 00:18:26.990
or if you have no school at all,
00:18:26.990 --> 00:18:29.850
Khan Academy, Schoolhouse.world,
the certification,
00:18:29.850 --> 00:18:33.390
the tutoring, you can get
to where you wanna go.
00:18:33.390 --> 00:18:37.960
So that's my best answer for an actual
00:18:37.960 --> 00:18:39.323
very unfortunate circumstances
00:18:39.323 --> 00:18:41.090
the world is in right now.
00:18:41.090 --> 00:18:42.370
- Thank you, Sal, for the answer.
00:18:42.370 --> 00:18:44.820
And could they also use your Khan Lab
00:18:44.820 --> 00:18:46.940
High School program to get admitted
00:18:46.940 --> 00:18:49.310
and especially if the
schools have shut been down?
00:18:49.310 --> 00:18:50.970
- Yeah, so good question.
00:18:50.970 --> 00:18:52.980
So Khan Lab High School,
some of y'all might know,
00:18:52.980 --> 00:18:56.520
I started a school Khan
Lab School seven years ago.
00:18:56.520 --> 00:18:57.580
It's now K through 12.
00:18:57.580 --> 00:18:59.590
There's a high school,
Khan Lab High School.
00:18:59.590 --> 00:19:00.490
I'm always sensitive.
00:19:00.490 --> 00:19:01.730
Everything has my name on it now,
00:19:01.730 --> 00:19:05.050
but people assure me it's
good for branding (laughs).
00:19:05.050 --> 00:19:05.970
I used to make fun of people
00:19:05.970 --> 00:19:08.443
who named things after
themselves, but it shows you.
00:19:11.060 --> 00:19:14.240
We are exploring doing
a virtual component.
00:19:14.240 --> 00:19:16.660
The original spirit of the
vision of Khan Lab High School
00:19:16.660 --> 00:19:18.570
is can we create a model
00:19:18.570 --> 00:19:20.490
that then can be replicated everywhere?
00:19:20.490 --> 00:19:23.590
Whether we replicated or
other people copy, awesome.
00:19:23.590 --> 00:19:25.570
We are now realizing
there might be interest
00:19:25.570 --> 00:19:27.840
in creating a virtual component
00:19:27.840 --> 00:19:31.300
that leans on Khan Academy
and Schoolhouse.world,
00:19:31.300 --> 00:19:33.833
but could also give people credit.
00:19:35.500 --> 00:19:39.210
What I will say, going back
to Shivam's original question,
00:19:39.210 --> 00:19:40.830
well, cause even Khan Lab school,
00:19:40.830 --> 00:19:42.330
even for the students who
are going there in person,
00:19:42.330 --> 00:19:43.870
it's a very non-traditional school.
00:19:43.870 --> 00:19:44.770
It's mastery-based.
00:19:44.770 --> 00:19:47.260
Kids have the opportunity
incentive to improve their grades.
00:19:47.260 --> 00:19:48.180
We don't use letter grades.
00:19:48.180 --> 00:19:49.890
We use a slightly
different form of grading,
00:19:49.890 --> 00:19:50.960
but it's unusual.
00:19:50.960 --> 00:19:53.670
So there's always the
question of these parents.
00:19:53.670 --> 00:19:56.020
It's like, are these kids
even gonna get into college?
00:19:56.020 --> 00:20:01.020
And what we have found
is in the U.S., at least,
00:20:01.890 --> 00:20:03.840
the private schools are very flexible
00:20:03.840 --> 00:20:06.740
and are very open to looking
at alternative things,
00:20:06.740 --> 00:20:08.120
especially if they can make sense of them.
00:20:08.120 --> 00:20:09.740
So that's where I think
the Schoolhouse.world
00:20:09.740 --> 00:20:12.010
certification tutoring
could have a lot of value,
00:20:12.010 --> 00:20:14.490
and we're seeing more and
more of the public schools
00:20:14.490 --> 00:20:17.850
are also opening their aperture to it.
00:20:17.850 --> 00:20:18.773
But you're right.
00:20:19.660 --> 00:20:21.740
If Khan Lab High School or other partners,
00:20:21.740 --> 00:20:23.420
we're talking to some
colleges that also might give
00:20:23.420 --> 00:20:25.770
college credit for
certain types of mastery
00:20:25.770 --> 00:20:27.880
on Khan Academy or Schoolhouse.world.
00:20:27.880 --> 00:20:29.130
That also could be interesting.
00:20:29.130 --> 00:20:31.693
So we wanna continue to explore that.
00:20:33.470 --> 00:20:36.770
So let's see, next question, Renee.
00:20:36.770 --> 00:20:39.700
I'm not sure if I'm going
in order, but I'll try to.
00:20:39.700 --> 00:20:42.340
- Yeah, thank you, Sal.
00:20:42.340 --> 00:20:44.290
And hi, everyone.
00:20:44.290 --> 00:20:45.850
First, I just wanna thank you.
00:20:45.850 --> 00:20:48.230
I used your Khan Academy many years ago,
00:20:48.230 --> 00:20:49.870
and I was able to got into,
00:20:49.870 --> 00:20:52.120
get into a really good university
00:20:52.120 --> 00:20:55.280
and then get into my
PhD degree program here.
00:20:55.280 --> 00:20:57.590
So I really just wanna thank you.
00:20:57.590 --> 00:21:01.050
And then, so my question
here is how do you deal
00:21:01.050 --> 00:21:03.003
with information overload?
00:21:04.350 --> 00:21:05.330
How do you learn something?
00:21:05.330 --> 00:21:07.260
Because every time you
search for something,
00:21:07.260 --> 00:21:08.790
there are thousands of thousand stuff.
00:21:08.790 --> 00:21:13.353
So how are you doing your
learning in this world?
00:21:14.224 --> 00:21:16.220
- It's a great question.
00:21:16.220 --> 00:21:19.363
I was once, I was giving a
talk in Spain two years ago.
00:21:21.022 --> 00:21:23.250
It was the most poetic
introduction I had ever gotten.
00:21:23.250 --> 00:21:26.470
But part of the
introduction was this notion
00:21:26.470 --> 00:21:29.030
that the irony is when there's a flood,
00:21:29.030 --> 00:21:31.710
that's when actually people
oftentimes die of dehydration
00:21:31.710 --> 00:21:33.830
or experience dehydration
when there's a flood.
00:21:33.830 --> 00:21:36.160
And the introducer, he
made the analogy is that
00:21:36.160 --> 00:21:38.320
the same thing is happening
in information today.
00:21:38.320 --> 00:21:42.060
There's a flood of
information, but we are still,
00:21:42.060 --> 00:21:46.253
but a lot of it we can't
trust or it messes with us.
00:21:47.560 --> 00:21:48.773
Even the news itself.
00:21:49.960 --> 00:21:51.550
I know there's a huge issue globally,
00:21:51.550 --> 00:21:53.790
but especially in the U.S.
about news being polarized.
00:21:53.790 --> 00:21:55.490
And we're all in our own bubble.
00:21:55.490 --> 00:21:58.990
But even if you assume
the news is not biased,
00:21:58.990 --> 00:22:01.060
although everything has
some kind of a bias,
00:22:01.060 --> 00:22:02.340
even if you assume it's not biased,
00:22:02.340 --> 00:22:04.910
the news by its very
nature is taking a world
00:22:04.910 --> 00:22:06.120
of seven or eight billion people
00:22:06.120 --> 00:22:07.960
and telling you the seven worst things
00:22:07.960 --> 00:22:09.545
that happened that day.
00:22:09.545 --> 00:22:13.263
Like our brains aren't
good at processing that.
00:22:14.580 --> 00:22:16.360
I wish they could tell us that,
00:22:16.360 --> 00:22:17.930
because the same day that those seven
00:22:17.930 --> 00:22:19.240
horrible things are happening,
00:22:19.240 --> 00:22:21.380
there's probably 700,000 beautiful things
00:22:21.380 --> 00:22:24.260
that happened that weren't "newsworthy."
00:22:24.260 --> 00:22:27.550
And so it messes with your head
and messes with your brain.
00:22:27.550 --> 00:22:30.640
So what I would say is
protect yourself from it.
00:22:30.640 --> 00:22:35.360
I think future health
professionals are going to realize
00:22:35.360 --> 00:22:37.260
that exposing yourself
to this type of thing
00:22:37.260 --> 00:22:39.020
can become really harmful.
00:22:39.020 --> 00:22:41.060
That doesn't mean put
your head in the sand.
00:22:41.060 --> 00:22:43.960
I read the news, but I really
do try to be conscientious
00:22:43.960 --> 00:22:45.910
of like, look, I can go to a website
00:22:45.910 --> 00:22:47.120
and I can read a few headlines.
00:22:47.120 --> 00:22:48.790
I got the essence of the news.
00:22:48.790 --> 00:22:51.700
If I were to go on these 24-hour channels
00:22:51.700 --> 00:22:53.790
or in social media,
I'm gonna start getting
00:22:53.790 --> 00:22:55.880
all of these other things that
are all designed, frankly,
00:22:55.880 --> 00:22:59.140
to get me worked up and I
don't wanna be worked up.
00:22:59.140 --> 00:23:01.320
So I'm gonna go do my work.
00:23:01.320 --> 00:23:05.050
But one foot in front of the
other, live my life, meditate.
00:23:05.050 --> 00:23:08.180
Sometimes when I am experiencing
the information overload,
00:23:08.180 --> 00:23:10.905
and it might not be from social media
00:23:10.905 --> 00:23:13.070
or from the news.
00:23:13.070 --> 00:23:14.640
It might be from work.
00:23:14.640 --> 00:23:16.650
I'm constantly getting emails in.
00:23:16.650 --> 00:23:18.680
I'm constantly, people are slacking me.
00:23:18.680 --> 00:23:19.960
People are this.
00:23:19.960 --> 00:23:21.320
There's 9, 10 decisions
00:23:21.320 --> 00:23:23.910
that are coming to my desk every day.
00:23:23.910 --> 00:23:26.040
And I can feel and I've become
more sensitive to saying,
00:23:26.040 --> 00:23:27.640
hey, Sal, you're feeling kinda off.
00:23:27.640 --> 00:23:30.740
You're not present right now.
00:23:30.740 --> 00:23:32.200
Then I just try to stop what I'm doing
00:23:32.200 --> 00:23:33.670
and even do a 10 minute meditation.
00:23:33.670 --> 00:23:35.853
Just sit quietly or go for a walk.
00:23:36.910 --> 00:23:38.870
I find is a great way to reset.
00:23:38.870 --> 00:23:41.130
And then on top of that, make
sure you're getting exercise,
00:23:41.130 --> 00:23:42.130
make sure you're eating well,
00:23:42.130 --> 00:23:44.010
drinking a lot of water and sleeping well.
00:23:44.010 --> 00:23:45.410
I do this stuff religiously.
00:23:47.391 --> 00:23:50.940
So that's my best advice
for the information overload
00:23:50.940 --> 00:23:53.790
or when you're feeling
angsty about the world,
00:23:53.790 --> 00:23:56.621
just find a place of
stillness, a place of quiet,
00:23:56.621 --> 00:23:59.820
and try to be careful on how
much that stuff sucks you in.
00:23:59.820 --> 00:24:01.400
And I've been sucked in.
00:24:01.400 --> 00:24:02.950
Some of the news that's
going on in the world,
00:24:02.950 --> 00:24:03.820
like, oh, we should watch it.
00:24:03.820 --> 00:24:06.470
I watch it, and it's like
you can't turn it off.
00:24:06.470 --> 00:24:08.060
And like an hour goes
later and you're like,
00:24:08.060 --> 00:24:09.810
I don't feel better right now.
00:24:09.810 --> 00:24:11.580
And I learned the important news
00:24:11.580 --> 00:24:12.980
within the first two minutes.
00:24:12.980 --> 00:24:14.740
The rest of the 58
minutes just made me feel
00:24:14.740 --> 00:24:16.460
kinda not so good.
00:24:16.460 --> 00:24:18.313
Let me go do something else.
00:24:19.640 --> 00:24:21.790
In terms of the question
of how do I learn,
00:24:24.330 --> 00:24:26.620
I'm constantly just asking questions.
00:24:26.620 --> 00:24:28.220
So I'm actually about
to make a middle school
00:24:28.220 --> 00:24:29.980
science video on the atmosphere.
00:24:29.980 --> 00:24:33.400
And some people on my team
sent me some standards
00:24:33.400 --> 00:24:35.380
that we need to cover
and they're pretty basic,
00:24:35.380 --> 00:24:37.130
but I'm like, okay, what
makes us interesting?
00:24:37.130 --> 00:24:38.153
And I'm like, okay,
00:24:39.310 --> 00:24:41.640
let me make sure that I can help explain
00:24:41.640 --> 00:24:43.220
where does officially,
00:24:43.220 --> 00:24:44.720
where does the atmosphere
end and space start?
00:24:44.720 --> 00:24:46.530
Now we know it's not
like there's some line
00:24:46.530 --> 00:24:47.370
where it actually does end.
00:24:47.370 --> 00:24:48.620
It's a gradation.
00:24:48.620 --> 00:24:50.900
But people have the Karman
line and they've defined it
00:24:50.900 --> 00:24:52.950
as roughly 60 something miles.
00:24:52.950 --> 00:24:57.010
And, okay, what are the
the lowest satellites?
00:24:57.010 --> 00:24:58.833
Okay, it's about a hundred miles.
00:25:00.140 --> 00:25:02.210
And I just keep asking these
questions of like, okay,
00:25:02.210 --> 00:25:03.840
if something's in low earth orbit,
00:25:03.840 --> 00:25:05.510
because it's still going
to have some atmosphere,
00:25:05.510 --> 00:25:07.730
still going to run into a few nitrogen
00:25:07.730 --> 00:25:10.020
and oxygen molecules every now and then,
00:25:10.020 --> 00:25:12.920
it's gonna slowly slow down
and slowly come back to earth.
00:25:13.958 --> 00:25:14.791
How long do they last?
00:25:14.791 --> 00:25:18.340
So for me, it's just
asking these fun questions
00:25:19.410 --> 00:25:20.350
over and over again,
00:25:20.350 --> 00:25:23.070
and having that sense
of curiosity about it.
00:25:23.070 --> 00:25:24.290
And then once I'm really jazzed
00:25:24.290 --> 00:25:25.340
about whatever I'm about to do,
00:25:25.340 --> 00:25:27.160
then I just press record and go.
00:25:27.160 --> 00:25:28.750
But that's something pretty simple.
00:25:28.750 --> 00:25:30.180
If something is more esoteric,
00:25:30.180 --> 00:25:31.410
I'd like to talk to people about it.
00:25:31.410 --> 00:25:32.543
I'll call up friends.
00:25:33.530 --> 00:25:36.620
Another thing I like to
do when something is dense
00:25:36.620 --> 00:25:39.030
or I'm trying to conceptually get it,
00:25:39.030 --> 00:25:42.700
read it one day and say, okay,
my brain will process it.
00:25:42.700 --> 00:25:45.600
I kind of delegate it
to my brain and my mind.
00:25:45.600 --> 00:25:46.570
And I'm like, by tomorrow,
00:25:46.570 --> 00:25:48.240
my mind will have insights about it.
00:25:48.240 --> 00:25:50.070
Don't worry about it, conscious Sal.
00:25:50.070 --> 00:25:51.940
Subconscious Sal has it covered.
00:25:51.940 --> 00:25:54.500
And it's amazing that
it works, but it does.
00:25:54.500 --> 00:25:56.500
I remember in college,
00:25:56.500 --> 00:25:58.210
when I would take the
theoretical math classes,
00:25:58.210 --> 00:26:01.600
sometimes you look at the
problem sets and you're like,
00:26:01.600 --> 00:26:03.100
I can't make sense of any of this.
00:26:03.100 --> 00:26:03.933
But you do it.
00:26:03.933 --> 00:26:05.940
You at least try every problem.
00:26:05.940 --> 00:26:07.850
You close the book, go to sleep.
00:26:07.850 --> 00:26:10.500
In the morning, I can do like 80% of them.
00:26:10.500 --> 00:26:12.060
I've done the same thing on tests,
00:26:12.060 --> 00:26:14.080
where I'm taking this
test, these really deep,
00:26:14.080 --> 00:26:18.260
theoretical math classes and
you see four or five questions.
00:26:18.260 --> 00:26:19.950
And you're like, I don't know.
00:26:19.950 --> 00:26:20.783
Let me just think about it.
00:26:20.783 --> 00:26:22.340
But then I kinda get
into a meditative place.
00:26:22.340 --> 00:26:23.870
And in about 20 minutes, I'm like, oh,
00:26:23.870 --> 00:26:25.890
my subconscious is starting
to give me the answers.
00:26:25.890 --> 00:26:28.640
I'm like, it's amazing what
the subconscious can do.
00:26:28.640 --> 00:26:30.300
So anyway, that's other advice.
00:26:30.300 --> 00:26:31.210
We're almost out of time.
00:26:31.210 --> 00:26:32.340
Let me see, I'm sorry I couldn't get,
00:26:32.340 --> 00:26:36.250
I'm giving you these long-winded answers.
00:26:36.250 --> 00:26:37.130
Let's see.
00:26:37.130 --> 00:26:38.243
Maybe Salil.
00:26:39.260 --> 00:26:41.743
No, Salik, Salik, Salik K.
00:26:44.950 --> 00:26:47.200
- Hello, Sal, it's great to meet you.
00:26:47.200 --> 00:26:51.430
I am 12 years old and
currently being homeschooled.
00:26:51.430 --> 00:26:54.857
And I'm also ahead of my class.
00:26:54.857 --> 00:26:57.670
I (indistinct) starting school.
00:26:57.670 --> 00:27:01.740
So I've been using the Khan
Academy platform since one year,
00:27:01.740 --> 00:27:05.775
and I have about 1.5
million energy points on it.
00:27:05.775 --> 00:27:07.192
- Another Shivam.
00:27:09.230 --> 00:27:10.773
Go ahead, sorry I interrupted you.
00:27:10.773 --> 00:27:13.350
- I'm sorry, it's all good.
00:27:13.350 --> 00:27:15.990
And I finished grade eight, grade five.
00:27:15.990 --> 00:27:18.000
Grade five and grade six
00:27:18.000 --> 00:27:20.730
and finished grade seven and grade eight
00:27:20.730 --> 00:27:22.550
and also finished all the JavaScript
00:27:22.550 --> 00:27:26.617
on the Khan Academy platform
and now learning RCM
00:27:28.720 --> 00:27:32.110
and looking forward to learning
all the other programming
00:27:32.110 --> 00:27:34.210
languages available on
the Khan Academy platform.
00:27:34.210 --> 00:27:38.040
So actually, I know it's a good,
00:27:38.040 --> 00:27:40.350
very, very good future
ahead in programming.
00:27:40.350 --> 00:27:45.350
So can you advise me
and advise me in this?
00:27:47.039 --> 00:27:47.872
- Yeah.
00:27:50.440 --> 00:27:55.440
- Since I'm from Pakistan
and it's past midnight here,
00:27:55.570 --> 00:27:57.883
I'll take advantage and ask two questions,
00:27:58.900 --> 00:27:59.733
if you don't mind.
00:27:59.733 --> 00:28:02.883
So my second question is I
have a great taste in gaming.
00:28:04.851 --> 00:28:07.113
Can I build a future out of it?
00:28:08.400 --> 00:28:10.620
- Yeah, well, first of all, Salik,
00:28:10.620 --> 00:28:13.400
I have no doubt.
00:28:13.400 --> 00:28:14.700
I mean, don't get over-confident,
00:28:14.700 --> 00:28:17.500
but I have no doubt that
you're gonna do very well.
00:28:17.500 --> 00:28:19.860
And I'll make my plug
'cause I have you now
00:28:19.860 --> 00:28:22.060
before anyone else is
asking for donations.
00:28:22.060 --> 00:28:23.830
When you become a billionaire,
00:28:23.830 --> 00:28:25.470
a founder of a gaming company,
00:28:25.470 --> 00:28:28.780
remember how much of that
was due to Khan Academy.
00:28:28.780 --> 00:28:31.171
And, you know, 10% maybe?
00:28:31.171 --> 00:28:33.463
I'm kidding (laughs).
00:28:35.868 --> 00:28:37.259
- I will thank you my whole life.
00:28:37.259 --> 00:28:38.320
(laughs)
00:28:38.320 --> 00:28:40.710
- Look, I'm only half joking.
00:28:40.710 --> 00:28:43.520
But to your point, yeah.
00:28:43.520 --> 00:28:46.990
Look, if you love coding and
you're the exact same age
00:28:46.990 --> 00:28:50.690
as my oldest son, you'll
probably get along.
00:28:50.690 --> 00:28:53.563
He's also really into
coding and all of the rest.
00:28:54.720 --> 00:28:55.780
Keep doing it.
00:28:55.780 --> 00:28:58.250
And I would say keep building things.
00:28:58.250 --> 00:29:00.500
Keep progressing academically.
00:29:00.500 --> 00:29:03.470
And I have no doubt that, and
your question about gaming,
00:29:03.470 --> 00:29:05.140
yeah, I only think
that's only gonna become
00:29:05.140 --> 00:29:06.920
a bigger and bigger industry,
00:29:06.920 --> 00:29:09.400
both in the gaming industry in particular.
00:29:09.400 --> 00:29:10.780
And look, you look at companies
00:29:10.780 --> 00:29:12.323
like Minecraft and Roblox.
00:29:12.323 --> 00:29:13.620
I mean, these are massive things.
00:29:13.620 --> 00:29:15.910
And in the next 10 or 15
years, there's gonna be things
00:29:15.910 --> 00:29:18.720
that are a whole order of
magnitude, even bigger.
00:29:18.720 --> 00:29:22.650
So I think there's unlimited
work to be done there.
00:29:22.650 --> 00:29:24.940
And also, I think every other industry
00:29:24.940 --> 00:29:27.410
is thinking about how do they automate
00:29:27.410 --> 00:29:28.550
and leverage technology more,
00:29:28.550 --> 00:29:30.100
and then how do they gamify more?
00:29:30.100 --> 00:29:31.640
Something we think a
lot about Khan Academy
00:29:31.640 --> 00:29:33.420
is how do we make better game mechanics
00:29:33.420 --> 00:29:36.820
so that we can addict
the Saliks of the world
00:29:36.820 --> 00:29:39.160
into learning and all of this.
00:29:39.160 --> 00:29:43.130
So, yeah, you're gonna keep
doing what you're doing.
00:29:43.130 --> 00:29:45.610
Remembering my answers to the
other one, don't burn out.
00:29:45.610 --> 00:29:47.910
Don't put too much pressure on yourself.
00:29:47.910 --> 00:29:50.397
Make sure you, you know, if you can,
00:29:50.397 --> 00:29:53.410
when my children were first born,
00:29:53.410 --> 00:29:55.680
I was a little bit of
a tiger dad thinking,
00:29:55.680 --> 00:29:58.870
oh, if they can master
their subject matter,
00:29:58.870 --> 00:30:00.400
if they can build some
of these hard skills,
00:30:00.400 --> 00:30:01.233
they're gonna be fine.
00:30:01.233 --> 00:30:03.010
And there is some truth to that.
00:30:03.010 --> 00:30:04.605
Obviously, every parent
wants their children
00:30:04.605 --> 00:30:08.400
to be able to support
themselves, support their family,
00:30:08.400 --> 00:30:09.970
have a healthy, productive life.
00:30:09.970 --> 00:30:13.020
But as I've grown, I realized,
yes, that's important.
00:30:13.020 --> 00:30:15.220
But the most important thing is having
00:30:15.220 --> 00:30:17.190
kind of a mental, emotional resilience.
00:30:17.190 --> 00:30:20.150
And that's where my first advice to Kai
00:30:20.150 --> 00:30:24.120
around the meditation and
making time for yourself
00:30:24.120 --> 00:30:26.440
and having a good social network.
00:30:26.440 --> 00:30:28.010
Incredibly, incredibly important.
00:30:28.010 --> 00:30:31.060
If you have the combination
of those two things,
00:30:31.060 --> 00:30:32.500
you really are gonna be unstoppable
00:30:32.500 --> 00:30:34.610
because everyone's journey is gonna have
00:30:34.610 --> 00:30:37.130
some high points and you're gonna get,
00:30:37.130 --> 00:30:40.290
I have more low points
than y'all might imagine.
00:30:40.290 --> 00:30:42.740
And I've definitely had them over my life.
00:30:42.740 --> 00:30:45.290
But it's that ability to
kind of detach yourself
00:30:45.290 --> 00:30:47.070
from your ego sometimes,
00:30:47.070 --> 00:30:49.440
to not get too worked
up about some things,
00:30:49.440 --> 00:30:52.543
have some tools at your
disposal to meditate,
00:30:53.400 --> 00:30:57.430
to exercise, to whatever it is.
00:30:57.430 --> 00:30:59.770
For some folks, it might be religion.
00:30:59.770 --> 00:31:02.400
But it takes you into
that meditative place.
00:31:02.400 --> 00:31:03.970
I think that'll make you
incredibly resilient.
00:31:03.970 --> 00:31:05.840
So if you've got the skills
and you've got the resilience,
00:31:05.840 --> 00:31:07.410
you're gonna be unstoppable.
00:31:07.410 --> 00:31:09.960
So that's my best advice there.
00:31:09.960 --> 00:31:10.870
Maybe time for one more.
00:31:10.870 --> 00:31:13.170
I know we're over, but
I'm having a good time.
00:31:14.150 --> 00:31:14.983
Daisy.
00:31:14.983 --> 00:31:16.850
I'm somewhat randomly picking.
00:31:17.880 --> 00:31:19.380
- Hi, Sal.
00:31:19.380 --> 00:31:21.960
So first, I just wanna say thank you
00:31:21.960 --> 00:31:23.880
for all that you have done to enrich
00:31:23.880 --> 00:31:27.870
the educational experiences
of learners on Khan Academy
00:31:27.870 --> 00:31:28.840
and now Schoolhouse.
00:31:28.840 --> 00:31:32.290
So I, myself, I'm a tutor at Schoolhouse
00:31:32.290 --> 00:31:36.000
and I'm sort of constantly
looking for ways
00:31:36.000 --> 00:31:41.000
that I can more effectively
like present or teach concepts.
00:31:41.790 --> 00:31:43.470
And so I'm sort of just wondering,
00:31:43.470 --> 00:31:45.930
do you have any tutoring
strategies or tips
00:31:45.930 --> 00:31:48.990
that you like to use and
has there perhaps been
00:31:48.990 --> 00:31:52.050
someone like a teacher
who's teaching style
00:31:52.050 --> 00:31:54.900
you really admire and who
has been an inspiration
00:31:54.900 --> 00:31:56.420
to you as an educator?
00:31:56.420 --> 00:31:57.253
Thanks.
00:31:57.253 --> 00:31:58.173
- Oh, a good question.
00:31:59.720 --> 00:32:01.110
Not that I have fully figured it out.
00:32:01.110 --> 00:32:03.420
I think there's two modes that I get into.
00:32:03.420 --> 00:32:06.590
One is the explaining mode.
00:32:06.590 --> 00:32:08.020
And that's the one that many of you all
00:32:08.020 --> 00:32:09.970
might be familiar with on Khan Academy.
00:32:09.970 --> 00:32:11.670
And when I'm in explaining mode,
00:32:11.670 --> 00:32:14.810
that's where I try not to script it.
00:32:14.810 --> 00:32:16.410
I try not to over plan it.
00:32:16.410 --> 00:32:17.980
I do try to make sure that I am excited
00:32:17.980 --> 00:32:19.360
about what I'm about to do,
00:32:19.360 --> 00:32:20.650
because I always tell anyone teaching,
00:32:20.650 --> 00:32:21.900
if you're not excited about it,
00:32:21.900 --> 00:32:22.980
there's no way that your students
00:32:22.980 --> 00:32:24.470
are gonna be excited about it.
00:32:24.470 --> 00:32:26.770
I also try to not be stressed about it
00:32:26.770 --> 00:32:28.640
because stress, humans are very good
00:32:28.640 --> 00:32:30.270
at sensing stress in other people.
00:32:30.270 --> 00:32:31.280
And for most learners,
00:32:31.280 --> 00:32:33.430
it's already a slightly
stressful experience
00:32:33.430 --> 00:32:34.720
or maybe a very stressful experience.
00:32:34.720 --> 00:32:36.400
And then if the teacher is stressed,
00:32:36.400 --> 00:32:38.490
that's only gonna make the
student even more stressed.
00:32:38.490 --> 00:32:39.383
So I like to,
00:32:40.230 --> 00:32:42.350
even though you don't see my
faces on Khan Academy videos,
00:32:42.350 --> 00:32:44.930
I actually do force myself to
smile no matter what happen.
00:32:44.930 --> 00:32:47.020
My car might've gotten
towed, whatever else,
00:32:47.020 --> 00:32:49.150
but I'll force myself to smile.
00:32:49.150 --> 00:32:50.670
Before making the video,
00:32:50.670 --> 00:32:52.560
I force myself to just kind of relax.
00:32:52.560 --> 00:32:54.100
If I'm not relaxed, I
will take a little bit
00:32:54.100 --> 00:32:55.460
of a one minute, two minute breather,
00:32:55.460 --> 00:32:58.340
just get into a good place,
'cause it's gonna show up.
00:32:58.340 --> 00:33:00.620
And then really trying
to focus on the intuition
00:33:00.620 --> 00:33:03.490
and the ahas and let your
personality shine as much as,
00:33:03.490 --> 00:33:04.720
whatever your personality is.
00:33:04.720 --> 00:33:07.780
I think when you show that
authenticity, you really connect.
00:33:07.780 --> 00:33:11.090
And then when I imagine
who I'm speaking to,
00:33:11.090 --> 00:33:13.560
I really just try to speak
to almost like a younger,
00:33:13.560 --> 00:33:15.800
not even a younger,
just a version of myself
00:33:15.800 --> 00:33:18.020
that just has not learned
this material yet.
00:33:18.020 --> 00:33:21.070
But I try to respect that,
okay, they are also curious.
00:33:21.070 --> 00:33:23.390
They also wanna connect the dots.
00:33:23.390 --> 00:33:24.760
I don't try to talk down to them
00:33:24.760 --> 00:33:26.280
or I don't try to talk above them.
00:33:26.280 --> 00:33:27.113
So that's that.
00:33:27.113 --> 00:33:29.440
Now the other mode is the
Schoolhouse.world mode.
00:33:29.440 --> 00:33:33.100
When you're actually with people
like we are now, tutoring,
00:33:33.100 --> 00:33:35.360
that's where I just keep
trying to remind myself,
00:33:35.360 --> 00:33:38.020
the more that I can be a question asker,
00:33:38.020 --> 00:33:40.670
and it can be directed
questions, the better.
00:33:40.670 --> 00:33:43.750
And I've had trouble sometimes
with awkward silence.
00:33:43.750 --> 00:33:45.880
Like even at dinner parties,
I'm always the guy that like,
00:33:45.880 --> 00:33:47.630
when there's like three
seconds of awkward silence,
00:33:47.630 --> 00:33:49.800
I'm trying to fill it in somehow (laughs).
00:33:49.800 --> 00:33:52.220
Like who saw the game last night?
00:33:52.220 --> 00:33:53.719
One of my things that I need to work on
00:33:53.719 --> 00:33:56.550
is being more comfortable
with that awkward silence.
00:33:56.550 --> 00:33:58.960
And also, when you're tutoring folks,
00:33:58.960 --> 00:34:00.600
you ask a question.
00:34:00.600 --> 00:34:02.410
People might not have
an answer immediately,
00:34:02.410 --> 00:34:04.170
but make sure they have
some space to do it,
00:34:04.170 --> 00:34:06.640
or give them context,
like the message board,
00:34:06.640 --> 00:34:08.260
where it's like, hey
everyone, put what you think.
00:34:08.260 --> 00:34:09.630
That might feel a little bit safer
00:34:09.630 --> 00:34:11.300
if someone's a little
bit more introverted.
00:34:11.300 --> 00:34:12.970
I think try to pull
people out of the screen
00:34:12.970 --> 00:34:14.220
as much as possible.
00:34:14.220 --> 00:34:15.880
In Schoolhouse.world, make them feel safe.
00:34:15.880 --> 00:34:17.220
But say, hey, you know.
00:34:17.220 --> 00:34:18.450
Call on them a little bit.
00:34:18.450 --> 00:34:19.420
What do you think?
00:34:19.420 --> 00:34:20.970
How would you approach this problem?
00:34:20.970 --> 00:34:23.780
But I think the more that
you can make them do the work
00:34:23.780 --> 00:34:26.240
and you're pulling it out of them,
00:34:26.240 --> 00:34:27.870
I think that's going to be
a really good experience.
00:34:27.870 --> 00:34:31.113
And you just bring this
joy and energy to it.
00:34:32.240 --> 00:34:34.303
I think it's gonna be quite wonderful.
00:34:35.220 --> 00:34:36.483
- Thank you so much.
00:34:38.333 --> 00:34:39.710
- All right, all right.
00:34:39.710 --> 00:34:40.725
This is super, okay,
00:34:40.725 --> 00:34:42.150
I'll do two more quick questions.
00:34:42.150 --> 00:34:45.860
I'll do two questions and I will go to,
00:34:45.860 --> 00:34:50.860
let's go to Jose and Sarah.
00:34:53.300 --> 00:34:54.810
Apologies to everyone else.
00:34:54.810 --> 00:34:55.643
Apologies to everyone.
00:34:55.643 --> 00:34:56.603
Jose and then Sarah.
00:34:57.830 --> 00:34:59.090
- Hi, Sal.
00:34:59.090 --> 00:35:00.420
My name's Jose, obviously.
00:35:00.420 --> 00:35:01.902
I'm 13.
00:35:01.902 --> 00:35:05.330
I'm a sophomore and an
international student.
00:35:05.330 --> 00:35:07.800
So first, I just really appreciate you
00:35:07.800 --> 00:35:12.800
taking the time to help us by
giving us this opportunity.
00:35:14.150 --> 00:35:19.037
Now, my question is for
students who want to advance
00:35:21.400 --> 00:35:23.810
more than what their
school might be offering,
00:35:23.810 --> 00:35:26.900
what the school teaches,
the school curriculum.
00:35:26.900 --> 00:35:30.113
And for me, specifically,
math and science.
00:35:32.190 --> 00:35:35.380
For students who have
already taken the time to,
00:35:35.380 --> 00:35:37.300
apart from doing the school assignments
00:35:37.300 --> 00:35:39.963
and preparing for standardized
tests and all of that,
00:35:42.210 --> 00:35:46.240
also taking the opportunity to participate
00:35:46.240 --> 00:35:50.180
in extracurricular, say, online activities
00:35:50.180 --> 00:35:53.150
such as Khan Academy, such as Schoolhouse,
00:35:53.150 --> 00:35:55.210
for me, it's Khan Academy and AoPS
00:35:56.900 --> 00:36:00.800
in order to advance their
knowledge for math and science,
00:36:00.800 --> 00:36:02.810
how they might be able to communicate
00:36:02.810 --> 00:36:07.810
to schools as well as other institutions,
00:36:07.850 --> 00:36:11.120
the knowledge that they've
gathered on their own
00:36:11.120 --> 00:36:14.470
using non-accredited institutions.
00:36:14.470 --> 00:36:16.180
And you've talked a little bit about this
00:36:16.180 --> 00:36:18.630
in some of your interviews
about how ideally,
00:36:18.630 --> 00:36:20.670
educational institutions
could be independent
00:36:20.670 --> 00:36:22.900
from accreditation, because that allows
00:36:22.900 --> 00:36:24.840
mastery learning to take place
00:36:24.840 --> 00:36:28.613
instead of just that grade mindset.
00:36:29.750 --> 00:36:30.890
I have to get a hundred percent.
00:36:30.890 --> 00:36:32.420
I have to get an A, right?
00:36:32.420 --> 00:36:36.810
Just to actually take the
time to learn those concepts.
00:36:36.810 --> 00:36:39.420
How do you communicate that to teachers?
00:36:39.420 --> 00:36:41.150
- Yeah, yeah, you know, the good thing...
00:36:41.150 --> 00:36:42.460
So there's two things.
00:36:42.460 --> 00:36:47.460
One is I think if any of
y'all, there are ways to do it
00:36:47.740 --> 00:36:50.760
even without any kind of
extra systemic support.
00:36:50.760 --> 00:36:51.900
I remember when I was in high school,
00:36:51.900 --> 00:36:54.100
I was going through a similar,
00:36:54.100 --> 00:36:56.220
I was taking courses.
00:36:56.220 --> 00:36:57.470
I was born and raised in New Orleans.
00:36:57.470 --> 00:36:59.210
So I was taking courses at
the University of New Orleans
00:36:59.210 --> 00:37:00.980
while I was in high
school, which back then
00:37:00.980 --> 00:37:03.150
was actually fairly
non-standard thing to do.
00:37:03.150 --> 00:37:04.660
And so actually, at first,
00:37:04.660 --> 00:37:06.830
I remember them not even
letting me take the courses
00:37:06.830 --> 00:37:09.060
'cause I wanted to take them
when I was roughly your age.
00:37:09.060 --> 00:37:10.350
And they're like, we don't do that.
00:37:10.350 --> 00:37:12.530
And I remember I kept going
to them and saying like,
00:37:12.530 --> 00:37:14.270
what do I need to do to
let you take the course?
00:37:14.270 --> 00:37:16.640
And you'd be surprised, if
you're persistent enough,
00:37:16.640 --> 00:37:18.127
people will eventually let you.
00:37:18.127 --> 00:37:20.320
And then I remember I
wanted to take more courses
00:37:20.320 --> 00:37:22.740
and then they wouldn't let me
'cause there's some policy.
00:37:22.740 --> 00:37:26.370
And then I said, well, see how I do.
00:37:26.370 --> 00:37:28.560
So I think you can always keep pushing,
00:37:28.560 --> 00:37:30.430
keep pushing the envelope there.
00:37:30.430 --> 00:37:33.010
Never doubt the power of that.
00:37:33.010 --> 00:37:34.440
The good thing is some of these ideas
00:37:34.440 --> 00:37:35.740
are a lot more mainstream now.
00:37:35.740 --> 00:37:38.330
And just the very fact that
you're thinking about this
00:37:38.330 --> 00:37:40.960
at age 13 is a, sorry,
00:37:40.960 --> 00:37:43.640
my kids are screaming in the other room.
00:37:43.640 --> 00:37:46.973
But just the fact that you're
thinking about this at age 13,
00:37:49.850 --> 00:37:51.770
I wouldn't worry, first of all.
00:37:51.770 --> 00:37:54.300
But we're working on it for you, too.
00:37:54.300 --> 00:37:57.170
So if you go on or maybe you already,
00:37:57.170 --> 00:37:58.970
if you tutor on Schoolhouse.world
00:37:58.970 --> 00:38:01.410
and build a strong reputation,
00:38:01.410 --> 00:38:06.410
as I said, already two
very strong universities
00:38:06.820 --> 00:38:09.340
are interested in looking
at Schoolhouse.world tutors.
00:38:09.340 --> 00:38:10.763
UChicago and MIT.
00:38:12.090 --> 00:38:14.290
And I talked to 30 others yesterday.
00:38:14.290 --> 00:38:16.070
By the time you are
actually going to college,
00:38:16.070 --> 00:38:17.240
I suspect we're gonna have 50
00:38:17.240 --> 00:38:19.770
or a hundred of them that will
take a serious look at it.
00:38:19.770 --> 00:38:22.320
I'm also working with some scholarships.
00:38:22.320 --> 00:38:25.570
I talked to a very prestigious
scholarship yesterday.
00:38:25.570 --> 00:38:27.860
Don't be surprised if in
the next two, three months,
00:38:27.860 --> 00:38:30.240
Schoolhouse.world, becoming
a highly reputed tutor
00:38:30.240 --> 00:38:31.310
on Schoolhouse.world
00:38:32.290 --> 00:38:33.780
puts you kind of at the front of the line
00:38:33.780 --> 00:38:36.010
for some of these really,
really good scholarships.
00:38:36.010 --> 00:38:37.890
I'm also gonna be talking to employers.
00:38:37.890 --> 00:38:39.170
Some of the employers
that I think many of you
00:38:39.170 --> 00:38:40.410
all would love to work at,
00:38:40.410 --> 00:38:43.480
where, hey, if someone is a great tutor,
00:38:43.480 --> 00:38:45.790
highly reputed tutor on Schoolhouse.world,
00:38:45.790 --> 00:38:48.500
why wouldn't you give them an internship?
00:38:48.500 --> 00:38:53.070
And going back to my example,
someone can tutor Algebra,
00:38:53.070 --> 00:38:55.130
Calculus, Statistics, Biology.
00:38:55.130 --> 00:38:56.400
Whatever it might be, by that point,
00:38:56.400 --> 00:38:58.610
we should hopefully have
tutoring in other subjects,
00:38:58.610 --> 00:39:02.430
in English and in History
and whatever else by then.
00:39:02.430 --> 00:39:04.980
Why not hire those folks?
00:39:04.980 --> 00:39:06.520
So the good thing is you're 13.
00:39:06.520 --> 00:39:09.610
So by that point, I will have
done more of the homework
00:39:09.610 --> 00:39:11.280
and you'll have more opportunities
00:39:11.280 --> 00:39:12.210
than you'll know what to deal with.
00:39:12.210 --> 00:39:14.050
But don't be complacent, keep working.
00:39:14.050 --> 00:39:15.150
And meditate (laughs).
00:39:16.080 --> 00:39:16.913
- Thank you.
00:39:18.160 --> 00:39:19.260
- Sarah, take us home.
00:39:23.850 --> 00:39:24.683
- Hi, Sal.
00:39:25.870 --> 00:39:28.460
You have been my role model ever since.
00:39:28.460 --> 00:39:31.120
I used your platform even
before there was even,
00:39:31.120 --> 00:39:32.990
just your YouTube videos even.
00:39:32.990 --> 00:39:35.330
And now I'm a PhD student.
00:39:35.330 --> 00:39:38.220
And I've shared those Sal Khan videos
00:39:38.220 --> 00:39:41.090
to almost everyone that
I've met across my journey.
00:39:41.090 --> 00:39:42.927
So I'm in awe of your work.
00:39:42.927 --> 00:39:45.240
And I actually started tutoring on my own
00:39:45.240 --> 00:39:46.620
because I'm motivated by you.
00:39:46.620 --> 00:39:48.240
And then I saw Schoolhouse.world.
00:39:48.240 --> 00:39:51.823
I started a similar
initiative in my university.
00:39:53.326 --> 00:39:54.159
Again, inspired by you.
00:39:54.159 --> 00:39:56.340
And I was like, oh, he
has something similar.
00:39:56.340 --> 00:39:59.110
So I just wanted to say thank
you for all that you do.
00:39:59.110 --> 00:40:03.810
And it really brings a lot
of joy to everyone learning.
00:40:03.810 --> 00:40:05.630
One of the things that I
want to talk to you about
00:40:05.630 --> 00:40:09.233
was the motto is you can
learn anything anywhere.
00:40:10.320 --> 00:40:11.970
You hit on this previously as well.
00:40:11.970 --> 00:40:14.200
The issue is what about these areas
00:40:14.200 --> 00:40:15.780
where there isn't internet access?
00:40:15.780 --> 00:40:16.860
That even in the United States,
00:40:16.860 --> 00:40:18.240
we have these low income areas.
00:40:18.240 --> 00:40:20.670
Now, have you ever considered partnering
00:40:20.670 --> 00:40:22.160
with these internet providers?
00:40:22.160 --> 00:40:23.120
Maybe creating,
00:40:23.120 --> 00:40:27.360
I know Comcast has the
internet essentials program.
00:40:27.360 --> 00:40:30.010
And other companies that also have
00:40:30.010 --> 00:40:34.000
these internet access
programs and might benefit,
00:40:34.000 --> 00:40:38.330
I mean, how do you plan on
overcoming this obstacle?
00:40:38.330 --> 00:40:39.450
- Yeah, great question.
00:40:39.450 --> 00:40:42.010
And something that we constantly discuss
00:40:42.010 --> 00:40:43.560
at Khan Academy over the years.
00:40:47.223 --> 00:40:49.810
If there is a silver
lining of the pandemic
00:40:49.810 --> 00:40:51.730
is it's put a bigger
spotlight on this issue
00:40:51.730 --> 00:40:53.040
than I've ever seen.
00:40:53.040 --> 00:40:56.920
And we know for the first
time, governments and industry
00:40:56.920 --> 00:40:58.370
and philanthropists around the world
00:40:58.370 --> 00:41:00.810
are more serious about it
than they've ever been.
00:41:00.810 --> 00:41:03.140
In the U.S., this latest
infrastructure around
00:41:03.140 --> 00:41:04.810
has 60 something billion dollars
00:41:04.810 --> 00:41:07.950
to close the digital divide,
which should go a long way.
00:41:07.950 --> 00:41:09.480
Now, that's just the U.S.
00:41:09.480 --> 00:41:11.570
What about the rest of the world?
00:41:11.570 --> 00:41:12.820
The simple answer is yes.
00:41:14.090 --> 00:41:15.830
We are relatively small organization.
00:41:15.830 --> 00:41:16.730
We're not gonna be the people
00:41:16.730 --> 00:41:18.280
who could put fiber in the ground.
00:41:18.280 --> 00:41:19.470
We have lobbyists in D.C.
00:41:19.470 --> 00:41:20.303
We can't do that kind of,
00:41:20.303 --> 00:41:22.030
we're not even allowed to lobby in D.C.
00:41:22.030 --> 00:41:23.300
as a not-for-profit.
00:41:23.300 --> 00:41:25.240
But we're not gonna be the
organization that does that,
00:41:25.240 --> 00:41:27.730
puts fiber in the ground or
put satellites in the air.
00:41:27.730 --> 00:41:29.797
But I think the existence of Khan Academy
00:41:29.797 --> 00:41:31.390
and Schoolhouse.world,
00:41:31.390 --> 00:41:35.160
I think only highlights the
importance of giving access.
00:41:35.160 --> 00:41:36.850
And access isn't just about academics.
00:41:36.850 --> 00:41:38.960
It's even just about economic empowerment
00:41:38.960 --> 00:41:41.540
and even social wellbeing to some degree,
00:41:41.540 --> 00:41:43.933
as long as you can stay off
of the really bad stuff.
00:41:45.909 --> 00:41:46.990
So we try to do what we can.
00:41:46.990 --> 00:41:49.680
Actually, Comcast has been
one of our longtime partners.
00:41:49.680 --> 00:41:51.470
I had a conversation with the SpaceX folks
00:41:51.470 --> 00:41:52.783
working on Starlink.
00:41:53.870 --> 00:41:56.240
If that works out, that's great.
00:41:56.240 --> 00:41:58.920
That we can get more internet
to more of the world.
00:41:58.920 --> 00:42:01.210
So yes, that's something that is,
00:42:01.210 --> 00:42:03.120
definitely something we think about.
00:42:03.120 --> 00:42:05.670
We have been signatories to
things with Common Sense Media
00:42:05.670 --> 00:42:07.590
to try to close the digital divide.
00:42:07.590 --> 00:42:08.760
And now there's talk
about the homework gap,
00:42:08.760 --> 00:42:10.840
which is really the
digital divide at home.
00:42:10.840 --> 00:42:12.670
But yes, we try to do whatever we can.
00:42:12.670 --> 00:42:14.060
Now, the good news is,
00:42:14.060 --> 00:42:16.330
it isn't happening fast
enough for any of us.
00:42:16.330 --> 00:42:18.370
All of us would love that five years ago,
00:42:18.370 --> 00:42:19.430
there should have been no digital divide.
00:42:19.430 --> 00:42:21.610
10 years ago, there still is one.
00:42:21.610 --> 00:42:23.620
But if you look at it historically,
00:42:23.620 --> 00:42:26.970
compared to almost any
other technology ramp up,
00:42:26.970 --> 00:42:30.890
the refrigerator,
television, it's quite fast.
00:42:30.890 --> 00:42:34.020
So I do try to think about let's build
00:42:34.020 --> 00:42:35.840
for where the world is going.
00:42:35.840 --> 00:42:39.400
So I believe in 10 years,
the type of internet access
00:42:39.400 --> 00:42:43.530
and the types of devices
that are currently fancy
00:42:43.530 --> 00:42:46.430
I think are gonna be fairly
mainstream in 10 years.
00:42:46.430 --> 00:42:48.630
And then if Khan Academy
and Schoolhouse.world
00:42:48.630 --> 00:42:49.780
can sit on top of those,
00:42:49.780 --> 00:42:52.560
then probably not
everyone's going to access.
00:42:52.560 --> 00:42:54.320
In fact, probably the biggest barrier
00:42:54.320 --> 00:42:55.410
for access won't be that.
00:42:55.410 --> 00:42:56.550
It will be like governments.
00:42:56.550 --> 00:42:58.140
It'll be like the Taliban.
00:42:58.140 --> 00:42:59.250
It'll be government, you know.
00:42:59.250 --> 00:43:02.890
It'll be stuff like that -
war - that disrupts people.
00:43:02.890 --> 00:43:05.500
But economically, it should
be hopefully feasible.
00:43:05.500 --> 00:43:09.340
So fingers crossed, but we just
gotta keep pushing on that.
00:43:09.340 --> 00:43:10.510
- One of the things I was thinking about
00:43:10.510 --> 00:43:11.800
maybe creating like these hubs.
00:43:11.800 --> 00:43:13.040
Like there's a lot of schools.
00:43:13.040 --> 00:43:14.140
Well, early in the pandemic,
00:43:14.140 --> 00:43:15.830
there's libraries closed
or schools closed.
00:43:15.830 --> 00:43:17.540
Maybe creating these hubs
and these, I don't know.
00:43:17.540 --> 00:43:18.810
Again, that branding of Khan,
00:43:18.810 --> 00:43:22.560
like these Khan hubs that
provide internet access
00:43:22.560 --> 00:43:24.280
in these low income areas,
00:43:24.280 --> 00:43:25.750
which obviously will have, you know,
00:43:25.750 --> 00:43:28.212
Khan Academy and Schoolhouse.world
00:43:28.212 --> 00:43:29.550
in the computers or whatever,
00:43:29.550 --> 00:43:33.320
but some kind of access to
these low income areas exactly.
00:43:33.320 --> 00:43:34.270
- You're 100% right.
00:43:34.270 --> 00:43:36.990
We've had ideas, and
I've talked to people.
00:43:36.990 --> 00:43:39.070
This actually is what libraries
of the future should be.
00:43:39.070 --> 00:43:39.920
- Yes.
- I mean,
00:43:40.780 --> 00:43:42.730
physical books have,
you know, that's good,
00:43:42.730 --> 00:43:44.870
but people need a hub.
00:43:44.870 --> 00:43:45.703
There's that.
00:43:45.703 --> 00:43:47.830
I've had conversations
with major retailers.
00:43:47.830 --> 00:43:49.040
I was just like, why don't you take
00:43:49.040 --> 00:43:50.670
that back right corner of your store
00:43:50.670 --> 00:43:52.240
that no one goes to right now,
00:43:52.240 --> 00:43:54.010
turn it into a learning lab.
00:43:54.010 --> 00:43:55.210
- Yes.
- And by the way,
00:43:55.210 --> 00:43:57.210
parents will come, drop
their kids off there
00:43:57.210 --> 00:43:58.630
for half an hour while they can learn
00:43:58.630 --> 00:44:00.520
from Khan Academy and Schoolhouse.world,
00:44:00.520 --> 00:44:02.060
and the parents are gonna buy something.
00:44:02.060 --> 00:44:03.850
They're gonna do their shopping.
00:44:03.850 --> 00:44:06.170
And you're giving them childcare, too.
00:44:06.170 --> 00:44:07.420
And then they pick up their kids
00:44:07.420 --> 00:44:08.280
and their kids would have learned.
00:44:08.280 --> 00:44:10.970
So yeah, open to all ideas.
00:44:10.970 --> 00:44:14.550
Museums, libraries, even big box retail.
00:44:14.550 --> 00:44:17.070
And then in really rural places
00:44:17.070 --> 00:44:18.100
or developing parts of the world,
00:44:18.100 --> 00:44:19.770
you could manage a shipping container
00:44:19.770 --> 00:44:22.073
with a internet connection to Starlink,
00:44:23.320 --> 00:44:25.590
put a couple of low-cost devices in there,
00:44:25.590 --> 00:44:27.640
hire someone from the village
who can just make sure
00:44:27.640 --> 00:44:30.660
that nothing shady happens and go.
00:44:30.660 --> 00:44:32.235
You have a school in a box, so to speak.
00:44:32.235 --> 00:44:33.068
- Yes.
00:44:33.970 --> 00:44:35.060
- Let's work on it.
- I was thinking
00:44:35.060 --> 00:44:37.040
like some kind of like to-go school.
00:44:37.040 --> 00:44:37.970
Yeah, exactly.
00:44:37.970 --> 00:44:38.830
- That's right.
00:44:38.830 --> 00:44:41.623
So yeah, I mean, it goes
back to what I said earlier.
00:44:42.530 --> 00:44:43.363
There's two scenarios.
00:44:43.363 --> 00:44:45.070
You have a school, which hopefully you do.
00:44:45.070 --> 00:44:46.840
And then hopefully Khan
Academy and Schoolhouse.world
00:44:46.840 --> 00:44:49.230
can make it even more
personalized, even better.
00:44:49.230 --> 00:44:53.700
But we also wanna be the
world's education safety net,
00:44:53.700 --> 00:44:55.630
so that no one has nothing.
00:44:55.630 --> 00:44:58.290
And actually, the safety
net's pretty darn good.
00:44:58.290 --> 00:44:59.930
So yeah, let's figure it out.
00:44:59.930 --> 00:45:00.980
It's not gonna be solved tomorrow,
00:45:00.980 --> 00:45:04.240
but it's an admirable
goal to keep pushing on.
00:45:04.240 --> 00:45:05.160
So I will stop.
- I think you have some
00:45:05.160 --> 00:45:06.330
great minds who'll figure it out.
00:45:06.330 --> 00:45:07.320
- Yes, yes.
00:45:07.320 --> 00:45:08.870
And congratulations.
00:45:08.870 --> 00:45:13.410
Just as I told Salik
to be a donor one day,
00:45:13.410 --> 00:45:15.240
either, depending if you
go to industry or academia,
00:45:15.240 --> 00:45:17.800
be a donor one day or when
you get the Nobel prize.
00:45:17.800 --> 00:45:19.360
I just want a small mention.
00:45:19.360 --> 00:45:21.690
- Yeah (laughs).
- If not for Khan Academy,
00:45:21.690 --> 00:45:23.528
we might not have cured this disease.
00:45:23.528 --> 00:45:24.590
- Oh, don't you worry, Sal.
00:45:24.590 --> 00:45:25.640
I'm donating to you already.
00:45:25.640 --> 00:45:27.786
Don't you worry.
- Oh, very good.
00:45:27.786 --> 00:45:29.513
- With my amazing stipend.
00:45:30.890 --> 00:45:33.880
- I feel somewhat guilty from that.
00:45:33.880 --> 00:45:35.720
But later on, when you're
making the big money,
00:45:35.720 --> 00:45:37.490
then you should.
00:45:37.490 --> 00:45:38.370
But, well, thanks everyone.
00:45:38.370 --> 00:45:39.840
The good thing is this is a series.
00:45:39.840 --> 00:45:41.630
We're gonna be doing this again next week.
00:45:41.630 --> 00:45:44.510
So everyone, I'm trying
to kind of remember
00:45:44.510 --> 00:45:48.490
the names and the faces of
people who I did not get to.
00:45:48.490 --> 00:45:52.700
And everyone else on - Zeeshan, Vinay,
00:45:52.700 --> 00:45:55.920
Christine, Jose A.,
00:45:55.920 --> 00:46:00.920
Evelyn, Maive, Athena, and Connall.
00:46:01.110 --> 00:46:01.943
We didn't get to you.
00:46:01.943 --> 00:46:03.460
And obviously, everyone
else can ask questions, too.
00:46:03.460 --> 00:46:04.610
So I look forward to hopefully getting
00:46:04.610 --> 00:46:06.800
to all of your questions next week.
00:46:06.800 --> 00:46:07.900
See you then, this was a lot of fun.
00:46:07.900 --> 00:46:09.319
Thanks everyone.
- See you next week, Sal.
00:46:09.319 --> 00:46:10.258
Thanks.
00:46:10.258 --> 00:46:11.840
- Thanks, Sal.
- Thanks so much, Sal.
00:46:11.840 --> 00:46:12.938
- Thank you.
- Thank you.
00:46:12.938 --> 00:46:14.855
- Thank you, thank you.
00:46:33.718 --> 00:46:35.301
- Are you still on?
00:46:36.960 --> 00:46:38.560
- Yeah, what's up?
00:46:38.560 --> 00:46:39.680
- Were you the one that joined in
00:46:39.680 --> 00:46:41.592
and let people in or is it Sal?
00:46:41.592 --> 00:46:42.609
- It was me.
00:46:42.609 --> 00:46:43.442
- Okay.
00:46:44.367 --> 00:46:47.313
You're gonna do this again
or should we make a note?
00:46:48.670 --> 00:46:51.190
- Sal, next time, is it
possible to, I guess,
00:46:51.190 --> 00:46:52.920
give someone co-host?
00:46:52.920 --> 00:46:54.323
To let people in?
00:46:55.300 --> 00:46:56.380
- Oh yeah, I'll do that.
00:46:56.380 --> 00:46:57.500
Just tell me how to do it.
00:46:57.500 --> 00:47:00.400
- Yeah, 'cause I got
like 10 chat requesting,
00:47:00.400 --> 00:47:02.177
like they're waiting for
people to join the meeting
00:47:02.177 --> 00:47:03.877
and I don't have the admin access.
00:47:05.300 --> 00:47:06.680
But it's okay, we got it now.
00:47:06.680 --> 00:47:07.513
- Let's do that.
00:47:11.910 --> 00:47:14.310
- I just don't wanna leave, that's all.
00:47:14.310 --> 00:47:16.050
- Oh yeah, you're still
part of the recording.
00:47:16.050 --> 00:47:18.450
- I'm reading all of the messages before-
00:47:18.450 --> 00:47:19.283
- Oh yeah, that's a ton.
00:47:19.283 --> 00:47:21.450
I think you can download
them too somewhere.
00:47:22.540 --> 00:47:24.474
- Actually, if one of
y'all can download them.
00:47:24.474 --> 00:47:26.190
- Yeah.
00:47:26.190 --> 00:47:27.023
- I think there's save chat.
- The three dots
00:47:27.023 --> 00:47:27.856
at the bottom.
00:47:27.856 --> 00:47:28.689
Yeah, save chat.
00:47:28.689 --> 00:47:30.223
Save it as a txt file.
00:47:34.230 --> 00:47:35.120
- All right, thanks everyone.
00:47:35.120 --> 00:47:36.480
See you all.
00:47:36.480 --> 00:47:37.313
- Bye.
00:47:37.313 --> 00:47:38.483
- Bye, everyone.
|
Buffer range | https://www.youtube.com/watch?v=yia1GeEEVaM | vtt | https://www.youtube.com/api/timedtext?v=yia1GeEEVaM&ei=0lWUZeaFJOShp-oP3tOD4AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=431CDE946C8095044E95FC826ACCED6F9E06D65F.24EFBF42E4DDCB0A71A57B33197DC126A96A9455&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.470 --> 00:00:02.730
- [Instructor] Buffers consists
of a significant amount
00:00:02.730 --> 00:00:06.170
of a weak acid, which
we will represent as HA
00:00:06.170 --> 00:00:08.670
and the conjugate base to the weak acid,
00:00:08.670 --> 00:00:11.120
which we will represent as A-.
00:00:11.120 --> 00:00:14.640
Buffer solutions resist
large changes in pH.
00:00:14.640 --> 00:00:16.720
However, buffers are only effective
00:00:16.720 --> 00:00:19.420
over a certain range of pH values.
00:00:19.420 --> 00:00:22.410
We are going to use the
Henderson-Hasselbalch equation
00:00:22.410 --> 00:00:26.750
to find the effective
pH range of a buffer.
00:00:26.750 --> 00:00:28.700
Looking at the
Henderson-Hasselbalch equation,
00:00:28.700 --> 00:00:30.280
the pH of the buffer solution
00:00:30.280 --> 00:00:33.300
is equal to the pKa of the weak acid,
00:00:33.300 --> 00:00:34.900
which would be HA,
00:00:34.900 --> 00:00:37.920
plus the log of the concentration
of the conjugate base
00:00:37.920 --> 00:00:41.120
divided by the concentration
of the weak acid.
00:00:41.120 --> 00:00:43.720
And it's this ratio of the concentration
00:00:43.720 --> 00:00:48.390
of the conjugate base to the
concentration of the weak acid
00:00:48.390 --> 00:00:52.650
that determines if a
buffer is effective or not.
00:00:52.650 --> 00:00:56.000
Buffer solutions are most
effective at resisting a change
00:00:56.000 --> 00:00:58.100
in pH in either direction
00:00:58.100 --> 00:01:00.250
when the concentration of the weak acid
00:01:00.250 --> 00:01:04.090
is equal to the concentration
of the conjugate base.
00:01:04.090 --> 00:01:06.660
And when the concentrations
are equal to each other,
00:01:06.660 --> 00:01:09.310
the ratio is equal to one,
00:01:09.310 --> 00:01:14.123
and the log of one is equal to zero.
00:01:15.200 --> 00:01:17.930
Therefore, when the concentrations
are equal to each other,
00:01:17.930 --> 00:01:22.390
the pH of the buffer
solution is equal to the pKa
00:01:22.390 --> 00:01:24.990
of the weak acid plus zero.
00:01:24.990 --> 00:01:28.870
So we could just say that
the pH is equal to the pKa
00:01:28.870 --> 00:01:30.690
when the concentration of the weak acid
00:01:30.690 --> 00:01:34.140
is equal to the concentration
of the conjugate base.
00:01:34.140 --> 00:01:37.450
So we usually try to choose
a buffer with a weak acid
00:01:37.450 --> 00:01:41.670
that has a pKa value
close to the desired pH
00:01:41.670 --> 00:01:43.500
of the solution.
00:01:43.500 --> 00:01:47.090
So buffers are effective at
resisting large changes in pH
00:01:47.090 --> 00:01:49.480
when the pH is approximately equal
00:01:49.480 --> 00:01:51.820
to the pKa of the weak acid.
00:01:51.820 --> 00:01:55.570
However, if the concentration
of one component of a buffer
00:01:55.570 --> 00:01:58.790
is more than 10 times the concentration
00:01:58.790 --> 00:02:00.870
of the other component in a buffer,
00:02:00.870 --> 00:02:05.690
buffers are not effective at
resisting large changes to pH.
00:02:05.690 --> 00:02:08.660
Therefore, to find the effective pH range,
00:02:08.660 --> 00:02:11.280
we're gonna use the
Henderson-Hasselbalch equation
00:02:11.280 --> 00:02:12.800
to calculate the pH
00:02:12.800 --> 00:02:15.580
when the concentration
of the conjugate base
00:02:15.580 --> 00:02:18.890
is 10 times the concentration
of the weak acid,
00:02:18.890 --> 00:02:21.230
and also to calculate the pH
00:02:21.230 --> 00:02:22.940
when the concentration of the weak acid
00:02:22.940 --> 00:02:26.810
is 10 times the concentration
of the conjugate base.
00:02:26.810 --> 00:02:28.420
Doing these two calculations
00:02:28.420 --> 00:02:30.350
gives us the upper and lower limits
00:02:30.350 --> 00:02:33.340
of the effective pH range.
00:02:33.340 --> 00:02:36.030
So let's calculate the
pH of the buffer solution
00:02:36.030 --> 00:02:38.570
when the concentration
of the conjugate base
00:02:38.570 --> 00:02:42.420
is 10 times the concentration
of the weak acid.
00:02:42.420 --> 00:02:44.540
Looking at the
Henderson-Hasselbalch equation,
00:02:44.540 --> 00:02:47.040
if the concentration of the conjugate base
00:02:47.040 --> 00:02:50.200
is 10 times the concentration
of the weak acid,
00:02:50.200 --> 00:02:53.510
the ratio is equal to 10 over one,
00:02:53.510 --> 00:02:56.520
and the log of 10 is equal to one.
00:02:56.520 --> 00:02:59.080
Therefore, the pH of the buffer solution
00:02:59.080 --> 00:03:04.080
is equal to the pKa value
of the weak acid plus one.
00:03:04.770 --> 00:03:08.160
This value for the pH
represents the upper limit
00:03:08.160 --> 00:03:10.710
of the effective pH range.
00:03:10.710 --> 00:03:13.420
Next, let's calculate the
pH of the buffer solution
00:03:13.420 --> 00:03:15.400
when the concentration of weak acid
00:03:15.400 --> 00:03:19.180
is 10 times the concentration
of the conjugate base.
00:03:19.180 --> 00:03:21.450
Looking at the
Henderson-Hasselbalch equation,
00:03:21.450 --> 00:03:23.100
if the concentration of HA
00:03:23.100 --> 00:03:27.130
is 10 times the concentration of A-,
00:03:27.130 --> 00:03:30.060
the ratio is equal to one over 10,
00:03:30.060 --> 00:03:34.350
and the log of one over 10
is equal to negative one.
00:03:34.350 --> 00:03:36.960
Therefore, the pH of the buffer solution
00:03:36.960 --> 00:03:41.900
is equal to the pKa value
of the weak acid minus one.
00:03:41.900 --> 00:03:45.130
This value for the pH
represents the lower limit
00:03:45.130 --> 00:03:47.440
of the effective pH range.
00:03:47.440 --> 00:03:49.770
By the calculations that we've just done,
00:03:49.770 --> 00:03:53.460
we've seen that the effective
pH range of a buffer
00:03:53.460 --> 00:03:58.080
is plus or minus one of the
pKa value of the weak acid.
00:03:58.080 --> 00:04:01.640
Let's use these concepts
of an effective pH range
00:04:01.640 --> 00:04:04.080
to choose a buffer solution.
00:04:04.080 --> 00:04:06.350
Let's say we want to buffer a solution
00:04:06.350 --> 00:04:11.020
at a pH of 9.00 at 25 degrees Celsius.
00:04:11.020 --> 00:04:12.950
And suppose that we have two choices,
00:04:12.950 --> 00:04:16.730
we could either choose an
acetic acid-acetate buffer
00:04:16.730 --> 00:04:20.200
or we could choose an
ammonium-ammonia buffer.
00:04:20.200 --> 00:04:22.620
Because the effective pH range of a buffer
00:04:22.620 --> 00:04:26.610
is plus or minus one the
pKa value of the weak acid,
00:04:26.610 --> 00:04:27.810
we don't wanna choose
00:04:27.810 --> 00:04:30.830
the acetic acid-acetate buffer solution.
00:04:30.830 --> 00:04:32.640
Because at 25 degrees Celsius,
00:04:32.640 --> 00:04:37.140
the pKa value for acetic
acid is equal to 4.74.
00:04:37.140 --> 00:04:39.950
Therefore, this buffer
would only be effective
00:04:39.950 --> 00:04:44.450
at a range of plus or minus one from 4.74,
00:04:44.450 --> 00:04:49.070
so about 3.74 to approximately 5.74.
00:04:49.070 --> 00:04:53.750
The ammonium cation has
a pKa value equal to 9.25
00:04:53.750 --> 00:04:56.200
at 25 degrees Celsius.
00:04:56.200 --> 00:04:58.720
Therefore, the ammonium-ammonia buffer
00:04:58.720 --> 00:05:02.880
is effective plus or minus
one of this pKa value,
00:05:02.880 --> 00:05:07.880
so approximately 8.25 to 10.25.
00:05:08.000 --> 00:05:11.930
Since our pH of nine
falls within that range,
00:05:11.930 --> 00:05:15.353
we would choose the
ammonium-ammonia buffer.
|
Methods for preparing buffers | https://www.youtube.com/watch?v=OCPQaKhVC_0 | vtt | https://www.youtube.com/api/timedtext?v=OCPQaKhVC_0&ei=0lWUZYS4I8HJp-oP0pKN2Ao&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=772883437ED7F8AEA25A8D351D560D2D26415F83.9CA240CEAFE149FAF5E9F5322F39BB8761A10123&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.400 --> 00:00:01.930
- [Instructor] Let's look
at two different methods
00:00:01.930 --> 00:00:04.890
for preparing buffer solutions.
00:00:04.890 --> 00:00:05.820
In the first method,
00:00:05.820 --> 00:00:07.400
we're gonna add an aqueous solution
00:00:07.400 --> 00:00:09.660
of a strong base, sodium hydroxide,
00:00:09.660 --> 00:00:13.240
to an aqueous solution of
a weak acid, acetic acid.
00:00:13.240 --> 00:00:16.130
Our goal is to calculate the
pH of the buffer solution
00:00:16.130 --> 00:00:20.500
that forms when we mix these
two aqueous solutions together.
00:00:20.500 --> 00:00:22.870
Our first step is to
figure out how many moles
00:00:22.870 --> 00:00:25.060
of acetic acid that we have.
00:00:25.060 --> 00:00:28.530
So if we have 100 milliliters
of a 1.00 molar solution
00:00:28.530 --> 00:00:31.040
of acetic acid, we can use the equation:
00:00:31.040 --> 00:00:34.420
molarity is equal to
moles divided by liters
00:00:34.420 --> 00:00:37.010
to figure out the moles of acetic acid.
00:00:37.010 --> 00:00:40.530
Since the concentration is 1.00 molar
00:00:40.530 --> 00:00:42.990
and the volume is 100 milliliters,
00:00:42.990 --> 00:00:46.910
which is equal to 0.100 liters,
00:00:46.910 --> 00:00:51.833
x is equal to 0.100 moles of acetic acid.
00:00:52.800 --> 00:00:54.640
We can do a similar calculation
00:00:54.640 --> 00:00:57.890
to determine the moles of strong base.
00:00:57.890 --> 00:01:00.310
So for our aqueous solution
of sodium hydroxide,
00:01:00.310 --> 00:01:02.070
we have 50 milliliters of it
00:01:02.070 --> 00:01:05.130
at a concentration of 1.00 molar.
00:01:05.130 --> 00:01:08.560
So we plug in the concentration 1.00 molar
00:01:08.560 --> 00:01:10.520
into the equation for molarity,
00:01:10.520 --> 00:01:12.260
and we plug in the volume,
00:01:12.260 --> 00:01:15.870
and 50 milliliters is
equal to 0.050 liters.
00:01:15.870 --> 00:01:17.060
So solving for x,
00:01:17.060 --> 00:01:22.060
we find the x is equal to 0.050
moles of sodium hydroxide.
00:01:22.920 --> 00:01:25.370
Since sodium hydroxide is a strong base,
00:01:25.370 --> 00:01:28.500
it dissociates completely in solution.
00:01:28.500 --> 00:01:32.650
Therefore, if we have 0.050
moles of sodium hydroxide,
00:01:32.650 --> 00:01:37.020
we also have 0.050 moles of
sodium cations in solution
00:01:37.020 --> 00:01:40.780
and also hydroxide anions in solution.
00:01:40.780 --> 00:01:42.970
When these two aqueous
solutions are mixed,
00:01:42.970 --> 00:01:46.470
we're mixing 100 milliliters
with 50 milliliters
00:01:46.470 --> 00:01:50.820
for a total volume of 150 milliliters.
00:01:50.820 --> 00:01:51.653
Let me just go ahead
00:01:51.653 --> 00:01:53.150
and write that down here really quickly.
00:01:53.150 --> 00:01:55.560
And when the two solutions are mixed,
00:01:55.560 --> 00:01:59.270
the acetic acid will react
with hydroxide anions
00:01:59.270 --> 00:02:02.730
to form the acetate anion and water.
00:02:02.730 --> 00:02:04.170
To figure out what's left over
00:02:04.170 --> 00:02:06.200
after the reaction goes to completion,
00:02:06.200 --> 00:02:08.150
we're gonna use an ICF table,
00:02:08.150 --> 00:02:10.410
where I stands for initial,
00:02:10.410 --> 00:02:13.810
C is for change, and F is for final.
00:02:13.810 --> 00:02:16.270
We've already calculated
the initial number of moles
00:02:16.270 --> 00:02:20.420
of acetic acid is equal to 0.100,
00:02:20.420 --> 00:02:23.630
and the initial number of
moles of hydroxide anions
00:02:23.630 --> 00:02:26.660
is equal to 0.050.
00:02:26.660 --> 00:02:29.360
And if we assume the
reaction hasn't happened yet,
00:02:29.360 --> 00:02:32.180
the initial number of
moles of the acetate anion
00:02:32.180 --> 00:02:34.170
would be zero.
00:02:34.170 --> 00:02:35.080
For this reaction,
00:02:35.080 --> 00:02:38.340
the hydroxide anion is
the limiting reactant.
00:02:38.340 --> 00:02:41.330
And therefore, we're gonna
use it all up in the reaction.
00:02:41.330 --> 00:02:46.330
So we write -0.050 under
hydroxide in our ICF table.
00:02:48.440 --> 00:02:49.840
Looking at the balanced equation,
00:02:49.840 --> 00:02:53.080
the mole ratio of a acetic
acid to hydroxide anion
00:02:53.080 --> 00:02:54.570
is one-to-one.
00:02:54.570 --> 00:02:59.570
Therefore, if we are losing
0.050 moles of hydroxide anions,
00:02:59.620 --> 00:03:04.620
we're also losing 0.050
moles of acetic acid.
00:03:05.310 --> 00:03:07.600
So when the reaction goes to completion,
00:03:07.600 --> 00:03:10.550
all of the hydroxide
anions have been used up.
00:03:10.550 --> 00:03:14.610
Therefore, we have zero moles
of hydroxide anions left over.
00:03:14.610 --> 00:03:17.920
For a acetic acid, if
we started with 0.100
00:03:17.920 --> 00:03:20.680
and we're losing 0.050,
00:03:20.680 --> 00:03:23.380
half of the acetic acid
has been neutralized
00:03:23.380 --> 00:03:25.150
by the hydroxide anions,
00:03:25.150 --> 00:03:29.340
and we're left with 0.050 moles
00:03:29.340 --> 00:03:32.200
when the reaction goes to completion.
00:03:32.200 --> 00:03:33.650
For the acetate anion,
00:03:33.650 --> 00:03:36.690
the coefficient in the
balanced equation is a one.
00:03:36.690 --> 00:03:39.730
Therefore, if we're losing 0.050
00:03:39.730 --> 00:03:41.210
on the left side of the equation,
00:03:41.210 --> 00:03:46.210
we're gonna be gaining
0.050 on the right side.
00:03:46.320 --> 00:03:49.230
So when the reaction goes to completion,
00:03:49.230 --> 00:03:54.230
we have 0.050 moles of the acetate anion.
00:03:54.950 --> 00:03:57.540
A buffer solution consists
of significant amounts
00:03:57.540 --> 00:03:59.990
of a weak acid and its conjugate base.
00:03:59.990 --> 00:04:04.400
Acetic acid is a weak acid
and its conjugate base
00:04:04.400 --> 00:04:06.660
is the acetate anion.
00:04:06.660 --> 00:04:10.420
Therefore, the addition of
the strong base, hydroxide,
00:04:10.420 --> 00:04:13.150
which neutralized half of the acetic acid
00:04:13.150 --> 00:04:15.060
created a buffer solution
00:04:15.060 --> 00:04:19.100
because we have significant
amounts of both acetic acid
00:04:19.100 --> 00:04:23.250
and its conjugate base, the
acetate anion, in solution.
00:04:23.250 --> 00:04:24.320
Remember that our goal
00:04:24.320 --> 00:04:27.430
was to calculate the pH
of this buffer solution.
00:04:27.430 --> 00:04:29.940
So first, we need to
calculate the concentration
00:04:29.940 --> 00:04:32.870
of acetic acid and of the acetate anion.
00:04:32.870 --> 00:04:35.090
To find the concentration of acetic acid,
00:04:35.090 --> 00:04:39.260
we take the moles of acetic
acid which is equal to 0.050,
00:04:39.260 --> 00:04:42.440
and we divide by the
total volume of solution.
00:04:42.440 --> 00:04:43.490
We already calculated
00:04:43.490 --> 00:04:45.220
when we mix the two solutions together,
00:04:45.220 --> 00:04:47.810
the total volume was 150 milliliters
00:04:47.810 --> 00:04:50.830
which is equal to 0.150 liters.
00:04:50.830 --> 00:04:54.980
So 0.050 moles divided by 0.150 liters
00:04:54.980 --> 00:04:59.423
gives the concentration of
acetic acid a 0.33 molar.
00:05:00.360 --> 00:05:04.200
For the acetate anion,
we also have 0.050 moles,
00:05:04.200 --> 00:05:08.300
and the total volume of
solution is also 0.150 liters.
00:05:08.300 --> 00:05:10.630
Therefore, the concentration
of the acetate anion
00:05:10.630 --> 00:05:13.570
is also 0.33 molar.
00:05:13.570 --> 00:05:15.440
To find the pH of the buffer solution,
00:05:15.440 --> 00:05:18.350
we can use the
Henderson-Hasselbalch equation.
00:05:18.350 --> 00:05:19.780
The Henderson-Hasselbalch equation
00:05:19.780 --> 00:05:21.480
says the pH of the buffer solution
00:05:21.480 --> 00:05:24.310
is equal to the pKa of the weak acid
00:05:24.310 --> 00:05:27.250
plus the log of the ratio
of the concentration
00:05:27.250 --> 00:05:30.110
of the conjugate base
divided by the concentration
00:05:30.110 --> 00:05:31.430
of the weak acid.
00:05:31.430 --> 00:05:34.970
The weak acid present in our
buffer solution is acetic acid.
00:05:34.970 --> 00:05:37.090
And at 25 degrees Celsius,
00:05:37.090 --> 00:05:41.960
the pKa value of acetic
acid is equal to 4.74.
00:05:41.960 --> 00:05:44.740
The acetate anion is our conjugated base
00:05:44.740 --> 00:05:47.070
and it has a concentration of 0.33 molar,
00:05:47.070 --> 00:05:50.060
so we can plug that into the
Henderson-Hasselbalch equation,
00:05:50.060 --> 00:05:51.980
and the concentration of our weak acid
00:05:51.980 --> 00:05:54.950
is also 0.33 molar.
00:05:54.950 --> 00:05:59.950
Molars cancel and 0.33 divided
by 0.33 is equal to one.
00:06:00.460 --> 00:06:04.710
And the log of one is equal to zero.
00:06:04.710 --> 00:06:06.900
Therefore, for this buffer solution,
00:06:06.900 --> 00:06:11.900
the pH is just equal to 4.74.
00:06:13.060 --> 00:06:15.760
And notice that even though I
calculated the concentration
00:06:15.760 --> 00:06:18.960
of the weak acid and
of the conjugate base,
00:06:18.960 --> 00:06:19.990
I didn't really have to,
00:06:19.990 --> 00:06:22.440
if you look at the
Henderson-Hasselbalch equation.
00:06:22.440 --> 00:06:25.800
Because we have concentration
divided by concentration,
00:06:25.800 --> 00:06:29.300
and concentration, molarity,
is moles per liter.
00:06:29.300 --> 00:06:32.390
And so it's moles divided
by liters, divided by moles,
00:06:32.390 --> 00:06:33.620
divided by liters.
00:06:33.620 --> 00:06:36.480
And since both the weak
acid and the conjugate base
00:06:36.480 --> 00:06:39.240
have the same total volume of solution,
00:06:39.240 --> 00:06:41.590
the total volume of solution would cancel.
00:06:41.590 --> 00:06:42.740
And so, if we want to,
00:06:42.740 --> 00:06:44.540
we could just do a ratio of the moles
00:06:44.540 --> 00:06:46.360
and we would have gotten the same answer,
00:06:46.360 --> 00:06:49.950
a final pH of 4.74.
00:06:49.950 --> 00:06:53.270
Let's look at another method
for making a buffer solution.
00:06:53.270 --> 00:06:55.410
In this case, we're gonna
mix an aqueous solution
00:06:55.410 --> 00:06:57.830
of a weak base with an aqueous solution
00:06:57.830 --> 00:07:01.570
that contains the conjugate
acid to the weak base.
00:07:01.570 --> 00:07:05.540
In this example, our weak
base is ammonia, NH3.
00:07:05.540 --> 00:07:10.490
The conjugate acid to ammonia
is the ammonium ion, NH4+.
00:07:10.490 --> 00:07:13.710
And if we have an aqueous
solution of ammonium chloride,
00:07:13.710 --> 00:07:17.500
in solution, there are
ammonium ions, NH4+.
00:07:19.190 --> 00:07:21.900
So we have a weak base, NH3,
00:07:21.900 --> 00:07:25.100
and its conjugate acid, NH4+.
00:07:25.100 --> 00:07:27.530
And when the two aqueous
solutions are mixed,
00:07:27.530 --> 00:07:31.060
we'll have a significant
amount of both our weak base
00:07:31.060 --> 00:07:33.050
and its conjugate acid.
00:07:33.050 --> 00:07:36.060
Therefore, we will have a buffer solution.
00:07:36.060 --> 00:07:39.510
I often say that a buffer
solution consists of a weak acid
00:07:39.510 --> 00:07:41.200
and its conjugate base.
00:07:41.200 --> 00:07:42.200
In this case,
00:07:42.200 --> 00:07:44.810
I've said the buffer solution
consists of a weak base
00:07:44.810 --> 00:07:46.540
and its conjugate acid.
00:07:46.540 --> 00:07:49.810
So a more general definition
for a buffer solution
00:07:49.810 --> 00:07:53.460
could be a weak conjugate acid-base pair.
00:07:53.460 --> 00:07:56.630
We can calculate the pH of
the buffer solution that forms
00:07:56.630 --> 00:07:58.310
when we mix the two solutions together
00:07:58.310 --> 00:08:01.540
using the Henderson-Hasselbalch equation.
00:08:01.540 --> 00:08:02.373
In this case,
00:08:02.373 --> 00:08:06.670
our numerator is our weak
base which is ammonia
00:08:06.670 --> 00:08:10.100
and our denominator is the
conjugate acid to ammonia
00:08:10.100 --> 00:08:12.650
which is the ammonium ion, NH4+.
00:08:13.570 --> 00:08:17.610
The ammonia solution had a
concentration of 0.16 molar,
00:08:17.610 --> 00:08:20.430
and when we mix 100 milliliters
of the ammonia solution
00:08:20.430 --> 00:08:23.760
with 100 milliliters of the
solution of ammonium chloride,
00:08:23.760 --> 00:08:25.390
the total volume would double.
00:08:25.390 --> 00:08:28.400
So we went from 100
milliliters to 200 milliliters.
00:08:28.400 --> 00:08:30.350
Therefore, since we're
doubling the volume,
00:08:30.350 --> 00:08:33.460
we're halving the
concentration of ammonia.
00:08:33.460 --> 00:08:36.850
So we can put in 0.080 molar
00:08:36.850 --> 00:08:39.620
for the concentration of ammonia.
00:08:39.620 --> 00:08:42.290
Ammonium chloride is a soluble salt.
00:08:42.290 --> 00:08:45.040
Therefore, if we have 0.20 molar
00:08:45.040 --> 00:08:47.930
for the initial concentration
of ammonium chloride,
00:08:47.930 --> 00:08:51.100
we have 0.20 more for
the initial concentration
00:08:51.100 --> 00:08:52.360
of ammonium ions.
00:08:52.360 --> 00:08:54.560
And since we're doubling the volume
00:08:54.560 --> 00:08:56.930
when we mix the two solutions together,
00:08:56.930 --> 00:08:59.350
we are halving the concentration.
00:08:59.350 --> 00:09:00.370
So the concentration
00:09:00.370 --> 00:09:04.810
of ammonium ions in
solution is 0.10 molar.
00:09:04.810 --> 00:09:05.770
So we could plug that
00:09:05.770 --> 00:09:08.750
into the Henderson-Hasselbalch equation.
00:09:08.750 --> 00:09:11.200
So here we have the
concentrations plugged in,
00:09:11.200 --> 00:09:14.320
0.080 molar is the
concentration of ammonia
00:09:14.320 --> 00:09:18.980
and 0.10 molar was the
concentration of the ammonium ion.
00:09:18.980 --> 00:09:20.680
In the Henderson-Hasselbalch equation,
00:09:20.680 --> 00:09:24.120
the pKa is the pKa value of the weak acid,
00:09:24.120 --> 00:09:27.150
which is the ammonium ion, NH4+.
00:09:27.150 --> 00:09:29.060
At 25 degrees Celsius,
00:09:29.060 --> 00:09:33.560
the pKa value of the ammonium
cation is equal to 9.25.
00:09:33.560 --> 00:09:38.096
Molar cancels and when we solve
for the pH of the solution,
00:09:38.096 --> 00:09:42.200
the pH is equal to 9.15.
00:09:42.200 --> 00:09:44.420
So this problem started with a weak base
00:09:44.420 --> 00:09:47.000
and a salt that contained
the conjugate acid
00:09:47.000 --> 00:09:48.560
to that weak base.
00:09:48.560 --> 00:09:50.850
It's also possible to
make a buffer solution
00:09:50.850 --> 00:09:53.960
starting with an aqueous
solution of a weak acid
00:09:53.960 --> 00:09:57.100
and adding a salt that
contains the conjugate base
00:09:57.100 --> 00:09:58.860
to that weak acid.
00:09:58.860 --> 00:10:00.990
For example, to make another buffer,
00:10:00.990 --> 00:10:01.823
we could have started
00:10:01.823 --> 00:10:04.320
with a solution of a
weak acid, acetic acid,
00:10:04.320 --> 00:10:05.490
and to that solution,
00:10:05.490 --> 00:10:08.830
we could have added something
like sodium acetate.
00:10:08.830 --> 00:10:10.797
Sodium acetate is a soluble salt
00:10:10.797 --> 00:10:14.070
that dissociates completely in solution
00:10:14.070 --> 00:10:17.270
to produce sodium cations
and acetate anions.
00:10:17.270 --> 00:10:20.220
And since we would have
a significant amount
00:10:20.220 --> 00:10:23.180
of both a weak acid
and its conjugate base,
00:10:23.180 --> 00:10:25.083
we would have a buffer solution.
|
Henderson–Hasselbalch equation | https://www.youtube.com/watch?v=7QgtdYiWH50 | vtt | https://www.youtube.com/api/timedtext?v=7QgtdYiWH50&ei=0lWUZfCII7a5mLAP-_6hoAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E747ABB518B6E669EA1A930ADCDE70B46DF2843B.04C22619FAEC8D197F5121F0056F414136199AD9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:02.400
- [Instructor] The
Henderson-Hasselbalch equation
00:00:02.400 --> 00:00:03.970
is an equation that's often used
00:00:03.970 --> 00:00:07.410
to calculate the pH of buffer solutions.
00:00:07.410 --> 00:00:10.470
Buffers consists of a weak
acid and its conjugate base.
00:00:10.470 --> 00:00:12.330
So for a generic weak acid,
00:00:12.330 --> 00:00:13.980
we could call that HA,
00:00:13.980 --> 00:00:16.507
and therefore, its
conjugate base would be A-.
00:00:17.370 --> 00:00:20.130
To calculate the pH of
the buffer solution,
00:00:20.130 --> 00:00:23.300
we would find the pKa of the weak acid,
00:00:23.300 --> 00:00:26.730
and to that we would add
the log of the concentration
00:00:26.730 --> 00:00:29.700
of the conjugate base
divided by the concentration
00:00:29.700 --> 00:00:31.510
of the weak acid.
00:00:31.510 --> 00:00:33.480
Let's use the
Henderson-Hasselbalch equation
00:00:33.480 --> 00:00:36.950
to calculate the pH of an
aqueous buffer solution
00:00:36.950 --> 00:00:40.290
that consists of acetic
acid and its conjugate base,
00:00:40.290 --> 00:00:42.040
the acetate anion.
00:00:42.040 --> 00:00:43.960
And let's use this particulate diagram
00:00:43.960 --> 00:00:47.520
to help us calculate the
pH of the buffer solution.
00:00:47.520 --> 00:00:49.920
Remember that the goal
of a particulate diagram
00:00:49.920 --> 00:00:52.480
is not to represent every
particle in the solution,
00:00:52.480 --> 00:00:54.500
but to give us an idea
about what's going on
00:00:54.500 --> 00:00:56.250
in the entire solution.
00:00:56.250 --> 00:00:58.640
And also, when looking at
the particulate diagrams
00:00:58.640 --> 00:01:00.060
of buffer solutions,
00:01:00.060 --> 00:01:04.160
water molecules and cations
are often left out for clarity.
00:01:04.160 --> 00:01:06.710
Let's count the number of
particles of acetic acid
00:01:06.710 --> 00:01:08.710
in our particulate diagram.
00:01:08.710 --> 00:01:12.730
So in our diagram, there are
five particles of acetic acid,
00:01:12.730 --> 00:01:17.730
and for the acetate anion,
there are also five.
00:01:18.120 --> 00:01:19.700
Because there are five particles
00:01:19.700 --> 00:01:22.250
of both acetic acid and the acetate anion,
00:01:22.250 --> 00:01:25.030
the concentration of acetic acid
00:01:25.030 --> 00:01:29.483
is equal to the concentration
of the acetate anion.
00:01:30.440 --> 00:01:32.980
Next, let's think about the
Henderson-Hasselbalch equation.
00:01:32.980 --> 00:01:35.810
Our goal is to calculate the
pH of this buffer solution
00:01:35.810 --> 00:01:38.030
represented in the particulate diagram.
00:01:38.030 --> 00:01:41.990
And so first, we need to know
the pKa of the weak acid,
00:01:41.990 --> 00:01:44.460
which is acetic acid.
00:01:44.460 --> 00:01:48.110
At 25 degrees Celsius, the
Ka value for acetic acid
00:01:48.110 --> 00:01:51.150
is equal to 1.8 times 10
to the negative fifth.
00:01:51.150 --> 00:01:53.870
The Ka value is less than
one because acetic acid
00:01:53.870 --> 00:01:55.490
is a weak acid.
00:01:55.490 --> 00:01:57.890
To find the pKa of acetic acid,
00:01:57.890 --> 00:02:01.040
we take the negative log of the Ka value.
00:02:01.040 --> 00:02:04.350
So the negative log of 1.8
times 10 to the negative fifth
00:02:04.350 --> 00:02:07.960
is equal to 4.74.
00:02:07.960 --> 00:02:10.500
So we can go back to the
Henderson-Hasselbalch equation
00:02:10.500 --> 00:02:14.820
and write that the pH is equal to the pKa,
00:02:14.820 --> 00:02:18.750
which we just calculated to be 4.74
00:02:18.750 --> 00:02:23.610
plus the log of the concentration
of the conjugate base.
00:02:23.610 --> 00:02:26.320
And the conjugate base
is the acetate anions,
00:02:26.320 --> 00:02:29.187
so let's write that in here, CH3COO-,
00:02:31.960 --> 00:02:35.430
and that's divided by the
concentration of the weak acid,
00:02:35.430 --> 00:02:39.723
which is acetic acid, CH3COOH.
00:02:40.820 --> 00:02:41.720
We've already figured out
00:02:41.720 --> 00:02:43.770
that the concentration of acetic acid
00:02:43.770 --> 00:02:47.790
is equal to the concentration
of the acetate anion.
00:02:47.790 --> 00:02:50.300
Therefore, the concentration
of the acetate anion
00:02:50.300 --> 00:02:53.060
divided by the
concentration of acetic acid
00:02:53.060 --> 00:02:55.100
is just equal to one.
00:02:55.100 --> 00:02:59.480
And the log of one is equal to zero.
00:02:59.480 --> 00:03:01.070
So let's go ahead and write that in here,
00:03:01.070 --> 00:03:04.140
the log of one is equal to zero.
00:03:04.140 --> 00:03:07.050
Therefore, the pH of the buffer solution
00:03:07.050 --> 00:03:12.050
is equal to 4.74 plus zero
00:03:12.080 --> 00:03:14.760
or just 4.74.
00:03:14.760 --> 00:03:17.070
So whenever the concentration
of the weak acid
00:03:17.070 --> 00:03:20.320
is equal to the concentration
of the conjugate base,
00:03:20.320 --> 00:03:22.000
the pH of the buffer solution
00:03:22.000 --> 00:03:25.890
is equal to the pKa of the weak acid.
00:03:25.890 --> 00:03:28.640
Let's look at another particulate diagram.
00:03:28.640 --> 00:03:32.640
We still have an acetic
acid-acetate buffer solution.
00:03:32.640 --> 00:03:34.770
However, this is a
different buffer solution
00:03:34.770 --> 00:03:36.750
than the previous problem.
00:03:36.750 --> 00:03:38.360
So let's count our particles.
00:03:38.360 --> 00:03:42.400
For acetic acid, there are six particles
00:03:42.400 --> 00:03:46.990
and for the acetate anion,
there are only four.
00:03:46.990 --> 00:03:50.410
Since we have more acetic acid particles
00:03:50.410 --> 00:03:51.720
than acetate particles,
00:03:51.720 --> 00:03:54.080
the concentration of acetic acid
00:03:54.080 --> 00:03:59.080
is greater than the concentration
of the acetate anion.
00:03:59.210 --> 00:04:01.310
We can use the
Henderson-Hasselbalch equation
00:04:01.310 --> 00:04:04.130
to think about the pH
of this buffer solution.
00:04:04.130 --> 00:04:07.010
So the pH is equal to the pKa,
00:04:07.010 --> 00:04:09.410
which we calculated in
the previous problem
00:04:09.410 --> 00:04:10.940
for acetic acid,
00:04:10.940 --> 00:04:14.120
it's 4.74 at 25 degrees Celsius,
00:04:14.120 --> 00:04:17.700
plus the log of the concentration
of the acetate anion,
00:04:17.700 --> 00:04:21.520
divided by the concentration
of acetic acid.
00:04:21.520 --> 00:04:23.750
In this case, the
concentration of acetic acid
00:04:23.750 --> 00:04:27.750
is greater than the concentration
of the acetate anion.
00:04:27.750 --> 00:04:31.280
Therefore, we have a smaller concentration
00:04:31.280 --> 00:04:34.090
divided by a larger concentration.
00:04:34.090 --> 00:04:36.270
So we have a number less than one.
00:04:36.270 --> 00:04:41.230
And the log of a number
less than one is negative.
00:04:41.230 --> 00:04:46.230
Therefore, all of this would
be negative or less than zero.
00:04:46.710 --> 00:04:51.540
So we would be subtracting
a number from 4.74.
00:04:51.540 --> 00:04:55.010
Therefore, we can say
the pH of the solution
00:04:55.010 --> 00:05:00.010
would be less than 4.74.
00:05:00.080 --> 00:05:02.160
Let's do one more particulate diagram
00:05:02.160 --> 00:05:05.460
of an acetic acid-acetate buffer solution.
00:05:05.460 --> 00:05:07.300
Once again, we count our particles.
00:05:07.300 --> 00:05:11.710
So for acetic acid, this
time, there are four particles
00:05:11.710 --> 00:05:14.160
and for the acetate anion,
00:05:14.160 --> 00:05:17.320
this time, there are six particles.
00:05:17.320 --> 00:05:21.340
Since we have only four
particles of acetic acid
00:05:21.340 --> 00:05:24.170
and six particles of the acetate anion,
00:05:24.170 --> 00:05:25.930
the concentration of acetic acid
00:05:25.930 --> 00:05:29.970
is less than the concentration
of the acetate anion
00:05:29.970 --> 00:05:32.660
or we could say the concentration
of the acetate anion
00:05:32.660 --> 00:05:36.220
is greater than the
concentration of acetic acid.
00:05:36.220 --> 00:05:38.420
Thinking about the
Henderson-Hasselbalch equation,
00:05:38.420 --> 00:05:42.320
once again, the pKa is equal to 4.74,
00:05:42.320 --> 00:05:44.050
and we need to think about the ratio
00:05:44.050 --> 00:05:46.910
of the concentration of the acetate anion
00:05:46.910 --> 00:05:49.760
to the concentration of acetic acid.
00:05:49.760 --> 00:05:52.570
For this example, the
concentration of the acetate anion
00:05:52.570 --> 00:05:56.110
is greater than the
concentration of acetic acid.
00:05:56.110 --> 00:05:59.680
Therefore, the ratio
would be greater than one,
00:05:59.680 --> 00:06:03.050
and the log of a number greater than one
00:06:03.050 --> 00:06:06.330
is positive or greater than zero.
00:06:06.330 --> 00:06:11.330
Therefore, we would be
adding a number to 4.74.
00:06:11.370 --> 00:06:13.250
So for this buffer solution,
00:06:13.250 --> 00:06:17.993
the pH would be greater than 4.74.
00:06:19.360 --> 00:06:21.320
Finally, let's summarize
what we've learned
00:06:21.320 --> 00:06:24.370
from our three different
particulate diagrams.
00:06:24.370 --> 00:06:25.560
In the first example,
00:06:25.560 --> 00:06:27.360
the concentration of the weak acid
00:06:27.360 --> 00:06:30.560
was equal to the concentration
of the conjugate base.
00:06:30.560 --> 00:06:33.410
And therefore, the pH
of the buffer solution
00:06:33.410 --> 00:06:37.110
was equal to the pKa of the weak acid.
00:06:37.110 --> 00:06:38.310
In the second example,
00:06:38.310 --> 00:06:40.040
the concentration of the weak acid
00:06:40.040 --> 00:06:43.420
was greater than the concentration
of the conjugate base.
00:06:43.420 --> 00:06:46.330
And therefore, the pH
of the buffer solution
00:06:46.330 --> 00:06:49.243
is less than the pKa of the weak acid.
00:06:50.330 --> 00:06:51.890
And in the third example,
00:06:51.890 --> 00:06:54.370
the concentration of the weak acid
00:06:54.370 --> 00:06:58.090
was less than the concentration
of the conjugate base.
00:06:58.090 --> 00:07:00.490
Therefore, the pH of the buffer solution
00:07:00.490 --> 00:07:04.080
was greater than the pKa of the weak acid.
00:07:04.080 --> 00:07:06.980
So if we know the pH of a buffer solution,
00:07:06.980 --> 00:07:10.030
we can think about the
Henderson-Hasselbalch equation
00:07:10.030 --> 00:07:12.640
to think about the relative concentrations
00:07:12.640 --> 00:07:15.690
of the weak acid and the conjugate base.
00:07:15.690 --> 00:07:18.550
For example, if we have a
particular buffer solution
00:07:18.550 --> 00:07:20.740
and we know the pH of the buffer solution
00:07:20.740 --> 00:07:23.360
is less than the pKa of the weak acid,
00:07:23.360 --> 00:07:26.110
we know that in that buffer
at that moment in time,
00:07:26.110 --> 00:07:28.190
the concentration of the weak acid
00:07:28.190 --> 00:07:32.523
is greater than the concentration
of the conjugate base.
|
Properties of buffers | https://www.youtube.com/watch?v=tZH6zvQ8Wl8 | vtt | https://www.youtube.com/api/timedtext?v=tZH6zvQ8Wl8&ei=0lWUZd--I-Gvp-oPjIm8yA0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7B713463F7EBF939CCA898885E984073B753FCE3.C0A56F8186A21671FB5B0AE1DEAE8CA153E5E4FA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.300 --> 00:00:01.830
- [Instructor] A buffer solution consists
00:00:01.830 --> 00:00:04.160
of a significant amount of a weak acid
00:00:04.160 --> 00:00:06.280
and its conjugate base.
00:00:06.280 --> 00:00:09.500
Let's say we have a generic weak acid, HA,
00:00:09.500 --> 00:00:11.820
and its conjugate base, A-.
00:00:11.820 --> 00:00:14.450
And we're gonna use some
particulate diagrams
00:00:14.450 --> 00:00:17.000
to try to understand how buffers work.
00:00:17.000 --> 00:00:19.060
So for our first particulate diagram,
00:00:19.060 --> 00:00:21.900
let's count out how many
particles we have of each.
00:00:21.900 --> 00:00:24.390
So first let's count how many HAs we have.
00:00:24.390 --> 00:00:27.953
So there's 1, 2, 3, 4, 5 HAs,
00:00:29.200 --> 00:00:34.200
and there's also, for A-,
there's 1, 2, 3, 4, 5 A minuses.
00:00:36.170 --> 00:00:38.890
And when looking at a
particulate diagram of a buffer,
00:00:38.890 --> 00:00:42.190
usually water molecules
are omitted for clarity.
00:00:42.190 --> 00:00:44.850
And also keep in mind that
this particulate diagram
00:00:44.850 --> 00:00:48.750
is just meant to represent a
small portion of the solution,
00:00:48.750 --> 00:00:50.470
so we can get an idea
about what's happening
00:00:50.470 --> 00:00:52.320
in the entire solution.
00:00:52.320 --> 00:00:54.313
Also notice that like water molecules,
00:00:54.313 --> 00:00:58.490
cations are also left out
of the particulate diagram.
00:00:58.490 --> 00:01:02.050
So we have five HA particles
and five A- particles
00:01:02.050 --> 00:01:03.840
in our aqueous solution.
00:01:03.840 --> 00:01:07.420
Having equal amounts of a weak
acid and its conjugate base
00:01:07.420 --> 00:01:09.720
is a good buffer solution.
00:01:09.720 --> 00:01:11.560
Let's see what happens
to the buffer solution
00:01:11.560 --> 00:01:14.330
if we add in a small amount of acid.
00:01:14.330 --> 00:01:17.240
So here I'm drawing in an H+ ion,
00:01:17.240 --> 00:01:19.850
and let's think about adding this H+ ion
00:01:19.850 --> 00:01:22.000
to our buffer solution.
00:01:22.000 --> 00:01:25.120
When the H+ ion is added to the solution,
00:01:25.120 --> 00:01:28.660
the base that is present
will react with the H+ ion
00:01:28.660 --> 00:01:29.960
to neutralize it.
00:01:29.960 --> 00:01:33.373
So the added H+ reacts with A- to form HA.
00:01:34.260 --> 00:01:36.030
So for the particulate diagrams,
00:01:36.030 --> 00:01:38.440
this added H+ is going to react
00:01:38.440 --> 00:01:42.140
with one of the A minuses
present in the buffer solution.
00:01:42.140 --> 00:01:46.070
So the H+ and the A- form an HA.
00:01:46.070 --> 00:01:50.210
So we're gonna go from
five HAs to six HAs.
00:01:50.210 --> 00:01:53.140
So let's look at this next
particulate diagram here.
00:01:53.140 --> 00:01:57.220
We can see there are now
six HAs in the solution,
00:01:57.220 --> 00:01:59.550
so let me write down six here.
00:01:59.550 --> 00:02:03.580
And since we started with five,
A minuses and we lost one,
00:02:03.580 --> 00:02:07.780
we should have only four
A minuses in solution now.
00:02:07.780 --> 00:02:09.340
So let's write down a four here.
00:02:09.340 --> 00:02:12.790
So you started off with
five HAs and five A minuses,
00:02:12.790 --> 00:02:15.180
and upon the addition of
a small amount of acid,
00:02:15.180 --> 00:02:18.180
the acid was neutralized by
the base that was present,
00:02:18.180 --> 00:02:22.210
and we formed six HAs and four A minuses.
00:02:22.210 --> 00:02:25.440
So a buffer solution
resists changes in pH.
00:02:25.440 --> 00:02:27.840
So the added H+ was neutralized
00:02:27.840 --> 00:02:29.770
by the presence of the base.
00:02:29.770 --> 00:02:31.920
If the buffer solution
had not been present,
00:02:31.920 --> 00:02:33.600
if we just had some water
00:02:33.600 --> 00:02:35.290
and we added some H+,
00:02:35.290 --> 00:02:37.990
the pH would have changed dramatically.
00:02:37.990 --> 00:02:41.080
One way to write the acid-base
neutralization reaction
00:02:41.080 --> 00:02:45.960
that occurred is to write
H+ plus A- goes to HA.
00:02:45.960 --> 00:02:48.690
However, since H3O+ and H+
00:02:48.690 --> 00:02:51.350
are used interchangeably in chemistry,
00:02:51.350 --> 00:02:54.170
we could have also written
the net ionic equation
00:02:54.170 --> 00:02:59.170
as H3O+ plus A- goes to HA and H2O.
00:02:59.570 --> 00:03:02.700
Next, let's go back to our
middle particulate diagram
00:03:02.700 --> 00:03:05.880
with five HA and five A-.
00:03:05.880 --> 00:03:09.430
And this time let's try
to add some hydroxide ions
00:03:09.430 --> 00:03:10.610
to the solution.
00:03:10.610 --> 00:03:12.040
So think about,
00:03:12.040 --> 00:03:13.320
let me go ahead and draw an arrow here,
00:03:13.320 --> 00:03:15.490
so we're gonna add a small amount of base
00:03:15.490 --> 00:03:18.120
to our buffer solution.
00:03:18.120 --> 00:03:21.010
The hydroxide anion will
react with the weak acid
00:03:21.010 --> 00:03:25.550
that is present, HA, to form H2O and A-.
00:03:25.550 --> 00:03:27.270
So for the particulate diagrams,
00:03:27.270 --> 00:03:30.973
we can think about this OH-
reacting with one of the HAs
00:03:31.960 --> 00:03:34.290
to form H2O and an A-.
00:03:35.760 --> 00:03:38.000
Since we're using up one of the HAs,
00:03:38.000 --> 00:03:43.000
we're gonna go from five
HAs down to four HAs.
00:03:43.150 --> 00:03:45.573
So let me write down here, four HAs.
00:03:46.890 --> 00:03:50.740
And when this HA reacts,
it's gonna turn into an A-.
00:03:50.740 --> 00:03:54.700
So we're gonna go from
five A minuses up to six.
00:03:54.700 --> 00:03:55.730
So let's count them over here.
00:03:55.730 --> 00:03:59.560
1, 2, 3, 4, 5, 6.
00:03:59.560 --> 00:04:02.440
So let's write in six A minuses.
00:04:02.440 --> 00:04:03.910
If there is no buffer present
00:04:03.910 --> 00:04:06.940
and we're just adding
hydroxide anions to water,
00:04:06.940 --> 00:04:09.560
the pH would change dramatically.
00:04:09.560 --> 00:04:11.770
However, with a buffer present,
00:04:11.770 --> 00:04:14.980
since there is a weak acid, HA, present
00:04:14.980 --> 00:04:19.040
to neutralize the added hydroxide anions,
00:04:19.040 --> 00:04:23.320
the buffer solution
resists a change to the pH.
00:04:23.320 --> 00:04:26.380
So let's summarize how
buffer solutions work.
00:04:26.380 --> 00:04:29.770
If we add a small amount of an acid, H+,
00:04:29.770 --> 00:04:31.380
to a buffer solution,
00:04:31.380 --> 00:04:34.130
the conjugate base that's present, A-,
00:04:34.130 --> 00:04:36.370
neutralizes the added acid.
00:04:36.370 --> 00:04:40.330
Therefore, the buffer solution
resists a change in pH.
00:04:40.330 --> 00:04:43.660
And if we add a small amount of a base,
00:04:43.660 --> 00:04:45.890
the weak acid that's present
00:04:45.890 --> 00:04:49.610
will neutralize the hydroxide anions.
00:04:49.610 --> 00:04:54.110
Therefore, the buffer solution
resists a change in pH.
00:04:54.110 --> 00:04:57.070
Let's say we have an aqueous
solution of acetic acid
00:04:57.070 --> 00:05:00.940
and an aqueous solution of sodium acetate.
00:05:00.940 --> 00:05:03.880
And let's say we have
equal moles of acetic acid
00:05:03.880 --> 00:05:06.170
and of sodium acetate.
00:05:06.170 --> 00:05:07.760
Mixing these two solutions together
00:05:07.760 --> 00:05:10.180
would form a buffer solution.
00:05:10.180 --> 00:05:12.980
To understand why this
forms a buffer solution,
00:05:12.980 --> 00:05:15.160
let's first think about acetic acid.
00:05:15.160 --> 00:05:17.130
Acetic acid is a weak acid
00:05:17.130 --> 00:05:21.040
and only partially ionizes
in aqueous solution.
00:05:21.040 --> 00:05:22.670
Therefore, in aqueous solution,
00:05:22.670 --> 00:05:25.953
we have mostly acetic acid, CH3COOH.
00:05:28.120 --> 00:05:30.710
Sodium acetate is a soluble salt
00:05:30.710 --> 00:05:34.090
and it dissociates completely
in aqueous solution.
00:05:34.090 --> 00:05:35.670
Therefore, in aqueous solution,
00:05:35.670 --> 00:05:38.220
we have sodium cations and
acetate anions, CH3COO-.
00:05:43.020 --> 00:05:47.030
The acetate anion is the
conjugate base to acetic acid.
00:05:47.030 --> 00:05:49.330
Therefore, in aqueous solution,
00:05:49.330 --> 00:05:52.410
we have a weak acid
and its conjugate base,
00:05:52.410 --> 00:05:54.950
and so we have a buffer solution.
00:05:54.950 --> 00:05:56.940
If we try adding a small amount of acid
00:05:56.940 --> 00:05:58.660
to the buffer solution,
00:05:58.660 --> 00:06:01.860
the conjugate base
that's present will react
00:06:01.860 --> 00:06:04.170
with the acid and neutralize it.
00:06:04.170 --> 00:06:06.930
So in the balanced net ionic equation,
00:06:06.930 --> 00:06:10.030
the added acid hydronium ion, H3O+,
00:06:10.030 --> 00:06:15.030
reacts with the acetate anion
to form acetic acid and water.
00:06:15.030 --> 00:06:18.300
So the added hydronium
ion was neutralized,
00:06:18.300 --> 00:06:22.330
and the buffer has resisted
a dramatic change in pH.
00:06:22.330 --> 00:06:24.380
If we try adding a small amount of base
00:06:24.380 --> 00:06:26.090
to the buffer solution,
00:06:26.090 --> 00:06:28.090
the weak acid that is present
00:06:28.090 --> 00:06:30.690
will neutralize the added base.
00:06:30.690 --> 00:06:33.340
So in the balanced net ionic equation,
00:06:33.340 --> 00:06:36.090
hydroxide anions react with acetic acid
00:06:36.090 --> 00:06:39.330
to form the acetate anion and water.
00:06:39.330 --> 00:06:42.670
So the added base was neutralized.
00:06:42.670 --> 00:06:43.820
So to summarize,
00:06:43.820 --> 00:06:46.380
the acetic acid-acetate buffer system
00:06:46.380 --> 00:06:48.600
resists dramatic changes in pH
00:06:48.600 --> 00:06:51.680
when small amounts of
acid or base are added.
00:06:51.680 --> 00:06:52.550
And I just noticed,
00:06:52.550 --> 00:06:55.650
I forgot to include the
L for liquid for water
00:06:55.650 --> 00:06:58.153
in the balanced net ionic equations.
|
Cellular respiration | https://www.youtube.com/watch?v=NUFbQUOLAXc | vtt | https://www.youtube.com/api/timedtext?v=NUFbQUOLAXc&ei=0lWUZePvIPScp-oP4LuSqAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=DB2E321643DA16A31B0CBE102EB83DE64B8FD269.6DDFDBF23FECE14DA00A974896745B446A592DAD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:01.153
- [Instructor] In this video,
00:00:01.153 --> 00:00:03.170
we're going to talk about
cellular respiration,
00:00:03.170 --> 00:00:04.865
which sounds like a very fancy thing,
00:00:04.865 --> 00:00:08.466
but it's really just about
the biochemical processes
00:00:08.466 --> 00:00:10.520
that can take things
00:00:10.520 --> 00:00:13.170
that we find in food and convert
00:00:13.170 --> 00:00:15.254
it into forms of energy that we can use
00:00:15.254 --> 00:00:19.130
to do things like run and
maintain our body temperature,
00:00:19.130 --> 00:00:21.321
and maintain body homeostasis.
00:00:21.321 --> 00:00:25.780
So to get into the chemistry
of cellular respiration,
00:00:25.780 --> 00:00:28.490
and this really is an overview video,
00:00:28.490 --> 00:00:32.460
we will start with the chemical
equation for respiration.
00:00:32.460 --> 00:00:34.686
And what it's all about is a series
00:00:34.686 --> 00:00:37.650
of steps that when you
look at them in aggregate,
00:00:37.650 --> 00:00:40.138
you're starting with the
glucose right over here,
00:00:40.138 --> 00:00:42.086
using oxygen, and that's why we have
00:00:42.086 --> 00:00:44.090
to breathe really hard in order
00:00:44.090 --> 00:00:46.080
to do our cellular respiration.
00:00:46.080 --> 00:00:48.450
And it's going to yield
some carbon dioxide,
00:00:48.450 --> 00:00:51.120
which we also need to
breathe hard to exhale,
00:00:51.120 --> 00:00:53.700
some water, and some energy.
00:00:53.700 --> 00:00:55.600
Now that energy he is in the form of heat,
00:00:55.600 --> 00:00:57.580
which can help us maintain
our body temperature,
00:00:57.580 --> 00:00:59.360
especially if it's cold outside side.
00:00:59.360 --> 00:01:01.322
But also ATP.
00:01:01.322 --> 00:01:05.449
Now you might be wondering, what is ATP?
00:01:05.449 --> 00:01:07.930
And to help us answer that question,
00:01:07.930 --> 00:01:10.110
I will show you a picture of ATP,
00:01:10.110 --> 00:01:11.691
and I will also show you a picture
00:01:11.691 --> 00:01:14.500
of glucose or a visualization of it.
00:01:14.500 --> 00:01:17.032
Now you don't have to memorize
what these structures are,
00:01:17.032 --> 00:01:20.793
but what's really going
on here is that glucose,
00:01:20.793 --> 00:01:23.970
as you are able to shape
it into other things,
00:01:23.970 --> 00:01:26.030
as you're able to break
the bonds in glucose,
00:01:26.030 --> 00:01:29.130
and having its constituents
form bonds with other things,
00:01:29.130 --> 00:01:31.200
that has a net release of energy.
00:01:31.200 --> 00:01:32.641
And that energy can be used
00:01:32.641 --> 00:01:34.190
to take what's known
00:01:34.190 --> 00:01:37.490
as ADP that has two phosphate groups,
00:01:37.490 --> 00:01:41.120
and add a third phosphate
group onto it right over here.
00:01:41.120 --> 00:01:43.010
Now you see it might
say, why is that useful?
00:01:43.010 --> 00:01:45.883
Why is that a more readily
usable form of energy?
00:01:45.883 --> 00:01:48.441
Well, as you go forward
in your biological journey
00:01:48.441 --> 00:01:50.410
or your understanding of biology,
00:01:50.410 --> 00:01:52.896
you'll see that ATP molecules like this,
00:01:52.896 --> 00:01:54.650
by losing that phosphate
00:01:54.650 --> 00:01:57.100
and allowing that phosphate
to bond to other things
00:01:57.100 --> 00:01:58.359
can actually release energy
00:01:58.359 --> 00:01:59.990
and can fuel muscles,
00:01:59.990 --> 00:02:02.352
can fuel other biological processes.
00:02:02.352 --> 00:02:04.180
Now to understand the steps of it,
00:02:04.180 --> 00:02:06.563
we will start in the cytosol of a cell,
00:02:06.563 --> 00:02:11.180
where a process known as
glycolysis takes place.
00:02:11.180 --> 00:02:15.410
And glycolysis literally
means the breaking of glucose.
00:02:15.410 --> 00:02:18.022
So let me write it down, glycolysis.
00:02:18.022 --> 00:02:21.690
And what it does is it
breaks each glucose molecule
00:02:21.690 --> 00:02:25.590
into two molecules known as pyruvate.
00:02:25.590 --> 00:02:27.340
Now just that process alone,
00:02:27.340 --> 00:02:29.146
and we'll go into much
more depth in other videos,
00:02:29.146 --> 00:02:31.686
does start to produce some ATPs,
00:02:31.686 --> 00:02:36.686
and also helps produce some
molecules known as NADH.
00:02:36.950 --> 00:02:38.920
And I know this is all
sounding very complex.
00:02:38.920 --> 00:02:42.784
But you will have a
molecule known as NAD+,
00:02:42.784 --> 00:02:44.890
if you want to know what it looks like,
00:02:44.890 --> 00:02:46.180
it looks like this.
00:02:46.180 --> 00:02:49.010
Once again, don't get too
bogged down in the details.
00:02:49.010 --> 00:02:50.120
It is worth noting,
00:02:50.120 --> 00:02:53.580
NAD stands for nicotinamide
adenine dinucleotide.
00:02:53.580 --> 00:02:54.880
And we also noticed that ATP stands
00:02:54.880 --> 00:02:57.670
for adenosine triphosphate.
00:02:57.670 --> 00:03:00.880
And so you have these
very molecular components
00:03:00.880 --> 00:03:02.930
that are showing up in
different places in biology,
00:03:02.930 --> 00:03:05.750
and you might also
recognize that adenosine
00:03:05.750 --> 00:03:08.550
is involved in the
formation of DNA as well.
00:03:08.550 --> 00:03:09.383
So once again,
00:03:09.383 --> 00:03:12.830
these molecules are adapted
and reused all over the place.
00:03:12.830 --> 00:03:14.641
But going back to our journey
00:03:14.641 --> 00:03:18.148
of cellular respiration, an NAD+ molecule,
00:03:18.148 --> 00:03:21.340
if you were to add to
that two hydrogen protons,
00:03:21.340 --> 00:03:23.457
and this is the important
part, two electrons,
00:03:23.457 --> 00:03:27.652
it will be reduced to NADH.
00:03:27.652 --> 00:03:30.760
And remember, reduction is
the gaining of electrons,
00:03:30.760 --> 00:03:32.150
which is happening right over here.
00:03:32.150 --> 00:03:34.410
And the reason why these two electrons
00:03:34.410 --> 00:03:35.609
are really interesting is,
00:03:35.609 --> 00:03:38.370
in NADH, they're in a
fairly high energy state.
00:03:38.370 --> 00:03:39.480
And as we'll see,
00:03:39.480 --> 00:03:41.112
as they're able to go to other molecules
00:03:41.112 --> 00:03:43.440
and go to lower and lower energy states,
00:03:43.440 --> 00:03:44.765
they're able to do useful things
00:03:44.765 --> 00:03:48.450
that can eventually end up
in the production of ATP.
00:03:48.450 --> 00:03:50.275
It's essentially a transfer of energy.
00:03:50.275 --> 00:03:53.660
So glycolysis is directly
producing some ATPs,
00:03:53.660 --> 00:03:57.780
and it's also reducing NAD
in this way to produce NADH.
00:03:57.780 --> 00:04:00.857
For the next stage, we have
to go into the mitochondria,
00:04:00.857 --> 00:04:04.710
which is often known as
the powerhouse of the cell,
00:04:04.710 --> 00:04:07.283
where now our pyruvate will enter
00:04:07.283 --> 00:04:11.050
into the mitochondrial
matrix right over here.
00:04:11.050 --> 00:04:15.102
And that's where the
citric acid cycle occurs.
00:04:15.102 --> 00:04:19.326
And the citric acid cycle
is going to use a derivative
00:04:19.326 --> 00:04:22.654
of the pyruvate, which
we got from glycolysis.
00:04:22.654 --> 00:04:24.450
You don't have to know all the details,
00:04:24.450 --> 00:04:25.709
it's called acetylcholine.
00:04:25.709 --> 00:04:28.690
But that's going to go through
a series of transformations.
00:04:28.690 --> 00:04:30.460
And the reason why it's called a cycle,
00:04:30.460 --> 00:04:33.280
there's some molecules that
react with the acetyl-CoA,
00:04:33.280 --> 00:04:35.180
and then through a series
of transformations,
00:04:35.180 --> 00:04:36.710
get back to where they started.
00:04:36.710 --> 00:04:38.740
And the reason why it's
called a citric acid cycle
00:04:38.740 --> 00:04:40.345
is one of those intermediaries is citrate.
00:04:40.345 --> 00:04:45.330
But this process, once again,
produces more ATPs directly,
00:04:45.330 --> 00:04:46.868
but it also produces more NADHs,
00:04:46.868 --> 00:04:49.788
and it also is able to
do something similar
00:04:49.788 --> 00:04:51.260
to another molecule.
00:04:51.260 --> 00:04:53.660
And once again, I'm not going
to go into all of the details.
00:04:53.660 --> 00:04:55.830
But we're able to go
from another molecule,
00:04:55.830 --> 00:04:59.343
known as flavin adenine dinucleotide, FAD,
00:04:59.343 --> 00:05:01.630
plus two hydrogen protons,
00:05:01.630 --> 00:05:04.733
plus two electrons to get to FADH2,
00:05:06.810 --> 00:05:09.102
which once again is an
interesting molecule,
00:05:09.102 --> 00:05:12.470
because it has these electrons
in a higher energy level,
00:05:12.470 --> 00:05:15.130
which, through a series
of molecular processes,
00:05:15.130 --> 00:05:17.716
which you'll go into much
detail in future courses on,
00:05:17.716 --> 00:05:19.860
you are able to do useful work.
00:05:19.860 --> 00:05:21.879
You're able to transfer energy.
00:05:21.879 --> 00:05:24.464
So once you have a few ATPs
00:05:24.464 --> 00:05:27.504
and a bunch of NADHs and FADHs,
00:05:27.504 --> 00:05:30.010
you then go into something known
00:05:30.010 --> 00:05:32.570
as the electron transport chain.
00:05:32.570 --> 00:05:35.000
And this is essentially
where those electrons go
00:05:35.000 --> 00:05:36.060
from a high energy state
00:05:36.060 --> 00:05:38.120
and they get transferred
from one molecule to another,
00:05:38.120 --> 00:05:40.480
actually along this
membrane right over here.
00:05:40.480 --> 00:05:41.491
And as they do, the proteins
00:05:41.491 --> 00:05:43.530
that they are interacting with are able
00:05:43.530 --> 00:05:45.010
to use that energy in order
00:05:45.010 --> 00:05:46.720
to pump hydrogen protons
00:05:46.720 --> 00:05:50.210
into this intermembrane
space of the mitochondria.
00:05:50.210 --> 00:05:53.078
And then that concentration
gradient of hydrogen protons,
00:05:53.078 --> 00:05:56.000
it's released through another enzyme,
00:05:56.000 --> 00:05:59.385
which is actually able to
produce the actual ATP.
00:05:59.385 --> 00:06:01.863
So I know that is a lot to process,
00:06:01.863 --> 00:06:04.440
but this is meant to be just an overview.
00:06:04.440 --> 00:06:06.040
I know you might have a lot of questions
00:06:06.040 --> 00:06:08.120
as I did the first time
that I learned this.
00:06:08.120 --> 00:06:09.499
But the important thing to realize,
00:06:09.499 --> 00:06:11.440
that glucose does store energy,
00:06:11.440 --> 00:06:12.840
but we don't use it directly.
00:06:12.840 --> 00:06:14.540
We have to go through cellular respiration
00:06:14.540 --> 00:06:17.060
to convert that glucose into ATPs,
00:06:17.060 --> 00:06:18.637
which is more readily used by cells.
00:06:18.637 --> 00:06:20.770
Now the various steps are also going
00:06:20.770 --> 00:06:22.570
to produce heat as they release energy,
00:06:22.570 --> 00:06:25.101
which could also be useful for the cell.
00:06:25.101 --> 00:06:28.660
Now, one final point, you
might say glucose, well,
00:06:28.660 --> 00:06:30.050
that's only one form of food.
00:06:30.050 --> 00:06:31.376
You showed a picture of bread initially.
00:06:31.376 --> 00:06:33.559
Well, carbohydrates are made up of chains
00:06:33.559 --> 00:06:35.425
of simple sugars like glucose.
00:06:35.425 --> 00:06:36.940
And if we're thinking about things
00:06:36.940 --> 00:06:39.255
like protein or fats, which
you could also use for energy,
00:06:39.255 --> 00:06:40.921
those are going to be adapted
00:06:40.921 --> 00:06:44.588
and enter at different phases
of cellular respiration.
00:06:44.588 --> 00:06:45.970
But at some point, you're going
00:06:45.970 --> 00:06:47.360
to have a very similar process.
00:06:47.360 --> 00:06:50.728
So I lied, I actually
have one last, last point.
00:06:50.728 --> 00:06:55.384
We talked a lot about glucose
as it enters into glycolysis,
00:06:55.384 --> 00:06:58.300
and then the pyruvate enters
into the mitochondria.
00:06:58.300 --> 00:06:59.379
But what about the oxygen?
00:06:59.379 --> 00:07:02.281
Where's that involvement as an input?
00:07:02.281 --> 00:07:05.915
Well, the oxygen is the
eventual electronic sector
00:07:05.915 --> 00:07:08.113
at the end of the
electron transport chain.
00:07:08.113 --> 00:07:10.546
And not only is it accepting electrons,
00:07:10.546 --> 00:07:12.539
it's accepting hydrogen protons.
00:07:12.539 --> 00:07:17.248
So the oxygen is an input into
the electron transport chain.
00:07:17.248 --> 00:07:20.070
And then once it gets those electrons
00:07:20.070 --> 00:07:21.670
and those hydrogen protons,
00:07:21.670 --> 00:07:23.680
well, you can imagine what the output is.
00:07:23.680 --> 00:07:25.959
You add some oxygen to some
hydrogen protons and electrons,
00:07:25.959 --> 00:07:28.730
you're going to get water.
00:07:28.730 --> 00:07:31.420
You're going to get this
output right over here.
00:07:31.420 --> 00:07:33.460
And what about the carbon dioxide?
00:07:33.460 --> 00:07:34.368
Well, the carbon dioxide
00:07:34.368 --> 00:07:38.713
is going to be an output
of the citric acid cycle.
|
Cell division and organism growth | https://www.youtube.com/watch?v=q2CSqC_waE8 | vtt | https://www.youtube.com/api/timedtext?v=q2CSqC_waE8&ei=0lWUZdyQI-Cjp-oPp-y7KA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=37F1851C3EB15A641AACF14AE85AA6BC7C595D32.BE67F18B0EA8FC2B9B867652A2ADFED5F531A17E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.340 --> 00:00:01.310
- [Lecturer] In this
video, we're gonna talk
00:00:01.310 --> 00:00:05.070
about cell division and organism growth.
00:00:05.070 --> 00:00:06.840
Or another way to think about it is,
00:00:06.840 --> 00:00:09.300
how do we start with fertilization?
00:00:09.300 --> 00:00:11.270
And we talk about this in other videos,
00:00:11.270 --> 00:00:14.010
but in sexually reproducing species,
00:00:14.010 --> 00:00:18.140
each individual starts off as a cell
00:00:18.140 --> 00:00:21.010
that is the result of the fusion
00:00:21.010 --> 00:00:24.990
between a sperm and an
egg, between two gametes.
00:00:24.990 --> 00:00:27.550
And each of these gametes have half
00:00:27.550 --> 00:00:31.700
of the genetic material
needed to make that organism.
00:00:31.700 --> 00:00:35.400
So once they fuse, once the
fertilization has happened,
00:00:35.400 --> 00:00:36.670
you are now diploid.
00:00:36.670 --> 00:00:38.570
So you're haploid when you have half
00:00:38.570 --> 00:00:40.860
of the genetic material, as
each of these individually
00:00:40.860 --> 00:00:42.270
have each of these gametes,
00:00:42.270 --> 00:00:45.340
and then you become
diploid once it's fused.
00:00:45.340 --> 00:00:48.370
Well, once it's fused, that fertilized egg
00:00:48.370 --> 00:00:51.840
will then start to divide and replicate.
00:00:51.840 --> 00:00:54.560
And so a short period of time later,
00:00:54.560 --> 00:00:57.310
you might have eight cells
that has divided in two,
00:00:57.310 --> 00:00:58.320
it'll first divide into two,
00:00:58.320 --> 00:00:59.580
then those two will become four,
00:00:59.580 --> 00:01:02.640
those four will become eight,
the eight will become 16,
00:01:02.640 --> 00:01:05.230
and you keep dividing,
and before you know it,
00:01:05.230 --> 00:01:07.210
you have trillions of cells
00:01:07.210 --> 00:01:09.420
on the order of 30 to 40 trillion
00:01:09.420 --> 00:01:11.740
and you could create this
very handsome organism
00:01:11.740 --> 00:01:13.340
right over here.
00:01:13.340 --> 00:01:14.860
But an interesting question is,
00:01:14.860 --> 00:01:16.830
how does that division happen?
00:01:16.830 --> 00:01:18.670
And are the cells identical?
00:01:18.670 --> 00:01:21.180
Do they have the same
identical genetic material?
00:01:21.180 --> 00:01:23.340
But if they are, how do they differentiate
00:01:23.340 --> 00:01:25.100
into all of the different types of cells
00:01:25.100 --> 00:01:26.980
that make this handsome organism?
00:01:26.980 --> 00:01:28.860
The skin cells versus the heart cells
00:01:28.860 --> 00:01:30.320
versus the nerve cells?
00:01:30.320 --> 00:01:32.390
And this process of cell division
00:01:32.390 --> 00:01:36.510
in which a parent cell divides
into two new daughter cells,
00:01:36.510 --> 00:01:39.470
each of which is genetically
identical to the parent cell,
00:01:39.470 --> 00:01:41.603
is known as mitosis.
00:01:42.600 --> 00:01:45.463
And so let's dig into
mitosis a little bit.
00:01:46.360 --> 00:01:48.900
So let's start with two daughter cells
00:01:48.900 --> 00:01:51.590
from a previous round of mitosis.
00:01:51.590 --> 00:01:53.910
Now, this would not be a human cell.
00:01:53.910 --> 00:01:57.600
What we're looking at is four
chromosomes in two pairs.
00:01:57.600 --> 00:01:59.300
And the way that they've color-coded it,
00:01:59.300 --> 00:02:02.590
two of these are blue
and two of these are red.
00:02:02.590 --> 00:02:06.910
While a human cell would have
23 pairs or 46 chromosomes,
00:02:06.910 --> 00:02:08.540
but this is a eukaryotic cell.
00:02:08.540 --> 00:02:10.420
The genetic material is inside
00:02:10.420 --> 00:02:12.660
of the nucleus right over here.
00:02:12.660 --> 00:02:15.970
And just to understand what
these long strands are,
00:02:15.970 --> 00:02:19.790
these are chromosomes in
their non-condensed form.
00:02:19.790 --> 00:02:21.720
And a chromosome you can really view
00:02:21.720 --> 00:02:24.520
as a long strand of DNA,
00:02:24.520 --> 00:02:27.230
and you're going to have
segments of that DNA
00:02:27.230 --> 00:02:29.830
that code for specific proteins,
00:02:29.830 --> 00:02:33.330
and those segments are what we call genes.
00:02:33.330 --> 00:02:35.350
In a given chromosome pair,
00:02:35.350 --> 00:02:38.290
you will code for the same genes,
00:02:38.290 --> 00:02:41.170
but you might have different
versions of the same gene.
00:02:41.170 --> 00:02:42.640
Maybe this gene right over here
00:02:42.640 --> 00:02:45.030
contributes to hair color in some way,
00:02:45.030 --> 00:02:47.710
and then this other one
contributes in the same way,
00:02:47.710 --> 00:02:49.980
but it might lead to a
different hair color.
00:02:49.980 --> 00:02:51.900
So each of these chromosomes in a pair,
00:02:51.900 --> 00:02:54.590
we call them homologous
or homologous pairs.
00:02:54.590 --> 00:02:56.640
They're coding for the same genes.
00:02:56.640 --> 00:02:58.200
They're the same set of genes,
00:02:58.200 --> 00:02:59.610
but they might have different versions
00:02:59.610 --> 00:03:02.360
of those genes or different alleles.
00:03:02.360 --> 00:03:04.010
So that's what we're seeing here.
00:03:04.010 --> 00:03:07.420
Now to prepare for mitosis,
what we need to see
00:03:07.420 --> 00:03:11.220
is each of these chromosomes
need to replicate,
00:03:11.220 --> 00:03:14.920
and once they do, the
cell might look like this.
00:03:14.920 --> 00:03:16.060
Now it's hard to see it here,
00:03:16.060 --> 00:03:18.400
but the two copies that are now replicated
00:03:18.400 --> 00:03:21.740
and connected at the center,
we call them sister chromatids.
00:03:21.740 --> 00:03:23.870
And we can see that a little bit clearer
00:03:23.870 --> 00:03:26.450
in the early phases of mitosis.
00:03:26.450 --> 00:03:29.210
So first, we see that the chromosomes
00:03:29.210 --> 00:03:32.620
have condensed into what
we classically imagine
00:03:32.620 --> 00:03:35.180
as chromosomes when we look
at it into a microscope.
00:03:35.180 --> 00:03:38.180
This is really happening
in preparation for mitosis,
00:03:38.180 --> 00:03:40.520
in preparation for cell division.
00:03:40.520 --> 00:03:43.360
And so you see those two homologous pairs,
00:03:43.360 --> 00:03:46.070
and you can see each of those chromosomes
00:03:46.070 --> 00:03:49.140
actually now consists of
two sister chromatids,
00:03:49.140 --> 00:03:51.810
one over here, one over there.
00:03:51.810 --> 00:03:53.070
As we go through mitosis,
00:03:53.070 --> 00:03:55.710
they're going to separate
into individual chromosomes
00:03:55.710 --> 00:03:58.220
that are actually just
copies of each other.
00:03:58.220 --> 00:03:59.650
Now, the other thing that we're seeing
00:03:59.650 --> 00:04:01.750
in this early phase of mitosis
00:04:01.750 --> 00:04:05.180
is that the nuclear envelope
starts to break down,
00:04:05.180 --> 00:04:06.500
and we're gonna see why that's important,
00:04:06.500 --> 00:04:08.530
because we're gonna have to
separate the chromosomes.
00:04:08.530 --> 00:04:10.160
Now, the other thing that we see,
00:04:10.160 --> 00:04:12.050
and in other future biology classes
00:04:12.050 --> 00:04:13.800
you'll go into much more detail,
00:04:13.800 --> 00:04:17.320
is the mitotic spindle
is starting to form.
00:04:17.320 --> 00:04:19.390
Now, we don't have to
go into all the details
00:04:19.390 --> 00:04:21.510
of the different parts
of the mitotic spindle,
00:04:21.510 --> 00:04:25.010
but imagine a bunch of structures
made primarily by protein
00:04:25.010 --> 00:04:27.300
that are actually going to act to allow
00:04:27.300 --> 00:04:29.990
the mitosis to happen,
to grab the chromosomes,
00:04:29.990 --> 00:04:33.800
to pull them apart, to allow
the cell to change its shape
00:04:33.800 --> 00:04:36.830
so that it will eventually
be able to divide.
00:04:36.830 --> 00:04:41.800
But after that, we go into
the middle phase of mitosis.
00:04:41.800 --> 00:04:44.610
So as we enter into the
middle phases of mitosis,
00:04:44.610 --> 00:04:46.190
we can see now that the chromosomes
00:04:46.190 --> 00:04:47.510
are aligned at the center,
00:04:47.510 --> 00:04:49.490
and they've actually now been attached
00:04:49.490 --> 00:04:51.740
to the mitotic spindle, which
is going to be important,
00:04:51.740 --> 00:04:54.440
because that's the machinery
that's going to pull them apart
00:04:54.440 --> 00:04:57.040
and bring them to the
different sides of the cell.
00:04:57.040 --> 00:04:59.520
And as we continue through
the middle phases of mitosis,
00:04:59.520 --> 00:05:01.340
we see that right over there,
00:05:01.340 --> 00:05:04.340
that those sister chromatids
are now pulled apart
00:05:04.340 --> 00:05:06.380
and they are copies of each other.
00:05:06.380 --> 00:05:08.410
They became copies of
each other back here,
00:05:08.410 --> 00:05:10.180
where the DNA originally replicated
00:05:10.180 --> 00:05:12.470
when it wasn't in its condensed form.
00:05:12.470 --> 00:05:14.290
But I think you see where this is going.
00:05:14.290 --> 00:05:17.150
As the mitotic spindle
pulls on these chromosomes,
00:05:17.150 --> 00:05:20.460
we then enter into the
late phases of mitosis.
00:05:20.460 --> 00:05:23.750
And you can see here that
the sister chromatids,
00:05:23.750 --> 00:05:25.390
which are now individual chromosomes,
00:05:25.390 --> 00:05:29.810
have been pulled to either side
of that now elongated cell.
00:05:29.810 --> 00:05:31.760
You can see that once they're there,
00:05:31.760 --> 00:05:35.850
a nuclear envelope begins to
form again on either side,
00:05:35.850 --> 00:05:38.160
and then the mitotic spindle breaks down
00:05:38.160 --> 00:05:40.520
and the splitting of the cytoplasm finally
00:05:40.520 --> 00:05:44.680
into two daughter cells
is known as cytokinesis.
00:05:44.680 --> 00:05:46.910
So it's pretty mind boggling to realize
00:05:46.910 --> 00:05:49.140
that this is going on in
your body continuously,
00:05:49.140 --> 00:05:51.380
and this is what allowed
all of us to start
00:05:51.380 --> 00:05:54.170
as a single-celled
organism, a fertilized egg,
00:05:54.170 --> 00:05:57.740
and become an organism made
of tens of trillions of cells.
00:05:57.740 --> 00:05:59.900
Now, I haven't gone into detail yet.
00:05:59.900 --> 00:06:01.640
Even though the great
majority of our cells
00:06:01.640 --> 00:06:03.410
have the exact same genetics,
00:06:03.410 --> 00:06:05.400
they are actually able to differentiate,
00:06:05.400 --> 00:06:07.460
express different parts of the genetics
00:06:07.460 --> 00:06:09.820
based on the roles that they need to play,
00:06:09.820 --> 00:06:12.870
but we will talk about
that in future videos.
00:06:12.870 --> 00:06:14.530
It's also important to realize
00:06:14.530 --> 00:06:17.240
that mitosis isn't just
about growing an organism.
00:06:17.240 --> 00:06:19.290
It's also about maintaining an organism
00:06:19.290 --> 00:06:21.760
and doing tissue repair for an organism.
00:06:21.760 --> 00:06:23.010
So I'll leave you there.
00:06:23.010 --> 00:06:24.900
Look at your hands, look at your arms,
00:06:24.900 --> 00:06:26.572
look in the mirror and just realize
00:06:26.572 --> 00:06:31.030
that you are an organism
of 30 to 40 trillion cells
00:06:31.030 --> 00:06:32.590
that all started with one cell
00:06:32.590 --> 00:06:36.023
through many, many,
many rounds of mitosis.
|
Natural selection and evolution | https://www.youtube.com/watch?v=ifyEocJ2Rog | vtt | https://www.youtube.com/api/timedtext?v=ifyEocJ2Rog&ei=0lWUZYH8I7qfp-oP4MqeKA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=94AAB86A3EA6D9119854FEA6E40936EE007441B9.9A3F1A6948DD67664724008A5AFB8919882BB4D1&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.224 --> 00:00:02.480
- [Instructor] Many of you
all are probably familiar
00:00:02.480 --> 00:00:04.640
with the term evolution,
and some of you all,
00:00:04.640 --> 00:00:05.820
I'm guessing, are also familiar
00:00:05.820 --> 00:00:08.040
with the term natural selection,
although it isn't used
00:00:08.040 --> 00:00:10.250
quite as much as evolution.
00:00:10.250 --> 00:00:11.550
And what we're going to do in this video
00:00:11.550 --> 00:00:13.980
is see how these are
connected, but we're also
00:00:13.980 --> 00:00:16.640
going to address some
potential misconceptions
00:00:16.640 --> 00:00:19.320
that folks have about evolution.
00:00:19.320 --> 00:00:21.860
So when a lot of people
think of evolution,
00:00:21.860 --> 00:00:23.830
they think of a diagram or an image
00:00:23.830 --> 00:00:25.400
that looks something like this.
00:00:25.400 --> 00:00:27.670
They can see what they
would consider to be
00:00:27.670 --> 00:00:31.190
a more primitive ancestor evolving into
00:00:31.190 --> 00:00:35.810
a more sophisticated, a more
modern type of organism.
00:00:35.810 --> 00:00:38.210
And this is going from
some type of primitive ape,
00:00:38.210 --> 00:00:40.880
all the way to human beings.
00:00:40.880 --> 00:00:43.040
Now there's some aspects of this diagram
00:00:43.040 --> 00:00:47.400
that give the right idea, that
evolution is the phenomenon
00:00:47.400 --> 00:00:50.510
that organisms over time can evolve,
00:00:50.510 --> 00:00:53.640
can change in their
traits, that can actually
00:00:53.640 --> 00:00:55.920
become different species.
00:00:55.920 --> 00:00:57.640
Now the one thing about
this diagram that might
00:00:57.640 --> 00:01:00.840
be misleading is calling
this character primitive
00:01:00.840 --> 00:01:03.140
and somehow imagining
that this one in the front
00:01:03.140 --> 00:01:06.080
is better or more advanced.
00:01:06.080 --> 00:01:07.940
Evolution doesn't necessarily go
00:01:07.940 --> 00:01:10.930
from good to bad or primitive to advanced.
00:01:10.930 --> 00:01:14.030
It's really just continual change based on
00:01:14.030 --> 00:01:16.740
what is most suitable for the environment
00:01:16.740 --> 00:01:18.780
in which the organisms are in.
00:01:18.780 --> 00:01:21.220
And this can take millions of years.
00:01:21.220 --> 00:01:23.990
For example, the common
ancestor of human beings
00:01:23.990 --> 00:01:27.850
and other apes like
chimpanzees or gorillas
00:01:27.850 --> 00:01:31.710
can be five, 10 million-plus
years in the past,
00:01:31.710 --> 00:01:33.900
but it can also happen
right before our eyes.
00:01:33.900 --> 00:01:36.270
For example, every year
we have a new flu virus
00:01:36.270 --> 00:01:39.280
because the flu virus
is constantly evolving
00:01:39.280 --> 00:01:40.990
through mutation.
00:01:40.990 --> 00:01:42.700
We have the Coronavirus and we're having
00:01:42.700 --> 00:01:44.240
new variants of that, it seems like,
00:01:44.240 --> 00:01:45.990
almost every few months.
00:01:45.990 --> 00:01:49.300
That is evolution happening
right before our eyes.
00:01:49.300 --> 00:01:52.780
But the key question is, how
does this actually happen?
00:01:52.780 --> 00:01:55.600
Does the DNA know to
change into something else?
00:01:55.600 --> 00:01:57.840
Well, clearly not. The
DNA is not sentient.
00:01:57.840 --> 00:02:00.310
It is not somehow constructing itself.
00:02:00.310 --> 00:02:03.260
And that's where natural
selection comes into the picture.
00:02:03.260 --> 00:02:06.220
So let's imagine a
population, and I'm gonna
00:02:06.220 --> 00:02:08.180
think about a very abstract population
00:02:08.180 --> 00:02:11.150
of these little circle-shaped things.
00:02:11.150 --> 00:02:13.760
And an important characteristic
for evolution to happen
00:02:13.760 --> 00:02:18.170
is that you need variation
in the population.
00:02:18.170 --> 00:02:20.550
And we talk about variation,
we're talking about
00:02:20.550 --> 00:02:23.677
different expressed
traits, and you might ask,
00:02:23.677 --> 00:02:26.960
"Where does that variation
actually come from?"
00:02:26.960 --> 00:02:29.350
Well, it's going to come from mutation.
00:02:29.350 --> 00:02:31.930
I talked about variation
when we think about viruses,
00:02:31.930 --> 00:02:34.050
the flu virus or the Coronavirus,
00:02:34.050 --> 00:02:36.890
and it can also come
from sexual reproduction,
00:02:36.890 --> 00:02:39.690
and we go into a lot of
detail in other videos
00:02:39.690 --> 00:02:42.940
how sexual reproduction mixes and matches
00:02:42.940 --> 00:02:45.900
all of the potential alleles
that are in a population
00:02:45.900 --> 00:02:47.810
so that different
members of the population
00:02:47.810 --> 00:02:50.370
are getting different
combinations of those alleles,
00:02:50.370 --> 00:02:53.120
and so that contributes to variation.
00:02:53.120 --> 00:02:57.290
And that variation by itself
does not lead to evolution.
00:02:57.290 --> 00:03:00.770
You need variation and selection pressure.
00:03:00.770 --> 00:03:02.307
And this is really where the term
00:03:02.307 --> 00:03:05.170
"natural selection" is coming from.
00:03:05.170 --> 00:03:07.700
What do I mean by selection pressure?
00:03:07.700 --> 00:03:09.720
Well, in this little example here,
00:03:09.720 --> 00:03:13.370
if these circles and
triangle-looking things
00:03:13.370 --> 00:03:15.440
could just keep
reproducing, they could find
00:03:15.440 --> 00:03:19.400
as many resources as they need,
there's no shortage of food,
00:03:19.400 --> 00:03:22.200
there's no shortage of
environments in which they can live
00:03:22.200 --> 00:03:24.610
and reproduce, they had no predators,
00:03:24.610 --> 00:03:26.400
well, you're not gonna
have selection pressure.
00:03:26.400 --> 00:03:29.230
And so all of these variations
might have an equal chance
00:03:29.230 --> 00:03:32.440
of living their life and then reproducing.
00:03:32.440 --> 00:03:34.930
But now let's introduce
some selection pressure
00:03:34.930 --> 00:03:36.740
and imagine what might happen.
00:03:36.740 --> 00:03:38.770
Let's say we introduce
the selection pressure
00:03:38.770 --> 00:03:43.770
of a predator that has a much
easier time seeing white.
00:03:46.810 --> 00:03:48.650
Well, then what's going to happen?
00:03:48.650 --> 00:03:51.050
Well over time, generation to generation,
00:03:51.050 --> 00:03:53.800
the white circles and
triangles here are going to be
00:03:53.800 --> 00:03:56.860
much more likely to be
eaten by that predator
00:03:56.860 --> 00:03:59.860
before they can reproduce
and pass on the allele
00:03:59.860 --> 00:04:03.140
or the alleles that might
result in this white trait,
00:04:03.140 --> 00:04:05.890
and so next generations
or future generations
00:04:05.890 --> 00:04:08.330
are going to have fewer and
fewer of these white shapes,
00:04:08.330 --> 00:04:11.970
so the next generation
might look a lot like this.
00:04:11.970 --> 00:04:15.970
A lot more of the purple we're seeing
00:04:15.970 --> 00:04:20.070
and a lot more of the blue.
00:04:20.070 --> 00:04:22.300
Now on the other hand,
you could have a scenario
00:04:22.300 --> 00:04:24.600
where instead of a
predator that sees white
00:04:24.600 --> 00:04:26.580
and can't see the other colors showing up,
00:04:26.580 --> 00:04:28.630
where there's a shortage of food.
00:04:28.630 --> 00:04:31.440
So that's another form
of selection pressure.
00:04:31.440 --> 00:04:34.360
Let's say a more triangular shape
00:04:34.360 --> 00:04:37.980
is useful for finding food.
00:04:37.980 --> 00:04:40.410
for food.
00:04:40.410 --> 00:04:42.260
Well, then what's going to happen?
00:04:42.260 --> 00:04:44.560
Well, generation by
generation, these shapes
00:04:44.560 --> 00:04:46.830
that are more triangular are going to have
00:04:46.830 --> 00:04:49.200
a better chance of
surviving and reproducing.
00:04:49.200 --> 00:04:52.720
And so maybe in the
first generation you have
00:04:52.720 --> 00:04:55.090
maybe something like that
does reasonably well,
00:04:55.090 --> 00:04:57.300
something like that could do very well.
00:04:57.300 --> 00:04:59.380
Something like that would do well.
00:04:59.380 --> 00:05:01.840
Something like this could do well,
00:05:01.840 --> 00:05:03.320
but we're gonna see, we might see
00:05:03.320 --> 00:05:06.020
a few of the circles still.
00:05:06.020 --> 00:05:08.020
We might see a few of these characters,
00:05:08.020 --> 00:05:09.600
but we'll see fewer have them.
00:05:09.600 --> 00:05:10.840
And we're gonna see more
00:05:11.848 --> 00:05:14.300
of these characters right over here.
00:05:14.300 --> 00:05:16.250
And now you can imagine if this
00:05:16.250 --> 00:05:18.390
environmental pressure continues,
00:05:18.390 --> 00:05:20.330
then over generation and generation,
00:05:20.330 --> 00:05:23.130
you keep selecting for more triangular,
00:05:23.130 --> 00:05:25.940
if you could go forward
many hundreds or thousands
00:05:25.940 --> 00:05:28.200
or hundreds of thousands
or millions of years,
00:05:28.200 --> 00:05:30.480
you might see some
subset of this population
00:05:30.480 --> 00:05:32.550
that lives in this environment.
00:05:32.550 --> 00:05:34.490
They might have a very triangular shape.
00:05:34.490 --> 00:05:37.940
They might not even look
anything like their ancestors.
00:05:37.940 --> 00:05:40.430
Now, does this mean that
this shape right over here
00:05:40.430 --> 00:05:42.800
is somehow more advanced
or better than what
00:05:42.800 --> 00:05:45.770
their ancestors saw, or maybe
there's a cousin species
00:05:45.770 --> 00:05:47.530
that was where the predators see white
00:05:47.530 --> 00:05:49.940
and the triangular shape
really doesn't help you,
00:05:49.940 --> 00:05:52.600
and so they have a cousin
species that looks like this.
00:05:52.600 --> 00:05:54.300
There's no way of saying that this species
00:05:54.300 --> 00:05:56.360
is more advanced or
better than this species,
00:05:56.360 --> 00:05:59.960
but what we can say is, it is
more fit for its environment.
00:05:59.960 --> 00:06:02.800
And this species is more
fit in its environment.
00:06:02.800 --> 00:06:04.850
So I will leave you there,
and it's important to realize
00:06:04.850 --> 00:06:06.570
this isn't some magical process.
00:06:06.570 --> 00:06:08.950
It's all due to variation
caused by mutation
00:06:08.950 --> 00:06:11.710
and sexual reproduction,
selection pressure,
00:06:11.710 --> 00:06:13.790
and then that change happens over time.
00:06:13.790 --> 00:06:15.670
And this isn't just something that happens
00:06:15.670 --> 00:06:17.900
over millions or tens
of millions of years.
00:06:17.900 --> 00:06:20.630
It happens before our eyes every day.
00:06:20.630 --> 00:06:22.830
When we talk about the
different flu strain
00:06:22.830 --> 00:06:24.620
or a different coronavirus strain
00:06:24.620 --> 00:06:26.520
or drug-resistant bacteria,
00:06:26.520 --> 00:06:29.393
it's very relevant to
our day-to-day lives.
|
Genes, traits, and the environment | https://www.youtube.com/watch?v=OR9j5hog1mQ | vtt | https://www.youtube.com/api/timedtext?v=OR9j5hog1mQ&ei=0lWUZevMJIK5mLAPgK6nsA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B2E7A4C85401315EEA87C9990A030B8721BF4895.78BACAB621BC54E4C4ACED00864930D1C31B14E8&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.480 --> 00:00:03.830
- [Instructor] This is a
prize-winning Himalayan rabbit,
00:00:03.830 --> 00:00:06.850
and it will help us see
that an organism's traits
00:00:06.850 --> 00:00:10.190
aren't only the results
of which genes they have,
00:00:10.190 --> 00:00:12.750
but also which environmental factors
00:00:12.750 --> 00:00:14.610
the organism is exposed to.
00:00:14.610 --> 00:00:16.580
So we're gonna look at a specific gene
00:00:16.580 --> 00:00:20.830
in the Himalayan rabbit
known as the C-gene,
00:00:20.830 --> 00:00:24.110
and to C-gene encodes a
protein which acts as an enzyme
00:00:24.110 --> 00:00:26.150
in the eventual production of pigment.
00:00:26.150 --> 00:00:29.550
And we can see where that
enzyme is more active,
00:00:29.550 --> 00:00:34.130
at the nose, on the feet,
on the ears right over here,
00:00:34.130 --> 00:00:37.180
and then you could also
see that it is inactive
00:00:37.180 --> 00:00:40.410
across the body and in
some parts of the head
00:00:40.410 --> 00:00:41.900
right over here.
00:00:41.900 --> 00:00:44.620
Now the question is
what's causing it to be
00:00:44.620 --> 00:00:46.890
inactive or active?
00:00:46.890 --> 00:00:50.510
Well, it turns out that the
enzyme that the C-gene codes for
00:00:50.510 --> 00:00:55.030
is optimally active at 15 degrees Celsius
00:00:55.030 --> 00:00:57.710
to 25 degrees Celsius,
00:00:57.710 --> 00:01:00.810
and this alone can actually explain
00:01:00.810 --> 00:01:02.700
the difference in pigmentation.
00:01:02.700 --> 00:01:04.120
How does that make sense?
00:01:04.120 --> 00:01:06.390
Well imagine that this rabbit over here
00:01:06.390 --> 00:01:10.350
was raised at 20 degrees Celsius.
00:01:10.350 --> 00:01:12.950
The body itself, it's a
mammal, it's warm blooded,
00:01:12.950 --> 00:01:15.120
it's going to be producing heat.
00:01:15.120 --> 00:01:20.120
So the body, this area right
over here, is going to be warm.
00:01:21.800 --> 00:01:25.080
And so, over here where we're
going to be greater than,
00:01:25.080 --> 00:01:27.800
let's say 35 degrees Celsius,
00:01:27.800 --> 00:01:30.870
where the enzyme that the C-gene
and codes for is inactive.
00:01:30.870 --> 00:01:32.420
This is where it's optimally active,
00:01:32.420 --> 00:01:34.340
and above 35 degrees Celsius
00:01:34.340 --> 00:01:36.700
it's actually not active at all.
00:01:36.700 --> 00:01:39.830
And once again, why is
it so warm over here?
00:01:39.830 --> 00:01:41.440
It's not just the ambient temperature.
00:01:41.440 --> 00:01:43.370
It's the combination of
the ambient temperature
00:01:43.370 --> 00:01:46.010
plus the heat from the rabbit itself.
00:01:46.010 --> 00:01:48.930
Now, if you go at some
of the further off parts
00:01:48.930 --> 00:01:49.860
of the rabbit's body,
00:01:49.860 --> 00:01:51.690
and this is actually true
of our bodies as well,
00:01:51.690 --> 00:01:54.020
if you go to the ears, you go to the nose,
00:01:54.020 --> 00:01:58.040
you go to the feet, you
have less body warmth.
00:01:58.040 --> 00:02:03.040
And so, it is going to be cooler
in these parts of the body,
00:02:03.700 --> 00:02:04.710
and it could be cool enough
00:02:04.710 --> 00:02:06.810
so that the protein encoded by the C-gene
00:02:06.810 --> 00:02:08.260
is actually active.
00:02:08.260 --> 00:02:10.260
And so, you see something very simple
00:02:10.260 --> 00:02:12.030
can create this very neat
00:02:12.030 --> 00:02:15.860
and, I would have to say,
cute pattern as well.
00:02:15.860 --> 00:02:17.920
Now, some of you might be wondering, well,
00:02:17.920 --> 00:02:20.020
could I then based on temperature,
00:02:20.020 --> 00:02:23.070
raise a completely white Himalayan rabbit,
00:02:23.070 --> 00:02:24.710
and the answer is yes.
00:02:24.710 --> 00:02:26.470
If you had a twin of this rabbit
00:02:26.470 --> 00:02:28.210
and you raised it in an environment
00:02:28.210 --> 00:02:32.140
that was, say, hotter
than 30 degrees Celsius,
00:02:32.140 --> 00:02:35.330
well then all of its
body would probably be
00:02:35.330 --> 00:02:38.320
of a temperature where the
protein encoded by the C-gene is
00:02:38.320 --> 00:02:40.570
not too active or not active at all,
00:02:40.570 --> 00:02:42.150
and it would be a white rabbit.
00:02:42.150 --> 00:02:44.190
And people have performed this experiment
00:02:44.190 --> 00:02:47.940
over 100 years ago and
they saw that exact result.
00:02:47.940 --> 00:02:50.470
And temperature is just
one of many factors.
00:02:50.470 --> 00:02:52.250
So there's research where
they're able to make
00:02:52.250 --> 00:02:54.400
a Cyclops fish, a fish with one eye,
00:02:54.400 --> 00:02:57.550
based on chemicals and
where it was reared.
00:02:57.550 --> 00:03:00.410
There's experiments with
the light that depending on
00:03:00.410 --> 00:03:02.270
the light or the lack of light,
00:03:02.270 --> 00:03:03.410
at the caterpillar stage,
00:03:03.410 --> 00:03:05.750
it can affect what the
butterfly looks like
00:03:05.750 --> 00:03:07.630
when it develops wings.
00:03:07.630 --> 00:03:10.710
Food can activate or
inactivate certain genes,
00:03:10.710 --> 00:03:13.410
not just in other animals,
but even in our own bodies.
00:03:13.410 --> 00:03:16.550
There's research around fasting
and how that might activate
00:03:16.550 --> 00:03:18.880
or inactivate certain genes.
00:03:18.880 --> 00:03:20.400
Stress can affect genes.
00:03:20.400 --> 00:03:22.150
Hormones can affect genes.
00:03:22.150 --> 00:03:24.880
So the big takeaway here
is an organism's traits
00:03:24.880 --> 00:03:28.480
are not just due to which
genes the organism has,
00:03:28.480 --> 00:03:32.353
but are influenced by
environmental factors as well.
|
Gene expression and regulation | https://www.youtube.com/watch?v=fdzsrTpUe4w | vtt | https://www.youtube.com/api/timedtext?v=fdzsrTpUe4w&ei=0lWUZZ2nHbjGmLAPtrKZ-Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=83D82D09ED33E46FEEB18D690C5CC2960430DFA3.DB6BDD70590BC4473758B1AAEAFDF4C7D981F9C1&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.950 --> 00:00:02.790
- [Instructor] By now
you're likely familiar
00:00:02.790 --> 00:00:07.240
with the idea that DNA,
deoxyribonucleic acid,
00:00:07.240 --> 00:00:10.340
is the molecular basis of inheritance.
00:00:10.340 --> 00:00:12.090
You might also have a sense
00:00:12.090 --> 00:00:15.190
that it is somehow
involved with chromosomes.
00:00:15.190 --> 00:00:18.120
And in this video, I wanna make
sure we can connect the dots
00:00:18.120 --> 00:00:19.940
with all of these concepts that we have
00:00:19.940 --> 00:00:21.440
when we come to genetics.
00:00:21.440 --> 00:00:22.670
What's a chromosome.
00:00:22.670 --> 00:00:24.750
How does it relate to DNA?
00:00:24.750 --> 00:00:27.050
How does that relate to genes?
00:00:27.050 --> 00:00:29.160
And then how do genes and DNA
00:00:29.160 --> 00:00:32.030
relate to proteins or other things?
00:00:32.030 --> 00:00:33.820
Well, as you can see in this diagram
00:00:33.820 --> 00:00:37.420
from the National Human
Genome Research Institute,
00:00:37.420 --> 00:00:39.210
they're showing us a blown up cell.
00:00:39.210 --> 00:00:41.280
So this is the outer membrane of the cell
00:00:41.280 --> 00:00:42.690
that you see right over here.
00:00:42.690 --> 00:00:47.660
And in here, they are showing
us the nucleus of the cell.
00:00:47.660 --> 00:00:52.660
And inside the nucleus of
eukaryotes, you have your DNA.
00:00:53.010 --> 00:00:54.480
Now, the way that they have shown it,
00:00:54.480 --> 00:00:58.040
the DNA all looks like
these Xes over here.
00:00:58.040 --> 00:00:59.150
Now, it's important to realize
00:00:59.150 --> 00:01:03.110
that DNA isn't always in this
condensed chromosome form.
00:01:03.110 --> 00:01:04.540
When DNA replicates,
00:01:04.540 --> 00:01:07.620
it is in it's loose or uncondensed form.
00:01:07.620 --> 00:01:11.640
When it condenses, maybe in
preparation for say mitosis,
00:01:11.640 --> 00:01:14.790
then it takes on an X shape.
00:01:14.790 --> 00:01:18.620
But this X actually has two
copies of the same chromosome.
00:01:18.620 --> 00:01:19.930
But while they are connected,
00:01:19.930 --> 00:01:22.050
consider that to be one chromosome.
00:01:22.050 --> 00:01:24.670
But then once they separate,
say during mitosis,
00:01:24.670 --> 00:01:27.530
then people would consider
it to be two chromosomes.
00:01:27.530 --> 00:01:29.910
Now, if we look at chromosomes
under a microscope,
00:01:29.910 --> 00:01:32.490
you might see something like this.
00:01:32.490 --> 00:01:34.640
As you notice, they come in pairs.
00:01:34.640 --> 00:01:36.170
And this is actually what chromosomes
00:01:36.170 --> 00:01:37.770
would look like for the human genome.
00:01:37.770 --> 00:01:39.420
You have 23 pairs.
00:01:39.420 --> 00:01:41.810
The way we know that
this is a biological male
00:01:41.810 --> 00:01:43.610
is by looking right over here.
00:01:43.610 --> 00:01:45.790
This short little
chromosome right over here,
00:01:45.790 --> 00:01:48.070
that is the Y chromosome.
00:01:48.070 --> 00:01:49.590
And you can see each of these pairs
00:01:49.590 --> 00:01:51.690
have what are called
homologous chromosomes,
00:01:51.690 --> 00:01:53.970
which we've talked about in other videos.
00:01:53.970 --> 00:01:57.000
But it's the view that
these two chromosomes
00:01:57.000 --> 00:01:59.390
code for the same genes,
00:01:59.390 --> 00:02:02.280
but they might have different
versions of the genes on them.
00:02:02.280 --> 00:02:06.370
You get one of the homologous
pair from your female parent,
00:02:06.370 --> 00:02:09.790
and one of the homologous
pair from your male parent.
00:02:09.790 --> 00:02:12.550
And we've gone into some
depth into other videos.
00:02:12.550 --> 00:02:14.380
Now, it's hard to see
it at this resolution,
00:02:14.380 --> 00:02:15.213
but in this image,
00:02:15.213 --> 00:02:17.290
each chromosome has been replicated
00:02:17.290 --> 00:02:20.510
and is actually two copies
connected at the centromere.
00:02:20.510 --> 00:02:21.850
If we were to spread it out,
00:02:21.850 --> 00:02:25.300
it would have that X
shape right over there.
00:02:25.300 --> 00:02:29.080
Now, the question is how does
a chromosome relate to DNA?
00:02:29.080 --> 00:02:32.280
And you can see it in this
broader diagram right over here.
00:02:32.280 --> 00:02:33.990
A chromosome is actually just a very,
00:02:33.990 --> 00:02:37.240
very long strand of DNA
that's all wrapped up.
00:02:37.240 --> 00:02:38.690
And there some other molecules
00:02:38.690 --> 00:02:39.930
and proteins that are involved,
00:02:39.930 --> 00:02:42.010
like histones like you
see right over here.
00:02:42.010 --> 00:02:43.800
that help package the DNA,
00:02:43.800 --> 00:02:46.910
but that's all a chromosome really is.
00:02:46.910 --> 00:02:48.780
In the entire human genome,
00:02:48.780 --> 00:02:53.780
we have 3.2 billion base pairs in our DNA.
00:02:54.720 --> 00:02:56.980
And just as a reminder,
a base pair you can view
00:02:56.980 --> 00:02:59.550
as each of the rungs of this ladder.
00:02:59.550 --> 00:03:03.210
Now, those 3.2 billion base pairs,
00:03:03.210 --> 00:03:07.360
they are divided into these 46 chromosomes
00:03:07.360 --> 00:03:09.520
in a complete human genome.
00:03:09.520 --> 00:03:10.520
So you're looking at the order
00:03:10.520 --> 00:03:12.610
of tens to hundreds of millions
00:03:12.610 --> 00:03:15.140
of base pairs per chromosome.
00:03:15.140 --> 00:03:16.720
Now you're probably
familiar with this idea
00:03:16.720 --> 00:03:18.090
that the genes on the DNA
00:03:18.090 --> 00:03:20.060
are actually what code for protein.
00:03:20.060 --> 00:03:21.720
And that is indeed the case.
00:03:21.720 --> 00:03:25.250
If you have a long strand
of DNA right over here,
00:03:25.250 --> 00:03:27.410
not all of it is protein coding,
00:03:27.410 --> 00:03:30.000
but you have protein coding genes on it.
00:03:30.000 --> 00:03:32.330
And if you look at the
entire human genome,
00:03:32.330 --> 00:03:37.330
you're looking at about 20,000
plus protein coding genes,
00:03:38.300 --> 00:03:39.310
each of which is made up
00:03:39.310 --> 00:03:41.710
an average of about 3000 base pairs,
00:03:41.710 --> 00:03:42.810
but it can vary a lot
00:03:42.810 --> 00:03:44.440
depending on the gene you're looking at.
00:03:44.440 --> 00:03:47.710
And the way that we go from
these protein coding genes,
00:03:47.710 --> 00:03:50.140
which are really just sections of the DNA
00:03:50.140 --> 00:03:52.600
on these chromosomes, to proteins,
00:03:52.600 --> 00:03:56.830
this idea is known as the
central dogma of biology
00:03:56.830 --> 00:04:00.000
or oftentimes the central
dogma of molecular biology.
00:04:00.000 --> 00:04:04.120
So this is a chain of DNA
in a protein coding gene.
00:04:04.120 --> 00:04:07.250
The process of transcription
is what takes us
00:04:07.250 --> 00:04:10.780
from one half of this to an mRNA strand,
00:04:10.780 --> 00:04:13.840
which you can view as a
cousin molecule of DNA.
00:04:13.840 --> 00:04:16.340
Now, messenger RNA in particular,
00:04:16.340 --> 00:04:18.670
that then goes to the ribosomes.
00:04:18.670 --> 00:04:20.590
It goes outside of the
nucleus of the cell,
00:04:20.590 --> 00:04:21.690
goes to the ribosomes.
00:04:21.690 --> 00:04:24.110
We talk about this in some
depth in other videos.
00:04:24.110 --> 00:04:25.840
And then at the ribosomes,
00:04:25.840 --> 00:04:29.360
that information is used to
actually construct proteins
00:04:29.360 --> 00:04:30.540
out of amino acids.
00:04:30.540 --> 00:04:32.470
And then those proteins,
those amino acids,
00:04:32.470 --> 00:04:33.450
will interact with each other
00:04:33.450 --> 00:04:35.750
and they'll form a shape of some protein
00:04:35.750 --> 00:04:38.770
that is valuable in the human body.
00:04:38.770 --> 00:04:40.220
Now, what's interesting
00:04:40.220 --> 00:04:44.380
is that even though we most
associate DNA with genes
00:04:44.380 --> 00:04:46.730
that code for proteins in this way,
00:04:46.730 --> 00:04:51.730
the reality is that only 1-2%
of DNA codes for proteins.
00:04:53.230 --> 00:04:54.610
So a natural question would be,
00:04:54.610 --> 00:04:58.710
what is the other 98-99% of DNA doing?
00:04:58.710 --> 00:05:01.310
And that's actually an
active area of research,
00:05:01.310 --> 00:05:03.110
but we have some good ideas.
00:05:03.110 --> 00:05:05.230
We know that some of that DNA
00:05:05.230 --> 00:05:08.910
helps regulate the coding of other DNA.
00:05:08.910 --> 00:05:10.920
What's interesting about the human genome,
00:05:10.920 --> 00:05:12.820
or actually the genome of any organism,
00:05:12.820 --> 00:05:15.970
is that nearly every
cell in the human body
00:05:15.970 --> 00:05:18.660
has this same set of chromosomes,
00:05:18.660 --> 00:05:21.340
has all of the information necessary
00:05:21.340 --> 00:05:24.480
to code for all of the proteins
that any cell might need.
00:05:24.480 --> 00:05:26.100
Exceptions are red blood cells,
00:05:26.100 --> 00:05:27.950
which lose their genetic material,
00:05:27.950 --> 00:05:30.040
and gametes, sperm, or egg cells,
00:05:30.040 --> 00:05:31.810
which have half of the genetic material,
00:05:31.810 --> 00:05:34.410
but almost every other cell
has all the genetic material.
00:05:34.410 --> 00:05:36.080
But obviously cells are different.
00:05:36.080 --> 00:05:38.070
Heart cells are different than neurons,
00:05:38.070 --> 00:05:39.860
which are different than skin cells.
00:05:39.860 --> 00:05:41.100
So a lot of the other DNA
00:05:41.100 --> 00:05:43.520
is part of the regulatory mechanism
00:05:43.520 --> 00:05:45.660
of which genes to express,
00:05:45.660 --> 00:05:48.550
which genes should be coded into proteins
00:05:48.550 --> 00:05:50.050
and which ones should not,
00:05:50.050 --> 00:05:53.060
as we have different types of
cells doing different things.
00:05:53.060 --> 00:05:56.730
And so this is known as
differential gene expression.
00:05:56.730 --> 00:05:58.620
And those parts of the DNA
00:05:58.620 --> 00:06:01.490
that aren't coding directly for proteins,
00:06:01.490 --> 00:06:04.470
we would call those
regulatory sections of DNA.
00:06:04.470 --> 00:06:06.920
Now, there's other stretches of DNA
00:06:06.920 --> 00:06:08.950
that instead of producing mRNA,
00:06:08.950 --> 00:06:12.210
which then gets translated
into polypeptides,
00:06:12.210 --> 00:06:14.360
it could code for other types of RNA,
00:06:14.360 --> 00:06:16.280
which we would call functional RNA
00:06:16.280 --> 00:06:18.810
because that type of
RNA is directly useful.
00:06:18.810 --> 00:06:21.780
It has a function. It's not
just transmitting information.
00:06:21.780 --> 00:06:24.020
For example, you have ribosomal RNA,
00:06:24.020 --> 00:06:26.690
which can be directly
transcribed from DNA,
00:06:26.690 --> 00:06:29.070
and it's used to make up
parts of the ribosome.
00:06:29.070 --> 00:06:30.820
You might've seen transfer RNA
00:06:30.820 --> 00:06:32.620
when we learned about translation.
00:06:32.620 --> 00:06:35.810
They're also involved in the
construction of proteins.
00:06:35.810 --> 00:06:37.000
So I will leave you there.
00:06:37.000 --> 00:06:38.500
Hopefully this connects the dots
00:06:38.500 --> 00:06:41.910
between the idea that most of
your cells in the human body,
00:06:41.910 --> 00:06:44.400
and we're talking about
tens of trillions of cells,
00:06:44.400 --> 00:06:49.320
have the entire complement
of 3.2 billion base pairs
00:06:49.320 --> 00:06:51.920
that are in these 46 chromosomes
00:06:51.920 --> 00:06:54.870
that are organized in 23 pairs
00:06:54.870 --> 00:06:57.730
that contain these 20,000+ genes,
00:06:57.730 --> 00:07:01.040
which only make up 1-2% of the base pairs.
00:07:01.040 --> 00:07:03.120
The rest we're still exploring,
00:07:03.120 --> 00:07:06.210
but it can be involved in
functional RNA and regulation,
00:07:06.210 --> 00:07:07.750
which helps different cells
00:07:07.750 --> 00:07:10.493
do different things at different times.
|
Stratospheric Ozone Depletion | https://www.youtube.com/watch?v=5CGtESB40Rc | vtt | https://www.youtube.com/api/timedtext?v=5CGtESB40Rc&ei=0lWUZd6FI_eKvdIP7oGqkAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E16401896D470A5121B3E5BF82C41B4C9D1096C1.CAA43FC7A1A8C1182EFD9649465CFB7EE3EEC032&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.490 --> 00:00:01.710
- In this video we're gonna talk about
00:00:01.710 --> 00:00:04.450
a molecule known as Ozone.
00:00:04.450 --> 00:00:07.930
And Ozone you can also view as O3,
00:00:07.930 --> 00:00:10.230
or three oxygens bonded this way,
00:00:10.230 --> 00:00:12.260
these dash lines show that sometimes
00:00:12.260 --> 00:00:13.600
the double bond is on this side,
00:00:13.600 --> 00:00:14.940
sometimes it's on that side.
00:00:14.940 --> 00:00:17.290
You might recognize that as resonance
00:00:17.290 --> 00:00:18.530
in molecular structures,
00:00:18.530 --> 00:00:20.530
or resonance in bonds.
00:00:20.530 --> 00:00:23.630
But it plays some very interesting roles.
00:00:23.630 --> 00:00:27.260
It can both protect
us, and it can hurt us.
00:00:27.260 --> 00:00:30.636
And to understand this,
let's look at this diagram
00:00:30.636 --> 00:00:32.880
of the atmosphere.
00:00:32.880 --> 00:00:34.900
So there's a lot of really interesting
00:00:34.900 --> 00:00:36.470
information in this diagram.
00:00:36.470 --> 00:00:38.360
Some of it relevant to
this video, some of it not,
00:00:38.360 --> 00:00:39.550
but I encourage you to look at it.
00:00:39.550 --> 00:00:41.460
There's all sorts of cool things,
00:00:41.460 --> 00:00:44.500
how temperature changes as
we increase in altitude.
00:00:44.500 --> 00:00:48.030
We see the labels of the major
layers of the atmosphere,
00:00:48.030 --> 00:00:51.040
we can compare it to Mount
Everest and where clouds are.
00:00:51.040 --> 00:00:54.170
But we see a few things,
we have a troposphere,
00:00:54.170 --> 00:00:57.210
and then above that we
have a stratosphere.
00:00:57.210 --> 00:00:59.910
Now in the stratosphere we see this thing
00:00:59.910 --> 00:01:02.990
known as an Ozone layer,
00:01:02.990 --> 00:01:07.990
which is 10 to 20 miles above
the surface of the earth.
00:01:08.120 --> 00:01:12.870
And Ozone in this part of
the atmosphere protects us.
00:01:12.870 --> 00:01:14.610
How does it protect us?
00:01:14.610 --> 00:01:18.210
Well the sun, which most
of us consider our friend,
00:01:18.210 --> 00:01:21.530
that lives 93 million miles away,
00:01:21.530 --> 00:01:24.420
we know that life wouldn't
exist without the sun.
00:01:24.420 --> 00:01:26.540
Most of the energy we have on this planet
00:01:26.540 --> 00:01:28.260
is because of the sun.
00:01:28.260 --> 00:01:32.070
But UV frequencies from the sun,
00:01:32.070 --> 00:01:33.150
if they aren't blocked,
00:01:33.150 --> 00:01:35.030
or if they aren't mitigated a little bit,
00:01:35.030 --> 00:01:36.800
they can cause a lot of damage.
00:01:36.800 --> 00:01:39.980
They have a lot of energy,
they can affect molecules,
00:01:39.980 --> 00:01:43.920
and in particular, they
can affect our DNA.
00:01:43.920 --> 00:01:46.050
And if you start messing with DNA,
00:01:46.050 --> 00:01:50.800
start mutating DNA, that can
lead to things like cancer.
00:01:50.800 --> 00:01:53.350
And so you can imagine, we human beings,
00:01:53.350 --> 00:01:55.020
and actually most organisms
00:01:55.020 --> 00:01:58.640
can only deal with a
certain amount of UV light.
00:01:58.640 --> 00:02:01.240
Now if we had no Ozone layer,
00:02:01.240 --> 00:02:04.260
a lot of that UV light
would come in unchecked.
00:02:04.260 --> 00:02:05.630
It's going to get absorbed a little bit
00:02:05.630 --> 00:02:07.610
by the various layers of the atmosphere,
00:02:07.610 --> 00:02:10.330
but it turns out that Ozone in particular
00:02:10.330 --> 00:02:13.730
is good at protecting us from UV light.
00:02:13.730 --> 00:02:16.420
So if we didn't have this
Ozone layer above us,
00:02:16.420 --> 00:02:18.020
you would see cancer rates go up.
00:02:18.020 --> 00:02:21.323
We would just get a lot more UV energy.
00:02:22.400 --> 00:02:23.640
Now an interesting question is,
00:02:23.640 --> 00:02:26.090
how does this Ozone layer form?
00:02:26.090 --> 00:02:28.570
We're not used to seeing
oxygen in this form.
00:02:28.570 --> 00:02:31.010
Most of the oxygen that
we see in our atmosphere
00:02:31.010 --> 00:02:35.236
is molecular oxygen in
the form of two oxygens
00:02:35.236 --> 00:02:37.500
which looks like that.
00:02:37.500 --> 00:02:39.770
Well is turns out that UV light
00:02:39.770 --> 00:02:41.840
actually helps create the thing
00:02:41.840 --> 00:02:43.910
that protects us from UV light.
00:02:43.910 --> 00:02:46.590
Because O2 in the presence of UV
00:02:46.590 --> 00:02:50.630
can be broken up and
then reformed as Ozone.
00:02:50.630 --> 00:02:51.500
So it's actually the fact
00:02:51.500 --> 00:02:54.050
that you have so much UV light up here,
00:02:54.050 --> 00:02:56.350
that it reacts with oxygen that has raised
00:02:56.350 --> 00:02:57.370
to the stratosphere,
00:02:57.370 --> 00:03:00.940
and some of that gets formed into Ozone.
00:03:00.940 --> 00:03:03.250
Now Ozone is very reactive,
00:03:03.250 --> 00:03:04.530
and it can be a little bit delicate,
00:03:04.530 --> 00:03:06.360
it has a very short half life.
00:03:06.360 --> 00:03:08.413
It is way less stable than O2.
00:03:09.710 --> 00:03:13.030
And so it has to keep getting
replenished in the atmosphere.
00:03:13.030 --> 00:03:15.380
And we also know that certain chemicals
00:03:15.380 --> 00:03:16.910
that we human beings have produced,
00:03:16.910 --> 00:03:18.640
in particular what's often known
00:03:18.640 --> 00:03:20.520
as chlorofloro carbons,
00:03:20.520 --> 00:03:22.910
that's just a fancy
way of saying molecules
00:03:22.910 --> 00:03:24.080
that are hydrocarbons,
00:03:24.080 --> 00:03:25.790
so a bunch of carbons and hydrogens,
00:03:25.790 --> 00:03:28.620
that also involve chlorine and fluorine.
00:03:28.620 --> 00:03:30.690
And these molecules were generated
00:03:30.690 --> 00:03:32.240
in industrial applications,
00:03:32.240 --> 00:03:35.520
things like aerosol
sprays used to have CFCs,
00:03:35.520 --> 00:03:38.900
but it turns out that CFCs
will deplete the ozone layer.
00:03:38.900 --> 00:03:41.670
They'll come up from our
little spray paint cans
00:03:41.670 --> 00:03:44.470
and they'll interact with the
Ozone, and they'll deplete it
00:03:44.470 --> 00:03:45.740
which is not a good thing.
00:03:45.740 --> 00:03:48.330
Once again it will make
us all more susceptible
00:03:48.330 --> 00:03:50.600
to things like cancer.
00:03:50.600 --> 00:03:52.290
Now everything we've talked about so far
00:03:52.290 --> 00:03:55.000
is Ozone in the stratosphere,
00:03:55.000 --> 00:03:56.330
but it turns out that Ozone
00:03:56.330 --> 00:03:59.300
can actually also form
lower in the atmosphere,
00:03:59.300 --> 00:04:01.920
in the place where we
tend to spend our lives,
00:04:01.920 --> 00:04:03.600
in the troposphere.
00:04:03.600 --> 00:04:07.380
And when Ozone is down there,
it's actually a bad thing.
00:04:07.380 --> 00:04:10.400
And to understand why it
might form down there,
00:04:10.400 --> 00:04:11.830
we need to understand the role
00:04:11.830 --> 00:04:13.850
once again that we're playing.
00:04:13.850 --> 00:04:16.920
Nitrous oxides are formed
from automobile exhaust,
00:04:16.920 --> 00:04:18.570
and coal-fired power plants,
00:04:18.570 --> 00:04:21.210
and when those in the
presence of UV light,
00:04:21.210 --> 00:04:24.320
and what's known as
volatile organic compounds,
00:04:24.320 --> 00:04:26.810
which is just a fancy way
of saying organic compounds
00:04:26.810 --> 00:04:28.000
that evaporate very easily,
00:04:28.000 --> 00:04:31.120
and most of these are
naturally produced, the VOCs,
00:04:31.120 --> 00:04:33.500
but when you have the
UV light in conjunction
00:04:33.500 --> 00:04:35.010
with the exhaust from automobiles
00:04:35.010 --> 00:04:37.650
and nitrous oxides from
coal-fired power plants,
00:04:37.650 --> 00:04:40.880
it can produce Ozone in
the lower atmosphere.
00:04:40.880 --> 00:04:43.890
And Ozone as I mentioned
is highly reactive,
00:04:43.890 --> 00:04:45.370
it can damage living tissue,
00:04:45.370 --> 00:04:47.690
it can damage our respiratory systems,
00:04:47.690 --> 00:04:49.730
so you don't want Ozone around.
00:04:49.730 --> 00:04:51.820
So it's good in the upper atmosphere,
00:04:51.820 --> 00:04:54.960
and it is bad in the lower atmosphere.
00:04:54.960 --> 00:04:56.390
So I will leave you there,
00:04:56.390 --> 00:04:58.430
you got your primer on Ozone,
00:04:58.430 --> 00:05:00.220
and just recognize the same thing
00:05:00.220 --> 00:05:01.670
that can help us in one place,
00:05:01.670 --> 00:05:03.530
can hurt us in another place.
00:05:03.530 --> 00:05:05.800
And the same thing that
it's protecting us from
00:05:05.800 --> 00:05:08.753
can actually help create
it, that UV light.
|
Pathogens and the environment | https://www.youtube.com/watch?v=wyd0ozxbWkk | vtt | https://www.youtube.com/api/timedtext?v=wyd0ozxbWkk&ei=0lWUZa-kI--ep-oPjIGkuAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=DDF3BFCC253A71791F58264781CA33346540705B.1405C9FE4A78039C0B66E46FB0441F8B79079B5D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.250 --> 00:00:01.120
- [Instructor] In this video,
00:00:01.120 --> 00:00:02.810
we're gonna be talking about pathogens
00:00:02.810 --> 00:00:04.930
and how an environment might help
00:00:04.930 --> 00:00:07.180
or hurt the spread of a pathogen.
00:00:07.180 --> 00:00:11.340
So first of all, let's make
sure we know what a pathogen is.
00:00:11.340 --> 00:00:13.520
Patho comes from Greek pathos,
00:00:13.520 --> 00:00:15.810
which is referring to disease.
00:00:15.810 --> 00:00:19.410
Gen, you might recognize that part of word
00:00:19.410 --> 00:00:22.130
from words like generate or genetics.
00:00:22.130 --> 00:00:23.570
It means to produce.
00:00:23.570 --> 00:00:28.510
So a pathogen is something
that produces disease.
00:00:28.510 --> 00:00:30.470
Now, a good example of a pathogen
00:00:30.470 --> 00:00:35.270
that we're still facing
on our planet is malaria.
00:00:35.270 --> 00:00:40.040
And malaria is a very,
very unpleasant disease.
00:00:40.040 --> 00:00:42.540
It involves the attack on red blood cells.
00:00:42.540 --> 00:00:44.950
It causes fever, chills, sweats,
00:00:44.950 --> 00:00:48.030
severe abdominal pain,
vomiting, headaches.
00:00:48.030 --> 00:00:51.320
It can make you more
susceptible to other diseases.
00:00:51.320 --> 00:00:55.010
And if it's not treated,
it can kill someone.
00:00:55.010 --> 00:00:59.570
Now, the pathogen that creates
or that produces malaria,
00:00:59.570 --> 00:01:02.860
that causes the disease malaria is known
00:01:02.860 --> 00:01:05.920
as plasmodium falciparum.
00:01:05.920 --> 00:01:08.280
And this right over here is a picture
00:01:08.280 --> 00:01:10.860
of it attacking red blood cells.
00:01:10.860 --> 00:01:13.540
We see healthy red blood
cells right over here,
00:01:13.540 --> 00:01:15.700
and then the ones that
are in this deep color,
00:01:15.700 --> 00:01:18.440
this is being attacked
by the malaria pathogen.
00:01:18.440 --> 00:01:21.740
And as it does that, it
destroys those red blood cells,
00:01:21.740 --> 00:01:25.260
and it leads to all of the
symptoms that I talked about.
00:01:25.260 --> 00:01:27.360
So let's think a little
bit about the environment
00:01:27.360 --> 00:01:30.790
in which malaria is likely to be spread.
00:01:30.790 --> 00:01:33.520
Well, there's a few things that we know.
00:01:33.520 --> 00:01:36.630
We know that the malaria
pathogen can only operate,
00:01:36.630 --> 00:01:38.800
can only go through its full life cycle
00:01:38.800 --> 00:01:40.880
in relatively warm conditions.
00:01:40.880 --> 00:01:44.500
It needs to be greater
than 20 degrees Celsius,
00:01:44.500 --> 00:01:49.170
which is the same thing
as 68 degrees Fahrenheit.
00:01:49.170 --> 00:01:52.130
We also know that it is
spread through mosquitoes,
00:01:52.130 --> 00:01:54.890
in particular this
mosquito right over here,
00:01:54.890 --> 00:01:56.870
the anopheles mosquito.
00:01:56.870 --> 00:01:58.450
And mosquitoes are unpleasant even
00:01:58.450 --> 00:02:00.070
when they aren't zoomed in like this,
00:02:00.070 --> 00:02:02.000
but this is actually quite frightening.
00:02:02.000 --> 00:02:04.810
And we all know what
mosquitoes like to do,
00:02:04.810 --> 00:02:06.590
at least to human beings.
00:02:06.590 --> 00:02:08.180
They drink our blood.
00:02:08.180 --> 00:02:09.730
And so you need an environment
00:02:09.730 --> 00:02:11.650
where both mosquitoes can thrive,
00:02:11.650 --> 00:02:13.480
and there's a lot of human hosts
00:02:13.480 --> 00:02:15.190
whose blood they can drink
00:02:15.190 --> 00:02:17.360
and where they can spread
the malaria pathogen
00:02:17.360 --> 00:02:19.710
from one host to another.
00:02:19.710 --> 00:02:24.710
So ideally, you'd like a
high population density.
00:02:25.400 --> 00:02:27.570
And for the mosquito spread,
00:02:27.570 --> 00:02:32.350
you definitely want a hot
and humid environment.
00:02:32.350 --> 00:02:35.110
So you might guess that if
you're looking for things
00:02:35.110 --> 00:02:37.870
that don't dip below this,
because if you dip below this,
00:02:37.870 --> 00:02:39.260
the malaria pathogen's not going
00:02:39.260 --> 00:02:41.090
to be able to go through its life cycle,
00:02:41.090 --> 00:02:44.040
you're likely looking at
regions in the Equator.
00:02:44.040 --> 00:02:47.290
And this map right over
here confirms our intuition.
00:02:47.290 --> 00:02:49.430
What you see in these orange regions are
00:02:49.430 --> 00:02:52.510
where you see the highest
prevalence of malaria.
00:02:52.510 --> 00:02:55.150
The yellow regions are
where you might see malaria,
00:02:55.150 --> 00:02:56.950
but not as high of a prevalence.
00:02:56.950 --> 00:03:00.730
And then the blue areas are
where you don't see malaria.
00:03:00.730 --> 00:03:03.120
And as we guessed, if you look generally
00:03:03.120 --> 00:03:05.500
at where the Equator is,
00:03:05.500 --> 00:03:07.770
that is where you're likely to see malaria
00:03:07.770 --> 00:03:09.440
because it is warmer there.
00:03:09.440 --> 00:03:11.210
You don't see temperatures dip.
00:03:11.210 --> 00:03:14.020
And then you also see
hot, humid environments
00:03:14.020 --> 00:03:15.710
in Sub-Saharan Africa.
00:03:15.710 --> 00:03:18.830
The Sahara Desert is
roughly right over there,
00:03:18.830 --> 00:03:21.000
and that is very dry,
not good for mosquitoes.
00:03:21.000 --> 00:03:22.900
But if you look at
Sub-Sahara right below this,
00:03:22.900 --> 00:03:26.390
you have a high prevalence of malaria.
00:03:26.390 --> 00:03:28.950
Now, one not so comforting realization is
00:03:28.950 --> 00:03:31.910
as the Earth warms, you're
going to have more regions
00:03:31.910 --> 00:03:33.540
that are not just tropical regions,
00:03:33.540 --> 00:03:35.290
not just equatorial regions,
00:03:35.290 --> 00:03:39.540
that are going to be suitable
for the spread of malaria.
00:03:39.540 --> 00:03:41.480
So easily you could have
00:03:41.480 --> 00:03:44.440
what are traditionally
sub-tropical environments
00:03:44.440 --> 00:03:46.660
or even temperate environments
00:03:46.660 --> 00:03:49.080
that if it gets warm and
hot and humid enough,
00:03:49.080 --> 00:03:53.440
you might see the spread
of malaria over time.
00:03:53.440 --> 00:03:56.970
And malaria and the malaria
pathogen aren't the only things
00:03:56.970 --> 00:03:57.980
that might spread.
00:03:57.980 --> 00:04:01.560
You have things like the
Zika virus, which is a virus,
00:04:01.560 --> 00:04:03.410
not a protist in the case of malaria,
00:04:03.410 --> 00:04:06.580
but a virus that's also
spread by mosquitoes.
00:04:06.580 --> 00:04:08.220
So it also thrives
00:04:08.220 --> 00:04:10.820
wherever mosquitoes
might be able to thrive.
00:04:10.820 --> 00:04:13.350
And a warming, more humid
environment isn't just going
00:04:13.350 --> 00:04:15.370
to support the spread of mosquitoes.
00:04:15.370 --> 00:04:18.700
It can support the spread of
other pathogens, like bacteria,
00:04:18.700 --> 00:04:20.600
which can cause diseases like cholera,
00:04:20.600 --> 00:04:23.370
which is caused by infected water.
00:04:23.370 --> 00:04:24.490
So I'll leave you there.
00:04:24.490 --> 00:04:26.810
I like to be a little bit
more upbeat about things.
00:04:26.810 --> 00:04:29.520
But it's just good to realize
that this is out there.
00:04:29.520 --> 00:04:30.890
And as our environment changes,
00:04:30.890 --> 00:04:33.570
it's not just the
environment that it affects,
00:04:33.570 --> 00:04:36.153
but it can also affect
the spread of disease.
|
Nonrenewable Energy Resources | https://www.youtube.com/watch?v=RCT5dIVhIWA | vtt | https://www.youtube.com/api/timedtext?v=RCT5dIVhIWA&ei=0lWUZeCdJL-PmLAP89KDgAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E5358761A98E86AF0C803335BB9EF4A4E70524A0.96B30D80CF44E0C4B67A36A65CFF046D0D11679E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.190 --> 00:00:03.890
- Today, let's talk
about energy resources.
00:00:03.890 --> 00:00:06.130
You've probably already
done something today
00:00:06.130 --> 00:00:08.170
that used energy resources.
00:00:08.170 --> 00:00:10.500
Even beginning from
the moment you woke up.
00:00:10.500 --> 00:00:12.330
For me, the beginning of my day,
00:00:12.330 --> 00:00:14.590
always starts with making tea.
00:00:14.590 --> 00:00:17.440
I use energy and every
step of this process,
00:00:17.440 --> 00:00:18.700
my car uses oil.
00:00:18.700 --> 00:00:21.160
When I drive to the grocery
store to get the tea,
00:00:21.160 --> 00:00:24.400
my stove uses natural
gas when I boil the water
00:00:24.400 --> 00:00:27.400
and my water heater uses
coal sourced electricity.
00:00:27.400 --> 00:00:30.030
When I wash my mug in
hot water afterwards,
00:00:30.030 --> 00:00:33.060
we use energy constantly
in our daily lives.
00:00:33.060 --> 00:00:35.577
Since the first law of
thermodynamics states that
00:00:35.577 --> 00:00:38.570
"energy cannot be created nor destroyed."
00:00:38.570 --> 00:00:40.110
Where does it all come from?
00:00:40.110 --> 00:00:42.570
And will we have enough?
00:00:42.570 --> 00:00:44.750
When we talk about energy resources,
00:00:44.750 --> 00:00:46.970
we could split it up into two groups,
00:00:46.970 --> 00:00:50.930
renewable energy and non renewable energy.
00:00:50.930 --> 00:00:53.430
I can always remember what
renewable resources are
00:00:53.430 --> 00:00:55.940
because the prefix re means again,
00:00:55.940 --> 00:00:59.230
and the root new refers to the
origin of the energy source.
00:00:59.230 --> 00:01:01.110
So renewable energy sources,
00:01:01.110 --> 00:01:03.480
are the sources that we
can use again and again,
00:01:03.480 --> 00:01:06.640
and are quickly restored
by natural processes.
00:01:06.640 --> 00:01:08.580
Renewable fuel sources include
00:01:08.580 --> 00:01:11.220
sunlight, wind, moving water,
00:01:11.220 --> 00:01:13.160
biomass from fast growing plants
00:01:13.160 --> 00:01:15.890
and geothermal heat from the earth.
00:01:15.890 --> 00:01:19.230
The lifespan of renewable
resources looks like a circle.
00:01:19.230 --> 00:01:21.450
We can use them and then
we can use them again
00:01:21.450 --> 00:01:23.300
without worrying about them running out.
00:01:23.300 --> 00:01:25.900
Non-renewable energy
sources on the other hand,
00:01:25.900 --> 00:01:28.260
are sources that exist in a fixed amount
00:01:28.260 --> 00:01:30.130
and cannot be easily replaced.
00:01:30.130 --> 00:01:33.430
These energy sources must
be extracted from the earth
00:01:33.430 --> 00:01:38.130
and they include things like
nuclear fuel and fossil fuels,
00:01:38.130 --> 00:01:42.240
which are things like
coal oil and natural gas.
00:01:42.240 --> 00:01:45.110
Fossil fuels performed
in the geologic past
00:01:45.110 --> 00:01:47.500
from the remains of ancient organisms,
00:01:47.500 --> 00:01:50.580
plants and animals that
died millions of years ago,
00:01:50.580 --> 00:01:52.350
became buried in the soil,
00:01:52.350 --> 00:01:54.430
partially decomposed,
00:01:54.430 --> 00:01:57.153
and were exposed to a
lot of heat and pressure.
00:01:58.380 --> 00:02:01.030
This heat and pressure
chemically rearranged
00:02:01.030 --> 00:02:03.140
the energy contained within their bodies
00:02:03.140 --> 00:02:05.660
into the fossil fuels we use today.
00:02:05.660 --> 00:02:08.190
Because they take so long to form,
00:02:08.190 --> 00:02:11.080
we have a finite amount
of non-renewable resources
00:02:11.080 --> 00:02:12.700
in the earth right now.
00:02:12.700 --> 00:02:15.990
The lifespan for fossil
fuels is a broken loop,
00:02:15.990 --> 00:02:17.840
a one-way ticket.
00:02:17.840 --> 00:02:20.380
First, the fossil fuel is found,
00:02:20.380 --> 00:02:22.980
then it has to be extracted.
00:02:22.980 --> 00:02:25.020
Extracting fossil fuels can involve
00:02:25.020 --> 00:02:26.650
destructive mining processes
00:02:26.650 --> 00:02:29.190
that can pollute surrounding habitats.
00:02:29.190 --> 00:02:32.770
It then has to be transported
to wherever it will be used.
00:02:32.770 --> 00:02:35.930
And using fossil fuels means burning them,
00:02:35.930 --> 00:02:37.720
which releases greenhouse gases
00:02:37.720 --> 00:02:40.280
and other pollutants into that atmosphere.
00:02:40.280 --> 00:02:42.510
Also, it can take energy to refine
00:02:42.510 --> 00:02:44.360
and process some types of fossil fuels,
00:02:44.360 --> 00:02:45.920
so that they're more helpful to us
00:02:45.920 --> 00:02:48.880
like turning crude oil
into petroleum gas, diesel,
00:02:48.880 --> 00:02:50.060
and jet fuel.
00:02:50.060 --> 00:02:53.080
And burning the fossil
fuels transforms that energy
00:02:53.080 --> 00:02:55.460
into a less organized form of energy,
00:02:55.460 --> 00:02:58.140
like heat and ash.
00:02:58.140 --> 00:03:00.720
Not all fossil fuels are the same.
00:03:00.720 --> 00:03:01.730
And this is because
00:03:01.730 --> 00:03:03.540
different kinds of organic material
00:03:03.540 --> 00:03:05.830
were heated and compressed
in different ways.
00:03:05.830 --> 00:03:08.680
Creating different kinds of fossil fuels.
00:03:08.680 --> 00:03:11.670
One of these kinds of
fossil fuels is petroleum.
00:03:11.670 --> 00:03:15.470
The word petroleum comes from
the Latin word for rock Petra
00:03:15.470 --> 00:03:18.190
and the Latin word for oil Oleum.
00:03:18.190 --> 00:03:20.640
This makes sense because
it's an oily substance
00:03:20.640 --> 00:03:23.280
that's found in reservoirs,
trapped in rock.
00:03:23.280 --> 00:03:26.560
Humans have been using
oil for a very long time.
00:03:26.560 --> 00:03:29.290
Early civilizations found it
bubbling up from the ground
00:03:29.290 --> 00:03:30.730
at natural Wells,
00:03:30.730 --> 00:03:32.570
the oil they saw coming
straight out of the earth
00:03:32.570 --> 00:03:35.690
is called crude oil or crude petroleum,
00:03:35.690 --> 00:03:39.120
which means that it is
unrefined and unprocessed.
00:03:39.120 --> 00:03:42.510
Crude oil was probably one of
the ingredients in Greek fire,
00:03:42.510 --> 00:03:44.810
which was a flame throwing
up in the Byzantines
00:03:44.810 --> 00:03:46.460
with fling at their enemies.
00:03:46.460 --> 00:03:49.420
Today we were fine crude
oil into many products
00:03:49.420 --> 00:03:52.030
like gasoline and diesel for vehicles,
00:03:52.030 --> 00:03:55.660
kerosene for heating and
asphalts for road construction.
00:03:55.660 --> 00:03:58.803
It's also used to make
plastics and synthetic fabrics.
00:03:59.800 --> 00:04:02.180
Another type of fossil fuel is coal,
00:04:02.180 --> 00:04:04.640
which we mostly burned
to make electricity,
00:04:04.640 --> 00:04:07.920
but it can also be used
for heating and cooking.
00:04:07.920 --> 00:04:10.890
It's a solid, shiny black flammable rock,
00:04:10.890 --> 00:04:13.320
which is mostly formed
from the carpenter remains
00:04:13.320 --> 00:04:16.120
of fossilized plants like MOS.
00:04:16.120 --> 00:04:17.590
Over thousands of years,
00:04:17.590 --> 00:04:19.050
plant material transforms
00:04:19.050 --> 00:04:22.060
into a carbon rich compound called peat.
00:04:22.060 --> 00:04:24.860
And then with some pressure,
it becomes soft coal,
00:04:24.860 --> 00:04:26.730
which is called lignite.
00:04:26.730 --> 00:04:30.630
And then with more pressure,
it becomes bituminous coal.
00:04:30.630 --> 00:04:34.560
And then finally it becomes a
hard coal called anthracite.
00:04:34.560 --> 00:04:36.840
The longer the plant remains
are put under pressure,
00:04:36.840 --> 00:04:39.260
the more energy dense it becomes.
00:04:39.260 --> 00:04:41.020
So if you burned anthracite,
00:04:41.020 --> 00:04:44.270
you would get a lot more
energy than if you burned peat,
00:04:44.270 --> 00:04:47.780
burning coal releases carbon
dioxide, sulfur dioxide,
00:04:47.780 --> 00:04:51.330
nitrogen oxides, and
other gases into the air.
00:04:51.330 --> 00:04:54.920
So coal is one of the
dirtiest fossil fuels.
00:04:54.920 --> 00:04:57.990
The cleanest burning
fossil fuel is natural gas,
00:04:57.990 --> 00:05:00.810
meaning that it admits the
least amount of carbon dioxide
00:05:00.810 --> 00:05:02.600
or other air prints.
00:05:02.600 --> 00:05:04.350
This is not the same type of gas
00:05:04.350 --> 00:05:06.130
as we put into our vehicles.
00:05:06.130 --> 00:05:07.940
That type comes from petroleum.
00:05:07.940 --> 00:05:10.140
Instead, natural gas is mostly used
00:05:10.140 --> 00:05:11.800
for generating electricity,
00:05:11.800 --> 00:05:14.600
heating homes and cooking food.
00:05:14.600 --> 00:05:17.230
Your oven, furnace, water heater, dryer,
00:05:17.230 --> 00:05:20.150
or grill all might run on natural gas.
00:05:20.150 --> 00:05:23.620
Natural gas is a naturally
occurring mixture of gases.
00:05:23.620 --> 00:05:26.570
And it's mostly made
up of methane, ethane,
00:05:26.570 --> 00:05:28.760
propane and butane.
00:05:28.760 --> 00:05:31.530
The gas is colorless and odorless.
00:05:31.530 --> 00:05:34.290
So natural gas companies
often add a rotten egg smell
00:05:35.125 --> 00:05:37.520
to the fuel to make
leaks easier to detect.
00:05:37.520 --> 00:05:40.510
But even though we can't
see or smell natural gas,
00:05:40.510 --> 00:05:44.320
humans have been detecting it
and using it for centuries.
00:05:44.320 --> 00:05:47.150
There is evidence that
more than 2000 years ago,
00:05:47.150 --> 00:05:49.530
people in China created bamboo pipelines
00:05:49.530 --> 00:05:51.010
to transport the gas,
00:05:51.010 --> 00:05:53.150
so that they could use
it to boil saltwater
00:05:53.150 --> 00:05:55.210
and separate out the salt.
00:05:55.210 --> 00:05:57.190
And today we still use pipelines
00:05:57.190 --> 00:05:59.010
to transport gas across land.
00:05:59.010 --> 00:06:01.363
Although they're no
longer made out of bamboo.
00:06:02.460 --> 00:06:06.500
Another kind of non-renewable
resource is nuclear fuel.
00:06:06.500 --> 00:06:09.800
Nuclear power plants
don't burn fossil fuels.
00:06:09.800 --> 00:06:12.070
Instead they split uranium
00:06:12.070 --> 00:06:14.750
through something called nuclear fission,
00:06:14.750 --> 00:06:17.070
just one kilogram of uranium,
00:06:17.070 --> 00:06:21.060
can produce 24 million
kilowatt hours of energy.
00:06:21.060 --> 00:06:23.280
Compare that with one kilogram of coal,
00:06:23.280 --> 00:06:26.630
which can produce eight
kilowatt hours of energy.
00:06:26.630 --> 00:06:30.710
In other words, nuclear fusion
produces a lot of energy.
00:06:30.710 --> 00:06:32.810
It also produces a lot of heat,
00:06:32.810 --> 00:06:34.853
which we mostly use to make electricity.
00:06:35.800 --> 00:06:39.230
Also nuclear energy is
known as a clean energy
00:06:39.230 --> 00:06:42.680
because the only greenhouse
gas emission is water vapor,
00:06:42.680 --> 00:06:44.960
which tends to cycle out
of the atmosphere faster
00:06:44.960 --> 00:06:47.170
than other greenhouse gases.
00:06:47.170 --> 00:06:49.320
But the downside is the spent fuel
00:06:49.320 --> 00:06:51.790
is a dangerous radioactive waste
00:06:51.790 --> 00:06:55.673
and recycling the nuclear waste
is dangerous and expensive.
00:06:57.320 --> 00:07:00.810
Petroleum, coal, natural
gas and nuclear fuel
00:07:00.810 --> 00:07:04.300
make up 85% of the world's
energy consumption.
00:07:04.300 --> 00:07:06.890
But as our populations
and our energy needs grow,
00:07:06.890 --> 00:07:08.270
it's becoming more important
00:07:08.270 --> 00:07:10.100
to integrate renewable resources.
00:07:10.100 --> 00:07:12.780
The sources that could be
restored by natural processes
00:07:12.780 --> 00:07:14.550
into our energy mix.
00:07:14.550 --> 00:07:17.170
I'm gonna go make some
tea now, but before I do,
00:07:17.170 --> 00:07:18.760
here's something to think about.
00:07:18.760 --> 00:07:21.750
What's something that you do
in your day that uses energy?
00:07:21.750 --> 00:07:24.120
Does that energy come from fossil fuels?
00:07:24.120 --> 00:07:26.690
And if so, which one?
00:07:26.690 --> 00:07:28.680
Understanding how you get your energy
00:07:28.680 --> 00:07:31.640
is part of understanding
what powers your community,
00:07:31.640 --> 00:07:33.963
your country, and the world.
|
Integrated pest management | https://www.youtube.com/watch?v=z2AMnP4nn2E | vtt | https://www.youtube.com/api/timedtext?v=z2AMnP4nn2E&ei=0lWUZcGwK-2Hp-oPh5qYwAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1C6FD72845548D70C7771FC4A25191B0859765AE.DB2A909A748B02A9FBC3BF9EB6DE08E3621AA5BD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.430 --> 00:00:02.360
- [Instructor] Let's
imagine your corn farmer
00:00:02.360 --> 00:00:05.120
and you would dream of having
nice, healthy corn crop,
00:00:05.120 --> 00:00:06.860
like we see in this picture.
00:00:06.860 --> 00:00:11.380
But being a farmer isn't as
simple as planting the seeds
00:00:11.380 --> 00:00:14.610
and making sure that the
crop gets enough sunshine
00:00:14.610 --> 00:00:19.610
and water and fertilizer, you
also have to deal with pests.
00:00:20.290 --> 00:00:22.840
And pests you can view as anything
00:00:22.840 --> 00:00:25.310
that might eat your crop
or destroy your crop,
00:00:25.310 --> 00:00:28.980
or make it just really hard
for you to have a good crop.
00:00:28.980 --> 00:00:30.120
Now, some of you all are familiar
00:00:30.120 --> 00:00:31.790
with the notion of pesticides,
00:00:31.790 --> 00:00:34.260
where you're essentially
poisoning the pests.
00:00:34.260 --> 00:00:37.250
Now for various reasons, that
might not be a good idea,
00:00:37.250 --> 00:00:38.600
and we'll talk more about it.
00:00:38.600 --> 00:00:42.410
And so there's a notion of
integrated pest management,
00:00:42.410 --> 00:00:45.610
which is how we can do multiple
things which might include
00:00:45.610 --> 00:00:48.810
pesticides or might not include
pesticides, to really keep
00:00:48.810 --> 00:00:50.610
things under control.
00:00:50.610 --> 00:00:54.680
And to get a good sense
of how bad a pest can be,
00:00:54.680 --> 00:00:59.003
I will introduce you to
the Western corn rootworm.
00:00:59.920 --> 00:01:01.430
Now, the reason why it's called a worm,
00:01:01.430 --> 00:01:02.650
even though in its adult phase,
00:01:02.650 --> 00:01:05.790
it does not look like a worm,
is that in its larval phase,
00:01:05.790 --> 00:01:08.220
when it's a baby, it looks like a worm.
00:01:08.220 --> 00:01:12.040
And even though the adult will
also feed on the corn silks,
00:01:12.040 --> 00:01:14.780
the real damage is done
in the larval stage.
00:01:14.780 --> 00:01:16.720
When they're feeding on the roots,
00:01:16.720 --> 00:01:20.080
that's why they're called corn rootworms.
00:01:20.080 --> 00:01:25.040
And the USDA estimates that
just in the United States,
00:01:25.040 --> 00:01:28.927
damage due to Western
corn rootworm is about
00:01:28.927 --> 00:01:33.020
$1 billion per year.
00:01:33.020 --> 00:01:36.790
About 800 million of that,
is just lost corn crop.
00:01:36.790 --> 00:01:40.360
And about 200 million of that
is all the costs in order
00:01:40.360 --> 00:01:44.500
to prevent this pest
from doing their damage.
00:01:44.500 --> 00:01:45.880
Now, as I mentioned, if we think about
00:01:45.880 --> 00:01:47.270
integrated pest management,
00:01:47.270 --> 00:01:49.960
there's many ways of addressing this.
00:01:49.960 --> 00:01:53.070
One way of course, that many
people think of, is pesticides.
00:01:53.070 --> 00:01:56.690
And this is an image of crop dusting.
00:01:56.690 --> 00:01:58.340
I don't think this is a corn field here,
00:01:58.340 --> 00:02:00.750
we can see the pesticides
coming from the biplane.
00:02:00.750 --> 00:02:02.570
And it's a way of
spreading the pesticides,
00:02:02.570 --> 00:02:05.180
not the only way, but for various reasons,
00:02:05.180 --> 00:02:06.610
this is not optimal.
00:02:06.610 --> 00:02:09.080
You could view it as
polluting the environment
00:02:09.080 --> 00:02:10.170
in certain ways.
00:02:10.170 --> 00:02:12.560
A lot of us aren't so keen on eating crops
00:02:12.560 --> 00:02:14.450
that have pesticides on them.
00:02:14.450 --> 00:02:18.030
And we've learned in other
videos on evolution and natural
00:02:18.030 --> 00:02:20.560
selection, there's
variation in any population.
00:02:20.560 --> 00:02:23.050
And the more that you expose
a population to something,
00:02:23.050 --> 00:02:25.040
and it kills off the ones
that are susceptible,
00:02:25.040 --> 00:02:27.570
the more chances that the ones
that aren't as susceptible,
00:02:27.570 --> 00:02:29.230
reproduce and thrive.
00:02:29.230 --> 00:02:32.930
So at some point you might
have an insecticide resistant
00:02:32.930 --> 00:02:35.080
pest on your hands and
then your insecticide,
00:02:35.080 --> 00:02:37.530
isn't going to be all that useful.
00:02:37.530 --> 00:02:39.540
So when we think about
integrated pest management,
00:02:39.540 --> 00:02:40.373
we think about art,
00:02:40.373 --> 00:02:41.830
what are other ways to address this?
00:02:41.830 --> 00:02:43.860
Maybe in conjunction, maybe ways
00:02:43.860 --> 00:02:46.600
that could be perceived
to be more natural?
00:02:46.600 --> 00:02:48.880
Well one obvious thing
is to think about, well,
00:02:48.880 --> 00:02:51.320
what are the predators of that pest?
00:02:51.320 --> 00:02:53.580
And this is the wasp spider,
00:02:53.580 --> 00:02:57.290
and this is what's known as
a ladybug in North America
00:02:57.290 --> 00:02:59.680
and ladybird in much of
the rest of the world.
00:02:59.680 --> 00:03:04.300
And they will actually feed
on the Western corn rootworm.
00:03:04.300 --> 00:03:07.070
So you might want to
introduce this onto your farm
00:03:07.070 --> 00:03:09.350
if you're trying to grow that corn.
00:03:09.350 --> 00:03:11.340
Another thing that farmers have done
00:03:11.340 --> 00:03:14.440
to some degree of success,
is early planting.
00:03:14.440 --> 00:03:16.490
By planting the crop early,
00:03:16.490 --> 00:03:20.400
it's less favorable for the
root worm to lay their eggs.
00:03:20.400 --> 00:03:24.350
And also it gives a chance
for the roots to get stronger,
00:03:24.350 --> 00:03:29.350
so that by the time that they're
attacked by the rootworm,
00:03:29.530 --> 00:03:31.600
they're going to be more resilient.
00:03:31.600 --> 00:03:33.940
You could also have
hybrid versions of corn
00:03:33.940 --> 00:03:36.250
that just have larger roots.
00:03:36.250 --> 00:03:38.020
So once again, they're going to be more
00:03:38.020 --> 00:03:40.200
resilient to the rootworm.
00:03:40.200 --> 00:03:43.400
Another technique is to
genetically modify the corn.
00:03:43.400 --> 00:03:45.760
And that also is a bit
of a controversial topic,
00:03:45.760 --> 00:03:47.370
depending on who you talk to.
00:03:47.370 --> 00:03:49.860
You might've heard things about GMO,
00:03:49.860 --> 00:03:52.160
genetically modified organism.
00:03:52.160 --> 00:03:53.680
Some people think they're fine.
00:03:53.680 --> 00:03:55.320
Some people are wary of them.
00:03:55.320 --> 00:03:57.890
But there is a transgenic version of corn.
00:03:57.890 --> 00:04:02.020
Transgenic means, that we took
DNA from some other organism
00:04:02.020 --> 00:04:03.470
and put it into the corn.
00:04:03.470 --> 00:04:07.970
And that transgenic version
is known as BT corn.
00:04:07.970 --> 00:04:10.690
That actually has DNA from a bacteria,
00:04:10.690 --> 00:04:12.890
which produces a protein,
00:04:12.890 --> 00:04:15.790
which is harmful to certain
types of root worms.
00:04:15.790 --> 00:04:17.880
Now, another really interesting technique,
00:04:17.880 --> 00:04:20.280
which people have used to
some degree of success,
00:04:20.280 --> 00:04:22.380
is known as crop rotation.
00:04:22.380 --> 00:04:24.450
Let's imagine looking down from the sky
00:04:24.450 --> 00:04:26.290
onto a corn crop here.
00:04:26.290 --> 00:04:28.290
So we're looking down from above.
00:04:28.290 --> 00:04:30.310
So what normally happens is,
00:04:30.310 --> 00:04:33.800
is that the eggs are laid near the corn
00:04:33.800 --> 00:04:36.090
and the larvae can't travel so far.
00:04:36.090 --> 00:04:37.930
So they, if they're near the corn,
00:04:37.930 --> 00:04:39.760
they get to the roots
and then they're able to,
00:04:39.760 --> 00:04:42.170
the reproduction cycle goes on.
00:04:42.170 --> 00:04:45.850
But if we rotate the crops so
that the next year we're not
00:04:45.850 --> 00:04:50.850
planting here, but maybe we
are planting the corn over here
00:04:50.980 --> 00:04:53.720
and then in that first place,
we're planting soybean.
00:04:53.720 --> 00:04:55.520
Well, that can solve the problem,
00:04:55.520 --> 00:04:57.080
because the eggs will be laid here.
00:04:57.080 --> 00:04:59.980
But next year the corn
is going to be here.
00:04:59.980 --> 00:05:02.820
And over here, we will have the soybean,
00:05:02.820 --> 00:05:06.890
which is not a suitable
food for the corn rootworm.
00:05:06.890 --> 00:05:08.250
Now what's really interesting,
00:05:08.250 --> 00:05:10.600
and this is another one of
those fascinating stories
00:05:10.600 --> 00:05:12.540
of evolution and natural selection,
00:05:12.540 --> 00:05:15.920
are there cases because there's
variation in populations,
00:05:15.920 --> 00:05:20.920
where some of the adult rootworm
actually doesn't lay their
00:05:21.320 --> 00:05:24.860
eggs in the same corn
crop, where they feed,
00:05:24.860 --> 00:05:27.240
they lay it in an adjacent corn crop.
00:05:27.240 --> 00:05:30.830
So that next year when
the crop rotation happens,
00:05:30.830 --> 00:05:34.170
then their larva are going
to have access to the corn
00:05:34.170 --> 00:05:35.620
in the other field.
00:05:35.620 --> 00:05:37.190
Now you might say, how did they know that?
00:05:37.190 --> 00:05:40.010
How did they know that the
farmers were planning to rotate?
00:05:40.010 --> 00:05:41.930
Well, generally the
rotations are pretty simple.
00:05:41.930 --> 00:05:43.920
You keep alternating between two crops
00:05:43.920 --> 00:05:45.470
like corn and soybean.
00:05:45.470 --> 00:05:48.810
And most of the Western corn rootworm
00:05:48.810 --> 00:05:50.010
would not have done that,
00:05:50.010 --> 00:05:52.880
but just some of them might
have started to randomly travel
00:05:52.880 --> 00:05:53.800
a little bit further.
00:05:53.800 --> 00:05:56.410
And then those would be
more likely to reproduce.
00:05:56.410 --> 00:05:58.920
So the ones are more likely to reproduce
00:05:58.920 --> 00:05:59.753
will then exist more.
00:05:59.753 --> 00:06:01.640
And then that behavior would be passed on,
00:06:01.640 --> 00:06:03.800
if it is a genetic trait.
00:06:03.800 --> 00:06:05.480
There's other situations once again,
00:06:05.480 --> 00:06:07.440
because of the variation in populations,
00:06:07.440 --> 00:06:10.680
where some of the eggs stay
dormant for an extra year.
00:06:10.680 --> 00:06:13.380
So even though you might
rotate to corn this year,
00:06:13.380 --> 00:06:15.440
the year after that,
you rotate back to corn
00:06:15.440 --> 00:06:19.070
and then the eggs hatch
and the larva can feed.
00:06:19.070 --> 00:06:21.800
So it's a fascinating, almost arms race,
00:06:21.800 --> 00:06:24.470
between the farmer and these pests.
00:06:24.470 --> 00:06:26.760
But I hope you appreciate,
it's far more interesting
00:06:26.760 --> 00:06:28.220
than you might have realized before.
00:06:28.220 --> 00:06:30.440
And I haven't even given
you a comprehensive list
00:06:30.440 --> 00:06:32.900
of all the types of
pests and all of the ways
00:06:32.900 --> 00:06:33.870
that you might want to manage it.
00:06:33.870 --> 00:06:36.330
You can do physical removal,
you could do barriers.
00:06:36.330 --> 00:06:38.560
Maybe you'll think of another creative way
00:06:38.560 --> 00:06:41.873
to have integrated pest management.
|
Demographic transition model | https://www.youtube.com/watch?v=kEOgW5Rg0o8 | vtt | https://www.youtube.com/api/timedtext?v=kEOgW5Rg0o8&ei=0lWUZeL6I7etp-oP3p-kyA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=4CA89AB0C4EE9BA6F701CD4EC6C3FE46586191B0.1071D1D67B89B14E7304ADD1E861DFE7FBC500BA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.710 --> 00:00:02.650
- [Narrator] In this video,
we're going to study something
00:00:02.650 --> 00:00:05.530
called the demographic transition model,
00:00:05.530 --> 00:00:07.510
which is something demographers use.
00:00:07.510 --> 00:00:11.140
Demographers are people who
study the makeup of populations
00:00:11.140 --> 00:00:13.410
and how those transition over time
00:00:13.410 --> 00:00:15.140
and why that might happen.
00:00:15.140 --> 00:00:18.240
And this model in particular
is one to think about
00:00:18.240 --> 00:00:21.450
how a country goes from
being pre-industrial
00:00:21.450 --> 00:00:25.150
to post-industrial, and what
happens to the birth rate,
00:00:25.150 --> 00:00:27.480
the death rate, and the total population
00:00:27.480 --> 00:00:29.850
over time as they make that transition.
00:00:29.850 --> 00:00:32.480
And as we'll see, it
happens over four stages.
00:00:32.480 --> 00:00:34.060
So let's just first understand
00:00:34.060 --> 00:00:36.860
what's going on in this graphic year.
00:00:36.860 --> 00:00:41.410
So our horizontal axis
we see is our time axis.
00:00:41.410 --> 00:00:43.690
And depending on the
country we're studying,
00:00:43.690 --> 00:00:44.870
this might occur.
00:00:44.870 --> 00:00:45.840
Oh, in fact, it's definitely
00:00:45.840 --> 00:00:47.330
going to occur over many decades,
00:00:47.330 --> 00:00:49.040
but some countries still
haven't even gotten
00:00:49.040 --> 00:00:50.640
through all of these phases.
00:00:50.640 --> 00:00:52.700
So it might've been a century already.
00:00:52.700 --> 00:00:55.230
And they might still be
in say this second phase
00:00:55.230 --> 00:00:57.500
which we'll describe in
a little bit more detail.
00:00:57.500 --> 00:01:01.130
The vertical axis, you can see
it says rates per thousand.
00:01:01.130 --> 00:01:04.900
And this is useful for
looking at the birth rate
00:01:04.900 --> 00:01:07.460
and the death rate, the
total population here
00:01:07.460 --> 00:01:09.170
which is in this light blue color,
00:01:09.170 --> 00:01:10.900
that really shouldn't be read as a rate,
00:01:10.900 --> 00:01:12.650
that is the total population.
00:01:12.650 --> 00:01:14.550
You could probably add another axis here
00:01:14.550 --> 00:01:16.450
to measure total population,
00:01:16.450 --> 00:01:17.640
but it's telling us indicatively
00:01:17.640 --> 00:01:20.040
where the total population is.
00:01:20.040 --> 00:01:23.170
Now we see the birth
rate in this blue color
00:01:23.170 --> 00:01:24.280
and we see the death rate
00:01:24.280 --> 00:01:27.760
in this salmon or this
pink, orange, red color.
00:01:27.760 --> 00:01:30.640
And we can see that as a country is,
00:01:30.640 --> 00:01:31.940
I guess you could say, starting out,
00:01:31.940 --> 00:01:33.650
or really according to this model,
00:01:33.650 --> 00:01:36.603
we would call it pre-industrial phase,
00:01:37.870 --> 00:01:39.900
which is pre-industrial,
00:01:39.900 --> 00:01:42.880
which is this phase right over here.
00:01:42.880 --> 00:01:45.040
You have relatively high birth rates
00:01:45.040 --> 00:01:47.140
and relatively high death rates.
00:01:47.140 --> 00:01:48.520
Why is that happening?
00:01:48.520 --> 00:01:50.330
Well, in most pre-industrial societies,
00:01:50.330 --> 00:01:53.660
you have a high death
rate because healthcare
00:01:53.660 --> 00:01:56.960
is either non-existent
or it isn't that good.
00:01:56.960 --> 00:01:59.040
So you could have high child mortality.
00:01:59.040 --> 00:02:01.920
A lot of people are dying from diseases
00:02:01.920 --> 00:02:04.540
that are easy to cure
in an industrial society
00:02:04.540 --> 00:02:07.000
or in a post-industrial
society, which we'll talk about.
00:02:07.000 --> 00:02:09.360
And why is there a high birth rate?
00:02:09.360 --> 00:02:11.640
Oftentimes, culturally women still haven't
00:02:11.640 --> 00:02:13.820
entered the workforce in a major way.
00:02:13.820 --> 00:02:16.410
Education generally is at a low level
00:02:16.410 --> 00:02:19.030
especially for women at this
stage because fundamentally
00:02:19.030 --> 00:02:21.420
of a lack of a healthcare
system for most people,
00:02:21.420 --> 00:02:23.990
you might not have things
like family planning.
00:02:23.990 --> 00:02:25.930
And so you could imagine that might lead
00:02:25.930 --> 00:02:28.070
to an overall higher birth rate.
00:02:28.070 --> 00:02:29.490
Now, because both the birth rate
00:02:29.490 --> 00:02:32.490
and the death rate are high,
but they're about the same,
00:02:32.490 --> 00:02:35.190
you can see that you
have a relatively stable
00:02:35.190 --> 00:02:38.600
but we'll say in absolute
terms, low population.
00:02:38.600 --> 00:02:42.550
And then countries might
start to industrialize.
00:02:42.550 --> 00:02:46.673
And so we call this state right
here the transitional state,
00:02:48.970 --> 00:02:51.690
and we can see that at
least on this graphic,
00:02:51.690 --> 00:02:54.660
it is elongated and different
countries go through this
00:02:54.660 --> 00:02:56.120
in different amounts of time.
00:02:56.120 --> 00:02:58.300
You might have a country like Japan
00:02:58.300 --> 00:03:01.410
that went through this in
less than half a century,
00:03:01.410 --> 00:03:02.670
but you might have other countries
00:03:02.670 --> 00:03:03.930
that are still going through this,
00:03:03.930 --> 00:03:07.920
even after a half a century
or even a century or more.
00:03:07.920 --> 00:03:09.560
But in the transitional state,
00:03:09.560 --> 00:03:13.390
this country will start to industrialize.
00:03:13.390 --> 00:03:15.390
And this whole model is based on
00:03:15.390 --> 00:03:18.950
looking at what happened in
Europe, in the 19th century,
00:03:18.950 --> 00:03:21.100
as much of Europe
industrialized and saying, okay,
00:03:21.100 --> 00:03:23.700
maybe other countries will
go through the same pattern
00:03:23.700 --> 00:03:26.600
of demographics as they industrialize.
00:03:26.600 --> 00:03:28.350
So let's think about
what is happening here.
00:03:28.350 --> 00:03:30.320
We see that the death rate
00:03:30.320 --> 00:03:32.880
is starting to come
down pretty reasonably.
00:03:32.880 --> 00:03:34.500
Now, the argument why that would happen
00:03:34.500 --> 00:03:37.290
as this country is industrializing
00:03:37.290 --> 00:03:40.270
is because they would now
have better healthcare,
00:03:40.270 --> 00:03:42.670
they might have better nutrition now.
00:03:42.670 --> 00:03:43.670
In fact, that's another reason
00:03:43.670 --> 00:03:46.260
why the pre-industrial society
might have a high death rate.
00:03:46.260 --> 00:03:49.410
People are even having illnesses
or dying from malnutrition.
00:03:49.410 --> 00:03:52.010
But now, because say farm
productivity is higher
00:03:52.010 --> 00:03:54.630
because they're able to
use more modern methods,
00:03:54.630 --> 00:03:58.000
the nutrition is better,
death rates start coming down.
00:03:58.000 --> 00:04:01.320
And birth rates might start
coming down a little bit,
00:04:01.320 --> 00:04:03.300
but not as quickly as the death rates.
00:04:03.300 --> 00:04:06.190
Now, why the birth rates
might start coming down?
00:04:06.190 --> 00:04:08.410
Well, once again, access to healthcare.
00:04:08.410 --> 00:04:10.660
More women might be able
to enter the workforce.
00:04:10.660 --> 00:04:13.040
You're having a higher level of education
00:04:13.040 --> 00:04:17.220
as the society starts to
develop and becomes wealthier.
00:04:17.220 --> 00:04:20.000
Now, with the death rate
going down at a faster rate
00:04:20.000 --> 00:04:21.770
than the birth rate,
00:04:21.770 --> 00:04:24.380
all of a sudden this will
add to the population.
00:04:24.380 --> 00:04:26.710
If fewer people are dying than being born,
00:04:26.710 --> 00:04:30.130
the population is increasing over time.
00:04:30.130 --> 00:04:33.150
And in fact, the rate of
population increase is increasing
00:04:33.150 --> 00:04:37.810
as this gap between birth
rate and death rate increases.
00:04:37.810 --> 00:04:42.470
Now, the next stage of our
demographic transition model,
00:04:42.470 --> 00:04:45.060
we would consider industrial.
00:04:45.060 --> 00:04:48.290
And the real marker of that
00:04:48.290 --> 00:04:51.200
is we see that in the industrial phase,
00:04:51.200 --> 00:04:55.980
our birth rate is starting to
catch up with our death rate.
00:04:55.980 --> 00:04:58.690
And so at this phase,
women might be entering
00:04:58.690 --> 00:05:00.170
in the workforce in a major way.
00:05:00.170 --> 00:05:02.480
Culturally, it is far more acceptable
00:05:02.480 --> 00:05:04.060
for things like family planning,
00:05:04.060 --> 00:05:05.800
culturally far more acceptable
00:05:05.800 --> 00:05:08.460
for people to delay giving birth,
00:05:08.460 --> 00:05:11.720
especially for women so that
they could get their education.
00:05:11.720 --> 00:05:12.980
And there's just more awareness
00:05:12.980 --> 00:05:14.670
that by having fewer children,
00:05:14.670 --> 00:05:17.280
the children you do have
will be more prosperous,
00:05:17.280 --> 00:05:18.730
will get better nutrition.
00:05:18.730 --> 00:05:21.640
The family is overall
likely to be wealthier.
00:05:21.640 --> 00:05:23.860
So as the birth rate
and the death rate curve
00:05:23.860 --> 00:05:26.010
get closer and closer together,
00:05:26.010 --> 00:05:29.280
the rate of population
growth starts to slow.
00:05:29.280 --> 00:05:31.850
And then this last phase
right here over here,
00:05:31.850 --> 00:05:35.060
the fourth phase in our
demographic transition model
00:05:35.060 --> 00:05:38.363
which we could call post industrial,
00:05:39.660 --> 00:05:42.540
we see that not only has the birth rate
00:05:42.540 --> 00:05:44.300
caught up to the death rate,
00:05:44.300 --> 00:05:47.940
that it actually can go
below the death rate.
00:05:47.940 --> 00:05:51.230
And so in that situation,
you have a stable population,
00:05:51.230 --> 00:05:52.440
but if the birth rate
00:05:52.440 --> 00:05:54.496
actually even goes below the death rate,
00:05:54.496 --> 00:05:58.200
you can even see the
population began to decline.
00:05:58.200 --> 00:06:01.030
And there are societies
that are already there.
00:06:01.030 --> 00:06:04.270
For example, Japan has
a declining population,
00:06:04.270 --> 00:06:06.110
even places like the United States.
00:06:06.110 --> 00:06:07.920
If we did not have immigration,
00:06:07.920 --> 00:06:10.090
you would have a declining population
00:06:10.090 --> 00:06:13.720
because we are in this
last phase right over here.
00:06:13.720 --> 00:06:16.610
And this post-industrial
declining population
00:06:16.610 --> 00:06:18.640
because birth rates have gotten so low,
00:06:18.640 --> 00:06:20.660
have its own set of issues.
00:06:20.660 --> 00:06:22.680
You now have an aging population.
00:06:22.680 --> 00:06:24.000
If birth rates are much lower
00:06:24.000 --> 00:06:25.750
and people are living much longer,
00:06:25.750 --> 00:06:28.750
a higher and higher percentage
of the population is older.
00:06:28.750 --> 00:06:31.670
Older people, especially once
they are out of the workforce,
00:06:31.670 --> 00:06:32.930
who's going to support them?
00:06:32.930 --> 00:06:34.870
Who's going to provide
the healthcare for them?
00:06:34.870 --> 00:06:37.430
Where are those resources
going to come from?
00:06:37.430 --> 00:06:40.550
If your population is shrinking,
00:06:40.550 --> 00:06:43.030
then your economy might
not be growing as fast,
00:06:43.030 --> 00:06:45.830
which would make it even
harder to support the costs
00:06:45.830 --> 00:06:47.320
of an aging population.
00:06:47.320 --> 00:06:48.570
So I'll leave you there.
00:06:48.570 --> 00:06:51.150
Once again, this is a
model, it's a hypothesis,
00:06:51.150 --> 00:06:53.690
but it's a useful one to
at least have a framework
00:06:53.690 --> 00:06:56.620
of how things might transition
in the society over time.
00:06:56.620 --> 00:06:59.260
And people use this type of
model to advise countries,
00:06:59.260 --> 00:07:01.770
especially ones that might be
in this transitional state.
00:07:01.770 --> 00:07:03.280
And the transitional state,
00:07:03.280 --> 00:07:05.830
sometimes is the place where
countries might get stuck
00:07:05.830 --> 00:07:08.650
because they're getting
delayed economic development.
00:07:08.650 --> 00:07:10.920
So they're not quite able
to get too industrial.
00:07:10.920 --> 00:07:13.800
And so demographers, economists,
others will think about,
00:07:13.800 --> 00:07:17.863
well, how can you make this
transition as well as possible?
|
Weak acid–weak base reactions | https://www.youtube.com/watch?v=G5FVxAzlmfM | vtt | https://www.youtube.com/api/timedtext?v=G5FVxAzlmfM&ei=0lWUZfL_IrvoxN8PscetEA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=425349A345A0A41340B17CFB383AF415532D8920.C33B30E17AFCD1DF5D845990A40AA66914C979A0&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:01.560
- [Instructor] Let's say the HA
00:00:01.560 --> 00:00:04.670
represents a generic weak acid
00:00:04.670 --> 00:00:08.680
and B represents a generic weak base.
00:00:08.680 --> 00:00:11.860
If our weak acid donates
a proton to our weak base,
00:00:11.860 --> 00:00:15.480
that would form A minus and HB plus.
00:00:15.480 --> 00:00:17.860
To identify conjugate acid base pairs
00:00:17.860 --> 00:00:21.260
remember there's only one
proton or one H plus difference
00:00:21.260 --> 00:00:24.590
between an acid and it's conjugate base.
00:00:24.590 --> 00:00:28.300
So when HA donates its proton
and turns into A minus,
00:00:28.300 --> 00:00:33.103
A minus must be the conjugate base to HA.
00:00:34.570 --> 00:00:38.760
So there's one H plus difference
between HA and A minus.
00:00:38.760 --> 00:00:41.650
They are a conjugate acid base pair.
00:00:41.650 --> 00:00:43.210
When B accepts a proton,
00:00:43.210 --> 00:00:48.130
it turns into HB plus
therefore HB plus must be
00:00:48.130 --> 00:00:52.490
the conjugate acid to B.
00:00:52.490 --> 00:00:56.210
Since there's one H plus
difference between B and HB plus,
00:00:56.210 --> 00:00:59.410
they are a conjugate acid base pair.
00:00:59.410 --> 00:01:02.240
Let's look at the situation
where the equilibrium constant
00:01:02.240 --> 00:01:04.600
for this reaction is greater than one.
00:01:04.600 --> 00:01:07.390
If K is greater than one, that
means that at equilibrium,
00:01:07.390 --> 00:01:09.840
there are more products than reactants
00:01:09.840 --> 00:01:13.170
therefore, the equilibrium
favors the formation
00:01:13.170 --> 00:01:15.100
of the products.
00:01:15.100 --> 00:01:17.270
For acid-base reactions the equilibrium
00:01:17.270 --> 00:01:19.770
always favors the side
with the weaker acid
00:01:19.770 --> 00:01:21.630
and the weaker base.
00:01:21.630 --> 00:01:24.730
Therefore, since the
equilibrium favors the products,
00:01:24.730 --> 00:01:27.090
the weaker acid and the weaker base,
00:01:27.090 --> 00:01:28.710
are on the product side
00:01:28.710 --> 00:01:31.170
and the stronger acid
and the stronger base
00:01:31.170 --> 00:01:33.000
are on the reactant side.
00:01:33.000 --> 00:01:34.750
So when comparing our two acids,
00:01:34.750 --> 00:01:39.750
HA and HB plus, HA is the
stronger acid of the two.
00:01:40.580 --> 00:01:44.660
And when comparing our
two bases B and A minus,
00:01:44.660 --> 00:01:47.273
B is the stronger base of the two.
00:01:48.110 --> 00:01:50.420
When the equilibrium
constant is less than one
00:01:50.420 --> 00:01:51.990
that means at equilibrium,
00:01:51.990 --> 00:01:54.520
there are more reactants
than there are products.
00:01:54.520 --> 00:01:55.720
Therefore, this time,
00:01:55.720 --> 00:01:59.470
the equilibrium favors the
formation of the reactants.
00:01:59.470 --> 00:02:01.820
And the equilibrium always favors the side
00:02:01.820 --> 00:02:04.640
with the weaker acid and the weaker base.
00:02:04.640 --> 00:02:07.760
Since the equilibrium
favors the reactants,
00:02:07.760 --> 00:02:09.840
the weaker acid and the weaker base,
00:02:09.840 --> 00:02:11.180
are on the reactant side
00:02:11.180 --> 00:02:13.530
and the stronger acid
and the stronger base
00:02:13.530 --> 00:02:15.520
are on the product side.
00:02:15.520 --> 00:02:19.340
So comparing our two acids, HA and HB plus
00:02:19.340 --> 00:02:22.570
this time, HB plus is the
stronger acid of the two
00:02:22.570 --> 00:02:25.490
and for our bases B and A minus
00:02:25.490 --> 00:02:29.720
this time, A minus is the
stronger base of the two.
00:02:29.720 --> 00:02:33.870
Let's look at an example of a
weak acid, weak base reaction.
00:02:33.870 --> 00:02:35.500
The Hydrogen Sulfate anion
00:02:35.500 --> 00:02:37.400
we'll react with the Carbonate anion
00:02:37.400 --> 00:02:39.470
to form the Sulfate anion
00:02:39.470 --> 00:02:42.150
and the Hydrogen Carbonate anion.
00:02:42.150 --> 00:02:44.760
Looking at the reaction,
the Hydrogen Sulfate anion
00:02:44.760 --> 00:02:48.000
is donating its proton
so that must be the acid
00:02:48.000 --> 00:02:51.610
and the Carbonate anion
is accepting a proton
00:02:51.610 --> 00:02:54.450
so that must be the base.
00:02:54.450 --> 00:02:57.210
After the Hydrogen Sulfate
anion donates it's proton
00:02:57.210 --> 00:03:00.870
it turns into the Sulfate
anion, SO four, two minus.
00:03:00.870 --> 00:03:05.320
Therefore the Sulfate anion
must be the conjugate base
00:03:05.320 --> 00:03:07.910
to HSO four minus.
00:03:07.910 --> 00:03:11.940
So one conjugate acid base
pair is HSO four minus
00:03:11.940 --> 00:03:14.390
and SO four, two minus.
00:03:14.390 --> 00:03:16.770
And when the Carbonate anion
and accepts the proton,
00:03:16.770 --> 00:03:19.760
it turns into the
Hydrogen Carbonate anion.
00:03:19.760 --> 00:03:21.980
Therefore the Hydrogen Carbonate anion,
00:03:21.980 --> 00:03:26.980
must be the conjugate acid
to the Carbonate anion.
00:03:29.170 --> 00:03:31.240
So our other conjugate acid-base pair
00:03:31.240 --> 00:03:33.490
consists of the Carbonate anion,
00:03:33.490 --> 00:03:36.000
and the Hydrogen Carbonate anion.
00:03:36.000 --> 00:03:38.380
The equilibrium constant for this reaction
00:03:38.380 --> 00:03:41.210
at 25 degrees Celsius is greater than one,
00:03:41.210 --> 00:03:43.350
therefore the equilibrium favors
00:03:43.350 --> 00:03:46.350
the formation of the products.
00:03:46.350 --> 00:03:48.050
And because the equilibrium favors
00:03:48.050 --> 00:03:50.920
the formation of the weaker
acid and the weaker base,
00:03:50.920 --> 00:03:53.110
we know that the weaker
acid and the weaker base
00:03:53.110 --> 00:03:54.560
must be on the product side
00:03:54.560 --> 00:03:56.860
and the stronger acid
and the stronger base
00:03:56.860 --> 00:03:58.630
are on the reactant side.
00:03:58.630 --> 00:04:02.339
Therefore the Hydrogen Sulfate
anion is a stronger acid
00:04:02.339 --> 00:04:04.503
than the Hydrogen Carbonate anion,
00:04:04.503 --> 00:04:07.330
and the Carbonate anion
in as a stronger base
00:04:07.330 --> 00:04:09.730
than the Sulfate anion.
00:04:09.730 --> 00:04:11.010
Let's look at another example
00:04:11.010 --> 00:04:13.630
of a weak acid, weak base reaction.
00:04:13.630 --> 00:04:14.463
In this case,
00:04:14.463 --> 00:04:16.740
Hydrofluoric acid reacts with Ammonia
00:04:16.740 --> 00:04:19.290
to form the Ammonium ion an NH four plus,
00:04:19.290 --> 00:04:22.090
and the Fluoride anion, F minus.
00:04:22.090 --> 00:04:26.100
Because Hydrofluoric acid
donates a proton, it's an acid
00:04:26.100 --> 00:04:29.650
and because Ammonia accepts a proton
00:04:29.650 --> 00:04:32.960
Ammonia functions as a base.
00:04:32.960 --> 00:04:35.020
And when HF donates a proton,
00:04:35.020 --> 00:04:37.760
it turns into F minus the Fluoride anion,
00:04:37.760 --> 00:04:42.760
therefore the Fluoride anion
is the conjugate base to HF.
00:04:43.560 --> 00:04:45.360
And when Ammonia accepts a proton,
00:04:45.360 --> 00:04:48.670
it turns into NH four
Plus the Ammonium ion,
00:04:48.670 --> 00:04:52.540
therefore the Ammonium
ion is the conjugate acid
00:04:52.540 --> 00:04:54.223
to NH three.
00:04:55.130 --> 00:04:58.860
Let's say that we mix equal
moles of our weak acid HF
00:04:58.860 --> 00:05:01.200
with our weak base NH three
00:05:01.200 --> 00:05:04.280
and our goal is to figure
out if the resulting solution
00:05:04.280 --> 00:05:07.310
is acidic, basic or neutral.
00:05:07.310 --> 00:05:09.860
First, we need to determine
if the reactants or products
00:05:09.860 --> 00:05:11.830
are favored at equilibrium.
00:05:11.830 --> 00:05:13.210
And to help us determine that
00:05:13.210 --> 00:05:15.660
here we have the Ka and Kb values
00:05:15.660 --> 00:05:17.630
for our acids and bases.
00:05:17.630 --> 00:05:20.380
So here's the Ka value
for Hydrofluoric acid
00:05:20.380 --> 00:05:22.400
at 25 degrees Celsius,
00:05:22.400 --> 00:05:24.520
so all of these are at 25 degrees Celsius.
00:05:24.520 --> 00:05:27.217
Here's the Kb value for Ammonia,
00:05:27.217 --> 00:05:29.709
the Ka value for the Ammonium ion
00:05:29.709 --> 00:05:33.070
and the Kb value for the Fluoride anion.
00:05:33.070 --> 00:05:36.160
So looking at our two acids
that was Hydrofluoric acid
00:05:36.160 --> 00:05:38.410
and the Ammonium cation,
00:05:38.410 --> 00:05:42.070
the Ka for Hydrofluoric
acid is a higher value
00:05:42.070 --> 00:05:44.640
than the Ka for the Ammonium cation.
00:05:44.640 --> 00:05:49.440
Therefore Hydrofluoric acid
is the stronger of the two,
00:05:49.440 --> 00:05:51.690
the stronger acid of the two.
00:05:51.690 --> 00:05:53.100
And for the two bases,
00:05:53.100 --> 00:05:56.180
we have Ammonia and we also
have the Fluoride anion,
00:05:56.180 --> 00:05:58.080
looking at the Kb values,
00:05:58.080 --> 00:06:01.240
for Ammonia the Kb value is higher
00:06:01.240 --> 00:06:03.410
than the Kb value for the Fluoride anion,
00:06:03.410 --> 00:06:07.283
therefore Ammonia is the
stronger base of the two.
00:06:08.200 --> 00:06:10.510
So we have the stronger
acid and the stronger base
00:06:10.510 --> 00:06:11.660
on the reactant side
00:06:11.660 --> 00:06:13.840
and the weaker acid and the weaker base
00:06:13.840 --> 00:06:15.400
on the product side.
00:06:15.400 --> 00:06:17.560
We know the equilibrium favors the side
00:06:17.560 --> 00:06:19.930
with the weaker acid and the weaker base.
00:06:19.930 --> 00:06:21.610
Therefore the equilibrium
00:06:21.610 --> 00:06:25.160
favors the formation of the products.
00:06:25.160 --> 00:06:27.800
So we could go ahead and
write the equilibrium constant
00:06:27.800 --> 00:06:31.110
for this reaction is greater than one.
00:06:31.110 --> 00:06:32.310
And at equilibrium
00:06:32.310 --> 00:06:33.640
we're going to have more of our products
00:06:33.640 --> 00:06:35.410
than we do of our reactants.
00:06:35.410 --> 00:06:38.240
So to determine at the solution
as acidic, basic or neutral,
00:06:38.240 --> 00:06:40.650
we have to think about the Ammonium cation
00:06:40.650 --> 00:06:44.160
and the Fluoride anion
in aqueous solution.
00:06:44.160 --> 00:06:46.666
Since the Ka value for the Ammonium cation
00:06:46.666 --> 00:06:47.573
is greater than the Kb value
for the Fluoride anion,
00:06:50.201 --> 00:06:53.005
the Ammonium cation is better
at producing Hydronium ions
00:06:53.005 --> 00:06:54.357
in aqueous solution
00:06:54.357 --> 00:06:57.773
than the Fluoride anion is
at producing Hydroxide anions
00:06:57.773 --> 00:06:59.710
in aqueous solution.
00:06:59.710 --> 00:07:02.040
So the concentration of Hydronium ions
00:07:02.040 --> 00:07:06.270
will be greater than the
concentration of Hydroxide anions
00:07:06.270 --> 00:07:10.253
and therefore the resulting
solution will be acidic.
|
Weak base–strong acid reactions | https://www.youtube.com/watch?v=78Sg3RdEPVk | vtt | https://www.youtube.com/api/timedtext?v=78Sg3RdEPVk&ei=0lWUZaa_I66Jp-oPqNeBgAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=474204F88C5A86443FCCDB465CBEA935879CB507.76A0803B0D485A2ACA226607C5545473DB4389FB&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:03.350
- [Instructor] Ammonia is
an example of a weak base.
00:00:03.350 --> 00:00:07.280
and hydrochloric acid is an
example of a strong acid.
00:00:07.280 --> 00:00:09.170
Ammonia reacts with hydrochloric acid
00:00:09.170 --> 00:00:12.280
to form an aqueous solution
of ammonium chloride.
00:00:12.280 --> 00:00:15.240
And because this is an acid-base
neutralization reaction,
00:00:15.240 --> 00:00:17.420
there's only a single
arrow going to the right,
00:00:17.420 --> 00:00:20.380
indicating the reaction
goes to completion.
00:00:20.380 --> 00:00:24.120
Next, let's write the overall
or complete ionic equation.
00:00:24.120 --> 00:00:25.760
Let's start with ammonia.
00:00:25.760 --> 00:00:27.230
Ammonia is a weak base,
00:00:27.230 --> 00:00:31.010
and weak bases only partly
ionize in aqueous solution.
00:00:31.010 --> 00:00:34.020
Therefore, since weak
bases only partly ionize,
00:00:34.020 --> 00:00:35.480
we're not gonna show this as an ion.
00:00:35.480 --> 00:00:39.550
We're simply gonna write
NH3 in our equation.
00:00:39.550 --> 00:00:41.350
However, for hydrochloric acid,
00:00:41.350 --> 00:00:43.320
hydrochloric acid is a strong acid,
00:00:43.320 --> 00:00:46.340
and strong acids ionize 100%.
00:00:46.340 --> 00:00:47.760
Therefore, an aqueous solution,
00:00:47.760 --> 00:00:49.760
we need to show this as the ions,
00:00:49.760 --> 00:00:53.593
so H plus and Cl minus.
00:00:54.860 --> 00:00:57.660
Ammonium chloride is a soluble salt,
00:00:57.660 --> 00:00:59.150
therefore, an aqueous solution,
00:00:59.150 --> 00:01:01.100
we show it as the ions.
00:01:01.100 --> 00:01:03.930
So ammonium chloride
consists of the ammonium ion,
00:01:03.930 --> 00:01:08.930
NH4 plus, and the
chloride anion, Cl minus.
00:01:09.410 --> 00:01:10.340
To save some time,
00:01:10.340 --> 00:01:12.320
I've drawn in the aqueous subscripts,
00:01:12.320 --> 00:01:15.530
and also put in the reaction
arrow and a plus sign.
00:01:15.530 --> 00:01:17.860
So this represents the overall,
00:01:17.860 --> 00:01:20.660
or the complete ionic equation.
00:01:20.660 --> 00:01:22.900
And we can use the complete ionic equation
00:01:22.900 --> 00:01:24.970
to find the net ionic equation
00:01:24.970 --> 00:01:27.740
for this weak base, strong acid reaction.
00:01:27.740 --> 00:01:31.150
To do that, we first need to
identify these spectator ions.
00:01:31.150 --> 00:01:33.440
And remember, these are the
ions that do not take part
00:01:33.440 --> 00:01:35.120
in the chemical reaction.
00:01:35.120 --> 00:01:37.460
Since there's a chloride
anion on the left side
00:01:37.460 --> 00:01:38.510
and on the right side,
00:01:38.510 --> 00:01:42.780
the chloride anion is the
spectator ion for this reaction.
00:01:42.780 --> 00:01:44.590
And once we take out our spectator ion,
00:01:44.590 --> 00:01:47.330
we're left with our net ionic equation,
00:01:47.330 --> 00:01:52.330
which is aqueous ammonia
plus H plus yields NH4 plus.
00:01:52.610 --> 00:01:55.920
So this is one way to write
our net ionic equation.
00:01:55.920 --> 00:01:59.480
However, remember that H plus and H3O plus
00:01:59.480 --> 00:02:02.070
are used interchangeably in chemistry.
00:02:02.070 --> 00:02:05.200
Therefore, another way to
write the net ionic equation
00:02:05.200 --> 00:02:08.080
is to show aqueous ammonia
plus the hydronium ion,
00:02:08.080 --> 00:02:12.683
H3O plus, yields the ammonium
ion, NH4 plus, plus water.
00:02:13.550 --> 00:02:15.420
Now that we have our net ionic equation,
00:02:15.420 --> 00:02:18.010
we're gonna consider three
different situations.
00:02:18.010 --> 00:02:19.470
In the first situation,
00:02:19.470 --> 00:02:23.350
we have equal moles of our
weak base and strong acid.
00:02:23.350 --> 00:02:24.990
Looking at our net ionic equation,
00:02:24.990 --> 00:02:28.750
the mole ratio of ammonia to
hydronium ion is one to one.
00:02:28.750 --> 00:02:31.800
Therefore, if we have equal
moles of our weak base
00:02:31.800 --> 00:02:33.500
and strong acid,
00:02:33.500 --> 00:02:34.870
the weak base and strong acid
00:02:34.870 --> 00:02:36.650
will completely neutralize each other
00:02:36.650 --> 00:02:40.450
and produce the ammonium ion NH4 plus.
00:02:40.450 --> 00:02:42.210
So if our goal is to figure out the pH
00:02:42.210 --> 00:02:43.480
of the resulting solution,
00:02:43.480 --> 00:02:45.440
we don't need to consider the weak base,
00:02:45.440 --> 00:02:47.010
or this strong acid.
00:02:47.010 --> 00:02:49.600
We need to think about the ammonium cation
00:02:49.600 --> 00:02:51.820
in aqueous solution.
00:02:51.820 --> 00:02:52.720
And in solution,
00:02:52.720 --> 00:02:55.170
the ammonium cation acts as a weak acid
00:02:55.170 --> 00:02:56.830
and donates a proton to water
00:02:56.830 --> 00:03:01.740
to form the hydronium ion,
H3O plus, and aqueous ammonia.
00:03:01.740 --> 00:03:05.240
The ammonium cation, NH4
plus, is a weak acid.
00:03:05.240 --> 00:03:08.410
Therefore, the Ka value is less than one.
00:03:08.410 --> 00:03:11.930
And since Ka is less
than one at equilibrium,
00:03:11.930 --> 00:03:15.050
there are mostly reactants
and not very many products.
00:03:15.050 --> 00:03:18.960
However, the concentration
of hydronium ions in solution
00:03:18.960 --> 00:03:21.270
is increased, and therefore,
00:03:21.270 --> 00:03:24.620
the resulting solution will be acidic.
00:03:24.620 --> 00:03:27.220
So the resulting solution
will be slightly acidic.
00:03:27.220 --> 00:03:29.240
And at 25 degrees Celsius,
00:03:29.240 --> 00:03:32.650
the pH of the solution
will be less than seven.
00:03:32.650 --> 00:03:34.860
If we wanted to calculate the actual pH,
00:03:34.860 --> 00:03:38.330
we would treat this like a
weak acid equilibrium problem.
00:03:38.330 --> 00:03:41.040
Also, it's important to
emphasize that the hydronium ions
00:03:41.040 --> 00:03:43.950
that gave the resulting
solution a pH less than seven
00:03:43.950 --> 00:03:47.740
came from the reaction of the
ammonium cation with water.
00:03:47.740 --> 00:03:50.630
The hydronium ions did not
come from the strong acid.
00:03:50.630 --> 00:03:52.900
All of those hydronium ions were used up
00:03:52.900 --> 00:03:56.050
in the acid-base neutralization reaction.
00:03:56.050 --> 00:03:57.290
For the second situation,
00:03:57.290 --> 00:04:00.180
we have more of the weak
base than the strong acid,
00:04:00.180 --> 00:04:03.240
therefore, we have the
weak base in excess.
00:04:03.240 --> 00:04:04.930
And because the mole
ratio of the weak base
00:04:04.930 --> 00:04:07.360
to the strong acid is one to one,
00:04:07.360 --> 00:04:10.400
if we have more of the weak
base than the strong acid,
00:04:10.400 --> 00:04:13.790
all of the strong acid will be used up.
00:04:13.790 --> 00:04:15.610
So when the reaction goes to completion,
00:04:15.610 --> 00:04:18.240
we'll have ammonium cations in solution,
00:04:18.240 --> 00:04:21.290
and we'll also have some leftover ammonia.
00:04:21.290 --> 00:04:24.540
So after the neutralization
reaction is complete
00:04:24.540 --> 00:04:26.800
and all the H3O plus is used up,
00:04:26.800 --> 00:04:28.880
we'll have some leftover ammonia.
00:04:28.880 --> 00:04:31.090
That ammonia will react with water
00:04:31.090 --> 00:04:35.730
to form hydroxide anions and NH4 plus.
00:04:35.730 --> 00:04:39.180
Because the concentration of
hydroxide ions in solution
00:04:39.180 --> 00:04:43.000
has increased at 25 degrees Celsius,
00:04:43.000 --> 00:04:45.230
the resulting solution will be basic
00:04:45.230 --> 00:04:48.690
and the pH will be greater than seven.
00:04:48.690 --> 00:04:50.920
If we wanted to calculate the actual pH,
00:04:50.920 --> 00:04:54.190
we would treat this like a
weak base equilibria problem.
00:04:54.190 --> 00:04:57.340
However, we have two sources
for the ammonium cation.
00:04:57.340 --> 00:05:00.190
One source is from ammonia
reacting with water
00:05:00.190 --> 00:05:01.740
to form NH4 plus,
00:05:01.740 --> 00:05:06.180
and the other source came from
the neutralization reaction.
00:05:06.180 --> 00:05:09.970
So actually, this would be
a common-ion effect problem.
00:05:09.970 --> 00:05:12.560
The other way to calculate
the pH of this solution
00:05:12.560 --> 00:05:16.270
is to realize that ammonium
NH4 plus is a weak acid,
00:05:16.270 --> 00:05:19.480
and ammonia NH3 is its conjugate base,
00:05:19.480 --> 00:05:22.350
therefore, if we have similar
amounts of a weak acid
00:05:22.350 --> 00:05:23.380
and its conjugate base,
00:05:23.380 --> 00:05:25.660
we have a buffer solution
and we could calculate
00:05:25.660 --> 00:05:29.100
the pH using the
Henderson-Hasselbalch equation.
00:05:29.100 --> 00:05:30.430
For our third situation,
00:05:30.430 --> 00:05:33.980
let's say we have the
strong acid in excess.
00:05:33.980 --> 00:05:36.500
Since the mole ratio of
weak base to strong acid
00:05:36.500 --> 00:05:37.740
is one to one,
00:05:37.740 --> 00:05:40.590
if we have more of the strong
acid than the weak base,
00:05:40.590 --> 00:05:43.650
all of the weak base will be used up
00:05:43.650 --> 00:05:46.740
and we'll have some strong acid in excess.
00:05:46.740 --> 00:05:50.660
Therefore, there'll be a
concentration of hydronium ions
00:05:50.660 --> 00:05:55.300
in solution, which would make
the resulting solution acidic.
00:05:55.300 --> 00:06:00.300
So at 25 degrees Celsius, the
pH would be less than seven.
00:06:00.480 --> 00:06:03.540
We could calculate the actual
pH of the resulting solution
00:06:03.540 --> 00:06:07.390
by doing a strong acid
pH calculation problem.
00:06:07.390 --> 00:06:09.260
And while it's true
that the ammonium cation
00:06:09.260 --> 00:06:10.660
can function as a weak acid
00:06:10.660 --> 00:06:13.910
and also increase the
concentration of hydronium ions,
00:06:13.910 --> 00:06:15.990
it's such a small increase compared to
00:06:15.990 --> 00:06:19.370
the hydronium ions we have in
solution from our strong acid
00:06:19.370 --> 00:06:21.790
that we don't need to worry
about the contribution
00:06:21.790 --> 00:06:23.310
of the ammonium cations.
00:06:23.310 --> 00:06:24.390
We can just treat this
00:06:24.390 --> 00:06:27.123
like a strong acid pH calculation problem.
|
Worked example: Calculating the pH after a weak acid–strong base reaction (excess acid) | https://www.youtube.com/watch?v=9rRlLPx6w7M | vtt | https://www.youtube.com/api/timedtext?v=9rRlLPx6w7M&ei=0lWUZYD7I63WxN8P5qOP8AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E27FF6DDE7A6D948F473A88BD5B69F72C748F3C8.5FD63CE6C4C10C67618450989FC472684947C21C&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.280 --> 00:00:01.280
- [Instructor] Let's look at a reaction
00:00:01.280 --> 00:00:03.850
between a weak acid, acetic acid,
00:00:03.850 --> 00:00:07.660
and a strong base, sodium hydroxide.
00:00:07.660 --> 00:00:11.800
Let's say we have 100 milliliters
of a 2.0 molar solution
00:00:11.800 --> 00:00:13.330
of aqueous acetic acid,
00:00:13.330 --> 00:00:15.300
and that's mixed with 100 milliliters
00:00:15.300 --> 00:00:19.190
of a 1.0 molar solution of
aqueous sodium hydroxide.
00:00:19.190 --> 00:00:22.180
Our goal is to find the pH
of the resulting solution
00:00:22.180 --> 00:00:24.830
at 25 degrees Celsius.
00:00:24.830 --> 00:00:26.950
When the weak acid reacts
with the strong base,
00:00:26.950 --> 00:00:29.320
a neutralization reaction occurs.
00:00:29.320 --> 00:00:30.990
So our first step is to figure out
00:00:30.990 --> 00:00:33.930
how many moles of our
weak acid are present
00:00:33.930 --> 00:00:37.330
and also how many moles of
our strong base are present.
00:00:37.330 --> 00:00:38.710
Let's start with the weak acid.
00:00:38.710 --> 00:00:40.350
We're gonna use the molarity equation.
00:00:40.350 --> 00:00:42.950
Molarity is equal to moles over liters.
00:00:42.950 --> 00:00:46.550
So for our weak acid, the
concentration is 2.0 molar,
00:00:46.550 --> 00:00:47.740
so we plug that in,
00:00:47.740 --> 00:00:49.930
and the volume is 100 milliliters
00:00:49.930 --> 00:00:53.140
which is equal to 0.100 liters.
00:00:53.140 --> 00:00:54.410
Solving for x,
00:00:54.410 --> 00:00:59.410
we find that there are
0.20 moles of acetic acid.
00:00:59.710 --> 00:01:03.230
For our strong base, the
concentration is 1.0 molar,
00:01:03.230 --> 00:01:07.420
and the volume is 100 milliliters
which is 0.100 liters.
00:01:07.420 --> 00:01:11.720
So solving for x, x is
equal to 0.10 moles of NaOH.
00:01:12.600 --> 00:01:16.700
And because NaOH is a strong
base, it dissociates 100%.
00:01:16.700 --> 00:01:19.200
So if there's 0.10 moles of NaOH,
00:01:19.200 --> 00:01:24.200
there's also 0.10 moles
of hydroxide ions, OH-.
00:01:26.130 --> 00:01:26.963
In solution,
00:01:26.963 --> 00:01:30.460
the hydroxide anions will
react with acetic acid.
00:01:30.460 --> 00:01:33.820
So our next step is to look
at the net ionic equation
00:01:33.820 --> 00:01:37.290
for this weak acid-strong base reaction.
00:01:37.290 --> 00:01:38.880
In the net ionic equation,
00:01:38.880 --> 00:01:41.640
acetic acid reacts with hydroxide anions
00:01:41.640 --> 00:01:44.640
to form the acetate anion and water.
00:01:44.640 --> 00:01:47.430
Because this neutralization
reaction goes to completion,
00:01:47.430 --> 00:01:49.230
we draw an arrow going to the right
00:01:49.230 --> 00:01:51.640
instead of an equilibrium arrow.
00:01:51.640 --> 00:01:52.970
And instead of an ICE table
00:01:52.970 --> 00:01:54.620
where the E stands for equilibrium,
00:01:54.620 --> 00:01:56.490
we use an ICF table,
00:01:56.490 --> 00:01:58.620
where I is the initial amount of moles,
00:01:58.620 --> 00:01:59.990
C is the change in moles,
00:01:59.990 --> 00:02:02.760
and F is the final amount of moles.
00:02:02.760 --> 00:02:04.980
We've already calculated
the initial amount of moles
00:02:04.980 --> 00:02:07.980
of acetic acid to be 0.20,
00:02:07.980 --> 00:02:09.250
and the initial amount of moles
00:02:09.250 --> 00:02:12.440
of hydroxide anions to be 0.10.
00:02:12.440 --> 00:02:14.550
If we assume the reaction
hasn't happened yet,
00:02:14.550 --> 00:02:18.570
the initial amount of moles
of acetate would be zero.
00:02:18.570 --> 00:02:20.030
Next, we look at the coefficients
00:02:20.030 --> 00:02:22.210
in our balanced net ionic equation.
00:02:22.210 --> 00:02:25.680
The mole ratio of hydroxide
anions to acetic acid
00:02:25.680 --> 00:02:27.130
is one-to-one.
00:02:27.130 --> 00:02:31.650
Therefore, if we have 0.10
moles of hydroxide anions,
00:02:31.650 --> 00:02:35.920
that's gonna react with
0.10 moles of acetic acid.
00:02:35.920 --> 00:02:36.900
So for the change,
00:02:36.900 --> 00:02:41.610
we can write minus 0.10
under hydroxide anions,
00:02:41.610 --> 00:02:46.010
and also minus 0.10 under acetic acid.
00:02:46.010 --> 00:02:48.700
For the acetate anion,
there's a coefficient of one
00:02:48.700 --> 00:02:51.010
in the balanced net ionic equation.
00:02:51.010 --> 00:02:55.190
Therefore, if we're losing 0.10
moles for our two reactants,
00:02:55.190 --> 00:03:00.190
we're going to gain 0.10
moles of the acetate anion.
00:03:00.560 --> 00:03:03.810
So when the reaction comes to
completion for acetic acid,
00:03:03.810 --> 00:03:07.800
we started with 0.20
moles and we lost 0.10,
00:03:07.800 --> 00:03:11.920
so we're gonna have 0.10 moles
of acetic acid left over.
00:03:11.920 --> 00:03:13.420
For hydroxide anions,
00:03:13.420 --> 00:03:16.960
we start with 0.10 moles
and we lost 0.10 moles.
00:03:16.960 --> 00:03:19.350
Therefore, when the reaction
comes to completion,
00:03:19.350 --> 00:03:22.390
there'll be zero moles
of hydroxide anions.
00:03:22.390 --> 00:03:23.730
And for the acetate anion,
00:03:23.730 --> 00:03:27.090
we started off with
zero and we gained 0.10.
00:03:27.090 --> 00:03:31.160
Therefore, we will have 0.10
moles of the acetate anion.
00:03:31.160 --> 00:03:33.620
So in this case, we started
with more of our weak acid
00:03:33.620 --> 00:03:35.620
than we did of our strong base.
00:03:35.620 --> 00:03:40.220
And therefore, we ended up
with acid being in excess.
00:03:40.220 --> 00:03:42.740
The next step is to
calculate the concentration
00:03:42.740 --> 00:03:45.300
of acetic acid in solution.
00:03:45.300 --> 00:03:48.870
So we ended up with 0.10
moles of acetic acid.
00:03:48.870 --> 00:03:51.540
So we plug that into our
equation for molarity.
00:03:51.540 --> 00:03:54.540
And when we mixed our
two solutions together,
00:03:54.540 --> 00:03:56.440
the 100 milliliters of our weak acid
00:03:56.440 --> 00:03:58.350
with the 100 milliliters
of our strong base,
00:03:58.350 --> 00:04:01.670
the total volume of the
solution is 200 milliliters
00:04:01.670 --> 00:04:04.620
or 0.200 liters.
00:04:04.620 --> 00:04:07.920
Therefore, 0.1 divided by 0.200,
00:04:07.920 --> 00:04:12.330
gives the concentration
of acetic of 0.50 molar.
00:04:12.330 --> 00:04:16.240
And for the acetate anion,
we also had 0.10 moles.
00:04:16.240 --> 00:04:17.820
The total volume is the same,
00:04:17.820 --> 00:04:19.980
so it's the same calculation as before.
00:04:19.980 --> 00:04:23.680
0.10 moles divided by 0.200 liters,
00:04:23.680 --> 00:04:28.500
gives the concentration of
acetate anions of 0.50 molar.
00:04:28.500 --> 00:04:30.790
Remember, our goal was to calculate the pH
00:04:30.790 --> 00:04:32.780
of the resulting solution.
00:04:32.780 --> 00:04:34.100
So to calculate the pH,
00:04:34.100 --> 00:04:36.730
we're gonna need the
concentration of acetic acid
00:04:36.730 --> 00:04:39.980
and the concentration of acetate anions.
00:04:39.980 --> 00:04:42.830
So we know we have some
acetic acid in solution,
00:04:42.830 --> 00:04:44.760
and acetic acid reacts with water
00:04:44.760 --> 00:04:47.580
to form the hydronium ion, H3O+,
00:04:47.580 --> 00:04:51.340
and the acetate anion, CH3COO-.
00:04:51.340 --> 00:04:54.450
This reaction is a weak
acid equilibrium problem,
00:04:54.450 --> 00:04:56.200
so we have an equilibrium arrow,
00:04:56.200 --> 00:04:58.240
and we're gonna set up an ICE table
00:04:58.240 --> 00:05:00.710
for initial concentration,
change in concentration,
00:05:00.710 --> 00:05:03.370
and equilibrium concentration.
00:05:03.370 --> 00:05:05.520
We just calculated the
initial concentration
00:05:05.520 --> 00:05:08.390
of acetic acid to be 0.50 molar.
00:05:08.390 --> 00:05:12.500
And if we pretend like the
acetic acid hasn't ionized yet,
00:05:12.500 --> 00:05:15.730
the initial concentration of
hydronium ions would be zero
00:05:15.730 --> 00:05:18.420
and the initial concentration
of acetate anions
00:05:18.420 --> 00:05:21.030
from the ionization would be zero.
00:05:21.030 --> 00:05:22.780
However, we just calculated
00:05:22.780 --> 00:05:25.730
that there is a concentration
of acetate anions
00:05:25.730 --> 00:05:27.580
already in solution,
00:05:27.580 --> 00:05:30.670
and that concentration was 0.50 molar.
00:05:30.670 --> 00:05:35.230
So on the ICE table, I'm
gonna write in here 0.50
00:05:35.230 --> 00:05:37.440
for the acetate anion.
00:05:37.440 --> 00:05:40.800
Next, we think about some
of the acetic acid ionizing,
00:05:40.800 --> 00:05:43.510
and we don't know how much,
so we're gonna call that x.
00:05:43.510 --> 00:05:46.520
So under the change,
we're gonna write minus x.
00:05:46.520 --> 00:05:49.450
The mole ratio of acetic
acid to hydronium ion
00:05:49.450 --> 00:05:50.820
is one-to-one.
00:05:50.820 --> 00:05:53.280
So if we write minus x under acetic acid,
00:05:53.280 --> 00:05:56.530
we need to write plus x
under the hydronium ion.
00:05:56.530 --> 00:05:57.850
And for the acetate anion,
00:05:57.850 --> 00:06:00.190
there's also a coefficient of one,
00:06:00.190 --> 00:06:03.980
so we're gonna write plus
x under the acetate anion.
00:06:03.980 --> 00:06:05.900
Therefore, the equilibrium concentration
00:06:05.900 --> 00:06:09.310
of acetic acid is 0.50 minus x.
00:06:09.310 --> 00:06:11.240
And for hydronium ion,
00:06:11.240 --> 00:06:13.950
it would be zero plus x or just x.
00:06:13.950 --> 00:06:15.510
And for the acetate anion,
00:06:15.510 --> 00:06:18.800
it would be zero plus 0.50 plus x
00:06:18.800 --> 00:06:22.930
or just 0.50 plus x.
00:06:22.930 --> 00:06:26.705
Notice that there are two
sources of the acetate anion.
00:06:26.705 --> 00:06:28.950
The 0.50 molar
00:06:28.950 --> 00:06:33.070
came from the weak acid-strong
base neutralization reaction
00:06:33.070 --> 00:06:35.120
that we previously discussed.
00:06:35.120 --> 00:06:37.400
The other source of the acetate anion
00:06:37.400 --> 00:06:40.970
comes from the ionization of acetic acid,
00:06:40.970 --> 00:06:42.430
and that's this x here.
00:06:42.430 --> 00:06:46.610
So 0.50 plus x indicates
there are two sources
00:06:46.610 --> 00:06:48.590
for this common ion.
00:06:48.590 --> 00:06:51.803
Therefore, this is a
common-ion effect problem.
00:06:52.680 --> 00:06:54.960
The next step is to
write the Ka expression
00:06:54.960 --> 00:06:56.840
for acetic acid.
00:06:56.840 --> 00:06:58.840
So we can get that from
the balanced equation.
00:06:58.840 --> 00:07:02.490
The Ka value for acetic
acid at 25 degrees Celsius
00:07:02.490 --> 00:07:05.440
is equal to the concentration
of hydronium ions
00:07:05.440 --> 00:07:06.880
raised to the first power
00:07:06.880 --> 00:07:09.480
times the concentration of acetate anions
00:07:09.480 --> 00:07:10.830
raised to the first power
00:07:10.830 --> 00:07:13.640
divided by the
concentration of acetic acid
00:07:13.640 --> 00:07:14.850
raised to the first power,
00:07:14.850 --> 00:07:15.980
with water being left
00:07:15.980 --> 00:07:18.750
out of our equilibrium
constant expression.
00:07:18.750 --> 00:07:21.460
Next, we plug in our
equilibrium concentrations
00:07:21.460 --> 00:07:22.660
from our ICE table.
00:07:22.660 --> 00:07:24.970
For the hydronium ion, it's x.
00:07:24.970 --> 00:07:28.550
For the acetate anion, it's 0.50 plus x.
00:07:28.550 --> 00:07:33.000
And for acetic acid it's 0.50 minus x.
00:07:33.000 --> 00:07:36.000
Here, we have our equilibrium
concentrations plugged in
00:07:36.000 --> 00:07:40.620
and also the Ka value for acetic
acid at 25 degrees Celsius.
00:07:40.620 --> 00:07:42.380
Next, we need to solve for x.
00:07:42.380 --> 00:07:46.040
And to make the math easier,
we can make an approximation.
00:07:46.040 --> 00:07:50.260
With a relatively low value
for Ka for acetic acid,
00:07:50.260 --> 00:07:52.570
acetic acid doesn't ionize very much.
00:07:52.570 --> 00:07:55.520
Therefore, we know that x is
gonna be a very small number.
00:07:55.520 --> 00:07:58.892
And if x is a very small
number compared to 0.50,
00:07:58.892 --> 00:08:03.420
0.50 plus x is
approximately equal to 0.50.
00:08:03.420 --> 00:08:06.010
The same idea applies to 0.50 minus x.
00:08:06.010 --> 00:08:08.949
If x is a very small
number compared to 0.50,
00:08:08.949 --> 00:08:13.440
0.50 minus x is
approximately equal to 0.50.
00:08:13.440 --> 00:08:14.730
And with our approximations,
00:08:14.730 --> 00:08:17.500
the 0.50s would cancel out and give us x
00:08:17.500 --> 00:08:20.520
is equal to 1.8 times 10
to the negative fifth.
00:08:20.520 --> 00:08:21.530
From our ICE table,
00:08:21.530 --> 00:08:25.750
we know that x is equal to
the equilibrium concentration
00:08:25.750 --> 00:08:27.820
of hydronium ions.
00:08:27.820 --> 00:08:29.930
Therefore, at equilibrium,
00:08:29.930 --> 00:08:31.420
the concentration of hydronium ions
00:08:31.420 --> 00:08:35.520
is equal to 1.8 times 10 to
the negative fifth molar.
00:08:35.520 --> 00:08:38.170
And because our goal was to
find the pH of the solution,
00:08:38.170 --> 00:08:40.700
pH is equal to the negative
log of the concentration
00:08:40.700 --> 00:08:42.160
of hydronium ions.
00:08:42.160 --> 00:08:44.970
So when we plug in that concentration,
00:08:44.970 --> 00:08:46.090
we get the pH is equal
00:08:46.090 --> 00:08:48.890
to negative log of 1.8 times
10 to the negative fifth
00:08:48.890 --> 00:08:52.100
which is equal to 4.74.
00:08:52.100 --> 00:08:55.570
So if you react a weak
acid with a strong base
00:08:55.570 --> 00:08:58.590
and the weak acid is in excess,
00:08:58.590 --> 00:09:02.620
the pH of the solution
will be less than seven.
00:09:02.620 --> 00:09:03.553
It'll be acidic.
|
Weak acid–strong base reactions | https://www.youtube.com/watch?v=VdAl4QK4-0Q | vtt | https://www.youtube.com/api/timedtext?v=VdAl4QK4-0Q&ei=0lWUZY7kI76KvdIPt8CEiAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C871BAC95E265D1C58BE5537CB1E89C031E68967.0B6ABBD3BC40D0BB2B20FECE7CC033254BEB5EE8&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.680 --> 00:00:04.540
- [Instructor] Acetic acid
is an example of a weak acid
00:00:04.540 --> 00:00:08.783
and sodium hydroxide is an
example of a strong base.
00:00:08.783 --> 00:00:12.040
When acetic acid reacts
with sodium hydroxide,
00:00:12.040 --> 00:00:14.480
an aqueous solution of
sodium acetate is formed
00:00:14.480 --> 00:00:16.070
along with water.
00:00:16.070 --> 00:00:19.830
Since this reaction is an
acid-base neutralization reaction,
00:00:19.830 --> 00:00:22.060
and these reactions go to completion,
00:00:22.060 --> 00:00:23.890
instead of using an equilibrium arrow,
00:00:23.890 --> 00:00:26.630
we simply draw an arrow
going to the right.
00:00:26.630 --> 00:00:29.610
Next, let's write the
overall ionic equation.
00:00:29.610 --> 00:00:33.270
This is also called the
complete ionic equation.
00:00:33.270 --> 00:00:34.890
Let's start with acetic acid.
00:00:34.890 --> 00:00:37.080
Acetic acid is a weak acid
00:00:37.080 --> 00:00:40.200
that only partly ionizes in solution.
00:00:40.200 --> 00:00:43.010
Therefore, an aqueous
solution of acetic acid,
00:00:43.010 --> 00:00:46.210
most of the acetic acid
molecules stay protonated
00:00:46.210 --> 00:00:48.500
and don't turn into acetate.
00:00:48.500 --> 00:00:53.230
Therefore, we're just gonna
write CH3COOH down here.
00:00:53.230 --> 00:00:56.420
We're not gonna show acetic acid ionizing
00:00:56.420 --> 00:00:59.400
into H+ and the conjugate base.
00:00:59.400 --> 00:01:01.770
However, things are different
for sodium hydroxide.
00:01:01.770 --> 00:01:03.730
Sodium hydroxide is a strong base,
00:01:03.730 --> 00:01:07.600
and strong bases dissociate
100% in solution.
00:01:07.600 --> 00:01:10.310
So an aqueous solution of sodium hydroxide
00:01:10.310 --> 00:01:15.310
consists of sodium cations
and hydroxide anions.
00:01:16.340 --> 00:01:17.910
Next, let's think about our products.
00:01:17.910 --> 00:01:21.040
We have an aqueous
solution of sodium acetate.
00:01:21.040 --> 00:01:23.840
Sodium acetate is a soluble salt.
00:01:23.840 --> 00:01:26.160
Therefore, in aqueous solution,
00:01:26.160 --> 00:01:29.290
we would have sodium cations, Na+,
00:01:29.290 --> 00:01:31.673
and the acetate anion, CH3COO-.
00:01:35.140 --> 00:01:38.080
Because water ionizes only
to an extremely small extent,
00:01:38.080 --> 00:01:39.690
we don't write it as the ions.
00:01:39.690 --> 00:01:42.950
We simply write H2O.
00:01:42.950 --> 00:01:45.770
To save some time, I've added
in some aqueous subscripts
00:01:45.770 --> 00:01:47.670
and a liquid one for water,
00:01:47.670 --> 00:01:50.050
some plus signs, and the reaction arrow.
00:01:50.050 --> 00:01:51.440
So this balanced equation
00:01:51.440 --> 00:01:54.960
represents the complete ionic equation.
00:01:54.960 --> 00:01:57.220
Next, we're gonna use the
complete ionic equation
00:01:57.220 --> 00:01:59.440
to write the net ionic equation
00:01:59.440 --> 00:02:01.900
for this weak acid-strong base reaction.
00:02:01.900 --> 00:02:02.733
And to do that,
00:02:02.733 --> 00:02:05.660
we first need to identify spectator ions.
00:02:05.660 --> 00:02:09.830
Remember, spectator ions don't
participate in the reaction.
00:02:09.830 --> 00:02:12.030
So looking at the complete ionic equation,
00:02:12.030 --> 00:02:13.920
there are sodium cations on the left
00:02:13.920 --> 00:02:15.720
and sodium cations on the right,
00:02:15.720 --> 00:02:17.720
so we can cross out the sodium cation,
00:02:17.720 --> 00:02:19.730
that's our spectator ion.
00:02:19.730 --> 00:02:21.580
After we take out the sodium cation,
00:02:21.580 --> 00:02:24.480
what's left over is
our net ionic equation.
00:02:24.480 --> 00:02:26.070
So for our net equation,
00:02:26.070 --> 00:02:29.410
we have acetic acid plus hydroxide anion,
00:02:29.410 --> 00:02:32.450
forms the acetate anion and water.
00:02:32.450 --> 00:02:34.280
Now that we have our net ionic equation,
00:02:34.280 --> 00:02:36.890
we're gonna think about
three different situations.
00:02:36.890 --> 00:02:38.450
And the first situation,
00:02:38.450 --> 00:02:42.710
we have equal moles of our
weak acid and our strong base.
00:02:42.710 --> 00:02:45.330
Looking at our balanced
net ionic equation,
00:02:45.330 --> 00:02:48.540
the mole ratio of our weak
acid to our strong base
00:02:48.540 --> 00:02:50.040
is one-to-one.
00:02:50.040 --> 00:02:52.700
Therefore, if we have equal
moles of our weak acid
00:02:52.700 --> 00:02:53.800
and our strong base
00:02:53.800 --> 00:02:56.100
and the mole ratio is one-to-one,
00:02:56.100 --> 00:02:57.410
the weak and the strong base
00:02:57.410 --> 00:02:59.730
are going to completely
neutralize each other
00:02:59.730 --> 00:03:02.250
and form the acetate anion.
00:03:02.250 --> 00:03:03.840
So if our goal is to figure out the pH
00:03:03.840 --> 00:03:05.380
of the resulting solution,
00:03:05.380 --> 00:03:07.370
we don't need to consider acetic acid
00:03:07.370 --> 00:03:09.730
and we don't need to
consider the hydroxide ions
00:03:09.730 --> 00:03:12.040
'cause these have been completely used up.
00:03:12.040 --> 00:03:14.560
We need to think about the acetate anion
00:03:14.560 --> 00:03:16.250
in aqueous solution.
00:03:16.250 --> 00:03:19.730
And in aqueous solution,
acetate anions react with water
00:03:19.730 --> 00:03:23.460
to form acetic acid and hydroxide ions.
00:03:23.460 --> 00:03:25.550
This reaction does come to an equilibrium
00:03:25.550 --> 00:03:27.880
and since Kb is less than one,
00:03:27.880 --> 00:03:31.140
at equilibrium, there will be
a large amount of reactants
00:03:31.140 --> 00:03:33.470
and only a small amount of products.
00:03:33.470 --> 00:03:36.230
However, since we are
increasing the concentration
00:03:36.230 --> 00:03:39.310
of hydroxide ions in solution,
00:03:39.310 --> 00:03:42.310
the resulting solution will be basic.
00:03:42.310 --> 00:03:44.690
Therefore, at 25 degrees Celsius,
00:03:44.690 --> 00:03:48.530
the pH of the resulting solution
will be greater than seven.
00:03:48.530 --> 00:03:50.500
If we wanted to calculate the actual pH,
00:03:50.500 --> 00:03:52.730
we would need some more information,
00:03:52.730 --> 00:03:53.563
but we would treat it
00:03:53.563 --> 00:03:56.720
just like a weak base equilibria problem.
00:03:56.720 --> 00:04:00.110
Also note that the hydroxide
ions that we wrote down here
00:04:00.110 --> 00:04:02.830
are not the same thing
as the hydroxide ions
00:04:02.830 --> 00:04:05.110
from our net ionic equation.
00:04:05.110 --> 00:04:08.490
The hydroxide ions from
our net ionic equation
00:04:08.490 --> 00:04:09.650
went away completely.
00:04:09.650 --> 00:04:13.820
They were neutralized by
reacting with the acetic acid.
00:04:13.820 --> 00:04:16.110
So these hydroxide ions were generated
00:04:16.110 --> 00:04:19.460
from the anion hydrolysis
reaction of acetate plus water,
00:04:19.460 --> 00:04:21.610
and even though it's only a small amount
00:04:21.610 --> 00:04:24.080
or a small concentration
of hydroxide ions,
00:04:24.080 --> 00:04:25.590
those are the hydroxide ions
00:04:25.590 --> 00:04:27.970
that make the pH greater than seven.
00:04:27.970 --> 00:04:29.310
For the second situation,
00:04:29.310 --> 00:04:33.100
let's think about the
weak acid being in excess.
00:04:33.100 --> 00:04:36.240
Since the mole ratio of our
weak acid to our strong base
00:04:36.240 --> 00:04:37.550
is one-to-one,
00:04:37.550 --> 00:04:39.240
if we have more of the weak acid
00:04:39.240 --> 00:04:40.630
than we do have the strong base,
00:04:40.630 --> 00:04:43.160
all of the strong base will be used up,
00:04:43.160 --> 00:04:46.070
and we will form the acetate anion.
00:04:46.070 --> 00:04:47.840
And when the reaction comes to completion,
00:04:47.840 --> 00:04:51.800
there'll be no more
hydroxide ion in solution.
00:04:51.800 --> 00:04:54.700
So if our goal is to find the
pH of the resulting solution,
00:04:54.700 --> 00:04:57.690
we don't need to consider
the hydroxide ion at all
00:04:57.690 --> 00:04:59.440
since it's all been used up.
00:04:59.440 --> 00:05:01.840
We need to think about the weak acid
00:05:01.840 --> 00:05:03.717
that was in excess, acetic acid,
00:05:03.717 --> 00:05:06.200
and we also have to think
about the acetate anion
00:05:06.200 --> 00:05:09.390
that was formed in the
neutralization reaction.
00:05:09.390 --> 00:05:12.560
First, let's think about the
weak acid that was in excess.
00:05:12.560 --> 00:05:14.730
Acetic acid will react with water
00:05:14.730 --> 00:05:17.200
to form the hydronium ion, H3O+,
00:05:17.200 --> 00:05:21.330
and the acetate anion, CH3COO-.
00:05:21.330 --> 00:05:24.050
Because the concentration
of hydronium ions
00:05:24.050 --> 00:05:26.410
in solution increases,
00:05:26.410 --> 00:05:29.210
that makes the solution more acidic.
00:05:29.210 --> 00:05:32.300
Therefore, when the
weak acid is in excess,
00:05:32.300 --> 00:05:35.530
the pH of the resulting
solution will be less than seven
00:05:35.530 --> 00:05:37.750
at 25 degrees Celsius.
00:05:37.750 --> 00:05:40.080
If our goal is to calculate the actual pH
00:05:40.080 --> 00:05:41.680
of the resulting solution,
00:05:41.680 --> 00:05:42.730
our first thought would be,
00:05:42.730 --> 00:05:45.250
this is a weak acid equilibria problem.
00:05:45.250 --> 00:05:46.740
And it is, however,
00:05:46.740 --> 00:05:49.620
there are two sources of acetate anion.
00:05:49.620 --> 00:05:51.750
One source of acetate anion
00:05:51.750 --> 00:05:54.630
is from the reaction of
acetic acid with water,
00:05:54.630 --> 00:05:57.280
and then the other source
of the acetate anion
00:05:57.280 --> 00:06:00.890
came from our acid-base
neutralization reaction.
00:06:00.890 --> 00:06:03.530
Therefore, one way to think
about this problem is,
00:06:03.530 --> 00:06:06.170
it's actually a common-ion effect problem
00:06:06.170 --> 00:06:09.710
where the common ion is the acetate anion.
00:06:09.710 --> 00:06:11.730
The presence of a common ion
00:06:11.730 --> 00:06:15.580
decreases the ionization
of acetic acid in water.
00:06:15.580 --> 00:06:18.380
However, since the
concentration of hydronium ions
00:06:18.380 --> 00:06:19.870
will still increase,
00:06:19.870 --> 00:06:23.220
the pH of the solution
will be less than seven.
00:06:23.220 --> 00:06:25.520
Another way to think
about this problem is,
00:06:25.520 --> 00:06:28.290
when we formed the acetate anion
00:06:28.290 --> 00:06:29.690
from the neutralization reaction,
00:06:29.690 --> 00:06:32.130
we had some of the weak acid in excess.
00:06:32.130 --> 00:06:35.900
And when we have a weak acid
and its conjugate base present,
00:06:35.900 --> 00:06:37.540
a buffer solution forms.
00:06:37.540 --> 00:06:40.670
And so we could also use the
Henderson-Hasselbalch equation
00:06:40.670 --> 00:06:43.920
to calculate the pH of
the resulting solution.
00:06:43.920 --> 00:06:45.130
For the third situation,
00:06:45.130 --> 00:06:48.510
let's think about the
strong base being in excess.
00:06:48.510 --> 00:06:50.330
Since the mole ratio of our weak acid
00:06:50.330 --> 00:06:52.520
to our strong base is one-to-one,
00:06:52.520 --> 00:06:55.100
if we have the strong base in excess,
00:06:55.100 --> 00:06:59.080
the strong base is going to
neutralize all of the weak acid.
00:06:59.080 --> 00:07:02.280
Therefore, when the reaction
comes to completion,
00:07:02.280 --> 00:07:05.950
there will be no more weak acid present.
00:07:05.950 --> 00:07:08.910
So if our goal is to find the
pH of the resulting solution,
00:07:08.910 --> 00:07:12.510
we would just have to think
about the extra hydroxide ions
00:07:12.510 --> 00:07:13.660
in solution.
00:07:13.660 --> 00:07:16.070
And since there are extra hydroxide ions
00:07:16.070 --> 00:07:17.660
from our strong base,
00:07:17.660 --> 00:07:19.960
we know at 25 degrees Celsius,
00:07:19.960 --> 00:07:23.480
the pH of the solution
will be greater than seven,
00:07:23.480 --> 00:07:26.300
so the resulting solution will be basic.
00:07:26.300 --> 00:07:29.240
If we wanted to calculate the
actual pH of the solution,
00:07:29.240 --> 00:07:33.410
this would become a strong
base pH calculation problem.
00:07:33.410 --> 00:07:35.900
And while it is true
that the acetate anions
00:07:35.900 --> 00:07:38.440
that were produced from
the neutralization reaction
00:07:38.440 --> 00:07:39.710
will react with water
00:07:39.710 --> 00:07:43.000
to also increase the
concentration of hydroxide ions,
00:07:43.000 --> 00:07:45.330
the concentration of hydroxide
ions that we would get
00:07:45.330 --> 00:07:48.350
from the anion hydrolysis
of the acetate anion
00:07:48.350 --> 00:07:50.860
would be negligible to the hydroxide ions
00:07:50.860 --> 00:07:52.340
that were left over.
00:07:52.340 --> 00:07:55.010
Therefore, we could just
consider the strong base
00:07:55.010 --> 00:07:56.550
to calculate the pH,
00:07:56.550 --> 00:07:59.190
and we don't need to worry
about anion hydrolysis
00:07:59.190 --> 00:08:01.073
for this particular situation.
|
Strong acid–strong base reactions | https://www.youtube.com/watch?v=SttbEmGj9uM | vtt | https://www.youtube.com/api/timedtext?v=SttbEmGj9uM&ei=0lWUZeymIKC8mLAPy4C8wAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0D012CAA6008C44C2A939DF77A88373FE64D7EF1.E16CA2DA83641C84C6CC51F4DA174569190589C9&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.210 --> 00:00:02.020
- [Instructor] Hydrochloric
acid is an example
00:00:02.020 --> 00:00:03.900
of a strong acid,
00:00:03.900 --> 00:00:08.170
and sodium hydroxide is an
example of a strong base.
00:00:08.170 --> 00:00:10.600
When an aqueous solution
of hydrochloric acid reacts
00:00:10.600 --> 00:00:12.940
with an aqueous solution
of sodium hydroxide,
00:00:12.940 --> 00:00:14.650
the products are an aqueous solution
00:00:14.650 --> 00:00:16.970
of sodium chloride and water.
00:00:16.970 --> 00:00:18.920
Since the reaction goes to completion,
00:00:18.920 --> 00:00:20.530
instead of an equilibrium arrow,
00:00:20.530 --> 00:00:22.780
there's just an arrow going to the right.
00:00:22.780 --> 00:00:26.360
And this is called an acid-base
neutralization reaction.
00:00:26.360 --> 00:00:28.590
Let's think about the
ions that are involved
00:00:28.590 --> 00:00:31.360
in this acid-base neutralization reaction.
00:00:31.360 --> 00:00:34.060
Since hydrochloric acid is a strong acid,
00:00:34.060 --> 00:00:37.400
HCl ionizes 100% in solution,
00:00:37.400 --> 00:00:38.950
and therefore, in solution,
00:00:38.950 --> 00:00:43.950
HCl consists of H plus
ions and Cl minus anions.
00:00:44.460 --> 00:00:46.640
Sodium hydroxide is a strong base,
00:00:46.640 --> 00:00:50.350
and strong bases dissociate
100% in solution.
00:00:50.350 --> 00:00:53.290
Therefore, an aqueous solution
of sodium hydroxide consists
00:00:53.290 --> 00:00:58.290
of sodium ions, Na plus, and
hydroxide anions, OH minus.
00:00:59.510 --> 00:01:00.343
For our products,
00:01:00.343 --> 00:01:02.160
sodium chloride is a soluble salt
00:01:02.160 --> 00:01:04.460
and therefore forms an aqueous solution.
00:01:04.460 --> 00:01:07.770
So in solution, we would
have sodium cations, Na plus,
00:01:07.770 --> 00:01:11.090
and chloride anions, Cl minus.
00:01:11.090 --> 00:01:14.170
Since water ionizes only
to a very small extent,
00:01:14.170 --> 00:01:15.960
we don't write it as the ions,
00:01:15.960 --> 00:01:17.197
we simply write H2O.
00:01:19.160 --> 00:01:20.170
To save some time,
00:01:20.170 --> 00:01:22.670
I went ahead and added
in aqueous subscripts,
00:01:22.670 --> 00:01:24.370
and for water, it'd be liquid,
00:01:24.370 --> 00:01:27.100
and some plus signs
and the reaction arrow.
00:01:27.100 --> 00:01:30.660
This is called the overall ionic equation
00:01:30.660 --> 00:01:33.850
for our strong acid-strong base reaction.
00:01:33.850 --> 00:01:36.580
Instead of calling it an
overall ionic equation,
00:01:36.580 --> 00:01:40.560
we could also call it a
complete ionic equation.
00:01:40.560 --> 00:01:43.160
And we can use the overall ionic equation
00:01:43.160 --> 00:01:45.510
to determine the net ionic equation
00:01:45.510 --> 00:01:48.230
for this strong acid-strong base reaction.
00:01:48.230 --> 00:01:50.150
To figure out the net ionic equation,
00:01:50.150 --> 00:01:53.120
we first need to determine
the spectator ions.
00:01:53.120 --> 00:01:55.950
Remember, spectator ions don't participate
00:01:55.950 --> 00:01:57.990
in the chemical reaction.
00:01:57.990 --> 00:02:00.690
Notice how we have a sodium
cation on the reactant side
00:02:00.690 --> 00:02:02.880
and a sodium cation on the product side,
00:02:02.880 --> 00:02:05.560
so we can cancel out the sodium cation.
00:02:05.560 --> 00:02:08.353
We also have a chloride
anion on the reactant side
00:02:08.353 --> 00:02:10.810
and a chloride anion on the product side.
00:02:10.810 --> 00:02:13.610
So we can cross that ion out as well.
00:02:13.610 --> 00:02:16.110
So the sodium cation
and the chloride anion
00:02:16.110 --> 00:02:18.490
are the spectator ions.
00:02:18.490 --> 00:02:20.540
And once we take out our spectator ions,
00:02:20.540 --> 00:02:22.970
we're left with the net ionic equation.
00:02:22.970 --> 00:02:26.330
So for the net ionic equation,
we would have H plus,
00:02:26.330 --> 00:02:30.730
plus OH minus yields H2O.
00:02:30.730 --> 00:02:34.480
So this is one way of writing
our net ionic equation.
00:02:34.480 --> 00:02:37.910
However, remember that H plus and H3O plus
00:02:37.910 --> 00:02:40.770
are used interchangeably in chemistry.
00:02:40.770 --> 00:02:44.360
So instead of writing H plus
in our net ionic equation,
00:02:44.360 --> 00:02:47.300
we could have also written H3O plus,
00:02:47.300 --> 00:02:50.050
and when H3O plus, or the hydronium ion,
00:02:50.050 --> 00:02:52.470
reacts with the hydroxide anion,
00:02:52.470 --> 00:02:53.610
we still form water.
00:02:53.610 --> 00:02:55.990
But notice, for this version
of the net ionic equation,
00:02:55.990 --> 00:02:59.640
we need to put a two as a
coefficient to balance everything.
00:02:59.640 --> 00:03:01.280
Next, let's think about a situation
00:03:01.280 --> 00:03:03.940
where we have equal
moles of our strong acid
00:03:03.940 --> 00:03:05.580
and strong base.
00:03:05.580 --> 00:03:06.413
For example,
00:03:06.413 --> 00:03:09.460
let's say we have one mole of HCl
00:03:09.460 --> 00:03:12.830
and one mole of NaOH.
00:03:12.830 --> 00:03:15.310
To help us think about what's
happening in this situation,
00:03:15.310 --> 00:03:17.550
we're gonna use an ICF table,
00:03:17.550 --> 00:03:20.330
where I stands for the
initial number of moles,
00:03:20.330 --> 00:03:22.080
C stands for the change in moles,
00:03:22.080 --> 00:03:24.980
and F stands for the
final amount of moles.
00:03:24.980 --> 00:03:27.250
The reason why we're using an ICF table
00:03:27.250 --> 00:03:29.710
instead of an ICE table
is in an ICE table,
00:03:29.710 --> 00:03:31.400
the E stands for equilibrium,
00:03:31.400 --> 00:03:34.510
and here we assume the
reaction goes to completion.
00:03:34.510 --> 00:03:35.940
Therefore, instead of E,
00:03:35.940 --> 00:03:39.100
we're writing F for final amount of moles.
00:03:39.100 --> 00:03:41.290
Let's fill out the rest of our ICF table.
00:03:41.290 --> 00:03:44.690
We have the initial amount
of moles of HCL and NaOH,
00:03:44.690 --> 00:03:47.500
and if we assume the
reaction hasn't happened yet,
00:03:47.500 --> 00:03:50.840
the initial amount of moles
of NaCl would be zero.
00:03:50.840 --> 00:03:52.440
Looking at the balanced equation,
00:03:52.440 --> 00:03:56.720
one mole of HCl reacts with
one mole of sodium hydroxide.
00:03:56.720 --> 00:03:58.700
And since the reaction goes to completion,
00:03:58.700 --> 00:04:00.950
we can go ahead and write,
under the change part here,
00:04:00.950 --> 00:04:02.780
we're gonna react one mole of HCl,
00:04:02.780 --> 00:04:04.940
so we're gonna lose that one mole of HCl.
00:04:04.940 --> 00:04:06.530
And since it's a one-to-one ratio,
00:04:06.530 --> 00:04:08.760
we're gonna lose one mole of NaOH.
00:04:09.750 --> 00:04:13.450
And since there's a one as a
coefficient in front of NaCl,
00:04:13.450 --> 00:04:15.640
under the change part on our ICF table,
00:04:15.640 --> 00:04:19.280
we would write plus one mole for NaCl.
00:04:19.280 --> 00:04:22.920
Since we started with one mole
of HCl, and we lost one mole,
00:04:22.920 --> 00:04:25.780
the final amount of moles
for HCl would be zero.
00:04:25.780 --> 00:04:27.450
Same thing for sodium hydroxide,
00:04:27.450 --> 00:04:29.340
the final amount of moles would be zero,
00:04:29.340 --> 00:04:30.850
because it's one minus one.
00:04:30.850 --> 00:04:33.820
For NaCl, we started off
with zero and we gained one.
00:04:33.820 --> 00:04:36.100
So we're ending up with
a final amount of moles
00:04:36.100 --> 00:04:38.310
of one mole of sodium chloride.
00:04:38.310 --> 00:04:40.550
So when the reaction goes to completion,
00:04:40.550 --> 00:04:42.360
the strong acid and the strong base
00:04:42.360 --> 00:04:44.400
have completely neutralized each other.
00:04:44.400 --> 00:04:46.700
And essentially, we
have an aqueous solution
00:04:46.700 --> 00:04:48.500
of sodium chloride.
00:04:48.500 --> 00:04:53.090
At 25 degrees Celsius,
the pH of water is seven,
00:04:53.090 --> 00:04:54.770
which is neutral,
00:04:54.770 --> 00:04:57.690
and the sodium cations
and the chloride anions
00:04:57.690 --> 00:04:59.180
do not react with water,
00:04:59.180 --> 00:05:01.790
so they don't affect the pH.
00:05:01.790 --> 00:05:05.010
Therefore, for the situation
where you have equal amount
00:05:05.010 --> 00:05:07.780
of moles of a strong
acid and a strong base,
00:05:07.780 --> 00:05:11.100
the pH of the resulting
solution will be seven.
00:05:11.100 --> 00:05:13.900
Let's do another strong
acid-strong base calculation.
00:05:13.900 --> 00:05:15.100
However, this time,
00:05:15.100 --> 00:05:18.900
the moles of strong acid and
strong base are not equal.
00:05:18.900 --> 00:05:21.440
So let's say we react 300 milliliters
00:05:21.440 --> 00:05:24.700
of a 1.0 molar solution of HCl
00:05:24.700 --> 00:05:28.220
with 100 milliliters
of a 1.0 molar solution
00:05:28.220 --> 00:05:29.630
of sodium hydroxide.
00:05:29.630 --> 00:05:32.510
And our goal is to calculate the pH
00:05:32.510 --> 00:05:34.470
of the resulting solution.
00:05:34.470 --> 00:05:36.510
And I should point out
these are aqueous solutions
00:05:36.510 --> 00:05:39.210
of HCl and NaOH.
00:05:39.210 --> 00:05:41.770
The first step is to
calculate moles of strong acid
00:05:41.770 --> 00:05:43.740
and moles of strong base.
00:05:43.740 --> 00:05:45.270
And the equation for molarity
00:05:45.270 --> 00:05:47.550
is equal to moles over liters.
00:05:47.550 --> 00:05:52.530
So for our strong acid,
HCl, the molarity is 1.0,
00:05:52.530 --> 00:05:55.150
and the volume is 300 milliliters,
00:05:55.150 --> 00:05:58.730
which is equal to .300 liters.
00:05:58.730 --> 00:06:00.580
So solving for x, we find that x
00:06:00.580 --> 00:06:04.470
is equal to .30 moles of HCl.
00:06:04.470 --> 00:06:06.650
For our strong base, sodium hydroxide,
00:06:06.650 --> 00:06:09.090
the concentration is one molar,
00:06:09.090 --> 00:06:11.500
and the volume is 100 milliliters,
00:06:11.500 --> 00:06:14.570
which is equal to .100 liters.
00:06:14.570 --> 00:06:15.750
So solving for x,
00:06:15.750 --> 00:06:19.860
we find that x is equal
to .10 moles of NaOH.
00:06:19.860 --> 00:06:21.080
Going back to HCl,
00:06:21.080 --> 00:06:24.830
since HCl is strong
acid that ionizes 100%,
00:06:24.830 --> 00:06:27.300
if we have .30 moles of HCl,
00:06:27.300 --> 00:06:30.780
we have .30 moles of H plus ions,
00:06:30.780 --> 00:06:35.780
or we could say .30 moles
of hydronium ions, H3O plus.
00:06:38.420 --> 00:06:39.870
And for sodium hydroxide,
00:06:39.870 --> 00:06:41.810
since sodium hydroxide is a strong base
00:06:41.810 --> 00:06:43.940
that dissociates 100%,
00:06:43.940 --> 00:06:46.900
if we have .10 moles of sodium hydroxide,
00:06:46.900 --> 00:06:49.220
we have .10 moles of sodium ions
00:06:49.220 --> 00:06:54.220
and also .10 moles of
hydroxide ions, OH minus.
00:06:55.940 --> 00:06:58.570
And if we think about
our net ionic equation,
00:06:58.570 --> 00:07:02.410
the .30 moles of hydronium
ions will react with
00:07:02.410 --> 00:07:05.890
the .10 moles of hydroxide ions.
00:07:05.890 --> 00:07:08.710
So here's one way to write
our net ionic equation.
00:07:08.710 --> 00:07:13.710
The hydronium ion plus the
hydroxide ion forms 2H2O.
00:07:13.930 --> 00:07:15.190
And to help us find the pH,
00:07:15.190 --> 00:07:17.780
we're gonna use another ICF table.
00:07:17.780 --> 00:07:20.730
The initial moles of hydronium ions,
00:07:20.730 --> 00:07:23.270
we calculated to be .30,
00:07:23.270 --> 00:07:25.760
and the initial moles of hydroxide ions,
00:07:25.760 --> 00:07:27.623
we calculated to be .10.
00:07:28.750 --> 00:07:30.900
Because we don't have
equal amounts of moles
00:07:30.900 --> 00:07:33.210
and the mole ratio is one to one.
00:07:33.210 --> 00:07:34.043
In this case,
00:07:34.043 --> 00:07:37.970
we're gonna have a limiting
reactant and an excess reactant.
00:07:37.970 --> 00:07:40.850
Since we only have .10
moles of hydroxide ions,
00:07:40.850 --> 00:07:44.060
all of the hydroxide ions will react.
00:07:44.060 --> 00:07:46.737
And since it's a one-to-one mole ratio,
00:07:46.737 --> 00:07:50.920
.10 moles of hydroxide ions
will react with .10 moles
00:07:50.920 --> 00:07:52.240
of hydronium ions,
00:07:52.240 --> 00:07:56.320
so we can write minus .10
under hydronium as well.
00:07:56.320 --> 00:07:58.950
Therefore, when the
reaction goes to completion,
00:07:58.950 --> 00:08:00.210
for the hydroxide ions,
00:08:00.210 --> 00:08:01.450
we'll have used all of them up.
00:08:01.450 --> 00:08:04.660
We started with .10
and we're using up .10,
00:08:04.660 --> 00:08:06.960
therefore, we'll have zero moles.
00:08:06.960 --> 00:08:08.220
For the hydronium ion,
00:08:08.220 --> 00:08:13.220
we started with .30 moles
minus .10 gives us .20 moles.
00:08:14.670 --> 00:08:16.943
So the hydroxide ions were
our limiting reactant,
00:08:16.943 --> 00:08:21.180
and the hydronium ions
where our excess reactant.
00:08:21.180 --> 00:08:24.760
So the strong base neutralized
some of the strong acid
00:08:24.760 --> 00:08:25.800
that was present,
00:08:25.800 --> 00:08:29.170
and we can calculate the pH
of the resulting solution
00:08:29.170 --> 00:08:33.070
by the number of moles
of excess hydronium ions.
00:08:33.070 --> 00:08:35.080
Next, we calculate the concentration
00:08:35.080 --> 00:08:37.450
of hydronium ions in solution.
00:08:37.450 --> 00:08:40.530
Since the number of moles
of hydronium ions is .20,
00:08:40.530 --> 00:08:42.450
we plug that into our
equation for molarity,
00:08:42.450 --> 00:08:45.110
so molarity is equal to moles over liters,
00:08:45.110 --> 00:08:47.450
and the total volume of our solution
00:08:47.450 --> 00:08:50.110
will be 300 milliliters
plus 100 milliliters,
00:08:50.110 --> 00:08:54.700
which is 400 milliliters, or .400 liters.
00:08:54.700 --> 00:08:55.900
So let me go and write this in here.
00:08:55.900 --> 00:09:00.480
So .20 moles divided by .400 liters
00:09:00.480 --> 00:09:05.470
is equal to a concentration of .50 molar.
00:09:05.470 --> 00:09:08.040
And because the pH is
equal to the negative log
00:09:08.040 --> 00:09:10.220
of the concentration of hydronium ions,
00:09:10.220 --> 00:09:13.920
if we plug in our concentration
of hydronium ions of .50,
00:09:13.920 --> 00:09:16.640
the pH is equal to the
negative log of .50,
00:09:16.640 --> 00:09:18.263
which is equal to .30.
00:09:19.900 --> 00:09:22.180
Having a low pH for our resulting solution
00:09:22.180 --> 00:09:25.000
at 25 degrees Celsius
makes a lot of sense,
00:09:25.000 --> 00:09:28.033
because we ended up
with an excess of acid.
|
Sal's back to school 2021 message | https://www.youtube.com/watch?v=mHsDodBfOVk | vtt | https://www.youtube.com/api/timedtext?v=mHsDodBfOVk&ei=0lWUZdrVJO-NmLAP-d2ZyAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5CA4CBA4438FA65A301A6603DC1457DAB197CE44.265EFE5FDE5DF4B5FD6224767D2D32261E68183D&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.450 --> 00:00:03.140
- Hi, everyone, Sal Khan
here from Khan Academy,
00:00:03.140 --> 00:00:06.000
and we're entering into
yet another back to school,
00:00:06.000 --> 00:00:08.000
but this is a back to
school that's very unusual
00:00:08.000 --> 00:00:09.710
compared to all others.
00:00:09.710 --> 00:00:12.100
We hope that we're finally going to get
00:00:12.100 --> 00:00:14.150
to some level of normalcy
00:00:14.150 --> 00:00:16.130
as we see the light at
the end of the tunnel
00:00:16.130 --> 00:00:18.320
with the pandemic, at
least in some places.
00:00:18.320 --> 00:00:21.010
I know a lot of parts of
the world are still going
00:00:21.010 --> 00:00:24.400
through some of the worst
impacts of the pandemic.
00:00:24.400 --> 00:00:28.400
But as we hopefully get to that
point and go back to school,
00:00:28.400 --> 00:00:30.190
I just wanted to say how excited we are
00:00:30.190 --> 00:00:31.390
to partner with y'all.
00:00:31.390 --> 00:00:33.080
The pandemic has been tough.
00:00:33.080 --> 00:00:35.320
It's been tough on many
dimensions of our life,
00:00:35.320 --> 00:00:37.230
but especially education.
00:00:37.230 --> 00:00:38.620
As I always say,
00:00:38.620 --> 00:00:40.770
and people are surprised
to hear it from me,
00:00:40.770 --> 00:00:43.230
if I had to pick between an
amazing in-person experience
00:00:43.230 --> 00:00:44.630
with an amazing educator
00:00:44.630 --> 00:00:46.240
versus the best technology in the world,
00:00:46.240 --> 00:00:48.150
I would pick the amazing
in-person experience.
00:00:48.150 --> 00:00:49.980
Now, I don't think there
has to be a trade off.
00:00:49.980 --> 00:00:52.230
I think the best is the
best of both worlds.
00:00:52.230 --> 00:00:54.900
But you can imagine, people
haven't had the benefit
00:00:54.900 --> 00:00:56.300
of being in the room together,
00:00:56.300 --> 00:00:57.770
being able to have all of the intangibles
00:00:57.770 --> 00:01:00.920
that goes with being an in-person school.
00:01:00.920 --> 00:01:02.730
So there's a lot of work to do.
00:01:02.730 --> 00:01:04.660
Obviously all of us here at Khan Academy
00:01:04.660 --> 00:01:07.200
have been doing our best to play a part
00:01:07.200 --> 00:01:08.830
in keeping everyone learning,
00:01:08.830 --> 00:01:11.970
supporting everyone as
the pandemic went on.
00:01:11.970 --> 00:01:13.930
But the real work is
actually going to be now,
00:01:13.930 --> 00:01:15.810
as we go into back to school.
00:01:15.810 --> 00:01:18.850
A lot of folks have been talking
about unfinished learning
00:01:18.850 --> 00:01:20.080
or learning loss.
00:01:20.080 --> 00:01:22.230
And every summer, there's
some learning loss.
00:01:22.230 --> 00:01:25.010
Kids forget things, and
they're not learning things.
00:01:25.010 --> 00:01:27.410
But we can imagine with a year,
00:01:27.410 --> 00:01:30.540
year and a half of pandemic schooling,
00:01:30.540 --> 00:01:33.130
some of the kids who
we're most concerned about
00:01:33.130 --> 00:01:34.310
actually fell off the radar.
00:01:34.310 --> 00:01:37.110
And many, many other kids
weren't able to learn as much,
00:01:37.110 --> 00:01:39.070
and even the kids and the
learners, I should say,
00:01:39.070 --> 00:01:41.200
of all ages who were able to learn,
00:01:41.200 --> 00:01:42.980
there's other things
that fell by the wayside,
00:01:42.980 --> 00:01:44.520
the socialization, the connection,
00:01:44.520 --> 00:01:46.520
the patterns of school.
00:01:46.520 --> 00:01:51.520
So for all of you parents,
students, teachers,
00:01:51.757 --> 00:01:53.470
donors to Khan Academy,
00:01:53.470 --> 00:01:56.760
first of all, thank you for
being on this journey with us.
00:01:56.760 --> 00:01:59.530
But I'm confident, as well,
that as we go into this period,
00:01:59.530 --> 00:02:02.170
it's not gonna be easy,
but if we work together,
00:02:02.170 --> 00:02:04.720
figure out ways to finish
that unfinished learning,
00:02:04.720 --> 00:02:06.680
there might be a post-pandemic world
00:02:06.680 --> 00:02:10.830
where we can accelerate learning
together faster than ever.
00:02:10.830 --> 00:02:12.520
So I look forward to
going on that journey,
00:02:12.520 --> 00:02:13.870
and welcome back to school.
|
LearnStorm 2021 - Khan Academy LearnStorm | https://www.youtube.com/watch?v=LYdhi1mZFl0 | vtt | https://www.youtube.com/api/timedtext?v=LYdhi1mZFl0&ei=0lWUZb2-JL6BmLAP7Z6FkA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=3C2BC14CD30F8030D7390B576AD1E1DE456F6AC5.1051895F45BDF30BCF338F02D49B0DC735511436&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.090 --> 00:00:01.240
- Hello teachers.
00:00:01.240 --> 00:00:04.800
I'm Sal Khan, founder of the
not-for-profit Khan Academy.
00:00:04.800 --> 00:00:07.460
And I'm here to announce a nationwide
00:00:07.460 --> 00:00:11.549
back to school learning
challenge called LearnStorm.
00:00:11.549 --> 00:00:15.340
LearnStorm is an exciting way
to jumpstart your school year
00:00:15.340 --> 00:00:17.400
around learning activities.
00:00:17.400 --> 00:00:19.590
It's designed to motivate your students
00:00:19.590 --> 00:00:22.390
and to help build their growth mindset.
00:00:22.390 --> 00:00:24.500
- This year was amazing with LearnStorm.
00:00:24.500 --> 00:00:27.140
I had a group of students
that couldn't add, subtract,
00:00:27.140 --> 00:00:29.070
multiply, or divide fractions.
00:00:29.070 --> 00:00:31.370
They avoided it at all costs.
00:00:31.370 --> 00:00:33.170
But since it was an assignment,
00:00:33.170 --> 00:00:36.650
they would try it and they
would eventually do much better.
00:00:36.650 --> 00:00:40.100
And what was amazing was that
the lower achieving students
00:00:40.100 --> 00:00:44.300
were able to see that they
were part of something huge.
00:00:44.300 --> 00:00:46.040
They were able to contribute,
00:00:46.040 --> 00:00:49.390
and that I thought boosted
their self-confidence,
00:00:49.390 --> 00:00:50.550
their self-esteem,
00:00:50.550 --> 00:00:52.590
and I didn't realize that would happen
00:00:52.590 --> 00:00:53.840
after doing LearnStorm.
00:00:53.840 --> 00:00:56.423
(upbeat music)
00:00:59.014 --> 00:01:03.060
- LearnStorm is a good
way to differentiate,
00:01:03.060 --> 00:01:07.500
and as well as motivate, and
with the growth mindset pieces,
00:01:07.500 --> 00:01:09.420
you can also educate them
00:01:09.420 --> 00:01:11.910
about why it's important to learn,
00:01:11.910 --> 00:01:12.970
how they learn,
00:01:12.970 --> 00:01:15.140
how their body is set up to learn,
00:01:15.140 --> 00:01:17.450
what strategies help them learn.
00:01:17.450 --> 00:01:18.450
It's amazing.
00:01:18.450 --> 00:01:19.995
It's amazing, and it's free.
00:01:19.995 --> 00:01:21.251
(laughing)
00:01:21.251 --> 00:01:22.720
It's free!
00:01:22.720 --> 00:01:25.180
- We think this is really
going to motivate your students
00:01:25.180 --> 00:01:26.940
to understand, to appreciate,
00:01:26.940 --> 00:01:29.760
that they truly can learn anything.
00:01:29.760 --> 00:01:31.870
The activities have been designed
00:01:31.870 --> 00:01:35.200
to have measurable gains
in learning attitudes.
00:01:35.200 --> 00:01:37.840
- One thing I learned from
the Growth Mindset Activities
00:01:37.840 --> 00:01:40.340
is that your intelligence can grow
00:01:40.340 --> 00:01:41.700
just like your muscles can grow.
00:01:41.700 --> 00:01:43.990
And that's something that
really stuck with me,
00:01:43.990 --> 00:01:46.490
'cause I didn't know that before.
00:01:46.490 --> 00:01:49.170
- I did over 300 lessons in one week.
00:01:49.170 --> 00:01:52.230
I felt proud of myself
getting all these good grades.
00:01:52.230 --> 00:01:54.720
- It helps the students tremendously.
00:01:54.720 --> 00:01:56.240
Their confidence is higher.
00:01:56.240 --> 00:01:57.190
They're able to do it.
00:01:57.190 --> 00:01:59.970
And it warms my heart that
they think that way now.
00:01:59.970 --> 00:02:02.100
And they know that they can keep going,
00:02:02.100 --> 00:02:05.850
and keep growing, and nothing
will stand in their way.
00:02:05.850 --> 00:02:08.530
- So together as we
jumpstart this school year,
00:02:08.530 --> 00:02:12.440
I look forward for all of us
living the LearnStorm motto,
00:02:12.440 --> 00:02:15.609
to keep going and to keep growing.
00:02:15.609 --> 00:02:18.276
(kids chanting)
|
Adaptation and environmental change | https://www.youtube.com/watch?v=XkhD_Rphlm0 | vtt | https://www.youtube.com/api/timedtext?v=XkhD_Rphlm0&ei=0lWUZeXeKt_wmLAP_qm5uAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=69C23FEC2D46A2D3D58AB35BDD96DBEEC0EFE9FA.35F698232F2F7B68F39049A37979343072E0B72B&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.170 --> 00:00:01.070
- [Dr. Sammy] Hi, everybody.
00:00:01.070 --> 00:00:03.680
Dr. Sammy here, your friendly
neighborhood entomologist
00:00:03.680 --> 00:00:06.390
here to talk to you about how adaptation,
00:00:06.390 --> 00:00:08.570
which is dependent on the environment,
00:00:08.570 --> 00:00:11.880
responds in contexts of
environmental change.
00:00:11.880 --> 00:00:15.040
Natural selection promotes
adaptation in populations.
00:00:15.040 --> 00:00:17.600
It encourages populations
to develop traits
00:00:17.600 --> 00:00:21.560
that better allow individuals
to survive and reproduce.
00:00:21.560 --> 00:00:23.740
Those adaptations are thus linked
00:00:23.740 --> 00:00:26.610
to the environment in
which they were forged.
00:00:26.610 --> 00:00:28.490
You can look at a lot of organisms
00:00:28.490 --> 00:00:31.950
and based on their physical
traits and/or their behavior,
00:00:31.950 --> 00:00:33.910
you can tell what sort of environment
00:00:33.910 --> 00:00:36.950
their population likely evolved in.
00:00:36.950 --> 00:00:40.000
So adaptations are products of,
00:00:40.000 --> 00:00:43.820
and are inextricably
connected to, the environment.
00:00:43.820 --> 00:00:45.860
But what happens when the environment
00:00:45.860 --> 00:00:49.040
which forges a specific set of adaptations
00:00:49.040 --> 00:00:51.660
no longer exists in that form?
00:00:51.660 --> 00:00:53.510
How do populations respond?
00:00:53.510 --> 00:00:55.630
Well, this happens to actually be
00:00:55.630 --> 00:00:57.640
a pretty common occurrence on Earth.
00:00:57.640 --> 00:01:00.860
I wouldn't be surprised if
the saying "things change"
00:01:00.860 --> 00:01:03.450
was first coined by a paleontologist.
00:01:03.450 --> 00:01:06.190
Studying the history of life on Earth
00:01:06.190 --> 00:01:07.940
means you'd be well-acquainted
00:01:07.940 --> 00:01:10.690
with the dogged persistence of change.
00:01:10.690 --> 00:01:12.660
Well, the good news is the forces
00:01:12.660 --> 00:01:14.430
that drive natural selection
00:01:14.430 --> 00:01:17.560
don't just disappear when
an environment changes.
00:01:17.560 --> 00:01:20.230
Because of the persistence
of heritable diversity
00:01:20.230 --> 00:01:22.800
and differential survivorship
and reproduction,
00:01:22.800 --> 00:01:26.340
natural selection is still
there to promote new adaptations
00:01:26.340 --> 00:01:29.360
suited to the new
environmental conditions.
00:01:29.360 --> 00:01:31.790
This means that when
the environment changes,
00:01:31.790 --> 00:01:34.010
the distribution of
traits in the population
00:01:34.010 --> 00:01:36.550
will often change as well.
00:01:36.550 --> 00:01:38.890
What those changes will ultimately be
00:01:38.890 --> 00:01:40.340
is based on the adaptations
00:01:40.340 --> 00:01:42.320
promoted by the previous environment
00:01:42.320 --> 00:01:45.070
and the pressures
presented by the new one.
00:01:45.070 --> 00:01:46.450
So let's look at some examples
00:01:46.450 --> 00:01:49.010
so I can make sure you're
picking up what I'm putting down.
00:01:49.010 --> 00:01:52.290
Okay, so in evolutionary biology,
00:01:52.290 --> 00:01:56.070
we like to discuss three
primary shift patterns
00:01:56.070 --> 00:02:00.090
that can be observed as a
result of environmental change:
00:02:00.090 --> 00:02:02.173
directional selection,
00:02:03.210 --> 00:02:05.543
disruptive selection,
00:02:06.960 --> 00:02:10.433
and stabilizing selection.
00:02:12.020 --> 00:02:13.400
For each of these,
00:02:13.400 --> 00:02:16.330
I'll show you a graph and tell you a story
00:02:16.330 --> 00:02:20.320
of the stubbornness
and resilience of life,
00:02:20.320 --> 00:02:23.160
because every graph has a story.
00:02:23.160 --> 00:02:24.640
And the first of these stories
00:02:24.640 --> 00:02:26.750
is that of directional selection.
00:02:26.750 --> 00:02:30.790
The snow vole is a mouse-like
mammal that even I,
00:02:30.790 --> 00:02:33.780
as an admittedly bug-biased scientist,
00:02:33.780 --> 00:02:36.060
have to admit is pretty cute.
00:02:36.060 --> 00:02:39.010
These rodents are born at high
elevations in the Swiss Alps
00:02:39.010 --> 00:02:40.870
and researchers have observed something
00:02:40.870 --> 00:02:43.470
that may seem obvious on its face.
00:02:43.470 --> 00:02:46.810
Large adult snow voles
have better survivorship
00:02:46.810 --> 00:02:49.050
than smaller adult snow voles.
00:02:49.050 --> 00:02:50.810
They're more difficult for predators
00:02:50.810 --> 00:02:53.540
to capture, overpower, and consume.
00:02:53.540 --> 00:02:55.680
They have greater temperature tolerance
00:02:55.680 --> 00:02:58.500
and typically more fat
stores for a long winter.
00:02:58.500 --> 00:03:01.710
So historically, that
distribution of snow bowls...
00:03:01.710 --> 00:03:02.543
Bowls.
00:03:02.543 --> 00:03:05.270
Snow voles (laughing) has been shifted
00:03:05.270 --> 00:03:08.363
toward the higher end of
the adult weight spectrum.
00:03:09.810 --> 00:03:12.570
However, climate change has led to changes
00:03:12.570 --> 00:03:14.450
in the snow vole's environment.
00:03:14.450 --> 00:03:17.390
Snow has been falling earlier
and earlier in the Alps,
00:03:17.390 --> 00:03:20.560
giving the voles less
time to actually develop.
00:03:20.560 --> 00:03:22.370
If the voles haven't reached maturity
00:03:22.370 --> 00:03:23.970
by the time the winter begins,
00:03:23.970 --> 00:03:26.770
they typically can't
continue their lifecycle.
00:03:26.770 --> 00:03:30.820
And because larger body sizes
require more time to develop,
00:03:30.820 --> 00:03:33.920
there's a strong, selective
pressure against the genes
00:03:33.920 --> 00:03:36.000
underlying larger body sizes
00:03:36.000 --> 00:03:39.410
as the environment shifts
towards earlier winter onset.
00:03:39.410 --> 00:03:41.030
This also means that the genes
00:03:41.030 --> 00:03:44.080
underlying smaller body sizes are favored.
00:03:44.080 --> 00:03:47.210
So the smallest individuals
in the original population
00:03:47.210 --> 00:03:49.000
likely had the most offspring,
00:03:49.000 --> 00:03:51.080
and the variation in those offspring
00:03:51.080 --> 00:03:53.740
likely included some
that were even smaller
00:03:53.740 --> 00:03:56.000
than in the original population.
00:03:56.000 --> 00:03:58.550
This means that as the
smallest individuals
00:03:58.550 --> 00:04:01.460
in each generation continue to be favored
00:04:01.460 --> 00:04:03.100
and have the most offspring,
00:04:03.100 --> 00:04:04.870
the distribution of the population
00:04:04.870 --> 00:04:07.840
will likely continue to march to the left
00:04:07.840 --> 00:04:10.190
until it reaches a point
where the individuals
00:04:10.190 --> 00:04:14.060
are too small to do well given
the environmental conditions.
00:04:14.060 --> 00:04:16.460
This shift can be represented by a graph
00:04:16.460 --> 00:04:19.350
that shows directional selection.
00:04:19.350 --> 00:04:21.580
Now let's go over the graph one more time
00:04:21.580 --> 00:04:23.380
to make sure that everything is clear.
00:04:23.380 --> 00:04:24.950
Here on the X-axis,
00:04:24.950 --> 00:04:28.090
you'll see the spectrum
of average adult body size
00:04:28.090 --> 00:04:31.330
ranging from the smallest
to the largest individuals.
00:04:31.330 --> 00:04:33.490
Traits are quite frequently on a spectrum,
00:04:33.490 --> 00:04:35.360
such that some individuals possess
00:04:35.360 --> 00:04:37.200
a greater or lesser expression
00:04:37.200 --> 00:04:39.450
and are thus differentially impacted
00:04:39.450 --> 00:04:41.330
by environmental change.
00:04:41.330 --> 00:04:43.420
On the Y-axis is the percent
00:04:43.420 --> 00:04:45.200
of individuals in the population,
00:04:45.200 --> 00:04:48.730
which allows you to see
proportionally how individuals fare
00:04:48.730 --> 00:04:51.940
by comparison to those of
greater or lesser size.
00:04:51.940 --> 00:04:54.580
The red arrow represents
selection pressure,
00:04:54.580 --> 00:04:56.440
which in this case is imposed
00:04:56.440 --> 00:04:58.790
by the abiotic factors of weather.
00:04:58.790 --> 00:05:00.430
When looking at these graphs,
00:05:00.430 --> 00:05:02.780
you wanna consider who is least able
00:05:02.780 --> 00:05:04.850
to handle the pressure imposed.
00:05:04.850 --> 00:05:07.970
It's typically the area
of the distribution
00:05:07.970 --> 00:05:09.890
where you'll see the greatest difference
00:05:09.890 --> 00:05:11.570
between the population before
00:05:11.570 --> 00:05:13.900
and after the environmental change.
00:05:13.900 --> 00:05:16.140
The white arrow then shows which direction
00:05:16.140 --> 00:05:19.020
the population as a
whole is then shifting.
00:05:19.020 --> 00:05:20.690
Directional selection events
00:05:20.690 --> 00:05:22.820
are those which favor one extreme
00:05:22.820 --> 00:05:24.810
while excluding another.
00:05:24.810 --> 00:05:27.510
However, change itself can be as diverse
00:05:27.510 --> 00:05:29.140
as the organisms it changes.
00:05:29.140 --> 00:05:31.490
And thus, you can also get circumstances
00:05:31.490 --> 00:05:34.440
where selection favors both extremes.
00:05:34.440 --> 00:05:37.000
This is called disruptive selection.
00:05:37.000 --> 00:05:38.070
For this example,
00:05:38.070 --> 00:05:41.450
we look to the pungent
world of dung beetles.
00:05:41.450 --> 00:05:45.220
Some populations of the
beetle Onthophagus acuminatus
00:05:45.220 --> 00:05:47.810
have a bimodaled size distribution
00:05:47.810 --> 00:05:50.460
where you'll see a large
number of large males
00:05:50.460 --> 00:05:53.170
in addition to a large
number of small males
00:05:53.170 --> 00:05:56.273
with very few representatives
of the sizes in between.
00:05:57.140 --> 00:05:59.890
The large males use their superior size,
00:05:59.890 --> 00:06:03.040
strength, and horns to fight other males
00:06:03.040 --> 00:06:05.240
for the opportunity to mate.
00:06:05.240 --> 00:06:08.850
A male having selected a mate
will spend most of his time
00:06:08.850 --> 00:06:11.440
guarding the entrance to the
borough where she dwells,
00:06:11.440 --> 00:06:15.910
grappling with males of
similar size who challenge him
00:06:15.910 --> 00:06:18.630
for the chance to depose
him and mate with her.
00:06:18.630 --> 00:06:21.640
Medium-sized males don't
do well in this context.
00:06:21.640 --> 00:06:24.460
They can't overcome the larger males.
00:06:24.460 --> 00:06:27.250
But why then are there small males
00:06:27.250 --> 00:06:29.860
and why are they so
abundant in the population?
00:06:29.860 --> 00:06:32.620
Well, they've actually got
a trick up their sleeves.
00:06:32.620 --> 00:06:34.410
Instead of trying to fight,
00:06:34.410 --> 00:06:36.550
they forgo the battle entirely
00:06:36.550 --> 00:06:38.840
and simply use their diminutive size
00:06:38.840 --> 00:06:40.900
to sneak past unnoticed.
00:06:40.900 --> 00:06:43.950
These small males typically lack horns,
00:06:43.950 --> 00:06:46.610
which leaves them similar
in appearance to females,
00:06:46.610 --> 00:06:48.110
which makes male dung beetles
00:06:48.110 --> 00:06:50.460
less inclined to engage them in battle.
00:06:50.460 --> 00:06:52.900
And the little guys further avoid trouble
00:06:52.900 --> 00:06:55.220
by deftly digging a backdoor entrance
00:06:55.220 --> 00:06:58.270
into the female beetle's
subterranean nesting chamber,
00:06:58.270 --> 00:06:59.950
such that they rarely have to encounter
00:06:59.950 --> 00:07:02.340
the large male guarding the front door.
00:07:02.340 --> 00:07:04.720
This allows them plenty of time to mate
00:07:04.720 --> 00:07:06.120
before making their exit,
00:07:06.120 --> 00:07:07.560
ensuring the representation
00:07:07.560 --> 00:07:10.250
of their sneaky genetics in the gene pool.
00:07:10.250 --> 00:07:12.040
Disruptive selection selects
00:07:12.040 --> 00:07:14.020
for both extremes on the spectrum
00:07:14.020 --> 00:07:17.230
to the exclusion of the moderate
trait in the distribution.
00:07:17.230 --> 00:07:19.370
But there's also a form of selection
00:07:19.370 --> 00:07:22.870
that is the opposite of
disruptive selection.
00:07:22.870 --> 00:07:24.853
It's called stabilizing selection.
00:07:25.780 --> 00:07:28.670
Stabilizing selection is
observed under circumstances
00:07:28.670 --> 00:07:31.250
where selection is favoring
the moderate set of traits
00:07:31.250 --> 00:07:34.620
in a distribution to the
exclusion of the extremes.
00:07:34.620 --> 00:07:36.780
For this story, we once again turn
00:07:36.780 --> 00:07:39.130
to the wondrous class Insecta,
00:07:39.130 --> 00:07:41.140
where insects have learned to make a home
00:07:41.140 --> 00:07:43.950
in some of the most
ingenious ways possible.
00:07:43.950 --> 00:07:45.640
In the world of gall flies,
00:07:45.640 --> 00:07:47.920
life begins when a female gall fly
00:07:47.920 --> 00:07:51.000
lays an egg in the stem
of a suitable host plant.
00:07:51.000 --> 00:07:53.110
The developing larva induces the plant
00:07:53.110 --> 00:07:56.130
to form a spherical growth
around it called a gall,
00:07:56.130 --> 00:07:58.830
which protects the
developing fly's squishy body
00:07:58.830 --> 00:08:00.790
and provides it with all the food it needs
00:08:00.790 --> 00:08:01.860
to reach adulthood,
00:08:01.860 --> 00:08:04.130
unless a parasitic wasps shows up
00:08:04.130 --> 00:08:07.710
and attempts to lay eggs
on the developing gall fly.
00:08:07.710 --> 00:08:11.220
If this happens, the
developing wasp kills the fly
00:08:11.220 --> 00:08:13.070
and takes over its living space.
00:08:13.070 --> 00:08:15.840
This is easiest to do with small galls
00:08:15.840 --> 00:08:18.940
because the wasp has to stick
his thin egg-laying tube
00:08:18.940 --> 00:08:21.750
through the gall to
access the developing fly.
00:08:21.750 --> 00:08:24.320
A large gall forms enough of a barrier
00:08:24.320 --> 00:08:27.190
between the gall fly and
the wasp's egg-laying tube
00:08:27.190 --> 00:08:29.260
that it can't quite make it.
00:08:29.260 --> 00:08:31.600
So this selects for larger galls
00:08:31.600 --> 00:08:33.670
and would promote directional selection,
00:08:33.670 --> 00:08:36.310
all the other factors in
the environment being equal.
00:08:36.310 --> 00:08:40.360
But what happens when
keen-eyed birds are introduced?
00:08:40.360 --> 00:08:44.250
Well, large galls become
an easy meal for them
00:08:44.250 --> 00:08:46.520
because they're conspicuous
in the environment.
00:08:46.520 --> 00:08:47.800
This creates a situation
00:08:47.800 --> 00:08:51.610
where small galls are selected
against as are large ones,
00:08:51.610 --> 00:08:54.820
ensuring that the medium-sized
galls are favored.
00:08:54.820 --> 00:08:57.000
To remember what this
distribution looks like,
00:08:57.000 --> 00:08:59.130
I tell myself that the trait distribution
00:08:59.130 --> 00:09:03.090
is being stabilized by
pressure on both sides.
00:09:03.090 --> 00:09:06.520
Environmental change
can be pretty diverse.
00:09:06.520 --> 00:09:10.170
Without the incredible adaptive
powers of natural selection,
00:09:10.170 --> 00:09:12.800
our dynamic world would be unsuitable
00:09:12.800 --> 00:09:17.403
for the unpredictability
that is life as we know it.
|
Factors affecting acid strength | https://www.youtube.com/watch?v=v_94NsuBwDM | vtt | https://www.youtube.com/api/timedtext?v=v_94NsuBwDM&ei=0lWUZZuvI7r0mLAPp_S72AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=870E4A83D689735589823D955272E8A88EC6405E.03DB009316C02E2842F762A8BA7100DFA6F00D77&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.370 --> 00:00:02.360
- [Instructor] Factors
that affect asset strength
00:00:02.360 --> 00:00:04.640
include bond polarity, bond strength,
00:00:04.640 --> 00:00:06.650
and conjugate base stability.
00:00:06.650 --> 00:00:09.070
Let's think about a generic acid, HA,
00:00:09.070 --> 00:00:11.570
that donates a proton to water
00:00:11.570 --> 00:00:14.470
to form the hydronium ion H3O plus,
00:00:14.470 --> 00:00:18.420
and the conjugate base
to HA, which is A minus.
00:00:18.420 --> 00:00:20.250
First let's consider the polarity
00:00:20.250 --> 00:00:23.000
of the bond between H and A.
00:00:23.000 --> 00:00:25.630
If A is more electronegative than H,
00:00:25.630 --> 00:00:28.090
A withdraws electron density.
00:00:28.090 --> 00:00:32.170
So we could draw an arrow
pointing towards the A, right,
00:00:32.170 --> 00:00:34.130
as the electrons and the bond between them
00:00:34.130 --> 00:00:36.670
are pulled closer to the A.
00:00:36.670 --> 00:00:40.330
As the electronegativity of A increases,
00:00:40.330 --> 00:00:44.913
there's an increase in
the polarity of the bond.
00:00:45.840 --> 00:00:47.800
As the bond polarity increases,
00:00:47.800 --> 00:00:51.180
more electron density is
drawn away from the H,
00:00:51.180 --> 00:00:54.730
which makes it easier for
HA to donate a proton.
00:00:54.730 --> 00:00:56.270
Therefore, in general,
00:00:56.270 --> 00:00:59.450
an increase in the
polarity of the HA bond,
00:00:59.450 --> 00:01:02.823
means an increase in the
strength of the acid.
00:01:03.800 --> 00:01:06.740
Next, let's think about the
factor of bond strength.
00:01:06.740 --> 00:01:10.800
And let's consider the strength
of the bond between H and A.
00:01:10.800 --> 00:01:12.100
The weaker the bond,
00:01:12.100 --> 00:01:15.160
the more easily the proton is donated.
00:01:15.160 --> 00:01:18.320
Therefore, in general, a
decrease in the bond strength,
00:01:18.320 --> 00:01:22.580
means an increase in the
strength of the acid.
00:01:22.580 --> 00:01:24.510
The stability of the conjugate base,
00:01:24.510 --> 00:01:27.060
can also affect the strength of the acid.
00:01:27.060 --> 00:01:28.830
The more stable the conjugate base,
00:01:28.830 --> 00:01:32.320
the more likely the asset
is to donate a proton.
00:01:32.320 --> 00:01:33.740
So if you think about that for HA,
00:01:33.740 --> 00:01:36.860
the conjugate base is A minus.
00:01:36.860 --> 00:01:39.040
And the more stable A minus is,
00:01:39.040 --> 00:01:43.100
the more likely HA will
donate a proton in solution.
00:01:43.100 --> 00:01:44.530
Therefore, in general,
00:01:44.530 --> 00:01:48.460
the more stable the conjugate
base, the stronger the acid.
00:01:48.460 --> 00:01:49.520
So let's go ahead and write here
00:01:49.520 --> 00:01:52.700
an increase in the stability
of the conjugate base,
00:01:52.700 --> 00:01:57.150
means an increase in the
strength of the acid.
00:01:57.150 --> 00:01:58.340
Even though acid strength
00:01:58.340 --> 00:02:00.740
is usually due to all
three of these factors,
00:02:00.740 --> 00:02:02.190
bond polarity, bond strength,
00:02:02.190 --> 00:02:04.010
and conjugate base stability,
00:02:04.010 --> 00:02:05.150
when we look at examples,
00:02:05.150 --> 00:02:07.540
we're only gonna consider
one or two factors
00:02:07.540 --> 00:02:11.590
that are the main
contributors to acid strength.
00:02:11.590 --> 00:02:15.190
Let's look at the binary
acids from group 7A
00:02:15.190 --> 00:02:18.020
on the periodic tables,
that's hydrofluoric acid,
00:02:18.020 --> 00:02:22.340
hydrochloric acid, hydrobromic
acid, and hydro ionic acid.
00:02:22.340 --> 00:02:25.110
As we go down the group
from fluorine to chlorine,
00:02:25.110 --> 00:02:26.890
to bromine, to iodine,
00:02:26.890 --> 00:02:29.600
there's an increase in
the strength of the acid.
00:02:29.600 --> 00:02:33.700
So out of these four, hydro
ionic acid, is the strongest.
00:02:33.700 --> 00:02:35.450
The main factor determining the strength
00:02:35.450 --> 00:02:40.380
of the binary acids in
group 7A, is bond strength.
00:02:40.380 --> 00:02:42.390
Looking at values for bond enthalpy,
00:02:42.390 --> 00:02:45.220
allows us to figure out the
strengths of these bonds.
00:02:45.220 --> 00:02:47.320
For example, the HF bond,
00:02:47.320 --> 00:02:51.480
has a bond enthalpy of
567 kilojoules per mole.
00:02:51.480 --> 00:02:53.040
While the HI bond,
00:02:53.040 --> 00:02:56.570
has a bond enthalpy of
299 kilojoules per mole.
00:02:56.570 --> 00:02:58.690
The lower the value for the bond enthalpy,
00:02:58.690 --> 00:03:01.120
the easier it is to break the bond.
00:03:01.120 --> 00:03:04.760
And because bond enthalpy
decrease as we go down the group,
00:03:04.760 --> 00:03:07.980
that means there's a
decrease in bond strength.
00:03:07.980 --> 00:03:09.330
A decrease in bond strength,
00:03:09.330 --> 00:03:12.210
means it's easier for the
asset to donate a proton.
00:03:12.210 --> 00:03:15.370
Therefore, we see an increase
in the strength of the asset
00:03:15.370 --> 00:03:17.330
as we go down the group.
00:03:17.330 --> 00:03:20.990
Next, let's compare the
strengths of some oxyacids.
00:03:20.990 --> 00:03:23.587
These oxyacids all have
the general formula XOH,
00:03:24.560 --> 00:03:26.660
where X is a halogen.
00:03:26.660 --> 00:03:27.830
The acidic proton,
00:03:27.830 --> 00:03:30.830
is the proton that's directly
bonded to the oxygen.
00:03:30.830 --> 00:03:34.420
And if an oxyacid donates
its proton to water,
00:03:34.420 --> 00:03:37.360
that forms the hydronium ion H3O plus,
00:03:37.360 --> 00:03:40.720
and the conjugate base to the oxyacid.
00:03:40.720 --> 00:03:42.170
For these three oxyacids,
00:03:42.170 --> 00:03:45.600
the halogens are iodine,
bromine, and chlorine.
00:03:45.600 --> 00:03:47.560
And as we go from iodine to bromine,
00:03:47.560 --> 00:03:50.730
to chlorine in group 7A
on the periodic table,
00:03:50.730 --> 00:03:54.450
that's an increase in
the electro negativity.
00:03:54.450 --> 00:03:57.110
So chlorine is the most electronegative
00:03:57.110 --> 00:03:59.560
out of these three halogens.
00:03:59.560 --> 00:04:02.610
And as we go up the group in our halogens,
00:04:02.610 --> 00:04:05.320
there's an increase in
the strength of the acid.
00:04:05.320 --> 00:04:09.060
So hypochlorous acid is
the strongest of the three.
00:04:09.060 --> 00:04:12.360
The main factor determining
the strength of these oxyacids,
00:04:12.360 --> 00:04:13.780
is the bond polarity,
00:04:13.780 --> 00:04:17.420
which is affected by the
electronegativity of the halogen.
00:04:17.420 --> 00:04:21.040
So the polarity of this
oxygen, hydrogen bond,
00:04:21.040 --> 00:04:24.120
is affected by the
presence of the halogen.
00:04:24.120 --> 00:04:27.760
As the electronegativity
of the halogen increases,
00:04:27.760 --> 00:04:30.730
the halogen is able to
withdraw more electron density
00:04:30.730 --> 00:04:33.210
away from the right side of the molecule.
00:04:33.210 --> 00:04:36.330
That increases the
polarity of the OH bond,
00:04:36.330 --> 00:04:39.040
it makes it easier to donate this proton.
00:04:39.040 --> 00:04:40.990
Therefore, as the electronegativity
00:04:40.990 --> 00:04:43.110
of the halogen increases,
00:04:43.110 --> 00:04:46.830
the acidity of the oxyacid increases.
00:04:46.830 --> 00:04:49.280
This effect of the electronegative atom
00:04:49.280 --> 00:04:51.200
increasing the acidity,
00:04:51.200 --> 00:04:54.770
is often referred to as
the inductive effect.
00:04:54.770 --> 00:04:59.110
Let's compare hypochlorous
acid to two other oxyacids,
00:04:59.110 --> 00:05:01.650
and notice how I've
left the formal charges
00:05:01.650 --> 00:05:03.270
off of these acids
00:05:03.270 --> 00:05:06.200
just so we can focus on general structure.
00:05:06.200 --> 00:05:08.410
Notice how the acidic proton
00:05:08.410 --> 00:05:10.630
is directly bonded to the oxygen
00:05:10.630 --> 00:05:13.370
and all three of these oxyacids.
00:05:13.370 --> 00:05:15.270
And in all three of these oxyacids,
00:05:15.270 --> 00:05:18.570
the oxygen is directly
bonded to a chlorine.
00:05:18.570 --> 00:05:20.010
Notice what happens to the structure
00:05:20.010 --> 00:05:21.560
as we move to the right.
00:05:21.560 --> 00:05:24.720
Comparing chlorous acid
to hypochlorous acid,
00:05:24.720 --> 00:05:26.590
chlorous acid has an additional oxygen
00:05:26.590 --> 00:05:28.060
bonded to the chlorine.
00:05:28.060 --> 00:05:30.260
And looking at perchloric acid,
00:05:30.260 --> 00:05:31.620
instead of only one additional oxygen,
00:05:31.620 --> 00:05:34.380
there are three additional oxygens.
00:05:34.380 --> 00:05:35.640
So as we move to the right,
00:05:35.640 --> 00:05:38.070
we're increasing in the number of oxygens
00:05:38.070 --> 00:05:40.180
bonded to the chlorine.
00:05:40.180 --> 00:05:43.100
Oxygen is a very electronegative element.
00:05:43.100 --> 00:05:44.490
So as we move to the right,
00:05:44.490 --> 00:05:48.240
we're increasing in the number
of electronegative atoms
00:05:48.240 --> 00:05:49.900
in the acid.
00:05:49.900 --> 00:05:52.920
And as the number of
electronegative atoms increases,
00:05:52.920 --> 00:05:57.310
more electron density is pulled
away from the acidic proton,
00:05:57.310 --> 00:06:01.590
which increases the polarity
of the oxygen hydrogen bond.
00:06:01.590 --> 00:06:04.980
So bond polarity increases
as we move to the right,
00:06:04.980 --> 00:06:08.260
which predicts an increase
in the strength of the acid
00:06:08.260 --> 00:06:10.210
as we move to the right.
00:06:10.210 --> 00:06:12.160
And that's what we observe experimentally,
00:06:12.160 --> 00:06:15.360
perchloric acid is the
strongest of the three.
00:06:15.360 --> 00:06:17.070
In reality, all three factors
00:06:17.070 --> 00:06:19.040
affect the strength of the acid.
00:06:19.040 --> 00:06:20.820
However, for simplicity sake,
00:06:20.820 --> 00:06:23.560
we could just say that
increasing bond polarity,
00:06:23.560 --> 00:06:26.440
is the main factor for the
increasing acid strength
00:06:26.440 --> 00:06:27.763
in these oxyacids.
00:06:29.490 --> 00:06:31.630
Carboxylic acids are a group of assets
00:06:31.630 --> 00:06:34.240
that all contain a carboxyl group.
00:06:34.240 --> 00:06:36.670
A carboxylic group consists of carbon,
00:06:36.670 --> 00:06:38.870
oxygen, oxygen and hydrogen.
00:06:38.870 --> 00:06:40.920
So if we look at acetic acid,
00:06:40.920 --> 00:06:43.810
I'll circle the carboxyl
group on acetic acid,
00:06:43.810 --> 00:06:48.040
and I can also circle the
carboxyl group on formic acid.
00:06:48.040 --> 00:06:50.440
The acidic proton in the carboxylic acid,
00:06:50.440 --> 00:06:53.150
is the one that's directly
bonded to the oxygen
00:06:53.150 --> 00:06:54.823
in the carboxyl group.
00:06:55.680 --> 00:06:57.990
One reason why this proton is acidic,
00:06:57.990 --> 00:07:00.097
is because of the presence of this oxygen
00:07:00.097 --> 00:07:02.210
in the carboxyl group.
00:07:02.210 --> 00:07:05.140
This oxygen hydrogen bond
is already polarized,
00:07:05.140 --> 00:07:08.380
but the presence of another
electronegative atom,
00:07:08.380 --> 00:07:12.670
further increases the polarity
of the oxygen hydrogen bond.
00:07:12.670 --> 00:07:14.150
Increasing the bond polarity,
00:07:14.150 --> 00:07:16.840
makes it more likely to donate the proton,
00:07:16.840 --> 00:07:19.460
which increases the acidity.
00:07:19.460 --> 00:07:20.730
For carboxylic acids,
00:07:20.730 --> 00:07:22.460
it's also important to consider
00:07:22.460 --> 00:07:25.400
the stability of the conjugate base.
00:07:25.400 --> 00:07:28.080
When acetic acid donates its proton,
00:07:28.080 --> 00:07:29.820
it turns into its conjugate base,
00:07:29.820 --> 00:07:31.860
which is the acetate anion.
00:07:31.860 --> 00:07:33.050
Notice that the oxygen
00:07:33.050 --> 00:07:34.670
that used to be bonded to the proton,
00:07:34.670 --> 00:07:37.320
now has a negative formal charge on it.
00:07:37.320 --> 00:07:39.160
There are two possible
resonance structures
00:07:39.160 --> 00:07:41.400
that you can draw for the acetate anion.
00:07:41.400 --> 00:07:42.820
The first is with the negative charge
00:07:42.820 --> 00:07:44.000
on this oxygen.
00:07:44.000 --> 00:07:46.330
And then we could draw
another resonance structure
00:07:46.330 --> 00:07:49.230
with a negative charge
on the other oxygen.
00:07:49.230 --> 00:07:51.280
In reality, neither resonant structure
00:07:51.280 --> 00:07:54.330
is a perfect representation
of the acetate anion.
00:07:54.330 --> 00:07:56.330
And we need to think about a hybrid
00:07:56.330 --> 00:07:59.020
of these two resonant structures.
00:07:59.020 --> 00:07:59.853
In the hybrid,
00:07:59.853 --> 00:08:02.670
the negative charge isn't
on one of the oxygens,
00:08:02.670 --> 00:08:03.790
that one negative charge,
00:08:03.790 --> 00:08:06.950
is spread out or de-localized over two,
00:08:06.950 --> 00:08:08.640
over the two oxygens.
00:08:08.640 --> 00:08:11.140
So it's like one oxygen
has negative one half,
00:08:11.140 --> 00:08:14.310
and the other oxygen
has negative one half.
00:08:14.310 --> 00:08:16.960
This de-localization
of the negative charge,
00:08:16.960 --> 00:08:19.500
stabilizes the conjugate base.
00:08:19.500 --> 00:08:21.700
And the more stable the conjugate base,
00:08:21.700 --> 00:08:23.720
the stronger the acid.
00:08:23.720 --> 00:08:25.810
Therefore, the stability
of the conjugate base
00:08:25.810 --> 00:08:29.490
also affects the acidity
of the carboxylic acid.
00:08:29.490 --> 00:08:31.160
So because carboxylic acids
00:08:31.160 --> 00:08:34.400
have conjugate bases that
are resonant stabilized,
00:08:34.400 --> 00:08:37.250
carboxylic acids like
acetic acid and formic acid,
00:08:37.250 --> 00:08:38.353
are more acidic.
|
Acid–base properties of salts | https://www.youtube.com/watch?v=EDvtwQLJzEg | vtt | https://www.youtube.com/api/timedtext?v=EDvtwQLJzEg&ei=0lWUZaraI7f4xN8P1JWMyAs&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=26D380CBBAE02BB454380733D3A04EC4C6DF92F7.EF8B35327DA06EF2C55A41EB6D5934484E027DD5&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.260 --> 00:00:02.290
- [Instructor] Salts can
form acidic solutions,
00:00:02.290 --> 00:00:03.390
neutral solutions,
00:00:03.390 --> 00:00:06.760
or basic solutions when
dissolved in water.
00:00:06.760 --> 00:00:10.200
For example, if we dissolve
sodium chloride in water,
00:00:10.200 --> 00:00:13.110
solid sodium chloride
turns into sodium cations
00:00:13.110 --> 00:00:16.100
and chloride anions in solution.
00:00:16.100 --> 00:00:17.910
At 25 degrees Celsius,
00:00:17.910 --> 00:00:20.960
the aqueous solution of
sodium chloride is neutral
00:00:20.960 --> 00:00:23.240
and has a pH of seven.
00:00:23.240 --> 00:00:25.480
The reason why the pH is equal to seven is
00:00:25.480 --> 00:00:29.520
because neither the cation nor
the anion reacts with water,
00:00:29.520 --> 00:00:33.730
and water has a pH of seven
at 25 degrees Celsius.
00:00:33.730 --> 00:00:37.380
And since neither the cation
nor the anion react with water,
00:00:37.380 --> 00:00:39.630
the pH remains seven.
00:00:39.630 --> 00:00:42.030
In a different solution,
it's possible for the cation
00:00:42.030 --> 00:00:44.230
or the anion to react with water
00:00:44.230 --> 00:00:48.100
and turn the solution
either acidic or basic.
00:00:48.100 --> 00:00:50.580
Therefore, to predict if
a salt solution is going
00:00:50.580 --> 00:00:52.830
to be acidic, neutral, or basic,
00:00:52.830 --> 00:00:55.280
we have to analyze
whether or not the cation
00:00:55.280 --> 00:00:58.160
and the anion will react with water.
00:00:58.160 --> 00:01:00.580
And there are four possible combinations
00:01:00.580 --> 00:01:01.937
of cation and anion.
00:01:02.850 --> 00:01:06.140
The first combination
is neither the cation
00:01:06.140 --> 00:01:09.240
nor the anion will react with water.
00:01:09.240 --> 00:01:10.660
And if that's the case,
00:01:10.660 --> 00:01:13.740
the resulting solution will be neutral.
00:01:13.740 --> 00:01:15.430
We've already talked
about an aqueous solution
00:01:15.430 --> 00:01:18.550
of sodium chloride being
a neutral solution.
00:01:18.550 --> 00:01:21.710
The way to approach this is to
look at the chemical formula
00:01:21.710 --> 00:01:26.080
and say sodium chloride
consists of a sodium cation
00:01:26.080 --> 00:01:28.460
and a chloride anion.
00:01:28.460 --> 00:01:31.300
The next step is to analyze
the cation and the anion
00:01:31.300 --> 00:01:34.240
and think about if they
react with water or not.
00:01:34.240 --> 00:01:37.020
To determine whether or not a
cation will react with water,
00:01:37.020 --> 00:01:40.890
it's helpful to think about
a list of common strong bases
00:01:40.890 --> 00:01:44.660
that consist of Group 1A metal hydroxides
00:01:44.660 --> 00:01:49.150
and the heavier Group 2A metal hydroxides.
00:01:49.150 --> 00:01:52.530
I the cation is from Group
1A or the heavier Group 2A,
00:01:52.530 --> 00:01:55.440
the cation will not react with water.
00:01:55.440 --> 00:01:58.480
For example, in our case,
we have the sodium cation.
00:01:58.480 --> 00:02:01.730
And since the sodium
cation is in Group 1A,
00:02:01.730 --> 00:02:04.590
the sodium cation will
not react with water.
00:02:04.590 --> 00:02:06.550
Next, we think about the anion.
00:02:06.550 --> 00:02:09.480
To determine whether or not the
anion will react with water,
00:02:09.480 --> 00:02:13.570
it's helpful to think about a
list of common strong acids.
00:02:13.570 --> 00:02:15.880
If the anion is the conjugate base
00:02:15.880 --> 00:02:17.640
to one of the strong acids,
00:02:17.640 --> 00:02:20.600
the anion will not react with water.
00:02:20.600 --> 00:02:23.850
For example, in our case,
we have the chloride anion,
00:02:23.850 --> 00:02:27.560
which is the conjugate base to HCl.
00:02:27.560 --> 00:02:30.530
Since Cl- is the conjugate base to HCl,
00:02:30.530 --> 00:02:33.730
Cl- will not react with water.
00:02:33.730 --> 00:02:35.380
A good way to think about this is
00:02:35.380 --> 00:02:38.430
to think about hydrochloric
acid being a strong acid.
00:02:38.430 --> 00:02:42.210
And the stronger the acid,
the weaker the conjugate base.
00:02:42.210 --> 00:02:45.650
Therefore, the chloride
anion is such a weak base,
00:02:45.650 --> 00:02:48.010
it will not react with water.
00:02:48.010 --> 00:02:52.100
So we say the chloride anion
is of negligible basicity.
00:02:52.100 --> 00:02:56.020
And since neither the cation
nor the anion react with water,
00:02:56.020 --> 00:02:59.840
an aqueous solution of sodium
chloride will be neutral.
00:02:59.840 --> 00:03:02.880
As another example, let's
think about barium nitrate.
00:03:02.880 --> 00:03:06.770
Barium nitrate consists
of the barium 2+ cation
00:03:06.770 --> 00:03:09.380
and the nitrate anion.
00:03:09.380 --> 00:03:14.160
Because the barium 2+ cation
is from the heavier Group 2A,
00:03:14.160 --> 00:03:17.430
the barium 2+ cation will
not react with water.
00:03:17.430 --> 00:03:21.800
And because the nitrate
anion is the conjugate base
00:03:21.800 --> 00:03:24.080
to a strong acid, which is nitric acid,
00:03:24.080 --> 00:03:26.920
the nitrate anion will
not react with water.
00:03:26.920 --> 00:03:28.360
Since neither the cation
00:03:28.360 --> 00:03:30.610
nor the anion will react with water,
00:03:30.610 --> 00:03:34.630
an aqueous solution of barium
nitrate will be neutral.
00:03:34.630 --> 00:03:37.860
The second possible combination
of cation and anion is
00:03:37.860 --> 00:03:40.110
where the cation does
not react with water,
00:03:40.110 --> 00:03:41.850
but the anion does.
00:03:41.850 --> 00:03:43.300
When this combination occurs,
00:03:43.300 --> 00:03:46.530
the resulting solution will be basic.
00:03:46.530 --> 00:03:48.490
An example of the second combination
00:03:48.490 --> 00:03:50.710
would be barium acetate.
00:03:50.710 --> 00:03:55.040
So barium acetate consists
of the barium 2+ cation
00:03:55.040 --> 00:03:57.643
and the acetate anion.
00:03:58.800 --> 00:04:02.777
Since barium 2+ is on our
list for heavier Group 2A,
00:04:02.777 --> 00:04:06.220
barium 2+ will not react with water.
00:04:06.220 --> 00:04:09.760
However, the acetate anion
is the conjugate base
00:04:09.760 --> 00:04:11.310
to acetic acid.
00:04:11.310 --> 00:04:13.840
And acetic acid is a weak acid
00:04:13.840 --> 00:04:16.830
and is not on our list of strong acids.
00:04:16.830 --> 00:04:19.270
Since acetic acid is a weak acid,
00:04:19.270 --> 00:04:23.690
its conjugate base is strong
enough to react with water.
00:04:23.690 --> 00:04:26.410
So the acetate anion
is a strong enough base
00:04:26.410 --> 00:04:27.690
to react with water.
00:04:27.690 --> 00:04:30.400
And when acetate anion reacts with water,
00:04:30.400 --> 00:04:33.540
it forms acetic acid and hydroxide ions.
00:04:33.540 --> 00:04:36.340
Since the concentration of hydroxide ions
00:04:36.340 --> 00:04:38.220
in solution have increased,
00:04:38.220 --> 00:04:41.000
that's what makes the solution basic.
00:04:41.000 --> 00:04:43.440
This is called anion hydrolysis
00:04:43.440 --> 00:04:45.580
when an anion reacts with water
00:04:45.580 --> 00:04:50.070
to increase the concentration
of hydroxide ions in solution.
00:04:50.070 --> 00:04:51.000
As another example,
00:04:51.000 --> 00:04:53.460
let's think about sodium hypochlorite,
00:04:53.460 --> 00:04:56.210
which consists of the sodium cation
00:04:56.210 --> 00:04:58.093
and the hypochlorite anion.
00:04:59.260 --> 00:05:02.540
Since the sodium cation is from Group 1A,
00:05:02.540 --> 00:05:05.023
the sodium cation will
not react with water.
00:05:05.023 --> 00:05:08.240
The hypochlorite anion
is the conjugate base
00:05:08.240 --> 00:05:10.140
to hypochlorous acid.
00:05:10.140 --> 00:05:12.110
Since hypochlorous acid is not
00:05:12.110 --> 00:05:16.400
on our list of common strong
acids, it must be a weak acid.
00:05:16.400 --> 00:05:18.840
And if it's a weak acid,
its conjugate base,
00:05:18.840 --> 00:05:20.673
the hypochlorite anion,
00:05:20.673 --> 00:05:23.220
is a strong enough base
to react with water,
00:05:23.220 --> 00:05:25.260
therefore increasing the concentration
00:05:25.260 --> 00:05:27.920
of hydroxide ions in solution.
00:05:27.920 --> 00:05:30.720
So since we have a cation
that does not react with water
00:05:30.720 --> 00:05:33.250
and an anion that does react with water,
00:05:33.250 --> 00:05:38.250
an aqueous solution of sodium
hypochlorite will be basic.
00:05:38.330 --> 00:05:41.520
The third possible combination
of cation and anion is
00:05:41.520 --> 00:05:43.750
where the cation will react with water,
00:05:43.750 --> 00:05:45.570
but the anion will not.
00:05:45.570 --> 00:05:48.420
In this case, the resulting
solution will be acidic.
00:05:48.420 --> 00:05:50.270
As an example of this third combination,
00:05:50.270 --> 00:05:53.680
let's consider an aqueous
solution of ammonium nitrate.
00:05:53.680 --> 00:05:56.320
Looking at the chemical
formula for ammonium nitrate,
00:05:56.320 --> 00:05:58.820
it consists of the ammonium cation NH4+
00:06:00.390 --> 00:06:04.450
and the nitrate anion NO3-.
00:06:04.450 --> 00:06:06.200
First, let's talk about the anion.
00:06:06.200 --> 00:06:10.740
The nitrate anion is the
conjugate base to nitric acid,
00:06:10.740 --> 00:06:12.230
which is HNO3.
00:06:12.230 --> 00:06:14.010
Since nitric acid is a strong acid,
00:06:14.010 --> 00:06:17.180
its conjugate base is
of negligible basicity,
00:06:17.180 --> 00:06:20.210
so the nitrate anion does not
affect the pH of the solution.
00:06:20.210 --> 00:06:22.040
It does not react with water.
00:06:22.040 --> 00:06:23.943
When thinking about the cation NH4+,
00:06:25.030 --> 00:06:30.030
NH4+ is the conjugate acid
to NH3, which is ammonia.
00:06:30.130 --> 00:06:33.750
And since NH3 or ammonia is a weak base,
00:06:33.750 --> 00:06:37.520
its conjugate acid NH4+ is strong enough
00:06:37.520 --> 00:06:39.390
to react with water.
00:06:39.390 --> 00:06:43.410
And when the ammonium cation
NH4+ reacts with water,
00:06:43.410 --> 00:06:47.000
it forms the hydronium
ion H3O+ and ammonia.
00:06:47.000 --> 00:06:50.810
So the NH4+ is increasing
the concentration
00:06:50.810 --> 00:06:53.390
of hydronium ion in solution,
00:06:53.390 --> 00:06:56.110
which is what's making the solution,
00:06:56.110 --> 00:06:59.100
this aqueous solution of
ammonium nitrate, acidic.
00:06:59.100 --> 00:07:01.680
As another example, let's
consider aluminum chloride,
00:07:01.680 --> 00:07:03.740
an aqueous solution of aluminum chloride.
00:07:03.740 --> 00:07:05.300
Looking at the chemical formula,
00:07:05.300 --> 00:07:09.200
aluminum chloride consists
of the aluminum 3+ cation
00:07:09.200 --> 00:07:11.250
and the chloride anion.
00:07:11.250 --> 00:07:13.430
The chloride anion is the conjugate base
00:07:13.430 --> 00:07:15.760
to hydrochloric acid,
which is a strong acid.
00:07:15.760 --> 00:07:18.950
Therefore, the chloride anion
does not react with water.
00:07:18.950 --> 00:07:23.240
The aluminum 3+ cation
is not from Group 1A
00:07:23.240 --> 00:07:25.520
or heavier Group 2A.
00:07:25.520 --> 00:07:27.560
Therefore, we can conclude
that this is going
00:07:27.560 --> 00:07:29.440
to react with water.
00:07:29.440 --> 00:07:31.700
So small cations with charges
00:07:31.700 --> 00:07:36.660
of 2+ or greater can react with water.
00:07:36.660 --> 00:07:37.760
Let's look in more detail
00:07:37.760 --> 00:07:42.070
how the aluminum 3+ cation
can function as an acid.
00:07:42.070 --> 00:07:45.220
In aqueous solution, the
aluminum 3+ cation interacts
00:07:45.220 --> 00:07:48.983
with water molecules to
form a hydrated metal ion.
00:07:50.020 --> 00:07:52.520
Water is a polar molecule,
00:07:52.520 --> 00:07:57.310
and the positively-charged
aluminum 3+ cation interacts
00:07:57.310 --> 00:08:00.150
with the negative end
of the water molecule.
00:08:00.150 --> 00:08:02.230
So there's an electrostatic attraction
00:08:02.230 --> 00:08:04.870
between the negative end
of the water molecule
00:08:04.870 --> 00:08:07.770
and the 3+ charge on the aluminum cation.
00:08:07.770 --> 00:08:09.900
I only drew in one water molecule.
00:08:09.900 --> 00:08:13.190
However, keep in mind there's
actually six water molecules
00:08:13.190 --> 00:08:16.020
interacting with one Al3+ cation
00:08:16.020 --> 00:08:18.320
in the hydrated metal ion.
00:08:18.320 --> 00:08:20.240
The strong electrostatic attraction
00:08:20.240 --> 00:08:24.920
withdraws electron density
from this oxygen-hydrogen bond,
00:08:24.920 --> 00:08:28.000
which makes this proton easier to remove.
00:08:28.000 --> 00:08:30.820
Therefore, when another
molecule comes along,
00:08:30.820 --> 00:08:33.090
so right here in the equation,
00:08:33.090 --> 00:08:35.860
this other water molecule
can take this proton,
00:08:35.860 --> 00:08:38.150
leaving these electrons
behind in the oxygen.
00:08:38.150 --> 00:08:43.150
And if you're adding an H+
onto H2O, you form H3O+.
00:08:43.450 --> 00:08:46.990
Losing an H+ means the charge
in the hydrated ion went
00:08:46.990 --> 00:08:50.802
from a 3+ down to only a 2+.
00:08:50.802 --> 00:08:53.300
An increase in the
concentration of hydronium ions
00:08:53.300 --> 00:08:57.770
in solution means the pH of
the solution will decrease.
00:08:57.770 --> 00:09:02.440
Therefore, a hydrated metal
ion can function as an acid.
00:09:02.440 --> 00:09:04.830
However, it's the strength
of this interaction
00:09:04.830 --> 00:09:08.420
between the cation and the
water molecules that determines
00:09:08.420 --> 00:09:12.070
if the hydrated metal ion will
function as an acid or not.
00:09:12.070 --> 00:09:15.610
For a small cation with
charge of 2+ or greater,
00:09:15.610 --> 00:09:17.720
that gives a large
electrostatic attraction
00:09:17.720 --> 00:09:18.750
to the water molecule,
00:09:18.750 --> 00:09:21.370
which makes this proton easier to donate.
00:09:21.370 --> 00:09:23.190
However, if the cation is too large
00:09:23.190 --> 00:09:24.650
or the charge is too small,
00:09:24.650 --> 00:09:27.170
the electrostatic attraction
is not strong enough
00:09:27.170 --> 00:09:29.460
to make the proton easy to donate,
00:09:29.460 --> 00:09:31.690
and that's the reason
why cations from Group 1A
00:09:31.690 --> 00:09:35.100
or the heavier Group 2A don't
interact strongly enough
00:09:35.100 --> 00:09:38.500
with water to affect
the pH of the solution.
00:09:38.500 --> 00:09:40.330
Therefore, if we have an aqueous solution
00:09:40.330 --> 00:09:42.070
of aluminum chloride,
00:09:42.070 --> 00:09:45.520
the cation aluminum 3+
will react with water,
00:09:45.520 --> 00:09:48.310
but the anion, the
chloride anion, will not.
00:09:48.310 --> 00:09:49.890
Since the cation reacts with water,
00:09:49.890 --> 00:09:52.670
the resulting solution will be acidic.
00:09:52.670 --> 00:09:54.450
The fourth possible combination is
00:09:54.450 --> 00:09:56.550
where a cation will react with water,
00:09:56.550 --> 00:09:59.300
and the anion will also react with water.
00:09:59.300 --> 00:10:02.350
In this case, the resulting
solution can be acidic,
00:10:02.350 --> 00:10:04.860
neutral, or basic.
00:10:04.860 --> 00:10:07.130
As an example, let's think
about an aqueous solution
00:10:07.130 --> 00:10:08.940
of ammonium carbonate.
00:10:08.940 --> 00:10:12.040
Looking at the chemical
formula for ammonium carbonate,
00:10:12.040 --> 00:10:16.380
the cation would be the
ammonium cation, so that's NH4+.
00:10:16.380 --> 00:10:19.900
And the anion would be the
carbonate anion, CO3 2-.
00:10:21.770 --> 00:10:23.470
We've already seen that
the ammonium cation
00:10:23.470 --> 00:10:25.430
will react with water.
00:10:25.430 --> 00:10:28.370
And the carbonate anion, if
you add a proton onto it,
00:10:28.370 --> 00:10:31.960
that doesn't give us an acid
on our list of strong acids.
00:10:31.960 --> 00:10:34.980
Therefore, the carbonate
anion is a strong enough base
00:10:34.980 --> 00:10:36.690
to react with water.
00:10:36.690 --> 00:10:38.010
First, let's look at the equation
00:10:38.010 --> 00:10:41.180
showing the ammonium
ion reacting with water.
00:10:41.180 --> 00:10:43.430
So this is cation hydrolysis
00:10:43.430 --> 00:10:45.640
since the cation is reacting with water.
00:10:45.640 --> 00:10:49.390
In this case, we would form
the hydronium ion and ammonia.
00:10:49.390 --> 00:10:52.180
Next, we think about the
carbonate anion reacting
00:10:52.180 --> 00:10:55.110
with water, so this is anion hydrolysis.
00:10:55.110 --> 00:10:57.780
When the carbonate
anion reacts with water,
00:10:57.780 --> 00:11:00.210
it forms hydroxide ions in solution
00:11:00.210 --> 00:11:02.890
and also hydrogen carbonate.
00:11:02.890 --> 00:11:07.430
Since the cation hydrolysis
forms hydronium ions,
00:11:07.430 --> 00:11:09.600
if we were to write an
equilibrium constant
00:11:09.600 --> 00:11:13.140
for this acid-base
reaction, it would be Ka.
00:11:13.140 --> 00:11:15.010
And since the anion hydrolysis
00:11:15.010 --> 00:11:17.610
forms hydroxide ions in solution,
00:11:17.610 --> 00:11:19.740
if we were to write an
equilibrium constant
00:11:19.740 --> 00:11:23.420
for this acid-base
reaction, it would be Kb.
00:11:23.420 --> 00:11:25.680
To figure out if the aqueous solution
00:11:25.680 --> 00:11:29.160
of ammonium carbonate is
acidic, neutral, or basic,
00:11:29.160 --> 00:11:32.550
we need to compare the
Ka value for ammonium
00:11:32.550 --> 00:11:35.880
to the Kb value for carbonate.
00:11:35.880 --> 00:11:37.673
If the Ka value is
greater than the Kb value,
00:11:39.220 --> 00:11:40.940
the solution is acidic.
00:11:40.940 --> 00:11:44.470
If the Ka and the Kb values
are approximately the same,
00:11:44.470 --> 00:11:46.190
the solution is about neutral.
00:11:46.190 --> 00:11:48.300
And if Ka is less than Kb,
00:11:48.300 --> 00:11:50.690
or you could say Kb is greater than Ka,
00:11:50.690 --> 00:11:53.090
the solution will be basic.
00:11:53.090 --> 00:11:55.800
To find the Ka for the ammonium cation,
00:11:55.800 --> 00:11:57.470
we're gonna use the following equation:
00:11:57.470 --> 00:12:00.697
Ka times Kb is equal to Kw.
00:12:00.697 --> 00:12:04.850
And this equation is true for
a conjugate acid-base pair.
00:12:04.850 --> 00:12:09.070
So what this is saying is the
Ka for the ammonium cation
00:12:09.070 --> 00:12:14.070
times the Kb for ammonia is equal to Kw,
00:12:14.070 --> 00:12:16.310
which at 25 degrees Celsius is equal
00:12:16.310 --> 00:12:19.460
to 1.0 times 10 to the -14th.
00:12:19.460 --> 00:12:21.730
Textbooks often have the Kb values
00:12:21.730 --> 00:12:24.340
for common weak bases like ammonia,
00:12:24.340 --> 00:12:29.310
and the Kb value for ammonia
is 1.8 times 10 to the -5th.
00:12:29.310 --> 00:12:31.620
So we solve for Ka,
00:12:31.620 --> 00:12:34.500
and we find that Ka for the
ammonium cation is equal
00:12:34.500 --> 00:12:36.833
to 5.6 times 10 to the -10th.
00:12:37.720 --> 00:12:40.500
To calculate the Kb value
for the carbonate anion,
00:12:40.500 --> 00:12:41.760
we use the same equation.
00:12:41.760 --> 00:12:44.650
Ka times Kb is equal to Kw.
00:12:44.650 --> 00:12:47.200
However, remember, this
is the Ka and the Kb
00:12:47.200 --> 00:12:49.260
for a conjugate acid-base pair,
00:12:49.260 --> 00:12:53.710
so we're talking about the
carbonate anion as the base
00:12:53.710 --> 00:12:54.840
and its conjugate acid,
00:12:54.840 --> 00:12:57.557
which would be a hydrogen
carbonate, HCO3-.
00:12:58.460 --> 00:13:01.860
So we plug in the Ka value for HCO3-
00:13:01.860 --> 00:13:04.430
and solve for Kb.
00:13:04.430 --> 00:13:07.820
So Kb for the carbonate anion is equal
00:13:07.820 --> 00:13:12.490
to 1.8 times 10 to the
-4th at 25 degrees Celsius.
00:13:12.490 --> 00:13:17.490
And this Ka value is also
at 25 degrees Celsius.
00:13:17.640 --> 00:13:20.640
Looking at the values for Ka and Kb,
00:13:20.640 --> 00:13:24.880
Ka is less than Kb.
00:13:24.880 --> 00:13:27.210
Since Ka is less than Kb,
00:13:27.210 --> 00:13:29.790
or you could say Kb is greater than Ka,
00:13:29.790 --> 00:13:31.653
this solution is basic.
|
Weak base equilibria | https://www.youtube.com/watch?v=cvcgH3ohcNg | vtt | https://www.youtube.com/api/timedtext?v=cvcgH3ohcNg&ei=0lWUZZ-gJMytmLAPya2b2As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=40E017F0D7797B680D7A3F446DD38F149E1972D2.E68BA2D7C0A3E1ECDC9460337279D8B121C2A840&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.670 --> 00:00:04.510
- [Instructor] An example of
a weak base is ammonia, NH3,
00:00:04.510 --> 00:00:06.550
and ammonia will react with water.
00:00:06.550 --> 00:00:07.410
And in this reaction,
00:00:07.410 --> 00:00:09.760
water functions as a Bronsted-Lowry acid
00:00:09.760 --> 00:00:12.410
and donates a proton to ammonia,
00:00:12.410 --> 00:00:14.340
which functions as a Bronsted-Lowry base
00:00:14.340 --> 00:00:16.000
and accepts a proton.
00:00:16.000 --> 00:00:17.400
A proton is H plus.
00:00:17.400 --> 00:00:20.410
So if you add on H plus onto NH3,
00:00:20.410 --> 00:00:23.720
you form NH4 plus, which
is the ammonium ion.
00:00:23.720 --> 00:00:26.770
And if you take away NH plus from H2O,
00:00:26.770 --> 00:00:30.640
you form the hydroxide
anion, which is OH minus.
00:00:30.640 --> 00:00:32.620
This reaction comes to an equilibrium,
00:00:32.620 --> 00:00:34.540
so we have an equilibrium arrow in here,
00:00:34.540 --> 00:00:38.370
and we can also write an
equilibrium constant expression.
00:00:38.370 --> 00:00:39.960
So first, we look at our products.
00:00:39.960 --> 00:00:41.480
We have NH4 plus,
00:00:41.480 --> 00:00:43.290
and there's a coefficient
of one in front of it,
00:00:43.290 --> 00:00:45.680
so it'd be the concentration
of NH4 plus raised
00:00:45.680 --> 00:00:48.160
to the first power times the concentration
00:00:48.160 --> 00:00:50.130
of the other product, hydroxide,
00:00:50.130 --> 00:00:51.810
which also has a coefficient of one,
00:00:51.810 --> 00:00:53.850
so it's the concentration
of hydroxide raised
00:00:53.850 --> 00:00:55.030
to the first power,
00:00:55.030 --> 00:00:58.720
divided by the concentration of ammonia,
00:00:58.720 --> 00:01:00.270
and the coefficient is also one,
00:01:00.270 --> 00:01:02.280
so that's also raised to the first power.
00:01:02.280 --> 00:01:03.480
And water is left out
00:01:03.480 --> 00:01:06.170
of our equilibrium constant expression.
00:01:06.170 --> 00:01:09.640
The equilibrium constant
K has a subscript of b,
00:01:09.640 --> 00:01:11.170
which stands for base.
00:01:11.170 --> 00:01:14.900
And this Kb is called the
base ionization constant,
00:01:14.900 --> 00:01:18.020
or the base dissociation constant.
00:01:18.020 --> 00:01:19.390
Ammonia is a weak base,
00:01:19.390 --> 00:01:22.530
which means it only
partially ionizes in water.
00:01:22.530 --> 00:01:25.760
And if it only partially
ionizes, at equilibrium,
00:01:25.760 --> 00:01:28.280
there's going to be a
small amount of products
00:01:28.280 --> 00:01:30.890
and a large amount of reactants.
00:01:30.890 --> 00:01:33.870
Therefore, looking at the
equilibrium constant expression,
00:01:33.870 --> 00:01:36.530
the numerator is gonna
be very small compared
00:01:36.530 --> 00:01:38.470
to the denominator.
00:01:38.470 --> 00:01:40.950
So with a small numerator
and a large denominator,
00:01:40.950 --> 00:01:44.260
that means that the Kb
value for a weak base
00:01:44.260 --> 00:01:46.330
will be less than one.
00:01:46.330 --> 00:01:49.220
Let's look at a few
examples of weak bases.
00:01:49.220 --> 00:01:50.940
Here's the dot structure for ammonia,
00:01:50.940 --> 00:01:53.010
and notice how ammonia has a nitrogen
00:01:53.010 --> 00:01:54.830
with a lone pair of electrons
00:01:54.830 --> 00:01:57.330
that's capable of accepting a proton.
00:01:57.330 --> 00:01:59.030
A proton is H plus.
00:01:59.030 --> 00:02:04.000
So if we add an H plus
onto NH3, we form NH4 plus,
00:02:04.000 --> 00:02:06.180
which is the ammonium ion,
00:02:06.180 --> 00:02:09.510
and it's the conjugate acid to ammonia.
00:02:09.510 --> 00:02:11.290
So think about this lone pair of electrons
00:02:11.290 --> 00:02:15.570
that I circled here picking
up a proton to form this bond.
00:02:15.570 --> 00:02:16.930
If we replace the hydrogen
00:02:16.930 --> 00:02:19.650
with what's called a methyl group, CH3,
00:02:19.650 --> 00:02:23.270
we form a new weak base
called methylamine.
00:02:23.270 --> 00:02:25.410
Like ammonia, methylamine has a nitrogen
00:02:25.410 --> 00:02:26.720
with a lone pair of electrons
00:02:26.720 --> 00:02:29.880
that's capable of accepting a proton.
00:02:29.880 --> 00:02:32.410
So if methylamine picks up a proton,
00:02:32.410 --> 00:02:34.733
it forms the methyl ammonium ion.
00:02:35.660 --> 00:02:37.410
Both ammonia and methylamine
00:02:37.410 --> 00:02:39.940
are examples of neutral substances.
00:02:39.940 --> 00:02:42.730
However, a weak base
doesn't have to be neutral.
00:02:42.730 --> 00:02:47.410
If we look at the
hypochlorite anion, ClO minus,
00:02:47.410 --> 00:02:49.650
if the hypochlorite
anion picks up a proton,
00:02:49.650 --> 00:02:51.180
let's say this lone pair of electrons
00:02:51.180 --> 00:02:52.963
in the oxygen picks up a proton,
00:02:54.832 --> 00:02:57.140
it would form hypochlorous acid,
00:02:57.140 --> 00:03:01.670
and hypochlorous is the
conjugate acid to hypochlorite.
00:03:01.670 --> 00:03:04.760
So these are three examples of weak bases,
00:03:04.760 --> 00:03:07.300
which we can tell by
looking at their Kb values
00:03:07.300 --> 00:03:08.920
at 25 degrees Celsius.
00:03:08.920 --> 00:03:12.450
Notice they all have Kb
values less than one.
00:03:12.450 --> 00:03:14.360
However, the higher the Kb value,
00:03:14.360 --> 00:03:17.760
the higher the equilibrium
concentration of hydroxide ion,
00:03:17.760 --> 00:03:20.070
and therefore the stronger the base.
00:03:20.070 --> 00:03:22.420
So out of these three week bases,
00:03:22.420 --> 00:03:26.060
the one with the higher Kb
value is the most basic.
00:03:26.060 --> 00:03:28.800
So looking at these three values, again,
00:03:28.800 --> 00:03:33.400
the Kb value for methylamine
is the highest of the three,
00:03:33.400 --> 00:03:35.550
so it's the strongest base of the three,
00:03:35.550 --> 00:03:38.770
although all three are
considered to be weak.
00:03:38.770 --> 00:03:41.470
Let's do a calculation with a weak base.
00:03:41.470 --> 00:03:44.770
Let's say we have a .14 molar solution,
00:03:44.770 --> 00:03:47.940
aqueous solution of ammonia
at 25 degrees Celsius,
00:03:47.940 --> 00:03:50.720
and our goal is to
calculate the concentration
00:03:50.720 --> 00:03:52.930
of hydroxide ions in solution,
00:03:52.930 --> 00:03:56.930
and also the pH of the
solution at 25 degrees Celsius.
00:03:56.930 --> 00:03:58.240
So first, we're gonna calculate
00:03:58.240 --> 00:04:01.070
the equilibrium concentration
of hydroxide ions,
00:04:01.070 --> 00:04:02.080
and to help us do that,
00:04:02.080 --> 00:04:03.800
we're gonna use an ICE table,
00:04:03.800 --> 00:04:05.910
where I stands for the
initial concentration,
00:04:05.910 --> 00:04:07.770
C is the change in concentration,
00:04:07.770 --> 00:04:10.690
and E is the equilibrium concentration.
00:04:10.690 --> 00:04:14.430
The initial concentration
of ammonia is .14 molar.
00:04:14.430 --> 00:04:16.850
So we can put that in on our ICE table.
00:04:16.850 --> 00:04:20.450
And if we assume that ammonia
hasn't ionized at all yet,
00:04:20.450 --> 00:04:23.050
the initial concentrations of ammonium
00:04:23.050 --> 00:04:26.720
and hydroxide ions would both be zero.
00:04:26.720 --> 00:04:29.500
Next, we think about some
of the ammonia ionizing,
00:04:29.500 --> 00:04:31.090
and we don't know how much,
00:04:31.090 --> 00:04:35.260
so we write minus x under
ammonia for the change.
00:04:35.260 --> 00:04:39.180
When NH3 gains a proton,
it turns into NH4 plus,
00:04:39.180 --> 00:04:43.600
and the mole ratio of ammonia
to ammonium is one to one.
00:04:43.600 --> 00:04:46.720
Therefore, if we write
minus x for ammonia,
00:04:46.720 --> 00:04:50.180
we must write plus x for ammonium.
00:04:50.180 --> 00:04:53.170
And the hydroxide ion also
has a one as a coefficient
00:04:53.170 --> 00:04:54.570
in a balanced equation.
00:04:54.570 --> 00:04:58.340
Therefore, it would also
be plus x in our ICE table.
00:04:58.340 --> 00:05:00.780
So the equilibrium
concentration of ammonia
00:05:00.780 --> 00:05:03.780
would be .14 four minus x.
00:05:03.780 --> 00:05:06.630
So let's write that in there, .14 minus x.
00:05:06.630 --> 00:05:09.130
For ammonium, it would be zero plus x,
00:05:09.130 --> 00:05:11.470
which is just x, and for hydroxide,
00:05:11.470 --> 00:05:15.220
it would also be zero
plus x, which is just x.
00:05:15.220 --> 00:05:16.340
The next step is to write out
00:05:16.340 --> 00:05:18.260
the equilibrium constant expression
00:05:18.260 --> 00:05:20.050
for the ionization of ammonia,
00:05:20.050 --> 00:05:21.410
which we've already talked about.
00:05:21.410 --> 00:05:22.970
And since the concentrations
00:05:22.970 --> 00:05:25.090
in our equilibrium constant expression
00:05:25.090 --> 00:05:27.310
are equilibrium concentrations,
00:05:27.310 --> 00:05:28.610
we can go ahead and plug in
00:05:28.610 --> 00:05:31.650
the equilibrium concentrations
of the ammonium ion,
00:05:31.650 --> 00:05:33.210
the hydroxide ion,
00:05:33.210 --> 00:05:36.840
and ammonia into our
equilibrium constant expression.
00:05:36.840 --> 00:05:39.810
We also need to plug in for Kb for ammonia
00:05:39.810 --> 00:05:42.550
at 25 degrees Celsius.
00:05:42.550 --> 00:05:44.490
Here's our equilibrium constant expression
00:05:44.490 --> 00:05:46.220
with everything plugged in.
00:05:46.220 --> 00:05:48.070
And our goal is to solve for x,
00:05:48.070 --> 00:05:50.970
because x represented the
equilibrium concentration
00:05:50.970 --> 00:05:52.760
of hydroxide ions.
00:05:52.760 --> 00:05:54.820
However, if we solve for x now,
00:05:54.820 --> 00:05:57.830
we would get a quadratic equation.
00:05:57.830 --> 00:05:59.330
So to simplify the math,
00:05:59.330 --> 00:06:01.420
we're gonna use an approximation.
00:06:01.420 --> 00:06:04.450
We're gonna say that .14 minus x
00:06:04.450 --> 00:06:06.947
is approximately equal to .14.
00:06:08.440 --> 00:06:10.300
The reason why we can
make this approximation
00:06:10.300 --> 00:06:14.140
is because the Kb value
for ammonia is quite small,
00:06:14.140 --> 00:06:17.300
which means that ammonia
doesn't ionize very much at all,
00:06:17.300 --> 00:06:19.670
which tells us the
equilibrium concentration
00:06:19.670 --> 00:06:22.870
of hydroxide ions will
be a very small number.
00:06:22.870 --> 00:06:25.857
And if x is a really small
number compared to .14,
00:06:26.897 --> 00:06:29.907
.14 minus x is just
approximately equal to .14.
00:06:31.190 --> 00:06:33.530
So instead of writing .14 minus x,
00:06:33.530 --> 00:06:34.907
we can just write in .14.
00:06:36.000 --> 00:06:37.960
So now we solve for x and we find
00:06:37.960 --> 00:06:41.420
that x is equal to 1.6 times
10 to the negative third molar,
00:06:41.420 --> 00:06:45.900
which is the equilibrium
concentration of hydroxide ions.
00:06:45.900 --> 00:06:48.480
Our goal is to calculate
the pH of our solution.
00:06:48.480 --> 00:06:50.790
And first, we could find the pOH,
00:06:50.790 --> 00:06:53.270
because pOH is equal to the negative log
00:06:53.270 --> 00:06:55.870
of the concentration of hydroxide ions.
00:06:55.870 --> 00:07:00.870
So the negative log of 1.6
times 10 to the negative third
00:07:00.900 --> 00:07:03.663
is equal to 2.80.
00:07:04.920 --> 00:07:07.420
And at 25 degrees Celsius,
00:07:07.420 --> 00:07:12.343
the pH plus the pOH is equal to 14.00,
00:07:14.280 --> 00:07:17.440
so we could plug in the
pOH into our equation
00:07:17.440 --> 00:07:19.220
and solve for the pH,
00:07:19.220 --> 00:07:23.523
and we would find the pH of
our solution is equal to 11.20.
00:07:25.570 --> 00:07:28.870
And this makes sense, because
we have a basic solution,
00:07:28.870 --> 00:07:31.860
so the pH should be greater than seven.
00:07:31.860 --> 00:07:35.200
Finally, to make sure that
we can use our approximation,
00:07:35.200 --> 00:07:39.800
let's find the percent
ionization for our weak base.
00:07:39.800 --> 00:07:43.050
To calculate the percent
ionization of ammonia,
00:07:43.050 --> 00:07:45.170
we take x, which you could think about
00:07:45.170 --> 00:07:47.930
as the concentration of
ammonia that ionized,
00:07:47.930 --> 00:07:48.800
or you could think about it
00:07:48.800 --> 00:07:51.910
as the equilibrium
concentration of hydroxide ions.
00:07:51.910 --> 00:07:55.710
And we divide x by the initial
concentration of ammonia
00:07:55.710 --> 00:07:59.650
and multiply it by 100 to
get a percent ionization.
00:07:59.650 --> 00:08:00.580
So for this problem,
00:08:00.580 --> 00:08:04.400
x is equal to 1.6 times 10
to the negative third molar.
00:08:04.400 --> 00:08:05.840
So we go ahead and plug that in here.
00:08:05.840 --> 00:08:08.740
So 1.6 times 10 to the
negative third molar,
00:08:08.740 --> 00:08:10.750
and the initial concentration of ammonia
00:08:10.750 --> 00:08:13.030
was equal to .14 molar.
00:08:13.030 --> 00:08:15.560
So molar cancels out and we end up
00:08:15.560 --> 00:08:20.560
with a percent ionization of 1.1%.
00:08:21.640 --> 00:08:23.880
Once you calculate the percent ionization,
00:08:23.880 --> 00:08:25.680
you need to think about the 5% rule.
00:08:27.232 --> 00:08:28.450
And the 5% rule says,
00:08:28.450 --> 00:08:31.874
if your percent ionization
is less than 5%,
00:08:31.874 --> 00:08:34.300
it's okay to use the approximation.
00:08:34.300 --> 00:08:38.130
So in our case, our percent
ionization was 1.1%,
00:08:38.130 --> 00:08:40.060
which is less than 5%.
00:08:40.060 --> 00:08:42.890
So it's okay to say that .14 minus x
00:08:42.890 --> 00:08:45.460
is approximately equal to .14,
00:08:45.460 --> 00:08:47.590
because with such a
low percent ionization,
00:08:47.590 --> 00:08:50.217
x is a really small value compared to .14.
00:08:51.130 --> 00:08:55.500
However, if you get a percent
ionization greater than 5%,
00:08:55.500 --> 00:08:57.540
you can't use the approximation
00:08:57.540 --> 00:09:01.890
and you need to use the quadratic
equation to calculate x.
00:09:01.890 --> 00:09:04.630
Finally, when we calculated
our equilibrium concentration
00:09:04.630 --> 00:09:06.050
of hydroxide ions,
00:09:06.050 --> 00:09:09.730
we only considered the
ionization of ammonia.
00:09:09.730 --> 00:09:12.050
It's true that the autoionization of water
00:09:12.050 --> 00:09:15.180
would produce a small amount
of hydroxide ions in solution.
00:09:15.180 --> 00:09:18.400
However, that concentration
is extremely small compared
00:09:18.400 --> 00:09:20.940
to the concentration of hydroxide ions
00:09:20.940 --> 00:09:22.460
from the ionization of ammonia.
00:09:22.460 --> 00:09:25.800
Therefore, we ignore the
contribution of hydroxide ions
00:09:25.800 --> 00:09:29.203
from the auto ionization of
water in our calculations.
|
Worked example: Finding the percent ionization of a weak acid | https://www.youtube.com/watch?v=_jEe0Tkyn3w | vtt | https://www.youtube.com/api/timedtext?v=_jEe0Tkyn3w&ei=0lWUZb7eI8S2vdIP65S2uAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=33D9D52F395BABD1CC7CA8624B02DAAAC975CD94.8947EA3E673872CE39EB56BD89AE733BC2DB9519&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.420 --> 00:00:01.253
- [Instructor] Let's say we have
00:00:01.253 --> 00:00:04.780
a 0.20 Molar aqueous
solution of acidic acid.
00:00:04.780 --> 00:00:07.120
And our goal is to calculate the pH
00:00:07.120 --> 00:00:09.840
and the percent ionization.
00:00:09.840 --> 00:00:11.970
The Ka value for acidic acid
00:00:11.970 --> 00:00:14.630
is equal to 1.8 times
10 to the negative fifth
00:00:14.630 --> 00:00:16.970
at 25 degrees Celsius.
00:00:16.970 --> 00:00:19.210
First, we need to write out
the balanced equation showing
00:00:19.210 --> 00:00:21.810
the ionization of acidic acid.
00:00:21.810 --> 00:00:25.277
So acidic acid reacts with
water to form the hydronium ion,
00:00:25.277 --> 00:00:26.570
H3O+,
00:00:26.570 --> 00:00:30.350
and acetate, which is the
conjugate base to acidic acid.
00:00:30.350 --> 00:00:32.150
Because acidic acid is a weak acid,
00:00:32.150 --> 00:00:34.500
it only partially ionizes.
00:00:34.500 --> 00:00:36.780
Therefore, we need to set up an ICE table
00:00:36.780 --> 00:00:37.730
so we can figure out
00:00:37.730 --> 00:00:41.000
the equilibrium concentration
of hydronium ion,
00:00:41.000 --> 00:00:43.010
which will allow us to calculate the pH
00:00:43.010 --> 00:00:45.060
and the percent ionization.
00:00:45.060 --> 00:00:48.250
In an ICE table, the I stands
for initial concentration,
00:00:48.250 --> 00:00:50.230
C is for change in concentration,
00:00:50.230 --> 00:00:53.140
and E is equilibrium concentration.
00:00:53.140 --> 00:00:57.240
The initial concentration of
acidic acid is 0.20 Molar.
00:00:57.240 --> 00:01:00.720
So we can put that in our
ICE table under acidic acid.
00:01:00.720 --> 00:01:03.850
And if we assume that the
reaction hasn't happened yet,
00:01:03.850 --> 00:01:06.160
the initial concentrations
of hydronium ion
00:01:06.160 --> 00:01:09.560
and acetate anion would both be zero.
00:01:09.560 --> 00:01:11.920
Some of the acidic acid will ionize,
00:01:11.920 --> 00:01:13.270
but since we don't know how much,
00:01:13.270 --> 00:01:14.600
we're gonna call that x.
00:01:14.600 --> 00:01:17.590
So we write -x under acidic acid
00:01:17.590 --> 00:01:20.010
for the change part of our ICE table.
00:01:20.010 --> 00:01:21.910
And when acidic acid reacts with water,
00:01:21.910 --> 00:01:24.830
we form hydronium and acetate.
00:01:24.830 --> 00:01:27.940
So we're going to gain in
the amount of our products.
00:01:27.940 --> 00:01:30.040
To figure out how much
we look at mole ratios
00:01:30.040 --> 00:01:31.380
from the balanced equation.
00:01:31.380 --> 00:01:33.650
There's a one to one mole ratio
00:01:33.650 --> 00:01:36.280
of acidic acid to hydronium ion.
00:01:36.280 --> 00:01:39.510
Therefore, if we write -x for acidic acid,
00:01:39.510 --> 00:01:42.360
we're gonna write +x under hydronium.
00:01:42.360 --> 00:01:45.010
And for the acetate
anion, there's also a one
00:01:45.010 --> 00:01:47.460
as a coefficient in the balanced equation.
00:01:47.460 --> 00:01:51.470
Therefore, we can write
+x under acetate as well.
00:01:51.470 --> 00:01:54.460
So the equilibrium
concentration of acidic acid
00:01:54.460 --> 00:01:56.820
would be 0.20 minus x.
00:01:56.820 --> 00:01:58.230
Let's go ahead and write that in here,
00:01:58.230 --> 00:02:00.580
0.20 minus x.
00:02:00.580 --> 00:02:02.560
The equilibrium concentration of hydronium
00:02:02.560 --> 00:02:05.550
would be zero plus x, which is just x.
00:02:05.550 --> 00:02:08.450
And for acetate, it would
also be zero plus x,
00:02:08.450 --> 00:02:10.720
so we can just write x here.
00:02:10.720 --> 00:02:13.310
Next, we brought out the
equilibrium constant expression,
00:02:13.310 --> 00:02:15.680
which we can get from
the balanced equation.
00:02:15.680 --> 00:02:18.530
So the Ka is equal to the concentration
00:02:18.530 --> 00:02:20.320
of the hydronium ion.
00:02:20.320 --> 00:02:21.840
And since there's a coefficient of one,
00:02:21.840 --> 00:02:22.680
that's the concentration
00:02:22.680 --> 00:02:24.870
of hydronium ion raised
to the first power,
00:02:24.870 --> 00:02:27.600
times the concentration
of the acetate anion
00:02:27.600 --> 00:02:29.600
also raised to the first power,
00:02:29.600 --> 00:02:31.370
divided by the concentration
00:02:31.370 --> 00:02:34.270
of acidic acid raised to the first power.
00:02:34.270 --> 00:02:35.630
And water is left out of
00:02:35.630 --> 00:02:38.070
our equilibrium constant expression.
00:02:38.070 --> 00:02:39.260
Because the concentrations
00:02:39.260 --> 00:02:41.130
in our equilibrium constant expression
00:02:41.130 --> 00:02:43.290
or equilibrium concentrations,
00:02:43.290 --> 00:02:45.750
we can plug in what we
have from our ICE table.
00:02:45.750 --> 00:02:48.470
So we can plug in x for the
equilibrium concentration
00:02:48.470 --> 00:02:50.030
of hydronium ion,
00:02:50.030 --> 00:02:52.330
x is also the equilibrium concentration
00:02:52.330 --> 00:02:53.690
of the acetate anion,
00:02:53.690 --> 00:02:57.570
and 0.20 minus x is the
equilibrium concentration
00:02:57.570 --> 00:02:58.950
of acidic acid.
00:02:58.950 --> 00:03:02.170
We also need to plug in the
Ka value for acidic acid
00:03:02.170 --> 00:03:04.940
at 25 degrees Celsius.
00:03:04.940 --> 00:03:07.580
Here we have our equilibrium
concentrations plugged in
00:03:07.580 --> 00:03:09.440
and also the Ka value.
00:03:09.440 --> 00:03:10.970
Our goal is to solve for x,
00:03:10.970 --> 00:03:13.190
which would give us the
equilibrium concentration
00:03:13.190 --> 00:03:14.760
of hydronium ions.
00:03:14.760 --> 00:03:17.030
However, if we solve for x here,
00:03:17.030 --> 00:03:19.940
we would need to use a quadratic equation.
00:03:19.940 --> 00:03:21.730
So to make the math a little bit easier,
00:03:21.730 --> 00:03:23.670
we're gonna use an approximation.
00:03:23.670 --> 00:03:27.520
We're gonna say that 0.20 minus x
00:03:27.520 --> 00:03:31.990
is approximately equal to 0.20.
00:03:31.990 --> 00:03:34.080
The reason why we can
make this approximation
00:03:34.080 --> 00:03:36.350
is because acidic acid is a weak acid,
00:03:36.350 --> 00:03:38.550
which we know from its Ka value.
00:03:38.550 --> 00:03:40.080
Ka is less than one.
00:03:40.080 --> 00:03:42.870
And that means it's only
going to partially ionize.
00:03:42.870 --> 00:03:45.400
It's going to ionize
to a very small extent,
00:03:45.400 --> 00:03:48.350
which means that x must
be a very small number.
00:03:48.350 --> 00:03:51.700
And if x is a really small
number compared to 0.20,
00:03:52.539 --> 00:03:56.290
0.20 minus x is approximately
just equal to 0.20.
00:03:57.300 --> 00:03:59.280
So we can go ahead and rewrite this.
00:03:59.280 --> 00:04:02.910
So we would have 1.8 times
10 to the negative fifth
00:04:02.910 --> 00:04:05.510
is equal to x squared over,
00:04:05.510 --> 00:04:07.640
and instead of 0.20 minus x,
00:04:07.640 --> 00:04:09.253
we're just gonna write 0.20.
00:04:10.970 --> 00:04:15.970
Solving for x, we would
find that x is equal to 1.9,
00:04:15.970 --> 00:04:18.790
times 10 to the negative third.
00:04:18.790 --> 00:04:23.170
And remember, this is equal to
the equilibrium concentration
00:04:23.170 --> 00:04:25.000
of hydronium ions.
00:04:25.000 --> 00:04:25.833
So let's write in here,
00:04:25.833 --> 00:04:28.590
the equilibrium concentration
of hydronium ions.
00:04:28.590 --> 00:04:32.100
So this is 1.9 times 10 to
the negative third Molar.
00:04:32.100 --> 00:04:34.820
If we would have used the
quadratic equation to solve for x,
00:04:34.820 --> 00:04:38.070
we would have also gotten 1.9
times 10 to the negative third
00:04:38.070 --> 00:04:40.160
to two significant figures.
00:04:40.160 --> 00:04:43.390
Therefore, using the approximation
got us the same answer
00:04:43.390 --> 00:04:45.320
and saved us some time.
00:04:45.320 --> 00:04:47.130
Also, now that we have a value for x,
00:04:47.130 --> 00:04:48.840
we can go back to our approximation
00:04:48.840 --> 00:04:52.930
and see that x is very
small compared to 0.20.
00:04:52.930 --> 00:04:57.570
So 0.20 minus x is
approximately equal to 0.20.
00:04:57.570 --> 00:05:00.580
Also, this concentration of hydronium ion
00:05:00.580 --> 00:05:03.360
is only from the
ionization of acidic acid.
00:05:03.360 --> 00:05:05.650
And it's true that
there's some contribution
00:05:05.650 --> 00:05:08.690
of hydronium ion from the
autoionization of water.
00:05:08.690 --> 00:05:11.680
However, that concentration
is much smaller than this.
00:05:11.680 --> 00:05:14.330
So for this problem, we
can ignore the contribution
00:05:14.330 --> 00:05:17.900
of hydronium ions from the
autoionization of water.
00:05:17.900 --> 00:05:20.030
Next, we can find the pH of our solution
00:05:20.030 --> 00:05:21.900
at 25 degrees Celsius.
00:05:21.900 --> 00:05:25.140
So pH is equal to the negative
log of the concentration
00:05:25.140 --> 00:05:26.510
of hydronium ions.
00:05:26.510 --> 00:05:30.530
So that's the negative log of 1.9 times 10
00:05:30.530 --> 00:05:32.600
to the negative third,
00:05:32.600 --> 00:05:35.603
which is equal to 2.72.
00:05:37.730 --> 00:05:40.940
We also need to calculate
the percent ionization.
00:05:40.940 --> 00:05:44.520
So the equation 4% ionization is equal to
00:05:44.520 --> 00:05:47.770
the equilibrium concentration
of hydronium ions,
00:05:47.770 --> 00:05:51.070
divided by the initial
concentration of the acid,
00:05:51.070 --> 00:05:52.900
times 100%.
00:05:52.900 --> 00:05:55.180
The equilibrium concentration
of hydronium ions
00:05:55.180 --> 00:05:58.540
is equal to 1.9 times 10
to negative third Molar.
00:05:58.540 --> 00:05:59.980
So we plug that in.
00:05:59.980 --> 00:06:03.520
And the initial concentration
of our weak acid,
00:06:03.520 --> 00:06:06.590
which was acidic acid is 0.20 Molar.
00:06:06.590 --> 00:06:07.780
So the Molars cancel,
00:06:07.780 --> 00:06:12.780
and we get a percent ionization of 0.95%.
00:06:12.950 --> 00:06:15.540
A low value for the percent
ionization makes sense
00:06:15.540 --> 00:06:18.750
because acidic acid is a weak acid.
00:06:18.750 --> 00:06:22.420
We can also use the percent
ionization to justify
00:06:22.420 --> 00:06:25.110
the approximation that
we made earlier using
00:06:25.110 --> 00:06:26.853
what's called the 5% rule.
00:06:28.100 --> 00:06:31.470
So let me write that
down here, the 5% rule.
00:06:31.470 --> 00:06:35.641
If the percent ionization is less than 5%
00:06:35.641 --> 00:06:38.690
as it was in our case, it
was less than 1% actually,
00:06:38.690 --> 00:06:41.110
then the approximation is valid.
00:06:41.110 --> 00:06:44.592
If the percent ionization
is greater than 5%,
00:06:44.592 --> 00:06:46.470
then the approximation is not valid
00:06:46.470 --> 00:06:49.033
and you have to use
the quadratic equation.
|
Weak acid equilibria | https://www.youtube.com/watch?v=nJLNlB-7Rhk | vtt | https://www.youtube.com/api/timedtext?v=nJLNlB-7Rhk&ei=0lWUZaDMJP2vhcIPmcmcuA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=386A55F68F86EC992C7B3D89A45929DA93123BA1.A9616E653CD81F67E8C12B633D2E8CDA027AD4D4&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.310 --> 00:00:01.520
- [Instructor] Before
we get into the topic
00:00:01.520 --> 00:00:06.520
of weak acid equilibria, let's
look at a strong acid first.
00:00:06.710 --> 00:00:10.380
So let's say that HA is a strong
acid and reacts with water
00:00:10.380 --> 00:00:13.800
to produce the hydronium ion and A-minus,
00:00:13.800 --> 00:00:16.140
the conjugate base to HA.
00:00:16.140 --> 00:00:18.840
Technically, the reaction
comes to an equilibrium.
00:00:18.840 --> 00:00:22.310
However, the equilibrium
favors the products so much
00:00:22.310 --> 00:00:24.110
that we don't draw an equilibrium arrow.
00:00:24.110 --> 00:00:26.410
We simply draw an arrow going to the right
00:00:26.410 --> 00:00:28.850
indicating at equilibrium,
we have essentially
00:00:28.850 --> 00:00:32.690
all H30-plus and A-minus, and no HA.
00:00:32.690 --> 00:00:37.690
So we assume that a strong
acid ionizes 100% in solution,
00:00:38.020 --> 00:00:41.600
and we can see that in
our particulate diagrams.
00:00:41.600 --> 00:00:43.820
And keep in mind that
these particulate diagrams
00:00:43.820 --> 00:00:46.430
are not meant to represent
the entire solution,
00:00:46.430 --> 00:00:48.730
just a small portion of
it so we can get an idea
00:00:48.730 --> 00:00:51.380
about what's happening
in the entire solution.
00:00:51.380 --> 00:00:54.310
We can think about the
particulate diagram on the left
00:00:54.310 --> 00:00:57.773
representing the initial
concentration of our acid, HA.
00:00:58.790 --> 00:01:03.060
So there are five HA particles in solution
00:01:03.060 --> 00:01:06.160
and also five water particles.
00:01:06.160 --> 00:01:08.540
Since the reaction goes to completion,
00:01:08.540 --> 00:01:12.060
the HA particles are going to
react with the water particles
00:01:12.060 --> 00:01:17.060
to produce five hydronium,
H3O-plus, and five A-minus.
00:01:17.100 --> 00:01:20.220
We can see that in our
second particulate diagram,
00:01:20.220 --> 00:01:22.920
which represents the equilibrium mixture
00:01:22.920 --> 00:01:25.670
and there are five hydroniums present
00:01:25.670 --> 00:01:28.786
and also five A-minuses.
00:01:28.786 --> 00:01:31.630
We can write the equilibrium
constant expression
00:01:31.630 --> 00:01:34.430
for this reaction from
the balanced equation.
00:01:34.430 --> 00:01:36.920
we look at our products and
say it'd be the concentration
00:01:36.920 --> 00:01:39.450
of H3O-plus, and since
there's a coefficient of one,
00:01:39.450 --> 00:01:41.110
it'd be the concentration of H30-plus
00:01:41.110 --> 00:01:43.550
raised to the first power,
times the concentration
00:01:43.550 --> 00:01:46.700
of A-minus also raised to
the first power, divided by
00:01:46.700 --> 00:01:49.810
the concentration of HA
raised to the first power,
00:01:49.810 --> 00:01:51.590
and pure water is left out
00:01:51.590 --> 00:01:54.170
of the equilibrium constant expression.
00:01:54.170 --> 00:01:57.180
So that's equal to the
equilibrium constant K,
00:01:57.180 --> 00:02:00.180
and since this shows the
ionization of an acid,
00:02:00.180 --> 00:02:02.330
we could call this Ka value,
00:02:02.330 --> 00:02:04.400
the acid ionization constant,
00:02:04.400 --> 00:02:07.160
or the acid dissociation constant.
00:02:07.160 --> 00:02:09.840
Since the equilibrium
lies so far to the right
00:02:09.840 --> 00:02:13.100
for a strong acid, at
equilibrium, there's going to be
00:02:13.100 --> 00:02:17.180
essentially all products and
very, very little reactants.
00:02:17.180 --> 00:02:20.560
That means the Ka value for a strong acid
00:02:20.560 --> 00:02:23.310
will be much greater than one.
00:02:23.310 --> 00:02:25.360
Now let's look at a weak acid.
00:02:25.360 --> 00:02:27.350
We're gonna use the same
general equation here.
00:02:27.350 --> 00:02:31.890
HA plus H2O yields H3O-plus plus A-minus.
00:02:31.890 --> 00:02:35.090
However, if HA is a generic weak acid,
00:02:35.090 --> 00:02:38.260
we're going to include an
equilibrium arrow here.
00:02:38.260 --> 00:02:40.450
The equilibrium arrow needs to be included
00:02:40.450 --> 00:02:43.560
because weak acids only partially ionize,
00:02:43.560 --> 00:02:47.340
and we can see that in
the particulate diagrams.
00:02:47.340 --> 00:02:49.280
In the particulate diagram on the left,
00:02:49.280 --> 00:02:52.220
this is supposed to represent
the initial concentration
00:02:52.220 --> 00:02:56.686
of our weak acid HA and there
are five particles of HA
00:02:56.686 --> 00:02:59.640
and five particles of water.
00:02:59.640 --> 00:03:02.430
Since weak acids only
partially ionize, let's say
00:03:02.430 --> 00:03:07.430
that only one HA particle
reacts with one water molecule
00:03:07.550 --> 00:03:12.470
to produce one hydronium
ion and one A-minus anion.
00:03:12.470 --> 00:03:17.060
So if one HA particle reacts
with one H2O particle,
00:03:17.060 --> 00:03:21.230
that gives us one hydronium,
H30-plus and one A-minus.
00:03:21.230 --> 00:03:25.780
So out of the original five HA particles,
00:03:25.780 --> 00:03:30.640
only one of them ionized,
leaving four HA particles
00:03:30.640 --> 00:03:34.400
still in solution at
equilibrium, therefore HA
00:03:34.400 --> 00:03:38.500
only partially ionized and is a weak acid,
00:03:38.500 --> 00:03:41.330
the equilibrium constant
expression for a weak acid
00:03:41.330 --> 00:03:43.530
looks the same as it
did for our strong acid,
00:03:43.530 --> 00:03:46.050
because we use the same general equation.
00:03:46.050 --> 00:03:49.610
However, since a weak acid
only partially ionizes
00:03:49.610 --> 00:03:52.270
at equilibrium, there's
gonna be a small amount
00:03:52.270 --> 00:03:56.200
of products and a large
amount of reactants.
00:03:56.200 --> 00:03:59.516
Therefore, the Ka value for a weak acid
00:03:59.516 --> 00:04:02.460
will be less than one.
00:04:02.460 --> 00:04:03.950
Let's look at some Ka values
00:04:03.950 --> 00:04:06.970
for some weak acids at 25 degrees Celsius.
00:04:06.970 --> 00:04:09.150
Hydrofluoric acid has a Ka value
00:04:09.150 --> 00:04:11.600
of 6.3 times 10 to the negative fourth,
00:04:11.600 --> 00:04:13.710
and acetic acid has a Ka value
00:04:13.710 --> 00:04:16.950
of 1.8 times 10 to the negative fifth.
00:04:16.950 --> 00:04:19.920
Since both of these have
Ka values less than one,
00:04:19.920 --> 00:04:22.580
they're both considered to be weak acids.
00:04:22.580 --> 00:04:26.730
However, the higher the Ka
value, the stronger the acid.
00:04:26.730 --> 00:04:31.060
So out of these two weak
acids, since hydrofluoric acid
00:04:31.060 --> 00:04:33.960
has the higher Ka value, hydrofluoric acid
00:04:33.960 --> 00:04:36.143
is the stronger acid of the two.
00:04:37.040 --> 00:04:40.420
Now let's do a calculation
using a weak acid.
00:04:40.420 --> 00:04:44.460
Let's say we have a 0.10 molar
solution of benzoic acid,
00:04:44.460 --> 00:04:46.910
which is a weak acid, and
the pH of the solution
00:04:46.910 --> 00:04:50.070
is 2.60 at 25 degrees Celsius.
00:04:50.070 --> 00:04:52.590
Our goal is to calculate the Ka value
00:04:52.590 --> 00:04:56.060
for benzoic acid at 25 degrees Celsius.
00:04:56.060 --> 00:04:58.090
Since we're given the pH in the problem,
00:04:58.090 --> 00:05:02.940
we can go ahead and plug the
pH of 2.60 into this equation.
00:05:02.940 --> 00:05:07.730
So 2.60 is equal to the negative
log of the concentration
00:05:07.730 --> 00:05:11.160
of hydronium ions, and to
solve for the concentration
00:05:11.160 --> 00:05:13.740
of hydronium ions, first
moved the negative sign
00:05:13.740 --> 00:05:16.100
to the left, which gives us negative 2.60,
00:05:16.100 --> 00:05:20.720
is equal to log of the
concentration of hydronium ions.
00:05:20.720 --> 00:05:25.330
And to get rid of the log,
we take 10 to both sides.
00:05:25.330 --> 00:05:28.590
This gives us the
concentration of hydronium ions
00:05:28.590 --> 00:05:33.590
is equal to 2.5 times 10 to
the negative third molar.
00:05:35.740 --> 00:05:37.420
It's also important to recognize this is
00:05:37.420 --> 00:05:41.820
the equilibrium concentration
of hydronium ions.
00:05:41.820 --> 00:05:43.610
The next step is to write out the equation
00:05:43.610 --> 00:05:46.640
showing benzoic acid reacting with water.
00:05:46.640 --> 00:05:49.580
So here's the chemical
formula for benzoic acid
00:05:49.580 --> 00:05:52.430
reacting with water to
form the hydronium ion
00:05:52.430 --> 00:05:54.620
and the conjugate base to benzoic acid,
00:05:54.620 --> 00:05:56.860
which is the benzoate anion.
00:05:56.860 --> 00:05:59.470
To help us find the Ka
value for benzoic acid,
00:05:59.470 --> 00:06:01.190
we're gonna use an ICE table,
00:06:01.190 --> 00:06:03.640
where I stands for the
initial concentration,
00:06:03.640 --> 00:06:05.610
C is the change in concentration,
00:06:05.610 --> 00:06:08.240
and E is the equilibrium concentration.
00:06:08.240 --> 00:06:11.190
In our problem, we were told
the initial concentration
00:06:11.190 --> 00:06:15.550
of benzoic acid was 0.10
molar, and if we assume
00:06:15.550 --> 00:06:17.910
that benzoic acid hasn't reacted yet,
00:06:17.910 --> 00:06:21.050
the initial concentration of
hydronium ion would be zero,
00:06:21.050 --> 00:06:23.430
and the initial concentration of benzoate
00:06:23.430 --> 00:06:25.170
would also be zero.
00:06:25.170 --> 00:06:28.100
We just calculated the
equilibrium concentration
00:06:28.100 --> 00:06:31.100
of hydronium ions, which we found to be
00:06:31.100 --> 00:06:34.960
2.5 times 10 to the negative third molar.
00:06:34.960 --> 00:06:38.023
So we're going to go
ahead and put that under
00:06:38.023 --> 00:06:41.570
our hydronium ion in for the
equilibrium concentration.
00:06:41.570 --> 00:06:44.890
So if the initial concentration
of hydronium ion was zero
00:06:44.890 --> 00:06:46.620
and the equilibrium concentration
00:06:46.620 --> 00:06:49.700
is 2.5 times 10 to the
negative third, there was
00:06:49.700 --> 00:06:53.730
an increase in 2.5 times
10 to the negative third,
00:06:53.730 --> 00:06:55.660
so we're going to write
that under hydronium
00:06:55.660 --> 00:06:58.600
for the change in the concentration.
00:06:58.600 --> 00:07:01.030
And looking at the mole
ratio of hydronium ion
00:07:01.030 --> 00:07:04.510
to benzoate, it's a one-to-one mole ratio.
00:07:04.510 --> 00:07:06.700
So if hydronium ion increased
00:07:06.700 --> 00:07:09.330
by 2.5 times 10 to the negative third,
00:07:09.330 --> 00:07:12.600
so did the benzoate anions,
I can go ahead and write here
00:07:12.600 --> 00:07:15.770
plus 2.5 times 10 to the negative third,
00:07:15.770 --> 00:07:18.040
which means the equilibrium concentration
00:07:18.040 --> 00:07:20.770
of benzoate anion would also be
00:07:20.770 --> 00:07:23.770
2.5 times 10 to the negative third.
00:07:23.770 --> 00:07:25.800
Since we saw an increase
in the concentration
00:07:25.800 --> 00:07:29.140
of hydronium ion and
benzoate, that increase
00:07:29.140 --> 00:07:30.390
in the concentration of the products
00:07:30.390 --> 00:07:34.290
came from the ionization
of our weak acids.
00:07:34.290 --> 00:07:36.000
In the balanced equation, there's a one
00:07:36.000 --> 00:07:38.570
in front of benzoic acid, so if we write
00:07:38.570 --> 00:07:42.440
plus 2.5 times 10 to the
negative third for hydronium,
00:07:42.440 --> 00:07:45.490
and it's a one-to-one
mole ratio from hydronium
00:07:45.490 --> 00:07:47.980
to benzoic acid, we would have to write
00:07:47.980 --> 00:07:51.520
minus 2.5 times 10 to the negative third,
00:07:51.520 --> 00:07:55.140
since we lost some of the
benzoic acid when it ionized,
00:07:55.140 --> 00:07:58.400
therefore the equilibrium
concentration of benzoic acid
00:07:58.400 --> 00:08:03.400
would be 0.10 minus 2.5 times
10 to the negative third.
00:08:06.890 --> 00:08:09.180
Since our goal is to
calculate the Ka value
00:08:09.180 --> 00:08:11.550
for benzoic acid, the
next step is to write out
00:08:11.550 --> 00:08:13.830
the equilibrium constant expression,
00:08:13.830 --> 00:08:15.870
which we get from the balanced equation.
00:08:15.870 --> 00:08:18.160
It would be the concentration
of hydronium ions
00:08:18.160 --> 00:08:21.280
times the concentration of benzoate anions
00:08:21.280 --> 00:08:24.420
divided by the concentration
of benzoic acid.
00:08:24.420 --> 00:08:27.050
Since these are
equilibrium concentrations,
00:08:27.050 --> 00:08:29.290
we can get the equilibrium concentrations
00:08:29.290 --> 00:08:31.340
from the ICE table and plug them in
00:08:31.340 --> 00:08:34.350
to our equilibrium constant expression.
00:08:34.350 --> 00:08:37.160
So we can plug in the
equilibrium concentration
00:08:37.160 --> 00:08:39.360
for hydronium ions, we can plug in
00:08:39.360 --> 00:08:43.200
the equilibrium concentration
for benzoate anions,
00:08:43.200 --> 00:08:45.857
and we can plug in the
equilibrium concentration
00:08:45.857 --> 00:08:48.434
for benzoic acid.
00:08:48.434 --> 00:08:50.930
Here we have the
equilibrium concentrations
00:08:50.930 --> 00:08:53.760
plugged in to the equilibrium
constant expression,
00:08:53.760 --> 00:08:56.626
and when we solve for Ka, we find that Ka
00:08:56.626 --> 00:08:59.000
for benzoic acid at 25 degrees Celsius
00:08:59.000 --> 00:09:02.420
is equal to 6.4 times 10
to the negative fifth.
00:09:02.420 --> 00:09:04.870
Notice that Ka is less than one
00:09:04.870 --> 00:09:07.970
because benzoic acid is a weak acid.
00:09:07.970 --> 00:09:12.470
Finally, let's talk about the
idea of percent ionization.
00:09:12.470 --> 00:09:14.620
And to help us think
about percent ionization.
00:09:14.620 --> 00:09:18.040
Let's go back to our
example with a strong acid.
00:09:18.040 --> 00:09:21.370
We started off with five HA particles
00:09:21.370 --> 00:09:24.930
and all five of those HA particles ionized
00:09:24.930 --> 00:09:28.070
to produce five hydronium ions in solution
00:09:28.070 --> 00:09:31.310
and five A-minus anions in solution.
00:09:31.310 --> 00:09:35.720
Therefore 100% of our acid ionized.
00:09:35.720 --> 00:09:39.350
So we can write 100% ionization
00:09:39.350 --> 00:09:42.940
for this hypothetical strong acid HA.
00:09:42.940 --> 00:09:45.390
Now let's go back to our weak acid.
00:09:45.390 --> 00:09:49.150
For our weak acid, we started
off with five HA particles,
00:09:49.150 --> 00:09:51.750
but only one of them ionized to produce
00:09:51.750 --> 00:09:54.500
one H3O-plus and one A-minus.
00:09:54.500 --> 00:09:58.330
So four remain unionized at equilibrium,
00:09:58.330 --> 00:10:03.120
therefore one out of five
ionized, so the percent ionization
00:10:03.120 --> 00:10:08.120
for this hypothetical
weak acid would be 20%.
00:10:08.132 --> 00:10:11.840
Notice that the one
particle of HA that ionized
00:10:11.840 --> 00:10:16.030
made one hydronium ion, so we can also use
00:10:16.030 --> 00:10:19.430
the concentration of
hydronium ion at equilibrium
00:10:19.430 --> 00:10:22.610
to calculate percent ionization.
00:10:22.610 --> 00:10:25.350
So the equation for percent Ionization
00:10:25.350 --> 00:10:28.470
is equal to the equilibrium concentration
00:10:28.470 --> 00:10:32.540
of hydronium ions divided
by the initial concentration
00:10:32.540 --> 00:10:37.200
of the acid HA times 100%.
00:10:37.200 --> 00:10:40.900
So looking at our ICE table
for our benzoic acid problem,
00:10:40.900 --> 00:10:44.320
the equilibrium concentration
of hydronium ions
00:10:44.320 --> 00:10:47.740
was 2.5 times 10 to the
negative third molar,
00:10:47.740 --> 00:10:52.740
and the initial concentration
of our acid was 0.10 molar,
00:10:53.210 --> 00:10:56.040
so we can plug those into our equation.
00:10:56.040 --> 00:10:59.770
So we plug in our concentrations
and molar cancels,
00:10:59.770 --> 00:11:03.850
and we find for the final
answer, the percent ionization
00:11:03.850 --> 00:11:08.850
of benzoic acid is equal to 2.5%.
|
Strong base solutions | https://www.youtube.com/watch?v=ffAiM67QomI | vtt | https://www.youtube.com/api/timedtext?v=ffAiM67QomI&ei=0lWUZcvwIrG-mLAP1N2p8AQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C6831E359348D8302F3BFEAD0E98AB87C3A39CD0.36DDEEB5E70825D2D6DE8335D4D238F5855C33FD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.640 --> 00:00:01.740
- [Instructor] When dissolved in water,
00:00:01.740 --> 00:00:04.670
a strong base like potassium hydroxide
00:00:04.670 --> 00:00:07.020
will dissociate completely in solution
00:00:07.020 --> 00:00:09.020
to form hydroxide ions.
00:00:09.020 --> 00:00:11.040
Potassium hydroxide is an example
00:00:11.040 --> 00:00:14.390
of a group 1A metal hydroxide.
00:00:14.390 --> 00:00:16.950
Other examples include lithium hydroxide
00:00:16.950 --> 00:00:19.100
and sodium hydroxide.
00:00:19.100 --> 00:00:21.840
Group 2A metal hydroxides
are also considered
00:00:21.840 --> 00:00:23.510
to be strong bases.
00:00:23.510 --> 00:00:25.790
For example, calcium hydroxide
00:00:25.790 --> 00:00:27.660
is a group 2A metal hydroxide,
00:00:27.660 --> 00:00:30.320
and so is strontium hydroxide.
00:00:30.320 --> 00:00:33.640
Let's do a problem with a
group 1A metal hydroxide,
00:00:33.640 --> 00:00:35.520
sodium hydroxide.
00:00:35.520 --> 00:00:38.930
Let's say the pH of the solution is 13.00
00:00:38.930 --> 00:00:42.230
and our goal is to calculate
the initial concentration
00:00:42.230 --> 00:00:44.330
of sodium hydroxide.
00:00:44.330 --> 00:00:46.780
First, we brought out
the disillusion equation.
00:00:46.780 --> 00:00:50.390
Solid sodium hydroxide
dissociates completely in water
00:00:50.390 --> 00:00:55.390
to form sodium cations and
hydroxide anions in solution.
00:00:55.550 --> 00:00:56.850
Looking at the balanced equation,
00:00:56.850 --> 00:00:59.310
there's a one in front of sodium hydroxide
00:00:59.310 --> 00:01:02.130
and a one in front of hydroxide ions,
00:01:02.130 --> 00:01:05.260
therefore the concentration
of hydroxide ions
00:01:05.260 --> 00:01:09.680
is equal to the initial
concentration of sodium hydroxide.
00:01:09.680 --> 00:01:12.200
And we can find the
concentration of hydroxide ions
00:01:12.200 --> 00:01:14.980
in solution from the pH.
00:01:14.980 --> 00:01:16.720
At 25 degrees Celsius,
00:01:16.720 --> 00:01:21.523
the pH plus the pOH is equal to 14.00.
00:01:24.470 --> 00:01:28.100
So we can plug the pH into our equation,
00:01:28.100 --> 00:01:31.340
which gives us 13.00,
00:01:31.340 --> 00:01:36.340
plus the pOH is equal to 14.00.
00:01:36.490 --> 00:01:40.943
So the pOH of the
solution is equal to 1.00,
00:01:43.290 --> 00:01:47.360
and the pOH is equal to the negative log
00:01:47.360 --> 00:01:51.410
of the concentration of hydroxide ions.
00:01:51.410 --> 00:01:55.890
So we can plug the pOH into this equation,
00:01:55.890 --> 00:02:00.890
which gives us 1.00 is
equal to the negative log
00:02:01.100 --> 00:02:04.053
of the concentration of hydroxide ions.
00:02:05.160 --> 00:02:06.530
To solve for the concentration
00:02:06.530 --> 00:02:08.670
of hydroxide ions in solution,
00:02:08.670 --> 00:02:11.960
first we move the negative
sign to the left side,
00:02:11.960 --> 00:02:15.570
which gives us negative
1.00 is equal to the log
00:02:15.570 --> 00:02:18.540
of the concentration of hydroxide ions.
00:02:18.540 --> 00:02:23.100
To get rid of the log,
we take 10 to both sides.
00:02:23.100 --> 00:02:27.870
So the concentration of
hydroxide ions in this solution
00:02:27.870 --> 00:02:31.160
is equal to 10 to the negative 1.00,
00:02:31.160 --> 00:02:35.810
which is equal to .10 molar.
00:02:35.810 --> 00:02:38.220
Because sodium hydroxide is a strong base
00:02:38.220 --> 00:02:40.670
that dissociates completely in solution
00:02:40.670 --> 00:02:42.520
to form hydroxide ions,
00:02:42.520 --> 00:02:44.390
if the concentration of hydroxide ions
00:02:44.390 --> 00:02:46.590
in solution is .10 molar,
00:02:46.590 --> 00:02:50.563
so is the initial concentration
of sodium hydroxide.
00:02:52.110 --> 00:02:55.980
Now let's do a problem with
a group 2A metal hydroxide.
00:02:55.980 --> 00:02:58.360
Let's say the initial
concentration of a solution
00:02:58.360 --> 00:03:02.570
of calcium hydroxide is .0010 molar,
00:03:02.570 --> 00:03:05.040
and our goal is to find
the pH of the solution
00:03:05.040 --> 00:03:07.550
at 25 degrees Celsius.
00:03:07.550 --> 00:03:09.730
Calcium hydroxide is a strong base
00:03:09.730 --> 00:03:11.920
that dissociates completely in solution
00:03:11.920 --> 00:03:16.150
to form calcium two plus
ions and hydroxide anions,
00:03:16.150 --> 00:03:19.280
and looking at the mole ratios
in this disillusion equation,
00:03:19.280 --> 00:03:22.070
there's a one in front
of calcium hydroxide,
00:03:22.070 --> 00:03:24.160
a one in front of calcium two plus,
00:03:24.160 --> 00:03:27.060
and a two in front of hydroxide ions.
00:03:27.060 --> 00:03:30.790
Since the mole ratio of
calcium hydroxide to calcium
00:03:30.790 --> 00:03:32.290
is one to one,
00:03:32.290 --> 00:03:34.760
if the initial concentration
of calcium hydroxide
00:03:34.760 --> 00:03:37.190
is .0010 molar,
00:03:37.190 --> 00:03:40.070
that's also the concentration
of calcium ions.
00:03:40.070 --> 00:03:44.600
So it's .0010 molar in solution.
00:03:44.600 --> 00:03:48.340
The mole ratio of calcium
hydroxide to hydroxide ions
00:03:48.340 --> 00:03:50.590
is one to two,
00:03:50.590 --> 00:03:53.130
so if the initial concentration
of calcium hydroxide
00:03:53.130 --> 00:03:55.560
is .0010 molar,
00:03:55.560 --> 00:03:58.440
the concentration of
hydroxide ions in solution
00:03:58.440 --> 00:04:00.800
is twice that concentration,
00:04:00.800 --> 00:04:05.453
so two times .0010 molar
is equal to .0020 molar.
00:04:08.630 --> 00:04:11.140
Now that we know the
concentration of hydroxide ions,
00:04:11.140 --> 00:04:14.440
we can calculate the pH of the solution.
00:04:14.440 --> 00:04:18.360
One way to calculate the
pH is to first find the pOH
00:04:18.360 --> 00:04:19.420
of the solution,
00:04:19.420 --> 00:04:23.060
and pOH is equal to the negative log
00:04:23.060 --> 00:04:27.110
of the concentration of hydroxide ions.
00:04:27.110 --> 00:04:30.490
So we can plug in the
concentration of hydroxide ions
00:04:30.490 --> 00:04:32.020
into our equation,
00:04:32.020 --> 00:04:34.730
which gives us the pOH of the solution
00:04:34.730 --> 00:04:38.263
is equal to the negative log of .0020,
00:04:42.140 --> 00:04:43.650
and when you do the calculation,
00:04:43.650 --> 00:04:48.590
the pOH is equal to 2.70.
00:04:48.590 --> 00:04:51.970
Notice, since we have
two significant figures
00:04:51.970 --> 00:04:53.200
for the concentration,
00:04:53.200 --> 00:04:56.563
we need two decimal places for our pOH.
00:04:57.480 --> 00:04:58.730
So to find the pH,
00:04:58.730 --> 00:05:03.730
we know that pH plus pOH is equal to 14.00
00:05:06.020 --> 00:05:08.760
at 25 degrees Celsius.
00:05:08.760 --> 00:05:13.140
So we can plug in the pOH of 2.70,
00:05:13.140 --> 00:05:18.140
and that gives us pH plus
2.70 is equal to 14.00.
00:05:20.380 --> 00:05:24.113
So the pH of the solution
is equal to 11.30.
|
Strong acid solutions | https://www.youtube.com/watch?v=pZ43GbTechI | vtt | https://www.youtube.com/api/timedtext?v=pZ43GbTechI&ei=0lWUZfaTJZ2cxN8Pus-4iAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=416A3E52681573F353F073ED9C1E8BBED3549136.38BC230625640A9D194651A8E813B82FA8B628C2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:02.100
- [Instructor] A strong acid is an acid
00:00:02.100 --> 00:00:05.340
that ionizes 100% in solution.
00:00:05.340 --> 00:00:09.230
For example, hydrochloric
acid, HCl, as a strong acid
00:00:09.230 --> 00:00:11.960
it donates a proton to water, H2O,
00:00:11.960 --> 00:00:14.810
to form the hydronium ion, H3O plus,
00:00:14.810 --> 00:00:16.650
and the conjugate base to HCl
00:00:16.650 --> 00:00:19.750
which is the chloride anion, Cl minus.
00:00:19.750 --> 00:00:22.300
In reality, this reaction
reaches an equilibrium.
00:00:22.300 --> 00:00:25.040
However, the equilibrium
lies so far to the right
00:00:25.040 --> 00:00:28.060
and favors the product so
much that we don't draw
00:00:28.060 --> 00:00:30.520
an equilibrium arrow,
we simply draw an arrow
00:00:30.520 --> 00:00:33.210
going to the right,
indicating the reaction
00:00:33.210 --> 00:00:35.750
essentially goes to completion.
00:00:35.750 --> 00:00:38.300
And if the reaction
essentially goes to completion,
00:00:38.300 --> 00:00:41.890
we can say that hydrochloric
acid ionizes 100%
00:00:41.890 --> 00:00:45.800
and forms hydronium ions
and chloride anions.
00:00:45.800 --> 00:00:47.980
So essentially there is no more HCl left,
00:00:47.980 --> 00:00:52.460
it's all turned into
H3O plus and Cl minus.
00:00:52.460 --> 00:00:54.860
It's also acceptable to
completely leave water
00:00:54.860 --> 00:00:59.070
out of the equation and to
show hydrochloric acid, HCl,
00:00:59.070 --> 00:01:02.420
turning into H plus and Cl minus.
00:01:02.420 --> 00:01:04.740
Once again, since HCl is a strong acid,
00:01:04.740 --> 00:01:06.950
there's only an arrow going to the right
00:01:06.950 --> 00:01:10.350
indicating HCl ionizes 100%.
00:01:10.350 --> 00:01:12.830
And since there's only one
water molecule difference
00:01:12.830 --> 00:01:17.370
between H plus and H3O
plus, H plus and H3O plus
00:01:17.370 --> 00:01:19.490
are used interchangeably.
00:01:19.490 --> 00:01:21.200
Hydrochloric acid is an example
00:01:21.200 --> 00:01:23.350
of a monoprotic strong acid.
00:01:23.350 --> 00:01:26.490
Monoprotic means, hydrochloric
acid has one proton
00:01:26.490 --> 00:01:28.890
that it can donate in solution.
00:01:28.890 --> 00:01:31.730
Other examples of monoprotic
strong acids include
00:01:31.730 --> 00:01:34.233
hydrobromic acid, HBr,
hydroiodic acid, HI,
00:01:36.300 --> 00:01:40.627
nitric acid, HNO3, and
perchloric acid, HClO4.
00:01:41.980 --> 00:01:45.680
Sulfuric acid is H2SO4
and it's a strong acid,
00:01:45.680 --> 00:01:49.050
but it's a diprotic acid,
meaning it has two protons
00:01:49.050 --> 00:01:52.550
that it can donate, however,
only the first ionization
00:01:52.550 --> 00:01:55.310
for sulfuric acid is strong.
00:01:55.310 --> 00:01:58.810
Let's calculate the pH of
a strong acid solution.
00:01:58.810 --> 00:02:03.220
In this case, we're gonna
do a 0.040M solution
00:02:03.220 --> 00:02:05.320
of nitric acid.
00:02:05.320 --> 00:02:10.180
Nitric acid is HNO3, and
nitric acid reacts with water
00:02:10.180 --> 00:02:14.690
to form hydronium, H3O plus,
and nitrate, NO3 minus,
00:02:14.690 --> 00:02:17.910
which is the conjugate base 2HNO3.
00:02:17.910 --> 00:02:20.060
Because nitric acid is a strong acid,
00:02:20.060 --> 00:02:22.670
we assume the reaction goes to completion.
00:02:22.670 --> 00:02:25.740
Therefore, if the initial
concentration of nitric acid
00:02:25.740 --> 00:02:30.310
is 0.040M, looking at our mole ratios
00:02:30.310 --> 00:02:32.210
in the balanced equation,
there's a one in front
00:02:32.210 --> 00:02:35.560
of nitric acid and there's also
a one in front of hydronium
00:02:35.560 --> 00:02:37.630
and a one in front of nitrate.
00:02:37.630 --> 00:02:39.740
Therefore, if the reaction
goes to completion,
00:02:39.740 --> 00:02:43.897
the concentration of
hydronium would also be 0.040M
00:02:45.250 --> 00:02:47.100
and the same with the nitrate anion,
00:02:47.100 --> 00:02:51.510
that would also have a
concentration of 0.040M.
00:02:51.510 --> 00:02:55.000
Since our goal is to calculate
the pH of this solution,
00:02:55.000 --> 00:02:57.950
we know that the equation
for pH is pH is equal
00:02:57.950 --> 00:03:02.950
to the negative log of the
concentration of hydronium ions.
00:03:03.010 --> 00:03:05.580
Therefore, we just need to
plug in the concentration
00:03:05.580 --> 00:03:09.000
of hydronium ions into our equation.
00:03:09.000 --> 00:03:10.580
This gives us the pH is equal
00:03:10.580 --> 00:03:14.073
to the negative log of 0.040,
00:03:17.400 --> 00:03:22.360
which is equal to 1.40.
00:03:22.360 --> 00:03:24.900
So even though this is
a pretty dilute solution
00:03:24.900 --> 00:03:28.560
of nitric acid, because
nitric acid is a strong acid,
00:03:28.560 --> 00:03:30.760
the pH is pretty low.
00:03:30.760 --> 00:03:33.220
Also note since we have
two significant figures
00:03:33.220 --> 00:03:35.490
for the concentration of hydronium ions,
00:03:35.490 --> 00:03:39.420
we need two decimal places
for our final answer.
00:03:39.420 --> 00:03:42.430
Let's do another problem
with a strong acid solution.
00:03:42.430 --> 00:03:45.510
Let's say we have 100 ml
of an aqueous solution
00:03:45.510 --> 00:03:48.400
of hydroiodic acid and
the pH of the solution
00:03:48.400 --> 00:03:50.170
is equal to 1.50.
00:03:50.170 --> 00:03:52.740
And our goal is to find the mass of HI
00:03:52.740 --> 00:03:55.340
that's present in solution.
00:03:55.340 --> 00:03:58.470
Hydroiodic acid reacts with
water to form the hydronium ion
00:03:58.470 --> 00:04:00.090
and the iodide anion.
00:04:00.090 --> 00:04:05.090
And the mole ratio of HI
to H3O plus is one-to-one.
00:04:05.500 --> 00:04:08.380
So if we can find the
concentration of hydronium ion
00:04:08.380 --> 00:04:10.600
and solution, that should also be
00:04:12.118 --> 00:04:15.070
the initial concentration
of hydroiodic acid.
00:04:15.070 --> 00:04:15.903
And once we find
00:04:15.903 --> 00:04:17.780
the initial concentration
of hydroiodic acid,
00:04:17.780 --> 00:04:20.620
we can find the mass of HI that's present.
00:04:20.620 --> 00:04:22.610
Since we are given the pH in the problem,
00:04:22.610 --> 00:04:25.680
we can plug that directly
into our equation,
00:04:25.680 --> 00:04:30.680
which gives us 1.50 is
equal to the negative log
00:04:31.960 --> 00:04:35.473
of the concentration of hydronium ions.
00:04:36.730 --> 00:04:38.980
To solve for the concentration
of hydronium ions,
00:04:38.980 --> 00:04:41.680
we can first move the negative
sign to the left side,
00:04:41.680 --> 00:04:45.440
which gives us negative
1.50 is equal to the log
00:04:45.440 --> 00:04:48.380
of the concentration of hydronium ions.
00:04:48.380 --> 00:04:53.380
And to get rid of the log,
we can take 10 to both sides.
00:04:53.380 --> 00:04:55.190
So the concentration of hydronium ions
00:04:55.190 --> 00:04:58.830
is equal to 10 to the negative 1.50,
00:04:58.830 --> 00:05:03.730
which is equal to 0.032.
00:05:03.730 --> 00:05:07.373
So the concentration of
hydronium ions is 0.032M.
00:05:08.390 --> 00:05:11.960
And because the mole ratio
of hydronium ion to HI
00:05:11.960 --> 00:05:15.320
is one-to-one, the initial
concentration of HI
00:05:15.320 --> 00:05:17.600
is also 0.032M.
00:05:19.660 --> 00:05:21.820
Now that we know the
initial concentration of HI,
00:05:21.820 --> 00:05:24.800
we're ready to find
the mass of HI present.
00:05:24.800 --> 00:05:26.370
Molarity is moles per liter,
00:05:26.370 --> 00:05:28.040
so let's go ahead and rewrite this
00:05:28.040 --> 00:05:33.040
as 0.032 moles per liter.
00:05:34.630 --> 00:05:38.180
The volume of the solution
is 100 milliliters,
00:05:38.180 --> 00:05:42.180
which is equal to 0.100 liters.
00:05:42.180 --> 00:05:45.810
So if we multiply moles
per liter by the volume,
00:05:45.810 --> 00:05:50.810
which is 0.100 liters, liters
will cancel and give us moles.
00:05:51.600 --> 00:05:52.960
So this is equal to
00:05:52.960 --> 00:05:57.683
0.0032 moles of HI.
00:05:58.640 --> 00:06:01.140
Since our goal is to find
the mass of HI present,
00:06:01.140 --> 00:06:03.300
the final step is to
multiply the moles of HI
00:06:03.300 --> 00:06:04.950
by the molar mass which is
00:06:04.950 --> 00:06:09.950
128 grams per one mole of HI.
00:06:10.400 --> 00:06:15.400
So most of HI would cancel out
and this gives us 0.41 grams
00:06:16.370 --> 00:06:17.553
as our final answer.
|
Worked examples: Calculating [H₃O⁺] and pH | https://www.youtube.com/watch?v=qK_YVKAat1w | vtt | https://www.youtube.com/api/timedtext?v=qK_YVKAat1w&ei=0lWUZcTAI8Odp-oP4YO3aA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245314&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C976504F4AA1BF6976C1B963F72FFB5A5A2F12E8.9AE4C06AC77AD3A5EA2D6939D8D55C55C866D0FB&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.300 --> 00:00:01.290
- [Instructor] Here are some equations
00:00:01.290 --> 00:00:04.270
that are often used in pH calculations.
00:00:04.270 --> 00:00:06.200
For example, let's say a solution
00:00:06.200 --> 00:00:08.770
is formed at 25 degrees Celsius
00:00:08.770 --> 00:00:12.310
and the solution has a pOH of 4.75,
00:00:12.310 --> 00:00:14.870
and our goal is to
calculate the concentration
00:00:14.870 --> 00:00:18.320
of hydronium ions in solution, H3O+.
00:00:18.320 --> 00:00:20.900
One way to start this problem
is to use this equation,
00:00:20.900 --> 00:00:25.170
pH plus pOH is equal to 14.00.
00:00:25.170 --> 00:00:28.670
And we have the pOH equal to 4.75,
00:00:28.670 --> 00:00:31.700
so we can plug that into our equation.
00:00:31.700 --> 00:00:34.880
That gives us pH plus 4.75
00:00:36.540 --> 00:00:40.380
is equal to 14.00.
00:00:40.380 --> 00:00:45.380
And solving for the pH, we get
that the pH is equal to 9.25.
00:00:47.770 --> 00:00:49.820
So we have the pH and our goal is to solve
00:00:49.820 --> 00:00:52.020
for the concentration of hydronium ions,
00:00:52.020 --> 00:00:54.630
and pH is equal to the negative log
00:00:54.630 --> 00:00:57.760
of the concentration of hydronium ions.
00:00:57.760 --> 00:01:02.260
So we can plug our pH
right into this equation.
00:01:02.260 --> 00:01:05.680
So that would give us the pH which is 9.25
00:01:07.100 --> 00:01:09.770
is equal to the negative log
00:01:09.770 --> 00:01:13.573
of the concentration of hydronium ions.
00:01:14.920 --> 00:01:16.750
Next, we need to solve
for the concentration
00:01:16.750 --> 00:01:18.010
of hydronium ions.
00:01:18.010 --> 00:01:20.620
So we could move the negative
sign over to the left side,
00:01:20.620 --> 00:01:22.910
which gives us negative 9.25
00:01:22.910 --> 00:01:26.410
is equal to the log of the
concentration of hydronium ions.
00:01:26.410 --> 00:01:30.550
And to get rid of that log,
we can take 10 to both sides.
00:01:30.550 --> 00:01:34.330
So that's gonna give us the
concentration of hydronium ions,
00:01:34.330 --> 00:01:39.330
H3O+, is equal to 10 to the negative 9.25.
00:01:42.337 --> 00:01:44.277
And 10 to the negative 9.25
00:01:44.277 --> 00:01:47.944
is equal to 5.6 times
10 to the negative 10.
00:01:49.970 --> 00:01:52.990
So the concentration of hydronium ions
00:01:52.990 --> 00:01:56.450
in our solution at 25 degrees Celsius
00:01:56.450 --> 00:02:01.330
is equal to 5.6 times 10
to the negative 10th molar.
00:02:01.330 --> 00:02:04.450
Also notice that because
we had two decimal places
00:02:04.450 --> 00:02:08.860
for our pH, we have the
concentration of hydronium ions
00:02:08.860 --> 00:02:11.860
to two significant figures.
00:02:11.860 --> 00:02:14.230
There's another way to
do the same problem.
00:02:14.230 --> 00:02:16.060
Since we have the pOH,
00:02:16.060 --> 00:02:20.200
we could use the pOH equation
to find the concentration
00:02:20.200 --> 00:02:23.000
of hydroxide ions in solution.
00:02:23.000 --> 00:02:28.000
So we would just need to plug
in the pOH into this equation
00:02:28.330 --> 00:02:32.600
which gives us 4.75,
00:02:32.600 --> 00:02:35.470
which is the pOH, is
equal to the negative log
00:02:35.470 --> 00:02:39.690
of the concentration of hydroxide ions.
00:02:39.690 --> 00:02:42.260
Next, we can move the negative
sign over to the left side.
00:02:42.260 --> 00:02:47.260
So negative 4.75 is equal to
the log of the concentration
00:02:47.930 --> 00:02:50.510
of hydroxide ions.
00:02:50.510 --> 00:02:54.653
And to get rid of the log, we
just take 10 to both sides.
00:02:55.570 --> 00:02:57.630
10 to the negative 4.75
00:02:57.630 --> 00:03:02.630
is equal to 1.8 times 10
to the negative fifth.
00:03:03.440 --> 00:03:06.320
So the concentration of hydroxide ions
00:03:06.320 --> 00:03:10.010
is equal to 1.8 times 10 to
the negative fifth molar.
00:03:10.010 --> 00:03:11.540
So our goal is to find the concentration
00:03:11.540 --> 00:03:13.150
of hydronium ions in solution,
00:03:13.150 --> 00:03:16.900
and we have the concentration
of hydroxide ions in solution,
00:03:16.900 --> 00:03:19.570
so we can use the Kw equation
00:03:19.570 --> 00:03:21.880
because the concentration
of hydronium ions
00:03:21.880 --> 00:03:25.440
times the concentration of
hydroxide ions is equal to Kw,
00:03:25.440 --> 00:03:29.420
which is equal to 1.0 times
10 to the negative 14th
00:03:29.420 --> 00:03:32.010
at 25 degrees Celsius.
00:03:32.010 --> 00:03:35.130
So we can plug in the
concentration of hydroxide ions
00:03:35.130 --> 00:03:37.680
into our equation.
00:03:37.680 --> 00:03:42.440
That gives us 1.8 times
10 to the negative fifth
00:03:42.440 --> 00:03:44.770
times the concentration of hydronium ions,
00:03:44.770 --> 00:03:47.710
which we'll just write
as x in our equation
00:03:47.710 --> 00:03:48.890
is equal to Kw
00:03:48.890 --> 00:03:53.063
which is equal to 1.0 times
10 to the negative 14.
00:03:54.370 --> 00:03:55.300
Solving for x,
00:03:55.300 --> 00:04:00.300
we find the x is equal to 5.6
times 10 to the negative 10th.
00:04:02.130 --> 00:04:04.360
So the concentration of hydronium ions
00:04:04.360 --> 00:04:08.230
is equal to 5.6 times 10
to the negative 10th molar.
00:04:08.230 --> 00:04:10.320
So even though we used
two different equations
00:04:10.320 --> 00:04:11.930
from the first time we did this problem,
00:04:11.930 --> 00:04:14.610
we ended up with the same answer
that we did the first time,
00:04:14.610 --> 00:04:17.560
5.6 times 10 to the negative 10th molar.
00:04:17.560 --> 00:04:20.220
So it doesn't really matter
which approach you take.
00:04:20.220 --> 00:04:21.750
Finally, let's look at an example
00:04:21.750 --> 00:04:25.950
where the temperature is
not 25 degrees Celsius.
00:04:25.950 --> 00:04:28.250
Let's say, we have a sample of pure water
00:04:28.250 --> 00:04:30.090
at 50 degrees Celsius,
00:04:30.090 --> 00:04:32.803
and our goal is to calculate the pH.
00:04:33.800 --> 00:04:36.620
Pure water is a neutral substance
00:04:36.620 --> 00:04:41.620
which means the concentration
of hydronium ions, H3O+,
00:04:41.910 --> 00:04:46.260
is equal to the concentration
of hydroxide ions, OH-.
00:04:46.260 --> 00:04:49.290
Right now, we don't know what
those concentrations are,
00:04:49.290 --> 00:04:51.860
but we know that the
concentration of hydronium ions
00:04:51.860 --> 00:04:53.910
times the concentration of hydroxide ions
00:04:53.910 --> 00:04:55.840
is equal to Kw.
00:04:55.840 --> 00:04:58.470
However, we have to be careful because Kw
00:04:58.470 --> 00:05:01.670
is only equal to 1.0
times 10 to negative 14th
00:05:01.670 --> 00:05:03.870
at 25 degrees Celsius.
00:05:03.870 --> 00:05:05.700
And at 50 degrees Celsius,
00:05:05.700 --> 00:05:09.350
Kw is equal to 5.5 times
10 to the negative 14th.
00:05:10.350 --> 00:05:11.183
So let's go ahead and write
00:05:11.183 --> 00:05:16.183
Kw is equal to 5.5 times
10 to the negative 14th.
00:05:16.630 --> 00:05:20.110
And if we make the concentration
of hydronium ions x,
00:05:20.110 --> 00:05:21.970
then the concentration of hydroxide ions
00:05:21.970 --> 00:05:25.560
would also have to be x
since the two are equal.
00:05:25.560 --> 00:05:28.400
So we would have x times x
00:05:28.400 --> 00:05:32.460
is equal to 5.5 times
10 to the negative 14th.
00:05:32.460 --> 00:05:34.230
So that gives us x squared
00:05:34.230 --> 00:05:38.660
is equal to 5.5 times
10 to the negative 14th.
00:05:38.660 --> 00:05:41.200
And if we take the square
root of both sides,
00:05:41.200 --> 00:05:42.790
we find that x is equal
00:05:42.790 --> 00:05:47.790
to 2.3 times 10 to the negative seventh.
00:05:48.380 --> 00:05:50.480
And since x is equal to the concentration
00:05:50.480 --> 00:05:52.530
of hydronium ions in solution,
00:05:52.530 --> 00:05:54.310
the concentration of hydronium ions
00:05:54.310 --> 00:05:57.660
is 2.3 times 10 to the
negative seventh molar.
00:05:57.660 --> 00:05:59.220
Now that we know the concentration
00:05:59.220 --> 00:06:01.160
of hydronium ions in solution,
00:06:01.160 --> 00:06:05.260
we can use our pH equation
to find the pH of water
00:06:05.260 --> 00:06:07.500
at 50 degrees Celsius.
00:06:07.500 --> 00:06:10.370
So we plug our concentration
of hydronium ions
00:06:10.370 --> 00:06:11.960
into our equation,
00:06:11.960 --> 00:06:13.750
and we take the negative log of that,
00:06:13.750 --> 00:06:17.340
and we get that the pH is equal to 6.64.
00:06:17.340 --> 00:06:21.380
Notice with two significant
figures for the concentration,
00:06:21.380 --> 00:06:24.800
we get two decimal places for our answer.
00:06:24.800 --> 00:06:26.180
If we had used Kw
00:06:26.180 --> 00:06:30.010
is equal to 1.0 times
10 to the negative 14th,
00:06:30.010 --> 00:06:34.170
we would've gotten a pH of 7.00,
00:06:34.170 --> 00:06:37.960
but that's only true
at 25 degrees Celsius.
00:06:37.960 --> 00:06:41.310
Since Kw is temperature dependent,
00:06:41.310 --> 00:06:43.210
if the temperature is something other
00:06:43.210 --> 00:06:48.210
than 25 degrees Celsius, the
pH of water will not be seven.
00:06:48.250 --> 00:06:51.530
So in this case, we
calculated it to be 6.64.
00:06:51.530 --> 00:06:55.540
The pH of pure water is
6.64 at 50 degrees Celsius.
00:06:55.540 --> 00:06:58.740
However, water is still
a neutral substance.
00:06:58.740 --> 00:07:00.572
The concentration of hydronium ions
00:07:00.572 --> 00:07:04.364
is equal to the concentration
of hydroxide ions.
|
The pH scale | https://www.youtube.com/watch?v=75j1b1l6PWU | vtt | https://www.youtube.com/api/timedtext?v=75j1b1l6PWU&ei=11WUZaPSLfa6p-oPjNm7mAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245319&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=87D3A1D9E5E6AA2CDC440BCE5E9226D1081801B7.5EE749311CB9D7E5E605816D86AAFDEF74677BBA&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.270 --> 00:00:01.610
- [Instructor] For a sample of pure water
00:00:01.610 --> 00:00:05.490
at 25 degrees Celsius, the
concentration of hydronium ion
00:00:05.490 --> 00:00:09.210
is equal to 1.0 times 10 to
the negative seventh molar.
00:00:09.210 --> 00:00:12.070
Because the concentrations
are often very small,
00:00:12.070 --> 00:00:14.720
it's much more convenient
to express the concentration
00:00:14.720 --> 00:00:17.320
of hydronium ion in terms of pH.
00:00:17.320 --> 00:00:20.470
And pH is defined as the negative log
00:00:20.470 --> 00:00:23.320
of the concentration of hydronium ion.
00:00:23.320 --> 00:00:28.030
Since H+ and H3O+ are used
interchangeably in chemistry,
00:00:28.030 --> 00:00:30.580
sometimes you'll see the
pH equation written out
00:00:30.580 --> 00:00:32.580
as pH is equal to the negative log
00:00:32.580 --> 00:00:35.540
of the concentration of H+ ion.
00:00:35.540 --> 00:00:37.720
So to find the pH of pure water,
00:00:37.720 --> 00:00:40.070
we just need to plug in the concentration
00:00:40.070 --> 00:00:43.450
of hydronium ions into our equation.
00:00:43.450 --> 00:00:45.820
So the pH is equal to the negative log
00:00:45.820 --> 00:00:48.650
of 1.0 times 10 to the negative seventh
00:00:48.650 --> 00:00:51.310
which is equal to 7.00.
00:00:51.310 --> 00:00:55.210
So the pH of pure water
at 25 degrees Celsius
00:00:55.210 --> 00:00:56.930
is equal to seven.
00:00:56.930 --> 00:00:59.160
Notice that there are
two significant figures
00:00:59.160 --> 00:01:00.520
for the concentration
00:01:00.520 --> 00:01:04.070
and there are two decimal
places for the final answer.
00:01:04.070 --> 00:01:06.270
And that's because for a logarithm,
00:01:06.270 --> 00:01:09.640
only the numbers to the
right of the decimal point
00:01:09.640 --> 00:01:11.560
are significant figures.
00:01:11.560 --> 00:01:14.710
Therefore, two significant
figures for a concentration
00:01:14.710 --> 00:01:17.023
means two decimal places.
00:01:18.340 --> 00:01:20.830
Let's say we have a sample of lemon juice
00:01:20.830 --> 00:01:23.170
and the measured concentration
of hydronium ions
00:01:23.170 --> 00:01:27.390
in solution is 3.6 times 10
to negative fourth molar.
00:01:27.390 --> 00:01:29.890
Since we have the concentration
of hydronium ions,
00:01:29.890 --> 00:01:32.460
we can simply plug in that concentration
00:01:32.460 --> 00:01:34.890
into the equation for a pH.
00:01:34.890 --> 00:01:37.720
So the pH is equal to the negative log
00:01:37.720 --> 00:01:41.530
of the concentration of 3.6
times 10 to the negative fourth
00:01:41.530 --> 00:01:43.850
which is 3.44.
00:01:43.850 --> 00:01:45.960
Notice that we have
two significant figures
00:01:45.960 --> 00:01:47.200
for the concentration
00:01:47.200 --> 00:01:50.763
therefore we have two decimal
places in our final answer.
00:01:51.940 --> 00:01:54.840
So plugging in negative
log of 3.6 times 10
00:01:54.840 --> 00:01:56.520
to the negative fourth on your calculator,
00:01:56.520 --> 00:01:59.450
it gives you 3.44 for the answer.
00:01:59.450 --> 00:02:01.640
However, there's a way
of estimating the pH
00:02:01.640 --> 00:02:03.940
without using a calculator.
00:02:03.940 --> 00:02:08.110
The first step is to say 3.6
times 10 to the negative fourth
00:02:08.110 --> 00:02:11.350
is between one times 10
to the negative fourth
00:02:11.350 --> 00:02:14.380
and 10 times 10 to the negative fourth.
00:02:14.380 --> 00:02:16.050
10 times 10 to the negative fourth
00:02:16.050 --> 00:02:19.330
is the same thing as one times
10 to the negative third.
00:02:19.330 --> 00:02:21.140
If the concentration of hydronium ions
00:02:21.140 --> 00:02:23.450
is one times 10 to the negative third,
00:02:23.450 --> 00:02:26.410
you can find the pH of that
without using a calculator
00:02:26.410 --> 00:02:28.270
if you know your logarithms.
00:02:28.270 --> 00:02:31.740
The pH would be equal to three.
00:02:31.740 --> 00:02:33.520
And if the concentration of hydronium ions
00:02:33.520 --> 00:02:35.700
is one times 10 to the negative fourth,
00:02:35.700 --> 00:02:37.640
this is a log base 10 system,
00:02:37.640 --> 00:02:41.290
so the negative log of one
times 10 to the negative fourth
00:02:41.290 --> 00:02:45.390
would be equal to a pH of four.
00:02:45.390 --> 00:02:48.310
Since 3.6 times 10 to the negative fourth
00:02:48.310 --> 00:02:51.220
is between one times 10
to the negative fourth
00:02:51.220 --> 00:02:53.880
and one times 10 to the negative third,
00:02:53.880 --> 00:02:58.360
the pH of this concentration
must be between a pH of four
00:02:58.360 --> 00:03:00.140
and a pH three.
00:03:00.140 --> 00:03:02.100
And we saw that with our calculator.
00:03:02.100 --> 00:03:04.043
The pH came out to be 3.44.
00:03:05.750 --> 00:03:08.120
Let's say we have some cleaning
solution at room temperature
00:03:08.120 --> 00:03:09.860
which is 25 degrees Celsius
00:03:09.860 --> 00:03:12.750
and the cleaning solution
has some ammonia in it.
00:03:12.750 --> 00:03:16.140
The concentration of hydroxide
ions in solution is measured
00:03:16.140 --> 00:03:19.340
to be 2.0 times 10 to
the negative third molar.
00:03:19.340 --> 00:03:22.810
And our goal is to calculate
the pH of the solution.
00:03:22.810 --> 00:03:25.680
The first step is to use the Kw equation
00:03:25.680 --> 00:03:27.970
which says that the
concentration of hydronium ions
00:03:27.970 --> 00:03:31.730
times the concentration of
hydroxide ions is equal to Kw
00:03:31.730 --> 00:03:33.560
which at 25 degrees Celsius
00:03:33.560 --> 00:03:37.170
is equal to 1.0 times
10 to the negative 14th.
00:03:37.170 --> 00:03:39.340
We can go ahead and plug
in the concentration
00:03:39.340 --> 00:03:43.120
of hydroxide ions into the Kw equation.
00:03:43.120 --> 00:03:48.120
So that's 2.0 times 10
to the negative third.
00:03:48.160 --> 00:03:51.240
And we don't know the
concentration of hydronium ions is,
00:03:51.240 --> 00:03:53.800
we'll make that X and so
we're gonna solve for X.
00:03:53.800 --> 00:03:58.760
And this is equal to one
times 10 to the negative 14th.
00:03:58.760 --> 00:04:02.210
Solving for X, X is equal to 5.0
00:04:02.210 --> 00:04:04.380
times 10 to the negative 12
00:04:04.380 --> 00:04:06.420
and this is the equal to the concentration
00:04:06.420 --> 00:04:08.010
of hydronium ions.
00:04:08.010 --> 00:04:11.280
So the concentration of
hydronium ions is equal to 5.0
00:04:11.280 --> 00:04:13.800
times 10 to the negative 12 molar.
00:04:13.800 --> 00:04:16.070
Now that we know the
concentration of hydronium ions
00:04:16.070 --> 00:04:20.030
in solution, we can plug that
into our equation for pH.
00:04:20.030 --> 00:04:23.300
So the pH is equal to
the negative log of 5.0
00:04:23.300 --> 00:04:28.300
times 10 to the negative
12 which gives a 11.30.
00:04:28.470 --> 00:04:31.190
Notice since we have
two significant figures
00:04:31.190 --> 00:04:32.380
for the concentration,
00:04:32.380 --> 00:04:36.440
we need two decimal places
for our final answer.
00:04:36.440 --> 00:04:37.860
Now that we've calculated the pH
00:04:37.860 --> 00:04:39.370
of three different substances,
00:04:39.370 --> 00:04:42.870
let's find where they rank on
what's called the pH scale.
00:04:42.870 --> 00:04:46.980
The pH scale normally
goes from zero to 14.
00:04:46.980 --> 00:04:51.660
However, it is possible to go
below zero or to go above 14.
00:04:51.660 --> 00:04:53.950
We calculate that a sample of pure water
00:04:53.950 --> 00:04:58.950
at 25 degrees Celsius has a pH of 7.00.
00:04:59.260 --> 00:05:02.520
That puts it right in the
middle of the pH scale.
00:05:02.520 --> 00:05:06.200
And we say that water
is a neutral substance.
00:05:06.200 --> 00:05:08.480
An aqueous solution has a pH of seven
00:05:08.480 --> 00:05:12.290
is considered to be a neutral solution.
00:05:12.290 --> 00:05:14.640
An aqueous solution with
a pH less than seven
00:05:14.640 --> 00:05:17.200
is considered to be an acidic solution.
00:05:17.200 --> 00:05:22.010
So for lemon juice, we
calculated the pH to be 3.44
00:05:22.010 --> 00:05:24.530
which is right about here on our pH scale
00:05:24.530 --> 00:05:26.580
so lemon juice is acidic.
00:05:26.580 --> 00:05:29.360
And as you go to the left on the pH scale,
00:05:29.360 --> 00:05:32.080
you increase in acidity.
00:05:32.080 --> 00:05:34.800
For example, if we had a
solution with a pH of six
00:05:34.800 --> 00:05:37.060
and another solution with a pH of five,
00:05:37.060 --> 00:05:40.520
the solution with a pH
of five is more acidic.
00:05:40.520 --> 00:05:42.700
And going back to our equation for pH,
00:05:42.700 --> 00:05:44.320
pH is equal to the negative log
00:05:44.320 --> 00:05:46.500
of the concentration of hydronium ions.
00:05:46.500 --> 00:05:48.170
This is log based 10.
00:05:48.170 --> 00:05:50.880
Therefore the solution with the pH of five
00:05:50.880 --> 00:05:55.680
is 10 times more acidic than
a solution with a pH of six.
00:05:55.680 --> 00:05:58.040
And because of the way
the equation written,
00:05:58.040 --> 00:06:03.040
the higher the concentration
of hydronium ions in solution,
00:06:03.800 --> 00:06:07.710
the lower the value for the pH.
00:06:07.710 --> 00:06:11.350
And the lower the concentration
for the hydronium ions
00:06:11.350 --> 00:06:15.473
in solution, the higher
the value for them pH.
00:06:17.090 --> 00:06:20.030
And if an aqueous solution
has a pH greater than seven,
00:06:20.030 --> 00:06:22.740
we say that aqueous solution is basic.
00:06:22.740 --> 00:06:26.530
For example, our cleaning
solution with some ammonia in it
00:06:26.530 --> 00:06:29.310
had a pH of 11.30
00:06:29.310 --> 00:06:32.160
so that's right about
here on the pH scale.
00:06:32.160 --> 00:06:34.550
So we would consider that
cleaning solution with ammonia
00:06:34.550 --> 00:06:36.510
to be a basic solution.
00:06:36.510 --> 00:06:38.920
As you move to the right on the pH scale,
00:06:38.920 --> 00:06:43.030
you increase in the
basicity of the solution.
00:06:43.030 --> 00:06:45.330
So we've seen that pH is
equal to the negative log
00:06:45.330 --> 00:06:47.230
of the concentration of hydronium ions
00:06:47.230 --> 00:06:49.230
which you could also write pH is equal
00:06:49.230 --> 00:06:51.690
to the negative log of H+.
00:06:51.690 --> 00:06:54.830
Running it this way on the
right makes it easier to see
00:06:54.830 --> 00:06:57.890
how the pattern works
for other situations.
00:06:57.890 --> 00:07:02.630
For example, pOH is
defined as the negative log
00:07:02.630 --> 00:07:05.080
of the concentration of hydroxide ions.
00:07:05.080 --> 00:07:06.773
So we have the pOH here
00:07:06.773 --> 00:07:08.582
and then we have the
concentration of hydroxide ions
00:07:08.582 --> 00:07:10.810
over here, the same way we wrote pH
00:07:10.810 --> 00:07:13.730
with the concentration
of H+ ions over here.
00:07:13.730 --> 00:07:18.573
And also pKw would be equal
to the negative log of Kw.
00:07:19.430 --> 00:07:21.570
Let's go back to the Kw equation
00:07:21.570 --> 00:07:23.750
which says that the
concentration of hydronium ions
00:07:23.750 --> 00:07:25.800
times the concentration of hydroxide ions
00:07:25.800 --> 00:07:28.060
is equal to Kw.
00:07:28.060 --> 00:07:31.890
If we take the negative log
of both sides of this equation
00:07:31.890 --> 00:07:33.830
and we use our log properties,
00:07:33.830 --> 00:07:36.080
we get that the negative
log of the concentration
00:07:36.080 --> 00:07:39.410
of H3O+ plus the negative
log of the concentration
00:07:39.410 --> 00:07:42.663
of OH- is equal to the negative log of Kw.
00:07:43.740 --> 00:07:46.790
The negative log of the
concentration of H3O+
00:07:46.790 --> 00:07:48.710
is just equal to the pH,
00:07:48.710 --> 00:07:50.920
so we can write the pH down here,
00:07:50.920 --> 00:07:53.030
plus the negative log of the concentration
00:07:53.030 --> 00:07:56.390
of hydroxide ions,
that's equal to the pOH.
00:07:56.390 --> 00:08:01.390
So we have pH plus pOH is
equal to the negative log of Kw
00:08:02.580 --> 00:08:04.803
is equal to pKw.
00:08:07.340 --> 00:08:11.340
At 25 degrees Celsius, Kw is equal to 1.0
00:08:11.340 --> 00:08:13.760
times 10 to the negative 14.
00:08:13.760 --> 00:08:18.550
Therefore the negative log of
Kw is the negative log of 1.0
00:08:18.550 --> 00:08:23.403
times 10 to the negative
14 which is equal to 14.00.
00:08:26.420 --> 00:08:29.297
So we can plug in 14.00 in for pKw
00:08:31.880 --> 00:08:34.700
which gives us a very useful equation
00:08:34.700 --> 00:08:39.700
that says that the pH plus
the pOH is equal to 14.00.
00:08:42.430 --> 00:08:44.550
And this equation is true
00:08:44.550 --> 00:08:47.653
when the temperature
is 25 degrees Celsius.
|
Autoionization of water | https://www.youtube.com/watch?v=vt6WjF1O_08 | vtt | https://www.youtube.com/api/timedtext?v=vt6WjF1O_08&ei=11WUZcPvJ86ep-oPirSHqAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245319&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D99A612A8F1FEA3963AE35493F4F14A3D8BB7409.BCF144349C5522220C7A130BF39E2F476B664688&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.150 --> 00:00:02.610
- [Instructor] The
autoionization of water refers
00:00:02.610 --> 00:00:06.130
to the reaction of water
molecules to form two ions,
00:00:06.130 --> 00:00:08.860
the hydronium ion, which is H3O+,
00:00:08.860 --> 00:00:11.237
and the hydroxide ion, which is OH-.
00:00:12.290 --> 00:00:14.810
Water can function as an acid or a base,
00:00:14.810 --> 00:00:15.930
and in this reaction,
00:00:15.930 --> 00:00:19.330
one water molecule functions
as a Bronsted-Lowry acid
00:00:19.330 --> 00:00:21.070
and donates a proton
00:00:21.070 --> 00:00:23.370
and another water molecule functions
00:00:23.370 --> 00:00:25.330
as a Bronsted-Lowry base
00:00:25.330 --> 00:00:27.640
and accepts a proton.
00:00:27.640 --> 00:00:28.473
In the reaction,
00:00:28.473 --> 00:00:32.160
the base takes an H+ ion from the acid
00:00:32.160 --> 00:00:36.180
and these two electrons are
left behind on this oxygen.
00:00:36.180 --> 00:00:40.963
Adding an H+ to H2O gives
the hydronium ion H3O+,
00:00:40.963 --> 00:00:45.963
and taking away an H+ from H2O
gives the hydroxide ion OH-.
00:00:46.700 --> 00:00:49.510
We can write an equilibrium
constant expression
00:00:49.510 --> 00:00:50.940
for this reaction.
00:00:50.940 --> 00:00:55.120
So we would write the equilibrium
constant K is equal to,
00:00:55.120 --> 00:00:56.490
we would start with our products.
00:00:56.490 --> 00:00:59.700
We'd have the concentration
of hydronium ions.
00:00:59.700 --> 00:01:03.900
And since we have a coefficient
of one in front of hydronium
00:01:03.900 --> 00:01:05.070
in the balanced equation,
00:01:05.070 --> 00:01:07.050
it'd be the concentration
of hydronium ions
00:01:07.050 --> 00:01:08.730
raised to the first power
00:01:08.730 --> 00:01:12.620
times the concentration of hydroxide ions.
00:01:12.620 --> 00:01:14.360
And once again, there's
a coefficient of one,
00:01:14.360 --> 00:01:15.390
the balanced equation.
00:01:15.390 --> 00:01:17.470
So it's the concentration
of hydroxide ions
00:01:17.470 --> 00:01:19.060
raised to the first power.
00:01:19.060 --> 00:01:20.250
For the reactants,
00:01:20.250 --> 00:01:21.470
liquid water is left out
00:01:21.470 --> 00:01:23.930
of the equilibrium constant expression.
00:01:23.930 --> 00:01:25.900
Normally we would write KC,
00:01:25.900 --> 00:01:27.780
where the C stands for concentration
00:01:27.780 --> 00:01:29.380
for the equilibrium constant,
00:01:29.380 --> 00:01:31.460
since we're dealing with concentrations.
00:01:31.460 --> 00:01:34.710
However, this is a special
equilibrium constant expression
00:01:34.710 --> 00:01:36.850
for the autoionization of water,
00:01:36.850 --> 00:01:38.410
so instead of writing KC,
00:01:38.410 --> 00:01:39.770
we're gonna write KW,
00:01:39.770 --> 00:01:42.190
where W stands for water.
00:01:42.190 --> 00:01:45.660
KW is equal to 1.0 times
10 to the negative 14
00:01:45.660 --> 00:01:47.730
at 25 degrees Celsius,
00:01:47.730 --> 00:01:50.500
And with such a low value for KW,
00:01:50.500 --> 00:01:52.710
so this value is much less than one,
00:01:52.710 --> 00:01:54.560
that tells us at equilibrium,
00:01:54.560 --> 00:01:57.600
we have an extremely small
concentration of hydronium
00:01:57.600 --> 00:02:00.000
and hydroxide ions.
00:02:00.000 --> 00:02:05.000
So mostly we have H2O
molecules at equilibrium.
00:02:05.070 --> 00:02:06.799
Let's go ahead and solve
for the concentration
00:02:06.799 --> 00:02:10.670
of hydronium ions and
hydroxide ions at equilibrium.
00:02:10.670 --> 00:02:11.740
In the balanced equation,
00:02:11.740 --> 00:02:12.960
there's a coefficient of one
00:02:12.960 --> 00:02:15.710
in front of both hydronium and hydroxide.
00:02:15.710 --> 00:02:17.450
Therefore, at equilibrium,
00:02:17.450 --> 00:02:20.280
these two concentrations are equal.
00:02:20.280 --> 00:02:22.840
Since we don't know what
those concentrations are,
00:02:22.840 --> 00:02:25.900
we're gonna represent
it by writing in here X.
00:02:25.900 --> 00:02:30.900
So this would be X times X is equal to 1.0
00:02:31.060 --> 00:02:34.090
times 10 to the negative 14.
00:02:34.090 --> 00:02:37.709
So we would have X squared is equal to 1.0
00:02:37.709 --> 00:02:40.250
times 10 to the negative 14.
00:02:40.250 --> 00:02:43.760
And taking the square root of both sides,
00:02:43.760 --> 00:02:47.380
we would find that X is equal to 1.0
00:02:47.380 --> 00:02:50.840
times 10 to the negative seven.
00:02:50.840 --> 00:02:52.860
Therefore, if we had
a sample of pure water
00:02:52.860 --> 00:02:55.000
at 25 degrees Celsius,
00:02:55.000 --> 00:02:56.980
the concentration of hydronium ions
00:02:56.980 --> 00:02:58.794
and the concentration of hydroxide ions
00:02:58.794 --> 00:03:00.329
would be equal to 1.0
00:03:00.329 --> 00:03:03.023
times 10 to the negative seventh molar.
00:03:04.080 --> 00:03:05.860
Instead of using two water molecules
00:03:05.860 --> 00:03:08.580
to show the autoionization of water,
00:03:08.580 --> 00:03:12.880
it's also possible to show it
using only one water molecule.
00:03:12.880 --> 00:03:16.717
So H2O could break up to form H+ and OH-.
00:03:18.235 --> 00:03:20.840
So H+, which is the hydrogen ion,
00:03:20.840 --> 00:03:24.360
is sometimes used
interchangeably with H3O+,
00:03:24.360 --> 00:03:26.630
which is the hydronium ion.
00:03:26.630 --> 00:03:28.920
We've just seen that pure
water has a concentration
00:03:28.920 --> 00:03:31.460
of hydronium ions equal
to the concentration
00:03:31.460 --> 00:03:33.160
of hydroxide ions.
00:03:33.160 --> 00:03:36.620
Therefore, pure water
is a neutral substance,
00:03:36.620 --> 00:03:39.280
and for any aqueous solution
where the concentration
00:03:39.280 --> 00:03:40.450
of hydronium ion is equal
00:03:40.450 --> 00:03:42.650
to the concentration of hydroxide ion,
00:03:42.650 --> 00:03:45.690
we would classify that
as a neutral solution.
00:03:45.690 --> 00:03:47.810
If an aqueous solution has a concentration
00:03:47.810 --> 00:03:50.153
of hydronium ions that's
greater than the concentration
00:03:50.153 --> 00:03:51.970
of hydroxide ions,
00:03:51.970 --> 00:03:55.830
we would classify the solution
as an acidic solution.
00:03:55.830 --> 00:03:57.970
And if an aqueous solution
has a concentration
00:03:57.970 --> 00:04:00.510
of hydronium ions that's
less than the concentration
00:04:00.510 --> 00:04:01.760
of hydroxide ions,
00:04:01.760 --> 00:04:03.930
or you could say the
concentration of hydroxide ions
00:04:03.930 --> 00:04:05.900
is greater than that of hydronium,
00:04:05.900 --> 00:04:09.210
the solution would be
considered a basic solution.
00:04:09.210 --> 00:04:11.560
In the equation that we've
already talked about,
00:04:11.560 --> 00:04:13.290
the concentration of hydronium ions
00:04:13.290 --> 00:04:15.210
times the concentration of hydroxide ions
00:04:15.210 --> 00:04:16.680
is equal to KW,
00:04:16.680 --> 00:04:20.070
which is equal to 1.0
times 10 to the negative 14
00:04:20.070 --> 00:04:22.400
at 25 degrees Celsius.
00:04:22.400 --> 00:04:24.150
This equation is true
00:04:24.150 --> 00:04:25.870
if you're dealing with an acidic solution,
00:04:25.870 --> 00:04:27.370
a neutral solution,
00:04:27.370 --> 00:04:29.090
or a basic solution.
00:04:29.090 --> 00:04:33.550
And I'll call this equation
the KW equation from now on.
00:04:33.550 --> 00:04:35.430
Let's say we have an aqueous solution
00:04:35.430 --> 00:04:38.240
and the concentration of
hydronium ions in the solution
00:04:38.240 --> 00:04:41.470
is equal to 4.0 times 10
to the negative six molar
00:04:41.470 --> 00:04:43.470
at 25 degrees Celsius,
00:04:43.470 --> 00:04:45.730
and our goal is to
calculate the concentration
00:04:45.730 --> 00:04:50.370
of hydroxide ions in the
solution at 25 degrees Celsius.
00:04:50.370 --> 00:04:52.960
To solve for the concentration
of hydroxide ion,
00:04:52.960 --> 00:04:56.250
we can use our KW equation.
00:04:56.250 --> 00:04:58.760
So we need to plug in
for the concentration
00:04:58.760 --> 00:05:00.940
of hydronium ion.
00:05:00.940 --> 00:05:05.940
So that gives us 4.0 times
10 to the negative six
00:05:06.030 --> 00:05:08.140
times the concentration of hydroxide ion,
00:05:08.140 --> 00:05:10.100
which we'll just go ahead and make X here,
00:05:10.100 --> 00:05:11.940
and all that's equal to KW,
00:05:11.940 --> 00:05:16.140
which is equal to 1.0 times
10 to the negative 14.
00:05:16.140 --> 00:05:17.300
Solving for X,
00:05:17.300 --> 00:05:22.300
we find the X is equal to 2.5
times 10 to the negative nine.
00:05:23.350 --> 00:05:27.770
And since X is equal to the
concentration of hydroxide ion,
00:05:27.770 --> 00:05:30.570
the concentration of
hydroxide ion is equal to 2.5
00:05:30.570 --> 00:05:33.350
times 10 to the negative ninth molar.
00:05:33.350 --> 00:05:34.810
For this aqueous solution,
00:05:34.810 --> 00:05:38.560
the concentration of
hydronium ion is greater
00:05:38.560 --> 00:05:42.150
than the concentration of hydroxide ion.
00:05:42.150 --> 00:05:45.180
Therefore, this is an acidic solution.
00:05:45.180 --> 00:05:46.510
So let me go ahead and write that in here.
00:05:46.510 --> 00:05:49.210
This is an acidic solution.
00:05:49.210 --> 00:05:51.380
An equilibrium constant is only constant
00:05:51.380 --> 00:05:52.990
at a specific temperature.
00:05:52.990 --> 00:05:55.690
For example, at 25 degrees Celsius,
00:05:55.690 --> 00:05:59.750
KW is equal to 1.0 times
10 to the negative 14.
00:05:59.750 --> 00:06:01.130
But if you change the temperature,
00:06:01.130 --> 00:06:03.530
you change the value for KW.
00:06:03.530 --> 00:06:05.000
At 50 degrees Celsius,
00:06:05.000 --> 00:06:09.310
KW is equal to 5.5 times
10 to the negative 14.
00:06:09.310 --> 00:06:12.340
So an increase in temperature
from 25 degrees Celsius
00:06:12.340 --> 00:06:15.840
to 50 degrees Celsius causes an increase
00:06:15.840 --> 00:06:18.480
in the value for KW.
00:06:18.480 --> 00:06:23.480
So increase in temperature
causes an increase in KW.
00:06:23.650 --> 00:06:26.210
And we can use Le Chatelier's
principle to predict
00:06:26.210 --> 00:06:29.730
if the autoionization of water
is an endothermic reaction
00:06:29.730 --> 00:06:31.900
or an exothermic reaction.
00:06:31.900 --> 00:06:35.360
An increase in KW means
an increased concentration
00:06:35.360 --> 00:06:39.240
of hydronium ion and
hydroxide ion at equilibrium.
00:06:39.240 --> 00:06:42.610
Therefore, the net reaction
must have gone to the right
00:06:42.610 --> 00:06:45.730
to increase the amount of our products.
00:06:45.730 --> 00:06:48.440
And if we treat heat as a reactant
00:06:49.400 --> 00:06:51.080
and we increase the temperature,
00:06:51.080 --> 00:06:52.360
it's as if we've increased
00:06:52.360 --> 00:06:54.420
the amount of one of our reactants.
00:06:54.420 --> 00:06:57.450
Therefore, according to
Le Chatelier's principle,
00:06:57.450 --> 00:06:59.740
the net reaction is
gonna shift to the right
00:06:59.740 --> 00:07:01.550
to make more of the product.
00:07:01.550 --> 00:07:02.850
Since that's what we observed
00:07:02.850 --> 00:07:04.700
by increasing the value for KW,
00:07:04.700 --> 00:07:06.990
we know that the autoionization of water
00:07:06.990 --> 00:07:09.840
is an endothermic reaction.
00:07:09.840 --> 00:07:11.610
If we had put heat on the product side
00:07:11.610 --> 00:07:14.090
and treated this like
an exothermic reaction,
00:07:14.090 --> 00:07:16.350
we would've gotten a shift
in the wrong direction.
00:07:16.350 --> 00:07:17.950
We would've got a shift back to the left.
00:07:17.950 --> 00:07:20.450
So we know it's not exothermic.
00:07:20.450 --> 00:07:23.510
Finally, let's calculate the
concentration of hydronium ions
00:07:23.510 --> 00:07:27.530
and hydroxide ions in
a sample of pure water
00:07:27.530 --> 00:07:29.940
at 50 degrees Celsius.
00:07:29.940 --> 00:07:32.070
We can still use the KW equation.
00:07:32.070 --> 00:07:34.810
So KW is equal to the
concentration of hydronium ions
00:07:34.810 --> 00:07:37.270
times the concentration of hydroxide ions.
00:07:37.270 --> 00:07:40.680
However, since the temperature
is now 50 degrees Celsius,
00:07:40.680 --> 00:07:43.980
we can't use 1.0 times
10 to the negative 14
00:07:43.980 --> 00:07:46.770
because that's the KW
at 25 degrees Celsius.
00:07:46.770 --> 00:07:49.500
We need to use the KW
at 50 degrees Celsius,
00:07:49.500 --> 00:07:52.970
which is 5.5 times 10 to the negative 14.
00:07:52.970 --> 00:07:54.540
For the autoionization of water,
00:07:54.540 --> 00:07:56.070
the mole ratio of hydronium ion
00:07:56.070 --> 00:07:58.400
to hydroxide ion is one-to-one.
00:07:58.400 --> 00:08:00.520
Therefore the concentration
of hydronium ion
00:08:00.520 --> 00:08:03.490
is equal to the concentration
of hydroxide ion.
00:08:03.490 --> 00:08:05.330
So when we plug in for hydronium,
00:08:05.330 --> 00:08:07.090
if we say that concentration is X,
00:08:07.090 --> 00:08:09.790
then the concentration of
hydroxide would also be X.
00:08:09.790 --> 00:08:12.510
So we have X times X is equal to KW,
00:08:12.510 --> 00:08:15.923
which is equal to 5.5 times
10 to the negative 14.
00:08:16.800 --> 00:08:21.800
So X squared is equal to 5.5
times 10 to the negative 14.
00:08:21.900 --> 00:08:23.230
And to solve for X,
00:08:23.230 --> 00:08:26.980
we simply take the square
root of both sides.
00:08:26.980 --> 00:08:31.980
So X is equal to 2.3 times
10 to the negative seven.
00:08:33.510 --> 00:08:35.550
So the concentration of hydronium ions
00:08:35.550 --> 00:08:38.460
is equal to the concentration
of hydroxide ions,
00:08:38.460 --> 00:08:42.100
which is 2.3 times 10 to
the negative seventh molar.
00:08:42.100 --> 00:08:44.640
Notice that this is a higher concentration
00:08:44.640 --> 00:08:47.040
than we got at 25 degrees Celsius,
00:08:47.040 --> 00:08:50.680
which makes sense because the
value for KW has increased.
00:08:50.680 --> 00:08:52.598
However, since the
concentration of hydronium
00:08:52.598 --> 00:08:57.598
is still equal to the
concentration of hydroxide ions,
00:08:58.140 --> 00:09:00.303
pure water is still neutral.
|
Digital and analog information | https://www.youtube.com/watch?v=oSZNQ1LZjHg | vtt | https://www.youtube.com/api/timedtext?v=oSZNQ1LZjHg&ei=2FWUZfb5AYSBp-oPjNyg2AE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245320&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=3C4390B7D830754D0B9F1A1B889364CAEA38B601.9C27CA9A8D3FBA4A5F22CDC26E7B4993921721E2&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:01.640
- [Instructor] In this
video, we're going to talk
00:00:01.640 --> 00:00:04.050
about analog versus digital.
00:00:04.050 --> 00:00:06.300
Something that's analog can be any value
00:00:06.300 --> 00:00:08.940
within a given range
while something digital
00:00:08.940 --> 00:00:13.070
is represented by a number of
discreet or separate levels.
00:00:13.070 --> 00:00:14.390
To distinguish these two ideas,
00:00:14.390 --> 00:00:16.320
I like to think about clocks.
00:00:16.320 --> 00:00:18.550
An analog clock has the
numbers in the hands
00:00:18.550 --> 00:00:20.400
and it's analog because the motion
00:00:20.400 --> 00:00:22.430
of those hands is continuous.
00:00:22.430 --> 00:00:23.950
They can sweep across the circle
00:00:23.950 --> 00:00:27.530
representing any of infinite
times on that clock.
00:00:27.530 --> 00:00:30.140
For example, between 3:06 and 3:07,
00:00:30.140 --> 00:00:32.250
the minute hand is actually
going to be at some point
00:00:32.250 --> 00:00:34.290
between those marks on the clock
00:00:34.290 --> 00:00:36.520
showing one of the
infinitely possible times
00:00:36.520 --> 00:00:38.280
that the clock can represent.
00:00:38.280 --> 00:00:40.460
Compare that to a digital clock.
00:00:40.460 --> 00:00:44.530
A digital clock is only going
to show you 3:06 or 3:07.
00:00:44.530 --> 00:00:47.600
It will never display any of
the many fractional seconds
00:00:47.600 --> 00:00:49.330
between those two times.
00:00:49.330 --> 00:00:52.440
Digital only takes on
certain discrete values
00:00:52.440 --> 00:00:55.520
and it has a finite
number of those values.
00:00:55.520 --> 00:00:58.190
So an analog wave or
signal will smoothly sweep
00:00:58.190 --> 00:01:01.300
across the infinitely many
possible values it has
00:01:01.300 --> 00:01:02.960
while a digital wave or signal
00:01:02.960 --> 00:01:05.870
will only be at one of a
number of discrete values.
00:01:05.870 --> 00:01:09.560
So the shape of the wave will
be more square or step like.
00:01:09.560 --> 00:01:10.520
Let's check out an example
00:01:10.520 --> 00:01:12.290
so this makes a little more sense.
00:01:12.290 --> 00:01:13.440
I like music.
00:01:13.440 --> 00:01:15.410
So we're gonna talk about sound.
00:01:15.410 --> 00:01:18.270
Sound is an analog signal or wave.
00:01:18.270 --> 00:01:21.120
So if we look at a graph
of sound, volume over time,
00:01:21.120 --> 00:01:24.750
it's going to have a smooth
continuous analog wave form,
00:01:24.750 --> 00:01:28.140
both the amplitude or the
volume, and the frequency,
00:01:28.140 --> 00:01:31.340
what we hear as pitch
are changing continuously
00:01:31.340 --> 00:01:33.490
between infinite possible values.
00:01:33.490 --> 00:01:35.460
All right, and that's because sound waves,
00:01:35.460 --> 00:01:38.390
the vibration of particles
propagating through the air
00:01:38.390 --> 00:01:40.550
actually changes continuously.
00:01:40.550 --> 00:01:43.300
The very first sound recording
and reproduction technology
00:01:43.300 --> 00:01:46.690
imprinted that analog wave
directly onto a material.
00:01:46.690 --> 00:01:50.260
For example, records imprint
that sound wave into vinyl
00:01:50.260 --> 00:01:53.780
and cassettes imprint
the sound wave onto tape.
00:01:53.780 --> 00:01:55.790
A major drawback of this technology
00:01:55.790 --> 00:01:59.190
is after the sound to play back
exactly as it was recorded,
00:01:59.190 --> 00:02:02.100
that wave form needs to
stay untouched, right?
00:02:02.100 --> 00:02:05.700
So think about scratching vinyl
or smudging a cassette tape,
00:02:05.700 --> 00:02:07.940
that's directly deforming the wave.
00:02:07.940 --> 00:02:10.080
So you'll never be able
to reproduce the sound
00:02:10.080 --> 00:02:11.920
exactly as it was recorded.
00:02:11.920 --> 00:02:16.020
So, technology advanced and
sound waves became digitized.
00:02:16.020 --> 00:02:16.853
Here's how.
00:02:17.850 --> 00:02:20.050
All right, so recall
our analog sound wave.
00:02:20.050 --> 00:02:22.980
We have a smooth analog wave
that's taking on any number
00:02:22.980 --> 00:02:25.700
of infinitely possible
values within this range.
00:02:25.700 --> 00:02:27.880
In order to digitize this wave,
00:02:27.880 --> 00:02:30.510
we're going to ascribe
numbers to the amplitude
00:02:30.510 --> 00:02:32.280
at different points, all right?
00:02:32.280 --> 00:02:33.740
Watch this magic.
00:02:33.740 --> 00:02:35.200
So we go over here and make a scale.
00:02:35.200 --> 00:02:36.780
So we're breaking up the amplitudes
00:02:36.780 --> 00:02:39.170
into discrete possibilities.
00:02:39.170 --> 00:02:41.810
Then we can go through the
wave and at specific points
00:02:41.810 --> 00:02:44.550
of the wave measure what is the amplitude
00:02:44.550 --> 00:02:46.010
based on that scale.
00:02:46.010 --> 00:02:48.470
So over here, we're at the
first point of the scale.
00:02:48.470 --> 00:02:51.120
At this peak, we're at the
second point of our scale.
00:02:51.120 --> 00:02:55.200
Then the first, the third,
the second, the fourth,
00:02:55.200 --> 00:02:56.483
back down to the first.
00:02:57.370 --> 00:03:00.020
Now that we have this way
broken up into levels, right?
00:03:00.020 --> 00:03:02.450
We can ascribe the
numbers and we effectively
00:03:02.450 --> 00:03:05.730
turn this analog wave
into a set of numbers,
00:03:05.730 --> 00:03:09.740
one, two, one, three, two, four, one.
00:03:09.740 --> 00:03:12.083
Our wave has been digitized.
00:03:12.930 --> 00:03:15.310
Now that digitize wave can be played back
00:03:15.310 --> 00:03:18.350
through a speaker to
recreate the analog wave.
00:03:18.350 --> 00:03:20.980
As long as the sampling
happens at a quick enough rate,
00:03:20.980 --> 00:03:22.950
humans can't tell the difference.
00:03:22.950 --> 00:03:24.650
All right, so the digitization of waves
00:03:24.650 --> 00:03:27.200
is all about ascribing specific numbers
00:03:27.200 --> 00:03:30.130
to some of those mechanical
properties of the wave.
00:03:30.130 --> 00:03:32.270
The important thing here
is that now that the wave
00:03:32.270 --> 00:03:34.890
has been digitized, the
digitized sound wave
00:03:34.890 --> 00:03:37.320
can be reliably stored, processed,
00:03:37.320 --> 00:03:39.550
and communicated with computers.
00:03:39.550 --> 00:03:41.830
So some information is
lost in translation,
00:03:41.830 --> 00:03:43.790
but once the wave is digitized,
00:03:43.790 --> 00:03:46.470
it's quality will never degrade, okay?
00:03:46.470 --> 00:03:49.300
And that allows for a lot
more reliable technology
00:03:49.300 --> 00:03:51.220
because the wave is
represented with numbers
00:03:51.220 --> 00:03:54.670
instead of it being physically
imprinted on some material.
00:03:54.670 --> 00:03:58.200
So humans prefer to store
information like sound digitally,
00:03:58.200 --> 00:04:00.720
and there are ways to turn analog signals,
00:04:00.720 --> 00:04:03.250
which can represent any of
infinite possible values
00:04:03.250 --> 00:04:05.100
into digital information,
00:04:05.100 --> 00:04:07.220
which is useful because
information is stored
00:04:07.220 --> 00:04:10.353
only at a number of
discreet or separate levels.
|
Wave properties | https://www.youtube.com/watch?v=ClHuscLyuLo | vtt | https://www.youtube.com/api/timedtext?v=ClHuscLyuLo&ei=2FWUZbufGq_pxN8P7qmqgAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245320&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=4EC120D44763EF1F372F64043FCFBDFCA4F9D553.44A557D956CE7E35C1A440D467B2DB02F4DE4127&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.890 --> 00:00:02.080
- [Instructor] Imagine
that I'm standing here
00:00:02.080 --> 00:00:03.640
holding the end of a rope.
00:00:03.640 --> 00:00:05.980
I'm over here on the left end,
and while holding the rope,
00:00:05.980 --> 00:00:08.610
I rapidly moved my hand up, down,
00:00:08.610 --> 00:00:10.820
and back to the starting position.
00:00:10.820 --> 00:00:12.700
If we were to take a snapshot of the rope
00:00:12.700 --> 00:00:15.150
immediately after I finished my motion,
00:00:15.150 --> 00:00:17.220
we're going to see something like this.
00:00:17.220 --> 00:00:19.220
The rope has a squiggly disturbance
00:00:19.220 --> 00:00:21.880
that mirrors the motion
I made with my hand,
00:00:21.880 --> 00:00:24.780
up, down, and back to the middle.
00:00:24.780 --> 00:00:27.340
And the rest of the rope is still flat.
00:00:27.340 --> 00:00:28.580
You might've seen something like this
00:00:28.580 --> 00:00:30.080
if you've ever played with a jump rope
00:00:30.080 --> 00:00:31.770
and wiggled it back and forth,
00:00:31.770 --> 00:00:33.900
or a slinky and you've seen that oscillate
00:00:33.900 --> 00:00:35.340
back and forth on the ground,
00:00:35.340 --> 00:00:36.530
or if you've been in the gym
00:00:36.530 --> 00:00:39.520
and seen somebody doing exercises
with large battle ropes,
00:00:39.520 --> 00:00:42.350
slamming them up and down repeatedly.
00:00:42.350 --> 00:00:44.360
And we know that over
time, this disturbance
00:00:44.360 --> 00:00:47.340
is actually going to make
its way through the rope.
00:00:47.340 --> 00:00:49.980
If this is what we observe
right after my hand motion,
00:00:49.980 --> 00:00:51.410
at some later point in time,
00:00:51.410 --> 00:00:53.040
we will observe that the
beginning of the rope
00:00:53.040 --> 00:00:56.170
is back to its original shape,
the squiggly disturbance
00:00:56.170 --> 00:00:58.420
has made its way further down the rope,
00:00:58.420 --> 00:01:00.150
and it will keep traveling
in this direction
00:01:00.150 --> 00:01:02.510
until it reaches the end of the rope.
00:01:02.510 --> 00:01:05.630
This is exactly what a wave is in physics.
00:01:05.630 --> 00:01:08.110
A wave is a disturbance, in this case,
00:01:08.110 --> 00:01:10.870
the squiggle in the rope
caused by my hand motion,
00:01:10.870 --> 00:01:12.960
and that disturbance can propagate,
00:01:12.960 --> 00:01:16.300
it can travel or move in
a particular direction.
00:01:16.300 --> 00:01:19.773
So a wave is a disturbance
that can propagate.
00:01:20.970 --> 00:01:24.210
This particular example is
called a mechanical wave.
00:01:24.210 --> 00:01:26.180
It's called a mechanical
wave because the disturbance
00:01:26.180 --> 00:01:29.440
is traveling through a medium,
in this case, the rope.
00:01:29.440 --> 00:01:31.783
So mechanical waves
travel through a medium.
00:01:32.670 --> 00:01:34.300
One important point about waves
00:01:34.300 --> 00:01:36.130
that is worth noting right now
00:01:36.130 --> 00:01:40.340
is that waves transfer energy
without transferring matter.
00:01:40.340 --> 00:01:41.173
So what that means
00:01:41.173 --> 00:01:42.720
is that the disturbance
that is moving here,
00:01:42.720 --> 00:01:45.450
this squiggly shape is
moving through the rope,
00:01:45.450 --> 00:01:48.580
but it isn't moving the rope
to a different position.
00:01:48.580 --> 00:01:50.280
Any part of the rope might go up and down
00:01:50.280 --> 00:01:52.530
as the wave travels through that section,
00:01:52.530 --> 00:01:55.340
but the rope itself is not going anywhere,
00:01:55.340 --> 00:01:57.020
rather it's the kinetic energy
00:01:57.020 --> 00:01:59.230
imparted to the rope by my hand
00:01:59.230 --> 00:02:01.680
that is transferring
from particle to particle
00:02:01.680 --> 00:02:03.800
and making its way through the rope.
00:02:03.800 --> 00:02:07.703
So waves transfer energy, but not matter.
00:02:09.510 --> 00:02:10.470
So in my first example,
00:02:10.470 --> 00:02:12.600
I only jerked my hand up and down once,
00:02:12.600 --> 00:02:14.290
which created a single wave pulse
00:02:14.290 --> 00:02:16.040
that moved through my rope.
00:02:16.040 --> 00:02:18.250
If instead, I were to keep moving my hand
00:02:18.250 --> 00:02:19.900
up and down consistently,
00:02:19.900 --> 00:02:22.660
I would see a wave form that
looks something like this.
00:02:22.660 --> 00:02:24.210
And when we model a wave,
00:02:24.210 --> 00:02:26.730
there are a few key characteristics
that we need to know
00:02:26.730 --> 00:02:28.180
about that wave.
00:02:28.180 --> 00:02:30.270
First is the period.
00:02:30.270 --> 00:02:32.710
Period is measured in
seconds and it tells us
00:02:32.710 --> 00:02:35.523
how long it takes for one
wave cycle to complete.
00:02:36.400 --> 00:02:37.930
Next is the wavelength.
00:02:37.930 --> 00:02:40.430
Measured in units of distance like meters,
00:02:40.430 --> 00:02:43.440
the wavelength is the distance
between identical points
00:02:43.440 --> 00:02:45.290
of adjacent waves.
00:02:45.290 --> 00:02:47.520
And finally there's frequency.
00:02:47.520 --> 00:02:50.650
So if the wave point that we've
drawn here takes one second,
00:02:50.650 --> 00:02:53.080
there are four cycles in that one second,
00:02:53.080 --> 00:02:55.610
that means it has a frequency of 4hz
00:02:55.610 --> 00:02:57.870
or four cycles per second.
00:02:57.870 --> 00:03:00.930
So the frequency measured
in cycles per second
00:03:00.930 --> 00:03:03.963
tells us how many wave cycles
there are every second.
00:03:05.130 --> 00:03:08.870
Now using just these basic
anatomical properties of a wave,
00:03:08.870 --> 00:03:09.703
we can start to pick out
00:03:09.703 --> 00:03:11.770
more interesting physical characteristics,
00:03:11.770 --> 00:03:14.980
like speed or distance over time.
00:03:14.980 --> 00:03:17.370
If we want to know how
fast a wave is traveling,
00:03:17.370 --> 00:03:18.960
we can take its wavelength,
00:03:18.960 --> 00:03:21.590
which is the distance
covered by a single cycle,
00:03:21.590 --> 00:03:23.770
and multiply that by the frequency,
00:03:23.770 --> 00:03:26.870
which is how many cycles
are completed in a second,
00:03:26.870 --> 00:03:28.560
a given amount of time.
00:03:28.560 --> 00:03:29.770
The cycles cancel out
00:03:29.770 --> 00:03:32.010
and we're left with units
of distance over time,
00:03:32.010 --> 00:03:33.630
the same as speed.
00:03:33.630 --> 00:03:35.860
And that's our equation
for the speed of the wave.
00:03:35.860 --> 00:03:38.660
Wavelength times frequency.
00:03:38.660 --> 00:03:41.210
The standard units for
speed are meters per second.
00:03:42.430 --> 00:03:43.263
There are a couple of factors
00:03:43.263 --> 00:03:45.330
that can affect the speed of a wave.
00:03:45.330 --> 00:03:47.230
The first is the wave type.
00:03:47.230 --> 00:03:50.370
So different types of waves
move at different speeds.
00:03:50.370 --> 00:03:52.210
A relatable example of different waves
00:03:52.210 --> 00:03:54.430
moving at different speeds is lightning.
00:03:54.430 --> 00:03:55.710
Have you ever seen lightning strike
00:03:55.710 --> 00:03:57.160
or been in a thunderstorm?
00:03:57.160 --> 00:03:58.680
You know that the first thing you see
00:03:58.680 --> 00:04:01.880
is the flash of lightning,
and then you hear the thunder
00:04:01.880 --> 00:04:04.800
associated with that lightning flash.
00:04:04.800 --> 00:04:07.723
So the lightning comes first
and the thunder comes second.
00:04:08.610 --> 00:04:10.330
That's because those
are two different waves
00:04:10.330 --> 00:04:12.380
that are part of the same phenomenon.
00:04:12.380 --> 00:04:15.170
When the lightning strike
hits, you see the flash first
00:04:15.170 --> 00:04:18.220
because that's an
electromagnetic wave, light.
00:04:18.220 --> 00:04:19.590
It travels much faster
00:04:19.590 --> 00:04:22.770
than the sound associated
with the lightning strike.
00:04:22.770 --> 00:04:24.370
Electromagnetic waves are special
00:04:24.370 --> 00:04:26.800
not only because they travel really fast,
00:04:26.800 --> 00:04:29.930
but they also don't need a
medium to travel through.
00:04:29.930 --> 00:04:32.390
The thunder on the other
hand is a sound wave
00:04:32.390 --> 00:04:34.260
traveling slower than the light.
00:04:34.260 --> 00:04:37.900
So you'll see the lightning
before you hear the thunder.
00:04:37.900 --> 00:04:40.993
Different wave types
move at different speeds.
00:04:42.180 --> 00:04:44.860
The second key factor that
can affect the speed of a wave
00:04:44.860 --> 00:04:47.620
is the medium through
which the wave travels
00:04:47.620 --> 00:04:50.240
and we'll consider sound
as an example here.
00:04:50.240 --> 00:04:51.610
So when someone is talking, right,
00:04:51.610 --> 00:04:53.770
we have this talking head
creating some vibrations
00:04:53.770 --> 00:04:55.430
of the particles in front of their mouth,
00:04:55.430 --> 00:04:56.770
that's the sound wave.
00:04:56.770 --> 00:04:58.680
It's the vibration of those particles
00:04:58.680 --> 00:05:00.500
propagating through the air.
00:05:00.500 --> 00:05:03.520
When you speak, your
vocal cords exert force
00:05:03.520 --> 00:05:05.610
on the particles just in front of you.
00:05:05.610 --> 00:05:08.710
They vibrate back and forth,
creating a compression
00:05:08.710 --> 00:05:11.630
that transfers to the
surrounding particles.
00:05:11.630 --> 00:05:15.580
As the vibrations continue to
propagate, the sound travels.
00:05:15.580 --> 00:05:16.760
You can imagine
00:05:16.760 --> 00:05:19.470
that if these particles
are packed closer together,
00:05:19.470 --> 00:05:22.640
those vibrations are going to
transfer a lot more quickly
00:05:22.640 --> 00:05:24.680
because the particles
are colliding much faster
00:05:24.680 --> 00:05:26.420
than if they're further apart.
00:05:26.420 --> 00:05:30.000
So sound travels much
faster in water, a liquid,
00:05:30.000 --> 00:05:32.860
than it does in air,
for that exact reason.
00:05:32.860 --> 00:05:35.630
The particles in the
liquid are closer together.
00:05:35.630 --> 00:05:38.380
Since they're closer
compacted, they collide more,
00:05:38.380 --> 00:05:41.530
and the propagation of
the wave happens faster.
00:05:41.530 --> 00:05:43.750
So different ways move at different speeds
00:05:43.750 --> 00:05:46.160
and the medium through
which a wave travels
00:05:46.160 --> 00:05:48.123
can also affect the speed of a wave.
00:05:49.300 --> 00:05:51.630
All right, so let's try to
summarize all this information.
00:05:51.630 --> 00:05:55.490
We have waves, a wave, a
disturbance that can propagate,
00:05:55.490 --> 00:05:57.930
and it has a few key characteristics.
00:05:57.930 --> 00:05:59.120
There's the period
00:05:59.120 --> 00:06:01.520
or how long it takes
one cycle to complete,
00:06:01.520 --> 00:06:02.830
there's the wavelength,
00:06:02.830 --> 00:06:04.710
the distance between identical points
00:06:04.710 --> 00:06:07.170
on two waves that are next to each other,
00:06:07.170 --> 00:06:08.740
and the frequency,
00:06:08.740 --> 00:06:11.860
which is how many waves
cycles complete in one second.
00:06:11.860 --> 00:06:14.590
In this case, we have
two cycles in one second
00:06:14.590 --> 00:06:15.917
for a frequency of 2hz.
00:06:17.170 --> 00:06:20.750
Wave speed is found by multiplying
wavelength and frequency,
00:06:20.750 --> 00:06:23.800
and that wave speed is
affected by the type of wave
00:06:23.800 --> 00:06:26.660
and the medium through
which the wave travels.
00:06:26.660 --> 00:06:29.150
Mechanical waves are ways
that travel through a medium,
00:06:29.150 --> 00:06:33.270
so sound, a slinky or rope, ocean waves,
00:06:33.270 --> 00:06:36.440
and electromagnetic waves
like light are special
00:06:36.440 --> 00:06:38.680
because they can travel through a vacuum.
00:06:38.680 --> 00:06:42.050
They don't have to have a
medium in order to propagate.
00:06:42.050 --> 00:06:44.440
But all waves, no matter what type,
00:06:44.440 --> 00:06:47.313
transfer energy, not matter.
|
Calculating height using energy | https://www.youtube.com/watch?v=PElpJbRxJgc | vtt | https://www.youtube.com/api/timedtext?v=PElpJbRxJgc&ei=2VWUZYSdEa6_mLAPk_qcmAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5CE8D00F6F66AE091A63A06ABE6EF34F54C7256C.2AFE1A7D317A6C1EAEC1DDA8BBCDC65C191DA242&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.340 --> 00:00:02.400
- [Instructor] So I have
an uncompressed spring here
00:00:02.400 --> 00:00:04.860
and the spring has a spring constant
00:00:04.860 --> 00:00:06.960
of four Newtons per meter.
00:00:06.960 --> 00:00:10.600
Then I take a 10 gram
mass, a 10 gram ball,
00:00:10.600 --> 00:00:13.040
and I put it at the top of
the spring and I push down
00:00:13.040 --> 00:00:15.980
to compress that spring by 10 centimeters.
00:00:15.980 --> 00:00:18.350
And so let's call that
scenario one right over there,
00:00:18.350 --> 00:00:21.890
where our mass is on top
of this compressed spring.
00:00:21.890 --> 00:00:23.600
And then let's say, we let go.
00:00:23.600 --> 00:00:26.490
And then the spring launches
this mass into the air,
00:00:26.490 --> 00:00:29.670
and then this mass is gonna
hit some maximum height.
00:00:29.670 --> 00:00:31.330
And let's call that scenario two
00:00:31.330 --> 00:00:33.550
when we are hitting that maximum height.
00:00:33.550 --> 00:00:37.310
And my question to you is,
what is that maximum height
00:00:37.310 --> 00:00:40.080
based on all of the information
that I have given you here?
00:00:40.080 --> 00:00:41.750
And I'll give you a hint.
00:00:41.750 --> 00:00:43.520
What we have to think about is the idea
00:00:43.520 --> 00:00:45.410
that energy is conserved.
00:00:45.410 --> 00:00:48.160
The total energy in scenario
one is gonna be equal
00:00:48.160 --> 00:00:50.820
to the total energy in scenario two.
00:00:50.820 --> 00:00:53.240
So pause this video and
see if you can figure out
00:00:53.240 --> 00:00:55.240
what that maximum height is going to be.
00:00:56.370 --> 00:00:59.700
All right, now let's work
through this together.
00:00:59.700 --> 00:01:02.570
I told you that the total
energy is gonna be conserved,
00:01:02.570 --> 00:01:05.290
but what's that total energy
going to be made up of?
00:01:05.290 --> 00:01:07.870
Well, it's gonna have
some potential energy
00:01:07.870 --> 00:01:11.670
and it's going to have
some kinetic energy.
00:01:11.670 --> 00:01:13.760
And so another way to think about it is,
00:01:13.760 --> 00:01:16.210
our potential energy in scenario one
00:01:16.210 --> 00:01:19.220
plus our kinetic energy in scenario one
00:01:19.220 --> 00:01:24.220
needs to be equal to our
potential energy in scenario two,
00:01:25.340 --> 00:01:30.070
plus our kinetic energy in scenario two.
00:01:30.070 --> 00:01:32.180
And there might be other energies here
00:01:32.180 --> 00:01:34.320
that you could think
about heat due to friction
00:01:34.320 --> 00:01:36.020
with the air, but we're not going to,
00:01:36.020 --> 00:01:38.240
we're going to ignore those
to just simplify the problem.
00:01:38.240 --> 00:01:40.250
We can assume that this
is happening in a vacuum,
00:01:40.250 --> 00:01:42.320
that might help us a little bit.
00:01:42.320 --> 00:01:44.170
So if we think about
the potential energies,
00:01:44.170 --> 00:01:46.690
there's actually two types of
potential energies at play.
00:01:46.690 --> 00:01:48.490
There's gravitational potential energy,
00:01:48.490 --> 00:01:50.730
and there is elastic potential energy
00:01:50.730 --> 00:01:52.520
due to the fact that this mass is sitting
00:01:52.520 --> 00:01:54.150
on a compressed spring.
00:01:54.150 --> 00:01:56.530
So our gravitational potential energy
00:01:56.530 --> 00:01:59.310
is going to be our mass times the strength
00:01:59.310 --> 00:02:01.050
of our gravitational field,
00:02:01.050 --> 00:02:04.020
times our height in position one,
00:02:04.020 --> 00:02:07.120
and our elastic potential energy
00:02:07.120 --> 00:02:12.120
is going to be equal to one
half times our spring constant,
00:02:12.430 --> 00:02:15.780
times how much that spring
is compressed, squared.
00:02:15.780 --> 00:02:19.250
And so this is all of our
potential energy in scenario one,
00:02:19.250 --> 00:02:20.083
right over here.
00:02:20.083 --> 00:02:21.750
And then we add our kinetic energy.
00:02:21.750 --> 00:02:25.920
So plus, we have one half times our mass,
00:02:25.920 --> 00:02:29.590
times our velocity in
scenario one, squared.
00:02:29.590 --> 00:02:31.590
And so the sum of this is gonna be the sum
00:02:31.590 --> 00:02:33.600
of all of this in scenario two.
00:02:33.600 --> 00:02:38.160
And so that is going to
be equal to mass times G
00:02:38.160 --> 00:02:40.229
times height in scenario two,
00:02:40.229 --> 00:02:44.300
plus one half times our spring constant
00:02:44.300 --> 00:02:46.910
times how much that's spring is compressed
00:02:46.910 --> 00:02:49.300
in scenario two squared,
00:02:49.300 --> 00:02:53.570
plus one half times our mass,
00:02:53.570 --> 00:02:56.680
times our velocity in
scenario two, squared.
00:02:56.680 --> 00:03:00.540
And just as a reminder, what
we have right over here,
00:03:00.540 --> 00:03:03.520
this is our potential
energy in scenario two.
00:03:03.520 --> 00:03:05.810
And then our kinetic
energy is right over there.
00:03:05.810 --> 00:03:08.250
Now this might look
really hairy and daunting,
00:03:08.250 --> 00:03:10.690
but there's a lot of simplification here.
00:03:10.690 --> 00:03:13.760
We can define our starting
point right over here,
00:03:13.760 --> 00:03:16.540
H one as being equal to zero,
00:03:16.540 --> 00:03:18.080
which will simplify this dramatically.
00:03:18.080 --> 00:03:20.940
Cause if H one is zero, then
this term right over here,
00:03:20.940 --> 00:03:23.870
zero, we also know that
our velocity is zero
00:03:23.870 --> 00:03:25.350
in our starting scenario.
00:03:25.350 --> 00:03:27.620
So that would make our
kinetic energy zero.
00:03:27.620 --> 00:03:29.634
So the left-hand side is really
00:03:29.634 --> 00:03:32.330
all about our elastic potential energy.
00:03:32.330 --> 00:03:35.030
So it's gonna be one half
times our spring constant,
00:03:35.030 --> 00:03:36.990
times how much we have
compressed the spring
00:03:36.990 --> 00:03:39.010
in scenario one, squared.
00:03:39.010 --> 00:03:41.870
And then on the right-hand
side, what's going on?
00:03:41.870 --> 00:03:45.160
Well, in this scenario, our
spring is no longer compressed.
00:03:45.160 --> 00:03:48.970
So our elastic potential
energy is now zero.
00:03:48.970 --> 00:03:51.060
And what about our kinetic energy?
00:03:51.060 --> 00:03:53.750
Well, at maximum height right over here,
00:03:53.750 --> 00:03:57.450
your ball is actually
stationary for an instant,
00:03:57.450 --> 00:03:58.840
for a moment.
00:03:58.840 --> 00:04:01.260
It's right at that
moment where it is going
00:04:01.260 --> 00:04:04.340
from moving up to starting to move down.
00:04:04.340 --> 00:04:07.820
And so our velocity is
actually zero right over here.
00:04:07.820 --> 00:04:12.040
So V2 is actually zero,
just like V1 was zero.
00:04:12.040 --> 00:04:13.550
So that's gonna be zero.
00:04:13.550 --> 00:04:16.750
And so you have a scenario
where our initial elastic
00:04:16.750 --> 00:04:21.180
potential energy is going to
be equal to our scenario two,
00:04:21.180 --> 00:04:24.090
gravitational potential energy.
00:04:24.090 --> 00:04:27.840
And so we just need to solve
for this right over here.
00:04:27.840 --> 00:04:30.340
That is going to be our maximum height.
00:04:30.340 --> 00:04:33.570
To do that, we can divide both sides by mg
00:04:33.570 --> 00:04:38.570
and we get h2 is equal to
1/2 k delta x, one squared,
00:04:42.740 --> 00:04:44.683
all of that over mg.
00:04:46.910 --> 00:04:48.850
And we know what all of these things are,
00:04:48.850 --> 00:04:50.780
and I'll write it out with the units.
00:04:50.780 --> 00:04:54.820
This is going to be equal to one half
00:04:54.820 --> 00:04:56.130
times our spring constant,
00:04:56.130 --> 00:05:00.223
which is four Newtons per meter.
00:05:01.080 --> 00:05:03.120
Now our change in x is 10 centimeters,
00:05:03.120 --> 00:05:04.320
but we have to be very careful.
00:05:04.320 --> 00:05:07.440
We can't just put a 10 centimeters
here and then square it.
00:05:07.440 --> 00:05:09.300
We want the units to match up.
00:05:09.300 --> 00:05:10.980
So we're not dealing with
centimeters and grams.
00:05:10.980 --> 00:05:13.030
We're dealing with meters and kilograms.
00:05:13.030 --> 00:05:15.680
So I wanna convert this
10 centimeters to meters.
00:05:15.680 --> 00:05:17.760
Well, that's gonna be 0.1 meters.
00:05:17.760 --> 00:05:21.580
So I will write this as times 0.1.
00:05:21.580 --> 00:05:23.150
That's how much the spring is compressed.
00:05:23.150 --> 00:05:25.390
That's our delta x in terms of meters.
00:05:25.390 --> 00:05:27.100
And so that is gonna be squared.
00:05:27.100 --> 00:05:30.350
And then all of that
over, what is our mass?
00:05:30.350 --> 00:05:32.960
And once again, we want
to express our mass
00:05:32.960 --> 00:05:34.710
in terms of kilograms.
00:05:34.710 --> 00:05:39.710
So our mass is 0.01 kilograms.
00:05:41.180 --> 00:05:46.180
G is 9.8 meters per second squared.
00:05:47.140 --> 00:05:51.750
And when you calculate it, this
is approximately 0.2 meters.
00:05:51.750 --> 00:05:53.910
And the units actually all do work out.
00:05:53.910 --> 00:05:55.940
Because if you look at
Newtons as being the same
00:05:55.940 --> 00:05:59.980
as kilogram meters per second squared,
00:05:59.980 --> 00:06:04.120
this kilograms cancels with
that kilograms right over there.
00:06:04.120 --> 00:06:06.850
You can see that this per second squared
00:06:06.850 --> 00:06:08.860
is gonna cancel with
that per second squared
00:06:08.860 --> 00:06:09.840
right over there.
00:06:09.840 --> 00:06:12.780
And then this meter is going
to cancel out with that meter.
00:06:12.780 --> 00:06:14.700
And so what you're left
with is a meter squared
00:06:14.700 --> 00:06:15.880
divided by meters,
00:06:15.880 --> 00:06:17.820
which is just going to
leave you with meters,
00:06:17.820 --> 00:06:18.780
just like that.
00:06:18.780 --> 00:06:19.800
And we're done.
00:06:19.800 --> 00:06:22.700
We figured out the maximum
height using just our knowledge
00:06:22.700 --> 00:06:27.700
of the conservation of energy
is approximately 0.2 meters.
|
Calculating velocity using energy | https://www.youtube.com/watch?v=8n_7bH5d2EE | vtt | https://www.youtube.com/api/timedtext?v=8n_7bH5d2EE&ei=2VWUZbTaKd2gp-oP7LCu2AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A0A661D03657948A06CC6301B4B51170A945E854.77FCCC4A30B7259E3E8DA10883F0A58EAE156F86&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.350 --> 00:00:01.700
- [Instructor] So we have a spring here
00:00:01.700 --> 00:00:04.550
that has a spring constant
of four Newtons per meter.
00:00:04.550 --> 00:00:06.830
What we then do is take a 10-gram mass
00:00:06.830 --> 00:00:08.200
and we put it on top of the spring
00:00:08.200 --> 00:00:11.750
and we push down to compress
the spring by 10 centimeters.
00:00:11.750 --> 00:00:13.290
We then let go.
00:00:13.290 --> 00:00:15.930
And what I'm curious about
is what is going to be
00:00:15.930 --> 00:00:19.460
the magnitude of the
velocity of our ball here,
00:00:19.460 --> 00:00:21.170
of our 10-gram mass,
00:00:21.170 --> 00:00:25.170
right as the spring is no
longer compressed or stretched,
00:00:25.170 --> 00:00:27.970
or essentially when the
ball is being launched?
00:00:27.970 --> 00:00:29.840
Pause this video and see
if you can figure that out.
00:00:29.840 --> 00:00:32.860
And I'll give you a hint, the
energy in this first state,
00:00:32.860 --> 00:00:35.880
the total energy has got to
be equal to the total energy
00:00:35.880 --> 00:00:36.840
of this second state.
00:00:36.840 --> 00:00:39.093
We can't create or destroy energy.
00:00:40.210 --> 00:00:43.470
All right, now let's work
through this together.
00:00:43.470 --> 00:00:47.550
So let's call this first
scenario state one.
00:00:47.550 --> 00:00:50.500
So in state one, what is the
total energy going to be?
00:00:50.500 --> 00:00:51.790
Well, it's going to be the sum
00:00:51.790 --> 00:00:53.750
of the gravitational potential energy,
00:00:53.750 --> 00:00:57.570
so that's mg times the
height in state one,
00:00:57.570 --> 00:00:59.870
plus our elastic potential energy,
00:00:59.870 --> 00:01:02.110
that's 1/2 times the spring constant times
00:01:02.110 --> 00:01:05.640
how much we've compressed that
spring in state one squared,
00:01:05.640 --> 00:01:07.100
plus our kinetic energy,
00:01:07.100 --> 00:01:10.850
so that's 1/2 times our
mass times the magnitude
00:01:10.850 --> 00:01:13.640
of our velocity in state one squared.
00:01:13.640 --> 00:01:15.540
And that has got to be equal to,
00:01:15.540 --> 00:01:20.320
as we just talked about, the
total energy in state two.
00:01:20.320 --> 00:01:21.810
Well, what's that going to be?
00:01:21.810 --> 00:01:24.140
Well, that's your
gravitational potential energy
00:01:24.140 --> 00:01:29.140
in state two plus your elastic
potential energy in state two
00:01:30.640 --> 00:01:35.640
plus your kinetic energy in state two.
00:01:35.650 --> 00:01:37.970
Now let's think about which
of these variables we know
00:01:37.970 --> 00:01:40.240
and which ones we need to solve for.
00:01:40.240 --> 00:01:43.493
So, first of all, mass,
your spring constant,
00:01:44.720 --> 00:01:46.820
the strength of your gravitational field,
00:01:46.820 --> 00:01:48.480
well, we know what these are going to be.
00:01:48.480 --> 00:01:53.480
These are going to be our
mass is equal to 10 grams.
00:01:53.970 --> 00:01:56.750
The strength of the gravitational field,
00:01:56.750 --> 00:01:58.360
also the acceleration due to gravity near
00:01:58.360 --> 00:02:03.360
the surface of the earth, is
9.8 meters per second squared.
00:02:04.810 --> 00:02:09.810
Our spring constant is
four Newtons per meter,
00:02:10.760 --> 00:02:13.100
and I like to remind
myself what a Newton is,
00:02:13.100 --> 00:02:15.680
a Newton is kilogram
meter per second squared.
00:02:15.680 --> 00:02:16.730
So this is also equal
00:02:16.730 --> 00:02:21.730
to four kilogram meter per second squared,
00:02:22.460 --> 00:02:24.330
and then we also have a meter over there.
00:02:24.330 --> 00:02:26.280
And actually, these
meters will cancel out.
00:02:26.280 --> 00:02:28.250
And that's useful
because it's reminding us
00:02:28.250 --> 00:02:31.600
that we want everything to
be in kilograms and meters.
00:02:31.600 --> 00:02:32.890
And with that in mind, actually,
00:02:32.890 --> 00:02:37.890
let me rewrite our mass right
over here as 0.01 kilograms.
00:02:41.130 --> 00:02:44.190
And then let's think about
what's going on specifically
00:02:44.190 --> 00:02:46.660
in each of those states.
00:02:46.660 --> 00:02:51.660
So what is going to be our
h one, our initial height?
00:02:52.640 --> 00:02:53.760
Well, I didn't give it to you,
00:02:53.760 --> 00:02:55.860
but what really matters is the difference
00:02:55.860 --> 00:02:58.360
between h one and h two.
00:02:58.360 --> 00:03:01.430
So we could just define
h one right over here
00:03:01.430 --> 00:03:03.880
to be equal to zero.
00:03:03.880 --> 00:03:05.260
So let me write that down.
00:03:05.260 --> 00:03:08.400
H one is equal to zero.
00:03:08.400 --> 00:03:11.490
And if we say that, then
what is h two going to be?
00:03:11.490 --> 00:03:14.620
H two would then be
equal to 10 centimeters,
00:03:14.620 --> 00:03:17.610
but remember, we want everything
in kilograms and meters,
00:03:17.610 --> 00:03:21.443
so 10 centimeters is the
same thing is 0.1 meters.
00:03:23.030 --> 00:03:24.800
What is our spring compression
00:03:24.800 --> 00:03:27.060
in scenario one going to be?
00:03:27.060 --> 00:03:29.760
Well, that is going to be 10 centimeters.
00:03:29.760 --> 00:03:32.490
But once again, we wanna
write that in terms of meters.
00:03:32.490 --> 00:03:35.470
So I'll write that as 0.1 meters.
00:03:35.470 --> 00:03:38.540
And then what is our spring compression
00:03:38.540 --> 00:03:41.220
in scenario two going to be?
00:03:41.220 --> 00:03:44.080
Well, we're completely
uncompressed and unstretched,
00:03:44.080 --> 00:03:46.830
so that is going to be zero meters.
00:03:46.830 --> 00:03:49.030
And then what is going to be our velocity,
00:03:49.030 --> 00:03:51.840
or at least the magnitude of
our velocity in state one?
00:03:51.840 --> 00:03:55.300
Well, we're stationary, so
it's zero meters per second.
00:03:55.300 --> 00:03:57.360
And what is going to be the magnitude
00:03:57.360 --> 00:03:59.950
of our velocity in state two?
00:03:59.950 --> 00:04:01.800
Well, that's exactly
what we wanna solve for.
00:04:01.800 --> 00:04:04.800
That is our launch velocity.
00:04:04.800 --> 00:04:06.560
So let's see if we can simplify this
00:04:06.560 --> 00:04:09.470
and then solve for v two.
00:04:09.470 --> 00:04:13.070
So we know that h one is equal to zero.
00:04:13.070 --> 00:04:16.320
So that simplifies that right
over there, that term is zero.
00:04:16.320 --> 00:04:18.360
We know that v one is zero.
00:04:18.360 --> 00:04:20.740
So that simplifies that term there.
00:04:20.740 --> 00:04:24.560
We know that delta x in
scenario two is equal to zero.
00:04:24.560 --> 00:04:28.830
So that simplifies that
term right over there.
00:04:28.830 --> 00:04:31.830
And so we can now rewrite all of this,
00:04:31.830 --> 00:04:34.810
and I'll switch to one color
just to speed things up
00:04:34.810 --> 00:04:39.810
a little bit, as 1/2 k
times delta x one squared
00:04:40.160 --> 00:04:45.160
is equal to mgh sub two
plus 1/2 mv sub two squared.
00:04:48.780 --> 00:04:52.260
And now let's just try to
solve for this character.
00:04:52.260 --> 00:04:56.280
So let's subtract mgh
sub two from both sides.
00:04:56.280 --> 00:05:01.280
So we're going to have 1/2 k
times delta x sub one squared
00:05:02.160 --> 00:05:07.160
minus mgh sub two is equal
to 1/2 mv sub two squared.
00:05:10.530 --> 00:05:15.530
Now let's see, if we multiply
both sides by two over m,
00:05:16.070 --> 00:05:18.510
then that will get rid
of this 1/2 m over here.
00:05:18.510 --> 00:05:20.340
So let me multiply that.
00:05:20.340 --> 00:05:22.640
I'm kind of doing two
steps at the same time.
00:05:22.640 --> 00:05:25.190
One way to think about it
is I'm multiplying times
00:05:25.190 --> 00:05:28.490
the reciprocal of the
coefficient on the v squared.
00:05:28.490 --> 00:05:30.420
So right over here, it's m over two,
00:05:30.420 --> 00:05:32.840
so the reciprocal is two over m.
00:05:32.840 --> 00:05:34.830
I'm gonna have to make sure
that I'm gonna multiply it times
00:05:34.830 --> 00:05:35.800
that whole side.
00:05:35.800 --> 00:05:37.870
And so what do we now have?
00:05:37.870 --> 00:05:40.820
This is going to be equal to, let's see,
00:05:40.820 --> 00:05:45.820
it's going to be k delta
x sub one squared over m
00:05:47.800 --> 00:05:52.800
minus two gh sub two
00:05:53.120 --> 00:05:55.610
is going to be equal to v sub two squared.
00:05:55.610 --> 00:05:57.750
And then to solve for our launch velocity,
00:05:57.750 --> 00:05:59.220
we just take the principal route,
00:05:59.220 --> 00:06:00.920
the square root of both sides.
00:06:00.920 --> 00:06:02.390
So I could say v sub two,
00:06:02.390 --> 00:06:04.260
which is equal to our launch velocity,
00:06:04.260 --> 00:06:08.350
is equal to the square
root of our spring constant
00:06:08.350 --> 00:06:13.350
times delta x sub one squared
over our mass minus two times
00:06:15.640 --> 00:06:19.870
the gravitational field times h two.
00:06:19.870 --> 00:06:22.170
And so we just have to
plug in the numbers now.
00:06:22.170 --> 00:06:23.500
This is going to be equal to,
00:06:23.500 --> 00:06:26.230
and I'll switch colors
just to ease the monotony.
00:06:26.230 --> 00:06:28.530
I'm gonna use a new color right over here.
00:06:28.530 --> 00:06:32.370
This is going to be equal
to the square root of,
00:06:32.370 --> 00:06:34.550
and I wanna make sure
all the units work out.
00:06:34.550 --> 00:06:36.170
So I'm actually gonna write this version
00:06:36.170 --> 00:06:39.050
of my spring constant, so I
can work with all the units.
00:06:39.050 --> 00:06:44.050
So it's gonna be four
kilograms per second squared.
00:06:44.320 --> 00:06:49.320
And now delta x one we know is 0.1 meters.
00:06:49.430 --> 00:06:50.500
So if we square it,
00:06:50.500 --> 00:06:55.500
it's going to be times
0.01 meters squared.
00:06:56.360 --> 00:07:00.700
And then all of that is
going to be over our mass,
00:07:00.700 --> 00:07:05.700
which we know is 0.01
kilograms, 0.01 kilograms,
00:07:09.080 --> 00:07:14.080
and then minus two times 9.8
meters per second squared
00:07:16.830 --> 00:07:19.200
times height in the second scenario,
00:07:19.200 --> 00:07:24.200
which we already know is 0.1
meters, so times 0.1 meters.
00:07:25.830 --> 00:07:28.090
Let me extend this
radical right over here.
00:07:28.090 --> 00:07:29.560
And let's look at the units first
00:07:29.560 --> 00:07:31.590
to just to make sure we're
getting the right units.
00:07:31.590 --> 00:07:35.660
So this kilogram is going to
cancel with this kilogram.
00:07:35.660 --> 00:07:38.233
And then we have, over here,
00:07:38.233 --> 00:07:39.669
we're going to have
something that's in terms
00:07:39.669 --> 00:07:42.097
of meters squared per second squared,
00:07:42.097 --> 00:07:43.074
and then over here,
00:07:43.074 --> 00:07:44.202
we're gonna have something in terms
00:07:44.202 --> 00:07:46.335
of meters squared per second squared.
00:07:46.335 --> 00:07:47.168
So that makes sense.
00:07:47.168 --> 00:07:48.001
We're gonna have a difference
00:07:48.001 --> 00:07:49.550
of two meters squared per second squared.
00:07:49.550 --> 00:07:51.120
And then when you take
the principal route,
00:07:51.120 --> 00:07:53.060
you're going to get meters per second,
00:07:53.060 --> 00:07:56.560
which is the unit for the
magnitude of velocity.
00:07:56.560 --> 00:07:58.120
So now we just have to
get our calculator out
00:07:58.120 --> 00:07:59.280
and calculate this.
00:07:59.280 --> 00:08:01.530
So the .01s will cancel out.
00:08:01.530 --> 00:08:04.690
So this part right over
here is going to be four.
00:08:04.690 --> 00:08:05.930
And then from that,
00:08:05.930 --> 00:08:10.930
I am going to subtract
two times 9.8 times .1,
00:08:14.800 --> 00:08:16.650
close the parentheses.
00:08:16.650 --> 00:08:18.310
That's going to be equal to that.
00:08:18.310 --> 00:08:19.910
And then I needed to take the square root
00:08:19.910 --> 00:08:23.240
of all of that business, and
I get this right over here.
00:08:23.240 --> 00:08:28.240
So this is approximately
1.43 meters per second,
00:08:29.170 --> 00:08:32.640
1.43 meters per second.
00:08:32.640 --> 00:08:33.483
And we're done.
|
Natural selection and adaptation | https://www.youtube.com/watch?v=giw2ELZr-bE | vtt | https://www.youtube.com/api/timedtext?v=giw2ELZr-bE&ei=2VWUZYOVNNGIp-oP97K-mAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=3C489F2A1D60F76591139E5BCAC1B0475F40D397.5F28BB0DB63734B32B3B651D92D280A1C3BD4E8B&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.840 --> 00:00:02.540
- [Dr. Samuel] Hi
everybody, Dr. Samuel here,
00:00:02.540 --> 00:00:04.200
your friendly neighborhood entomologist.
00:00:04.200 --> 00:00:06.570
And I was hoping that we
could take a few minutes
00:00:06.570 --> 00:00:08.680
to talk about adaptation.
00:00:08.680 --> 00:00:11.810
What comes to mind when
you think about adaptation?
00:00:11.810 --> 00:00:13.720
You might think of cryptic morphology
00:00:13.720 --> 00:00:15.960
that helps organisms hide from predators,
00:00:15.960 --> 00:00:20.060
scaly armor or spines to
protect organisms in a scuffle,
00:00:20.060 --> 00:00:23.020
or increased melanin
pigmentation in the skin
00:00:23.020 --> 00:00:25.632
to shield an organism
from the damaging impacts
00:00:25.632 --> 00:00:29.030
of harsh sunlight in really sunny areas.
00:00:29.030 --> 00:00:31.520
And if this is the sort of
thing that you thought of,
00:00:31.520 --> 00:00:34.500
you're right, these are all adaptations.
00:00:34.500 --> 00:00:37.210
But what people often
miss about adaptations
00:00:37.210 --> 00:00:41.187
is that they all help
organisms survive and reproduce
00:00:41.187 --> 00:00:44.240
in a particular environment.
00:00:44.240 --> 00:00:49.086
The word adaptation can refer to a trait
00:00:49.086 --> 00:00:54.086
that makes an organism more
suited to its environment.
00:00:55.560 --> 00:00:57.430
But it can also mean
00:00:57.430 --> 00:01:01.030
the process by which a population
00:01:01.030 --> 00:01:04.340
becomes dominated by organisms
00:01:04.340 --> 00:01:08.180
that are suited to their environment.
00:01:08.180 --> 00:01:11.890
The point is that adaptation
happens in a population
00:01:11.890 --> 00:01:15.890
as its organisms accumulate adaptations.
00:01:15.890 --> 00:01:18.660
And this all happens through the process
00:01:18.660 --> 00:01:20.250
of natural selection,
00:01:20.250 --> 00:01:22.010
which you may have heard about.
00:01:22.010 --> 00:01:24.670
With natural selection, we see organisms
00:01:24.670 --> 00:01:26.910
with beneficial heritable traits,
00:01:26.910 --> 00:01:30.120
increasing their share of the
gene pool in the population
00:01:30.120 --> 00:01:33.870
because they're more likely
to mate and produce offspring.
00:01:33.870 --> 00:01:38.870
This means these well-adapted
organisms have higher fitness,
00:01:39.320 --> 00:01:44.110
a measure of an organism's ability
00:01:44.110 --> 00:01:48.420
to survive and reproduce
00:01:48.420 --> 00:01:51.540
in its specific environment.
00:01:51.540 --> 00:01:56.130
These traits or adaptations
make the organisms better suited
00:01:56.130 --> 00:01:58.200
to survive and reproduce
00:01:58.200 --> 00:01:59.400
because they're better suited
00:01:59.400 --> 00:02:02.740
to the specific environmental
context that they live in.
00:02:02.740 --> 00:02:05.110
That is our green caterpillars blend in,
00:02:05.110 --> 00:02:07.090
and thus, survive better
on the green leaves,
00:02:07.090 --> 00:02:09.440
and the orange caterpillars
on the orange leaves.
00:02:09.440 --> 00:02:11.360
As you can see, natural selection
00:02:11.360 --> 00:02:14.190
is intimately intertwined
with the environment
00:02:14.190 --> 00:02:15.690
in which it takes place.
00:02:15.690 --> 00:02:19.980
And this is why natural
selection can lead to adaptation.
00:02:19.980 --> 00:02:22.960
Even the concept of adaptation is diverse.
00:02:22.960 --> 00:02:25.292
Adaptations can be anatomical,
00:02:25.292 --> 00:02:30.292
changes to physical
structures, or physiological,
00:02:30.520 --> 00:02:34.710
changes in the function
of these structures,
00:02:34.710 --> 00:02:39.710
or adaptations can be changes to behavior.
00:02:39.740 --> 00:02:43.161
We see this with honeybees
adapted to life in Africa,
00:02:43.161 --> 00:02:45.750
sometimes called by the suboptimal names,
00:02:45.750 --> 00:02:49.870
Africanized honeybees or killer bees.
00:02:49.870 --> 00:02:54.090
They're the same species
as and look identical too.
00:02:54.090 --> 00:02:57.650
Populations of honeybees
adapted to North America,
00:02:57.650 --> 00:03:01.090
but their behaviors diverge dramatically.
00:03:01.090 --> 00:03:02.780
Because the African populations
00:03:02.780 --> 00:03:05.980
are adapted to life in a
hot, tropical environment,
00:03:05.980 --> 00:03:09.180
sometimes, they construct nests
right out in the open air,
00:03:09.180 --> 00:03:12.300
nests in open air.
00:03:12.300 --> 00:03:14.810
This is extremely rare for populations
00:03:14.810 --> 00:03:17.160
adapted to the temperate
climate of North America,
00:03:17.160 --> 00:03:19.560
where the temperature
range is far too broad
00:03:19.560 --> 00:03:22.960
between winter and
summer for open air nests
00:03:22.960 --> 00:03:24.173
to be successful.
00:03:25.050 --> 00:03:27.730
So, North American honeybee populations
00:03:27.730 --> 00:03:30.660
much prefer to live inside
of protected structures
00:03:30.660 --> 00:03:33.170
like inside of the trunks of hollow trees
00:03:33.170 --> 00:03:35.790
or the boxes that beekeepers provide,
00:03:35.790 --> 00:03:40.150
nests in protected structures.
00:03:40.150 --> 00:03:41.860
And in Africa,
00:03:41.860 --> 00:03:45.040
there are also more
large, fearsome predators
00:03:45.040 --> 00:03:47.730
interested in getting into the bees' nest.
00:03:47.730 --> 00:03:51.580
So, the frequency of traits
related to hyper defensiveness
00:03:51.580 --> 00:03:53.310
is much more common
00:03:53.310 --> 00:03:56.000
than in populations
adapted to North America,
00:03:56.000 --> 00:03:59.220
where there are fewer
aggressive predators,
00:03:59.220 --> 00:04:02.467
heightened defensiveness, low
00:04:04.630 --> 00:04:08.563
to moderate defensiveness.
00:04:10.040 --> 00:04:13.040
The success of honeybees
adapted to life in Africa
00:04:13.040 --> 00:04:14.470
left a lot of people worried
00:04:14.470 --> 00:04:17.270
that they would be similarly
successful in North America
00:04:17.270 --> 00:04:19.220
and replace the honeybees there.
00:04:19.220 --> 00:04:21.640
But those concerns ignored the connection
00:04:21.640 --> 00:04:24.740
between adaptation and the environment.
00:04:24.740 --> 00:04:27.650
Traits that helped those
bees survive in Africa
00:04:27.650 --> 00:04:29.540
and even helped them
in similar environments
00:04:29.540 --> 00:04:31.230
found in many regions of tropical,
00:04:31.230 --> 00:04:33.030
South and Central America,
00:04:33.030 --> 00:04:35.830
well, those same exact traits
00:04:35.830 --> 00:04:39.140
were liabilities in much of North America.
00:04:39.140 --> 00:04:41.890
Okay, so, this is all fascinating,
00:04:41.890 --> 00:04:43.640
but you may be wondering,
00:04:43.640 --> 00:04:47.060
if natural selection is
passing out adaptations,
00:04:47.060 --> 00:04:50.620
why doesn't it choose better stuff?
00:04:50.620 --> 00:04:55.620
Fish tend to get eaten
by birds and bears a lot.
00:04:56.080 --> 00:05:00.420
And that's gone on for
literally millions of years.
00:05:00.420 --> 00:05:02.220
So, why I haven't fish populations
00:05:02.220 --> 00:05:06.630
developed something like
laser eyes or teleportation?
00:05:06.630 --> 00:05:10.440
Instead, when a population
of fish does evolve defense,
00:05:10.440 --> 00:05:13.150
it's typically something like a few bones,
00:05:13.150 --> 00:05:16.350
that it already has,
getting longer and sharper
00:05:16.350 --> 00:05:18.320
and protruding out of their fins,
00:05:18.320 --> 00:05:21.488
like in the case of the
three-spined stickleback fish.
00:05:21.488 --> 00:05:24.300
These spines protect the stickleback
00:05:24.300 --> 00:05:26.730
from birds and other predators,
00:05:26.730 --> 00:05:28.950
but only if the spines are long enough
00:05:28.950 --> 00:05:31.390
to make it difficult for
that specific predator
00:05:31.390 --> 00:05:32.530
to swallow them.
00:05:32.530 --> 00:05:35.350
Birds with wider throats
are still able to eat
00:05:35.350 --> 00:05:39.640
even fully grown fish with
fully elongated spines.
00:05:39.640 --> 00:05:43.660
Laser eyes really do seem like
they would be more effective.
00:05:43.660 --> 00:05:46.030
It's almost like natural selection
00:05:46.030 --> 00:05:48.541
is just tinkering with
whatever it has lying around
00:05:48.541 --> 00:05:51.680
instead of going out
and buying something new
00:05:51.680 --> 00:05:54.180
and perfectly suited to the task.
00:05:54.180 --> 00:05:56.840
And that is exactly what's happening.
00:05:56.840 --> 00:06:00.380
Populations don't adapt by
accessing a bottomless well
00:06:00.380 --> 00:06:03.150
of awesome problem-solving options.
00:06:03.150 --> 00:06:06.360
Quite the contrary, with
natural selection as the driver,
00:06:06.360 --> 00:06:08.970
adaptations can be pretty limited.
00:06:08.970 --> 00:06:11.130
You might already be
tracking with the idea
00:06:11.130 --> 00:06:13.040
that if an increase in fitness
00:06:13.040 --> 00:06:15.180
is what natural selection is after,
00:06:15.180 --> 00:06:17.800
you don't need an adaptation
that allows you to incinerate
00:06:17.800 --> 00:06:18.890
all of your enemies.
00:06:18.890 --> 00:06:22.400
You just need one good enough
to solve whatever problem
00:06:22.400 --> 00:06:24.410
is keeping others in your population
00:06:24.410 --> 00:06:26.410
from surviving in mating.
00:06:26.410 --> 00:06:29.300
If that's a kingfisher
bird eating the other fish,
00:06:29.300 --> 00:06:31.760
the resolution might be just a spine
00:06:31.760 --> 00:06:34.040
that's only a half a centimeter longer
00:06:34.040 --> 00:06:35.420
than the other fishes.
00:06:35.420 --> 00:06:37.940
That's the reason why we see adaptations
00:06:37.940 --> 00:06:40.350
that look like natural
selection just grabbed
00:06:40.350 --> 00:06:43.690
whatever happened to be
lying around and modified it
00:06:43.690 --> 00:06:46.150
because it kinda did.
00:06:46.150 --> 00:06:48.470
A turtle's remarkably protective shell
00:06:48.470 --> 00:06:50.230
may look fancy and novel,
00:06:50.230 --> 00:06:53.070
but it's literally the
turtle's overgrown ribs
00:06:53.070 --> 00:06:54.850
fused with its spine.
00:06:54.850 --> 00:06:57.030
A narwhal's face spear,
00:06:57.030 --> 00:06:59.035
that there is just a tooth
00:06:59.035 --> 00:07:02.640
that grew all the way out of its face.
00:07:02.640 --> 00:07:04.860
Natural selection only has the options
00:07:04.860 --> 00:07:06.940
currently in the genes of a population
00:07:06.940 --> 00:07:08.080
with the occasional addition
00:07:08.080 --> 00:07:10.110
of new genetic sequences through mutation
00:07:10.110 --> 00:07:12.000
to work with when a problem arises.
00:07:12.000 --> 00:07:14.070
And you might be thinking, "Oh great!
00:07:14.070 --> 00:07:15.910
Mutations, those will help!
00:07:15.910 --> 00:07:18.720
That's how my favorite
superhero got her powers."
00:07:18.720 --> 00:07:21.240
Well, unlike what we see in movies,
00:07:21.240 --> 00:07:23.970
most mutations either have no real effect
00:07:23.970 --> 00:07:26.110
or result in problematic gene expression
00:07:26.110 --> 00:07:28.060
or nonfunctional proteins
00:07:28.060 --> 00:07:32.090
which is pretty bad
news for living things.
00:07:32.090 --> 00:07:35.510
So, adaptations are not
likely to be super weapons
00:07:35.510 --> 00:07:38.150
that ensure survival in all circumstances.
00:07:38.150 --> 00:07:39.609
Instead, they're useful traits
00:07:39.609 --> 00:07:42.270
that help increase an organism's fitness
00:07:42.270 --> 00:07:45.020
as the environmental
conditions apply pressure.
00:07:45.020 --> 00:07:47.810
So, adaptation is a remarkable system,
00:07:47.810 --> 00:07:50.790
but one with some pretty
pronounced limitations.
00:07:50.790 --> 00:07:54.140
Natural selection has to work
with what an organism has.
00:07:54.140 --> 00:07:56.950
But consider for a moment
what it has given us
00:07:56.950 --> 00:07:59.130
despite those limitations.
00:07:59.130 --> 00:08:00.790
Pistol shrimp have the ability
00:08:00.790 --> 00:08:03.230
to slam their claws shut so quickly
00:08:03.230 --> 00:08:06.090
that the water around them
collapses in on itself.
00:08:06.090 --> 00:08:10.490
It implodes knocking
nearby fish unconscious.
00:08:10.490 --> 00:08:12.520
Some honeybees can bundle together
00:08:12.520 --> 00:08:15.370
and vibrate their flight
muscles so rapidly
00:08:15.370 --> 00:08:18.190
that they can create a
biological convection oven
00:08:18.190 --> 00:08:20.400
which can cook predators to death.
00:08:20.400 --> 00:08:22.600
And there are parasitic wasps
00:08:22.600 --> 00:08:26.060
that have evolved to live
inside of parasitic wasps
00:08:26.060 --> 00:08:28.630
that live inside of parasitic wasps
00:08:28.630 --> 00:08:31.130
that live inside of caterpillars,
00:08:31.130 --> 00:08:34.720
like tiny, strange, little
Russian nesting dolls.
00:08:34.720 --> 00:08:37.880
And don't even get me
started on the hornets
00:08:37.880 --> 00:08:39.940
that have yellow patches on their abdomen
00:08:39.940 --> 00:08:41.770
that absorb solar energy
00:08:41.770 --> 00:08:44.450
to supplement the energy
provided by their diet.
00:08:44.450 --> 00:08:47.132
They have solar panels!
00:08:47.132 --> 00:08:51.293
I'd say natural selection has
done pretty well for itself.
|
Acid Rain | https://www.youtube.com/watch?v=P4I-abHPa-I | vtt | https://www.youtube.com/api/timedtext?v=P4I-abHPa-I&ei=2lWUZfgii7-YsA-7g7fgDQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245322&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A8239C10A25D1EE3D268E372D7138C020239B2D8.5BE292E843B290E966FD35733D6E789470F81F90&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.190 --> 00:00:02.590
- [Narrator] Acid rain
sounds like something
00:00:02.590 --> 00:00:04.570
straight out of a sci-fi film,
00:00:04.570 --> 00:00:07.260
like strange raindrops that fall in a city
00:00:07.260 --> 00:00:09.250
and corrode everything.
00:00:09.250 --> 00:00:10.860
The truth is not far off,
00:00:10.860 --> 00:00:12.760
but the good news is that we know a lot
00:00:12.760 --> 00:00:14.510
about what causes acid rain
00:00:14.510 --> 00:00:16.990
and how to address its
impact on the environment,
00:00:16.990 --> 00:00:19.250
our bodies and the built world.
00:00:19.250 --> 00:00:21.130
Interestingly, normal rain
00:00:21.130 --> 00:00:24.030
is actually slightly acidic as well.
00:00:24.030 --> 00:00:26.000
If you think back to the pH scale,
00:00:26.000 --> 00:00:29.840
you'll remember that it
goes from zero to 14,
00:00:29.840 --> 00:00:31.600
acidic to basic,
00:00:31.600 --> 00:00:35.260
and that seven, right in
the middle, is neutral.
00:00:35.260 --> 00:00:40.260
Normal rain is around 5 or 5
1/2, so it's slightly acidic,
00:00:42.380 --> 00:00:45.160
but acid rain is even more acidic
00:00:45.160 --> 00:00:47.993
and typically around a pH of four.
00:00:49.070 --> 00:00:51.530
Now this might not sound
like a big difference,
00:00:51.530 --> 00:00:54.280
but remember that this
is a logarithmic scale.
00:00:54.280 --> 00:00:56.810
So each increment, like from four to five,
00:00:56.810 --> 00:00:59.120
is actually a tenfold difference.
00:00:59.120 --> 00:01:01.860
So if we're comparing
normal rain, at about 5 1/2,
00:01:01.860 --> 00:01:04.760
and acid rain at four,
that's a pretty big deal.
00:01:04.760 --> 00:01:07.830
So now the questions are,
how does acid rain form?
00:01:07.830 --> 00:01:08.930
Why does it matter?
00:01:08.930 --> 00:01:13.110
And what effects can acid
rain have on our communities?
00:01:13.110 --> 00:01:15.740
So the short answer to
how it forms is pollution.
00:01:15.740 --> 00:01:17.900
So let me try to bring
that to life for you
00:01:17.900 --> 00:01:21.030
with my imaginary hand-drawn drawn city.
00:01:21.030 --> 00:01:22.350
Now remember that most of the fuels
00:01:22.350 --> 00:01:25.080
we burn to make energy
are from fossil fuels,
00:01:25.080 --> 00:01:26.730
so that animal and plant matter
00:01:26.730 --> 00:01:29.630
that has been in the ground
for millions of years.
00:01:29.630 --> 00:01:31.420
And when we burn these fuels,
00:01:31.420 --> 00:01:34.110
they tend to have remaining
traces of sulfur in them,
00:01:34.110 --> 00:01:35.450
especially coal.
00:01:35.450 --> 00:01:38.530
And both coal and oil burn
at such high temperatures
00:01:38.530 --> 00:01:41.470
that they can cause nitrogen
and oxygen in the air
00:01:41.470 --> 00:01:43.830
to form different compounds.
00:01:43.830 --> 00:01:46.190
So imagine we have here an oil refinery
00:01:46.190 --> 00:01:48.890
and a coal burning
plant, and a lot of cars.
00:01:48.890 --> 00:01:52.320
A common byproduct of coal
burning plants or smelters
00:01:52.320 --> 00:01:56.690
and other industrial facilities
is sulfur dioxide, SO2.
00:01:56.690 --> 00:02:00.290
At the same time, high temperatures
from combustion engines
00:02:00.290 --> 00:02:02.950
and oil refineries provide enough energy
00:02:02.950 --> 00:02:07.150
to break apart nitrogen and
oxygen molecules in the air.
00:02:07.150 --> 00:02:09.160
These molecules can then recombine
00:02:09.160 --> 00:02:14.160
to form different nitrogen
oxides, like nitric oxide, NO,
00:02:14.475 --> 00:02:17.220
and nitrogen dioxide, NO2.
00:02:17.220 --> 00:02:20.580
Together, these are referred
to as nitrogen oxides,
00:02:20.580 --> 00:02:23.900
which you can abbreviate by NOx.
00:02:23.900 --> 00:02:26.240
So the same can be said
about sulfur dioxide.
00:02:26.240 --> 00:02:31.240
That falls into the category
of sulfur oxide, SOx, or SOX.
00:02:31.940 --> 00:02:34.450
So a fun way to remember the precursors
00:02:34.450 --> 00:02:37.670
to acid rain are SOX and NOX.
00:02:37.670 --> 00:02:40.870
Now these precursors belonging
to the SOX and NOX family
00:02:40.870 --> 00:02:42.850
are hanging out up in the air.
00:02:42.850 --> 00:02:45.530
When they interact with
UV radiation from the sun
00:02:45.530 --> 00:02:48.430
and water molecules that
are also in the air,
00:02:48.430 --> 00:02:52.270
they form different
vapors, these acid vapors,
00:02:52.270 --> 00:02:55.680
sulfuric acid vapor, H2SO4,
00:02:55.680 --> 00:02:58.453
and nitric acid vapor, HNO3.
00:02:59.545 --> 00:03:01.370
And these acids are no joke.
00:03:01.370 --> 00:03:05.560
Sulfuric acid is highly
corrosive. It can burn your skin.
00:03:05.560 --> 00:03:08.690
The vapors can irritate
your respiratory tract.
00:03:08.690 --> 00:03:10.219
And nitric acid is known to be used
00:03:10.219 --> 00:03:13.130
in explosives and rocket launches.
00:03:13.130 --> 00:03:14.490
And these are the acids
00:03:14.490 --> 00:03:17.190
that make up the phenomenon of acid rain.
00:03:17.190 --> 00:03:20.860
Over time, these smoke stacks
have actually gotten taller.
00:03:20.860 --> 00:03:23.030
One example in the early 1970s,
00:03:23.030 --> 00:03:25.820
when the EPA wanted to reduce emissions
00:03:25.820 --> 00:03:29.450
from these coal burning
facilities and oil refineries
00:03:29.450 --> 00:03:32.930
to control the air quality
around those communities.
00:03:32.930 --> 00:03:37.080
What these facilities did was
build larger smoke stacks,
00:03:37.080 --> 00:03:38.530
or taller smoke stacks,
00:03:38.530 --> 00:03:42.150
so that those pollutants
would disperse and spread out
00:03:42.150 --> 00:03:45.870
over a larger area and not
fall over the local community
00:03:45.870 --> 00:03:48.370
as much or as fast.
00:03:48.370 --> 00:03:51.360
Instead, what ended up happening
is that these pollutants
00:03:51.360 --> 00:03:53.100
were carried by the wind
00:03:53.100 --> 00:03:56.550
to communities and natural
environments downwind
00:03:56.550 --> 00:03:58.960
of where they were being created,
00:03:58.960 --> 00:04:03.170
up to 1,000 kilometers, or over 600 miles.
00:04:03.170 --> 00:04:06.370
And when these acid
vapors cause acid rain,
00:04:06.370 --> 00:04:08.420
it's not always rain like we think of
00:04:08.420 --> 00:04:10.730
with water falling from the sky.
00:04:10.730 --> 00:04:12.900
Acid rain is just a general term
00:04:12.900 --> 00:04:15.950
and it really includes all
forms of precipitation,
00:04:15.950 --> 00:04:19.370
like snow, fog, cloud vapor,
00:04:19.370 --> 00:04:22.230
and dry deposition, like dust particles.
00:04:22.230 --> 00:04:25.453
And also it can have different
combinations of these forms.
00:04:26.560 --> 00:04:29.940
And now the other big question
is why does it matter, right?
00:04:29.940 --> 00:04:31.180
How are we affected?
00:04:31.180 --> 00:04:34.160
And also does that acid burn your skin,
00:04:34.160 --> 00:04:37.570
a very logical thing
(laughs) to want to know.
00:04:37.570 --> 00:04:40.990
So for cities, first of
all, acid rain is bad news
00:04:40.990 --> 00:04:43.600
because it can damage
buildings and statues,
00:04:43.600 --> 00:04:45.960
particularly those that
are made of limestone,
00:04:45.960 --> 00:04:47.930
marble, and some metals.
00:04:47.930 --> 00:04:51.640
Here in this photo is a gargoyle
from the Munich Town Hall,
00:04:51.640 --> 00:04:54.470
which is almost unrecognizable
00:04:54.470 --> 00:04:58.500
because of all the damage
it sustained from acid rain.
00:04:58.500 --> 00:05:01.330
There's also been a lot
of studies over the years,
00:05:01.330 --> 00:05:03.410
looking at the US Capitol
00:05:03.410 --> 00:05:06.410
and a lot of the surfaces
there that are made of marble
00:05:06.410 --> 00:05:08.620
and how they can strengthen them
00:05:08.620 --> 00:05:13.090
to protect them from acid
rain before it's too late.
00:05:13.090 --> 00:05:16.400
Now, if we go a little
deeper, acid rain can leach
00:05:16.400 --> 00:05:19.160
or pull out heavy metals, like aluminum,
00:05:19.160 --> 00:05:21.060
from the soil or rocks,
00:05:21.060 --> 00:05:23.380
which can then be washed out to lakes,
00:05:23.380 --> 00:05:26.500
and as you can imagine, can
lead to a lot of bad things
00:05:26.500 --> 00:05:28.910
like contaminating drinking water
00:05:28.910 --> 00:05:31.770
and harming aquatic ecosystems.
00:05:31.770 --> 00:05:34.950
Many fish can't survive at a lower pH.
00:05:34.950 --> 00:05:39.150
Acid rain also has impacts on
other natural environments,
00:05:39.150 --> 00:05:42.520
especially because of how far it reaches.
00:05:42.520 --> 00:05:46.090
Acid rain can damage and
weaken forests and trees
00:05:46.090 --> 00:05:48.560
by stripping nutrients from the soil
00:05:48.560 --> 00:05:51.830
and even damaging the waxy outer coat,
00:05:51.830 --> 00:05:56.430
leaving them much more vulnerable
to losing more nutrients.
00:05:56.430 --> 00:05:59.510
Now, when it comes to
humans, these acid vapors
00:05:59.510 --> 00:06:02.820
and the different
precipitation that they create
00:06:02.820 --> 00:06:06.340
are very harmful to
our respiratory system,
00:06:06.340 --> 00:06:09.023
and especially those that have asthma.
00:06:10.260 --> 00:06:12.260
And of course, I have
to answer the question,
00:06:12.260 --> 00:06:14.560
does acid rain burn your skin?
00:06:14.560 --> 00:06:18.010
The answer is no, it's
just not acidic enough.
00:06:18.010 --> 00:06:21.100
Remember acid rain is around a pH of four
00:06:21.100 --> 00:06:23.070
and for something to burn your skin,
00:06:23.070 --> 00:06:27.023
it has to be much more acidic,
usually around a pH of one.
00:06:28.950 --> 00:06:32.410
There is some good news
when it comes to acid rain.
00:06:32.410 --> 00:06:36.230
In 1990, the EPA created
the Acid Rain Program
00:06:36.230 --> 00:06:38.800
to help power plants reduce emissions.
00:06:38.800 --> 00:06:43.800
In 2019, when they looked at
the levels compared to 1990,
00:06:44.090 --> 00:06:46.650
they saw pretty great reductions,
00:06:46.650 --> 00:06:50.270
a 94% reduction in sulfur dioxide
00:06:50.270 --> 00:06:54.520
and an 86% reduction in nitric oxides.
00:06:54.520 --> 00:06:57.360
Now this is in the United
States, but around the world,
00:06:57.360 --> 00:06:59.510
acid rain is still a problem,
00:06:59.510 --> 00:07:02.520
particularly nitrates getting into the air
00:07:02.520 --> 00:07:07.510
from sources like fertilizer
and livestock feed.
00:07:07.510 --> 00:07:11.720
And even though we've had
great reductions since 1990,
00:07:11.720 --> 00:07:13.890
there is still some work to be done.
00:07:13.890 --> 00:07:16.080
And one of the ways that we can improve
00:07:16.080 --> 00:07:20.130
is by switching over to
cleaner burning fuels,
00:07:20.130 --> 00:07:22.990
or we can use renewable energy sources
00:07:22.990 --> 00:07:26.500
like solar power, wind
power, and hydro-power
00:07:26.500 --> 00:07:30.690
that ultimately reduce our
dependence on coal and oil.
00:07:30.690 --> 00:07:33.330
So now I hope you learned a
little bit about acid rain,
00:07:33.330 --> 00:07:35.830
how it's made, the impacts it can have,
00:07:35.830 --> 00:07:38.040
and I hope you don't lose any sleep
00:07:38.040 --> 00:07:39.773
over it burning your skin.
|
Evolution of group behavior | https://www.youtube.com/watch?v=61Zii5J8qoI | vtt | https://www.youtube.com/api/timedtext?v=61Zii5J8qoI&ei=21WUZYmANey2vdIP__6H4Ao&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245323&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D7B19374FC059E74C36902F0042AC9CC7ADD4060.3B1EC49FF7A337AEBD55015DCB0B21360B27BACD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.390 --> 00:00:02.740
- [Instructor] In our
journey, studying evolution
00:00:02.740 --> 00:00:05.590
and natural selection, we often index on
00:00:05.590 --> 00:00:07.000
individual organisms.
00:00:07.000 --> 00:00:10.430
If we look at a species or
population of a certain species,
00:00:10.430 --> 00:00:13.470
we've talked about how
there could be variation
00:00:13.470 --> 00:00:15.500
in that population, which I will depict
00:00:15.500 --> 00:00:19.280
by these colors and
these shapes over here.
00:00:19.280 --> 00:00:22.410
And sometimes the variation
really doesn't confer
00:00:22.410 --> 00:00:25.710
any advantage or disadvantage
for reproduction,
00:00:25.710 --> 00:00:27.540
but sometimes it might.
00:00:27.540 --> 00:00:29.267
And if a certain variation
00:00:29.267 --> 00:00:31.220
maybe because the environment changed
00:00:31.220 --> 00:00:33.700
or maybe this population finds themselves
00:00:33.700 --> 00:00:36.097
in a new ecosystem confers an advantage,
00:00:36.097 --> 00:00:40.320
well, that variant will be
more likely to multiply.
00:00:40.320 --> 00:00:43.210
And the genes which produce that phenotype
00:00:43.210 --> 00:00:45.520
are more likely to become
a larger and larger
00:00:45.520 --> 00:00:47.080
part of the gene pool.
00:00:47.080 --> 00:00:48.900
Similarly, if there's some disadvantage,
00:00:48.900 --> 00:00:51.990
maybe because the environment
has changed some way,
00:00:51.990 --> 00:00:54.920
well, that might select
out certain variants
00:00:54.920 --> 00:00:57.530
and the underlying genetics that cause it.
00:00:57.530 --> 00:00:59.090
But this is when we're
thinking about traits
00:00:59.090 --> 00:01:02.420
that primarily affect an
individual's chances of survival
00:01:02.420 --> 00:01:03.670
and reproduction.
00:01:03.670 --> 00:01:05.100
But what we're going to do in this video
00:01:05.100 --> 00:01:07.390
as this title implies, is focus on...
00:01:07.390 --> 00:01:09.810
it's not just about individual traits.
00:01:09.810 --> 00:01:12.628
There is also evolution of group behavior,
00:01:12.628 --> 00:01:15.660
and we see that right over
here in a school of fish.
00:01:15.660 --> 00:01:19.300
Why does it make sense
for these fish to ball up
00:01:19.300 --> 00:01:21.140
into this huge school?
00:01:21.140 --> 00:01:22.760
It might seem like it makes it very easy
00:01:22.760 --> 00:01:26.300
for a predator to just go
right into the middle of that
00:01:26.300 --> 00:01:28.930
and open its mouth and
get as much as it wants,
00:01:28.930 --> 00:01:31.440
an all you can eat buffet, so to speak.
00:01:31.440 --> 00:01:34.110
Well, it turns out that
this type of behavior
00:01:34.110 --> 00:01:36.200
does confer a benefit.
00:01:36.200 --> 00:01:39.210
The benefit is yes, this
shark that I just drew
00:01:39.210 --> 00:01:41.820
might be able to get a mouth full of fish,
00:01:41.820 --> 00:01:43.290
but the great majority of the fish
00:01:43.290 --> 00:01:44.730
are going to be protected.
00:01:44.730 --> 00:01:47.190
And by being in a big ball like this,
00:01:47.190 --> 00:01:48.740
instead of just having your own eyes,
00:01:48.740 --> 00:01:49.870
looking for a predator,
00:01:49.870 --> 00:01:52.420
as soon as any one of
these tens of thousands,
00:01:52.420 --> 00:01:55.180
or maybe hundreds of thousands
of fish spot a predator,
00:01:55.180 --> 00:01:56.920
well, the whole school will know it.
00:01:56.920 --> 00:01:59.470
So they're able to share information.
00:01:59.470 --> 00:02:02.850
Also, even though some
fish might get eaten up,
00:02:02.850 --> 00:02:06.240
the probability that any one
will be eaten by this shark
00:02:06.240 --> 00:02:07.810
is actually lower versus
00:02:07.810 --> 00:02:09.510
if there was just one of these fish,
00:02:09.510 --> 00:02:11.060
just swimming by itself,
00:02:11.060 --> 00:02:13.640
that one is much more
likely to be picked off.
00:02:13.640 --> 00:02:15.570
And we see this type of behavior in
00:02:15.570 --> 00:02:17.560
many, many, many types of animals.
00:02:17.560 --> 00:02:19.876
This right over here is
a herd of wildebeest.
00:02:19.876 --> 00:02:22.491
And once again, if you have
an individual wildebeest,
00:02:22.491 --> 00:02:24.750
it would be easy to be surrounded by say,
00:02:24.750 --> 00:02:28.175
hyenas, by predators, that
could be caught by surprise.
00:02:28.175 --> 00:02:31.860
The younger of the wildebeest
would be easy to pick off
00:02:31.860 --> 00:02:33.320
if they were by themselves.
00:02:33.320 --> 00:02:34.430
But if they're in a herd,
00:02:34.430 --> 00:02:36.120
maybe they can be in
the middle of the herd.
00:02:36.120 --> 00:02:39.880
Here's an example of adult
elephants protecting their young
00:02:39.880 --> 00:02:41.680
when they see a threat approaching.
00:02:41.680 --> 00:02:44.040
And notice, more than just the parents
00:02:44.040 --> 00:02:45.480
are protecting the young.
00:02:45.480 --> 00:02:47.870
These elephants are probably
related to each other.
00:02:47.870 --> 00:02:51.130
And so even though one elephant
might sacrifice themselves,
00:02:51.130 --> 00:02:52.890
maybe from some type of a threat,
00:02:52.890 --> 00:02:54.530
if they're able to protect the young,
00:02:54.530 --> 00:02:56.440
even though it might not be their child,
00:02:56.440 --> 00:02:58.660
it might be their nephew,
it might be their cousin,
00:02:58.660 --> 00:03:02.400
their shared genetics are
more likely to be passed on.
00:03:02.400 --> 00:03:04.670
You've sometimes heard
people say things like
00:03:04.670 --> 00:03:07.730
I'd be willing to die for two
brothers or eight cousins.
00:03:07.730 --> 00:03:09.180
And that would actually make sense
00:03:09.180 --> 00:03:11.100
from a genetic point of view,
00:03:11.100 --> 00:03:13.130
but it's not just about protection,
00:03:13.130 --> 00:03:15.190
where we see the evolution
of group behavior.
00:03:15.190 --> 00:03:17.746
We could also see it
in terms of predation.
00:03:17.746 --> 00:03:20.123
So this right over here
as a pack of wolves
00:03:20.123 --> 00:03:23.400
that are attacking this
bison here, and first of all,
00:03:23.400 --> 00:03:25.990
you can see how much more
vulnerable this bison is
00:03:25.990 --> 00:03:28.640
when it's alone than if
it were part of a herd.
00:03:28.640 --> 00:03:29.580
If it was part of a herd,
00:03:29.580 --> 00:03:31.350
it would be much harder to surround it.
00:03:31.350 --> 00:03:33.770
You'd have a ton of these
other bison all around
00:03:33.770 --> 00:03:36.380
that could run and
chase individual wolves.
00:03:36.380 --> 00:03:38.510
But when this bison is
surrounded like this,
00:03:38.510 --> 00:03:40.760
when it's outnumbered,
it is more vulnerable.
00:03:40.760 --> 00:03:41.890
And these wolves, which are
00:03:41.890 --> 00:03:44.570
much, much smaller
individually than this bison
00:03:44.570 --> 00:03:47.190
have a decent chance of taking it down.
00:03:47.190 --> 00:03:49.240
So once again, this group
behavior of these wolves
00:03:49.240 --> 00:03:51.486
to not hunt by themselves,
but to hunt together,
00:03:51.486 --> 00:03:54.420
to surround animals, to
coordinate with each other,
00:03:54.420 --> 00:03:56.650
that allows them to prey on animals
00:03:56.650 --> 00:03:59.160
much, much larger than themselves.
00:03:59.160 --> 00:04:01.240
So I encourage you to
think about this idea
00:04:01.240 --> 00:04:03.110
because it's happening all around us,
00:04:03.110 --> 00:04:05.257
including in human beings.
00:04:05.257 --> 00:04:07.530
We are social animals.
00:04:07.530 --> 00:04:10.250
This is occurring through
out the animal kingdom.
00:04:10.250 --> 00:04:12.400
And it's a really
fascinating thing to observe
00:04:12.400 --> 00:04:13.293
all around you.
|
Ocean acidification | https://www.youtube.com/watch?v=8JUEga3MYsM | vtt | https://www.youtube.com/api/timedtext?v=8JUEga3MYsM&ei=2VWUZZrLKpfJmLAP_8WhkAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=43AEC206851BB8CCA4F219A1893EEF5E01BD96E5.3B15B5AD0D5006E89FCD3AF378D5208403CB6600&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.400 --> 00:00:01.233
- [Instructor] In this video,
00:00:01.233 --> 00:00:05.670
we're going to talk a little
bit about ocean acidification.
00:00:05.670 --> 00:00:06.970
And as we'll see,
00:00:06.970 --> 00:00:11.270
it's all related to increased
carbon dioxide concentrations
00:00:11.270 --> 00:00:12.520
in the atmosphere.
00:00:12.520 --> 00:00:15.180
And we have talked about
this in other videos,
00:00:15.180 --> 00:00:18.280
but we can see if we look at
carbon dioxide concentrations
00:00:18.280 --> 00:00:21.390
over the last 800,000 years,
00:00:21.390 --> 00:00:24.450
which is well before modern
human beings existed,
00:00:24.450 --> 00:00:28.030
it has oscillated between
roughly 200 parts per million
00:00:28.030 --> 00:00:29.790
and 300 parts per million.
00:00:29.790 --> 00:00:32.280
But then if we look at modern times,
00:00:32.280 --> 00:00:35.150
the spike has gone well beyond that range.
00:00:35.150 --> 00:00:38.450
And this axis right over here,
it's covering so much time.
00:00:38.450 --> 00:00:41.870
It might not be obvious when
or why the spike has happened.
00:00:41.870 --> 00:00:43.570
So let's zoom in a little bit
00:00:43.570 --> 00:00:46.393
on the last several hundred years or so.
00:00:48.620 --> 00:00:49.970
And when you do that,
00:00:49.970 --> 00:00:52.240
this graph is showing us two things.
00:00:52.240 --> 00:00:55.100
In blue, we're seeing the actual emissions
00:00:55.100 --> 00:00:56.570
of carbon dioxide.
00:00:56.570 --> 00:00:58.330
And if we go pre-industrial revolution,
00:00:58.330 --> 00:01:00.750
or the early stages of
the industrial revolution,
00:01:00.750 --> 00:01:03.710
our emissions of carbon
dioxide were very low
00:01:03.710 --> 00:01:04.660
and fairly flat,
00:01:04.660 --> 00:01:07.490
and we have seen that they
have gone up dramatically,
00:01:07.490 --> 00:01:10.290
especially over the last 100 or so years.
00:01:10.290 --> 00:01:12.150
And that carbon dioxide
00:01:12.150 --> 00:01:14.490
doesn't just immediately
leave the atmosphere.
00:01:14.490 --> 00:01:16.520
It stays in the atmosphere for a while.
00:01:16.520 --> 00:01:18.130
So as we increase our emissions,
00:01:18.130 --> 00:01:21.890
the cumulative concentration
of carbon dioxide has gone up
00:01:21.890 --> 00:01:23.840
to those levels that we just saw.
00:01:23.840 --> 00:01:26.400
Before the industrial
revolution, or the early stages,
00:01:26.400 --> 00:01:27.850
we were within that range
00:01:27.850 --> 00:01:30.210
that we saw over the last 800,000 years,
00:01:30.210 --> 00:01:32.210
but then it cumulatively has increased
00:01:32.210 --> 00:01:35.770
so to get us to this place
that is far out of that range.
00:01:35.770 --> 00:01:38.800
And to appreciate what
it's doing to our oceans,
00:01:38.800 --> 00:01:41.680
we just have to recognize that
the carbon dioxide in the air
00:01:41.680 --> 00:01:44.330
is in interaction with the ocean,
00:01:44.330 --> 00:01:46.340
actually with water everywhere.
00:01:46.340 --> 00:01:50.700
So if I were to have some H2O, or water,
00:01:50.700 --> 00:01:53.770
in reaction with carbon dioxide,
00:01:53.770 --> 00:01:56.660
that is going to react, or
it could be in equilibrium,
00:01:56.660 --> 00:02:00.473
to form what is known as
carbonic acid, which is H2CO3.
00:02:02.210 --> 00:02:03.710
If you wanna know how
the bonds are structured,
00:02:03.710 --> 00:02:07.160
it looks like this,
00:02:07.160 --> 00:02:11.560
where each of the oxygens
are attached to a hydrogen.
00:02:11.560 --> 00:02:13.870
And the reason why this
is called carbonic acid,
00:02:13.870 --> 00:02:17.380
is because it can easily
release a hydrogen ion.
00:02:17.380 --> 00:02:21.180
So this can be in
equilibrium with bicarbonate,
00:02:21.180 --> 00:02:24.910
which is HCO3 minus.
00:02:24.910 --> 00:02:28.650
So it's really just our carbonic
acid minus a hydrogen ion,
00:02:28.650 --> 00:02:31.700
plus a hydrogen ion.
00:02:31.700 --> 00:02:34.070
So as you have more
carbon dioxide in the air
00:02:34.070 --> 00:02:36.520
that reacts with water in the ocean,
00:02:36.520 --> 00:02:39.000
well, then you're going
to have more carbonic acid
00:02:39.000 --> 00:02:42.670
and you're going to have
more of your hydrogen ions.
00:02:42.670 --> 00:02:44.730
The reaction is going to go this way
00:02:44.730 --> 00:02:47.180
as you have more of this stuff,
00:02:47.180 --> 00:02:50.220
and especially more of the carbon dioxide.
00:02:50.220 --> 00:02:52.870
And we have observed that
in the oceans themselves.
00:02:52.870 --> 00:02:55.870
We have seen that ocean pH,
00:02:55.870 --> 00:02:58.020
if we go to the early
industrial revolution,
00:02:58.020 --> 00:03:02.250
it was around 8.2 and it has gone to 8.1.
00:03:02.250 --> 00:03:04.170
And you might recognize
that the lower the pH,
00:03:04.170 --> 00:03:06.857
the more acidic it is, but
you also might be saying,
00:03:06.857 --> 00:03:09.460
"Hey, that doesn't look
like that much of a change,"
00:03:09.460 --> 00:03:11.710
but it actually turns
out that pH is measured
00:03:11.710 --> 00:03:13.520
on a logarithmic scale,
00:03:13.520 --> 00:03:15.860
so we're actually talking
about powers of 10.
00:03:15.860 --> 00:03:18.680
So this change, if you really
wanna get into the math,
00:03:18.680 --> 00:03:22.200
pH is the negative log of the
hydrogen ion concentration,
00:03:22.200 --> 00:03:24.470
and so the hydrogen ion concentration
00:03:24.470 --> 00:03:26.680
here relative to there,
if we wanted to compare,
00:03:26.680 --> 00:03:28.260
if we wanted see how much it grew,
00:03:28.260 --> 00:03:32.570
you would say 10 to the
negative 8.1 over 10
00:03:32.570 --> 00:03:34.710
to the negative 8.2.
00:03:34.710 --> 00:03:36.210
And if you look at this analysis,
00:03:36.210 --> 00:03:39.530
you'll see that this
is approximately 1.26,
00:03:39.530 --> 00:03:40.700
or another way of thinking about it,
00:03:40.700 --> 00:03:42.560
over the course of the
industrial revolution,
00:03:42.560 --> 00:03:45.220
because of the trends we
have seen in this graph
00:03:45.220 --> 00:03:49.640
that our oceans are about 26% more acidic.
00:03:49.640 --> 00:03:52.450
And to appreciate why this is a big deal,
00:03:52.450 --> 00:03:56.250
I will remind you that
things like coral reefs
00:03:56.250 --> 00:03:58.600
or shells in sea animals,
00:03:58.600 --> 00:04:02.210
these are formed with calcium carbonate.
00:04:02.210 --> 00:04:04.050
In calcium carbonate,
00:04:04.050 --> 00:04:09.050
you have a positively charged
calcium ion forming ionic bond
00:04:09.690 --> 00:04:14.690
with a carbonate ion, and
carbonate looks like this,
00:04:15.870 --> 00:04:18.810
which looks a awful lot of
what we see right over here
00:04:18.810 --> 00:04:21.630
in the carbonic acid, or the bicarbonate.
00:04:21.630 --> 00:04:23.840
And so if all of a sudden
you have a lot more
00:04:23.840 --> 00:04:27.190
of these hydrogen ions in
the water and dissolved,
00:04:27.190 --> 00:04:28.810
everything's more acidic now,
00:04:28.810 --> 00:04:31.110
it might disrupt this
process of formation.
00:04:31.110 --> 00:04:32.880
Some of this carbonate might go
00:04:32.880 --> 00:04:34.750
and nab some of these hydrogen ions,
00:04:34.750 --> 00:04:37.610
less likely to form an
ionic bond with the calcium.
00:04:37.610 --> 00:04:39.640
It also doesn't just
directly affect things
00:04:39.640 --> 00:04:42.000
like calcium carbonate,
which is everywhere,
00:04:42.000 --> 00:04:43.940
it's actually the main
constituent of pearls.
00:04:43.940 --> 00:04:45.480
It's the structure of so many,
00:04:45.480 --> 00:04:48.550
especially rigid structures
in life, including sea life,
00:04:48.550 --> 00:04:49.970
it's actually also antacid.
00:04:49.970 --> 00:04:52.020
TUMS is mainly calcium carbonate,
00:04:52.020 --> 00:04:53.520
but this acidity in general
00:04:53.520 --> 00:04:56.040
is going to throw all
sorts of organisms off
00:04:56.040 --> 00:04:57.620
of their homeostasis.
00:04:57.620 --> 00:05:01.120
Organisms are highly, highly
sensitive to changes in pH,
00:05:01.120 --> 00:05:02.600
to changes in acidity.
00:05:02.600 --> 00:05:04.530
But the big picture takeaway,
00:05:04.530 --> 00:05:06.900
a lot of talk is about global warming
00:05:06.900 --> 00:05:09.730
and carbon dioxide
concentrations in the air,
00:05:09.730 --> 00:05:12.300
but it's also not only warming the ocean
00:05:12.300 --> 00:05:14.120
because of the greenhouse effect,
00:05:14.120 --> 00:05:16.990
but it's also making
the oceans more acidic,
00:05:16.990 --> 00:05:19.650
which is having some
obvious consequences now,
00:05:19.650 --> 00:05:21.910
and probably some follow on consequences
00:05:21.910 --> 00:05:24.513
that we are just beginning to understand.
|
Science, technology, and the environment | https://www.youtube.com/watch?v=FIYVnvHa2dc | vtt | https://www.youtube.com/api/timedtext?v=FIYVnvHa2dc&ei=2VWUZeDlKZbVxN8PybqV2A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8CC7A739FFB9778C76A1B14AEB13B52AF152247F.4F55A2193AF6B5F203EBC5B3FA9E8C3B06BE3E24&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.290 --> 00:00:02.620
- [Narrator] So I really
like to snack and one
00:00:02.620 --> 00:00:04.200
of my most favorite snacks
00:00:04.200 --> 00:00:06.760
of all time happens to be bananas.
00:00:06.760 --> 00:00:08.930
I mean, you can have them in a smoothie,
00:00:08.930 --> 00:00:13.390
with some peanut butter, on
some toast, in any way, really.
00:00:13.390 --> 00:00:15.050
And usually like most people,
00:00:15.050 --> 00:00:17.740
I just throw away the peels
after I'm done eating,
00:00:17.740 --> 00:00:19.680
but did you know that banana peels
00:00:19.680 --> 00:00:22.810
and leaves can be used to
make all kinds of things now?
00:00:22.810 --> 00:00:25.580
In fact, since over 100 billion bananas
00:00:25.580 --> 00:00:28.030
are consumed annually around the world,
00:00:28.030 --> 00:00:30.050
scientists have developed technologies
00:00:30.050 --> 00:00:32.100
that convert banana peels and leaves
00:00:32.100 --> 00:00:35.860
into useful materials that
are also bio-degradable.
00:00:35.860 --> 00:00:39.010
For example, bananas can
be used to make shoe soles,
00:00:39.010 --> 00:00:40.980
which is truly mind blowing.
00:00:40.980 --> 00:00:44.400
So a designer named Sarah
Harbarth used banana peel waste
00:00:44.400 --> 00:00:49.180
to create a durable material
called Kouri, K-U-O-R-I,
00:00:49.180 --> 00:00:52.510
which is used for everything
from glasses, to belts,
00:00:52.510 --> 00:00:56.020
and even phone cases and shoe soles.
00:00:56.020 --> 00:00:58.680
Banana leaves are also
used for making things
00:00:58.680 --> 00:01:01.840
like disposable tableware or containers.
00:01:01.840 --> 00:01:05.890
So in 2010, a young inventor
named Tenith Adithyaa saw
00:01:05.890 --> 00:01:07.800
how banana leaves were going to waste
00:01:07.800 --> 00:01:11.100
and developed a technology that
would preserve banana leaves
00:01:11.100 --> 00:01:13.040
for up to three years.
00:01:13.040 --> 00:01:14.500
And these could also be used
00:01:14.500 --> 00:01:17.130
to create biodegradable containers.
00:01:17.130 --> 00:01:19.200
So you're probably
wondering why I'm rambling
00:01:19.200 --> 00:01:20.880
so much about bananas
00:01:20.880 --> 00:01:23.020
and as much as I love them as a snack,
00:01:23.020 --> 00:01:25.560
I personally think that
it's even more awesome
00:01:25.560 --> 00:01:27.040
that scientists and engineers
00:01:27.040 --> 00:01:31.010
are creating useful, biodegradable
materials out of them.
00:01:31.010 --> 00:01:33.480
Technologies like Sarah and Tenith's
00:01:33.480 --> 00:01:36.450
that help reduce plastic
waste are super great
00:01:36.450 --> 00:01:38.730
for our planet and its biodiversity
00:01:38.730 --> 00:01:41.270
because they prevent
more plastic microfibers
00:01:41.270 --> 00:01:43.070
from polluting our environment.
00:01:43.070 --> 00:01:44.730
And that's the great news.
00:01:44.730 --> 00:01:46.510
With science and engineering,
00:01:46.510 --> 00:01:48.930
we humans can create technologies
00:01:48.930 --> 00:01:51.430
that prevent ecosystem degradation,
00:01:51.430 --> 00:01:55.700
reduce pollution and
improve sustainability.
00:01:55.700 --> 00:01:57.230
So let's take a look at a couple
00:01:57.230 --> 00:01:59.200
of other really cool examples.
00:01:59.200 --> 00:02:02.590
Since I live in the sunny all
year long state of Arizona,
00:02:02.590 --> 00:02:05.370
it's not uncommon to
see residents making use
00:02:05.370 --> 00:02:07.520
of solar panels here.
00:02:07.520 --> 00:02:10.840
So this kind of technology
was created to allow photons,
00:02:10.840 --> 00:02:14.810
or light particles, to
generate a flow of electricity.
00:02:14.810 --> 00:02:17.440
And since it harnesses
energy from the sun,
00:02:17.440 --> 00:02:21.400
this kind of electricity doesn't
require using fossil fuels.
00:02:21.400 --> 00:02:23.840
So this means that solar panels help limit
00:02:23.840 --> 00:02:26.690
greenhouse gas emissions, which contribute
00:02:26.690 --> 00:02:28.740
to global warming and pose a threat
00:02:28.740 --> 00:02:32.360
to the biodiversity
present on earth right now.
00:02:32.360 --> 00:02:35.880
And even cooler for people
who want a more sleek option
00:02:35.880 --> 00:02:38.480
to use for their homes,
we now have this thing
00:02:38.480 --> 00:02:40.760
called solar roof tiles.
00:02:40.760 --> 00:02:43.910
So these are roof tiles
that generate solar energy
00:02:43.910 --> 00:02:45.520
and isn't that so cool?
00:02:45.520 --> 00:02:48.970
Well technologies like this
will only continue improving,
00:02:48.970 --> 00:02:51.140
which will help us combat climate change
00:02:51.140 --> 00:02:53.810
and preserve biodiversity.
00:02:53.810 --> 00:02:56.140
Now, if we drive westwards from Arizona
00:02:56.140 --> 00:02:58.550
to California, the chances are you'll spot
00:02:58.550 --> 00:03:01.550
these huge white
windmills lining the Hills
00:03:01.550 --> 00:03:04.830
and windmills are another
source of clean energy.
00:03:04.830 --> 00:03:07.030
They are designed to harness wind
00:03:07.030 --> 00:03:08.970
and convert it to electricity.
00:03:08.970 --> 00:03:12.640
So windmills function in a
similar way to solar panels.
00:03:12.640 --> 00:03:14.570
thanks to the people who designed them,
00:03:14.570 --> 00:03:17.630
we have another alternative
to fossil fuels,
00:03:17.630 --> 00:03:19.813
which is super great for our planet.
00:03:20.750 --> 00:03:23.070
And I could go on and on about all
00:03:23.070 --> 00:03:25.670
of the amazing new technology
that's being created
00:03:25.670 --> 00:03:27.200
to protect the environment.
00:03:27.200 --> 00:03:29.810
Even now people are developing things
00:03:29.810 --> 00:03:34.810
like eco-friendly vehicles,
buildings, household devices,
00:03:35.080 --> 00:03:36.840
even waste management systems.
00:03:36.840 --> 00:03:38.750
And as you can probably tell from all
00:03:38.750 --> 00:03:40.410
of these unique technologies,
00:03:40.410 --> 00:03:42.710
scientists and engineers
have already found
00:03:42.710 --> 00:03:44.880
many different solutions to try
00:03:44.880 --> 00:03:47.310
and address environmental issues.
00:03:47.310 --> 00:03:48.947
But we also have to ask,
00:03:48.947 --> 00:03:52.470
"Are there any drawbacks to all
of these new contributions?"
00:03:52.470 --> 00:03:55.520
Well, there are some cons
that we have to consider.
00:03:55.520 --> 00:03:58.070
For instance, since these
environmental friendly
00:03:58.070 --> 00:04:01.650
technologies, or green
technologies are still
00:04:01.650 --> 00:04:04.100
relatively new ideas, we have to do a lot
00:04:04.100 --> 00:04:05.880
of research on them to make sure that
00:04:05.880 --> 00:04:08.730
the technology can make
a significant impact
00:04:08.730 --> 00:04:11.070
and succeed, and that we minimize
00:04:11.070 --> 00:04:14.950
the environmental impacts that
these technologies can have.
00:04:14.950 --> 00:04:18.740
So for example, solar panels
can take up a lot of space
00:04:18.740 --> 00:04:20.900
and impact sensitive habitats.
00:04:20.900 --> 00:04:24.870
So we need to research ways
to mitigate these effects.
00:04:24.870 --> 00:04:26.910
So this requires large amounts of money
00:04:26.910 --> 00:04:28.440
to be spent on researching
00:04:28.440 --> 00:04:30.310
and developing these technologies,
00:04:30.310 --> 00:04:32.770
which means that companies
may be less willing to switch
00:04:32.770 --> 00:04:35.400
and pay so much for green alternatives.
00:04:35.400 --> 00:04:38.110
And the high implementation
costs also means
00:04:38.110 --> 00:04:40.290
that at first consumers like you
00:04:40.290 --> 00:04:42.630
and me will probably
have to pay higher prices
00:04:42.630 --> 00:04:44.200
for these technologies compared
00:04:44.200 --> 00:04:45.960
to traditional products.
00:04:45.960 --> 00:04:48.570
Going back to our
discussion on solar panels,
00:04:48.570 --> 00:04:50.220
the drawback to installing panels
00:04:50.220 --> 00:04:52.900
at home is usually a higher price.
00:04:52.900 --> 00:04:55.760
So even though solar panels
would save homeowners money
00:04:55.760 --> 00:04:58.380
in the long run on electricity,
00:04:58.380 --> 00:05:00.130
some consumers might not be willing
00:05:00.130 --> 00:05:03.320
or able to pay for the
higher initial price.
00:05:03.320 --> 00:05:05.640
And last but not least,
some people who work
00:05:05.640 --> 00:05:07.740
in conventional industries may go out
00:05:07.740 --> 00:05:09.840
of business or lose their jobs.
00:05:09.840 --> 00:05:12.140
So in order for the world to go greener,
00:05:12.140 --> 00:05:14.530
we have to figure out ways
to protect these workers
00:05:14.530 --> 00:05:16.550
and businesses as well.
00:05:16.550 --> 00:05:18.870
So clearly there are many
challenges that we have
00:05:18.870 --> 00:05:21.270
to address if we want
to implement technology
00:05:21.270 --> 00:05:23.100
that's better for the environment,
00:05:23.100 --> 00:05:26.120
but there's plenty of pros
to, seeing how scientists
00:05:26.120 --> 00:05:29.500
and engineers can do so
much for the environment.
00:05:29.500 --> 00:05:31.340
With science and
engineering we can come up
00:05:31.340 --> 00:05:35.680
with methods to save
energy, reduce pollution,
00:05:35.680 --> 00:05:38.740
conserve our planet's precious resources,
00:05:38.740 --> 00:05:40.370
even feed more people
00:05:40.370 --> 00:05:42.170
and also create new business
00:05:42.170 --> 00:05:44.720
opportunities and jobs for people.
00:05:44.720 --> 00:05:45.800
And that's the great thing.
00:05:45.800 --> 00:05:48.170
Scientists and engineers and thinkers
00:05:48.170 --> 00:05:50.270
around the world can use our existing pool
00:05:50.270 --> 00:05:54.430
of knowledge to address some
of the biggest issues of today.
00:05:54.430 --> 00:05:56.900
So to wrap up this video, today we learned
00:05:56.900 --> 00:05:59.380
that scientists and
engineers can find solutions
00:05:59.380 --> 00:06:01.790
to preserve the environment and make way
00:06:01.790 --> 00:06:03.600
for a better future.
00:06:03.600 --> 00:06:05.540
So the next time you have a banana,
00:06:05.540 --> 00:06:08.700
or any fruit for that
matter, spot solar panels
00:06:08.700 --> 00:06:10.520
or a drive by some windmills,
00:06:10.520 --> 00:06:12.200
I hope you can reflect on the fact
00:06:12.200 --> 00:06:15.610
that these green
innovations start as ideas.
00:06:15.610 --> 00:06:18.200
So if you ever have an
idea for a technology
00:06:18.200 --> 00:06:20.210
that you think can help our environment,
00:06:20.210 --> 00:06:21.530
you should write it down.
00:06:21.530 --> 00:06:23.763
It just might be useful one day.
|
Solid waste disposal | https://www.youtube.com/watch?v=LOzMugtKmN4 | vtt | https://www.youtube.com/api/timedtext?v=LOzMugtKmN4&ei=3FWUZaLlC4fBmLAPh5KRsA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245324&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=91804DEDCCC65DA27FBA29AD8EC7E1073AA7AB5E.551E84E93CFB2345DBE2D0BD39B8D8E7CA56DC21&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.760 --> 00:00:03.180
- [Narrator] Time for a little trash talk,
00:00:03.180 --> 00:00:06.640
the United States produces
more solid waste each year,
00:00:06.640 --> 00:00:11.160
than any other nation and as
we make more and more trash,
00:00:11.160 --> 00:00:13.580
we're running out of places to put it,
00:00:13.580 --> 00:00:16.380
there are two main types of solid waste,
00:00:16.380 --> 00:00:20.830
industrial solid waste
and municipal solid waste.
00:00:20.830 --> 00:00:23.540
Industrial solid waste
comes from industries,
00:00:23.540 --> 00:00:27.980
like factories, mines and farms,
00:00:27.980 --> 00:00:31.140
municipal waste on the
other hand comes from homes
00:00:31.140 --> 00:00:33.350
and workplaces like offices,
00:00:33.350 --> 00:00:35.880
it's basically the stuff
you'd put in your trash can
00:00:35.880 --> 00:00:40.770
or dumpster like paper, plastic
bags, cardboard, food waste,
00:00:40.770 --> 00:00:43.910
cans, bottles and yard waste.
00:00:43.910 --> 00:00:46.740
Suppose you're on a
picnic with your friends,
00:00:46.740 --> 00:00:49.300
being an AP Environmental
Science student and all,
00:00:49.300 --> 00:00:52.030
you brought reusable utensils,
00:00:52.030 --> 00:00:55.650
you see an old empty potato
chip bag on the ground,
00:00:55.650 --> 00:00:58.140
you're able to identify
it as a fine specimen
00:00:58.140 --> 00:01:00.280
of municipal solid waste,
00:01:00.280 --> 00:01:03.180
you decide to pick it up
and put it in the trash
00:01:03.180 --> 00:01:06.270
but now that it's in the
trash where will it go?
00:01:06.270 --> 00:01:09.210
Most likely it'll end up in a landfill,
00:01:09.210 --> 00:01:10.350
just like more than half
00:01:10.350 --> 00:01:12.980
of the United States
municipal solid waste,
00:01:12.980 --> 00:01:17.100
to store so much waste
landfills have to be really big,
00:01:17.100 --> 00:01:19.950
one kind of landfill is an open dump,
00:01:19.950 --> 00:01:23.740
which is a large field
or pit filled with trash
00:01:23.740 --> 00:01:26.350
and let's think about
the pros of an open dump
00:01:26.350 --> 00:01:28.620
for one thing they're really big,
00:01:28.620 --> 00:01:32.240
so, they allow a lot of people
to get rid of a lot of waste,
00:01:32.240 --> 00:01:34.210
this is why they're often
used near big cities
00:01:34.210 --> 00:01:36.160
with large populations,
00:01:36.160 --> 00:01:38.970
they're also pretty
inexpensive to maintain
00:01:38.970 --> 00:01:41.330
and they do a great job at keeping waste,
00:01:41.330 --> 00:01:44.190
away from people's homes and workplaces
00:01:44.190 --> 00:01:46.850
but if we take a closer
look at open dumps,
00:01:46.850 --> 00:01:49.980
we can see that there are
some potential problems too,
00:01:49.980 --> 00:01:52.870
first off open dumps can be smelly,
00:01:52.870 --> 00:01:54.440
which could be unpleasant for the people,
00:01:54.440 --> 00:01:55.920
who live around them
00:01:55.920 --> 00:01:59.840
because open dumps are
uncovered and uncompacted,
00:01:59.840 --> 00:02:02.340
the wildlife and the weather
could spread the waste,
00:02:02.340 --> 00:02:04.310
into the surrounding environment.
00:02:04.310 --> 00:02:07.820
The trash in open dumps
can emit dangerous gases
00:02:07.820 --> 00:02:09.853
and even catch on fire,
00:02:11.220 --> 00:02:14.160
so, we can add gases and
fires to our list of cons
00:02:14.160 --> 00:02:17.350
because these could be
dangerous to wildlife.
00:02:17.350 --> 00:02:20.480
Another problem happens when it rains,
00:02:20.480 --> 00:02:24.400
the water seeps into the
landfill and as it goes through,
00:02:24.400 --> 00:02:27.360
it gets contaminated with toxic materials,
00:02:27.360 --> 00:02:29.470
like heavy metals from electronics
00:02:29.470 --> 00:02:32.740
or waste from discarded
prescription drugs,
00:02:32.740 --> 00:02:35.420
this contaminated water
that comes out of landfill
00:02:35.420 --> 00:02:39.130
is called leachate and
when you think about it,
00:02:39.130 --> 00:02:42.830
the word leachate makes sense
because the root word leach,
00:02:42.830 --> 00:02:44.350
means that this water absorbs
00:02:44.350 --> 00:02:47.860
and carries some of the
dissolved waste material with it
00:02:47.860 --> 00:02:49.630
and leachate can be dangerous
00:02:49.630 --> 00:02:51.560
because it can seep into the soil
00:02:51.560 --> 00:02:52.810
and contaminate groundwater,
00:02:52.810 --> 00:02:54.750
that people rely on for drinking,
00:02:54.750 --> 00:02:58.310
so, this can make the water
supply toxic to humans.
00:02:58.310 --> 00:03:00.190
Another problem with open dumps
00:03:00.190 --> 00:03:02.330
is that they require a lot of land,
00:03:02.330 --> 00:03:04.483
which means they cause
habitat destruction.
00:03:07.640 --> 00:03:10.490
Another kind of landfill
is a sanitary landfill
00:03:11.530 --> 00:03:12.550
and you may be thinking,
00:03:12.550 --> 00:03:16.440
how can a landfill, a
pit of trash be sanitary?
00:03:16.440 --> 00:03:17.880
Well, sanitary landfills,
00:03:17.880 --> 00:03:21.100
have something that open
dumps don't a liner,
00:03:21.100 --> 00:03:25.560
which is a layer of clay or
plastic that keeps the trash in
00:03:25.560 --> 00:03:28.890
and every day when trash
is put in the landfill,
00:03:28.890 --> 00:03:31.240
it's covered by a layer
of construction debris
00:03:31.240 --> 00:03:34.920
or low quality soil and then
it's compacted into a cell
00:03:35.880 --> 00:03:37.253
and the process repeats.
00:03:38.290 --> 00:03:40.910
With all of it's tightly
sealed and compacted cells,
00:03:40.910 --> 00:03:43.570
it's very hard for water
to get into the landfill,
00:03:43.570 --> 00:03:46.070
so, sanitary landfills keep
the environment inside,
00:03:46.070 --> 00:03:48.750
really dry but over time,
00:03:48.750 --> 00:03:51.260
rainwater will eventually
infiltrate the layers
00:03:51.260 --> 00:03:52.720
and form leachate,
00:03:52.720 --> 00:03:55.970
the tightly sealed cells
prevent water from leaving too,
00:03:55.970 --> 00:03:58.960
so, leachate can build
up inside the landfill,
00:03:58.960 --> 00:04:01.740
some sanitary landfills are
built with double liners
00:04:01.740 --> 00:04:05.720
and pipes so that leachate
can be stored and treated.
00:04:05.720 --> 00:04:08.130
If you went inside a sanitary landfill,
00:04:08.130 --> 00:04:10.100
you wouldn't be able to breathe
00:04:10.100 --> 00:04:12.370
and not because it would be super smelly,
00:04:12.370 --> 00:04:15.190
this is because the cells
are sealed up so tightly,
00:04:15.190 --> 00:04:17.960
that it's hard for oxygen
to get in and circulate,
00:04:17.960 --> 00:04:21.440
the environment inside
is mostly anaerobic,
00:04:21.440 --> 00:04:23.830
which means that there is little oxygen,
00:04:23.830 --> 00:04:26.900
you see the prefix an means not or without
00:04:26.900 --> 00:04:30.810
and the word aerobic means
involving or requiring oxygen,
00:04:30.810 --> 00:04:34.023
so, the word anaerobic describes
a place without oxygen.
00:04:34.960 --> 00:04:38.370
So, aerobic decomposition
which is a process of decay,
00:04:38.370 --> 00:04:41.040
that takes place in aerobic environments
00:04:41.040 --> 00:04:44.660
and involves microorganisms
that need oxygen to survive,
00:04:44.660 --> 00:04:48.990
can't occur instead
anaerobic decomposition,
00:04:48.990 --> 00:04:50.770
which is decay by microorganisms,
00:04:50.770 --> 00:04:54.070
that don't need oxygen takes place,
00:04:54.070 --> 00:04:57.220
this process produces
methane, a greenhouse gas,
00:04:57.220 --> 00:04:59.440
that contributes to global warming,
00:04:59.440 --> 00:05:02.960
it could take several decades
or even hundreds of years
00:05:02.960 --> 00:05:04.370
for the tightly compacted waste
00:05:04.370 --> 00:05:06.580
in a sanitary landfill to decompose,
00:05:06.580 --> 00:05:08.610
so, this type of landfill can contribute,
00:05:08.610 --> 00:05:10.673
to global warming for a long time.
00:05:11.710 --> 00:05:15.580
So, what are the pros and
cons of sanitary landfills?
00:05:15.580 --> 00:05:19.950
Compared with open dumps sanitary
landfills are less smelly
00:05:19.950 --> 00:05:22.510
and less likely to catch on fire
00:05:22.510 --> 00:05:25.370
and because sanitary landfills
keep the waste inside,
00:05:25.370 --> 00:05:28.630
covered and compacted we
don't have the same problem
00:05:28.630 --> 00:05:31.640
of the wildlife and the
weather moving around the waste
00:05:31.640 --> 00:05:34.490
but no landfill is perfectly sealed,
00:05:34.490 --> 00:05:37.580
so, leachate can still seep out,
00:05:37.580 --> 00:05:42.010
adding and compacting layers
of trash causes dust and noise,
00:05:42.010 --> 00:05:44.420
also remember that the
anaerobic decomposition
00:05:44.420 --> 00:05:48.140
in sanitary landfills produces
methane, a greenhouse gas
00:05:48.140 --> 00:05:50.900
but some sanitary landfills
capture the methane,
00:05:50.900 --> 00:05:52.330
emitted by the decomposition,
00:05:52.330 --> 00:05:54.840
so, that it can be burned
to generate electricity,
00:05:54.840 --> 00:05:56.980
this can capture 60% to 90%
00:05:56.980 --> 00:05:59.030
of the methane produced by the landfill,
00:05:59.030 --> 00:06:01.150
so, that methane capture could be a pro
00:06:01.150 --> 00:06:03.960
because it generates electricity.
00:06:03.960 --> 00:06:07.780
Sanitary landfills are really expensive,
00:06:07.780 --> 00:06:09.210
so, they are a lot more common
00:06:09.210 --> 00:06:11.810
in more economically developed countries
00:06:11.810 --> 00:06:16.210
and like open dumps they
require a lot of land.
00:06:16.210 --> 00:06:18.270
One way to reduce the amount of material,
00:06:18.270 --> 00:06:19.830
that needs to be landfilled
00:06:19.830 --> 00:06:22.170
is by burning it in an incinerator,
00:06:22.170 --> 00:06:24.170
this reduction in the volume of the waste
00:06:24.170 --> 00:06:27.410
is really helpful in areas
with limited land space,
00:06:27.410 --> 00:06:29.530
so, reducing the volume of trash
00:06:29.530 --> 00:06:31.660
is one of incineration's pros,
00:06:31.660 --> 00:06:34.700
modern high-tech waste
to energy incinerators,
00:06:34.700 --> 00:06:37.690
have another pro they
can produce electricity
00:06:37.690 --> 00:06:39.800
and sell it to consumers,
00:06:39.800 --> 00:06:41.770
some of the cons of burning trash,
00:06:41.770 --> 00:06:46.020
are that it emits CO2,
ash waste, hazardous gases
00:06:46.020 --> 00:06:47.970
and other air pollutants.
00:06:47.970 --> 00:06:50.730
Incinerators could be built to
help reduce these emissions,
00:06:50.730 --> 00:06:52.980
by using a series of filters,
00:06:52.980 --> 00:06:56.880
to remove mercury and dioxins
from the exhaust gases.
00:06:56.880 --> 00:06:59.330
Another way to lessen the
danger of burning trash
00:06:59.330 --> 00:07:01.540
is by sorting out the hazardous materials,
00:07:01.540 --> 00:07:04.890
before the incineration
but these safety features,
00:07:04.890 --> 00:07:06.550
like the filters and the sorting,
00:07:06.550 --> 00:07:09.273
make waste incineration
much more expensive.
00:07:10.340 --> 00:07:12.800
Despite all these ways
of getting rid of waste,
00:07:12.800 --> 00:07:15.600
we're still having trouble
finding places to put it,
00:07:15.600 --> 00:07:17.570
the landfill near my home filled up,
00:07:17.570 --> 00:07:19.890
so, my county transfers its waste,
00:07:19.890 --> 00:07:22.490
to a sanitary landfill
in a neighboring state
00:07:22.490 --> 00:07:25.280
and this transportation burns fossil fuels
00:07:25.280 --> 00:07:27.173
and produces greenhouse gases.
00:07:28.450 --> 00:07:30.170
But what can we do with the landfills,
00:07:30.170 --> 00:07:31.780
that are already filled up?
00:07:31.780 --> 00:07:34.780
Some old landfills are
mined for valuable metals
00:07:34.780 --> 00:07:36.720
and recyclable materials,
00:07:36.720 --> 00:07:39.580
my home state of Virginia,
turned an old closed landfill
00:07:39.580 --> 00:07:41.840
in Virginia Beach into a public park,
00:07:41.840 --> 00:07:44.460
called Mount Trashmore park,
00:07:44.460 --> 00:07:48.350
it's actually one of the most
popular parks in the area,
00:07:48.350 --> 00:07:51.100
so if you ever feel like
picnicking on a landfill,
00:07:51.100 --> 00:07:52.550
that might be the one to try.
|
Extinction | https://www.youtube.com/watch?v=gmr5QYeFJ4g | vtt | https://www.youtube.com/api/timedtext?v=gmr5QYeFJ4g&ei=2VWUZf3HMPu4vdIPus-juAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=30D951B9FB516C2B73BCC720D55AAF4D9A2DAF08.07C8C02C7176C7B7DFE75BABC9506FC1A30B2A31&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:01.035 --> 00:00:03.200
- [Instructor] When we think
of the term extinction,
00:00:03.200 --> 00:00:05.950
we tend to think of
events like what happened,
00:00:05.950 --> 00:00:09.020
what we believe happened
63 million years ago
00:00:09.020 --> 00:00:11.430
when a large meteor hit the earth
00:00:11.430 --> 00:00:14.260
and killed most of the dinosaurs.
00:00:14.260 --> 00:00:15.580
And I say most of them,
00:00:15.580 --> 00:00:17.510
because a lot of animals
that we know today
00:00:17.510 --> 00:00:19.550
especially birds, birds like chickens,
00:00:19.550 --> 00:00:20.990
we believe are actually descended
00:00:20.990 --> 00:00:24.050
from some of the dinosaurs that survived.
00:00:24.050 --> 00:00:26.300
And other species not just dinosaurs
00:00:26.300 --> 00:00:27.490
would have gone extinct,
00:00:27.490 --> 00:00:30.140
but clearly some other
species did survive.
00:00:30.140 --> 00:00:31.740
Our ancestors might've been
00:00:31.740 --> 00:00:34.650
some type of burrowing
squirrel rodent like thing
00:00:34.650 --> 00:00:36.190
that maybe was under the ground
00:00:36.190 --> 00:00:38.990
and was able to survive
the immediate shocks
00:00:38.990 --> 00:00:40.680
and then somehow find food
00:00:40.680 --> 00:00:43.020
even when the earth was covered by dust
00:00:43.020 --> 00:00:44.960
and there wasn't a lot of
photosynthesis going on,
00:00:44.960 --> 00:00:47.770
but they were able to survive somehow.
00:00:47.770 --> 00:00:49.870
What we're gonna do in this
video though is think about
00:00:49.870 --> 00:00:52.200
more subtle notion of extinction.
00:00:52.200 --> 00:00:53.580
It's not always caused
00:00:53.580 --> 00:00:56.530
by these massive changes
in the environment.
00:00:56.530 --> 00:00:58.040
But one thread,
00:00:58.040 --> 00:01:00.960
one theme that we will be
talking about in extinction
00:01:00.960 --> 00:01:04.430
is that the environment is to
some degree always changing.
00:01:04.430 --> 00:01:07.580
And when there is
variation in a population,
00:01:07.580 --> 00:01:09.600
so I'm gonna draw some variation as I do
00:01:09.600 --> 00:01:12.170
with the different colored circles.
00:01:12.170 --> 00:01:14.820
If the environment changes gradually
00:01:14.820 --> 00:01:16.820
or in certain slow ways,
00:01:16.820 --> 00:01:20.750
there will oftentimes be variants,
members of the population
00:01:20.750 --> 00:01:23.350
that will be more likely
to succeed than others.
00:01:23.350 --> 00:01:26.050
And so those variants
that are more suitable
00:01:26.050 --> 00:01:28.000
for those changes in the environment,
00:01:28.000 --> 00:01:30.810
well, they will reproduce
more, they will survive more.
00:01:30.810 --> 00:01:32.330
They will become the dominant variant
00:01:32.330 --> 00:01:36.330
and over time they can
even become a new species.
00:01:36.330 --> 00:01:39.420
And so over time you have
species won't go extinct,
00:01:39.420 --> 00:01:41.620
but they would be adapting
or maybe even evolving
00:01:41.620 --> 00:01:45.510
into other species that are
more suited to the environment.
00:01:45.510 --> 00:01:47.850
But our meteorite dinosaur example
00:01:47.850 --> 00:01:50.790
shows us that change is
not always a gradual.
00:01:50.790 --> 00:01:54.140
And clearly in a situation
where the sky is burning
00:01:54.140 --> 00:01:56.010
as you have in the dinosaur example,
00:01:56.010 --> 00:01:58.110
very few organisms we're
gonna be able to adapt
00:01:58.110 --> 00:02:00.420
to those types of circumstances.
00:02:00.420 --> 00:02:02.120
But you can also have fast change
00:02:02.120 --> 00:02:05.790
that might not seem so
fast to us as human beings.
00:02:05.790 --> 00:02:08.420
For example, this chart right over here
00:02:08.420 --> 00:02:11.110
shows extinctions since 1500.
00:02:11.110 --> 00:02:12.290
And I encourage you to pause this video
00:02:12.290 --> 00:02:14.680
and make sure you're processing
what is going on here,
00:02:14.680 --> 00:02:16.570
because that's a skill in and of itself,
00:02:16.570 --> 00:02:18.000
but it's really interesting.
00:02:18.000 --> 00:02:19.980
This tells us the cumulative percentage
00:02:19.980 --> 00:02:24.600
of species driven extinct
over the last 500 years or so.
00:02:24.600 --> 00:02:25.450
And so you can see
00:02:25.450 --> 00:02:28.520
relative to the species
that were there in 1500,
00:02:28.520 --> 00:02:31.610
if we follow let's say
the line for amphibians,
00:02:31.610 --> 00:02:35.440
amphibians it looks like
someplace between 2% and 2 1/2%
00:02:35.440 --> 00:02:38.350
of all species of amphibians
have gone extinct.
00:02:38.350 --> 00:02:41.670
This is not saying 2% to 2 1/2%
of the amphibians have died.
00:02:41.670 --> 00:02:44.130
This is saying the species of amphibians,
00:02:44.130 --> 00:02:45.720
they don't exist anymore.
00:02:45.720 --> 00:02:48.490
That variant of amphibian genotypes
00:02:48.490 --> 00:02:51.310
don't exist in our world anymore.
00:02:51.310 --> 00:02:52.970
And it's pretty bad for amphibians
00:02:52.970 --> 00:02:54.370
but we can see it's pretty bad
00:02:54.370 --> 00:02:56.670
for other types of animals as well.
00:02:56.670 --> 00:02:57.503
And you might say,
00:02:57.503 --> 00:03:00.500
well, this isn't so bad, 2% to 2 1/2%.
00:03:00.500 --> 00:03:01.430
But once again,
00:03:01.430 --> 00:03:04.640
these are entire species
that we will never see again
00:03:04.640 --> 00:03:06.300
and what's also troubling
00:03:06.300 --> 00:03:09.430
is how these curves are
just rocketing upwards.
00:03:09.430 --> 00:03:10.590
And some of you all might be thinking,
00:03:10.590 --> 00:03:13.240
isn't there always some
baseline level of extinction?
00:03:13.240 --> 00:03:15.690
Maybe this isn't so much
worse than that baseline.
00:03:15.690 --> 00:03:18.170
And what's interesting
about this graphic here is
00:03:18.170 --> 00:03:19.890
it shows us the baseline.
00:03:19.890 --> 00:03:21.400
This little gray square they're saying
00:03:21.400 --> 00:03:23.690
that's the cumulative
percentage of species
00:03:23.690 --> 00:03:28.340
based on background rate
of 0.1 to 2 extinctions
00:03:28.340 --> 00:03:31.210
per million species per year.
00:03:31.210 --> 00:03:33.900
And so you see the baseline
in this little gray
00:03:33.900 --> 00:03:35.030
right down here.
00:03:35.030 --> 00:03:37.960
If we didn't have unusual
amounts of extinction,
00:03:37.960 --> 00:03:41.090
we would just be charting
roughly close to this line.
00:03:41.090 --> 00:03:44.430
But you can see since 1500,
we have gone well above it
00:03:44.430 --> 00:03:46.440
and we know why this is happening.
00:03:46.440 --> 00:03:49.650
Their environments are
changing very, very quickly.
00:03:49.650 --> 00:03:51.530
And who is the main culprit here
00:03:51.530 --> 00:03:54.500
of changing the environment
very, very quickly?
00:03:54.500 --> 00:03:57.980
Well, what group's population
has really expanded
00:03:57.980 --> 00:04:00.140
over the last 500 years?
00:04:00.140 --> 00:04:03.580
And you would of course say human beings.
00:04:03.580 --> 00:04:05.790
And human beings, it's
not just where they live
00:04:05.790 --> 00:04:07.180
and they're taking habitats away,
00:04:07.180 --> 00:04:10.130
you can imagine this
environment is very different
00:04:10.130 --> 00:04:12.900
than the environment of
what modern day Los Angeles
00:04:12.900 --> 00:04:15.700
would have been say 500 years ago.
00:04:15.700 --> 00:04:17.720
And it's not just where we live,
00:04:17.720 --> 00:04:20.370
it's also the food we
need and we do need food.
00:04:20.370 --> 00:04:22.750
But that takes up ecosystems environments
00:04:22.750 --> 00:04:24.790
where other animals might have lived
00:04:24.790 --> 00:04:25.960
and it could be a dramatic change
00:04:25.960 --> 00:04:28.390
where they can't live anymore.
00:04:28.390 --> 00:04:30.920
And so human land and
agricultural land use
00:04:30.920 --> 00:04:33.330
is a major source of extinctions.
00:04:33.330 --> 00:04:34.630
But on top of that,
00:04:34.630 --> 00:04:37.930
we go into the sea and we
sometimes will over fish.
00:04:37.930 --> 00:04:40.520
That can be a source of extinction.
00:04:40.520 --> 00:04:42.020
Lack of diversity.
00:04:42.020 --> 00:04:45.060
As more and more species
learn to live with humans
00:04:45.060 --> 00:04:47.123
and maybe our lack of diversity,
00:04:47.960 --> 00:04:49.530
we only have a few types of crops,
00:04:49.530 --> 00:04:51.500
a few types of cattle that we grow.
00:04:51.500 --> 00:04:53.480
There might be certain species
that live well with them
00:04:53.480 --> 00:04:55.320
that are able to live off of them,
00:04:55.320 --> 00:04:56.870
but they might not have as much variation
00:04:56.870 --> 00:04:59.390
because the ecosystem is so not diverse
00:04:59.390 --> 00:05:00.810
and so there's some change,
00:05:00.810 --> 00:05:04.660
the species won't have the
variation necessarily to survive.
00:05:04.660 --> 00:05:07.320
On top of that, you throw
in things like pollution,
00:05:07.320 --> 00:05:09.710
global warming, invasive species,
00:05:09.710 --> 00:05:12.320
and you can see why
these curves are going up
00:05:12.320 --> 00:05:14.660
in a very, very, very troubling way.
00:05:14.660 --> 00:05:15.493
And I will add,
00:05:15.493 --> 00:05:17.640
this isn't just for us
to care about animals,
00:05:17.640 --> 00:05:18.980
although that is a good motivation
00:05:18.980 --> 00:05:20.190
for us to care about the species,
00:05:20.190 --> 00:05:21.970
because once a species has gone,
00:05:21.970 --> 00:05:23.840
you're never going to get it back again.
00:05:23.840 --> 00:05:25.290
But in general,
00:05:25.290 --> 00:05:28.050
the less diversity that
earth as a whole has,
00:05:28.050 --> 00:05:30.130
it means that our ecosystems
are going to become
00:05:30.130 --> 00:05:32.663
less and less robust to change.
|
Species and the environment | https://www.youtube.com/watch?v=YdZqK60bxjs | vtt | https://www.youtube.com/api/timedtext?v=YdZqK60bxjs&ei=2VWUZazvOru_p-oPreKsuA0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245322&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8F251CB32E950B09446B7D8E4B3AE3317747C9C8.7732BF58D69B6DBA65992962AE6E511855BA31AE&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.170 --> 00:00:01.960
- [Instructor] So we
tend to view evolution
00:00:01.960 --> 00:00:05.530
and natural selection and
the formation of new species,
00:00:05.530 --> 00:00:07.550
which is often called speciation,
00:00:07.550 --> 00:00:10.260
as a slow process that could take
00:00:10.260 --> 00:00:12.300
tens or hundreds of thousands of years,
00:00:12.300 --> 00:00:14.350
or, in many cases, millions of years.
00:00:14.350 --> 00:00:17.110
And that's why it's always
interesting to see examples
00:00:17.110 --> 00:00:18.840
of when it might actually be happening
00:00:18.840 --> 00:00:21.360
more on a human timeframe.
00:00:21.360 --> 00:00:22.880
So this right over here is a picture
00:00:22.880 --> 00:00:26.480
of a male Central European blackcap.
00:00:26.480 --> 00:00:30.100
So historically Central European blackcaps
00:00:30.100 --> 00:00:33.270
would spend their
summers in Central Europe
00:00:33.270 --> 00:00:34.103
right over here,
00:00:34.103 --> 00:00:36.510
in what we would now consider Germany.
00:00:36.510 --> 00:00:39.550
So let me write summer right over here.
00:00:39.550 --> 00:00:42.150
And then, when it gets
colder in Central Europe,
00:00:42.150 --> 00:00:46.460
they would migrate and spend
their winters in Spain.
00:00:46.460 --> 00:00:49.090
So this is where they
would spend their winters.
00:00:49.090 --> 00:00:52.340
Now, whenever we talk about
migratory patterns like this,
00:00:52.340 --> 00:00:53.880
it's always interesting to note
00:00:53.880 --> 00:00:56.004
that it's not that all
of the birds always go
00:00:56.004 --> 00:00:58.780
on the exact same migration path.
00:00:58.780 --> 00:01:00.480
As we've talked about in many videos,
00:01:00.480 --> 00:01:03.150
you tend to have
variation in a population.
00:01:03.150 --> 00:01:06.120
There are birds that because
of genetic differences,
00:01:06.120 --> 00:01:07.610
they might go in other directions.
00:01:07.610 --> 00:01:10.360
They might go that way,
they might go that way,
00:01:10.360 --> 00:01:11.830
they might go that way.
00:01:11.830 --> 00:01:14.670
But those variants probably
weren't successful.
00:01:14.670 --> 00:01:16.570
Some of them might end
up in the North Sea.
00:01:16.570 --> 00:01:18.750
Some of them might end
up freezing to death.
00:01:18.750 --> 00:01:21.540
Some of them might not be
able to have sources of food
00:01:21.540 --> 00:01:24.870
while the dominant variant
that wintered in Spain
00:01:24.870 --> 00:01:25.720
was successful.
00:01:25.720 --> 00:01:26.960
It was warmer there.
00:01:26.960 --> 00:01:28.810
They had access to food.
00:01:28.810 --> 00:01:31.200
Now, this is where it gets interesting.
00:01:31.200 --> 00:01:36.150
In the 1960s and 1970s, it
became more and more popular
00:01:36.150 --> 00:01:39.930
to put backyard bird feeders in England.
00:01:39.930 --> 00:01:43.710
And so some of those
Central European blackcaps
00:01:43.710 --> 00:01:46.020
just happened to go in that direction.
00:01:46.020 --> 00:01:48.160
They might've always been
happening to go there,
00:01:48.160 --> 00:01:50.690
some small percentage of the population,
00:01:50.690 --> 00:01:52.260
but those didn't do so well.
00:01:52.260 --> 00:01:55.480
But now all of a sudden you
had these backyard bird feeders
00:01:55.480 --> 00:01:57.710
in England, and so these birds were able
00:01:57.710 --> 00:01:59.120
to be quite successful.
00:01:59.120 --> 00:02:00.750
They were able to get food.
00:02:00.750 --> 00:02:02.270
They were able to thrive.
00:02:02.270 --> 00:02:05.920
And so over time, this became
a larger and larger proportion
00:02:05.920 --> 00:02:09.130
that was able to successfully
go in that direction
00:02:09.130 --> 00:02:12.720
and then migrate back in the
summer and then reproduce.
00:02:12.720 --> 00:02:15.890
Now, not only did that gene
not get selected against,
00:02:15.890 --> 00:02:17.590
and now the birds that had the genes
00:02:17.590 --> 00:02:19.508
to go in that direction were thriving,
00:02:19.508 --> 00:02:21.443
but they also started
mating with each other
00:02:21.443 --> 00:02:23.070
more and more frequently
00:02:23.070 --> 00:02:25.910
because they would all get
back to Germany earlier.
00:02:25.910 --> 00:02:27.360
Because when the winter ended,
00:02:27.360 --> 00:02:30.450
they had a shorter distance
to travel on the way back
00:02:30.450 --> 00:02:31.794
than the ones that went to Spain.
00:02:31.794 --> 00:02:34.820
And so as they started
reproducing with each other
00:02:34.820 --> 00:02:36.560
more, and more, and more,
00:02:36.560 --> 00:02:40.420
we started to see differences
beyond migration direction
00:02:40.420 --> 00:02:43.930
in these two groups of
Central European blackcaps.
00:02:43.930 --> 00:02:46.700
The ones that traveled northwest
00:02:46.700 --> 00:02:48.860
started to see rounder wings
00:02:49.910 --> 00:02:53.160
versus pointier wings for the ones
00:02:53.160 --> 00:02:55.170
that were historically going to Spain.
00:02:55.170 --> 00:02:58.320
Well, pointier wings are better
for traveling long distances
00:02:58.320 --> 00:03:00.210
and rounder wings are more maneuverable,
00:03:00.210 --> 00:03:02.400
and if you don't have to
travel as long of a distance
00:03:02.400 --> 00:03:03.930
that is more desirable.
00:03:03.930 --> 00:03:05.590
Now, it's not like these birds knew
00:03:05.590 --> 00:03:07.180
that they needed rounder wings.
00:03:07.180 --> 00:03:09.450
But once again, even in
the pool that was going
00:03:09.450 --> 00:03:11.830
to the northwest, you
would have had variation,
00:03:11.830 --> 00:03:14.480
some pointy wings, some round wings.
00:03:14.480 --> 00:03:16.760
But the round wings might've
been more successful
00:03:16.760 --> 00:03:20.290
so that became a more
pronounced trait in that group.
00:03:20.290 --> 00:03:22.740
While, similarly, the
ones that went to Spain,
00:03:22.740 --> 00:03:24.500
some of them might've had rounder wings,
00:03:24.500 --> 00:03:26.630
but they might not have been as successful
00:03:26.630 --> 00:03:28.370
to get all the way to Spain and back
00:03:28.370 --> 00:03:32.760
so the pointier wings, that
phenotype, seemed to thrive.
00:03:32.760 --> 00:03:35.850
So this is an example how
an environmental change,
00:03:35.850 --> 00:03:37.830
and here the environmental
change is people deciding
00:03:37.830 --> 00:03:40.180
to put bird feeders in
their backyards in England
00:03:40.180 --> 00:03:42.300
in the 1960s and 1970s,
00:03:42.300 --> 00:03:44.610
has actually over just
the course of roughly
00:03:44.610 --> 00:03:47.980
30 or 40 generations
began what some biologists
00:03:47.980 --> 00:03:50.130
view as a speciation event.
00:03:50.130 --> 00:03:52.640
The ones that go northwest
can still interbreed
00:03:52.640 --> 00:03:54.830
with the ones that go to the southwest.
00:03:54.830 --> 00:03:56.717
But over time, if the
two groups keep breeding
00:03:56.717 --> 00:03:59.890
amongst themselves because of
the timing of their migration,
00:03:59.890 --> 00:04:01.940
they might not be able
to interbreed anymore
00:04:01.940 --> 00:04:04.880
and then you would have
two different species.
00:04:04.880 --> 00:04:06.600
So this is just one example.
00:04:06.600 --> 00:04:08.312
There are many other examples
about how the physical
00:04:08.312 --> 00:04:11.970
environment can contribute to
the expansion of some species,
00:04:11.970 --> 00:04:15.010
the emergence of new distinct species,
00:04:15.010 --> 00:04:16.700
or, in certain situations,
00:04:16.700 --> 00:04:18.130
cause a decline in the species
00:04:18.130 --> 00:04:19.609
and, in the extreme. an extinction,
00:04:19.609 --> 00:04:21.913
which we'll talk about in another video.
|
Introduction to sustainability | https://www.youtube.com/watch?v=k6jUaaQNY28 | vtt | https://www.youtube.com/api/timedtext?v=k6jUaaQNY28&ei=2VWUZaDeJcLDmLAPneut-Ao&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0C7E5F6F17A6B07D8D6FA0E7EACF3FAC83E777A4.27AFBB6AD06EB9C054836103383671B388C5E4CD&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.340 --> 00:00:02.420
- [Instructor] Let's talk
about sustainability.
00:00:02.420 --> 00:00:04.370
You've probably come across
the word "sustainable"
00:00:04.370 --> 00:00:05.790
at some point in your life.
00:00:05.790 --> 00:00:08.240
If I decided to continue to
talk for the rest of this video
00:00:08.240 --> 00:00:10.067
without taking a breath,
you might tell me,
00:00:10.067 --> 00:00:12.380
"Mia, that's just not sustainable."
00:00:12.380 --> 00:00:13.280
In this scenario,
00:00:13.280 --> 00:00:16.770
which I obviously would never
even dream of attempting,
00:00:16.770 --> 00:00:18.980
I'd be depleting the oxygen in my lungs
00:00:18.980 --> 00:00:20.550
without replacing it.
00:00:20.550 --> 00:00:23.230
Using resources faster than
they can be replenished
00:00:23.230 --> 00:00:24.760
is not sustainable.
00:00:24.760 --> 00:00:27.920
But what does
"sustainability" really mean?
00:00:27.920 --> 00:00:32.660
Well, the word "sustain" means
"to maintain" or "to hold,"
00:00:32.660 --> 00:00:34.930
so sustainability is
the ability of something
00:00:34.930 --> 00:00:37.800
to be maintained over a period of time.
00:00:37.800 --> 00:00:41.040
In environmental science, when
we talk about sustainability,
00:00:41.040 --> 00:00:43.450
we're talking about the
ability of the Earth's systems
00:00:43.450 --> 00:00:46.660
to survive and adapt to changing
environmental conditions
00:00:46.660 --> 00:00:49.470
and maintain the health of ecosystems.
00:00:49.470 --> 00:00:51.470
It's like a delicate balance
00:00:51.470 --> 00:00:55.350
where each process doesn't take
too much or produce too much
00:00:55.350 --> 00:00:58.210
so that all the other
processes can keep on going.
00:00:58.210 --> 00:01:00.760
And theoretically, when
all these processes
00:01:00.760 --> 00:01:04.860
are doing their jobs, this
balance could last forever.
00:01:04.860 --> 00:01:08.110
But some things that humans
do can disrupt this balance.
00:01:08.110 --> 00:01:10.570
Let's take a look at an example.
00:01:10.570 --> 00:01:12.770
In the early years of the United States,
00:01:12.770 --> 00:01:15.770
enslaved and free farm
workers in the American South
00:01:15.770 --> 00:01:18.980
planted or were forced to plant cotton,
00:01:18.980 --> 00:01:21.080
a plant that needs to use the nitrogen
00:01:21.080 --> 00:01:22.940
in the soil to survive.
00:01:22.940 --> 00:01:24.250
But when they planted cotton
00:01:24.250 --> 00:01:26.780
in the same fields year after year,
00:01:26.780 --> 00:01:29.260
the cotton plants would
deplete the nitrogen levels
00:01:29.260 --> 00:01:30.280
in the soil.
00:01:30.280 --> 00:01:34.100
This constant depletion of
nitrogen was not sustainable
00:01:34.100 --> 00:01:36.360
and the cotton crops suffered.
00:01:36.360 --> 00:01:38.010
In the early 20th century,
00:01:38.010 --> 00:01:41.340
agricultural scientist and
inventor George Washington Carver
00:01:41.340 --> 00:01:43.550
suggested that farmers could alternate
00:01:43.550 --> 00:01:47.360
between growing cotton and
growing nitrogen-fixing plants
00:01:47.360 --> 00:01:49.243
like peanuts or sweet potatoes.
00:01:50.200 --> 00:01:52.370
This is a more sustainable way of farming,
00:01:52.370 --> 00:01:55.320
as the nitrogen-fixing plants
would replace the nitrogen
00:01:55.320 --> 00:01:57.770
that the cotton plants
took out of the soil.
00:01:57.770 --> 00:01:59.420
Since then, we've discovered a way
00:01:59.420 --> 00:02:01.550
of putting nitrogen back into the soil
00:02:01.550 --> 00:02:04.610
using chemically-synthesized fertilizers.
00:02:04.610 --> 00:02:06.870
But sustainability is more complicated
00:02:06.870 --> 00:02:09.490
than just replacing depleted resources.
00:02:09.490 --> 00:02:11.600
When farmers use too much fertilizer
00:02:11.600 --> 00:02:14.550
or use poor methods of
fertilizer application,
00:02:14.550 --> 00:02:18.160
all that fertilizer can run
off into neighboring waterways.
00:02:18.160 --> 00:02:20.040
This excess nitrogen in the water
00:02:20.040 --> 00:02:22.920
could cause a lot of algae to grow.
00:02:22.920 --> 00:02:25.830
The thing about algae is that
when it grows too rapidly,
00:02:25.830 --> 00:02:27.740
it also dies rapidly,
00:02:27.740 --> 00:02:30.130
and the microbes that decompose the algae
00:02:30.130 --> 00:02:32.340
hog the available oxygen in the water,
00:02:32.340 --> 00:02:34.470
which makes it difficult
for other organisms
00:02:34.470 --> 00:02:36.320
living in the water to breathe.
00:02:36.320 --> 00:02:37.650
So, when the fertilizer runoff
00:02:37.650 --> 00:02:39.780
causes too much algae to grow,
00:02:39.780 --> 00:02:42.470
it creates an imbalance in the ecosystem
00:02:42.470 --> 00:02:44.210
and harms the other organisms
00:02:44.210 --> 00:02:46.890
that rely on the dissolved
oxygen in the water,
00:02:46.890 --> 00:02:49.040
so the addition of too much fertilizer
00:02:49.040 --> 00:02:51.240
is also unsustainable.
00:02:51.240 --> 00:02:52.640
But how could a farmer know
00:02:52.640 --> 00:02:55.490
whether they're using
fertilizer sustainably?
00:02:55.490 --> 00:02:58.793
Well, they could look out
for environmental indicators.
00:02:59.710 --> 00:03:01.750
Environmental indicators are basically
00:03:01.750 --> 00:03:03.217
when the Earth tells us,
00:03:03.217 --> 00:03:06.910
"Hey, there's something
unsustainable in this ecosystem."
00:03:06.910 --> 00:03:09.420
But instead of just telling
us that straight out,
00:03:09.420 --> 00:03:12.370
it tells us in a variety of clues.
00:03:12.370 --> 00:03:14.930
For our farmer, environmental
indicators can be things
00:03:14.930 --> 00:03:17.970
like the amount of dissolved
oxygen in the water,
00:03:17.970 --> 00:03:20.380
the biological diversity in the area,
00:03:20.380 --> 00:03:24.090
or even how much algae goes
in nearby water sources.
00:03:24.090 --> 00:03:27.090
The series of events triggered
by fertilizer pollution
00:03:27.090 --> 00:03:29.750
could deplete the amount
of oxygen in the water,
00:03:29.750 --> 00:03:31.330
so species that live in the water
00:03:31.330 --> 00:03:33.920
that require a lot of oxygen to survive
00:03:33.920 --> 00:03:36.000
could begin to die off.
00:03:36.000 --> 00:03:38.673
These species are called
indicator species.
00:03:39.810 --> 00:03:41.230
Because they're known to survive
00:03:41.230 --> 00:03:44.030
in very specific circumstances,
00:03:44.030 --> 00:03:46.310
spotting these species is an indication
00:03:46.310 --> 00:03:48.770
that there is a lot of
oxygen in the water.
00:03:48.770 --> 00:03:52.240
If these species are absent,
then that will be an indication
00:03:52.240 --> 00:03:53.810
that the pollution has reduced
00:03:53.810 --> 00:03:56.870
the amount of dissolved
oxygen in the pond.
00:03:56.870 --> 00:03:59.390
The farmer could then
change their behavior.
00:03:59.390 --> 00:04:02.580
In this way, environmental
indicators can guide humans
00:04:02.580 --> 00:04:04.910
to make sustainable choices.
00:04:04.910 --> 00:04:07.390
Another way humans can use
environmental indicators
00:04:07.390 --> 00:04:09.620
to make decisions about natural resources
00:04:09.620 --> 00:04:13.570
is by monitoring populations
and estimating their growth.
00:04:13.570 --> 00:04:16.270
Imagine that you have a
pond in your backyard.
00:04:16.270 --> 00:04:17.750
And let's imagine that you have searched
00:04:17.750 --> 00:04:20.290
for all of the correct
environmental indicators
00:04:20.290 --> 00:04:21.950
so you know that the fish in your pond
00:04:21.950 --> 00:04:23.723
are not suffering from pollution.
00:04:24.730 --> 00:04:27.120
One day, you decide to go fishing.
00:04:27.120 --> 00:04:29.770
It might be tempting to
fish as much as you can
00:04:29.770 --> 00:04:31.560
so that you can invite all of your friends
00:04:31.560 --> 00:04:34.200
and have a big happy fish feast.
00:04:34.200 --> 00:04:37.620
But if you decided to take all
of the fish out of the pond,
00:04:37.620 --> 00:04:40.280
then there wouldn't be
any left to reproduce,
00:04:40.280 --> 00:04:43.163
so your feast next year
would be pretty sad.
00:04:44.650 --> 00:04:47.900
Even if you just left a
couple of fish in the pool,
00:04:47.900 --> 00:04:49.660
they might not be able to reproduce enough
00:04:49.660 --> 00:04:52.010
to replenish the population.
00:04:52.010 --> 00:04:53.330
Other environmental factors
00:04:53.330 --> 00:04:55.160
might cause the small fish population
00:04:55.160 --> 00:04:56.960
to go down even further.
00:04:56.960 --> 00:05:00.480
The fish might catch
diseases, run out of food,
00:05:00.480 --> 00:05:03.133
or end up being some
other creature's feast.
00:05:04.010 --> 00:05:07.040
There's some maximum number
of fish that you could take
00:05:07.040 --> 00:05:09.050
so that there's enough
fish left in the pond
00:05:09.050 --> 00:05:12.000
to reproduce and replenish the population.
00:05:12.000 --> 00:05:15.223
This number is called the
maximum sustainable yield.
00:05:16.530 --> 00:05:19.270
Basically, you want to catch the most fish
00:05:19.270 --> 00:05:23.670
to have the maximum yield
while still being sustainable.
00:05:23.670 --> 00:05:26.370
If you fish more than the
maximum sustainable yield,
00:05:26.370 --> 00:05:27.710
then the fish will be captured
00:05:27.710 --> 00:05:29.650
more quickly than they can reproduce
00:05:29.650 --> 00:05:32.270
and the population will slowly decline.
00:05:32.270 --> 00:05:34.970
If you fish less than the
maximum sustainable yield,
00:05:34.970 --> 00:05:38.040
then the fish population
will grow exponentially
00:05:38.040 --> 00:05:39.980
until they reach the maximum capacity
00:05:39.980 --> 00:05:42.100
that the ecosystem can support.
00:05:42.100 --> 00:05:43.770
Some of the fish will eventually die
00:05:43.770 --> 00:05:45.420
from density-dependent factors
00:05:45.420 --> 00:05:48.170
like lack of food and disease.
00:05:48.170 --> 00:05:50.850
On a bigger scale than
your imaginary pond,
00:05:50.850 --> 00:05:53.520
natural resource managers try to estimate
00:05:53.520 --> 00:05:55.450
what the maximum sustainable yield will be
00:05:55.450 --> 00:05:57.030
each fishing season.
00:05:57.030 --> 00:05:58.590
This is why fishery managers
00:05:58.590 --> 00:06:00.520
regulate the amount of
certain types of fish
00:06:00.520 --> 00:06:02.840
each fisher is allowed to catch per year.
00:06:02.840 --> 00:06:06.113
This is to make sure that next
year we will still have fish.
00:06:07.060 --> 00:06:09.210
So, if we study the Earth's ecosystems
00:06:09.210 --> 00:06:12.020
and understand how we
impact the environment,
00:06:12.020 --> 00:06:14.560
then we can find ways to
interact with ecosystems
00:06:14.560 --> 00:06:15.800
more sustainably.
00:06:15.800 --> 00:06:19.093
And, really, that's what
environmental science is all about.
|
Heat transfer | https://www.youtube.com/watch?v=FPPv1mkRpKw | vtt | https://www.youtube.com/api/timedtext?v=FPPv1mkRpKw&ei=21WUZda9Nam2mLAPoNuCgA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245323&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EDADF46BD7EC78BC2362A9CA6CD9B7EF3BEA0E45.46D5E9A865F717F8B2E85D9070C1767207B8C99E&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.930 --> 00:00:02.240
- [Instructor] All right,
so I don't know about you,
00:00:02.240 --> 00:00:04.190
but I feel like talking about pizza.
00:00:04.190 --> 00:00:05.510
It's pizza night over here.
00:00:05.510 --> 00:00:07.900
I am smelling pizza as it's in the oven.
00:00:07.900 --> 00:00:09.240
It's on my mind.
00:00:09.240 --> 00:00:11.980
And I know we're supposed
to be talking about heat
00:00:11.980 --> 00:00:15.540
and thermal equilibrium, but
I think we can make this work.
00:00:15.540 --> 00:00:16.920
Now, if you're impatient like me,
00:00:16.920 --> 00:00:18.890
you probably put a slice
of pizza on your plate
00:00:18.890 --> 00:00:20.760
as soon as it comes out of the oven
00:00:20.760 --> 00:00:21.990
and you've probably noticed
00:00:21.990 --> 00:00:24.450
that the bottom of the plate warms up.
00:00:24.450 --> 00:00:26.900
So let's think about what's going on here.
00:00:26.900 --> 00:00:31.330
We have the temperature
of the pizza, T pizza,
00:00:31.330 --> 00:00:36.293
which is warmer than the
temperature of our plate, T plate.
00:00:37.650 --> 00:00:40.900
So, since the temperature
of the pizza is higher
00:00:40.900 --> 00:00:45.010
than that of the plate, the
plate starts to warm up.
00:00:45.010 --> 00:00:47.350
The pizza's temperature,
on the other hand,
00:00:47.350 --> 00:00:48.803
will actually start to lower.
00:00:49.960 --> 00:00:52.310
And this will happen
anytime the temperature
00:00:52.310 --> 00:00:53.940
of object one isn't the same
00:00:53.940 --> 00:00:55.590
as the temperature of object two.
00:00:57.500 --> 00:00:59.610
We know temperature is how we express
00:00:59.610 --> 00:01:01.360
that something is hot or cold.
00:01:01.360 --> 00:01:03.120
What does hot or cold mean?
00:01:03.120 --> 00:01:04.970
Temperature is actually the measure
00:01:04.970 --> 00:01:08.380
of the average kinetic energy
of the particles in an object.
00:01:08.380 --> 00:01:11.420
So let's digest that for a
second and break it down.
00:01:11.420 --> 00:01:12.920
So temperature, temperature
00:01:15.340 --> 00:01:19.093
is the average kinetic
energy of particles.
00:01:20.730 --> 00:01:25.023
And kinetic energy, as we
know, is 1/2 mv squared.
00:01:27.090 --> 00:01:28.640
So when the pizza is warm,
00:01:28.640 --> 00:01:32.520
its particles are moving
faster than if it was cold.
00:01:32.520 --> 00:01:34.760
And when particles and objects are moving,
00:01:34.760 --> 00:01:36.420
they're actually vibrating around.
00:01:36.420 --> 00:01:38.930
So what's happening in the hotter object
00:01:38.930 --> 00:01:42.210
is that the particles are vibrating faster
00:01:42.210 --> 00:01:44.270
than when the object is colder,
00:01:44.270 --> 00:01:47.570
and that's what it
means to be hot or cold.
00:01:47.570 --> 00:01:49.650
This type of kinetic energy,
00:01:49.650 --> 00:01:54.650
the motion of particles, is
also known as thermal energy.
00:01:56.440 --> 00:01:58.267
Now, you might be wondering,
00:01:58.267 --> 00:02:03.267
"If temperature is the measure
of kinetic energy in objects,
00:02:03.970 --> 00:02:05.870
and we have the pizza on the plate
00:02:05.870 --> 00:02:08.090
with their temperatures changing,
00:02:08.090 --> 00:02:10.160
does this mean there's some sort
00:02:10.160 --> 00:02:13.170
of energy transfer going on here?"
00:02:13.170 --> 00:02:15.100
And you would be spot on.
00:02:15.100 --> 00:02:18.430
Heat is the transfer of
energy between objects
00:02:18.430 --> 00:02:20.040
at different temperatures.
00:02:20.040 --> 00:02:22.000
This is a really important concept,
00:02:22.000 --> 00:02:24.740
so let's write that definition out.
00:02:24.740 --> 00:02:28.880
Heat is the transfer
00:02:28.880 --> 00:02:33.067
of energy between objects
00:02:35.280 --> 00:02:40.003
at different temperatures.
00:02:41.890 --> 00:02:43.840
As you can see with our pizza and plate,
00:02:43.840 --> 00:02:47.540
heat is transferring from the
hot pizza to the cold plate,
00:02:47.540 --> 00:02:50.750
from the hot object to the cold object.
00:02:50.750 --> 00:02:52.060
Why is that?
00:02:52.060 --> 00:02:55.060
Well, let's go ahead and
break down our problem
00:02:55.060 --> 00:02:57.480
and really dig into what's happening
00:02:57.480 --> 00:02:59.440
with everything in the system.
00:02:59.440 --> 00:03:00.570
In real life,
00:03:00.570 --> 00:03:03.450
a lot of energy is also
going to be transferred
00:03:03.450 --> 00:03:07.040
from the pizza into the air
around it, but for this problem,
00:03:07.040 --> 00:03:09.800
we're going to simplify it
to just look at the pizza
00:03:09.800 --> 00:03:10.633
and the plate.
00:03:12.040 --> 00:03:14.610
So we said that the
higher the temperature,
00:03:14.610 --> 00:03:17.460
the more all the particles
that make up the object
00:03:17.460 --> 00:03:18.960
are moving and vibrating.
00:03:18.960 --> 00:03:22.313
So let's go ahead and draw
that for the pizza particles.
00:03:23.240 --> 00:03:26.430
We're gonna use yellow
to represent the pizza,
00:03:26.430 --> 00:03:28.910
and I'm going to give the pizza particles
00:03:28.910 --> 00:03:32.480
a longer velocity vector
than those of the plate.
00:03:32.480 --> 00:03:33.593
And I'm going to assume that the particles
00:03:33.593 --> 00:03:36.780
in the pizza and the
plate have the same mass.
00:03:36.780 --> 00:03:39.610
That way, we can ignore the
mass part of kinetic energy
00:03:39.610 --> 00:03:41.350
and simplify the situation.
00:03:41.350 --> 00:03:43.600
Now, we can just focus on the velocities
00:03:43.600 --> 00:03:45.890
of all the particles in the system.
00:03:45.890 --> 00:03:48.760
When you put the slice
of pizza on the plate,
00:03:48.760 --> 00:03:51.090
the particles at the
surface of the objects
00:03:51.090 --> 00:03:53.010
will come into contact.
00:03:53.010 --> 00:03:56.020
So let's look at what happens
when these faster particles
00:03:56.020 --> 00:03:58.850
from the pizza collide
with the slower particles
00:03:58.850 --> 00:04:00.250
on the surface of the plate.
00:04:01.240 --> 00:04:02.810
When the particles collide,
00:04:02.810 --> 00:04:05.890
kinetic energy transfers
between the particles.
00:04:05.890 --> 00:04:08.130
Since the hotter object's particles,
00:04:08.130 --> 00:04:11.020
in this case, the pizza, have more energy,
00:04:11.020 --> 00:04:13.140
they're able to give some of that energy
00:04:13.140 --> 00:04:15.400
to the colder object's particles,
00:04:15.400 --> 00:04:18.410
which is why he always
transfers from the hotter object
00:04:18.410 --> 00:04:19.803
to the colder object.
00:04:20.880 --> 00:04:23.620
When the hotter object's
particles transfer some
00:04:23.620 --> 00:04:26.220
of their energy to the
colder object's particles,
00:04:26.220 --> 00:04:29.380
the hotter object particles
have now lost some energy
00:04:29.380 --> 00:04:30.490
and slow down.
00:04:30.490 --> 00:04:33.633
So we can show that by using
a smaller velocity vector.
00:04:34.780 --> 00:04:35.990
At the same time,
00:04:35.990 --> 00:04:38.580
the colder object's
particles have gained energy
00:04:38.580 --> 00:04:40.240
and sped up.
00:04:40.240 --> 00:04:42.020
So now this particle in the pizza
00:04:42.020 --> 00:04:44.690
is at a different velocity
than its neighboring particle
00:04:44.690 --> 00:04:45.660
in the pizza.
00:04:45.660 --> 00:04:48.110
So when they collide, guess what?
00:04:48.110 --> 00:04:50.040
We transfer energy again.
00:04:50.040 --> 00:04:52.950
The faster particle will give
some energy to the slower one,
00:04:52.950 --> 00:04:55.250
and in the process, it slows down.
00:04:55.250 --> 00:04:57.390
And this domino effect carries through
00:04:57.390 --> 00:04:59.370
to all the particles in the system,
00:04:59.370 --> 00:05:01.270
in the plate and in the pizza,
00:05:01.270 --> 00:05:04.493
until all the particles have
the same kinetic energy.
00:05:05.340 --> 00:05:07.610
And when the particles in both objects
00:05:07.610 --> 00:05:09.590
have the same kinetic energy,
00:05:09.590 --> 00:05:12.630
energy will no longer transfer
between the two objects
00:05:12.630 --> 00:05:15.220
and the system has reached
a state of stability,
00:05:15.220 --> 00:05:17.670
and we call this thermal equilibrium.
00:05:17.670 --> 00:05:19.520
You know when you leave your
pizza on the counter too long
00:05:19.520 --> 00:05:21.100
and you come back and it's cold?
00:05:21.100 --> 00:05:22.773
If you were to actually
measure the temperature
00:05:22.773 --> 00:05:25.230
of the pizza and the plate,
they're going to be the same.
00:05:25.230 --> 00:05:29.590
And we now know that
heat transfer only occurs
00:05:29.590 --> 00:05:32.430
when the temperature is
different between objects.
00:05:32.430 --> 00:05:34.550
So when the temperature is the same,
00:05:34.550 --> 00:05:36.210
no heat is transferring,
00:05:36.210 --> 00:05:39.300
and this is what is defined
as thermal equilibrium.
00:05:39.300 --> 00:05:41.319
So thermal equilibrium,
00:05:41.319 --> 00:05:46.120
equilibrium occurs when
there is no heat transfer
00:05:46.120 --> 00:05:46.953
in the system.
00:05:48.810 --> 00:05:50.780
So it turns out pizza
is actually pretty good
00:05:50.780 --> 00:05:54.210
for learning about heat transfer
and thermal equilibrium.
00:05:54.210 --> 00:05:55.530
And if you don't mind,
00:05:55.530 --> 00:05:57.820
that pizza and the other
room is calling my name,
00:05:57.820 --> 00:05:58.830
and personally,
00:05:58.830 --> 00:06:01.740
I prefer to eat it before it
reaches thermal equilibrium
00:06:01.740 --> 00:06:02.573
with my plate.
|
The photoelectric effect | https://www.youtube.com/watch?v=3O0xl8f2mSs | vtt | https://www.youtube.com/api/timedtext?v=3O0xl8f2mSs&ei=3FWUZZzjC8PXxN8P_6qLwAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245324&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=65C2B88C2073130F78980FCE7BE45E1D66ACFC1B.E0F9A19A2735A013CADBF97C4C01552A91EEF2BF&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.380 --> 00:00:01.580
- [Instructor] The photoelectric effect
00:00:01.580 --> 00:00:03.500
is another one of these
cool things in physics
00:00:03.500 --> 00:00:05.710
that sounds like it should be sci-fi,
00:00:05.710 --> 00:00:09.350
but actually describes an
everyday phenomenon around us.
00:00:09.350 --> 00:00:12.880
This and related effects are
used for all sorts of things,
00:00:12.880 --> 00:00:16.780
like solar panels and cameras.
00:00:16.780 --> 00:00:19.320
And the name itself is the biggest hint
00:00:19.320 --> 00:00:21.270
into what's going on.
00:00:21.270 --> 00:00:26.203
Photo, photon, electric, electron.
00:00:27.250 --> 00:00:30.310
So what is the photoelectric effect?
00:00:30.310 --> 00:00:33.960
It's the emission of
electrons from a metal
00:00:33.960 --> 00:00:37.140
that has absorbed
electromagnetic radiation
00:00:37.140 --> 00:00:39.463
like light over a certain frequency.
00:00:40.370 --> 00:00:43.300
A particle of light is called a photon,
00:00:43.300 --> 00:00:45.460
and when a photon has enough energy,
00:00:45.460 --> 00:00:48.380
it can actually knock an electron free.
00:00:48.380 --> 00:00:51.180
What happens is that the photon collides
00:00:51.180 --> 00:00:53.833
with the metal surface,
hitting an electron.
00:00:55.020 --> 00:00:56.540
When these particles collide,
00:00:56.540 --> 00:00:58.580
some of the energy of the photon is used
00:00:58.580 --> 00:01:00.390
to dislodge the electron.
00:01:00.390 --> 00:01:04.140
That electron is then shot
out of the metal, or emitted.
00:01:04.140 --> 00:01:06.960
The rest of the photon's
energy is then transferred
00:01:06.960 --> 00:01:08.433
to the emitted electron.
00:01:09.890 --> 00:01:12.457
We know that energy
transfers between objects
00:01:12.457 --> 00:01:14.400
and is conserved in a system,
00:01:14.400 --> 00:01:17.760
so maybe this photoelectric
effect sounds simple,
00:01:17.760 --> 00:01:20.290
but that's actually why
it's such a big deal,
00:01:20.290 --> 00:01:21.280
so big that it's
00:01:21.280 --> 00:01:24.980
what Albert Einstein
received his Nobel Prize for.
00:01:24.980 --> 00:01:27.060
Why was this such a big deal?
00:01:27.060 --> 00:01:29.270
By understanding the photoelectric effect,
00:01:29.270 --> 00:01:31.220
we also learned a lot about
00:01:31.220 --> 00:01:33.630
the fundamental properties of light.
00:01:33.630 --> 00:01:36.690
Today, we know that light
can behave as both a particle
00:01:36.690 --> 00:01:40.140
and a wave, but that wasn't always known.
00:01:40.140 --> 00:01:41.810
When this effect was discovered,
00:01:41.810 --> 00:01:45.540
it was clear that light
had wave-like properties,
00:01:45.540 --> 00:01:48.900
but the photo electric effect
was a big piece of evidence
00:01:48.900 --> 00:01:51.383
that light could also
behave as a particle.
00:01:52.580 --> 00:01:56.600
It also showed that the
energy of those particles
00:01:56.600 --> 00:01:59.423
was related to the frequency of the light.
00:02:01.260 --> 00:02:03.960
So how did scientists figure all this out?
00:02:03.960 --> 00:02:05.350
Well, let's start by thinking about
00:02:05.350 --> 00:02:07.860
how to make a metal emit an electron.
00:02:07.860 --> 00:02:10.510
This sounds an awful lot like work,
00:02:10.510 --> 00:02:13.470
and we need energy to perform work.
00:02:13.470 --> 00:02:16.230
It turns out that electrons
have what is called
00:02:16.230 --> 00:02:18.113
a binding energy.
00:02:19.400 --> 00:02:23.090
Binding energy, which I'm
going to refer to as Eb,
00:02:23.090 --> 00:02:24.990
refers to the amount of energy needed
00:02:24.990 --> 00:02:28.920
to pull an electron away from
the atom that it's orbiting,
00:02:28.920 --> 00:02:30.590
or that it's bound to,
00:02:30.590 --> 00:02:32.693
and hence the name binding energy.
00:02:33.820 --> 00:02:36.810
Electrons are happy to
remain where they are,
00:02:36.810 --> 00:02:39.570
unless something gives them enough energy
00:02:39.570 --> 00:02:41.350
to overcome this binding energy
00:02:41.350 --> 00:02:43.200
and bounce them out of place.
00:02:43.200 --> 00:02:47.270
So the energy hitting an
electron has to be greater
00:02:47.270 --> 00:02:50.053
than its binding energy to cause emission.
00:02:52.090 --> 00:02:55.360
Scientists had observed
the photoelectric effect,
00:02:55.360 --> 00:02:58.640
but they wanted to know how
it worked, because, well,
00:02:58.640 --> 00:03:00.400
that's what scientists do.
00:03:00.400 --> 00:03:01.630
So over the years,
00:03:01.630 --> 00:03:04.480
various scientists designed
experiments that tested
00:03:04.480 --> 00:03:06.680
the effects of different types of light
00:03:06.680 --> 00:03:08.620
on different materials.
00:03:08.620 --> 00:03:10.320
And let's look at what they found.
00:03:11.820 --> 00:03:14.340
They found that if a light
was shining on a metal
00:03:14.340 --> 00:03:16.920
and the metal wasn't emitting electrons,
00:03:16.920 --> 00:03:20.580
changing the intensity of the
light didn't change things,
00:03:20.580 --> 00:03:23.150
but they did notice that
raising the frequency
00:03:23.150 --> 00:03:24.083
of the light did.
00:03:24.950 --> 00:03:26.680
So, for example,
00:03:26.680 --> 00:03:29.440
if you set up an experiment
where you're shining a lamp
00:03:29.440 --> 00:03:33.180
on a piece of metal and it's
not ejecting any electrons,
00:03:33.180 --> 00:03:35.720
shining two of those lamps on the metal
00:03:35.720 --> 00:03:37.400
won't change anything.
00:03:37.400 --> 00:03:39.520
But if you replace the bulb
00:03:39.520 --> 00:03:42.570
with one that emits a
higher frequency of light,
00:03:42.570 --> 00:03:44.290
this might change things.
00:03:44.290 --> 00:03:47.320
And this was a big hint
that light might be behaving
00:03:47.320 --> 00:03:48.333
as a particle.
00:03:49.350 --> 00:03:51.160
Why is that?
00:03:51.160 --> 00:03:52.900
If this was a normal wave,
00:03:52.900 --> 00:03:56.060
we would expect that by sending
more energy at the metal,
00:03:56.060 --> 00:03:58.350
by increasing the intensity,
00:03:58.350 --> 00:04:01.630
electrons would gain enough
energy to be emitted.
00:04:01.630 --> 00:04:03.470
But since that didn't happen,
00:04:03.470 --> 00:04:06.630
it was clear something else was going on.
00:04:06.630 --> 00:04:09.020
And that eventually led to the idea
00:04:09.020 --> 00:04:11.950
that light was composed of photons.
00:04:11.950 --> 00:04:13.320
And these photons need
00:04:13.320 --> 00:04:18.320
to individually transfer
enough energy to an electron
00:04:18.330 --> 00:04:20.840
that it can bounce out of place.
00:04:20.840 --> 00:04:24.740
So by changing the frequency of a light,
00:04:24.740 --> 00:04:27.453
we can change the energy of a photon.
00:04:28.980 --> 00:04:32.250
Once this energy is higher than that
00:04:32.250 --> 00:04:34.840
of the binding energy
we talked about earlier,
00:04:34.840 --> 00:04:37.140
it can knock an electron loose.
00:04:37.140 --> 00:04:40.600
Any extra energy then
contributes to the energy
00:04:40.600 --> 00:04:42.283
of the emitted electron.
00:04:44.390 --> 00:04:47.190
This is a big deal and enables us
00:04:47.190 --> 00:04:49.160
to do some pretty cool things.
00:04:49.160 --> 00:04:53.420
So let's go back to one of
the examples at the beginning,
00:04:53.420 --> 00:04:54.930
solar panels.
00:04:54.930 --> 00:04:57.060
They have these things called photo cells,
00:04:57.060 --> 00:04:59.620
which we're pretending
I'm drawing right now,
00:04:59.620 --> 00:05:01.490
and these photo cells use a version
00:05:01.490 --> 00:05:04.680
of the photoelectric effect
to generate electricity.
00:05:04.680 --> 00:05:08.420
When sunlight hits the
cells, they emit electrons.
00:05:08.420 --> 00:05:09.610
The cells are designed
00:05:09.610 --> 00:05:14.180
so that these electrons moving
around generate a voltage,
00:05:14.180 --> 00:05:17.210
and voltage can power devices.
00:05:17.210 --> 00:05:19.450
Now we can see why the
photoelectric effect
00:05:19.450 --> 00:05:21.070
is such a big deal.
00:05:21.070 --> 00:05:24.370
Not only did it revolutionize
our understanding of physics,
00:05:24.370 --> 00:05:28.223
but it and similar effects are
used in tons of technology.
|
Solar Energy | https://www.youtube.com/watch?v=OVODBZUJAYE | vtt | https://www.youtube.com/api/timedtext?v=OVODBZUJAYE&ei=2VWUZab4Kc7Mp-oPirqOwAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245321&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C454A4E102F216C0C138158E706AACB02DE27CF1.2D8A3151025D38EE0BCAF09EC8AE48DAE8DD97BF&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.000 --> 00:00:03.880
- [Narrator] The sun is
about 93 million miles away,
00:00:03.880 --> 00:00:05.580
which means it takes about eight minutes
00:00:05.580 --> 00:00:07.700
for light from the sun to reach Earth,
00:00:07.700 --> 00:00:09.330
but it's still close enough for us
00:00:09.330 --> 00:00:11.550
to take advantage of solar energy.
00:00:11.550 --> 00:00:13.260
And why wouldn't we want to?
00:00:13.260 --> 00:00:15.840
After all, solar energy is renewable
00:00:15.840 --> 00:00:18.390
and essentially inexhaustible.
00:00:18.390 --> 00:00:20.780
It's also a clean energy source.
00:00:20.780 --> 00:00:23.690
So more and more we're
turning to solar energy
00:00:23.690 --> 00:00:25.920
to directly warm our homes
00:00:25.920 --> 00:00:29.440
or indirectly generate electricity.
00:00:29.440 --> 00:00:31.890
The first type of solar
heating we'll talking about
00:00:31.890 --> 00:00:33.720
is called passive.
00:00:33.720 --> 00:00:36.390
As the name suggests, passive happens
00:00:36.390 --> 00:00:38.180
without much work on your end.
00:00:38.180 --> 00:00:40.180
In my mind it's the equivalent of you
00:00:40.180 --> 00:00:41.820
just lying out in the sun,
00:00:41.820 --> 00:00:43.770
which is why throughout the world,
00:00:43.770 --> 00:00:48.100
this method is the most widely
accessible and inexpensive.
00:00:48.100 --> 00:00:51.580
Some examples of how homes
can be passively heated
00:00:51.580 --> 00:00:53.790
are through the actual materials
00:00:53.790 --> 00:00:55.630
that the home is made out of.
00:00:55.630 --> 00:01:00.630
So materials like stone, concrete, adobe,
00:01:00.640 --> 00:01:03.600
they absorb a lot of the
sun's heat during the day
00:01:03.600 --> 00:01:06.950
and then slowly release it at night.
00:01:06.950 --> 00:01:09.810
If we use this adobe house as an example,
00:01:09.810 --> 00:01:12.780
the thick walls and
small sunken in windows
00:01:12.780 --> 00:01:15.910
keep the house sheltered
from the sun during the day.
00:01:15.910 --> 00:01:19.490
And then at night, the clay
material that it's made out of
00:01:19.490 --> 00:01:23.610
releases that heat energy that
it stored throughout the day.
00:01:23.610 --> 00:01:27.990
So this particular home is
located in Santa Fe, New Mexico
00:01:27.990 --> 00:01:32.160
and a lot of homes that are
in desert areas like this
00:01:32.160 --> 00:01:34.750
are made out of clay and for good reason.
00:01:34.750 --> 00:01:37.150
Because during the day,
in desert locations,
00:01:37.150 --> 00:01:40.780
it can get very hot and that
clay will absorb the heat,
00:01:40.780 --> 00:01:43.520
keeping the inside of
the house pretty cool.
00:01:43.520 --> 00:01:47.470
And then at night desert
areas can get very, very cold.
00:01:47.470 --> 00:01:49.620
And so that clay will release the heat
00:01:49.620 --> 00:01:53.100
and keep the house moderately comfortable.
00:01:53.100 --> 00:01:55.340
Or in the Northern hemisphere,
00:01:55.340 --> 00:01:58.700
some homes are built with
South facing windows,
00:01:58.700 --> 00:02:00.460
which increases the number of hours
00:02:00.460 --> 00:02:02.810
that sunlight comes into the home.
00:02:02.810 --> 00:02:05.690
So these are ways to
passively warm a home,
00:02:05.690 --> 00:02:07.370
but there may be situations
00:02:07.370 --> 00:02:10.420
in which you wanna just block
the sun's heat and light
00:02:10.420 --> 00:02:12.440
to cool down the home instead.
00:02:12.440 --> 00:02:16.240
For example, the color of the
roof can make a big difference
00:02:16.240 --> 00:02:20.270
in how much heat does or
doesn't get stored in the home.
00:02:20.270 --> 00:02:21.960
Painting the roof a light color
00:02:21.960 --> 00:02:24.650
will reflect the sun's heat energy,
00:02:24.650 --> 00:02:26.880
much like choosing to wear a white T-shirt
00:02:26.880 --> 00:02:30.230
instead of a black shirt
on a hot summer day.
00:02:30.230 --> 00:02:34.600
There's also a specialty type
of roof called a green roof
00:02:34.600 --> 00:02:37.290
where plants are grown on top of the home
00:02:37.290 --> 00:02:40.440
to provide an additional
layer of insulation.
00:02:40.440 --> 00:02:42.880
Now, I haven't personally been on one,
00:02:42.880 --> 00:02:46.090
but I can only imagine in the spring time,
00:02:46.090 --> 00:02:48.690
if there are flowers
planted in the green roofs,
00:02:48.690 --> 00:02:52.490
they must smell and look amazing.
00:02:52.490 --> 00:02:55.030
And, of course, you can also create shade
00:02:55.030 --> 00:02:57.300
by planting trees around the home
00:02:57.300 --> 00:03:00.380
or adding awnings above the windows.
00:03:00.380 --> 00:03:03.040
To use solar energy in a different way,
00:03:03.040 --> 00:03:06.840
we can move from passive
techniques to active ones.
00:03:06.840 --> 00:03:09.730
For example, some homes have big panels
00:03:09.730 --> 00:03:13.230
attached to the roofs
called solar collectors.
00:03:13.230 --> 00:03:14.880
These solar collectors work
00:03:14.880 --> 00:03:17.400
by heating up a fluid inside of them
00:03:17.400 --> 00:03:21.700
and then use pumps or fans
to circulate that fluid
00:03:21.700 --> 00:03:24.360
and transfer heat into the home
00:03:24.360 --> 00:03:27.970
to warm up the air or water in the home.
00:03:27.970 --> 00:03:30.500
So the use of these pumps or fans
00:03:30.500 --> 00:03:32.190
to move the heat into the home
00:03:32.190 --> 00:03:36.800
is what makes this active
heating rather than just passive.
00:03:36.800 --> 00:03:39.860
A different alternative
if you happen to have
00:03:39.860 --> 00:03:42.020
a very large area of space
00:03:42.020 --> 00:03:47.020
is a concentrated solar power
system or CSP for short,
00:03:48.210 --> 00:03:50.620
which is basically a lot of reflectors
00:03:50.620 --> 00:03:54.000
that concentrate that solar energy.
00:03:54.000 --> 00:03:56.600
One specific type uses mirrors
00:03:56.600 --> 00:04:01.430
to reflect that solar
energy onto a single tower.
00:04:01.430 --> 00:04:04.320
That energy can then
be used to boil water,
00:04:04.320 --> 00:04:08.800
create steam, and ultimately
generate electricity.
00:04:08.800 --> 00:04:13.750
The largest CSP in the United
States is in the Mojave Desert
00:04:13.750 --> 00:04:17.260
very near California's border with Nevada.
00:04:17.260 --> 00:04:20.870
It's called the Ivanpah
Solar Power Facility.
00:04:20.870 --> 00:04:22.920
You'll see here that there are three sets
00:04:22.920 --> 00:04:25.440
of concentric circles with mirrors
00:04:25.440 --> 00:04:29.753
that are reflecting heat
energy onto individual towers.
00:04:30.620 --> 00:04:34.270
And there are hundreds
of thousands of mirrors.
00:04:34.270 --> 00:04:38.940
The plant takes up 3,500 acres of land
00:04:38.940 --> 00:04:43.880
and can power more than
100,000 homes in California.
00:04:43.880 --> 00:04:45.760
The downsides of these systems though
00:04:45.760 --> 00:04:49.040
is that they do cost a lot
of money and space up front
00:04:49.040 --> 00:04:52.150
and if the weather's bad
they don't work as well.
00:04:52.150 --> 00:04:54.400
There are also stories a few years back
00:04:54.400 --> 00:04:56.640
where there are hundreds of birds
00:04:56.640 --> 00:04:59.530
quite literally being burned up
00:04:59.530 --> 00:05:03.230
as they flew between the
mirrors and the towers.
00:05:03.230 --> 00:05:06.500
So you can imagine the
enormous amount of heat energy
00:05:06.500 --> 00:05:09.190
that's being reflected off these mirrors.
00:05:09.190 --> 00:05:12.570
On the upside, these reflectors
can be cheaper to maintain
00:05:12.570 --> 00:05:16.390
than other technologies and
can make use of large stretches
00:05:16.390 --> 00:05:20.243
of desert that are already
empty all over the world.
00:05:21.120 --> 00:05:25.060
And finally, one other way to
harness the power of the sun
00:05:25.060 --> 00:05:27.510
is through photovoltaic cells.
00:05:27.510 --> 00:05:31.350
If we break down that big
word, photo meaning light,
00:05:31.350 --> 00:05:35.930
and volt meaning a unit of electric force,
00:05:35.930 --> 00:05:38.920
then photovoltaic becomes using light
00:05:38.920 --> 00:05:40.980
to produce electric force.
00:05:40.980 --> 00:05:43.670
This idea dates back to 1905
00:05:43.670 --> 00:05:46.330
when Einstein first
published a paper about it.
00:05:46.330 --> 00:05:48.590
He then went on to win the Nobel Prize
00:05:48.590 --> 00:05:52.320
for this concept of the
photoelectric effect
00:05:52.320 --> 00:05:54.800
that when light shines on a metal,
00:05:54.800 --> 00:05:57.220
it causes electrons to be ejected
00:05:57.220 --> 00:05:59.950
and generates an electric current.
00:05:59.950 --> 00:06:03.410
Photovoltaic cells are
used in solar farms,
00:06:03.410 --> 00:06:06.450
on the roofs of houses,
and you might even have
00:06:06.450 --> 00:06:09.580
your very own solar powered calculator.
00:06:09.580 --> 00:06:13.160
You'll notice these types of
calculators work best outside
00:06:13.160 --> 00:06:14.660
or in a bright room,
00:06:14.660 --> 00:06:18.640
which can definitely be a
disadvantage in some cases.
00:06:18.640 --> 00:06:21.230
Another disadvantage is that sometimes
00:06:21.230 --> 00:06:24.050
you'll have to install
large amounts of these
00:06:24.050 --> 00:06:27.980
to generate enough
electricity for say a home,
00:06:27.980 --> 00:06:30.020
which can get expensive,
00:06:30.020 --> 00:06:33.730
and you also have to be sure
you're not moving anytime soon.
00:06:33.730 --> 00:06:36.500
On the other hand, installing
solar panels on a home
00:06:36.500 --> 00:06:40.380
reduces electricity costs
and your carbon footprint.
00:06:40.380 --> 00:06:42.300
So there you go, lot's of ways
00:06:42.300 --> 00:06:44.270
to harness the power of the sun,
00:06:44.270 --> 00:06:46.513
both its heat and its light.
|
The Indefinite Article | https://www.youtube.com/watch?v=z-SFzbp6Y08 | vtt | https://www.youtube.com/api/timedtext?v=z-SFzbp6Y08&ei=3FWUZeHQDJS2vdIP85Gq4As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245324&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=AA3D57CCFEDE73B9FED1CBD9B4D9B7F93CBC14B9.2E85461D8FD9FF90A71FCE4478D0D28CB1BD6D59&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.320 --> 00:00:02.020
- Hello Grammarians,
00:00:02.020 --> 00:00:03.860
we've talked a little about the difference
00:00:03.860 --> 00:00:07.163
between these special adjectives
'a,' and 'an,' and 'the,'
00:00:08.230 --> 00:00:11.250
also known as the articles.
00:00:11.250 --> 00:00:12.823
I want to go a little deeper.
00:00:13.790 --> 00:00:17.110
Now we know that 'the'
is the definite article
00:00:17.110 --> 00:00:21.260
and 'a,' or 'an is the indefinite.
00:00:21.260 --> 00:00:23.170
If you're being non-specific in language,
00:00:23.170 --> 00:00:27.410
you'd use an indefinite article,
as in may I have an orange,
00:00:27.410 --> 00:00:29.220
if you want to talk about
one orange in particular,
00:00:29.220 --> 00:00:30.800
you'd use the definite article:
00:00:30.800 --> 00:00:33.220
may I have the orange.
00:00:33.220 --> 00:00:35.480
Now into this framework,
I'd like to introduce
00:00:35.480 --> 00:00:38.960
a complication into
that indefinite article,
00:00:38.960 --> 00:00:41.180
something to chew on,
something to think about.
00:00:41.180 --> 00:00:46.120
You'll notice I said the
indefinite article is 'a' or 'an,'
00:00:47.150 --> 00:00:48.745
well what's with that or?
00:00:48.745 --> 00:00:50.170
We use 'a' and when do we use 'an'?
00:00:51.010 --> 00:00:54.030
And the answer to that question
comes down to one thing
00:00:54.030 --> 00:00:56.170
and one thing only.
00:00:56.170 --> 00:00:58.593
The next sound to come out of your mouth.
00:00:59.820 --> 00:01:02.110
Let us take, for example, two apes,
00:01:02.110 --> 00:01:04.963
the orangutan and the bonobo.
00:01:05.860 --> 00:01:07.477
Orangutan starts with 'o,'
00:01:08.420 --> 00:01:10.320
bonobo starts with 'b.'
00:01:10.320 --> 00:01:12.500
Marvelous great apes, cousins to humans,
00:01:12.500 --> 00:01:14.900
treat them with love and respect.
00:01:14.900 --> 00:01:17.840
When you say a word that
begins with a consonant,
00:01:17.840 --> 00:01:20.810
which is to say any sound
that you make when your lips
00:01:20.810 --> 00:01:22.950
or your teeth or your tongue are touching,
00:01:22.950 --> 00:01:25.700
you say 'a.'
00:01:25.700 --> 00:01:26.683
A bonobo.
00:01:28.341 --> 00:01:31.070
The 'b' sound requires
my lips to come together
00:01:31.070 --> 00:01:32.800
and then pop apart.
00:01:32.800 --> 00:01:34.840
Ba, ba.
00:01:34.840 --> 00:01:37.190
When you say a word that
begins with a vowel sound,
00:01:37.190 --> 00:01:39.500
which is any sound that
you make with an open mouth
00:01:39.500 --> 00:01:43.617
and no teeth, lips, toungey
business, you say 'an.'
00:01:43.617 --> 00:01:45.910
An orangutan.
00:01:45.910 --> 00:01:48.680
Orangutan starts with an 'o' sound:
00:01:48.680 --> 00:01:52.960
oh, ah, ee, ahh, little vocal warmup.
00:01:52.960 --> 00:01:55.653
So you can see how this
is going to break down.
00:01:55.653 --> 00:01:59.190
Whatever sound comes after
the indefinite article
00:01:59.190 --> 00:02:01.030
is going to determine the shape
00:02:01.030 --> 00:02:03.880
the indefinite article takes.
00:02:03.880 --> 00:02:08.880
A pencil, an open door, a zebra,
00:02:09.280 --> 00:02:13.630
an extra pudding cup, a sailboat,
00:02:13.630 --> 00:02:17.420
an NBA player, a unicorn,
00:02:17.420 --> 00:02:20.720
wait, whoa, hold up.
00:02:20.720 --> 00:02:23.110
Do you notice something weird
about those last two examples?
00:02:23.110 --> 00:02:26.750
NBA player, well that
begins with 'n' doesn't it?
00:02:26.750 --> 00:02:29.400
And unicorn begins with 'u,'
00:02:29.400 --> 00:02:33.940
so why isn't it a NBA
player and an unicorn,
00:02:33.940 --> 00:02:37.060
because, and this is the
crucial, complicated,
00:02:37.060 --> 00:02:40.660
confusing part, it's not about the letter
00:02:40.660 --> 00:02:42.940
that the word begins with in spelling,
00:02:42.940 --> 00:02:46.053
it's about the sound that letter makes.
00:02:47.300 --> 00:02:50.809
So NBA doesn't begin with the 'nuh' sound,
00:02:50.809 --> 00:02:54.950
it's not nuh-BA, it's Eh, Ehn-BA.
00:02:54.950 --> 00:02:59.300
And unicorn doesn't begin with
an 'uh' or an 'ohh' sound,
00:02:59.300 --> 00:03:04.140
it begins with 'yuh,' yuh-icorn.
00:03:04.140 --> 00:03:07.840
It's not about the letter,
it's about the sound.
00:03:07.840 --> 00:03:12.840
'Eh' in NBA is a vowel
sound, so it's an NBA player.
00:03:13.890 --> 00:03:17.660
And 'yuh' in unicorn is a consonant sound.
00:03:17.660 --> 00:03:19.870
Notice how you lift your
tongue as you practice
00:03:19.870 --> 00:03:24.290
the difference between
un-icorn and une-icorn.
00:03:24.290 --> 00:03:28.090
- Ohh, yu, ohh, yu, so
it's a consonant sound.
00:03:28.090 --> 00:03:30.163
It's a unicorn.
00:03:31.440 --> 00:03:34.620
Same deal with words to
begin with silent 'h,'
00:03:34.620 --> 00:03:39.620
like herb, or heirloom, or hour.
00:03:39.670 --> 00:03:42.540
An hour had passed, ow,
00:03:42.540 --> 00:03:45.823
I'm going to start an herb garden, er,
00:03:46.800 --> 00:03:51.330
that cuckoo clock is an heirloom, air.
00:03:51.330 --> 00:03:52.630
Why does this happen?
00:03:52.630 --> 00:03:55.200
What's the difference
between 'a' and 'an?'
00:03:55.200 --> 00:03:58.710
The 'nuh' sound in 'an'
helps separate sounds.
00:03:58.710 --> 00:04:01.110
Here, listen to this incorrect example:
00:04:01.110 --> 00:04:03.860
for my snack today, I ate a apple.
00:04:03.860 --> 00:04:04.930
Sounds weird, right?
00:04:04.930 --> 00:04:07.308
One right after the other, ah, ah.
00:04:07.308 --> 00:04:08.410
And now listen to this:
00:04:08.410 --> 00:04:11.920
for my snack today, I ate an apple.
00:04:11.920 --> 00:04:15.140
The 'nuh' in 'an' is ind
of like a springboard
00:04:15.140 --> 00:04:17.470
from one vowel sound into the next.
00:04:17.470 --> 00:04:18.453
An-napel.
00:04:19.570 --> 00:04:21.680
And that's what I want you to
take away from this lesson,
00:04:21.680 --> 00:04:25.180
because it can be very
confusing and, well, indefinite.
00:04:25.180 --> 00:04:28.660
But think about the sound
that the word makes,
00:04:28.660 --> 00:04:30.783
not the letter that it begins with.
00:04:32.070 --> 00:04:37.070
An orangutan, a bonobo,
an NBA player, a unicorn,
00:04:38.050 --> 00:04:41.743
a you can learn anything, David out.
|
Pollution and human health | https://www.youtube.com/watch?v=miaewHG2-X0 | vtt | https://www.youtube.com/api/timedtext?v=miaewHG2-X0&ei=2lWUZfOMD42_mLAPhsCM-AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245322&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=21AB3E28187A4905DEBEDA19FC5CC8CE28428C35.4461DFD2C965C6F9D867149D913B4F271386CF3A&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.960 --> 00:00:02.480
- [Narrator] Hey there friends,
00:00:02.480 --> 00:00:03.660
all of my life,
00:00:03.660 --> 00:00:05.900
I've struggled with asthma.
00:00:05.900 --> 00:00:08.300
And normally it doesn't
bother me too much,
00:00:08.300 --> 00:00:09.965
but when it's really cold outside,
00:00:09.965 --> 00:00:12.770
or if I've worked out really hard,
00:00:12.770 --> 00:00:15.480
my asthma symptoms get worse.
00:00:15.480 --> 00:00:16.360
When this happens,
00:00:16.360 --> 00:00:19.710
or in other words, when
I get an asthma attack,
00:00:19.710 --> 00:00:23.230
the airways in my lungs
become inflamed and swollen.
00:00:23.230 --> 00:00:26.100
And then also start to
narrow and fill with mucus,
00:00:26.100 --> 00:00:29.690
making it harder and harder
for me to breathe normally.
00:00:29.690 --> 00:00:31.440
However, it's not just the cold
00:00:31.440 --> 00:00:33.340
and CrossFit that trigger my asthma,
00:00:33.340 --> 00:00:35.510
but it's also air pollution.
00:00:35.510 --> 00:00:37.380
If I'm running around outside,
00:00:37.380 --> 00:00:39.100
or even just walking in areas
00:00:39.100 --> 00:00:42.020
where there's a lot of traffic
and cars driving around,
00:00:42.020 --> 00:00:44.840
my asthma will flare up immediately.
00:00:44.840 --> 00:00:45.860
But why?
00:00:45.860 --> 00:00:47.520
Well today, we're going to learn
00:00:47.520 --> 00:00:51.210
about the connections between
pollution and human health.
00:00:51.210 --> 00:00:53.659
This figure illustrates the
three main sources of pollution
00:00:53.659 --> 00:00:55.940
in our surrounding environment,
00:00:55.940 --> 00:00:59.320
namely air, water, and soil pollution.
00:00:59.320 --> 00:01:02.080
Exposure to these pollutants can in turn
00:01:02.080 --> 00:01:05.470
lead to a variety of
health issues and diseases.
00:01:05.470 --> 00:01:06.900
And today we're going to focus
00:01:06.900 --> 00:01:08.900
on air pollution in particular.
00:01:08.900 --> 00:01:11.140
Toxic gases, particulate matter,
00:01:11.140 --> 00:01:13.160
and chemicals released into the air
00:01:13.160 --> 00:01:15.230
can cause a variety of health issues,
00:01:15.230 --> 00:01:19.110
including respiratory and
cardiovascular illnesses,
00:01:19.110 --> 00:01:21.230
as well as headaches, fatigue,
00:01:21.230 --> 00:01:24.173
cancer, nausea, and skin irritation.
00:01:25.250 --> 00:01:27.520
Yet doctors and researchers
00:01:27.520 --> 00:01:29.400
are still learning about the connections
00:01:29.400 --> 00:01:32.190
between pollutants in our environment
00:01:32.190 --> 00:01:33.700
and human health issues,
00:01:33.700 --> 00:01:36.240
mainly because we humans
00:01:36.240 --> 00:01:39.190
collectively experienced
different levels of exposure
00:01:39.190 --> 00:01:42.510
to a variety of pollutants and toxins.
00:01:42.510 --> 00:01:43.830
So in short,
00:01:43.830 --> 00:01:47.250
it can be really hard to
pin down the exact cause
00:01:47.250 --> 00:01:48.500
of certain diseases
00:01:48.500 --> 00:01:51.970
because pollutants and
toxins can enter our bodies
00:01:51.970 --> 00:01:54.460
from the air, water and soil,
00:01:54.460 --> 00:01:56.100
as shown by this figure,
00:01:56.100 --> 00:01:59.120
which indicates the many
anthropogenic sources,
00:01:59.120 --> 00:02:02.490
that is to say sources
caused by human activities,
00:02:02.490 --> 00:02:05.730
of air, land, and water pollution.
00:02:05.730 --> 00:02:09.080
If we take a closer look of
air pollutants in particular,
00:02:09.080 --> 00:02:11.560
we see a cluster of industrial facilities
00:02:11.560 --> 00:02:13.360
releasing chlorofluorocarbons, CFCs,
00:02:15.230 --> 00:02:16.910
which are anthropogenic compounds
00:02:16.910 --> 00:02:20.700
that contribute to ozone
depletion in the stratosphere.
00:02:20.700 --> 00:02:24.860
We also see nitrous
oxides and sulfur dioxide,
00:02:24.860 --> 00:02:28.440
which can contribute to air
pollution as well as acid rain,
00:02:28.440 --> 00:02:32.330
and carbon dioxide, which
is a common greenhouse gas.
00:02:32.330 --> 00:02:36.223
So how do these common air
pollutants affect human health?
00:02:38.870 --> 00:02:41.090
One of them or well-studied connections
00:02:41.090 --> 00:02:43.780
between air pollution and human health
00:02:43.780 --> 00:02:47.440
is the link between
asbestos and mesothelioma.
00:02:47.440 --> 00:02:49.940
Many studies have shown
that the repeated act
00:02:49.940 --> 00:02:53.780
of inhaling or accidentally
swallowing asbestos
00:02:53.780 --> 00:02:56.900
is the most common cause of mesothelioma,
00:02:56.900 --> 00:02:58.210
which is a type of cancer
00:02:58.210 --> 00:03:00.130
that develops the lining of the lungs
00:03:00.130 --> 00:03:03.710
and sometimes in the
abdomen and heart as well.
00:03:03.710 --> 00:03:07.310
It might be a little difficult
to see in this chest x-ray,
00:03:07.310 --> 00:03:09.530
but this area is circled in orange
00:03:09.530 --> 00:03:11.120
shows affected lung tissue
00:03:11.120 --> 00:03:14.160
where mesothelioma has started to spread.
00:03:14.160 --> 00:03:15.710
Normally the lung tissue
00:03:15.710 --> 00:03:18.240
should appear fairly
transparent in x-rays,
00:03:18.240 --> 00:03:22.063
but it becomes opaque when
mesothelioma is present.
00:03:23.020 --> 00:03:25.660
Asbestos is a naturally occurring mineral
00:03:25.660 --> 00:03:27.410
composed of millions of fibers
00:03:27.410 --> 00:03:29.660
which bind together to create a light
00:03:29.660 --> 00:03:32.800
yet virtually indestructible material.
00:03:32.800 --> 00:03:34.890
The fiber structure of asbestos
00:03:34.890 --> 00:03:38.090
makes it a really effective
electrical insulator,
00:03:38.090 --> 00:03:39.700
and it's also heat resistant.
00:03:39.700 --> 00:03:43.880
So it was widely used in
construction and fireproofing.
00:03:43.880 --> 00:03:45.300
When I was growing up,
00:03:45.300 --> 00:03:48.020
my parents actually had
asbestos in their ceiling.
00:03:48.020 --> 00:03:51.120
And I also remembered that
both my elementary school
00:03:51.120 --> 00:03:52.380
and middle school,
00:03:52.380 --> 00:03:55.420
which were built in the late 1970s,
00:03:55.420 --> 00:03:58.900
had gymnasiums with asbestos ceilings.
00:03:58.900 --> 00:04:00.920
But as public health awareness
00:04:00.920 --> 00:04:03.780
about the dangers of asbestos has grown,
00:04:03.780 --> 00:04:07.440
the business of asbestos
removal has also grown.
00:04:07.440 --> 00:04:10.210
Although asbestos isn't
commonly used anymore
00:04:10.210 --> 00:04:12.860
in construction, some consumer products
00:04:12.860 --> 00:04:15.590
can still contain trace
amounts of asbestos,
00:04:15.590 --> 00:04:17.650
such as roofing materials.
00:04:17.650 --> 00:04:20.450
And sometimes when you're watching TV,
00:04:20.450 --> 00:04:22.920
you might see ads for asbestos abatement,
00:04:22.920 --> 00:04:24.470
which is the safe containment
00:04:24.470 --> 00:04:27.363
and removal of asbestos by professionals.
00:04:28.550 --> 00:04:31.200
The link between exposure to asbestos
00:04:31.200 --> 00:04:34.390
and mesothelioma has been heavily studied.
00:04:34.390 --> 00:04:38.840
And in turn, asbestos use has
greatly declined over time.
00:04:38.840 --> 00:04:40.540
Unfortunately though,
00:04:40.540 --> 00:04:43.030
symptoms or signs of mesothelioma
00:04:43.030 --> 00:04:46.860
may not appear until 20
or 50 years later or more
00:04:46.860 --> 00:04:50.210
after exposure to asbestos
with initial symptoms,
00:04:50.210 --> 00:04:53.280
including shortness of
breath and chest pain.
00:04:53.280 --> 00:04:55.180
However, over time,
00:04:55.180 --> 00:04:57.990
as we can see in the
lower part of this figure,
00:04:57.990 --> 00:05:00.470
asbestosis exposure can result in damage
00:05:00.470 --> 00:05:02.980
to and cancer of the pleura,
00:05:02.980 --> 00:05:05.120
which are membranes that cover the lungs
00:05:05.120 --> 00:05:08.120
and the inside of the
surrounding chest walls.
00:05:08.120 --> 00:05:10.600
These pleura, and even the diaphragm,
00:05:10.600 --> 00:05:12.140
which helps you breathe,
00:05:12.140 --> 00:05:15.650
can become scarred, damaged,
and hardened from asbestos.
00:05:15.650 --> 00:05:17.060
And of course,
00:05:17.060 --> 00:05:19.313
mesothelioma can develop too.
00:05:20.190 --> 00:05:21.350
What's even worse though
00:05:21.350 --> 00:05:24.150
is that mesothelioma
is generally resistant
00:05:24.150 --> 00:05:26.480
to radiation and chemotherapy treatments.
00:05:26.480 --> 00:05:31.130
So long-term survival and
cures are exceedingly rare.
00:05:31.130 --> 00:05:35.170
But mesothelioma can be
diagnosed and treated early
00:05:35.170 --> 00:05:38.030
through regular cancer
screenings and blood tests
00:05:38.030 --> 00:05:41.800
for those who may be most
vulnerable to this cancer.
00:05:41.800 --> 00:05:45.190
That is to say folks who
have had exposure to asbestos
00:05:45.190 --> 00:05:47.090
through their work like miners,
00:05:47.090 --> 00:05:49.670
factory workers, insulation, installers,
00:05:49.670 --> 00:05:51.283
and construction workers.
00:05:52.160 --> 00:05:53.930
So take a breath,
00:05:53.930 --> 00:05:55.340
take a sip of water.
00:05:55.340 --> 00:05:58.190
These are simple things that
we take for granted each day,
00:05:58.190 --> 00:06:01.990
yet pollution can threaten these
basic aspects of our lives.
00:06:01.990 --> 00:06:03.820
When my asthma starts to act up,
00:06:03.820 --> 00:06:06.920
I become acutely aware of
just how much pollution
00:06:06.920 --> 00:06:08.730
affects my day-to-day health.
00:06:08.730 --> 00:06:11.280
And thanks to regulatory legislation
00:06:11.280 --> 00:06:12.380
like the Clean Air Act
00:06:12.380 --> 00:06:14.780
and the Clean Water Act
in the United States,
00:06:14.780 --> 00:06:17.020
we have longer and healthier lives here.
00:06:17.020 --> 00:06:18.650
But this isn't the case everywhere,
00:06:18.650 --> 00:06:20.330
nor is it the case for everyone.
00:06:20.330 --> 00:06:22.800
So do your part and help to ensure
00:06:22.800 --> 00:06:24.763
safe air and water for all.
|
Mendelian inheritance and Punnett squares | https://www.youtube.com/watch?v=OhYOfTczCk4 | vtt | https://www.youtube.com/api/timedtext?v=OhYOfTczCk4&ei=3FWUZdaHLMmavdIPhLuBUA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245324&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0F91F4F3F0692C2CDEEBA4CD6BC982DAFAD4227A.33282A611355D54E5B7FF29EF51709E3FF130188&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.780 --> 00:00:02.960
- [Narrator] This is a
photo of Gregor Mendel,
00:00:02.960 --> 00:00:04.970
who is often known as
the father of genetics.
00:00:04.970 --> 00:00:07.360
And we'll see in a few seconds why,
00:00:07.360 --> 00:00:10.950
and he was an Abbot of
a monastery in Moravia,
00:00:10.950 --> 00:00:13.570
which is in modern day Czech Republic.
00:00:13.570 --> 00:00:17.860
And many people had bred plants
for agricultural purposes
00:00:17.860 --> 00:00:21.270
for hundreds, if not thousands
of years before Mendel,
00:00:21.270 --> 00:00:24.110
but he really gave us a
glimpse, gave us insights
00:00:24.110 --> 00:00:26.420
in how traits are really passed.
00:00:26.420 --> 00:00:29.020
And he did this through
his pea plant experiments
00:00:29.020 --> 00:00:32.230
that he conducted from 1856 to 1863.
00:00:32.230 --> 00:00:37.060
Over that time period, he
bred roughly 28,000 pea plants
00:00:37.060 --> 00:00:38.750
in order to get a better understanding
00:00:38.750 --> 00:00:40.970
of how they passed down different traits.
00:00:40.970 --> 00:00:44.090
And he studied things like
properties of the seeds,
00:00:44.090 --> 00:00:45.750
properties of the pea prods,
00:00:45.750 --> 00:00:48.990
and things like the height of the plant.
00:00:48.990 --> 00:00:52.610
And in his time, the mainstream theory
00:00:52.610 --> 00:00:56.830
was that if you bred a tall
parent with a short parent,
00:00:56.830 --> 00:00:59.050
you would get a medium offspring,
00:00:59.050 --> 00:01:01.160
but that's not what Mendel saw.
00:01:01.160 --> 00:01:04.350
When he bred tall pea plants
with short pea plants,
00:01:04.350 --> 00:01:06.630
all of the offspring were tall.
00:01:06.630 --> 00:01:08.610
But then when he self
fertilized those plants
00:01:08.610 --> 00:01:10.670
and plants have the interesting property
00:01:10.670 --> 00:01:12.950
that they can fertilize themselves.
00:01:12.950 --> 00:01:16.310
So the same plant can contribute
both the female gamete
00:01:16.310 --> 00:01:18.020
and the male gametes.
00:01:18.020 --> 00:01:20.580
In other words the same plant can be both
00:01:20.580 --> 00:01:23.820
the female parent and the male parent.
00:01:23.820 --> 00:01:26.870
Well, then he saw that
roughly there was a ratio
00:01:26.870 --> 00:01:28.710
of three to one, tall to short.
00:01:28.710 --> 00:01:29.970
Those weren't the exact numbers,
00:01:29.970 --> 00:01:33.280
but pretty close to three to one.
00:01:33.280 --> 00:01:35.830
And so there's a lot of really
interesting things here.
00:01:35.830 --> 00:01:37.600
First of all, at least for this trait,
00:01:37.600 --> 00:01:39.620
he didn't see any blending occur.
00:01:39.620 --> 00:01:43.240
And then the other thing is,
this short trait reappeared
00:01:43.240 --> 00:01:45.870
in this second generation.
00:01:45.870 --> 00:01:48.600
In order to explain these
results, he hypothesized
00:01:48.600 --> 00:01:51.140
that there are inheritable factors
00:01:51.140 --> 00:01:54.300
that are inherited from
an organism's parents
00:01:54.300 --> 00:01:56.280
and they're related to a specific trait.
00:01:56.280 --> 00:01:59.950
So in this case it would be around height.
00:01:59.950 --> 00:02:02.340
Now we know what he called
these inheritable factors.
00:02:02.340 --> 00:02:06.220
We now call genes, although
he did not use the term,
00:02:06.220 --> 00:02:08.930
and he also hypothesized
that these factors
00:02:08.930 --> 00:02:12.060
could come in different versions.
00:02:12.060 --> 00:02:15.010
Now, today we know that the
different versions of a gene,
00:02:15.010 --> 00:02:18.830
we call alleles, although
he did not use that term,
00:02:18.830 --> 00:02:22.010
but in this case, the versions
that we have at our disposal,
00:02:22.010 --> 00:02:23.670
you could have a tall height,
00:02:23.670 --> 00:02:27.700
which we can shorthand say,
capital T, capital T for tall,
00:02:27.700 --> 00:02:29.150
or you could have a short height,
00:02:29.150 --> 00:02:33.240
which I will use lowercase
t for, for a short height.
00:02:33.240 --> 00:02:36.830
Now generally speaking,
organisms will have two versions
00:02:36.830 --> 00:02:38.330
of their genes like this.
00:02:38.330 --> 00:02:41.680
For example, an organism
could have two tall alleles,
00:02:41.680 --> 00:02:44.240
or two short, or one of each,
00:02:44.240 --> 00:02:47.260
but when it produces its
gametes, the sex cells,
00:02:47.260 --> 00:02:50.280
so the sperm for a male
and the egg for a female,
00:02:50.280 --> 00:02:52.780
it will generally contribute
one of its two versions
00:02:52.780 --> 00:02:53.800
to its offspring.
00:02:53.800 --> 00:02:57.150
And this contribution of
one allele or the other
00:02:57.150 --> 00:03:00.540
is known as Mendel's law of segregation.
00:03:00.540 --> 00:03:03.520
And we can draw, what's
known as a Punnett square
00:03:03.520 --> 00:03:04.980
to depict this.
00:03:04.980 --> 00:03:08.300
So let me draw a little
bit of a grid here.
00:03:08.300 --> 00:03:11.040
And Mendel actually did not
invent the Punnett square,
00:03:11.040 --> 00:03:13.750
although he was thinking in these terms.
00:03:13.750 --> 00:03:17.580
It was actually invented by
Reginald Punnett in 1905.
00:03:17.580 --> 00:03:20.010
And this is useful to think
about the probabilities
00:03:20.010 --> 00:03:22.470
of various combinations based on what
00:03:22.470 --> 00:03:24.330
each parent could contribute.
00:03:24.330 --> 00:03:27.020
So let's say we're talking
about the tall plant,
00:03:27.020 --> 00:03:30.290
and let's say it has two tall versions.
00:03:30.290 --> 00:03:34.400
So it can contribute a
capital T or a capital T.
00:03:34.400 --> 00:03:36.800
And let's say that this
short plant over here
00:03:36.800 --> 00:03:39.060
has two of the short versions for now.
00:03:39.060 --> 00:03:41.680
So it could contribute
either a lowercase t,
00:03:41.680 --> 00:03:43.520
or a lowercase t.
00:03:43.520 --> 00:03:45.850
And so what are all the
possible combinations
00:03:45.850 --> 00:03:47.640
for its offspring?
00:03:47.640 --> 00:03:51.870
Well, in one scenario, you
could get this capital T
00:03:51.870 --> 00:03:55.060
from the male parent,
and this lowercase t,
00:03:55.060 --> 00:03:56.350
from the female parent.
00:03:56.350 --> 00:03:58.550
In another scenario, you
could get this capital T
00:03:58.550 --> 00:04:01.370
from the male parent, and a lowercase t
00:04:01.370 --> 00:04:03.200
from the female parent.
00:04:03.200 --> 00:04:05.920
In this scenario, and I know
these look very similar,
00:04:05.920 --> 00:04:09.870
a capital T from the male
parent and this lowercase t
00:04:09.870 --> 00:04:12.270
from the female parent, and
then last but not least,
00:04:12.270 --> 00:04:14.770
I know this looks repetitive,
you could get this capital T
00:04:14.770 --> 00:04:17.810
from the male parent and this lowercase t
00:04:17.810 --> 00:04:19.430
from the female parent.
00:04:19.430 --> 00:04:22.530
And the reason why in all of these cases,
00:04:22.530 --> 00:04:27.530
you see a tall plant, is
because the tall version,
00:04:28.060 --> 00:04:30.920
and he coined this term, is dominant.
00:04:30.920 --> 00:04:32.840
And once again, this
was all his hypothesis
00:04:32.840 --> 00:04:34.660
to explain his results.
00:04:34.660 --> 00:04:37.980
So this is dominant and
the short is recessive.
00:04:37.980 --> 00:04:40.370
So even if you have one of each,
00:04:40.370 --> 00:04:43.500
you're actually going to
show the dominant trait.
00:04:43.500 --> 00:04:45.410
We now call that your phenotype,
00:04:45.410 --> 00:04:48.010
what you show is going to be tall.
00:04:48.010 --> 00:04:50.250
Now, what's interesting
about this hypothesis
00:04:50.250 --> 00:04:54.410
is it seems to explain what
happens in the next generation.
00:04:54.410 --> 00:04:56.040
Just so a little bit of notation.
00:04:56.040 --> 00:04:57.610
The first generation is usually called
00:04:57.610 --> 00:04:59.450
the P generation for parental,
00:04:59.450 --> 00:05:01.760
and then the first generation of offspring
00:05:01.760 --> 00:05:04.330
is known as the F1, F for filial.
00:05:04.330 --> 00:05:07.260
And that comes filials,
which means sun in Greek,
00:05:07.260 --> 00:05:09.613
and then the generation
after that would be F2,
00:05:10.520 --> 00:05:12.600
that's just a little
bit of notation there,
00:05:12.600 --> 00:05:13.840
but let's think about what would happen
00:05:13.840 --> 00:05:17.600
at the F2 generation,
if you self fertilized,
00:05:17.600 --> 00:05:20.910
some of these characters right over here.
00:05:20.910 --> 00:05:25.180
Well, in that situation, let
me draw another Punnett square,
00:05:25.180 --> 00:05:27.480
on the male parents side,
you could contribute
00:05:27.480 --> 00:05:29.210
either your capital T version,
00:05:29.210 --> 00:05:31.800
which we now call your dominant allele,
00:05:31.800 --> 00:05:34.490
or you could contribute
the lowercase t version,
00:05:34.490 --> 00:05:37.300
and on the female parents side
and once again for a plant,
00:05:37.300 --> 00:05:39.520
you can have the same plant
that has both the male
00:05:39.520 --> 00:05:40.800
and the female parent.
00:05:40.800 --> 00:05:43.350
You could contribute the
dominant version, the capital T,
00:05:43.350 --> 00:05:46.200
or the recessive version, the lowercase t.
00:05:46.200 --> 00:05:49.370
Now we see something interesting
happen in the offspring.
00:05:49.370 --> 00:05:52.060
There is a one in four chance
you get both capital Ts.
00:05:52.060 --> 00:05:54.600
So capital T, capital T.
00:05:54.600 --> 00:05:58.790
There's also a one in four
chance that you get a lowercase t
00:05:58.790 --> 00:06:03.000
from the male parent up here,
and then you get a capital T
00:06:03.000 --> 00:06:05.050
from the female parent.
00:06:05.050 --> 00:06:09.500
There is another one in four
chance you get a capital T
00:06:09.500 --> 00:06:12.970
from the male parent, and a lowercase t
00:06:12.970 --> 00:06:14.460
from the female parent.
00:06:14.460 --> 00:06:16.330
And then there's a one in four chance
00:06:16.330 --> 00:06:18.350
that you get two lowercase ts,
00:06:18.350 --> 00:06:21.000
one each from the male and female parent.
00:06:21.000 --> 00:06:23.860
Now, if we accept the dominant
and recessive hypothesis,
00:06:23.860 --> 00:06:26.380
we would expect that plants
that got both capital Ts
00:06:26.380 --> 00:06:29.450
would be tall, but we would
also expect that these over here
00:06:29.450 --> 00:06:32.620
would be tall as well, because
the capital T is dominant.
00:06:32.620 --> 00:06:35.380
They would exhibit the tall phenotype.
00:06:35.380 --> 00:06:36.960
And then you would
expect probabilistically
00:06:36.960 --> 00:06:40.530
that one fourth of your plants
over time, would be short
00:06:40.530 --> 00:06:42.820
because they only have
the recessive alleles,
00:06:42.820 --> 00:06:45.980
the recessive traits in this situation.
00:06:45.980 --> 00:06:48.860
And that's actually what Mendel saw.
00:06:48.860 --> 00:06:50.890
Now what's amazing is that Mendel was able
00:06:50.890 --> 00:06:53.890
to figure this out without
knowing about chromosomes,
00:06:53.890 --> 00:06:56.280
without knowing all that we know today.
00:06:56.280 --> 00:06:58.280
Today we know this works because we have
00:06:58.280 --> 00:07:02.320
23 pair of chromosomes, and
each of those pairs have copies,
00:07:02.320 --> 00:07:05.590
have different versions
of usually the same gene,
00:07:05.590 --> 00:07:08.580
and that when meiosis occurs
and you have gamete formation,
00:07:08.580 --> 00:07:11.160
one member of each pair
will segregate randomly
00:07:11.160 --> 00:07:15.350
into the newly formed sex cell,
into the sperm or the egg.
00:07:15.350 --> 00:07:17.320
That's why this occur and we
go into some detail on that
00:07:17.320 --> 00:07:19.240
in other videos, but it's pretty cool,
00:07:19.240 --> 00:07:22.453
that Mendel was able to figure
this out in the 19th century.
|
Sources of genetic variation | https://www.youtube.com/watch?v=D0XYWKm_LoM | vtt | https://www.youtube.com/api/timedtext?v=D0XYWKm_LoM&ei=21WUZc2MLJnWxN8Pwp624AQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245323&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=778D328CA6F74D9E0547ACAA066E485C5E9BFD30.D3D36BF43646668AC723ACA4153ACCEB9B0B4D15&key=yt8&lang=en&name=Default&fmt=vtt | en | WEBVTT
Kind: captions
Language: en
00:00:00.240 --> 00:00:01.820
- [Instructor] In this video,
we're going to talk about
00:00:01.820 --> 00:00:04.370
sources of genetic variation,
00:00:04.370 --> 00:00:09.010
which is key for evolution and
natural selection to happen.
00:00:09.010 --> 00:00:11.820
Just as a little bit of a
primer, natural selection,
00:00:11.820 --> 00:00:13.670
you can have a bunch
of different organisms
00:00:13.670 --> 00:00:16.260
with different genetics,
different genotypes,
00:00:16.260 --> 00:00:18.830
and they can express themselves
as different phenotypes.
00:00:18.830 --> 00:00:21.530
And I'll just do this as
different colored circles
00:00:21.530 --> 00:00:22.800
right over here.
00:00:22.800 --> 00:00:24.910
So there are all of these
different phenotypes,
00:00:24.910 --> 00:00:28.000
and I'm just expressing different
phenotypes of one trait.
00:00:28.000 --> 00:00:30.670
And then depending on what's
going on in the environment,
00:00:30.670 --> 00:00:33.500
some of these phenotypes
might be more favorable
00:00:33.500 --> 00:00:35.700
for survival and reproducing
00:00:35.700 --> 00:00:39.010
and therefore passing on those
genes to the next generation.
00:00:39.010 --> 00:00:42.470
And if you do that over many,
many, many, many generations,
00:00:42.470 --> 00:00:44.560
you can have a change in your gene pool
00:00:44.560 --> 00:00:48.090
because the genes that provide
the variants of phenotypes
00:00:48.090 --> 00:00:51.050
that are more successful will exist more.
00:00:51.050 --> 00:00:52.200
But an interesting question is,
00:00:52.200 --> 00:00:55.070
where does this variation come from?
00:00:55.070 --> 00:00:57.740
And there's several sources of it.
00:00:57.740 --> 00:01:00.490
So one of the key and probably
the most primitive version
00:01:00.490 --> 00:01:03.910
of genetic variation is mutation.
00:01:03.910 --> 00:01:08.890
Cells are incredibly accurate
when they are copying DNA,
00:01:08.890 --> 00:01:11.310
but there are going to be some errors.
00:01:11.310 --> 00:01:14.050
Now, most of these errors can oftentimes
00:01:14.050 --> 00:01:17.810
break the organism in some way
or might not matter at all,
00:01:17.810 --> 00:01:20.080
but every now and then,
some of these errors,
00:01:20.080 --> 00:01:22.600
either as an individual base pair change,
00:01:22.600 --> 00:01:25.840
or maybe cumulatively can
produce a different phenotype
00:01:25.840 --> 00:01:29.170
and potentially a phenotype
that has an advantage.
00:01:29.170 --> 00:01:31.910
And so this has always been the case.
00:01:31.910 --> 00:01:34.870
Now, another major source
of genetic variation
00:01:34.870 --> 00:01:37.240
is sexual reproduction.
00:01:37.240 --> 00:01:40.920
And to remind ourselves
of sexual reproduction,
00:01:40.920 --> 00:01:45.500
I will show you this diagram of meiosis.
00:01:45.500 --> 00:01:47.790
Now sexual reproduction is the process
00:01:47.790 --> 00:01:49.910
by which we form gametes.
00:01:49.910 --> 00:01:51.160
So for a male organism,
00:01:51.160 --> 00:01:52.810
that would be producing the sperm cells,
00:01:52.810 --> 00:01:54.430
or for a female organism,
00:01:54.430 --> 00:01:56.730
that would be producing the egg cells.
00:01:56.730 --> 00:01:58.970
This meiosis diagram is for an organism
00:01:58.970 --> 00:02:01.900
that has two pairs of chromosomes,
00:02:01.900 --> 00:02:05.750
while we know that human
beings actually have 23 pairs.
00:02:05.750 --> 00:02:07.670
But if we saw a diagram with 23 pairs,
00:02:07.670 --> 00:02:09.560
it would get very complicated, very fast,
00:02:09.560 --> 00:02:12.110
so the two pairs help us
understand what's going on
00:02:12.110 --> 00:02:15.150
and help us understand where
some of this genetic variation
00:02:15.150 --> 00:02:16.410
is going to come from.
00:02:16.410 --> 00:02:19.380
So I've already pre-labeled the
homologous chromosomes here.
00:02:19.380 --> 00:02:20.500
And just as a reminder,
00:02:20.500 --> 00:02:22.820
homologous chromosomes are ones
00:02:22.820 --> 00:02:25.400
that have the same genes on them.
00:02:25.400 --> 00:02:28.440
Now they could have different
versions of the genes on them,
00:02:28.440 --> 00:02:31.300
but they're fundamentally
coding for the same genes.
00:02:31.300 --> 00:02:36.300
You can view chromosomes as
really long stretches of DNA
00:02:36.610 --> 00:02:40.630
that has all been rolled
in and bunched in together,
00:02:40.630 --> 00:02:41.590
something like this.
00:02:41.590 --> 00:02:44.040
A human chromosome can
have on the order of
00:02:44.040 --> 00:02:46.930
100 million base pairs in it.
00:02:46.930 --> 00:02:49.590
Now, if you were to
straighten that string of DNA,
00:02:49.590 --> 00:02:51.180
if you were to unwind it,
00:02:51.180 --> 00:02:54.100
you would see different section's
code for different genes.
00:02:54.100 --> 00:02:55.900
So that might be one gene there,
00:02:55.900 --> 00:02:57.530
that might be another gene there.
00:02:57.530 --> 00:03:00.030
You might have one long
gene right over there.
00:03:00.030 --> 00:03:03.320
On average, the genes are about
27,000 base pairs in length
00:03:03.320 --> 00:03:05.670
but some of them could be
millions of base pairs.
00:03:05.670 --> 00:03:07.390
So on one of these chromosomes,
00:03:07.390 --> 00:03:10.800
you can actually have
thousands of genes being coded.
00:03:10.800 --> 00:03:13.010
And so if you were to pick this chromosome
00:03:13.010 --> 00:03:15.020
and this chromosome right over here,
00:03:15.020 --> 00:03:16.940
they would be coding for the same genes
00:03:16.940 --> 00:03:18.130
because they're homologous.
00:03:18.130 --> 00:03:19.760
But once again, they could
have different alleles,
00:03:19.760 --> 00:03:21.960
different versions of those genes on them.
00:03:21.960 --> 00:03:26.280
And similarly, this
chromosome and this chromosome
00:03:26.280 --> 00:03:27.430
are also homologous.
00:03:27.430 --> 00:03:30.390
They're also coding for the same genes.
00:03:30.390 --> 00:03:32.510
Now, as we go into meiosis,
00:03:32.510 --> 00:03:35.250
the first step is that the chromosomes
00:03:35.250 --> 00:03:37.220
are essentially going to copy themselves
00:03:37.220 --> 00:03:39.290
into two sister chromatids.
00:03:39.290 --> 00:03:43.250
So, for example, this one right over here
00:03:43.250 --> 00:03:47.120
has now copied itself and it
has that telltale X shape.
00:03:47.120 --> 00:03:50.020
But this side of this now chromosome,
00:03:50.020 --> 00:03:51.510
which we would call a chromatid,
00:03:51.510 --> 00:03:54.320
and this sister chromatid
should be identical.
00:03:54.320 --> 00:03:55.660
Now there might be some errors
00:03:55.660 --> 00:03:57.590
that got introduced through mutation.
00:03:57.590 --> 00:04:00.390
But if we don't assume mutation,
they would be identical.
00:04:00.390 --> 00:04:03.820
Likewise, this side and this side,
00:04:03.820 --> 00:04:06.850
assuming no mutations,
they would be identical.
00:04:06.850 --> 00:04:08.700
Now what's interesting about this
00:04:08.700 --> 00:04:11.280
is what happens in the next phase.
00:04:11.280 --> 00:04:15.340
In the next phase, you have
the independent assortment
00:04:15.340 --> 00:04:17.680
of homologous chromosomes.
00:04:17.680 --> 00:04:21.730
So as we said, this and
this might be coding
00:04:21.730 --> 00:04:24.770
for the same genes, it might
just have different versions.
00:04:24.770 --> 00:04:26.420
But as we go into this phase,
00:04:26.420 --> 00:04:30.130
as we do meiosis I, as it's
often known right over here,
00:04:30.130 --> 00:04:32.280
this blue chromosome could go here,
00:04:32.280 --> 00:04:35.750
while the homologous red
chromosome would go there.
00:04:35.750 --> 00:04:38.060
The purple chromosome is going here
00:04:38.060 --> 00:04:40.710
and the light blue
chromosome is going there.
00:04:40.710 --> 00:04:41.790
And this is really interesting
00:04:41.790 --> 00:04:44.380
because there's a lot of
different ways this could happen.
00:04:44.380 --> 00:04:47.390
In this situation, you have two pairs.
00:04:47.390 --> 00:04:50.330
Each of these intermediary
steps in meiosis
00:04:50.330 --> 00:04:53.070
could randomly have one from each pair.
00:04:53.070 --> 00:04:57.170
So just in this example,
you have two to the number
00:04:57.170 --> 00:05:00.950
of pairs combinations at
this stage right over here.
00:05:00.950 --> 00:05:02.520
Now this was only when we have two pairs.
00:05:02.520 --> 00:05:04.000
If we're talking about a human being,
00:05:04.000 --> 00:05:08.490
we're talking about two to the
23rd different combinations
00:05:08.490 --> 00:05:11.450
of which of the two homologous
chromosomes you get.
00:05:11.450 --> 00:05:13.610
So there's a lot of variation here.
00:05:13.610 --> 00:05:14.720
Now on top of that,
00:05:14.720 --> 00:05:17.240
some of y'all might have
noticed something interesting.
00:05:17.240 --> 00:05:19.090
If you just follow the colors here,
00:05:19.090 --> 00:05:22.670
it looks like a little chunk
of this chromosome got swapped
00:05:22.670 --> 00:05:24.530
with a little chunk of this chromosome.
00:05:24.530 --> 00:05:25.600
You could see it here.
00:05:25.600 --> 00:05:28.200
The red is now on the big blue X
00:05:28.200 --> 00:05:30.500
and the blue is now on the big red X.
00:05:30.500 --> 00:05:33.500
This is another source
of genetic variation
00:05:33.500 --> 00:05:35.863
and it is known as crossover.
00:05:36.940 --> 00:05:37.860
And what it does is,
00:05:37.860 --> 00:05:41.280
it can actually mix DNA
between chromosomes.
00:05:41.280 --> 00:05:43.210
Once again, these are
homologous chromosomes,
00:05:43.210 --> 00:05:45.500
they are encoding the same genes,
00:05:45.500 --> 00:05:47.620
but now alleles that were
sitting on the blue one
00:05:47.620 --> 00:05:49.360
could now sit with the rest of the red one
00:05:49.360 --> 00:05:51.340
and the alleles that was
sitting with the red one
00:05:51.340 --> 00:05:53.330
can now sit with the
rest of the blue ones.
00:05:53.330 --> 00:05:56.530
And crossover is actually
reasonably common during meiosis.
00:05:56.530 --> 00:05:59.220
So once again, it's
mixing things up even more
00:05:59.220 --> 00:06:01.890
than this two to the 23rd combinations.
00:06:01.890 --> 00:06:04.300
So a lot of variation that you can produce
00:06:04.300 --> 00:06:05.600
through sexual reproduction.
00:06:05.600 --> 00:06:08.800
And then as we go into this
last phase into meiosis II,
00:06:08.800 --> 00:06:11.180
and we're actually producing the gametes,
00:06:11.180 --> 00:06:14.480
if this meiosis is going
on in the gonads of a male,
00:06:14.480 --> 00:06:17.170
this would be the chromosomal
makeup of the sperm cells.
00:06:17.170 --> 00:06:19.520
If this is going on within the female,
00:06:19.520 --> 00:06:24.030
then this would be the DNA
makeup of the egg cells.
00:06:24.030 --> 00:06:25.590
And what you see, and
just to make it clear
00:06:25.590 --> 00:06:28.080
what's happened here is
that your sister chromatids
00:06:28.080 --> 00:06:30.260
have now spread apart, although
they're no longer identical,
00:06:30.260 --> 00:06:32.060
especially if you have the crossover.
00:06:32.060 --> 00:06:35.870
So for example, this one went over here
00:06:35.870 --> 00:06:40.260
and this one went over here as well.
00:06:40.260 --> 00:06:44.180
And then you have another
scenario where you have this one
00:06:44.180 --> 00:06:46.830
and this one ended up in this gamete,
00:06:46.830 --> 00:06:48.220
and we can go on and on.
00:06:48.220 --> 00:06:49.350
So actually you can have,
00:06:49.350 --> 00:06:51.160
especially if you consider crossover,
00:06:51.160 --> 00:06:55.530
more than two to the 23rd
possible combinations.
00:06:55.530 --> 00:06:58.180
Now two to the 23rd power is approximately
00:06:58.180 --> 00:07:01.840
a little bit more than
eight million combinations.
00:07:01.840 --> 00:07:03.530
And if do you want a little math trick
00:07:03.530 --> 00:07:05.180
for estimating powers of two,
00:07:05.180 --> 00:07:07.190
you can just recognize
that two to the 10th power
00:07:07.190 --> 00:07:08.970
is a little bit more than 1,000.
00:07:08.970 --> 00:07:10.780
So this is going to be two to the 20th,
00:07:10.780 --> 00:07:12.840
which is about a million,
and then two to the third,
00:07:12.840 --> 00:07:15.380
which is eight, so a little
bit more than 8 million.
00:07:15.380 --> 00:07:16.213
And once again,
00:07:16.213 --> 00:07:19.090
that's before considering
crossover and mutation,
00:07:19.090 --> 00:07:22.000
which is going to make the
combinations even larger.
00:07:22.000 --> 00:07:24.970
And I'll also point out
these are the combinations
00:07:24.970 --> 00:07:28.300
for the gametes, and
the gametes are haploid.
00:07:28.300 --> 00:07:31.870
They have half the DNA of a full organism.
00:07:31.870 --> 00:07:33.750
And so when the gametes combine,
00:07:33.750 --> 00:07:36.540
you're actually going
to have two to the 23rd
00:07:36.540 --> 00:07:40.110
times two to the 23rd combinations,
00:07:40.110 --> 00:07:42.210
just from sexual reproduction,
00:07:42.210 --> 00:07:44.880
and you'll have even more
from mutation and crossover.
00:07:44.880 --> 00:07:46.780
And so that's going to lead you
00:07:46.780 --> 00:07:51.690
to more than 70 trillion combinations
00:07:51.690 --> 00:07:53.953
just from these two parents.
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