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Summarizing stories

https://www.youtube.com/watch?v=SmnR4AZ-XM8

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https://www.youtube.com/api/timedtext?v=SmnR4AZ-XM8&ei=bViUZa-LH_bDp-oPpoG28A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=51375CEA4DC235788FF81A797C3C1C2D91614D80.403D3E694060E2301E6FEA44A846639E075EA51D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.750 --> 00:00:01.720 - [David] Hello, readers. 00:00:01.720 --> 00:00:05.090 Today, I'll make a video about summaries. 00:00:05.090 --> 00:00:07.920 A summary retells the main ideas of a passage, 00:00:07.920 --> 00:00:10.173 but in a much shorter version. 00:00:11.360 --> 00:00:14.763 Cool, great, done, you can learn anything. David out. 00:00:15.871 --> 00:00:17.140 (David snort-laughs. It is charming and not gross.) 00:00:17.140 --> 00:00:19.030 Sorry, I made a goof, see, 00:00:19.030 --> 00:00:21.660 I summarized what was gonna happen in this video, 00:00:21.660 --> 00:00:23.860 right, I took the information I was gonna tell you, 00:00:23.860 --> 00:00:25.140 and I shortened it. 00:00:25.140 --> 00:00:27.230 This is what the skill of summarizing is. 00:00:27.230 --> 00:00:30.650 I just applied it to this video instead of to a story. 00:00:30.650 --> 00:00:32.810 When you summarize, you have to ask yourself, 00:00:32.810 --> 00:00:35.700 what are the most important facts? 00:00:35.700 --> 00:00:37.220 What are the most important details? 00:00:37.220 --> 00:00:40.910 You're a reporter, a stringer, a journal, 00:00:40.910 --> 00:00:44.570 your job is to get in, get the facts and get out. 00:00:44.570 --> 00:00:47.560 It's the news in brief, just the facts, man. 00:00:47.560 --> 00:00:49.620 Take The Three Little Pigs, for instance. 00:00:49.620 --> 00:00:51.491 I'll summarize it now. 00:00:51.491 --> 00:00:52.600 (clearing throat) 00:00:52.600 --> 00:00:54.960 Three little pigs live in houses that they built. 00:00:54.960 --> 00:00:57.980 One used straw, one used wood, and the third pig, 00:00:57.980 --> 00:01:00.800 who worked hardest of all, built a brick house. 00:01:00.800 --> 00:01:02.770 Along comes a big, bad wolf, 00:01:02.770 --> 00:01:04.980 pictured here with a big, bad top hat, 00:01:04.980 --> 00:01:08.220 and a big, bad house wrecking hammer, I don't know, 00:01:08.220 --> 00:01:10.940 and he successfully knocks down the first two houses 00:01:10.940 --> 00:01:13.100 in order to eat the pigs inside, 00:01:13.100 --> 00:01:14.870 but they escaped to the brick house, 00:01:14.870 --> 00:01:17.560 which the wolf is unable to knock down. 00:01:17.560 --> 00:01:19.060 That's the important parts of the story, 00:01:19.060 --> 00:01:21.430 and I bet I can even cut that down a little bit. 00:01:21.430 --> 00:01:22.770 But here's what's there. 00:01:22.770 --> 00:01:24.310 All the important characters, 00:01:24.310 --> 00:01:25.820 all their major decisions, 00:01:25.820 --> 00:01:27.820 and the outcome of the story. 00:01:27.820 --> 00:01:30.830 We have the beginning, the middle and the end. 00:01:30.830 --> 00:01:34.410 Now let me show you what too little information looks like. 00:01:34.410 --> 00:01:35.650 There were three pigs. 00:01:35.650 --> 00:01:36.750 They build houses. 00:01:36.750 --> 00:01:38.970 A big, bad wolf tried to get them. 00:01:38.970 --> 00:01:39.930 Not enough. 00:01:39.930 --> 00:01:40.980 That's not enough information, 00:01:40.980 --> 00:01:43.530 it doesn't tell us whether or not the wolf succeeded 00:01:43.530 --> 00:01:46.680 or the important differences between the three pig houses. 00:01:46.680 --> 00:01:49.010 Not enough as far as facts go. 00:01:49.010 --> 00:01:51.410 You know, it's gotta be specific, 00:01:51.410 --> 00:01:52.243 and look, it's possible to live 00:01:52.243 --> 00:01:53.920 on the opposite direction too. 00:01:53.920 --> 00:01:56.260 Too many irrelevant facts. 00:01:56.260 --> 00:01:57.380 So there were three pigs. 00:01:57.380 --> 00:01:59.520 One's name is Horace, another's name was Pansy, 00:01:59.520 --> 00:02:01.240 and the third's name was Flustopher, 00:02:01.240 --> 00:02:03.250 they had all been friends since middle school, 00:02:03.250 --> 00:02:04.880 and when the market was in a good place, 00:02:04.880 --> 00:02:06.470 all three of them decided to go in 00:02:06.470 --> 00:02:09.500 for plots of land right next to each other. 00:02:09.500 --> 00:02:12.010 Ah, right, but that's too much. 00:02:12.010 --> 00:02:14.520 In a summary, I don't need the whole story. 00:02:14.520 --> 00:02:17.270 If it were the whole story, it wouldn't be a summary. 00:02:17.270 --> 00:02:19.520 It'll just be the whole story all over again. 00:02:20.430 --> 00:02:21.520 Keep it simple. 00:02:21.520 --> 00:02:23.010 We need the events of the story 00:02:23.010 --> 00:02:24.770 in the order they happened in. 00:02:24.770 --> 00:02:27.700 We need the characters and we need the problems they face, 00:02:27.700 --> 00:02:30.640 and for a summary, that's kind of it. 00:02:30.640 --> 00:02:33.440 You can learn anything; David out, 00:02:33.440 --> 00:02:35.123 for real this time. Bye.

Finding connections between ideas within a passage

https://www.youtube.com/watch?v=Ox_JaA6nX_Q

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https://www.youtube.com/api/timedtext?v=Ox_JaA6nX_Q&ei=bViUZavwFL-khcIP-siQyAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C5B46C2F2CD2E322A34A2481158B584605F30C42.B12DB6286EC9B0A3B8AF242BA1269BF2B169622F&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.850 --> 00:00:01.790 - [David] Hello, Readers! 00:00:01.790 --> 00:00:04.890 Today we are going to talk about making connections. 00:00:04.890 --> 00:00:09.280 So I don't mean to brag, but I have at least one friend. 00:00:09.280 --> 00:00:10.113 (I'm kind of a big deal.) 00:00:10.113 --> 00:00:13.240 I have friends at work, friends from the school I attended, 00:00:13.240 --> 00:00:15.690 friends in my apartment building and my neighborhood, 00:00:15.690 --> 00:00:17.880 friends from places I used to live. 00:00:17.880 --> 00:00:19.960 Each friend is connected to me in some way. 00:00:19.960 --> 00:00:22.540 May be we met in an elevator or on the train, 00:00:22.540 --> 00:00:24.050 or at the community garden. 00:00:24.050 --> 00:00:26.170 In some cases, I introduced my friends 00:00:26.170 --> 00:00:27.600 and now they're friends with each other 00:00:27.600 --> 00:00:29.830 and even hang out without me. 00:00:29.830 --> 00:00:31.430 Each friend is connected to me 00:00:31.430 --> 00:00:33.350 or to each other in a different way 00:00:33.350 --> 00:00:34.690 and for a different reason. 00:00:34.690 --> 00:00:37.640 And just in a way the people can be friends with each other 00:00:37.640 --> 00:00:40.100 ideas can be friends with each other too. 00:00:40.100 --> 00:00:42.283 Understanding how ideas that tends to connect 00:00:42.283 --> 00:00:45.000 with each other and the topic of text 00:00:45.000 --> 00:00:47.530 will help me understand what I'm reading. 00:00:47.530 --> 00:00:51.070 Good readers make connections between ideas in the text. 00:00:51.070 --> 00:00:53.560 When I look at a passage, I ask myself 00:00:53.560 --> 00:00:56.560 what do all these sentences have in common. 00:00:56.560 --> 00:00:58.010 How are they connected? 00:00:58.010 --> 00:01:01.183 Let's explain with a brief passage about building ships. 00:01:02.070 --> 00:01:05.040 Long ago, shipbuilders used iron nails 00:01:05.040 --> 00:01:07.810 and bolts because iron was easy to find. 00:01:07.810 --> 00:01:09.620 They soon learned the disadvantages 00:01:09.620 --> 00:01:11.570 of using this metal on a boat! 00:01:11.570 --> 00:01:13.710 Iron quickly rusts and decays, 00:01:13.710 --> 00:01:16.110 especially near the salty ocean. 00:01:16.110 --> 00:01:19.190 They switched to using brass, which lasts longer. 00:01:19.190 --> 00:01:22.430 I wanna use this paragraph to describe three common ways 00:01:22.430 --> 00:01:24.550 authors show connections. 00:01:24.550 --> 00:01:27.690 Comparison, cause-and-effect and sequence. 00:01:27.690 --> 00:01:31.930 Comparison; what's the same or different between two ideas? 00:01:31.930 --> 00:01:35.450 So what's similar between brass and iron is one example. 00:01:35.450 --> 00:01:37.750 We can say okay, both of these are metals 00:01:37.750 --> 00:01:40.320 and both were used in shipbuilding. 00:01:40.320 --> 00:01:42.470 Now what's different between them? 00:01:42.470 --> 00:01:45.040 Well, iron rusts quickly in the ocean 00:01:45.040 --> 00:01:47.890 and it does so faster than brass. 00:01:47.890 --> 00:01:49.523 Brass lasts longer. 00:01:50.750 --> 00:01:52.790 Now let's talk about cause and effect. 00:01:52.790 --> 00:01:57.000 How does one event or idea cause another event or idea. 00:01:57.000 --> 00:01:59.375 Well what happens when you put a ship 00:01:59.375 --> 00:02:01.980 with iron bolts into salt water? It rusts and decays. 00:02:01.980 --> 00:02:05.190 The ocean causes the iron to corrode and rust. 00:02:05.190 --> 00:02:07.160 So what did shipbuilders do as a result, 00:02:07.160 --> 00:02:09.230 they switch to using brass. 00:02:09.230 --> 00:02:10.740 And finally sequence. 00:02:10.740 --> 00:02:12.660 What order did things happen in? 00:02:12.660 --> 00:02:15.170 Now the paragraph begins with long ago 00:02:15.170 --> 00:02:18.490 and talks about iron before it talks about brass. 00:02:18.490 --> 00:02:21.280 It then describes how shipbuilders switched to brass. 00:02:21.280 --> 00:02:24.110 So iron came first in the sequence. 00:02:24.110 --> 00:02:26.100 So when I read this passage on shipbuilding 00:02:26.100 --> 00:02:27.540 even though it is very short, 00:02:27.540 --> 00:02:30.620 I'm able to make a lot of connections between ideas. 00:02:30.620 --> 00:02:33.328 Doing this deepened my understanding 00:02:33.328 --> 00:02:35.450 and helps me to become a better reader. 00:02:35.450 --> 00:02:38.200 Now not every sentence or idea is connected 00:02:38.200 --> 00:02:41.060 to every other sentence or idea. 00:02:41.060 --> 00:02:43.470 Just like not every single one of my friends is friends 00:02:43.470 --> 00:02:45.080 with all of my other friends. 00:02:45.080 --> 00:02:46.760 And that's okay too. 00:02:46.760 --> 00:02:49.050 Our goal is to think about how those sentences connect 00:02:49.050 --> 00:02:50.820 to the topic overall. 00:02:50.820 --> 00:02:53.440 Think about the big picture. 00:02:53.440 --> 00:02:55.440 Understanding the connections between sentences 00:02:55.440 --> 00:02:57.290 is one of many ways you can strengthen 00:02:57.290 --> 00:02:59.590 your skills as a reader. 00:02:59.590 --> 00:03:01.100 You can learn anything. 00:03:01.100 --> 00:03:01.933 Dave it out!

Making inferences in literary texts

https://www.youtube.com/watch?v=INFWXZ_tl4M

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https://www.youtube.com/api/timedtext?v=INFWXZ_tl4M&ei=bViUZbGlILD9mLAPtoSp0AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6AD2D546AD4ECD27032CA715CF76579D0CFE22AB.2A6E9A640EE9845B8E412DF9007EC00F764CC88B&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.530 --> 00:00:01.470 - [David] Hello, readers. 00:00:01.470 --> 00:00:04.330 I'm here in the legendary study of the famous 00:00:04.330 --> 00:00:06.740 fictional dogtective Sherlock Bones 00:00:06.740 --> 00:00:09.100 of 221 B Barker Street. 00:00:09.100 --> 00:00:11.140 Mr. Bones, you're here to teach me about 00:00:11.140 --> 00:00:13.950 using details from a text to make inferences, aren't you? 00:00:13.950 --> 00:00:15.140 - [Sherlock Bones] Yes, my boy! 00:00:15.140 --> 00:00:16.770 It's simplicity itself. 00:00:16.770 --> 00:00:20.220 But first, let me deduce a few things about you, shall I? 00:00:20.220 --> 00:00:21.880 - [David] Well, Mr. Bones, we're trying to do this 00:00:21.880 --> 00:00:24.180 about writing, not about people, so... 00:00:24.180 --> 00:00:25.013 - [Bones] Give me your hand. 00:00:25.013 --> 00:00:25.846 - [David] Waugh! 00:00:25.846 --> 00:00:27.670 - [Bones] Ah, you like to cook, 00:00:27.670 --> 00:00:29.060 you have a nervous disposition 00:00:29.060 --> 00:00:30.480 and you work for Khan Academy. 00:00:30.480 --> 00:00:32.537 - [David] Now how did you know that? 00:00:32.537 --> 00:00:34.240 - [Bones] You have a callus on your finger 00:00:34.240 --> 00:00:35.830 from how you hold a knife, 00:00:35.830 --> 00:00:38.300 your fingernails are bitten, not clipped 00:00:38.300 --> 00:00:40.720 and your messenger bag says Khan Academy. 00:00:40.720 --> 00:00:42.320 - [David] Well and I told you who I was 00:00:42.320 --> 00:00:43.450 before I showed up. 00:00:43.450 --> 00:00:44.283 - [Bones] That too. 00:00:44.283 --> 00:00:45.270 - [David] But what does this have to do with 00:00:45.270 --> 00:00:46.150 reading a book? 00:00:46.150 --> 00:00:47.950 - [Bones] I correctly deduced several truths 00:00:47.950 --> 00:00:50.790 about your person based on clues, my good David. 00:00:50.790 --> 00:00:54.590 Indeed, all inference is making sense of clues. 00:00:54.590 --> 00:00:58.320 When you read a story, you are constantly making inferences. 00:00:58.320 --> 00:00:59.300 - [David] I see. 00:00:59.300 --> 00:01:01.540 Okay, I'll read a passage and then see 00:01:01.540 --> 00:01:03.150 what I can make of it. 00:01:03.150 --> 00:01:06.460 An hour later, thick smoke poured up the stairs. 00:01:06.460 --> 00:01:08.120 The smoke detector screamed 00:01:08.120 --> 00:01:10.320 and I could hear Uncle Paleo stumbling around 00:01:10.320 --> 00:01:11.850 with the fire extinguisher. 00:01:11.850 --> 00:01:14.150 When he came upstairs afterward, his footsteps 00:01:14.150 --> 00:01:15.970 sounded slow and heavy. 00:01:15.970 --> 00:01:19.760 He was a wreck, broken glasses, black smudges on his face 00:01:19.760 --> 00:01:21.580 and singed hair. 00:01:21.580 --> 00:01:23.941 Okay, so I can surmise that there was some kind of 00:01:23.941 --> 00:01:26.860 fire or explosion downstairs, 00:01:26.860 --> 00:01:29.400 where the character Uncle Paleo was. 00:01:29.400 --> 00:01:30.690 - [Bones] Hm, how do you know? 00:01:30.690 --> 00:01:31.970 - [David] Well his hair was singed, 00:01:31.970 --> 00:01:33.940 that's another word for burned and his face 00:01:33.940 --> 00:01:36.420 was covered in black smudges like you get 00:01:36.420 --> 00:01:39.500 from soot from a fire and there was all the smoke 00:01:39.500 --> 00:01:41.171 and the smoke detector went off. 00:01:41.171 --> 00:01:43.110 - [Bones] And there is also the matter 00:01:43.110 --> 00:01:44.500 of the fire extinguisher. 00:01:44.500 --> 00:01:45.810 - [David] Also that. 00:01:45.810 --> 00:01:47.807 - [Bones] I see something else in that passage too. 00:01:47.807 --> 00:01:49.510 - [David] What's that, Mr. Bones? 00:01:49.510 --> 00:01:51.480 - [Bones] Uncle Paleo was exhausted 00:01:51.480 --> 00:01:52.830 by putting out the fire. 00:01:52.830 --> 00:01:53.663 - [David] How can you tell? 00:01:53.663 --> 00:01:54.920 Where does it say that? 00:01:54.920 --> 00:01:56.420 - [Bones] Well, it doesn't. 00:01:56.420 --> 00:01:58.400 That's inference, my lad. 00:01:58.400 --> 00:02:02.750 Note here how it said his footsteps sounded slow and heavy. 00:02:02.750 --> 00:02:03.730 Why might that be? 00:02:03.730 --> 00:02:05.850 - [David] He stepped in something sticky. 00:02:05.850 --> 00:02:08.300 No, oo, he's wearing shoes made of lead. 00:02:08.300 --> 00:02:11.280 - [Bones] Well, those are indeed possible explanations 00:02:11.280 --> 00:02:14.010 but you want to think of the most likely option. 00:02:14.010 --> 00:02:16.680 - [David] He was running around to put the fire out 00:02:16.680 --> 00:02:18.040 and it made him tired. 00:02:18.040 --> 00:02:19.260 - [Bones] So, you were reading 00:02:19.260 --> 00:02:20.830 between the lines, were you? 00:02:20.830 --> 00:02:23.040 Drawing conclusions from the text? 00:02:23.040 --> 00:02:23.873 - [David] I was. 00:02:23.873 --> 00:02:25.950 So we know for sure Uncle Paleo was tired, right? 00:02:25.950 --> 00:02:27.510 - [Bones] WE DO NOT, SIR. 00:02:27.510 --> 00:02:28.343 - [David] Oh!! 00:02:28.343 --> 00:02:31.420 - [Bones] An inference is only one possible conclusion 00:02:31.420 --> 00:02:33.930 but is not the only conclusion. 00:02:33.930 --> 00:02:35.740 - [David] So what are we to do? 00:02:35.740 --> 00:02:37.330 - [Bones] The more clues you discover, 00:02:37.330 --> 00:02:40.210 the stronger your inferences will become. 00:02:40.210 --> 00:02:42.140 You have to look at what you already know 00:02:42.140 --> 00:02:45.240 about a character, about the setting of the story, 00:02:45.240 --> 00:02:47.910 the events of a story's plot and piece it 00:02:47.910 --> 00:02:49.477 together from there. 00:02:49.477 --> 00:02:53.720 You know that fires create lots of black dust or soot 00:02:53.720 --> 00:02:57.400 so it strengthens your argument in favor of a fire. 00:02:57.400 --> 00:02:59.790 And it's background knowledge like that, 00:02:59.790 --> 00:03:02.260 about the way the world works that will serve you 00:03:02.260 --> 00:03:05.540 as a reader and as a maker of inferences. 00:03:05.540 --> 00:03:07.820 Apply what you know to the world of the story 00:03:07.820 --> 00:03:10.050 and make inferences based on that. 00:03:10.050 --> 00:03:11.660 - [David] And then, I can become the world's 00:03:11.660 --> 00:03:13.080 greatest consulting detective? 00:03:13.080 --> 00:03:15.410 - [Bones] You can become like the world's 50th 00:03:15.410 --> 00:03:17.330 greatest consulting detective, 00:03:17.330 --> 00:03:19.290 top of the heap's rather full, I'm afraid. 00:03:19.290 --> 00:03:22.260 - [David] Well, thank you for your time today, Mr. Bones. 00:03:22.260 --> 00:03:23.780 Best of luck with your case work. 00:03:23.780 --> 00:03:25.444 - [Bones] Thank you; I shan't need it. 00:03:25.444 --> 00:03:26.340 (barks) 00:03:26.340 --> 00:03:28.690 - [David] You can learn anything. David out.

Using context clues to figure out new words

https://www.youtube.com/watch?v=CiNggzdWkIo

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https://www.youtube.com/api/timedtext?v=CiNggzdWkIo&ei=bViUZce-FJqEmLAPsIeE0AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=15BA014DF38DC1468446E2972BF70278A6F584B8.583780F7079118B8C03BFF87DE9F64E2F18AD2FF&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.310 --> 00:00:01.600 - [Instructor] Hello readers. 00:00:01.600 --> 00:00:03.770 You know that feeling when you're reading 00:00:03.770 --> 00:00:05.790 and you see a word you've never seen before 00:00:05.790 --> 00:00:06.623 and you don't really know how 00:00:06.623 --> 00:00:07.840 to figure out what it means? 00:00:07.840 --> 00:00:09.980 Well, that's what we're talking about today: 00:00:09.980 --> 00:00:13.820 strategies for figuring out new words through context. 00:00:13.820 --> 00:00:16.240 You're always going to be encountering new words. 00:00:16.240 --> 00:00:18.350 At the time of this recording, I'm 31 00:00:18.350 --> 00:00:21.800 and I run into new and confusing words every day. 00:00:21.800 --> 00:00:24.020 I read a lot and it's always a fun challenge 00:00:24.020 --> 00:00:25.520 to run into words like, I don't know, 00:00:25.520 --> 00:00:29.250 glabrous or limned or nacreous. 00:00:29.250 --> 00:00:30.470 I know a lot about language 00:00:30.470 --> 00:00:32.540 and even I have trouble figuring out 00:00:32.540 --> 00:00:34.400 what those words mean on their own. 00:00:34.400 --> 00:00:37.130 So it's important to rely on context, 00:00:37.130 --> 00:00:40.320 the language that surrounds the word. 00:00:40.320 --> 00:00:41.480 Let's say you're reading a text 00:00:41.480 --> 00:00:42.750 and you come across a sentence 00:00:42.750 --> 00:00:45.390 that has a word in it you don't recognize. 00:00:45.390 --> 00:00:46.670 Here's a bit from a passage 00:00:46.670 --> 00:00:49.883 about the famous chimpanzee researcher Jane Goodall. 00:00:50.857 --> 00:00:52.947 "Jane Goodall arrived at Tanzania's 00:00:52.947 --> 00:00:56.137 "Gombee Stream National Park in 1960. 00:00:56.137 --> 00:00:58.317 "She was considered somewhat unconventional 00:00:58.317 --> 00:01:00.227 "among other animal researchers. 00:01:00.227 --> 00:01:03.630 "After all, she had not yet been to college." 00:01:03.630 --> 00:01:05.630 So let's pause on unconventional. 00:01:05.630 --> 00:01:07.350 What does that word mean? 00:01:07.350 --> 00:01:10.320 Well, let me give you some ideas, 00:01:10.320 --> 00:01:12.340 that's the memory aid I use to keep it straight. 00:01:12.340 --> 00:01:16.400 IDEAS, it stands for inference, definition, 00:01:16.400 --> 00:01:21.400 example, antonym, synonym, I-D-E-A-S, IDEAS, 00:01:21.900 --> 00:01:24.980 which are all different kinds of context clues. 00:01:24.980 --> 00:01:27.120 Every word will have a different context, 00:01:27.120 --> 00:01:29.553 so you might need to vary your approach. 00:01:31.000 --> 00:01:34.130 The way this snippet is written let's try inference first, 00:01:34.130 --> 00:01:35.970 then I'll rewrite the sentence a few times 00:01:35.970 --> 00:01:37.670 to show you the other methods. 00:01:37.670 --> 00:01:40.330 Okay, the I in IDEAS, inference. 00:01:40.330 --> 00:01:43.220 We can draw conclusions from the context. 00:01:43.220 --> 00:01:45.220 If we don't know what unconventional means, 00:01:45.220 --> 00:01:47.080 we can take a look at the rest of the sentence 00:01:47.080 --> 00:01:49.670 or other nearby sentences to figure it out. 00:01:49.670 --> 00:01:51.930 Being unconventional seems to make Goodall 00:01:51.930 --> 00:01:53.930 different from other researchers. 00:01:53.930 --> 00:01:55.630 She hadn't yet been to college 00:01:55.630 --> 00:01:58.400 which implies that the rest of them had. 00:01:58.400 --> 00:01:59.750 That doesn't give us a full answer 00:01:59.750 --> 00:02:02.560 but it does tell us that she's different somehow. 00:02:02.560 --> 00:02:05.400 So I think unconventional might mean 00:02:05.400 --> 00:02:06.960 different than what is normal. 00:02:06.960 --> 00:02:08.260 And because I'm making an inference 00:02:08.260 --> 00:02:10.750 about this word's meaning I wanna keep an eye out for it 00:02:10.750 --> 00:02:12.810 in other places to see if I can confirm 00:02:12.810 --> 00:02:15.890 or revise that working definition later. 00:02:15.890 --> 00:02:17.890 D - definition. 00:02:17.890 --> 00:02:20.130 Context clues like these will just give you 00:02:20.130 --> 00:02:22.070 the definition of the word in question. 00:02:22.070 --> 00:02:23.947 So a good example of that would be: 00:02:23.947 --> 00:02:26.157 "She was considered somewhat unconventional 00:02:26.157 --> 00:02:28.047 "among other animal researchers. 00:02:28.047 --> 00:02:29.507 "She hadn't been to college yet, 00:02:29.507 --> 00:02:32.720 "and this made her different and unexpected." 00:02:32.720 --> 00:02:35.390 Different and unexpected is a great definition 00:02:35.390 --> 00:02:37.540 for the word unconventional. 00:02:37.540 --> 00:02:39.390 This style of context clue occurs 00:02:39.390 --> 00:02:41.360 when the author expects a word to be unfamiliar 00:02:41.360 --> 00:02:43.670 to you and builds in a guide for you 00:02:43.670 --> 00:02:45.490 right there in the text. 00:02:45.490 --> 00:02:47.900 The E in IDEAS stands for example, 00:02:47.900 --> 00:02:51.020 and this is somewhere between inference and definition. 00:02:51.020 --> 00:02:54.040 If the author describes Goodall as unconventional, 00:02:54.040 --> 00:02:56.190 they'll go on to talk about something unconventional 00:02:56.190 --> 00:02:57.827 that Goodall did. 00:02:57.827 --> 00:02:59.827 "She was considered somewhat unconventional 00:02:59.827 --> 00:03:01.117 "among animal researchers. 00:03:01.117 --> 00:03:03.760 "For one thing, she hadn't been to college yet." 00:03:03.760 --> 00:03:06.060 So this is very similar to that initial sentence, 00:03:06.060 --> 00:03:08.620 except for the transition phrase for one thing, 00:03:08.620 --> 00:03:10.930 which is a way to set up examples. 00:03:10.930 --> 00:03:13.930 Antonym - an antonym is a word whose meaning is 00:03:13.930 --> 00:03:17.150 the opposite of another word, like how night is 00:03:17.150 --> 00:03:21.430 the opposite of day, or how love is the opposite of hate. 00:03:21.430 --> 00:03:23.250 So if there's an example in the text 00:03:23.250 --> 00:03:25.330 of what Jane Goodall was not, 00:03:25.330 --> 00:03:28.410 we can use that to figure out what she was. 00:03:28.410 --> 00:03:29.777 So let's say the passage said: 00:03:29.777 --> 00:03:31.537 "Goodall was unconventional. 00:03:31.537 --> 00:03:34.710 "She didn't conform, and she wasn't ordinary." 00:03:34.710 --> 00:03:38.610 There we have two antonyms and our answer. 00:03:38.610 --> 00:03:41.730 Similarly, synonym just means write another word 00:03:41.730 --> 00:03:44.577 with the same meaning similar to a definition. 00:03:44.577 --> 00:03:46.637 "Jane Goodall was unconventional. 00:03:46.637 --> 00:03:47.967 "She was a nonconformist. 00:03:47.967 --> 00:03:49.590 "She went against the grain." 00:03:49.590 --> 00:03:52.340 You can see that I had to rewrite the sentences each time 00:03:52.340 --> 00:03:54.610 to apply to each context clue strategy, 00:03:54.610 --> 00:03:56.570 which shows me that you won't find 00:03:56.570 --> 00:03:59.100 all five context clues every time you need 00:03:59.100 --> 00:04:00.900 to search for a word's meaning. 00:04:00.900 --> 00:04:02.070 You need to find the approach 00:04:02.070 --> 00:04:04.360 that makes the most sense in context. 00:04:04.360 --> 00:04:05.900 See what I did there, ah huh? 00:04:06.750 --> 00:04:08.550 And failing that, you can always look up 00:04:08.550 --> 00:04:10.270 an unfamiliar word in a dictionary. 00:04:10.270 --> 00:04:11.260 I love to do that. 00:04:11.260 --> 00:04:14.250 I think that's great, but I also feel a sense of victory 00:04:14.250 --> 00:04:16.820 when I correctly figure out what a new word means, 00:04:16.820 --> 00:04:18.540 when I've put it together from context. 00:04:18.540 --> 00:04:20.720 And maybe if I'm still curious, I look it up later 00:04:20.720 --> 00:04:22.040 and then I turn out to be right, 00:04:22.040 --> 00:04:25.200 and I'm all like "Victory at sea, I did it!" 00:04:25.200 --> 00:04:26.900 Oh, and if you were curious, 00:04:26.900 --> 00:04:29.720 glabrous means smooth and hairless 00:04:29.720 --> 00:04:31.810 like a leaf or the skin of a frog. 00:04:31.810 --> 00:04:34.950 Nacreous means shiny and rainbow colored 00:04:34.950 --> 00:04:37.310 like the inside of an oyster shell. 00:04:37.310 --> 00:04:41.080 And to limn something means to draw the outline of 00:04:41.080 --> 00:04:43.293 or to be highlighted in light. 00:04:44.300 --> 00:04:46.483 You can learn anything, David out.

Making inferences in informational texts

https://www.youtube.com/watch?v=gUW2jit3uvo

vtt

https://www.youtube.com/api/timedtext?v=gUW2jit3uvo&ei=bViUZZXzHqCyvdIP4LKHGA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=778EB1A4BB0A699D016790DB93BCC49C50E83618.B1C0D38F64AC7AA3C62B8B19743EE06F8B608527&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:01.000 --> 00:00:03.200 - [David] From the moment she strolled into my office, 00:00:03.200 --> 00:00:04.300 I could tell she was gonna be 00:00:04.300 --> 00:00:06.510 a difficult sentence to read. 00:00:06.510 --> 00:00:07.880 You could tell from the way she walked 00:00:07.880 --> 00:00:09.840 she was carrying a lot of information, 00:00:09.840 --> 00:00:12.320 but getting it out of her wouldn't be easy. 00:00:12.320 --> 00:00:15.113 I was gonna need to make an inference. 00:00:16.590 --> 00:00:17.510 Hey, what's up readers? 00:00:17.510 --> 00:00:18.343 David here. 00:00:18.343 --> 00:00:20.630 I'm taking advantage of the cold that I have 00:00:20.630 --> 00:00:23.030 by doing my serious detective voice 00:00:23.030 --> 00:00:25.781 in order to teach you about inferences. 00:00:25.781 --> 00:00:26.700 (phone ringing) 00:00:26.700 --> 00:00:28.390 Hold on, let me get that. 00:00:28.390 --> 00:00:29.880 Hi, this is David. 00:00:29.880 --> 00:00:31.210 I'm in the middle of doing a video. 00:00:31.210 --> 00:00:32.540 Now isn't a great time. 00:00:32.540 --> 00:00:34.480 - [Man On Phone] Hello, I have information about 00:00:34.480 --> 00:00:35.460 what an inference is. 00:00:35.460 --> 00:00:36.973 - [David] Oh, oh that's great. 00:00:38.240 --> 00:00:40.270 Cool, follow me over to the next screen. 00:00:40.270 --> 00:00:42.566 What is an inference, please? 00:00:42.566 --> 00:00:44.912 - [Man On Phone] An inference is a conclusion that you make 00:00:44.912 --> 00:00:47.851 based on clues given in a piece of writing. 00:00:47.851 --> 00:00:48.887 It's more than a guess, 00:00:48.887 --> 00:00:50.827 but it's not just an observation either. 00:00:50.827 --> 00:00:52.747 - [David] Great, thank you. 00:00:52.747 --> 00:00:53.938 Was that all you needed? 00:00:53.938 --> 00:00:55.150 - [Man On Phone] Yeah, that was my only thing. 00:00:55.150 --> 00:00:56.787 - [David] All right, thanks, bye. 00:00:56.787 --> 00:00:58.130 - [Man On Phone] Goodbye. 00:00:58.130 --> 00:00:59.930 - [David] So an inference is a conclusion 00:00:59.930 --> 00:01:01.160 that you draw from writing. 00:01:01.160 --> 00:01:03.740 It's an idea that you pull from a sentence 00:01:03.740 --> 00:01:06.190 or a passage that isn't literally printed there. 00:01:06.190 --> 00:01:08.310 It's the detective work of reading, 00:01:08.310 --> 00:01:10.370 finding clues that help you make sense 00:01:10.370 --> 00:01:12.330 of what's being said. 00:01:12.330 --> 00:01:13.360 I feel like we're kind of getting 00:01:13.360 --> 00:01:15.810 bogged down in theory land so let's take a look 00:01:15.810 --> 00:01:16.840 at an example. 00:01:16.840 --> 00:01:19.763 I went outside and made an enormous snow fort. 00:01:20.670 --> 00:01:21.910 There's my snow fort. 00:01:21.910 --> 00:01:25.080 It's a D on the flag to represent me. 00:01:25.080 --> 00:01:26.640 There's me little hot cocoa, 00:01:26.640 --> 00:01:28.650 couple marshmallows floating in there, 00:01:28.650 --> 00:01:30.400 my Khan Academy mug. 00:01:30.400 --> 00:01:31.830 They don't make Khan Academy mugs. 00:01:31.830 --> 00:01:33.680 I want a Khan Academy mug. 00:01:33.680 --> 00:01:35.870 Okay, so what conclusions can we draw 00:01:35.870 --> 00:01:37.460 from these two sentences? 00:01:37.460 --> 00:01:39.860 I went outside and made an enormous snow fort. 00:01:39.860 --> 00:01:41.640 Beautiful, brilliant, enormous. 00:01:41.640 --> 00:01:45.090 Then I came inside and had a big mug of hot chocolate. 00:01:45.090 --> 00:01:47.220 Same deal, brilliant, beautiful, enormous. 00:01:47.220 --> 00:01:50.120 What conclusions can I draw about this situation? 00:01:50.120 --> 00:01:51.640 Well if you're making things out of snow 00:01:51.640 --> 00:01:53.730 and then you're coming inside and having hot chocolate, 00:01:53.730 --> 00:01:56.040 it's probably not the height of summer. 00:01:56.040 --> 00:01:58.190 One inference that I can draw 00:01:58.190 --> 00:01:59.720 from these two sentences together 00:01:59.720 --> 00:02:04.000 is that it is winter time when this sentence takes place. 00:02:04.000 --> 00:02:05.600 Where I live, these are not activities 00:02:05.600 --> 00:02:09.330 that one pursues in the height of summer outside. 00:02:09.330 --> 00:02:12.430 I'm looking for clues within the text. 00:02:12.430 --> 00:02:15.640 Snow fort, I'm outside, I came inside 00:02:15.640 --> 00:02:17.410 and then I had hot chocolate 00:02:17.410 --> 00:02:19.390 which is not traditionally a beverage 00:02:19.390 --> 00:02:21.900 that is consumed when it's warm out. 00:02:21.900 --> 00:02:23.780 Let's take a look at another example. 00:02:23.780 --> 00:02:26.420 This paragraph is part of a longer passage 00:02:26.420 --> 00:02:29.360 that is about a young ballet dancer named Michaela. 00:02:29.360 --> 00:02:31.190 Michaela danced so wonderfully 00:02:31.190 --> 00:02:32.790 that she was awarded a scholarship 00:02:32.790 --> 00:02:35.380 to attend the Jacqueline Kennedy Onassis School 00:02:35.380 --> 00:02:37.450 at the American Ballet Theater. 00:02:37.450 --> 00:02:40.460 That was only the beginning of her dancing success. 00:02:40.460 --> 00:02:42.700 When she was 17, Michaela danced with 00:02:42.700 --> 00:02:45.360 the Dance Theater of Harlem professional company. 00:02:45.360 --> 00:02:48.280 Later, she joined the Dutch National Junior Company. 00:02:48.280 --> 00:02:52.440 Today, Michaela is a soloist with the Dutch National Ballet. 00:02:52.440 --> 00:02:53.840 So very quickly without getting 00:02:53.840 --> 00:02:55.800 bogged down in this passage, 00:02:55.800 --> 00:02:58.320 what are some conclusions, what are some inferences 00:02:58.320 --> 00:03:00.790 that we can draw about Michaela? 00:03:00.790 --> 00:03:02.440 Who is Michaela? 00:03:02.440 --> 00:03:03.290 What do we know about her? 00:03:03.290 --> 00:03:05.110 We know that she's a dancer. 00:03:05.110 --> 00:03:07.160 We know that she's very good at it, right? 00:03:07.160 --> 00:03:10.370 She danced so wonderfully that she got a scholarship. 00:03:10.370 --> 00:03:13.070 So I'm gonna say Michaela is very talented 00:03:13.070 --> 00:03:15.240 and we know that her talent led to success 00:03:15.240 --> 00:03:16.730 because her getting the scholarship 00:03:16.730 --> 00:03:20.200 was only the beginning of her dancing success. 00:03:20.200 --> 00:03:22.140 We can see from the passage that she was part of 00:03:22.140 --> 00:03:24.130 at least three different dance companies, 00:03:24.130 --> 00:03:25.920 the Dance Theater of Harlem, 00:03:25.920 --> 00:03:27.610 the Dutch National Junior Company, 00:03:27.610 --> 00:03:30.430 and as a soloist with the Dutch National Ballet today. 00:03:30.430 --> 00:03:34.050 So I'm gonna say that Michaela is a very hard worker. 00:03:34.050 --> 00:03:37.212 Now notice no where in the passage does it say 00:03:37.212 --> 00:03:40.730 Michaela is a very talented, hard working dancer. 00:03:40.730 --> 00:03:42.430 Just like in the previous example, 00:03:42.430 --> 00:03:44.720 it didn't say, it was winter outside 00:03:44.720 --> 00:03:46.710 so I made a snow fort. 00:03:46.710 --> 00:03:48.810 What the skill of inference is 00:03:48.810 --> 00:03:50.820 requires you to be a detective 00:03:50.820 --> 00:03:54.018 and take your magnifying glass to the passage 00:03:54.018 --> 00:03:55.600 to discover clues. 00:03:55.600 --> 00:03:57.650 Imagine you're a detective like this dog. 00:03:58.510 --> 00:04:00.480 He's wearing a little deer stalker cap. 00:04:00.480 --> 00:04:03.870 Let's call him, let's call him Sherlock Bones, 00:04:03.870 --> 00:04:06.920 the famous dog detective that I just made up. 00:04:06.920 --> 00:04:09.010 I feel like Sherlock Holmes is always smoking a pipe 00:04:09.010 --> 00:04:11.040 so I'm gonna give this dog like a, 00:04:11.040 --> 00:04:14.170 I don't know a bone or a piece of rawhide or something. 00:04:14.170 --> 00:04:16.660 Imagine that you are a detective or a dog detective 00:04:16.660 --> 00:04:20.270 if you like and every time you read a text, 00:04:20.270 --> 00:04:22.700 let's say a book, that you are searching 00:04:22.700 --> 00:04:24.810 for clues within it. 00:04:24.810 --> 00:04:26.840 What you're doing when you make an inference 00:04:26.840 --> 00:04:29.540 is you are taking the information that you already know 00:04:29.540 --> 00:04:31.890 about the world and the places and people in it 00:04:31.890 --> 00:04:33.417 and how they behave and what they look like 00:04:33.417 --> 00:04:34.470 and what they do 00:04:34.470 --> 00:04:37.200 and you're applying that knowledge to the text. 00:04:37.200 --> 00:04:38.680 When do people build snowmen? 00:04:38.680 --> 00:04:40.320 When do people build snow forts? 00:04:40.320 --> 00:04:41.720 When do they drink hot cocoa? 00:04:41.720 --> 00:04:43.370 In the winter time. 00:04:43.370 --> 00:04:44.840 An important thing to remember though 00:04:44.840 --> 00:04:47.060 is that inferring is not guessing. 00:04:47.060 --> 00:04:48.710 Any time you make an inference, 00:04:48.710 --> 00:04:51.550 you have to be pulling it directly from the text. 00:04:51.550 --> 00:04:53.260 That's your jumping off point. 00:04:53.260 --> 00:04:56.490 It can't just be a wild guess out of no where. 00:04:56.490 --> 00:04:59.960 It comes from information that you've got there on the page. 00:04:59.960 --> 00:05:01.260 Now if you'll excuse me, 00:05:01.260 --> 00:05:04.320 I'm going to go eat my weight in cough drops. 00:05:04.320 --> 00:05:06.423 You can learn anything, David out.

Groups influencing policy outcomes

https://www.youtube.com/watch?v=6PfDtm8vvqI

vtt

https://www.youtube.com/api/timedtext?v=6PfDtm8vvqI&ei=bViUZZXAFMyFhcIP6cey8AQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=084E68B593004F9F18D7EDD1D803BDDC4EAF99AE.0FBC94920E7E7C43A30A0770A39C55BEE696FFEC&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.240 --> 00:00:01.530 - [Instructor] In previous videos 00:00:01.530 --> 00:00:04.140 we've talked about how various groups 00:00:04.140 --> 00:00:07.250 attempt to influence public policy. 00:00:07.250 --> 00:00:11.740 Political parties, interest groups, bureaucratic agencies, 00:00:11.740 --> 00:00:13.580 even social movements. 00:00:13.580 --> 00:00:16.900 And we've talked about The Policy Process Model. 00:00:16.900 --> 00:00:19.230 This is how a problem is identified 00:00:19.230 --> 00:00:20.770 and potentially addresses, 00:00:20.770 --> 00:00:22.930 through a policy solution. 00:00:22.930 --> 00:00:23.830 So in this video, 00:00:23.830 --> 00:00:26.090 let's bring these two things together 00:00:26.090 --> 00:00:28.660 by thinking through when and how 00:00:28.660 --> 00:00:30.580 each of these groups might influence 00:00:30.580 --> 00:00:32.080 the policy process. 00:00:32.080 --> 00:00:36.050 So let's say that our problem is climate change. 00:00:36.050 --> 00:00:37.750 As we've discussed in other videos, 00:00:37.750 --> 00:00:40.050 climate change has only recently 00:00:40.050 --> 00:00:41.050 become an issue 00:00:41.050 --> 00:00:43.840 that voters wanna see politicians address. 00:00:43.840 --> 00:00:46.190 Social movements have put climate change 00:00:46.190 --> 00:00:47.560 on the policy agenda, 00:00:47.560 --> 00:00:49.320 with climate activists leading 00:00:49.320 --> 00:00:50.650 marches and strikes 00:00:50.650 --> 00:00:53.100 to demand action from politicians. 00:00:53.100 --> 00:00:54.960 You will most often see 00:00:54.960 --> 00:00:56.680 the influence of social movements 00:00:56.680 --> 00:00:59.330 at this point in the Policy Process, 00:00:59.330 --> 00:01:02.180 or at the Policy Evaluation step. 00:01:02.180 --> 00:01:04.350 Take a moment to think about why that is. 00:01:04.350 --> 00:01:06.170 What are the characteristics 00:01:06.170 --> 00:01:09.010 of broad based social movements 00:01:09.010 --> 00:01:10.460 that make it more difficult 00:01:10.460 --> 00:01:12.630 for them to engage at other parts 00:01:12.630 --> 00:01:14.780 of the policy process. 00:01:14.780 --> 00:01:17.190 Well, social movements are large, 00:01:17.190 --> 00:01:19.430 often led at the grassroots level, 00:01:19.430 --> 00:01:22.030 and so they may not have a central body 00:01:22.030 --> 00:01:23.790 that could get into the weeds 00:01:23.790 --> 00:01:25.410 with crafting policy. 00:01:25.410 --> 00:01:27.110 When people go out to protest, 00:01:27.110 --> 00:01:28.670 it's usually because they want 00:01:28.670 --> 00:01:31.790 a policy to be enacted to solve a problem, 00:01:31.790 --> 00:01:35.010 or because they're not happy with an existing policy 00:01:35.010 --> 00:01:37.810 and they want it to be removed or revised. 00:01:37.810 --> 00:01:39.580 So that's why you might also see 00:01:39.580 --> 00:01:41.870 social movements influencing policy 00:01:41.870 --> 00:01:44.980 at the Evaluation and Change stage. 00:01:44.980 --> 00:01:47.590 Okay, so say that climate activists 00:01:47.590 --> 00:01:50.150 have gotten their issue onto the agenda, 00:01:50.150 --> 00:01:53.080 now it's time for Policy Formation. 00:01:53.080 --> 00:01:55.340 Coming up with a potential solution 00:01:55.340 --> 00:01:56.470 to the problem, 00:01:56.470 --> 00:01:59.180 which groups might be involved with that? 00:01:59.180 --> 00:02:00.920 This is a time when interest groups 00:02:00.920 --> 00:02:02.710 might play a large role, 00:02:02.710 --> 00:02:05.620 and environmental group may have a strong opinion 00:02:05.620 --> 00:02:08.360 about what goals the government should work toward 00:02:08.360 --> 00:02:10.020 in curbing climate change. 00:02:10.020 --> 00:02:12.410 Whether that's reducing carbon emissions, 00:02:12.410 --> 00:02:14.740 or incentivizing clean energy. 00:02:14.740 --> 00:02:15.820 In fact an interest group 00:02:15.820 --> 00:02:18.160 might even write potential legislation 00:02:18.160 --> 00:02:19.570 for members of Congress. 00:02:19.570 --> 00:02:22.160 In the Policy Legitimation stage, 00:02:22.160 --> 00:02:24.680 when the proposed solution is debated 00:02:24.680 --> 00:02:26.530 and set to become law, 00:02:26.530 --> 00:02:28.780 you may see political parties 00:02:28.780 --> 00:02:30.710 exerting a great deal of influence. 00:02:30.710 --> 00:02:32.210 A party member in Congress 00:02:32.210 --> 00:02:33.880 may champion the legislation 00:02:33.880 --> 00:02:37.210 as a representation of their party's goals, 00:02:37.210 --> 00:02:39.950 or work against it because it conflicts 00:02:39.950 --> 00:02:41.580 with their party's goals. 00:02:41.580 --> 00:02:44.270 This stage is also when the federal budget 00:02:44.270 --> 00:02:45.600 process takes places. 00:02:45.600 --> 00:02:48.900 So you might find bureaucratic agencies or departments 00:02:48.900 --> 00:02:51.420 campaigning to spend more or less money 00:02:51.420 --> 00:02:52.403 on the policy. 00:02:54.200 --> 00:02:56.030 Now the law's on the books. 00:02:56.030 --> 00:02:59.520 Let's say it's a law to reduce carbon emissions 00:02:59.520 --> 00:03:01.670 by 25% over 10 years, 00:03:01.670 --> 00:03:03.550 and the money is lined up to fund it. 00:03:03.550 --> 00:03:05.890 It's time for the Implementation Stage. 00:03:05.890 --> 00:03:08.130 So which groups might attempt 00:03:08.130 --> 00:03:09.510 to exert influence 00:03:09.510 --> 00:03:11.800 in this stage of the process? 00:03:11.800 --> 00:03:14.490 Well, definitely bureaucratic agencies, 00:03:14.490 --> 00:03:16.370 at least one of which will be tasked 00:03:16.370 --> 00:03:18.110 with implementing the new law. 00:03:18.110 --> 00:03:20.490 This is also a time when interest groups 00:03:20.490 --> 00:03:21.680 will be really prominent. 00:03:21.680 --> 00:03:25.090 Remember, the law might have an overarching goal, 00:03:25.090 --> 00:03:27.830 reducing carbon emissions by 25%, 00:03:27.830 --> 00:03:29.990 but it's up to the bureaucracy 00:03:29.990 --> 00:03:31.960 to come up with the specific rules 00:03:31.960 --> 00:03:33.280 that will make that happen. 00:03:33.280 --> 00:03:36.260 So interest groups representing coal, 00:03:36.260 --> 00:03:38.480 oil, or solar power, 00:03:38.480 --> 00:03:41.350 might attempt to influence those rules 00:03:41.350 --> 00:03:42.440 in their favor. 00:03:42.440 --> 00:03:46.070 Now the last stage of the process, Evaluation. 00:03:46.070 --> 00:03:47.800 Who do you think will wanna have a say 00:03:47.800 --> 00:03:50.500 in how effective the policy has been 00:03:50.500 --> 00:03:51.710 in solving the problem? 00:03:51.710 --> 00:03:53.380 If you guessed everyone, 00:03:53.380 --> 00:03:55.610 you're getting the hang of this policy making thing. 00:03:55.610 --> 00:03:57.330 Experts in the bureaucracy 00:03:57.330 --> 00:04:00.600 may undertake a formal analysis of data 00:04:00.600 --> 00:04:03.070 to understand how well policy goals 00:04:03.070 --> 00:04:04.100 have been met. 00:04:04.100 --> 00:04:06.370 Political parties may want to tout 00:04:06.370 --> 00:04:07.870 how effective a program 00:04:07.870 --> 00:04:11.240 they sponsored was, or critique how ineffective 00:04:11.240 --> 00:04:13.470 a program they opposed was. 00:04:13.470 --> 00:04:15.680 Interest groups may request adjustments 00:04:15.680 --> 00:04:16.513 to the program 00:04:16.513 --> 00:04:18.210 to better serve their members. 00:04:18.210 --> 00:04:19.360 And social movements, 00:04:19.360 --> 00:04:20.910 as we've already mentioned, 00:04:20.910 --> 00:04:22.780 might turn out to protest, 00:04:22.780 --> 00:04:24.470 or on rare occasions, 00:04:24.470 --> 00:04:27.160 to celebrate the outcome of a policy, 00:04:27.160 --> 00:04:30.353 and then the whole process starts again.

Getting started with Khan Academy Kids

https://www.youtube.com/watch?v=GbrtpAd-fVE

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WEBVTT Kind: captions Language: en 00:00:00.210 --> 00:00:02.100 - [Instructor] So the first thing you want to do 00:00:02.100 --> 00:00:06.793 is go to your App Store and download Khan Academy Kids. 00:00:07.980 --> 00:00:11.000 Once you've done that, you can open our app, 00:00:11.000 --> 00:00:15.182 and you'll be greeted by our fun characters, 00:00:15.182 --> 00:00:17.973 Cody, Orlov, Sandy, Raya and Peck. 00:00:18.920 --> 00:00:21.850 You'll be taken to a signup screen, click Sign up 00:00:21.850 --> 00:00:23.973 and enter your email. 00:00:26.730 --> 00:00:29.100 We use this email to create your account, 00:00:29.100 --> 00:00:32.010 and we're going to ask you to verify it. 00:00:32.010 --> 00:00:34.230 So once you've entered it and clicked next, 00:00:34.230 --> 00:00:37.990 you'll receive an email in your email inbox. 00:00:37.990 --> 00:00:42.990 And you want to click the verify email button in that email, 00:00:43.950 --> 00:00:46.830 and then you're set to go back into the app 00:00:46.830 --> 00:00:49.323 and start creating accounts for your kids. 00:00:50.730 --> 00:00:54.440 Click next here, and here you are. 00:00:54.440 --> 00:00:58.660 First we're going to add the name of our first child Kim. 00:00:58.660 --> 00:01:03.660 Kim is six, and we'll select an avatar for Kim, a dolphin. 00:01:04.260 --> 00:01:06.770 Ready to start learning now, but we'll quickly show you 00:01:06.770 --> 00:01:10.150 how to create a profile for another child. 00:01:10.150 --> 00:01:13.430 If you swipe up into the parent section, 00:01:13.430 --> 00:01:16.480 you'll see Kim's account there, tap the new button, 00:01:16.480 --> 00:01:21.480 swipe up, and enter the name of the next child, Oscar. 00:01:22.880 --> 00:01:25.760 Oscar is actually older, he's seven 00:01:25.760 --> 00:01:28.663 and he is going to be a tiger. 00:01:29.520 --> 00:01:34.520 And now we have two children's profiles, Kim and Oscar. 00:01:35.360 --> 00:01:38.950 We're going to start learning with Kim so we tap Kim, 00:01:38.950 --> 00:01:41.150 and if we press the play button, 00:01:41.150 --> 00:01:43.680 he will be in our personalized learning path. 00:01:43.680 --> 00:01:46.730 It will serve up age appropriate activities 00:01:46.730 --> 00:01:48.663 for your child like this one. 00:01:49.738 --> 00:01:54.010 - (Character) And together they have five toy dinosaurs. 00:01:54.010 --> 00:01:55.620 - If you wanted to do self serve, 00:01:55.620 --> 00:01:59.100 you could click in the top left corner on the library icon. 00:01:59.100 --> 00:02:02.050 Then you can scroll through all of our activities, 00:02:02.050 --> 00:02:05.980 books, videos, our reading, our logic, 00:02:05.980 --> 00:02:09.000 social emotional learning, and you can pick out 00:02:09.000 --> 00:02:11.160 what your child works on. 00:02:11.160 --> 00:02:13.620 We've partnered with National Geographic 00:02:13.620 --> 00:02:17.740 and Bellwether Media to offer a range of characters 00:02:17.740 --> 00:02:21.220 and stories and formats to keep your child busy. 00:02:21.220 --> 00:02:23.320 And there's always the offline functionality, 00:02:23.320 --> 00:02:25.890 that suitcase under the word library. 00:02:25.890 --> 00:02:28.970 We can't wait for you to discover everything there is to do 00:02:28.970 --> 00:02:30.603 on Khan Academy Kids.

Getting Started with Khan Academy and Khan Academy Kids for Remote Learning

https://www.youtube.com/watch?v=s5M0UqFv9jQ

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WEBVTT Kind: captions Language: en 00:00:07.540 --> 00:00:10.690 - All right, hello everybody. 00:00:10.690 --> 00:00:12.620 And thank you for all taking time 00:00:12.620 --> 00:00:15.120 out of what's gotta be an incredibly busy day 00:00:15.120 --> 00:00:17.700 to join us for this webinar. 00:00:17.700 --> 00:00:20.540 My name is Karen White, and I am on the Product Team 00:00:20.540 --> 00:00:22.240 here at Khan Academy. 00:00:22.240 --> 00:00:26.700 I am also the mother of two girls, ages 12 and 17, 00:00:26.700 --> 00:00:29.660 both of whom have been out of school since last Friday. 00:00:29.660 --> 00:00:31.400 One with a distance learning plan 00:00:31.400 --> 00:00:33.060 and one with no plan at all. 00:00:33.060 --> 00:00:35.160 So we are definitely winging it here 00:00:35.160 --> 00:00:39.000 in San Jose, California, while we shelter in place. 00:00:39.000 --> 00:00:41.333 I'm sure many of you are as well. 00:00:42.450 --> 00:00:45.680 With me today, we have Dan Tieu from our Marketing Team. 00:00:45.680 --> 00:00:49.240 You can see him if you go to the next slide, 00:00:49.240 --> 00:00:53.490 see him pictured there with his nieces and nephews. 00:00:53.490 --> 00:00:56.030 And we have Sophie Turnbull in that picture 00:00:56.030 --> 00:00:57.230 with a helicopter. 00:00:57.230 --> 00:00:59.640 She's going to be talking to those of you 00:00:59.640 --> 00:01:01.540 with little ones about how to get started 00:01:01.540 --> 00:01:04.640 on our Khan Kids app which is designed 00:01:04.640 --> 00:01:06.883 as a mobile app for kids two through seven. 00:01:07.930 --> 00:01:10.640 I wanna thank our friends at Bank of America 00:01:10.640 --> 00:01:12.610 for generously supporting our ability 00:01:12.610 --> 00:01:16.023 to bring school closures resources to you at this time. 00:01:16.920 --> 00:01:18.310 And finally, before we dive in, 00:01:18.310 --> 00:01:21.390 I just wanna mention that this session will be recorded 00:01:21.390 --> 00:01:24.120 and it will be sent out by email soon after 00:01:24.120 --> 00:01:25.310 we finish this session. 00:01:25.310 --> 00:01:27.690 Also uploaded to YouTube for easy access. 00:01:27.690 --> 00:01:31.100 So if you need to step away, if you miss parts, 00:01:31.100 --> 00:01:33.640 don't worry about it, it will be available to you 00:01:33.640 --> 00:01:36.373 to review and to share with your friends and family. 00:01:37.790 --> 00:01:41.390 So with that, today, we're going to help you 00:01:41.390 --> 00:01:45.020 and your child get started on Khan Academy. 00:01:45.020 --> 00:01:48.161 If you are a teacher, we're not gonna be going 00:01:48.161 --> 00:01:50.250 through the teacher experience in this webinar, 00:01:50.250 --> 00:01:51.830 but we're gonna send these slides out, 00:01:51.830 --> 00:01:53.500 and that link on the right over there 00:01:53.500 --> 00:01:55.160 that says watch this webinar, 00:01:55.160 --> 00:01:57.950 that will take you to teacher webinar we recorded 00:01:57.950 --> 00:02:01.400 earlier this week, it's fantastic and it'll give you 00:02:01.400 --> 00:02:03.890 everything you need to get started there. 00:02:03.890 --> 00:02:06.590 We're also not going to be doing a step by step 00:02:06.590 --> 00:02:09.520 walkthrough of the setup, but in a couple slides 00:02:09.520 --> 00:02:11.530 you're gonna see our quick start guides 00:02:11.530 --> 00:02:14.163 that actually will do that for you quite well. 00:02:16.410 --> 00:02:19.993 So, a little bit more about Khan Academy. 00:02:21.410 --> 00:02:24.160 First of all, this came up in a number of questions 00:02:24.160 --> 00:02:26.730 from the pre-webinar survey. 00:02:26.730 --> 00:02:28.920 Khan Academy is free. 00:02:28.920 --> 00:02:31.500 We are a nonprofit organization 00:02:31.500 --> 00:02:35.110 and all of our instruction and practice is always free 00:02:35.110 --> 00:02:38.133 to learners and parents and their teachers. 00:02:39.270 --> 00:02:42.870 Khan Academy is a trusted source. 00:02:42.870 --> 00:02:46.220 You can trust us because we've been doing this 00:02:46.220 --> 00:02:48.700 for a long time, more than 10 years 00:02:48.700 --> 00:02:51.820 with millions of users around the world. 00:02:51.820 --> 00:02:54.770 All of our math courses are Common Core aligned 00:02:54.770 --> 00:02:57.180 and our other non-AP math courses 00:02:57.180 --> 00:03:01.320 include both Common Core material and additional content. 00:03:01.320 --> 00:03:04.390 Our AP math courses are aligned to the AP standards 00:03:04.390 --> 00:03:08.450 and as I mentioned, we served, even before 00:03:08.450 --> 00:03:10.390 the school closure started, we were serving 00:03:10.390 --> 00:03:13.340 well over 10 million learners around the globe every month. 00:03:14.400 --> 00:03:17.700 And finally, Khan Academy is flexible. 00:03:17.700 --> 00:03:20.150 The Khan Academy main app which is what I'm gonna be 00:03:20.150 --> 00:03:23.190 talking to you about is available on desktop, web, 00:03:23.190 --> 00:03:26.880 iOS, or Android, anytime, anywhere, 00:03:26.880 --> 00:03:29.610 translated into over 40 languages. 00:03:29.610 --> 00:03:31.420 Sophie's gonna talk to you later 00:03:31.420 --> 00:03:35.390 about the Khan Kids app which is a mobile app only. 00:03:35.390 --> 00:03:36.810 But Khan Academy is a main, 00:03:36.810 --> 00:03:39.183 Khan Academy we're gonna be talking about 00:03:39.183 --> 00:03:40.350 for the next 10 minutes or so, 00:03:40.350 --> 00:03:42.513 is available on desktop as well. 00:03:44.670 --> 00:03:47.800 So, now let's get into what it really means 00:03:47.800 --> 00:03:49.440 to learn on Khan Academy. 00:03:49.440 --> 00:03:52.000 And in our pre-webinar survey, 00:03:52.000 --> 00:03:54.320 the most common question we got, 00:03:54.320 --> 00:03:57.223 and thanks everyone who took the time to fill it out. 00:03:59.948 --> 00:04:01.788 The most common question we got 00:04:01.788 --> 00:04:05.600 was how do I figure out what my child should be learning? 00:04:05.600 --> 00:04:08.290 That's a great question because if you're like me 00:04:08.290 --> 00:04:11.340 you might not know exactly what your kids were up to 00:04:11.340 --> 00:04:14.380 right before the school closure started 00:04:14.380 --> 00:04:17.240 and you're certainly not used to teaching it, right? 00:04:17.240 --> 00:04:20.410 I've been a mother to my younger daughter for 12 years 00:04:20.410 --> 00:04:22.900 and I've been her teacher for about 12 hours. 00:04:22.900 --> 00:04:26.300 So, I would say the first thing to do 00:04:26.300 --> 00:04:29.730 is pat yourself on the back for trying to pull this off 00:04:29.730 --> 00:04:32.350 during a time that has a lot of other stressors 00:04:32.350 --> 00:04:33.743 in play as well. 00:04:34.900 --> 00:04:38.330 So with that preamble, here are a few tips 00:04:38.330 --> 00:04:40.590 to getting started. 00:04:40.590 --> 00:04:43.430 First things first, look at your child's homework 00:04:43.430 --> 00:04:45.060 and their textbooks. 00:04:45.060 --> 00:04:49.620 If you have access to a parent or a student portal 00:04:49.620 --> 00:04:52.620 for your school, you might be able to log in 00:04:52.620 --> 00:04:55.200 and see what assignments your teachers, 00:04:55.200 --> 00:04:58.740 your child's teacher have lined up before school let out. 00:04:58.740 --> 00:05:01.680 That'll give you some clues as to where to start 00:05:01.680 --> 00:05:02.823 their learning path. 00:05:03.910 --> 00:05:06.430 If you don't have that, that's okay. 00:05:06.430 --> 00:05:08.280 You can select a course on Khan Academy 00:05:08.280 --> 00:05:11.030 based on your child's age and grade. 00:05:11.030 --> 00:05:12.940 And you can navigate your way through that 00:05:12.940 --> 00:05:13.960 any number of ways. 00:05:13.960 --> 00:05:16.520 You can start with their very first lesson. 00:05:16.520 --> 00:05:18.502 We're gonna talk in a few minutes 00:05:18.502 --> 00:05:19.770 about how to start with the Course Challenge 00:05:19.770 --> 00:05:21.853 to identify learning gaps quickly. 00:05:22.790 --> 00:05:25.470 Or you can let your child choose where to start. 00:05:25.470 --> 00:05:28.240 And even if your child chooses something 00:05:28.240 --> 00:05:31.700 that kind of feels easy to you, that's okay. 00:05:31.700 --> 00:05:34.230 Those early math skills are foundational 00:05:34.230 --> 00:05:38.850 to more advanced math, and it's not necessarily 00:05:38.850 --> 00:05:41.900 a bad thing to have your child review that material 00:05:41.900 --> 00:05:44.290 and gain confidence and really just keep 00:05:44.290 --> 00:05:46.800 the brain training going while we're in this 00:05:46.800 --> 00:05:48.623 really unusual time. 00:05:50.030 --> 00:05:52.170 Finally, for high school students 00:05:52.170 --> 00:05:55.720 who are enrolled in AP or are studying for the SATs, 00:05:55.720 --> 00:05:59.290 we have most pop, the most popular AP courses 00:05:59.290 --> 00:06:03.610 on Khan Academy, and we also have our Official SAT prep. 00:06:03.610 --> 00:06:07.023 I can vouch for that as a parent of a senior. 00:06:08.028 --> 00:06:10.660 It is incredibly valuable. 00:06:10.660 --> 00:06:12.420 My daughter used it as her sole way 00:06:12.420 --> 00:06:15.610 to prepare for the SAT and was really, really happy 00:06:15.610 --> 00:06:16.460 with her results. 00:06:17.340 --> 00:06:19.900 So, overall, if I had to give you one mantra 00:06:19.900 --> 00:06:21.890 to remember, it's this. 00:06:21.890 --> 00:06:25.300 Some learning is better than no learning. 00:06:25.300 --> 00:06:27.500 Don't let perfect be the enemy of good. 00:06:27.500 --> 00:06:29.690 There's all sorts of things that are being demand of you 00:06:29.690 --> 00:06:32.140 right now and just get started, 00:06:32.140 --> 00:06:35.120 it's very easy to course correct, 00:06:35.120 --> 00:06:37.210 to change your learning path and make adjustments 00:06:37.210 --> 00:06:38.653 as you go with Khan Academy. 00:06:40.900 --> 00:06:44.790 So, next up, I wanna share those quick start guides 00:06:44.790 --> 00:06:45.643 I was mentioning. 00:06:47.060 --> 00:06:49.300 These links, again, this will be provided to you 00:06:49.300 --> 00:06:50.570 after the webinar. 00:06:50.570 --> 00:06:52.360 There are three different guides here. 00:06:52.360 --> 00:06:56.220 Two for Khan Academy and one for Khan Academy Kids. 00:06:56.220 --> 00:06:57.610 Just for a little bit of context 00:06:57.610 --> 00:06:59.480 on why we have different guides 00:06:59.480 --> 00:07:02.210 for younger and older children on Khan Academy. 00:07:02.210 --> 00:07:04.420 It basically comes down to the fact that 00:07:04.420 --> 00:07:06.700 there are some regulatory requirements 00:07:06.700 --> 00:07:09.822 around setting up accounts for younger kids 00:07:09.822 --> 00:07:11.910 that require your approval. 00:07:11.910 --> 00:07:13.520 And so what we wanted to do was give you 00:07:13.520 --> 00:07:17.020 the absolute fastest most efficient way to get started 00:07:17.020 --> 00:07:19.030 based on your child's situation, 00:07:19.030 --> 00:07:20.930 and these guides are customized 00:07:20.930 --> 00:07:22.770 for the fastest path through 00:07:22.770 --> 00:07:24.580 to get your child learning and then to get you 00:07:24.580 --> 00:07:25.583 set up as a parent. 00:07:26.800 --> 00:07:30.000 So, lots of support in there in those guides. 00:07:30.000 --> 00:07:32.570 What I'm gonna do now is jump into what happens 00:07:32.570 --> 00:07:34.090 once you're signed up. 00:07:34.090 --> 00:07:36.090 And this is what you're gonna see first. 00:07:36.930 --> 00:07:40.100 You're going to be offered the opportunity 00:07:40.100 --> 00:07:42.410 to personalize your child's learning 00:07:43.470 --> 00:07:45.320 by selecting their grade level 00:07:45.320 --> 00:07:47.770 and seeing what courses we recommend. 00:07:47.770 --> 00:07:49.810 Now, regardless of our suggestion, 00:07:49.810 --> 00:07:53.400 your child can choose any course on Khan Academy. 00:07:53.400 --> 00:07:57.200 So if you have a child who's really into math 00:07:57.200 --> 00:08:00.320 and is generally performing above grade level 00:08:00.320 --> 00:08:03.500 and loves a challenge, you can choose any course 00:08:03.500 --> 00:08:05.040 that's right for that child. 00:08:05.040 --> 00:08:06.708 Same the other way. 00:08:06.708 --> 00:08:08.287 If you have someone who's struggling, 00:08:08.287 --> 00:08:10.463 don't feel bound to the grade level suggestions. 00:08:11.590 --> 00:08:16.280 And after you've done that, so you've selected a course, 00:08:16.280 --> 00:08:18.270 you can select more than one, 00:08:18.270 --> 00:08:20.760 you can always go back and add, 00:08:20.760 --> 00:08:24.090 this is what your child's experience is going to look like. 00:08:24.090 --> 00:08:27.270 The courses will show up on the home page 00:08:27.270 --> 00:08:28.573 whenever they log in. 00:08:29.570 --> 00:08:32.410 And you'll see that Khan Academy is designed 00:08:32.410 --> 00:08:34.880 to give your child a lot of agency 00:08:34.880 --> 00:08:37.130 in terms of where they're going to go 00:08:37.130 --> 00:08:38.550 to do their next task. 00:08:38.550 --> 00:08:39.650 And that can be great. 00:08:39.650 --> 00:08:43.650 If you've got a child whose engaged and motivated, 00:08:43.650 --> 00:08:45.750 let them roam around, let them take these things 00:08:45.750 --> 00:08:49.510 in the order that sparks their interest and energy. 00:08:49.510 --> 00:08:52.790 It can also be a little challenging and overwhelming 00:08:52.790 --> 00:08:56.050 if you've got a younger child to have so many choices. 00:08:56.050 --> 00:08:57.980 So one of the things we like to do 00:08:57.980 --> 00:09:00.470 when we're in the classroom with young children 00:09:00.470 --> 00:09:02.870 is say, follow the blue button. 00:09:02.870 --> 00:09:05.236 You can see there that red arrow 00:09:05.236 --> 00:09:07.420 is pointed at a blue start button. 00:09:07.420 --> 00:09:10.440 That's pretty much always gonna be a good call. 00:09:10.440 --> 00:09:14.120 It will essentially take the child linearly 00:09:14.120 --> 00:09:17.730 through the course, starting with the most basic skills 00:09:17.730 --> 00:09:19.610 and advancing from there. 00:09:19.610 --> 00:09:23.110 So, always an option if you wanna give your child 00:09:23.110 --> 00:09:26.163 a little bit more of a sense of where to go next. 00:09:29.000 --> 00:09:32.470 So, once you've done that, if you were to click 00:09:32.470 --> 00:09:36.360 into any one of those units, 00:09:36.360 --> 00:09:41.360 those then turn into lessons that include instruction, 00:09:42.300 --> 00:09:45.120 practice, and assessments. 00:09:45.120 --> 00:09:46.690 If you look at where those arrows are, 00:09:46.690 --> 00:09:49.900 you can see the practice exercise is on the right 00:09:49.900 --> 00:09:53.970 and the instructional resources on the left. 00:09:53.970 --> 00:09:57.830 So, if your child is practicing and is finding 00:09:57.830 --> 00:09:59.800 that the material is a little bit challenging, 00:09:59.800 --> 00:10:01.570 but not so challenging that they wanna move 00:10:01.570 --> 00:10:03.150 to a different level. 00:10:03.150 --> 00:10:06.210 They're likely to find an article or a video 00:10:06.210 --> 00:10:09.330 or a series of them right next to that practice content 00:10:09.330 --> 00:10:12.590 that can support them as they're practicing 00:10:12.590 --> 00:10:14.043 and reinforce those skills. 00:10:17.830 --> 00:10:19.900 And then, the other thing I wanted to mention 00:10:19.900 --> 00:10:21.788 is this course challenge. 00:10:21.788 --> 00:10:24.430 So every, most of our math courses 00:10:24.430 --> 00:10:26.013 are gonna have this challenge, 00:10:27.050 --> 00:10:30.330 and it's a great way to accelerate the process 00:10:30.330 --> 00:10:32.710 of getting your child to that learning edge, 00:10:32.710 --> 00:10:35.420 that place where they're struggling a little bit 00:10:35.420 --> 00:10:37.650 in a productive way, but not so much 00:10:37.650 --> 00:10:39.510 that they get discouraged. 00:10:39.510 --> 00:10:42.200 And the way to do this is you scroll to the bottom 00:10:42.200 --> 00:10:44.020 of the course page and you'll see this button 00:10:44.020 --> 00:10:46.403 that says, start course challenge. 00:10:47.450 --> 00:10:49.350 These do take a little bit of time, 00:10:49.350 --> 00:10:51.610 so you wanna leave 30 or 45 minutes 00:10:51.610 --> 00:10:54.380 for the child to get through that, 00:10:54.380 --> 00:10:55.940 but what you're gonna come out of it with 00:10:55.940 --> 00:10:58.086 is the sense of the skills 00:10:58.086 --> 00:10:59.170 that they're really comfortable with 00:10:59.170 --> 00:11:03.640 and the skills where they might need some more practice. 00:11:03.640 --> 00:11:06.500 Especially given where we are in the school year, 00:11:06.500 --> 00:11:08.980 this is a pretty good option for you 00:11:08.980 --> 00:11:10.980 because there's going to be a lot of content 00:11:10.980 --> 00:11:14.040 that feels familiar in most cases. 00:11:14.040 --> 00:11:16.003 So starting at the beginning may not be 00:11:16.003 --> 00:11:17.710 what you need to do. 00:11:17.710 --> 00:11:21.580 The one caveat I'll say is at least if you've got 00:11:21.580 --> 00:11:25.940 a child who is generally in the mode of performing, 00:11:25.940 --> 00:11:28.670 being a high performer, the course challenge 00:11:28.670 --> 00:11:31.300 can feel a little bit like a test 00:11:31.300 --> 00:11:33.190 that they didn't get to study for. 00:11:33.190 --> 00:11:35.670 I know for my daughter when I put this in front of her, 00:11:35.670 --> 00:11:39.570 she was still in that mindset of I have to get an A, 00:11:39.570 --> 00:11:41.620 but really what the course challenge is for 00:11:41.620 --> 00:11:44.200 is identifying where she needs to practice. 00:11:44.200 --> 00:11:46.530 So I needed to really kind of encourage her 00:11:46.530 --> 00:11:49.410 and coax her along to make her comfortable with the idea 00:11:49.410 --> 00:11:52.120 that this wasn't a test, she didn't need to get an A, 00:11:52.120 --> 00:11:53.750 and this was really about finding 00:11:53.750 --> 00:11:56.733 the best ways for her to spend time on Khan Academy. 00:11:59.810 --> 00:12:03.570 So, when they're practicing, we've really designed 00:12:03.570 --> 00:12:08.040 Khan Academy to be a delightful learning experience. 00:12:08.040 --> 00:12:10.610 We celebrate when they've leveled up, 00:12:10.610 --> 00:12:15.610 they'll see confetti, there are bells when you're on a roll, 00:12:15.860 --> 00:12:19.299 you'll get a nice surprise every time 00:12:19.299 --> 00:12:21.840 you answer a question right, 00:12:21.840 --> 00:12:24.440 and there are videos and hints 00:12:24.440 --> 00:12:27.830 to get in the moment support as you go. 00:12:27.830 --> 00:12:31.400 We really try with Khan Academy to celebrate grit 00:12:31.400 --> 00:12:34.060 and perseverance, not just leveling up, 00:12:34.060 --> 00:12:37.643 because that's what having a growth mindset is all about. 00:12:40.070 --> 00:12:44.090 So now, I'm gonna very briefly talk about the parent tools 00:12:44.090 --> 00:12:48.170 that you can access as part of your parent account. 00:12:48.170 --> 00:12:49.670 And the main thing you're going to do 00:12:49.670 --> 00:12:51.580 when you're logged in as a parent 00:12:51.580 --> 00:12:54.260 is look at your child's progress. 00:12:54.260 --> 00:12:57.640 This report is essentially like being in the room 00:12:57.640 --> 00:13:00.070 with your child, looking over their shoulder, 00:13:00.070 --> 00:13:01.230 seeing what they're working on, 00:13:01.230 --> 00:13:03.370 except without the looking over their shoulder part. 00:13:03.370 --> 00:13:06.220 So, it's almost like an audit trail 00:13:06.220 --> 00:13:08.640 that shows you every exercise, how much time 00:13:08.640 --> 00:13:10.830 they've spent on it and how they did. 00:13:10.830 --> 00:13:12.570 And there's really three values I think 00:13:12.570 --> 00:13:15.240 that are going to be helpful to you 00:13:15.240 --> 00:13:16.980 as you're coaching your child 00:13:16.980 --> 00:13:20.860 or thinking about how to motivate their work. 00:13:20.860 --> 00:13:23.708 There are two numbers you'll see in there, 00:13:23.708 --> 00:13:26.683 the two numbers, both say three in this particular case. 00:13:26.683 --> 00:13:29.420 One is the time spent on exercises 00:13:29.420 --> 00:13:32.580 which is the real practice of applying the skills, 00:13:32.580 --> 00:13:35.810 and the other is the total learning time on Khan Academy 00:13:35.810 --> 00:13:38.460 which includes things like watching videos 00:13:38.460 --> 00:13:40.150 or reading articles. 00:13:40.150 --> 00:13:42.880 You're looking for in general a mix of those things, 00:13:42.880 --> 00:13:46.973 not just the instruction, but also the practice. 00:13:48.140 --> 00:13:49.680 And then, the third thing you're going to see 00:13:49.680 --> 00:13:51.990 are those little arrows, you can see a little green one 00:13:51.990 --> 00:13:54.370 there on the screen. 00:13:54.370 --> 00:13:56.800 That's going to tell you when a skill 00:13:56.800 --> 00:13:59.660 is leveling up or down. 00:13:59.660 --> 00:14:01.270 And what we essentially mean by that 00:14:01.270 --> 00:14:04.270 is your child is in, if the skill is going up 00:14:04.270 --> 00:14:07.250 it means they're making progress towards mastery 00:14:07.250 --> 00:14:09.130 of that skill. 00:14:09.130 --> 00:14:12.410 If mastery sounds like a fancy term, 00:14:12.410 --> 00:14:15.450 what it really means is this child is getting 00:14:15.450 --> 00:14:17.360 so good at this skill that they could 00:14:17.360 --> 00:14:19.020 probably explain it to somebody else, 00:14:19.020 --> 00:14:20.370 they could almost teach it. 00:14:21.660 --> 00:14:24.330 There also are going to be red arrows 00:14:24.330 --> 00:14:28.070 if the child is struggling and maybe going down a level 00:14:28.070 --> 00:14:30.050 on a skill, and those are your opportunities 00:14:30.050 --> 00:14:32.480 to say hey, let's lean in a little bit here, 00:14:32.480 --> 00:14:37.480 maybe review some videos and support them with instruction. 00:14:38.430 --> 00:14:42.080 So, this is all a good segway into the last few minutes 00:14:42.080 --> 00:14:43.570 I'm gonna spend on Khan Academy 00:14:43.570 --> 00:14:46.270 before turning it over to Sophie. 00:14:46.270 --> 00:14:50.450 And it's really about how do we motivate 00:14:50.450 --> 00:14:53.033 and structure the student's day. 00:14:53.890 --> 00:14:57.840 Let's face it, it's hard, it's a lot competing 00:14:57.840 --> 00:15:01.070 for your child's attention right now, let alone your own, 00:15:01.070 --> 00:15:06.070 and just be kind to yourselves. 00:15:06.130 --> 00:15:08.040 But I always like to remind myself 00:15:08.040 --> 00:15:10.060 that at the end of the day, yes, I want my kids 00:15:10.060 --> 00:15:12.250 to be learning, but the most important thing 00:15:12.250 --> 00:15:14.580 is we're all gonna be stuck in this house a lot together, 00:15:14.580 --> 00:15:17.200 so we have better get along. 00:15:17.200 --> 00:15:20.130 So, in terms of setting goals, 00:15:20.130 --> 00:15:23.140 it's great to include your children in the process, 00:15:23.140 --> 00:15:26.093 they're going to be more invested if you do it that way, 00:15:27.330 --> 00:15:28.750 and take it one day at a time. 00:15:28.750 --> 00:15:31.310 If the goals you set for your first day 00:15:31.310 --> 00:15:33.440 don't turn out to be particularly realistic 00:15:33.440 --> 00:15:36.530 given your situation, stay flexible, 00:15:36.530 --> 00:15:40.280 let yourself, give yourself some slack, 00:15:40.280 --> 00:15:43.390 we're all in uncharted territory right now. 00:15:43.390 --> 00:15:45.630 And then recognize milestones. 00:15:45.630 --> 00:15:48.700 We always like to celebrate both the progress 00:15:48.700 --> 00:15:50.180 and the effort. 00:15:50.180 --> 00:15:53.170 So when you look at those numbers around time, 00:15:53.170 --> 00:15:55.530 that's one of the ways you can congratulate your child 00:15:55.530 --> 00:15:59.570 for making the effort, and then look for those level ups 00:15:59.570 --> 00:16:02.170 as an indication that your child is making progress. 00:16:03.560 --> 00:16:05.450 All right, one last thing. 00:16:05.450 --> 00:16:07.560 I think some of you probably have seen 00:16:07.560 --> 00:16:12.290 we have posted online a number of templates 00:16:12.290 --> 00:16:14.620 for daily schedules that can help you 00:16:14.620 --> 00:16:18.020 just get a little bit more of that structure 00:16:18.020 --> 00:16:20.670 that helps your child be calm, creates a sense 00:16:20.670 --> 00:16:24.230 of predictability, and gives you some room to maneuver 00:16:24.230 --> 00:16:27.020 because you have a sense of how your day is going to go. 00:16:27.020 --> 00:16:29.710 So feel free to click through on those 00:16:29.710 --> 00:16:33.940 when you get the materials and hope that they are helpful 00:16:33.940 --> 00:16:35.430 to you as they have been to me 00:16:35.430 --> 00:16:38.370 in terms of giving your children some structure 00:16:38.370 --> 00:16:40.983 and order in what is kind of a chaotic time. 00:16:42.450 --> 00:16:44.993 And with that, I will turn it over to you Sophie. 00:16:46.480 --> 00:16:50.320 - Hi everyone, I'm Sophie from Khan Academy Kids. 00:16:50.320 --> 00:16:53.080 And tonight, I'm really excited to walk you 00:16:53.080 --> 00:16:55.370 through the basics on getting set up, 00:16:55.370 --> 00:17:00.203 how to learn at home with your kids on Khan Academy Kids. 00:17:01.450 --> 00:17:05.240 Khan Academy Kids is made by Khan Academy. 00:17:05.240 --> 00:17:09.120 It's a mobile app that is separate to the Khan Academy app 00:17:09.120 --> 00:17:11.820 or the Khan Academy desktop experience 00:17:11.820 --> 00:17:14.700 and it's designed especially for children 00:17:14.700 --> 00:17:17.420 ages two through seven. 00:17:17.420 --> 00:17:22.420 It's available on your mobile, be it an Apple iOS or Android 00:17:23.290 --> 00:17:26.220 as well as touch screen Chromebooks, 00:17:26.220 --> 00:17:30.110 and you can find it in the app store that you use. 00:17:30.110 --> 00:17:32.440 So, what we're going to do right now 00:17:32.440 --> 00:17:35.170 is quickly watch a demo of how to get set up 00:17:35.170 --> 00:17:38.973 on Khan Academy Kids in about three minutes. 00:17:58.730 --> 00:18:00.630 So the first thing you want to do 00:18:00.630 --> 00:18:05.303 is go to your app store and download Khan Academy Kids. 00:18:06.490 --> 00:18:09.510 Once you've done that, you can open our app 00:18:09.510 --> 00:18:12.830 and you'll be greeted by our fun characters. 00:18:12.830 --> 00:18:13.900 - Khan Academy Kids. 00:18:13.900 --> 00:18:16.483 - [Sophie] Cody, Ollo, Sandy, Rhea, and Peck. 00:18:17.430 --> 00:18:19.110 You'll be taken to a signup screen. 00:18:19.110 --> 00:18:22.493 Click signup and enter your email. 00:18:25.250 --> 00:18:27.610 We use this email to create your account 00:18:27.610 --> 00:18:30.520 and we're going to ask you to verify it. 00:18:30.520 --> 00:18:32.760 So once you've entered it and clicked next, 00:18:32.760 --> 00:18:36.500 you'll receive an email in your email inbox 00:18:36.500 --> 00:18:41.500 and you want to click the verify email button in that email, 00:18:42.490 --> 00:18:45.340 and then you are set to go back into the app 00:18:45.340 --> 00:18:47.853 and start creating accounts for your kids. 00:18:49.250 --> 00:18:51.973 Click next here and here you are. 00:18:52.960 --> 00:18:57.170 First, we're going to add the name of our first child, Kim. 00:18:57.170 --> 00:19:02.170 Kim is six and we'll select an avatar for Kim, a dolphin. 00:19:02.780 --> 00:19:05.280 Ready to start learning now, but we'll quickly show you 00:19:05.280 --> 00:19:08.670 how to create a profile for another child. 00:19:08.670 --> 00:19:11.940 If you swipe up into the parents section 00:19:11.940 --> 00:19:14.990 you'll see Kim's account there, tap the new button, 00:19:14.990 --> 00:19:19.990 swipe up, and enter the name of the next child, Oscar. 00:19:21.410 --> 00:19:24.290 Oscar is actually older, he's seven, 00:19:24.290 --> 00:19:28.040 and he is going to be a tiger. 00:19:28.040 --> 00:19:33.040 And now we have two children's profiles, Kim and Oscar. 00:19:33.880 --> 00:19:37.470 We're going to start learning with Kim, so we tap Kim. 00:19:37.470 --> 00:19:39.870 And if we press the play button here, 00:19:39.870 --> 00:19:42.210 we'll be in our personalized learning path. 00:19:42.210 --> 00:19:46.410 It'll serve up age appropriate activities for your child 00:19:46.410 --> 00:19:47.243 like this one. 00:19:48.630 --> 00:19:52.530 - And together they have five toy dinosaurs. 00:19:52.530 --> 00:19:54.130 - If you wanted to do self serve 00:19:54.130 --> 00:19:55.770 you could click in the top left corner 00:19:55.770 --> 00:19:59.040 on the library icon, then you can scroll through 00:19:59.040 --> 00:20:02.730 all of our activities, books, and videos, 00:20:02.730 --> 00:20:06.200 our reading, our logic, social emotional learning, 00:20:06.200 --> 00:20:09.680 and you can pick out what your child works on. 00:20:09.680 --> 00:20:12.130 We've partnered with National Geographic 00:20:12.130 --> 00:20:16.250 and Bellwether Media to offer a range of characters 00:20:16.250 --> 00:20:19.680 and stories and formats to keep your child busy. 00:20:19.680 --> 00:20:21.840 And there's always the offline functionality, 00:20:21.840 --> 00:20:24.420 that suitcase under the word library. 00:20:24.420 --> 00:20:26.360 We can't wait for you to discover 00:20:26.360 --> 00:20:29.133 everything there is to do on Khan Academy Kids. 00:20:47.060 --> 00:20:50.390 So now, you should be ready to get started learning. 00:20:50.390 --> 00:20:53.130 And I wanna run through a few of the questions 00:20:53.130 --> 00:20:55.540 that we've been getting from parents learning at home 00:20:55.540 --> 00:20:56.850 with their kids. 00:20:56.850 --> 00:20:58.710 I mentioned the home screen. 00:20:58.710 --> 00:21:02.660 If you press that big green play button on the homepage, 00:21:02.660 --> 00:21:05.330 you'll go into the personalized learning path. 00:21:05.330 --> 00:21:08.860 And if you press the top left library icon, 00:21:08.860 --> 00:21:10.810 you'll go into the library. 00:21:10.810 --> 00:21:13.220 Well, what's the difference between those two? 00:21:13.220 --> 00:21:17.190 The personalized learning path is an automatic playlist 00:21:17.190 --> 00:21:20.940 of all of our activities, math and reading, 00:21:20.940 --> 00:21:24.080 social emotional learning, books and videos, 00:21:24.080 --> 00:21:26.810 and they get served up to your child 00:21:26.810 --> 00:21:28.930 to meet them where they're at, 00:21:28.930 --> 00:21:30.410 so they're age appropriate 00:21:30.410 --> 00:21:33.200 and they're automatically served up. 00:21:33.200 --> 00:21:35.730 The learning path might be a good idea 00:21:35.730 --> 00:21:38.040 if you just can't be there to pick and choose 00:21:38.040 --> 00:21:40.240 every activity that your child is doing 00:21:40.240 --> 00:21:41.793 for a certain part of the day. 00:21:42.660 --> 00:21:45.200 The library is where is where you can self serve 00:21:45.200 --> 00:21:46.940 out of our catalog of activities. 00:21:46.940 --> 00:21:51.880 It's the blue, the book icon in the top left hand corner 00:21:51.880 --> 00:21:53.670 of the home screen. 00:21:53.670 --> 00:21:56.270 All of the activities are the same. 00:21:56.270 --> 00:21:58.410 It's just about how they're served up to you. 00:21:58.410 --> 00:22:01.390 Do you want to pick and choose what your child is doing 00:22:01.390 --> 00:22:03.350 from one activity to the next 00:22:03.350 --> 00:22:05.300 or are you happy to let them work their way 00:22:05.300 --> 00:22:07.030 through the personalized learning path? 00:22:07.030 --> 00:22:08.603 That's totally up to you. 00:22:10.810 --> 00:22:13.060 Now, I wanna cover some quick tips 00:22:13.060 --> 00:22:16.640 for learning at home with Khan Academy Kids. 00:22:16.640 --> 00:22:19.650 All of Karen's points about having a daily schedule, 00:22:19.650 --> 00:22:22.470 but being flexible, and motivating kids at home 00:22:22.470 --> 00:22:26.550 being terribly difficult apply to two to seven year olds. 00:22:26.550 --> 00:22:28.790 On the technical side though, I wanna point out 00:22:28.790 --> 00:22:30.130 a couple of things. 00:22:30.130 --> 00:22:33.640 If you have to go offline, I mentioned the suitcase icon 00:22:33.640 --> 00:22:35.050 in the library, tap that. 00:22:35.050 --> 00:22:37.010 All your child's progress will be saved 00:22:37.010 --> 00:22:39.870 and uploaded when you go online next. 00:22:39.870 --> 00:22:43.020 If you want to view progress, go into your child's 00:22:43.020 --> 00:22:45.440 library view and you'll see green, yellow, 00:22:45.440 --> 00:22:48.680 and red check marks indicating whether they've mastered 00:22:48.680 --> 00:22:50.500 something, they're still working on it, 00:22:50.500 --> 00:22:51.950 or they're yet to work on it. 00:22:53.350 --> 00:22:57.690 On the content side, there are a few things 00:22:57.690 --> 00:22:59.560 that parents have pointed out to us. 00:22:59.560 --> 00:23:03.050 Parents are loving using out the thousands of books 00:23:03.050 --> 00:23:04.970 that we have to read to their children. 00:23:04.970 --> 00:23:07.610 We have books on everything from animals 00:23:07.610 --> 00:23:09.100 to feeling frustrated. 00:23:09.100 --> 00:23:12.646 So, have at it in the book section. 00:23:12.646 --> 00:23:15.310 Parents have also been saying that they're enjoying 00:23:15.310 --> 00:23:17.400 the healthy habits throughout the act. 00:23:17.400 --> 00:23:19.920 There are activities on things like saying hello 00:23:19.920 --> 00:23:22.590 and making friends, even getting dressed in the morning. 00:23:22.590 --> 00:23:24.930 Some of these habits that are so important 00:23:24.930 --> 00:23:26.700 when we're couped up inside. 00:23:26.700 --> 00:23:31.670 And so, I encourage you to check those out in the logic tab. 00:23:31.670 --> 00:23:34.560 And then, finally, in the create tab, 00:23:34.560 --> 00:23:38.310 your child can do something creative like drawing, 00:23:38.310 --> 00:23:41.210 making a card for a friend, you can screenshot it 00:23:41.210 --> 00:23:44.950 and send it on, and Khan Academy Kids is really focused 00:23:44.950 --> 00:23:49.070 on not just math and reading the core academic subjects 00:23:49.070 --> 00:23:51.530 for two to seven year olds, but also making sure 00:23:51.530 --> 00:23:53.890 kids are creative, that they're interacting with you, 00:23:53.890 --> 00:23:56.530 that they're moving around, getting up and jumping 00:23:56.530 --> 00:23:59.860 and making zoo animal noises 00:23:59.860 --> 00:24:02.553 and really developing their whole selves. 00:24:05.230 --> 00:24:06.600 The last thing I wanna mention 00:24:06.600 --> 00:24:08.320 is that there is some places you can go 00:24:08.320 --> 00:24:09.900 for more information. 00:24:09.900 --> 00:24:12.590 So teachers should look out for the Teacher Guide 00:24:12.590 --> 00:24:15.470 that is linked in the quick start handout 00:24:15.470 --> 00:24:17.560 that we are posting on this webinar. 00:24:17.560 --> 00:24:20.560 It has a whole lot about how you might teach remotely 00:24:20.560 --> 00:24:22.640 with Khan Academy Kids. 00:24:22.640 --> 00:24:25.790 And if you have any questions about getting started, 00:24:25.790 --> 00:24:30.790 please email khan, that's K-H-A-N, kids@khanacademy.org. 00:24:32.610 --> 00:24:34.950 And you should follow us on social media 00:24:34.950 --> 00:24:37.700 if you're into that for daily activities, 00:24:37.700 --> 00:24:40.940 things like circle time and what to do with your kids 00:24:40.940 --> 00:24:42.760 on Khan Academy Kids. 00:24:42.760 --> 00:24:43.783 Thanks so much. 00:24:45.600 --> 00:24:47.350 - All right, thank you Sophie and Karen. 00:24:47.350 --> 00:24:49.130 Hi everyone, it's Dan here. 00:24:49.130 --> 00:24:51.220 I'd like to for y'all to do two steps 00:24:51.220 --> 00:24:54.300 before we open it up to live questions. 00:24:54.300 --> 00:24:56.810 First, if you can all go out to the handout section 00:24:56.810 --> 00:24:58.487 and grab the cheat sheet, it contains guides 00:24:58.487 --> 00:25:01.940 for this entire process, from finding the right content 00:25:01.940 --> 00:25:04.550 for your kids, to tracking their progress, 00:25:04.550 --> 00:25:06.830 and to creating structure and motivation. 00:25:06.830 --> 00:25:08.870 It also contains step by step instructions 00:25:08.870 --> 00:25:10.850 on how to set up an account and links 00:25:10.850 --> 00:25:12.370 to other parent resources. 00:25:12.370 --> 00:25:14.910 So feel free to download it and share it with other parents, 00:25:14.910 --> 00:25:16.430 friends and families. 00:25:16.430 --> 00:25:18.490 And secondly, if you have any questions, 00:25:18.490 --> 00:25:20.640 please add them to the question box. 00:25:20.640 --> 00:25:22.540 I'll be facilitating while Karen and Sophie 00:25:22.540 --> 00:25:24.860 provide their expert answers. 00:25:24.860 --> 00:25:27.270 So, let's go ahead and start with some good questions 00:25:27.270 --> 00:25:30.483 that are coming in, and thank you everyone for submitting. 00:25:31.670 --> 00:25:35.760 So we have a question, Karen, for you. 00:25:35.760 --> 00:25:39.593 Should my child have separate account for me as a parent? 00:25:40.560 --> 00:25:42.547 - Yeah, that's a great question. 00:25:42.547 --> 00:25:44.300 And absolutely, we would recommend 00:25:44.300 --> 00:25:49.300 that you and your child have separate accounts. 00:25:49.610 --> 00:25:53.410 First of all, you have a set of controls and settings 00:25:53.410 --> 00:25:56.300 that are particular to the parent account, 00:25:56.300 --> 00:25:58.570 but there's a second reason that I wanna emphasize 00:25:58.570 --> 00:26:01.190 which is that you actually may wanna do 00:26:01.190 --> 00:26:03.520 some learning on Khan Academy yourself. 00:26:03.520 --> 00:26:06.380 I have personally found that seventh grade math 00:26:06.380 --> 00:26:09.030 feels like it was a really, really long time ago, 00:26:09.030 --> 00:26:13.780 and so while your child is learning in their own account 00:26:13.780 --> 00:26:16.600 you can actually go in as a learner, 00:26:16.600 --> 00:26:18.370 and this is in the quick start guide, 00:26:18.370 --> 00:26:19.710 and practice yourself. 00:26:19.710 --> 00:26:21.430 So you'll have your own learning path 00:26:21.430 --> 00:26:22.860 if you have a separate account 00:26:22.860 --> 00:26:24.810 from the one you set up for your child. 00:26:26.340 --> 00:26:28.060 - Awesome, thank you Karen. 00:26:28.060 --> 00:26:31.000 This next one I think it's most appropriate for you Sophie. 00:26:31.000 --> 00:26:33.070 Is Khan Academy Kids integrated 00:26:33.070 --> 00:26:35.420 with the desktop Khan Academy, 00:26:35.420 --> 00:26:37.920 and can I see their progress from the kids app 00:26:37.920 --> 00:26:38.883 on the desktop? 00:26:41.479 --> 00:26:42.990 - So the short answer is no. 00:26:42.990 --> 00:26:45.310 Khan Academy Kids is a mobile app 00:26:45.310 --> 00:26:47.460 and the progress that your child makes 00:26:47.460 --> 00:26:49.540 on the Khan Academy Kids mobile app 00:26:49.540 --> 00:26:54.310 will not be present on the Khan Academy desktop experience. 00:26:54.310 --> 00:26:56.740 We've designed it so that it's touch screen 00:26:56.740 --> 00:26:59.250 and it's especially for two to seven year olds. 00:26:59.250 --> 00:27:01.300 And I think in the future, we look forward 00:27:01.300 --> 00:27:04.203 to linking those two experiences, but for now, no. 00:27:05.730 --> 00:27:07.220 - Okay, great, thank you. 00:27:07.220 --> 00:27:09.490 Here's a question that either of you can answer, 00:27:09.490 --> 00:27:11.650 perhaps Karen you tackle it first 00:27:11.650 --> 00:27:14.210 and Sophie, you can go next on this one. 00:27:14.210 --> 00:27:17.250 So we have a question from Matteas Devereus, 00:27:17.250 --> 00:27:19.600 apologies if I pronounced the name incorrectly. 00:27:20.745 --> 00:27:23.770 So the question is, how much should we supervise our kids 00:27:23.770 --> 00:27:25.380 while they learn? 00:27:25.380 --> 00:27:27.380 - Yeah, great question. 00:27:27.380 --> 00:27:30.710 I guess my first response would be, how much can you? 00:27:30.710 --> 00:27:33.900 I know at least for me, I am working during the day 00:27:33.900 --> 00:27:36.710 even though I'm here at home, so my ability to supervise 00:27:36.710 --> 00:27:39.290 is fairly limited, and I imagine many of you 00:27:39.290 --> 00:27:40.610 are in the same position. 00:27:40.610 --> 00:27:43.100 And we have designed Khan Academy 00:27:43.100 --> 00:27:48.100 so that most children can progress independently. 00:27:49.270 --> 00:27:52.320 I like to make myself available to be nearby, 00:27:52.320 --> 00:27:55.130 but if you're supervising because you want to hold 00:27:55.130 --> 00:27:57.760 your child accountable, that's where that progress report 00:27:57.760 --> 00:28:00.020 becomes really, really valuable. 00:28:00.020 --> 00:28:04.180 Your child cannot practice on Khan Academy 00:28:04.180 --> 00:28:06.040 without you seeing it and vice versa. 00:28:06.040 --> 00:28:09.880 So, that report will be your way of staying connected 00:28:09.880 --> 00:28:11.040 with what your child is learning 00:28:11.040 --> 00:28:15.380 even when you don't have the ability to sit side by side. 00:28:15.380 --> 00:28:18.090 Having said that, if you do have the ability 00:28:18.090 --> 00:28:20.140 and if your child welcomes it, 00:28:20.140 --> 00:28:21.640 it's a great, it's a great chance 00:28:21.640 --> 00:28:23.840 to really be part of their learning journey. 00:28:24.930 --> 00:28:27.210 - Yeah, I would just quickly echo that. 00:28:27.210 --> 00:28:29.420 It's great for parents to be interacting 00:28:29.420 --> 00:28:32.859 with Khan Academy Kids while their child is using it, 00:28:32.859 --> 00:28:34.170 particularly in the library mode. 00:28:34.170 --> 00:28:36.650 But if you needed to step away for a time 00:28:36.650 --> 00:28:38.410 and have your child learn independently, 00:28:38.410 --> 00:28:40.750 the personalized learning path is really taking care 00:28:40.750 --> 00:28:42.680 of things while you have to do that, 00:28:42.680 --> 00:28:45.460 and you'll be able to see a comprehensive view 00:28:45.460 --> 00:28:49.100 of their progress when you go back into the library. 00:28:49.100 --> 00:28:49.933 - Yeah. 00:28:49.933 --> 00:28:52.150 And keep in mind, Khan Academy is used 00:28:52.150 --> 00:28:55.150 in schools all over the place, 00:28:55.150 --> 00:28:58.310 and that's a situation where one teacher 00:28:58.310 --> 00:28:59.870 has a group of 30 kids. 00:28:59.870 --> 00:29:02.210 So, it's definitely designed for kids 00:29:02.210 --> 00:29:04.750 to be able to make independent progress 00:29:04.750 --> 00:29:07.540 through a combination of instruction and practice 00:29:07.540 --> 00:29:11.043 paired together without direct supervision. 00:29:12.300 --> 00:29:15.550 - All right, so I think we have time for one more question. 00:29:15.550 --> 00:29:17.600 Karen, this one's from Heather. 00:29:17.600 --> 00:29:21.450 Will there be an answer key to help grade if I'm a parent 00:29:21.450 --> 00:29:23.283 and not in a teacher account? 00:29:24.140 --> 00:29:24.973 - Yeah, great question. 00:29:24.973 --> 00:29:28.040 So, you will not get an answer key, 00:29:28.040 --> 00:29:31.820 but you actually won't need to grade your child's practice, 00:29:31.820 --> 00:29:33.910 because they are getting real-time feedback 00:29:33.910 --> 00:29:35.440 with every question. 00:29:35.440 --> 00:29:37.830 So, as the questions are answered, 00:29:37.830 --> 00:29:40.410 they will immediately know whether they got the question 00:29:40.410 --> 00:29:43.840 right or wrong, they'll have access to a hint, 00:29:43.840 --> 00:29:46.620 and they'll have access in many cases to a rationale 00:29:46.620 --> 00:29:48.020 even if they do get it right. 00:29:48.020 --> 00:29:50.950 So, there's really no need for an answer key. 00:29:50.950 --> 00:29:51.783 - All right. 00:29:51.783 --> 00:29:54.840 So, thank you Karen and Sophie for sharing your expertise 00:29:54.840 --> 00:29:57.440 with our audience, and thank you to our audience 00:29:57.440 --> 00:30:00.400 for taking the time out of your busy evening to be with us. 00:30:00.400 --> 00:30:01.830 We know there's so much going on 00:30:01.830 --> 00:30:03.940 and we really appreciate you investing your time 00:30:03.940 --> 00:30:05.730 into this session. 00:30:05.730 --> 00:30:07.380 We know that we hit our limit in terms 00:30:07.380 --> 00:30:09.540 of the number of people who wanted to join the webinar, 00:30:09.540 --> 00:30:11.630 so we apologize for that. 00:30:11.630 --> 00:30:14.180 So for those of you who or may know folks 00:30:14.180 --> 00:30:15.680 who were not able to get in, 00:30:15.680 --> 00:30:19.000 this will be, this will be record, this is recorded, 00:30:19.000 --> 00:30:21.110 and we'll be posting live online 00:30:21.110 --> 00:30:22.660 and available to everyone. 00:30:22.660 --> 00:30:25.870 And so, rest assured that this information 00:30:25.870 --> 00:30:27.870 will be available to you. 00:30:27.870 --> 00:30:30.960 And secondly, we also have quite a few other resources 00:30:30.960 --> 00:30:33.920 available on our website at khanacademy.org. 00:30:33.920 --> 00:30:35.930 There's currently a blue ribbon at the very top. 00:30:35.930 --> 00:30:37.830 We're adding new resources every day 00:30:37.830 --> 00:30:39.550 and making changes quite frequently, 00:30:39.550 --> 00:30:42.250 so feel free to go there and click through 00:30:42.250 --> 00:30:43.930 for more information. 00:30:43.930 --> 00:30:46.620 Before we sign off, please do us one more favor 00:30:46.620 --> 00:30:48.790 and take the poll that pops up at the very end 00:30:48.790 --> 00:30:51.550 of this webinar and let us know two things. 00:30:51.550 --> 00:30:54.480 First, how could we make future iterations of this session 00:30:54.480 --> 00:30:55.970 even better for you all? 00:30:55.970 --> 00:30:58.090 And secondly, what kind of sessions 00:30:58.090 --> 00:30:59.580 would you like to see next? 00:30:59.580 --> 00:31:02.110 So this was obviously a relatively high level session 00:31:02.110 --> 00:31:04.070 to get you all started, but if you wanted us 00:31:04.070 --> 00:31:07.300 to dive deeper into things like motivation, 00:31:07.300 --> 00:31:09.810 specific courses like math or science, 00:31:09.810 --> 00:31:12.160 please let us know, we're here to support you, 00:31:12.160 --> 00:31:14.450 this is the first of future webinars 00:31:14.450 --> 00:31:16.330 that we wanna create to be able to support you 00:31:16.330 --> 00:31:17.720 through this time. 00:31:17.720 --> 00:31:19.830 So with that, from all of us at Khan Academy, 00:31:19.830 --> 00:31:22.453 thank you again for joining us, and good night.

A message from Sal on school closures and remote learning on Khan Academy.

https://www.youtube.com/watch?v=2B1EAhgAvPs

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WEBVTT Kind: captions Language: en 00:00:00.900 --> 00:00:04.340 - Hi everyone, it's Sal here from Khan Academy. 00:00:04.340 --> 00:00:06.630 I am back in the walk-in closet 00:00:06.630 --> 00:00:09.940 where Khan Academy all began, socially distanced. 00:00:09.940 --> 00:00:13.640 Obviously the entire globe is going through 00:00:13.640 --> 00:00:18.390 a very unusual crisis right now, and as part of that crisis, 00:00:18.390 --> 00:00:20.200 people are worried about three things. 00:00:20.200 --> 00:00:21.330 They're worried about their health, 00:00:21.330 --> 00:00:23.760 both physical and mental health, 00:00:23.760 --> 00:00:25.250 they are worried about the economy, 00:00:25.250 --> 00:00:27.180 and then they're worried about how do we ensure 00:00:27.180 --> 00:00:31.680 that kids can keep learning with now nearly a billion kids 00:00:31.680 --> 00:00:34.280 that otherwise would be in school are now out of school 00:00:34.280 --> 00:00:37.590 in order to protect people from this virus. 00:00:37.590 --> 00:00:40.040 All of us here at Khan Academy, as a not for profit 00:00:40.040 --> 00:00:42.550 with a mission of providing a free world class education 00:00:42.550 --> 00:00:46.310 for anyone, anywhere, recognize that it's our duty 00:00:46.310 --> 00:00:48.870 to step up in this crisis. 00:00:48.870 --> 00:00:52.430 We never could have foreseen this type of situation, 00:00:52.430 --> 00:00:56.510 but we want to be there to support you, support students, 00:00:56.510 --> 00:01:01.181 parents, teachers to get us through this situation. 00:01:01.181 --> 00:01:04.090 We've always been working on resources 00:01:04.090 --> 00:01:07.020 starting from pre-K with Khan Academy Kids 00:01:07.020 --> 00:01:09.440 that covers math, reading, writing, 00:01:09.440 --> 00:01:12.130 social/emotional learning, all the way through 00:01:12.130 --> 00:01:14.550 the main Khan Academy website and app 00:01:14.550 --> 00:01:17.700 that goes from kindergarten through the core of college, 00:01:17.700 --> 00:01:19.150 including middle school and high school 00:01:19.150 --> 00:01:22.550 in math, English language arts, the sciences. 00:01:22.550 --> 00:01:25.110 We have history, economics. 00:01:25.110 --> 00:01:27.770 We also have official SAT practice for you. 00:01:27.770 --> 00:01:30.420 But as we saw the school closures begin to happen 00:01:30.420 --> 00:01:33.220 over the last few days and now it's accelerating, 00:01:33.220 --> 00:01:34.920 we realize that we need to do more, 00:01:34.920 --> 00:01:38.460 so on top of that we are publishing resources 00:01:38.460 --> 00:01:41.220 for parents, for students, for teachers 00:01:41.220 --> 00:01:45.090 to be able to understand how to navigate the situation. 00:01:45.090 --> 00:01:47.620 Just recently we published schedules 00:01:47.620 --> 00:01:49.410 so that students, parents and teachers 00:01:49.410 --> 00:01:51.070 can structure students' days, 00:01:51.070 --> 00:01:52.740 and there's different schedules for students 00:01:52.740 --> 00:01:54.570 of different age groups. 00:01:54.570 --> 00:01:57.040 And we are doing daily live streams 00:01:57.040 --> 00:01:59.380 so that in this time of social distancing, 00:01:59.380 --> 00:02:01.620 we all can feel connected and make sure 00:02:01.620 --> 00:02:03.970 that we're there to support each other. 00:02:03.970 --> 00:02:07.090 The team here at Khan Academy is very focused 00:02:07.090 --> 00:02:09.650 on making sure we can support you all through this crisis. 00:02:09.650 --> 00:02:11.820 We're seeing the server load increase, 00:02:11.820 --> 00:02:13.910 and so the engineering team is reassuring me 00:02:13.910 --> 00:02:15.944 that we think we have it. 00:02:15.944 --> 00:02:19.742 We're also exploring other ways that we can support you, 00:02:19.742 --> 00:02:21.810 and we're looking at ways that we can get 00:02:21.810 --> 00:02:24.530 more help for folks, things like that. 00:02:24.530 --> 00:02:27.340 I will remind folks that we are not for profit. 00:02:27.340 --> 00:02:30.120 Even before this crisis, we were operating 00:02:30.120 --> 00:02:33.970 at a bit of a deficit, and so if you're in the position, 00:02:33.970 --> 00:02:36.210 especially as our demands on our server 00:02:36.210 --> 00:02:39.000 and our costs are going up as people use us more, 00:02:39.000 --> 00:02:42.700 if you are in a position, I hope you could think about 00:02:42.700 --> 00:02:44.650 supporting us philanthropically. 00:02:44.650 --> 00:02:47.460 I want to really thank Bank of America. 00:02:47.460 --> 00:02:49.740 Just over this past weekend they stepped up. 00:02:49.740 --> 00:02:51.980 They realized that our costs were going up, 00:02:51.980 --> 00:02:53.790 that we had to have a better response effort, 00:02:53.790 --> 00:02:57.000 so they have helped us there, but we need more help. 00:02:57.000 --> 00:02:58.800 For any of you all out there who are in a position, 00:02:58.800 --> 00:03:01.090 whether individual or corporation, 00:03:01.090 --> 00:03:03.780 if you're finding use out of the resources we're providing, 00:03:03.780 --> 00:03:06.380 please think about making a donation to Khan Academy. 00:03:06.380 --> 00:03:10.210 It will allow us to support the nation and the world 00:03:10.210 --> 00:03:15.210 as we go through this very, very unusual crisis together. 00:03:15.600 --> 00:03:17.890 Last but not least, I just want to say 00:03:17.890 --> 00:03:20.390 as one human being talking to another, 00:03:20.390 --> 00:03:22.550 this is a new frontier for all of us, 00:03:22.550 --> 00:03:24.920 but I've been very heartened by the humanity 00:03:24.920 --> 00:03:26.140 that I'm seeing in everyone. 00:03:26.140 --> 00:03:28.190 Everyone is just trying to help everyone else 00:03:28.190 --> 00:03:31.200 as a human being, and I'm confident 00:03:31.200 --> 00:03:33.290 that if we just do the next right thing, 00:03:33.290 --> 00:03:35.630 one step after another, that we're all going to be able 00:03:35.630 --> 00:03:39.050 to get each other through this situation. 00:03:39.050 --> 00:03:39.883 Thank you.

How Khan Academy is Here to Help During COVID-19

https://www.youtube.com/watch?v=RK-tezfrjJs

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WEBVTT Kind: captions Language: en 00:00:00.900 --> 00:00:03.820 - Hi everyone, Sal here from Khan Academy. 00:00:03.820 --> 00:00:05.210 As I'm sure you're aware, 00:00:05.210 --> 00:00:07.900 we are finding ourselves collectively, our planet, 00:00:07.900 --> 00:00:09.730 in a very interesting situation right now 00:00:09.730 --> 00:00:11.570 and a lot of unfortunate things are happening. 00:00:11.570 --> 00:00:13.320 And one of those unfortunate things is 00:00:13.320 --> 00:00:15.480 the potential for school closures. 00:00:15.480 --> 00:00:17.430 And so, all of us here at Khan Academy, 00:00:17.430 --> 00:00:19.930 we've essentially stopped what we're doing 00:00:19.930 --> 00:00:21.860 and we view it as our duty 00:00:21.860 --> 00:00:24.040 to be able to support you through this, 00:00:24.040 --> 00:00:28.730 to help you help ensure that students continue to learn. 00:00:28.730 --> 00:00:30.900 I know a lot of districts are facing 00:00:30.900 --> 00:00:33.440 a lot of difficult decisions to make, 00:00:33.440 --> 00:00:35.280 thinking about whether to close, 00:00:35.280 --> 00:00:36.500 whether to virtualize, 00:00:36.500 --> 00:00:38.360 there's a lot of equity issues at stake, 00:00:38.360 --> 00:00:40.864 who has access to internet and computers at home? 00:00:40.864 --> 00:00:43.210 There's other things around childcare, 00:00:43.210 --> 00:00:44.740 free and reduced lunch. 00:00:44.740 --> 00:00:46.240 But we're gonna try and do our part 00:00:46.240 --> 00:00:49.200 to support everyone as much as possible. 00:00:49.200 --> 00:00:52.410 Big picture, if you have younger kids, 00:00:52.410 --> 00:00:54.480 if you're a parent and you have younger kids at home, 00:00:54.480 --> 00:00:56.650 early elementary or even Pre-K, 00:00:56.650 --> 00:00:59.330 I think the key is to focus on the basics, 00:00:59.330 --> 00:01:02.000 even if students are able to put in a solid 00:01:02.000 --> 00:01:03.930 two hours of learning per day, 00:01:03.930 --> 00:01:06.180 that will at least keep them on track. 00:01:06.180 --> 00:01:09.230 I would focus on reading. 00:01:09.230 --> 00:01:11.410 So that could be, if they aren't able 00:01:11.410 --> 00:01:13.750 to read on their own yet, reading with them. 00:01:13.750 --> 00:01:15.960 We're going to be sending out reading lists, 00:01:15.960 --> 00:01:18.580 different activities you could with your students, 00:01:18.580 --> 00:01:20.490 and some form of mathematics. 00:01:20.490 --> 00:01:23.780 We have Khan Academy Kids free app, 00:01:23.780 --> 00:01:26.080 non-commercial, anyone can download it. 00:01:26.080 --> 00:01:28.460 And that has over a hundred books available 00:01:28.460 --> 00:01:30.140 that you could read with your child. 00:01:30.140 --> 00:01:32.110 It will also read to your child. 00:01:32.110 --> 00:01:35.810 We think the best use case of Khan Academy Kids is maybe 00:01:35.810 --> 00:01:37.860 in sessions of about 20 minutes. 00:01:37.860 --> 00:01:40.440 Ideally, with your child next to an adult, 00:01:40.440 --> 00:01:42.000 you or an older sibling. 00:01:42.000 --> 00:01:44.330 And that covers not just Pre-K 00:01:44.330 --> 00:01:45.990 through 1st grade standards math, 00:01:45.990 --> 00:01:48.090 but it also covers reading, writing 00:01:48.090 --> 00:01:50.320 and social emotional learning. 00:01:50.320 --> 00:01:52.270 On top of that, if your student has time 00:01:52.270 --> 00:01:54.680 to do some handwriting practice, we think that is great. 00:01:54.680 --> 00:01:55.900 Or some type of journaling 00:01:55.900 --> 00:01:57.770 if they are already at that level. 00:01:57.770 --> 00:02:01.300 As we get into later elementary, middle school, 00:02:01.300 --> 00:02:03.970 Khan Academy Math, we think can be really valuable for them, 00:02:03.970 --> 00:02:05.330 help them stay on track. 00:02:05.330 --> 00:02:06.980 You can start them at their grade level. 00:02:06.980 --> 00:02:08.810 We're often times seeing a lot of success 00:02:08.810 --> 00:02:10.750 if kids start well before grade level, 00:02:10.750 --> 00:02:13.380 and then are able to master their way 00:02:13.380 --> 00:02:15.080 all the way through grade level. 00:02:15.080 --> 00:02:17.350 I would recommend also for the older elementary 00:02:17.350 --> 00:02:18.530 and the middle school students to have 00:02:18.530 --> 00:02:21.510 at least an hour day of reading that could be broken up 00:02:21.510 --> 00:02:24.480 into two 30 minute sessions if needed. 00:02:24.480 --> 00:02:25.730 Once again, we're gonna try to provide 00:02:25.730 --> 00:02:27.780 some reading lists and things like that. 00:02:27.780 --> 00:02:29.770 As you get into middle school, early high school 00:02:29.770 --> 00:02:33.580 and high school, we have even more resources for students 00:02:33.580 --> 00:02:34.910 on top of what I just talked about, 00:02:34.910 --> 00:02:36.358 about the mathematics, which we have, 00:02:36.358 --> 00:02:40.210 it goes from Pre-K all the way through early college. 00:02:40.210 --> 00:02:43.340 We can help those students with enrichment. 00:02:43.340 --> 00:02:44.760 Things like computer programming. 00:02:44.760 --> 00:02:47.140 We'll also provide reading lists for them. 00:02:47.140 --> 00:02:50.390 Also, in the sciences, I think students as early 00:02:50.390 --> 00:02:53.340 as middle school and definitely in high school. 00:02:53.340 --> 00:02:56.030 Obviously, biology is of interest today. 00:02:56.030 --> 00:02:58.490 Glass half-full, that could be a learning opportunity. 00:02:58.490 --> 00:03:00.920 Learn about viruses, learning how disease spread. 00:03:00.920 --> 00:03:02.750 Learn about exponential growth. 00:03:02.750 --> 00:03:04.370 I think a lot of students at the middle school 00:03:04.370 --> 00:03:06.400 and high school level could begin to engage 00:03:06.400 --> 00:03:08.560 in our high school level biology, 00:03:08.560 --> 00:03:10.980 or even some of our high school level chemistry. 00:03:10.980 --> 00:03:14.200 As you get into the core of high school, 00:03:14.200 --> 00:03:15.630 above and beyond those things, 00:03:15.630 --> 00:03:17.810 we have high school level physics. 00:03:17.810 --> 00:03:20.630 We have economics, macro/micro economics, 00:03:20.630 --> 00:03:23.860 American history, civics and government 00:03:23.860 --> 00:03:26.430 at both the high school and the advanced placement, 00:03:26.430 --> 00:03:27.790 early college level. 00:03:27.790 --> 00:03:29.960 And on top that we have official SAT practice. 00:03:29.960 --> 00:03:33.178 So if you're an older student, I would recommend 00:03:33.178 --> 00:03:34.900 you could structure your day even longer. 00:03:34.900 --> 00:03:36.730 We're gonna be giving out some schedules 00:03:36.730 --> 00:03:39.700 that you could work from, so that you can stay on track, 00:03:39.700 --> 00:03:41.700 to be prepared, to get college ready, 00:03:41.700 --> 00:03:45.000 and make sure that you don't have any lost learning. 00:03:45.000 --> 00:03:47.465 So we'll be setting out more details, 00:03:47.465 --> 00:03:51.010 more videos, more information, as we learn more. 00:03:51.010 --> 00:03:53.900 But we are doing everything we can to make sure 00:03:53.900 --> 00:03:55.410 that we can have you covered. 00:03:55.410 --> 00:03:57.520 It's our duty as a not-for-profit with a mission 00:03:57.520 --> 00:04:00.160 of free, world class education for anyone anywhere 00:04:00.160 --> 00:04:03.973 to support you in this very challenging time.

Estimating actual COVID 19 cases (novel corona virus infections) in an area based on deaths

https://www.youtube.com/watch?v=mCa0JXEwDEk

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WEBVTT Kind: captions Language: en 00:00:00.200 --> 00:00:01.080 - [Narrator] The goal of this video 00:00:01.080 --> 00:00:02.740 is to help us all estimate 00:00:02.740 --> 00:00:07.740 the actual new COVID-19 cases per day in your area. 00:00:09.212 --> 00:00:11.750 And it's based on analysis by Thomas Pueyo, 00:00:11.750 --> 00:00:14.400 he wrote an incredible blog post on Medium. 00:00:14.400 --> 00:00:16.040 This is the link and I'll also include it 00:00:16.040 --> 00:00:17.300 in the description below. 00:00:17.300 --> 00:00:21.130 This is the data that he uses to do some of his analysis. 00:00:21.130 --> 00:00:22.840 Now, some of you might be thinking, 00:00:22.840 --> 00:00:25.460 I know the number of COVID cases in my area, 00:00:25.460 --> 00:00:27.630 they're reporting it on the news every day. 00:00:27.630 --> 00:00:29.450 But that's the reported number of cases 00:00:29.450 --> 00:00:31.080 and that's based on the people 00:00:31.080 --> 00:00:32.730 that happened to get the test. 00:00:32.730 --> 00:00:35.470 There are a lot of people who might not have symptoms yet 00:00:35.470 --> 00:00:38.880 or their symptoms are not severe enough to get the test yet. 00:00:38.880 --> 00:00:41.780 So the actual cases are likely far larger 00:00:41.780 --> 00:00:43.770 than the number of confirmed cases. 00:00:43.770 --> 00:00:46.040 And we can see that in graphical form. 00:00:46.040 --> 00:00:50.030 Once again, this is a diagram put together by Thomas Pueyo. 00:00:50.030 --> 00:00:52.120 It's a screenshot from his blog post 00:00:52.120 --> 00:00:53.590 which once again could be found here. 00:00:53.590 --> 00:00:57.140 This is all his analysis, or based off of his analysis, 00:00:57.140 --> 00:00:59.850 but this shows you what was happening in Hubei Province, 00:00:59.850 --> 00:01:02.360 which is the province where Wuhan is. 00:01:02.360 --> 00:01:05.130 And there's several interesting things here. 00:01:05.130 --> 00:01:07.774 The vertical axis is the number of cases 00:01:07.774 --> 00:01:12.110 and what we see on the horizontal axis is per day. 00:01:12.110 --> 00:01:15.126 And so for example, we could pick January 23. 00:01:15.126 --> 00:01:20.126 The yellow bar tells us the number of confirmed new cases 00:01:20.740 --> 00:01:21.940 that day. 00:01:21.940 --> 00:01:24.300 So these are people who would have been tested 00:01:24.300 --> 00:01:25.700 and then they tested positive, 00:01:25.700 --> 00:01:28.197 and it looks like that number is about 300. 00:01:29.070 --> 00:01:30.960 But then we have this gray bar. 00:01:30.960 --> 00:01:34.750 This gray bar is the actual number of new cases that day, 00:01:34.750 --> 00:01:37.680 which is close to 2,500. 00:01:37.680 --> 00:01:40.430 So roughly eight times as high. 00:01:40.430 --> 00:01:41.700 Now you might be saying, 00:01:41.700 --> 00:01:44.400 how did they know the actual number of cases 00:01:44.400 --> 00:01:46.660 if they didn't test everyone? 00:01:46.660 --> 00:01:47.980 Well, the way they did that is 00:01:47.980 --> 00:01:51.250 when someone tested positive, they asked them, 00:01:51.250 --> 00:01:53.410 when did you first get the symptoms? 00:01:53.410 --> 00:01:57.300 And if they said, Hey, I first got the symptoms 10 days ago, 00:01:57.300 --> 00:01:59.990 they would be included as a true new case. 00:01:59.990 --> 00:02:04.690 An actual new case 10 days before that on January 13, 00:02:04.690 --> 00:02:07.084 so that Chinese officials were able 00:02:07.084 --> 00:02:09.520 to actually make these gray bars in hindsight, 00:02:09.520 --> 00:02:13.110 based on when people said they first got the symptoms. 00:02:13.110 --> 00:02:16.570 And there's a lot of really interesting information here. 00:02:16.570 --> 00:02:19.260 First of all, we can see that Wuhan 00:02:19.260 --> 00:02:22.020 was shut down on January 23. 00:02:22.020 --> 00:02:24.640 So let's draw a line between the pre shut down 00:02:24.640 --> 00:02:26.310 and post shut down. 00:02:26.310 --> 00:02:27.900 And you can see just as the city officials 00:02:27.900 --> 00:02:29.780 were starting to see confirmed cases, 00:02:29.780 --> 00:02:32.720 the actual cases were far higher, 00:02:32.720 --> 00:02:35.120 but then they shut down the city 00:02:35.120 --> 00:02:38.090 essentially significantly slowing down the spread rate. 00:02:38.090 --> 00:02:41.220 And a few days later, the actual cases 00:02:41.220 --> 00:02:43.560 which were they were able to calculate in hindsight, 00:02:43.560 --> 00:02:46.060 start to flatten out and then go down. 00:02:46.060 --> 00:02:47.740 But even though they were going down, 00:02:47.740 --> 00:02:50.660 the confirmed new cases continued to go up 00:02:50.660 --> 00:02:52.490 because there is a delay. 00:02:52.490 --> 00:02:54.810 You can even see the delay right over here. 00:02:54.810 --> 00:02:56.560 And that is roughly the amount of time 00:02:56.560 --> 00:02:58.790 between when people show symptoms 00:02:58.790 --> 00:03:00.690 and they are actually tested. 00:03:00.690 --> 00:03:03.190 Now you might be saying, all right, this isn't too bad. 00:03:03.190 --> 00:03:06.410 It looks like things eventually became okay for Wuhan. 00:03:06.410 --> 00:03:09.710 But this is because they did a very serious shut down. 00:03:09.710 --> 00:03:11.820 If they did not do this shut down 00:03:11.820 --> 00:03:13.440 and slow the spread of the virus, 00:03:13.440 --> 00:03:16.625 you would have seen this exponential growth continue. 00:03:16.625 --> 00:03:19.710 It's also worth remembering what I just drew this curve on. 00:03:19.710 --> 00:03:21.700 This isn't the total number of cases. 00:03:21.700 --> 00:03:24.910 This is the number of new cases per day. 00:03:24.910 --> 00:03:26.880 If you want the total number of cases 00:03:26.880 --> 00:03:28.690 at a given point in time, 00:03:28.690 --> 00:03:32.140 you would have to sum up the gray or the yellow bars 00:03:32.140 --> 00:03:34.149 depending on whether you want to look 00:03:34.149 --> 00:03:35.460 at actual or confirmed cases. 00:03:35.460 --> 00:03:38.300 So as of January 22, if you total up 00:03:38.300 --> 00:03:42.982 all of these gray bars over here, as of January 22, 00:03:42.982 --> 00:03:47.420 you get approximately 12,000 cases, 00:03:47.420 --> 00:03:49.344 while if you add up all of the yellow bars, 00:03:49.344 --> 00:03:54.344 that is roughly only 444 confirmed cases. 00:03:54.800 --> 00:03:57.700 So before the city even went into shutdown, 00:03:57.700 --> 00:04:00.870 and this is what the Chinese doing reasonably good testing, 00:04:00.870 --> 00:04:03.121 you had a far higher number of cases 00:04:03.121 --> 00:04:06.280 than the confirmed cases would make you believe. 00:04:06.280 --> 00:04:08.170 And as large as the ratio is on a given day 00:04:08.170 --> 00:04:10.140 before the city shut down, 00:04:10.140 --> 00:04:13.170 between the number of actual new cases per day 00:04:13.170 --> 00:04:15.840 and the number of confirmed new cases per day, 00:04:15.840 --> 00:04:17.130 it's probably higher 00:04:17.130 --> 00:04:19.810 in a lot of the geographies where we live, 00:04:19.810 --> 00:04:22.690 because we're not testing as well as the Chinese did. 00:04:22.690 --> 00:04:24.410 For example. 00:04:24.410 --> 00:04:27.630 This is data once again compiled by Thomas Pueyo 00:04:27.630 --> 00:04:28.500 on his blog post. 00:04:28.500 --> 00:04:29.970 This is just a screen capture of it 00:04:29.970 --> 00:04:32.270 and I'm really just giving his analysis. 00:04:32.270 --> 00:04:34.550 This shows the total test performed, 00:04:34.550 --> 00:04:39.460 and the tests performed per million citizens as of March 3, 00:04:39.460 --> 00:04:41.160 and you can see for example, 00:04:41.160 --> 00:04:45.060 where I live the United States is not doing so well. 00:04:45.060 --> 00:04:47.450 And so the number of reported cases 00:04:47.450 --> 00:04:48.880 in places like the United States 00:04:48.880 --> 00:04:52.281 where we are really just starting to ramp up testing 00:04:52.281 --> 00:04:57.281 is far understating the number of actual cases out there. 00:04:58.250 --> 00:04:59.530 So how do we go about estimating 00:04:59.530 --> 00:05:02.980 the actual number of cases in our area? 00:05:02.980 --> 00:05:06.170 Well, once again, I'm going to use Thomas's analysis, 00:05:06.170 --> 00:05:08.360 we're gonna be looking at the number of deaths 00:05:08.360 --> 00:05:10.530 and estimations of mortality rate, 00:05:10.530 --> 00:05:12.200 time from infection to death, 00:05:12.200 --> 00:05:15.300 and how fast the virus actually spreads. 00:05:15.300 --> 00:05:17.300 So in other videos, I'll talk more about 00:05:17.300 --> 00:05:19.000 some of Thomas's analysis. 00:05:19.000 --> 00:05:21.870 But for mortality rate, it'll make the math simple. 00:05:21.870 --> 00:05:24.870 And this actually does seem to be a pretty good estimate, 00:05:24.870 --> 00:05:27.680 we can assume that there's a 1% mortality rate, 00:05:27.680 --> 00:05:30.460 the reports are as low as point 0.6% in South Korea, 00:05:30.460 --> 00:05:34.010 and then as high as roughly 5% in places like Iran. 00:05:34.010 --> 00:05:35.310 But it looks like the higher numbers 00:05:35.310 --> 00:05:38.490 are where the hospital system is being overwhelmed. 00:05:38.490 --> 00:05:41.460 And then the lower numbers at the 0.6%, 00:05:41.460 --> 00:05:44.180 might not be fully accounting for all of the mortality 00:05:44.180 --> 00:05:46.130 that will happen due to the cases 00:05:46.130 --> 00:05:47.580 that are actually out there. 00:05:47.580 --> 00:05:50.870 So we'll assume a mortality rate of 1%. 00:05:50.870 --> 00:05:52.410 The other thing we need to think about 00:05:52.410 --> 00:05:57.410 is the time from infection to death in those 1% of cases 00:05:59.970 --> 00:06:01.610 where someone does die. 00:06:01.610 --> 00:06:02.890 And to figure that out, 00:06:02.890 --> 00:06:05.510 I will look at this data right over here. 00:06:05.510 --> 00:06:08.030 This top chart, and it comes from this link, 00:06:08.030 --> 00:06:09.260 which Thomas cites. 00:06:09.260 --> 00:06:11.520 And I'll give the link in the description below. 00:06:11.520 --> 00:06:13.050 This is the incubation period. 00:06:13.050 --> 00:06:14.930 This is an estimate of the time 00:06:14.930 --> 00:06:16.600 from when someone gets infected 00:06:16.600 --> 00:06:18.450 to when they start to show symptoms. 00:06:18.450 --> 00:06:20.750 And this estimate is roughly five days. 00:06:20.750 --> 00:06:22.730 And then once you see symptoms, 00:06:22.730 --> 00:06:25.660 how long does it take to death in those 1% of cases, 00:06:25.660 --> 00:06:27.520 or whatever the percentage is? 00:06:27.520 --> 00:06:29.300 Well, there's varying estimates, 00:06:29.300 --> 00:06:31.850 but it looks like to make the numbers easy, 00:06:31.850 --> 00:06:34.920 we can estimate roughly 15 days. 00:06:34.920 --> 00:06:36.070 So one way to think about it 00:06:36.070 --> 00:06:39.320 is five days from infection to showing the symptoms, 00:06:39.320 --> 00:06:43.170 and then another 15 days from showing the symptoms to death 00:06:43.170 --> 00:06:48.100 for a total of 20 days from infection to death, 00:06:48.100 --> 00:06:51.790 in what we're assuming the 1% of cases. 00:06:51.790 --> 00:06:54.530 So I'll write 20 days. 00:06:54.530 --> 00:06:56.210 And now the other thing we're gonna estimate 00:06:56.210 --> 00:06:58.980 is the days to doubling, 00:06:58.980 --> 00:07:00.940 days to double. 00:07:00.940 --> 00:07:03.370 This is how long does it take for the infection 00:07:03.370 --> 00:07:04.960 to double in the population. 00:07:04.960 --> 00:07:06.620 And this is gonna be heavily dependent 00:07:06.620 --> 00:07:08.140 on what the population is doing, 00:07:08.140 --> 00:07:10.570 how dense they are, how much they're interacting. 00:07:10.570 --> 00:07:12.600 But we'll look at some of these estimates. 00:07:12.600 --> 00:07:14.760 And they're in very different contexts. 00:07:14.760 --> 00:07:16.520 And the lower the doubling rate, 00:07:16.520 --> 00:07:18.980 that means a virus is spreading very fast. 00:07:18.980 --> 00:07:20.100 While if you have a population 00:07:20.100 --> 00:07:21.400 that's doing all the right things, 00:07:21.400 --> 00:07:22.790 they're taking all the precaution, 00:07:22.790 --> 00:07:24.840 the doubling rate will be lower. 00:07:24.840 --> 00:07:26.590 So we could look at a conservative estimate 00:07:26.590 --> 00:07:28.990 and take a higher doubling rate than all of these estimates, 00:07:28.990 --> 00:07:30.670 it'll make our math a little bit easier. 00:07:30.670 --> 00:07:32.960 Let's just assume a doubling rate of five days 00:07:32.960 --> 00:07:35.930 and I'm using slightly different numbers than Thomas used, 00:07:35.930 --> 00:07:37.220 but it will be indicative 00:07:37.220 --> 00:07:39.020 and you can do the same analysis 00:07:39.020 --> 00:07:41.650 with whatever estimates that you choose to do. 00:07:41.650 --> 00:07:44.850 So let's assume five days to double, 00:07:44.850 --> 00:07:46.070 which might be conservative, 00:07:46.070 --> 00:07:47.870 especially for places like the United States 00:07:47.870 --> 00:07:50.490 where we have not taken anywhere near the action 00:07:50.490 --> 00:07:54.340 of a place like China or South Korea, or Japan. 00:07:54.340 --> 00:07:56.240 So now let's use these numbers 00:07:56.240 --> 00:07:59.770 to figure out what might actually be happening in our areas 00:07:59.770 --> 00:08:02.460 based on the data that we are presented with. 00:08:02.460 --> 00:08:06.094 So let's say that we unfortunately here on some day, 00:08:06.094 --> 00:08:11.094 that there is one death in our region or in our city. 00:08:11.630 --> 00:08:12.740 Now, based on our estimates, 00:08:12.740 --> 00:08:15.130 we're saying that the average time from infection to death 00:08:15.130 --> 00:08:16.660 is about 20 days. 00:08:16.660 --> 00:08:18.350 That means that that person 00:08:18.350 --> 00:08:23.070 would have likely contracted the virus roughly 20 days ago, 00:08:23.070 --> 00:08:26.220 20 days ago. 00:08:26.220 --> 00:08:27.610 And so I'm gonna make a timeline. 00:08:27.610 --> 00:08:32.270 This is 20 days ago, this would be 10 days ago, 00:08:32.270 --> 00:08:36.770 10 days ago, this would be 15 days ago, 00:08:36.770 --> 00:08:39.380 and then this would be five days ago. 00:08:39.380 --> 00:08:41.800 Now it's possible that they were the only person 00:08:41.800 --> 00:08:44.220 who contracted the virus on that day, 00:08:44.220 --> 00:08:48.080 and then they happen to unfortunately get very sick 00:08:48.080 --> 00:08:50.920 and then pass away 20 days later. 00:08:50.920 --> 00:08:54.100 But if we assume that the mortality rate is roughly correct, 00:08:54.100 --> 00:08:57.380 it's quite possible that 100 people were infected that day. 00:08:57.380 --> 00:08:59.960 The person that we know about is that one in 100 00:08:59.960 --> 00:09:02.850 who actually gets sick enough to pass away. 00:09:02.850 --> 00:09:05.840 And so if we assume that on 20 days ago 00:09:05.840 --> 00:09:09.040 that not one person, but 100 people. 00:09:09.040 --> 00:09:12.290 So the actual number of people who are infected that day 00:09:12.290 --> 00:09:16.050 is 100 infected that day. 00:09:16.050 --> 00:09:18.840 Once again, because it's a 1% mortality rate. 00:09:18.840 --> 00:09:21.640 If we assumed a 0.5% mortality rate, 00:09:21.640 --> 00:09:22.690 then we would say, all right, 00:09:22.690 --> 00:09:25.849 there might have been 200 people infected that day, 00:09:25.849 --> 00:09:29.460 0.5% of whom get all the way to death 20 days later. 00:09:29.460 --> 00:09:31.890 If you assume a 5% mortality rate, 00:09:31.890 --> 00:09:33.920 which would be a very unfortunate situation, 00:09:33.920 --> 00:09:35.690 but that is a mortality rate that we are seeing 00:09:35.690 --> 00:09:37.250 in different parts of the world, 00:09:37.250 --> 00:09:38.760 then you would have say, 00:09:38.760 --> 00:09:41.210 well, maybe there were 20 people infected that day. 00:09:41.210 --> 00:09:44.420 When you only have one or two or three deaths in a region 00:09:44.420 --> 00:09:47.070 that will make the estimates more difficult. 00:09:47.070 --> 00:09:48.330 But as unfortunately, 00:09:48.330 --> 00:09:50.790 we are likely to see a larger number of deaths 00:09:50.790 --> 00:09:52.260 in various regions 00:09:52.260 --> 00:09:54.860 that will make this these backward estimates 00:09:54.860 --> 00:09:57.230 more and more reasonable. 00:09:57.230 --> 00:10:00.070 Now if the infection rate in the population doubles 00:10:00.070 --> 00:10:03.440 every five days, what is now going to happen? 00:10:03.440 --> 00:10:06.803 After five days, you're going to have 200 cases 00:10:08.173 --> 00:10:12.280 in your region, 200 cases. 00:10:12.280 --> 00:10:14.030 Now, these wouldn't just be new cases, 00:10:14.030 --> 00:10:17.100 this would be the cumulative total number of cases 00:10:17.100 --> 00:10:18.670 due to those hundred. 00:10:18.670 --> 00:10:21.230 Now, this is actually quite conservative, 00:10:21.230 --> 00:10:23.440 because this is assuming that those 100 00:10:23.440 --> 00:10:25.110 that were infected 20 days ago 00:10:25.110 --> 00:10:27.820 are the only infected cases in your region. 00:10:27.820 --> 00:10:29.720 There might be other infected cases 00:10:29.720 --> 00:10:32.040 that were infected before that date. 00:10:32.040 --> 00:10:33.530 But I'm just assuming that the hundred 00:10:33.530 --> 00:10:36.240 that were infected that day are the only cases 00:10:36.240 --> 00:10:39.430 to be conservative, and so they double after five days, 00:10:39.430 --> 00:10:42.480 and then they'll double again after five more days. 00:10:42.480 --> 00:10:45.540 And so you will get to 400 cases 00:10:47.040 --> 00:10:48.450 after five more days. 00:10:48.450 --> 00:10:51.520 And then you will, after five more days, 00:10:51.520 --> 00:10:53.350 you will have doubled and I can't even fit it 00:10:53.350 --> 00:10:55.060 on the screen anymore. 00:10:55.060 --> 00:10:57.710 You're going to have 800 cases 00:10:57.710 --> 00:11:00.330 and then that means today just by evidence 00:11:00.330 --> 00:11:01.640 of that one death, 00:11:01.640 --> 00:11:04.270 you probably have on the order of 00:11:04.270 --> 00:11:06.590 and I can't even draw the whole bar, 00:11:06.590 --> 00:11:09.900 approximately 1,600 cases. 00:11:09.900 --> 00:11:12.940 And so this is just to be a little bit sobering 00:11:12.940 --> 00:11:14.910 about how serious this is, 00:11:14.910 --> 00:11:17.670 and how much the data that we actually get 00:11:17.670 --> 00:11:20.980 is actually lagging the circumstances on the ground, 00:11:20.980 --> 00:11:23.600 particularly in places like the United States, 00:11:23.600 --> 00:11:26.680 where we are barely even getting started testing. 00:11:26.680 --> 00:11:27.960 For example, in my county, 00:11:27.960 --> 00:11:30.750 which is Santa Clara County in California. 00:11:30.750 --> 00:11:32.110 We just had our second death 00:11:32.110 --> 00:11:33.620 unfortunately reported yesterday 00:11:33.620 --> 00:11:36.390 and there was another death five days before that. 00:11:36.390 --> 00:11:40.740 Now, there's only under 100 reported cases in my county, 00:11:40.740 --> 00:11:42.310 but based on this analysis, 00:11:42.310 --> 00:11:45.470 the actual number of infected persons in my county 00:11:45.470 --> 00:11:48.910 is likely to be at least a factor of 10 more than that, 00:11:48.910 --> 00:11:52.780 and it could be as high as 1,000, 2,000, 3,000 people. 00:11:52.780 --> 00:11:54.030 We won't know for sure 00:11:54.030 --> 00:11:56.180 until we can do the type of hindsight analysis 00:11:56.180 --> 00:11:57.400 that the Chinese had, 00:11:57.400 --> 00:11:59.660 but this is to just remind us how serious 00:11:59.660 --> 00:12:02.160 the situation actually is. 00:12:02.160 --> 00:12:03.560 So the big takeaway here 00:12:03.560 --> 00:12:06.360 is to take all of this very seriously, 00:12:06.360 --> 00:12:09.850 especially because the mortality rate itself can change 00:12:09.850 --> 00:12:11.160 depending on how well equipped 00:12:11.160 --> 00:12:14.140 the hospital system can handle the situation. 00:12:14.140 --> 00:12:17.720 If we all socially isolate and take the proper precaution, 00:12:17.720 --> 00:12:19.460 the spread rate will lower 00:12:19.460 --> 00:12:21.760 and we won't overwhelm the hospital system. 00:12:21.760 --> 00:12:23.890 And we'll hopefully be able to keep the mortality rate 00:12:23.890 --> 00:12:25.580 as low as possible. 00:12:25.580 --> 00:12:28.080 But if we don't take the precaution, 00:12:28.080 --> 00:12:29.240 and if we're just complacent 00:12:29.240 --> 00:12:31.000 because we see this lagging data 00:12:31.000 --> 00:12:33.300 that's being reported to us because of the lack of testing 00:12:33.300 --> 00:12:34.950 in places like the United States, 00:12:34.950 --> 00:12:36.100 then it's very possible 00:12:36.100 --> 00:12:39.110 that we eventually overwhelm the hospital system 00:12:39.110 --> 00:12:40.540 in the next few weeks, 00:12:40.540 --> 00:12:43.223 which would cause the mortality rate to go higher.

Policy and the branches of government

https://www.youtube.com/watch?v=F6ZhV09DgMA

vtt

https://www.youtube.com/api/timedtext?v=F6ZhV09DgMA&ei=bViUZYS3GY-zvdIP_qmJ6A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B14E2BF67DEC5F63D3F55CA20B2B63D81B796723.A3AAAFF4F4E014479D37472C9E926B9FC3A48121&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.230 --> 00:00:02.280 - [Instructor] As we've discussed in other videos, 00:00:02.280 --> 00:00:05.670 the federal bureaucracy is a huge part of the US government, 00:00:05.670 --> 00:00:08.010 sometimes even called the fourth branch. 00:00:08.010 --> 00:00:10.820 It has more than two million employees 00:00:10.820 --> 00:00:12.360 who work in various agencies 00:00:12.360 --> 00:00:14.610 dedicated to implementing the law. 00:00:14.610 --> 00:00:17.430 So the bureaucracy has a lot of discretion 00:00:17.430 --> 00:00:21.010 to decide how best to achieve a policy goal. 00:00:21.010 --> 00:00:23.650 But the sheer size of the bureaucracy, 00:00:23.650 --> 00:00:25.300 along with its independence, 00:00:25.300 --> 00:00:27.870 can make it difficult to monitor. 00:00:27.870 --> 00:00:30.470 What happens when a bureaucratic agency 00:00:30.470 --> 00:00:32.400 fails to carry out its mission, 00:00:32.400 --> 00:00:36.610 or deviates from the letter or the intent of a law? 00:00:36.610 --> 00:00:39.440 What can the other branches do to keep it accountable? 00:00:39.440 --> 00:00:43.380 Let's use a real example to make things a bit more concrete. 00:00:43.380 --> 00:00:47.280 In 2014, a whistleblower came forward, reporting that 00:00:47.280 --> 00:00:50.040 a hospital in the Department of Veterans Affairs 00:00:50.040 --> 00:00:52.420 was deceiving federal regulators 00:00:52.420 --> 00:00:56.610 about how long veterans were waiting to receive healthcare. 00:00:56.610 --> 00:01:00.150 Because officials at the VA got pay bonuses 00:01:00.150 --> 00:01:02.210 based on ensuring that patients 00:01:02.210 --> 00:01:04.800 had short wait times for medical care, 00:01:04.800 --> 00:01:07.330 they were falsifying electronic records 00:01:07.330 --> 00:01:10.950 to keep wait times within those acceptable guidelines. 00:01:10.950 --> 00:01:14.320 In reality though, the average wait time for medical care 00:01:14.320 --> 00:01:18.740 was greater than 100 days, and dozens of veterans died 00:01:18.740 --> 00:01:20.920 while waiting for delayed appointments. 00:01:20.920 --> 00:01:23.200 Now, this is a pretty complex story, 00:01:23.200 --> 00:01:25.220 so I'm just giving you the broad strokes here. 00:01:25.220 --> 00:01:28.050 But for our purposes, what you need to know is 00:01:28.050 --> 00:01:31.610 this was a case of very serious mismanagement 00:01:31.610 --> 00:01:33.480 in a bureaucratic agency. 00:01:33.480 --> 00:01:35.230 So now, let's think about 00:01:35.230 --> 00:01:38.160 what the other branches of government could do, 00:01:38.160 --> 00:01:41.280 using their formal and informal powers, 00:01:41.280 --> 00:01:43.340 in response to this situation. 00:01:43.340 --> 00:01:46.220 I encourage you to pause the video here, 00:01:46.220 --> 00:01:49.200 and see if you can list at least one action 00:01:49.200 --> 00:01:51.650 that the executive branch, Congress, 00:01:51.650 --> 00:01:53.810 or the judicial branch could take. 00:01:53.810 --> 00:01:55.430 Ready, go. 00:01:55.430 --> 00:01:57.910 Okay, so let's go through some of the actions 00:01:57.910 --> 00:01:59.670 that the other branches did take 00:01:59.670 --> 00:02:01.440 in response to the VA scandal, 00:02:01.440 --> 00:02:04.340 and you can check to see if you came up with any of them. 00:02:04.340 --> 00:02:06.670 So what steps did the executive take? 00:02:06.670 --> 00:02:08.940 Remember that the bureaucracy itself 00:02:08.940 --> 00:02:10.790 is under the executive branch. 00:02:10.790 --> 00:02:14.070 So first, we saw internal investigations 00:02:14.070 --> 00:02:17.920 from the Secretary of Veterans Affairs, Eric Shinseki. 00:02:17.920 --> 00:02:20.770 The VA used its rulemaking authority 00:02:20.770 --> 00:02:24.060 to abandon the unrealistic wait time goal 00:02:24.060 --> 00:02:27.190 in order to remove that perverse incentive. 00:02:27.190 --> 00:02:29.990 It was within the power of Barack Obama, 00:02:29.990 --> 00:02:32.000 who was president at the time, 00:02:32.000 --> 00:02:34.200 to fire the cabinet secretary, 00:02:34.200 --> 00:02:36.980 but instead, Shinseki resigned. 00:02:36.980 --> 00:02:39.590 Then the president used his nomination power 00:02:39.590 --> 00:02:43.490 to replace him with a new VA secretary, Bob McDonald. 00:02:43.490 --> 00:02:47.670 Obama also introduced a number of executive actions 00:02:47.670 --> 00:02:49.090 to address the problem, 00:02:49.090 --> 00:02:51.290 including establishing an independent 00:02:51.290 --> 00:02:53.130 accountability review board, 00:02:53.130 --> 00:02:56.050 a board of physicians to advise the secretary, 00:02:56.050 --> 00:02:59.310 a plan to upgrade the electronic health record system, 00:02:59.310 --> 00:03:02.033 and protections for whistleblowers. 00:03:04.060 --> 00:03:06.210 What steps did Congress take? 00:03:06.210 --> 00:03:11.210 First, Congress used its oversight power to call hearings, 00:03:11.210 --> 00:03:13.700 investigating what was going on at the VA. 00:03:13.700 --> 00:03:16.690 They subpoenaed Secretary Shinseki to testify. 00:03:16.690 --> 00:03:19.420 They also passed reform measures, 00:03:19.420 --> 00:03:23.150 using their lawmaking powers and the power of the purse 00:03:23.150 --> 00:03:25.730 to fix the larger problems at the VA, 00:03:25.730 --> 00:03:30.730 funding a $16 billion plan to hire more doctors and nurses, 00:03:31.200 --> 00:03:34.020 upgrade facilities, and allow veterans 00:03:34.020 --> 00:03:36.380 to see private doctors if necessary. 00:03:36.380 --> 00:03:38.090 And as part of this reform, 00:03:38.090 --> 00:03:40.890 Congress included legislation that made it easier 00:03:40.890 --> 00:03:44.460 to hold VA officials accountable for misconduct. 00:03:44.460 --> 00:03:46.290 Congress also used its power 00:03:46.290 --> 00:03:48.810 to approve presidential nominations 00:03:48.810 --> 00:03:51.483 by confirming the new VA secretary. 00:03:52.800 --> 00:03:54.950 The judicial branch, for its part, 00:03:54.950 --> 00:03:57.880 reviewed the constitutionality of the new rules 00:03:57.880 --> 00:04:00.160 holding VA employees accountable. 00:04:00.160 --> 00:04:02.240 The federal court system heard a case 00:04:02.240 --> 00:04:04.190 about whether it was constitutional 00:04:04.190 --> 00:04:07.090 to fire civil servants who weren't appointed, 00:04:07.090 --> 00:04:09.070 without giving them a chance to appeal. 00:04:09.070 --> 00:04:11.640 The courts ruled that that was unconstitutional, 00:04:11.640 --> 00:04:15.170 so in 2017, Congress passed a new bill, 00:04:15.170 --> 00:04:17.640 adding a grievance process for civil servants, 00:04:17.640 --> 00:04:19.963 which President Trump then signed into law. 00:04:20.840 --> 00:04:24.490 So it's been a few years since the VA scandal, 00:04:24.490 --> 00:04:25.970 so how are things doing? 00:04:25.970 --> 00:04:28.030 Did the reform measures work? 00:04:28.030 --> 00:04:30.890 In 2015, The New York Times reported 00:04:30.890 --> 00:04:33.620 that only three people had been fired 00:04:33.620 --> 00:04:35.320 as a response to the scandal, 00:04:35.320 --> 00:04:37.700 despite Bob McDonald's public statements 00:04:37.700 --> 00:04:40.150 that 60 employees had been fired. 00:04:40.150 --> 00:04:44.060 In 2019, Debra Draper, the healthcare director 00:04:44.060 --> 00:04:46.090 at the Government Accountability Office, 00:04:46.090 --> 00:04:48.300 told the House Veterans Affairs Committee 00:04:48.300 --> 00:04:50.870 that although the VA had made progress 00:04:50.870 --> 00:04:52.570 in wait times and scheduling, 00:04:52.570 --> 00:04:54.260 there was still room for improvement. 00:04:54.260 --> 00:04:56.300 She said that the VA's new system 00:04:56.300 --> 00:04:59.580 was still not accurately recording patient wait times, 00:04:59.580 --> 00:05:01.170 and that veterans might still wait 00:05:01.170 --> 00:05:03.750 up to 70 days for an appointment, 00:05:03.750 --> 00:05:07.580 even though the VA was reporting a much shorter delay. 00:05:07.580 --> 00:05:10.030 On the positive side, the VA completed 00:05:10.030 --> 00:05:12.310 one million more appointments for veterans 00:05:12.310 --> 00:05:15.590 in 2018 than in 2017, showing that 00:05:15.590 --> 00:05:19.570 access to care for veterans had definitely improved. 00:05:19.570 --> 00:05:20.750 So what do you think? 00:05:20.750 --> 00:05:22.200 Were the other branches of government 00:05:22.200 --> 00:05:24.380 able to hold the VA accountable? 00:05:24.380 --> 00:05:26.100 If you had to solve this problem, 00:05:26.100 --> 00:05:29.920 either as a member of Congress, a judge, or the president, 00:05:29.920 --> 00:05:31.553 what other steps could you take?

Ideology and policymaking

https://www.youtube.com/watch?v=6Zzcd90Cqag

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https://www.youtube.com/api/timedtext?v=6Zzcd90Cqag&ei=bViUZYy_Huu4mLAPtuOK8AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7D9A01A1C857161EBB20A92AC6A817ADDC7454B7.20CF67A7648DBA7BFC522E23D9D5A053A54F9A71&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.140 --> 00:00:02.070 - [Instructor] Let's take a look at this chart, 00:00:02.070 --> 00:00:06.070 based on survey data from the Pew Research Center. 00:00:06.070 --> 00:00:09.410 Researchers asked U.S. adults in early 2020 00:00:09.410 --> 00:00:12.810 which issues they think should be top priorities 00:00:12.810 --> 00:00:14.580 for the President and Congress. 00:00:14.580 --> 00:00:19.580 The top two issues were the economy and the environment. 00:00:19.980 --> 00:00:22.080 Now, as we compare that to other years, 00:00:22.080 --> 00:00:24.180 you can see that these two policy issues 00:00:24.180 --> 00:00:26.610 haven't always been top of mind, 00:00:26.610 --> 00:00:30.350 although the economy has ranked 1st since 2002. 00:00:30.350 --> 00:00:33.000 Until recently, jobs were second. 00:00:33.000 --> 00:00:36.910 The environment was last place for several years, 00:00:36.910 --> 00:00:41.410 and climate change didn't even make the list until 2015. 00:00:41.410 --> 00:00:43.119 So what's going on here? 00:00:43.119 --> 00:00:46.780 Questions like these help political scientists 00:00:46.780 --> 00:00:50.620 measure the policy mood of the public, 00:00:50.620 --> 00:00:54.620 people's preferences toward policy choices. 00:00:54.620 --> 00:00:58.450 As you can see, policy mood changes over time, 00:00:58.450 --> 00:01:01.830 in response to problems and issues that arise. 00:01:01.830 --> 00:01:06.830 For example, in 2009, as a response to the economic crash, 00:01:06.860 --> 00:01:09.230 surveyed adults responded that jobs 00:01:09.230 --> 00:01:12.055 should be a top priority, but in 2020, 00:01:12.055 --> 00:01:16.750 after a period of economic recovery and low unemployment, 00:01:16.750 --> 00:01:19.999 jobs had fallen as a main concern and new issues 00:01:19.999 --> 00:01:21.780 had taken its place. 00:01:21.780 --> 00:01:24.360 Climate change has become a major concern 00:01:24.360 --> 00:01:26.596 for many people, which wasn't even a term 00:01:26.596 --> 00:01:29.240 that people knew a few decades ago. 00:01:29.240 --> 00:01:33.550 Conversely, a poll like this taken in 1980, 00:01:33.550 --> 00:01:37.730 might have shown containing Communism as a main concern, 00:01:37.730 --> 00:01:39.610 but since the fall of the Soviet Union, 00:01:39.610 --> 00:01:41.600 that has dropped off the list. 00:01:41.600 --> 00:01:45.233 These measures of policy mood help politicians 00:01:45.233 --> 00:01:49.000 and political parties craft their policy agendas, 00:01:49.000 --> 00:01:52.640 in order to attract voters and serve their constituents. 00:01:52.640 --> 00:01:54.960 But if so many people think that the economy 00:01:54.960 --> 00:01:57.357 should be a major priority, why don't voters 00:01:57.357 --> 00:02:00.170 all just agree on a course of action? 00:02:00.170 --> 00:02:03.210 Here's where ideological differences come into play. 00:02:03.210 --> 00:02:06.850 Political scientists sometimes divide policy issues 00:02:06.850 --> 00:02:11.050 into position issues and valence issues. 00:02:11.050 --> 00:02:15.980 Position issues are issues that divide voters, 00:02:15.980 --> 00:02:20.360 like abortion or gun control, where there isn't much room 00:02:20.360 --> 00:02:22.700 for overlapping opinions. 00:02:22.700 --> 00:02:27.060 Valence issues are issues that most voters will agree with, 00:02:27.060 --> 00:02:30.220 like our communities should be free of crime 00:02:30.220 --> 00:02:32.780 or we should care for the elderly. 00:02:32.780 --> 00:02:37.450 These are high level values that cut across partisan lines, 00:02:37.450 --> 00:02:39.170 but the parties might differ 00:02:39.170 --> 00:02:41.440 on how to achieve those outcomes. 00:02:41.440 --> 00:02:44.820 For example, although both Democrats and Republicans 00:02:44.820 --> 00:02:49.400 might want to reduce drug use, Republicans might argue 00:02:49.400 --> 00:02:53.460 that tougher drug laws are most likely to achieve that goal, 00:02:53.460 --> 00:02:55.886 while Democrats might argue that prevention 00:02:55.886 --> 00:02:59.010 and education programs would be more effective. 00:02:59.010 --> 00:03:01.860 So policy mood tells us what the public thinks 00:03:01.860 --> 00:03:04.300 is most important at any given time, 00:03:04.300 --> 00:03:08.050 but differing ideological beliefs about how best 00:03:08.050 --> 00:03:11.490 to achieve those priorities lead to different approaches 00:03:11.490 --> 00:03:12.963 on the left and the right.

Metallic solids

https://www.youtube.com/watch?v=eJqBMPE1PLw

vtt

https://www.youtube.com/api/timedtext?v=eJqBMPE1PLw&ei=bViUZa_jGdX7vdIP-7yiwAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E44BAA7C3EC097C54DC752B9675F2F307C1299C2.92370E6E61C3593DB8BF885993D4A2E69C6E91F4&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.710 --> 00:00:01.543 - [Instructor] Let's talk a little bit 00:00:01.543 --> 00:00:03.290 about metallic solids. 00:00:03.290 --> 00:00:05.810 And here is an example of what 00:00:05.810 --> 00:00:08.350 a metallic solid might look like. 00:00:08.350 --> 00:00:11.080 They tend to be shiny like this. 00:00:11.080 --> 00:00:12.780 Some would say lustrous. 00:00:12.780 --> 00:00:14.970 Some of you might be guessing maybe this is some type 00:00:14.970 --> 00:00:17.990 of aluminum or silver. 00:00:17.990 --> 00:00:20.280 It actually turns out that this is sodium. 00:00:20.280 --> 00:00:23.760 Our same friend sodium that we saw bonding with chlorine 00:00:23.760 --> 00:00:27.140 to form sodium chloride and form ionic solids, 00:00:27.140 --> 00:00:30.360 it can actually bond with itself with metallic bonds. 00:00:30.360 --> 00:00:31.840 This right over here, 00:00:31.840 --> 00:00:35.330 you might guess is silver or something. 00:00:35.330 --> 00:00:37.830 It actually turns out this is calcium. 00:00:37.830 --> 00:00:38.730 And I know what you're thinking. 00:00:38.730 --> 00:00:41.260 Isn't calcium kind of this chalky white powder? 00:00:41.260 --> 00:00:43.920 Well no, those are compounds formed with calcium, 00:00:43.920 --> 00:00:46.280 things like calcium oxide. 00:00:46.280 --> 00:00:48.240 But this right over here is pure calcium. 00:00:48.240 --> 00:00:50.200 And the reason why it has to be in this container, 00:00:50.200 --> 00:00:52.410 it is highly reactive with oxygen. 00:00:52.410 --> 00:00:54.550 So that's not oxygen that is in this container. 00:00:54.550 --> 00:00:56.680 It's some form of inert gas. 00:00:56.680 --> 00:00:58.730 But calcium when it just bonds to itself 00:00:58.730 --> 00:01:01.630 with metallic bonds, which we'll talk about in a little bit, 00:01:01.630 --> 00:01:03.460 it also looks kind of similar. 00:01:03.460 --> 00:01:08.030 It's this shiny, metallic, or lustrous look to it. 00:01:08.030 --> 00:01:10.260 And what do you think this is? 00:01:10.260 --> 00:01:12.230 Well this is something we're used to associating 00:01:12.230 --> 00:01:14.220 with metals, this is gold. 00:01:14.220 --> 00:01:17.640 But once again, you can see it has this lustrous property. 00:01:17.640 --> 00:01:21.200 So what is it about metals or metallic solids 00:01:21.200 --> 00:01:23.160 that allow them to be lustrous in this way 00:01:23.160 --> 00:01:25.680 and have other properties that we're about to see? 00:01:25.680 --> 00:01:28.210 And to understand that, we just have to look at 00:01:28.210 --> 00:01:31.000 the periodic table of elements. 00:01:31.000 --> 00:01:33.870 And that most of the periodic table of elements 00:01:33.870 --> 00:01:36.310 is actually some form of metal. 00:01:36.310 --> 00:01:39.360 You have in red right over here, this group one elements, 00:01:39.360 --> 00:01:40.760 not including hydrogen. 00:01:40.760 --> 00:01:42.320 Those are your alkali metals, 00:01:42.320 --> 00:01:43.720 and you have your alkaline earth metals, 00:01:43.720 --> 00:01:44.870 your transition metals, 00:01:44.870 --> 00:01:47.610 your post-transition metals, your metalloids. 00:01:47.610 --> 00:01:50.090 It's really only what you see in yellow and blue here 00:01:50.090 --> 00:01:52.550 that are not your metals. 00:01:52.550 --> 00:01:55.950 So how do metals form solids when you just have 00:01:55.950 --> 00:01:57.940 a pure sample of them? 00:01:57.940 --> 00:02:01.470 Well the general idea, you can look at your alkali metals, 00:02:01.470 --> 00:02:03.850 they all have that one valence electron. 00:02:03.850 --> 00:02:05.450 And to get to that stable outer shell, 00:02:05.450 --> 00:02:08.800 it's much easier for them to give away a valence electron. 00:02:08.800 --> 00:02:11.850 And that's why we often see these folks are dissipating 00:02:11.850 --> 00:02:13.050 in ionic bonds. 00:02:13.050 --> 00:02:15.150 They can be ionized quite easily. 00:02:15.150 --> 00:02:17.240 But if you have a pure sample of them, 00:02:17.240 --> 00:02:18.870 they can contribute electrons 00:02:18.870 --> 00:02:21.510 to a sea of electron, one each. 00:02:21.510 --> 00:02:23.250 These alkaline earth metals, 00:02:23.250 --> 00:02:24.910 they have two valence electrons. 00:02:24.910 --> 00:02:27.990 They too can be ionized or if you have a pure sample 00:02:27.990 --> 00:02:31.990 like in a calcium, they can contribute two valence electrons 00:02:31.990 --> 00:02:33.400 to a sea of electrons. 00:02:33.400 --> 00:02:35.760 And the transition metals here have a similar ability 00:02:35.760 --> 00:02:37.960 to contribute valence electrons. 00:02:37.960 --> 00:02:41.450 And so in general, we can view metallic solids 00:02:41.450 --> 00:02:46.130 as having cations, these positively charged cations 00:02:47.720 --> 00:02:50.850 in a sea of electrons. 00:02:50.850 --> 00:02:53.400 So you have all these electrons here. 00:02:53.400 --> 00:02:56.110 I'll just draw all these minus charges that they're in. 00:02:56.110 --> 00:02:58.070 Where do those electrons come from? 00:02:58.070 --> 00:03:00.270 Well if you're looking at the alkali metals, 00:03:00.270 --> 00:03:04.610 each of those atoms could give one electron to that sea 00:03:04.610 --> 00:03:07.060 because it doesn't really want that valence electron. 00:03:07.060 --> 00:03:08.750 If you're talking about alkaline earth metals, 00:03:08.750 --> 00:03:12.050 they could each donate two electrons to that sea. 00:03:12.050 --> 00:03:14.670 Now given that you have this positive charge 00:03:14.670 --> 00:03:16.570 in this sea of electrons, 00:03:16.570 --> 00:03:18.400 what are you think of the properties? 00:03:18.400 --> 00:03:19.470 How good do you think this will be 00:03:19.470 --> 00:03:21.350 at conducting electricity or heat? 00:03:21.350 --> 00:03:23.550 And many of you might guessed, if you looked at a wire, 00:03:23.550 --> 00:03:26.420 wires are made out of metals, because they are excellent 00:03:26.420 --> 00:03:29.180 at conducting electricity, or they tend to be excellent 00:03:29.180 --> 00:03:31.210 at conducting electricity, because you have 00:03:31.210 --> 00:03:34.330 all of these electrons that can move around. 00:03:34.330 --> 00:03:37.670 And so if you apply a voltage, they will start moving 00:03:37.670 --> 00:03:39.060 and conduct electricity. 00:03:39.060 --> 00:03:41.680 And those electrons can also be good at conducting 00:03:41.680 --> 00:03:43.950 thermal energy or heat. 00:03:43.950 --> 00:03:46.050 Now what would be, we already talked about them 00:03:46.050 --> 00:03:48.240 having the shiny, lustrous property, 00:03:48.240 --> 00:03:51.050 but how easy would it be to bend them? 00:03:51.050 --> 00:03:52.800 Ionic solids, we talked about 00:03:52.800 --> 00:03:54.300 they can be strong but brittle. 00:03:54.300 --> 00:03:57.170 As soon as you try to shift them around a little bit, 00:03:57.170 --> 00:03:58.280 they can break. 00:03:58.280 --> 00:04:00.060 But what do you think is going to happen here? 00:04:00.060 --> 00:04:02.860 If let's say right over here, I were to push really hard 00:04:02.860 --> 00:04:05.950 and on the top I would have pushed really hard to the left. 00:04:05.950 --> 00:04:07.170 Do you think this will be brittle? 00:04:07.170 --> 00:04:09.090 Or do you think it will be malleable? 00:04:09.090 --> 00:04:10.600 It's easy to bend. 00:04:10.600 --> 00:04:12.450 Well if you have a pure metallic solid, 00:04:12.450 --> 00:04:14.210 it's actually quite malleable. 00:04:14.210 --> 00:04:18.100 If you just took this top part and pushed it 00:04:18.100 --> 00:04:21.350 to the left like this, no big deal. 00:04:21.350 --> 00:04:23.550 You have those cations that are still in those 00:04:23.550 --> 00:04:25.150 that sea of electrons. 00:04:25.150 --> 00:04:28.200 And that's generally true of metallic solids. 00:04:28.200 --> 00:04:29.510 They're very malleable. 00:04:29.510 --> 00:04:30.720 They are not brittle. 00:04:30.720 --> 00:04:33.430 In fact, so much so that often times we want them 00:04:33.430 --> 00:04:35.020 to be a little bit more rigid. 00:04:35.020 --> 00:04:37.090 We want them to be a little bit harder. 00:04:37.090 --> 00:04:40.380 And that's why we might do things like add other elements 00:04:40.380 --> 00:04:42.270 into the metallic solid. 00:04:42.270 --> 00:04:45.080 For example, pure iron is reasonably malleable. 00:04:45.080 --> 00:04:46.480 But if you wanna make it stronger, 00:04:46.480 --> 00:04:48.660 you could stick carbon atoms in between. 00:04:48.660 --> 00:04:51.140 For example, you could put a carbon atom there, 00:04:51.140 --> 00:04:53.860 or carbon atom over there. 00:04:53.860 --> 00:04:56.520 And that way, it kind of disrupts 00:04:56.520 --> 00:04:59.660 this electron sea a little bit. 00:04:59.660 --> 00:05:01.660 So it's not quite as malleable. 00:05:01.660 --> 00:05:04.950 It'll be stronger and more rigid. 00:05:04.950 --> 00:05:05.920 So I'll leave you here. 00:05:05.920 --> 00:05:08.170 This is just an extension of what we've already learned 00:05:08.170 --> 00:05:10.640 about metals and metallic bonds. 00:05:10.640 --> 00:05:13.620 To just realize why most of the periodic table of elements 00:05:13.620 --> 00:05:16.590 that we're familiar with has some of these properties 00:05:16.590 --> 00:05:19.483 when they are, when you have pure solids of them.

Ionic solids

https://www.youtube.com/watch?v=zax0lYlOdiI

vtt

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en

WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:02.860 - [Instructor] Let's talk a little bit about ionic solids, 00:00:02.860 --> 00:00:07.010 which you can imagine are solids formed by ions. 00:00:07.010 --> 00:00:09.326 So, let's think a little bit about these ions. 00:00:09.326 --> 00:00:12.610 So, for example, we could look at group one elements here, 00:00:12.610 --> 00:00:16.430 especially things like lithium, or sodium, or potassium. 00:00:16.430 --> 00:00:18.340 And in many other videos we have talked 00:00:18.340 --> 00:00:22.640 about these elements wanting maybe not so much 00:00:22.640 --> 00:00:24.990 to keep their outermost electron 00:00:24.990 --> 00:00:26.490 because they only have one electron 00:00:26.490 --> 00:00:28.210 in their outermost shell. 00:00:28.210 --> 00:00:31.310 And it'd be pretty easy for them to loose that electron 00:00:31.310 --> 00:00:33.300 to get to a noble gas configuration 00:00:33.300 --> 00:00:35.180 to have a full outer shell. 00:00:35.180 --> 00:00:37.600 So, these characters like to lose one electron 00:00:37.600 --> 00:00:39.991 the group two elements like to lose two electrons. 00:00:39.991 --> 00:00:43.130 While if you go on the other side of the periodic table, 00:00:43.130 --> 00:00:45.990 if you look at the halogens right over here, 00:00:45.990 --> 00:00:47.770 they're one electron away 00:00:47.770 --> 00:00:50.560 from having a noble gas electron configuration, 00:00:50.560 --> 00:00:52.740 from having a full outer shell. 00:00:52.740 --> 00:00:55.860 So, they really like to grab electrons. 00:00:55.860 --> 00:00:58.913 And, if you look at elements like oxygen and sulfur, 00:00:58.913 --> 00:01:03.180 they really like to grab two electrons, if they can. 00:01:03.180 --> 00:01:06.750 So, what do you think happens if you have some metals 00:01:06.750 --> 00:01:09.890 on the left end here mixed with some nonmetals 00:01:09.890 --> 00:01:11.310 on the right end here? 00:01:11.310 --> 00:01:14.670 Well, you might imagine there would be a reaction. 00:01:14.670 --> 00:01:18.039 So, for example, if you mixed sodium with chlorine, 00:01:18.039 --> 00:01:22.690 the sodiums might lose an electron to the chlorines, 00:01:22.690 --> 00:01:26.120 in which case you're going to have sodium cations, 00:01:26.120 --> 00:01:28.080 positively charged ions. 00:01:28.080 --> 00:01:31.660 And if the chlorines are now taking those electrons, 00:01:31.660 --> 00:01:34.437 they then become chloride anions. 00:01:35.320 --> 00:01:37.470 And now if you have a bunch of positive ions 00:01:37.470 --> 00:01:40.750 hanging around a bunch of negative ions, 00:01:40.750 --> 00:01:42.440 what do you think is going to happen? 00:01:42.440 --> 00:01:44.370 They're going to get attracted to each other. 00:01:44.370 --> 00:01:46.040 And they're going to get attracted to each other 00:01:46.040 --> 00:01:49.000 and form a lattice structure, like this. 00:01:49.000 --> 00:01:51.330 I like to use sodium chloride as an example 00:01:51.330 --> 00:01:52.380 because this is probably the one 00:01:52.380 --> 00:01:55.800 that we see most in our life, this is table salt. 00:01:55.800 --> 00:01:58.290 If you were to lick it, it'd taste salty. 00:01:58.290 --> 00:02:00.304 But, there's many other ionic salt solids, 00:02:00.304 --> 00:02:03.030 many of them would actually be categorized 00:02:03.030 --> 00:02:04.600 as salt, generally. 00:02:04.600 --> 00:02:07.130 You could have a potassium chloride. 00:02:07.130 --> 00:02:10.360 You could have a sodium chloride. 00:02:10.360 --> 00:02:14.330 You could have, for example, a magnesium oxide. 00:02:14.330 --> 00:02:15.710 What's going on there? 00:02:15.710 --> 00:02:19.750 Well, in that situation, the magnesium, each magnesium 00:02:19.750 --> 00:02:22.130 might lose two electrons, 00:02:22.130 --> 00:02:26.320 so they become a ion with a positive two charge, 00:02:26.320 --> 00:02:30.760 and each of the oxygens would gain two electrons. 00:02:30.760 --> 00:02:35.690 So then they are anions with a negative two charge. 00:02:35.690 --> 00:02:38.640 And these characters once again are going to be attracted 00:02:38.640 --> 00:02:42.380 to each other and form an ionic solid in a regular 00:02:42.380 --> 00:02:44.640 lattice structure like this. 00:02:44.640 --> 00:02:47.670 So let's think a little bit about their properties. 00:02:47.670 --> 00:02:51.070 So first of all, let's think about the melting points. 00:02:51.070 --> 00:02:55.808 So, these solids, the electrostatic attraction between 00:02:55.808 --> 00:02:58.230 these ions is strong. 00:02:58.230 --> 00:03:01.920 And so they tend to have high melting points. 00:03:01.920 --> 00:03:03.680 Now what if we were to compare melting points 00:03:03.680 --> 00:03:05.630 between ionic solids? 00:03:05.630 --> 00:03:08.130 So for example, if you wanted to compare the melting point 00:03:08.130 --> 00:03:11.980 of sodium chloride to the melting point 00:03:11.980 --> 00:03:15.670 of magnesium oxide which one do you think 00:03:15.670 --> 00:03:16.760 has a higher melting point? 00:03:16.760 --> 00:03:19.000 Pause this video and think about it. 00:03:19.000 --> 00:03:21.640 Well, as you can imagine the electrostatic attraction, 00:03:21.640 --> 00:03:23.840 it's going to be dependent on two things. 00:03:23.840 --> 00:03:27.590 The magnitude of the charge and the radius 00:03:27.590 --> 00:03:30.630 of the atoms that ae forming this lattice structure. 00:03:30.630 --> 00:03:33.230 And the magnitude of the charge here is clear. 00:03:33.230 --> 00:03:36.020 Here you have a plus two charge being attracted 00:03:36.020 --> 00:03:39.210 to a negative two charge so this has a stronger 00:03:39.210 --> 00:03:41.580 electrostatic attraction and so you're going to have 00:03:41.580 --> 00:03:44.710 a higher melting point right over here. 00:03:44.710 --> 00:03:47.320 The melting point of magnesium oxide? 00:03:47.320 --> 00:03:52.320 2,825 degrees Celsius, while the melting point of table salt 00:03:54.050 --> 00:03:58.670 or sodium chloride is 801 degrees Celsius. 00:03:58.670 --> 00:04:01.760 You could also try to compare sodium chloride 00:04:01.760 --> 00:04:06.346 to something like sodium fluoride. 00:04:06.346 --> 00:04:07.730 Which one do you think is going to 00:04:07.730 --> 00:04:09.650 have a higher melting point? 00:04:09.650 --> 00:04:13.031 Sodium chloride or sodium fluoride? 00:04:13.031 --> 00:04:16.300 Well fluorines are smaller than chlorines and each of them 00:04:16.300 --> 00:04:19.490 gain an electron, then the fluoride anion 00:04:19.490 --> 00:04:21.160 is still going to be a reasonable bit smaller 00:04:21.160 --> 00:04:22.870 than the chloride anion. 00:04:22.870 --> 00:04:25.630 Or when you have smaller constituent ions, 00:04:25.630 --> 00:04:28.268 the electrostatic attraction is actually stronger. 00:04:28.268 --> 00:04:31.110 Remember, we've seen in Coulomb's law, 00:04:31.110 --> 00:04:33.870 that the closer two charges are to each other, 00:04:33.870 --> 00:04:36.710 the stronger the attractive or the repulsive force, 00:04:36.710 --> 00:04:37.870 and if they're opposite charges, 00:04:37.870 --> 00:04:39.570 it's going to be an attractive force. 00:04:39.570 --> 00:04:43.090 So, sodium fluoride is actually gonna have a higher 00:04:43.090 --> 00:04:46.410 melting point than sodium chloride, by a little bit. 00:04:46.410 --> 00:04:48.210 It actually turns out that the melting point 00:04:48.210 --> 00:04:52.500 of sodium fluoride is 996 degrees Celsius. 00:04:52.500 --> 00:04:54.280 But if you're comparing these three, 00:04:54.280 --> 00:04:57.100 the highest melting point is magnesium oxide, 00:04:57.100 --> 00:05:01.110 followed by sodium fluoride, followed by sodium chloride. 00:05:01.110 --> 00:05:04.770 So charge is what's really dominating over here. 00:05:04.770 --> 00:05:06.590 Now the next question you might be wondering 00:05:06.590 --> 00:05:10.040 is all right I can imagine these solids are really hard, 00:05:10.040 --> 00:05:12.290 but what would happen if I were to try to break it? 00:05:12.290 --> 00:05:14.890 Would it bend like a lot of the metals we know 00:05:14.890 --> 00:05:16.540 and we'll study that in other videos, 00:05:16.540 --> 00:05:18.200 or would something else happen? 00:05:18.200 --> 00:05:20.980 And to understand that, let me draw a two dimensional 00:05:20.980 --> 00:05:22.140 representation of this. 00:05:22.140 --> 00:05:24.360 So let me draw the chlorine, 00:05:24.360 --> 00:05:26.577 or I should say the chloride anions. 00:05:27.652 --> 00:05:31.810 And this is just a two dimensional version of that lattice. 00:05:31.810 --> 00:05:34.150 Obviously not drawing it to scale. 00:05:34.150 --> 00:05:36.870 And then let me draw the sodiums. 00:05:37.874 --> 00:05:39.413 Sodium cations. 00:05:40.665 --> 00:05:42.960 As you can see, the positives are attracted to the negative, 00:05:42.960 --> 00:05:44.220 that's why they're next to each other, 00:05:44.220 --> 00:05:46.060 the negatives aren't next each other 00:05:46.060 --> 00:05:47.280 because they repel each other. 00:05:47.280 --> 00:05:49.310 The positives aren't next to each other, 00:05:49.310 --> 00:05:53.140 but what would happen if I were to try to, 00:05:53.140 --> 00:05:55.760 or I were to press down really hard on this side 00:05:55.760 --> 00:06:00.690 and if I were to press really hard up on this side? 00:06:00.690 --> 00:06:02.451 So what would happen if I press had enough 00:06:02.451 --> 00:06:06.010 that this side begins to budge? 00:06:06.010 --> 00:06:07.540 So it begins to budge. 00:06:07.540 --> 00:06:10.780 Would it just bend, or what do you think's gonna happen 00:06:10.780 --> 00:06:13.340 when I get right about there? 00:06:13.340 --> 00:06:15.630 Well, when I get right about there, 00:06:15.630 --> 00:06:19.170 all of a sudden I've, not only have I broken the lattice, 00:06:19.170 --> 00:06:20.800 but the negatives are next to the negatives 00:06:20.800 --> 00:06:22.362 and the positives are next to the positives 00:06:22.362 --> 00:06:24.870 and so it's not just going to bend, 00:06:24.870 --> 00:06:27.700 and be malleable like a lot of the metals we've seen, 00:06:27.700 --> 00:06:29.680 it's just going to break. 00:06:29.680 --> 00:06:31.910 So this is going to be, even though it's going to be hard, 00:06:31.910 --> 00:06:33.800 it is going to be brittle. 00:06:33.800 --> 00:06:36.610 Now the last question we'll address in this video 00:06:36.610 --> 00:06:40.600 is how good do you think ionic solids conduct electricity? 00:06:40.600 --> 00:06:43.130 Pause this video and think about that. 00:06:43.130 --> 00:06:44.720 Well, in order to conduct electricity, 00:06:44.720 --> 00:06:47.900 either electrons or charge generally has to be able 00:06:47.900 --> 00:06:48.950 to move about. 00:06:48.950 --> 00:06:52.010 And when it's just in its solid form like this, 00:06:52.010 --> 00:06:54.037 the, even though you do have these ions 00:06:54.037 --> 00:06:56.100 they're not going to move about. 00:06:56.100 --> 00:06:58.406 So ionic solids in their solid form, 00:06:58.406 --> 00:07:01.580 they aren't good at conducting electricity. 00:07:01.580 --> 00:07:04.150 They can be good at conducting electricity 00:07:04.150 --> 00:07:06.410 if you were to dissolve it in a solution. 00:07:06.410 --> 00:07:08.410 For example, if you were to dissolve this salt 00:07:08.410 --> 00:07:10.708 in water, now the ions can move around 00:07:10.708 --> 00:07:13.580 and then they're good at conducting electricity. 00:07:13.580 --> 00:07:16.210 Or, if you were to heat this sodium chloride 00:07:16.210 --> 00:07:20.270 up beyond 801 degrees Celsius and it turns into a liquid, 00:07:20.270 --> 00:07:23.290 then once again the ions can move around 00:07:23.290 --> 00:07:26.120 and you can actually conduct electricity. 00:07:26.120 --> 00:07:29.020 Take everything I say with a grain of salt. 00:07:29.020 --> 00:07:31.210 Sorry, I know, I couldn't help it. 00:07:31.210 --> 00:07:32.380 But hopefully you know a little bit more 00:07:32.380 --> 00:07:33.913 about ionic solids now.

Information for congruency

https://www.youtube.com/watch?v=ygqvHLE3IKE

vtt

https://www.youtube.com/api/timedtext?v=ygqvHLE3IKE&ei=bViUZaK7GfK2vdIPzvuNuAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6FDB8D56273268F5683B3D58167C0F1BBCE1318D.D9CD68001D29EA8DD0AD460EB1A0DDA78D60AFEB&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.140 --> 00:00:02.260 - [Instructor] So I have two triangles depicted here 00:00:02.260 --> 00:00:05.340 and we have some information about each of those triangles. 00:00:05.340 --> 00:00:08.390 We know that this side of this left triangle 00:00:08.390 --> 00:00:09.960 has length eight. 00:00:09.960 --> 00:00:12.440 We know that this side has length seven 00:00:12.440 --> 00:00:15.330 and then we know that this angle is 50 degrees. 00:00:15.330 --> 00:00:18.600 And on this triangle we see some things that look 00:00:18.600 --> 00:00:20.130 a little bit familiar. 00:00:20.130 --> 00:00:23.740 This triangle, this side has length eight. 00:00:23.740 --> 00:00:26.320 This side has length seven. 00:00:26.320 --> 00:00:30.730 And this angle right over here has a measure of 50 degrees. 00:00:30.730 --> 00:00:32.570 So my question to you is, 00:00:32.570 --> 00:00:35.440 can you definitively say, not assuming 00:00:35.440 --> 00:00:36.660 that these are drawn to scale, 00:00:36.660 --> 00:00:39.580 because they actually aren't, can you definitively say 00:00:39.580 --> 00:00:41.760 that these triangles are congruent? 00:00:41.760 --> 00:00:44.470 Or could you definitively say that they aren't congruent? 00:00:44.470 --> 00:00:46.460 Or can you not say either? 00:00:46.460 --> 00:00:49.010 Would you have to say that there's not enough information? 00:00:49.010 --> 00:00:51.210 Pause this video and think about that. 00:00:51.210 --> 00:00:54.440 So essentially what we have here are two pairs of sides 00:00:54.440 --> 00:00:56.580 that have the same length and and angle, 00:00:56.580 --> 00:00:59.830 but that angle is not between those two sides. 00:00:59.830 --> 00:01:02.400 If the angle were here and here, 00:01:02.400 --> 00:01:07.130 then we could use side, angle, side, side, angle, side 00:01:07.130 --> 00:01:09.970 to deduce that, hey, these are congruent, 00:01:09.970 --> 00:01:11.350 but that's not what we're dealing with. 00:01:11.350 --> 00:01:14.240 We are dealing with side, side, angle. 00:01:14.240 --> 00:01:16.110 Side, side, angle. 00:01:16.110 --> 00:01:18.230 I'm saying the side and the side before the angle, 00:01:18.230 --> 00:01:21.440 because if I don't do that it becomes a little bit crass. 00:01:21.440 --> 00:01:22.273 So what we're really saying 00:01:22.273 --> 00:01:27.273 is side, side, angle sufficient to prove congruency? 00:01:27.330 --> 00:01:28.590 And the reason why it's not, 00:01:28.590 --> 00:01:31.680 is that you can actually construct different triangles 00:01:31.680 --> 00:01:33.800 with the same constraints. 00:01:33.800 --> 00:01:36.060 For example, on this right most triangle 00:01:36.060 --> 00:01:37.490 it could look like this, 00:01:37.490 --> 00:01:39.290 or it could look like this. 00:01:39.290 --> 00:01:43.480 The seven side could go down like this 00:01:43.480 --> 00:01:46.400 and intersect just like that. 00:01:46.400 --> 00:01:48.380 Now you might be saying, hey, that's not what it looks like. 00:01:48.380 --> 00:01:50.390 It looks very similar, but remember, 00:01:50.390 --> 00:01:52.120 we're not going on looks. 00:01:52.120 --> 00:01:54.940 We have to go based on the information they've given us 00:01:54.940 --> 00:01:57.760 and so you could just as easily, based on the information, 00:01:57.760 --> 00:01:59.440 the constraints they've given us, 00:01:59.440 --> 00:02:01.350 have a triangle like this. 00:02:01.350 --> 00:02:03.320 And so the very fact that you can create 00:02:03.320 --> 00:02:06.240 two different triangles that are clearly not congruent, 00:02:06.240 --> 00:02:08.440 based on the exact same information, 00:02:08.440 --> 00:02:10.580 the exact same constraints, tells you that 00:02:10.580 --> 00:02:12.070 that information, those constraints, 00:02:12.070 --> 00:02:13.990 are not enough to tell you 00:02:13.990 --> 00:02:15.763 that these are congruent triangles.

Non-congruent shapes & transformations

https://www.youtube.com/watch?v=7Rb3V-HyVD8

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WEBVTT Kind: captions Language: en 00:00:00.210 --> 00:00:02.510 - [Instructor] We are told, Brenda was able to map 00:00:02.510 --> 00:00:06.050 circle M onto circle N 00:00:06.050 --> 00:00:09.690 using a translation and a dilation. 00:00:09.690 --> 00:00:11.550 This is circle M right over here. 00:00:11.550 --> 00:00:13.100 Here's the center of it. 00:00:13.100 --> 00:00:17.310 This is circle M, this circle right over here. 00:00:17.310 --> 00:00:19.850 It looks like at first, she translates it. 00:00:19.850 --> 00:00:23.390 The center goes from this point to this point here. 00:00:23.390 --> 00:00:27.230 After the translation, we have the circle 00:00:27.230 --> 00:00:28.800 right over here. 00:00:28.800 --> 00:00:30.820 Then she dilates it. 00:00:30.820 --> 00:00:34.170 The center of dilation looks like it is point N. 00:00:34.170 --> 00:00:36.990 She dilates it with some type of a scale factor 00:00:36.990 --> 00:00:40.600 in order to map it exactly onto N. 00:00:40.600 --> 00:00:42.990 That all seems right. 00:00:42.990 --> 00:00:47.177 Brenda concluded, "I was able to map circle M 00:00:47.177 --> 00:00:50.307 "onto circle N using a sequence 00:00:50.307 --> 00:00:52.357 "of rigid transformations, 00:00:52.357 --> 00:00:56.020 "so the figures are congruent." 00:00:56.020 --> 00:00:57.723 Is she correct? 00:00:59.218 --> 00:01:01.813 Pause this video and think about that. 00:01:03.210 --> 00:01:05.920 Let's work on this together. 00:01:05.920 --> 00:01:10.560 She was able to map circle M onto circle N 00:01:10.560 --> 00:01:13.700 using a sequence of transformations. 00:01:13.700 --> 00:01:15.660 She did a translation and then a dilation. 00:01:15.660 --> 00:01:17.330 Those are all transformations, 00:01:17.330 --> 00:01:19.910 but they are not all rigid transformations. 00:01:19.910 --> 00:01:21.950 I'll put a question mark right over there. 00:01:21.950 --> 00:01:25.000 A translation is a rigid transformation. 00:01:25.000 --> 00:01:26.670 Remember, rigid transformations are ones 00:01:26.670 --> 00:01:28.100 that preserve distances, 00:01:28.100 --> 00:01:30.850 preserve angle measures, preserve lengths, 00:01:30.850 --> 00:01:33.700 while a dilation is not a rigid transformation. 00:01:33.700 --> 00:01:35.240 As you can see very clearly, 00:01:35.240 --> 00:01:36.920 it is not preserving lengths. 00:01:36.920 --> 00:01:39.050 It is not, for example, preserving the radius 00:01:39.050 --> 00:01:40.270 of the circle. 00:01:40.270 --> 00:01:43.230 In order for two figures to be congruent, 00:01:43.230 --> 00:01:47.630 the mapping has to be only with rigid transformations. 00:01:47.630 --> 00:01:49.760 Because she used a dilation, 00:01:49.760 --> 00:01:51.730 in fact, you have to use a dilation 00:01:51.730 --> 00:01:53.890 if you wanna be able to map M onto N 00:01:53.890 --> 00:01:55.633 because they have different radii, 00:01:56.510 --> 00:01:58.320 then she's not correct. 00:01:58.320 --> 00:01:59.740 These are not congruent figures. 00:01:59.740 --> 00:02:01.843 She cannot make this conclusion.

Congruent shapes and transformations

https://www.youtube.com/watch?v=KZMRhWdzEPo

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en

WEBVTT Kind: captions Language: en 00:00:00.380 --> 00:00:02.497 - [Instructor] We're told, "Kason was curious 00:00:02.497 --> 00:00:06.837 "if triangle ABC and triangle GFE were congruent, 00:00:06.837 --> 00:00:10.107 "so he tried to map one figure onto the other 00:00:10.107 --> 00:00:12.140 "using a rotation." 00:00:12.140 --> 00:00:15.610 So let's see, this is triangle ABC, and it looks like, 00:00:15.610 --> 00:00:20.610 at first, he rotates triangle ABC about point C, 00:00:21.150 --> 00:00:24.350 to get it right over here, so that's what they're depicting 00:00:24.350 --> 00:00:25.610 in this diagram. 00:00:25.610 --> 00:00:28.717 And then they say, "Kason concluded: 00:00:28.717 --> 00:00:31.697 "It is not possible to map triangle ABC 00:00:31.697 --> 00:00:34.647 "onto triangle GFE using a sequence 00:00:34.647 --> 00:00:36.407 "of rigid transformations, 00:00:36.407 --> 00:00:39.560 "so the triangles are not congruent." 00:00:39.560 --> 00:00:41.580 So what I want you to do is pause this video 00:00:41.580 --> 00:00:43.870 and think about, is Kason correct 00:00:43.870 --> 00:00:46.048 that they are not congruent, because you can not map 00:00:46.048 --> 00:00:49.180 ABC, triangle ABC onto triangle GFE 00:00:49.180 --> 00:00:50.703 with rigid transformations? 00:00:51.890 --> 00:00:54.410 All right, so the way I think about it, 00:00:54.410 --> 00:00:55.792 he was able to do the rotation 00:00:55.792 --> 00:00:58.740 that got us right over here, 00:00:58.740 --> 00:01:01.040 so it is rotation about point C, 00:01:01.040 --> 00:01:02.590 and so this point right over here, 00:01:02.590 --> 00:01:03.650 let me make sure I get this right, 00:01:03.650 --> 00:01:05.830 this would've become B prime, 00:01:05.830 --> 00:01:07.650 and then this is A prime, 00:01:07.650 --> 00:01:12.110 and then C is mapped to itself, so C is equal to C prime. 00:01:12.110 --> 00:01:15.040 But he's not done, there's another rigid transformation 00:01:15.040 --> 00:01:17.470 he could do, and that would be a reflection 00:01:17.470 --> 00:01:20.090 about the line FG. 00:01:20.090 --> 00:01:22.610 So if he reflects about the line FG, 00:01:22.610 --> 00:01:25.620 then this point is going to be mapped to point E, 00:01:25.620 --> 00:01:26.530 just like that. 00:01:26.530 --> 00:01:28.720 And then if you did that, you would see that there is 00:01:28.720 --> 00:01:30.340 a series of rigid transformations 00:01:30.340 --> 00:01:34.340 that maps triangle ABC onto triangle GFE. 00:01:34.340 --> 00:01:38.980 So Kason is not correct, he missed one more transformation 00:01:38.980 --> 00:01:41.703 he could've done, which is a reflection.

Dilating triangles: find the error

https://www.youtube.com/watch?v=Kry9Bhp4PQg

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WEBVTT Kind: captions Language: en 00:00:00.470 --> 00:00:01.810 - [Instructor] We are told triangle 00:00:01.810 --> 00:00:04.380 A-prime, B-prime, C-prime is the image 00:00:04.380 --> 00:00:07.290 of triangle ABC under a dilation 00:00:07.290 --> 00:00:12.270 whose center is P and scale factor is 3/4. 00:00:12.270 --> 00:00:14.880 Which figure correctly shows triangle 00:00:14.880 --> 00:00:18.990 A-prime, B-prime, C-prime using the solid line. 00:00:18.990 --> 00:00:20.370 So pause this video and see 00:00:20.370 --> 00:00:22.320 if you can figure this out on your own. 00:00:23.280 --> 00:00:25.760 All right, now before I even look at the choices, 00:00:25.760 --> 00:00:26.710 I like to just think about, 00:00:26.710 --> 00:00:29.240 what would that dilation actually look like? 00:00:29.240 --> 00:00:31.680 So our center of dilation is P. 00:00:31.680 --> 00:00:34.560 And it's a scale factor of 3/4. 00:00:34.560 --> 00:00:36.140 So one way to think about it is, 00:00:36.140 --> 00:00:38.730 however far any point was from P before, 00:00:38.730 --> 00:00:43.270 is now going to be 3/4 as far, but along the same line. 00:00:43.270 --> 00:00:44.900 So I'm just going to estimate it. 00:00:44.900 --> 00:00:48.400 So if C was there, 3/2 would be this far. 00:00:48.400 --> 00:00:50.190 So 3/4 would be right about there. 00:00:50.190 --> 00:00:52.580 So C-prime should be about there. 00:00:52.580 --> 00:00:57.580 If we have this line connecting B and P like this, 00:00:58.200 --> 00:01:00.070 let's see, half of that is there. 00:01:00.070 --> 00:01:02.170 3/4 is going to be there. 00:01:02.170 --> 00:01:04.610 So B-prime should be there. 00:01:04.610 --> 00:01:09.020 And then on this line, halfway is roughly there. 00:01:09.020 --> 00:01:09.980 I'm just eyeballing it. 00:01:09.980 --> 00:01:11.690 So 3/4 is there. 00:01:11.690 --> 00:01:15.240 So A-prime, A-prime, should be there. 00:01:15.240 --> 00:01:18.280 And so A-prime, B-prime, C-prime 00:01:18.280 --> 00:01:22.930 should look something like this. 00:01:22.930 --> 00:01:27.930 Which we can see is exactly what we see for choice C. 00:01:28.700 --> 00:01:30.470 So choice C, it looks correct. 00:01:30.470 --> 00:01:32.400 So I'm gonna just circle that, 00:01:32.400 --> 00:01:34.390 or select it just like that. 00:01:34.390 --> 00:01:35.800 But let's just make sure we understand why 00:01:35.800 --> 00:01:38.820 these other two choices were not correct. 00:01:38.820 --> 00:01:42.450 So choice A, it looks like it is a dilation 00:01:42.450 --> 00:01:44.600 with a 3/4 scale factor. 00:01:44.600 --> 00:01:46.540 Each of the dimensions, each of the sides 00:01:46.540 --> 00:01:48.360 of these triangles, of this triangle, 00:01:48.360 --> 00:01:51.310 looks like it's about 3/4 of what it originally was. 00:01:51.310 --> 00:01:54.620 But it doesn't look like the center of dilation is P. 00:01:54.620 --> 00:01:56.690 Here the center of dilation looks 00:01:56.690 --> 00:02:01.690 like it is probably the midpoint of segment AC. 00:02:02.570 --> 00:02:05.410 Because now it looks like everything is 3/4 00:02:05.410 --> 00:02:08.140 of the distance it was to that point. 00:02:08.140 --> 00:02:12.290 So they have this other center of dilation in choice A. 00:02:12.290 --> 00:02:14.040 The center of dilation is not P, 00:02:14.040 --> 00:02:16.020 and that's why we can rule that one out. 00:02:16.020 --> 00:02:19.240 And then for choice B right over here, 00:02:19.240 --> 00:02:21.290 it looks like they just got the scale factor wrong. 00:02:21.290 --> 00:02:22.590 Actually they got the center of dilation 00:02:22.590 --> 00:02:23.670 and the scale factor wrong. 00:02:23.670 --> 00:02:26.320 It still looks like they are using this 00:02:26.320 --> 00:02:27.830 as a center of dilation. 00:02:27.830 --> 00:02:30.680 But this scale factor looks like it's much closer 00:02:30.680 --> 00:02:34.290 to 1/4 or 1/3, not 3/4. 00:02:34.290 --> 00:02:36.940 So that's why we can rule that one out as well. 00:02:36.940 --> 00:02:38.483 We like our choice, C.

Proving the ASA and AAS triangle congruence criteria using transformations

https://www.youtube.com/watch?v=5EX7tYQEB_M

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en

WEBVTT Kind: captions Language: en 00:00:00.550 --> 00:00:02.550 - [Instructor] What we're going to do in this video is show 00:00:02.550 --> 00:00:05.450 that if we have two different triangles 00:00:05.450 --> 00:00:09.980 that have one pair of sides that have the same length, 00:00:09.980 --> 00:00:11.530 so these blue sides in each 00:00:11.530 --> 00:00:13.740 of these triangles have the same length, 00:00:13.740 --> 00:00:18.420 and they have two pairs of angles where, for each pair, 00:00:18.420 --> 00:00:21.090 the corresponding angles have the same measure, 00:00:21.090 --> 00:00:23.370 so this gray angle here has the same measure 00:00:23.370 --> 00:00:27.350 as this angle here, and then these double orange arcs show 00:00:27.350 --> 00:00:31.040 that this angle ACB has the same measure 00:00:31.040 --> 00:00:32.123 as angle DFE. 00:00:33.520 --> 00:00:36.950 And so we're gonna show that if you have two of your angles 00:00:36.950 --> 00:00:40.570 and a side that had the same measure or length, 00:00:40.570 --> 00:00:44.820 that we can always create a series of rigid transformations 00:00:44.820 --> 00:00:46.930 that maps one triangle onto the other. 00:00:46.930 --> 00:00:49.400 Or another way to say it, they must be congruent 00:00:49.400 --> 00:00:53.700 by the rigid transformation definition of congruency. 00:00:53.700 --> 00:00:56.510 And the reason why I wrote angle side angle here 00:00:56.510 --> 00:00:59.240 and angle angle side is to realize 00:00:59.240 --> 00:01:01.060 that these are equivalent. 00:01:01.060 --> 00:01:03.500 Because if you have two angles, 00:01:03.500 --> 00:01:06.300 then you know what the third angle is going to be. 00:01:06.300 --> 00:01:08.660 So for example, in this case right over here, 00:01:08.660 --> 00:01:10.170 if we know that we have two pairs 00:01:10.170 --> 00:01:12.230 of angles that have the same measure, 00:01:12.230 --> 00:01:14.060 then that means that the third pair 00:01:14.060 --> 00:01:17.170 must have the same measure as well. 00:01:17.170 --> 00:01:18.670 So we'll know this as well. 00:01:18.670 --> 00:01:20.090 So if you really think about it, 00:01:20.090 --> 00:01:22.860 if you have the side between the two angles, 00:01:22.860 --> 00:01:26.310 that's equivalent to having an angle, an angle, and a side. 00:01:26.310 --> 00:01:28.170 Because as long as you have two angles, 00:01:28.170 --> 00:01:30.600 the third angle is also going to have the same measure 00:01:30.600 --> 00:01:34.040 as the corresponding third angle on the other triangle. 00:01:34.040 --> 00:01:36.820 So let's just show a series of rigid transformations 00:01:36.820 --> 00:01:39.583 that can get us from ABC to DEF. 00:01:41.030 --> 00:01:44.180 So the first step, you might imagine, we've already shown 00:01:44.180 --> 00:01:46.660 that if you have two segments of equal length 00:01:46.660 --> 00:01:48.010 that they are congruent. 00:01:48.010 --> 00:01:50.300 You can have a series of rigid transformations 00:01:50.300 --> 00:01:52.000 that maps one onto the other. 00:01:52.000 --> 00:01:54.440 So what I want to do is 00:01:54.440 --> 00:01:56.440 map segment AC 00:01:58.710 --> 00:02:00.383 onto DF. 00:02:01.285 --> 00:02:03.780 And the way that I could do that 00:02:03.780 --> 00:02:07.330 is I could translate point A 00:02:07.330 --> 00:02:09.630 to be on top of point D, 00:02:09.630 --> 00:02:11.980 so then I'll call this A prime. 00:02:11.980 --> 00:02:13.630 And then when I do that, 00:02:13.630 --> 00:02:16.250 this segment AC is going to look something like this. 00:02:16.250 --> 00:02:17.410 I'm just sketching it right now. 00:02:17.410 --> 00:02:19.020 It's going to be in that direction. 00:02:19.020 --> 00:02:20.000 But then, and the whole, 00:02:20.000 --> 00:02:21.700 the rest of the triangle is going to come with it. 00:02:21.700 --> 00:02:25.060 So let's see, the rest of that orange side, side AB, 00:02:25.060 --> 00:02:27.920 is going to look something like that. 00:02:27.920 --> 00:02:29.810 But then we could do another rigid transformation, 00:02:29.810 --> 00:02:33.080 which is rotate about point D or point A prime, 00:02:33.080 --> 00:02:34.560 they're the same point now, 00:02:34.560 --> 00:02:39.060 so that point C coincides with point F. 00:02:39.060 --> 00:02:40.490 And so just like that, 00:02:40.490 --> 00:02:43.120 you would have two rigid transformations that get us, 00:02:43.120 --> 00:02:46.800 that map AC onto DF. 00:02:46.800 --> 00:02:50.220 And so A prime, where A is mapped, is now equal to D, 00:02:50.220 --> 00:02:52.940 and F is now equal to C prime. 00:02:52.940 --> 00:02:57.690 But the question is where does point B now sit? 00:02:57.690 --> 00:02:59.570 And the realization here is 00:02:59.570 --> 00:03:02.840 that angle measures are preserved. 00:03:02.840 --> 00:03:05.570 And since angle measures are preserved, 00:03:05.570 --> 00:03:10.160 we are either going to have a situation where this angle, 00:03:10.160 --> 00:03:12.713 let's see, this angle is angle CAB 00:03:14.660 --> 00:03:15.890 gets preserved. 00:03:15.890 --> 00:03:19.770 So then it would be C prime, A prime, 00:03:19.770 --> 00:03:23.206 and then B prime would have to sit someplace on this ray. 00:03:23.206 --> 00:03:26.783 Or if we're gonna preserve the measure of angle CAB, 00:03:27.660 --> 00:03:31.910 B prime is going to sit someplace along that ray. 00:03:31.910 --> 00:03:34.420 Because an angle is defined by two rays 00:03:34.420 --> 00:03:38.030 that intersect at the vertex or start at the vertex. 00:03:38.030 --> 00:03:40.530 And because this angle is preserved, 00:03:40.530 --> 00:03:43.960 that's the angle that is formed by these two rays. 00:03:43.960 --> 00:03:46.980 You could say ray CA and ray CB. 00:03:46.980 --> 00:03:49.520 We know that B prime also has to sit someplace 00:03:49.520 --> 00:03:51.510 on this ray as well. 00:03:51.510 --> 00:03:55.970 So B prime also has to sit someplace on this ray, 00:03:55.970 --> 00:03:58.290 and I think you see where this is going. 00:03:58.290 --> 00:04:01.890 If B prime, because these two angles are preserved, 00:04:01.890 --> 00:04:03.990 because this angle and this angle are preserved, 00:04:03.990 --> 00:04:07.020 have to sit someplace on both of these rays, 00:04:07.020 --> 00:04:08.650 they intersect at one point, 00:04:08.650 --> 00:04:12.000 this point right over here that coincides with point E. 00:04:12.000 --> 00:04:14.300 So this is where B prime would be. 00:04:14.300 --> 00:04:16.910 So that's one scenario, in which case we've shown 00:04:16.910 --> 00:04:19.590 that you can get a series of rigid transformations 00:04:19.590 --> 00:04:21.580 from this triangle to this triangle. 00:04:21.580 --> 00:04:22.790 But there's another one. 00:04:22.790 --> 00:04:26.550 There is a circumstance where the angles get preserved. 00:04:26.550 --> 00:04:29.260 But instead of being on, 00:04:29.260 --> 00:04:31.150 instead of the angles being on the, 00:04:31.150 --> 00:04:32.690 I guess you could say the bottom right side 00:04:32.690 --> 00:04:33.840 of this blue line, 00:04:33.840 --> 00:04:35.900 you could imagine the angles get preserved 00:04:35.900 --> 00:04:38.560 such that they are on the other side. 00:04:38.560 --> 00:04:41.090 So the angles get preserved 00:04:41.090 --> 00:04:45.220 so that they are on the other side of that blue line. 00:04:45.220 --> 00:04:47.490 And then the question is, in that situation, 00:04:47.490 --> 00:04:49.560 where would B prime end up? 00:04:49.560 --> 00:04:51.810 Well, actually, let me draw this a little bit, 00:04:51.810 --> 00:04:53.950 let me do this a little bit more exact. 00:04:53.950 --> 00:04:56.690 Let me replicate these angles. 00:04:56.690 --> 00:05:01.690 So I'm going to draw an arc like this, an arc like this, 00:05:01.910 --> 00:05:03.823 and then I'll measure this distance. 00:05:05.497 --> 00:05:06.570 It's just like this. 00:05:06.570 --> 00:05:07.940 We've done this in other videos, 00:05:07.940 --> 00:05:10.433 when we're trying to replicate angles. 00:05:11.490 --> 00:05:12.730 So it's like that far, 00:05:12.730 --> 00:05:15.730 and so let me draw that on this point right over here, 00:05:15.730 --> 00:05:16.890 this far. 00:05:16.890 --> 00:05:19.830 So if the angles are on that side of line, 00:05:19.830 --> 00:05:22.950 I guess we could say DF or A prime, C prime, 00:05:22.950 --> 00:05:25.100 we know that B prime 00:05:25.100 --> 00:05:28.850 would have to sit someplace on this ray. 00:05:28.850 --> 00:05:32.260 So let me draw that as neatly as I can, 00:05:32.260 --> 00:05:35.023 someplace on this ray. 00:05:36.890 --> 00:05:38.670 And it would have to sit someplace 00:05:38.670 --> 00:05:41.060 on the ray formed by the other angle. 00:05:41.060 --> 00:05:44.720 So let me see if I can draw that as neatly as possible. 00:05:44.720 --> 00:05:45.730 So let me 00:05:48.760 --> 00:05:51.340 make a arc like this. 00:05:51.340 --> 00:05:53.990 I probably did that a little bit bigger than I need to, 00:05:53.990 --> 00:05:56.620 but hopefully it serves our purposes. 00:05:56.620 --> 00:05:59.230 I measured this distance right over here. 00:05:59.230 --> 00:06:01.970 If I measure that distance over here, 00:06:01.970 --> 00:06:05.380 it would get us right over there. 00:06:05.380 --> 00:06:10.380 So B prime either sits on this ray, or it could sit, 00:06:10.500 --> 00:06:15.260 or and it has to sit, I should really say, on this ray, 00:06:15.260 --> 00:06:17.910 that goes through this point and this point. 00:06:17.910 --> 00:06:19.730 And it has to sit on this ray. 00:06:19.730 --> 00:06:23.270 And you can see where these two rays intersect 00:06:23.270 --> 00:06:24.120 is right over there. 00:06:24.120 --> 00:06:26.690 So the other scenario is if the angles get preserved 00:06:26.690 --> 00:06:29.700 in a way that they're on the other side of that blue line, 00:06:29.700 --> 00:06:31.750 well, then B prime is there. 00:06:31.750 --> 00:06:34.910 And then we could just add one more rigid transformation 00:06:34.910 --> 00:06:37.150 to our series of rigid transformations, 00:06:37.150 --> 00:06:41.310 which is essentially or is a reflection across 00:06:41.310 --> 00:06:44.570 line DF or A prime, C prime. 00:06:44.570 --> 00:06:48.210 Why will that work, to map B prime onto E? 00:06:48.210 --> 00:06:51.460 Well, because reflection is also a rigid transformation, 00:06:51.460 --> 00:06:53.010 so angles are preserved. 00:06:53.010 --> 00:06:55.360 And so as this angle gets flipped over, it's preserved. 00:06:55.360 --> 00:06:56.890 As this angle gets flipped over, 00:06:56.890 --> 00:06:59.460 the measure of it, I should say, is preserved. 00:06:59.460 --> 00:07:02.000 And so that means we'll go to that first case 00:07:02.000 --> 00:07:04.490 where then these rays would be flipped onto these rays, 00:07:04.490 --> 00:07:07.170 and B prime would have to sit on that intersection. 00:07:07.170 --> 00:07:08.430 And there you have it. 00:07:08.430 --> 00:07:09.970 If you have two angles, 00:07:09.970 --> 00:07:12.140 and if you have two angles, you're gonna know the third, 00:07:12.140 --> 00:07:14.370 if you have two angles and a side 00:07:14.370 --> 00:07:17.130 that have the same measure or length, 00:07:17.130 --> 00:07:18.880 if we're talking about angle or a side, 00:07:18.880 --> 00:07:20.370 well, that means that they are going 00:07:20.370 --> 00:07:22.293 to be congruent triangles.

Proving the SAS triangle congruence criterion using transformations

https://www.youtube.com/watch?v=CMTeCNILzwU

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en

WEBVTT Kind: captions Language: en 00:00:00.420 --> 00:00:01.970 - [Instructor] What we're going to do in this video 00:00:01.970 --> 00:00:04.390 is see that if we have two different triangles, 00:00:04.390 --> 00:00:07.880 and we have two sets of corresponding sides 00:00:07.880 --> 00:00:10.140 that have the same length, 00:00:10.140 --> 00:00:12.830 for example this blue side has the same length 00:00:12.830 --> 00:00:14.710 as this blue side here, 00:00:14.710 --> 00:00:16.900 and this orange side has the same length side 00:00:16.900 --> 00:00:18.827 as this orange side here. 00:00:18.827 --> 00:00:22.150 And the angle that is formed between those sides, 00:00:22.150 --> 00:00:25.030 so we have two corresponding angles right over here, 00:00:25.030 --> 00:00:27.420 that they also have the equal measure. 00:00:27.420 --> 00:00:29.900 So we could think about we have a side, an angle, 00:00:29.900 --> 00:00:33.060 a side, a side, an angle and a side. 00:00:33.060 --> 00:00:36.340 If those have the same lengths or measures, 00:00:36.340 --> 00:00:38.270 then we can deduce 00:00:38.270 --> 00:00:41.220 that these two triangles must be congruent 00:00:41.220 --> 00:00:44.880 by the rigid motion definition of congruency. 00:00:44.880 --> 00:00:46.450 Or the short hand is, 00:00:46.450 --> 00:00:48.920 if we have side, angle, side in common, 00:00:48.920 --> 00:00:51.260 and the angle is between the two sides, 00:00:51.260 --> 00:00:54.430 then the two triangles will be congruent. 00:00:54.430 --> 00:00:55.840 So to be able to prove this, 00:00:55.840 --> 00:00:57.210 in order to make this deduction, 00:00:57.210 --> 00:00:58.650 we just have to say that there's always 00:00:58.650 --> 00:01:00.810 a rigid transformation if we have 00:01:00.810 --> 00:01:02.720 a side, angle, side in common 00:01:02.720 --> 00:01:05.270 that will allow us to map one triangle onto the other. 00:01:05.270 --> 00:01:06.510 Because if there is a series 00:01:06.510 --> 00:01:08.640 of rigid transformations that allow us to do it, 00:01:08.640 --> 00:01:10.660 then by the rigid transformation definition 00:01:10.660 --> 00:01:13.130 the two triangles are congruent. 00:01:13.130 --> 00:01:14.750 So the first thing that we could do 00:01:14.750 --> 00:01:17.410 is we could reference back to where we saw 00:01:17.410 --> 00:01:21.130 that if we have two segments that have the same length, 00:01:21.130 --> 00:01:24.950 like segment AB and segment DE. 00:01:24.950 --> 00:01:27.220 If we have two segments with the same length 00:01:27.220 --> 00:01:28.600 that they are congruent. 00:01:28.600 --> 00:01:30.850 You can always map one segment onto the other 00:01:30.850 --> 00:01:33.070 with a series of rigid transformations. 00:01:33.070 --> 00:01:34.900 The way that we could do that in this case 00:01:34.900 --> 00:01:39.850 is we could map point B onto point E. 00:01:39.850 --> 00:01:44.390 So this would be now I'll put B prime right over here. 00:01:44.390 --> 00:01:47.320 And if we just did a transformation to do that, 00:01:47.320 --> 00:01:49.320 if we just translated like that, 00:01:49.320 --> 00:01:54.320 then side, woops, then side B A would, 00:01:54.440 --> 00:01:56.730 that orange side would be something like that. 00:01:56.730 --> 00:01:58.470 But then we could do another rigid transformation 00:01:58.470 --> 00:02:02.650 that rotates about point E, or B prime, 00:02:02.650 --> 00:02:04.260 that rotates that orange side, 00:02:04.260 --> 00:02:07.970 and the whole triangle with it, onto DE. 00:02:07.970 --> 00:02:10.670 In which case, once we do that second rigid transformation, 00:02:10.670 --> 00:02:13.280 point A will now coincide with D. 00:02:13.280 --> 00:02:16.400 Or we could say A prime is equal to D. 00:02:16.400 --> 00:02:20.870 But the question is, where would C now sit? 00:02:20.870 --> 00:02:24.040 Well, we can see the distance between A and C. 00:02:24.040 --> 00:02:25.940 In fact, we can use our compass for it. 00:02:25.940 --> 00:02:30.930 The distance between A and C is just like that. 00:02:30.930 --> 00:02:32.170 And so since all 00:02:32.170 --> 00:02:35.570 of these rigid transformations preserve distance, 00:02:35.570 --> 00:02:39.270 we know that C prime, the point that C gets mapped to 00:02:39.270 --> 00:02:41.540 after those first two transformations. 00:02:41.540 --> 00:02:43.620 C prime it's distance is going 00:02:43.620 --> 00:02:45.360 to stay the same from A prime. 00:02:45.360 --> 00:02:48.010 So C prime is going to be some place, 00:02:48.010 --> 00:02:53.010 some place along this curve right over here. 00:02:54.260 --> 00:02:55.530 We also know 00:02:55.530 --> 00:02:59.600 that the rigid transformations preserve angle measures. 00:02:59.600 --> 00:03:02.770 And so we also know that as we do the mapping, 00:03:02.770 --> 00:03:04.410 the angle will be preserved. 00:03:04.410 --> 00:03:08.100 So either side AC will be mapped 00:03:08.100 --> 00:03:11.570 to this side right over here, and if that's the case 00:03:11.570 --> 00:03:13.710 then F would be equal to C prime, 00:03:13.710 --> 00:03:16.200 and we would have found our rigid transformation 00:03:16.200 --> 00:03:18.730 based on SAS, and so therefore 00:03:18.730 --> 00:03:20.550 the two triangles would be congruent. 00:03:20.550 --> 00:03:21.730 But there's another possibility 00:03:21.730 --> 00:03:23.480 that the angle gets conserved, 00:03:23.480 --> 00:03:28.020 but side AC is mapped down here. 00:03:28.020 --> 00:03:31.020 So there's another possibility that side AC, 00:03:31.020 --> 00:03:32.540 due to our rigid transformations, 00:03:32.540 --> 00:03:36.370 or after our first set of rigid transformations, 00:03:36.370 --> 00:03:38.660 looks something like this. 00:03:41.599 --> 00:03:44.160 It looks something like that. 00:03:44.160 --> 00:03:48.320 In which case, C prime would be mapped right over there. 00:03:48.320 --> 00:03:49.153 And in that case, 00:03:49.153 --> 00:03:51.500 we can just do one more rigid transformation. 00:03:51.500 --> 00:03:55.830 We can just do a reflection about DE, 00:03:55.830 --> 00:03:59.340 or A prime B prime, to reflect point C prime 00:03:59.340 --> 00:04:00.990 over that to get right over there. 00:04:00.990 --> 00:04:04.000 How do we know that C prime would then be mapped to F? 00:04:04.000 --> 00:04:06.410 Well, this angle would be preserved 00:04:06.410 --> 00:04:07.950 due to the rigid transformation. 00:04:07.950 --> 00:04:11.900 So as we flip it over, as we do the reflection over DE, 00:04:11.900 --> 00:04:13.790 the angle will be preserved. 00:04:13.790 --> 00:04:17.340 And A prime C prime will then map to DF. 00:04:17.340 --> 00:04:18.590 And then we'd be done. 00:04:18.590 --> 00:04:20.980 We have just shown that there's always a series 00:04:20.980 --> 00:04:22.380 of rigid transformations, 00:04:22.380 --> 00:04:25.270 as long as you meet this SAS criteria, 00:04:25.270 --> 00:04:27.980 that can map one triangle onto the other. 00:04:27.980 --> 00:04:29.933 And therefore, they are congruent.

Proving the SSS triangle congruence criterion using transformations

https://www.youtube.com/watch?v=OIRZd5mDu_o

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https://www.youtube.com/api/timedtext?v=OIRZd5mDu_o&ei=bViUZYvJHsvwvdIPhqC-0AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=23E5B57E3651E7C0A4F9482D0D31C2E32FF4756F.D9D6F65B92500EB14BF637EE294C386D7D3C1DB4&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.220 --> 00:00:02.050 - [Instructor] What we're going to do in this video 00:00:02.050 --> 00:00:04.220 is see that if we have two different triangles 00:00:04.220 --> 00:00:06.570 where the corresponding sides have the same measure, 00:00:06.570 --> 00:00:09.840 so this orange side has the same length as this orange side, 00:00:09.840 --> 00:00:12.460 this blue side has the same length as this blue side, 00:00:12.460 --> 00:00:15.960 this gray side has the same length as this gray side, 00:00:15.960 --> 00:00:18.210 then we can deduce that these two triangles 00:00:18.210 --> 00:00:19.990 are congruent to each other 00:00:19.990 --> 00:00:24.390 based on the rigid transformation definition of congruence. 00:00:24.390 --> 00:00:26.100 And to show that, we just have to show 00:00:26.100 --> 00:00:29.200 that there's always a series of rigid transformations 00:00:29.200 --> 00:00:34.200 that maps triangle ABC onto triangle EDF. 00:00:35.010 --> 00:00:36.620 So how do we do that? 00:00:36.620 --> 00:00:38.200 Well, first of all, in other videos, 00:00:38.200 --> 00:00:41.110 we showed that if we have two line segments 00:00:41.110 --> 00:00:43.750 that have the same measure, they are congruent. 00:00:43.750 --> 00:00:47.770 You can map one onto the other using rigid transformations. 00:00:47.770 --> 00:00:50.570 So let's do a series of rigid transformations 00:00:50.570 --> 00:00:53.950 that maps AB onto ED. 00:00:53.950 --> 00:00:56.170 And you could imagine how to do that. 00:00:56.170 --> 00:00:57.960 You would translate point A. 00:00:57.960 --> 00:01:00.600 You would translate this entire left triangle 00:01:00.600 --> 00:01:03.810 so that point A coincides with point E, 00:01:03.810 --> 00:01:07.300 and then side AB would be moving in this, 00:01:07.300 --> 00:01:08.670 would be on this direction over here. 00:01:08.670 --> 00:01:11.640 And then you would rotate around this point right over here. 00:01:11.640 --> 00:01:12.920 You could call that A prime. 00:01:12.920 --> 00:01:15.200 So this is going to be equal to A prime. 00:01:15.200 --> 00:01:16.770 You rotate around that 00:01:16.770 --> 00:01:21.240 so that side AB coincides with side ED. 00:01:21.240 --> 00:01:23.090 And we've talked about that in other videos. 00:01:23.090 --> 00:01:26.950 So at that point, D would be equal to B prime, 00:01:26.950 --> 00:01:29.220 the point to which B is mapped. 00:01:29.220 --> 00:01:31.750 But the question is where is C? 00:01:31.750 --> 00:01:35.900 If we can show that for sure C is either at point F 00:01:35.900 --> 00:01:37.670 or, with another rigid transformation, 00:01:37.670 --> 00:01:39.480 we can get C to point F, 00:01:39.480 --> 00:01:41.330 then we would have completed our proof. 00:01:41.330 --> 00:01:42.340 We would have been able to show 00:01:42.340 --> 00:01:44.450 that with a series of rigid transformations, 00:01:44.450 --> 00:01:46.060 you can go from this triangle 00:01:46.060 --> 00:01:49.180 or you can map this triangle onto that triangle. 00:01:49.180 --> 00:01:50.990 And to think about where point C is, 00:01:50.990 --> 00:01:54.520 this is where this compass is going to prove useful. 00:01:54.520 --> 00:01:59.520 We know that point C is exactly this far away from point A. 00:02:00.040 --> 00:02:02.380 I will measure that with my compass. 00:02:02.380 --> 00:02:04.210 So I could do it this way as well. 00:02:04.210 --> 00:02:08.990 Point C is exactly that far from point A. 00:02:08.990 --> 00:02:13.990 And so that means that point C needs to be someplace, 00:02:14.190 --> 00:02:17.300 someplace on this curve right over here, 00:02:17.300 --> 00:02:18.940 on this arc that I'm doing. 00:02:18.940 --> 00:02:23.520 These are some of the points that are exactly that far away. 00:02:23.520 --> 00:02:27.730 I can do a complete circle, but you see where this is going. 00:02:27.730 --> 00:02:30.410 So point C, I guess we could save C prime or C 00:02:30.410 --> 00:02:31.950 will be mapped to some point 00:02:31.950 --> 00:02:35.090 on that circle if you take it from A's perspective, 00:02:35.090 --> 00:02:37.240 because that's how far C is from A, 00:02:37.240 --> 00:02:41.150 but then we also know that C is this far from B. 00:02:41.150 --> 00:02:43.600 So let me adjust my compass again. 00:02:43.600 --> 00:02:47.390 C is that far from B, 00:02:47.390 --> 00:02:49.840 and so if B is mapped to this point, 00:02:49.840 --> 00:02:53.890 this is where B prime is then C prime where C is mapped 00:02:53.890 --> 00:02:57.370 is going to be someplace along this curve, 00:02:57.370 --> 00:03:00.200 and so you could view those two curves as constraints 00:03:00.200 --> 00:03:03.940 so we know that C prime has to sit on both of these curves. 00:03:03.940 --> 00:03:07.160 So it's either going to sit right over here where F is 00:03:07.160 --> 00:03:09.780 and so if my rigid transformation got us to a point 00:03:09.780 --> 00:03:11.960 where C sits exactly where F is, 00:03:11.960 --> 00:03:13.740 well then our proof is complete. 00:03:13.740 --> 00:03:16.500 We've come up with a rigid transformation. 00:03:16.500 --> 00:03:17.800 Now another possibility is 00:03:17.800 --> 00:03:19.500 when we do that transformation 00:03:19.500 --> 00:03:22.550 C prime ends up right over here. 00:03:22.550 --> 00:03:24.110 So what could we then do 00:03:24.110 --> 00:03:27.150 to continue to transform rigidly 00:03:27.150 --> 00:03:29.150 so that C prime ends up with F? 00:03:29.150 --> 00:03:30.460 Remember the other two points 00:03:30.460 --> 00:03:35.130 have already coincided on with E and D 00:03:35.130 --> 00:03:38.440 so we just have to get C prime to coincide with F. 00:03:38.440 --> 00:03:40.570 Well one way to think about it is, 00:03:40.570 --> 00:03:43.560 if we if we think about it, 00:03:43.560 --> 00:03:48.560 E, point E is equidistant to C Prime and F. 00:03:49.450 --> 00:03:52.123 We see this is going to be equal to, 00:03:53.071 --> 00:03:54.220 we could put three hashtags there, 00:03:54.220 --> 00:03:55.800 because once again that defined the radius 00:03:55.800 --> 00:04:00.130 of this arc and we know that point C Prime 00:04:00.130 --> 00:04:03.960 in this case the point C prime in this case 00:04:03.960 --> 00:04:08.770 is the same distance from D as F is, as F is. 00:04:08.770 --> 00:04:10.120 And so one way to think about it, 00:04:10.120 --> 00:04:12.620 imagine a line between F and, 00:04:12.620 --> 00:04:14.170 I could get my straight edge here 00:04:14.170 --> 00:04:16.310 so it looks a little bit neater, 00:04:16.310 --> 00:04:21.310 imagine a line that connects F and this C Prime, 00:04:21.460 --> 00:04:22.560 and once again we're in the case 00:04:22.560 --> 00:04:24.420 where C prime immediately didn't go to F, 00:04:24.420 --> 00:04:28.990 where C prime ended up being on this side so to speak, 00:04:28.990 --> 00:04:31.450 and you can see that point E, 00:04:31.450 --> 00:04:35.310 because it is equidistant to C Prime and F, 00:04:35.310 --> 00:04:38.840 it must sit on the perpendicular bisector 00:04:38.840 --> 00:04:41.560 of the segment FC. 00:04:41.560 --> 00:04:44.910 Same thing about point D or B prime. 00:04:44.910 --> 00:04:47.080 This must be the perpendicular bisector, 00:04:47.080 --> 00:04:48.880 because this point is equidistant to F 00:04:48.880 --> 00:04:51.180 as it is to C prime. 00:04:51.180 --> 00:04:54.010 This point is equidistant to F as it is to C prime. 00:04:54.010 --> 00:04:55.940 The set of points whose distance 00:04:55.940 --> 00:04:59.970 is equal to F and C prime they will form 00:04:59.970 --> 00:05:02.930 the perpendicular bisector of FC. 00:05:02.930 --> 00:05:04.580 So we know that this orange line 00:05:04.580 --> 00:05:07.200 is a perpendicular bisector of FC. 00:05:07.200 --> 00:05:08.510 Why is that helpful? 00:05:08.510 --> 00:05:09.680 Well that tells us is 00:05:09.680 --> 00:05:11.540 if when we do that first transformation 00:05:11.540 --> 00:05:14.190 to make AB coincide with EF, 00:05:14.190 --> 00:05:16.750 if C Prime doesn't end up here and it ends up there, 00:05:16.750 --> 00:05:18.500 we just have to do one more transformation. 00:05:18.500 --> 00:05:21.580 We just have to do a reflection about ED 00:05:21.580 --> 00:05:23.330 or about A prime B prime, 00:05:23.330 --> 00:05:24.200 however you want to view it, 00:05:24.200 --> 00:05:25.580 about this orange line, 00:05:25.580 --> 00:05:28.710 and then C will coincide with F, 00:05:28.710 --> 00:05:31.040 because orange is a perpendicular bisector. 00:05:31.040 --> 00:05:32.720 So I could do something like this. 00:05:32.720 --> 00:05:35.840 This length is the same as this length, 00:05:35.840 --> 00:05:36.703 and since it's perpendicular bisector, 00:05:36.703 --> 00:05:39.430 when you do the reflection 00:05:39.430 --> 00:05:42.010 C prime will then coincide with F. 00:05:42.010 --> 00:05:44.360 And a reflection is a rigid transformation, 00:05:44.360 --> 00:05:45.953 so we would be all good.

Geometric constructions: perpendicular line through a point off the line

https://www.youtube.com/watch?v=-ltjjKgGY7o

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WEBVTT Kind: captions Language: en 00:00:00.270 --> 00:00:02.270 - [Instructor] What I have here is a line, 00:00:02.270 --> 00:00:05.140 and I have a point that is not on that line, 00:00:05.140 --> 00:00:08.240 and my goal is to draw a new line 00:00:08.240 --> 00:00:10.010 that goes through this point, 00:00:10.010 --> 00:00:12.550 and is perpendicular to my original line. 00:00:12.550 --> 00:00:14.480 How do I do that? 00:00:14.480 --> 00:00:16.740 Well you might imagine that our compass 00:00:16.740 --> 00:00:17.680 will come in handy, 00:00:17.680 --> 00:00:19.140 it's been handy before. 00:00:19.140 --> 00:00:22.390 And so what I will do is, I'll pick an arbitrary point 00:00:22.390 --> 00:00:23.223 on our original line, 00:00:23.223 --> 00:00:25.400 let's say this point right over here. 00:00:25.400 --> 00:00:27.400 And then I'll adjust my compass, 00:00:27.400 --> 00:00:30.940 so the distance between the pivot point 00:00:30.940 --> 00:00:32.890 and my pencil tip, 00:00:32.890 --> 00:00:35.420 is the same as the distance between those two points. 00:00:35.420 --> 00:00:38.320 And then I can now use my compass 00:00:38.320 --> 00:00:41.290 to trace out an arc of that radius. 00:00:41.290 --> 00:00:42.963 So there you go. 00:00:43.900 --> 00:00:46.000 Now my next step is to find another point 00:00:46.000 --> 00:00:47.880 on my original line 00:00:47.880 --> 00:00:49.740 that has the same distance 00:00:49.740 --> 00:00:51.960 from that point that is off the line. 00:00:51.960 --> 00:00:55.720 And I can do that by centering my compass 00:00:55.720 --> 00:00:58.170 on that offline point, 00:00:58.170 --> 00:00:59.940 and then drawing another arc. 00:00:59.940 --> 00:01:02.230 And I can see very clearly 00:01:02.230 --> 00:01:05.480 that this point also has the same distance 00:01:05.480 --> 00:01:07.760 from this point up here. 00:01:07.760 --> 00:01:11.200 And then I can center my compass on that point, 00:01:11.200 --> 00:01:12.880 and notice I haven't changed the radius 00:01:12.880 --> 00:01:14.570 of my compass, 00:01:14.570 --> 00:01:18.910 to draw another arc like this, 00:01:18.910 --> 00:01:21.063 to draw another arc like this. 00:01:22.240 --> 00:01:25.080 And then what I can do is connect 00:01:25.080 --> 00:01:27.623 this point and that point, 00:01:28.770 --> 00:01:30.930 and it at least looks perpendicular, 00:01:30.930 --> 00:01:32.460 but we're going to prove to ourselves 00:01:32.460 --> 00:01:34.320 that it is indeed perpendicular 00:01:34.320 --> 00:01:35.960 to our original line. 00:01:35.960 --> 00:01:40.043 So let me just draw it, so you have that like that. 00:01:40.950 --> 00:01:42.260 So how do we feel good 00:01:42.260 --> 00:01:44.000 that this new line that I just drew 00:01:44.000 --> 00:01:46.460 is perpendicular to our original one? 00:01:46.460 --> 00:01:48.670 Well let's connect the dots 00:01:48.670 --> 00:01:49.940 that we made. 00:01:49.940 --> 00:01:52.240 So if we connect all the dots 00:01:52.240 --> 00:01:53.720 we're going to get a rhombus. 00:01:53.720 --> 00:01:55.483 We know that this distance, 00:01:56.570 --> 00:02:01.067 this distance is the same as this distance. 00:02:01.067 --> 00:02:05.150 The same as this one right over here, 00:02:05.150 --> 00:02:08.089 which is the same as this distance, 00:02:08.089 --> 00:02:10.800 so let me make sure I got my straight edge right. 00:02:10.800 --> 00:02:13.290 Same as that distance, 00:02:13.290 --> 00:02:17.490 which is the same as this distance, 00:02:17.490 --> 00:02:22.490 same as that distance. 00:02:24.100 --> 00:02:28.480 And then, so this is a rhombus, 00:02:28.480 --> 00:02:30.450 and we know that the diagonals 00:02:30.450 --> 00:02:31.790 of a rhombus 00:02:31.790 --> 00:02:34.240 intersect at right angles. 00:02:34.240 --> 00:02:35.073 So there you have it. 00:02:35.073 --> 00:02:36.240 I have drawn a new line 00:02:36.240 --> 00:02:38.750 that goes through that offline point, 00:02:38.750 --> 00:02:41.253 and is perpendicular to our original line.

Geometric constructions: congruent angles

https://www.youtube.com/watch?v=D9UXfNc1ePs

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WEBVTT Kind: captions Language: en 00:00:01.110 --> 00:00:02.560 - [Instructor] What we're gonna do in this video 00:00:02.560 --> 00:00:04.970 is learn to construct congruent angles, 00:00:04.970 --> 00:00:06.360 and we're gonna do it, with of course, 00:00:06.360 --> 00:00:08.050 a pen or a pencil here. 00:00:08.050 --> 00:00:11.080 I'm gonna use a ruler as a straight edge. 00:00:11.080 --> 00:00:12.380 And then I'm gonna use a tool 00:00:12.380 --> 00:00:13.600 known as a compass. 00:00:13.600 --> 00:00:15.360 Which looks a little bit fancy, 00:00:15.360 --> 00:00:16.710 but what it allows us to do 00:00:16.710 --> 00:00:19.420 it'll apply using it in a little bit, 00:00:19.420 --> 00:00:21.530 is it allows us to draw perfect circles, 00:00:21.530 --> 00:00:23.030 or arcs, of a given radius. 00:00:23.030 --> 00:00:24.720 You pivot on one point here 00:00:24.720 --> 00:00:26.570 and then you use your pen or your pencil 00:00:26.570 --> 00:00:28.810 to trace out the arc, 00:00:28.810 --> 00:00:30.200 or the circle. 00:00:30.200 --> 00:00:32.570 So let's just start with this angle 00:00:32.570 --> 00:00:33.520 right over here, 00:00:33.520 --> 00:00:35.470 and I'm going to construct an angle 00:00:35.470 --> 00:00:37.750 that is congruent to it. 00:00:37.750 --> 00:00:40.650 So let me make the vertex of my second angle 00:00:40.650 --> 00:00:42.020 right over there, 00:00:42.020 --> 00:00:44.500 and then let me draw one of the rays 00:00:44.500 --> 00:00:46.690 that originates at that vertex. 00:00:46.690 --> 00:00:47.750 And I'm gonna put this angle 00:00:47.750 --> 00:00:48.850 in a different orientation, 00:00:48.850 --> 00:00:50.010 just to show that they don't even have 00:00:50.010 --> 00:00:53.290 to have the same orientation. 00:00:53.290 --> 00:00:54.260 So it's going to look 00:00:54.260 --> 00:00:57.480 something like that, that's one of the rays. 00:00:57.480 --> 00:00:58.313 But then we have to figure out 00:00:58.313 --> 00:00:59.410 where do we put, 00:00:59.410 --> 00:01:01.190 where do we put the other ray 00:01:01.190 --> 00:01:03.330 so that the two angles are congruent? 00:01:03.330 --> 00:01:05.890 And this is where our compass 00:01:05.890 --> 00:01:07.910 is going to be really useful. 00:01:07.910 --> 00:01:10.740 So what I'm going to do is put the pivot point 00:01:10.740 --> 00:01:12.100 of a compass, of the compass, 00:01:12.100 --> 00:01:14.170 right at the vertex of the first angle, 00:01:14.170 --> 00:01:19.170 and I'm going to draw out an arc like this. 00:01:19.240 --> 00:01:20.355 And what's useful about the compass 00:01:20.355 --> 00:01:24.210 is you can keep the radius constant, 00:01:24.210 --> 00:01:26.810 and you can see it intersects 00:01:26.810 --> 00:01:29.910 our first two rays at points, 00:01:29.910 --> 00:01:33.020 let's just call this B and C. 00:01:33.020 --> 00:01:34.850 And I could call this point A, 00:01:34.850 --> 00:01:35.980 right over here. 00:01:35.980 --> 00:01:37.140 And so let me, 00:01:37.140 --> 00:01:39.390 now that I have my compass with the exact 00:01:39.390 --> 00:01:41.130 right radius right now, 00:01:41.130 --> 00:01:44.290 let me draw that right over here. 00:01:44.290 --> 00:01:47.350 But this alone won't allow us to draw 00:01:47.350 --> 00:01:48.753 the angle just yet, 00:01:49.850 --> 00:01:52.320 but let me draw it like this, 00:01:52.320 --> 00:01:55.073 and that is pretty good. 00:01:56.220 --> 00:01:59.626 And let's call this point right over here D, 00:01:59.626 --> 00:02:01.550 and I'll call this one E, 00:02:01.550 --> 00:02:02.780 and I wanna figure out where to put 00:02:02.780 --> 00:02:04.630 my third point F, 00:02:04.630 --> 00:02:06.230 so I can define ray E F, 00:02:06.230 --> 00:02:08.390 so that these two angles are congruent. 00:02:08.390 --> 00:02:12.140 And what I can do is take my compass again 00:02:12.140 --> 00:02:15.680 and get a clear sense of the distance 00:02:15.680 --> 00:02:16.990 between C and B, 00:02:16.990 --> 00:02:18.980 by adjusting my compass. 00:02:18.980 --> 00:02:20.420 So one point is on C, 00:02:20.420 --> 00:02:22.610 and my pencil is on B. 00:02:22.610 --> 00:02:24.860 So I have, get this right, 00:02:24.860 --> 00:02:27.430 so I have this distance right over here. 00:02:27.430 --> 00:02:29.280 I know this distance, 00:02:29.280 --> 00:02:31.520 and I've adjusted my compass accordingly, 00:02:31.520 --> 00:02:34.250 so I can get that same distance 00:02:34.250 --> 00:02:35.893 right over there. 00:02:36.860 --> 00:02:38.760 And so you can now image 00:02:38.760 --> 00:02:40.800 where I'm going to draw that second ray. 00:02:40.800 --> 00:02:42.190 That second ray, 00:02:42.190 --> 00:02:46.720 if I put point F right over here, 00:02:46.720 --> 00:02:47.870 my second ray, 00:02:47.870 --> 00:02:51.860 I can just draw between, starting at point E 00:02:51.860 --> 00:02:52.870 right over here, 00:02:52.870 --> 00:02:55.080 going through point F. 00:02:55.080 --> 00:02:57.620 I could draw a little bit neater, 00:02:57.620 --> 00:03:00.580 so it would look like that, my second ray. 00:03:00.580 --> 00:03:02.210 Ignore that first little line I drew, 00:03:02.210 --> 00:03:03.043 I'm using a pen, 00:03:03.043 --> 00:03:04.390 which I don't recommend for you to do it. 00:03:04.390 --> 00:03:05.450 I'm doing it so that you can see 00:03:05.450 --> 00:03:06.970 it on this video. 00:03:06.970 --> 00:03:09.480 Now how do we know that this angle 00:03:09.480 --> 00:03:11.920 is now congruent to this angle 00:03:11.920 --> 00:03:13.360 right over here? 00:03:13.360 --> 00:03:14.690 Well one way to do it, is to think 00:03:14.690 --> 00:03:17.620 about triangle B A C, 00:03:17.620 --> 00:03:19.440 triangle B A C, 00:03:19.440 --> 00:03:23.230 and triangle, let's just call it D F E. 00:03:23.230 --> 00:03:25.740 So this triangle right over here. 00:03:25.740 --> 00:03:27.570 When we drew that first arc, 00:03:27.570 --> 00:03:30.760 we know that the distance between A C 00:03:30.760 --> 00:03:33.450 is equivalent to the distance between A B, 00:03:33.450 --> 00:03:36.300 and we kept the compass radius the same. 00:03:36.300 --> 00:03:39.110 So we know that's also the distance between E F, 00:03:39.110 --> 00:03:41.730 and the distance between E D. 00:03:41.730 --> 00:03:43.300 And then the second time, 00:03:43.300 --> 00:03:45.910 when we adjusted our compass radius, 00:03:45.910 --> 00:03:48.580 we now know that the distance between B C 00:03:48.580 --> 00:03:51.940 is the same as the distance between F and D. 00:03:51.940 --> 00:03:53.180 Or the length of B C 00:03:53.180 --> 00:03:56.380 is the same as the length of F D. 00:03:56.380 --> 00:04:00.430 So it's very clear that we have congruent triangles. 00:04:00.430 --> 00:04:01.670 All of the three sides 00:04:01.670 --> 00:04:03.380 have the same measure, 00:04:03.380 --> 00:04:06.130 and therefore the corresponding angles 00:04:06.130 --> 00:04:08.153 must be congruent as well.

Geometric constructions: parallel line

https://www.youtube.com/watch?v=BHLre3UiIho

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https://www.youtube.com/api/timedtext?v=BHLre3UiIho&ei=bViUZaf7GZCFp-oPhoWiKA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B3E4156EC8731E87450A2F7C7A9CBC4EC82E9A28.CD9E9560E0F555998E8D70AFF77596C3562F9C4B&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.510 --> 00:00:02.940 - [David] Let's say that we have a line, 00:00:02.940 --> 00:00:05.070 drawing it right over there, 00:00:05.070 --> 00:00:09.470 and our goal is to construct another line 00:00:09.470 --> 00:00:11.340 that is parallel to this line 00:00:11.340 --> 00:00:13.790 that goes through this point. 00:00:13.790 --> 00:00:15.740 How would we do that? 00:00:15.740 --> 00:00:17.840 Well, the way that we can approach it is 00:00:17.840 --> 00:00:20.630 by creating what will eventually be a transversal 00:00:20.630 --> 00:00:22.950 between the two parallel lines. 00:00:22.950 --> 00:00:24.450 So let me draw that. 00:00:24.450 --> 00:00:26.530 So I'm just drawing a line that goes through my point 00:00:26.530 --> 00:00:28.878 and intersects my original line. 00:00:28.878 --> 00:00:32.020 Do that, so it's going to look like that. 00:00:32.020 --> 00:00:34.430 And then, I'm really just going to use the idea 00:00:34.430 --> 00:00:38.470 of corresponding angled congruents for parallel lines. 00:00:38.470 --> 00:00:41.660 So what I can do is now take my compass 00:00:42.750 --> 00:00:46.363 and think about this angle right over here. 00:00:47.210 --> 00:00:49.263 So I'll draw it like that. 00:00:50.190 --> 00:00:53.600 And say, all right, if I draw an arc 00:00:53.600 --> 00:00:56.230 of the same radius over here, 00:00:56.230 --> 00:00:59.280 can I reconstruct that angle? 00:00:59.280 --> 00:01:03.440 And so where should the point be on this left end? 00:01:03.440 --> 00:01:06.480 Well, to do that, I can just measure 00:01:07.640 --> 00:01:09.450 the distance between these two points 00:01:09.450 --> 00:01:12.200 using my compass, so I'm adjusting it a little bit 00:01:12.200 --> 00:01:14.950 to get the distance between those two points. 00:01:14.950 --> 00:01:19.550 And then I can use that up over here to figure out, 00:01:19.550 --> 00:01:21.240 I got a little bit shaky. 00:01:21.240 --> 00:01:23.540 I can figure out that point right over there. 00:01:23.540 --> 00:01:28.540 And just like that, I now have two corresponding angles 00:01:29.010 --> 00:01:31.810 to find my transversal and parallel lines, 00:01:31.810 --> 00:01:34.780 so what I can do is take my straightedge 00:01:34.780 --> 00:01:39.290 and make it go through those points that I just created, 00:01:39.290 --> 00:01:41.350 so let's see, make sure I'm going through, 00:01:41.350 --> 00:01:43.180 and it would look like that, 00:01:43.180 --> 00:01:46.880 and I have just constructed two parallel lines. 00:01:46.880 --> 00:01:50.090 And once again, how do I know that this line 00:01:50.090 --> 00:01:51.950 is parallel to this line? 00:01:51.950 --> 00:01:55.160 Because we have a transversal that intersects both of them 00:01:55.160 --> 00:01:58.240 and these two angles, which are corresponding angles, 00:01:58.240 --> 00:01:59.073 are congruent. 00:01:59.073 --> 00:02:02.303 So these two lines must be parallel.

Angle congruence equivalent to having same measure

https://www.youtube.com/watch?v=t41aV0XkYPQ

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WEBVTT Kind: captions Language: en 00:00:00.360 --> 00:00:01.460 - [Instructor] What we're going to do in this video 00:00:01.460 --> 00:00:04.500 is demonstrate that angles are congruent if and only 00:00:04.500 --> 00:00:07.540 if they have the same measure, 00:00:07.540 --> 00:00:10.440 and for our definition of congruence, 00:00:10.440 --> 00:00:13.750 we will use the rigid transformation definition, 00:00:13.750 --> 00:00:16.420 which tells us two figures are congruent if and only 00:00:16.420 --> 00:00:20.100 if there exists a series of rigid transformations 00:00:20.100 --> 00:00:23.620 which will map one figure onto the other. 00:00:23.620 --> 00:00:26.200 And then, what are rigid transformations? 00:00:26.200 --> 00:00:29.010 Those are transformations that preserve distance 00:00:29.010 --> 00:00:31.860 between points and angle measures. 00:00:31.860 --> 00:00:33.920 So, let's get to it. 00:00:33.920 --> 00:00:36.350 So, let's start with two angles that are congruent, 00:00:36.350 --> 00:00:39.070 and I'm going to show that they have the same measure. 00:00:39.070 --> 00:00:42.660 I'm going to demonstrate that, so they start congruent, 00:00:42.660 --> 00:00:45.380 so these two angles are congruent to each other. 00:00:45.380 --> 00:00:49.680 Now, this means by the rigid transformation 00:00:49.680 --> 00:00:54.680 definition of congruence, there is a series 00:00:56.500 --> 00:00:59.630 of rigid transformations, 00:00:59.630 --> 00:01:04.550 transformations that map 00:01:04.550 --> 00:01:09.023 angle ABC onto angle, 00:01:10.400 --> 00:01:13.073 I'll do it here, onto angle DEF. 00:01:16.408 --> 00:01:20.510 By definition, by definition of rigid transformations, 00:01:20.510 --> 00:01:25.510 they preserve angle measure, preserve angle measure. 00:01:26.750 --> 00:01:30.000 So, if you're able to map the left angle 00:01:30.000 --> 00:01:32.730 onto the right angle, and in doing so, you did it 00:01:32.730 --> 00:01:35.250 with transformations that preserved angle measure, 00:01:35.250 --> 00:01:38.400 they must now have the same angle measure. 00:01:38.400 --> 00:01:43.160 We now know that the measure of angle ABC is equal 00:01:43.160 --> 00:01:45.133 to the measure of angle DEF. 00:01:46.430 --> 00:01:50.060 So, we've demonstrated this green statement the first way, 00:01:50.060 --> 00:01:51.620 that if things are congruent, 00:01:51.620 --> 00:01:53.110 they will have the same measure. 00:01:53.110 --> 00:01:55.550 Now, let's prove it the other way around. 00:01:55.550 --> 00:01:59.453 So now, let's start with the idea that measure of angle ABC 00:02:01.090 --> 00:02:04.043 is equal to the measure of angle DEF, 00:02:04.930 --> 00:02:07.220 and to demonstrate that these are going to be congruent, 00:02:07.220 --> 00:02:09.000 we just have to show that there's always a series 00:02:09.000 --> 00:02:12.880 of rigid transformations that will map angle ABC 00:02:12.880 --> 00:02:16.130 onto angle DEF, and to help us there, 00:02:16.130 --> 00:02:18.380 let's just visualize these angles, 00:02:18.380 --> 00:02:21.957 so, draw this really fast, angle ABC, 00:02:24.480 --> 00:02:28.690 and angle is defined by two rays that start at a point. 00:02:28.690 --> 00:02:32.090 That point is the vertex, so that's ABC, 00:02:32.090 --> 00:02:35.453 and then let me draw angle DEF. 00:02:37.158 --> 00:02:39.408 So, that might look something like this, DEF, 00:02:42.840 --> 00:02:46.000 and what we will now do is let's do 00:02:46.000 --> 00:02:48.350 our first rigid transformation. 00:02:48.350 --> 00:02:53.273 Let's translate, translate angle ABC 00:02:56.780 --> 00:03:01.780 so that B mapped to point E, 00:03:05.330 --> 00:03:08.470 and if we did that, so we're gonna translate it like that, 00:03:08.470 --> 00:03:12.514 then ABC is going to look something like, 00:03:12.514 --> 00:03:13.347 ABC is gonna look something like this. 00:03:15.753 --> 00:03:17.000 It's going to look something like this. 00:03:17.000 --> 00:03:20.430 B is now mapped onto E. 00:03:20.430 --> 00:03:23.120 This would be where A would get mapped to. 00:03:23.120 --> 00:03:24.610 This would where C would get mapped to. 00:03:24.610 --> 00:03:27.450 Sometimes you might see a notation A prime, C prime, 00:03:27.450 --> 00:03:30.120 and this is where B would get mapped to, 00:03:30.120 --> 00:03:32.150 and then the next thing I would do 00:03:32.150 --> 00:03:37.150 is I would rotate angle ABC about its vertex, 00:03:41.040 --> 00:03:45.327 about B, so that ray BC, 00:03:48.600 --> 00:03:53.600 ray BC, coincides, coincides with ray EF. 00:03:57.870 --> 00:04:02.300 Now, you're just gonna rotate the whole angle that way 00:04:02.300 --> 00:04:07.080 so that now, ray BC coincides with ray EF. 00:04:07.080 --> 00:04:08.657 Well, you might be saying, "Hey, C doesn't necessarily have 00:04:08.657 --> 00:04:11.017 "to sit on F 'cause they might be different distances 00:04:11.017 --> 00:04:13.480 "from their vertices," but that's all right. 00:04:13.480 --> 00:04:17.410 The ray can be defined by any point that sits on that ray, 00:04:17.410 --> 00:04:21.780 so now, if you do this rotation, and ray BC coincides 00:04:21.780 --> 00:04:24.960 with ray EF, now those two rays would be equivalent 00:04:24.960 --> 00:04:29.550 because measure of angle ABC is equal to the measure 00:04:29.550 --> 00:04:30.383 of angle DEF. 00:04:32.060 --> 00:04:37.060 That will also tell us that ray BA, ray BA now coincides, 00:04:41.200 --> 00:04:45.920 coincides with ray ED, and just like that, 00:04:45.920 --> 00:04:47.990 I've given you a series of rigid transformations 00:04:47.990 --> 00:04:49.500 that will always work. 00:04:49.500 --> 00:04:51.810 If you translate so that the vertices are mapped 00:04:51.810 --> 00:04:54.160 onto each other and then you rotate it 00:04:54.160 --> 00:04:55.990 so that the bottom ray of one angle coincides 00:04:55.990 --> 00:04:57.820 with the bottom ray of the other angle, 00:04:57.820 --> 00:05:00.190 then you could say the top ray of the two angles 00:05:00.190 --> 00:05:02.930 will now coincide because the angles have the same measure, 00:05:02.930 --> 00:05:06.800 and because of that, the angles now completely coincide, 00:05:06.800 --> 00:05:11.800 and so we know that angle ABC is congruent to angle DEF, 00:05:13.200 --> 00:05:14.033 and we're now done. 00:05:14.033 --> 00:05:17.210 We've proven both sides of this statement. 00:05:17.210 --> 00:05:18.920 If they're congruent, they have the same measure. 00:05:18.920 --> 00:05:21.903 If they have the same measure, then they are congruent.

Introduction to Khan Academy Kids

https://www.youtube.com/watch?v=01VlLMdM65k

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WEBVTT Kind: captions Language: en 00:00:00.170 --> 00:00:01.270 - [Voice-over] Khan Academy Kids 00:00:01.270 --> 00:00:04.750 includes thousands of activities, books, and videos 00:00:04.750 --> 00:00:08.870 helping kids read, play, learn, and grow. 00:00:08.870 --> 00:00:10.730 Narrator Kodi Bear and her friends 00:00:10.730 --> 00:00:12.170 guide kids through the app, 00:00:12.170 --> 00:00:15.950 encouraging creativity, curiosity, and kindness. 00:00:15.950 --> 00:00:17.380 Because we believe that everyone 00:00:17.380 --> 00:00:19.060 should have access to learning, 00:00:19.060 --> 00:00:21.620 Khan Academy Kids is completely free. 00:00:21.620 --> 00:00:24.170 No ads, no subscriptions. 00:00:24.170 --> 00:00:26.933 Download now, and let the joyful learning begin!

Khan Academy Kids: Celebrating First Words Through First Grade

https://www.youtube.com/watch?v=ayMkrsbW3Vw

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WEBVTT Kind: captions Language: en 00:00:00.200 --> 00:00:02.210 - [Narrator] Growing up is exciting. 00:00:02.210 --> 00:00:05.200 There are so many firsts to discover: 00:00:05.200 --> 00:00:08.180 your first word, your first book, 00:00:08.180 --> 00:00:10.230 your first day of school, 00:00:10.230 --> 00:00:12.913 and with each new thing you learn, you grow. 00:00:13.800 --> 00:00:16.640 At Khan Academy, we embrace and celebrate learning 00:00:16.640 --> 00:00:18.210 at all ages. 00:00:18.210 --> 00:00:20.000 We created Khan Academy Kids 00:00:20.000 --> 00:00:21.330 to spark the joy of learning 00:00:21.330 --> 00:00:24.010 in kids ages two through seven. 00:00:24.010 --> 00:00:27.440 Through thousands of activities, books, and videos, 00:00:27.440 --> 00:00:30.933 kids can read, play, learn, and grow. 00:00:31.880 --> 00:00:33.740 Narrator Kodi Bear and her friends 00:00:33.740 --> 00:00:35.470 guide kids through the app, 00:00:35.470 --> 00:00:39.930 encouraging creativity, curiosity, and kindness. 00:00:39.930 --> 00:00:41.450 Because we believe that everyone 00:00:41.450 --> 00:00:43.300 should have access to learning, 00:00:43.300 --> 00:00:45.940 Khan Academy Kids is completely free, 00:00:45.940 --> 00:00:48.143 no ads, no subscriptions. 00:00:49.070 --> 00:00:50.630 Khan Academy Kids, 00:00:50.630 --> 00:00:53.540 now celebrating first words through first grade. 00:00:53.540 --> 00:00:56.823 Available in the App Store, Google Play, and Amazon.

Introduction to meditation to reduce test prep anxiety

https://www.youtube.com/watch?v=gOjKzh8z33U

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WEBVTT Kind: captions Language: en 00:00:00.450 --> 00:00:03.100 - Hello, Sal here from Khan Academy. 00:00:03.100 --> 00:00:05.590 So when you hear the word meditation, 00:00:05.590 --> 00:00:07.830 for many of y'all, it might evoke some type of 00:00:07.830 --> 00:00:10.620 new age thing that has nothing to do 00:00:10.620 --> 00:00:12.270 with standardize tests. 00:00:12.270 --> 00:00:14.250 And if you're about to take a standardize test, 00:00:14.250 --> 00:00:16.890 I'm sure there's many thoughts about 00:00:16.890 --> 00:00:19.300 am I prepared, am I going to do well, 00:00:19.300 --> 00:00:22.180 I hope I don't bomb the exam. 00:00:22.180 --> 00:00:23.624 That stress and that anxiety 00:00:23.624 --> 00:00:26.160 is, if anything, going to hurt your performance 00:00:26.160 --> 00:00:27.850 on these things that you wanna do well. 00:00:27.850 --> 00:00:31.140 And so, meditation is a way to help still that. 00:00:31.140 --> 00:00:33.970 But it's really just for you to observe your thoughts, 00:00:33.970 --> 00:00:35.810 not get stressed out about it if your thoughts start 00:00:35.810 --> 00:00:37.890 to wander, but then just bring them back 00:00:37.890 --> 00:00:39.440 and try to not think. 00:00:39.440 --> 00:00:42.170 Or think about just very positive thoughts. 00:00:42.170 --> 00:00:44.420 I think if you do that you're gonna find you're gonna be 00:00:44.420 --> 00:00:46.620 happier, you're gonna be more positive, 00:00:46.620 --> 00:00:48.870 all sorts of positive energy is going to be attracted 00:00:48.870 --> 00:00:51.360 to you, and, even though that's not the most important 00:00:51.360 --> 00:00:54.080 thing in the world, you'll do just fine on these tests 00:00:54.080 --> 00:00:56.230 that right now you might be worrying about.

Introduction to meditation for students

https://www.youtube.com/watch?v=U_v6qr18sOo

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en

WEBVTT Kind: captions Language: en 00:00:00.330 --> 00:00:03.300 - Hi everyone, Sal here from Khan Academy. 00:00:03.300 --> 00:00:05.960 So for most of human history, 00:00:05.960 --> 00:00:09.440 when we were either hunter gatherers or early farmers, 00:00:09.440 --> 00:00:12.760 we had a lot of time where we would just look at things 00:00:12.760 --> 00:00:16.890 and not be overstimulated, there'd just be a bubbling brook. 00:00:16.890 --> 00:00:19.170 But now we're constantly stimulated 00:00:19.170 --> 00:00:22.190 by social media, by things we have to do at school, 00:00:22.190 --> 00:00:23.870 things that we have to do at work, 00:00:23.870 --> 00:00:26.800 our cell phones ringing, getting different text messages 00:00:26.800 --> 00:00:28.000 and before we know it, 00:00:28.000 --> 00:00:30.580 in modern society, our brains, 00:00:30.580 --> 00:00:34.370 our thoughts are taking control of us. 00:00:34.370 --> 00:00:36.840 And we actually don't have as much peace 00:00:36.840 --> 00:00:39.450 and as much stillness as we would like. 00:00:39.450 --> 00:00:41.041 And so one thing that I found in my life 00:00:41.041 --> 00:00:43.901 is that everyday you take some time out 00:00:43.901 --> 00:00:46.630 to just let your mind be still, 00:00:46.630 --> 00:00:48.520 you start to observe your thoughts, 00:00:48.520 --> 00:00:50.160 that it can be incredibly powerful, 00:00:50.160 --> 00:00:51.880 it's going to improve your mood, 00:00:51.880 --> 00:00:54.250 and it's going to just make you a overall happier 00:00:54.250 --> 00:00:55.723 and more functional person.

Guided visualization to calm your mind

https://www.youtube.com/watch?v=ZEYuSRHgmCg

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WEBVTT Kind: captions Language: en 00:00:00.380 --> 00:00:02.980 - [Instructor] Welcome, and thanks for taking out the time 00:00:02.980 --> 00:00:05.490 for yourself for what will hopefully be 00:00:05.490 --> 00:00:08.590 a nice inward journey. 00:00:08.590 --> 00:00:12.290 So just start off sitting upright, 00:00:12.290 --> 00:00:14.140 feet planted on the ground 00:00:14.140 --> 00:00:17.790 if you're ideally on some type of a firm chair. 00:00:17.790 --> 00:00:22.790 And start to soften your gaze if your eyes are still open. 00:00:23.130 --> 00:00:25.240 Gently close them. 00:00:25.240 --> 00:00:28.640 I like to leave my hands on my lap, 00:00:28.640 --> 00:00:31.180 palms up to the sky, 00:00:31.180 --> 00:00:33.493 but whatever feels comfortable for you. 00:00:34.930 --> 00:00:36.980 And then with your eyes closed, 00:00:36.980 --> 00:00:40.383 gently become a little bit more aware of your breaths. 00:00:41.500 --> 00:00:45.283 Make them a little bit deeper and a little bit slower. 00:00:47.070 --> 00:00:50.143 At your own time breathe in, 00:00:52.900 --> 00:00:57.280 breathe out, just a little bit deeper 00:00:57.280 --> 00:00:58.833 and a little bit slower. 00:01:01.850 --> 00:01:05.100 So the whole idea behind meditation 00:01:05.100 --> 00:01:08.610 is trying to ease all the chatter 00:01:08.610 --> 00:01:10.550 that exists in our brains, 00:01:10.550 --> 00:01:12.913 trying to still our thoughts. 00:01:13.770 --> 00:01:15.280 And so as we do that, 00:01:15.280 --> 00:01:18.170 and every meditation I'm going to try to introduce 00:01:18.170 --> 00:01:22.000 some frameworks, ways of thinking about your mind. 00:01:22.000 --> 00:01:25.260 But as you try to quiet the mind, 00:01:25.260 --> 00:01:28.120 it will inevitably get distracted. 00:01:28.120 --> 00:01:31.640 It might get distracted by some noise in the room 00:01:31.640 --> 00:01:35.370 or some noise outside, or more likely, 00:01:35.370 --> 00:01:37.620 it'll get distracted by thoughts 00:01:37.620 --> 00:01:40.470 that are just surfacing into your consciousness. 00:01:40.470 --> 00:01:43.780 And if that happens, don't let it make you anxious. 00:01:43.780 --> 00:01:45.660 A lot of folks, when they meditate, 00:01:45.660 --> 00:01:47.330 they worry that they're doing it wrong, 00:01:47.330 --> 00:01:48.750 and then if they get distracted, 00:01:48.750 --> 00:01:50.640 it actually makes things worse. 00:01:50.640 --> 00:01:52.557 They say, "I'm never going to be able 00:01:52.557 --> 00:01:54.940 "to do this meditation thing." 00:01:54.940 --> 00:01:57.670 The important thing is to approach the meditation 00:01:57.670 --> 00:02:00.970 with a spirit of fun, a spirit of curiosity. 00:02:00.970 --> 00:02:02.490 Have a sense of humor about it. 00:02:02.490 --> 00:02:04.520 We are all literally human, 00:02:04.520 --> 00:02:06.360 and we do very human things. 00:02:06.360 --> 00:02:09.230 And so when you find your mind wandering a bit, 00:02:09.230 --> 00:02:12.190 just laugh it off and say, "Oh, there you go, mind." 00:02:12.190 --> 00:02:14.940 Just come back to the stillness, not a big deal. 00:02:14.940 --> 00:02:17.100 Don't beat up on yourself over it. 00:02:17.100 --> 00:02:19.470 And as part of that, as we go over to this meditation, 00:02:19.470 --> 00:02:21.900 as much as possible try to keep a little bit 00:02:21.900 --> 00:02:24.860 of a smile on your face. 00:02:24.860 --> 00:02:25.920 Your eyes are closed, 00:02:25.920 --> 00:02:27.490 but you can still smile a little bit 00:02:27.490 --> 00:02:29.800 or at least smile with your mind. 00:02:29.800 --> 00:02:32.730 Reminds you that this should be fun. 00:02:32.730 --> 00:02:34.403 This is relaxing. 00:02:36.280 --> 00:02:41.280 So with that said, let's keep breathing in, breathing out, 00:02:41.700 --> 00:02:44.313 a little bit deeper, a little bit slower. 00:02:48.820 --> 00:02:51.210 In the framework that I'm going to introduce 00:02:51.210 --> 00:02:53.390 for how you can still your mind 00:02:53.390 --> 00:02:54.990 is one that I use a lot, 00:02:54.990 --> 00:02:57.830 which is imagining all the thoughts 00:02:57.830 --> 00:03:01.350 in your subconscious as the ocean. 00:03:01.350 --> 00:03:04.180 And the surface of the ocean is the interface 00:03:04.180 --> 00:03:08.150 between your subconscious and your consciousness. 00:03:08.150 --> 00:03:11.520 And most of us have a pretty choppy surface. 00:03:11.520 --> 00:03:12.960 There's a lot of thoughts 00:03:12.960 --> 00:03:16.030 that are jumping up and down out of our subconscious. 00:03:16.030 --> 00:03:19.123 And sometimes we're drowning in those thoughts. 00:03:20.050 --> 00:03:21.570 And one way to think about it 00:03:21.570 --> 00:03:24.680 is we can elevate ourselves. 00:03:24.680 --> 00:03:29.680 We can elevate ourselves above the surface of that water. 00:03:29.710 --> 00:03:32.160 And when you start to elevate yourself, 00:03:32.160 --> 00:03:35.010 you're not suppressing the thoughts, 00:03:35.010 --> 00:03:37.670 but you're just looking down on them. 00:03:37.670 --> 00:03:39.250 You see that they're still there. 00:03:39.250 --> 00:03:40.940 The surface is still choppy. 00:03:40.940 --> 00:03:42.550 There's still waves. 00:03:42.550 --> 00:03:44.910 But as you rise and you look down on it, 00:03:44.910 --> 00:03:47.470 you realize that you are not those thoughts. 00:03:47.470 --> 00:03:50.380 You are not the surface of the water. 00:03:50.380 --> 00:03:52.820 So whether the thing that's bothering you 00:03:52.820 --> 00:03:54.610 is an assignment you have to do 00:03:54.610 --> 00:03:58.170 or some interpersonal relations 00:03:58.170 --> 00:03:59.630 or just something in your life 00:03:59.630 --> 00:04:02.630 not working out the way that you would like it to, 00:04:02.630 --> 00:04:04.910 remind yourself that that is not you. 00:04:04.910 --> 00:04:08.370 You are not defined by the outcome of that situation. 00:04:08.370 --> 00:04:11.243 Those are just waves on that ocean. 00:04:14.730 --> 00:04:16.760 And the more that you surface above them 00:04:16.760 --> 00:04:20.630 and you look at them and analyze them, 00:04:20.630 --> 00:04:23.970 you realize that they have no control over you. 00:04:23.970 --> 00:04:28.230 And once that happens, things start to slow down. 00:04:28.230 --> 00:04:29.910 The surface of that water begins 00:04:29.910 --> 00:04:33.573 to get calmer and calmer and calmer. 00:04:35.130 --> 00:04:38.850 And there you are floating above that surface, 00:04:38.850 --> 00:04:40.803 just pure awareness. 00:04:41.940 --> 00:04:44.570 And you realize that you're a lot more 00:04:44.570 --> 00:04:45.943 than you thought you were. 00:04:46.950 --> 00:04:50.103 You aren't just your physical body. 00:04:50.960 --> 00:04:53.430 You aren't just those thoughts 00:04:53.430 --> 00:04:56.463 that you see as waves on the surface of that ocean. 00:04:57.920 --> 00:05:00.510 You aren't even just that identity 00:05:00.510 --> 00:05:02.550 that you associate yourself with, 00:05:02.550 --> 00:05:04.840 your name, your position in the world, 00:05:04.840 --> 00:05:07.793 your status, what people think of you, your relations. 00:05:09.020 --> 00:05:12.103 Those are aspects of you, but they aren't you. 00:05:13.200 --> 00:05:16.573 You are something much bigger than all of them. 00:05:17.410 --> 00:05:20.600 You are the space in which they occur, 00:05:20.600 --> 00:05:24.590 in which they happen, but they aren't you. 00:05:24.590 --> 00:05:27.850 And now let's just try to sit in that pure awareness 00:05:27.850 --> 00:05:29.040 for the next minute or so. 00:05:29.040 --> 00:05:32.000 And once again, if your thoughts wander, not a big deal. 00:05:32.000 --> 00:05:34.450 That's just the choppiness on the surface of that water, 00:05:34.450 --> 00:05:36.150 and you need to elevate yourself back 00:05:36.150 --> 00:05:38.050 to that pure awareness. 00:05:38.050 --> 00:05:40.410 And if the quiet bothers you, don't worry. 00:05:40.410 --> 00:05:43.003 I will be back in about a minute. 00:06:42.860 --> 00:06:47.090 All right, so that was a relatively short amount of time 00:06:47.090 --> 00:06:48.940 for you to be on your own. 00:06:48.940 --> 00:06:49.910 And as you'll see, 00:06:49.910 --> 00:06:53.410 as we do more and more advanced meditations, 00:06:53.410 --> 00:06:55.750 give yourself more and more time. 00:06:55.750 --> 00:06:58.550 And over time you won't need me talking. 00:06:58.550 --> 00:07:00.660 In fact, that will probably annoy you. 00:07:00.660 --> 00:07:04.270 You'll just be able to sit down and still your mind 00:07:04.270 --> 00:07:07.000 and realize that you are not your thoughts 00:07:07.000 --> 00:07:08.930 and that these things that are bothering you, 00:07:08.930 --> 00:07:10.330 they're only going to bother you 00:07:10.330 --> 00:07:12.273 as much as you let them bother you. 00:07:13.437 --> 00:07:15.310 In the whole scheme of things, 00:07:15.310 --> 00:07:17.640 in all of time and space, 00:07:17.640 --> 00:07:21.520 none of them are really what should define you 00:07:21.520 --> 00:07:23.940 or are anywhere near as important 00:07:23.940 --> 00:07:26.890 as we sometimes make them out to be. 00:07:26.890 --> 00:07:28.690 I'll see you in the next meditation.

Guided meditation to help with test anxiety

https://www.youtube.com/watch?v=5nm7WwS80Xs

vtt

https://www.youtube.com/api/timedtext?v=5nm7WwS80Xs&ei=bViUZd_sGa6hp-oPxsGiyAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=64DD3415740E911B64EF2FDED8375DF9764E3437.79B49C6E22E16ADB23E8988975309DE28BCBBD42&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.310 --> 00:00:02.830 - [Instructor] Welcome to this meditation 00:00:02.830 --> 00:00:05.650 and I'll assume that if you are listening 00:00:05.650 --> 00:00:09.140 that you have some type of major test or exam coming up 00:00:09.140 --> 00:00:13.000 because that's what the title of this meditation is about. 00:00:13.000 --> 00:00:16.510 Now the word meditation can conjure up different ideas 00:00:16.510 --> 00:00:20.500 to different folks, but all it is is a way for us 00:00:20.500 --> 00:00:25.110 to observe our thoughts and maybe quiet our thoughts down, 00:00:25.110 --> 00:00:27.260 especially in a way that makes us feel 00:00:27.260 --> 00:00:30.000 just a little bit lighter, a little bit more peaceful, 00:00:30.000 --> 00:00:34.610 a little bit happier, and less stressed or anxious. 00:00:34.610 --> 00:00:38.210 Oftentimes by doing that, it helps us do better 00:00:38.210 --> 00:00:41.780 on the thing that we were stressed about in the first place. 00:00:41.780 --> 00:00:42.833 Let's get started. 00:00:44.310 --> 00:00:46.460 The first thing that I always emphasize, 00:00:46.460 --> 00:00:48.200 this is true whenever I meditate, 00:00:48.200 --> 00:00:53.110 is posture and breathing and environment can matter a lot. 00:00:53.110 --> 00:00:55.410 Find someplace nice that you can sit down, 00:00:55.410 --> 00:00:58.010 ideally a little bit quiet or at least where the sound 00:00:58.010 --> 00:01:02.223 doesn't bother you, and sit upright as well as you can. 00:01:03.440 --> 00:01:05.960 If there is a little bit of ambient sound, 00:01:05.960 --> 00:01:08.370 don't let it bother you or irritate you. 00:01:08.370 --> 00:01:11.910 Just accept that's the universe making its noises, 00:01:11.910 --> 00:01:13.700 just something to observe. 00:01:13.700 --> 00:01:16.020 It's almost a little bit funny. 00:01:16.020 --> 00:01:18.600 As you accept your environment, 00:01:18.600 --> 00:01:20.410 whether it's your external environment 00:01:20.410 --> 00:01:23.573 or even sensations that you have from your body, 00:01:24.420 --> 00:01:28.630 start to breathe a little bit deeper and a little bit slower 00:01:28.630 --> 00:01:30.913 than you were before this meditation began. 00:01:31.800 --> 00:01:32.913 Breathe in. 00:01:34.920 --> 00:01:35.893 Pause. 00:01:39.280 --> 00:01:40.333 Breathe out. 00:01:42.750 --> 00:01:45.390 You can set your own pace for breathing in 00:01:45.390 --> 00:01:48.910 and breathing out, but just try to go a little bit deeper 00:01:48.910 --> 00:01:50.110 and a little bit slower. 00:01:51.150 --> 00:01:53.630 Now when I do this, I like to sit upright, 00:01:53.630 --> 00:01:57.470 usually on a chair, and keep my hands on my lap face up, 00:01:57.470 --> 00:02:00.220 but you can do whatever feels comfortable for yourself. 00:02:01.160 --> 00:02:03.280 The other thing that I'll ask you to do, 00:02:03.280 --> 00:02:05.170 it might feel a little unnatural, 00:02:05.170 --> 00:02:08.190 is force a smile. 00:02:08.190 --> 00:02:09.810 Try to make it as real as possible, 00:02:09.810 --> 00:02:11.260 but if you have to, force it. 00:02:12.836 --> 00:02:14.960 What I find is, obviously when we're happy, 00:02:14.960 --> 00:02:18.230 we tend to smile, but you can actually make the wiring 00:02:18.230 --> 00:02:19.430 go the other way. 00:02:19.430 --> 00:02:21.930 That by forcing a smile, it can actually make you 00:02:21.930 --> 00:02:25.720 feel a little bit better, a little bit more positive. 00:02:25.720 --> 00:02:28.570 Try to keep that smile on your face 00:02:28.570 --> 00:02:29.670 throughout the meditation 00:02:29.670 --> 00:02:32.300 and ideally well beyond the meditation. 00:02:32.300 --> 00:02:33.610 It doesn't have to be a fake smile, 00:02:33.610 --> 00:02:36.620 it could just be a very slight, gentle smirk, if you like. 00:02:36.620 --> 00:02:38.983 But something that makes you feel a little bit better. 00:02:40.260 --> 00:02:44.213 With that, continue to breathe in, breathe out. 00:02:45.080 --> 00:02:47.560 If you haven't closed your eyes already, 00:02:47.560 --> 00:02:50.173 you can gently close your eyes. 00:02:52.260 --> 00:02:56.050 Before I give you a chance to just be with yourself quietly 00:02:56.050 --> 00:02:59.190 and observe and maybe still your thoughts, 00:02:59.190 --> 00:03:01.223 I'll give you some ideas to think about. 00:03:02.090 --> 00:03:06.490 A lot of the stress of an exam 00:03:06.490 --> 00:03:09.363 comes from identifying with the outcome. 00:03:10.290 --> 00:03:13.940 We get caught up with, "What if I don't do well?" 00:03:13.940 --> 00:03:17.020 Or "I need to do well." 00:03:17.020 --> 00:03:20.487 Or "I am going to do so awesome that when I do awesome, 00:03:20.487 --> 00:03:23.387 "all these amazing things are going to happen in my life." 00:03:24.240 --> 00:03:27.100 The problem with getting attached to the outcome 00:03:27.100 --> 00:03:29.640 is the outcome may or may not happen. 00:03:29.640 --> 00:03:33.170 All those fears that you have may or may not happen. 00:03:33.170 --> 00:03:36.720 All those hopes you have may or may not happen. 00:03:36.720 --> 00:03:39.450 When you identify with those, and if they don't happen, 00:03:39.450 --> 00:03:42.920 well that might create a little bit of a disconnect 00:03:42.920 --> 00:03:45.370 between yourself and reality and that's one 00:03:45.370 --> 00:03:49.440 of the number one reasons why people get unhappy. 00:03:49.440 --> 00:03:52.960 Reality isn't working out the way they want it to. 00:03:52.960 --> 00:03:57.330 Instead, you could identify a bit more with the process, 00:03:57.330 --> 00:03:58.380 the adventure. 00:03:58.380 --> 00:04:01.797 Saying, "Look, I have this thing coming up 00:04:01.797 --> 00:04:04.457 "and I'm going to put my best foot forward. 00:04:04.457 --> 00:04:08.147 "I am going to put in the work to prepare 00:04:08.147 --> 00:04:10.957 "and I'm going to enjoy that work. 00:04:10.957 --> 00:04:13.537 "I am the sentient being on this planet, 00:04:13.537 --> 00:04:15.387 "in this mystery that we call life 00:04:15.387 --> 00:04:20.297 "and I get to engage on this challenge called this test. 00:04:20.297 --> 00:04:22.770 "Let me enjoy these moments." 00:04:22.770 --> 00:04:24.480 Before you know it, you're going to be a lot older 00:04:24.480 --> 00:04:26.760 and you're going to reminisce about this moment 00:04:26.760 --> 00:04:28.610 in your life right now. 00:04:28.610 --> 00:04:30.257 You're going to laugh at yourself, 00:04:30.257 --> 00:04:32.550 "Why didn't I enjoy it more?" 00:04:32.550 --> 00:04:35.380 Now with that notion of focusing on the adventure 00:04:35.380 --> 00:04:38.300 of preparation, I'll give you another visualization 00:04:38.300 --> 00:04:39.600 that I find really useful. 00:04:40.790 --> 00:04:45.790 Imagine that your subconscious is a massive ocean 00:04:46.110 --> 00:04:49.417 and your consciousness, the part that thinks to itself, 00:04:49.417 --> 00:04:50.307 "Here I am! 00:04:50.307 --> 00:04:53.767 "I'm some type of pure awareness trying to observe 00:04:53.767 --> 00:04:55.640 "and make sense of the universe." 00:04:55.640 --> 00:05:00.363 That's a sky that's clear and full of sunlight. 00:05:01.850 --> 00:05:06.090 Most of us are operating on the surface of that ocean 00:05:06.090 --> 00:05:07.860 most of the time. 00:05:07.860 --> 00:05:09.680 There are all these random thoughts 00:05:09.680 --> 00:05:12.430 that are just bubbling up from that ocean, 00:05:12.430 --> 00:05:15.433 waves that are crashing into our consciousness. 00:05:17.070 --> 00:05:20.410 For many of you, it might be thoughts, ruminations 00:05:20.410 --> 00:05:22.750 about how you're doing on that test 00:05:22.750 --> 00:05:26.443 or thinking about consequences of doing well or not well. 00:05:27.830 --> 00:05:28.760 It could be other things. 00:05:28.760 --> 00:05:31.240 It could be things going on in your social life, 00:05:31.240 --> 00:05:33.310 assignments that you have due, 00:05:33.310 --> 00:05:35.863 things in the broader world that are troubling you. 00:05:37.100 --> 00:05:40.890 But one of the ideas behind meditation is to realize 00:05:40.890 --> 00:05:42.760 that those thoughts that are surfacing 00:05:42.760 --> 00:05:46.310 from your subconscious, they aren't you 00:05:46.310 --> 00:05:50.030 and you can actually rise above those thoughts, 00:05:50.030 --> 00:05:53.050 rise above the surface of that ocean. 00:05:53.050 --> 00:05:57.010 Imagine yourself as just a pure awareness rising above 00:05:57.010 --> 00:06:00.330 that surface and you're realizing all of those thoughts 00:06:00.330 --> 00:06:02.340 that were thrashing around, 00:06:02.340 --> 00:06:05.230 that were splashing against your pure awareness, 00:06:05.230 --> 00:06:07.730 your consciousness, they don't have to. 00:06:07.730 --> 00:06:09.780 Now you're above them and there's just a few drops 00:06:09.780 --> 00:06:13.640 that every now and then you can giggle and wipe off a bit. 00:06:13.640 --> 00:06:16.330 You can look down on the surface of that ocean 00:06:16.330 --> 00:06:19.290 and from a distance, those thoughts really don't seem 00:06:19.290 --> 00:06:21.660 like that big of a deal. 00:06:21.660 --> 00:06:25.480 As you look down on those thoughts, you begin to appreciate 00:06:25.480 --> 00:06:27.830 that they're starting to slow down. 00:06:27.830 --> 00:06:31.603 The ocean is starting to become a little more still. 00:06:32.710 --> 00:06:37.710 As you continue to breathe in and breathe out, 00:06:37.750 --> 00:06:41.900 there you are, just in that sun-drenched sky 00:06:41.900 --> 00:06:43.400 above the ocean. 00:06:43.400 --> 00:06:46.650 You are that sun-drenched sky above that ocean 00:06:46.650 --> 00:06:48.220 that is your subconsciousness. 00:06:48.220 --> 00:06:50.083 You are that pure sunlight. 00:06:51.230 --> 00:06:55.720 With that idea in mind, I'll give you a minute of silence 00:06:55.720 --> 00:06:58.680 where you can just breathe in, breathe out 00:06:59.570 --> 00:07:03.550 and experience joy in that sunlight that you are in. 00:07:03.550 --> 00:07:07.930 Experience joy in not getting caught up in those thoughts. 00:07:07.930 --> 00:07:11.370 If your brain wanders off, if your consciousness goes back 00:07:11.370 --> 00:07:13.540 to the surface of that ocean and that starts 00:07:13.540 --> 00:07:17.630 to get a little bit choppier, no reason to worry about that. 00:07:17.630 --> 00:07:20.020 Just remind yourself, giggle a little bit, 00:07:20.020 --> 00:07:22.077 and say, "Oh! I got lost in the ocean again 00:07:22.077 --> 00:07:23.687 "on the surface with those waves. 00:07:23.687 --> 00:07:26.030 "Let me just rise up again." 00:07:26.030 --> 00:07:27.653 I'll be back in about a minute. 00:07:53.920 --> 00:07:56.383 All right so we are back. 00:07:57.900 --> 00:08:01.700 Continue to breathe in, breathe out. 00:08:01.700 --> 00:08:04.360 Hopefully you experienced just a little bit of stillness, 00:08:04.360 --> 00:08:06.310 even if it was for five or 10 seconds, 00:08:06.310 --> 00:08:10.460 the experience of knowing that you aren't your thoughts, 00:08:10.460 --> 00:08:12.560 knowing that you can observe your thoughts, 00:08:12.560 --> 00:08:15.040 knowing that there can be moments in your life 00:08:15.040 --> 00:08:17.183 where you are free of your thoughts. 00:08:18.540 --> 00:08:22.630 Now as we are winding down this meditation, 00:08:22.630 --> 00:08:25.760 keep a couple of big ideas in your head. 00:08:25.760 --> 00:08:28.770 Remind yourself not to focus on the outcome, 00:08:28.770 --> 00:08:32.240 but to focus on the process and to enjoy it. 00:08:32.240 --> 00:08:35.210 That smile that hopefully you still have on your face, 00:08:35.210 --> 00:08:38.310 have that smile the whole time that you're preparing. 00:08:38.310 --> 00:08:41.500 Have that smile as you go into whatever type of test 00:08:41.500 --> 00:08:43.963 or exam you are about to take on. 00:08:44.910 --> 00:08:48.400 If you can, try to take a little bit of time out every day, 00:08:48.400 --> 00:08:50.470 even if you can do it for a minute, two minutes, 00:08:50.470 --> 00:08:54.610 three minutes, where you can sit silently with good posture, 00:08:54.610 --> 00:08:58.920 breathe slowly, deeply, put a smile on your face, 00:08:58.920 --> 00:09:01.400 and rise above your thoughts. 00:09:01.400 --> 00:09:03.300 I feel confident that not only are you going 00:09:03.300 --> 00:09:05.740 to enjoy this experience, 00:09:05.740 --> 00:09:08.680 but you're going to put your best foot forward on that test 00:09:08.680 --> 00:09:11.110 and you're also going to realize over time 00:09:11.110 --> 00:09:14.240 that this test isn't that big of a deal. 00:09:14.240 --> 00:09:15.520 Many things in our life 00:09:15.520 --> 00:09:18.150 that in the moment seem like a big deal, 00:09:18.150 --> 00:09:20.670 with a little bit of distance of time and space, 00:09:20.670 --> 00:09:22.173 aren't that big of a deal. 00:09:23.390 --> 00:09:25.930 If you haven't already, I encourage you 00:09:25.930 --> 00:09:28.160 at your own time and pace, while you're continuing 00:09:28.160 --> 00:09:30.710 to smile and continuing to breathe in 00:09:30.710 --> 00:09:35.710 and breathe out deeply, gently open up your eyes 00:09:36.070 --> 00:09:38.010 and take joy in this adventure, 00:09:38.010 --> 00:09:40.423 this mystery that we call life.

Guided meditation to help you stop procrastinating

https://www.youtube.com/watch?v=SXMBkHlL2Dc

vtt

https://www.youtube.com/api/timedtext?v=SXMBkHlL2Dc&ei=bViUZaKeGoCjp-oPn863yAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EB20AB97756FD258F862B4F6776ABEDFD4013453.A839D46527965C8FA8D23158B29D9D3492D59139&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.631 --> 00:00:04.880 - [Instructor] Welcome to the meditation on procrastination. 00:00:04.880 --> 00:00:06.510 And somewhat ironically, 00:00:06.510 --> 00:00:09.600 I've been procrastinating making this meditation. 00:00:09.600 --> 00:00:12.513 So we're all in the same boat together. 00:00:13.510 --> 00:00:16.250 So as with all meditations, 00:00:16.250 --> 00:00:18.450 posture and breathing makes a big difference. 00:00:18.450 --> 00:00:19.770 So I really encourage you 00:00:19.770 --> 00:00:22.510 to find a nice, firm seat to sit on. 00:00:22.510 --> 00:00:23.810 If your legs don't fall asleep, 00:00:23.810 --> 00:00:25.510 you can sit on the ground as well. 00:00:25.510 --> 00:00:29.523 But try to sit with your back upright, really good posture. 00:00:30.450 --> 00:00:33.590 Breathe in, breathe out, 00:00:33.590 --> 00:00:37.910 a little bit slower, a little bit deeper every time. 00:00:37.910 --> 00:00:40.650 You can lay your hands on your lap. 00:00:40.650 --> 00:00:42.193 I like to leave them face up. 00:00:43.260 --> 00:00:44.215 And when you're ready, 00:00:44.215 --> 00:00:49.215 you can soften your gaze, and slowly close your eyes, 00:00:53.650 --> 00:00:56.563 breathing in, breathing out. 00:01:00.140 --> 00:01:03.150 Now procrastination is an interesting thing. 00:01:03.150 --> 00:01:05.930 I'm not sure whether we human beings 00:01:05.930 --> 00:01:09.430 are the only animals we know of that procrastinate. 00:01:09.430 --> 00:01:12.110 It's maybe worth some research for somebody 00:01:12.110 --> 00:01:13.530 to figure that out. 00:01:13.530 --> 00:01:14.763 But we clearly do it. 00:01:15.730 --> 00:01:16.977 And a lot of meditation 00:01:16.977 --> 00:01:21.110 is about becoming aware of our thoughts, 00:01:21.110 --> 00:01:22.730 and observing our thoughts, 00:01:22.730 --> 00:01:26.450 and realizing that we are not our thoughts, 00:01:26.450 --> 00:01:29.290 even though many times, our thoughts seem to control us, 00:01:29.290 --> 00:01:30.913 or even overwhelm us. 00:01:33.720 --> 00:01:34.931 And so let's do that. 00:01:34.931 --> 00:01:38.629 Let's try to observe those thoughts 00:01:38.629 --> 00:01:42.060 that are making us put off something 00:01:42.060 --> 00:01:43.823 that we know we need to do. 00:01:47.303 --> 00:01:51.073 Why do you think you are putting that thing off? 00:01:53.271 --> 00:01:55.570 I'll tell you what happens to be usually 00:01:55.570 --> 00:01:56.650 for my experience. 00:01:56.650 --> 00:01:59.926 It usually is, I'm afraid to start, 00:01:59.926 --> 00:02:04.110 because I might realize that it's harder than I expected, 00:02:04.110 --> 00:02:08.503 or I might not do as well as I expected, 00:02:09.640 --> 00:02:12.800 or I might make a mistake. 00:02:12.800 --> 00:02:15.743 Maybe I don't think I'm prepared enough to start. 00:02:17.400 --> 00:02:18.840 Another way to think about it is, 00:02:18.840 --> 00:02:20.939 we're getting too caught up in the outcome 00:02:20.939 --> 00:02:24.410 versus enjoying the journey, 00:02:24.410 --> 00:02:26.210 or enjoying whatever the thing is 00:02:26.210 --> 00:02:27.080 that you're putting off, 00:02:27.080 --> 00:02:29.903 'cause that's just a part of this fun experience. 00:02:30.936 --> 00:02:35.101 And so I find that when I tell myself, 00:02:35.101 --> 00:02:40.101 self, define yourself by the action, not the outcome. 00:02:42.040 --> 00:02:45.823 Don't define yourself by whether you succeed or fail. 00:02:46.780 --> 00:02:51.780 Define yourself as making the effort, showing up, 00:02:53.130 --> 00:02:57.170 and enjoying it, laughing at yourself, 00:02:57.170 --> 00:03:00.100 laughing at this mystery that we call life, 00:03:00.100 --> 00:03:03.800 and just putting one foot in front of the other, 00:03:03.800 --> 00:03:06.570 and realizing it's not so bad. 00:03:06.570 --> 00:03:07.620 And then you can put the other foot 00:03:07.620 --> 00:03:09.763 in front of that one, and keep going. 00:03:12.340 --> 00:03:13.630 And slowly but surely, 00:03:13.630 --> 00:03:17.370 you realize that you're making a lot of progress. 00:03:17.370 --> 00:03:20.050 And the more you make that progress, 00:03:20.050 --> 00:03:22.250 the more that you actually enjoy it, 00:03:22.250 --> 00:03:25.180 especially if you're not doing it at the last minute. 00:03:25.180 --> 00:03:27.360 And now, I'll give you about a minute 00:03:27.360 --> 00:03:30.348 for you to repeat something in your mind 00:03:30.348 --> 00:03:35.300 that can hopefully short-circuit any of those thoughts 00:03:35.300 --> 00:03:38.059 that have been keeping you from taking action. 00:03:38.059 --> 00:03:42.909 For the next minute or so, repeat to yourself, 00:03:42.909 --> 00:03:45.963 that you really enjoy taking action. 00:03:47.140 --> 00:03:48.680 You're lucky that you're in a position 00:03:48.680 --> 00:03:51.143 to be able to take action. 00:03:52.346 --> 00:03:53.959 The outcome? 00:03:53.959 --> 00:03:56.053 It is what it is. 00:03:57.950 --> 00:03:59.613 You enjoy action. 00:04:00.700 --> 00:04:02.913 You're lucky to be able to take action. 00:04:04.520 --> 00:04:07.823 The outcome is what it is. 00:04:08.975 --> 00:04:11.780 Keep thinking that for the next minute or so, 00:04:11.780 --> 00:04:14.143 and I'll be back, don't worry. 00:05:16.921 --> 00:05:18.223 All right. 00:05:20.270 --> 00:05:22.793 So when you're ready, really at your own time, 00:05:25.050 --> 00:05:28.640 just become a little bit more aware of your surroundings, 00:05:28.640 --> 00:05:30.490 a little bit more aware of your body, 00:05:32.020 --> 00:05:34.020 a little bit more aware of your breaths, 00:05:35.840 --> 00:05:38.763 and slowly open your eyes. 00:05:40.810 --> 00:05:42.923 And so I'll finish with one last tip: 00:05:44.100 --> 00:05:45.760 Sometimes we put something off 00:05:45.760 --> 00:05:49.483 because it just feels big, or overwhelming. 00:05:50.405 --> 00:05:53.570 What I like to do then is say hey, 00:05:53.570 --> 00:05:56.960 let me just put 20 minutes towards it, 00:05:56.960 --> 00:06:00.060 and see where I am at the end of 20 minutes. 00:06:00.060 --> 00:06:03.330 If I didn't make any progress, no big deal. 00:06:03.330 --> 00:06:04.693 It was juts 20 minutes. 00:06:05.540 --> 00:06:07.940 But if I did make some progress, great. 00:06:07.940 --> 00:06:10.945 I did the 20 minutes, I deserve a break. 00:06:10.945 --> 00:06:13.190 If after a five or 10-minute break 00:06:13.190 --> 00:06:15.531 I'm ready to put in another 20 minutes, awesome. 00:06:15.531 --> 00:06:18.242 If at the end of the 20 minutes, I wanna keep going, 00:06:18.242 --> 00:06:20.150 I shouldn't stop myself. 00:06:20.150 --> 00:06:21.129 I should keep going. 00:06:21.129 --> 00:06:21.962 (laughs) 00:06:21.962 --> 00:06:24.172 But when you view things as hey, 00:06:24.172 --> 00:06:27.570 I'm just committing 20 minutes to something, 00:06:27.570 --> 00:06:29.483 it doesn't feel as intimidating. 00:06:30.520 --> 00:06:31.353 You just own it. 00:06:31.353 --> 00:06:34.610 You say hey, I can do anything for 20 minutes. 00:06:34.610 --> 00:06:38.270 And I can enjoy anything for 20 minutes. 00:06:38.270 --> 00:06:39.690 And then you'll wanna do it. 00:06:39.690 --> 00:06:43.113 Put a smile on your face and own that action. 00:06:44.180 --> 00:06:45.800 And not only will you make progress, 00:06:45.800 --> 00:06:48.020 but you're gonna have a good time. 00:06:48.020 --> 00:06:51.400 And so take it wit that playful mindset. 00:06:51.400 --> 00:06:52.270 Enjoy it. 00:06:52.270 --> 00:06:53.510 Smile. 00:06:53.510 --> 00:06:55.275 And just get started. 00:06:55.275 --> 00:06:57.200 And I think you'll find 00:06:57.200 --> 00:06:59.533 you'll be procrastinating a lot, lot less.

Guided meditation for students

https://www.youtube.com/watch?v=K4YoQHjaziI

vtt

https://www.youtube.com/api/timedtext?v=K4YoQHjaziI&ei=bViUZdLSGZz1mLAPlIaf0AU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6AB2D7468208A8C13BE4E4C18ABE570DE8FF31E3.0177A99E3476E62CF0C3D58BD2801D6B6AEA0F77&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.630 --> 00:00:02.900 - [Instructor] Welcome, and thanks for joining me 00:00:02.900 --> 00:00:06.790 on this, let's call it a voyage of the mind. 00:00:06.790 --> 00:00:11.020 So before we begin, posture and breathing 00:00:11.020 --> 00:00:14.010 make a big difference in meditation. 00:00:14.010 --> 00:00:17.920 So if you're not already on a nice, firm chair 00:00:17.920 --> 00:00:21.270 with your back straight, pause this recording 00:00:21.270 --> 00:00:24.550 and go find a nice, firm chair with your back straight, 00:00:24.550 --> 00:00:28.363 ideally in a place that's kind of quiet and peaceful. 00:00:29.800 --> 00:00:33.920 So now that you're there, sit with your back straight. 00:00:33.920 --> 00:00:37.040 Try to put your feet firmly on the floor. 00:00:37.040 --> 00:00:40.570 When I do this, I like to rest my hands on my lap, 00:00:40.570 --> 00:00:43.563 palms up, gently curled, so really no effort. 00:00:44.840 --> 00:00:48.220 And now start to slowly breathe, 00:00:48.220 --> 00:00:52.313 a bit deeper than you were just now and a bit slower. 00:00:53.460 --> 00:00:55.770 In, and out. 00:00:55.770 --> 00:00:58.770 At your own time, but just a little bit deeper, 00:00:58.770 --> 00:01:00.173 a little bit slower. 00:01:01.290 --> 00:01:04.250 If you like, a lot of folks like to breathe in 00:01:04.250 --> 00:01:08.100 through their nose, out through their mouth, 00:01:08.100 --> 00:01:12.130 but the key, once again, a little bit deeper, 00:01:12.130 --> 00:01:13.393 a little bit slower. 00:01:15.050 --> 00:01:18.810 And as you do so, start to soften your gaze 00:01:18.810 --> 00:01:21.230 if your eyes are still open. 00:01:21.230 --> 00:01:26.223 And when you feel comfortable, gently close your eyes. 00:01:29.250 --> 00:01:32.550 Now, before we get into the heart of the meditation, 00:01:32.550 --> 00:01:35.080 I'm gonna give you a few reminders. 00:01:35.080 --> 00:01:40.080 This whole exercise is about exploring your inner being, 00:01:41.150 --> 00:01:44.550 it's about curiosity, it's about relaxation. 00:01:44.550 --> 00:01:47.230 There's no perfect way to meditate. 00:01:47.230 --> 00:01:50.070 Sometimes folks think that they're not doing it right 00:01:50.070 --> 00:01:52.180 or their mind is wandering too much 00:01:52.180 --> 00:01:53.610 and then it causes stress. 00:01:53.610 --> 00:01:56.600 And that's the exact opposite of what you want meditation 00:01:56.600 --> 00:02:00.510 to be, it should be fun, it could even by funny at moments. 00:02:00.510 --> 00:02:02.010 You should be curious. 00:02:02.010 --> 00:02:03.943 You should be enjoying it. 00:02:04.870 --> 00:02:07.080 If there are some random distractions, 00:02:07.080 --> 00:02:08.640 and there inevitably will be. 00:02:08.640 --> 00:02:10.770 It could be sounds around you, 00:02:10.770 --> 00:02:15.260 it might be part of your body that itches or tingles. 00:02:15.260 --> 00:02:18.630 Don't let it stress you out, just accept it. 00:02:18.630 --> 00:02:20.720 It's part of the universe, 00:02:20.720 --> 00:02:23.160 it's just atoms doing what they do, 00:02:23.160 --> 00:02:25.890 it's the universe doing its thing. 00:02:25.890 --> 00:02:28.420 And no worries if you need to scratch 00:02:28.420 --> 00:02:32.473 or adjust part of your body, no reason to stress. 00:02:33.940 --> 00:02:36.650 Now to add to the idea that this shouldn't 00:02:36.650 --> 00:02:38.970 be a stressful experience, I'm gonna ask you 00:02:38.970 --> 00:02:43.470 to do something that may or may not feel completely natural. 00:02:43.470 --> 00:02:45.130 I want you to smile right now. 00:02:45.130 --> 00:02:46.630 Give yourself a good smile. 00:02:46.630 --> 00:02:49.470 With your eyes closed, just smile. 00:02:49.470 --> 00:02:51.210 Obviously we smile when we're happy, 00:02:51.210 --> 00:02:53.400 but sometimes making us smile 00:02:53.400 --> 00:02:55.480 can actually make us a little bit happier. 00:02:55.480 --> 00:02:57.910 It can make us a little bit less stressed. 00:02:57.910 --> 00:03:00.570 So even if you need to force it, smile. 00:03:00.570 --> 00:03:03.440 And as much as possible as we go through this meditation, 00:03:03.440 --> 00:03:05.490 as long as you don't have to force it too much, 00:03:05.490 --> 00:03:08.363 try to keep a gentle smile on your face the whole time. 00:03:10.860 --> 00:03:13.183 All right, now let's get into it. 00:03:14.150 --> 00:03:17.900 So one thing to keep in mind as we start 00:03:17.900 --> 00:03:21.720 trying to still our minds is to just appreciate 00:03:21.720 --> 00:03:26.720 that you're alive, you're in this vast mystery we call life, 00:03:27.710 --> 00:03:29.860 and that you're taking pause to appreciate 00:03:29.860 --> 00:03:31.600 who you really are, 00:03:31.600 --> 00:03:33.980 and the beauty of this mystery, this existence, 00:03:33.980 --> 00:03:36.710 this universe that we share. 00:03:36.710 --> 00:03:40.900 So as you breathe deeper and slower, 00:03:40.900 --> 00:03:45.900 your eyes are closed, try to become aware of your thoughts. 00:03:46.280 --> 00:03:47.680 What are you thinking about? 00:03:49.920 --> 00:03:51.800 Are they random thoughts? 00:03:51.800 --> 00:03:53.700 Something you saw on TV? 00:03:53.700 --> 00:03:55.623 Is it something going on at school? 00:03:56.870 --> 00:03:58.990 Are you thinking about some test 00:03:58.990 --> 00:04:01.180 you might have coming up? 00:04:01.180 --> 00:04:05.590 Or is someone at your school you tend to think about a lot? 00:04:05.590 --> 00:04:08.220 Just observe your thoughts, don't try to fight them, 00:04:08.220 --> 00:04:09.273 just observe them. 00:04:12.420 --> 00:04:14.720 And as you observe your thoughts, 00:04:14.720 --> 00:04:19.290 start to appreciate that you are not your thoughts. 00:04:19.290 --> 00:04:22.640 You are something different than your thoughts. 00:04:22.640 --> 00:04:25.370 They're all in there in your head with you, 00:04:25.370 --> 00:04:27.010 but clearly you can observe them. 00:04:27.010 --> 00:04:29.620 You can see them go by. 00:04:29.620 --> 00:04:32.240 Sometimes we can get lost in them, 00:04:32.240 --> 00:04:33.380 but I think you're seeing right now 00:04:33.380 --> 00:04:34.690 that you are not your thoughts. 00:04:34.690 --> 00:04:36.893 You can actually observe your thoughts. 00:04:39.710 --> 00:04:42.530 One metaphor that folks sometimes use 00:04:42.530 --> 00:04:44.620 is that your thoughts are cars on a road 00:04:44.620 --> 00:04:47.140 or cars on a highway, and oftentimes 00:04:47.140 --> 00:04:48.200 we're in the middle of the highway 00:04:48.200 --> 00:04:50.640 and those cars are bombarding us, 00:04:50.640 --> 00:04:52.860 they're hitting us, or we have to dodge them in some way 00:04:52.860 --> 00:04:54.410 or they're overwhelming us. 00:04:54.410 --> 00:04:55.940 And one thing to do to observe them 00:04:55.940 --> 00:04:57.710 is just get out of the highway. 00:04:57.710 --> 00:04:59.000 You don't have to fight the thoughts, 00:04:59.000 --> 00:05:01.330 those cars will keep on going by. 00:05:01.330 --> 00:05:03.200 But now that you're on the median, 00:05:03.200 --> 00:05:06.423 you're no longer on the highway, you can see them go by. 00:05:07.730 --> 00:05:10.530 And what you'll often find is when you're observing 00:05:10.530 --> 00:05:12.893 your thoughts, they start to slow down. 00:05:14.610 --> 00:05:17.130 And so if your thoughts start to slow down, great, 00:05:17.130 --> 00:05:18.980 really embrace that, start to realize 00:05:18.980 --> 00:05:21.940 what that feels like when your thoughts slow down. 00:05:21.940 --> 00:05:23.960 And then there's even going to be moments 00:05:23.960 --> 00:05:25.703 when you have no thoughts. 00:05:26.780 --> 00:05:29.330 For the next few breaths, try that. 00:05:29.330 --> 00:05:31.650 Try to have no thoughts. 00:05:31.650 --> 00:05:34.213 Just breathe in, breathe out. 00:05:35.360 --> 00:05:38.710 No thoughts, just stillness. 00:05:38.710 --> 00:05:42.060 Just your consciousness here in this universe. 00:05:42.060 --> 00:05:47.030 No time, no space, it's all in your mind, 00:05:47.030 --> 00:05:49.313 no thoughts, stillness. 00:05:56.920 --> 00:05:59.100 Now as you try to keep that state, 00:05:59.100 --> 00:06:01.810 your mind will inevitably wander, 00:06:01.810 --> 00:06:02.910 you're going to start thinking 00:06:02.910 --> 00:06:05.790 about an assignment that you have due soon. 00:06:05.790 --> 00:06:07.800 You're going to think about something 00:06:07.800 --> 00:06:09.260 that you have to do this weekend, 00:06:09.260 --> 00:06:13.530 or someone that you think a lot about. 00:06:13.530 --> 00:06:17.250 That's okay, don't beat yourself up if your mind wanders. 00:06:17.250 --> 00:06:19.970 Just remind yourself, just gently nudge it back. 00:06:19.970 --> 00:06:21.380 Try to get back to the stillness. 00:06:21.380 --> 00:06:23.880 Say, oh, look, I got a little bit distracted, 00:06:23.880 --> 00:06:25.600 I started thinking about something. 00:06:25.600 --> 00:06:29.640 That's funny, I'm gonna get my mind back to the stillness. 00:06:29.640 --> 00:06:31.623 I'm gonna try to slow down those cars. 00:06:35.500 --> 00:06:38.770 And so gently breathe in and breathe out, 00:06:38.770 --> 00:06:40.320 and I'm gonna give you a few minutes 00:06:40.320 --> 00:06:45.320 to just sit there, still, breathing in, breathing out, 00:06:46.160 --> 00:06:48.290 being still with your thoughts. 00:06:48.290 --> 00:06:51.180 If your mind wanders, no big deal, 00:06:51.180 --> 00:06:53.540 just try to nudge it back when you can. 00:06:53.540 --> 00:06:55.660 And if the silence starts to get to you a little bit, 00:06:55.660 --> 00:06:59.910 don't worry, I will be back for sure in a few minutes. 00:08:06.890 --> 00:08:09.070 Now that you've had a little bit of time on your own, 00:08:09.070 --> 00:08:10.920 I'm gonna give you some ideas 00:08:10.920 --> 00:08:14.373 that just might help appreciate who you really are. 00:08:15.690 --> 00:08:18.620 A lot of times we get caught up in the day-to-day, 00:08:18.620 --> 00:08:20.780 we start worrying about test scores 00:08:20.780 --> 00:08:24.563 or things we have due or what people think about us, 00:08:25.440 --> 00:08:28.113 but remind yourself that you are not that. 00:08:29.400 --> 00:08:32.700 You are not defined by your test scores. 00:08:32.700 --> 00:08:35.113 You are not defined by your grades. 00:08:36.480 --> 00:08:39.653 And you are not defined by what people think of you. 00:08:42.130 --> 00:08:43.983 You are pure consciousness. 00:08:45.660 --> 00:08:48.520 You associate yourself with your body, 00:08:48.520 --> 00:08:53.000 with your thoughts, but they're part of you. 00:08:53.000 --> 00:08:54.333 They aren't you. 00:08:55.400 --> 00:08:59.103 You're something deeper, and you're something far larger. 00:09:00.810 --> 00:09:03.083 Think about how vast the universe is. 00:09:03.930 --> 00:09:06.853 Not just vast in space, but vast in time. 00:09:07.760 --> 00:09:10.940 That puts some of our problems in perspective. 00:09:10.940 --> 00:09:15.140 A hundred years from now, a thousand years from now, 00:09:15.140 --> 00:09:17.623 will these problems really be that significant? 00:09:19.410 --> 00:09:24.300 When you think about where you are on this planet, 00:09:24.300 --> 00:09:27.930 part of the cosmos, are these issues 00:09:27.930 --> 00:09:29.393 really that significant? 00:09:31.000 --> 00:09:32.550 So I'll give you a few more moments 00:09:32.550 --> 00:09:34.300 to just think about those ideas, 00:09:34.300 --> 00:09:37.270 to just think about the vastness of the universe 00:09:37.270 --> 00:09:39.210 and what a privilege it is to be able 00:09:39.210 --> 00:09:41.990 to participate in it, to see the beauty of it, 00:09:41.990 --> 00:09:43.830 and how small some of the things 00:09:43.830 --> 00:09:47.283 that we often define ourselves by really are. 00:09:50.350 --> 00:09:52.323 And so now when you get a chance, 00:09:53.940 --> 00:09:55.620 gently, with your eyes closed, 00:09:55.620 --> 00:09:59.230 start to feel and hear the room around you a little bit. 00:09:59.230 --> 00:10:01.530 Get a little bit more in touch with your body. 00:10:02.920 --> 00:10:05.253 And when you're ready, open your eyes. 00:10:08.070 --> 00:10:10.710 And take these ideas, take that stillness with you 00:10:10.710 --> 00:10:11.913 to the rest of your day. 00:10:13.800 --> 00:10:16.910 And you should thank yourself for taking the time out 00:10:16.910 --> 00:10:18.870 for doing this today. 00:10:18.870 --> 00:10:21.370 And I encourage you to make it a practice. 00:10:21.370 --> 00:10:23.070 Some of you might be skeptical. 00:10:23.070 --> 00:10:25.633 What would a few minute meditation do for me? 00:10:26.660 --> 00:10:29.170 But I can guarantee you if you do it day in, day out, 00:10:29.170 --> 00:10:32.353 if you make a practice of it, do it regularly, 00:10:33.290 --> 00:10:35.360 over a few weeks, a few months, 00:10:35.360 --> 00:10:37.690 you're gonna notice some changes. 00:10:37.690 --> 00:10:40.750 You're gonna see yourself be more open to experience. 00:10:40.750 --> 00:10:44.290 You're going to see more beauty in more things. 00:10:44.290 --> 00:10:46.520 You're going to just have a positive energy 00:10:46.520 --> 00:10:49.210 that people are going to want to connect with, 00:10:49.210 --> 00:10:51.700 that people are going to be drawn to. 00:10:51.700 --> 00:10:54.260 And you'll also see that you're doing better 00:10:54.260 --> 00:10:56.340 at some of those things we talked about before 00:10:56.340 --> 00:10:58.120 because you're not stressed about them anymore, 00:10:58.120 --> 00:10:59.510 you're enjoying them. 00:10:59.510 --> 00:11:01.620 You're doing what you can, 00:11:01.620 --> 00:11:05.470 but you're not attached to the outcome. 00:11:05.470 --> 00:11:09.683 You do your best, wherever the chips fall, that's okay. 00:11:10.830 --> 00:11:13.880 If things don't turn out the way you wanted, that's okay. 00:11:13.880 --> 00:11:15.913 You just accept where things are, 00:11:16.890 --> 00:11:20.320 and then you decide, what other actions can you take? 00:11:20.320 --> 00:11:22.790 Assemble your actions piece by piece 00:11:22.790 --> 00:11:25.130 so that you can get to another outcome. 00:11:25.130 --> 00:11:28.210 But once again, if the outcome is what you want, awesome. 00:11:28.210 --> 00:11:31.433 If it isn't, accept it and move on from there. 00:11:32.940 --> 00:11:35.040 So I'll leave you in this meditation. 00:11:35.040 --> 00:11:38.170 Thank you for joining, and once again thanks 00:11:38.170 --> 00:11:40.013 for taking time out for yourself.

Influence of political events on ideology

https://www.youtube.com/watch?v=uj1Kqhs_xB0

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WEBVTT Kind: captions Language: en 00:00:00.140 --> 00:00:02.260 - [Instructor] In discussing political socialization, 00:00:02.260 --> 00:00:06.380 we've talked a lot about factors that go into how people 00:00:06.380 --> 00:00:10.210 develop their opinions on government and politics. 00:00:10.210 --> 00:00:14.220 Your family, your friends, your demographic characteristics, 00:00:14.220 --> 00:00:15.940 like your race, your gender, 00:00:15.940 --> 00:00:18.080 they all contribute to your views. 00:00:18.080 --> 00:00:21.210 In this video, I wanna talk about another set of factors 00:00:21.210 --> 00:00:24.230 that influence a person's political views, 00:00:24.230 --> 00:00:26.760 and that's political events. 00:00:26.760 --> 00:00:30.960 And political events include not just elections or debates 00:00:30.960 --> 00:00:34.225 or laws, but things like terrorist attacks, 00:00:34.225 --> 00:00:38.840 or international incidents, or economic recessions. 00:00:38.840 --> 00:00:43.840 These are external events that shape a person's beliefs, 00:00:46.490 --> 00:00:49.050 either in the short-term or maybe even 00:00:49.050 --> 00:00:50.773 for the rest of their lives. 00:00:52.740 --> 00:00:54.431 So what are some examples 00:00:54.431 --> 00:00:58.570 of how political events influence ideology? 00:00:58.570 --> 00:01:02.880 Some events can change a person's party identification 00:01:04.860 --> 00:01:08.530 or how strongly they identify with a party. 00:01:08.530 --> 00:01:11.940 For example, researchers have found that people 00:01:11.940 --> 00:01:14.950 who lost family members in the September 11th 00:01:14.950 --> 00:01:18.660 terrorist attacks became more politically active 00:01:18.660 --> 00:01:21.160 and have identified more strongly 00:01:21.160 --> 00:01:23.810 with the Republican party since then. 00:01:23.810 --> 00:01:27.340 Sometimes events can influence a person's attitudes 00:01:27.340 --> 00:01:31.100 toward government and the political process as a whole. 00:01:31.100 --> 00:01:34.300 And here we're not talking about which party a person 00:01:34.300 --> 00:01:38.750 favors, but rather their ideas about government itself, 00:01:38.750 --> 00:01:41.450 like is the government trustworthy? 00:01:41.450 --> 00:01:43.530 Does my vote really count? 00:01:43.530 --> 00:01:46.694 One example of this is the lasting influence 00:01:46.694 --> 00:01:50.450 of the Vietnam War and Watergate scandal 00:01:50.450 --> 00:01:53.120 on public trust in government. 00:01:53.120 --> 00:01:56.470 You can see in this graph by the Pew Research Center 00:01:56.470 --> 00:02:01.470 that since polls started asking Americans whether they trust 00:02:01.840 --> 00:02:06.840 Washington to do what is right always or most of the time, 00:02:06.960 --> 00:02:11.563 trust peaked in the early Johnson administration, 00:02:12.710 --> 00:02:17.710 then crashed in the mid-1960s and 1970s 00:02:18.880 --> 00:02:22.290 and has never really recovered since. 00:02:22.290 --> 00:02:26.820 So events that happened more than 50 years ago have left 00:02:26.820 --> 00:02:30.440 a mark on public trust in government that hasn't gone away. 00:02:30.440 --> 00:02:33.230 But not all political events have 00:02:33.230 --> 00:02:36.140 such a lasting effect on beliefs. 00:02:36.140 --> 00:02:40.040 Some events influence opinions for just a short term, 00:02:40.040 --> 00:02:42.950 like international events that influence 00:02:42.950 --> 00:02:46.150 Americans' attitudes towards other countries. 00:02:46.150 --> 00:02:50.600 For example, you can see in this poll data done by Gallup, 00:02:50.600 --> 00:02:55.279 that the public's favorable opinion about Russia has changed 00:02:55.279 --> 00:02:58.600 a great deal over the last 20 years, 00:02:58.600 --> 00:03:03.300 with revelations about Russian hacking coming in 2015 00:03:03.300 --> 00:03:07.557 leading to a sharp decline in favorable opinions. 00:03:07.557 --> 00:03:10.930 The last thing I wanna note here is that researchers 00:03:10.930 --> 00:03:13.380 have discovered that political events that happen 00:03:13.380 --> 00:03:17.650 when someone is in their formative age, or the age 00:03:17.650 --> 00:03:21.800 from about 18 to 24, when people are just getting out 00:03:21.800 --> 00:03:25.460 on their own and starting to form an independent identity. 00:03:25.460 --> 00:03:29.270 Events that happen then are more likely to have long lasting 00:03:29.270 --> 00:03:33.510 effects on a person's political beliefs and behaviors. 00:03:33.510 --> 00:03:38.510 The great recession in 2008 had a strong effect on people 00:03:38.570 --> 00:03:42.100 in the millennial generation, many of whom were just getting 00:03:42.100 --> 00:03:43.950 out into the workforce when it hit. 00:03:43.950 --> 00:03:46.940 Studies have shown that this had an especially 00:03:46.940 --> 00:03:50.670 strong influence on their ideas about government 00:03:50.670 --> 00:03:53.690 and money compared to other generations. 00:03:53.690 --> 00:03:57.610 So events can have both short and long-term effects 00:03:57.610 --> 00:04:00.890 on people's political beliefs, not just about whether 00:04:00.890 --> 00:04:03.300 they lean more liberal or conservative, 00:04:03.300 --> 00:04:06.120 but also about how they think about government itself. 00:04:06.120 --> 00:04:10.160 And those effects may be felt more strongly depending 00:04:10.160 --> 00:04:12.990 on what stage a person is in their life 00:04:12.990 --> 00:04:16.673 or how deeply an event impacts them personally.

Segment congruence equivalent to having same length

https://www.youtube.com/watch?v=WDHW-VZK3YI

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WEBVTT Kind: captions Language: en 00:00:00.560 --> 00:00:02.310 - [Instructor] So, what I have here are a few definitions 00:00:02.310 --> 00:00:05.020 that will be useful for a proof we're going to do 00:00:05.020 --> 00:00:08.840 that connects the worlds of congruence of line segments 00:00:08.840 --> 00:00:11.930 to the idea of them having the same length. 00:00:11.930 --> 00:00:13.390 So, first of all, there's this idea 00:00:13.390 --> 00:00:15.930 of rigid transformations, which we've talked about 00:00:15.930 --> 00:00:18.480 in other videos, but just as a refresher, 00:00:18.480 --> 00:00:19.970 these are transformations 00:00:19.970 --> 00:00:23.440 that preserve distance between points. 00:00:23.440 --> 00:00:27.920 So, for example, if I have points A and B, 00:00:27.920 --> 00:00:31.610 a rigid transformation could be something like a translation 00:00:31.610 --> 00:00:34.840 because after I've translated them, notice the distance 00:00:34.840 --> 00:00:38.010 between the points is still the same. 00:00:38.010 --> 00:00:40.300 It could be like that. 00:00:40.300 --> 00:00:41.440 It includes rotation. 00:00:41.440 --> 00:00:44.660 Let's say I rotated about point A as the center of rotation. 00:00:44.660 --> 00:00:49.070 That still would not change, that still would not change 00:00:49.070 --> 00:00:51.410 my distance between points A and B. 00:00:51.410 --> 00:00:54.620 It could even be things like taking the mirror image. 00:00:54.620 --> 00:00:56.690 Once again, that's not going to change the distance 00:00:56.690 --> 00:00:57.860 between A and B. 00:00:57.860 --> 00:00:59.790 What's not a rigid transformation? 00:00:59.790 --> 00:01:02.470 Well, one thing you might imagine is dilating, 00:01:02.470 --> 00:01:03.970 scaling it up or down. 00:01:03.970 --> 00:01:06.310 That is going to change the distance, 00:01:06.310 --> 00:01:09.080 so rigid transformation are any transformations 00:01:09.080 --> 00:01:11.850 that preserve the distance between points. 00:01:11.850 --> 00:01:14.470 Now, another idea is congruence, 00:01:14.470 --> 00:01:18.060 and in the context of this video, we're going to be viewing 00:01:18.060 --> 00:01:21.630 the definition of congruence as two figures are congruent 00:01:21.630 --> 00:01:24.910 if and only if there exists a series 00:01:24.910 --> 00:01:28.530 of rigid transformations which will map one figure 00:01:28.530 --> 00:01:30.710 onto the other. 00:01:30.710 --> 00:01:33.520 You might see other definitions of congruence in your life, 00:01:33.520 --> 00:01:36.160 but this is the rigid transformation definition 00:01:36.160 --> 00:01:38.990 of congruence that we will use, and we're going to use 00:01:38.990 --> 00:01:42.900 these two definitions to prove the following, 00:01:42.900 --> 00:01:46.240 to prove that saying two segments are congruent 00:01:46.240 --> 00:01:50.323 is equivalent to saying that they have the same length. 00:01:52.040 --> 00:01:54.760 So, let me get some space here to do that in. 00:01:54.760 --> 00:01:59.760 So first, let me prove that if segment AB 00:01:59.760 --> 00:02:04.570 is congruent to segment CD, 00:02:04.570 --> 00:02:08.060 then the length of segment AB, 00:02:08.060 --> 00:02:11.110 which we'll just denote as AB without the line over it, 00:02:11.110 --> 00:02:15.840 is equal to the length of segment CD. 00:02:15.840 --> 00:02:18.700 How do we do that? 00:02:18.700 --> 00:02:23.700 Well, the first thing to realize is if AB, 00:02:24.010 --> 00:02:27.130 if AB is 00:02:27.130 --> 00:02:29.990 congruent to CD, 00:02:29.990 --> 00:02:34.840 then AB can 00:02:34.840 --> 00:02:39.330 be mapped onto CD 00:02:42.010 --> 00:02:47.010 with rigid transformations, rigid transformations. 00:02:47.260 --> 00:02:51.880 That comes out of the definition of congruence. 00:02:51.880 --> 00:02:53.980 And then we could say, "Since 00:02:55.187 --> 00:03:00.163 "the transformations are rigid, 00:03:02.137 --> 00:03:06.533 "distance is preserved, 00:03:07.627 --> 00:03:10.860 "preserved," and so, that would imply 00:03:10.860 --> 00:03:12.490 that the distance between the points 00:03:12.490 --> 00:03:14.180 are going to be the same. 00:03:14.180 --> 00:03:17.360 AB, the distance between points AB, or the length 00:03:17.360 --> 00:03:21.890 of segment AB, is equal to the length of segment CD. 00:03:21.890 --> 00:03:24.330 That might almost seem too intuitive for you, 00:03:24.330 --> 00:03:26.230 but that's all we're talking about. 00:03:26.230 --> 00:03:28.430 So, now, let's see if we can prove the other way. 00:03:28.430 --> 00:03:32.830 Let's see if we can prove that if the length of segment AB 00:03:32.830 --> 00:03:37.507 is equal to the length of segment CD, then segment AB 00:03:39.770 --> 00:03:44.643 is congruent to segment CD, and let me draw them 00:03:46.410 --> 00:03:50.150 right over here, just to, so, let's say I have segment AB 00:03:51.800 --> 00:03:53.330 right over there, and I'll draw another segment 00:03:53.330 --> 00:03:56.900 that has the same length, so maybe it looks something 00:03:56.900 --> 00:03:59.970 like this, and this is obviously hand-drawn. 00:03:59.970 --> 00:04:02.313 So, then, let's call this CD. 00:04:03.870 --> 00:04:05.697 So, in order to prove this, I have to show, 00:04:05.697 --> 00:04:08.597 "Hey, if I have two segments with the same length, 00:04:08.597 --> 00:04:11.807 "that there's always a set of rigid transformations 00:04:11.807 --> 00:04:14.717 "that will map one segment onto the other, 00:04:14.717 --> 00:04:17.840 "which means, by definition, they are congruent." 00:04:17.840 --> 00:04:21.130 So, let me just construct those transformations. 00:04:21.130 --> 00:04:24.480 So, my first rigid transformation that I could do 00:04:24.480 --> 00:04:29.480 is to translate, translate, and I'll underline the name 00:04:29.930 --> 00:04:34.930 of the transformation, segment AB, so that point A is 00:04:38.030 --> 00:04:43.030 on top of point C, or A is mapped onto C, 00:04:44.030 --> 00:04:46.120 and you could see that there's always a translation 00:04:46.120 --> 00:04:46.953 to do that. 00:04:46.953 --> 00:04:50.600 It would be doing that, and of course we would translate. 00:04:50.600 --> 00:04:55.600 B would end up like that, and so, after this translation, 00:04:56.500 --> 00:04:59.280 it's going to be A right over there. 00:04:59.280 --> 00:05:03.180 A is going to be there, and then B is going 00:05:03.180 --> 00:05:05.630 to be right over there. 00:05:05.630 --> 00:05:10.630 Now, the second step I would do is then rotate AB 00:05:13.930 --> 00:05:18.720 about A, so A is the center of rotation, 00:05:18.720 --> 00:05:22.910 so I'm gonna rotate it so that 00:05:22.910 --> 00:05:27.910 point B lies on ray CD. 00:05:30.400 --> 00:05:32.170 Well, what does this transformation do? 00:05:32.170 --> 00:05:34.250 Well, since point A is the center of rotation, 00:05:34.250 --> 00:05:37.230 A is going to stay mapped on top of C 00:05:37.230 --> 00:05:41.310 from our first translation, but now B is rotated, 00:05:41.310 --> 00:05:44.620 so it sits on top of the ray that starts at C 00:05:44.620 --> 00:05:48.000 and goes through D and keeps going, 00:05:48.000 --> 00:05:50.950 and where will B be on that ray? 00:05:50.950 --> 00:05:54.330 Well, since the distance between B and A is the same 00:05:54.330 --> 00:05:57.070 as the distance between D and C, 00:05:57.070 --> 00:05:58.980 and A and C are the same point, 00:05:58.980 --> 00:06:03.700 and now B sits on that ray, B will now sit right on top 00:06:03.700 --> 00:06:08.700 of D because AB is equal to CD. 00:06:10.110 --> 00:06:14.700 B will be mapped onto, 00:06:16.890 --> 00:06:19.500 onto D, and just like that, 00:06:19.500 --> 00:06:22.550 we've shown that if the segment lengths are equal, 00:06:22.550 --> 00:06:26.090 there is always a set of rigid transformations 00:06:26.090 --> 00:06:29.270 that will map one segment onto the other. 00:06:29.270 --> 00:06:33.780 Therefore, since A and B have been mapped onto C and D, 00:06:33.780 --> 00:06:38.780 we know that A, that segment AB is congruent to segment CD, 00:06:39.370 --> 00:06:40.540 and we are done. 00:06:40.540 --> 00:06:43.633 We have proven what we set out to prove both ways.

Area model for multiplying polynomials with negative terms

https://www.youtube.com/watch?v=_PC1JMBZKUQ

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https://www.youtube.com/api/timedtext?v=_PC1JMBZKUQ&ei=bViUZcvwGdqOmLAP3cGzuAY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=DDA2D11025F429CF6E4F16ECA5FF938C70CFCD95.EAD04CE9DD4607F1B6C21FFC00A92BC49F15F309&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.260 --> 00:00:01.320 - [Instructor] In previous videos, 00:00:01.320 --> 00:00:03.330 we've already looked at using area models 00:00:03.330 --> 00:00:05.590 to think about multiplying expressions, 00:00:05.590 --> 00:00:09.050 like multiplying x plus seven times x plus three. 00:00:09.050 --> 00:00:11.850 In those videos, we saw that we could think about it 00:00:11.850 --> 00:00:14.140 as finding the area of a rectangle, 00:00:14.140 --> 00:00:17.090 where we could break up the length of the rectangle 00:00:17.090 --> 00:00:20.700 as part of the length has length x, 00:00:20.700 --> 00:00:23.800 and then the rest of it has length seven. 00:00:23.800 --> 00:00:26.420 So this would be seven here, and then the total length 00:00:26.420 --> 00:00:29.020 of this side would be x plus seven. 00:00:29.020 --> 00:00:34.020 And then the total length of this side would be x plus, 00:00:34.110 --> 00:00:36.540 and then you have three right over here. 00:00:36.540 --> 00:00:40.160 And what area models did is they helped us visualize 00:00:40.160 --> 00:00:42.400 why we multiply the different terms 00:00:42.400 --> 00:00:44.470 or how we multiply the different terms. 00:00:44.470 --> 00:00:47.300 Because if we're looking for the entire area, 00:00:47.300 --> 00:00:50.100 the entire area is going to be x plus seven, 00:00:50.100 --> 00:00:53.500 x plus seven times x plus three, 00:00:53.500 --> 00:00:55.290 times x plus three. 00:00:55.290 --> 00:00:57.460 And then of course, we can break that down 00:00:57.460 --> 00:01:00.000 into these sub-rectangles. 00:01:00.000 --> 00:01:02.700 This rectangle, and this is actually going to be a square, 00:01:02.700 --> 00:01:04.860 would have an area of x squared. 00:01:04.860 --> 00:01:07.700 This one over here will have an area of seven x, 00:01:07.700 --> 00:01:09.670 seven times x. 00:01:09.670 --> 00:01:12.490 This one over here will have an area of three x. 00:01:12.490 --> 00:01:14.430 And then this one over here will have an area 00:01:14.430 --> 00:01:17.820 of three times seven, or 21. 00:01:17.820 --> 00:01:20.660 And so we can figure out that the ultimate product here 00:01:20.660 --> 00:01:24.690 is going to be x squared plus seven x 00:01:24.690 --> 00:01:27.440 plus three x plus 21. 00:01:27.440 --> 00:01:29.790 That's going to be the area of the entire rectangle. 00:01:29.790 --> 00:01:31.510 Of course, we could add the seven x 00:01:31.510 --> 00:01:34.140 to the three x to get to 10x. 00:01:34.140 --> 00:01:36.260 But some of you might be wondering, 00:01:36.260 --> 00:01:37.630 well, this is all nice 00:01:37.630 --> 00:01:40.690 when I have plus seven and plus three. 00:01:40.690 --> 00:01:43.250 I can think about positive lengths. 00:01:43.250 --> 00:01:45.740 I can think about positive areas. 00:01:45.740 --> 00:01:47.440 But what if it wasn't that way? 00:01:47.440 --> 00:01:50.860 What if we were dealing with negatives instead? 00:01:50.860 --> 00:01:55.060 For example, if we now try to do the same thing, 00:01:55.060 --> 00:01:56.680 we could say, all right, 00:01:56.680 --> 00:01:59.130 this top length right over here 00:01:59.130 --> 00:02:02.830 would be x minus seven. 00:02:02.830 --> 00:02:04.440 So let's just keep going with it, 00:02:04.440 --> 00:02:07.800 and let's call this length negative seven up here. 00:02:07.800 --> 00:02:10.260 So it has a negative seven length, and we're not 00:02:10.260 --> 00:02:12.060 necessarily used to thinking about lengths as negative. 00:02:12.060 --> 00:02:13.080 Let's just go with it. 00:02:13.080 --> 00:02:15.580 And then the height right over here, 00:02:15.580 --> 00:02:17.490 it would be x minus three. 00:02:17.490 --> 00:02:20.060 So we could write an x there for that part of the height. 00:02:20.060 --> 00:02:21.720 And for this part of the height, 00:02:21.720 --> 00:02:24.990 we could put a negative three. 00:02:24.990 --> 00:02:27.400 So let's see, if we kept going with what we did last time, 00:02:27.400 --> 00:02:29.590 the area here would be x squared. 00:02:29.590 --> 00:02:32.580 The area here would be negative seven times x, 00:02:32.580 --> 00:02:35.250 so that would be negative seven x. 00:02:35.250 --> 00:02:38.040 This green area would be negative three x. 00:02:38.040 --> 00:02:40.380 And then this orange area would be negative three 00:02:40.380 --> 00:02:43.770 times negative seven, which is positive 21. 00:02:43.770 --> 00:02:47.180 And then we would say that the entire product is x squared 00:02:47.180 --> 00:02:51.670 minus seven x minus three x plus 21. 00:02:51.670 --> 00:02:52.570 And we can, of course, 00:02:52.570 --> 00:02:55.800 add these two together to get negative 10x. 00:02:55.800 --> 00:02:57.810 But does this make sense? 00:02:57.810 --> 00:03:00.170 Well, one way to think about it is that a negative area 00:03:00.170 --> 00:03:04.550 is an area that you would take away from the total area. 00:03:04.550 --> 00:03:07.290 So if x happens to be a positive number here, 00:03:07.290 --> 00:03:09.070 then this pink area would be negative, 00:03:09.070 --> 00:03:10.850 and so we would take it away from the whole. 00:03:10.850 --> 00:03:14.450 And that's exactly what is happening in this expression. 00:03:14.450 --> 00:03:16.640 And it's worth mentioning 00:03:16.640 --> 00:03:19.090 that even before when this wasn't a negative seven, 00:03:19.090 --> 00:03:20.420 when it was a positive seven 00:03:20.420 --> 00:03:22.970 and this was a positive seven x, 00:03:22.970 --> 00:03:25.580 it's completely possible that x is negative, 00:03:25.580 --> 00:03:29.090 in which case you would've had a negative area anyway. 00:03:29.090 --> 00:03:32.330 But to appreciate that this will all work out, 00:03:32.330 --> 00:03:33.870 even with negative numbers, 00:03:33.870 --> 00:03:37.640 I'll give an example, if x were equal to 10. 00:03:37.640 --> 00:03:39.950 That will help us make sense of things. 00:03:39.950 --> 00:03:42.330 So if x were equal to 10, 00:03:42.330 --> 00:03:44.700 we would get an area model that looks like this. 00:03:44.700 --> 00:03:48.720 We're having 10 minus seven, 00:03:48.720 --> 00:03:51.680 so I'll put minus seven right over here, 00:03:51.680 --> 00:03:56.680 times 10 minus three. 00:03:56.720 --> 00:03:58.060 Now, you can figure out in your heads 00:03:58.060 --> 00:03:58.900 what's that going to be. 00:03:58.900 --> 00:04:00.750 10 minus seven is three. 00:04:00.750 --> 00:04:02.750 10 minus three is seven. 00:04:02.750 --> 00:04:06.250 So this should all add up to positive 21. 00:04:06.250 --> 00:04:08.100 Let's make sure that's actually occurring. 00:04:08.100 --> 00:04:11.940 So this blue area is going to be 10 times 10, which is 100. 00:04:11.940 --> 00:04:15.000 This pink area now is 10 times negative seven. 00:04:15.000 --> 00:04:16.550 So it's negative 70, 00:04:16.550 --> 00:04:19.450 so we're gonna take it away from the total area. 00:04:19.450 --> 00:04:21.600 This green area is negative three times 10, 00:04:21.600 --> 00:04:23.260 so that's negative 30. 00:04:23.260 --> 00:04:26.410 And then negative three times negative seven, 00:04:26.410 --> 00:04:29.150 this orange area is positive 21. 00:04:29.150 --> 00:04:30.820 Does that all work out? 00:04:30.820 --> 00:04:35.820 Let's see, if we take this positive area, 100 minus 70 00:04:36.430 --> 00:04:40.130 minus 30 and then add 21, 00:04:40.130 --> 00:04:43.340 100 minus 70 is going to be 30, 00:04:43.340 --> 00:04:44.820 minus 30 again is zero, 00:04:44.820 --> 00:04:46.370 and then you just have 21 left over, 00:04:46.370 --> 00:04:48.920 which is exactly what you would expect. 00:04:48.920 --> 00:04:51.170 You could actually move this pink area over 00:04:51.170 --> 00:04:53.520 and subtract it from this blue area. 00:04:53.520 --> 00:04:55.110 And then you could take this green area 00:04:55.110 --> 00:04:56.340 and then you could turn it vertical, 00:04:56.340 --> 00:04:59.010 and then that would subtract out the rest of the blue area. 00:04:59.010 --> 00:05:02.450 And then all you would have left is this orange area. 00:05:02.450 --> 00:05:04.940 So hopefully this helps you appreciate 00:05:04.940 --> 00:05:09.110 that area models for multiplying expressions also works 00:05:09.110 --> 00:05:10.970 if the terms are negative. 00:05:10.970 --> 00:05:13.600 And also, reminder, when we just had x's here, 00:05:13.600 --> 00:05:15.700 they could've been negative to begin with.

Hydrogen bonding

https://www.youtube.com/watch?v=ltxqQbiI6-o

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https://www.youtube.com/api/timedtext?v=ltxqQbiI6-o&ei=bViUZaumE6ezvdIPisibkAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A85BF9BF5D60A5D09BE82639914557F3A2DFFF86.34500B8935022A34FDD36ACD5E7D02C20085C28B&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:02.850 - [Instructor] Let's talk about hydrogen bonds. 00:00:02.850 --> 00:00:05.790 Depicted here, I have three different types of molecules. 00:00:05.790 --> 00:00:07.470 On the left, I have ammonia. 00:00:07.470 --> 00:00:11.060 Each ammonia molecule has one nitrogen bonded 00:00:11.060 --> 00:00:12.440 to three hydrogens. 00:00:12.440 --> 00:00:13.273 In the middle, 00:00:13.273 --> 00:00:15.980 I have something you're probably very familiar with, 00:00:15.980 --> 00:00:18.910 in fact, you're made up of it, which is water. 00:00:18.910 --> 00:00:22.330 Each oxygen is bonded to two hydrogens. 00:00:22.330 --> 00:00:25.500 And then here on the right, I have hydrogen fluoride. 00:00:25.500 --> 00:00:28.900 Each fluorine is bonded to one hydrogen. 00:00:28.900 --> 00:00:32.720 Now, why are these types of molecules interesting? 00:00:32.720 --> 00:00:35.020 And what does that have to do with hydrogen bonds? 00:00:35.020 --> 00:00:38.220 And the simple answer is, in each of these cases, 00:00:38.220 --> 00:00:40.010 you have hydrogen bonded 00:00:40.010 --> 00:00:43.480 to a much more electronegative atom. 00:00:43.480 --> 00:00:45.660 Even though these are covalent bonds, 00:00:45.660 --> 00:00:47.980 they're going to be polar covalent bonds. 00:00:47.980 --> 00:00:51.740 You are going to have a bond dipole moment that goes 00:00:51.740 --> 00:00:55.630 from the hydrogen to the more electronegative atom, 00:00:55.630 --> 00:00:58.650 from the hydrogen to the more electronegative atom, 00:00:58.650 --> 00:01:02.530 from the hydrogen to the more electronegative atom. 00:01:02.530 --> 00:01:05.320 The more electronegative atom is going to hog the electrons. 00:01:05.320 --> 00:01:07.390 The electrons are gonna spend more time around that. 00:01:07.390 --> 00:01:09.610 So that end of the molecule is going 00:01:09.610 --> 00:01:11.320 to have a partial negative charge. 00:01:11.320 --> 00:01:13.200 And then the ends with the hydrogens, 00:01:13.200 --> 00:01:17.000 those are gonna have partial positive charges. 00:01:17.000 --> 00:01:18.170 Another way to think about it is, 00:01:18.170 --> 00:01:20.410 if you added these dipole moments, 00:01:20.410 --> 00:01:24.440 you would have a net dipole for the entire molecule 00:01:26.812 --> 00:01:27.653 that would look something like that. 00:01:28.900 --> 00:01:31.320 So we are dealing with polar molecules. 00:01:31.320 --> 00:01:34.680 And the polarity comes from both the asymmetry, 00:01:34.680 --> 00:01:39.680 and you have a very electronegative atom bonded to hydrogen, 00:01:40.090 --> 00:01:43.740 oxygen, very electronegative atom, bonded to hydrogen. 00:01:43.740 --> 00:01:46.720 So this end of the molecule is partially negative. 00:01:46.720 --> 00:01:47.890 This end of the molecule 00:01:47.890 --> 00:01:50.250 or these ends of the molecule are partially positive. 00:01:50.250 --> 00:01:53.500 For hydrogen fluoride, this end is partially positive. 00:01:53.500 --> 00:01:55.280 This end is partially negative. 00:01:55.280 --> 00:01:56.540 And so what do you think could happen 00:01:56.540 --> 00:01:59.090 when these molecules interact with each other? 00:01:59.090 --> 00:02:01.950 The nitrogen end right over here, of this ammonia, 00:02:01.950 --> 00:02:04.370 could be attracted to one of these hydrogens 00:02:04.370 --> 00:02:07.220 that has a partially positive charge right over there. 00:02:07.220 --> 00:02:11.670 Or this hydrogen, the partial positive charge, 00:02:11.670 --> 00:02:13.690 might be attracted to that nitrogen 00:02:13.690 --> 00:02:15.870 that has a partial negative charge. 00:02:15.870 --> 00:02:16.970 And this attraction 00:02:16.970 --> 00:02:19.460 between the partial positive hydrogen end 00:02:19.460 --> 00:02:23.470 and the partially negative end of another molecule, 00:02:23.470 --> 00:02:26.210 those are hydrogen bonds. 00:02:26.210 --> 00:02:30.260 And they are an intermolecular force that will be additive 00:02:30.260 --> 00:02:31.990 to the total intermolecular force 00:02:31.990 --> 00:02:35.320 from, say, things like London dispersion forces, 00:02:35.320 --> 00:02:37.570 which makes you have a higher boiling point 00:02:37.570 --> 00:02:39.170 than you would have if you just thought 00:02:39.170 --> 00:02:41.070 about London dispersion forces. 00:02:41.070 --> 00:02:44.350 And to make that clear, you can look at this chart. 00:02:44.350 --> 00:02:47.810 You can see all of these molecules are formed 00:02:47.810 --> 00:02:50.990 between period two elements and hydrogen. 00:02:50.990 --> 00:02:55.300 In fact, all of these molecules have similar molar masses, 00:02:55.300 --> 00:02:58.690 methane, ammonia, hydrogen fluoride, and water. 00:02:58.690 --> 00:03:01.350 If we were just thinking about London dispersion forces, 00:03:01.350 --> 00:03:03.540 London dispersion forces are proportional 00:03:03.540 --> 00:03:07.030 to the polarizability of a molecule, 00:03:07.030 --> 00:03:10.760 which is proportional to the electron cloud size, 00:03:10.760 --> 00:03:13.100 which is proportional to the molar mass. 00:03:13.100 --> 00:03:15.590 And generally speaking, as you go from molecules formed 00:03:15.590 --> 00:03:18.150 with period two elements to period three elements 00:03:18.150 --> 00:03:21.100 to period four elements to period five elements, 00:03:21.100 --> 00:03:23.620 you do see that as the molar mass 00:03:23.620 --> 00:03:25.390 of those molecules increase, 00:03:25.390 --> 00:03:29.780 there is that general upward trend of the boiling point, 00:03:29.780 --> 00:03:32.810 and that's due to the London dispersion forces. 00:03:32.810 --> 00:03:36.400 But for any given period, you do see the separation. 00:03:36.400 --> 00:03:37.233 And in particular, 00:03:37.233 --> 00:03:39.500 you see a lot of separation for the molecules formed 00:03:39.500 --> 00:03:41.830 with oxygen, fluorine, and nitrogen. 00:03:41.830 --> 00:03:45.190 These molecules, despite having similar molar masses, 00:03:45.190 --> 00:03:47.750 have very different boiling points. 00:03:47.750 --> 00:03:51.470 So there must be some other type of intermolecular forces 00:03:51.470 --> 00:03:55.260 at play above and beyond London dispersion forces. 00:03:55.260 --> 00:03:58.130 And the simple answer is yes. 00:03:58.130 --> 00:04:02.200 What you have at play are the hydrogen bonds. 00:04:02.200 --> 00:04:03.500 Now, some of you might be wondering, 00:04:03.500 --> 00:04:04.900 well, look at these molecules formed 00:04:04.900 --> 00:04:06.900 with period three elements and hydrogen 00:04:06.900 --> 00:04:09.070 or period four elements and hydrogen, 00:04:09.070 --> 00:04:11.980 they also don't have the same boiling point, 00:04:11.980 --> 00:04:13.310 even though you would expect 00:04:13.310 --> 00:04:15.360 similar London dispersion forces 00:04:15.360 --> 00:04:17.650 because they have similar molar masses. 00:04:17.650 --> 00:04:20.470 And the separation that you see here in boiling points, 00:04:20.470 --> 00:04:22.970 this, too, would be due to other things, 00:04:22.970 --> 00:04:24.920 other than London dispersion forces. 00:04:24.920 --> 00:04:29.370 In particular, dipole-dipole forces would be at play. 00:04:29.370 --> 00:04:31.490 But what you can see is the spread is much higher 00:04:31.490 --> 00:04:34.870 for these molecules formed with nitrogen and hydrogen, 00:04:34.870 --> 00:04:37.830 fluorine and hydrogen, and oxygen and hydrogen. 00:04:37.830 --> 00:04:40.870 And that's because hydrogen bonds can be viewed 00:04:40.870 --> 00:04:45.870 as the strongest form of dipole-dipole forces. 00:04:46.440 --> 00:04:51.440 Hydrogen bonds are a special case of dipole-dipole forces. 00:04:52.120 --> 00:04:54.240 When we're talking about hydrogen bonds, 00:04:54.240 --> 00:04:58.110 we're usually talking about a specific bond dipole, 00:04:58.110 --> 00:05:01.880 the bond between hydrogen and a more electronegative atom 00:05:01.880 --> 00:05:04.440 like nitrogen, oxygen, and fluorine. 00:05:04.440 --> 00:05:05.860 And so we're specifically talking 00:05:05.860 --> 00:05:07.630 about that part of the molecule, 00:05:07.630 --> 00:05:10.890 that hydrogen part that has a partially positive charge 00:05:10.890 --> 00:05:13.220 being attracted to the partially negative end 00:05:13.220 --> 00:05:14.670 of another molecule. 00:05:14.670 --> 00:05:18.130 So it's really about a bond dipole with hydrogen bonds 00:05:18.130 --> 00:05:20.580 versus a total molecular dipole 00:05:20.580 --> 00:05:23.870 when we talk about dipole-dipole interactions in general. 00:05:23.870 --> 00:05:25.200 And so you could imagine, 00:05:25.200 --> 00:05:27.170 it doesn't even just have to be hydrogen bonds 00:05:27.170 --> 00:05:29.170 between a like molecule. 00:05:29.170 --> 00:05:31.750 You could have hydrogen bonds between an ammonia molecule 00:05:31.750 --> 00:05:34.110 and a water molecule or between a water molecule 00:05:34.110 --> 00:05:36.430 and a hydrogen fluoride molecule. 00:05:36.430 --> 00:05:40.630 And I mentioned that these are really important in biology. 00:05:40.630 --> 00:05:43.890 This right over here is a closeup of DNA. 00:05:43.890 --> 00:05:46.700 You can see that the base pairs in DNA, 00:05:46.700 --> 00:05:48.550 you can imagine the rungs of the ladder, 00:05:48.550 --> 00:05:52.940 those are formed by hydrogen bonds between base pairs. 00:05:52.940 --> 00:05:54.930 So those hydrogen bonds are strong enough 00:05:54.930 --> 00:05:57.170 to keep that double helix together, 00:05:57.170 --> 00:05:58.750 but then they're not so strong 00:05:58.750 --> 00:06:00.690 that they can't be pulled apart 00:06:00.690 --> 00:06:04.870 when it's time to replicate or transcribe the DNA. 00:06:04.870 --> 00:06:07.830 Hydrogen bonds are also a big deal in proteins. 00:06:07.830 --> 00:06:10.370 You learn in biology class that proteins are made up 00:06:10.370 --> 00:06:12.290 of chains of amino acids, 00:06:12.290 --> 00:06:13.910 and the function is heavily influenced 00:06:13.910 --> 00:06:15.620 by the shape of that protein. 00:06:15.620 --> 00:06:19.280 And that shape is influenced by hydrogen bonds 00:06:19.280 --> 00:06:22.300 that might form between the amino acids 00:06:22.300 --> 00:06:24.720 that make up the protein. 00:06:24.720 --> 00:06:27.040 So hydrogen bonds are everywhere. 00:06:27.040 --> 00:06:30.130 There are many hydrogen bonds in your body right now mainly, 00:06:30.130 --> 00:06:31.290 not just because of the DNA, 00:06:31.290 --> 00:06:33.360 mainly because you're mostly water. 00:06:33.360 --> 00:06:36.450 So life, as we know it, would not exist 00:06:36.450 --> 00:06:38.353 without hydrogen bonds.

Intermolecular forces and vapor pressure

https://www.youtube.com/watch?v=eubN8DwUh48

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en

WEBVTT Kind: captions Language: en 00:00:00.630 --> 00:00:03.270 - [Instructor] So we have four different molecules here. 00:00:03.270 --> 00:00:04.350 And what I want you to think about, 00:00:04.350 --> 00:00:05.860 if you had a pure sample of each, 00:00:05.860 --> 00:00:07.280 which of those pure samples would have 00:00:07.280 --> 00:00:09.460 the highest boiling point, second highest, 00:00:09.460 --> 00:00:11.400 third highest, and fourth highest? 00:00:11.400 --> 00:00:14.180 Pause this video, and try to figure that out. 00:00:14.180 --> 00:00:16.380 All right, now to figure that out, 00:00:16.380 --> 00:00:17.780 it really just boils down to 00:00:17.780 --> 00:00:20.450 which of these has the highest intermolecular forces 00:00:20.450 --> 00:00:21.910 when they're in a liquid state? 00:00:21.910 --> 00:00:24.160 Because if you have high intermolecular forces, 00:00:24.160 --> 00:00:27.480 it would take a lot of energy or a higher boiling point 00:00:27.480 --> 00:00:30.120 to really overcome those intermolecular forces 00:00:30.120 --> 00:00:32.420 and get to a gas state. 00:00:32.420 --> 00:00:34.790 So let's think about the intermolecular forces 00:00:34.790 --> 00:00:35.950 that we have studied. 00:00:35.950 --> 00:00:38.800 So I will start with hydrogen bonds, 00:00:38.800 --> 00:00:41.630 hydrogen bonds. 00:00:41.630 --> 00:00:42.850 'Cause you could really view those, 00:00:42.850 --> 00:00:46.620 those are the strongest of the dipole-dipole interactions, 00:00:46.620 --> 00:00:48.040 and they're going to be stronger 00:00:48.040 --> 00:00:50.340 than your London dispersion forces. 00:00:50.340 --> 00:00:53.370 We can see that diethyl ether won't form hydrogen bonds. 00:00:53.370 --> 00:00:56.040 We don't see any bonds between hydrogen 00:00:56.040 --> 00:00:59.130 and an oxygen, a nitrogen, or a fluorine. 00:00:59.130 --> 00:01:02.440 Ethanol has one oxygen-hydrogen bond. 00:01:02.440 --> 00:01:05.850 Methanol also has one oxygen-hydrogen bond. 00:01:05.850 --> 00:01:09.900 Water has two oxygen-hydrogen bonds. 00:01:09.900 --> 00:01:12.340 So if I had to rank the hydrogen bond contribution 00:01:12.340 --> 00:01:13.730 to the intermolecular forces, 00:01:13.730 --> 00:01:15.570 I would put water as number one 00:01:15.570 --> 00:01:18.210 'cause it can form the most hydrogen bonds. 00:01:18.210 --> 00:01:22.090 I would put methanol and ethanol as a tie for second. 00:01:22.090 --> 00:01:24.530 And then I would put diethyl ether last 00:01:24.530 --> 00:01:26.330 'cause it can't form hydrogen bonds. 00:01:26.330 --> 00:01:28.240 So just looking at this, 00:01:28.240 --> 00:01:30.800 I know that water's going to have the highest boiling point. 00:01:30.800 --> 00:01:33.480 Diethyl ether is going to have the lowest boiling point. 00:01:33.480 --> 00:01:37.080 But what about the difference between methanol and ethanol? 00:01:37.080 --> 00:01:40.530 And we could think about other types of dipole forces, 00:01:40.530 --> 00:01:43.740 but not a lot that you could intuit just by eyeballing them. 00:01:43.740 --> 00:01:45.890 They might actually have similar dipole moments 00:01:45.890 --> 00:01:47.310 on a molecular basis. 00:01:47.310 --> 00:01:50.170 But we can think about London dispersion forces. 00:01:50.170 --> 00:01:51.270 I'll do this in a different color. 00:01:51.270 --> 00:01:54.130 So London dispersion forces. 00:01:54.130 --> 00:01:55.740 And if we're just trying to, 00:01:55.740 --> 00:01:57.740 actually I'll rank all of them. 00:01:57.740 --> 00:02:00.747 So London dispersion forces are proportional to 00:02:00.747 --> 00:02:03.430 how polarizable a molecule is, 00:02:03.430 --> 00:02:05.850 which is proportional to how large its electron cloud is, 00:02:05.850 --> 00:02:07.630 which is proportional to its molar mass. 00:02:07.630 --> 00:02:09.440 And it's clear that diethyl ether 00:02:09.440 --> 00:02:11.190 has the highest molar mass, 00:02:11.190 --> 00:02:12.810 followed by ethanol, 00:02:12.810 --> 00:02:15.310 followed by methanol, 00:02:15.310 --> 00:02:16.500 followed by water. 00:02:16.500 --> 00:02:17.660 How did I know that? 00:02:17.660 --> 00:02:19.710 Well, you literally can take atoms away 00:02:19.710 --> 00:02:23.630 from the diethyl ether to get to an ethanol. 00:02:23.630 --> 00:02:25.040 And you can literally take atoms away 00:02:25.040 --> 00:02:26.670 from that to get to a methanol. 00:02:26.670 --> 00:02:28.020 And you can literally take atoms away 00:02:28.020 --> 00:02:29.610 from that to get to a water. 00:02:29.610 --> 00:02:33.630 So we know that this is the order of molar mass. 00:02:33.630 --> 00:02:35.900 And so London dispersion forces, 00:02:35.900 --> 00:02:37.750 I wouldn't make that change the ranking 00:02:37.750 --> 00:02:40.260 between water or diethyl ether because these are going 00:02:40.260 --> 00:02:42.530 to be a lot weaker than those hydrogen bonds. 00:02:42.530 --> 00:02:44.530 But they can be useful for the tiebreaker 00:02:44.530 --> 00:02:46.790 between ethanol and methanol. 00:02:46.790 --> 00:02:49.790 And so my overall ranking on boiling points, 00:02:49.790 --> 00:02:52.980 the highest boiling point I would put would be water, 00:02:52.980 --> 00:02:56.630 followed by, since ethanol won the tiebreaker, 00:02:56.630 --> 00:02:58.510 followed by ethanol, 00:02:58.510 --> 00:03:01.320 followed by methanol, 00:03:01.320 --> 00:03:04.650 and then the lowest boiling point would be diethyl ether. 00:03:04.650 --> 00:03:06.660 And if we look at the actual data, 00:03:06.660 --> 00:03:10.060 it's consistent with what we just talked about. 00:03:10.060 --> 00:03:11.430 We can see very clearly 00:03:11.430 --> 00:03:13.520 that water has the highest boiling point, 00:03:13.520 --> 00:03:14.920 ethanol is second, 00:03:14.920 --> 00:03:16.270 methanol is third, 00:03:16.270 --> 00:03:18.570 and diethyl ether was fourth, 00:03:18.570 --> 00:03:21.550 completely consistent with our intuition. 00:03:21.550 --> 00:03:23.160 Now, what's also interesting here, 00:03:23.160 --> 00:03:25.980 you might have noticed, is this thing called vapor pressure. 00:03:25.980 --> 00:03:29.960 And you might have also noticed that vapor pressure seems 00:03:29.960 --> 00:03:32.430 to trend the opposite way as boiling point. 00:03:32.430 --> 00:03:34.110 The things that have the high boiling point 00:03:34.110 --> 00:03:35.500 have the low vapor pressure, 00:03:35.500 --> 00:03:37.510 and the things that have the low boiling point 00:03:37.510 --> 00:03:39.520 have a high vapor pressure. 00:03:39.520 --> 00:03:41.130 So what are we talking about, why, 00:03:41.130 --> 00:03:44.870 about vapor pressure, and why do we see this relationship? 00:03:44.870 --> 00:03:47.040 And I'm not going to go deep into vapor pressure. 00:03:47.040 --> 00:03:49.260 There'll be other videos on that on Khan Academy. 00:03:49.260 --> 00:03:51.290 But just to get you a sense, 00:03:51.290 --> 00:03:54.670 imagine a closed container here. 00:03:54.670 --> 00:03:56.990 And I put one of these, 00:03:56.990 --> 00:03:59.370 a sample of one of these molecules in a liquid state, 00:03:59.370 --> 00:04:00.820 and I'm gonna just draw the molecules, 00:04:00.820 --> 00:04:04.890 clearly not drawn to scale, as these little circles. 00:04:04.890 --> 00:04:06.850 And the temperature matters, 00:04:06.850 --> 00:04:10.000 so let's say that this is at 20 degrees Celsius. 00:04:10.000 --> 00:04:11.880 Now, you might notice, at 20 degrees Celsius, 00:04:11.880 --> 00:04:13.460 it's lower than the boiling point 00:04:13.460 --> 00:04:15.820 of all of these characters. 00:04:15.820 --> 00:04:18.770 So for the most part, they're going to be in a liquid state, 00:04:18.770 --> 00:04:22.870 but we know that not every one of these molecules is moving 00:04:22.870 --> 00:04:25.050 with the exact same kinetic energy. 00:04:25.050 --> 00:04:26.840 The temperature, you could view as a measure 00:04:26.840 --> 00:04:29.400 of the average kinetic energy of the molecules, 00:04:29.400 --> 00:04:31.690 but they're all bumping around into each other, 00:04:31.690 --> 00:04:34.930 in different positions, with different amounts of velocities 00:04:34.930 --> 00:04:36.710 and therefore different kinetic energies. 00:04:36.710 --> 00:04:40.490 And so every now and then, you're going to have a molecule 00:04:40.490 --> 00:04:43.320 that has the right position and the right kinetic energy 00:04:43.320 --> 00:04:47.190 to escape and get into the vapor state, 00:04:47.190 --> 00:04:48.940 into a gaseous state. 00:04:48.940 --> 00:04:51.120 And so that's going to keep happening. 00:04:51.120 --> 00:04:53.270 But then the things that are in the gaseous state, 00:04:53.270 --> 00:04:55.020 every now and then they're bumping into each other, 00:04:55.020 --> 00:04:57.200 and they're bumping into the sides of the container. 00:04:57.200 --> 00:04:58.280 And every now and then, 00:04:58.280 --> 00:05:00.660 they might approach the surface 00:05:00.660 --> 00:05:03.730 with the right kinetic energy, with the right position, 00:05:03.730 --> 00:05:06.430 so that they get recaptured by the intermolecular forces 00:05:06.430 --> 00:05:07.720 and enter a liquid state. 00:05:07.720 --> 00:05:09.840 And so you can imagine, this will keep happening 00:05:09.840 --> 00:05:13.130 where things go from liquid, and then they go to vapor. 00:05:13.130 --> 00:05:15.710 But then when that vapor gets high enough 00:05:15.710 --> 00:05:17.900 or when you could say the vapor pressure gets high enough, 00:05:17.900 --> 00:05:19.260 remember, that pressure's just from 00:05:19.260 --> 00:05:21.210 the vapor molecules bouncing around, 00:05:21.210 --> 00:05:24.320 then you will get to some form of an equilibrium. 00:05:24.320 --> 00:05:25.620 And you could imagine, 00:05:25.620 --> 00:05:28.220 the things that have a lower boiling point, 00:05:28.220 --> 00:05:30.840 that means they have lower intermolecular forces, 00:05:30.840 --> 00:05:33.280 more of the vapor is going to form, 00:05:33.280 --> 00:05:35.630 and so you're going to have a higher vapor pressure 00:05:35.630 --> 00:05:37.470 before you get to equilibrium. 00:05:37.470 --> 00:05:40.730 On the other hand, things with high intermolecular forces, 00:05:40.730 --> 00:05:43.750 fewer of those molecules are going to break away, 00:05:43.750 --> 00:05:46.100 and so you're going to have a lower vapor pressure 00:05:46.100 --> 00:05:48.550 when you get to that equilibrium. 00:05:48.550 --> 00:05:51.220 And you can see that very clearly here. 00:05:51.220 --> 00:05:52.820 So I will leave you there. 00:05:52.820 --> 00:05:54.330 We got a little bit of practice, 00:05:54.330 --> 00:05:56.010 seeing everything we've seen so far, 00:05:56.010 --> 00:05:58.700 and we learned a little bit about vapor pressure 00:05:58.700 --> 00:06:01.940 and how that relates to intermolecular forces 00:06:01.940 --> 00:06:02.843 and boiling point.

Ion–dipole forces

https://www.youtube.com/watch?v=7HCAGSkK1Do

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WEBVTT Kind: captions Language: en 00:00:00.450 --> 00:00:01.283 - [Instructor] Let's talk a little bit 00:00:01.283 --> 00:00:03.950 about ion-dipole forces. 00:00:03.950 --> 00:00:05.697 And before we think about how ions 00:00:05.697 --> 00:00:07.480 and dipoles might interact, 00:00:07.480 --> 00:00:09.190 let's just remind ourselves 00:00:09.190 --> 00:00:12.610 what the difference is between ions and dipoles. 00:00:12.610 --> 00:00:14.020 And I encourage you to pause this video 00:00:14.020 --> 00:00:15.580 and try to refresh your own memory 00:00:15.580 --> 00:00:17.580 before we refresh our memories together. 00:00:18.710 --> 00:00:21.920 All right, now let's first think about ions. 00:00:21.920 --> 00:00:26.920 Ions are atoms or molecules that have a net charge. 00:00:27.250 --> 00:00:32.250 So for example, when chlorine gains an electron 00:00:32.430 --> 00:00:35.060 and becomes the chloride ion, 00:00:35.060 --> 00:00:39.320 it's an ion because it now has a net negative charge. 00:00:39.320 --> 00:00:42.910 Similarly, when sodium loses an electron, 00:00:42.910 --> 00:00:45.070 it now has a net positive charge. 00:00:45.070 --> 00:00:48.310 So this is the sodium ion. 00:00:48.310 --> 00:00:50.930 Now what's the difference between that and a dipole? 00:00:50.930 --> 00:00:53.900 Well, generally speaking when we're talking about dipoles, 00:00:53.900 --> 00:00:55.420 we're not talking about something 00:00:55.420 --> 00:00:57.910 that has necessarily a net charge, 00:00:57.910 --> 00:01:01.587 we're talking about something where the charge is separated 00:01:01.587 --> 00:01:04.030 on different ends of the molecule, 00:01:04.030 --> 00:01:05.660 that you have a partially positive end 00:01:05.660 --> 00:01:08.000 and you have a partial negative end, 00:01:08.000 --> 00:01:12.220 that there is a molecular dipole moment. 00:01:12.220 --> 00:01:16.400 And a good example of a molecule that is a dipole 00:01:16.400 --> 00:01:20.980 or has a dipole moment at a molecular level is water. 00:01:20.980 --> 00:01:24.030 Water is a very polar molecule. 00:01:24.030 --> 00:01:26.320 We've talked about this many times. 00:01:26.320 --> 00:01:30.510 You have your oxygen which is quite electronegative, 00:01:30.510 --> 00:01:32.770 covalently bonded to two hydrogens, 00:01:32.770 --> 00:01:34.740 and those are really polar covalent bonds 00:01:34.740 --> 00:01:37.090 because the oxygen's so much more electronegative 00:01:37.090 --> 00:01:40.200 that it hogs the electrons, it's selfish of the electrons. 00:01:40.200 --> 00:01:43.470 And since the electrons spend more time around the oxygen 00:01:43.470 --> 00:01:45.880 than around the hydrogen, 00:01:45.880 --> 00:01:47.460 you have a partial negative charge 00:01:47.460 --> 00:01:48.730 at this end of the molecule 00:01:48.730 --> 00:01:50.960 and you have partial positive charges 00:01:50.960 --> 00:01:53.060 at the other end of the molecules. 00:01:53.060 --> 00:01:54.310 And we describe this 00:01:54.310 --> 00:01:56.210 when we talked about hydrogen bonding 00:01:56.210 --> 00:01:59.670 where the partial negative end of one water molecule 00:01:59.670 --> 00:02:02.330 would be attracted to the partial positive end 00:02:02.330 --> 00:02:04.160 of another water molecule. 00:02:04.160 --> 00:02:06.670 But, as we've talked about, hydrogen bonds, 00:02:06.670 --> 00:02:08.550 which are an intermolecular force 00:02:08.550 --> 00:02:12.570 are just a special case of dipole forces. 00:02:12.570 --> 00:02:14.600 Things that are able to form hydrogen bonds 00:02:14.600 --> 00:02:16.820 just have a very strong dipole moment, 00:02:16.820 --> 00:02:19.950 because you have hydrogen bonded to an oxygen, 00:02:19.950 --> 00:02:23.840 a nitrogen, and a fluorine, that is quite electronegative. 00:02:23.840 --> 00:02:26.760 So now that we know the difference between ions and dipoles, 00:02:26.760 --> 00:02:28.690 how might they interact? 00:02:28.690 --> 00:02:31.730 Well you might guess Coulomb forces are at play. 00:02:31.730 --> 00:02:36.290 The partial negative end of a dipole would be attracted 00:02:36.290 --> 00:02:38.450 to a positively charged ion. 00:02:38.450 --> 00:02:41.430 And I have prearranged these water molecules 00:02:41.430 --> 00:02:43.750 so that you have the partial negative end 00:02:43.750 --> 00:02:48.127 is facing towards this sodium positive ion. 00:02:48.127 --> 00:02:50.490 And so what I'm drawing right over here, 00:02:50.490 --> 00:02:54.200 these are ion-dipole forces. 00:02:54.200 --> 00:02:59.060 Similarly, if you have a chloride anion, or a negative ion, 00:02:59.060 --> 00:03:02.260 well then the partially positive ends of the dipoles 00:03:02.260 --> 00:03:04.010 are going to be attracted, 00:03:04.010 --> 00:03:07.740 and so water might arrange itself in this way 00:03:07.740 --> 00:03:11.350 where the partial positive ends, the ends with the hydrogen, 00:03:11.350 --> 00:03:13.530 are facing the chlorine. 00:03:13.530 --> 00:03:15.070 And this is one of the reasons 00:03:15.070 --> 00:03:19.010 why it's so easy to dissolve sodium chloride, 00:03:19.010 --> 00:03:22.120 to dissolve table salt in water. 00:03:22.120 --> 00:03:24.760 Those ions are able to separate 00:03:24.760 --> 00:03:27.800 and be attracted to the water molecules which are polar, 00:03:27.800 --> 00:03:30.933 which have molecular dipoles. 00:03:30.933 --> 00:03:34.610 Now, if I were to ask you what's gonna dictate the strength 00:03:34.610 --> 00:03:38.780 of the ion-dipole forces, think about that. 00:03:38.780 --> 00:03:42.160 Pause this video, and what do you think is going to matter? 00:03:42.160 --> 00:03:44.950 Well, as you can imagine, these are Coulomb forces. 00:03:44.950 --> 00:03:47.420 So the strength of the charges matter. 00:03:47.420 --> 00:03:50.260 So you're gonna have a stronger ion-dipole force 00:03:50.260 --> 00:03:53.570 if you have stronger charges on the ions. 00:03:53.570 --> 00:03:56.710 So instead of a sodium with a positive one charge, 00:03:56.710 --> 00:04:00.410 if you had a calcium ion that had a positive two charge, 00:04:00.410 --> 00:04:03.070 then the partially negative ends of the water molecules 00:04:03.070 --> 00:04:05.000 would be even more strongly attracted. 00:04:05.000 --> 00:04:08.160 You would have stronger ion-dipole forces. 00:04:08.160 --> 00:04:10.660 Similarly if you have stronger dipole moments, 00:04:10.660 --> 00:04:13.890 that will also make the ion-dipole forces stronger, 00:04:13.890 --> 00:04:14.890 or vice versa. 00:04:14.890 --> 00:04:17.200 If you had a molecule that had a weaker dipole moment, 00:04:17.200 --> 00:04:21.180 you're not going to have as strong ion-dipole forces. 00:04:21.180 --> 00:04:22.990 Coulomb forces are inversely proportional 00:04:22.990 --> 00:04:24.940 to the distance between the charges. 00:04:24.940 --> 00:04:28.490 So you're also going to have stronger ion-dipole forces 00:04:28.490 --> 00:04:31.730 the closer that these things get to each other. 00:04:31.730 --> 00:04:33.400 But to some degree that's true of a lot 00:04:33.400 --> 00:04:36.060 of the intermolecular forces we've talked about, 00:04:36.060 --> 00:04:38.933 because on some level they are all Coulomb forces.

Dipole–dipole forces

https://www.youtube.com/watch?v=hg7jN32q9A0

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en

WEBVTT Kind: captions Language: en 00:00:00.840 --> 00:00:02.560 - [Instructor] So I have these two molecules here, 00:00:02.560 --> 00:00:06.140 propane on the left and acetaldehyde here on the right. 00:00:06.140 --> 00:00:09.540 And we've already calculated their molar masses for you, 00:00:09.540 --> 00:00:13.370 and you see that they have very close molar masses. 00:00:13.370 --> 00:00:16.710 And so based on what you see in front of you, 00:00:16.710 --> 00:00:18.160 which of these, you think, 00:00:18.160 --> 00:00:20.520 would have a higher boiling point, 00:00:20.520 --> 00:00:22.810 a sample of pure propane 00:00:22.810 --> 00:00:26.210 or a sample of pure acetaldehyde? 00:00:26.210 --> 00:00:28.160 Pause this video, and think about that. 00:00:29.520 --> 00:00:32.080 All right, well, in previous videos, 00:00:32.080 --> 00:00:33.740 when we talked about boiling points 00:00:33.740 --> 00:00:34.930 and why they might be different, 00:00:34.930 --> 00:00:37.530 we talked about intermolecular forces. 00:00:37.530 --> 00:00:40.500 Because you could imagine, if you have a bunch of molecules, 00:00:40.500 --> 00:00:42.780 let's say, in a liquid state, 00:00:42.780 --> 00:00:45.390 the boiling point is going to be dependent 00:00:45.390 --> 00:00:48.630 on how much energy you need to put into the system 00:00:48.630 --> 00:00:53.630 in order for the intermolecular forces between the molecules 00:00:53.660 --> 00:00:57.140 to be overcome so that molecules could break free 00:00:57.140 --> 00:01:00.430 and enter into a gaseous state. 00:01:00.430 --> 00:01:02.380 And so when we're thinking about 00:01:02.380 --> 00:01:04.800 which might have a higher boiling point, 00:01:04.800 --> 00:01:06.310 we really just need to think about 00:01:06.310 --> 00:01:11.160 which one would have higher intermolecular forces. 00:01:11.160 --> 00:01:12.110 Now, in a previous video, 00:01:12.110 --> 00:01:14.580 we talked about London dispersion forces, 00:01:14.580 --> 00:01:18.170 which you can view as random dipoles forming 00:01:18.170 --> 00:01:21.010 in one molecule, and then that can induce dipoles 00:01:21.010 --> 00:01:22.310 in a neighboring molecule. 00:01:22.310 --> 00:01:25.630 And then the positive end, even temporarily positive end, 00:01:25.630 --> 00:01:28.000 of one could be attracted to the temporarily 00:01:28.000 --> 00:01:30.840 negative end of another and vice versa, 00:01:30.840 --> 00:01:34.030 and that whole phenomenon can domino. 00:01:34.030 --> 00:01:35.730 And we said that you're going to have more 00:01:35.730 --> 00:01:37.820 of those London dispersion forces 00:01:37.820 --> 00:01:40.960 the more polarizable your molecule is, 00:01:40.960 --> 00:01:44.260 which is related to how large of an electron cloud it has, 00:01:44.260 --> 00:01:46.430 which is related to its molar mass. 00:01:46.430 --> 00:01:49.440 And when we look at these two molecules, 00:01:49.440 --> 00:01:53.190 they have near identical molar masses. 00:01:53.190 --> 00:01:54.570 So you might expect them 00:01:54.570 --> 00:01:57.220 to have near identical boiling points, 00:01:57.220 --> 00:01:59.660 but it turns out that that is not the case. 00:01:59.660 --> 00:02:02.440 The boiling point of propane 00:02:02.440 --> 00:02:06.440 is negative 42.1 degrees Celsius, 00:02:06.440 --> 00:02:09.150 while the boiling point of acetaldehyde 00:02:09.150 --> 00:02:12.450 is 20.1 degrees Celsius. 00:02:12.450 --> 00:02:15.000 So what makes the difference? 00:02:15.000 --> 00:02:18.350 Why does acetaldehyde have such a higher boiling point? 00:02:18.350 --> 00:02:20.360 Why does it take more energy 00:02:20.360 --> 00:02:24.430 for the molecules in liquid acetaldehyde 00:02:24.430 --> 00:02:26.250 to be able to break free of each other 00:02:26.250 --> 00:02:28.773 to overcome their intermolecular forces? 00:02:29.620 --> 00:02:32.850 Well, the answer, you might imagine, is other things are 00:02:32.850 --> 00:02:36.290 at play on top of the London dispersion forces. 00:02:36.290 --> 00:02:38.810 And what we're going to talk about in this video is 00:02:38.810 --> 00:02:42.360 dipole-dipole forces. 00:02:42.360 --> 00:02:46.100 So you might already imagine where this is going. 00:02:46.100 --> 00:02:48.320 In the video on London dispersion forces, 00:02:48.320 --> 00:02:51.160 we talked about a temporary dipole 00:02:51.160 --> 00:02:53.760 inducing a dipole in a neighboring molecule 00:02:53.760 --> 00:02:56.390 and then them being attracted to each other. 00:02:56.390 --> 00:03:00.540 Now we're going to talk about permanent dipoles. 00:03:00.540 --> 00:03:03.530 So when you look at both of these molecules, 00:03:03.530 --> 00:03:07.440 which one would you think has a stronger permanent dipole? 00:03:07.440 --> 00:03:08.910 Or another way of thinking about it is 00:03:08.910 --> 00:03:12.063 which one has a larger dipole moment? 00:03:12.900 --> 00:03:17.460 Remember, molecular dipole moments are just the vector sum 00:03:17.460 --> 00:03:20.290 of all of the dipole moments of the individual bonds, 00:03:20.290 --> 00:03:23.100 and the dipole moments are all proportional 00:03:23.100 --> 00:03:26.010 to the differences in electronegativity. 00:03:26.010 --> 00:03:28.490 When we look at propane here on the left, 00:03:28.490 --> 00:03:31.720 carbon is a little bit more electronegative than hydrogen 00:03:31.720 --> 00:03:33.680 but not a lot more electronegative. 00:03:33.680 --> 00:03:37.690 So you will have these dipole moments on each of the bonds 00:03:37.690 --> 00:03:40.200 that might look something like this. 00:03:40.200 --> 00:03:42.870 So you would have these things that look like that. 00:03:42.870 --> 00:03:44.790 If that is looking unfamiliar to you, 00:03:44.790 --> 00:03:49.790 I encourage you to review the videos on dipole moments. 00:03:50.170 --> 00:03:53.610 But as you can see, there's a symmetry to propane as well. 00:03:53.610 --> 00:03:57.250 So if you were to take all of these arrows that I'm drawing, 00:03:57.250 --> 00:03:59.240 if you were to take all of these arrows 00:03:59.240 --> 00:04:01.220 that I'm drawing and net them together, 00:04:01.220 --> 00:04:05.090 you're not going to get much of a molecular dipole moment. 00:04:05.090 --> 00:04:06.280 You will get a little bit of one, 00:04:06.280 --> 00:04:08.383 but they, for the most part, cancel out. 00:04:09.270 --> 00:04:11.968 Now what about acetaldehyde? 00:04:11.968 --> 00:04:15.030 Well, acetaldehyde, there's a few giveaways here. 00:04:15.030 --> 00:04:18.640 One is it's an asymmetric molecule. 00:04:18.640 --> 00:04:21.230 So asymmetric molecules are good suspects 00:04:21.230 --> 00:04:24.530 for having a higher dipole moment. 00:04:24.530 --> 00:04:27.940 Another good indicator is you have some character here 00:04:27.940 --> 00:04:29.730 that's quite electronegative. 00:04:29.730 --> 00:04:32.410 In this case, oxygen is quite electronegative. 00:04:32.410 --> 00:04:33.540 And even more important, 00:04:33.540 --> 00:04:36.780 it's a good bit more electronegative than carbon. 00:04:36.780 --> 00:04:40.470 So right over here, this carbon-oxygen double bond, 00:04:40.470 --> 00:04:43.310 you're going to have a pretty significant dipole moment 00:04:43.310 --> 00:04:44.830 just on this double bond. 00:04:44.830 --> 00:04:46.590 It might look like that. 00:04:46.590 --> 00:04:48.950 And all of the other dipole moments 00:04:48.950 --> 00:04:50.800 for all of the other bonds aren't going 00:04:50.800 --> 00:04:53.130 to cancel this large one out. 00:04:53.130 --> 00:04:55.480 In fact, they might add to it a little bit 00:04:55.480 --> 00:04:58.260 because of the molecule's asymmetry. 00:04:58.260 --> 00:05:01.100 And so net-net, your whole molecule 00:05:01.100 --> 00:05:04.380 is going to have a pretty significant dipole moment. 00:05:04.380 --> 00:05:06.160 It'll look something like this, 00:05:06.160 --> 00:05:08.120 and I'm just going to approximate it. 00:05:08.120 --> 00:05:11.190 But we're going to point towards the more negative end, 00:05:11.190 --> 00:05:14.260 so it might look something like this, 00:05:14.260 --> 00:05:16.330 pointing towards the more negative end. 00:05:16.330 --> 00:05:17.920 And I'll put this little cross here 00:05:17.920 --> 00:05:19.200 at the more positive end. 00:05:19.200 --> 00:05:22.230 And so you would expect a partial negative charge 00:05:22.230 --> 00:05:26.550 at that end and a partial positive charge at this end. 00:05:26.550 --> 00:05:28.200 And so what's going to happen 00:05:28.200 --> 00:05:30.350 if it's next to another acetaldehyde? 00:05:30.350 --> 00:05:33.310 Well, the partially negative end of one acetaldehyde 00:05:33.310 --> 00:05:36.440 is going to be attracted to the partially positive end 00:05:36.440 --> 00:05:38.320 of another acetaldehyde. 00:05:38.320 --> 00:05:40.220 And so this is what people are talking about 00:05:40.220 --> 00:05:42.970 when they say dipole-dipole forces. 00:05:42.970 --> 00:05:46.010 We are talking about a permanent dipole 00:05:46.010 --> 00:05:48.980 being attracted to another permanent dipole. 00:05:48.980 --> 00:05:51.570 And so acetaldehyde is experiencing that 00:05:51.570 --> 00:05:54.030 on top of the London dispersion forces, 00:05:54.030 --> 00:05:57.280 which is why it has a higher boiling point. 00:05:57.280 --> 00:05:58.900 Now some of you might be wondering, 00:05:58.900 --> 00:06:01.770 hey, can a permanent dipole 00:06:01.770 --> 00:06:05.010 induce a dipole in a neighboring molecule 00:06:05.010 --> 00:06:07.940 and then those get attracted to each other? 00:06:07.940 --> 00:06:10.950 And the simple answer is yes, it makes a lot of sense. 00:06:10.950 --> 00:06:14.330 You can absolutely have a dipole 00:06:14.330 --> 00:06:15.710 and then induced 00:06:17.837 --> 00:06:20.240 dipole interaction. 00:06:20.240 --> 00:06:23.340 And we might cover that in a few examples in the future, 00:06:23.340 --> 00:06:25.480 but this can also occur. 00:06:25.480 --> 00:06:26.930 You can have a temporary dipole 00:06:26.930 --> 00:06:28.620 inducing a dipole in the neighbor, 00:06:28.620 --> 00:06:30.440 and then they get attracted to each other. 00:06:30.440 --> 00:06:32.410 And you could have a bit of a domino effect. 00:06:32.410 --> 00:06:35.340 You can have a permanent dipole interacting 00:06:35.340 --> 00:06:36.930 with another permanent dipole. 00:06:36.930 --> 00:06:38.820 They get attracted to each other. 00:06:38.820 --> 00:06:42.280 And you could have a permanent dipole inducing a dipole 00:06:42.280 --> 00:06:43.593 in a neighboring molecule.

Guided meditation for procrastination

https://www.youtube.com/watch?v=OoTimXPT8ec

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https://www.youtube.com/api/timedtext?v=OoTimXPT8ec&ei=bViUZazwGZPpxN8Pyu2w6As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7EF0184B99D3C4B2277716372014A339CCF147F1.4B839E2736BE7C35742F157690A9CF5205346E9D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.930 --> 00:00:04.840 - [Instructor] Welcome to the meditation on procrastination 00:00:04.840 --> 00:00:07.730 and somewhat ironically, I've been procrastinating 00:00:07.730 --> 00:00:09.530 making this meditation, 00:00:09.530 --> 00:00:12.463 so we're all in the same boat together. 00:00:13.470 --> 00:00:16.220 So, as with all meditations, 00:00:16.220 --> 00:00:18.390 posture and breathing makes a big difference. 00:00:18.390 --> 00:00:22.460 So, I really encourage you find a nice firm seat to sit on. 00:00:22.460 --> 00:00:23.760 If your legs don't fall asleep, 00:00:23.760 --> 00:00:25.460 you could sit on the ground as well. 00:00:25.460 --> 00:00:29.483 But try to sit with your back upright, really good posture. 00:00:30.420 --> 00:00:33.550 Breathe in, breathe out, 00:00:33.550 --> 00:00:37.123 a little bit slower a little bit deeper every time, 00:00:38.330 --> 00:00:40.580 you could lay your hands on your lap, 00:00:40.580 --> 00:00:42.143 I like to leave them face up, 00:00:43.220 --> 00:00:46.290 and when you're ready, you can soften your gaze 00:00:46.290 --> 00:00:49.853 and slowly close your eyes. 00:00:53.620 --> 00:00:56.343 Breathing in, breathing out. 00:01:00.090 --> 00:01:03.110 Now, procrastination is an interesting thing. 00:01:03.110 --> 00:01:07.410 I'm not sure whether we human beings are the only animals 00:01:07.410 --> 00:01:09.390 we know of that procrastinate, 00:01:09.390 --> 00:01:12.070 it's may be worth some research for somebody 00:01:12.070 --> 00:01:14.713 to figure that out, but we clearly do it. 00:01:16.210 --> 00:01:18.900 And a lot of meditation is about 00:01:18.900 --> 00:01:22.680 becoming aware of our thoughts and observing our thoughts 00:01:22.680 --> 00:01:26.400 and realizing that we are not our thoughts, 00:01:26.400 --> 00:01:29.240 even though many times our thoughts seem to control us 00:01:29.240 --> 00:01:30.873 or even overwhelm us. 00:01:33.670 --> 00:01:38.670 And so let's do that, let's try to observe those thoughts 00:01:39.350 --> 00:01:42.010 that are making us put off something, 00:01:42.010 --> 00:01:43.793 that we know we need to do. 00:01:47.640 --> 00:01:51.033 Why do you think you are putting that thing off? 00:01:53.860 --> 00:01:55.530 I'll tell you what happens to be usually 00:01:55.530 --> 00:01:58.360 from my experience, it usually is 00:01:58.360 --> 00:02:01.820 I'm afraid to start because I might realize 00:02:01.820 --> 00:02:04.140 it's harder than I expected 00:02:05.180 --> 00:02:08.380 or I might not do as well as I expected 00:02:09.580 --> 00:02:12.750 or I might make a mistake, 00:02:12.750 --> 00:02:15.713 maybe I don't think I'm prepared enough to start. 00:02:17.360 --> 00:02:20.170 Another way to think about it is we're getting too caught up 00:02:20.170 --> 00:02:24.370 in the outcome versus enjoying the journey 00:02:24.370 --> 00:02:27.040 or enjoying whatever the thing is that you're putting off, 00:02:27.040 --> 00:02:29.853 'cause that's just a part of this fun experience. 00:02:31.940 --> 00:02:34.893 And so I find that when I tell myself, 00:02:36.039 --> 00:02:40.763 define yourself by the action not the outcome, 00:02:41.990 --> 00:02:45.783 don't define yourself by whether you succeed or fail, 00:02:46.730 --> 00:02:51.710 define yourself as making the effort, 00:02:51.710 --> 00:02:56.710 showing up and enjoying it, laughing at yourself, 00:02:57.120 --> 00:03:00.530 laughing at this mystery that we call life 00:03:00.530 --> 00:03:03.750 and just putting one foot in front of the other 00:03:03.750 --> 00:03:06.530 and realizing it's not so bad, 00:03:06.530 --> 00:03:08.560 and then you can put the other foot in front of that one 00:03:08.560 --> 00:03:09.713 and keep going. 00:03:12.290 --> 00:03:14.440 And slowly but surely you realize 00:03:14.440 --> 00:03:17.320 that you're making a lot of progress. 00:03:17.320 --> 00:03:20.010 And the more you make that progress, 00:03:20.010 --> 00:03:22.210 the more that you actually enjoy it, 00:03:22.210 --> 00:03:25.130 especially if you're not going it the last minute. 00:03:25.130 --> 00:03:27.310 And I will give you about a minute 00:03:27.310 --> 00:03:31.380 for you to repeat something in your mind 00:03:31.380 --> 00:03:35.250 that can hopefully short-circuit any of those thoughts 00:03:35.250 --> 00:03:37.550 that have been keeping you from taking action. 00:03:39.200 --> 00:03:42.360 For the next minute or so repeat to yourself 00:03:43.230 --> 00:03:45.903 that you really enjoy taking action, 00:03:47.090 --> 00:03:48.640 you're lucky that you're in a position 00:03:48.640 --> 00:03:51.103 to be able to take action. 00:03:53.020 --> 00:03:56.023 The outcome, it is what it is. 00:03:57.900 --> 00:04:02.853 You enjoy action, you are lucky to be able to take action, 00:04:04.480 --> 00:04:07.773 the outcome is what it is. 00:04:09.510 --> 00:04:11.730 Keep thinking that for the next minute or so 00:04:11.730 --> 00:04:14.093 and I'll be back, don't worry. 00:05:17.430 --> 00:05:22.430 All right, so when you're ready, really at your own time, 00:05:24.990 --> 00:05:28.600 just become a little bit more aware of your surroundings, 00:05:28.600 --> 00:05:30.450 a little bit more aware of your body, 00:05:31.980 --> 00:05:34.093 a little bit more aware of your every breath, 00:05:35.780 --> 00:05:38.723 and slowly open your eyes. 00:05:40.690 --> 00:05:42.873 And so, I'll finished with one last tip: 00:05:44.050 --> 00:05:45.730 sometimes we put something off 00:05:45.730 --> 00:05:49.433 because it just feels big or overwhelming. 00:05:50.740 --> 00:05:52.320 What I like to do is say, 00:05:52.320 --> 00:05:56.910 Hey, let me just put 20 minutes towards it 00:05:56.910 --> 00:06:00.010 and see where I am at the end of 20 minutes. 00:06:00.010 --> 00:06:03.280 If I didn't make any progress, no big deal, 00:06:03.280 --> 00:06:04.653 it was just 20 minutes, 00:06:05.490 --> 00:06:07.900 but if I did make some progress, great! 00:06:07.900 --> 00:06:10.523 I did the 20 minutes, I deserve a break. 00:06:11.370 --> 00:06:13.130 If after a five or 10 minute break 00:06:13.130 --> 00:06:16.150 I'm ready to put another 20 minutes, awesome. 00:06:16.150 --> 00:06:18.670 If at the end of the 20 minutes I wanna keep going, 00:06:18.670 --> 00:06:21.373 I shouldn't stop myself, I should keep going. 00:06:22.390 --> 00:06:24.430 For when you view things as, hey, 00:06:24.430 --> 00:06:27.530 I'm just committing 20 minutes to something, 00:06:27.530 --> 00:06:29.443 it doesn't feel as intimidating. 00:06:30.470 --> 00:06:31.770 You just own it, you say, 00:06:31.770 --> 00:06:34.570 Hey, I can do anything for 20 minutes, 00:06:34.570 --> 00:06:38.250 and I can enjoy anything for 20 minutes 00:06:38.250 --> 00:06:40.980 and then you'll wanna do it, put a smile on your face 00:06:40.980 --> 00:06:43.063 and own that action. 00:06:44.150 --> 00:06:45.730 And not only will you make progress, 00:06:45.730 --> 00:06:47.940 but you're gonna have a good time. 00:06:47.940 --> 00:06:52.940 And so take it with that playful mindset, enjoy it, smile 00:06:53.460 --> 00:06:54.853 and just get started. 00:06:55.750 --> 00:06:57.160 And I think you'll find 00:06:57.160 --> 00:06:59.353 you'll be procrastinating a lot less.

Guided meditation visualizing thoughts as the surface of an ocean

https://www.youtube.com/watch?v=J1V5Txop1kw

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https://www.youtube.com/api/timedtext?v=J1V5Txop1kw&ei=bViUZdXgHtiKp-oPiJyo0A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=17BDEB3B49CCA9FD2B2D4900733CD582344013B6.E2EEA6139224942D6A7DAEC25B718E8DAA5FF09D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.330 --> 00:00:02.940 - [Instructor] Welcome and thanks for taking out the time 00:00:02.940 --> 00:00:04.060 for yourself 00:00:04.060 --> 00:00:08.530 for what will hopefully be a nice inward journey. 00:00:08.530 --> 00:00:12.240 So just start off sitting upright 00:00:12.240 --> 00:00:14.080 feet planted on the ground 00:00:14.080 --> 00:00:17.730 if you're ideally on some type of a firm chair 00:00:17.730 --> 00:00:21.030 and start to soften your gaze. 00:00:21.030 --> 00:00:25.200 If your eyes are still open, gently close them. 00:00:25.200 --> 00:00:30.200 I like to leave my hands on my lap, palms up to the sky 00:00:31.130 --> 00:00:33.370 but whatever feels comfortable for you 00:00:34.890 --> 00:00:36.940 and then with your eyes closed, 00:00:36.940 --> 00:00:40.343 gently become a little bit more aware of your breaths. 00:00:41.460 --> 00:00:45.233 Make them a little bit deeper and a little bit slower. 00:00:47.030 --> 00:00:50.083 At your own time, breathe in. 00:00:52.850 --> 00:00:54.920 Breathe out. 00:00:54.920 --> 00:00:58.793 Just a little bit deeper and a little bit slower. 00:01:01.810 --> 00:01:05.060 So the whole idea behind meditation 00:01:05.060 --> 00:01:10.060 is trying to ease all the chatter that exists in our brains, 00:01:10.510 --> 00:01:12.780 trying to still our thoughts 00:01:13.730 --> 00:01:16.490 and so as we do that and every meditation 00:01:16.490 --> 00:01:19.270 I'm going to try to introduce some frameworks, 00:01:19.270 --> 00:01:21.950 ways of thinking about your mind 00:01:21.950 --> 00:01:25.220 but as you try to quiet the mind, 00:01:25.220 --> 00:01:28.070 it will inevitably get distracted. 00:01:28.070 --> 00:01:31.590 It might get distracted by some noise in the room 00:01:31.590 --> 00:01:35.330 or some noise outside or more likely, 00:01:35.330 --> 00:01:37.570 it'll get distracted by thoughts 00:01:37.570 --> 00:01:40.400 that are just surfacing into your consciousness 00:01:40.400 --> 00:01:43.730 and if that happens, don't let it make you anxious. 00:01:43.730 --> 00:01:45.640 A lot of folks when they meditate, 00:01:45.640 --> 00:01:47.270 they worry that they're doing it wrong 00:01:47.270 --> 00:01:48.720 and then if they get distracted, 00:01:48.720 --> 00:01:50.580 it actually makes things worse. 00:01:50.580 --> 00:01:52.590 They say I'm never going to be able 00:01:52.590 --> 00:01:54.890 to do this meditation thing. 00:01:54.890 --> 00:01:57.610 The important thing is to approach the meditation 00:01:57.610 --> 00:02:00.940 with a spirit of fun, a spirit of curiosity, 00:02:00.940 --> 00:02:02.440 have a sense of humor about it. 00:02:02.440 --> 00:02:06.280 We are all literally human and we do very human things 00:02:06.280 --> 00:02:09.190 and so when you find your mind wandering a bit, 00:02:09.190 --> 00:02:12.150 just laugh it off and say, oh, there you go, mind. 00:02:12.150 --> 00:02:13.920 Just come back to the stillness. 00:02:13.920 --> 00:02:17.070 Not a big deal, don't beat up on yourself over it 00:02:17.070 --> 00:02:19.420 and as part of that as we go through this meditation, 00:02:19.420 --> 00:02:20.910 as much as possible, 00:02:20.910 --> 00:02:24.810 try to keep a little bit of a smile on your face. 00:02:24.810 --> 00:02:27.450 Your eyes are closed but you can still smile a little bit 00:02:27.450 --> 00:02:29.760 or at least smile with your mind. 00:02:29.760 --> 00:02:34.363 Reminds you that this should be fun, this is relaxing. 00:02:36.230 --> 00:02:40.790 So with that said, let's keep breathing in, breathing out 00:02:41.660 --> 00:02:44.180 a little bit deeper, a little bit slower 00:02:48.760 --> 00:02:51.150 and the framework that I'm going to introduce 00:02:51.150 --> 00:02:54.960 for how you can still your mind is one that I use a lot 00:02:54.960 --> 00:02:59.060 which is imagining all the thoughts in your subconscious 00:02:59.060 --> 00:03:04.060 as the ocean and the surface of the ocean is the interface 00:03:04.140 --> 00:03:08.070 between your subconscious and your consciousness 00:03:08.070 --> 00:03:11.480 and most of us have a pretty choppy surface. 00:03:11.480 --> 00:03:14.360 There's a lot of thoughts that are jumping up and down 00:03:14.360 --> 00:03:15.900 out of our subconscious 00:03:15.900 --> 00:03:18.990 and sometimes we're drowning in those thoughts 00:03:19.990 --> 00:03:24.640 and one way to think about it is we can elevate ourselves. 00:03:24.640 --> 00:03:29.640 We can elevate ourselves above the surface of that water 00:03:29.660 --> 00:03:32.110 and when you start to elevate yourself, 00:03:32.110 --> 00:03:34.970 you're not suppressing the thoughts 00:03:34.970 --> 00:03:37.620 but you're just looking down on them. 00:03:37.620 --> 00:03:39.200 You see that they're still there, 00:03:39.200 --> 00:03:42.520 the surface is still choppy, there's still waves 00:03:42.520 --> 00:03:44.860 but as you rise and you look down on it, 00:03:44.860 --> 00:03:47.420 you realize that you are not those thoughts, 00:03:47.420 --> 00:03:50.330 you are not the surface of the water. 00:03:50.330 --> 00:03:52.780 So whether the thing that's bothering you 00:03:52.780 --> 00:03:54.560 is an assignment you have to do 00:03:54.560 --> 00:03:58.140 or some interpersonal relations 00:03:58.140 --> 00:03:59.570 or just something in your life 00:03:59.570 --> 00:04:02.570 not working out the way that you would like it to, 00:04:02.570 --> 00:04:04.870 remind yourself that that is not you. 00:04:04.870 --> 00:04:08.330 You are not defined by the outcome of that situation. 00:04:08.330 --> 00:04:11.140 Those are just waves on that ocean 00:04:14.690 --> 00:04:16.730 and the more that you surface above them 00:04:16.730 --> 00:04:20.580 and you look at them and analyze them, 00:04:20.580 --> 00:04:23.080 you realize that they have no control over you 00:04:23.930 --> 00:04:28.180 and once that happens, things start to slow down. 00:04:28.180 --> 00:04:31.450 The surface of that water begins to get calmer 00:04:31.450 --> 00:04:33.440 and calmer and calmer 00:04:35.080 --> 00:04:38.800 and there you are floating above that surface. 00:04:38.800 --> 00:04:40.680 Just pure awareness 00:04:41.900 --> 00:04:44.540 and you realize that you're a lot more 00:04:44.540 --> 00:04:45.883 than you thought you were. 00:04:46.900 --> 00:04:50.063 You aren't just your physical body. 00:04:50.910 --> 00:04:53.400 You aren't just those thoughts 00:04:53.400 --> 00:04:56.423 that you see as waves on the surface of that ocean. 00:04:57.870 --> 00:05:00.460 You aren't even just that identity 00:05:00.460 --> 00:05:02.510 that you associate yourself with, 00:05:02.510 --> 00:05:05.530 your name, your position in the world, your status, 00:05:05.530 --> 00:05:07.743 what people think of you, your relations. 00:05:08.970 --> 00:05:12.053 Those are aspects of you but they aren't you. 00:05:13.150 --> 00:05:16.523 You are something much bigger than all of them. 00:05:17.370 --> 00:05:22.160 You are the space in which they occur, in which they happen 00:05:22.160 --> 00:05:23.680 but they aren't you 00:05:24.530 --> 00:05:27.800 and now let's just try to sit in that pure awareness 00:05:27.800 --> 00:05:29.530 for the next minute or so and once again, 00:05:29.530 --> 00:05:31.940 if your thoughts wander, not a big deal. 00:05:31.940 --> 00:05:34.410 That's just the choppiness on the surface of that water 00:05:34.410 --> 00:05:38.010 and you need to elevate yourself back to that pure awareness 00:05:38.010 --> 00:05:40.370 and if the quiet bothers you, don't worry, 00:05:40.370 --> 00:05:42.963 I will be back in about a minute. 00:06:42.830 --> 00:06:47.040 All right, so that was a relatively short amount of time 00:06:47.040 --> 00:06:49.870 for you to be on your own and as you'll see 00:06:49.870 --> 00:06:53.340 as we do more and more advanced meditations, 00:06:53.340 --> 00:06:55.710 give yourself more and more time 00:06:55.710 --> 00:06:58.510 and over time, you won't need me talking. 00:06:58.510 --> 00:07:00.620 In fact, that will probably annoy you. 00:07:00.620 --> 00:07:04.210 You'll just be able to sit down and still your mind 00:07:04.210 --> 00:07:06.890 and realize that you are not your thoughts 00:07:06.890 --> 00:07:08.880 and these things that are bothering you, 00:07:08.880 --> 00:07:10.290 they're only going to bother you 00:07:10.290 --> 00:07:12.223 as much as you let them bother you. 00:07:13.237 --> 00:07:17.600 In the whole scheme of things, in all of time and space, 00:07:17.600 --> 00:07:21.480 none of them are really what should define you 00:07:21.480 --> 00:07:23.890 or are anywhere near as important 00:07:23.890 --> 00:07:26.840 as we sometimes make them out to be. 00:07:26.840 --> 00:07:28.640 I'll see you in the next meditation.

Guided meditation for high school students

https://www.youtube.com/watch?v=qZYxc6VcRGA

vtt

https://www.youtube.com/api/timedtext?v=qZYxc6VcRGA&ei=bViUZfG8Fp_evdIPnZGiwAs&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=CA0F7F67F359B54422327518BB02967A8AD95FE9.50CB09E66B3C8AC9C069882873F4D12A4A78853D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.600 --> 00:00:03.700 - [Instructor] Welcome, and thanks for joining me on this, 00:00:03.700 --> 00:00:06.750 let's call it a voyage of the mind. 00:00:06.750 --> 00:00:10.970 So before we begin, posture and breathing 00:00:10.970 --> 00:00:13.960 make a big difference in meditation. 00:00:13.960 --> 00:00:17.860 So if you're not already on a nice firm chair 00:00:17.860 --> 00:00:21.220 with your back straight, pause this recording 00:00:21.220 --> 00:00:24.500 and go find a nice firm chair with your back straight, 00:00:24.500 --> 00:00:28.313 ideally in a place that's kind of quiet and peaceful. 00:00:29.750 --> 00:00:33.870 So now that you're there, sit with your back straight, 00:00:33.870 --> 00:00:37.000 try to put your feet firmly on the floor. 00:00:37.000 --> 00:00:40.520 When I do this, I like to rest my hands on my lap, 00:00:40.520 --> 00:00:43.513 palms up gently curled, so really no effort. 00:00:44.790 --> 00:00:49.400 And now start to slowly breathe a bit deeper 00:00:49.400 --> 00:00:52.263 than you were just now and a bit slower. 00:00:53.420 --> 00:00:58.420 In and out, at your own time but just a little bit deeper, 00:00:58.720 --> 00:01:00.143 a little bit slower. 00:01:01.240 --> 00:01:03.870 If you like, a lot of folks like to breathe 00:01:03.870 --> 00:01:06.190 in through their nose, 00:01:06.190 --> 00:01:08.060 out through their mouth, 00:01:08.060 --> 00:01:12.090 but the key, once again, a little bit deeper, 00:01:12.090 --> 00:01:13.353 a little bit slower. 00:01:14.930 --> 00:01:18.770 And as you do so, start to soften your gaze 00:01:18.770 --> 00:01:21.180 if your eyes are still open, 00:01:21.180 --> 00:01:26.163 and when you feel comfortable, gently close your eyes. 00:01:29.210 --> 00:01:32.510 Now, before we get into the heart of the meditation, 00:01:32.510 --> 00:01:35.030 I'm going to give you a few reminders. 00:01:35.030 --> 00:01:40.030 This whole exercise is about exploring your inner being. 00:01:41.120 --> 00:01:42.580 It's about curiosity. 00:01:42.580 --> 00:01:44.500 It's about relaxation. 00:01:44.500 --> 00:01:47.180 There's no perfect way to meditate. 00:01:47.180 --> 00:01:50.010 Sometimes folks think that they're not doing it right 00:01:50.010 --> 00:01:52.120 or their mind is wandering too much. 00:01:52.120 --> 00:01:53.580 And then it causes stress. 00:01:53.580 --> 00:01:55.130 And that's the exact opposite 00:01:55.130 --> 00:01:57.350 of what you want meditation to be. 00:01:57.350 --> 00:02:00.460 It should be fun, it could even be funny at moments. 00:02:00.460 --> 00:02:01.970 You should be curious. 00:02:01.970 --> 00:02:03.883 You should be enjoying it. 00:02:04.830 --> 00:02:07.040 If there are some random distractions, 00:02:07.040 --> 00:02:08.600 and there inevitably will be, 00:02:08.600 --> 00:02:10.720 it could be sounds around you, 00:02:10.720 --> 00:02:15.210 it might be part of your body that itches or tingles. 00:02:15.210 --> 00:02:18.580 Don't let it stress you out, just accept it. 00:02:18.580 --> 00:02:20.670 It's part of the universe. 00:02:20.670 --> 00:02:23.120 It's just atoms doing what they do. 00:02:23.120 --> 00:02:25.840 It's the universe doing its thing. 00:02:25.840 --> 00:02:28.390 And no worries if you need to scratch 00:02:28.390 --> 00:02:32.403 or adjust part of your body, no reason to stress. 00:02:33.900 --> 00:02:36.080 Now to add to the idea 00:02:36.080 --> 00:02:38.220 that this shouldn't be a stressful experience, 00:02:38.220 --> 00:02:39.750 I'm going to ask you to do something 00:02:39.750 --> 00:02:43.420 that may or may not feel completely natural. 00:02:43.420 --> 00:02:45.080 I want you to smile right now. 00:02:45.080 --> 00:02:46.580 Give yourself a good smile 00:02:46.580 --> 00:02:49.430 with your eyes closed, just smile. 00:02:49.430 --> 00:02:51.160 Obviously, we smile when we're happy. 00:02:51.160 --> 00:02:53.350 But sometimes, making a smile 00:02:53.350 --> 00:02:55.430 can actually make us a little bit happier. 00:02:55.430 --> 00:02:57.870 It can make us a little bit less stressed. 00:02:57.870 --> 00:03:00.550 So even if you need to force it, smile. 00:03:00.550 --> 00:03:03.410 And as much as possible, as we go through this meditation, 00:03:03.410 --> 00:03:05.440 as long as you don't have to force it too much, 00:03:05.440 --> 00:03:08.303 try to keep a gentle smile on your face the whole time. 00:03:10.820 --> 00:03:13.133 All right, now let's get into it. 00:03:14.110 --> 00:03:16.790 So, one thing to keep in mind 00:03:16.790 --> 00:03:19.950 as we start trying to still our minds, 00:03:19.950 --> 00:03:23.730 is to just appreciate that you're alive. 00:03:23.730 --> 00:03:27.640 You're in this vast mystery we call life 00:03:27.640 --> 00:03:28.990 and that you're taking pause 00:03:28.990 --> 00:03:31.550 to appreciate who you really are. 00:03:31.550 --> 00:03:32.980 And the beauty of this mystery, 00:03:32.980 --> 00:03:36.670 this existence, this universe that we share. 00:03:36.670 --> 00:03:41.670 So as you breathe deeper and slower, your eyes are closed. 00:03:43.590 --> 00:03:46.250 Try to become aware of your thoughts. 00:03:46.250 --> 00:03:47.650 What are you thinking about? 00:03:49.870 --> 00:03:53.660 Are they random thoughts, something you saw on TV? 00:03:53.660 --> 00:03:55.563 Is it something going on at school? 00:03:56.840 --> 00:04:01.150 Are you thinking about some tests you might have coming up? 00:04:01.150 --> 00:04:05.550 Or someone at your school, you tend to think about a lot? 00:04:05.550 --> 00:04:06.820 Just observe your thoughts. 00:04:06.820 --> 00:04:09.223 Don't try to fight them, just observe them. 00:04:12.350 --> 00:04:14.680 And as you observe your thoughts, 00:04:14.680 --> 00:04:19.250 start to appreciate that you are not your thoughts. 00:04:19.250 --> 00:04:22.600 You are something different than your thoughts. 00:04:22.600 --> 00:04:25.320 They're all in there in your head with you. 00:04:25.320 --> 00:04:26.950 But clearly, you can observe them. 00:04:26.950 --> 00:04:29.560 You can see them go by. 00:04:29.560 --> 00:04:32.200 Sometimes we can get lost in them. 00:04:32.200 --> 00:04:33.350 But I think you're seeing right now 00:04:33.350 --> 00:04:34.630 that you are not your thoughts, 00:04:34.630 --> 00:04:36.843 you can actually observe your thoughts. 00:04:39.660 --> 00:04:42.480 One metaphor that folks sometimes use 00:04:42.480 --> 00:04:44.560 is that your thoughts are cars on a road 00:04:44.560 --> 00:04:46.080 or cars on a highway. 00:04:46.080 --> 00:04:48.160 And oftentimes, we're in the middle of the highway 00:04:48.160 --> 00:04:50.600 and those cars are bombarding us. 00:04:50.600 --> 00:04:52.820 They're hitting us, or we have to dodge them in some way 00:04:52.820 --> 00:04:54.240 or they're overwhelming us. 00:04:54.240 --> 00:04:55.900 And one thing to do to observe them 00:04:55.900 --> 00:04:57.670 is just get out of the highway. 00:04:57.670 --> 00:04:58.960 You don't have to fight the thoughts, 00:04:58.960 --> 00:05:01.290 those cars will keep on going by. 00:05:01.290 --> 00:05:03.170 But now that you're on the median, 00:05:03.170 --> 00:05:06.333 you're no longer on the highway, you can see them go by. 00:05:07.700 --> 00:05:09.240 And what you'll often find is 00:05:09.240 --> 00:05:11.210 when you're observing your thoughts, 00:05:11.210 --> 00:05:12.853 they start to slow down. 00:05:14.560 --> 00:05:17.080 And so if your thoughts start to slow down, great, 00:05:17.080 --> 00:05:19.850 really embrace that, start to realize what that feels like 00:05:19.850 --> 00:05:21.910 when your thoughts slow down. 00:05:21.910 --> 00:05:23.910 And then there's even going to be moments 00:05:23.910 --> 00:05:25.653 when you have no thoughts. 00:05:26.730 --> 00:05:29.280 For the next few breaths, try that. 00:05:29.280 --> 00:05:31.600 Try to have no thoughts. 00:05:31.600 --> 00:05:34.173 Just breathe in, breathe out. 00:05:35.320 --> 00:05:36.860 No thoughts. 00:05:36.860 --> 00:05:38.650 Just stillness. 00:05:38.650 --> 00:05:42.020 Just your consciousness here in this universe. 00:05:42.020 --> 00:05:46.990 No time, no space, it's all in your mind. 00:05:46.990 --> 00:05:49.263 No thoughts, stillness. 00:05:56.870 --> 00:05:59.060 Now as you try to keep that state, 00:05:59.060 --> 00:06:01.760 your mind will inevitably wander. 00:06:01.760 --> 00:06:03.940 You're going to start thinking about an assignment 00:06:03.940 --> 00:06:05.750 that you have due soon, 00:06:05.750 --> 00:06:07.750 you're going to think about something 00:06:07.750 --> 00:06:09.200 that you have to do this weekend 00:06:09.200 --> 00:06:14.200 or someone that you think a lot about, that's okay. 00:06:14.860 --> 00:06:17.210 Don't beat yourself up, if your mind wanders, 00:06:17.210 --> 00:06:19.910 just remind yourself, just gently nudge it back. 00:06:19.910 --> 00:06:21.340 Try to get back to the stillness. 00:06:21.340 --> 00:06:23.830 Say, oh, look, I got a little bit distracted, 00:06:23.830 --> 00:06:25.550 I started thinking about something. 00:06:25.550 --> 00:06:26.640 That's funny. 00:06:26.640 --> 00:06:29.580 I'm going to get my mind back to the stillness. 00:06:29.580 --> 00:06:31.630 I'm going to try to slow down those cars. 00:06:35.450 --> 00:06:38.730 And so gently breathe in and breathe out. 00:06:38.730 --> 00:06:40.270 And I'm going to give you a few minutes 00:06:40.270 --> 00:06:42.980 to just sit there, still. 00:06:42.980 --> 00:06:46.120 Breathing in, breathing out. 00:06:46.120 --> 00:06:48.280 Being still with your thoughts. 00:06:48.280 --> 00:06:51.140 If your mind wanders, no big deal. 00:06:51.140 --> 00:06:53.510 Just try to nudge it back when you can. 00:06:53.510 --> 00:06:55.610 And if the silence starts to get to you a little bit, 00:06:55.610 --> 00:06:59.860 don't worry, I will be back for sure in a few minutes. 00:08:06.840 --> 00:08:09.030 Now that you've had a little bit of time on your own, 00:08:09.030 --> 00:08:10.880 I'm going to give you some ideas 00:08:10.880 --> 00:08:14.323 that just might help appreciate who you really are. 00:08:15.650 --> 00:08:18.580 A lot of times we get caught up in the day to day, 00:08:18.580 --> 00:08:20.740 we start worrying about test scores 00:08:20.740 --> 00:08:24.493 or things we have due or what people think about us. 00:08:25.400 --> 00:08:28.053 But remind yourself that you are not that. 00:08:29.340 --> 00:08:32.650 You are not defined by your test scores. 00:08:32.650 --> 00:08:35.063 You are not defined by your grades. 00:08:36.440 --> 00:08:39.603 And you are not defined by what people think of you. 00:08:42.080 --> 00:08:43.923 You are pure consciousness. 00:08:45.610 --> 00:08:49.563 You associate yourself with your body with your thoughts. 00:08:50.790 --> 00:08:54.293 But they're part of you, they aren't you. 00:08:55.490 --> 00:08:59.053 You're something deeper and you're something far larger. 00:09:01.330 --> 00:09:05.210 Like the whole universe, if you really think about it, 00:09:05.210 --> 00:09:06.860 it's a construction of your mind. 00:09:07.840 --> 00:09:11.193 Your mind has set up the simulation for you to enjoy. 00:09:12.080 --> 00:09:15.410 In theory, there's a universe out there, 00:09:15.410 --> 00:09:18.590 sound waves stimulating your ear. 00:09:18.590 --> 00:09:21.610 Photons stimulate your eye, 00:09:21.610 --> 00:09:23.843 air particles bouncing into your skin. 00:09:25.650 --> 00:09:26.963 But from that input, 00:09:28.120 --> 00:09:30.893 your mind creates the reality that you're in. 00:09:32.120 --> 00:09:33.870 When you realize that, 00:09:33.870 --> 00:09:36.883 that everything you see is a construct. 00:09:37.890 --> 00:09:40.740 It's a construct of your mind 00:09:40.740 --> 00:09:42.853 to make sense of all of that information. 00:09:44.170 --> 00:09:47.130 You realize that you're a lot more central 00:09:47.130 --> 00:09:49.453 than you might have appreciated before. 00:09:50.330 --> 00:09:52.600 And you also realize 00:09:52.600 --> 00:09:55.560 that the things that you might have been thinking about 00:09:55.560 --> 00:09:57.710 things at school, what people think of you, 00:09:57.710 --> 00:10:00.950 your test scores, those are nice, 00:10:00.950 --> 00:10:03.020 you should try to do what you can. 00:10:03.020 --> 00:10:05.500 But they don't define who you are. 00:10:05.500 --> 00:10:07.453 They don't define your reality. 00:10:08.690 --> 00:10:10.963 Think about how vast the universe is, 00:10:11.810 --> 00:10:14.723 not just vast in space, but vast in time. 00:10:15.860 --> 00:10:18.820 Let put some of our problems in perspective. 00:10:18.820 --> 00:10:23.020 100 years from now, 1,000 years from now, 00:10:23.020 --> 00:10:25.513 will these problems really be that significant? 00:10:27.300 --> 00:10:32.190 When you think about where you are, on this planet, 00:10:32.190 --> 00:10:33.683 part of the cosmos, 00:10:34.770 --> 00:10:37.283 are these issues really that significant? 00:10:38.900 --> 00:10:40.450 So I'll give you a few more moments 00:10:40.450 --> 00:10:42.180 to just think about those ideas, 00:10:42.180 --> 00:10:45.160 to just think about the vastness of the universe 00:10:45.160 --> 00:10:48.180 and what a privilege it is to be able to participate in it, 00:10:48.180 --> 00:10:49.890 to see the beauty of it. 00:10:49.890 --> 00:10:51.710 And how small some of the things 00:10:51.710 --> 00:10:55.173 that we often define ourselves by really are. 00:10:58.240 --> 00:11:00.110 And so now when you get a chance 00:11:01.830 --> 00:11:03.530 gently with your eyes closed, 00:11:03.530 --> 00:11:07.110 start to feel and hear the room around you a little bit, 00:11:07.110 --> 00:11:09.410 get a little bit more in touch with your body. 00:11:10.810 --> 00:11:13.123 And when you're ready, open your eyes. 00:11:15.960 --> 00:11:17.250 And take these ideas, 00:11:17.250 --> 00:11:20.150 take that stillness with you through the rest of your day. 00:11:21.680 --> 00:11:23.630 And you should thank yourself 00:11:23.630 --> 00:11:26.760 for taking the time out for doing this today. 00:11:26.760 --> 00:11:29.240 And I encourage you to make it a practice. 00:11:29.240 --> 00:11:30.940 Some of you might be skeptical, 00:11:30.940 --> 00:11:33.523 what would a few minute meditation do for me? 00:11:34.550 --> 00:11:37.060 But I can guarantee you if you do it day in day out, 00:11:37.060 --> 00:11:40.253 if you make a practice of it, do it regularly. 00:11:41.180 --> 00:11:43.260 Over a few weeks, a few months, 00:11:43.260 --> 00:11:45.580 you're going to notice some changes. 00:11:45.580 --> 00:11:48.640 You're going to see yourself be more open to experience, 00:11:48.640 --> 00:11:52.180 you're going to see more beauty in more things. 00:11:52.180 --> 00:11:54.410 You're going to just have a positive energy 00:11:54.410 --> 00:11:57.090 that people are going to want to connect with, 00:11:57.090 --> 00:11:59.590 that people are going to be drawn to. 00:11:59.590 --> 00:12:02.150 And you'll also see that you're doing better 00:12:02.150 --> 00:12:04.240 at some of those things we talked about before, 00:12:04.240 --> 00:12:06.010 because you're not stressed about them anymore. 00:12:06.010 --> 00:12:07.410 You're enjoying them. 00:12:07.410 --> 00:12:09.500 You're doing what you can, 00:12:09.500 --> 00:12:13.360 but you're not attached to the outcome. 00:12:13.360 --> 00:12:17.573 You do your best, wherever the chips fall, that's okay. 00:12:18.710 --> 00:12:21.780 If things don't turn out the way you want it, that's okay. 00:12:21.780 --> 00:12:23.803 You just accept where things are. 00:12:24.770 --> 00:12:28.210 And then you decide what other actions can you take. 00:12:28.210 --> 00:12:30.670 Assemble your actions piece by piece, 00:12:30.670 --> 00:12:33.010 so that you can get to another outcome. 00:12:33.010 --> 00:12:36.090 But once again, if the outcome is what you want, awesome, 00:12:36.090 --> 00:12:39.323 if it isn't, accept it and move on from there. 00:12:40.830 --> 00:12:42.920 So I'll leave you in this meditation. 00:12:42.920 --> 00:12:44.580 Thank you for joining. 00:12:44.580 --> 00:12:47.883 And once again, thanks for taking time out for yourself.

The development of an American culture

https://www.youtube.com/watch?v=-zr1NBxTgG8

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WEBVTT Kind: captions Language: en 00:00:00.450 --> 00:00:02.530 - [Instructor] In this video I'm gonna take some time 00:00:02.530 --> 00:00:05.860 to talk about the culture of the young United States 00:00:05.860 --> 00:00:08.740 that developed in the early 19th century. 00:00:08.740 --> 00:00:10.270 At the beginning of this period, 00:00:10.270 --> 00:00:13.550 most of the dominant artistic and cultural productions 00:00:13.550 --> 00:00:16.670 in the United States, the paintings, architecture, 00:00:16.670 --> 00:00:19.110 literature, and even philosophy, 00:00:19.110 --> 00:00:21.709 were either borrowed from or imitations 00:00:21.709 --> 00:00:24.890 of what was being produced in Europe. 00:00:24.890 --> 00:00:27.080 The United States itself was born 00:00:27.080 --> 00:00:29.730 in the midst of an intellectual movement 00:00:29.730 --> 00:00:33.180 that crossed the Atlantic from Europe, the Enlightenment. 00:00:33.180 --> 00:00:35.570 And if you read the Declaration of Independence, 00:00:35.570 --> 00:00:38.467 you can hear the echoes of the Enlightenment: 00:00:38.467 --> 00:00:41.477 "We hold these truths to be self-evident, 00:00:41.477 --> 00:00:43.067 "that all men are created equal, 00:00:43.067 --> 00:00:45.087 "that they are endowed by their Creator 00:00:45.087 --> 00:00:47.037 "with certain unalienable Rights, 00:00:47.037 --> 00:00:49.127 "that among these are Life, Liberty, 00:00:49.127 --> 00:00:50.767 "and the pursuit of Happiness. 00:00:50.767 --> 00:00:52.327 "That to secure these rights, 00:00:52.327 --> 00:00:54.487 "Governments are instituted among Men, 00:00:54.487 --> 00:00:56.847 "deriving their just powers from the consent 00:00:56.847 --> 00:00:57.700 "of the governed..." 00:00:57.700 --> 00:00:59.910 Jefferson looks at the evidence, 00:00:59.910 --> 00:01:02.710 the rational reasons for self-government. 00:01:02.710 --> 00:01:05.443 Now contrast that with a piece of writing 00:01:05.443 --> 00:01:08.870 from an American at the end of this period. 00:01:08.870 --> 00:01:12.280 Here's the last stanza from Edgar Allan Poe's 00:01:12.280 --> 00:01:16.787 poem The Raven, first published in 1845: 00:01:16.787 --> 00:01:19.097 "...And the Raven, never flitting, 00:01:19.097 --> 00:01:21.882 "still is sitting, still is sitting 00:01:21.882 --> 00:01:26.287 "On the pallid bust of Pallas just above my chamber door; 00:01:26.287 --> 00:01:29.467 "And his eyes have all the seeming of a demon's 00:01:29.467 --> 00:01:30.417 "that is dreaming. 00:01:30.417 --> 00:01:32.827 "And the lamp-light o'er him streaming 00:01:32.827 --> 00:01:34.827 "throws his shadow on the floor; 00:01:34.827 --> 00:01:38.007 "And my soul from out that shadow that lies floating 00:01:38.007 --> 00:01:38.840 "on the floor 00:01:38.840 --> 00:01:41.810 "Shall be lifted, nevermore!" 00:01:41.810 --> 00:01:43.330 What is going on here? 00:01:43.330 --> 00:01:46.570 Poe's talking about demons, and souls, and shadows. 00:01:46.570 --> 00:01:49.840 He's clearly not interested in reason or logic. 00:01:49.840 --> 00:01:52.350 Where Jefferson is cold, Poe is hot, 00:01:52.350 --> 00:01:55.680 emotional, imaginative, concentrating 00:01:55.680 --> 00:01:59.310 on the unseen world instead of the observable world 00:01:59.310 --> 00:02:00.820 that Jefferson prizes. 00:02:00.820 --> 00:02:04.470 This is because Poe, writing nearly 70 years later, 00:02:04.470 --> 00:02:07.130 was a product of the Romantic era. 00:02:07.130 --> 00:02:10.340 The Romantics rebelled against the Enlightenment ideas 00:02:10.340 --> 00:02:13.300 of pure reason and the scientific method, 00:02:13.300 --> 00:02:16.186 arguing instead that individual experience 00:02:16.186 --> 00:02:18.620 and emotion mattered more. 00:02:18.620 --> 00:02:21.180 So why do we care about this transition 00:02:21.180 --> 00:02:24.150 from the Enlightenment to the Romantic era 00:02:24.150 --> 00:02:25.970 in the history of the United States? 00:02:25.970 --> 00:02:27.690 Well, for one thing, because it helps 00:02:27.690 --> 00:02:29.950 us explain the Second Great Awakening, 00:02:29.950 --> 00:02:32.930 that period of intense religious devotion 00:02:32.930 --> 00:02:35.780 that emerged in the first half of the 19th century, 00:02:35.780 --> 00:02:37.270 and drove not only the creation 00:02:37.270 --> 00:02:39.480 of new religious moments in the United States, 00:02:39.480 --> 00:02:41.927 but also major reform movements. 00:02:41.927 --> 00:02:45.000 But we also care because it was during this time 00:02:45.000 --> 00:02:48.640 of transition that the first truly American art 00:02:48.640 --> 00:02:51.000 and literary movements emerged. 00:02:51.000 --> 00:02:54.830 Artists and writers stopped merely imitating 00:02:54.830 --> 00:02:57.330 European styles, although they were certainly 00:02:57.330 --> 00:02:58.870 still influenced by them, 00:02:58.870 --> 00:03:01.590 and began trying to capture a unique 00:03:01.590 --> 00:03:04.100 and different American culture. 00:03:04.100 --> 00:03:06.190 What they produced not only tells us a lot 00:03:06.190 --> 00:03:10.040 about their time period, but also created the foundation 00:03:10.040 --> 00:03:12.300 of what's considered American art 00:03:12.300 --> 00:03:15.030 or American literature today. 00:03:15.030 --> 00:03:17.160 One of the ways that Americans began 00:03:17.160 --> 00:03:20.440 to distinguish their culture was through architecture. 00:03:20.440 --> 00:03:23.490 In the late 1700s, American architecture started 00:03:23.490 --> 00:03:26.060 to move away from the Georgian style 00:03:26.060 --> 00:03:27.460 it had borrowed from Britain, 00:03:27.460 --> 00:03:29.570 the very symmetrical brick homes 00:03:29.570 --> 00:03:31.610 that were built during the era 00:03:31.610 --> 00:03:33.800 when kings named George were in power, 00:03:33.800 --> 00:03:36.236 and they started to draw more from the models 00:03:36.236 --> 00:03:39.270 of Roman and Greek architecture. 00:03:39.270 --> 00:03:43.160 Americans saw themselves as carrying on the traditions 00:03:43.160 --> 00:03:45.830 of the Roman Republic and Greek democracy, 00:03:45.830 --> 00:03:47.550 so they started employing some 00:03:47.550 --> 00:03:49.990 of the same architectural language. 00:03:49.990 --> 00:03:53.620 The Federal style started incorporating Roman elements 00:03:53.620 --> 00:03:56.780 into Georgian buildings, like Roman arches. 00:03:56.780 --> 00:03:59.470 Here you can see a bit of the transition 00:03:59.470 --> 00:04:01.987 from this Georgian building on Harvard's campus 00:04:01.987 --> 00:04:05.720 to this Federal building in Salem, Massachusetts. 00:04:05.720 --> 00:04:08.090 You go from square windows and doors 00:04:08.090 --> 00:04:09.830 to Roman arches. 00:04:09.830 --> 00:04:13.790 And this transition continued as the U.S. Capitol was built 00:04:13.790 --> 00:04:15.320 in Washington D.C. 00:04:15.320 --> 00:04:19.002 Starting in the 1820s, the Greek Revival style 00:04:19.002 --> 00:04:22.028 became prominent for monumental buildings, 00:04:22.028 --> 00:04:25.130 incorporating triangular pediments 00:04:25.130 --> 00:04:26.920 and Greek columns. 00:04:26.920 --> 00:04:28.730 Here you can see the original design 00:04:28.730 --> 00:04:31.840 of the U.S. Capitol building, which houses Congress. 00:04:31.840 --> 00:04:35.200 It has a central dome like the Pantheon in Rome, 00:04:35.200 --> 00:04:38.060 and then a full-on Greek temple pasted to its face. 00:04:38.060 --> 00:04:39.174 By adopting these elements, 00:04:39.174 --> 00:04:41.820 American architects sent the message 00:04:41.820 --> 00:04:45.270 that the United States wasn't just imitating British styles. 00:04:45.270 --> 00:04:48.300 Instead they were crafting an architectural form 00:04:48.300 --> 00:04:50.720 that was suitable for a republic. 00:04:50.720 --> 00:04:53.340 American art also began to diverge 00:04:53.340 --> 00:04:57.140 from its European forbears during the early 19th century. 00:04:57.140 --> 00:05:00.190 American-born painters in the Revolutionary era, 00:05:00.190 --> 00:05:02.230 like Gilbert Stuart, went to Europe 00:05:02.230 --> 00:05:04.240 to study and start their careers 00:05:04.240 --> 00:05:06.630 before heading back to the United States. 00:05:06.630 --> 00:05:09.470 Stuart's portraits of important American figures 00:05:09.470 --> 00:05:12.370 like George Washington followed the conventions 00:05:12.370 --> 00:05:14.330 of classical portraiture. 00:05:14.330 --> 00:05:17.300 It wasn't until the 1820s that American art began 00:05:17.300 --> 00:05:20.290 to come into its own with the Hudson River School. 00:05:20.290 --> 00:05:22.900 This was started by a group of painters working 00:05:22.900 --> 00:05:26.512 in Upstate New York who captured the majestic nature 00:05:26.512 --> 00:05:28.750 of the American landscape. 00:05:28.750 --> 00:05:32.010 They were influenced by the Romantic movement's emphasis 00:05:32.010 --> 00:05:34.590 on emotion and the sublime, 00:05:34.590 --> 00:05:38.380 which is the awe-inspiring, untamed aspect 00:05:38.380 --> 00:05:40.550 of nature that you find in mountains, 00:05:40.550 --> 00:05:42.420 and storms, and wilderness. 00:05:42.420 --> 00:05:45.610 The painters of the Hudson River School explored 00:05:45.610 --> 00:05:49.000 the relationship between the American environment 00:05:49.000 --> 00:05:50.940 and the march of settlement. 00:05:50.940 --> 00:05:54.270 Let's take a look at one Hudson River School painting, 00:05:54.270 --> 00:05:59.190 The Oxbow, which was painted in 1836 by Thomas Cole. 00:05:59.190 --> 00:06:02.900 The painting depicts a bend in the Connecticut River 00:06:02.900 --> 00:06:04.830 in Western Massachusetts. 00:06:04.830 --> 00:06:07.340 You can see that a thunderstorm is passing 00:06:07.340 --> 00:06:09.810 with dark clouds here on the left. 00:06:09.810 --> 00:06:13.040 And there's this twisted tree and downed limbs, 00:06:13.040 --> 00:06:16.070 which show how violent the storm was up on the mountain. 00:06:16.070 --> 00:06:18.870 It feels dangerous and unpredictable. 00:06:18.870 --> 00:06:20.570 That's the sublime right there. 00:06:20.570 --> 00:06:24.110 Then, on the right side, you have this river valley 00:06:24.110 --> 00:06:27.660 with farms and little plumes of smoke from houses. 00:06:27.660 --> 00:06:28.773 There's a boat on the river 00:06:28.773 --> 00:06:31.200 and some sheep grazing down here, 00:06:31.200 --> 00:06:33.760 and just barely visible in the foreground 00:06:33.760 --> 00:06:36.440 is a little self-portrait of Thomas Cole 00:06:36.440 --> 00:06:37.470 out with his easel. 00:06:37.470 --> 00:06:39.087 He's kind of saying, "Yeah, that's right. 00:06:39.087 --> 00:06:40.857 "I'm out here dodging lightning to show you 00:06:40.857 --> 00:06:42.420 "how the real deal looks." 00:06:42.420 --> 00:06:43.810 So you can see in this painting 00:06:43.810 --> 00:06:45.340 that there's kind of a tension 00:06:45.340 --> 00:06:48.320 between the settled society on the right side 00:06:48.320 --> 00:06:50.550 and the wilderness on the left side. 00:06:50.550 --> 00:06:52.932 The vastness of the American West 00:06:52.932 --> 00:06:55.790 and the march of the first wave 00:06:55.790 --> 00:06:58.040 of industrialization gave painters 00:06:58.040 --> 00:07:01.650 a unique American subject for their art. 00:07:01.650 --> 00:07:06.250 Lastly, the first American writers and thinkers came 00:07:06.250 --> 00:07:08.080 on the scene during this era. 00:07:08.080 --> 00:07:11.483 Remember the Romantics glorified the experience 00:07:11.483 --> 00:07:14.730 of the individual and their emotions. 00:07:14.730 --> 00:07:16.950 The first American fiction writers 00:07:16.950 --> 00:07:20.380 to gain traction for an international audience described 00:07:20.380 --> 00:07:23.370 unique aspects of American society. 00:07:23.370 --> 00:07:26.290 Washington Irving, who we remember today 00:07:26.290 --> 00:07:29.300 for the Headless Horseman in "The Legend of Sleepy Hollow," 00:07:29.300 --> 00:07:33.270 another romantic ghost story like Poe's The Raven, 00:07:33.270 --> 00:07:36.430 achieved renown by telling folk tales 00:07:36.430 --> 00:07:40.310 about the lingering Dutch culture in Upstate New York. 00:07:40.310 --> 00:07:42.700 James Fenimore Cooper's protagonist 00:07:42.700 --> 00:07:45.660 in his "Leatherstocking Tales," Natty Bumppo, 00:07:45.660 --> 00:07:48.520 was a white frontiersman who grew up 00:07:48.520 --> 00:07:50.850 among the indigenous Delaware People. 00:07:50.850 --> 00:07:52.700 His nickname was Hawkeye, 00:07:52.700 --> 00:07:55.310 and yes, the Marvel character is named after him, 00:07:55.310 --> 00:07:56.760 which gives you a sense of how 00:07:56.760 --> 00:07:59.820 these first American characters have continued 00:07:59.820 --> 00:08:02.940 to live on in our contemporary culture. 00:08:02.940 --> 00:08:05.970 In New England, particularly Boston 00:08:05.970 --> 00:08:07.540 and the surrounding areas, 00:08:07.540 --> 00:08:11.190 American intellectuals embraced Romanticism 00:08:11.190 --> 00:08:14.510 in the philosophy of Transcendentalism. 00:08:14.510 --> 00:08:17.390 The Transcendentalists were a group of writers, 00:08:17.390 --> 00:08:20.410 poets, and philosophers who believed 00:08:20.410 --> 00:08:23.736 that truth transcended the observable world 00:08:23.736 --> 00:08:26.970 of the Enlightenment, and that spiritual meaning 00:08:26.970 --> 00:08:28.810 could be found in nature. 00:08:28.810 --> 00:08:30.870 Henry David Thoreau is probably 00:08:30.870 --> 00:08:32.790 the most famous Transcendentalist. 00:08:32.790 --> 00:08:35.117 He wrote a book about his two years living simply 00:08:35.117 --> 00:08:38.059 in a cabin he built on the edge of Walden Pond, 00:08:38.059 --> 00:08:42.380 on fellow Transcendentalist Ralph Waldo Emerson's property. 00:08:42.380 --> 00:08:45.861 The Transcendentalists also emphasized the individual 00:08:45.861 --> 00:08:47.850 and freedom of thought. 00:08:47.850 --> 00:08:50.332 Emerson, who's generally considered the founder 00:08:50.332 --> 00:08:52.570 of the Transcendentalist movement, 00:08:52.570 --> 00:08:54.950 wrote essays encouraging Americans 00:08:54.950 --> 00:08:57.530 to think for themselves, not just go along 00:08:57.530 --> 00:08:58.500 with the crowd. 00:08:58.500 --> 00:09:01.800 Some of the most influential Transcendentalists were women, 00:09:01.800 --> 00:09:04.180 like Margaret Fuller, who wrote about the state 00:09:04.180 --> 00:09:05.990 of women in the 19th century 00:09:05.990 --> 00:09:09.183 and edited the Transcendentalist magazine The Dial. 00:09:09.183 --> 00:09:12.270 Poet Emily Dickinson has sometimes been classed 00:09:12.270 --> 00:09:13.860 among the Transcendentalists, 00:09:13.860 --> 00:09:17.520 as has Louisa May Alcott, the author of "Little Women." 00:09:17.520 --> 00:09:20.013 The freedom of thought that the Transcendentalists 00:09:20.013 --> 00:09:22.173 espoused also led them to become some 00:09:22.173 --> 00:09:26.370 of the strongest opponents of the institution of slavery. 00:09:26.370 --> 00:09:29.370 Thoreau refused to pay his taxes 00:09:29.370 --> 00:09:31.960 in protest of the Mexican American War, 00:09:31.960 --> 00:09:33.760 which he and many Northerners saw 00:09:33.760 --> 00:09:37.610 as an unjust land-grab to extend southern territory 00:09:37.610 --> 00:09:39.310 and spread slavery west. 00:09:39.310 --> 00:09:41.807 He wrote an essay about his experience called 00:09:41.807 --> 00:09:43.970 "Resistance to Civil Government," 00:09:43.970 --> 00:09:46.871 sometimes shortened to "Civil Disobedience," 00:09:46.871 --> 00:09:49.110 which encouraged individuals not 00:09:49.110 --> 00:09:51.350 to obey unjust laws. 00:09:51.350 --> 00:09:54.420 His ideas would go on to influence Mahatma Gandhi 00:09:54.420 --> 00:09:56.653 and later Martin Luther King, Junior.

Showing segment congruence equivalent to having same length

https://www.youtube.com/watch?v=Ko12Tf-lulQ

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https://www.youtube.com/api/timedtext?v=Ko12Tf-lulQ&ei=bViUZbKHIJ_BmLAP3rqT8A4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2021390F05B9C0FFA0000B1174F573DB9AFE68B2.BA05E60702C8CAE458EE2467D5295DDBBF3359A3&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.280 --> 00:00:01.113 - [Instructor] In this video, 00:00:01.113 --> 00:00:05.590 we're gonna talk a little bit about segment congruence. 00:00:05.590 --> 00:00:09.340 And what we have here, let's call this statement one, 00:00:09.340 --> 00:00:12.590 this is the definition of line segment congruence, 00:00:12.590 --> 00:00:14.770 or at least the one that we will use. 00:00:14.770 --> 00:00:17.900 Two segments are congruent, that means that we can map 00:00:17.900 --> 00:00:22.900 one segment onto the other using rigid transformations. 00:00:23.180 --> 00:00:25.720 And examples of rigid transformations are reflections, 00:00:25.720 --> 00:00:29.470 rotations, translations, and combinations of them. 00:00:29.470 --> 00:00:31.180 Now what we're going to see in this video 00:00:31.180 --> 00:00:32.820 is that statement one 00:00:32.820 --> 00:00:37.100 is actually equivalent to statement two. 00:00:37.100 --> 00:00:40.970 Or another way of saying it is if statement one is true, 00:00:40.970 --> 00:00:42.720 then statement two is true, 00:00:42.720 --> 00:00:46.200 and if statement two is true, then statement one is true. 00:00:46.200 --> 00:00:47.750 Or we can write it like this, 00:00:47.750 --> 00:00:49.820 we can map one segment onto another 00:00:49.820 --> 00:00:54.820 using rigid transformations if and only, only if, 00:00:56.950 --> 00:00:59.280 the two segments have the same length. 00:00:59.280 --> 00:01:01.140 So how do we go about proving it? 00:01:01.140 --> 00:01:04.700 Well the first thing that we'd want to prove is 00:01:04.700 --> 00:01:09.700 that if statement one is true, then, 00:01:11.500 --> 00:01:16.050 then statement two is true. 00:01:16.050 --> 00:01:17.600 So how would we go about doing this? 00:01:17.600 --> 00:01:18.580 And like always, I encourage you 00:01:18.580 --> 00:01:20.623 to pause the video and have a go at it. 00:01:21.670 --> 00:01:23.600 All right, now let's work through it together. 00:01:23.600 --> 00:01:25.660 Some proofs like this might be difficult 00:01:25.660 --> 00:01:28.090 because they feel so intuitive. 00:01:28.090 --> 00:01:33.060 But one way to prove this is to first say that by definition 00:01:33.060 --> 00:01:36.400 rigid transformations preserve length. 00:01:36.400 --> 00:01:41.400 So by definition, by definition, definition, 00:01:42.850 --> 00:01:47.850 rigid transformations, that's what makes them rigid, 00:01:48.040 --> 00:01:52.297 rigid transformations preserve length. 00:01:59.709 --> 00:02:01.409 So if one segment, if one segment, 00:02:06.190 --> 00:02:10.130 can be mapped onto, 00:02:12.530 --> 00:02:17.110 onto a second segment 00:02:18.960 --> 00:02:23.960 with rigid transformations, with rigid transformations, 00:02:27.770 --> 00:02:31.020 they must have had the original, the same original length, 00:02:31.020 --> 00:02:35.620 they must have had the same original length, 00:02:35.620 --> 00:02:40.620 they must have had same original length. 00:02:43.420 --> 00:02:46.400 Or another way to say it is, then two is true. 00:02:46.400 --> 00:02:50.570 Then we can try to do it the other way around. 00:02:50.570 --> 00:02:54.710 So let's see if we can prove that if two, 00:02:54.710 --> 00:02:58.890 if statement two is true, then statement one is true, 00:02:58.890 --> 00:03:03.000 then statement one, and why don't you pause this video 00:03:03.000 --> 00:03:05.083 and have a go at that as well. 00:03:06.700 --> 00:03:11.700 So let's assume, assume, I have segment AB 00:03:13.220 --> 00:03:16.600 and then I have another segment, let's call it CD, 00:03:16.600 --> 00:03:20.773 have the same length, have same length. 00:03:21.680 --> 00:03:25.263 So they meet the number two statement right over there. 00:03:26.620 --> 00:03:30.370 To map, to map AB onto CD, 00:03:37.100 --> 00:03:41.350 all I have to do, I can do this in two rotations every time, 00:03:41.350 --> 00:03:46.350 I first will, I will translate so that A is on top of C, 00:03:48.550 --> 00:03:53.550 so I will translate, translate AB, 00:03:53.760 --> 00:03:58.760 so that point A is on top of point C. 00:04:06.520 --> 00:04:10.630 And then the next thing I would do is rotate, 00:04:10.630 --> 00:04:15.630 rotate AB so that point B, 00:04:17.350 --> 00:04:22.350 point B, is on top of point D. 00:04:25.860 --> 00:04:27.000 And there you have it. 00:04:27.000 --> 00:04:29.440 For any two segments with the same length, 00:04:29.440 --> 00:04:31.380 I can always translate it 00:04:31.380 --> 00:04:33.770 so that I have one set of points overlap, 00:04:33.770 --> 00:04:35.770 and then to get the other points to overlap 00:04:35.770 --> 00:04:36.700 I just have to rotate it. 00:04:36.700 --> 00:04:37.810 I know that's going to work 00:04:37.810 --> 00:04:39.980 because they have the same length. 00:04:39.980 --> 00:04:43.890 So I've just shown you, if we can map one segment 00:04:43.890 --> 00:04:45.840 onto another using rigid transformations, 00:04:45.840 --> 00:04:47.620 then we know they have the same length, 00:04:47.620 --> 00:04:49.830 and if two segments have the same length, 00:04:49.830 --> 00:04:52.060 then we know that we can map one segment 00:04:52.060 --> 00:04:54.953 onto the other using rigid transformations.

Idea behind hypothesis testing

https://www.youtube.com/watch?v=cn4S3QqEBRg

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https://www.youtube.com/api/timedtext?v=cn4S3QqEBRg&ei=bViUZfDDEtPDhcIPlOqA0Ak&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=45FBEA21FFEF84247F3D22CC25F1A8099D18E0B6.D1F1D573BB696DACD8669D4C5CA9303707DD09F8&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.300 --> 00:00:01.630 - [Instructor] What we're going to do in this video 00:00:01.630 --> 00:00:04.930 is talk about hypothesis testing, 00:00:04.930 --> 00:00:07.640 which is the heart of all of inferential statistics, 00:00:07.640 --> 00:00:10.840 statistics that allow us to make inferences about the world. 00:00:10.840 --> 00:00:12.560 So, to give us the gist of this, 00:00:12.560 --> 00:00:14.890 let's start with a tangible example. 00:00:14.890 --> 00:00:16.950 Let's say, hypothetically, 00:00:16.950 --> 00:00:20.350 you run a website that has the mission 00:00:20.350 --> 00:00:24.200 of giving everyone on the planet a free education, 00:00:24.200 --> 00:00:27.330 and you wanna think about how you might change 00:00:27.330 --> 00:00:29.090 the amount of time people spend on the site. 00:00:29.090 --> 00:00:30.830 Ideally, you wanna increase the amount of time 00:00:30.830 --> 00:00:31.663 people spend on the site 00:00:31.663 --> 00:00:33.940 so there's more learning on the planet. 00:00:33.940 --> 00:00:38.380 Well, currently the website has a white background like this 00:00:38.380 --> 00:00:42.050 and the mean amount of time people spend 00:00:42.050 --> 00:00:44.540 when you have a white background, 00:00:44.540 --> 00:00:46.610 the mean amount of time when you have a white background 00:00:46.610 --> 00:00:48.400 is 20 minutes. 00:00:48.400 --> 00:00:50.160 And you or someone on your team, 00:00:50.160 --> 00:00:52.680 maybe you read some type of study that says 00:00:52.680 --> 00:00:54.800 people like to spend more time on yellow backgrounds. 00:00:54.800 --> 00:00:56.360 I don't actually think that's true, 00:00:56.360 --> 00:00:58.680 but let's just go with that for the sake of this video. 00:00:58.680 --> 00:01:00.820 And so you have a hypothesis 00:01:00.820 --> 00:01:02.790 that if you actually have a yellow background, 00:01:02.790 --> 00:01:05.420 if you change your background to yellow, 00:01:05.420 --> 00:01:08.240 that the mean amount of time that people spend 00:01:08.240 --> 00:01:11.540 on a yellow background, on yellow, 00:01:11.540 --> 00:01:15.690 is going to be different, is not going to be equal to 00:01:15.690 --> 00:01:20.690 the mean amount of time people spend on a white background. 00:01:21.450 --> 00:01:23.700 So, the question is how do you test this, 00:01:23.700 --> 00:01:25.710 and how do you feel good about your inferences 00:01:25.710 --> 00:01:27.110 that you make from your test? 00:01:27.110 --> 00:01:30.060 And that is the heart of hypothesis testing. 00:01:30.060 --> 00:01:33.440 And medical research, actually almost all research 00:01:33.440 --> 00:01:36.800 involves some form of hypothesis testing. 00:01:36.800 --> 00:01:38.410 So, how would you do this? 00:01:38.410 --> 00:01:40.120 Well, the standard why to do this 00:01:40.120 --> 00:01:42.640 is to set up a couple of hypothesis. 00:01:42.640 --> 00:01:44.630 Hypotheses, I should say. 00:01:44.630 --> 00:01:48.350 The first one is known as your null hypothesis, 00:01:48.350 --> 00:01:50.910 and I often think about this as the skeptic's hypothesis. 00:01:50.910 --> 00:01:52.310 Skeptics think that, 00:01:52.310 --> 00:01:54.430 hey, it's hard to make a difference in this world, 00:01:54.430 --> 00:01:55.750 or cynics feel like it's hard 00:01:55.750 --> 00:01:57.040 to make a difference in the world 00:01:57.040 --> 00:01:59.550 and so they always have this null hypothesis 00:01:59.550 --> 00:02:01.597 that's saying, "Hey, you think you're making a difference, 00:02:01.597 --> 00:02:02.720 "but you aren't." 00:02:02.720 --> 00:02:05.850 So, the null hypothesis is that 00:02:05.850 --> 00:02:09.260 the mean amount of time people spend on the yellow site, 00:02:09.260 --> 00:02:11.490 or on a yellow site, 00:02:11.490 --> 00:02:15.450 is going to be equal to the mean amount of time 00:02:15.450 --> 00:02:16.840 that people spend on the current site 00:02:16.840 --> 00:02:20.280 or the existing site or on a white site, 00:02:20.280 --> 00:02:22.267 while the people who are thinking about, 00:02:22.267 --> 00:02:23.387 "Hey, how do I make change? 00:02:23.387 --> 00:02:24.860 "How do I make improvements in the world?" 00:02:24.860 --> 00:02:26.560 they had some type of hypothesis 00:02:26.560 --> 00:02:30.630 and we call that the alternative hypothesis. 00:02:30.630 --> 00:02:35.460 And so the alternative hypothesis, A for alternative, 00:02:35.460 --> 00:02:39.770 is that the mean time on the yellow site, 00:02:39.770 --> 00:02:41.300 on the yellow site, 00:02:41.300 --> 00:02:42.930 is actually different. 00:02:42.930 --> 00:02:43.900 Is actually different. 00:02:43.900 --> 00:02:47.570 It is not equal to the mean amount of time 00:02:47.570 --> 00:02:49.610 on the white site. 00:02:49.610 --> 00:02:50.820 So, how do we think about this 00:02:50.820 --> 00:02:53.040 now that we set up these hypotheses? 00:02:53.040 --> 00:02:55.100 Well, what we're going to do is 00:02:55.100 --> 00:02:57.460 we are going to assume, 00:02:57.460 --> 00:03:00.023 we assume the null hypothesis. 00:03:00.970 --> 00:03:04.630 Then we build this yellow site 00:03:04.630 --> 00:03:06.240 and then we take a sample 00:03:06.240 --> 00:03:09.100 of the people using the yellow site, 00:03:09.100 --> 00:03:11.127 and we say, "What is the probability 00:03:11.127 --> 00:03:13.010 "of getting that sample mean," 00:03:13.010 --> 00:03:16.007 which is an approximation of the parameter of the true mean, 00:03:16.007 --> 00:03:19.307 "what is the probability of getting that sample mean 00:03:19.307 --> 00:03:22.040 "if we assume the null hypothesis?" 00:03:22.040 --> 00:03:25.300 And if the probability of getting that sample mean 00:03:25.300 --> 00:03:26.340 on the yellow site, 00:03:26.340 --> 00:03:29.620 assuming the null hypothesis, is really low, 00:03:29.620 --> 00:03:32.170 then we reject the null hypothesis, 00:03:32.170 --> 00:03:34.330 which suggests the alternative. 00:03:34.330 --> 00:03:37.360 On the other hand, if we get a sample mean 00:03:37.360 --> 00:03:39.380 that seems pretty reasonable to get 00:03:39.380 --> 00:03:41.670 if you assume the null hypothesis, 00:03:41.670 --> 00:03:44.150 then we fail to reject the null hypothesis 00:03:44.150 --> 00:03:47.310 and then that would not suggest the alternative. 00:03:47.310 --> 00:03:49.450 Now, to make this a little bit more tangible, 00:03:49.450 --> 00:03:52.360 and we'll go over this into a lot of videos, 00:03:52.360 --> 00:03:54.620 if you assume the null hypothesis, 00:03:54.620 --> 00:03:57.440 then there's a few things you can think about. 00:03:57.440 --> 00:03:59.980 You can think about just the general distribution 00:03:59.980 --> 00:04:02.640 of the amount of time people spend on the site. 00:04:02.640 --> 00:04:03.930 It would look something like this. 00:04:03.930 --> 00:04:05.550 We will, for this sake, 00:04:05.550 --> 00:04:07.290 assume that it's a normal distribution, 00:04:07.290 --> 00:04:09.750 and normal distributions are very important, 00:04:09.750 --> 00:04:11.910 and/or things that are close to normal distributions, 00:04:11.910 --> 00:04:13.500 for hypothesis testing. 00:04:13.500 --> 00:04:15.260 But let's say that it's a normal distribution 00:04:15.260 --> 00:04:17.200 of the amount of time people spend on the site 00:04:17.200 --> 00:04:19.410 and so there is some mean. 00:04:19.410 --> 00:04:20.530 We know that mean, 00:04:20.530 --> 00:04:23.740 so the mean that people spend on that white site 00:04:23.740 --> 00:04:27.790 is equal to 20 minutes. 00:04:27.790 --> 00:04:30.090 And, remember, we're assuming the null hypothesis, 00:04:30.090 --> 00:04:33.020 so we're assuming that this is also the amount of time 00:04:33.020 --> 00:04:35.150 that people would spend on the yellow site. 00:04:35.150 --> 00:04:39.660 We've assumed, assuming, the null hypothesis, 00:04:39.660 --> 00:04:43.380 and you could view this as time or distribution 00:04:44.470 --> 00:04:47.023 of time spent. 00:04:48.520 --> 00:04:50.330 Now, one of the things we're going to talk about 00:04:50.330 --> 00:04:53.340 in future videos is if you have this distribution, 00:04:53.340 --> 00:04:56.210 you can actually come up with another distribution 00:04:56.210 --> 00:04:59.550 of the means of samples you might get. 00:04:59.550 --> 00:05:03.720 So, there's something else called the sampling distribution, 00:05:03.720 --> 00:05:05.390 and I know it's very confusing at first. 00:05:05.390 --> 00:05:10.390 Sampling distribution of the sample 00:05:10.670 --> 00:05:14.210 of the sample mean, 00:05:14.210 --> 00:05:16.150 and it'll be for a given sample size, 00:05:16.150 --> 00:05:20.980 for sample size, sample size. 00:05:20.980 --> 00:05:24.760 Let's say this is sample size 1,000. 00:05:24.760 --> 00:05:25.720 I'm just making things up. 00:05:25.720 --> 00:05:26.780 I could've said N, 00:05:26.780 --> 00:05:30.150 but I'm just gonna make this a little bit more tangible. 00:05:30.150 --> 00:05:31.920 Well, we're going to get statistical methods 00:05:31.920 --> 00:05:33.770 for how you can think about this distribution 00:05:33.770 --> 00:05:36.060 assuming this distribution we have on the left. 00:05:36.060 --> 00:05:38.290 And it turns out this distribution 00:05:38.290 --> 00:05:40.530 is going to look like the one on the left, 00:05:40.530 --> 00:05:44.120 but it's going to be narrower around that mean. 00:05:44.120 --> 00:05:46.670 It's going to look something like this. 00:05:46.670 --> 00:05:49.700 And, actually, the larger your sample sizes are going to be, 00:05:49.700 --> 00:05:51.740 the narrower it's going to get. 00:05:51.740 --> 00:05:53.700 Now, remember, this isn't just the distribution 00:05:53.700 --> 00:05:56.310 of the amount of time people spend on the site. 00:05:56.310 --> 00:06:01.220 This is the distribution that if I were to take a sample 00:06:01.220 --> 00:06:03.440 of the amount of time people spend on the site 00:06:03.440 --> 00:06:05.210 and calculate the means, 00:06:05.210 --> 00:06:08.600 this is the distribution of those sample means I might get. 00:06:08.600 --> 00:06:11.550 Now, the center of this distribution is still 00:06:11.550 --> 00:06:15.550 our mean for white which is equal to the mean for yellow. 00:06:15.550 --> 00:06:18.270 Remember, we're assuming the null hypothesis. 00:06:18.270 --> 00:06:21.380 The mean for yellow. 00:06:21.380 --> 00:06:23.480 But each of these points, 00:06:23.480 --> 00:06:25.010 for example, if I think about this, 00:06:25.010 --> 00:06:27.200 this is amount of time that someone might spend 00:06:27.200 --> 00:06:29.760 and you can see that there's a low probability about it. 00:06:29.760 --> 00:06:33.740 This over here, this would be a sample mean you might get 00:06:33.740 --> 00:06:36.830 for a time that you sampled 1,000 people 00:06:36.830 --> 00:06:38.350 and you calculated the mean, 00:06:38.350 --> 00:06:40.720 and you see that there's a low probability for it. 00:06:40.720 --> 00:06:42.560 So, then what you would do is, 00:06:42.560 --> 00:06:45.350 if you were able to statistically generate these things 00:06:45.350 --> 00:06:47.210 assuming the null hypothesis, 00:06:47.210 --> 00:06:48.320 and don't worry too much, 00:06:48.320 --> 00:06:50.550 we'll find out the techniques for doing this 00:06:50.550 --> 00:06:52.713 and the assumptions we need to make for doing this, 00:06:52.713 --> 00:06:56.020 what we do is then take a sample of 1,000. 00:06:56.020 --> 00:06:58.834 So, you take your sample of 1,000, 00:06:58.834 --> 00:07:00.167 so sample 1,000, 00:07:02.560 --> 00:07:07.560 and then from that you are able to calculate a sample mean. 00:07:07.740 --> 00:07:09.360 You are able to calculate that. 00:07:09.360 --> 00:07:13.713 And let's say you get a sample mean of 30 minutes. 00:07:14.590 --> 00:07:17.470 And let's say, actually, that that is right over here, 00:07:17.470 --> 00:07:19.170 that this is 30 minutes right over here. 00:07:19.170 --> 00:07:21.260 The center was 20 minutes. 00:07:21.260 --> 00:07:23.657 The next thing, what you do is you say, 00:07:23.657 --> 00:07:25.247 "What's the probability of getting a result 00:07:25.247 --> 00:07:28.880 "at least that extreme assuming the null hypothesis?" 00:07:28.880 --> 00:07:31.350 And that high probability on these curves, 00:07:31.350 --> 00:07:33.330 it would be this right tail here 00:07:33.330 --> 00:07:34.620 and it would be the left tail 00:07:34.620 --> 00:07:36.270 that is equally far on the left side, 00:07:36.270 --> 00:07:37.560 so it'd be like that. 00:07:37.560 --> 00:07:38.850 And what you do is you look. 00:07:38.850 --> 00:07:40.290 You look at this probability, 00:07:40.290 --> 00:07:43.370 which would be these yellow areas there, 00:07:43.370 --> 00:07:47.650 and then we think about the probability 00:07:47.650 --> 00:07:52.430 of getting a result at least as extreme as 30 minutes. 00:07:52.430 --> 00:07:55.060 So, probability of getting, 00:07:55.060 --> 00:07:58.950 getting a sample mean at least 00:08:00.160 --> 00:08:02.080 as extreme 00:08:04.110 --> 00:08:08.790 as the sample mean equaling 30 minutes, 00:08:08.790 --> 00:08:11.550 assuming, assuming 00:08:13.330 --> 00:08:14.960 your null hypothesis, 00:08:14.960 --> 00:08:19.470 and that's exactly what those yellow areas are all about. 00:08:19.470 --> 00:08:24.270 And you compare that to some pre-specified threshold. 00:08:24.270 --> 00:08:27.510 So, that threshold is oftentimes 5%. 00:08:27.510 --> 00:08:29.220 Sometimes it's 1%. 00:08:29.220 --> 00:08:34.220 But if this probability is less than or equal to, 00:08:35.010 --> 00:08:37.723 if it's less than or equal to your threshold, 00:08:38.760 --> 00:08:41.060 and the threshold is oftentimes denoted 00:08:41.060 --> 00:08:42.980 by the Greek letter alpha, 00:08:42.980 --> 00:08:46.237 well, we say, "Hey, that was a very low probability 00:08:46.237 --> 00:08:48.967 "of getting a result at least this extreme 00:08:48.967 --> 00:08:51.080 "if we assume the null hypothesis," 00:08:51.080 --> 00:08:54.670 and so that will allow us to reject, 00:08:54.670 --> 00:08:57.480 reject the null hypothesis, 00:08:57.480 --> 00:09:01.890 which would suggest, suggest the alternative. 00:09:01.890 --> 00:09:04.250 Notice we haven't proven the alternative. 00:09:04.250 --> 00:09:06.710 We also haven't proven the the null hypothesis 00:09:06.710 --> 00:09:08.560 is for sure false. 00:09:08.560 --> 00:09:11.440 We've just said if we assume the null hypothesis, 00:09:11.440 --> 00:09:13.990 there's a very low probability of getting a result 00:09:13.990 --> 00:09:16.870 at least as extreme as what we just got, 00:09:16.870 --> 00:09:19.280 so we will reject the null. 00:09:19.280 --> 00:09:21.920 Now, if it's the other way around, 00:09:21.920 --> 00:09:25.120 if the probability of getting a sample mean 00:09:25.120 --> 00:09:28.220 at least as extreme as this is still reasonable, 00:09:28.220 --> 00:09:33.190 if it's greater than your pre-specified threshold, 00:09:33.190 --> 00:09:35.970 then you fail to reject the null. 00:09:35.970 --> 00:09:39.040 You fail to reject 00:09:39.990 --> 00:09:42.570 your null hypothesis. 00:09:42.570 --> 00:09:43.550 So, I'll leave you there. 00:09:43.550 --> 00:09:44.400 In future videos, 00:09:44.400 --> 00:09:46.620 we'll go into much more depth into all of this, 00:09:46.620 --> 00:09:50.950 but this is to give you a sense of how hypothesis testing 00:09:50.950 --> 00:09:54.340 allows science or all of us in the world 00:09:54.340 --> 00:09:57.743 to start making inferences that we can feel good about.

Conclusion for a two sample t test using a P value

https://www.youtube.com/watch?v=9s8jiskyso0

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https://www.youtube.com/api/timedtext?v=9s8jiskyso0&ei=bViUZYvSFqm_mLAPmKCa2AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C57629BF85115893A7E3A3F1C3271BA62F6B5B53.495039B816F1CBD91BC3234736ABC965FBFBE0F4&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.810 --> 00:00:03.210 - [Instructor] We're told a sociologist studying fertility 00:00:03.210 --> 00:00:05.830 in Argentina and Bolivia wanted to test 00:00:05.830 --> 00:00:08.100 if there was a difference in the average number 00:00:08.100 --> 00:00:10.300 of babies women in each country have. 00:00:10.300 --> 00:00:12.820 The sociologist obtained a random sample 00:00:12.820 --> 00:00:14.490 of women from each country. 00:00:14.490 --> 00:00:16.910 Here are the results of their test. 00:00:16.910 --> 00:00:21.910 So they take a sample of 75 women in Argentina, 00:00:22.220 --> 00:00:26.740 and these women had a mean of 2.4 babies each, 00:00:26.740 --> 00:00:29.063 with a standard deviation of 1.5. 00:00:30.490 --> 00:00:34.260 And then the standard error of the mean was 0.17. 00:00:34.260 --> 00:00:38.500 And then they calculated similar statistics for Bolivia. 00:00:38.500 --> 00:00:41.010 And then they give us the t test 00:00:41.010 --> 00:00:43.690 for the means being different, 00:00:43.690 --> 00:00:46.750 and we were able to calculate these statistics. 00:00:46.750 --> 00:00:49.410 And they say assume that all conditions 00:00:49.410 --> 00:00:51.890 for inference have been met. 00:00:51.890 --> 00:00:56.580 At the alpha equals 0.05 level of significance, 00:00:56.580 --> 00:00:59.410 is there sufficient evidence to conclude 00:00:59.410 --> 00:01:02.700 that there is a difference in the average number 00:01:02.700 --> 00:01:05.980 of babies women in each country have? 00:01:05.980 --> 00:01:08.923 So pause this video, and see if you can answer that. 00:01:10.340 --> 00:01:13.450 All right, now let's work through this together. 00:01:13.450 --> 00:01:17.020 So this is classic hypothesis testing right over here, 00:01:17.020 --> 00:01:20.010 where your null hypothesis is actually going to be 00:01:20.010 --> 00:01:21.770 that your means are the same, 00:01:21.770 --> 00:01:24.530 so that the mean in Argentina is equal 00:01:24.530 --> 00:01:27.020 to the mean in Bolivia. 00:01:27.020 --> 00:01:30.590 And then your alternative hypothesis is 00:01:30.590 --> 00:01:34.600 that your means are different. 00:01:34.600 --> 00:01:36.700 And what you do is you say, all right, 00:01:36.700 --> 00:01:41.700 if we assume the null hypothesis, what is the probability 00:01:41.700 --> 00:01:45.320 that we would have gotten means this far apart? 00:01:45.320 --> 00:01:49.040 And that's what our p-value tells us, 00:01:49.040 --> 00:01:52.720 that we have a 0.31 probability, 00:01:52.720 --> 00:01:57.480 or a 31% probability, of getting means this far apart. 00:01:57.480 --> 00:02:00.720 Now, if your probability, assuming the null hypothesis, 00:02:00.720 --> 00:02:03.350 is below your level of significance, 00:02:03.350 --> 00:02:05.190 your alpha right over here, 00:02:05.190 --> 00:02:06.550 then you would say, all right, 00:02:06.550 --> 00:02:08.380 that seems like such a low probability. 00:02:08.380 --> 00:02:10.530 I'll reject the null hypothesis, 00:02:10.530 --> 00:02:13.530 which suggests the alternative hypothesis. 00:02:13.530 --> 00:02:15.440 But in this situation here, 00:02:15.440 --> 00:02:18.730 if we compare our p to our alpha, 00:02:18.730 --> 00:02:23.730 we see that our p-value is for sure greater than our alpha. 00:02:23.830 --> 00:02:25.180 So in this situation, 00:02:25.180 --> 00:02:26.290 I mean you could see it right over here, 00:02:26.290 --> 00:02:31.290 0.31 is for sure greater than 0.05. 00:02:31.620 --> 00:02:35.150 So in this situation, we cannot reject the null hypothesis, 00:02:35.150 --> 00:02:38.100 cannot reject 00:02:38.100 --> 00:02:39.850 our null hypothesis. 00:02:39.850 --> 00:02:42.530 And so there is not sufficient evidence 00:02:42.530 --> 00:02:44.530 to conclude that there is a difference 00:02:44.530 --> 00:02:47.953 in the average number of babies women in each country have.

Dilating shapes: shrinking

https://www.youtube.com/watch?v=xAxgxUHzgaY

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en

WEBVTT Kind: captions Language: en 00:00:00.720 --> 00:00:02.930 - [Instructor] We're told draw the image 00:00:02.930 --> 00:00:06.630 of triangle ABC under a dilation 00:00:06.630 --> 00:00:11.630 whose center is P and scale factor is 1/4. 00:00:12.640 --> 00:00:17.010 And what we see here is the widget on Khan Academy 00:00:17.010 --> 00:00:19.400 where we can do that. 00:00:19.400 --> 00:00:22.617 So we have this figure, this triangle ABC, 00:00:23.558 --> 00:00:27.270 A, B, C, right over here, 00:00:27.270 --> 00:00:29.620 and what we wanna do is dilate it, 00:00:29.620 --> 00:00:32.020 so that means scaling it up or down, 00:00:32.020 --> 00:00:36.170 and the center of that dilation is this point P. 00:00:36.170 --> 00:00:38.480 So one way to think about it is let's think 00:00:38.480 --> 00:00:40.470 about the distance between point P 00:00:40.470 --> 00:00:41.840 and each of these points, 00:00:41.840 --> 00:00:44.350 and we wanna scale it by 1/4. 00:00:44.350 --> 00:00:46.160 So the distance is going to be 1/4 00:00:46.160 --> 00:00:47.910 of what it was before. 00:00:47.910 --> 00:00:50.100 So, for example, this point right over here, 00:00:50.100 --> 00:00:53.010 if we just even look diagonally from P to A, 00:00:53.010 --> 00:00:55.450 we can see that we are crossing one square, 00:00:55.450 --> 00:00:58.560 two squares, three squares, four squares. 00:00:58.560 --> 00:01:00.900 So if we have a scale factor of 1/4, 00:01:00.900 --> 00:01:03.590 instead of crossing four squares diagonally, 00:01:03.590 --> 00:01:05.880 we would only cross one square diagonally. 00:01:05.880 --> 00:01:09.470 So I'll put the corresponding point to A right over there. 00:01:09.470 --> 00:01:10.970 Now, what about for point C? 00:01:10.970 --> 00:01:13.570 It's not quite as obvious, 00:01:13.570 --> 00:01:15.230 but one way we could think about it 00:01:15.230 --> 00:01:18.080 is we can think about how far are we going horizontally 00:01:18.080 --> 00:01:21.760 from P to C, and then how far do we go vertically? 00:01:21.760 --> 00:01:24.100 So horizontally, we're going one, two, 00:01:24.100 --> 00:01:29.100 three, four, five, six, seven, eight of these units, 00:01:29.160 --> 00:01:33.610 and then vertically we're going one, two, three, four. 00:01:33.610 --> 00:01:36.290 So we're going to the left eight and up four. 00:01:36.290 --> 00:01:38.300 Now, if we have a scale factor of 1/4, 00:01:38.300 --> 00:01:40.580 we just multiply each of those by 1/4. 00:01:40.580 --> 00:01:42.410 So instead of going to the left eight, 00:01:42.410 --> 00:01:44.100 we would go to the left two. 00:01:44.100 --> 00:01:45.930 Eight times 1/4 is two. 00:01:45.930 --> 00:01:49.250 Instead of going up four, we would go up one. 00:01:49.250 --> 00:01:51.970 So this would be the corresponding point to point C. 00:01:51.970 --> 00:01:54.480 And then we'll do the same thing for point B. 00:01:54.480 --> 00:01:57.680 When we go from P to B, we're going one, two, 00:01:57.680 --> 00:02:02.570 three, four, five, six, seven, eight up, 00:02:02.570 --> 00:02:04.630 and we're going four to the left. 00:02:04.630 --> 00:02:06.300 So if we have a scale factor of 1/4, 00:02:06.300 --> 00:02:08.320 instead of going eight up, we'll go two up, 00:02:08.320 --> 00:02:09.540 and instead of going four to the left, 00:02:09.540 --> 00:02:11.600 we'll go one to the left. 00:02:11.600 --> 00:02:12.960 So there you have it. 00:02:12.960 --> 00:02:16.450 We have just dilated triangle ABC 00:02:16.450 --> 00:02:21.450 around point P with a scale factor of 1/4, 00:02:23.410 --> 00:02:25.083 and we are done.

Health insurance primer

https://www.youtube.com/watch?v=jdP0bBU0rV8

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https://www.youtube.com/api/timedtext?v=jdP0bBU0rV8&ei=bViUZeCZE8f2xN8PstSDoAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B5055CBAE42DE51C466A408D41C94989945DA89A.9879E702BAE7914BCF2598F39D469CC880AC2A7B&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.650 --> 00:00:01.920 - [Narrator] What we're gonna do in this video 00:00:01.920 --> 00:00:04.920 is try to break down the terminology 00:00:04.920 --> 00:00:08.410 and a little bit of the math of health insurance. 00:00:08.410 --> 00:00:11.490 So the first question that you might wonder is, 00:00:11.490 --> 00:00:14.770 how much does an insurance plan cost? 00:00:14.770 --> 00:00:16.840 In many cases, you might have an employer 00:00:16.840 --> 00:00:19.740 who pays for all or part of your insurance, 00:00:19.740 --> 00:00:22.210 but in many cases, you have to get your own insurance. 00:00:22.210 --> 00:00:25.140 And so I'm going to focus on the second case. 00:00:25.140 --> 00:00:29.150 What I did is, I went to my state's insurance exchange, 00:00:29.150 --> 00:00:33.140 and I just looked up an indicative plan for a family of four 00:00:33.140 --> 00:00:37.280 that makes a combined $100,000 a year. 00:00:37.280 --> 00:00:39.150 And this is just one of the plans that I found. 00:00:39.150 --> 00:00:40.950 I got rid of the company's name. 00:00:40.950 --> 00:00:45.030 And what it has here is the monthly premium. 00:00:45.030 --> 00:00:48.330 So whenever people talk about premiums in insurance, 00:00:48.330 --> 00:00:51.220 they're talking about the amount that you have to pay 00:00:51.220 --> 00:00:53.230 to get the insurance. 00:00:53.230 --> 00:00:54.400 So this saying that 00:00:54.400 --> 00:00:59.380 you to have to pay $629.51 a month 00:00:59.380 --> 00:01:02.070 in order to get this insurance. 00:01:02.070 --> 00:01:03.450 You might also hear things 00:01:03.450 --> 00:01:06.580 in terms of annual premiums 00:01:06.580 --> 00:01:09.000 and you might guess how to go from a monthly 00:01:09.000 --> 00:01:11.040 to an annual premium. 00:01:11.040 --> 00:01:15.280 If you multiply this number, $629.51, 00:01:15.280 --> 00:01:18.630 times 12, you're going to get an annual premium 00:01:18.630 --> 00:01:23.630 of $7,554.12. 00:01:23.790 --> 00:01:26.400 So this is how much someone would have to pay, 00:01:26.400 --> 00:01:29.130 likely you, in order to get this insurance. 00:01:29.130 --> 00:01:31.150 And what this is telling me on my exchange 00:01:31.150 --> 00:01:33.070 is that this is actually after 00:01:33.070 --> 00:01:35.590 a pretty big subsidy that I'm getting 00:01:35.590 --> 00:01:37.440 from the federal and state government. 00:01:37.440 --> 00:01:41.180 And most of this is happening from the federal government, 00:01:41.180 --> 00:01:43.570 but we can talk about that in future videos. 00:01:43.570 --> 00:01:45.490 The big picture here is, 00:01:45.490 --> 00:01:47.790 if you wanna know how much a policy costs, 00:01:47.790 --> 00:01:48.850 that's the premium. 00:01:48.850 --> 00:01:52.770 This is how much per month, and this is how much per year. 00:01:52.770 --> 00:01:55.260 Now, the next thing that you are very likely to see 00:01:55.260 --> 00:01:59.820 when getting a policy is a term called a deductible. 00:01:59.820 --> 00:02:02.240 And one way to think about a deductible is, 00:02:02.240 --> 00:02:04.990 this is how much you will have to pay 00:02:04.990 --> 00:02:06.670 out of your own pocket 00:02:06.670 --> 00:02:10.320 until the insurance really starts to kick in. 00:02:10.320 --> 00:02:13.560 So here, we're looking at actually two columns, 00:02:13.560 --> 00:02:15.810 in network and out of network. 00:02:15.810 --> 00:02:19.130 In network are doctors and healthcare providers 00:02:19.130 --> 00:02:22.350 that the insurance company already has put in their network, 00:02:22.350 --> 00:02:24.260 they already have some type of an arrangement with, 00:02:24.260 --> 00:02:26.640 while out of network, they don't have an arrangement 00:02:26.640 --> 00:02:28.250 with those parties. 00:02:28.250 --> 00:02:32.230 So for this insurer, if you go in network, 00:02:32.230 --> 00:02:33.800 you would have to spend 00:02:33.800 --> 00:02:37.840 up to $6,300 on an individual 00:02:37.840 --> 00:02:40.910 before the insurance really starts to kick in. 00:02:40.910 --> 00:02:44.350 So if you had to go and get some type of a surgery 00:02:44.350 --> 00:02:46.810 that costs $6,000, 00:02:46.810 --> 00:02:48.640 even if you've been paying the premium, 00:02:48.640 --> 00:02:52.010 you would have to pay $6,000 on top of the premium 00:02:52.010 --> 00:02:53.840 in order to get that surgery. 00:02:53.840 --> 00:02:56.540 If that surgery, on the other hand, for just one person, 00:02:56.540 --> 00:02:59.683 let's say that surgery costs $10,300. 00:03:01.880 --> 00:03:03.650 Well, in that situation, 00:03:03.650 --> 00:03:06.940 you would have to pay the first 6,300, 00:03:06.940 --> 00:03:08.473 so minus 6,300, 00:03:09.490 --> 00:03:11.080 which means that the insurance company 00:03:11.080 --> 00:03:12.190 would pay the remainder. 00:03:12.190 --> 00:03:14.650 It would pay the remaining $4,000. 00:03:14.650 --> 00:03:17.640 And in that year, if you were to get other surgeries 00:03:17.640 --> 00:03:19.880 for that individual, let's say it's you, 00:03:19.880 --> 00:03:21.790 it would then be covered. 00:03:21.790 --> 00:03:24.520 The insurance company would pay above and beyond, 00:03:24.520 --> 00:03:27.530 anything above and beyond the $6,300. 00:03:27.530 --> 00:03:30.360 Now, you also have a deductible for the entire family. 00:03:30.360 --> 00:03:31.300 So they're not just totalling 00:03:31.300 --> 00:03:33.300 what each individual is spending. 00:03:33.300 --> 00:03:35.950 They're also totalling what the whole family is spending. 00:03:35.950 --> 00:03:39.070 So let's say I have four people in my family, 00:03:39.070 --> 00:03:42.240 and over the course of the year, 00:03:42.240 --> 00:03:44.390 I've had to, for each of them, 00:03:44.390 --> 00:03:48.480 I have spent 3,150. 00:03:48.480 --> 00:03:50.380 I'm just using this as an example. 00:03:50.380 --> 00:03:52.830 So each of them have not gotten 00:03:52.830 --> 00:03:55.430 to their individual deductible yet. 00:03:55.430 --> 00:03:57.880 But in total, my family of four, 00:03:57.880 --> 00:04:02.067 3,150 times four, is $12,600. 00:04:03.080 --> 00:04:05.710 After this point, even though no individual 00:04:05.710 --> 00:04:07.970 has maxed out their deductible yet, 00:04:07.970 --> 00:04:11.170 now the insurance will also kick in. 00:04:11.170 --> 00:04:13.680 Now when they talk about a drug deductible, 00:04:13.680 --> 00:04:16.340 this is a separate deductible for the drugs. 00:04:16.340 --> 00:04:17.760 So the one that I looked at before, 00:04:17.760 --> 00:04:19.900 that could be general procedures 00:04:19.900 --> 00:04:22.510 or certain types of care you might need, 00:04:22.510 --> 00:04:25.910 while this right over here is specific 00:04:25.910 --> 00:04:28.620 to what you might need for medications. 00:04:28.620 --> 00:04:30.150 But it's the same idea. 00:04:30.150 --> 00:04:31.930 If it's for any one individual, 00:04:31.930 --> 00:04:34.720 the first $500 on medication in that year, 00:04:34.720 --> 00:04:36.600 they're going to have to pay out of pocket, 00:04:36.600 --> 00:04:39.350 but then after that, the insurance kicks in. 00:04:39.350 --> 00:04:44.350 And then once again, $1,000 for the entire family. 00:04:44.410 --> 00:04:48.300 Now, out-of-pocket maximum, this says, no matter what, 00:04:48.300 --> 00:04:50.470 no individual on an individual basis 00:04:50.470 --> 00:04:54.970 should you have to put out more than $7,800 00:04:54.970 --> 00:04:57.990 for an individual, no matter what happens. 00:04:57.990 --> 00:05:02.620 And no more than $15,600 for an entire family. 00:05:02.620 --> 00:05:04.810 So this is real money here, but it's saying that 00:05:04.810 --> 00:05:07.530 you won't have to pay more than that 00:05:07.530 --> 00:05:09.400 out of your actual pocket. 00:05:09.400 --> 00:05:13.060 And then here, the maximum cost per prescription, 00:05:13.060 --> 00:05:16.060 this is the most that you will ever have to pay 00:05:16.060 --> 00:05:17.590 to get a prescription. 00:05:17.590 --> 00:05:20.300 So even if there's some type of exotic drug 00:05:20.300 --> 00:05:23.540 that costs $1,000 per prescription, 00:05:23.540 --> 00:05:24.990 the most that you would have to pay 00:05:24.990 --> 00:05:28.310 is $500 per prescription for that. 00:05:28.310 --> 00:05:31.000 Now that we've dissected deductibles a good bit, 00:05:31.000 --> 00:05:35.640 another term that you are likely to see is copay. 00:05:35.640 --> 00:05:37.820 Copay, one way to think about it is, 00:05:37.820 --> 00:05:42.100 something that you pay every time you go into that service. 00:05:42.100 --> 00:05:44.940 So, for example, a primary care visit. 00:05:44.940 --> 00:05:47.340 This says the first three visits 00:05:47.340 --> 00:05:51.020 are a $65 copay before the deductible. 00:05:51.020 --> 00:05:53.420 So this is saying, even if you haven't used up 00:05:53.420 --> 00:05:57.250 your $6,300 individual deductible, 00:05:57.250 --> 00:06:00.460 your primary care visits are covered, 00:06:00.460 --> 00:06:04.203 but every visit, you have to pay $65. 00:06:04.203 --> 00:06:05.840 Now, the reason why they call it copay 00:06:05.840 --> 00:06:08.640 is that you and the insurance company are paying. 00:06:08.640 --> 00:06:11.640 That visit might cost the insurance company 00:06:11.640 --> 00:06:15.490 another 150, 200, $250, 00:06:15.490 --> 00:06:18.120 but you're paying $65 on every visit. 00:06:18.120 --> 00:06:21.000 So the insurance company, the insurance is kicking in 00:06:21.000 --> 00:06:23.860 even before the deductible has been reached. 00:06:23.860 --> 00:06:25.360 Now specialists visits. 00:06:25.360 --> 00:06:27.260 If you go to specialist doctors 00:06:27.260 --> 00:06:31.820 like a cardiologist or a rheumatologist or a dermatologist, 00:06:31.820 --> 00:06:35.990 these copays only kick in after the deductible. 00:06:35.990 --> 00:06:37.090 So what that means is, 00:06:37.090 --> 00:06:40.100 before you reach your deductible ceiling, 00:06:40.100 --> 00:06:42.880 you're going to pay whatever it costs out of pocket. 00:06:42.880 --> 00:06:46.140 So if that specialist visit costs $500, 00:06:46.140 --> 00:06:48.030 you're going to pay $500. 00:06:48.030 --> 00:06:50.820 But once you've reached your deductible, 00:06:50.820 --> 00:06:53.590 then every visit after that 00:06:53.590 --> 00:06:57.100 is going to cost $95 is what you would contribute, 00:06:57.100 --> 00:07:00.120 and then the insurance company would pay the rest. 00:07:00.120 --> 00:07:04.330 Now, the last term I'm going to introduce into this video 00:07:04.330 --> 00:07:08.110 is that of coinsurance. 00:07:08.110 --> 00:07:09.610 So what this is telling us, 00:07:09.610 --> 00:07:11.700 right here they're telling us how we are covered 00:07:11.700 --> 00:07:13.740 for various drugs. 00:07:13.740 --> 00:07:15.840 So, for example, if it's a generic drug, 00:07:15.840 --> 00:07:18.070 these are things that are off patent, 00:07:18.070 --> 00:07:22.330 then you pay $18 after you have reached your deductible. 00:07:22.330 --> 00:07:24.260 So no matter what the drug costs, 00:07:24.260 --> 00:07:25.780 after you've reached your deductible, 00:07:25.780 --> 00:07:28.110 every prescription, you pay $18. 00:07:28.110 --> 00:07:29.780 Now these tier two drugs, 00:07:29.780 --> 00:07:31.530 and I'm not gonna go into detail about this, 00:07:31.530 --> 00:07:34.270 but these are drugs that tend to still be on patent, 00:07:34.270 --> 00:07:36.400 and they tend to be more expensive. 00:07:36.400 --> 00:07:39.600 What this coinsurance is telling us is, 00:07:39.600 --> 00:07:42.250 you're going to pay the drugs out of pocket 00:07:42.250 --> 00:07:45.250 until you reach your deductible for this insurance plan, 00:07:45.250 --> 00:07:47.820 and then after you've reached the deductible, 00:07:47.820 --> 00:07:50.530 you're going to pay 40% of the cost. 00:07:50.530 --> 00:07:52.820 So whenever someone talks about coinsurance, 00:07:52.820 --> 00:07:54.740 that means that you are splitting the cost 00:07:54.740 --> 00:07:56.800 with the insurance company at that point, 00:07:56.800 --> 00:07:59.510 and it's usually specified as a percentage. 00:07:59.510 --> 00:08:03.280 So the 40% is what you would pay for that drug. 00:08:03.280 --> 00:08:05.240 So let's say it's $100 a month. 00:08:05.240 --> 00:08:08.230 You would pay 40% of that, so $40, 00:08:08.230 --> 00:08:10.940 and you'd only get the 60% subsidy 00:08:10.940 --> 00:08:12.470 from the insurance company 00:08:12.470 --> 00:08:16.290 after your drug deductible has been reached. 00:08:16.290 --> 00:08:17.650 So I will leave you there. 00:08:17.650 --> 00:08:19.560 I've already introduced a lot of ideas to you, 00:08:19.560 --> 00:08:22.780 but hopefully that will already start to help you 00:08:22.780 --> 00:08:25.713 dissect how insurance plans work.

Mapping shapes

https://www.youtube.com/watch?v=l3NpQPdbK3k

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https://www.youtube.com/api/timedtext?v=l3NpQPdbK3k&ei=bViUZfaBJtbSxN8PioWo6AQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5C6363F1F13A306A8FEB1826D496359503E0E4EF.221178CE9D290E17D24FEF54ADC5B81F87CDBBC1&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.200 --> 00:00:02.010 - [Instructor] We're told that triangles, 00:00:02.010 --> 00:00:03.640 let's see, we have triangle PQR 00:00:03.640 --> 00:00:07.000 and triangle ABC are congruent. 00:00:07.000 --> 00:00:11.740 The side length of each square on the grid is one unit. 00:00:11.740 --> 00:00:14.270 So each of these is one unit. 00:00:14.270 --> 00:00:16.000 Which of the following sequences 00:00:16.000 --> 00:00:21.000 of transformations maps triangle PQR onto triangle ABC? 00:00:23.420 --> 00:00:27.720 So we have four different sequences of transformations. 00:00:27.720 --> 00:00:30.490 And so why don't you pause this video and figure out 00:00:30.490 --> 00:00:34.720 which of these actually does map triangle PQR, 00:00:34.720 --> 00:00:38.150 so this is PQR, onto ABC. 00:00:38.150 --> 00:00:40.340 And it could be more than one of these. 00:00:40.340 --> 00:00:43.210 So pause this video and have a go at that. 00:00:43.210 --> 00:00:45.200 All right, now let's do this together. 00:00:45.200 --> 00:00:47.730 So let's first think about sequence A. 00:00:47.730 --> 00:00:50.600 And I will do sequence A in this purple color. 00:00:50.600 --> 00:00:53.120 So remember, we're starting with triangle PQR. 00:00:53.120 --> 00:00:57.620 So first it says a rotation 90 degrees about the point R. 00:00:59.860 --> 00:01:02.850 So let's do that and then we'll do the rest of this sequence 00:01:02.850 --> 00:01:05.780 So if we rotate this 90 degrees, 00:01:05.780 --> 00:01:07.680 so one way to think about it is 00:01:07.680 --> 00:01:12.100 a line like that is then going to be like that. 00:01:12.100 --> 00:01:13.500 So we're gonna go like that. 00:01:14.358 --> 00:01:16.960 And so R is going to stay where it is. 00:01:16.960 --> 00:01:20.910 You're rotating about it, but P is now going 00:01:20.910 --> 00:01:23.400 to be right over here. 00:01:23.400 --> 00:01:26.330 One way to think about it is to go from R to P, 00:01:26.330 --> 00:01:29.270 we went down one and three to the right. 00:01:29.270 --> 00:01:32.250 Now when you do the rotation, you're going to go 00:01:32.250 --> 00:01:34.980 to the right one and then up three. 00:01:34.980 --> 00:01:37.330 So P is going to be there and you could see that. 00:01:37.330 --> 00:01:39.380 That's the rotation. 00:01:39.380 --> 00:01:43.200 So that side will look like this. 00:01:43.200 --> 00:01:48.200 So that is P and then Q is going to go right over here. 00:01:52.080 --> 00:01:56.340 Once again also do a 90 degree rotation about R. 00:01:56.340 --> 00:02:00.490 And so after you do the 90 degree rotation PQR 00:02:00.490 --> 00:02:02.400 is going to look like this. 00:02:02.400 --> 00:02:04.350 So that is Q. 00:02:04.350 --> 00:02:05.460 So we've done that first part. 00:02:05.460 --> 00:02:10.460 Then a translation six units to the left and seven units up. 00:02:11.560 --> 00:02:14.890 So each of these points are gonna go six units 00:02:14.890 --> 00:02:16.620 to the left and seven up. 00:02:16.620 --> 00:02:20.670 So if we take point P, six to the left one, two, 00:02:20.670 --> 00:02:22.540 three, four, five, six. 00:02:22.540 --> 00:02:27.540 Seven units up one, two, three, four, five, six, seven. 00:02:27.880 --> 00:02:29.640 It'll put it right over there. 00:02:29.640 --> 00:02:31.520 So that is point P. 00:02:31.520 --> 00:02:34.600 If we take point R, we take six units to the left. 00:02:34.600 --> 00:02:38.310 One, two, three, four, five, six. 00:02:38.310 --> 00:02:43.310 Seven up, one, two, three, four, five, six, seven 00:02:43.540 --> 00:02:47.470 it gets us right over there and then point Q. 00:02:47.470 --> 00:02:50.670 If we go six units to the left one, two, 00:02:50.670 --> 00:02:52.880 three, four, five, six. 00:02:52.880 --> 00:02:57.880 Seven up is one, two, three, four, five, six, seven 00:02:58.170 --> 00:03:00.660 puts us right over there. 00:03:00.660 --> 00:03:02.430 So this looks like it worked. 00:03:02.430 --> 00:03:04.790 Sequence A is good. 00:03:04.790 --> 00:03:08.917 It maps PQR on to ABC. 00:03:10.430 --> 00:03:13.830 This last one isn't an R this is a Q right over here. 00:03:13.830 --> 00:03:16.840 So that worked, sequence A. 00:03:16.840 --> 00:03:20.370 Now let's work on sequence B on this in different color. 00:03:20.370 --> 00:03:24.870 A translation eight units to the left and three up. 00:03:24.870 --> 00:03:26.080 So let's do that first. 00:03:26.080 --> 00:03:29.810 So if we take point Q, eight to the left and three up. 00:03:29.810 --> 00:03:34.740 One, two, three, four, five, six, seven, eight. 00:03:34.740 --> 00:03:38.120 Three up, one, two, three. 00:03:38.120 --> 00:03:41.010 So this will be my red Q for now 00:03:41.010 --> 00:03:43.630 and now if I do this point R. 00:03:43.630 --> 00:03:48.630 One, two, three, four, five, six, seven, eight. 00:03:48.920 --> 00:03:50.875 Let me make sure I do that right. 00:03:50.875 --> 00:03:53.460 One, two, three, four, five, six, seven, eight. 00:03:53.460 --> 00:03:55.536 Three up, one, two, three. 00:03:55.536 --> 00:03:58.750 So my new R is going to be there 00:03:58.750 --> 00:04:03.500 and then last but not least point P, eight to the left, 00:04:03.500 --> 00:04:07.420 One, two, three, four, five, six, seven, eight. 00:04:07.420 --> 00:04:09.960 Three up, one, two, three. 00:04:09.960 --> 00:04:11.160 Goes right there. 00:04:11.160 --> 00:04:16.160 So just that translation will get us to this point. 00:04:19.270 --> 00:04:20.700 It'll get us to that point. 00:04:20.700 --> 00:04:22.290 So we're clearly not done mapping yet, 00:04:22.290 --> 00:04:26.110 but there's more transformation to be done. 00:04:26.110 --> 00:04:27.650 So it looks something like that. 00:04:27.650 --> 00:04:29.330 It says then a reflection 00:04:29.330 --> 00:04:33.600 over the horizontal line through point A. 00:04:33.600 --> 00:04:36.630 So point A is right over here. 00:04:36.630 --> 00:04:40.100 The horizontal line is right like that. 00:04:40.100 --> 00:04:42.320 So if I were to reflect, point A wouldn't change. 00:04:42.320 --> 00:04:45.510 Point R right now is three below that horizontal line. 00:04:45.510 --> 00:04:48.120 Point R will then be three above that horizontal line, 00:04:48.120 --> 00:04:52.370 so point R will then go right over there. 00:04:52.370 --> 00:04:55.430 Just from that, I can see that this sequence 00:04:55.430 --> 00:04:57.410 of transformations is not going to work. 00:04:57.410 --> 00:04:59.550 It's putting R in the wrong place. 00:04:59.550 --> 00:05:03.240 So I'm going to rule out sequence B. 00:05:03.240 --> 00:05:07.760 Sequence C, let me do that with another color. 00:05:07.760 --> 00:05:10.530 I don't know I will do it with this orange color. 00:05:10.530 --> 00:05:15.530 A reflection over the vertical point through point Q, 00:05:15.870 --> 00:05:19.310 sorry, a reflection over the vertical line through point Q. 00:05:19.310 --> 00:05:20.220 So let me do that. 00:05:20.220 --> 00:05:23.840 So the vertical line through point Q looks like this. 00:05:23.840 --> 00:05:25.800 You can draw that vertical line. 00:05:25.800 --> 00:05:28.460 So if you reflect it Q is going to be, 00:05:28.460 --> 00:05:29.930 it's going to stay in place. 00:05:29.930 --> 00:05:31.950 R is one to the right of that, 00:05:31.950 --> 00:05:33.850 so now it's going to be one to the left once 00:05:33.850 --> 00:05:34.970 you do the reflection. 00:05:34.970 --> 00:05:38.030 And point P is four to the right 00:05:38.030 --> 00:05:39.160 so that's gonna be for the left. 00:05:39.160 --> 00:05:41.050 One, two, three, four. 00:05:41.050 --> 00:05:44.090 So P is going to be there after the reflection. 00:05:44.090 --> 00:05:47.290 And so it's going to look something like this 00:05:47.290 --> 00:05:49.220 after that first transformation, 00:05:49.220 --> 00:05:51.600 unless it's getting a little bit messy. 00:05:51.600 --> 00:05:54.300 But this is what you probably have to go through as well. 00:05:54.300 --> 00:05:56.240 So I'll go through it with you. 00:05:56.240 --> 00:05:58.270 All right, so we did that first part the reflection, 00:05:58.270 --> 00:06:02.070 then a translation for to the left and seven units up. 00:06:02.070 --> 00:06:04.280 So four to the left and seven up. 00:06:04.280 --> 00:06:05.930 So let me try that. 00:06:05.930 --> 00:06:07.010 So four to the left, 00:06:07.010 --> 00:06:09.470 one, two, three, four, seven up. 00:06:09.470 --> 00:06:14.170 One, two, three, four, five, six, seven. 00:06:14.170 --> 00:06:17.170 So it's putting Q right over here. 00:06:17.170 --> 00:06:19.870 I'm already suspicious of it because sequence A worked 00:06:19.870 --> 00:06:21.700 where we put P right over there. 00:06:21.700 --> 00:06:24.400 So I'm already suspicious of this but let's keep trying. 00:06:24.400 --> 00:06:27.070 So four to the left and seven up. 00:06:27.070 --> 00:06:28.900 One, two, three, four. 00:06:28.900 --> 00:06:33.630 Seven up One, two, three, four, five, six, seven. 00:06:33.630 --> 00:06:37.630 So R is going to the same place that sequence A put it 00:06:37.630 --> 00:06:41.950 and then point P one, two, three, four. 00:06:41.950 --> 00:06:45.780 One, two, three, four, five, six, seven. 00:06:45.780 --> 00:06:47.323 Actually it worked. 00:06:49.007 --> 00:06:53.540 And it works because this is actually an isosceles triangle. 00:06:53.540 --> 00:06:55.240 So this one actually worked out. 00:06:55.240 --> 00:06:59.830 We were able to map a PQR onto ABC with sequence C. 00:06:59.830 --> 00:07:03.260 So I like I like this one as well 00:07:03.260 --> 00:07:06.740 and then last but not least, let's try sequence D. 00:07:06.740 --> 00:07:09.290 I'll do that in black so that we can see it. 00:07:09.290 --> 00:07:11.260 So first we do a translation eight units 00:07:11.260 --> 00:07:12.853 to the left and three up. 00:07:13.715 --> 00:07:15.610 So we start here. 00:07:15.610 --> 00:07:19.380 One, two, three, four, five, six, seven, eight, 00:07:19.380 --> 00:07:21.674 three up, one, two, three. 00:07:21.674 --> 00:07:25.580 So I'll put my black Q right over there. 00:07:25.580 --> 00:07:29.960 So eight to the left One, two, three, four, 00:07:29.960 --> 00:07:31.860 five, six, seven, eight. 00:07:31.860 --> 00:07:34.390 Three up, one, two, three. 00:07:34.390 --> 00:07:37.140 I'll put my black R right over there. 00:07:37.140 --> 00:07:37.973 That's actually exactly 00:07:37.973 --> 00:07:40.090 what we did in sequence B the first time. 00:07:40.090 --> 00:07:42.980 So P is going to show up right over there. 00:07:42.980 --> 00:07:45.680 So after that translation sequence... 00:07:45.680 --> 00:07:49.630 First translation in sequence D it gets us right over there 00:07:49.630 --> 00:07:54.630 Then it says a rotation negative 270 degrees about point A. 00:07:56.370 --> 00:07:58.800 So this is point A right over here 00:07:58.800 --> 00:08:02.260 and negative 270 degrees. 00:08:02.260 --> 00:08:05.020 It's negative, so it's going to go clockwise 00:08:05.020 --> 00:08:06.970 and I'll see 180 degrees. 00:08:06.970 --> 00:08:09.810 Let's say if we were to take this line right over here 00:08:09.810 --> 00:08:11.910 if we were to go 180 degrees, 00:08:11.910 --> 00:08:16.850 it would go to this line like that 00:08:16.850 --> 00:08:19.003 and then if we go to another 90 degrees, 00:08:20.074 --> 00:08:24.670 it actually does look like it would map on to that. 00:08:24.670 --> 00:08:27.500 So this is actually looking pretty good. 00:08:27.500 --> 00:08:29.930 If you were to this line right over here 00:08:29.930 --> 00:08:32.680 well then if you go negative 270 degrees, 00:08:32.680 --> 00:08:37.200 we'll map on to this right over here 00:08:37.200 --> 00:08:40.260 and then that point R will kind of go along for the ride. 00:08:40.260 --> 00:08:41.939 It is one way to think about it 00:08:41.939 --> 00:08:43.130 and so it'll go right over there as well. 00:08:43.130 --> 00:08:45.840 So I'm actually liking sequence D as well. 00:08:45.840 --> 00:08:49.193 So all of these work except for sequence B.

The Court in Action

https://www.youtube.com/watch?v=Y0jFVNCVqsg

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en

WEBVTT Kind: captions Language: en 00:00:00.280 --> 00:00:02.910 - [Instructor] Of the three branches of the U.S. Government, 00:00:02.910 --> 00:00:04.730 the Judicial branch is the one 00:00:04.730 --> 00:00:08.390 that is least bound by public opinion. 00:00:08.390 --> 00:00:11.800 Supreme Court Justices aren't elected, they're appointed, 00:00:11.800 --> 00:00:15.280 and they serve for life or until they decide to retire. 00:00:15.280 --> 00:00:18.300 Usually a Justices serve on the court for many years 00:00:18.300 --> 00:00:20.590 after the end of the term of the President 00:00:20.590 --> 00:00:21.560 who appointed them. 00:00:21.560 --> 00:00:24.060 One Justice, William O. Douglas, 00:00:24.060 --> 00:00:28.690 was appointed by Franklin Delano Roosevelt in 1939 00:00:28.690 --> 00:00:33.560 and didn't retire until 1975 when Gerald Ford was President. 00:00:33.560 --> 00:00:35.460 Can you imagine how much changed 00:00:35.460 --> 00:00:37.470 during his tenure on the court? 00:00:37.470 --> 00:00:39.240 The framers designed things this way 00:00:39.240 --> 00:00:42.900 so that the Supreme Court Justices can be independent 00:00:42.900 --> 00:00:46.670 consulting the Constitution and precedent to decide 00:00:46.670 --> 00:00:50.020 whether laws an executive actions are permissible 00:00:50.020 --> 00:00:52.060 without having to worry about keeping 00:00:52.060 --> 00:00:54.240 the public happy to get reelected, 00:00:54.240 --> 00:00:56.850 but this also means that it's not unusual 00:00:56.850 --> 00:01:00.430 that the Supreme Court makes decisions that the public, 00:01:00.430 --> 00:01:04.280 the President or members of Congress don't like. 00:01:04.280 --> 00:01:08.820 Brown versus Board of Education in 1954 is a good example. 00:01:08.820 --> 00:01:12.190 White southerners resisted the ruling refusing 00:01:12.190 --> 00:01:15.000 to integrate segregated public schools. 00:01:15.000 --> 00:01:18.530 Although it wasn't popular with the majority population 00:01:18.530 --> 00:01:20.860 of the states that it most affected, 00:01:20.860 --> 00:01:24.680 the ruling protecting minority rights in Brown versus Board 00:01:24.680 --> 00:01:28.650 was made possible by the independence of the Judiciary. 00:01:28.650 --> 00:01:30.250 In that case, the Supreme Court 00:01:30.250 --> 00:01:33.080 had the backing of Presidents Dwight Eisenhower 00:01:33.080 --> 00:01:35.700 and John F. Kennedy who sent Federal troops 00:01:35.700 --> 00:01:38.490 into the south to enforce the ruling. 00:01:38.490 --> 00:01:40.450 Even though the court is independent, 00:01:40.450 --> 00:01:42.610 it's still important that it maintains 00:01:42.610 --> 00:01:45.530 it's legitimacy in the eyes of the public, 00:01:45.530 --> 00:01:48.760 so that citizens believe that the court is impartial 00:01:48.760 --> 00:01:52.580 and that it's possible to challenge the other branches 00:01:52.580 --> 00:01:54.510 through the actions of the court. 00:01:54.510 --> 00:01:56.610 To maintain it's legitimacy, 00:01:56.610 --> 00:01:58.670 Justices on the court are careful 00:01:58.670 --> 00:02:02.980 not to give the appearance of favoring one political party 00:02:02.980 --> 00:02:05.240 over another by ruling too often 00:02:05.240 --> 00:02:08.510 for or against one parties policies. 00:02:08.510 --> 00:02:10.900 But what happens when the President 00:02:10.900 --> 00:02:14.660 or Congress doesn't support the Supreme Court's rulings? 00:02:14.660 --> 00:02:18.430 What measures can they take to affect the court's decisions? 00:02:18.430 --> 00:02:19.450 There are three main ways 00:02:19.450 --> 00:02:21.340 that we'll talk about in this video. 00:02:21.340 --> 00:02:23.480 Future appointments to the court, 00:02:23.480 --> 00:02:25.630 changing the court's jurisdiction 00:02:25.630 --> 00:02:29.170 and refusing to implement the court's decisions. 00:02:29.170 --> 00:02:32.010 One of the ways that Presidents can influence the court 00:02:32.010 --> 00:02:34.280 is by appointing Justices. 00:02:34.280 --> 00:02:37.300 Presidents tend to nominate Supreme Court Justices 00:02:37.300 --> 00:02:40.060 who share their interpretation of the Constitution, 00:02:40.060 --> 00:02:41.700 so their appointments change 00:02:41.700 --> 00:02:44.320 the ideological composition of the court. 00:02:44.320 --> 00:02:47.980 For example, President Richard Nixon appointed four Justices 00:02:47.980 --> 00:02:49.790 to the Supreme Court that altered 00:02:49.790 --> 00:02:51.680 the court's ideological leaning. 00:02:51.680 --> 00:02:54.510 He ushered in a transition from a liberal court 00:02:54.510 --> 00:02:58.900 under Chief Justice Earl Warren to a more conservative court 00:02:58.900 --> 00:03:01.460 under Chief Justice Warren Burger. 00:03:01.460 --> 00:03:03.240 Congress can also influence the court 00:03:03.240 --> 00:03:05.530 by changing the number of Justices. 00:03:05.530 --> 00:03:06.890 But today, we accept that there are 00:03:06.890 --> 00:03:09.000 nine Justices on the Supreme Court, 00:03:09.000 --> 00:03:12.120 but Article III of the Constitution doesn't actually specify 00:03:12.120 --> 00:03:13.930 how many Justices are on the court. 00:03:13.930 --> 00:03:17.880 Over time, there have been as few as six and as many as 10. 00:03:17.880 --> 00:03:19.850 There have been nine since Congress passed 00:03:19.850 --> 00:03:22.330 the Judiciary Act of 1869, 00:03:22.330 --> 00:03:26.150 but Congress had actually eliminated seats in the 1860's. 00:03:26.150 --> 00:03:29.420 Then in the 1930's, Franklin Roosevelt proposed 00:03:29.420 --> 00:03:31.500 adding more court seats to the Supreme Court 00:03:31.500 --> 00:03:34.470 so that it's ideological balance would move in favor 00:03:34.470 --> 00:03:36.490 of his new deal legislation. 00:03:36.490 --> 00:03:39.710 So, although, the number of Justices on the court 00:03:39.710 --> 00:03:43.210 hasn't actually changed in 150 years, 00:03:43.210 --> 00:03:47.320 Congress does retain the power to adjust that number. 00:03:47.320 --> 00:03:50.410 Another way that Congress can influence the Supreme Court 00:03:50.410 --> 00:03:52.730 is by changing it's jurisdiction 00:03:52.730 --> 00:03:54.400 or the field of authority 00:03:54.400 --> 00:03:57.550 that it has to hear and decide cases. 00:03:57.550 --> 00:03:59.290 There are two places in the Constitution 00:03:59.290 --> 00:04:01.550 that say that Congress can do this. 00:04:01.550 --> 00:04:04.090 Article I, Section 8, which says 00:04:04.090 --> 00:04:08.220 that Congress has the power to constitute tribunals inferior 00:04:08.220 --> 00:04:09.640 to the Supreme Court, 00:04:09.640 --> 00:04:12.040 and Article III, Section 1, which says 00:04:12.040 --> 00:04:16.020 that judicial power shall be vested in the Supreme Court, 00:04:16.020 --> 00:04:18.760 and such inferior courts as the congress 00:04:18.760 --> 00:04:21.620 may from time to time ordain and establish. 00:04:21.620 --> 00:04:24.080 So Congress may add new Federal courts 00:04:24.080 --> 00:04:26.210 by splitting up an existing District 00:04:26.210 --> 00:04:29.610 or subtract them by combining Districts. 00:04:29.610 --> 00:04:32.170 Congress may also pass legislation 00:04:32.170 --> 00:04:34.330 stripping the Supreme Court's jurisdiction 00:04:34.330 --> 00:04:37.810 to hear certain types of cases on appeal. 00:04:37.810 --> 00:04:40.410 Some recent examples of Congress attempting 00:04:40.410 --> 00:04:43.660 to strip the Supreme Court of jurisdiction concern 00:04:43.660 --> 00:04:47.600 the detainees at Guantanamo Bay detention camp in Cuba. 00:04:47.600 --> 00:04:48.810 In the mid 2000's, 00:04:48.810 --> 00:04:52.050 the detainee's petitioned the Supreme Court to review 00:04:52.050 --> 00:04:54.060 whether their detention was legal, 00:04:54.060 --> 00:04:57.520 and Congress passed two laws stripping detainees 00:04:57.520 --> 00:05:00.220 of the right to petition courts for review. 00:05:00.220 --> 00:05:03.270 The Supreme Court overturned both of those laws. 00:05:03.270 --> 00:05:06.350 The last way that the other branches can push back 00:05:06.350 --> 00:05:10.230 against a court decision is by refusing to implement it 00:05:10.230 --> 00:05:13.560 or by doing as little as possible to implement it. 00:05:13.560 --> 00:05:17.060 Remember, the court itself has no enforcement power. 00:05:17.060 --> 00:05:19.750 It has to rely on the executive branch 00:05:19.750 --> 00:05:21.610 to enforce it's rulings. 00:05:21.610 --> 00:05:24.130 So what happens when the President disagrees 00:05:24.130 --> 00:05:25.320 with the ruling? 00:05:25.320 --> 00:05:27.750 In most cases, Presidents enforce 00:05:27.750 --> 00:05:30.510 the Supreme Court's rulings whether they like them or not 00:05:30.510 --> 00:05:33.370 seeing it as part of their duty to uphold the government. 00:05:33.370 --> 00:05:34.700 But in rare cases, 00:05:34.700 --> 00:05:37.960 a President might choose not to enforce a court ruling, 00:05:37.960 --> 00:05:40.710 especially if their party controls Congress. 00:05:40.710 --> 00:05:43.060 An early example of this was in 1808 00:05:43.060 --> 00:05:46.910 when the Supreme Court ruled Thomas Jefferson's Embargo Act, 00:05:46.910 --> 00:05:49.230 the one with the famous, Oh Grab Me cartoon, 00:05:49.230 --> 00:05:50.800 was unconstitutional. 00:05:50.800 --> 00:05:53.100 Jefferson instructed customs agents 00:05:53.100 --> 00:05:56.410 to keep on enforcing the Embargo and they did. 00:05:56.410 --> 00:05:59.280 So the important takeaway here is that even though 00:05:59.280 --> 00:06:02.320 the Supreme Court determines the law of the land, 00:06:02.320 --> 00:06:05.640 the system of checks and balances still applies to it. 00:06:05.640 --> 00:06:08.190 Congress and the President have several ways 00:06:08.190 --> 00:06:11.353 to influence the court's power, present and future.

Help Jason Give Back to Khan Academy

https://www.youtube.com/watch?v=Na67UzhSYMg

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https://www.youtube.com/api/timedtext?v=Na67UzhSYMg&ei=bViUZfPnGe-sxN8P28aG6AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=76CF01756D95D3665D7D5E492AF5F490A8EB7CE3.77813B4294DE55E4BF38B6944DA271F27910B07E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:01.450 --> 00:00:04.080 - My name is Jason Spyres, and at the age of 19, 00:00:04.080 --> 00:00:06.500 I made a stupid decision to sell cannabis 00:00:06.500 --> 00:00:08.420 and ended up in prison. 00:00:08.420 --> 00:00:11.560 Fortunately, my mother sent me Khan Academy transcripts 00:00:11.560 --> 00:00:13.800 to start improving my education. 00:00:13.800 --> 00:00:16.240 And while I was doing that, other inmates noticed 00:00:16.240 --> 00:00:19.530 and would come up to me and ask if I could help them. 00:00:19.530 --> 00:00:21.117 When I'd ask them, "Why don't you try to get 00:00:21.117 --> 00:00:22.560 "in the GED classes?" 00:00:22.560 --> 00:00:25.120 Some of the waiting lists was too long. 00:00:25.120 --> 00:00:27.960 Others, I realize, what it is is, 00:00:27.960 --> 00:00:30.990 it's hard to admit you don't know something, 00:00:30.990 --> 00:00:33.420 and it's embarrassing when you're a full-grown man 00:00:33.420 --> 00:00:34.600 to say that you don't know 00:00:34.600 --> 00:00:37.500 that there's three different ways to spell the word there. 00:00:38.570 --> 00:00:39.573 So I'd help them. 00:00:40.470 --> 00:00:43.970 And when I got out, I used Khan Academy's SAT program 00:00:43.970 --> 00:00:45.270 to prepare myself, 00:00:45.270 --> 00:00:47.623 and I ended up getting a 1440 on the SATs. 00:00:48.870 --> 00:00:51.150 And after that, I applied and was accepted 00:00:51.150 --> 00:00:53.423 into Stanford University. 00:00:55.710 --> 00:00:57.160 I'm making this video today 00:00:57.160 --> 00:01:00.300 'cause I wanna tell you that when you support Khan Academy, 00:01:00.300 --> 00:01:02.550 you're not only supporting people like me 00:01:02.550 --> 00:01:05.330 and helping me get to places like Stanford. 00:01:05.330 --> 00:01:08.180 You're supporting a mission that strips away 00:01:08.180 --> 00:01:11.270 the embarrassment factor of having to admit 00:01:11.270 --> 00:01:12.500 you don't know something 00:01:12.500 --> 00:01:14.950 because you wanna learn something. 00:01:14.950 --> 00:01:17.620 The best teacher can only help the student 00:01:17.620 --> 00:01:20.140 if they'll walk into the classroom, 00:01:20.140 --> 00:01:21.630 and what Khan Academy does 00:01:21.630 --> 00:01:25.000 is they put a classroom in everybody's home 00:01:25.000 --> 00:01:27.800 on their time, on their schedule 00:01:27.800 --> 00:01:30.890 without any embarrassment. 00:01:30.890 --> 00:01:32.820 So I hope you will continue to support 00:01:32.820 --> 00:01:34.820 Khan Academy's mission, 00:01:34.820 --> 00:01:37.200 and I hope to continue to support the mission 00:01:37.200 --> 00:01:39.400 of increasing a world-class education 00:01:39.400 --> 00:01:41.463 for everybody everywhere.

Formal charge

https://www.youtube.com/watch?v=Kv5y3t9jsi4

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https://www.youtube.com/api/timedtext?v=Kv5y3t9jsi4&ei=bViUZZCIGrSCp-oP0KebuAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=27FB79E6A24643B54411F160C0405E063CFA13BB.6385BFD4EBA5DF1DE59BB6D8AA66E57B7465FEBB&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.150 --> 00:00:01.290 - [Instructor] In this video, we're going 00:00:01.290 --> 00:00:06.050 to introduce ourselves to the idea of formal charge, 00:00:06.050 --> 00:00:09.220 and as we will see, it is a tool that we can use 00:00:09.220 --> 00:00:12.890 as chemists to analyze molecules. 00:00:12.890 --> 00:00:15.780 It is not the charge on the molecule as a whole, 00:00:15.780 --> 00:00:17.640 it's actually a number that we can calculate 00:00:17.640 --> 00:00:21.060 for each of the individual atoms in a molecule, 00:00:21.060 --> 00:00:22.610 and as we'll see in future videos, 00:00:22.610 --> 00:00:25.670 it'll help us think about which resonance structures, 00:00:25.670 --> 00:00:29.480 which configurations of a molecule will contribute most 00:00:29.480 --> 00:00:31.520 to a resonance hybrid. 00:00:31.520 --> 00:00:33.610 So before going too deep into that, 00:00:33.610 --> 00:00:36.740 let's just give ourselves a definition for formal charge, 00:00:36.740 --> 00:00:38.660 and then as practice, we're going to calculate 00:00:38.660 --> 00:00:41.090 the formal charge on the various atoms 00:00:41.090 --> 00:00:45.500 in each of these resonance structures for nitrous acid. 00:00:45.500 --> 00:00:47.630 These are both legitimate Lewis diagrams. 00:00:47.630 --> 00:00:49.900 They're both legitimate resonance structures 00:00:49.900 --> 00:00:52.040 for nitrous acid, but we'll think about 00:00:52.040 --> 00:00:54.630 which one contributes more to the resonance hybrid 00:00:54.630 --> 00:00:57.220 based on formal charge. 00:00:57.220 --> 00:00:59.500 So the definition of formal charge, 00:00:59.500 --> 00:01:02.430 and we're going to do this for each atom in our molecule, 00:01:02.430 --> 00:01:06.250 for each atom, we're going to calculate the number 00:01:06.250 --> 00:01:10.470 of valence electrons in free, 00:01:10.470 --> 00:01:13.000 in free neutral, 00:01:13.000 --> 00:01:14.423 neutral atom, 00:01:15.290 --> 00:01:16.780 atom. 00:01:16.780 --> 00:01:21.610 From that, we are going to subtract the number 00:01:21.610 --> 00:01:25.890 of valence electrons allocated, 00:01:25.890 --> 00:01:28.993 allocated to bonded, 00:01:30.050 --> 00:01:31.690 bonded atom. 00:01:31.690 --> 00:01:33.170 And so you're next question is, 00:01:33.170 --> 00:01:36.230 what does is mean to be allocated? 00:01:36.230 --> 00:01:39.430 Well, I will break up this definition a little bit. 00:01:39.430 --> 00:01:41.130 So if we want to think about the valence electrons 00:01:41.130 --> 00:01:44.480 that are allocated to a bonded atom, 00:01:44.480 --> 00:01:49.470 these are going to be the number of lone pair electrons, 00:01:49.470 --> 00:01:53.543 number of lone pair electrons 00:01:56.290 --> 00:02:01.290 plus one half of the number of shared electrons. 00:02:03.780 --> 00:02:05.240 So lets try and make sense of this 00:02:05.240 --> 00:02:07.940 by applying this definition of formal charge 00:02:07.940 --> 00:02:10.680 to the constituents of nitrous acid. 00:02:10.680 --> 00:02:14.290 So let's start with this hydrogen over here. 00:02:14.290 --> 00:02:16.330 So what's the number of valence electrons 00:02:16.330 --> 00:02:18.720 in a free, neutral atom of hydrogen? 00:02:18.720 --> 00:02:20.080 Well we've seen this multiple times, 00:02:20.080 --> 00:02:22.540 you could look at this on the periodic table of elements, 00:02:22.540 --> 00:02:25.380 free neutral hydrogen has one valence electron. 00:02:25.380 --> 00:02:27.640 Now how many valence electrons 00:02:27.640 --> 00:02:30.400 are allocated to the bonded atom? 00:02:30.400 --> 00:02:31.680 Well one way to think about it is, 00:02:31.680 --> 00:02:36.390 draw a circle around that atom in the molecule, 00:02:36.390 --> 00:02:38.530 and you want to capture all of the lone pairs, 00:02:38.530 --> 00:02:40.000 and you want to capture, you can think of it 00:02:40.000 --> 00:02:42.990 as half the bond, you could say for each bond, 00:02:42.990 --> 00:02:44.670 it's going to be one electron 00:02:44.670 --> 00:02:46.510 'cause it's half of the shared electrons, 00:02:46.510 --> 00:02:49.100 each bond is two shared electrons, 00:02:49.100 --> 00:02:50.430 but you're gonna say half of those, 00:02:50.430 --> 00:02:52.800 and then you have no lone pairs over here, 00:02:52.800 --> 00:02:56.000 so the number of valence electrons allocated to bonded atom, 00:02:56.000 --> 00:02:58.420 in the case of hydrogen here, is one, 00:02:58.420 --> 00:03:01.170 and so we are dealing with a formal charge 00:03:01.170 --> 00:03:03.910 of zero for this hydrogen. 00:03:03.910 --> 00:03:05.580 Now what about this oxygen here? 00:03:05.580 --> 00:03:07.300 Well we do the same exercise, 00:03:07.300 --> 00:03:11.070 I like to draw a little bit of a circle around it. 00:03:11.070 --> 00:03:12.970 And so the number of valence electrons 00:03:12.970 --> 00:03:15.750 in a free, neutral oxygen we've seen multiple times, 00:03:15.750 --> 00:03:18.320 that is six, and then from that, 00:03:18.320 --> 00:03:21.000 we're going to subtract the number of valence electrons 00:03:21.000 --> 00:03:22.880 allocated to the bonded atom. 00:03:22.880 --> 00:03:26.350 So the bonded atom has two lone pair electrons, 00:03:26.350 --> 00:03:28.520 and then it gets half of the shared electrons, 00:03:28.520 --> 00:03:30.810 so half of the shared electrons would be one from this bond, 00:03:30.810 --> 00:03:33.030 one from that bond, and one from that bond. 00:03:33.030 --> 00:03:35.940 So you add them all together, two, three, four, five. 00:03:35.940 --> 00:03:40.940 So six minus five is equal to positive one, 00:03:41.150 --> 00:03:44.000 and so the formal charge on this oxygen atom, 00:03:44.000 --> 00:03:48.590 in this configuration of nitrous acid is positive one. 00:03:48.590 --> 00:03:50.010 Now what about the nitrogen? 00:03:50.010 --> 00:03:52.710 Well we'll do a similar exercise there. 00:03:52.710 --> 00:03:56.260 A free neutral nitrogen has five valence electrons, 00:03:56.260 --> 00:03:57.450 we've seen that multiple times, 00:03:57.450 --> 00:03:59.540 you can look at that from the periodic table of elements, 00:03:59.540 --> 00:04:02.200 and then from that, we're going to subtract 00:04:02.200 --> 00:04:03.470 the number of valence electrons 00:04:03.470 --> 00:04:06.340 allocated to the bonded to nitrogen, 00:04:06.340 --> 00:04:09.930 well we see one, two, three, 00:04:09.930 --> 00:04:14.030 and then two more lone pair electrons, so that is five, 00:04:14.030 --> 00:04:16.870 and so you have zero formal charge there. 00:04:16.870 --> 00:04:19.460 And then let's look at this last oxygen. 00:04:19.460 --> 00:04:22.550 So this last oxygen, a free neutral oxygen 00:04:22.550 --> 00:04:24.600 has six valence electrons, 00:04:24.600 --> 00:04:27.140 from that, we're going to subtract the number 00:04:27.140 --> 00:04:29.610 of valence electrons allocated to the bonded atom, 00:04:29.610 --> 00:04:33.440 so two, four, six lone pair electrons, 00:04:33.440 --> 00:04:36.650 plus half of this bond, so that's seven 00:04:36.650 --> 00:04:38.330 allocated valence electrons, 00:04:38.330 --> 00:04:43.170 six minus seven equals negative one. 00:04:43.170 --> 00:04:46.926 So this oxygen has a formal charge of negative one, 00:04:46.926 --> 00:04:48.940 and I really want to remind you, 00:04:48.940 --> 00:04:51.800 we're not talking about the charge of the entire molecule, 00:04:51.800 --> 00:04:54.730 formal charge is really a mathematical tool 00:04:54.730 --> 00:04:58.210 we use to analyze this configuration, 00:04:58.210 --> 00:05:01.200 but one way you can kind of conceptualize it is, 00:05:01.200 --> 00:05:04.460 in this configuration, this oxygen on average 00:05:04.460 --> 00:05:06.900 has one more electron hanging around it, 00:05:06.900 --> 00:05:09.110 one more valence electron hanging around it 00:05:09.110 --> 00:05:11.010 than a free neutral oxygen would. 00:05:11.010 --> 00:05:15.060 This oxygen has one less valence electron hanging around it 00:05:15.060 --> 00:05:18.300 than a neutral free oxygen would. 00:05:18.300 --> 00:05:20.860 Now let's look at this configuration down here, 00:05:20.860 --> 00:05:23.080 well this hydrogen is identical to this hydrogen, 00:05:23.080 --> 00:05:24.910 it has no lone pair electrons 00:05:24.910 --> 00:05:27.670 and it just has one covalent bond to an oxygen, 00:05:27.670 --> 00:05:29.550 so we would do the same analysis 00:05:29.550 --> 00:05:32.630 to get that its formal charge is a zero, 00:05:32.630 --> 00:05:35.870 but now let's think about this oxygen right over here. 00:05:35.870 --> 00:05:39.940 A free neutral oxygen has six valence electrons, 00:05:39.940 --> 00:05:41.920 the number of valence electrons allocated to this one 00:05:41.920 --> 00:05:46.500 is two, four, five, and six, 00:05:46.500 --> 00:05:50.220 so six minus six is zero, no formal charge, 00:05:50.220 --> 00:05:52.150 and we go to this nitrogen. 00:05:52.150 --> 00:05:56.010 Free nitrogen has five valence electrons, 00:05:56.010 --> 00:06:00.600 this nitrogen has two, three, four, 00:06:00.600 --> 00:06:03.690 five valence electrons allocated to it, 00:06:03.690 --> 00:06:06.520 so minus five, it has zero formal charge. 00:06:06.520 --> 00:06:09.800 And then last but not least, this oxygen right over here. 00:06:09.800 --> 00:06:12.900 A free neutral oxygen has six valence electrons, 00:06:12.900 --> 00:06:17.900 this one has two, four, five, six valence electrons 00:06:18.800 --> 00:06:21.240 allocated to the bonded atom, 00:06:21.240 --> 00:06:23.650 and so minus six is equal to zero. 00:06:23.650 --> 00:06:26.410 And so what we see is this first configuration, 00:06:26.410 --> 00:06:28.090 or you could say this first resonance structure 00:06:28.090 --> 00:06:30.720 for nitrous acid had some formal charge, 00:06:30.720 --> 00:06:32.210 it had a plus one on this oxygen 00:06:32.210 --> 00:06:33.710 and minus one on this oxygen, 00:06:33.710 --> 00:06:36.330 while the one down here had no formal charge, 00:06:36.330 --> 00:06:39.250 everything had a formal charge of zero, 00:06:39.250 --> 00:06:41.370 and as we'll see in future videos, 00:06:41.370 --> 00:06:46.060 the closer the individual atom formal charges are to zero, 00:06:46.060 --> 00:06:48.270 the more likely that that structure, 00:06:48.270 --> 00:06:49.550 that resonance structure, 00:06:49.550 --> 00:06:52.960 will contribute more to the resonance hybrid, 00:06:52.960 --> 00:06:55.420 but we'll talk about that more in future videos, 00:06:55.420 --> 00:06:56.380 the whole pint of this one 00:06:56.380 --> 00:06:59.420 is just to get comfortable calculating formal charge 00:06:59.420 --> 00:07:02.063 for the individual atoms in a molecule.

Millions Learn for Free, Made Possible by People Like You

https://www.youtube.com/watch?v=UfMnag3FOaE

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https://www.youtube.com/api/timedtext?v=UfMnag3FOaE&ei=bViUZczHHv-Lp-oP2YWTKA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7F2996D6B33CF3627B22230C615AB67334751F58.D26A27E262B277CA8597CD47C39DF4C65441F39F&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.063 --> 00:00:02.730 (upbeat music)

Resonance

https://www.youtube.com/watch?v=XRM9o1Sq5hg

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https://www.youtube.com/api/timedtext?v=XRM9o1Sq5hg&ei=bViUZc3kGfyip-oP8oCNyAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=074C6EA6D1E52E1C0F136D729CD66CED96124F6A.6651AF6C7C49E9C471B45361AE64F7B82F586303&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.610 --> 00:00:02.790 - [Instructor] Let's see if we can draw the Lewis diagram 00:00:02.790 --> 00:00:05.530 for a nitrate anion. 00:00:05.530 --> 00:00:10.530 So a nitrate anion has one nitrogen and three oxygens, 00:00:10.960 --> 00:00:14.030 and it has a negative charge. 00:00:14.030 --> 00:00:15.460 I'll do that in another color. 00:00:15.460 --> 00:00:16.470 It has a negative charge. 00:00:16.470 --> 00:00:18.550 So pause this video and see if you can draw that, 00:00:18.550 --> 00:00:21.033 the Lewis structure for a nitrate anion. 00:00:21.890 --> 00:00:24.020 All right, well we've done this many times. 00:00:24.020 --> 00:00:25.470 The first step is to just account 00:00:25.470 --> 00:00:27.230 for the valence electrons. 00:00:27.230 --> 00:00:31.890 Nitrogen has one, two, three, four, five valence electrons 00:00:31.890 --> 00:00:34.090 in its outer shell, and in that second shell, 00:00:34.090 --> 00:00:36.990 if it's a neutral, free nitrogen atom. 00:00:36.990 --> 00:00:39.710 So we have five valence electrons there. 00:00:39.710 --> 00:00:43.030 Oxygen has one, two, three, four, five, 00:00:43.030 --> 00:00:44.610 six valence electrons. 00:00:44.610 --> 00:00:45.670 But if you have three oxygens, 00:00:45.670 --> 00:00:47.860 you're going to have six times three. 00:00:47.860 --> 00:00:50.470 And so if you just add up the valence electrons, 00:00:50.470 --> 00:00:52.900 if these were free, neutral atoms, 00:00:52.900 --> 00:00:57.900 you would get five plus 18, which is 23 valence electrons. 00:00:59.010 --> 00:01:00.390 Now the next thing we have to keep 00:01:00.390 --> 00:01:02.250 in mind is this is an anion. 00:01:02.250 --> 00:01:05.190 This has a negative one charge right over here. 00:01:05.190 --> 00:01:08.430 So it's going to have one more extra electron, 00:01:08.430 --> 00:01:10.660 one more extra valence electron than you would expect 00:01:10.660 --> 00:01:12.920 if these were just free atoms that were neutral. 00:01:12.920 --> 00:01:16.600 So let's add one valance electron here. 00:01:16.600 --> 00:01:20.210 So that gets us to 24 valence electrons. 00:01:20.210 --> 00:01:21.640 And then the next step is let's try 00:01:21.640 --> 00:01:23.880 to actually draw this structure. 00:01:23.880 --> 00:01:25.610 And the way we do it is we try 00:01:25.610 --> 00:01:27.460 to pick the least electronegative atom 00:01:27.460 --> 00:01:29.960 that is not hydrogen to be the central atom. 00:01:29.960 --> 00:01:31.700 And in this case it is nitrogen. 00:01:31.700 --> 00:01:34.270 It's to the left of oxygen in that second period. 00:01:34.270 --> 00:01:37.930 So let's put nitrogen in the center, 00:01:37.930 --> 00:01:38.763 right over there. 00:01:38.763 --> 00:01:40.544 And around it let's put three oxygens. 00:01:40.544 --> 00:01:45.544 So one, two, three oxygens. 00:01:45.570 --> 00:01:48.890 Let's put a single bond between them. 00:01:48.890 --> 00:01:50.960 And so so far we, and let me do that 00:01:50.960 --> 00:01:53.150 in another color, so we can account for it better. 00:01:53.150 --> 00:01:54.860 So I'll do them in purple. 00:01:54.860 --> 00:01:56.970 So so far we have accounted for two, four, 00:01:56.970 --> 00:01:58.370 six valence electrons. 00:01:58.370 --> 00:02:01.780 So minus six valence electrons gets us 00:02:01.780 --> 00:02:04.510 to 18 valence electrons. 00:02:04.510 --> 00:02:07.020 The next step is we would try to allocate 00:02:07.020 --> 00:02:11.100 as many of these as possible to our terminal atoms, 00:02:11.100 --> 00:02:12.240 the oxygens over here. 00:02:12.240 --> 00:02:14.700 Try to get them to a full octet. 00:02:14.700 --> 00:02:15.753 So let's do that. 00:02:15.753 --> 00:02:17.670 This, each of these oxygens, 00:02:17.670 --> 00:02:19.170 they're already participating in one 00:02:19.170 --> 00:02:20.230 of these covalent bonds, 00:02:20.230 --> 00:02:23.090 so they already have two valence electrons hanging out. 00:02:23.090 --> 00:02:25.940 So let's see if we can give them each another six, 00:02:25.940 --> 00:02:26.840 to get to eight. 00:02:26.840 --> 00:02:30.583 So two, four, six. 00:02:31.660 --> 00:02:34.976 Two, four, six. 00:02:34.976 --> 00:02:39.520 And then two, four, and six. 00:02:39.520 --> 00:02:40.650 And so just like that 00:02:40.650 --> 00:02:43.550 we have allocated 18 valence electrons, 00:02:43.550 --> 00:02:45.120 six, 12, 18. 00:02:45.120 --> 00:02:48.390 So minus 18 valence electrons. 00:02:48.390 --> 00:02:52.830 And we are now left with no further valence electrons 00:02:52.830 --> 00:02:54.080 to allocate. 00:02:54.080 --> 00:02:56.220 But let's see how our atoms are doing. 00:02:56.220 --> 00:02:58.250 We know the oxygens have a full octet, 00:02:58.250 --> 00:03:00.680 but the nitrogen only has two, four, 00:03:00.680 --> 00:03:04.290 six valance electrons hanging around. 00:03:04.290 --> 00:03:06.580 It would be great if there was a Lewis structure 00:03:06.580 --> 00:03:09.010 where we could have eight valence electrons 00:03:09.010 --> 00:03:10.470 for that nitrogen. 00:03:10.470 --> 00:03:13.110 Well one way to do that is to take one 00:03:13.110 --> 00:03:15.650 of these lone pairs from one of the oxygens 00:03:15.650 --> 00:03:19.120 and turn that into another covalent bond. 00:03:19.120 --> 00:03:20.278 So let's do that. 00:03:20.278 --> 00:03:23.893 So let me just erase this pair right over here, 00:03:24.760 --> 00:03:26.030 and I'm just going to turn that 00:03:26.030 --> 00:03:28.460 into another covalent bond. 00:03:28.460 --> 00:03:30.814 And this is looking pretty good. 00:03:30.814 --> 00:03:32.800 We have eight valence electrons around each 00:03:32.800 --> 00:03:34.170 of the oxygens. 00:03:34.170 --> 00:03:35.840 And now we have eight for the nitrogen, 00:03:35.840 --> 00:03:37.180 two, four, six, eight. 00:03:37.180 --> 00:03:38.780 And we have to remind ourselves 00:03:38.780 --> 00:03:40.720 that this is an anion. 00:03:40.720 --> 00:03:42.580 It has a negative one charge. 00:03:42.580 --> 00:03:44.020 So to finish the Lewis diagram 00:03:44.020 --> 00:03:45.880 we would just put that negative charge there. 00:03:45.880 --> 00:03:48.200 And this is all well and good, 00:03:48.200 --> 00:03:51.590 but if this was the only way that nitrate existed 00:03:51.590 --> 00:03:55.040 when we observed nitrate anions in the world, 00:03:55.040 --> 00:03:58.060 we would expect to see one shorter bond 00:03:58.060 --> 00:04:01.010 and two longer bonds, and we would expect one 00:04:01.010 --> 00:04:02.400 of the bonds to have a different energy 00:04:02.400 --> 00:04:03.890 than the other two. 00:04:03.890 --> 00:04:06.200 But in the real world we don't see that. 00:04:06.200 --> 00:04:10.480 We see that all of the bonds actually have the same length, 00:04:10.480 --> 00:04:12.920 and they actually have the same energy. 00:04:12.920 --> 00:04:15.370 And so an interesting question is why is that? 00:04:15.370 --> 00:04:17.610 And one thing that you might appreciate is, 00:04:17.610 --> 00:04:19.230 when I took that lone pair 00:04:19.230 --> 00:04:20.460 to create this covalent bond, 00:04:20.460 --> 00:04:22.160 I could have done it with that top oxygen. 00:04:22.160 --> 00:04:24.400 I could have done it with this bottom-left oxygen. 00:04:24.400 --> 00:04:26.740 Or I could have done it with that bottom-right oxygen. 00:04:26.740 --> 00:04:30.490 And so there's actually three valid Lewis structures 00:04:30.490 --> 00:04:31.470 that we could have had. 00:04:31.470 --> 00:04:33.353 Not only could we have had this Lewis structure, 00:04:33.353 --> 00:04:35.360 we could have had this one, 00:04:35.360 --> 00:04:38.405 and I'll draw it all in yellow to save us some time, 00:04:38.405 --> 00:04:40.220 where you have this nitrogen. 00:04:40.220 --> 00:04:42.660 It has a single bond with that top oxygen. 00:04:42.660 --> 00:04:44.793 And so that top oxygen still has six electrons 00:04:44.793 --> 00:04:46.289 in lone pairs. 00:04:46.289 --> 00:04:48.130 And maybe it forms a double bond 00:04:48.130 --> 00:04:50.010 with the bottom-left oxygen. 00:04:50.010 --> 00:04:52.970 So this bottom-left oxygen only has two lone pairs. 00:04:52.970 --> 00:04:55.155 One of them would have gone to form the double bond. 00:04:55.155 --> 00:04:58.010 And then this oxygen would look the same. 00:04:58.010 --> 00:05:02.826 So what I am drawing here is another valid Lewis structure. 00:05:02.826 --> 00:05:04.819 Or the double bond might have formed 00:05:04.819 --> 00:05:06.500 with this bottom-right oxygen, 00:05:06.500 --> 00:05:09.740 so let me draw that. 00:05:09.740 --> 00:05:12.560 So another valid Lewis structure could look like this. 00:05:12.560 --> 00:05:17.560 So nitrogen bonded to that oxygen has three lone pairs. 00:05:18.160 --> 00:05:22.450 This oxygen also has three lone pairs. 00:05:22.450 --> 00:05:24.260 And now this one has the double bond 00:05:24.260 --> 00:05:27.200 and only has two lone pairs. 00:05:27.200 --> 00:05:28.690 And whenever we see a situation 00:05:28.690 --> 00:05:31.633 where we have three valid Lewis structures, 00:05:31.633 --> 00:05:34.690 we call this resonance. 00:05:34.690 --> 00:05:36.253 Resonance. 00:05:37.220 --> 00:05:38.350 Resonance. 00:05:38.350 --> 00:05:39.610 And we'll put an arrow, 00:05:39.610 --> 00:05:42.000 these two-way arrows between these structures. 00:05:42.000 --> 00:05:43.780 And when you hear the word resonance, 00:05:43.780 --> 00:05:45.460 it sometimes conjures up this image 00:05:45.460 --> 00:05:47.790 that you're bouncing back, you're resonating 00:05:47.790 --> 00:05:49.050 between these structures. 00:05:49.050 --> 00:05:50.760 But that's actually not right. 00:05:50.760 --> 00:05:52.690 What the right way to think about it is, 00:05:52.690 --> 00:05:55.540 these different ways of visualizing the nitrate, 00:05:55.540 --> 00:05:58.160 these contribute to a resonance hybrid, 00:05:58.160 --> 00:05:59.670 which is really the true way 00:05:59.670 --> 00:06:01.040 that the nitrate exists. 00:06:01.040 --> 00:06:03.330 And so, if we wanted to draw a resonance hybrid, 00:06:03.330 --> 00:06:05.230 it would look like this. 00:06:05.230 --> 00:06:07.140 You have the nitrogen in the center. 00:06:07.140 --> 00:06:11.670 You have your oxygens, one, two, three. 00:06:11.670 --> 00:06:15.430 I can draw our first covalent bond like that. 00:06:15.430 --> 00:06:16.430 And then you would show the bond 00:06:16.430 --> 00:06:17.420 between nitrogen and each 00:06:17.420 --> 00:06:21.220 of these oxygens are a hybrid between someplace 00:06:21.220 --> 00:06:23.680 between a single bond and a double bond. 00:06:23.680 --> 00:06:26.510 And so instead of just one of them having the double bond 00:06:26.510 --> 00:06:28.270 and the other two having single bonds, 00:06:28.270 --> 00:06:30.120 they're all somewhere in between. 00:06:30.120 --> 00:06:32.148 So maybe you draw a dotted line, 00:06:32.148 --> 00:06:37.148 something like that, to show what the reality is, 00:06:37.460 --> 00:06:39.590 is that you actually have three bonds 00:06:39.590 --> 00:06:41.720 that are someplace in between a single 00:06:41.720 --> 00:06:44.159 and a double bond, because the electrons 00:06:44.159 --> 00:06:46.880 in this molecule are delocalized throughout. 00:06:46.880 --> 00:06:48.550 And of course you wanna make sure, 00:06:48.550 --> 00:06:50.950 you always wanna make sure that people recognize 00:06:50.950 --> 00:06:53.320 that this is a anion. 00:06:53.320 --> 00:06:55.110 So this is the idea of resonance. 00:06:55.110 --> 00:06:57.650 You have multiple valid Lewis structures. 00:06:57.650 --> 00:07:01.380 They all contribute to a resonance hybrid, 00:07:01.380 --> 00:07:03.070 which is actually what we observe. 00:07:03.070 --> 00:07:04.093 We're not just bouncing between 00:07:04.093 --> 00:07:05.980 these different structures. 00:07:05.980 --> 00:07:09.870 The actual observation will be a hybrid of the three. 00:07:09.870 --> 00:07:11.030 Now what we just drew here, 00:07:11.030 --> 00:07:12.804 these three are all equivalent. 00:07:12.804 --> 00:07:14.580 But in certain cases, we'll see this 00:07:14.580 --> 00:07:17.500 in future videos, you don't have equivalent structures, 00:07:17.500 --> 00:07:19.620 and some of them might contribute more 00:07:19.620 --> 00:07:21.230 to the resonance hybrid than others. 00:07:21.230 --> 00:07:23.083 But we'll see that in future videos.

Exceptions to the octet rule

https://www.youtube.com/watch?v=Tkb1OemB2KI

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https://www.youtube.com/api/timedtext?v=Tkb1OemB2KI&ei=bViUZaiPFqeip-oPhfOt4Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0F1175DF39A17FCCFF0808A55045794997F598BA.66ADB49914160375EFF69B4C50D2A343325A7B3E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.270 --> 00:00:02.040 - [Instructor] In this video, we're gonna start talking 00:00:02.040 --> 00:00:04.250 about exceptions to the octet rule, 00:00:04.250 --> 00:00:05.850 which we've talked about in many other videos. 00:00:05.850 --> 00:00:07.070 The octet rule is this notion 00:00:07.070 --> 00:00:09.490 that atoms tend to react in ways 00:00:09.490 --> 00:00:12.100 that they're able to have a full outer shell. 00:00:12.100 --> 00:00:14.550 They're able to have eight valence electrons. 00:00:14.550 --> 00:00:16.610 Now, we've already talked about some exceptions, 00:00:16.610 --> 00:00:17.930 things like hydrogen. 00:00:17.930 --> 00:00:19.730 Its outer shell is that first shell 00:00:19.730 --> 00:00:22.460 which gets full with two electrons. 00:00:22.460 --> 00:00:25.090 So it's trying to get to that duet rule. 00:00:25.090 --> 00:00:27.090 But as we'll see, there are other exceptions. 00:00:27.090 --> 00:00:29.420 Boron and aluminum, for example, 00:00:29.420 --> 00:00:31.960 they can form stable molecules where the boron 00:00:31.960 --> 00:00:36.630 or the aluminum only have six valence electrons, not eight. 00:00:36.630 --> 00:00:38.720 And there are exceptions in the other direction. 00:00:38.720 --> 00:00:41.630 As you get to the third period and beyond, 00:00:41.630 --> 00:00:44.650 we'll actually see atoms that can maintain more 00:00:44.650 --> 00:00:46.330 than eight valence electrons. 00:00:46.330 --> 00:00:47.650 And we're actually going to see an example 00:00:47.650 --> 00:00:50.070 of that with xenon. 00:00:50.070 --> 00:00:51.870 So let's just go into a few examples. 00:00:51.870 --> 00:00:53.740 Given what I've told you, 00:00:53.740 --> 00:00:57.620 see if you can come up with the Lewis diagram 00:00:57.620 --> 00:01:00.070 for aluminum hydride. 00:01:00.070 --> 00:01:03.850 So aluminum hydride has one aluminum 00:01:03.850 --> 00:01:05.470 and three hydrogens. 00:01:05.470 --> 00:01:08.600 See if you can draw the Lewis diagram for that. 00:01:08.600 --> 00:01:10.220 All right, now let's do this together. 00:01:10.220 --> 00:01:12.070 So the first thing you wanna do is account 00:01:12.070 --> 00:01:14.174 for all of the valence electrons. 00:01:14.174 --> 00:01:16.080 Aluminum's outer shell is the third shell, 00:01:16.080 --> 00:01:17.180 so the third period here, 00:01:17.180 --> 00:01:20.740 and it has one, two, three valence electrons. 00:01:20.740 --> 00:01:23.500 And then we have three hydrogens, 00:01:23.500 --> 00:01:26.890 and each hydrogen has one valence electron. 00:01:26.890 --> 00:01:29.510 And so you add all of this up together, 00:01:29.510 --> 00:01:34.380 three plus three is equal to six valence electrons 00:01:34.380 --> 00:01:36.760 in aluminum hydride. 00:01:36.760 --> 00:01:39.400 Now, the next step after that is 00:01:39.400 --> 00:01:43.350 to try to draw the structure with some covalent bonds. 00:01:43.350 --> 00:01:45.590 We don't wanna make hydrogen our central atom. 00:01:45.590 --> 00:01:48.240 That would be very atypical. 00:01:48.240 --> 00:01:51.030 And so let's put aluminum in the center. 00:01:51.030 --> 00:01:53.300 And then we're gonna have three hydrogens. 00:01:53.300 --> 00:01:57.060 So one, two, and three. 00:01:57.060 --> 00:02:00.220 And then let's put some covalent bonds in here. 00:02:00.220 --> 00:02:03.550 And so let's see, how many valence electrons 00:02:03.550 --> 00:02:04.810 have we now accounted for? 00:02:04.810 --> 00:02:06.530 This is two in this covalent bond. 00:02:06.530 --> 00:02:07.900 Another two gets us to four. 00:02:07.900 --> 00:02:09.570 Another two gets us to six. 00:02:09.570 --> 00:02:14.120 So we have just accounted for all six valence electrons. 00:02:14.120 --> 00:02:16.470 So we have no more valence electrons to play with. 00:02:16.470 --> 00:02:19.190 Let's think about how the various atoms are doing. 00:02:19.190 --> 00:02:22.170 So the hydrogens are all meeting their duet rule. 00:02:22.170 --> 00:02:25.720 These two electrons in this bond are hanging around hydrogen 00:02:25.720 --> 00:02:27.230 and around the aluminum. 00:02:27.230 --> 00:02:30.130 But from hydrogen's point of view, it has a full duet, 00:02:30.130 --> 00:02:32.410 that hydrogen as well and that hydrogen as well. 00:02:32.410 --> 00:02:34.410 But notice the aluminum over here, 00:02:34.410 --> 00:02:37.120 it has two, four, six electrons, 00:02:37.120 --> 00:02:41.140 valence electrons around it, and so it's not a full octet. 00:02:41.140 --> 00:02:43.470 But aluminum hydride is actually something 00:02:43.470 --> 00:02:45.860 that has been observed. 00:02:45.860 --> 00:02:47.690 Let's think about another example. 00:02:47.690 --> 00:02:51.793 Let's think about xenon pentafluoride. 00:02:53.520 --> 00:02:57.870 Xenon pentafluoride cations, 00:02:57.870 --> 00:03:00.400 a positively charged ion here. 00:03:00.400 --> 00:03:01.260 Pause this video and see 00:03:01.260 --> 00:03:03.853 if you can draw the Lewis diagram for this. 00:03:05.010 --> 00:03:06.080 All right, now let's do this together. 00:03:06.080 --> 00:03:07.170 If any of this seems unfamiliar, 00:03:07.170 --> 00:03:09.360 I encourage you to watch the video 00:03:09.360 --> 00:03:11.920 on introduction to drawing Lewis diagrams. 00:03:11.920 --> 00:03:13.830 But what we'd wanna do is first think 00:03:13.830 --> 00:03:16.360 about our valence electrons. 00:03:16.360 --> 00:03:19.890 So xenon right over here, it's actually a noble gas. 00:03:19.890 --> 00:03:23.600 It already has a full octet in its outer shell, 00:03:23.600 --> 00:03:26.120 so it has eight valence electrons. 00:03:26.120 --> 00:03:28.620 So xenon has eight valence electrons. 00:03:28.620 --> 00:03:31.640 And then fluorine, we've seen this multiple times, 00:03:31.640 --> 00:03:34.160 has one, two, three, four, five, six, 00:03:34.160 --> 00:03:37.510 seven valence electrons, but there's five of them. 00:03:37.510 --> 00:03:39.400 So five times seven. 00:03:39.400 --> 00:03:41.370 I'm gonna be drawing a lot of electrons in this. 00:03:41.370 --> 00:03:44.440 So this gives us a total of eight plus 35, 00:03:44.440 --> 00:03:48.380 which is 43 valence electrons. 00:03:48.380 --> 00:03:50.120 But we have to be careful. 00:03:50.120 --> 00:03:51.350 This is a cation. 00:03:51.350 --> 00:03:53.640 It is a positively charged molecule. 00:03:53.640 --> 00:03:55.520 It has a positive one charge. 00:03:55.520 --> 00:03:58.350 So we have to take one electron away because of that. 00:03:58.350 --> 00:04:03.350 So let's take away one valence electron to get that cation. 00:04:03.380 --> 00:04:06.060 And so we are left with 42. 00:04:06.060 --> 00:04:08.700 42 valence electrons. 00:04:08.700 --> 00:04:11.180 So the next step is to try to draw its structure 00:04:11.180 --> 00:04:13.800 with some basic single covalent bonds. 00:04:13.800 --> 00:04:16.470 And xenon would be our preferred central atom 00:04:16.470 --> 00:04:19.060 because fluorine is more electronegative. 00:04:19.060 --> 00:04:21.510 It's actually the most electronegative element. 00:04:21.510 --> 00:04:23.483 So let's put xenon in the middle, 00:04:24.410 --> 00:04:26.890 and then let's put some fluorines around it, 00:04:26.890 --> 00:04:28.790 five of them to be specific. 00:04:28.790 --> 00:04:31.183 So one, two, 00:04:32.130 --> 00:04:34.860 three, four. 00:04:34.860 --> 00:04:36.440 I'm having trouble writing an F. 00:04:36.440 --> 00:04:39.900 Four and then five fluorines. 00:04:39.900 --> 00:04:42.510 And now let me make five covalent bonds. 00:04:42.510 --> 00:04:45.930 One, two, three, four, five. 00:04:45.930 --> 00:04:48.410 So just like that, I have accounted for 10 valence electrons 00:04:48.410 --> 00:04:49.620 because you have two valence electrons 00:04:49.620 --> 00:04:50.850 in each of these covalent bonds, 00:04:50.850 --> 00:04:52.780 two, four, six, eight, 10. 00:04:52.780 --> 00:04:55.990 So let me subtract 10 valence electrons. 00:04:55.990 --> 00:05:00.020 And then we are left with 32 valence electrons. 00:05:00.020 --> 00:05:02.880 Now, the next step is to try to allocate some more 00:05:02.880 --> 00:05:05.170 of these valence electrons to the terminal atom 00:05:05.170 --> 00:05:06.780 so that they get to a full octet. 00:05:06.780 --> 00:05:08.340 So let me do that to the fluorines. 00:05:08.340 --> 00:05:10.510 Each of these fluorines already are participating 00:05:10.510 --> 00:05:13.100 in a covalent bond, so they already have 00:05:13.100 --> 00:05:15.400 two valence electrons hanging out with them, 00:05:15.400 --> 00:05:17.270 so let's give 'em each six more. 00:05:17.270 --> 00:05:21.080 So let's give that fluorine six, 00:05:21.080 --> 00:05:23.780 and that fluorine gets six, 00:05:23.780 --> 00:05:28.570 and that fluorine gets six valence electrons, 00:05:28.570 --> 00:05:31.550 and that fluorine gets six valence electrons, 00:05:31.550 --> 00:05:32.890 and then last but not least, 00:05:32.890 --> 00:05:35.610 this fluorine gets six valence electrons. 00:05:35.610 --> 00:05:38.750 So I have just given away six valence electrons 00:05:38.750 --> 00:05:41.110 to each of five fluorine atoms. 00:05:41.110 --> 00:05:45.560 So that is 30 valence electrons that I have just allocated. 00:05:45.560 --> 00:05:48.470 And then what does that leave me with? 00:05:48.470 --> 00:05:51.760 That leaves me with two valence electrons 00:05:51.760 --> 00:05:53.370 that have gone unallocated. 00:05:53.370 --> 00:05:56.560 And the only place to now put them is on the xenon. 00:05:56.560 --> 00:05:58.440 And as I said, things that are lower down 00:05:58.440 --> 00:05:59.950 in that periodic table of elements, 00:05:59.950 --> 00:06:03.770 especially as we get below the third period, 00:06:03.770 --> 00:06:06.440 these can defy the octet rule. 00:06:06.440 --> 00:06:08.820 Xenon already has 10 valence electrons, 00:06:08.820 --> 00:06:13.460 and I'm about to allocate it two more to it just like that. 00:06:13.460 --> 00:06:15.360 So you allocate those two more. 00:06:15.360 --> 00:06:18.260 And then we have allocated all of our valence electrons. 00:06:18.260 --> 00:06:22.730 And I wanna make sure I remind myself and everyone 00:06:22.730 --> 00:06:24.700 that this is a cation. 00:06:24.700 --> 00:06:28.030 So I have to put that plus charge just like this, 00:06:28.030 --> 00:06:31.050 but this is something that has been observed 00:06:31.050 --> 00:06:34.990 where you can actually have a central atom like this 00:06:34.990 --> 00:06:38.610 that goes beyond an octet number of valence electrons. 00:06:38.610 --> 00:06:41.290 In this case, it has two, four, six, 00:06:41.290 --> 00:06:45.470 eight, 10, 12 valence electrons. 00:06:45.470 --> 00:06:48.560 Now, an interesting question is how do these atoms 00:06:48.560 --> 00:06:51.690 that are in the third period or beyond handle more 00:06:51.690 --> 00:06:53.570 than eight valence electrons? 00:06:53.570 --> 00:06:56.300 And it is a matter of debate, 00:06:56.300 --> 00:06:59.150 but some chemists believe that it's possible 00:06:59.150 --> 00:07:01.560 because they're able to place their electrons 00:07:01.560 --> 00:07:04.210 in their empty valence d-orbitals. 00:07:04.210 --> 00:07:05.890 But once again, this is controversial 00:07:05.890 --> 00:07:08.113 in the chemistry community.

Worked example: Lewis diagram of xenon difluoride (XeF₂)

https://www.youtube.com/watch?v=kfTm72uWt9o

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WEBVTT Kind: captions Language: en 00:00:00.310 --> 00:00:01.530 - [Instructor] Let's do one more example 00:00:01.530 --> 00:00:03.460 of constructing a Lewis diagram 00:00:03.460 --> 00:00:05.680 that might be a little bit interesting. 00:00:05.680 --> 00:00:08.130 So let's say we wanted to construct the Lewis structure 00:00:08.130 --> 00:00:11.963 or Lewis diagram for xenon difluoride. 00:00:13.589 --> 00:00:16.193 So pause this video and have a go of that. 00:00:17.070 --> 00:00:20.090 All right, now let's work through this together. 00:00:20.090 --> 00:00:20.940 So first step, 00:00:20.940 --> 00:00:23.920 we just have to account for the valence electrons. 00:00:23.920 --> 00:00:25.640 Xenon right over here. 00:00:25.640 --> 00:00:27.700 It is a noble gas. 00:00:27.700 --> 00:00:30.280 It has eight valence electrons. 00:00:30.280 --> 00:00:34.620 One, two, three, four, five, six, seven, eight 00:00:34.620 --> 00:00:36.700 in that fifth shell. 00:00:36.700 --> 00:00:38.220 It's in the fifth period. 00:00:38.220 --> 00:00:40.930 So it has eight valence electrons. 00:00:40.930 --> 00:00:42.740 And then fluorine, 00:00:42.740 --> 00:00:44.850 we have looked at fluorine multiple times, 00:00:44.850 --> 00:00:47.210 we know that it has seven valence electrons. 00:00:47.210 --> 00:00:50.830 One, two, three, four, five, six, seven 00:00:50.830 --> 00:00:52.760 in that second shell. 00:00:52.760 --> 00:00:54.450 And we have two of these fluorines. 00:00:54.450 --> 00:00:56.390 So two times seven. 00:00:56.390 --> 00:00:59.210 And then this gives us a total of 00:00:59.210 --> 00:01:02.430 eight plus 14 valence electrons 00:01:02.430 --> 00:01:07.430 which gets us to 22 valence electrons in total. 00:01:07.510 --> 00:01:09.900 Now the next step, and we've done this multiple times, 00:01:09.900 --> 00:01:11.160 in multiple videos now, 00:01:11.160 --> 00:01:14.730 is we would try to draw the structure 00:01:14.730 --> 00:01:16.840 with some single covalent bonds 00:01:16.840 --> 00:01:20.250 and we would put xenon as our central atom 00:01:20.250 --> 00:01:23.560 because it is less electronegative than fluorine. 00:01:23.560 --> 00:01:26.040 So let's put a xenon there. 00:01:26.040 --> 00:01:29.620 And let's put two fluorines on either side. 00:01:29.620 --> 00:01:31.170 So fluorine there 00:01:31.170 --> 00:01:32.850 and a fluorine there. 00:01:32.850 --> 00:01:36.820 And let's set up some single covalent bonds. 00:01:36.820 --> 00:01:39.870 And so how many of our valence electrons 00:01:39.870 --> 00:01:41.400 have we now accounted for? 00:01:41.400 --> 00:01:44.610 Well two in that bond and then two in that bond. 00:01:44.610 --> 00:01:45.870 So we've accounted for four. 00:01:45.870 --> 00:01:48.670 So minus four valence electrons. 00:01:48.670 --> 00:01:52.970 We now have a total of 18 valence electrons. 00:01:52.970 --> 00:01:55.520 Now the next step is we wanna allocate them 00:01:55.520 --> 00:02:00.520 to our terminal atoms and try to get them to a full octet. 00:02:00.650 --> 00:02:05.170 Each of these fluorines already have two valence electrons 00:02:05.170 --> 00:02:06.130 that they are sharing. 00:02:06.130 --> 00:02:08.380 So we need to give each of them six more. 00:02:08.380 --> 00:02:12.260 So two, four, six. 00:02:12.260 --> 00:02:15.660 Two, four, six. 00:02:15.660 --> 00:02:18.940 So I've just allocated 12 more valence electrons. 00:02:18.940 --> 00:02:21.970 So minus 12 valence electrons 00:02:21.970 --> 00:02:24.910 means that we still have six valence electrons 00:02:24.910 --> 00:02:25.860 left to allocate. 00:02:25.860 --> 00:02:27.340 And there's only one place 00:02:27.340 --> 00:02:31.100 where we can allocate those left over six valence electrons 00:02:31.100 --> 00:02:32.240 and that's at the central atom. 00:02:32.240 --> 00:02:33.500 At the xenon. 00:02:33.500 --> 00:02:34.333 So let's do that. 00:02:34.333 --> 00:02:39.320 So, two, four, and six. 00:02:39.320 --> 00:02:40.350 And there you have it. 00:02:40.350 --> 00:02:43.310 We have the Lewis diagram, the Lewis structure 00:02:43.310 --> 00:02:45.340 for xenon difluoride. 00:02:45.340 --> 00:02:47.020 Now what's interesting here is 00:02:47.020 --> 00:02:50.300 our fluorines they have an octet of valence electrons. 00:02:50.300 --> 00:02:52.120 But what's going on with xenon? 00:02:52.120 --> 00:02:56.180 Xenon has two, four, six, eight, 00:02:56.180 --> 00:02:59.370 10 valence electrons hanging around. 00:02:59.370 --> 00:03:00.840 So this is one of those examples 00:03:00.840 --> 00:03:02.880 of an exception to the octet rule 00:03:02.880 --> 00:03:05.600 where we go beyond eight valence electrons 00:03:05.600 --> 00:03:07.860 which is possible for elements 00:03:07.860 --> 00:03:10.173 in the third or higher period.

Worked example: Lewis diagram of the cyanide ion (CN⁻)

https://www.youtube.com/watch?v=Y8p4cthWB8I

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WEBVTT Kind: captions Language: en 00:00:00.210 --> 00:00:01.470 - [Instructor] In this video we're gonna try to get 00:00:01.470 --> 00:00:04.210 more practice constructing Lewis diagrams. 00:00:04.210 --> 00:00:08.750 And we're gonna try to do that for a cyanide anion. 00:00:08.750 --> 00:00:09.660 So this is interesting. 00:00:09.660 --> 00:00:11.280 This is the first time we're constructing 00:00:11.280 --> 00:00:13.960 a Lewis diagram for an ion. 00:00:13.960 --> 00:00:17.550 So pause this video and see if you can have a go at that. 00:00:17.550 --> 00:00:20.780 All right, now let's do this together. 00:00:20.780 --> 00:00:23.030 So we've already seen in many videos, 00:00:23.030 --> 00:00:25.990 the first step is to essentially count 00:00:25.990 --> 00:00:29.210 the total valence electrons that we're dealing with. 00:00:29.210 --> 00:00:30.610 And the reason why we do that is to make sure 00:00:30.610 --> 00:00:32.940 that we're allocating all the valence electrons. 00:00:32.940 --> 00:00:33.773 To help us there 00:00:33.773 --> 00:00:35.790 we can look at a periodic table of elements. 00:00:35.790 --> 00:00:37.440 You might already know that carbon has 00:00:37.440 --> 00:00:40.100 one, two, three, four valence electrons 00:00:40.100 --> 00:00:42.670 in that second shell, it's in the second period, 00:00:42.670 --> 00:00:45.010 so you have four valence electrons from carbon. 00:00:45.010 --> 00:00:48.691 Nitrogen has one, two, three, four, five valence electrons 00:00:48.691 --> 00:00:51.780 in its second shell, it's in that second period. 00:00:51.780 --> 00:00:55.730 And so the valence electrons from a neutral carbon 00:00:55.730 --> 00:00:57.730 and a neutral nitrogen-free atom 00:00:57.730 --> 00:01:01.310 would be a total of nine valence electrons. 00:01:01.310 --> 00:01:02.730 But we are not done yet. 00:01:02.730 --> 00:01:04.910 Because this is not a neutral molecule. 00:01:04.910 --> 00:01:06.370 We have a negative charge here. 00:01:06.370 --> 00:01:08.630 It is an anion, it has a negative one charge. 00:01:08.630 --> 00:01:10.460 And so because of that negative one 00:01:10.460 --> 00:01:13.630 we can think about it having an extra valence electron. 00:01:13.630 --> 00:01:16.200 So let's add a valence electron here. 00:01:16.200 --> 00:01:17.180 Why do we do it? 00:01:17.180 --> 00:01:19.056 Because of this negative charge. 00:01:19.056 --> 00:01:24.056 So we're dealing with a total of 10 valence electrons. 00:01:24.100 --> 00:01:28.190 Now, the next step is to try to draw single bonds. 00:01:28.190 --> 00:01:33.190 Try single bonds, and identify a central atom. 00:01:33.860 --> 00:01:35.770 Now, we only have two atoms here, 00:01:35.770 --> 00:01:39.300 so really neither feels central, 00:01:39.300 --> 00:01:41.440 so let me just put a carbon 00:01:41.440 --> 00:01:44.090 and a nitrogen next to each other here. 00:01:44.090 --> 00:01:47.830 And then let me draw one single bond. 00:01:47.830 --> 00:01:49.530 So by drawing that one single bond 00:01:49.530 --> 00:01:52.544 I have now accounted for two valence electrons. 00:01:52.544 --> 00:01:56.440 So now I am left with eight valence electrons, 00:01:56.440 --> 00:01:58.130 and so that's the next step, 00:01:58.130 --> 00:02:00.330 allocate remaining valence electrons, 00:02:00.330 --> 00:02:03.690 allocate valence electrons. 00:02:03.690 --> 00:02:05.950 So let me start with the more electronegative. 00:02:05.950 --> 00:02:07.340 Let's try to get nitrogen to eight. 00:02:07.340 --> 00:02:08.680 It already has two. 00:02:08.680 --> 00:02:11.070 So let's give it three more lone pairs. 00:02:11.070 --> 00:02:16.070 So we have two, four, six, eight. 00:02:16.230 --> 00:02:19.350 So I have just used up six 00:02:19.350 --> 00:02:23.160 of these remaining valence electrons, six, so minus six, 00:02:23.160 --> 00:02:25.860 so I have two left to allocate. 00:02:25.860 --> 00:02:30.390 So let me give carbon two valence electrons, like that. 00:02:30.390 --> 00:02:33.658 And there I have used up all of my, 00:02:33.658 --> 00:02:36.640 all of my valence electrons. 00:02:36.640 --> 00:02:38.830 Now let's see how happy everyone is. 00:02:38.830 --> 00:02:41.790 Nitrogen has eight valence electrons hanging around, 00:02:41.790 --> 00:02:44.070 two, four, six, eight. 00:02:44.070 --> 00:02:47.550 But carbon only has four, two and four. 00:02:47.550 --> 00:02:49.200 So this is where we think about 00:02:49.200 --> 00:02:53.500 whether we would want to have some extra bonds, 00:02:53.500 --> 00:02:57.470 extra bonds, or higher-order bonds. 00:02:57.470 --> 00:03:00.227 So how can we give carbon more valence electrons? 00:03:00.227 --> 00:03:01.710 Well, what we could do is 00:03:01.710 --> 00:03:03.800 we could take some of these lone pairs around nitrogen 00:03:03.800 --> 00:03:06.310 and then use them, turn this single covalent bond 00:03:06.310 --> 00:03:08.270 into a higher-order bond. 00:03:08.270 --> 00:03:11.190 So let's see, if we were to take these two 00:03:11.190 --> 00:03:14.320 and turn it into another covalent bond, 00:03:14.320 --> 00:03:15.810 what is going to happen? 00:03:15.810 --> 00:03:17.560 Let me erase all of these, 00:03:17.560 --> 00:03:22.560 and then I'll just draw another covalent bond. 00:03:25.430 --> 00:03:28.360 So nitrogen still has eight electrons hanging around. 00:03:28.360 --> 00:03:29.820 Carbon now has six. 00:03:29.820 --> 00:03:32.550 So maybe we can do that again. 00:03:32.550 --> 00:03:36.150 So let me erase these two characters. 00:03:36.150 --> 00:03:38.670 Let me erase these two characters 00:03:38.670 --> 00:03:41.380 and make another covalent bond out of them. 00:03:41.380 --> 00:03:46.110 So let me make a covalent bond out of them. 00:03:46.110 --> 00:03:48.050 And so now what's going on? 00:03:48.050 --> 00:03:50.930 Carbon has two, four, six, eight 00:03:50.930 --> 00:03:52.380 valence electrons hanging around. 00:03:52.380 --> 00:03:55.230 Nitrogen has two, four, six, eight 00:03:55.230 --> 00:03:57.370 valence electrons hanging around. 00:03:57.370 --> 00:03:59.125 So this is looking pretty good. 00:03:59.125 --> 00:04:01.410 But are we done yet? 00:04:01.410 --> 00:04:02.670 The simple answer is no. 00:04:02.670 --> 00:04:05.810 We still haven't represented this negative charge 00:04:05.810 --> 00:04:07.490 in our Lewis diagram. 00:04:07.490 --> 00:04:09.130 The way that we would do that is say hey, 00:04:09.130 --> 00:04:11.850 this entire molecule, you put brackets around it, 00:04:11.850 --> 00:04:13.840 has a negative charge. 00:04:13.840 --> 00:04:15.100 And now we're done. 00:04:15.100 --> 00:04:17.640 We've allocated all of our valence electrons, 00:04:17.640 --> 00:04:20.380 we have our octet rule on all of our atoms 00:04:20.380 --> 00:04:22.260 that are not hydrogen, there's no hydrogen here, 00:04:22.260 --> 00:04:25.360 and we're showing that this indeed is an anion, 00:04:25.360 --> 00:04:27.053 and now we are done.

Drawing Lewis diagrams

https://www.youtube.com/watch?v=9BZFphoY-vo

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WEBVTT Kind: captions Language: en 00:00:00.540 --> 00:00:01.830 - [Sal] In this video we're going 00:00:01.830 --> 00:00:04.530 to think about constructing Lewis diagrams, 00:00:04.530 --> 00:00:06.000 which you've probably seen before. 00:00:06.000 --> 00:00:07.840 They're nice ways of visualizing 00:00:07.840 --> 00:00:10.980 how the atoms in a molecule are bonded to each other 00:00:10.980 --> 00:00:14.580 and what other lone pairs of valence electrons 00:00:14.580 --> 00:00:16.780 various atoms might have. 00:00:16.780 --> 00:00:18.820 And so let's just start with an example, 00:00:18.820 --> 00:00:20.570 then we'll come up with some rules 00:00:20.570 --> 00:00:23.100 for trying to draw these Lewis diagrams. 00:00:23.100 --> 00:00:25.300 So the first example that we will look at 00:00:25.300 --> 00:00:30.300 is silicon tetrafluoride, and tetrafluoride 00:00:30.580 --> 00:00:32.860 is just a fancy way of saying four fluorines, 00:00:32.860 --> 00:00:33.903 so tetrafluoride. 00:00:35.810 --> 00:00:37.297 Now the first step is to say, 00:00:37.297 --> 00:00:40.400 "Well, what are the electrons that are of interest to us?" 00:00:40.400 --> 00:00:41.873 And if we're talking about the electrons 00:00:41.873 --> 00:00:43.830 that are likely to react, we're talking 00:00:43.830 --> 00:00:47.790 about the valence electrons, so V.E. for short, 00:00:47.790 --> 00:00:49.240 valence electrons. 00:00:49.240 --> 00:00:51.520 So first let's think about how many total valence electrons 00:00:51.520 --> 00:00:55.020 are involved in silicon tetrafluoride. 00:00:55.020 --> 00:00:56.390 Well, to think about that, we could think 00:00:56.390 --> 00:00:59.130 about how many valence electrons does silicon have, 00:00:59.130 --> 00:01:00.490 and then how many valence electrons 00:01:00.490 --> 00:01:02.910 does each of the fluorines have 00:01:02.910 --> 00:01:05.490 if they were just free atoms and neutral, 00:01:05.490 --> 00:01:06.960 and then multiply that times four, 00:01:06.960 --> 00:01:08.080 'cause you have four fluorines. 00:01:08.080 --> 00:01:11.140 So let's get out our periodic table of elements, 00:01:11.140 --> 00:01:14.380 and then you can see here that silicon, 00:01:14.380 --> 00:01:16.690 its outer shell is the third shell, 00:01:16.690 --> 00:01:19.096 and in that third shell it has one, two, 00:01:19.096 --> 00:01:22.620 three, four valence electrons. 00:01:22.620 --> 00:01:26.520 So silicon here has four valence electrons, 00:01:26.520 --> 00:01:29.270 and then to that, we're going to add the valence electrons 00:01:29.270 --> 00:01:31.040 from the four fluorines. 00:01:31.040 --> 00:01:34.430 A free, neutral fluorine atom, 00:01:34.430 --> 00:01:36.210 its outer shell is the second shell, 00:01:36.210 --> 00:01:38.680 and in that outer shell, it has one, two, 00:01:38.680 --> 00:01:42.080 three, four, five, six, seven electrons. 00:01:42.080 --> 00:01:45.320 So each of these fluorines has seven valence electrons, 00:01:45.320 --> 00:01:46.830 but there are four of them. 00:01:46.830 --> 00:01:49.790 So one silicon tetrafluoride molecule 00:01:49.790 --> 00:01:53.840 is gonna have four plus 28 valence electrons. 00:01:53.840 --> 00:01:57.743 So this is going to be a total of 32. 00:01:58.640 --> 00:02:00.630 Now the next step is to think 00:02:00.630 --> 00:02:03.490 about how might these be configured? 00:02:03.490 --> 00:02:05.020 And as a general rule of thumb, 00:02:05.020 --> 00:02:07.370 we'd wanna put the least electronegative atom 00:02:07.370 --> 00:02:09.720 that is not hydrogen at the center. 00:02:09.720 --> 00:02:11.870 And we've talked about this before, 00:02:11.870 --> 00:02:14.070 but you can even see from the periodic table of elements, 00:02:14.070 --> 00:02:17.110 fluorine is actually the most electronegative element, 00:02:17.110 --> 00:02:20.680 and so we would at least try to put silicon at the center 00:02:20.680 --> 00:02:23.140 and make fluorine a terminal atom, 00:02:23.140 --> 00:02:24.630 something on the outside. 00:02:24.630 --> 00:02:26.070 So let's try to do that. 00:02:26.070 --> 00:02:29.200 So let's put silicon in the center, 00:02:29.200 --> 00:02:31.870 and then we have to put the four fluorines some place. 00:02:31.870 --> 00:02:34.880 Let's just put one fluorine there, one fluorine there, 00:02:34.880 --> 00:02:38.780 one fluorine there, and one fluorine there. 00:02:38.780 --> 00:02:40.820 Now the next step is, well let's just say 00:02:40.820 --> 00:02:43.230 for simplicity that we just have single bonds 00:02:43.230 --> 00:02:45.530 between the silicon and each of the fluorines. 00:02:45.530 --> 00:02:46.990 So let's do that. 00:02:46.990 --> 00:02:50.770 So one bond, a bond, a bond, a bond. 00:02:50.770 --> 00:02:52.700 Now each of these covalent bonds, 00:02:52.700 --> 00:02:55.380 each of these lines in our Lewis diagram, 00:02:55.380 --> 00:02:57.190 they represent two electrons. 00:02:57.190 --> 00:03:00.590 So for example, this one right over here 00:03:00.590 --> 00:03:03.590 that I'm doing in yellow, that represents two electrons 00:03:03.590 --> 00:03:06.460 that are shared by this fluorine and this silicon. 00:03:06.460 --> 00:03:08.260 This represents another two electrons 00:03:08.260 --> 00:03:10.830 that is shared between this fluorine and the silicon. 00:03:10.830 --> 00:03:12.235 This is another two electrons that's shared 00:03:12.235 --> 00:03:14.787 between this fluorine and this silicon. 00:03:14.787 --> 00:03:16.980 And this is another two electrons 00:03:16.980 --> 00:03:19.910 shared between that fluorine and the silicon. 00:03:19.910 --> 00:03:22.900 So, so far, how many electrons have we accounted for? 00:03:22.900 --> 00:03:25.240 Well, each of these represent two electrons, 00:03:25.240 --> 00:03:28.520 so two, four, six, eight electrons. 00:03:28.520 --> 00:03:31.550 So if we subtract eight from this, we are left 00:03:31.550 --> 00:03:36.550 with 24 electrons to account for, 24 valence electrons. 00:03:37.830 --> 00:03:40.660 So now, our general rule of thumb would be, 00:03:40.660 --> 00:03:43.150 try to put those on those terminal atoms 00:03:43.150 --> 00:03:45.130 with the goal of getting those terminal atoms 00:03:45.130 --> 00:03:47.620 to having eight valence electrons. 00:03:47.620 --> 00:03:49.220 In general we try to get the octet rule 00:03:49.220 --> 00:03:50.720 for any atom except for hydrogen. 00:03:50.720 --> 00:03:53.300 Hydrogen, you just need to get to two in that outer shell. 00:03:53.300 --> 00:03:54.760 But fluorine, you want to get it to eight. 00:03:54.760 --> 00:03:57.500 It already has two that it can share, 00:03:57.500 --> 00:03:59.970 so it needs six more, so let's add that. 00:03:59.970 --> 00:04:03.460 Two, four, six. 00:04:03.460 --> 00:04:05.140 Let's do that again for this fluorine. 00:04:05.140 --> 00:04:08.860 Two, four, six. 00:04:08.860 --> 00:04:10.430 Do it again for this fluorine. 00:04:10.430 --> 00:04:13.780 Two, four, six. 00:04:13.780 --> 00:04:15.570 And then last but not least, for this fluorine. 00:04:15.570 --> 00:04:19.450 Two, four, and six. 00:04:19.450 --> 00:04:21.580 Now how many more electrons are now accounted for? 00:04:21.580 --> 00:04:24.190 Well, six in this fluorine, six in this fluorine, 00:04:24.190 --> 00:04:26.520 six in this fluorine, six in this fluorine, 00:04:26.520 --> 00:04:28.860 so six times four, we've now accounted 00:04:28.860 --> 00:04:30.960 for 24 more electrons. 00:04:30.960 --> 00:04:34.360 We've now used up all of the valence electrons. 00:04:34.360 --> 00:04:36.890 Now that's good, because we wanted to account 00:04:36.890 --> 00:04:38.270 for all of the valence electrons. 00:04:38.270 --> 00:04:41.020 We wanna represent them somehow in this Lewis diagram. 00:04:41.020 --> 00:04:44.450 The next thing to check for is how satisfied 00:04:44.450 --> 00:04:48.670 the various atoms are relative to to the octet rule. 00:04:48.670 --> 00:04:50.530 We've already seen that the fluorines 00:04:50.530 --> 00:04:51.840 are feeling pretty good. 00:04:51.840 --> 00:04:55.290 They each have six electrons that are not in a bond, 00:04:55.290 --> 00:04:57.360 and then they're able to share two electrons 00:04:57.360 --> 00:04:58.806 that are in a bond, so each of them 00:04:58.806 --> 00:05:01.720 can kind of feel like they have eight outer electrons, 00:05:01.720 --> 00:05:03.940 eight valence electrons hanging out with them. 00:05:03.940 --> 00:05:07.610 And then the silicon is able to share in four bonds. 00:05:07.610 --> 00:05:10.150 Each of those bonds have two electrons, 00:05:10.150 --> 00:05:13.710 so the silicon is also feeling good about the octet rule. 00:05:13.710 --> 00:05:15.730 So I would feel very confident 00:05:15.730 --> 00:05:18.790 in this being the Lewis diagram, 00:05:18.790 --> 00:05:20.330 sometimes called the Lewis structure, 00:05:20.330 --> 00:05:22.340 for silicon tetrafluoride. 00:05:22.340 --> 00:05:24.860 So just to hit the point home on what we just did, 00:05:24.860 --> 00:05:26.360 I will give you these steps, 00:05:26.360 --> 00:05:28.400 but hopefully you find them pretty intuitive. 00:05:28.400 --> 00:05:30.144 That's why I didn't wanna show you from the beginning. 00:05:30.144 --> 00:05:32.410 But as you see, step one was, 00:05:32.410 --> 00:05:34.250 find the total number of valence electrons. 00:05:34.250 --> 00:05:35.083 We did that. 00:05:35.083 --> 00:05:36.340 That's the four from silicon 00:05:36.340 --> 00:05:38.640 and then the 28 from the fluorines. 00:05:38.640 --> 00:05:41.210 It says add an electron for every negative charge. 00:05:41.210 --> 00:05:43.290 Subtract an electron for every positive charge. 00:05:43.290 --> 00:05:44.780 We didn't have to do that in this example 00:05:44.780 --> 00:05:46.650 because it's a neutral molecule. 00:05:46.650 --> 00:05:48.630 Then it says decide the central atom, 00:05:48.630 --> 00:05:51.360 which should be the electronegative except for hydrogen. 00:05:51.360 --> 00:05:52.510 That's why we picked silicon, 00:05:52.510 --> 00:05:55.100 because fluorine is the most electronegative atom. 00:05:55.100 --> 00:05:57.290 And then we drew the bonds. 00:05:57.290 --> 00:06:00.610 We saw that the bonds accounted for eight electrons, 00:06:00.610 --> 00:06:02.220 and we subtracted those electrons 00:06:02.220 --> 00:06:04.660 from the total in step one, and that's just 00:06:04.660 --> 00:06:06.933 to keep track of the number of valence electrons 00:06:06.933 --> 00:06:09.340 that we are accounting for. 00:06:09.340 --> 00:06:11.200 And then we had 24 left over. 00:06:11.200 --> 00:06:13.850 And then the next step, it says assign the valence electrons 00:06:13.850 --> 00:06:15.180 to the terminal atoms. 00:06:15.180 --> 00:06:18.160 That's where we assigned these extra lone pair electrons 00:06:18.160 --> 00:06:21.370 to the various fluorines, giving them an extra six each 00:06:21.370 --> 00:06:24.530 so that they were all able to fulfill the octet rule. 00:06:24.530 --> 00:06:26.820 And then we subtracted that from the total, 00:06:26.820 --> 00:06:28.090 really just to account, to make sure 00:06:28.090 --> 00:06:29.890 that we're using all of our electrons. 00:06:29.890 --> 00:06:31.610 It says it right here: subtract the electrons 00:06:31.610 --> 00:06:32.850 from the total in step two. 00:06:32.850 --> 00:06:35.070 And then we saw that all of our electrons 00:06:35.070 --> 00:06:36.230 were accounted for. 00:06:36.230 --> 00:06:38.710 But then in step four, it says if necessary, 00:06:38.710 --> 00:06:41.350 assign any leftover electrons to the central atom. 00:06:41.350 --> 00:06:43.230 We didn't have to do that in this example. 00:06:43.230 --> 00:06:45.110 If the central atom has an octet 00:06:45.110 --> 00:06:47.540 or exceeds an octet, you are usually done. 00:06:47.540 --> 00:06:50.400 In this case, it had an octet, so we felt done. 00:06:50.400 --> 00:06:52.110 And it finally says, if a central atom 00:06:52.110 --> 00:06:55.200 does not have an octet, create multiple bonds. 00:06:55.200 --> 00:06:56.820 Once again, in this example we were able 00:06:56.820 --> 00:06:59.000 to stay pretty simple with just single bonds. 00:06:59.000 --> 00:07:00.620 But in future examples, we're going to see 00:07:00.620 --> 00:07:03.930 where we might have to do some of these more nuanced steps. 00:07:03.930 --> 00:07:05.350 So I will leave you there, 00:07:05.350 --> 00:07:07.200 and I'll see you in the next example.

Worked example: Lewis diagram of formaldehyde (CH₂O)

https://www.youtube.com/watch?v=s0VM7WKnPeA

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WEBVTT Kind: captions Language: en 00:00:00.950 --> 00:00:01.950 - [Instructor] What we're gonna do in this video 00:00:01.950 --> 00:00:03.320 is get a little bit more practice 00:00:03.320 --> 00:00:05.990 constructing Lewis diagrams, 00:00:05.990 --> 00:00:08.170 and in particular, we're going to try 00:00:08.170 --> 00:00:11.650 to construct the Lewis diagram for formaldehyde. 00:00:11.650 --> 00:00:15.750 Formaldehyde has one carbon, two hydrogens, 00:00:15.750 --> 00:00:18.710 and an oxygen, CH2O. 00:00:18.710 --> 00:00:20.470 So pause this video and have a go at it. 00:00:20.470 --> 00:00:23.630 Try to construct a valid Lewis structure, 00:00:23.630 --> 00:00:26.133 or a Lewis diagram for formaldehyde. 00:00:27.050 --> 00:00:29.950 All right, now let's do this together. 00:00:29.950 --> 00:00:32.870 Now the first step, and we saw this in a previous video, 00:00:32.870 --> 00:00:35.190 we want to think about all of the valence electrons 00:00:35.190 --> 00:00:36.930 for this molecule. 00:00:36.930 --> 00:00:39.190 So we want to account, 00:00:39.190 --> 00:00:42.560 account for the valence electrons. 00:00:42.560 --> 00:00:43.830 Now the reason why we wanna do that 00:00:43.830 --> 00:00:46.640 is so that while we're trying to create this structure, 00:00:46.640 --> 00:00:49.320 we are making use of all of the valence electrons. 00:00:49.320 --> 00:00:52.160 And to figure out how many total valence electrons we have, 00:00:52.160 --> 00:00:54.230 we can look at a periodic table of elements. 00:00:54.230 --> 00:00:56.720 We can see that carbon, 00:00:56.720 --> 00:00:58.750 it's in that second row, in that second period, 00:00:58.750 --> 00:01:01.140 so its second shell is its outer shell. 00:01:01.140 --> 00:01:02.170 And in that shell, 00:01:02.170 --> 00:01:05.660 it has one, two, three, four valence electrons. 00:01:05.660 --> 00:01:08.660 So, carbon has four valence electrons. 00:01:08.660 --> 00:01:10.400 A neutral free hydrogen atom 00:01:10.400 --> 00:01:12.270 is going to have one valence electron, 00:01:12.270 --> 00:01:14.090 but we have two of them here, 00:01:14.090 --> 00:01:15.980 so it's gonna be two times one. 00:01:15.980 --> 00:01:20.290 And then, oxygen, it also is in the second period, 00:01:20.290 --> 00:01:21.720 and in its second shell 00:01:21.720 --> 00:01:26.320 it has one, two, three, four, five, six valence electrons. 00:01:26.320 --> 00:01:28.860 And so the total valence electrons in this molecule 00:01:28.860 --> 00:01:32.660 are gonna be four plus two, which is six, plus six, 00:01:32.660 --> 00:01:37.330 which is equal to 12 valence electrons. 00:01:37.330 --> 00:01:41.580 Now the next step is to try to draw a structure. 00:01:41.580 --> 00:01:44.640 Try to draw, 00:01:44.640 --> 00:01:49.140 draw single bonds, I'll say, single bonds. 00:01:49.140 --> 00:01:50.320 And a key question is, 00:01:50.320 --> 00:01:52.690 what do we think is going to be our central atom? 00:01:52.690 --> 00:01:56.420 And the rule of thumb is the least electronegative atom, 00:01:56.420 --> 00:01:58.530 that is not hydrogen, 00:01:58.530 --> 00:02:01.300 is a good candidate for our central atom. 00:02:01.300 --> 00:02:02.630 So we can rule out hydrogen. 00:02:02.630 --> 00:02:05.500 So between carbon and oxygen, we know that oxygen 00:02:05.500 --> 00:02:07.980 is one of the most electronegative atoms, 00:02:07.980 --> 00:02:09.490 well one of the most electronegative elements 00:02:09.490 --> 00:02:10.750 on the periodic table of elements. 00:02:10.750 --> 00:02:12.170 It's very close to fluorine. 00:02:12.170 --> 00:02:15.810 And so carbon is a good candidate for the central atom. 00:02:15.810 --> 00:02:20.600 So let's put the carbon right over here, 00:02:20.600 --> 00:02:24.000 and then let's put these other atoms around it. 00:02:24.000 --> 00:02:25.830 We could call them terminal atoms. 00:02:25.830 --> 00:02:29.340 So, let's put our oxygen right over there, 00:02:29.340 --> 00:02:31.340 and then we have two hydrogens. 00:02:31.340 --> 00:02:33.840 Hydrogen there, a hydrogen there. 00:02:33.840 --> 00:02:35.980 And let me draw the bonds. 00:02:35.980 --> 00:02:37.130 So that's a single bond. 00:02:37.130 --> 00:02:39.380 That accounts for two valence electrons. 00:02:39.380 --> 00:02:41.490 That accounts for two valence electrons. 00:02:41.490 --> 00:02:43.070 That accounts for two valence electrons. 00:02:43.070 --> 00:02:46.260 So I've just used two, four, six valence electrons. 00:02:46.260 --> 00:02:49.410 So if I subtract six valence electrons, 00:02:49.410 --> 00:02:53.580 I am now left with six valence electrons, 00:02:53.580 --> 00:02:55.910 six valence electrons. 00:02:55.910 --> 00:02:57.410 So the next step is 00:02:57.410 --> 00:02:59.660 allocate the remaining valence electrons, 00:02:59.660 --> 00:03:01.970 trying to get to the octet rule 00:03:01.970 --> 00:03:04.690 for atoms that are not hydrogen, and then for hydrogen, 00:03:04.690 --> 00:03:06.880 trying to get it to have two valence electrons. 00:03:06.880 --> 00:03:11.480 So allocate, allocate the remaining, 00:03:11.480 --> 00:03:15.890 remaining valence electrons. 00:03:15.890 --> 00:03:17.650 All right, so let's start with this oxygen. 00:03:17.650 --> 00:03:19.940 This oxygen already has these two electrons 00:03:19.940 --> 00:03:21.760 that it's sharing hanging around. 00:03:21.760 --> 00:03:25.150 So in order to get to the octet rule, it needs six more. 00:03:25.150 --> 00:03:27.910 So let's give it six electrons. 00:03:27.910 --> 00:03:32.910 So, one, two, three, four, five, six. 00:03:33.560 --> 00:03:38.100 Well I've just used up the remaining six valence electrons. 00:03:38.100 --> 00:03:40.480 So I don't really have any more to play with, 00:03:40.480 --> 00:03:43.020 but let's see how the other atoms are feeling. 00:03:43.020 --> 00:03:46.880 So hydrogen here, it's able to share these two electrons 00:03:46.880 --> 00:03:49.080 that are in this covalent bond, so it's feeling good. 00:03:49.080 --> 00:03:52.430 It can kind of pretend that it has a full outer shell, 00:03:52.430 --> 00:03:54.310 'cause its outer shell is just that one, 00:03:54.310 --> 00:03:56.970 that first shell, that's filled with two electrons. 00:03:56.970 --> 00:03:58.840 Same thing for this other hydrogen. 00:03:58.840 --> 00:04:00.560 So at least the terminal atoms, 00:04:00.560 --> 00:04:02.480 the oxygen and the two hydrogens, 00:04:02.480 --> 00:04:05.070 are feeling like they have a full outer shell. 00:04:05.070 --> 00:04:06.580 But then in the fourth step, 00:04:06.580 --> 00:04:09.540 we're going to look at our central atom. 00:04:09.540 --> 00:04:14.470 So, let's focus on the central atom, central atom, 00:04:14.470 --> 00:04:16.660 and do we need more bonds, 00:04:16.660 --> 00:04:19.430 or do we need to do something interesting here? 00:04:19.430 --> 00:04:22.030 And what we see is that carbon, 00:04:22.030 --> 00:04:25.610 it's able to have two, four, six electrons 00:04:25.610 --> 00:04:28.670 hanging around it, but it would love to have eight. 00:04:28.670 --> 00:04:31.450 Carbon would love to have a full outer shell, 00:04:31.450 --> 00:04:33.280 so how could we do that? 00:04:33.280 --> 00:04:36.000 Well, we could add more bonds. 00:04:36.000 --> 00:04:37.930 Where could the bonds come from? 00:04:37.930 --> 00:04:40.230 Well it would come from some lone pair of electrons. 00:04:40.230 --> 00:04:41.850 Well the only lone pairs of electrons 00:04:41.850 --> 00:04:43.570 are hanging around this oxygen. 00:04:43.570 --> 00:04:45.730 So what if we were to take, 00:04:45.730 --> 00:04:48.300 say, this lone pair of electrons, 00:04:48.300 --> 00:04:51.980 and then construct another covalent bond with that? 00:04:51.980 --> 00:04:55.950 Then, our Lewis diagram will look like this. 00:04:55.950 --> 00:04:57.610 I will actually redraw it. 00:04:57.610 --> 00:04:59.370 So you have your carbon, 00:04:59.370 --> 00:05:04.370 you have your three original covalent bonds, 00:05:05.220 --> 00:05:08.460 you had a hydrogen, a hydrogen, 00:05:08.460 --> 00:05:13.460 and then you had your oxygen, right over here, 00:05:13.490 --> 00:05:18.490 and now we've formed a new covalent bond, just like this, 00:05:18.680 --> 00:05:21.360 and then you have these two other lone pairs 00:05:21.360 --> 00:05:22.510 around the oxygen. 00:05:22.510 --> 00:05:24.210 So let me draw that. 00:05:24.210 --> 00:05:28.430 So, two, then another two around the oxygen. 00:05:28.430 --> 00:05:31.660 And this is looking pretty good, because the oxygen, 00:05:31.660 --> 00:05:33.880 it still has eight electrons hanging around, 00:05:33.880 --> 00:05:35.050 four in lone pairs, 00:05:35.050 --> 00:05:37.680 and then four, they're in this double bond 00:05:37.680 --> 00:05:39.070 that it is sharing. 00:05:39.070 --> 00:05:41.520 The hydrogens still have two electrons hanging around. 00:05:41.520 --> 00:05:43.670 They're able to share the electrons 00:05:43.670 --> 00:05:45.270 in each of these covalent bonds. 00:05:45.270 --> 00:05:47.890 And now the carbon is participating in, 00:05:47.890 --> 00:05:49.710 you could think of it as four covalent bonds, 00:05:49.710 --> 00:05:51.620 two single bonds and one double bond, 00:05:51.620 --> 00:05:54.410 so each of those have two electrons associated with it, 00:05:54.410 --> 00:05:56.790 so it has eight electrons hanging around. 00:05:56.790 --> 00:05:59.680 So this is looking really good 00:05:59.680 --> 00:06:03.330 as a legitimate Lewis structure, 00:06:03.330 --> 00:06:06.603 or Lewis diagram for formaldehyde.

Give a gift that will change a life.

https://www.youtube.com/watch?v=fuJxn3yG2gA

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WEBVTT Kind: captions Language: en 00:00:00.239 --> 00:00:03.572 (soft uplifting music)

Causation from 1980-2020

https://www.youtube.com/watch?v=6JXYNT5wD2A

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WEBVTT Kind: captions Language: en 00:00:00.360 --> 00:00:01.510 - [Instructor] From our first lesson 00:00:01.510 --> 00:00:03.970 focusing on the migration of indigenous people 00:00:03.970 --> 00:00:07.520 to the landmass that today comprises the United States, 00:00:07.520 --> 00:00:10.460 we've made it all the way to the present, 00:00:10.460 --> 00:00:14.250 a journey in time of more than 15,000 years. 00:00:14.250 --> 00:00:17.870 We've looked most closely at the last 500 years 00:00:17.870 --> 00:00:21.480 starting with the arrival of Europeans in the Americas. 00:00:21.480 --> 00:00:23.880 Now, in this last unit we're focused 00:00:23.880 --> 00:00:27.820 just on the last 40 years of American history 00:00:27.820 --> 00:00:30.590 from 1980 until the present. 00:00:30.590 --> 00:00:32.010 How can we examine something 00:00:32.010 --> 00:00:34.570 that's so close to us in time? 00:00:34.570 --> 00:00:36.550 We're still in this era. 00:00:36.550 --> 00:00:37.930 It doesn't have a name, 00:00:37.930 --> 00:00:41.620 not like the Gilded Age or the Revolutionary Era, 00:00:41.620 --> 00:00:42.860 at least not yet. 00:00:42.860 --> 00:00:46.150 Maybe this is the post-Cold War era 00:00:46.150 --> 00:00:49.210 or the post-9/11 era? 00:00:49.210 --> 00:00:51.450 Maybe it will be defined by the changes 00:00:51.450 --> 00:00:52.580 brought by technology 00:00:52.580 --> 00:00:55.020 and we'll call it the Information Age. 00:00:55.020 --> 00:00:57.940 Trying to think historically about the present 00:00:57.940 --> 00:00:59.820 gives us a better understanding 00:00:59.820 --> 00:01:02.360 of what it was like to live in the past, 00:01:02.360 --> 00:01:04.330 to not know what was coming next 00:01:04.330 --> 00:01:07.980 or how to interpret all the complex threads 00:01:07.980 --> 00:01:11.380 of politics, society, and culture 00:01:11.380 --> 00:01:13.050 weaving together around you. 00:01:13.050 --> 00:01:15.010 Life is messy and confusing. 00:01:15.010 --> 00:01:17.780 We don't know if we're living in a tragic era 00:01:17.780 --> 00:01:19.540 or a triumphant one, 00:01:19.540 --> 00:01:22.330 neither did the people who lived in 1940 00:01:22.330 --> 00:01:25.040 or 1860 or 1770. 00:01:25.040 --> 00:01:27.500 So years from now when historians 00:01:27.500 --> 00:01:30.990 write about the period from 1980 to 2020 00:01:30.990 --> 00:01:32.230 in the United States 00:01:32.230 --> 00:01:33.500 what will they say? 00:01:33.500 --> 00:01:35.890 Well, let's pretend for a few minutes 00:01:35.890 --> 00:01:39.030 that we are those historians from the future. 00:01:39.030 --> 00:01:41.410 Maybe we're living on a space station 00:01:41.410 --> 00:01:43.120 a few hundred years from now 00:01:43.120 --> 00:01:46.060 enjoying a Raktajino by the Replicator 00:01:46.060 --> 00:01:47.700 and discussing the United States 00:01:47.700 --> 00:01:50.290 at the turn of the 21st century. 00:01:50.290 --> 00:01:53.840 Would we be discussing a golden age or a dark period? 00:01:53.840 --> 00:01:55.640 Let's apply some of our historical 00:01:55.640 --> 00:01:57.290 thinking skills to this era 00:01:57.290 --> 00:01:59.120 and see if we can determine 00:01:59.120 --> 00:02:02.210 what effects changes in this period had 00:02:02.210 --> 00:02:04.540 on American national identity. 00:02:04.540 --> 00:02:08.040 First, let's talk about America's role in the world. 00:02:08.040 --> 00:02:10.770 In 1980, the United States was still locked 00:02:10.770 --> 00:02:12.950 in a Cold War with the Soviet Union, 00:02:12.950 --> 00:02:15.660 and when Ronald Reagan took over as president 00:02:15.660 --> 00:02:18.930 he moved the country away from the policy of Detente, 00:02:18.930 --> 00:02:21.420 or relaxation of tension, 00:02:21.420 --> 00:02:24.080 kind of live and let live with the soviets 00:02:24.080 --> 00:02:26.170 that was pursued in the 1970s 00:02:26.170 --> 00:02:30.460 towards a more active, anticommunist stance. 00:02:30.460 --> 00:02:33.910 The end of the decade saw the collapse of the Soviet Union. 00:02:33.910 --> 00:02:38.030 So after more then 40 years of foreign policy 00:02:38.030 --> 00:02:40.710 that was aimed at containing communism 00:02:40.710 --> 00:02:42.730 and the influence of the Soviet Union, 00:02:42.730 --> 00:02:45.180 capitalism and democracy were now 00:02:45.180 --> 00:02:47.800 the dominant economic and political systems, 00:02:47.800 --> 00:02:51.790 and the United States was the world's lone superpower. 00:02:51.790 --> 00:02:53.100 After the Cold War ended 00:02:53.100 --> 00:02:55.010 it wasn't immediately clear 00:02:55.010 --> 00:02:58.350 what the new US role in the world should be. 00:02:58.350 --> 00:03:01.510 Should it return to an isolationist stance 00:03:01.510 --> 00:03:03.540 like it had before World War II. 00:03:03.540 --> 00:03:06.780 Should it serve as the world's police officer 00:03:06.780 --> 00:03:09.720 keeping the peace and countering the actions 00:03:09.720 --> 00:03:12.530 of hostile powers that might try to arise. 00:03:12.530 --> 00:03:15.240 During the 1990s, the United States had 00:03:15.240 --> 00:03:18.240 a few limited engagements abroad 00:03:18.240 --> 00:03:21.210 and the Gulf War, the United States defended Kuwait 00:03:21.210 --> 00:03:23.180 from an Iraqi invasion, 00:03:23.180 --> 00:03:25.430 and it sent troops to Kosovo 00:03:25.430 --> 00:03:28.410 as part of a NATO peacekeeping force. 00:03:28.410 --> 00:03:32.460 But the terrorist attacks of September 11th, 2001 00:03:32.460 --> 00:03:35.120 on the World Trade Center in New York City 00:03:35.120 --> 00:03:37.620 and the Pentagon in Washington, D.C. 00:03:37.620 --> 00:03:41.610 began a new era of American foreign policy. 00:03:41.610 --> 00:03:44.460 US President George W. Bush articulated 00:03:44.460 --> 00:03:46.630 what's been called the Bush Doctrine 00:03:46.630 --> 00:03:48.350 which asserted that the United States 00:03:48.350 --> 00:03:51.660 has the right to secure itself against countries 00:03:51.660 --> 00:03:54.810 that harbor or give aid to terrorist groups. 00:03:54.810 --> 00:03:57.200 So under this doctrine, the United States 00:03:57.200 --> 00:04:02.200 went to war with Afghanistan in 2001 and Iraq in 2003 00:04:02.780 --> 00:04:05.270 after those countries refused to surrender 00:04:05.270 --> 00:04:08.100 Osama bin Laden and the terrorists responsible 00:04:08.100 --> 00:04:09.510 for September 11th. 00:04:09.510 --> 00:04:12.980 The war in Afghanistan became the longest war 00:04:12.980 --> 00:04:16.380 in US history continuing through 2019. 00:04:16.380 --> 00:04:20.860 At the end of this era from 1980 to 2020, 00:04:20.860 --> 00:04:23.590 Americans were continuing to debate 00:04:23.590 --> 00:04:25.810 the proper US role in the world. 00:04:25.810 --> 00:04:28.770 Should the United States withdraw from wars abroad 00:04:28.770 --> 00:04:31.010 to save the lives of American troops 00:04:31.010 --> 00:04:34.010 and the massive budget expenditures of war? 00:04:34.010 --> 00:04:35.670 Or would leaving the Middle East 00:04:35.670 --> 00:04:37.650 further destabilize the region 00:04:37.650 --> 00:04:40.170 and lead to even bigger problems in the future? 00:04:40.170 --> 00:04:41.980 Some questions that we might think about 00:04:41.980 --> 00:04:44.720 in the broader scope of US history, 00:04:44.720 --> 00:04:47.340 how does the Bush doctrine compare to 00:04:47.340 --> 00:04:50.470 earlier presidential doctrines on foreign policy 00:04:50.470 --> 00:04:53.520 like the Nixon Doctrine, the Truman Doctrine, 00:04:53.520 --> 00:04:55.550 or even the Monroe Doctrine? 00:04:55.550 --> 00:04:57.780 And how does the war in Afghanistan 00:04:57.780 --> 00:05:00.990 compare to the United States' second longest war, 00:05:00.990 --> 00:05:02.470 the war in Vietnam. 00:05:02.470 --> 00:05:03.990 The end of the Cold War 00:05:03.990 --> 00:05:06.410 and the rise of the war on terror 00:05:06.410 --> 00:05:09.700 weren't the only major changes in this time period. 00:05:09.700 --> 00:05:12.790 There were also far-reaching social changes. 00:05:12.790 --> 00:05:14.580 How work was done, 00:05:14.580 --> 00:05:16.370 how much people were paid for it, 00:05:16.370 --> 00:05:17.810 and who did that work. 00:05:17.810 --> 00:05:19.480 In the late 20th century, 00:05:19.480 --> 00:05:22.950 the emergence of the personal computer and the internet 00:05:22.950 --> 00:05:24.640 made it possible to communicate 00:05:24.640 --> 00:05:28.280 and to do business all over the world in an instant. 00:05:28.280 --> 00:05:32.320 At the same time, barriers to trade fell between countries. 00:05:32.320 --> 00:05:35.030 In 1994, the United States signed 00:05:35.030 --> 00:05:38.510 the North American Free Trade Agreement or NAFTA 00:05:38.510 --> 00:05:41.500 to reduce or eliminate tariffs on trade goods 00:05:41.500 --> 00:05:44.550 between the United States, Mexico and Canada. 00:05:44.550 --> 00:05:49.460 The growing international interdependence of business 00:05:49.460 --> 00:05:51.510 and the mixing of cultures that business 00:05:51.510 --> 00:05:55.060 carries along with it is called globalization. 00:05:55.060 --> 00:05:58.240 But the availability of cheap goods and cheap labor 00:05:58.240 --> 00:06:00.370 that globalization made possible 00:06:00.370 --> 00:06:04.550 also had some economic consequences for American workers. 00:06:04.550 --> 00:06:07.410 Manufacturing generally moved overseas 00:06:07.410 --> 00:06:10.510 to take advantage of lower wages and regulations 00:06:10.510 --> 00:06:13.640 and union membership fell to a record low. 00:06:13.640 --> 00:06:15.880 Meanwhile, the share of Americans 00:06:15.880 --> 00:06:18.820 working in service-oriented jobs rose. 00:06:18.820 --> 00:06:21.250 The largest employer in the United States 00:06:21.250 --> 00:06:23.820 in 2019 was Walmart. 00:06:23.820 --> 00:06:26.010 Wages have stagnated for low 00:06:26.010 --> 00:06:27.990 and middle class American workers 00:06:27.990 --> 00:06:31.000 while wages have soared for the richest Americans. 00:06:31.000 --> 00:06:33.250 A study by the federal reserve found that 00:06:33.250 --> 00:06:36.580 although the total net worth of US households 00:06:36.580 --> 00:06:40.500 more than quadrupled between 1989 and 2018, 00:06:40.500 --> 00:06:42.450 most of those gains were for the wealthy, 00:06:42.450 --> 00:06:45.090 with the top 10% of households controlling 00:06:45.090 --> 00:06:47.640 64% of overall wealth. 00:06:47.640 --> 00:06:51.130 The top 1% alone controlled 32%. 00:06:51.130 --> 00:06:53.270 Another social change of the late 20th 00:06:53.270 --> 00:06:56.680 and early 21st century was the growth of immigration. 00:06:56.680 --> 00:06:59.370 The 1965 immigration act ended 00:06:59.370 --> 00:07:01.410 national quotas in immigration 00:07:01.410 --> 00:07:04.070 which had barred immigration for most countries 00:07:04.070 --> 00:07:05.700 other than Western Europe. 00:07:05.700 --> 00:07:08.440 As a result, immigration from Latin America, 00:07:08.440 --> 00:07:10.770 Asia and Africa grew 00:07:10.770 --> 00:07:13.900 changing the racial demographics of the United States. 00:07:13.900 --> 00:07:16.620 Some of the biggest questions of American politics 00:07:16.620 --> 00:07:18.230 at the end of this era 00:07:18.230 --> 00:07:21.930 concerned the effects of globalization and immigration. 00:07:21.930 --> 00:07:24.730 Putting this in a broader historical context 00:07:24.730 --> 00:07:26.970 we might ask how did the developments 00:07:26.970 --> 00:07:29.510 in this time period compare with 00:07:29.510 --> 00:07:33.420 say the Second Industrial Revolution in the Gilded Age 00:07:33.420 --> 00:07:36.220 when new manufacturing technology opened up 00:07:36.220 --> 00:07:37.920 many new factory jobs, 00:07:37.920 --> 00:07:40.920 and lured many immigrants to American cities, 00:07:40.920 --> 00:07:43.920 but also bred great inequality of wealth. 00:07:43.920 --> 00:07:47.500 Politics in this period also differed sharply 00:07:47.500 --> 00:07:49.770 from the era that came before it. 00:07:49.770 --> 00:07:52.710 From 1932 to 1980, 00:07:52.710 --> 00:07:56.700 liberal ideas had dominated American politics 00:07:56.700 --> 00:07:58.710 that government should be active 00:07:58.710 --> 00:08:00.580 in securing the welfare of people, 00:08:00.580 --> 00:08:03.540 and that taxation should pay for those initiatives. 00:08:03.540 --> 00:08:06.190 But there was a growing conservative movement 00:08:06.190 --> 00:08:07.970 starting in the 1960s 00:08:07.970 --> 00:08:10.550 and Ronald Reagan's election in 1980 00:08:10.550 --> 00:08:13.750 began a period of limiting government regulation 00:08:13.750 --> 00:08:15.220 and lowering taxes. 00:08:15.220 --> 00:08:19.050 And when democrat Bill Clinton took office in 1993, 00:08:19.050 --> 00:08:21.530 he largely adopted that same stance. 00:08:21.530 --> 00:08:24.630 He declared that the era of big government is over 00:08:24.630 --> 00:08:27.160 and reduced welfare benefits significantly. 00:08:27.160 --> 00:08:31.230 The 1990s saw the emergence of the culture wars. 00:08:31.230 --> 00:08:34.580 Battles over the growing multiculturalism, 00:08:34.580 --> 00:08:37.340 secularism, and cultural acceptance 00:08:37.340 --> 00:08:40.990 of non-traditional marriage and family relationships. 00:08:40.990 --> 00:08:43.360 Many conservative Christians feared that 00:08:43.360 --> 00:08:46.200 the traditional American nuclear family 00:08:46.200 --> 00:08:49.240 with Christian, heterosexual married parents 00:08:49.240 --> 00:08:50.400 was disappearing. 00:08:50.400 --> 00:08:53.000 Meanwhile, liberal progressive celebrated 00:08:53.000 --> 00:08:56.190 the growing acceptance of LGBTQ citizens 00:08:56.190 --> 00:08:58.050 in diversity and public life. 00:08:58.050 --> 00:09:01.710 This was also a time of bitter partisan divisions 00:09:01.710 --> 00:09:03.810 with citizens not only more strongly 00:09:03.810 --> 00:09:05.400 identifying with one party 00:09:05.400 --> 00:09:08.410 but increasingly vilifying members of the other party 00:09:08.410 --> 00:09:11.090 is immoral or unpatriotic. 00:09:11.090 --> 00:09:14.130 To put this in a broader historical context 00:09:14.130 --> 00:09:16.670 we might ask, do these partisan divisions 00:09:16.670 --> 00:09:19.380 suggest that American national identity 00:09:19.380 --> 00:09:21.400 was fractured beyond repair 00:09:21.400 --> 00:09:24.450 or that a party realignment was underway? 00:09:24.450 --> 00:09:27.740 How does this period compare with the 1850s 00:09:27.740 --> 00:09:29.970 when the beliefs of the north and south diverged 00:09:29.970 --> 00:09:32.870 sharply over the institution of slavery? 00:09:32.870 --> 00:09:34.780 These are very difficult question 00:09:34.780 --> 00:09:37.170 and I'm glad we're here in the 23rd century 00:09:37.170 --> 00:09:38.900 enjoying the benefits of hindsight 00:09:38.900 --> 00:09:42.753 to assess that strange period from 1980 to 2020.

Worked example: Using formal charges to evaluate nonequivalent resonance structures

https://www.youtube.com/watch?v=N8qKGrChGC4

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https://www.youtube.com/api/timedtext?v=N8qKGrChGC4&ei=bViUZZySEqClvdIPuNaMkAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=16222CF63834DD8E2DA17DE70C476F060D0ECCF4.6AE4CC1996DF640FE6F9AEFA52757EFA1978DC55&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:01.322 --> 00:00:02.229 - [Instructor] We're told 00:00:02.229 --> 00:00:04.242 that three possible resonance structures 00:00:04.242 --> 00:00:08.060 for the thiocyanate ion are shown below. 00:00:08.060 --> 00:00:09.213 All right, there we have them. 00:00:10.092 --> 00:00:11.673 Based on formal charges, 00:00:12.579 --> 00:00:15.531 which of the three structures contributes most 00:00:15.531 --> 00:00:19.183 to the resonance hybrid of thiocyanate? 00:00:20.402 --> 00:00:22.470 And they have given us some extra information. 00:00:22.470 --> 00:00:24.925 They've given us the various elements 00:00:24.925 --> 00:00:26.686 in these resonance structures, 00:00:26.686 --> 00:00:30.055 and they've told us their Pauling scale electronegativity, 00:00:30.055 --> 00:00:32.286 so maybe that is going to be useful 00:00:32.286 --> 00:00:34.000 for thinking about basing on the, 00:00:34.000 --> 00:00:35.457 based on the formal charges, 00:00:35.457 --> 00:00:37.020 which of the three structures contributes most 00:00:37.020 --> 00:00:40.948 to the resonance hybrid of thiocyanate? 00:00:40.948 --> 00:00:42.723 So pause this video and see if you can figure that out. 00:00:44.025 --> 00:00:45.960 All right, now let's work through this together. 00:00:45.960 --> 00:00:50.180 So there's really two things we want to optimize for 00:00:50.180 --> 00:00:51.476 when we're thinking about which 00:00:51.476 --> 00:00:53.110 of these resonance structures contributes most 00:00:53.110 --> 00:00:54.523 to the resonance hybrid? 00:00:55.650 --> 00:00:58.770 One, we want to figure out the resonance structures 00:00:59.647 --> 00:01:03.340 where individual atoms have formal charges 00:01:03.340 --> 00:01:05.932 as close to zero as possible. 00:01:05.932 --> 00:01:07.316 So let me write that down. 00:01:07.316 --> 00:01:08.149 Individual, 00:01:09.218 --> 00:01:10.680 individual atoms 00:01:12.150 --> 00:01:16.480 have formal charge 00:01:19.014 --> 00:01:20.613 as close to zero as possible. 00:01:21.464 --> 00:01:25.082 As close to zero as possible. 00:01:25.082 --> 00:01:27.044 We're not talking about the charge of the entire ion. 00:01:27.044 --> 00:01:29.723 We're talking about individual atoms' formal charges, 00:01:30.659 --> 00:01:31.959 close to zero as possible. 00:01:33.198 --> 00:01:35.198 And then the electronegativity is useful 00:01:36.098 --> 00:01:38.241 because we also want to see 00:01:38.241 --> 00:01:40.669 if there's any negative formal charge 00:01:40.669 --> 00:01:42.467 on an individual atom 00:01:42.467 --> 00:01:45.204 that ideally, that would be on the most electronegative 00:01:45.204 --> 00:01:46.755 of the atoms. 00:01:46.755 --> 00:01:49.300 So any formal charge, 00:01:49.300 --> 00:01:50.133 so once again, we're not talking about the charge 00:01:50.133 --> 00:01:51.343 of the entire ion. 00:01:52.258 --> 00:01:53.283 Any formal charge, 00:01:55.230 --> 00:01:56.886 any negative, 00:01:56.886 --> 00:01:58.450 any negative formal charge 00:01:58.450 --> 00:02:00.183 on individual atom, 00:02:01.207 --> 00:02:03.493 individual atom, 00:02:05.762 --> 00:02:07.570 ideally, ideally 00:02:09.038 --> 00:02:11.113 on most electronegative ones, 00:02:12.204 --> 00:02:13.604 or most electronegative one. 00:02:14.456 --> 00:02:15.789 Electronegative. 00:02:17.080 --> 00:02:19.959 All right, now with these two principles, 00:02:19.959 --> 00:02:22.980 let's figure out which of these resonance structures 00:02:23.923 --> 00:02:26.263 get closest to these ideals. 00:02:26.263 --> 00:02:27.183 So to do that, 00:02:27.183 --> 00:02:29.288 let's just calculate the formal charges 00:02:29.288 --> 00:02:31.519 in each of these resonance structures. 00:02:31.519 --> 00:02:35.009 So the way that we do that is for each of these elements, 00:02:35.009 --> 00:02:37.742 if you had just a free atom of it that was neutral, 00:02:37.742 --> 00:02:39.852 how many valence electrons would it have? 00:02:39.852 --> 00:02:42.318 And actually, let me make another column right over here, 00:02:42.318 --> 00:02:44.459 which is just the valence electrons. 00:02:44.459 --> 00:02:46.623 You can look it up on a periodic table of elements 00:02:46.623 --> 00:02:47.595 or you might already know 00:02:47.595 --> 00:02:51.393 that carbon has four valence electrons, six total, 00:02:51.393 --> 00:02:52.813 but four in that second shell. 00:02:53.786 --> 00:02:56.751 Nitrogen has five valence electrons, 00:02:56.751 --> 00:02:58.180 a neutral nitrogen, 00:02:58.180 --> 00:02:59.637 seven overall electrons, 00:02:59.637 --> 00:03:01.905 but it has five in its outer shell, 00:03:01.905 --> 00:03:03.893 and sulfur has six valence electrons. 00:03:05.034 --> 00:03:07.375 And the way that we calculate formal charge 00:03:07.375 --> 00:03:09.120 of the individual atoms 00:03:09.120 --> 00:03:11.481 in each of these resonance structures 00:03:11.481 --> 00:03:12.314 is we say, all right, 00:03:12.314 --> 00:03:15.329 how many valence electrons would say, sulfur, 00:03:15.329 --> 00:03:18.033 a neutral, free sulfur atom typically have? 00:03:18.033 --> 00:03:20.207 And we know that that is six. 00:03:20.207 --> 00:03:21.184 And then we say, well, 00:03:21.184 --> 00:03:23.210 how many outer electrons are hanging out 00:03:23.210 --> 00:03:26.073 around the sulfur in this resonance structure? 00:03:27.191 --> 00:03:29.152 And the outer electrons that we see here, 00:03:29.152 --> 00:03:30.952 it's really from this Lewis diagram, 00:03:31.799 --> 00:03:33.783 we can see one, two, 00:03:34.809 --> 00:03:36.663 three, four, five. 00:03:37.721 --> 00:03:41.534 So five electrons versus six valence electrons 00:03:41.534 --> 00:03:43.723 in a typically neutral sulfur free atom, 00:03:44.705 --> 00:03:46.142 and so it's one less electron. 00:03:46.142 --> 00:03:49.454 So you would expect a plus one formal charge here. 00:03:49.454 --> 00:03:50.550 Another way you could think about it is typically, 00:03:50.550 --> 00:03:52.833 six valence electrons and, 00:03:53.704 --> 00:03:55.880 but we are only seeing five hanging out 00:03:56.801 --> 00:03:58.800 in this Lewis structure, 00:03:58.800 --> 00:04:01.286 so that's where we get our plus one from. 00:04:01.286 --> 00:04:04.688 Now we can do the same exercise for the carbon here. 00:04:04.688 --> 00:04:07.874 Carbon typically has four valence electrons 00:04:07.874 --> 00:04:08.825 when it's neutral, 00:04:08.825 --> 00:04:10.251 and this Lewis structure, 00:04:10.251 --> 00:04:11.526 in this resonance structure, 00:04:11.526 --> 00:04:15.110 we can see that four outer electrons are hanging out, 00:04:15.110 --> 00:04:16.605 the same as you would expect 00:04:16.605 --> 00:04:18.658 for a neutral carbon atom. 00:04:18.658 --> 00:04:21.508 And so four minus four, you have zero formal charge here. 00:04:22.682 --> 00:04:24.144 And then for the nitrogen, 00:04:24.144 --> 00:04:26.667 we have one, two, three, 00:04:26.667 --> 00:04:28.703 four, five, six, seven. 00:04:29.666 --> 00:04:31.820 We can say outer electrons hanging out. 00:04:31.820 --> 00:04:34.983 Neutral nitrogen would have five valence electrons, 00:04:36.061 --> 00:04:37.300 so five valence electrons, 00:04:37.300 --> 00:04:38.828 we have two more than that. 00:04:38.828 --> 00:04:41.135 Five minus seven is negative two. 00:04:41.135 --> 00:04:44.483 So since we have two more outer electrons hanging out 00:04:44.483 --> 00:04:46.986 than we would typically have for a neutral nitrogen, 00:04:46.986 --> 00:04:49.363 we have a negative two formal charge. 00:04:50.371 --> 00:04:52.743 Now let's go to this resonance structure here. 00:04:52.743 --> 00:04:53.803 So same idea. 00:04:54.760 --> 00:04:56.960 Here, we have one, two, three, 00:04:56.960 --> 00:05:01.623 four, five, six outer electrons hanging out, the sulfur. 00:05:02.628 --> 00:05:06.202 Now that's the same as a neutral sulfur valence electrons. 00:05:06.202 --> 00:05:07.943 So here, we have no formal charge. 00:05:08.944 --> 00:05:09.813 You could think about it, 00:05:09.813 --> 00:05:11.363 six minus six is equal to zero. 00:05:12.220 --> 00:05:16.776 Carbon, we have four outer electrons hanging around 00:05:16.776 --> 00:05:17.976 from this Lewis diagram, 00:05:19.378 --> 00:05:21.160 and that's typical of the valence electrons 00:05:21.160 --> 00:05:22.253 of a neutral carbon, 00:05:23.141 --> 00:05:25.433 so once again, four minus four, 00:05:25.433 --> 00:05:27.774 we have no formal charge there, 00:05:27.774 --> 00:05:29.827 and then we move onto the nitrogen. 00:05:29.827 --> 00:05:32.470 We have one, two, three, 00:05:32.470 --> 00:05:35.973 four, five, six outer electrons hanging out. 00:05:37.098 --> 00:05:38.848 Nitrogen would typically have five. 00:05:39.724 --> 00:05:43.103 Five minus six, we have one extra electron hanging out, 00:05:44.043 --> 00:05:46.655 which gives us a negative one formal charge, 00:05:46.655 --> 00:05:49.857 the nitrogen right over there in this resonance structure, 00:05:49.857 --> 00:05:52.000 and then last, but not least, 00:05:52.000 --> 00:05:53.692 in this resonance structure, 00:05:53.692 --> 00:05:56.530 we have one, two, three, four, five, 00:05:56.530 --> 00:05:59.941 six, seven electrons hanging around, 00:05:59.941 --> 00:06:02.241 outer electrons hanging out around the sulfur. 00:06:03.249 --> 00:06:05.716 Neutral sulfur would have six valence electrons. 00:06:05.716 --> 00:06:07.133 Six minus this seven, 00:06:08.036 --> 00:06:09.763 we have one extra electron. 00:06:09.763 --> 00:06:12.363 That's what gives us this negative one formal charge 00:06:13.441 --> 00:06:15.975 for the sulfur in that resonance structure. 00:06:15.975 --> 00:06:19.173 The carbon is still having four hanging out, 00:06:20.350 --> 00:06:21.698 which is typical of carbon 00:06:21.698 --> 00:06:23.283 and neutral carbon's valence electrons, 00:06:23.283 --> 00:06:25.138 so no formal charge there, 00:06:25.138 --> 00:06:28.420 and then the nitrogen has one, two, three, 00:06:28.420 --> 00:06:31.563 four, five outer electrons hanging out, 00:06:32.572 --> 00:06:33.472 which is equivalent 00:06:33.472 --> 00:06:36.363 to a neutral nitrogen's valence electrons, 00:06:37.306 --> 00:06:38.999 and so five minus five, 00:06:38.999 --> 00:06:40.854 you have no formal charge. 00:06:40.854 --> 00:06:41.752 So there you have it. 00:06:41.752 --> 00:06:43.644 We've looked at the formal charges on all of these, 00:06:43.644 --> 00:06:45.123 and now let's look at these ideals. 00:06:46.036 --> 00:06:48.681 So individual atoms have formal charges close 00:06:48.681 --> 00:06:49.681 to zero as possible. 00:06:50.827 --> 00:06:52.786 In this first resonance structure, 00:06:52.786 --> 00:06:54.240 we have two individual atoms 00:06:55.127 --> 00:06:57.010 whose formal charges are not zero, and in fact, 00:06:57.010 --> 00:06:59.103 nitrogen is quite far from zero, 00:07:00.096 --> 00:07:02.359 while in these other two resonance structures, 00:07:02.359 --> 00:07:05.623 we only have one atom whose formal charge is not zero. 00:07:06.595 --> 00:07:09.129 So I'm liking, just based on this first principle, 00:07:09.129 --> 00:07:11.976 I'm liking these second two resonance structures 00:07:11.976 --> 00:07:13.690 as contributing more to the resonance hybrid 00:07:13.690 --> 00:07:14.983 than this first one. 00:07:15.915 --> 00:07:17.403 So I will rule that one out, 00:07:18.503 --> 00:07:20.345 and then if we had to pick between these two, 00:07:20.345 --> 00:07:21.941 we could go to the second principle. 00:07:21.941 --> 00:07:24.755 Any negative formal charge on an individual atom, 00:07:24.755 --> 00:07:26.083 ideally on the most electronegative. 00:07:27.367 --> 00:07:29.126 So in this resonance structure here, 00:07:29.126 --> 00:07:30.983 I guess the second resonance structure, 00:07:30.983 --> 00:07:33.376 the negative formal charge is on nitrogen. 00:07:33.376 --> 00:07:34.347 While on this third one, 00:07:34.347 --> 00:07:36.709 the negative formal charge is on sulfur. 00:07:36.709 --> 00:07:38.826 And we can see from this table 00:07:38.826 --> 00:07:41.653 that nitrogen is more electronegative than sulfur. 00:07:42.645 --> 00:07:45.005 So it's in the second resonance structure, 00:07:45.005 --> 00:07:48.030 you have the negative formal charge on an atom 00:07:48.030 --> 00:07:50.784 that is more electronegative than nitrogen 00:07:50.784 --> 00:07:53.448 than in this third resonance structure, 00:07:53.448 --> 00:07:54.548 and so this is the one 00:07:55.553 --> 00:07:57.160 that I believe contributes most 00:07:57.160 --> 00:08:00.611 to the resonance hybrid of thiocyanate 00:08:00.611 --> 00:08:01.711 for these two reasons.

Representing alloys using particulate models

https://www.youtube.com/watch?v=LTH-WH97zbo

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https://www.youtube.com/api/timedtext?v=LTH-WH97zbo&ei=bViUZZ6TIrSjp-oPo5a-6A8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=32488C9B7EFFC7CDF171C50861056E527BA84EB5.6077019AC7DE6B03CA98BAC7207CF0CF50B8D12F&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.230 --> 00:00:02.620 - [Instructor] In many videos we have already talked about 00:00:02.620 --> 00:00:05.410 metals and metallic bonds. 00:00:05.410 --> 00:00:08.210 And in this video we're going to dig a little bit deeper 00:00:08.210 --> 00:00:11.720 and in particular, we're going to talk about alloys, 00:00:11.720 --> 00:00:13.850 which are mixtures of elements, 00:00:13.850 --> 00:00:17.600 but still have metallic properties. 00:00:17.600 --> 00:00:20.490 So first of all, what are metallic properties? 00:00:20.490 --> 00:00:23.170 Well those tend to be things like they're shiny, 00:00:23.170 --> 00:00:24.130 they reflect light. 00:00:24.130 --> 00:00:27.040 This is actually a pure iron sample right over here. 00:00:27.040 --> 00:00:28.980 You can see that it reflects light. 00:00:28.980 --> 00:00:30.440 It tends to be malleable, 00:00:30.440 --> 00:00:32.810 which means you can bend it without breaking it. 00:00:32.810 --> 00:00:35.610 And it tends to conduct electricity. 00:00:35.610 --> 00:00:37.560 And alloys are when you can mix 00:00:37.560 --> 00:00:39.040 multiple elements together 00:00:39.040 --> 00:00:41.980 and still have most of these properties. 00:00:41.980 --> 00:00:45.460 And just as a review of where these properties come from, 00:00:45.460 --> 00:00:47.910 we can imagine metallic bonds. 00:00:47.910 --> 00:00:50.010 And there's a whole video on this, 00:00:50.010 --> 00:00:51.730 but in metallic bonds, let's say we were 00:00:51.730 --> 00:00:54.630 to take a bunch of iron and you can see right over here, 00:00:54.630 --> 00:00:58.250 iron, Fe, it is a transition metal. 00:00:58.250 --> 00:01:00.310 And what happens with metals is, 00:01:00.310 --> 00:01:02.330 is when they form bonds with each other, 00:01:02.330 --> 00:01:03.760 they're valence electrons, 00:01:03.760 --> 00:01:06.380 because each of the atoms aren't that electronegative, 00:01:06.380 --> 00:01:07.910 they don't want to hog the electrons. 00:01:07.910 --> 00:01:09.720 They don't want them, just for themselves. 00:01:09.720 --> 00:01:11.900 They're willing to share their valence electrons 00:01:11.900 --> 00:01:14.950 into a bit of a communal pool of electrons. 00:01:14.950 --> 00:01:17.950 And so even though you have a bunch of neutral, 00:01:17.950 --> 00:01:21.080 let's say iron atoms, you could actually view them 00:01:21.080 --> 00:01:26.080 as positively charged ions in a sea of electrons. 00:01:29.070 --> 00:01:32.850 And so you have a bunch of electrons here. 00:01:32.850 --> 00:01:35.010 And where did these electrons come from? 00:01:35.010 --> 00:01:36.830 Well these are the valence electrons 00:01:36.830 --> 00:01:40.880 from the neutral atoms that get contributed to this sea. 00:01:40.880 --> 00:01:42.630 And this is why most metals are good 00:01:42.630 --> 00:01:44.210 at conducting electricity. 00:01:44.210 --> 00:01:46.463 This is why they are malleable. 00:01:47.613 --> 00:01:48.446 And depending on the metal, 00:01:48.446 --> 00:01:51.180 if you're talking about a Group one metal, 00:01:51.180 --> 00:01:52.570 you could imagine that the charge 00:01:52.570 --> 00:01:55.990 of these ions right over here would be a plus one. 00:01:55.990 --> 00:01:57.810 But if we're talking about a Group two metal 00:01:57.810 --> 00:02:01.380 or a transition metal, they have more valence electrons 00:02:01.380 --> 00:02:03.700 that they might be able to contribute to this pool. 00:02:03.700 --> 00:02:05.480 And so if you're thinking about these ions, 00:02:05.480 --> 00:02:07.460 they can even have a positive two charge 00:02:07.460 --> 00:02:09.780 or a positive three charge. 00:02:09.780 --> 00:02:13.160 But as promised in this video we're gonna talk about 00:02:13.160 --> 00:02:15.190 the notion of alloys. 00:02:15.190 --> 00:02:17.720 And we're going to do these particulate diagrams 00:02:17.720 --> 00:02:19.240 that we have seen in other videos. 00:02:19.240 --> 00:02:20.940 And in the particulate diagrams, 00:02:20.940 --> 00:02:24.310 we're not going to show this sea of electrons, 00:02:24.310 --> 00:02:25.840 but they're going to help us visualize 00:02:25.840 --> 00:02:27.840 the structure of the alloys. 00:02:27.840 --> 00:02:29.690 So let's imagine what iron could look like. 00:02:29.690 --> 00:02:32.030 And we're just going to look at a two-dimensional slice 00:02:32.030 --> 00:02:35.270 of a solid of iron, where all the iron atoms 00:02:35.270 --> 00:02:36.680 have formed metallic bonds. 00:02:36.680 --> 00:02:37.850 And as I said, we're not going 00:02:37.850 --> 00:02:39.620 to draw this sea of electrons, 00:02:39.620 --> 00:02:42.230 but they might form a pretty regular structure, 00:02:42.230 --> 00:02:43.960 something like this. 00:02:43.960 --> 00:02:48.130 And so each of these circles represent an iron atom. 00:02:48.130 --> 00:02:51.150 But as promised, this video is about alloys. 00:02:51.150 --> 00:02:53.840 So let's imagine what steel might look like. 00:02:53.840 --> 00:02:57.090 This is a steel blade and steel is a bunch of iron, 00:02:57.090 --> 00:03:01.330 so once again, we can visualize each of these 00:03:01.330 --> 00:03:05.140 as an iron atom, but mixed in with that iron 00:03:05.140 --> 00:03:07.090 is a little bit of carbon. 00:03:07.090 --> 00:03:09.190 And when you look at the periodic table of elements 00:03:09.190 --> 00:03:12.380 you can see that carbon is a good bit higher 00:03:12.380 --> 00:03:13.510 on the periodic table of elements 00:03:13.510 --> 00:03:16.080 and to the right of iron. 00:03:16.080 --> 00:03:19.300 Neutral iron has 26 protons and 26 electrons, 00:03:19.300 --> 00:03:22.720 and neutral carbon only has six protons and six electrons. 00:03:22.720 --> 00:03:25.490 The valence electrons in carbon are in their second shell. 00:03:25.490 --> 00:03:29.050 The valence electrons of iron are in the fourth shell. 00:03:29.050 --> 00:03:32.000 So carbon is a good bit smaller. 00:03:32.000 --> 00:03:34.570 And so, when you mix that carbon in, 00:03:34.570 --> 00:03:35.910 because it is smaller, 00:03:35.910 --> 00:03:39.130 it's able to fit in the gaps between the irons. 00:03:39.130 --> 00:03:41.380 So you might have, I'll draw this right here. 00:03:41.380 --> 00:03:43.240 You might have a little bit of carbon there. 00:03:43.240 --> 00:03:45.703 You might have a little bit of carbon there. 00:03:46.689 --> 00:03:48.230 You might have a little bit of carbon there. 00:03:48.230 --> 00:03:50.400 And so when you form an alloy, 00:03:50.400 --> 00:03:53.690 where one atom has a larger radius 00:03:53.690 --> 00:03:56.100 or a significantly larger radius than the other, 00:03:56.100 --> 00:03:58.297 you tend to form things like this, 00:03:58.297 --> 00:04:00.297 which are known as interstitial alloys, 00:04:04.160 --> 00:04:09.050 and basic carbon steel is a good example of it. 00:04:09.050 --> 00:04:11.730 Now you have other situations where you have alloys 00:04:11.730 --> 00:04:14.610 between atoms of similar size. 00:04:14.610 --> 00:04:17.550 And this right over here, this is a brass, 00:04:17.550 --> 00:04:19.460 I don't know if this is a clock or an astrolabe, 00:04:19.460 --> 00:04:20.870 or something like this, 00:04:20.870 --> 00:04:25.870 but brass is made up of a mix of copper and zinc. 00:04:27.040 --> 00:04:28.660 And so when you have an alloy like this, 00:04:28.660 --> 00:04:32.010 that's between atoms of similar radius, 00:04:32.010 --> 00:04:34.480 this is called a substitutional alloy. 00:04:34.480 --> 00:04:36.560 You can imagine that some of the copper 00:04:36.560 --> 00:04:39.390 has been substituted with zinc. 00:04:39.390 --> 00:04:42.860 So this is substitutional alloy. 00:04:42.860 --> 00:04:44.880 Now the last thing you might be wondering about is 00:04:44.880 --> 00:04:46.870 can you have a combination of both? 00:04:46.870 --> 00:04:48.910 And you indeed can. 00:04:48.910 --> 00:04:50.270 This is over here are panels 00:04:50.270 --> 00:04:52.290 on the International Space Station, 00:04:52.290 --> 00:04:54.160 and it's made out of stainless steel. 00:04:54.160 --> 00:04:56.840 You're likely to have stainless steel in your kitchen. 00:04:56.840 --> 00:04:59.510 And stainless steel, you could view it as 00:04:59.510 --> 00:05:03.590 it's basic steel but instead of just iron and carbon, 00:05:03.590 --> 00:05:06.730 It also has a little bit of chromium mixed in. 00:05:06.730 --> 00:05:09.690 And so we can visualize this. 00:05:09.690 --> 00:05:11.760 If this is stainless steel, 00:05:11.760 --> 00:05:15.360 maybe the blue ones, we say are iron, 00:05:15.360 --> 00:05:16.990 but it has a little bit of chromium. 00:05:16.990 --> 00:05:18.550 I'll do that with red. 00:05:18.550 --> 00:05:21.570 Chromium has a similar radius to iron. 00:05:21.570 --> 00:05:24.170 It's not exactly the same, but it is close. 00:05:24.170 --> 00:05:26.210 So maybe a little chromium there, 00:05:26.210 --> 00:05:29.340 a little bit of chromium right over there, 00:05:29.340 --> 00:05:33.367 a little bit of chromium right over there. 00:05:33.367 --> 00:05:34.200 And if it was just iron chromium 00:05:34.200 --> 00:05:35.530 we would call it substitutional, 00:05:35.530 --> 00:05:39.210 but it also has carbon and carbon has a smaller radius. 00:05:39.210 --> 00:05:41.110 So maybe a little bit of carbon fitting 00:05:41.110 --> 00:05:43.940 in the gaps between the larger atoms there. 00:05:43.940 --> 00:05:45.490 A little bit of carbon there. 00:05:45.490 --> 00:05:47.960 A little bit of carbon right over here. 00:05:47.960 --> 00:05:51.170 And so this is an example of an alloy, 00:05:51.170 --> 00:05:55.340 that is both interstitial and substitutional. 00:05:55.340 --> 00:05:56.610 Now one final question, you're like okay 00:05:56.610 --> 00:05:57.760 this is all interesting, 00:05:57.760 --> 00:06:02.380 but why have we decided to put things like carbon in iron? 00:06:02.380 --> 00:06:04.390 Well it turns out that even by putting 00:06:04.390 --> 00:06:06.220 a little bit of carbon in or mixing in 00:06:06.220 --> 00:06:09.620 with other metals, you're able to change 00:06:09.620 --> 00:06:13.100 the properties and for example, steel as an alloy, 00:06:13.100 --> 00:06:17.290 is much stronger than iron, by itself. 00:06:17.290 --> 00:06:20.210 And stainless steel once you mix that chromium in, 00:06:20.210 --> 00:06:24.270 it's much more resistant to corrosion, than basic steel. 00:06:24.270 --> 00:06:25.510 So I'll leave you there. 00:06:25.510 --> 00:06:29.293 You just learned a little bit more about metals and alloys.

Representing ionic solids using particulate models

https://www.youtube.com/watch?v=sAhRvgX4tQk

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https://www.youtube.com/api/timedtext?v=sAhRvgX4tQk&ei=bViUZdLcEJq-mLAP28OzuAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245981&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C465B7D97A4931B9FAFD194F36A1DDC4831699BE.E343D314AB889E0EF888949AC0380A54346B5102&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.290 --> 00:00:01.770 - [Instructor] In this video, we're gonna think about 00:00:01.770 --> 00:00:04.102 how ions will arrange themselves 00:00:04.102 --> 00:00:07.120 when they form solid crystals. 00:00:07.120 --> 00:00:10.310 When they form these lattice structures. 00:00:10.310 --> 00:00:12.380 So just in very broad brush terms, 00:00:12.380 --> 00:00:17.030 let's say that we have a bunch of this white cation, 00:00:17.030 --> 00:00:22.030 and we have a bunch of this green, or this blue-green anion. 00:00:22.890 --> 00:00:25.050 So let's say they're in a one-to-one ratio. 00:00:25.050 --> 00:00:26.846 How will that look? 00:00:26.846 --> 00:00:28.320 How will the solid look, if you were to take 00:00:28.320 --> 00:00:30.080 a two-dimensional slice of it? 00:00:30.080 --> 00:00:31.890 To imagine that, we can draw 00:00:31.890 --> 00:00:34.010 what we could call particulate models. 00:00:34.010 --> 00:00:36.930 We're just imagining a two-dimensional slice of the solid, 00:00:36.930 --> 00:00:40.250 and we're just drawing these ions as particles. 00:00:40.250 --> 00:00:42.060 Would it look something like this, 00:00:42.060 --> 00:00:47.060 where maybe the positive ion is all on one side, 00:00:49.240 --> 00:00:54.110 and then the negative ion is on the other side, 00:00:54.110 --> 00:00:57.190 is on the bottom if we were to take a slice? 00:00:57.190 --> 00:01:01.410 Would something like this make sense? 00:01:01.410 --> 00:01:03.000 Or maybe it's random. 00:01:03.000 --> 00:01:05.460 Maybe you have a positive there, 00:01:05.460 --> 00:01:09.810 and then you have some negatives right over there. 00:01:09.810 --> 00:01:14.130 And then, maybe you have a positive and a positive, 00:01:14.130 --> 00:01:16.760 and then a positive right over there. 00:01:16.760 --> 00:01:21.054 And then maybe you have some negatives right over there. 00:01:21.054 --> 00:01:23.810 Would this be a reasonable configuration, 00:01:23.810 --> 00:01:26.493 as they form these ionic bonds? 00:01:27.400 --> 00:01:29.340 Well, when we think about Coulomb forces, 00:01:29.340 --> 00:01:31.840 we know that like charges repel each other 00:01:31.840 --> 00:01:35.180 and unlike charges, or opposite charges, attract each other. 00:01:35.180 --> 00:01:37.820 And so, when these ionic solids form, 00:01:37.820 --> 00:01:39.810 they're unlikely to form in this way, 00:01:39.810 --> 00:01:41.830 or even in this way, because they're gonna form 00:01:41.830 --> 00:01:44.950 in a way that maximizes the attractive forces 00:01:44.950 --> 00:01:48.580 and minimizes the repulsive, the repelling forces. 00:01:48.580 --> 00:01:50.820 And so what would be an arrangement that does that? 00:01:50.820 --> 00:01:53.210 Pause this video and think about it. 00:01:53.210 --> 00:01:54.440 Well, all the positive charges 00:01:54.440 --> 00:01:55.920 are gonna try to get as close as possible 00:01:55.920 --> 00:01:57.940 to the negative charges and as far as possible 00:01:57.940 --> 00:01:59.500 from other positive charges. 00:01:59.500 --> 00:02:01.113 And the same thing is going to be true of negative charges. 00:02:01.113 --> 00:02:02.880 They're gonna try to get as far away 00:02:02.880 --> 00:02:04.770 from other negative charges as possible, 00:02:04.770 --> 00:02:07.780 and as close to other positive charges as possible. 00:02:07.780 --> 00:02:10.350 So the arrangement that you are likely to see 00:02:10.350 --> 00:02:13.090 is going to look something more like a checkerboard pattern. 00:02:13.090 --> 00:02:14.990 So it may be a positive there, 00:02:14.990 --> 00:02:18.610 a positive there, a positive there, 00:02:18.610 --> 00:02:21.020 a positive there, and a positive there. 00:02:21.020 --> 00:02:22.000 These are all the same ion, 00:02:22.000 --> 00:02:24.340 I'm not drawing it perfectly, they'd be the same size. 00:02:24.340 --> 00:02:27.010 And when you do these two-dimensional representations, 00:02:27.010 --> 00:02:28.000 these particulate models, 00:02:28.000 --> 00:02:29.480 it is important to get the size right, 00:02:29.480 --> 00:02:31.280 'cause we're gonna think about that in a second. 00:02:31.280 --> 00:02:34.720 And then the negative charges would be in between. 00:02:34.720 --> 00:02:35.553 So notice. 00:02:35.553 --> 00:02:37.660 In this configuration, 00:02:37.660 --> 00:02:39.620 every negative is surrounded by positives, 00:02:39.620 --> 00:02:41.480 and every positive is surrounded by negatives. 00:02:41.480 --> 00:02:43.671 So it's maximizing the attractive forces 00:02:43.671 --> 00:02:46.630 and it's minimizing the repulsive forces. 00:02:46.630 --> 00:02:48.550 And if you were to think about it in three dimensions, 00:02:48.550 --> 00:02:49.790 you would have a lattice structure 00:02:49.790 --> 00:02:51.200 that looks something like that. 00:02:51.200 --> 00:02:54.580 And we have seen this in other videos. 00:02:54.580 --> 00:02:56.970 Now another interesting thing to think about 00:02:56.970 --> 00:03:01.970 is the size of the ions that form that ionic solid. 00:03:02.150 --> 00:03:07.150 Let's say we wanted to deal with rubidium bromide. 00:03:07.580 --> 00:03:10.080 Rubidium bromide. 00:03:10.080 --> 00:03:12.180 What would this look like if I were to draw it 00:03:12.180 --> 00:03:14.670 in a two-dimensional particulate model like this, 00:03:14.670 --> 00:03:17.850 and I wanted to make the size roughly comparable 00:03:17.850 --> 00:03:21.390 to what we would see between the rubidium and the bromide? 00:03:21.390 --> 00:03:22.670 Pause this video and think about that, 00:03:22.670 --> 00:03:24.470 and I'll give you a little bit of a hint. 00:03:24.470 --> 00:03:25.740 It might be useful to look at 00:03:25.740 --> 00:03:27.543 this periodic table of elements. 00:03:29.020 --> 00:03:32.550 All right, if we were to separate this out into its ions, 00:03:32.550 --> 00:03:36.757 it is a rubidium cation, and a bromide anion. 00:03:41.486 --> 00:03:44.800 Now a rubidium cation, it has lost an electron. 00:03:44.800 --> 00:03:46.980 So even though it still has 37 protons, 00:03:46.980 --> 00:03:51.240 its electron configuration now looks like that of krypton. 00:03:51.240 --> 00:03:56.210 Now, the bromide anion, even though it only has 35 protons, 00:03:56.210 --> 00:03:58.960 it's going to gain an electron to become a bromide anion, 00:03:58.960 --> 00:04:02.060 and it also has an electron configuration of krypton. 00:04:02.060 --> 00:04:06.030 So both of these have the same number of electrons, 00:04:06.030 --> 00:04:09.970 but rubidium has two more protons than bromide does. 00:04:09.970 --> 00:04:13.040 And so the rubidium is going to attract 00:04:13.040 --> 00:04:14.570 that outer shell of electrons, 00:04:14.570 --> 00:04:16.220 that fourth shell of electrons, 00:04:16.220 --> 00:04:20.210 more than the bromide nucleus is going to. 00:04:20.210 --> 00:04:23.130 And so, the rubidium in this example 00:04:23.130 --> 00:04:27.740 is going to be smaller than the bromide. 00:04:27.740 --> 00:04:31.990 And so if I were to draw one of these diagrams, 00:04:31.990 --> 00:04:33.880 it would look something like this. 00:04:33.880 --> 00:04:36.990 Let me draw the bromide first. 00:04:36.990 --> 00:04:41.880 So I have a bromide anion, I have another bromide anion, 00:04:41.880 --> 00:04:45.702 another bromide anion, maybe I have a bromide anion 00:04:45.702 --> 00:04:49.480 right over here, bromide anion over there, 00:04:49.480 --> 00:04:51.180 maybe a few more. 00:04:51.180 --> 00:04:53.890 Make 'em a little bit, if I was doing this with a computer, 00:04:53.890 --> 00:04:56.490 I would make them all the same size. 00:04:56.490 --> 00:04:59.000 So these are our bromide anions. 00:04:59.000 --> 00:05:02.250 And then your rubidium cations would be a bit smaller. 00:05:02.250 --> 00:05:06.080 And so, our particulate model right over here 00:05:06.080 --> 00:05:07.300 might look something like this. 00:05:07.300 --> 00:05:09.900 We wanna make it clear that the cation 00:05:09.900 --> 00:05:13.740 is a bit smaller than the anion. 00:05:13.740 --> 00:05:16.580 It would arrange, it would likely arrange 00:05:16.580 --> 00:05:18.400 in a pattern that looks like this. 00:05:18.400 --> 00:05:21.050 And notice, I am trying to make the sizes 00:05:24.040 --> 00:05:26.060 roughly accurate, to show that the cation 00:05:26.060 --> 00:05:28.580 is indeed smaller than the anion. 00:05:28.580 --> 00:05:30.290 Although it wouldn't be dramatically smaller. 00:05:30.290 --> 00:05:31.830 Remember, they have the same number of electrons. 00:05:31.830 --> 00:05:33.190 And they don't have that dramatically 00:05:33.190 --> 00:05:34.840 different number of protons. 00:05:34.840 --> 00:05:37.200 And this is just a very rough drawing. 00:05:37.200 --> 00:05:38.890 If they were dramatically different, 00:05:38.890 --> 00:05:41.693 you might show that in the sizes on this diagram.

Lattice energy

https://www.youtube.com/watch?v=paXRIINiYlQ

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WEBVTT Kind: captions Language: en 00:00:00.660 --> 00:00:02.220 - [Instructor] You may already be familiar 00:00:02.220 --> 00:00:04.740 with Coulomb's law, 00:00:04.740 --> 00:00:07.310 which is really the most important 00:00:07.310 --> 00:00:10.400 or underlying law behind all of what we know 00:00:10.400 --> 00:00:12.690 about electrostatics 00:00:12.690 --> 00:00:16.730 and how things with charge attract or repulse each other, 00:00:16.730 --> 00:00:19.160 but a simplified version of Coulomb's law 00:00:19.160 --> 00:00:23.200 is just that the force between charged particles, 00:00:23.200 --> 00:00:24.940 the magnitude of the force 00:00:24.940 --> 00:00:29.940 is going to be proportional to the product of the charges, 00:00:30.280 --> 00:00:31.900 so q one would be the charge 00:00:31.900 --> 00:00:33.320 of one of the charged particles. 00:00:33.320 --> 00:00:34.900 Maybe this is an ion. 00:00:34.900 --> 00:00:38.250 Q two would the charge of the other particle. 00:00:38.250 --> 00:00:39.710 Maybe that's an ion, 00:00:39.710 --> 00:00:42.200 divided by r squared. 00:00:42.200 --> 00:00:43.570 And if we're talking about ions, 00:00:43.570 --> 00:00:47.840 r is going to be the distance between their nuclei, 00:00:47.840 --> 00:00:49.460 and if the charges are different, 00:00:49.460 --> 00:00:50.940 it's going to be force of attraction. 00:00:50.940 --> 00:00:52.380 If the charges are the same, 00:00:52.380 --> 00:00:54.680 it's going to be a force of repulsion. 00:00:54.680 --> 00:00:59.680 And we can use Coulomb's law to think about ionic compounds. 00:00:59.710 --> 00:01:03.430 So let's go with maybe the most common ionic compound 00:01:03.430 --> 00:01:06.450 in our daily life, and that is table salt. 00:01:06.450 --> 00:01:09.010 Table salt is sodium chloride, 00:01:09.010 --> 00:01:12.230 so sodium chloride. 00:01:12.230 --> 00:01:14.810 We have talked about this in other videos. 00:01:14.810 --> 00:01:19.810 It is made up of positively-charged sodium cations, 00:01:20.350 --> 00:01:23.040 so you have an Na plus, 00:01:23.040 --> 00:01:25.230 so sodium is a group one element. 00:01:25.230 --> 00:01:28.100 It's very easy to nab an electron off of it 00:01:28.100 --> 00:01:29.830 and then it has a positive charge, 00:01:29.830 --> 00:01:33.220 and it's made up of a chloride anion, 00:01:33.220 --> 00:01:35.770 so Cl minus. 00:01:35.770 --> 00:01:39.130 Chloride is a group seven element. 00:01:39.130 --> 00:01:41.730 It really wants to get that extra electron 00:01:41.730 --> 00:01:45.100 to have eight valence electrons in its outermost shell, 00:01:45.100 --> 00:01:48.570 and so it's very likely to grab an electron maybe 00:01:48.570 --> 00:01:49.530 from a sodium, 00:01:49.530 --> 00:01:52.610 and so these two characters are going to be attracted 00:01:52.610 --> 00:01:53.443 to each other. 00:01:53.443 --> 00:01:55.400 Notice, they have opposite charges. 00:01:55.400 --> 00:01:59.830 And when you have a bunch of sodium and chloride together, 00:01:59.830 --> 00:02:03.510 you'll have a structure that looks something like this. 00:02:03.510 --> 00:02:08.340 And in chemistry, we call this a lattice. 00:02:08.340 --> 00:02:09.910 Now in everyday language, 00:02:09.910 --> 00:02:12.580 you might associate things like lattices 00:02:12.580 --> 00:02:16.750 with kind of a crossing pattern like that, 00:02:16.750 --> 00:02:18.950 and in chemistry, when we're talking about a lattice, 00:02:18.950 --> 00:02:21.470 we're talking about a three-dimensional structure 00:02:21.470 --> 00:02:24.650 of atoms or three-dimensional structure of ions 00:02:24.650 --> 00:02:26.840 that have a repeating pattern to them, 00:02:26.840 --> 00:02:27.840 and you can see that here, 00:02:27.840 --> 00:02:30.320 and in future videos, we'll go into more detail 00:02:30.320 --> 00:02:32.010 onto lattice structures, 00:02:32.010 --> 00:02:34.870 but you can see in this picture, 00:02:34.870 --> 00:02:38.091 the purples are the sodium cations 00:02:38.091 --> 00:02:43.091 and the greens are the chloride anions. 00:02:43.142 --> 00:02:47.270 And the reason why the sodium cations are so small, 00:02:47.270 --> 00:02:49.840 you can see that if you look at the periodic table 00:02:49.840 --> 00:02:51.100 of elements here. 00:02:51.100 --> 00:02:52.920 We have said that as you go to the right, 00:02:52.920 --> 00:02:55.150 your radius decreases, 00:02:55.150 --> 00:02:57.900 but what's happening is when sodium loses 00:02:57.900 --> 00:02:59.830 that outermost electron, 00:02:59.830 --> 00:03:04.470 then its electrons have a noble gas configuration of neon. 00:03:04.470 --> 00:03:07.850 So it really loses that third shell, it gets smaller, 00:03:07.850 --> 00:03:09.090 and not only does it lose that third shell, 00:03:09.090 --> 00:03:10.540 but it has 11 protons, 00:03:10.540 --> 00:03:12.880 so it's going to have a very strong pull 00:03:12.880 --> 00:03:15.880 on those electrons in that second shell. 00:03:15.880 --> 00:03:18.950 And similarly, chloride is going to gain an electron 00:03:18.950 --> 00:03:22.270 so it's going to have a noble gas configuration of argon. 00:03:22.270 --> 00:03:24.853 So it is going to be bigger. 00:03:25.700 --> 00:03:27.410 Now when we talked about covalent bonds, 00:03:27.410 --> 00:03:29.200 we talked about the bond energy, 00:03:29.200 --> 00:03:31.130 the energy needed to pull apart the atoms 00:03:31.130 --> 00:03:33.700 that were forming the covalent bonds. 00:03:33.700 --> 00:03:37.730 There's a similar notion for ionic bonds like this 00:03:37.730 --> 00:03:39.560 and that is lattice energy, 00:03:39.560 --> 00:03:42.110 and that is energy necessary 00:03:42.110 --> 00:03:44.320 to pull the ions apart 00:03:44.320 --> 00:03:47.470 so that they are infinitely far apart from each other, 00:03:47.470 --> 00:03:51.530 and lattice energy is usually measured 00:03:51.530 --> 00:03:54.090 in kilojoules per mole, 00:03:54.090 --> 00:03:57.540 which is also what we measure bond energy in 00:03:57.540 --> 00:03:59.730 because they're really the same notion, 00:03:59.730 --> 00:04:00.750 except lattice energy, 00:04:00.750 --> 00:04:02.810 you're breaking up a lattice of ions, 00:04:02.810 --> 00:04:03.800 while in bond energy, 00:04:03.800 --> 00:04:06.770 you're normally talking about covalent bonds. 00:04:06.770 --> 00:04:08.290 Now I want you to think about something. 00:04:08.290 --> 00:04:11.000 What's going to have a higher lattice energy? 00:04:11.000 --> 00:04:13.740 Would it be sodium chloride, 00:04:13.740 --> 00:04:16.060 or let's pick something else. 00:04:16.060 --> 00:04:20.690 Let's say we had rubidium. 00:04:20.690 --> 00:04:23.600 Rubidium chloride, 00:04:23.600 --> 00:04:26.720 which is going to have a higher lattice energy? 00:04:26.720 --> 00:04:28.820 What's going to take more energy 00:04:28.820 --> 00:04:31.180 to pull the ions apart? 00:04:31.180 --> 00:04:32.460 And I'll give you a hint 00:04:32.460 --> 00:04:35.083 with this periodic table of elements. 00:04:36.500 --> 00:04:38.640 All right, well, rubidium chloride, 00:04:38.640 --> 00:04:41.770 that's made up, instead of a sodium cation, 00:04:41.770 --> 00:04:44.520 that's made up of a rubidium cation, 00:04:44.520 --> 00:04:47.010 so you have Rb plus, and of course, 00:04:47.010 --> 00:04:51.120 you have the chloride anion, Cl minus, 00:04:51.120 --> 00:04:52.780 and so what's the difference here? 00:04:52.780 --> 00:04:56.830 The anion is both, is chloride in both cases, 00:04:56.830 --> 00:04:59.430 but when you look at rubidium versus sodium, 00:04:59.430 --> 00:05:01.250 rubidium, when it loses an electron, 00:05:01.250 --> 00:05:03.280 it's going to have a noble gas structure, 00:05:03.280 --> 00:05:05.520 electron structure of krypton, 00:05:05.520 --> 00:05:07.860 while sodium, once it loses an electron, 00:05:07.860 --> 00:05:09.130 it's, its electron, 00:05:09.130 --> 00:05:12.810 its electron configuration is going to look like neon. 00:05:12.810 --> 00:05:16.030 So the sodium cation is smaller, 00:05:16.030 --> 00:05:17.743 and what does that tell us? 00:05:18.640 --> 00:05:21.370 Well, if this one right over here, 00:05:21.370 --> 00:05:23.030 let me circle it like this. 00:05:23.030 --> 00:05:25.533 If this is smaller, 00:05:26.750 --> 00:05:28.830 and we have similar charges on top, 00:05:28.830 --> 00:05:31.930 you have a plus one and a negative one on top, 00:05:31.930 --> 00:05:34.480 that's the charges between the two ions, 00:05:34.480 --> 00:05:37.730 but now you have a smaller radius between the nuclei 00:05:37.730 --> 00:05:40.550 because sodium is smaller than rubidium. 00:05:40.550 --> 00:05:42.210 While the radius goes down, 00:05:42.210 --> 00:05:44.430 the force goes up, 00:05:44.430 --> 00:05:47.460 so you're going to have stronger Coulomb forces 00:05:47.460 --> 00:05:49.510 in a lattice of sodium chloride 00:05:49.510 --> 00:05:51.970 than in a lattice of rubidium chloride. 00:05:51.970 --> 00:05:54.070 Because the force of attraction is stronger, 00:05:54.070 --> 00:05:56.560 it's going to take more energy to pull it apart. 00:05:56.560 --> 00:05:57.520 So because of that, 00:05:57.520 --> 00:05:59.690 you're going to have a higher, 00:05:59.690 --> 00:06:02.330 higher lattice energy. 00:06:02.330 --> 00:06:07.330 Lattice energy for sodium chloride than rubidium chloride. 00:06:07.700 --> 00:06:09.410 Let's think about another ionic compound. 00:06:09.410 --> 00:06:14.410 Let's say we were to think about magnesium fluoride, F two, 00:06:16.040 --> 00:06:20.340 and this is made up of a magnesium cation 00:06:20.340 --> 00:06:22.950 that has a positive two charge, 00:06:22.950 --> 00:06:27.950 so two plus, in a lattice with a bunch of fluoride anions, 00:06:28.290 --> 00:06:31.660 so with a bunch of fluoride anions. 00:06:31.660 --> 00:06:33.280 So how would the lattice energy 00:06:33.280 --> 00:06:35.860 of magnesium fluoride compare 00:06:35.860 --> 00:06:38.080 to what we just saw up here? 00:06:38.080 --> 00:06:40.560 So magnesium has a larger charge 00:06:40.560 --> 00:06:42.860 than these cations up here, 00:06:42.860 --> 00:06:46.220 so if you viewed the charge of magnesium as q one, 00:06:46.220 --> 00:06:49.090 you're going to have something larger up there 00:06:49.090 --> 00:06:54.090 and that fluoride is a smaller anion than chloride. 00:06:54.500 --> 00:06:57.850 We can see that if we look at the periodic table 00:06:57.850 --> 00:06:59.150 of elements again. 00:06:59.150 --> 00:07:01.860 Florine is smaller than chlorine, 00:07:01.860 --> 00:07:04.150 and so even if you added an electron to both of them, 00:07:04.150 --> 00:07:06.070 fluoride is still going to be smaller, 00:07:06.070 --> 00:07:09.950 and magnesium, when you take two electrons off of it, 00:07:09.950 --> 00:07:11.770 it's going to have the noble gas configure, 00:07:11.770 --> 00:07:14.020 electron configuration of neon, 00:07:14.020 --> 00:07:16.480 but it's going to pull even more on those, 00:07:16.480 --> 00:07:18.380 that, those second shell electrons 00:07:18.380 --> 00:07:22.520 because it has 12 protons versus sodium only has 11. 00:07:22.520 --> 00:07:27.510 So what we see here is not only does magnesium have a larger 00:07:27.510 --> 00:07:31.090 positive charge than the sodium cation does, 00:07:31.090 --> 00:07:33.160 but it's going to be smaller. 00:07:33.160 --> 00:07:37.530 And the fluoride has a comparable charge to the chloride, 00:07:37.530 --> 00:07:39.650 but it too is going to be smaller. 00:07:39.650 --> 00:07:42.160 So we have a larger charge on top, 00:07:42.160 --> 00:07:43.840 at least for the magnesium, 00:07:43.840 --> 00:07:47.110 and you have smaller radii for the bottom, 00:07:47.110 --> 00:07:48.510 so in magnesium fluoride, 00:07:48.510 --> 00:07:51.490 the Coulomb forces between the ions and the lattice 00:07:51.490 --> 00:07:53.120 are even stronger, 00:07:53.120 --> 00:07:54.530 and so the lattice energy, 00:07:54.530 --> 00:07:56.480 the energy necessary to pull it apart, 00:07:56.480 --> 00:07:58.720 is going to be higher, 00:07:58.720 --> 00:08:00.780 so out of the three we just looked at, 00:08:00.780 --> 00:08:03.880 the highest lattice energy is going to be magnesium fluoride 00:08:03.880 --> 00:08:06.490 followed by sodium chloride 00:08:06.490 --> 00:08:08.683 followed by rubidium chloride.

All in for Education with Khan Academy. Give today!

https://www.youtube.com/watch?v=PrN9QB8HDNM

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WEBVTT Kind: captions Language: en 00:00:00.780 --> 00:00:01.613 - Hi, everyone. 00:00:01.613 --> 00:00:04.330 Sal Khan here from the not-for-profit Khan Academy 00:00:04.330 --> 00:00:06.980 and I just wanted to announce our first-ever 00:00:06.980 --> 00:00:09.830 fundraising campaign on YouTube. 00:00:09.830 --> 00:00:12.780 As you know, we are a not-for-profit organization 00:00:12.780 --> 00:00:14.740 and we are able to do the work we do 00:00:14.740 --> 00:00:17.890 because of donations from folks like yourself, 00:00:17.890 --> 00:00:21.830 so we are trying to raise $10000 on YouTube. 00:00:21.830 --> 00:00:25.940 Every dollar is equal to three hours of learning some place 00:00:25.940 --> 00:00:26.860 on the planet. 00:00:26.860 --> 00:00:29.620 This is learning for you, learning for your family, 00:00:29.620 --> 00:00:32.450 or learning for a young child in some part of the world 00:00:32.450 --> 00:00:35.440 that might not have resources otherwise. 00:00:35.440 --> 00:00:38.450 So please donate by clicking on the blue button 00:00:38.450 --> 00:00:40.380 which is either there or there, 00:00:40.380 --> 00:00:41.213 but you'll find it. 00:00:41.213 --> 00:00:43.500 There should be a blue button around me someplace, 00:00:43.500 --> 00:00:46.010 and please support us on this mission 00:00:46.010 --> 00:00:48.250 of a free, world-class education 00:00:48.250 --> 00:00:49.950 for anyone, anywhere. 00:00:49.950 --> 00:00:50.783 Thank you.

Worked example: Interpreting potential energy curves of diatomic molecules

https://www.youtube.com/watch?v=-mZAsdJnnMM

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en

WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:01.330 - [Instructor] In a previous video, 00:00:01.330 --> 00:00:04.450 we began to think about potential energy as a function 00:00:04.450 --> 00:00:09.210 of internuclear distance for diatomic molecules. 00:00:09.210 --> 00:00:11.190 What do I mean by diatomic molecules? 00:00:11.190 --> 00:00:13.957 Well, we looked at molecular hydrogen, or H2, 00:00:14.953 --> 00:00:18.080 which is just two hydrogens covalently bonded to each other. 00:00:18.080 --> 00:00:20.580 And at standard temperature and pressure, 00:00:20.580 --> 00:00:22.720 there, they would naturally, 00:00:22.720 --> 00:00:25.770 the distance between the two nuclei 00:00:26.948 --> 00:00:28.360 would be based on where there is 00:00:28.360 --> 00:00:30.200 the lowest potential energy. 00:00:30.200 --> 00:00:32.070 And if you were to squeeze them together, 00:00:32.070 --> 00:00:34.030 you would have to put energy into the system 00:00:34.030 --> 00:00:35.650 and have a higher potential energy. 00:00:35.650 --> 00:00:36.980 Or if you were to pull them apart, 00:00:36.980 --> 00:00:38.660 you would have to put energy into the system 00:00:38.660 --> 00:00:41.260 and have a higher potential energy. 00:00:41.260 --> 00:00:42.610 What I want to do in this video 00:00:42.610 --> 00:00:44.750 is do a little bit of a worked example. 00:00:44.750 --> 00:00:47.360 Over here, I have three potential energies 00:00:47.360 --> 00:00:50.200 as a function of internuclear distance graphs. 00:00:50.200 --> 00:00:52.150 And what I'm going to tell you is 00:00:52.150 --> 00:00:55.900 one of these is molecular hydrogen, 00:00:55.900 --> 00:01:00.090 one of these is molecular nitrogen or diatomic nitrogen, N2, 00:01:00.090 --> 00:01:02.980 and one of these is diatomic oxygen. 00:01:02.980 --> 00:01:05.500 And what I want you to think about, pause this video, 00:01:05.500 --> 00:01:08.830 is which graph is the potential energy 00:01:08.830 --> 00:01:10.700 as a function of internuclear distance 00:01:10.700 --> 00:01:13.640 for each of these diatomic molecules. 00:01:13.640 --> 00:01:15.980 And I'll give you a hint. 00:01:15.980 --> 00:01:18.370 Look at the low point in potential energy. 00:01:18.370 --> 00:01:20.750 The low point in potential energy is 00:01:20.750 --> 00:01:22.610 what you would typically observe 00:01:22.610 --> 00:01:25.300 that diatomic molecule's internuclear distance 00:01:25.300 --> 00:01:27.680 to be at standard temperature and pressure. 00:01:27.680 --> 00:01:29.520 And this distance right over here is going 00:01:29.520 --> 00:01:33.200 to be a function of two things. 00:01:33.200 --> 00:01:35.050 It's going to be a function of 00:01:35.050 --> 00:01:37.620 how small the atoms actually are, 00:01:37.620 --> 00:01:39.650 how small their radii are. 00:01:39.650 --> 00:01:41.790 So smaller atoms are, in general, 00:01:41.790 --> 00:01:44.650 going to have a shorter stable internuclear distance. 00:01:44.650 --> 00:01:47.540 But the other thing to think about is the bond order 00:01:47.540 --> 00:01:49.280 between these atoms, 00:01:49.280 --> 00:01:51.130 and I'll give you a little bit of a hint. 00:01:51.130 --> 00:01:55.480 Diatomic hydrogen, you just have a single covalent bond. 00:01:55.480 --> 00:01:59.380 For diatomic nitrogen, it is a triple bond. 00:01:59.380 --> 00:02:03.600 And for diatomic oxygen, it is a double bond. 00:02:03.600 --> 00:02:05.730 So the higher order the bond, 00:02:05.730 --> 00:02:09.150 that will also bring the two atoms closer together, 00:02:09.150 --> 00:02:13.460 and it also makes it have a higher bond energy, 00:02:13.460 --> 00:02:16.090 the energy required to separate the atoms. 00:02:16.090 --> 00:02:18.190 Remember, we talked about it in the previous video. 00:02:18.190 --> 00:02:22.910 This right over here is the bond energy. 00:02:22.910 --> 00:02:25.410 And so with that said, pause the video, 00:02:25.410 --> 00:02:26.790 and try to figure it out. 00:02:26.790 --> 00:02:29.100 Which of these is the graphs of H2, 00:02:29.100 --> 00:02:30.983 which is N2, and which is O2? 00:02:32.110 --> 00:02:35.500 So let's first just think about it in terms of bond energy. 00:02:35.500 --> 00:02:36.333 If you look at it, 00:02:36.333 --> 00:02:39.170 the single bond, double bond, triple bond here, 00:02:39.170 --> 00:02:41.650 you would expect the highest order bond here 00:02:41.650 --> 00:02:43.670 to have the highest bond energy, 00:02:43.670 --> 00:02:45.040 and the highest bond energy 00:02:45.040 --> 00:02:48.360 is this salmon-colored one right over here. 00:02:48.360 --> 00:02:50.150 So just based on that, 00:02:50.150 --> 00:02:54.020 I would say that this is a good candidate for N2. 00:02:54.020 --> 00:02:56.630 So this one right over here, 00:02:56.630 --> 00:03:00.493 this looks like diatomic nitrogen to me. 00:03:01.340 --> 00:03:04.740 Then the next highest bond energy, 00:03:04.740 --> 00:03:06.180 if you look at it carefully, 00:03:06.180 --> 00:03:09.540 it looks like this purple one right over here. 00:03:09.540 --> 00:03:13.030 And so just based on bond order, 00:03:13.030 --> 00:03:16.260 I would say this is a good candidate for O2. 00:03:16.260 --> 00:03:19.950 And then the lowest bond energy 00:03:19.950 --> 00:03:23.030 is this one right over here. 00:03:23.030 --> 00:03:25.810 And so just based on the bond order here, 00:03:25.810 --> 00:03:27.670 it's just a single covalent bond, 00:03:27.670 --> 00:03:31.810 this looks like a good candidate for diatomic hydrogen. 00:03:31.810 --> 00:03:36.460 But let's also think about the radii of these atoms. 00:03:36.460 --> 00:03:40.280 If we get a periodic table of elements here, 00:03:40.280 --> 00:03:43.190 we can see that hydrogen only has one electron 00:03:43.190 --> 00:03:44.750 in that first shell, 00:03:44.750 --> 00:03:47.320 and so it's going to be the smallest. 00:03:47.320 --> 00:03:51.000 So that makes sense over here, that your distance, 00:03:51.000 --> 00:03:52.830 where you have the lowest potential energy, 00:03:52.830 --> 00:03:56.420 is shortest for the diatomic molecule 00:03:56.420 --> 00:03:59.040 that's made up of the smallest atoms. 00:03:59.040 --> 00:04:00.920 But then when you look at the other two, 00:04:00.920 --> 00:04:02.610 something interesting happens. 00:04:02.610 --> 00:04:06.160 Remember, your radius for an atom increases 00:04:06.160 --> 00:04:08.310 as you go down a column. 00:04:08.310 --> 00:04:11.640 But as you go to the right on a row, your radius decreases. 00:04:11.640 --> 00:04:13.120 'Cause you're adding more and more electrons 00:04:13.120 --> 00:04:16.690 to the same shell, but the Coulomb forces are increasing 00:04:16.690 --> 00:04:20.630 between that outermost shell and your nucleus. 00:04:20.630 --> 00:04:22.800 And so if you just look at that trend, 00:04:22.800 --> 00:04:25.070 as you go from nitrogen to oxygen, 00:04:25.070 --> 00:04:27.200 you would actually expect your atomic radius 00:04:27.200 --> 00:04:28.970 to get a little bit smaller. 00:04:28.970 --> 00:04:30.210 They're right next to each other. 00:04:30.210 --> 00:04:32.390 They might be close, but you say, okay, oxygen, 00:04:32.390 --> 00:04:35.040 you have one extra electron in that same second shell, 00:04:35.040 --> 00:04:37.390 maybe it's going to be a little bit smaller. 00:04:37.390 --> 00:04:39.440 So if you were to base things just on that, 00:04:39.440 --> 00:04:42.200 you'd say, all right, well, the internuclear distance 00:04:42.200 --> 00:04:44.290 for this salmon-colored one is a little bit shorter, 00:04:44.290 --> 00:04:48.380 maybe that one is oxygen, and maybe this one is nitrogen. 00:04:48.380 --> 00:04:50.870 But they would be close, and I would say, in general, 00:04:50.870 --> 00:04:52.870 the bond order would trump things. 00:04:52.870 --> 00:04:56.810 And the bond order, because you see this high bond energy, 00:04:56.810 --> 00:04:58.690 that's the biggest giveaway that this is going 00:04:58.690 --> 00:05:03.690 to be the higher bond order diatomic molecule or N2. 00:05:04.180 --> 00:05:06.140 They're close in atomic radius, 00:05:06.140 --> 00:05:09.970 but this is what makes all of the difference. 00:05:09.970 --> 00:05:12.260 And we'll take those two nitrogen atoms 00:05:12.260 --> 00:05:15.420 and squeeze them together just a little bit more, 00:05:15.420 --> 00:05:18.200 even though they might be a little bit bigger. 00:05:18.200 --> 00:05:20.553 And so I feel pretty good with this labeling.

You Can Learn Anything (30 sec)

https://www.youtube.com/watch?v=beSsSAUf-oc

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https://www.youtube.com/api/timedtext?v=beSsSAUf-oc&ei=cViUZaOrEJL7mLAPnPiVyA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=AA1B65FC3C2C2D06FCD4E01A82825686FA733470.053FB6F6677F19AFB1A7B91DC8E8F688BE2FAFE9&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.670 --> 00:00:02.890 - [Narrator] Nobody's born smart. 00:00:02.890 --> 00:00:05.890 There was a time when Einstein couldn't count to 10 00:00:05.890 --> 00:00:08.030 and Shakespeare had to learn his ABC's 00:00:08.030 --> 00:00:10.110 just like the rest of us. 00:00:10.110 --> 00:00:13.430 You stumble, slip, crawl, fall, and fail. 00:00:13.430 --> 00:00:16.130 But failing is just another word for growing 00:00:16.130 --> 00:00:17.630 and you keep going. 00:00:17.630 --> 00:00:19.920 One foot in front of the other, one idea 00:00:19.920 --> 00:00:22.810 on top of the next until you get it. 00:00:22.810 --> 00:00:24.600 This is learning. 00:00:24.600 --> 00:00:26.200 You only have to know one thing, 00:00:27.130 --> 00:00:28.793 you can learn anything.

Bond length and bond energy

https://www.youtube.com/watch?v=EMCWvehKpd4

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en

WEBVTT Kind: captions Language: en 00:00:00.160 --> 00:00:02.340 - [Instructor] If you were to find a pure sample 00:00:02.340 --> 00:00:04.320 of hydrogen, 00:00:04.320 --> 00:00:07.950 odds are that the individual hydrogen atoms in that sample 00:00:07.950 --> 00:00:10.750 aren't just going to be separate atoms floating around, 00:00:10.750 --> 00:00:13.270 that many of them, and if not most of them, 00:00:13.270 --> 00:00:15.610 would have bonded with each other, 00:00:15.610 --> 00:00:18.640 forming what's known as diatomic hydrogen, 00:00:18.640 --> 00:00:20.710 which we would write as H2. 00:00:20.710 --> 00:00:23.920 Another way to write it is you have each hydrogen 00:00:23.920 --> 00:00:27.290 in diatomic hydrogen would have bonded to another hydrogen, 00:00:27.290 --> 00:00:29.730 to form a diatomic molecule like this. 00:00:29.730 --> 00:00:31.900 This molecule's only made up of hydrogen, 00:00:31.900 --> 00:00:33.720 but it's two atoms of hydrogen. 00:00:33.720 --> 00:00:35.820 And this makes sense, why it's stable, 00:00:35.820 --> 00:00:40.390 because each individual hydrogen has one valence electron 00:00:40.390 --> 00:00:41.440 if it is neutral. 00:00:41.440 --> 00:00:43.110 So that's one hydrogen there. 00:00:43.110 --> 00:00:44.200 That's another one there. 00:00:44.200 --> 00:00:47.640 And if they could share their valence electrons, 00:00:47.640 --> 00:00:51.720 they can both feel like they have a complete outer shell. 00:00:51.720 --> 00:00:54.280 And so this dash right over here, 00:00:54.280 --> 00:00:56.770 you can view as a pair of electrons being shared 00:00:56.770 --> 00:00:58.810 in a covalent bond. 00:00:58.810 --> 00:01:00.660 Now, what we're going to do in this video 00:01:00.660 --> 00:01:04.730 is think about the distance between the atoms. 00:01:04.730 --> 00:01:08.570 So just as an example, imagine two hydrogens like this. 00:01:08.570 --> 00:01:09.910 So that's one hydrogen atom, 00:01:09.910 --> 00:01:11.860 and that is another hydrogen atom. 00:01:11.860 --> 00:01:14.690 It turns out, at standard temperature, pressure, 00:01:14.690 --> 00:01:17.990 the distance between the centers of the atoms 00:01:17.990 --> 00:01:21.020 that we observe, that distance right over there, 00:01:21.020 --> 00:01:24.640 is approximately 74 picometers. 00:01:24.640 --> 00:01:27.630 And just as a refresher of how small a picometer is, 00:01:27.630 --> 00:01:30.840 a picometer is one trillionth of a meter. 00:01:30.840 --> 00:01:33.920 So this is 74 trillionths of a meter, 00:01:33.920 --> 00:01:36.390 so we're talking about a very small distance. 00:01:36.390 --> 00:01:39.260 But one interesting question is why is it this distance? 00:01:39.260 --> 00:01:41.940 What would happen if we tried to squeeze them together? 00:01:41.940 --> 00:01:44.370 What would happen if we tried to pull them apart? 00:01:44.370 --> 00:01:45.800 And to think about that, 00:01:45.800 --> 00:01:47.320 I'm gonna make a little bit of a graph 00:01:47.320 --> 00:01:51.020 that deals with potential energy and distance. 00:01:51.020 --> 00:01:53.170 So in the vertical axis, 00:01:53.170 --> 00:01:56.100 this is going to be potential energy, 00:01:56.100 --> 00:01:58.230 potential energy. 00:01:58.230 --> 00:01:59.560 And I won't give the units just yet. 00:01:59.560 --> 00:02:02.280 I'll just think in very broad-brush conceptual terms, 00:02:02.280 --> 00:02:04.900 then we could think about the units in a little bit. 00:02:04.900 --> 00:02:07.433 And then this over here is the distance, 00:02:08.330 --> 00:02:10.810 distance between the centers of the atoms. 00:02:10.810 --> 00:02:13.290 You could view it as the distance between the nuclei. 00:02:13.290 --> 00:02:16.290 And let's give this in picometers. 00:02:16.290 --> 00:02:18.110 Now, potential energy, when you think about it, 00:02:18.110 --> 00:02:20.160 it's all relative to something else. 00:02:20.160 --> 00:02:22.140 And so let's just arbitrarily say 00:02:22.140 --> 00:02:25.620 that at a distance of 74 picometers, 00:02:25.620 --> 00:02:27.540 our potential energy is right over here. 00:02:27.540 --> 00:02:30.760 I'm not even going to label this axis yet. 00:02:30.760 --> 00:02:33.810 Now, what's going to happen to the potential energy 00:02:33.810 --> 00:02:37.373 if we wanted to pull these two atoms apart? 00:02:38.230 --> 00:02:40.270 Well, this is what we typically find them at. 00:02:40.270 --> 00:02:41.730 This is probably a low point, 00:02:41.730 --> 00:02:44.290 or this is going to be a low point in potential energy. 00:02:44.290 --> 00:02:46.500 So if you make the distances go apart, 00:02:46.500 --> 00:02:47.840 you're going to have to put energy into it, 00:02:47.840 --> 00:02:51.800 and that makes the potential energy go higher. 00:02:51.800 --> 00:02:54.930 And to think about why that makes sense, 00:02:54.930 --> 00:02:57.180 imagine a spring right over here. 00:02:57.180 --> 00:02:59.490 If you want to pull it apart, 00:02:59.490 --> 00:03:01.960 if you pull on either sides of a spring, 00:03:01.960 --> 00:03:03.740 you are putting energy in, 00:03:03.740 --> 00:03:05.610 which increases the potential energy. 00:03:05.610 --> 00:03:09.510 Because if you let go, they're just going to come back to, 00:03:09.510 --> 00:03:11.240 they're going to accelerate back to each other. 00:03:11.240 --> 00:03:12.570 So as you pull it apart, 00:03:12.570 --> 00:03:14.430 you're adding potential energy to it. 00:03:14.430 --> 00:03:16.690 So as you have further and further distances 00:03:16.690 --> 00:03:19.730 between the nuclei, the potential energy goes up. 00:03:19.730 --> 00:03:21.750 And if you go really far, 00:03:21.750 --> 00:03:24.030 it's going to asymptote towards some value, 00:03:24.030 --> 00:03:26.180 and that value's essentially going to be the 00:03:26.180 --> 00:03:30.170 potential energy if these two atoms were not bonded at all, 00:03:30.170 --> 00:03:32.800 if they, to some degree, weren't associated with each other, 00:03:32.800 --> 00:03:35.060 if they weren't interacting with each other. 00:03:35.060 --> 00:03:37.150 And so that's actually the point 00:03:37.150 --> 00:03:39.260 at which most chemists or physicists 00:03:39.260 --> 00:03:43.440 or scientists would label zero potential energy, 00:03:43.440 --> 00:03:45.410 the energy at which they are infinitely 00:03:45.410 --> 00:03:46.550 far away from each other. 00:03:46.550 --> 00:03:48.800 And that's what this is asymptoting towards, 00:03:48.800 --> 00:03:51.490 and so let me just draw that line right over here. 00:03:51.490 --> 00:03:54.840 So let's call this zero right over here. 00:03:54.840 --> 00:03:56.310 And actually, let me now give units. 00:03:56.310 --> 00:04:00.113 Let's say all of this is in kilojoules per mole. 00:04:01.610 --> 00:04:04.060 Now, once again, if you're pulling them apart, 00:04:04.060 --> 00:04:06.050 as you pull further and further and further apart, 00:04:06.050 --> 00:04:08.260 you're getting closer and closer to these, 00:04:08.260 --> 00:04:10.400 these two atoms not interacting. 00:04:10.400 --> 00:04:11.280 Why is that? 00:04:11.280 --> 00:04:14.150 Because as you get further and further and further apart, 00:04:14.150 --> 00:04:16.510 the Coulomb forces between them are going 00:04:16.510 --> 00:04:19.410 to get weaker and weaker and weaker and weaker. 00:04:19.410 --> 00:04:20.470 And so that's why they like 00:04:20.470 --> 00:04:23.430 to think about that as zero potential energy. 00:04:23.430 --> 00:04:25.010 Now, what if we think about it the other way around? 00:04:25.010 --> 00:04:28.290 What if we want to squeeze these two together? 00:04:28.290 --> 00:04:31.140 Well, once again, if you think about a spring, 00:04:31.140 --> 00:04:33.020 if you imagine a spring like this, 00:04:33.020 --> 00:04:35.210 just as you would have to add energy 00:04:35.210 --> 00:04:36.940 or increase the potential energy of the spring 00:04:36.940 --> 00:04:39.150 if you want to pull the spring apart, 00:04:39.150 --> 00:04:42.320 you would also have to do it to squeeze the spring more. 00:04:42.320 --> 00:04:43.760 And so to get these two atoms 00:04:43.760 --> 00:04:46.400 to be closer and closer and closer together, 00:04:46.400 --> 00:04:49.650 you have to add energy into the system 00:04:49.650 --> 00:04:51.870 and increase the potential energy. 00:04:51.870 --> 00:04:55.300 And why, why are you having to put more energy into it? 00:04:55.300 --> 00:04:58.520 Because the more that you squeeze these two things together, 00:04:58.520 --> 00:05:00.670 you're going to have the positive charges 00:05:00.670 --> 00:05:02.930 of the nuclei repelling each other, 00:05:02.930 --> 00:05:04.660 so you're gonna have to try to overcome that. 00:05:04.660 --> 00:05:06.750 That puts potential energy into the system. 00:05:06.750 --> 00:05:08.480 And these electrons are starting 00:05:08.480 --> 00:05:10.310 to really overlap with each other, 00:05:10.310 --> 00:05:12.770 and they will also want to repel each other. 00:05:12.770 --> 00:05:16.110 And so what we've drawn here, just as just conceptually, 00:05:16.110 --> 00:05:17.560 is this idea of if you wanted them 00:05:17.560 --> 00:05:19.920 to really overlap with each other, 00:05:19.920 --> 00:05:22.490 you're going to have a pretty high potential energy. 00:05:22.490 --> 00:05:24.020 And if you're going to have them 00:05:24.020 --> 00:05:25.590 very separate from each other, 00:05:25.590 --> 00:05:28.040 you're not going to have as high of a potential energy, 00:05:28.040 --> 00:05:29.910 but this is still going to be higher 00:05:29.910 --> 00:05:32.240 than if you're at this stable point. 00:05:32.240 --> 00:05:35.350 This stable point is stable because that is a minimum point. 00:05:35.350 --> 00:05:38.460 It is a low point in this potential energy graph. 00:05:38.460 --> 00:05:40.660 You could view this as just right. 00:05:40.660 --> 00:05:44.110 And it turns out that for diatomic hydrogen, 00:05:44.110 --> 00:05:47.740 this difference between zero and where you will find it 00:05:47.740 --> 00:05:49.790 at standard temperature and pressure, 00:05:49.790 --> 00:05:54.790 this distance right over here is 432 kilojoules per mole. 00:05:55.120 --> 00:05:59.050 So this is at the point negative 432 kilojoules per mole. 00:05:59.050 --> 00:06:00.380 And so one interesting thing 00:06:00.380 --> 00:06:02.550 to think about a diagram like this is 00:06:02.550 --> 00:06:05.790 how much energy would it take to separate these two atoms, 00:06:05.790 --> 00:06:07.700 to completely break this bond? 00:06:07.700 --> 00:06:10.610 Well, it'd be the energy of completely pulling them apart. 00:06:10.610 --> 00:06:13.240 And so it would be this energy. 00:06:13.240 --> 00:06:16.080 It would be this energy right over here, 00:06:16.080 --> 00:06:19.100 or 432 kilojoules. 00:06:19.100 --> 00:06:22.140 And that's what people will call the bond energy, 00:06:22.140 --> 00:06:26.110 the energy required to separate the atoms. 00:06:26.110 --> 00:06:27.910 And we'll see in future videos, 00:06:27.910 --> 00:06:30.400 the smaller the individual atoms 00:06:30.400 --> 00:06:32.700 and the higher the order of the bonds, 00:06:32.700 --> 00:06:35.520 so from a single bond to a double bond to a triple bond, 00:06:35.520 --> 00:06:37.220 the higher order of the bonds, 00:06:37.220 --> 00:06:41.113 the higher of a bond energy you're going to be dealing with.

Predicting bond type (electronegativity)

https://www.youtube.com/watch?v=AHUHpVQXRsw

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https://www.youtube.com/api/timedtext?v=AHUHpVQXRsw&ei=cViUZc_VEoeep-oPxLC8wAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=DD8F1E5A7419D912C54BBC592E809023873CCE1C.CEE4C011B02F9A68757E2355248E9C583056BB0D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.180 --> 00:00:02.120 - In other videos, we had started talking 00:00:02.120 --> 00:00:04.520 about the types of bonds that might form 00:00:04.520 --> 00:00:06.890 between atoms of a given element. 00:00:06.890 --> 00:00:11.830 For example, if you have two metals forming a bond, 00:00:11.830 --> 00:00:15.700 well, you are going to have a metallic bond. 00:00:15.700 --> 00:00:18.623 If you have two nonmetals, 00:00:21.756 --> 00:00:24.232 engaged in some type of bonding activity, 00:00:24.232 --> 00:00:27.802 this is likely to be a covalent bond. 00:00:27.802 --> 00:00:29.708 And the general rule of thumb is 00:00:29.708 --> 00:00:31.625 if you have one metal, 00:00:33.673 --> 00:00:35.090 and one nonmetal, 00:00:38.970 --> 00:00:41.840 that this is likely to be an ionic bond. 00:00:41.840 --> 00:00:44.160 These are the general rules of thumb. 00:00:44.160 --> 00:00:46.850 What I wanna do in this video is to better appreciate 00:00:46.850 --> 00:00:50.270 that bonding is really more of a spectrum. 00:00:50.270 --> 00:00:51.200 There are bonds, 00:00:51.200 --> 00:00:53.920 and we've talked about things like polar covalent bonds, 00:00:53.920 --> 00:00:56.190 that start to look a little bit more and more 00:00:56.190 --> 00:00:57.570 ionic in nature. 00:00:57.570 --> 00:00:59.899 And so that's what we're gonna talk about in this video 00:00:59.899 --> 00:01:02.990 and think about it in the context of electronegativity. 00:01:02.990 --> 00:01:06.180 Just as a reminder, we talk about electronegativity 00:01:06.180 --> 00:01:07.630 in many videos, 00:01:07.630 --> 00:01:11.140 but this is the property of an atom that's in a bond 00:01:11.140 --> 00:01:12.700 to hog electrons, 00:01:12.700 --> 00:01:16.059 to want the electron density to be closer to it 00:01:16.059 --> 00:01:18.619 for the electron pairs to spend more time 00:01:18.619 --> 00:01:21.640 around that particular atom. 00:01:21.640 --> 00:01:23.670 So, something with a high electronegativity 00:01:23.670 --> 00:01:26.660 is going to be greedier with the electrons 00:01:26.660 --> 00:01:29.750 than something with a low electronegativity. 00:01:29.750 --> 00:01:32.780 We can think about the spectrum between 00:01:32.780 --> 00:01:35.069 at this end you have ionic, 00:01:35.069 --> 00:01:39.050 and at this end you have covalent. 00:01:39.050 --> 00:01:42.140 And one way to think about it is at the extreme left end, 00:01:42.140 --> 00:01:46.010 you don't have much difference in electronegativities. 00:01:46.010 --> 00:01:48.500 Both atoms that are participating in the bond 00:01:48.500 --> 00:01:51.628 are roughly equal in how badly they want the electrons. 00:01:51.628 --> 00:01:53.510 While in an ionic bond, 00:01:53.510 --> 00:01:56.586 you have a very big difference in electronegativities, 00:01:56.586 --> 00:02:00.165 so much so that one of the atoms swipes an electron 00:02:00.165 --> 00:02:01.910 from the other. 00:02:01.910 --> 00:02:03.880 So, one way to think about it is, 00:02:03.880 --> 00:02:06.500 let me draw a little bit of an arrow here, 00:02:06.500 --> 00:02:10.390 so this is increased electronegativity 00:02:13.100 --> 00:02:16.520 difference as you go from left to right. 00:02:16.520 --> 00:02:18.290 And some place in the middle, 00:02:18.290 --> 00:02:20.240 or as you go from left to right, 00:02:20.240 --> 00:02:23.550 you're becoming more and more polar covalent. 00:02:23.550 --> 00:02:25.520 So for example, if you have a bond 00:02:25.520 --> 00:02:27.540 between oxygen and hydrogen, 00:02:27.540 --> 00:02:29.520 these are both nonmetals. 00:02:29.520 --> 00:02:31.380 So this will be a covalent bond 00:02:31.380 --> 00:02:33.540 by just our general rule of thumb. 00:02:33.540 --> 00:02:35.680 And actually the division between metals and nonmetals, 00:02:35.680 --> 00:02:36.730 I'm gonna make it right over here, 00:02:36.730 --> 00:02:39.730 it's this blue line is one division you could view, 00:02:39.730 --> 00:02:41.000 although things that straddle it 00:02:41.000 --> 00:02:43.360 are a little bit more interesting. 00:02:43.360 --> 00:02:46.203 But oxygen and hydrogen are both nonmetals, 00:02:47.190 --> 00:02:51.350 but you have a pretty big difference in electronegativities. 00:02:51.350 --> 00:02:53.190 This right over here is electronegativity 00:02:53.190 --> 00:02:54.760 measured on a Pauling scale, 00:02:54.760 --> 00:02:58.090 named after the famous biologist and chemist, Linus Pauling, 00:02:58.090 --> 00:03:01.160 and you can see on that scale oxygen is a 3.44, 00:03:01.160 --> 00:03:03.511 one of the most electronegative atoms. 00:03:03.511 --> 00:03:06.310 Electronegativity trends, we talk about in other videos, 00:03:06.310 --> 00:03:08.470 goes from bottom left to top right. 00:03:08.470 --> 00:03:11.540 The things at the top right that are not the noble gases, 00:03:11.540 --> 00:03:13.860 these are the ones that really are greedy with electrons. 00:03:13.860 --> 00:03:15.820 And oxygen is one of the greediest. 00:03:15.820 --> 00:03:19.060 While hydrogen, it's not not electronegative, 00:03:19.060 --> 00:03:21.660 but it's lower, at 2.20. 00:03:21.660 --> 00:03:23.490 So in this scenario, 00:03:23.490 --> 00:03:25.430 those electrons are going to spend more time 00:03:25.430 --> 00:03:26.640 around the oxygen. 00:03:26.640 --> 00:03:28.300 If they spent an equal amount of time, 00:03:28.300 --> 00:03:30.080 that oxygen might be neutral, 00:03:30.080 --> 00:03:31.850 but since they're spending a little bit more time here, 00:03:31.850 --> 00:03:34.970 we'll say that has a partial negative charge, 00:03:34.970 --> 00:03:37.010 the Greek lowercase letter delta, 00:03:37.010 --> 00:03:38.270 and on the hydrogen side 00:03:38.270 --> 00:03:40.900 because the shared electrons are spending more time 00:03:40.900 --> 00:03:42.860 around the oxygen than around the hydrogen, 00:03:42.860 --> 00:03:46.360 you would have a partially positive charge right over there. 00:03:46.360 --> 00:03:48.690 And so this would be a polar covalent bond. 00:03:48.690 --> 00:03:52.290 Maybe on the spectrum it sits right over there, 00:03:52.290 --> 00:03:53.640 depending on how you wanna, 00:03:53.640 --> 00:03:55.750 how you view this scale. 00:03:55.750 --> 00:03:56.790 Now the other question you say is 00:03:56.790 --> 00:03:59.560 okay, this is a spectrum between covalent and ionic, 00:03:59.560 --> 00:04:01.090 what about metallic? 00:04:01.090 --> 00:04:03.918 Well, metallic bonds are in general going to be formed 00:04:03.918 --> 00:04:07.530 if you have two things that are not so different 00:04:07.530 --> 00:04:09.870 in electronegativity, 00:04:09.870 --> 00:04:13.530 and they both have reasonably low electronegativities. 00:04:13.530 --> 00:04:16.840 So that's why things on the bottom left right over here, 00:04:16.840 --> 00:04:18.770 if you have two of these forming bonds 00:04:18.770 --> 00:04:20.220 with each other somehow, 00:04:20.220 --> 00:04:23.540 that you're likely to have metallic bonds. 00:04:23.540 --> 00:04:25.480 And that makes sense because in metallic bonds 00:04:25.480 --> 00:04:27.760 you have all the electrons kind of mixing in 00:04:27.760 --> 00:04:28.740 in a shared pool, 00:04:28.740 --> 00:04:32.020 which gives some of the properties like conductivity. 00:04:32.020 --> 00:04:34.310 And so if you have a lot of things 00:04:34.310 --> 00:04:36.652 that are fairly similar in electronegativity, 00:04:36.652 --> 00:04:38.390 and they're all low in electronegativity, 00:04:38.390 --> 00:04:41.470 they might be more willing to share those valence electrons 00:04:41.470 --> 00:04:42.743 in a communal pool.

Predicting bond type (metals vs. nonmetals)

https://www.youtube.com/watch?v=B9GkAsd8EK8

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en

WEBVTT Kind: captions Language: en 00:00:00.480 --> 00:00:01.450 - [Instructor] In a previous video, 00:00:01.450 --> 00:00:06.270 we introduced ourselves to the idea of bonds between atoms, 00:00:06.270 --> 00:00:08.500 and we talked about the types of bonds, 00:00:08.500 --> 00:00:11.140 ionic, covalent 00:00:12.240 --> 00:00:14.210 and metallic. 00:00:14.210 --> 00:00:16.570 In this video we're going to dig a little bit deeper 00:00:16.570 --> 00:00:18.530 and talk about the types of bonds 00:00:18.530 --> 00:00:22.350 that are likely to be formed between different elements. 00:00:22.350 --> 00:00:24.700 And to understand that, I'm going to introduce 00:00:24.700 --> 00:00:27.980 a broad classification of the elements, 00:00:27.980 --> 00:00:29.900 and in general, we're just going to think about things 00:00:29.900 --> 00:00:33.147 as metals and as nonmetals. 00:00:34.640 --> 00:00:37.450 So before I even point out on the periodic table of elements 00:00:37.450 --> 00:00:39.290 what are the metals and what are the nonmetals 00:00:39.290 --> 00:00:41.430 and maybe what are the ones that are in between, 00:00:41.430 --> 00:00:44.140 what are the properties of metals? 00:00:44.140 --> 00:00:47.500 Well, generally speaking, they conduct electricity. 00:00:47.500 --> 00:00:49.423 Conduct electricity. 00:00:53.950 --> 00:00:56.860 They tend to be malleable, which is just a fancy way 00:00:56.860 --> 00:00:59.610 of saying that you can bend them without breaking. 00:00:59.610 --> 00:01:03.290 And generally speaking, and there's exceptions to this, 00:01:03.290 --> 00:01:05.590 they are solid at room temperature. 00:01:05.590 --> 00:01:10.590 So I'll say solid at room temperature. 00:01:12.120 --> 00:01:13.240 Now what do you think the properties 00:01:13.240 --> 00:01:14.730 of nonmetals are going to be? 00:01:14.730 --> 00:01:15.900 Well generally speaking, 00:01:15.900 --> 00:01:17.920 they're going to be the opposite of this. 00:01:17.920 --> 00:01:20.240 Nonmetals, generally speaking, 00:01:20.240 --> 00:01:23.090 at room temperature are often not solid, 00:01:23.090 --> 00:01:25.170 they're often times gasses. 00:01:25.170 --> 00:01:29.510 They are not going to conduct electricity well. 00:01:29.510 --> 00:01:31.280 Now when you look at a periodic table of elements, 00:01:31.280 --> 00:01:34.320 how do you divide the metals from the nonmetals? 00:01:34.320 --> 00:01:36.950 Well that's what this little scratchy yellow line 00:01:36.950 --> 00:01:39.320 I'm drawing is trying to indicate. 00:01:39.320 --> 00:01:43.310 So everything above and to the right of this yellow line 00:01:43.310 --> 00:01:46.410 is a nonmetal and if you look at the color code 00:01:46.410 --> 00:01:48.750 from the folks who made this periodic table of elements, 00:01:48.750 --> 00:01:50.960 everything in this yellow color that we have here, 00:01:50.960 --> 00:01:53.730 so hydrogen and carbon and nitrogen 00:01:53.730 --> 00:01:57.990 and oxygen and fluorine, chlorine, I could keep going, 00:01:57.990 --> 00:02:00.420 these are all nonmetals. 00:02:00.420 --> 00:02:02.330 And it is the case that generally speaking 00:02:02.330 --> 00:02:05.520 at room temperature, they will be in a gas form 00:02:05.520 --> 00:02:08.560 and they will not conduct electricity well. 00:02:08.560 --> 00:02:11.570 These things in blue we've talked about in other videos, 00:02:11.570 --> 00:02:13.590 these are the noble gasses. 00:02:13.590 --> 00:02:15.550 So these are also nonmetals. 00:02:15.550 --> 00:02:17.410 The people who made this periodic table of elements 00:02:17.410 --> 00:02:18.690 put them in their own color 00:02:18.690 --> 00:02:21.790 'cause then you could view them as a subclass of nonmetals 00:02:22.840 --> 00:02:25.100 and they tend to be very inert, 00:02:25.100 --> 00:02:27.150 they don't interact with other things. 00:02:27.150 --> 00:02:30.520 They don't tend to form any of these bonds. 00:02:30.520 --> 00:02:32.740 Now everything else, you can consider 00:02:32.740 --> 00:02:36.490 in some form to be a metal 00:02:36.490 --> 00:02:38.610 and the reason why this periodic table of elements 00:02:38.610 --> 00:02:41.690 has different colors is that there's subclassifications 00:02:41.690 --> 00:02:43.110 of the metals 00:02:43.110 --> 00:02:45.500 but generally speaking, all of these things 00:02:45.500 --> 00:02:47.000 that you see right over here 00:02:47.000 --> 00:02:49.820 below this scratchy yellow line 00:02:49.820 --> 00:02:51.870 have the properties, generally speaking, 00:02:51.870 --> 00:02:54.220 of conducting electricity, being malleable, 00:02:54.220 --> 00:02:56.990 being solid at room temperature. 00:02:56.990 --> 00:02:58.660 And these things that straddle 00:02:58.660 --> 00:02:59.830 this yellow line right over here, 00:02:59.830 --> 00:03:01.270 these things that are in this kind 00:03:01.270 --> 00:03:03.790 of bluish-green kind of color, 00:03:03.790 --> 00:03:06.420 these are sometimes viewed as metalloids 00:03:06.420 --> 00:03:08.390 because they have some properties of metals 00:03:08.390 --> 00:03:10.233 and some properties of nonmetals. 00:03:11.070 --> 00:03:13.170 But generally speaking, if you know whether 00:03:13.170 --> 00:03:15.830 the things reacting are metals or nonmetals, 00:03:15.830 --> 00:03:18.680 you can oftentimes predict what type of bond 00:03:18.680 --> 00:03:20.220 is going to form. 00:03:20.220 --> 00:03:24.790 So for example, if I have a bond between a metal, 00:03:24.790 --> 00:03:28.217 a metal and a nonmetal, and a nonmetal, 00:03:29.257 --> 00:03:32.475 what type of bond do you think is going to form? 00:03:32.475 --> 00:03:34.502 Well when you bond between a net metal 00:03:34.502 --> 00:03:36.770 and a nonmetal, and we saw an example of that 00:03:36.770 --> 00:03:38.550 in that first video on bonding, 00:03:38.550 --> 00:03:42.600 say a metal like sodium, and then a nonmetal like chlorine, 00:03:42.600 --> 00:03:45.900 we saw that that chlorine will swipe an electron, 00:03:45.900 --> 00:03:47.570 the sodium might lose one, 00:03:47.570 --> 00:03:52.000 then the chlorine atom becomes a chloride anion, 00:03:52.000 --> 00:03:56.060 and then the sodium atom becomes a sodium cation 00:03:56.060 --> 00:03:57.640 and then they become attracted to each other 00:03:57.640 --> 00:03:59.990 and then you form an ionic bond. 00:03:59.990 --> 00:04:04.053 So this tends to form ionic bonds. 00:04:05.020 --> 00:04:09.987 Now what if you were to have a nonmetal with a nonmetal? 00:04:09.987 --> 00:04:14.010 Nonmetal times two, 00:04:14.010 --> 00:04:16.200 so two nonmetals bind, 00:04:16.200 --> 00:04:18.390 bound, I'm having trouble saying it, 00:04:18.390 --> 00:04:20.570 two nonmetals bonding to each other. 00:04:20.570 --> 00:04:23.050 What do you think is going to happen? 00:04:23.050 --> 00:04:25.960 Well we saw as an example in that first video 00:04:25.960 --> 00:04:29.460 where we say well what happens if oxygen bonds to oxygen? 00:04:29.460 --> 00:04:31.760 Well we saw that was a covalent bond 00:04:31.760 --> 00:04:33.810 and that is generally the case 00:04:33.810 --> 00:04:38.080 when you have two nonmetals form bonds, it is covalent. 00:04:38.080 --> 00:04:39.930 And then last but not least, 00:04:39.930 --> 00:04:42.700 and this might be the most obvious one of them all, 00:04:42.700 --> 00:04:45.070 what do you think happens when you have 00:04:45.070 --> 00:04:47.983 two metals forming a bond? 00:04:49.110 --> 00:04:53.340 Well you can imagine that will be a metallic bond 00:04:53.340 --> 00:04:55.830 where they contribute electrons to this kind 00:04:55.830 --> 00:04:58.960 of sea of electrons and that's what makes them 00:04:58.960 --> 00:05:01.930 conduct electricity so well and malleable. 00:05:01.930 --> 00:05:03.180 So I'll leave you there. 00:05:03.180 --> 00:05:05.660 There are exceptions to everything I just talked about 00:05:05.660 --> 00:05:06.840 but generally speaking, 00:05:06.840 --> 00:05:08.650 these notions will serve you well, 00:05:08.650 --> 00:05:11.053 especially in an introductory chemistry class.

Electron configurations of ions

https://www.youtube.com/watch?v=oCajIGPK-WM

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https://www.youtube.com/api/timedtext?v=oCajIGPK-WM&ei=cViUZZ6AH_ifp-oPg42coAU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1F4F3FDADB1A9376B3C10FFEF608ACE8D3BCD970.12A3D7BEF1FB03C2C576CF7C845B32D19FE0AB70&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.160 - [Instructor] In many videos 00:00:01.160 --> 00:00:05.640 we have already talked about electron configuration 00:00:05.640 --> 00:00:07.180 and now in this video 00:00:07.180 --> 00:00:09.730 we're going to extend that understanding 00:00:09.730 --> 00:00:13.820 by thinking about the electron configuration of ions. 00:00:13.820 --> 00:00:17.270 These are going to be charged atoms. 00:00:17.270 --> 00:00:19.820 Let's just start looking at some examples. 00:00:19.820 --> 00:00:23.550 Let's say we are dealing with fluorine. 00:00:23.550 --> 00:00:26.630 Now, we know what a neutral fluorine atom's 00:00:26.630 --> 00:00:28.600 electron configuration would be. 00:00:28.600 --> 00:00:30.680 In fact, if you want a little bit of practice, 00:00:30.680 --> 00:00:31.610 try to pause this video 00:00:31.610 --> 00:00:33.640 and think about what is the electron configuration 00:00:33.640 --> 00:00:37.393 of a neutral fluorine atom? 00:00:38.260 --> 00:00:40.290 All right, now let's work through this together. 00:00:40.290 --> 00:00:43.510 A neutral fluorine atom has nine electrons, 00:00:43.510 --> 00:00:45.950 and we could just use our Periodic Table of Elements. 00:00:45.950 --> 00:00:49.010 So first, we're going to have two electrons in 1s. 00:00:49.010 --> 00:00:51.640 So we'll have 1s two. 00:00:51.640 --> 00:00:54.480 And then we're going to go to the second shell. 00:00:54.480 --> 00:00:56.670 So then we go to 2s two. 00:00:56.670 --> 00:01:00.200 So far we have filled in four electrons. 00:01:00.200 --> 00:01:04.340 And next we got to the 2p sub-shell. 00:01:04.340 --> 00:01:05.610 And we are going to have, 00:01:05.610 --> 00:01:07.640 we're talking about a neutral fluorine, 00:01:07.640 --> 00:01:12.300 we are going to have one two three four five electrons 00:01:12.300 --> 00:01:14.030 in that 2p sub-shell. 00:01:14.030 --> 00:01:16.920 So it's 2p five. 00:01:16.920 --> 00:01:20.080 So if that's the electron configuration for fluorine, 00:01:20.080 --> 00:01:22.050 what do you think the electron configuration 00:01:22.050 --> 00:01:24.120 for fluoride would be? 00:01:24.120 --> 00:01:28.630 This is just the anion that has one extra electron. 00:01:28.630 --> 00:01:31.160 It is a negatively charged ion. 00:01:31.160 --> 00:01:33.260 Pause this video and try to figure it out. 00:01:34.450 --> 00:01:38.750 Well, here you're now going to have one extra electron. 00:01:38.750 --> 00:01:42.060 The fluorine has nabbed an electron from someplace 00:01:42.060 --> 00:01:44.710 and so where will that extra electron go? 00:01:44.710 --> 00:01:48.330 Well our 2p sub-shell has space for one more electron. 00:01:48.330 --> 00:01:50.140 So that's where it will go. 00:01:50.140 --> 00:01:52.120 So the fluoride anion is going to have 00:01:52.120 --> 00:01:57.120 an electron configuration of 1s two, 2s two, 2p, 00:01:58.480 --> 00:02:02.638 now it's going to have an extra electron here, 2p six. 00:02:02.638 --> 00:02:05.410 2p six. 00:02:05.410 --> 00:02:07.190 Now let's do another example. 00:02:07.190 --> 00:02:10.600 Let's say we wanted to figure out the electron configuration 00:02:10.600 --> 00:02:14.150 of a part positively charged calcium ion. 00:02:14.150 --> 00:02:15.840 So calcium, let's make it two plus. 00:02:15.840 --> 00:02:18.063 It has a positive charge of two. 00:02:18.970 --> 00:02:20.740 You could do this as a neutral calcium 00:02:20.740 --> 00:02:23.210 that has lost two electrons. 00:02:23.210 --> 00:02:25.900 What would be its electron configuration? 00:02:25.900 --> 00:02:28.638 Pause this video and try to figure that out. 00:02:28.638 --> 00:02:31.350 All right, well one way to figure this out is 00:02:31.350 --> 00:02:33.610 first we could figure out the electron configuration 00:02:33.610 --> 00:02:35.077 of a neutral calcium atom 00:02:39.440 --> 00:02:41.699 and then from that, we can take two 00:02:41.699 --> 00:02:45.460 of the highest energy electrons away. 00:02:45.460 --> 00:02:48.710 And so neutral calcium, you could view it, 00:02:48.710 --> 00:02:51.340 actually let's do it in noble gas configuration. 00:02:51.340 --> 00:02:53.620 Neutral calcium, the noble gas that comes 00:02:53.620 --> 00:02:56.150 right before calcium is argon. 00:02:56.150 --> 00:02:59.440 So it's going to have the electron configuration of argon 00:02:59.440 --> 00:03:02.540 and then we are going to have two electrons 00:03:02.540 --> 00:03:03.650 for that fourth shell. 00:03:03.650 --> 00:03:06.880 It's going to fill in the 4s sub-shell. 00:03:06.880 --> 00:03:08.700 And so we're going to have argon 00:03:08.700 --> 00:03:12.830 and then we're going to have, let me do this in a new color, 00:03:12.830 --> 00:03:16.370 let's call this 4s two. 00:03:16.370 --> 00:03:17.620 Now what do you think is going to happen 00:03:17.620 --> 00:03:20.650 if we were to lose two electrons? 00:03:20.650 --> 00:03:23.900 Well those two electrons in that 4s sub-shell, 00:03:23.900 --> 00:03:25.940 in the fourth shell, are gonna go away. 00:03:25.940 --> 00:03:27.970 And so the electron configuration here 00:03:27.970 --> 00:03:30.590 for calcium with a positive two charge, 00:03:30.590 --> 00:03:33.170 this calcium cation, is going to be 00:03:33.170 --> 00:03:36.830 the electron configuration of argon and no 4s two. 00:03:36.830 --> 00:03:37.770 So it's actually going to have 00:03:37.770 --> 00:03:42.380 the exact same electron configuration as argon. 00:03:42.380 --> 00:03:44.850 So I will leave you there, just a couple of examples. 00:03:44.850 --> 00:03:47.410 And I encourage you, if you're in the mood, 00:03:47.410 --> 00:03:50.050 just pick any of these atoms, any of these elements, 00:03:50.050 --> 00:03:51.040 and think about what would happen 00:03:51.040 --> 00:03:52.700 if they gained or lost an electron 00:03:52.700 --> 00:03:55.203 and what their electron configurations might be.

Khan Stories: Jason Spyres

https://www.youtube.com/watch?v=edMjF4Tcst8

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en

WEBVTT Kind: captions Language: en 00:00:02.420 --> 00:00:04.430 - My name's Jason Spires. 00:00:04.430 --> 00:00:07.950 It's nice to be able to use that name because, 00:00:07.950 --> 00:00:10.260 for many years, the only name that mattered 00:00:10.260 --> 00:00:15.260 in my life was Mr. K99397 'cause that was my prison number. 00:00:18.070 --> 00:00:21.230 Unfortunately, at a very young age, 00:00:21.230 --> 00:00:24.290 I made a stupid decision to sell cannabis, 00:00:24.290 --> 00:00:26.500 and I ended up in prison, 00:00:26.500 --> 00:00:27.950 and I was never really the type 00:00:27.950 --> 00:00:29.500 that was real good at school. 00:00:29.500 --> 00:00:31.140 Like, I was smart, 00:00:31.140 --> 00:00:33.853 but I wouldn't sit around and wouldn't focus. 00:00:34.800 --> 00:00:36.310 Not trying to make excuses, 00:00:36.310 --> 00:00:39.680 but my parents had drug addictions. 00:00:39.680 --> 00:00:42.150 I probably didn't have the best guidance, 00:00:42.150 --> 00:00:44.180 but I still knowingly made my own choices. 00:00:44.180 --> 00:00:48.570 So I own up to that, but when I got to prison, 00:00:48.570 --> 00:00:51.290 I had moments in my life that made me realize 00:00:51.290 --> 00:00:54.563 I had a distorted notion of what success really was, 00:00:55.503 --> 00:00:57.200 and fortunately, when I got arrested, 00:00:57.200 --> 00:00:59.190 it helped my mother get clean and sober, 00:00:59.190 --> 00:01:01.760 and it helped my father get clean and sober. 00:01:01.760 --> 00:01:04.170 So I now had parents that were actively involved 00:01:04.170 --> 00:01:06.900 in trying to do good things for me, 00:01:06.900 --> 00:01:10.610 and I decided that I wanted to improve my education, 00:01:10.610 --> 00:01:15.050 and one of the things that I remember is 00:01:15.050 --> 00:01:18.270 my mother went online to Khan Academy, 00:01:18.270 --> 00:01:20.420 and she would get printed out transcripts 00:01:20.420 --> 00:01:22.720 of what the videos were talking about in math, 00:01:23.580 --> 00:01:26.753 and she'd send me the transcripts, and I'd read over 'em, 00:01:27.650 --> 00:01:31.410 and from that, I started realizing I understand 00:01:31.410 --> 00:01:32.500 how fractions work. 00:01:32.500 --> 00:01:34.730 I understand math on a deeper level. 00:01:34.730 --> 00:01:35.880 I was always good with it, 00:01:35.880 --> 00:01:36.960 but now I was getting to the point 00:01:36.960 --> 00:01:39.650 where I could actually perform well with it. 00:01:39.650 --> 00:01:40.640 While I was in prison, 00:01:40.640 --> 00:01:44.350 I was able to, with Khan Academy's transcripts, 00:01:44.350 --> 00:01:47.600 learn how to do many of the math procedures 00:01:47.600 --> 00:01:50.250 that helped me perform better on the SAT, 00:01:50.250 --> 00:01:52.760 and when I got towards the end of my sentence, 00:01:52.760 --> 00:01:55.140 I was able to get to a work-release program, 00:01:55.140 --> 00:01:57.520 which allowed me to go to community college, 00:01:57.520 --> 00:01:59.002 and I had to take the SAT 00:01:59.002 --> 00:02:02.610 in anticipation of transferring to a university, 00:02:02.610 --> 00:02:06.550 and I used the Khan Academy SAT prep, 00:02:06.550 --> 00:02:10.790 and fortunately, I was accepted as a transfer student 00:02:10.790 --> 00:02:12.273 at Stanford University, 00:02:13.210 --> 00:02:16.540 and little did I know that a year later I would go 00:02:16.540 --> 00:02:21.540 to my classroom, and Mr. Khan would be our guest speaker, 00:02:21.590 --> 00:02:24.980 and I got to tell him something 00:02:27.160 --> 00:02:28.780 that was very difficult to say 00:02:28.780 --> 00:02:31.470 but was the truest words I could think of, 00:02:31.470 --> 00:02:32.733 and that was thank you, 00:02:35.110 --> 00:02:39.100 and it's not just who he is 'cause, like he said, 00:02:39.100 --> 00:02:40.970 he did nothing personally for me. 00:02:40.970 --> 00:02:42.840 It was his organization. 00:02:42.840 --> 00:02:46.460 It was having videos that were easy to understand. 00:02:46.460 --> 00:02:49.320 It was being able to learn knowledge without having to admit 00:02:49.320 --> 00:02:52.220 that I'm stupid because I didn't already know it. 00:02:52.220 --> 00:02:54.130 It took away the embarrassment factor 00:02:54.130 --> 00:02:56.410 of having to ask someone else, 00:02:56.410 --> 00:03:01.040 and so if you're a part of that organization, 00:03:01.040 --> 00:03:06.040 if you're a donor, if you're Miss Door who gave Mr. Khan 00:03:07.800 --> 00:03:12.523 the impetus he needed to make this actually happen, 00:03:14.100 --> 00:03:18.160 thank you because you played a role 00:03:18.160 --> 00:03:21.420 in me now being a Stanford University student 00:03:21.420 --> 00:03:24.860 and studying computer science after being locked up 15 years 00:03:24.860 --> 00:03:27.160 without access to technology. 00:03:27.160 --> 00:03:31.230 So I appreciate everything that's been done 00:03:31.230 --> 00:03:32.980 for me in my life, 00:03:32.980 --> 00:03:35.300 and there's been so many people that's contributed to it, 00:03:35.300 --> 00:03:38.010 but I can honestly say that Khan Academy 00:03:38.010 --> 00:03:40.530 and everyone involved with the organization 00:03:40.530 --> 00:03:43.120 and everyone who has supported its expansion and growth 00:03:43.120 --> 00:03:46.920 to other students has made an impact upon me, 00:03:46.920 --> 00:03:51.370 and I can only tell you that there's so many other people 00:03:52.690 --> 00:03:56.410 that have the potential to make my story nothing 00:03:56.410 --> 00:03:59.130 if they can just get their hands 00:03:59.130 --> 00:04:03.700 on the ability to learn the way that I was able to, 00:04:03.700 --> 00:04:05.513 which Khan Academy was a part of.

What to do the night before an exam: 3 tips from Sal Khan

https://www.youtube.com/watch?v=7hfcmct9lgc

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en

WEBVTT Kind: captions Language: en 00:00:00.740 --> 00:00:03.102 - Here are my three tips to reducing stress 00:00:03.102 --> 00:00:05.833 the night before a test. 00:00:05.833 --> 00:00:09.850 Tip one, stay physically healthy. 00:00:09.850 --> 00:00:11.211 There's a tendency that the night before 00:00:11.211 --> 00:00:12.650 you wanna cram, 00:00:12.650 --> 00:00:13.640 you wanna stay up late, 00:00:13.640 --> 00:00:14.860 you're stressed, you're anxious. 00:00:14.860 --> 00:00:16.620 That's the exact wrong thing to do. 00:00:16.620 --> 00:00:19.340 The night before you have to get good rest. 00:00:19.340 --> 00:00:20.210 You have to relax, 00:00:20.210 --> 00:00:21.410 maybe meditate, 00:00:21.410 --> 00:00:23.851 watch a fun show, laugh a little bit, 00:00:23.851 --> 00:00:25.740 hang out with your family, 00:00:25.740 --> 00:00:27.690 and eat a healthy light meal. 00:00:27.690 --> 00:00:29.900 You don't wanna have stomach issues 00:00:29.900 --> 00:00:30.930 as you go into the test. 00:00:30.930 --> 00:00:34.986 Tip two, organize your logistics. 00:00:34.986 --> 00:00:36.670 It's really important that 00:00:36.670 --> 00:00:37.820 as you go into the test 00:00:37.820 --> 00:00:39.354 that you have to worry about as little as possible. 00:00:39.354 --> 00:00:40.830 So the best way to do that 00:00:40.830 --> 00:00:42.640 is to organize everything ahead of time. 00:00:42.640 --> 00:00:43.930 Know where you're going. 00:00:43.930 --> 00:00:45.310 If you have to print out something, 00:00:45.310 --> 00:00:46.366 print it out ahead of time. 00:00:46.366 --> 00:00:48.240 Get your pencils in shape 00:00:48.240 --> 00:00:49.073 and sharpened. 00:00:49.073 --> 00:00:51.410 Even your clothes ready for the morning of 00:00:51.410 --> 00:00:52.243 so that you just have to 00:00:52.243 --> 00:00:55.940 have nice night of sleep, wake up, do some simple tasks 00:00:55.940 --> 00:00:58.140 and then go to the test. 00:00:58.140 --> 00:00:59.558 The less you have to worry about that morning the better. 00:00:59.558 --> 00:01:04.451 Tip three, stay positive and confident. 00:01:04.451 --> 00:01:05.798 And perhaps the most important thing 00:01:05.798 --> 00:01:07.367 is as you go to the test itself, 00:01:07.367 --> 00:01:10.137 keep a relaxed and positive attitude. 00:01:10.137 --> 00:01:11.758 If you're stressed, if you're anxious, 00:01:11.758 --> 00:01:13.581 that's going to become a self-fulfilling prophecy. 00:01:13.581 --> 00:01:17.248 So take a deep breath, breathe out slowly, 00:01:17.248 --> 00:01:19.193 and say I got this.

Ionic bonds

https://www.youtube.com/watch?v=FaeAurHnQJs

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en

WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.840 - [Instructor] Most of what we've talked about so far 00:00:01.840 --> 00:00:04.260 has been atoms in isolation. 00:00:04.260 --> 00:00:05.880 We have thought about the number 00:00:05.880 --> 00:00:08.260 of electrons and protons and neutrons 00:00:08.260 --> 00:00:10.980 and the electron configuration of atoms. 00:00:10.980 --> 00:00:14.160 But atoms don't just operate in isolation. 00:00:14.160 --> 00:00:16.710 If that were the case, the whole universe including us 00:00:16.710 --> 00:00:19.400 would just be a bunch of atoms drifting around. 00:00:19.400 --> 00:00:21.050 What begins to be interesting is 00:00:21.050 --> 00:00:24.300 how the atoms actually interact with each other. 00:00:24.300 --> 00:00:27.910 And one of the most interesting forms of interaction is 00:00:27.910 --> 00:00:31.760 when they stick to each other in some way shape or form. 00:00:31.760 --> 00:00:35.240 And this sticking together of atoms is 00:00:35.240 --> 00:00:38.060 what we are going to study in this video. 00:00:38.060 --> 00:00:42.770 Another way to talk about it is, how do atoms bond? 00:00:42.770 --> 00:00:46.370 Now as we will see, there are several types of bonds 00:00:46.370 --> 00:00:47.690 and it's really a spectrum. 00:00:47.690 --> 00:00:49.480 But let's just start with what I would consider 00:00:49.480 --> 00:00:51.940 one of the more extreme type of bonds. 00:00:51.940 --> 00:00:54.660 And to understand it, let's get a periodic table of elements 00:00:54.660 --> 00:00:56.350 out right over here. 00:00:56.350 --> 00:01:00.950 So let's say that we are dealing with a group one element. 00:01:00.950 --> 00:01:03.860 Let's say sodium right over here. 00:01:03.860 --> 00:01:06.290 What's interesting about group one elements is 00:01:06.290 --> 00:01:09.080 that they have one valence electron. 00:01:09.080 --> 00:01:12.040 If we want to visualize the valence electrons 00:01:12.040 --> 00:01:14.490 for, say, sodium we could do it 00:01:14.490 --> 00:01:17.110 with what's known as a Lewis dot structure 00:01:17.110 --> 00:01:19.220 or a Lewis electron dot structure, 00:01:19.220 --> 00:01:22.150 sometimes just called a dot structure for short. 00:01:22.150 --> 00:01:25.740 But because a neutral sodium has one valence electron, 00:01:25.740 --> 00:01:30.690 we would just draw that one valence electron like that. 00:01:30.690 --> 00:01:33.360 Now let's go to the other end of the periodic table 00:01:33.360 --> 00:01:35.530 and say, look at chlorine. 00:01:35.530 --> 00:01:37.490 Chlorine is a halogen. 00:01:37.490 --> 00:01:41.380 Halogens have seven valence electrons 00:01:41.380 --> 00:01:44.970 so chlorine's valence electrons would look like this. 00:01:44.970 --> 00:01:49.970 It has one two three four five six seven valence electrons. 00:01:54.800 --> 00:01:57.670 And so you could imagine chlorine would love 00:01:57.670 --> 00:01:58.880 to get another electron 00:01:58.880 --> 00:02:01.240 in order to complete its outer shell. 00:02:01.240 --> 00:02:04.300 And we've also studied in other videos these atoms, 00:02:04.300 --> 00:02:06.850 these elements at the top right of the periodic table 00:02:06.850 --> 00:02:08.650 which are not the noble gases, 00:02:08.650 --> 00:02:11.260 but especially the top of these halogens, 00:02:11.260 --> 00:02:13.170 things like oxygen, nitrogen. 00:02:13.170 --> 00:02:14.830 These are very electronegative. 00:02:14.830 --> 00:02:18.610 They like to pull electrons, hog electrons. 00:02:18.610 --> 00:02:20.100 And so what do you think is going to happen 00:02:20.100 --> 00:02:22.720 when you put these characters together? 00:02:22.720 --> 00:02:25.010 This guy wants to lose the electrons 00:02:25.010 --> 00:02:28.300 and chlorine wants to gain an electron. 00:02:28.300 --> 00:02:30.980 Well, maybe the chlorine will take an electron 00:02:30.980 --> 00:02:31.940 from the sodium. 00:02:31.940 --> 00:02:33.320 On a real chemical reaction, 00:02:33.320 --> 00:02:34.880 you would have trillions of these 00:02:34.880 --> 00:02:36.170 and they're bouncing around 00:02:36.170 --> 00:02:37.800 and different things are happening 00:02:37.800 --> 00:02:38.740 but just for simplicity, 00:02:38.740 --> 00:02:40.800 let's just imagine that these are the only two. 00:02:40.800 --> 00:02:43.330 And let's imagine that this chlorine is able 00:02:43.330 --> 00:02:46.810 to nab an electron from this sodium. 00:02:46.810 --> 00:02:48.980 So what is going to happen? 00:02:48.980 --> 00:02:53.980 This sodium is then going to become positively charged, 00:02:54.160 --> 00:02:56.400 'cause it's going to lose an electron. 00:02:56.400 --> 00:03:00.340 And then the chlorine, the chlorine is now going 00:03:00.340 --> 00:03:02.040 to gain an electron. 00:03:02.040 --> 00:03:04.663 So it's going to become a chloride anion. 00:03:04.663 --> 00:03:06.510 Anion is a negative ion. 00:03:06.510 --> 00:03:09.260 It's a sodium cation, a positive ion. 00:03:09.260 --> 00:03:10.560 Ion means it's charged. 00:03:10.560 --> 00:03:13.290 And now it's a chloride anion. 00:03:13.290 --> 00:03:15.430 So it has the valence electrons that it had before 00:03:15.430 --> 00:03:16.800 and then you could imagine 00:03:16.800 --> 00:03:18.980 that it gains one from the sodium. 00:03:18.980 --> 00:03:22.780 And now it has a negative charge. 00:03:22.780 --> 00:03:25.730 Now what do we know about positively charged ions 00:03:25.730 --> 00:03:27.780 and negatively charged ions? 00:03:27.780 --> 00:03:29.490 Opposites attract. 00:03:29.490 --> 00:03:30.410 Coulomb forces. 00:03:30.410 --> 00:03:31.930 So these two characters are going 00:03:31.930 --> 00:03:33.810 to be attracted to each other, 00:03:33.810 --> 00:03:34.810 or another way to think of it, 00:03:34.810 --> 00:03:35.780 they're gonna stick together, 00:03:35.780 --> 00:03:37.250 or another way you could think about it, 00:03:37.250 --> 00:03:39.440 they are going to be bonded. 00:03:39.440 --> 00:03:44.440 And they will form a compound of sodium chloride. 00:03:45.300 --> 00:03:49.380 And notice the whole compound here is neutral. 00:03:49.380 --> 00:03:51.820 It has a plus one charge for the sodium, 00:03:51.820 --> 00:03:53.680 a negative one charge for the chloride, 00:03:53.680 --> 00:03:55.290 but taken together it is neutral 00:03:55.290 --> 00:03:57.523 because these are hanging out together. 00:03:58.410 --> 00:04:01.470 And this type of bond between ions, 00:04:01.470 --> 00:04:03.670 you might guess what it's called. 00:04:03.670 --> 00:04:06.490 It is called an ionic bond. 00:04:06.490 --> 00:04:08.963 Ionic bond.

Covalent bonds

https://www.youtube.com/watch?v=kS5iU4v0QZk

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en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:01.480 - [Instructor] In a previous video, 00:00:01.480 --> 00:00:04.200 we introduced ourselves to the idea of bonds 00:00:04.200 --> 00:00:06.330 and the idea of ionic bonds, 00:00:06.330 --> 00:00:08.730 where one atom essentially is able 00:00:08.730 --> 00:00:11.380 to take electrons from another atom. 00:00:11.380 --> 00:00:13.620 But then because one becomes positively charged 00:00:13.620 --> 00:00:15.220 and the other becomes negatively charged, 00:00:15.220 --> 00:00:16.910 they get attracted to each other. 00:00:16.910 --> 00:00:18.720 Now we're going to go to the other end 00:00:18.720 --> 00:00:20.060 of the bonding spectrum, 00:00:20.060 --> 00:00:22.610 where instead of stealing electrons from each other, 00:00:22.610 --> 00:00:24.430 we're going to share them. 00:00:24.430 --> 00:00:27.690 Let's say we're dealing with two oxygen atoms. 00:00:27.690 --> 00:00:30.380 So let me draw one oxygen here. 00:00:30.380 --> 00:00:33.060 A neutral oxygen has eight electrons total, 00:00:33.060 --> 00:00:34.910 but six of them are in its outer shell. 00:00:34.910 --> 00:00:37.420 So it has one, 00:00:37.420 --> 00:00:39.320 two, three, 00:00:39.320 --> 00:00:41.800 four, five, 00:00:41.800 --> 00:00:44.260 six valence electrons. 00:00:44.260 --> 00:00:48.510 And the way that I arrange them is I pair them up last. 00:00:48.510 --> 00:00:50.810 So you have these two valence electrons 00:00:50.810 --> 00:00:53.000 that are not paired with another electron. 00:00:53.000 --> 00:00:54.770 And now let me draw another oxygen, 00:00:54.770 --> 00:00:56.730 and I'm going do it with a different color, 00:00:56.730 --> 00:01:00.520 so we can keep track of the electrons. 00:01:00.520 --> 00:01:01.920 So another oxygen right over there, 00:01:01.920 --> 00:01:06.440 also has six valence electrons, one, two, three, 00:01:06.440 --> 00:01:11.440 four, five, six valence electrons. 00:01:11.920 --> 00:01:13.870 Now this oxygen on the left, 00:01:13.870 --> 00:01:15.690 in order to become more stable, 00:01:15.690 --> 00:01:17.740 it would love to somehow gain 00:01:17.740 --> 00:01:19.960 or maybe share two more electrons. 00:01:19.960 --> 00:01:22.830 And of course, this oxygen on the right, it's still oxygen. 00:01:22.830 --> 00:01:24.400 It also would love to gain 00:01:24.400 --> 00:01:27.810 or share two more valence electrons. 00:01:27.810 --> 00:01:29.280 So how could it do it? 00:01:29.280 --> 00:01:33.390 Well, what if the oxygen on the left shared this electron 00:01:33.390 --> 00:01:35.600 and this electron with the oxygen on the right, 00:01:35.600 --> 00:01:38.070 and the oxygen on the right shared this electron 00:01:38.070 --> 00:01:41.380 and this electron with the oxygen on the left? 00:01:41.380 --> 00:01:43.020 Well, if they did that, 00:01:43.020 --> 00:01:45.340 you would have something that looks like this. 00:01:45.340 --> 00:01:47.240 You have your oxygen on the left. 00:01:47.240 --> 00:01:50.950 You have the oxygen on the right. 00:01:50.950 --> 00:01:54.750 And the way we show two electrons that are being shared, 00:01:54.750 --> 00:01:57.590 let's say these two electrons are being shared, 00:01:57.590 --> 00:02:00.310 is just a line like this. 00:02:00.310 --> 00:02:01.960 This shows that there are two electrons 00:02:01.960 --> 00:02:04.670 that are being shared by these two oxygens. 00:02:04.670 --> 00:02:07.330 And let's say that these two electrons 00:02:07.330 --> 00:02:09.290 are also being shared. 00:02:09.290 --> 00:02:11.190 You would do that with a line like this. 00:02:11.190 --> 00:02:12.600 And then we could draw the remainder 00:02:12.600 --> 00:02:13.650 of the valence electrons. 00:02:13.650 --> 00:02:15.600 This oxygen on the left had, 00:02:15.600 --> 00:02:17.670 outside of the electrons that are being shared, 00:02:17.670 --> 00:02:20.573 it had four more valence electrons. 00:02:21.870 --> 00:02:23.680 And then the oxygen on the right 00:02:23.680 --> 00:02:25.900 had four more valence electrons, 00:02:25.900 --> 00:02:28.630 one, two, three, four. 00:02:28.630 --> 00:02:31.340 Now what's interesting here is the shared electrons, 00:02:31.340 --> 00:02:35.580 these are going to cause these oxygens to stick together. 00:02:35.580 --> 00:02:36.560 If they don't stick together, 00:02:36.560 --> 00:02:38.770 these electrons aren't going to be shared. 00:02:38.770 --> 00:02:43.220 So what we have formed here is known as a covalent bond, 00:02:43.220 --> 00:02:46.130 covalent bond. 00:02:46.130 --> 00:02:49.820 And what's interesting is it allows both of these oxygens 00:02:49.820 --> 00:02:52.130 in some ways to be more stable. 00:02:52.130 --> 00:02:54.390 From the left oxygen's point of view, 00:02:54.390 --> 00:02:56.350 it had six valence electrons, 00:02:56.350 --> 00:02:58.880 but now it's able to share two more. 00:02:58.880 --> 00:03:00.720 Remember, each of these bonds, 00:03:00.720 --> 00:03:03.390 each of these lines represent two electrons. 00:03:03.390 --> 00:03:05.090 So this oxygen could say, hey, 00:03:05.090 --> 00:03:07.850 I get to have one, two, three, four, 00:03:07.850 --> 00:03:10.880 six, eight electrons that I'm dealing with, 00:03:10.880 --> 00:03:12.530 and the same thing is going to be true 00:03:12.530 --> 00:03:15.280 of this oxygen on the right. 00:03:15.280 --> 00:03:16.780 Now there are some covalent bonds 00:03:16.780 --> 00:03:19.090 that are between not-so-equals. 00:03:19.090 --> 00:03:22.630 So for example, if we're talking about water 00:03:22.630 --> 00:03:25.800 and if we're talking about how oxygen bonds with hydrogen. 00:03:25.800 --> 00:03:28.100 So if we have oxygen right over here, 00:03:28.100 --> 00:03:31.890 once again, I can draw its six valence electrons, one, two, 00:03:31.890 --> 00:03:35.050 three, four, five, 00:03:35.050 --> 00:03:38.400 and let me just draw the sixth one right over there. 00:03:38.400 --> 00:03:40.140 And if I have hydrogen, 00:03:40.140 --> 00:03:42.880 hydrogen has one valence electron. 00:03:42.880 --> 00:03:44.630 So let's say that's a hydrogen right over there 00:03:44.630 --> 00:03:45.820 with one valence electron, 00:03:45.820 --> 00:03:47.610 maybe another hydrogen right over there 00:03:47.610 --> 00:03:49.600 with one valence electron. 00:03:49.600 --> 00:03:51.950 Oxygen and hydrogen form covalent bonds. 00:03:51.950 --> 00:03:54.610 In fact, that is how water is formed. 00:03:54.610 --> 00:03:56.650 And so what would that look like? 00:03:56.650 --> 00:03:57.880 Well, it would look like this. 00:03:57.880 --> 00:03:59.720 You have oxygen right over here. 00:03:59.720 --> 00:04:03.540 You have these two pairs of electrons that I keep drawing. 00:04:03.540 --> 00:04:06.560 And then this electron right over here 00:04:06.560 --> 00:04:08.810 could be shared with the hydrogen, 00:04:08.810 --> 00:04:10.270 and that hydrogen's electron could be shared 00:04:10.270 --> 00:04:11.260 with the oxygen. 00:04:11.260 --> 00:04:15.100 So that forms a covalent bond with this hydrogen. 00:04:15.100 --> 00:04:17.170 And then this electron 00:04:17.170 --> 00:04:19.630 from the oxygen can be shared with the hydrogen, 00:04:19.630 --> 00:04:21.100 and that electron from the hydrogen can be shared 00:04:21.100 --> 00:04:21.940 with the oxygen. 00:04:21.940 --> 00:04:24.400 And so that would form a covalent bond 00:04:24.400 --> 00:04:26.003 with that other hydrogen. 00:04:27.720 --> 00:04:31.200 And now here, once again, oxygen can kinda pretend 00:04:31.200 --> 00:04:33.370 like it has eight valence electrons, 00:04:33.370 --> 00:04:35.930 two, four, six, eight. 00:04:35.930 --> 00:04:37.980 And the hydrogens can kind of pretend 00:04:37.980 --> 00:04:39.910 that it has two valence electrons. 00:04:39.910 --> 00:04:42.370 But the one difference here is that oxygen 00:04:42.370 --> 00:04:45.280 is a lot more electronegative than hydrogen. 00:04:45.280 --> 00:04:46.960 It's to the right of hydrogen. 00:04:46.960 --> 00:04:49.590 It's in this top-right corner, outside of, 00:04:49.590 --> 00:04:51.060 other than the noble gases, 00:04:51.060 --> 00:04:53.290 that really like to hog electrons. 00:04:53.290 --> 00:04:55.370 So what do you think is going to happen here? 00:04:55.370 --> 00:04:58.120 Well, the electrons in each of these covalent bonds 00:04:58.120 --> 00:05:00.280 are going to hang out around the oxygen 00:05:00.280 --> 00:05:02.420 more often than around the hydrogen. 00:05:02.420 --> 00:05:04.560 So if the electrons spend more time around the oxygen, 00:05:04.560 --> 00:05:05.700 you're going to have, in general, 00:05:05.700 --> 00:05:08.020 more negative charge around the oxygen. 00:05:08.020 --> 00:05:11.840 And so you're going to have a partial negative charge 00:05:11.840 --> 00:05:14.860 on the oxygen end of the water molecule, 00:05:14.860 --> 00:05:17.440 and then you're going to have partial positive charges 00:05:17.440 --> 00:05:20.750 on the hydrogen ends of the molecules. 00:05:20.750 --> 00:05:21.610 And in case you're curious, 00:05:21.610 --> 00:05:23.320 that little symbol I'm using for partial, 00:05:23.320 --> 00:05:25.980 that's the lowercase Greek letter delta, 00:05:25.980 --> 00:05:27.820 which is just the convention in chemistry. 00:05:27.820 --> 00:05:30.690 And so this type of covalent bond, 00:05:30.690 --> 00:05:32.550 because there is some polarity, 00:05:32.550 --> 00:05:35.240 one side has more charge than the other, 00:05:35.240 --> 00:05:38.390 this is known as a polar covalent bond, 00:05:38.390 --> 00:05:41.933 polar covalent bond.

Metallic bonds

https://www.youtube.com/watch?v=N5MAFQlnu18

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en

WEBVTT Kind: captions Language: en 00:00:00.240 --> 00:00:01.860 - [Instructor] Now the last type of bond 00:00:01.860 --> 00:00:06.860 I'm going to talk about is known as the metallic bond, 00:00:07.040 --> 00:00:08.810 which I think I know a little bit about 00:00:08.810 --> 00:00:10.400 because I was the lead singer 00:00:10.400 --> 00:00:12.730 of a metallic bond in high school. 00:00:12.730 --> 00:00:15.540 I'll talk about that in future videos. 00:00:15.540 --> 00:00:20.070 But let's just take one of our metallic atoms here. 00:00:20.070 --> 00:00:21.740 Iron is a good example. 00:00:21.740 --> 00:00:25.823 Iron is maybe one of the most referred to metals. 00:00:26.950 --> 00:00:29.430 Let's say we have a bunch of iron atoms. 00:00:29.430 --> 00:00:33.333 So Fe, Fe, Fe, Fe, hope you can read that. 00:00:36.930 --> 00:00:38.150 These are all iron atoms. 00:00:38.150 --> 00:00:39.990 And if they're just atoms by themselves 00:00:39.990 --> 00:00:41.350 they're going to be neutral. 00:00:41.350 --> 00:00:44.340 But when they are mushed together, 00:00:44.340 --> 00:00:46.330 they will form a metallic bond. 00:00:46.330 --> 00:00:47.930 Makes sense because they're metals. 00:00:47.930 --> 00:00:50.100 And what's interesting about metallic bonds, 00:00:50.100 --> 00:00:51.510 I'll draw it down here, is 00:00:51.510 --> 00:00:54.940 that metals like to share their electrons 00:00:54.940 --> 00:00:56.330 with the other metals. 00:00:56.330 --> 00:00:58.860 It kinda forms this sea of electrons. 00:00:58.860 --> 00:01:01.250 So what it can look like is, 00:01:01.250 --> 00:01:03.450 each of the irons lose an electron, 00:01:03.450 --> 00:01:04.460 I'll draw it a little bit bigger. 00:01:04.460 --> 00:01:08.473 So let's say this is Fe plus, so it has a positive charge. 00:01:09.580 --> 00:01:12.521 Fe plus has a positive charge. 00:01:12.521 --> 00:01:16.544 Fe plus, these are all iron ions, you can imagine. 00:01:16.544 --> 00:01:19.010 Fe plus, and we're imagining 00:01:19.010 --> 00:01:20.300 that they have this positive charge 00:01:20.300 --> 00:01:22.340 because they've all contributed an electron 00:01:22.340 --> 00:01:24.570 to this sea of electrons. 00:01:24.570 --> 00:01:27.260 So you have an electron here which has a negative charge. 00:01:27.260 --> 00:01:29.260 And electrons are not this big, 00:01:29.260 --> 00:01:31.130 but this is just so that you can see it. 00:01:31.130 --> 00:01:33.630 Electron here that has a negative charge. 00:01:33.630 --> 00:01:37.930 And so you can imagine these positive ions are attracted 00:01:37.930 --> 00:01:42.640 to the sea of negativity, the sea of negative electrons. 00:01:42.640 --> 00:01:44.020 Another way to think about it is, 00:01:44.020 --> 00:01:48.110 is that metals, when they bond in metallic bonds, 00:01:48.110 --> 00:01:50.420 they will have overlapping valence electrons. 00:01:50.420 --> 00:01:52.540 And those valence electrons are not fixed 00:01:52.540 --> 00:01:56.010 to just one of the atoms, they can move around. 00:01:56.010 --> 00:01:58.740 And this is what gives metals many of the characteristics 00:01:58.740 --> 00:02:00.460 we associate with metals. 00:02:00.460 --> 00:02:01.580 It conducts electricity 00:02:01.580 --> 00:02:05.390 because these electrons can move around quite easily. 00:02:05.390 --> 00:02:08.100 It makes them malleable, you can bend it easily. 00:02:08.100 --> 00:02:09.980 You can imagine these iron ions 00:02:09.980 --> 00:02:13.090 in this pudding, or this sea of electrons. 00:02:13.090 --> 00:02:15.040 So you can bend it, it doesn't break. 00:02:15.040 --> 00:02:18.300 Well if you were to take a bar of a salt right over here, 00:02:18.300 --> 00:02:20.650 if you were to try to bend it, it's very rigid. 00:02:20.650 --> 00:02:23.130 It is going to break. 00:02:23.130 --> 00:02:25.740 So there we have it, the types of bonds. 00:02:25.740 --> 00:02:27.550 It's important to realize that you can view it 00:02:27.550 --> 00:02:28.700 as something of a spectrum. 00:02:28.700 --> 00:02:31.360 At one end, you have things like ionic bonds 00:02:31.360 --> 00:02:33.420 where one character swipes an electron 00:02:33.420 --> 00:02:34.367 from another character and says, 00:02:34.367 --> 00:02:36.600 "Hey, but now we're attracted to each other," 00:02:36.600 --> 00:02:39.070 and you get something like salt. 00:02:39.070 --> 00:02:40.930 Or you have covalent bonds 00:02:40.930 --> 00:02:43.470 where we outright share electrons. 00:02:43.470 --> 00:02:45.580 And then you have things in between covalent bonds 00:02:45.580 --> 00:02:49.080 and ionic bonds where the sharing is not so equal 00:02:49.080 --> 00:02:50.800 and you get polar covalent bonds. 00:02:50.800 --> 00:02:52.810 And then another form, I guess you could say, 00:02:52.810 --> 00:02:55.770 of extreme sharing is the metallic bonds 00:02:55.770 --> 00:02:59.343 where you just have this communal sea of electrons.

Isotopes

https://www.youtube.com/watch?v=ShC3VoxxW3g

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WEBVTT Kind: captions Language: en 00:00:00.250 --> 00:00:01.610 - [Instructor] In other videos we have talked 00:00:01.610 --> 00:00:03.850 about that the type of element that we are dealing 00:00:03.850 --> 00:00:06.270 with is defined by the number of protons 00:00:06.270 --> 00:00:07.970 in an atom's nucleus. 00:00:07.970 --> 00:00:11.080 So for example, any atom with exactly one proton 00:00:11.080 --> 00:00:14.350 in its nucleus is by definition hydrogen. 00:00:14.350 --> 00:00:17.040 Any atom with six protons in its nucleus 00:00:17.040 --> 00:00:19.320 is by definition carbon, 00:00:19.320 --> 00:00:22.720 any atom with 17 protons in its nucleus 00:00:22.720 --> 00:00:25.200 is by definition chlorine, 00:00:25.200 --> 00:00:27.960 and so these numbers that I'm circling on a periodic table 00:00:27.960 --> 00:00:30.750 of elements, that's known as the atomic number, 00:00:30.750 --> 00:00:34.540 but it's really just the number of protons in an atom 00:00:34.540 --> 00:00:36.630 of that element types nucleus. 00:00:36.630 --> 00:00:40.660 And that defines what type of element it is. 00:00:40.660 --> 00:00:42.880 But in this video we're going to dig a little bit deeper 00:00:42.880 --> 00:00:46.260 and realize that you can still have different versions 00:00:46.260 --> 00:00:51.260 of the same element and these versions in chemistry speak 00:00:51.490 --> 00:00:54.150 are known as isotopes. 00:00:54.150 --> 00:00:57.480 Now how can you have different versions of the same element 00:00:57.480 --> 00:01:01.180 if the number of protons defines what the element is? 00:01:01.180 --> 00:01:04.510 Well, the versions the various isotopes are going to happen 00:01:04.510 --> 00:01:07.490 based on the number of neutrons you have. 00:01:07.490 --> 00:01:12.490 So for example, there are two stable isotopes of chlorine, 00:01:13.200 --> 00:01:17.520 there's one version of chlorine known as chlorine 35. 00:01:17.520 --> 00:01:20.360 Let me write it over here, chlorine 35. 00:01:20.360 --> 00:01:21.970 It's sometimes written like this, 00:01:21.970 --> 00:01:25.880 in fact it's often written like this, chlorine 35 00:01:25.880 --> 00:01:29.560 and this isotope notation that you see over here 00:01:29.560 --> 00:01:31.640 where we have 35 in the top left, 00:01:31.640 --> 00:01:35.100 that 35 is the sum of this version, 00:01:35.100 --> 00:01:39.600 this isotope of chlorines protons and neutrons. 00:01:39.600 --> 00:01:44.550 This number 35 is this isotope of chlorines mass number. 00:01:44.550 --> 00:01:47.610 So it has a total of 35 protons and neutrons, 00:01:47.610 --> 00:01:50.663 how many neutrons does this version of chlorine have? 00:01:51.900 --> 00:01:54.510 Well it's going to have 17 protons. 00:01:54.510 --> 00:01:57.250 17 protons, I know that because we are dealing 00:01:57.250 --> 00:02:00.130 with chlorine, so how many neutrons will it have? 00:02:00.130 --> 00:02:05.130 Well 35 minus 17 is 18, 18 neutrons. 00:02:06.860 --> 00:02:10.920 And there's another version of chlorine that is stable 00:02:10.920 --> 00:02:14.610 and that is chlorine 37. 00:02:14.610 --> 00:02:17.250 Now how many protons is that going to have? 00:02:17.250 --> 00:02:18.250 Well that's a trick question, 00:02:18.250 --> 00:02:21.530 by definition it's chlorine, it's going to have 17 protons. 00:02:21.530 --> 00:02:24.500 This is going to have 17 protons, 00:02:24.500 --> 00:02:26.620 but then how many neutrons will it have? 00:02:26.620 --> 00:02:29.340 Well the protons plus the neutrons is 37, 00:02:29.340 --> 00:02:32.850 so 17 plus 20 is going to be 37. 00:02:32.850 --> 00:02:36.510 So it's going to be 20 neutrons, 00:02:36.510 --> 00:02:41.103 and this would be written out as chlorine, chlorine 37. 00:02:42.280 --> 00:02:45.700 So you can see these are two different versions of chlorine, 00:02:45.700 --> 00:02:48.920 same number of protons which make them chlorine, 00:02:48.920 --> 00:02:51.820 but different number of neutrons. 00:02:51.820 --> 00:02:54.240 Now you can imagine these different versions are going 00:02:54.240 --> 00:02:56.940 to have different atomic masses, 00:02:56.940 --> 00:03:00.100 but here on a periodic table of elements there's only one 00:03:00.100 --> 00:03:01.770 average atomic mass listed, 00:03:01.770 --> 00:03:05.670 and the key word here is this is an average atomic mass. 00:03:05.670 --> 00:03:10.510 It's the weighted average of the masses of the chlorines, 00:03:10.510 --> 00:03:13.180 the stable chlorines that you will find. 00:03:13.180 --> 00:03:18.180 So for example, in nature 75.77% of the chlorine 00:03:21.810 --> 00:03:25.070 found is chlorine 35, 00:03:25.070 --> 00:03:30.070 and then the remaining 24.23% of the chlorine found 00:03:31.520 --> 00:03:33.870 is chlorine 37. 00:03:33.870 --> 00:03:36.970 So when they calculate this average atomic mass, 00:03:36.970 --> 00:03:39.610 what they do is they would take, or you would take, 00:03:39.610 --> 00:03:44.610 if you're calculating it, so this would be 75.77% 00:03:47.410 --> 00:03:50.485 times the atomic mass, 00:03:50.485 --> 00:03:55.485 atomic mass of chlorine 35 plus, 00:03:59.520 --> 00:04:04.520 and now the weight here would be 24.23% 00:04:04.720 --> 00:04:09.720 times the atomic mass, atomic mass of chlorine 37. 00:04:14.910 --> 00:04:17.090 And if you were to do this calculation you would get 00:04:17.090 --> 00:04:20.310 this number right over here, 35.45 unified 00:04:20.310 --> 00:04:22.080 atomic mass units. 00:04:22.080 --> 00:04:25.440 Now, how do you figure out the atomic mass of chlorine 35? 00:04:25.440 --> 00:04:28.040 You might be tempted to say it's just 35 unified 00:04:28.040 --> 00:04:30.740 atomic mass units, and you would be close 00:04:30.740 --> 00:04:34.900 because the mass of a proton is close to one 00:04:34.900 --> 00:04:36.400 universal atomic mass unit, 00:04:36.400 --> 00:04:39.010 and the mass of a neutron is close to one 00:04:39.010 --> 00:04:40.480 universal atomic mass unit, 00:04:40.480 --> 00:04:42.670 and then the electrons are have a much, much, 00:04:42.670 --> 00:04:44.020 much smaller mass. 00:04:44.020 --> 00:04:46.170 You can also almost consider them negligible 00:04:46.170 --> 00:04:48.450 for atomic mass purposes, 00:04:48.450 --> 00:04:51.780 and so you will get an atomic mass close to 35. 00:04:51.780 --> 00:04:53.870 But it actually turns out it's a little bit different 00:04:53.870 --> 00:04:57.140 because not only are the masses of each individual proton 00:04:57.140 --> 00:05:01.060 or neutron a little bit more actually than one unified 00:05:01.060 --> 00:05:02.400 atomic mass unit, 00:05:02.400 --> 00:05:05.230 but when you put all those protons and neutrons together 00:05:05.230 --> 00:05:08.810 in a nucleus, their combined masses is actually 00:05:08.810 --> 00:05:12.260 a little bit less than their individual masses 00:05:12.260 --> 00:05:13.500 if you were to just add them up, 00:05:13.500 --> 00:05:15.610 and that's actually known as a mass defect. 00:05:15.610 --> 00:05:17.820 And so if you actually want to know the atomic mass 00:05:17.820 --> 00:05:21.610 of chlorine 35, you can look that up in a lot of tables, 00:05:21.610 --> 00:05:24.420 and you will see that it's actually slightly under 00:05:24.420 --> 00:05:27.053 35 unified atomic mass units.

Mass spectrometry

https://www.youtube.com/watch?v=myolF-h1kKI

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https://www.youtube.com/api/timedtext?v=myolF-h1kKI&ei=cViUZeq3DP3DmLAPm4CcuA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6D85A4BF71D631012CA0981ADF39036D2DF78D27.A3846A4BAE490C485E315F4B25D41FEBD75A464D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.370 --> 00:00:01.320 - [Instructor] In other videos, 00:00:01.320 --> 00:00:03.860 we have talked about the idea that, 00:00:03.860 --> 00:00:05.210 even for a given element, 00:00:05.210 --> 00:00:07.540 you might have different versions of that element, 00:00:07.540 --> 00:00:09.890 and we call those different versions isotopes. 00:00:09.890 --> 00:00:12.020 And each isotope of an element 00:00:12.020 --> 00:00:14.450 can have a different atomic mass. 00:00:14.450 --> 00:00:17.570 And that stems from the idea that, if it's a given element, 00:00:17.570 --> 00:00:19.490 it's going to have the same number of protons, 00:00:19.490 --> 00:00:22.360 but you could have a different number of neutrons. 00:00:22.360 --> 00:00:25.330 Now one question that you might have been asking yourself is 00:00:25.330 --> 00:00:28.260 how have chemists been able to figure out 00:00:28.260 --> 00:00:31.030 what the various isotopes of an element are 00:00:31.030 --> 00:00:32.820 and their relative abundance? 00:00:32.820 --> 00:00:34.710 What percentage of an element that we find 00:00:34.710 --> 00:00:37.920 in the universe is of isotope A 00:00:37.920 --> 00:00:40.070 versus, say, isotope B? 00:00:40.070 --> 00:00:42.330 And the answer to your question is 00:00:42.330 --> 00:00:46.300 they use a technique known as mass spectrometry. 00:00:46.300 --> 00:00:50.190 I can never say it right, mass spectrometry. 00:00:50.190 --> 00:00:52.960 Sometimes you'll hear the word mass spectroscopy, 00:00:52.960 --> 00:00:55.980 and they're essentially referring to the same idea. 00:00:55.980 --> 00:00:58.440 And what this technique is, 00:00:58.440 --> 00:01:01.630 is that you put a little bit of a sample right over here, 00:01:01.630 --> 00:01:04.870 let's say we're talking about zirconium in this example, 00:01:04.870 --> 00:01:07.200 and you heat it up. 00:01:07.200 --> 00:01:08.820 So you have it, 00:01:08.820 --> 00:01:11.820 you have a bunch of the zirconium floating around, 00:01:11.820 --> 00:01:13.300 and then you beam it. 00:01:13.300 --> 00:01:15.800 You will bombard it with a bunch of electrons. 00:01:15.800 --> 00:01:18.440 And what the electron bombardment does is, 00:01:18.440 --> 00:01:22.410 it can knock off electrons from the atoms in your sample, 00:01:22.410 --> 00:01:24.240 and it can ionize them. 00:01:24.240 --> 00:01:28.650 And by ionizing some of your atoms, they now have charge. 00:01:28.650 --> 00:01:30.400 And because they have charge, 00:01:30.400 --> 00:01:34.660 they can be accelerated through these electric plates. 00:01:34.660 --> 00:01:38.170 So now you have these ions, in this case, of zirconium, 00:01:38.170 --> 00:01:41.750 moving quite rapidly through this chamber, 00:01:41.750 --> 00:01:44.290 and then they enter into a magnetic field. 00:01:44.290 --> 00:01:47.230 And a magnetic field, a strong magnetic field, 00:01:47.230 --> 00:01:51.860 can bend the path, can deflect ions with charge. 00:01:51.860 --> 00:01:52.960 For a given charge, 00:01:52.960 --> 00:01:55.580 the force of the deflection will be the same. 00:01:55.580 --> 00:01:57.400 But if you have a larger mass, 00:01:57.400 --> 00:01:58.960 you're going to be deflected less. 00:01:58.960 --> 00:02:00.060 And if you have a lower mass, 00:02:00.060 --> 00:02:01.830 you're going to be deflected more. 00:02:01.830 --> 00:02:03.540 And so what you see here 00:02:03.540 --> 00:02:07.430 are the different isotopes being deflected different amounts 00:02:07.430 --> 00:02:09.940 as they go through the magnetic field. 00:02:09.940 --> 00:02:11.700 And then you have the detector. 00:02:11.700 --> 00:02:14.030 And at different points of the detector, 00:02:14.030 --> 00:02:17.240 you will detect each of these isotopes. 00:02:17.240 --> 00:02:20.460 And the more ions that hit a certain part of the detector, 00:02:20.460 --> 00:02:22.360 that means that, hey, I have more 00:02:22.360 --> 00:02:24.710 of that type of isotope in nature. 00:02:24.710 --> 00:02:26.110 And then from that, 00:02:26.110 --> 00:02:29.420 you can generate a chart that looks like this, 00:02:29.420 --> 00:02:32.500 where you see, on the horizontal axis, 00:02:32.500 --> 00:02:35.080 sometimes you'll see it labeled atomic mass. 00:02:35.080 --> 00:02:37.150 And here, it's in unified atomic mass units. 00:02:37.150 --> 00:02:39.320 And you can see, when you put the zirconium 00:02:39.320 --> 00:02:42.420 through the mass spectrometer like this, 00:02:42.420 --> 00:02:46.960 you get a little bit that has a mass number of 96, 00:02:46.960 --> 00:02:49.670 you have a little bit more that gets a mass number of 94, 00:02:49.670 --> 00:02:54.220 92, 91, and most of the zirconium, over 50%, 00:02:54.220 --> 00:02:57.330 has a mass number of 90. 00:02:57.330 --> 00:02:58.570 Now in other cases, 00:02:58.570 --> 00:03:00.940 you won't see it just in terms of atomic mass, 00:03:00.940 --> 00:03:03.150 given in unified atomic mass units. 00:03:03.150 --> 00:03:05.060 Sometimes in this horizontal axis, 00:03:05.060 --> 00:03:09.350 they'll give it in terms of mass-to-charge ratio, 00:03:09.350 --> 00:03:11.390 where mass is the mass, 00:03:11.390 --> 00:03:15.240 but then charge is essentially the charge of the ions. 00:03:15.240 --> 00:03:17.870 Now in a case where your charge is one, 00:03:17.870 --> 00:03:21.070 for example, if you knock one electron off of the atoms 00:03:21.070 --> 00:03:22.730 and you have a plus-one charge, 00:03:22.730 --> 00:03:25.720 well, then the mass-to-charge ratio would be the same thing 00:03:25.720 --> 00:03:29.880 as atomic mass measured in unified atomic mass units. 00:03:29.880 --> 00:03:31.920 If your ions have a different charge, 00:03:31.920 --> 00:03:32.900 well, then you would have 00:03:32.900 --> 00:03:34.800 to make the appropriate adjustment. 00:03:34.800 --> 00:03:36.940 But in introductory chemistry class, 00:03:36.940 --> 00:03:38.970 most of the time you will get things 00:03:38.970 --> 00:03:42.310 in terms of just straight-up atomic mass. 00:03:42.310 --> 00:03:45.500 If you happen to get something in terms of mass to charge, 00:03:45.500 --> 00:03:48.510 just make sure that if the charge is, say, plus two, 00:03:48.510 --> 00:03:51.840 that you make the appropriate adjustment for the masses. 00:03:51.840 --> 00:03:54.670 But this right over here will tell you the various isotopes, 00:03:54.670 --> 00:03:56.520 and it will tell you its abundance. 00:03:56.520 --> 00:04:00.680 And it all comes from this process of ionizing those atoms, 00:04:00.680 --> 00:04:04.020 speeding them up, deflecting them through a magnetic field. 00:04:04.020 --> 00:04:07.060 And the ions that have a higher mass-to-charge ratio 00:04:07.060 --> 00:04:08.940 will be deflected less, 00:04:08.940 --> 00:04:11.810 and the ions that have a lower mass-to-charge ratio 00:04:11.810 --> 00:04:13.350 will be deflected more. 00:04:13.350 --> 00:04:16.853 And you can use that information to make a graph like this.

Making line plots with fractional data

https://www.youtube.com/watch?v=NG51xCPse5Y

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https://www.youtube.com/api/timedtext?v=NG51xCPse5Y&ei=cViUZf7nFcugp-oP-4aFQA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=33EC917E4AD2A77191FF584BDCFFBD548C28FF74.15051CA7B3284CC72FDB3B1E925210A72A34DEFF&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.550 --> 00:00:02.590 - [Instructor] We are told that for four days 00:00:02.590 --> 00:00:06.570 you record the number of hours you sleep each night. 00:00:06.570 --> 00:00:11.480 You round each time to the nearest 1/4 of an hour. 00:00:11.480 --> 00:00:13.632 And then here on this table they tell us 00:00:13.632 --> 00:00:15.460 that our different days, 00:00:15.460 --> 00:00:17.360 they tell us how many hours we slept. 00:00:17.360 --> 00:00:19.030 Day one we slept seven and 1/4 hours, 00:00:19.030 --> 00:00:20.517 day two seven and 3/4, 00:00:20.517 --> 00:00:22.220 day three seven and 3/4, 00:00:22.220 --> 00:00:24.950 day four eight 1/2 hours. 00:00:24.950 --> 00:00:28.080 Then it says, create a line plot 00:00:28.080 --> 00:00:30.140 that shows all of the measurements 00:00:30.140 --> 00:00:31.870 on the number line below. 00:00:31.870 --> 00:00:34.830 And it says click above the tick marks to add dots, 00:00:34.830 --> 00:00:36.630 click on tick marks to remove dots. 00:00:38.330 --> 00:00:40.548 So we can see if I click right over here, 00:00:40.548 --> 00:00:42.380 a tick mark shows up. 00:00:42.380 --> 00:00:45.720 And if I click again, it gets removed. 00:00:45.720 --> 00:00:50.570 So let's see, day one you slept seven and 1/4 hours. 00:00:50.570 --> 00:00:53.510 So, that's one day where you sleep seven and 1/4. 00:00:53.510 --> 00:00:57.390 So, seven and 1/4 is right between seven and seven and 1/2. 00:00:57.390 --> 00:01:00.880 So that's right over there. 00:01:00.880 --> 00:01:02.480 There we go. 00:01:02.480 --> 00:01:05.610 On day two you sleep seven and 3/4 hours. 00:01:05.610 --> 00:01:09.490 So, that's 1/4, 2/4, 3/4. 00:01:09.490 --> 00:01:11.432 So that's day two. 00:01:11.432 --> 00:01:14.980 Day three you also sleep seven and 3/4 hours, 00:01:14.980 --> 00:01:18.140 so that's another day that you sleep seven and 3/4 hours. 00:01:18.140 --> 00:01:20.450 And then on day four you sleep eight and 1/2 hours, 00:01:20.450 --> 00:01:21.860 which is right over there. 00:01:21.860 --> 00:01:23.640 And so, here we go. 00:01:23.640 --> 00:01:24.940 We have created a line plot 00:01:24.940 --> 00:01:26.600 that shows all of the measurements. 00:01:26.600 --> 00:01:28.800 On one day, day one it was, 00:01:28.800 --> 00:01:31.760 I slept seven and 1/4 hours. 00:01:31.760 --> 00:01:34.257 There were two days where I slept seven and 3/4 hours, 00:01:34.257 --> 00:01:37.357 and there was one day where I slept eight and 1/2 hours. 00:01:37.357 --> 00:01:38.963 Let's do another example. 00:01:42.990 --> 00:01:45.960 Amy ran many miles during September. 00:01:45.960 --> 00:01:49.030 She recorded how long it took her to run each mile, 00:01:49.030 --> 00:01:54.020 rounded to the nearest 1/4 of a minute on the table below. 00:01:54.020 --> 00:01:55.380 We can see it right over here, 00:01:55.380 --> 00:01:57.610 actually let me move my window a little bit 00:01:57.610 --> 00:01:58.830 so you can see everything. 00:01:58.830 --> 00:02:00.600 And then it says, create a line plot 00:02:00.600 --> 00:02:04.120 that shows all of the measurements on the number line below. 00:02:04.120 --> 00:02:07.130 All right, so three times she was able to run a mile 00:02:07.130 --> 00:02:09.810 in eight and 3/4 minutes. 00:02:09.810 --> 00:02:12.910 So, there are three that were eight and 3/4. 00:02:12.910 --> 00:02:16.030 Notice, this is, if we look at the space between 00:02:16.030 --> 00:02:18.860 eight and nine, there is one, two, three, 00:02:18.860 --> 00:02:20.400 four equal intervals. 00:02:20.400 --> 00:02:22.840 And so, 3/4 is going to be three of those. 00:02:22.840 --> 00:02:24.506 One, two, three. 00:02:24.506 --> 00:02:27.970 She ran a mile in eight and 3/4 minutes three times. 00:02:27.970 --> 00:02:29.820 That's what we saw from that table. 00:02:29.820 --> 00:02:32.250 So, that's three times she did that. 00:02:32.250 --> 00:02:36.240 She ran a mile in nine and 1/4 minutes two times. 00:02:36.240 --> 00:02:39.130 So nine and 1/4. 00:02:39.130 --> 00:02:40.920 That is 1/4 of the way to 10, 00:02:40.920 --> 00:02:44.490 we can see 1/4, 2/4, 3/4, 4/4. 00:02:44.490 --> 00:02:48.350 So nine and 1/4 she did two times. 00:02:48.350 --> 00:02:50.930 So that's going to be one, two. 00:02:50.930 --> 00:02:53.100 And then let's see, nine and 1/2 00:02:54.080 --> 00:02:55.560 she did four times. 00:02:55.560 --> 00:02:58.640 Nine and 1/2 is here, so one, two, three, four. 00:02:58.640 --> 00:03:02.360 And then eight and 1/2 she did one time. 00:03:02.360 --> 00:03:04.120 So that's eight and 1/2 right over there. 00:03:04.120 --> 00:03:07.430 And then she ran a mile in nine minutes five times. 00:03:07.430 --> 00:03:08.790 Nine minutes right over here. 00:03:08.790 --> 00:03:12.460 One, two, three, four, five. 00:03:12.460 --> 00:03:13.293 And we're done.

Interpreting line plots

https://www.youtube.com/watch?v=78zFg2F3HsI

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https://www.youtube.com/api/timedtext?v=78zFg2F3HsI&ei=cViUZYGJFeiMp-oP3bqW4Ao&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=35DFFFBD6F5AEF5A1D8460923F8783857350E13D.E012971133ACCCC91B68DFB0419EDFBE0E29BBDF&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.420 --> 00:00:01.570 - [Instructor] We're told that the weights 00:00:01.570 --> 00:00:05.810 of 11 different babies are recorded on the line plot below 00:00:05.810 --> 00:00:07.700 and we see there is one, two, three, four, 00:00:07.700 --> 00:00:09.650 five, six, seven, eight, nine, 00:00:09.650 --> 00:00:11.010 10, 11 data points. 00:00:11.010 --> 00:00:13.390 Each one represents a different baby 00:00:13.390 --> 00:00:16.100 whose weight is recorded. 00:00:16.100 --> 00:00:19.510 Each weight was rounded to the nearest 1/8 of a pound. 00:00:19.510 --> 00:00:21.080 All right, then they ask us, 00:00:21.080 --> 00:00:23.090 what is the difference, in weight, 00:00:23.090 --> 00:00:26.610 between the two heaviest babies? 00:00:26.610 --> 00:00:27.940 So pause this video 00:00:27.940 --> 00:00:28.920 and try to figure that out 00:00:28.920 --> 00:00:31.160 before we work through it together. 00:00:31.160 --> 00:00:34.520 All right, now where are the two heaviest babies? 00:00:34.520 --> 00:00:35.990 So this one out here, 00:00:35.990 --> 00:00:38.010 this is the heaviest baby, 00:00:38.010 --> 00:00:39.700 and what is its weight? 00:00:39.700 --> 00:00:40.533 Well, let's see. 00:00:40.533 --> 00:00:42.590 Its weight is right over there, 00:00:42.590 --> 00:00:46.060 and what is that number or what is that weight? 00:00:46.060 --> 00:00:48.970 So this is nine and this is 10, 00:00:48.970 --> 00:00:52.590 and we have one, two, three, four, 00:00:52.590 --> 00:00:56.220 five, six, seven, eight equal spaces. 00:00:56.220 --> 00:00:57.950 So each of these is an eighth. 00:00:57.950 --> 00:01:01.610 So this is nine and one, two, 00:01:01.610 --> 00:01:03.400 nine and 2/8. 00:01:03.400 --> 00:01:05.900 So this one is, let me write this. 00:01:05.900 --> 00:01:07.830 This is nine and 2/8. 00:01:07.830 --> 00:01:09.570 Another way to think about it is, 00:01:09.570 --> 00:01:11.260 2/8 is the same thing as 1/4, 00:01:11.260 --> 00:01:12.093 'cause if you think about it, 00:01:12.093 --> 00:01:15.920 it's one, two, three, four equal spaces. 00:01:15.920 --> 00:01:19.600 This is also nine and 1/4 of the way to 10, 00:01:19.600 --> 00:01:21.833 so this is the same thing as nine and 1/4. 00:01:22.760 --> 00:01:25.670 And then what's the second heaviest babies? 00:01:25.670 --> 00:01:26.690 'Cause we want the weight difference 00:01:26.690 --> 00:01:28.380 between the two heaviest. 00:01:28.380 --> 00:01:31.040 So the second heaviest baby is right over here 00:01:31.040 --> 00:01:36.040 and we know that it is eight and a half pounds. 00:01:36.040 --> 00:01:38.490 So what we really need to do is figure out 00:01:38.490 --> 00:01:42.000 what is the difference between nine and 2/8 00:01:42.000 --> 00:01:43.660 or nine and 1/4 00:01:43.660 --> 00:01:46.870 and eight and a half right over here? 00:01:46.870 --> 00:01:50.010 So we could set this up as a subtraction. 00:01:50.010 --> 00:01:51.800 This is going to be nine and, 00:01:51.800 --> 00:01:53.900 let's call it nine and 1/4, 00:01:53.900 --> 00:01:57.910 minus, minus eight and a half, 00:01:57.910 --> 00:02:00.140 and we can actually use this, 00:02:00.140 --> 00:02:02.610 this, these measurement scales 00:02:02.610 --> 00:02:03.820 or you can even view this as something 00:02:03.820 --> 00:02:04.800 of a number line 00:02:04.800 --> 00:02:06.320 to help us think about this. 00:02:06.320 --> 00:02:10.580 The difference is this length right over here. 00:02:10.580 --> 00:02:12.880 And we could think about it in terms of eighths, 00:02:12.880 --> 00:02:14.970 'cause each of these hash marks is an eighth, 00:02:14.970 --> 00:02:19.970 so 1/8, 2/8, 3/8, 4/8, 5/8 and 6/8. 00:02:21.800 --> 00:02:24.160 So this is equal to 6/8. 00:02:24.160 --> 00:02:27.150 We could also think about it in terms of fourths, 00:02:27.150 --> 00:02:32.150 so this is 1/4, 2/4, and 3/4. 00:02:33.250 --> 00:02:36.460 So this is equal to 3/4. 00:02:36.460 --> 00:02:38.040 So what's the difference in weight 00:02:38.040 --> 00:02:40.040 between the two heaviest babies? 00:02:40.040 --> 00:02:43.343 It is 3/4 of a pound.

Line plots with fractions

https://www.youtube.com/watch?v=Ocs3NUNhhPk

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https://www.youtube.com/api/timedtext?v=Ocs3NUNhhPk&ei=cViUZY7cFauMvdIPmtazwAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1E2EACBE615FB4E3B609F050EA809687FE885142.323FA0D0C021568A98F0BD37B9205F3FD71259E2&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.690 --> 00:00:02.030 - [Instructor] What we're going to do in this video 00:00:02.030 --> 00:00:04.900 is review what we know about line plots, 00:00:04.900 --> 00:00:06.920 but apply them in a situation 00:00:06.920 --> 00:00:09.370 where some of our data involves fractions. 00:00:09.370 --> 00:00:11.900 So they tell us the lengths of some caterpillars 00:00:11.900 --> 00:00:14.380 are shown below, and so we can see 00:00:14.380 --> 00:00:15.960 that here in the line plot, 00:00:15.960 --> 00:00:18.670 just to refresh our minds how to read a line plot, 00:00:18.670 --> 00:00:21.860 this tells us that we have two caterpillars 00:00:21.860 --> 00:00:24.240 that are four centimeters long. 00:00:24.240 --> 00:00:26.390 These three show that we have three caterpillars 00:00:26.390 --> 00:00:28.870 that are seven centimeters long. 00:00:28.870 --> 00:00:31.490 Each dot represents a caterpillar 00:00:31.490 --> 00:00:33.730 whose length we are measuring. 00:00:33.730 --> 00:00:37.650 It allows us to see how those lengths are distributed. 00:00:37.650 --> 00:00:40.390 For example, we have a lot of caterpillars at this length. 00:00:40.390 --> 00:00:41.820 What is that length? 00:00:41.820 --> 00:00:44.120 Well we can see that is exactly 00:00:44.120 --> 00:00:46.260 half way between four and five, 00:00:46.260 --> 00:00:50.350 so that is four and one half centimeters long. 00:00:50.350 --> 00:00:52.230 We divide the section between four and five 00:00:52.230 --> 00:00:54.140 into two equal sections, and we're going 00:00:54.140 --> 00:00:56.940 one of those two equal sections towards five, 00:00:56.940 --> 00:00:59.550 so this is four and a half centimeters. 00:00:59.550 --> 00:01:01.880 I can ask you some questions. 00:01:01.880 --> 00:01:04.330 How many total caterpillars were measured? 00:01:04.330 --> 00:01:06.860 Pause this video and think about that. 00:01:06.860 --> 00:01:09.140 Well each dot represents a caterpillar measurement, 00:01:09.140 --> 00:01:12.260 and we have one, two, three, four, five, six, seven, 00:01:12.260 --> 00:01:17.120 eight, nine, 10, 11, 12, 13, 14, 15, 16, 17. 00:01:17.120 --> 00:01:19.450 So we have a total of 17 caterpillars. 00:01:19.450 --> 00:01:21.210 Now another question we could ask ourselves 00:01:21.210 --> 00:01:24.680 is how many of the caterpillars 00:01:24.680 --> 00:01:28.930 are five and one fourth centimeters long? 00:01:28.930 --> 00:01:30.780 Pause the video and think about that. 00:01:31.740 --> 00:01:34.800 Well five and one fourth is going to be more than five, 00:01:34.800 --> 00:01:37.560 and what we'd want to do to get to five and one fourth 00:01:37.560 --> 00:01:41.690 is divide the interval or the length between five and six 00:01:41.690 --> 00:01:43.470 into four equal sections, they already did that, 00:01:43.470 --> 00:01:46.550 one, two, three, four, and then we want to go 00:01:46.550 --> 00:01:48.700 one of those four equal sections. 00:01:48.700 --> 00:01:51.130 So five and one fourth is right over here 00:01:51.130 --> 00:01:53.410 and we can see that there's one caterpillar 00:01:53.410 --> 00:01:56.450 that is five and one fourth centimeters long. 00:01:56.450 --> 00:01:58.660 We can ask ourselves other questions. 00:01:58.660 --> 00:02:01.830 How many caterpillars, let me write it over here, 00:02:01.830 --> 00:02:06.080 how many have length 00:02:09.340 --> 00:02:14.340 more than six and one half centimeters? 00:02:15.390 --> 00:02:17.790 Pause the video and try to answer that. 00:02:17.790 --> 00:02:19.760 Where is six and a half centimeters? 00:02:19.760 --> 00:02:23.950 Well, we can divide the section between six and seven 00:02:23.950 --> 00:02:26.360 into two equal sections, and if you go 00:02:26.360 --> 00:02:28.680 one of those two equal sections, that is six and a half, 00:02:28.680 --> 00:02:30.580 so that is six and a half right over there. 00:02:30.580 --> 00:02:32.910 How many have a length more than or greater than 00:02:32.910 --> 00:02:34.330 six and a half centimeters? 00:02:34.330 --> 00:02:36.660 Well we can see it right over here. 00:02:36.660 --> 00:02:39.830 One, two, three, four, five, six. 00:02:39.830 --> 00:02:41.660 Six of them do. 00:02:41.660 --> 00:02:45.510 And we can even try to answer questions like 00:02:45.510 --> 00:02:50.510 how many more have a length 00:02:55.180 --> 00:02:58.910 of nine and a half centimeters 00:03:00.424 --> 00:03:04.400 than five and one fourth centimeters? 00:03:04.400 --> 00:03:05.800 Try to answer that question. 00:03:07.130 --> 00:03:08.850 Well nine and a half centimeters, 00:03:08.850 --> 00:03:11.660 that's half way between nine and 10, right over there. 00:03:11.660 --> 00:03:14.201 We can see two of them have a length of 00:03:14.201 --> 00:03:15.706 nine and a half centimeters. 00:03:15.706 --> 00:03:17.292 And we already know that one of them 00:03:17.292 --> 00:03:18.807 has a length of five and one fourth, 00:03:18.807 --> 00:03:20.930 so how many more have nine and a half centimeters 00:03:20.930 --> 00:03:22.580 versus five and one fourth? 00:03:22.580 --> 00:03:25.400 Well that would be two minus one, or one more. 00:03:25.400 --> 00:03:27.160 We have one more caterpillar with a length 00:03:27.160 --> 00:03:28.750 of nine and a half centimeters 00:03:28.750 --> 00:03:31.540 than we do with five and one fourth. 00:03:31.540 --> 00:03:32.460 I'll leave you there. 00:03:32.460 --> 00:03:34.330 We have plenty of examples on Khan Academy 00:03:34.330 --> 00:03:35.753 for you to practice this.

Measure lengths to nearest 1/4

https://www.youtube.com/watch?v=k29Hyub0wqM

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https://www.youtube.com/api/timedtext?v=k29Hyub0wqM&ei=cViUZYu-EIvXxwK0uqHQCA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0337CA2806E98EEBEA11FF1C86E49D6083885F11.4BB41C917FEF4915F63CD55082FE0EA4D5AF1E5F&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:02.410 - [Instructor] We are asked what is the height 00:00:02.410 --> 00:00:03.950 of the sunflower? 00:00:03.950 --> 00:00:06.420 So pause this video and think about it. 00:00:06.420 --> 00:00:07.690 All right, so let's see. 00:00:07.690 --> 00:00:11.000 The bottom of the sunflower is right aligned 00:00:11.000 --> 00:00:12.310 with the bottom of the ruler, 00:00:12.310 --> 00:00:14.140 so there ruler's in the right place. 00:00:14.140 --> 00:00:15.670 And let's see, the sunflower goes 00:00:15.670 --> 00:00:18.610 all the way up to this point right over here. 00:00:18.610 --> 00:00:23.610 So this is one, two, three, four, five, 00:00:24.210 --> 00:00:26.320 and then a little bit more. 00:00:26.320 --> 00:00:27.530 So we're going to get into a fraction. 00:00:27.530 --> 00:00:29.522 So what is this extra amount? 00:00:29.522 --> 00:00:33.098 So if we can see the space between five 00:00:33.098 --> 00:00:38.050 and six is divided into four equal sections. 00:00:38.050 --> 00:00:41.860 So we have, one, two, three, four. 00:00:41.860 --> 00:00:42.810 Or we could see it here. 00:00:42.810 --> 00:00:45.850 They've divided it with these little hash marks 00:00:45.850 --> 00:00:49.600 into one, two, three, four equal sections. 00:00:49.600 --> 00:00:52.850 And this goes one of those four equal sections 00:00:52.850 --> 00:00:57.850 towards six, so this is 5 1/4 feet. 00:00:58.450 --> 00:01:01.630 That's how tall the sunflower is. 00:01:01.630 --> 00:01:04.603 All right, let's do another example. 00:01:07.410 --> 00:01:10.680 So here we are told, or we are asked, 00:01:10.680 --> 00:01:14.200 which pencil measures 2 3/4 of an inch? 00:01:14.200 --> 00:01:17.320 So pause this video and try to think about it. 00:01:17.320 --> 00:01:21.510 All right, so we go one inch, two inches, 00:01:21.510 --> 00:01:23.050 and then we have to think about how far 00:01:23.050 --> 00:01:25.930 between two and three is 3/4? 00:01:25.930 --> 00:01:27.300 So to think about 3/4, we have 00:01:27.300 --> 00:01:29.900 to divide the part, or the part of this ruler, 00:01:29.900 --> 00:01:33.170 between two and three into four equal sections. 00:01:33.170 --> 00:01:34.360 So let's see. 00:01:34.360 --> 00:01:37.380 If I were to just split it like this, 00:01:37.380 --> 00:01:39.330 that's two equal sections. 00:01:39.330 --> 00:01:40.260 So if I were to take each 00:01:40.260 --> 00:01:41.750 of those two equals sections 00:01:41.750 --> 00:01:45.740 and then split them, now that's four equal sections. 00:01:45.740 --> 00:01:50.740 Notice one, two, three, four equal sections. 00:01:52.000 --> 00:01:54.800 So when we're thinking about 3/4, 00:01:54.800 --> 00:01:57.170 we wanna go three of those four equal sections. 00:01:57.170 --> 00:02:00.150 One, two, three. 00:02:00.150 --> 00:02:03.070 And so you can see right over here, 00:02:03.070 --> 00:02:06.880 that is 2 3/4. 00:02:06.880 --> 00:02:09.700 This is 2 3/4 right over here. 00:02:09.700 --> 00:02:11.773 And that is pencil A.

Multiplication and division relationship for fractions

https://www.youtube.com/watch?v=jXA-nMI4Nt4

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WEBVTT Kind: captions Language: en 00:00:00.180 --> 00:00:02.040 - [Instructor] You are likely already familiar 00:00:02.040 --> 00:00:05.360 with the relationship between multiplication and division. 00:00:05.360 --> 00:00:09.230 For example, we know that three times six 00:00:09.230 --> 00:00:11.600 is equal to 18. 00:00:11.600 --> 00:00:16.080 But another way to express that same relationship 00:00:16.080 --> 00:00:19.700 is to say, all right, if three times six is 18, 00:00:19.700 --> 00:00:23.640 then if I were to start with 18 and divide it by three, 00:00:23.640 --> 00:00:25.540 that would be equal to six. 00:00:25.540 --> 00:00:27.840 Or you could say something like this, 00:00:27.840 --> 00:00:30.980 that 18 divided by, 00:00:30.980 --> 00:00:34.090 divided by six 00:00:34.090 --> 00:00:37.730 is equal to three. 00:00:37.730 --> 00:00:41.050 Now we're just going to extend this same relationship 00:00:41.050 --> 00:00:43.840 between multiplication and division 00:00:43.840 --> 00:00:47.820 to expressions that deal with fractions. 00:00:47.820 --> 00:00:50.150 So for example, 00:00:50.150 --> 00:00:55.150 if I were to tell you that 1/4 divided by, 00:00:55.610 --> 00:01:00.040 and I'm going to color-code it, divided by two 00:01:00.040 --> 00:01:02.440 is equal to 1/8, 00:01:02.440 --> 00:01:04.530 is equal to 1/8, 00:01:04.530 --> 00:01:06.830 how could we express this relationship, 00:01:06.830 --> 00:01:08.823 but using multiplication? 00:01:09.960 --> 00:01:13.520 Well, if 1/4 divided by two is equal to 1/8, 00:01:13.520 --> 00:01:18.410 that means that 1/8 times two is equal to 1/4. 00:01:18.410 --> 00:01:21.030 Let me write this down, or I could write it like this. 00:01:21.030 --> 00:01:26.030 I could write that 1/4 is going to be equal to, 00:01:26.580 --> 00:01:31.160 is going to be equal to 1/8 times two, 00:01:31.160 --> 00:01:33.580 times two. 00:01:33.580 --> 00:01:35.970 And we could do another example. 00:01:35.970 --> 00:01:38.840 Let's say that I were to walk up to you on the street 00:01:38.840 --> 00:01:43.650 and I were to tell you that, hey, you, 42 00:01:43.650 --> 00:01:45.270 is equal to 00:01:46.200 --> 00:01:48.040 seven, 00:01:48.040 --> 00:01:52.030 seven divided by 1/6. 00:01:52.030 --> 00:01:55.230 In the future, we will learn to compute things like this. 00:01:55.230 --> 00:01:57.330 But just based on what you see here, 00:01:57.330 --> 00:02:00.070 how could we express this same relationship 00:02:00.070 --> 00:02:03.190 between 42, seven, and 1/6, 00:02:03.190 --> 00:02:04.870 but express it with multiplication? 00:02:04.870 --> 00:02:06.753 Pause this video, and think about that. 00:02:08.070 --> 00:02:12.760 Well, if 42 is equal to seven divided by 1/6, 00:02:12.760 --> 00:02:16.340 that means that 42 times 1/6 00:02:16.340 --> 00:02:18.320 is equal to seven. 00:02:18.320 --> 00:02:19.410 Let me write that down. 00:02:19.410 --> 00:02:24.410 This is the same relationship as saying that 42 times 00:02:24.621 --> 00:02:26.120 1/6, 00:02:26.120 --> 00:02:29.180 1/6 is equal 00:02:29.180 --> 00:02:30.913 to seven. 00:02:32.020 --> 00:02:34.210 Now let's say I walk up to you on the street 00:02:34.210 --> 00:02:36.560 and I were to say, all right, you, 00:02:36.560 --> 00:02:40.890 I'm telling you that 1/4 divided by, 00:02:40.890 --> 00:02:42.980 divided by six 00:02:42.980 --> 00:02:45.310 is equal to some number 00:02:45.310 --> 00:02:48.860 that we will express as t. 00:02:48.860 --> 00:02:53.620 So can we rewrite this relationship between 1/4, six, and t, 00:02:53.620 --> 00:02:56.560 but instead of using division, use multiplication? 00:02:56.560 --> 00:02:59.150 Pause this video, and try to think about it. 00:02:59.150 --> 00:03:03.000 So if 1/4 divided by six is equal to t, 00:03:03.000 --> 00:03:05.200 based on all of the examples we've just seen, 00:03:05.200 --> 00:03:08.210 that means that if we were to take t times six, 00:03:08.210 --> 00:03:10.210 we would get 1/4. 00:03:10.210 --> 00:03:14.260 So we could write it this way, t times six, 00:03:14.260 --> 00:03:19.260 times six is going to be equal to 1/4. 00:03:19.280 --> 00:03:20.630 If this isn't making sense, 00:03:20.630 --> 00:03:23.240 I really want you to think about how this relationship 00:03:23.240 --> 00:03:26.260 is really just the same relationship we saw up here. 00:03:26.260 --> 00:03:27.820 The only new thing here is 00:03:27.820 --> 00:03:29.840 instead of always having whole numbers, 00:03:29.840 --> 00:03:31.070 we're having fractions 00:03:31.070 --> 00:03:34.753 and representing some of the numbers with letters.

Fraction division in context

https://www.youtube.com/watch?v=dnZ0fykw_w0

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en

WEBVTT Kind: captions Language: en 00:00:00.380 --> 00:00:01.750 - [Instructor] We're told that a group 00:00:01.750 --> 00:00:05.480 of three friends is practicing for the track meet. 00:00:05.480 --> 00:00:10.090 The group is going to run 1/2 of a mile total. 00:00:10.090 --> 00:00:13.310 If they each run the same distance, 00:00:13.310 --> 00:00:16.360 how far will each person run? 00:00:16.360 --> 00:00:19.450 Which expression could represent this situation? 00:00:19.450 --> 00:00:22.663 So pause this video and try to figure this out on your own. 00:00:23.730 --> 00:00:25.690 All right, the way I think about it is 00:00:25.690 --> 00:00:29.380 there's some distance that they're going to try to travel. 00:00:29.380 --> 00:00:31.480 So in this case, it's half of a mile 00:00:31.480 --> 00:00:33.490 and they're going to divide that distance 00:00:33.490 --> 00:00:35.680 amongst the three friends. 00:00:35.680 --> 00:00:37.920 And so the distance that each of them are going to run 00:00:37.920 --> 00:00:39.720 is the total distance divided 00:00:39.720 --> 00:00:42.070 by the number of folks that are running. 00:00:42.070 --> 00:00:44.990 So an expression that represents this is 1/2, 00:00:44.990 --> 00:00:47.100 the total distance they're running, 00:00:47.100 --> 00:00:49.880 divided by the number of people 00:00:49.880 --> 00:00:53.460 who are going to split that distance, divided by three. 00:00:53.460 --> 00:00:57.150 And so that is choice C right over here. 00:00:57.150 --> 00:00:58.760 Now it might have confused you a little 00:00:58.760 --> 00:01:02.420 because you're not used to dividing a smaller number, 00:01:02.420 --> 00:01:05.380 especially a fraction, by a lager number 00:01:05.380 --> 00:01:07.250 but that's exactly what's going on over here. 00:01:07.250 --> 00:01:08.800 You're taking the total distance 00:01:08.800 --> 00:01:11.550 and it's being split amongst three friends. 00:01:11.550 --> 00:01:14.740 So the total distance divided by three friends 00:01:14.740 --> 00:01:18.580 will tell you how far each of them has to run. 00:01:18.580 --> 00:01:20.563 Let's do another example. 00:01:21.980 --> 00:01:25.270 So here, we are, actually they're telling us 00:01:25.270 --> 00:01:27.100 that there's some problem that can be solved 00:01:27.100 --> 00:01:28.690 with 1/2 divided by seven. 00:01:28.690 --> 00:01:30.240 They say which problem can we solve 00:01:30.240 --> 00:01:31.890 with 1/2 divided by seven? 00:01:31.890 --> 00:01:34.400 And then they give us three different scenarios 00:01:34.400 --> 00:01:36.050 that we could try to solve. 00:01:36.050 --> 00:01:37.460 So pause this video and think 00:01:37.460 --> 00:01:38.890 of which of these three scenarios 00:01:38.890 --> 00:01:41.463 can be solved with this expression. 00:01:42.560 --> 00:01:45.200 All right, let's go through each of the choices. 00:01:45.200 --> 00:01:49.680 Cara ordered seven pizzas for her birthday party. 00:01:49.680 --> 00:01:53.840 Her parents ate 1/2 of a pizza before the party. 00:01:53.840 --> 00:01:58.020 How much pizza is left for the party? 00:01:58.020 --> 00:01:59.400 All right, so what's going on here? 00:01:59.400 --> 00:02:03.280 She started with seven pizzas, she starts with seven. 00:02:03.280 --> 00:02:06.340 Her parents ate 1/2 of a pizza. 00:02:06.340 --> 00:02:09.550 So 1/2 of a pizza is taken away. 00:02:09.550 --> 00:02:12.090 And so that would tell you how much is left. 00:02:12.090 --> 00:02:14.580 So this is definitely, this is the expression 00:02:14.580 --> 00:02:16.910 you would solve to figure out A, 00:02:16.910 --> 00:02:18.380 not this expression up here. 00:02:18.380 --> 00:02:20.320 So I would rule this out. 00:02:20.320 --> 00:02:22.140 Walt has seven hamsters. 00:02:22.140 --> 00:02:25.250 Each hamster weighs 1/2 of a kilogram. 00:02:25.250 --> 00:02:28.110 What is the total weight of the hamsters? 00:02:28.110 --> 00:02:29.330 Well to figure out the total weight, 00:02:29.330 --> 00:02:31.570 you would start with the number of hamsters 00:02:31.570 --> 00:02:32.850 and you would multiply that 00:02:32.850 --> 00:02:35.200 times the weight of each hamster. 00:02:35.200 --> 00:02:37.080 So that would be seven times 1/2, 00:02:37.080 --> 00:02:38.750 so we could rule that one out. 00:02:38.750 --> 00:02:40.250 So it's likely going to be C 00:02:40.250 --> 00:02:42.671 but let's figure this, let's make sure it makes sense. 00:02:42.671 --> 00:02:47.671 Jenae has 1/2 kilogram of trail mix. 00:02:48.010 --> 00:02:52.060 She splits her trail mix evenly between seven friends. 00:02:52.060 --> 00:02:55.660 How much trail mix will each friend get? 00:02:55.660 --> 00:02:59.440 All right, she has a total amount, 1/2 of a kilogram 00:02:59.440 --> 00:03:01.740 and she's going to divide that total amount, 00:03:01.740 --> 00:03:05.550 she splits her trail mix evenly between seven friends 00:03:05.550 --> 00:03:08.600 so she's going to take this 1/2 and split it evenly 00:03:08.600 --> 00:03:13.330 amongst seven friends to get a certain amount per friend. 00:03:13.330 --> 00:03:15.260 How much trail mix will each friend get? 00:03:15.260 --> 00:03:17.810 And that's exactly what that expression up there is 00:03:17.810 --> 00:03:20.453 so I am liking this choice.

Dividing fractions and whole number word problems

https://www.youtube.com/watch?v=HUT8eL1sGhk

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WEBVTT Kind: captions Language: en 00:00:00.530 --> 00:00:01.390 - [Instructor] We are told 00:00:01.390 --> 00:00:04.820 that Billy has 1/4 of a pound of trail mix. 00:00:04.820 --> 00:00:06.920 He wants to share it equally 00:00:06.920 --> 00:00:09.580 between himself and his brother. 00:00:09.580 --> 00:00:12.810 How much trail mix would they each get? 00:00:12.810 --> 00:00:15.950 So pause this video and try to figure that out. 00:00:15.950 --> 00:00:18.380 All right, now let's work through this together. 00:00:18.380 --> 00:00:22.620 So Billy starts with 1/4 of a pound of trail mix. 00:00:22.620 --> 00:00:24.970 So how can we represent 1/4? 00:00:24.970 --> 00:00:28.550 Well, if this is a whole pound, 00:00:28.550 --> 00:00:31.100 let's just imagine this rectangle is a whole pound, 00:00:31.100 --> 00:00:33.350 I could divide it into four equal sections. 00:00:33.350 --> 00:00:37.520 So let's see, this would be roughly two equal sections, 00:00:37.520 --> 00:00:40.460 and then if I were to divide each of those into two, 00:00:40.460 --> 00:00:42.903 now I have four equal sections. 00:00:44.440 --> 00:00:47.950 So Billy is starting with 1/4 of a pound. 00:00:47.950 --> 00:00:51.350 Draw a little bit, try to make it a little bit more equal. 00:00:51.350 --> 00:00:53.570 Billy is starting with 1/4 of a pound, 00:00:53.570 --> 00:00:55.570 so let's say that is that 1/4 of a pound 00:00:55.570 --> 00:00:56.690 that he starts with. 00:00:56.690 --> 00:00:58.750 He's starting with 1/4 of a pound, 00:00:58.750 --> 00:01:00.370 and he wants to share it equally 00:01:00.370 --> 00:01:02.110 between himself and his brother. 00:01:02.110 --> 00:01:03.700 So he wants to share it equally 00:01:03.700 --> 00:01:06.300 between two people right over here. 00:01:06.300 --> 00:01:08.810 So what we wanna do is essentially say, 00:01:08.810 --> 00:01:11.200 let's start with our total amount of trail mix, 00:01:11.200 --> 00:01:15.910 and then we're going to divide it into two equal shares. 00:01:15.910 --> 00:01:19.100 So when they ask us how much trail mix would they each get, 00:01:19.100 --> 00:01:20.040 we're really trying to figure out 00:01:20.040 --> 00:01:24.170 what is this 1/4 divided by two? 00:01:24.170 --> 00:01:25.498 So what would that be? 00:01:25.498 --> 00:01:27.690 Well, what if we were to take 00:01:27.690 --> 00:01:31.700 all of these four equal sections and divide them into two? 00:01:31.700 --> 00:01:34.350 So I'll divide that one into two. 00:01:34.350 --> 00:01:36.690 I will divide this one into two. 00:01:36.690 --> 00:01:38.830 I will divide this one into two, 00:01:38.830 --> 00:01:41.670 and then I would divide this one into two. 00:01:41.670 --> 00:01:43.600 And now what are each of these sections? 00:01:43.600 --> 00:01:45.620 Well, each of these are now 1/8. 00:01:45.620 --> 00:01:47.350 That's a 1/8 right over there, 00:01:47.350 --> 00:01:49.690 the whole is divided into eight equal sections. 00:01:49.690 --> 00:01:53.500 And so you can see, that when you start with that 1/4, 00:01:53.500 --> 00:01:57.060 and you divide it into two equal sections, 00:01:57.060 --> 00:02:01.940 so one section and two equal sections right over there, 00:02:01.940 --> 00:02:06.130 each of these is equal to 1/8. 00:02:06.130 --> 00:02:11.130 So 1/4 divided by two is equal to 1/8. 00:02:12.230 --> 00:02:13.643 Let's do another example. 00:02:14.578 --> 00:02:18.360 So we are told Matt is filling containers of rice. 00:02:18.360 --> 00:02:23.360 Each container holds 1/4 of a kilogram of rice. 00:02:23.660 --> 00:02:28.240 And then they tell us if Matt has three kilograms of rice, 00:02:28.240 --> 00:02:31.100 how many containers can he fill? 00:02:31.100 --> 00:02:32.800 So like always, pause this video, 00:02:32.800 --> 00:02:35.160 and see if you can figure that out. 00:02:35.160 --> 00:02:37.110 All right, so let's think about what's going on. 00:02:37.110 --> 00:02:40.630 We're starting with a total amount, three kilograms of rice, 00:02:40.630 --> 00:02:43.430 and we're trying to divide it into equal sections. 00:02:43.430 --> 00:02:46.120 In this case we're trying to divide it into equal sections 00:02:46.120 --> 00:02:48.400 of 1/4 of a kilogram. 00:02:48.400 --> 00:02:49.710 So we are trying to figure out 00:02:49.710 --> 00:02:54.710 what three divided by 1/4 is going to be equal to. 00:02:55.080 --> 00:02:57.510 Now to imagine that, let's imagine three wholes, 00:02:57.510 --> 00:02:59.550 this would be three whole kilograms. 00:02:59.550 --> 00:03:04.360 So that is one whole, this is two wholes, 00:03:04.360 --> 00:03:06.450 trying to make them all the same, but it's hand-drawn, 00:03:06.450 --> 00:03:09.610 so it's not as exact as I would like. 00:03:09.610 --> 00:03:12.400 So that's three whole kilograms here. 00:03:12.400 --> 00:03:15.300 And he wants to divide it into sections of 1/4. 00:03:15.300 --> 00:03:17.240 So if you divide it into fourths, 00:03:17.240 --> 00:03:19.200 how many fourths are you going to have? 00:03:19.200 --> 00:03:20.540 Well, let's do that. 00:03:20.540 --> 00:03:22.700 So let's see, if we were to divide it into halves, 00:03:22.700 --> 00:03:24.457 it would look like this. 00:03:25.960 --> 00:03:29.310 If you divide these three wholes into halves. 00:03:29.310 --> 00:03:31.840 But then if you want to divide it into fourths, 00:03:31.840 --> 00:03:34.450 it would look like this, 00:03:36.270 --> 00:03:38.863 I'm trying to get it as close to equal sections. 00:03:39.770 --> 00:03:42.101 They should be exactly equal sections. 00:03:42.101 --> 00:03:45.330 So I am almost there. 00:03:45.330 --> 00:03:48.220 So there you have it. 00:03:48.220 --> 00:03:50.070 So I've just taken three wholes 00:03:50.070 --> 00:03:52.410 and I've divided it into fourths. 00:03:52.410 --> 00:03:54.440 So how many fourths are there? 00:03:54.440 --> 00:03:58.190 Well, there are one, two, three, four, five, six, 00:03:58.190 --> 00:04:02.810 seven, eight, nine, 10, 11, 12 fourths. 00:04:02.810 --> 00:04:07.313 So three divided by 1/4 is equal to 12. 00:04:09.150 --> 00:04:10.840 And I encourage you to really think about 00:04:10.840 --> 00:04:12.770 why this is the case, 00:04:12.770 --> 00:04:14.357 that if we take a whole number like three 00:04:14.357 --> 00:04:15.850 and you divide it by 1/4, 00:04:15.850 --> 00:04:18.420 we're getting a value larger than three. 00:04:18.420 --> 00:04:21.410 And we're getting a value that is four times three. 00:04:21.410 --> 00:04:23.543 Think about why that is the case.

Worked example: Identifying an element from its mass spectrum

https://www.youtube.com/watch?v=vU7MDe4ph5A

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https://www.youtube.com/api/timedtext?v=vU7MDe4ph5A&ei=cViUZdy7EKWdxN8P2uSlwAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=DF1217C5D03DA668550125EB4F6016887E0ACD8A.96BE18E682F32B8BE16CD9C0BFB1DDF98CABAC97&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.200 --> 00:00:01.360 - [Instructor] So let's say that we have 00:00:01.360 --> 00:00:03.000 some mystery substance here, 00:00:03.000 --> 00:00:04.660 and we know that it's a pure element, 00:00:04.660 --> 00:00:07.510 and we need to figure out what it is. 00:00:07.510 --> 00:00:10.040 Well, scientists have a method, 00:00:10.040 --> 00:00:11.240 and we go into the details, 00:00:11.240 --> 00:00:13.630 or more details, in other videos, 00:00:13.630 --> 00:00:18.630 called mass, sometimes it's known as mass spectrometry 00:00:20.149 --> 00:00:21.899 or mass spectroscopy. 00:00:24.182 --> 00:00:26.860 It's a technique where you can take a sample of a substance 00:00:26.860 --> 00:00:31.040 and think about the various atomic masses 00:00:31.040 --> 00:00:34.210 of the different isotopes in that substance. 00:00:34.210 --> 00:00:36.230 And that's what we have right over here. 00:00:36.230 --> 00:00:38.990 They tell us the mass spectrum for an average sample 00:00:38.990 --> 00:00:40.500 of a pure element is shown below. 00:00:40.500 --> 00:00:42.860 So let's say it's this pure element. 00:00:42.860 --> 00:00:44.360 So what this is telling us is, 00:00:44.360 --> 00:00:45.680 this looks like maybe, I don't know, 00:00:45.680 --> 00:00:50.110 let's call this 82% of our sample 00:00:50.110 --> 00:00:55.110 has an atomic mass of 88 universal atomic mass units. 00:00:55.330 --> 00:01:00.200 About, this looks like about 7% of our sample 00:01:00.200 --> 00:01:04.460 has an atomic mass of 87 universal atomic mass units. 00:01:04.460 --> 00:01:07.390 It looks like 10% has an atomic mass 00:01:07.390 --> 00:01:09.830 of 86 universal atomic mass units, 00:01:09.830 --> 00:01:14.190 and it looks like about 1% of our sample 00:01:14.190 --> 00:01:18.140 has an atomic mass of 84 universal atomic mass units. 00:01:18.140 --> 00:01:20.260 And so from this information, 00:01:20.260 --> 00:01:23.390 we can try to estimate what the average atomic mass 00:01:23.390 --> 00:01:25.320 of this mystery element is. 00:01:25.320 --> 00:01:30.013 We could calculate it as 0.82 times 88, 00:01:32.443 --> 00:01:35.610 plus, let's call this 7%, 00:01:35.610 --> 00:01:37.443 so 0.07 times 87, 00:01:41.329 --> 00:01:43.746 plus 10%, 0.1, times 86, 00:01:46.860 --> 00:01:48.823 plus, let's see, it should add up to 100%. 00:01:48.823 --> 00:01:50.740 This is 89, 00:01:50.740 --> 00:01:52.120 and then this gets us to 99, 00:01:52.120 --> 00:01:54.406 so then another 1%, 00:01:54.406 --> 00:01:58.270 0.01 times 84. 00:01:58.270 --> 00:02:01.410 And so if we were to do this calculation, 00:02:01.410 --> 00:02:02.750 this is our estimate 00:02:02.750 --> 00:02:05.810 of the average atomic mass of this element. 00:02:05.810 --> 00:02:07.330 We could type this into a calculator 00:02:07.330 --> 00:02:08.410 and get some number 00:02:08.410 --> 00:02:10.940 and then look that up on a periodic table of elements, 00:02:10.940 --> 00:02:12.870 or we could just try to estimate it. 00:02:12.870 --> 00:02:16.150 We can see that it's going to be close to 88 00:02:16.150 --> 00:02:18.385 because that's where the highest percentage is. 00:02:18.385 --> 00:02:20.050 When we're taking the weighted average, 00:02:20.050 --> 00:02:22.440 we have the highest weight right over there. 00:02:22.440 --> 00:02:24.250 But these other isotopes, 00:02:24.250 --> 00:02:26.780 these other versions of the element 00:02:26.780 --> 00:02:28.270 that have a different number of neutrons, 00:02:28.270 --> 00:02:30.680 which changes its atomic mass, 00:02:30.680 --> 00:02:32.950 they're going to bring the average down. 00:02:32.950 --> 00:02:35.590 So our average atomic mass 00:02:35.590 --> 00:02:38.680 is going to be a little bit less than 88. 00:02:38.680 --> 00:02:40.980 So let's look up a periodic table of elements. 00:02:41.960 --> 00:02:43.980 What element here has an atomic mass 00:02:43.980 --> 00:02:46.167 a little bit less than 88? 00:02:46.167 --> 00:02:48.980 Well, yttrium is 88.91, 00:02:48.980 --> 00:02:51.610 but we know it can't be that because none of the isotopes 00:02:51.610 --> 00:02:54.110 have an atomic mass above 88. 00:02:54.110 --> 00:02:55.860 So we can rule out yttrium. 00:02:55.860 --> 00:02:57.660 Strontium is looking pretty good. 00:02:57.660 --> 00:02:58.990 It's exactly what we predicted, 00:02:58.990 --> 00:03:01.120 a little bit less than 88, 00:03:01.120 --> 00:03:03.520 and rubidium is a lot less than 88. 00:03:03.520 --> 00:03:05.500 So our, even if we were to do the calculation, 00:03:05.500 --> 00:03:06.333 we could feel confident 00:03:06.333 --> 00:03:08.170 we're not going to be as low as rubidium. 00:03:08.170 --> 00:03:11.030 So I'm feeling very confident just eyeballing it, 00:03:11.030 --> 00:03:11.940 just estimating, 00:03:11.940 --> 00:03:13.090 this is going to be a little bit, 00:03:13.090 --> 00:03:15.890 have an average atomic mass a little bit less than 88, 00:03:15.890 --> 00:03:19.373 which tells me that this is strontium.

Worked example: Calculating mass percent

https://www.youtube.com/watch?v=enTtIDEtda8

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WEBVTT Kind: captions Language: en 00:00:00.570 --> 00:00:01.450 - [Instructor] So right over here, 00:00:01.450 --> 00:00:03.850 I have the molecular formula for glucose. 00:00:03.850 --> 00:00:05.950 And so let's just say that I had a sample 00:00:05.950 --> 00:00:07.660 of pure glucose right over here, 00:00:07.660 --> 00:00:09.620 this is my little pile of glucose. 00:00:09.620 --> 00:00:11.560 I'm not even gonna tell you its mass, 00:00:11.560 --> 00:00:14.220 but based on the molecular formula, 00:00:14.220 --> 00:00:17.570 can you figure out the percentage of carbon 00:00:17.570 --> 00:00:20.170 by mass of my sample? 00:00:20.170 --> 00:00:21.580 Pause this video and think about it. 00:00:21.580 --> 00:00:24.470 And as a hint, I've given you the average atomic masses 00:00:24.470 --> 00:00:26.173 of carbon, hydrogen, and oxygen. 00:00:27.840 --> 00:00:30.410 All right, now let's work through this together. 00:00:30.410 --> 00:00:34.040 Now, the reason why the amount of glucose doesn't matter 00:00:34.040 --> 00:00:35.750 is because the percent carbon by mass 00:00:35.750 --> 00:00:38.130 should be the same regardless of the amount. 00:00:38.130 --> 00:00:39.600 But to help us think this through, 00:00:39.600 --> 00:00:41.030 we can imagine amount. 00:00:41.030 --> 00:00:44.170 Let's just assume that this is a mole, 00:00:44.170 --> 00:00:47.320 this is a mole of glucose. 00:00:47.320 --> 00:00:49.340 So one way we could think about it is, 00:00:49.340 --> 00:00:51.790 we say okay, for every mole of glucose, 00:00:51.790 --> 00:00:53.400 we have six moles of carbon. 00:00:53.400 --> 00:00:56.960 Because every glucose molecule has six carbon atoms. 00:00:56.960 --> 00:01:01.300 So we could say, what is going to be the mass 00:01:01.300 --> 00:01:06.190 of six moles of carbon divided by 00:01:07.360 --> 00:01:12.360 the mass of one mole of glucose? 00:01:13.890 --> 00:01:16.890 And once again, the reason why it's six moles of carbon 00:01:16.890 --> 00:01:19.420 divided by one mole of glucose is because this, 00:01:19.420 --> 00:01:21.660 if we assume this is a mole of glucose, 00:01:21.660 --> 00:01:23.820 every molecule of glucose has six carbons. 00:01:23.820 --> 00:01:27.170 So it's going to be six times as many carbon atoms 00:01:27.170 --> 00:01:30.350 or six moles of carbon. 00:01:30.350 --> 00:01:32.640 Now, what is this going to be? 00:01:32.640 --> 00:01:36.570 Well, this is going to be equal to, 00:01:36.570 --> 00:01:38.350 it's going to be in our numerator, 00:01:38.350 --> 00:01:43.220 we're going to have six moles of carbon 00:01:43.220 --> 00:01:44.830 times the molar mass of carbon. 00:01:44.830 --> 00:01:46.270 Well, what's that going to be? 00:01:46.270 --> 00:01:47.103 Well, we can get that 00:01:47.103 --> 00:01:48.670 from the average atomic mass of carbon. 00:01:48.670 --> 00:01:49.830 If the average atomic mass 00:01:49.830 --> 00:01:52.700 is 12.01 universal atomic mass units, 00:01:52.700 --> 00:01:53.670 the molar mass is going to be 00:01:53.670 --> 00:01:58.670 12.01 grams per mole of carbon. 00:01:58.890 --> 00:02:03.890 So times 12.01 grams per mole of carbon. 00:02:05.940 --> 00:02:09.050 And notice the numerator will be just left with grams. 00:02:09.050 --> 00:02:11.840 And then in the denominator, 00:02:11.840 --> 00:02:13.430 what are we going to have? 00:02:13.430 --> 00:02:15.420 Well, the mass of one mole of glucose, 00:02:15.420 --> 00:02:16.253 for every glucose molecule, 00:02:16.253 --> 00:02:19.580 we have six carbons, 12 hydrogens, and six oxygens. 00:02:19.580 --> 00:02:23.540 So it's going to be the mass of six moles of carbon, 00:02:23.540 --> 00:02:27.230 12 moles of hydrogen, and six moles of oxygen. 00:02:27.230 --> 00:02:29.880 So it's going to be what we just had up here, 00:02:29.880 --> 00:02:33.370 it's going to be six moles of carbon 00:02:33.370 --> 00:02:35.340 times the molar mass of carbon, 00:02:35.340 --> 00:02:39.770 12.01 grams per mole of carbon. 00:02:39.770 --> 00:02:43.590 To that, we are going to add 00:02:43.590 --> 00:02:47.370 the mass of 12 moles of hydrogen. 00:02:47.370 --> 00:02:50.960 So 12 moles of hydrogen 00:02:50.960 --> 00:02:52.570 times the molar mass of hydrogen, 00:02:52.570 --> 00:02:57.570 which is going to be 1.008 grams per mole of hydrogen. 00:02:58.820 --> 00:03:03.290 Plus six moles of oxygen, 00:03:03.290 --> 00:03:04.980 times the molar mass of oxygen, 00:03:04.980 --> 00:03:09.980 which is going to be 16.00 grams per mole of oxygen. 00:03:11.890 --> 00:03:14.480 And the good thing is, down here, the units cancel out, 00:03:14.480 --> 00:03:17.690 so we're left with just grams in the denominator. 00:03:17.690 --> 00:03:18.523 And that makes sense. 00:03:18.523 --> 00:03:19.880 We're gonna end up with grams in the numerator, 00:03:19.880 --> 00:03:21.620 grams in the denominator, the units will cancel out, 00:03:21.620 --> 00:03:24.700 and we'll get a pure percentage at the end. 00:03:24.700 --> 00:03:26.450 So let's see, in the numerator, 00:03:26.450 --> 00:03:28.420 six times 12.01 00:03:28.420 --> 00:03:32.840 is 72.06. 00:03:32.840 --> 00:03:35.900 And then in the denominator, 00:03:35.900 --> 00:03:37.870 I'm just going to do the pure calculation first, 00:03:37.870 --> 00:03:40.200 and then I'm gonna worry about significant figures. 00:03:40.200 --> 00:03:41.500 So in the denominator, 00:03:41.500 --> 00:03:46.250 we have 72.06 plus, 00:03:46.250 --> 00:03:49.447 let's see, 12 times 1.008 is 12.096, 00:03:52.710 --> 00:03:57.710 and then we have plus six times 16 is 96.00, 00:04:01.240 --> 00:04:05.270 and this will be equal to 72, 00:04:05.270 --> 00:04:07.070 if we're just thinking about the pure calculation, 00:04:07.070 --> 00:04:08.560 before we think about significant figures, 00:04:08.560 --> 00:04:11.690 72.06 divided by, 00:04:11.690 --> 00:04:14.070 let's see, if I add 72 to 12, I get 84, 00:04:14.070 --> 00:04:15.370 plus 96, 00:04:15.370 --> 00:04:16.850 I get 180.156. 00:04:22.520 --> 00:04:24.250 Did I do that right? 00:04:24.250 --> 00:04:25.640 If I were just to add up everything, 00:04:25.640 --> 00:04:28.340 not even think about significant figures. 00:04:28.340 --> 00:04:30.210 So we can type this into a calculator 00:04:30.210 --> 00:04:32.010 but we should remind ourselves 00:04:32.010 --> 00:04:33.560 that our final answer should have 00:04:33.560 --> 00:04:36.490 no more than four significant figures. 00:04:36.490 --> 00:04:37.890 Because even down here, 00:04:37.890 --> 00:04:40.620 if we were just doing this blue calculation here, 00:04:40.620 --> 00:04:42.770 that should only have four significant figures, 00:04:42.770 --> 00:04:45.060 it would have gotten us to the hundredths place, 00:04:45.060 --> 00:04:46.620 and so when we add things together, 00:04:46.620 --> 00:04:48.650 we should get no more than the hundredths place, 00:04:48.650 --> 00:04:50.500 but even if we rounded over there 00:04:50.500 --> 00:04:52.180 for significant figures purposes, 00:04:52.180 --> 00:04:54.410 we would still have at least four, 00:04:54.410 --> 00:04:56.070 we'd actually have five significant figures. 00:04:56.070 --> 00:04:57.990 So this four significant figures 00:04:57.990 --> 00:05:00.530 is our significant figures limiting factor. 00:05:00.530 --> 00:05:02.120 So we just have to calculate this 00:05:02.120 --> 00:05:05.058 and round to four significant figures. 00:05:05.058 --> 00:05:09.217 72.06 divided by 180.156 00:05:12.180 --> 00:05:13.580 is equal to, 00:05:13.580 --> 00:05:15.860 and if we round to four significant figures, 00:05:15.860 --> 00:05:19.140 this will be .4000. 00:05:19.140 --> 00:05:20.950 So this will be, I'll say, 00:05:20.950 --> 00:05:24.800 approximately equal to 0.4000. 00:05:24.800 --> 00:05:27.560 Or we could say 40% 00:05:28.920 --> 00:05:32.600 or 40.00% carbon by mass 00:05:32.600 --> 00:05:35.640 when we round to four significant figures. 00:05:35.640 --> 00:05:36.953 And we are done.

Worked example: Calculating molar mass and number of moles

https://www.youtube.com/watch?v=PAqzpZ-nMlg

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WEBVTT Kind: captions Language: en 00:00:00.150 --> 00:00:01.420 - [Instructor] We are asked to calculate 00:00:01.420 --> 00:00:06.420 the number of moles in a 1.52 kilogram sample of glucose. 00:00:07.070 --> 00:00:08.970 So like always, pause this video 00:00:08.970 --> 00:00:10.830 and try to figure this out on your own 00:00:10.830 --> 00:00:13.743 and this periodic table of elements will prove useful. 00:00:14.830 --> 00:00:16.750 All right, now if we're trying to figure out 00:00:16.750 --> 00:00:21.190 the number of moles, remember, mole is really, 00:00:21.190 --> 00:00:23.440 you can view it as a quantity of something. 00:00:23.440 --> 00:00:24.910 If I said a dozen of something, 00:00:24.910 --> 00:00:26.480 you'd say oh, that's 12 of that thing. 00:00:26.480 --> 00:00:28.140 If I say a mole of something, 00:00:28.140 --> 00:00:31.030 I'm saying that's Avogadro's number of that thing. 00:00:31.030 --> 00:00:34.620 And so we have a 1.52 kilograms sample 00:00:34.620 --> 00:00:37.560 of our molecule in question, of glucose 00:00:37.560 --> 00:00:39.900 so if we can figure out the mass per mole, 00:00:39.900 --> 00:00:40.780 or another way to think about it, 00:00:40.780 --> 00:00:44.490 the molar mass of glucose, well then we just divide 00:00:44.490 --> 00:00:47.600 the mass of our sample by the mass per mole 00:00:47.600 --> 00:00:49.960 and we'll know how many moles we have. 00:00:49.960 --> 00:00:54.960 So what is the molar mass of glucose? 00:00:55.120 --> 00:00:56.570 Well to figure that out, and that's why 00:00:56.570 --> 00:00:58.600 this periodic table of elements is useful, 00:00:58.600 --> 00:01:00.320 we just have to figure out the molar mass 00:01:00.320 --> 00:01:02.870 of the constituent elements. 00:01:02.870 --> 00:01:05.450 So if we first look at carbon, 00:01:05.450 --> 00:01:08.790 carbon, we see from this periodic table of elements, 00:01:08.790 --> 00:01:12.820 has a molar mass of 12.01 grams per mole. 00:01:12.820 --> 00:01:14.630 We've talked about it in other videos, 00:01:14.630 --> 00:01:18.220 you could view this 12.01 as a relative atomic mass 00:01:18.220 --> 00:01:19.480 of a carbon atom, 00:01:19.480 --> 00:01:22.270 of as the average atomic mass of a carbon atom, 00:01:22.270 --> 00:01:24.070 or what's useful, and this is where 00:01:24.070 --> 00:01:25.800 Avogadro's Number is valuable, 00:01:25.800 --> 00:01:28.400 if you have Avogadro's Number of carbons, 00:01:28.400 --> 00:01:31.750 it is going to have a mass of 12.01 grams. 00:01:31.750 --> 00:01:36.750 So carbon has a molar mass of 12.01 grams per mole 00:01:37.040 --> 00:01:41.230 and now we can think about hydrogen in the same way. 00:01:41.230 --> 00:01:46.230 Hydrogen has a molar mass of 1.008 grams per mole, 00:01:46.620 --> 00:01:49.840 008 grams per mole. 00:01:49.840 --> 00:01:53.670 And then last but not least, we have oxygen here. 00:01:53.670 --> 00:01:56.540 Oxygen, we can see from our periodic table of elements, 00:01:56.540 --> 00:02:01.540 it has a molar mass of 16.00 grams per mole. 00:02:01.950 --> 00:02:04.500 And so now we have all the information we need 00:02:04.500 --> 00:02:06.550 from our periodic table of elements. 00:02:06.550 --> 00:02:09.280 So the molar mass of glucose is going to be six 00:02:09.280 --> 00:02:11.400 times the molar mass of carbon 00:02:11.400 --> 00:02:14.250 plus 12 times the molar mass of hydrogen 00:02:14.250 --> 00:02:17.750 plus six times the molar mass of oxygen. 00:02:17.750 --> 00:02:22.750 So it's going to be six times 12.01 grams per mole 00:02:23.780 --> 00:02:28.780 plus 12 times 1.008 grams per mole 00:02:32.680 --> 00:02:36.200 plus every molecule of glucose has six oxygen 00:02:36.200 --> 00:02:41.200 plus six times 16.00 grams per mole. 00:02:42.680 --> 00:02:47.240 Six times 12.01 00:02:48.330 --> 00:02:52.943 plus 12 times 1.008 00:02:55.300 --> 00:03:00.300 plus six times 16 00:03:00.350 --> 00:03:03.320 is equal to, and if we're thinking 00:03:03.320 --> 00:03:05.070 about significant figures here, 00:03:05.070 --> 00:03:07.890 the molar mass of hydrogen goes to the thousandths place 00:03:07.890 --> 00:03:10.180 but we only go to the hundredths for carbon 00:03:10.180 --> 00:03:13.290 and for oxygen, we're adding all of these up together 00:03:13.290 --> 00:03:15.340 so it's going to be 180. 00:03:15.340 --> 00:03:16.690 I can only go to the hundredths place 00:03:16.690 --> 00:03:20.510 for significant figures, so 180.16. 00:03:20.510 --> 00:03:25.510 So that's equal to 180.16 grams per mole. 00:03:26.350 --> 00:03:29.900 And we could say grams of glucose, C6H12O6 00:03:32.250 --> 00:03:37.250 per mole of glucose, C6H12O6 00:03:37.610 --> 00:03:40.700 and then we can use this 1.52 kilograms 00:03:40.700 --> 00:03:43.130 to figure out how many moles we have. 00:03:43.130 --> 00:03:48.130 So if we start off with 1.52 kilograms of glucose, 00:03:48.730 --> 00:03:50.903 so that's C6H12O6, 00:03:52.570 --> 00:03:54.500 well first we can convert it to grams 00:03:54.500 --> 00:03:57.400 'cause here, our molar mass is given in terms of grams, 00:03:57.400 --> 00:03:59.860 so times, we're going to want kilograms 00:03:59.860 --> 00:04:01.640 in the denominator and grams in the numerator, 00:04:01.640 --> 00:04:03.930 so how many grams are there per kilograms? 00:04:03.930 --> 00:04:07.520 Well, we have 1,000 grams 00:04:07.520 --> 00:04:10.390 for every one kilogram. 00:04:10.390 --> 00:04:11.960 So when you multiply these two out, 00:04:11.960 --> 00:04:14.170 this is going to give you the number of grams 00:04:14.170 --> 00:04:17.100 we have of glucose which would be 1,520 00:04:17.100 --> 00:04:19.270 and if you have your mass in terms of grams, 00:04:19.270 --> 00:04:22.260 you can then divide by your molar mass 00:04:22.260 --> 00:04:26.540 or you can view it as multiplying it by the moles per gram. 00:04:26.540 --> 00:04:31.423 So for every one mole of glucose, C6H12O6, 00:04:33.840 --> 00:04:38.840 we have 180.16 grams of glucose, 00:04:40.065 --> 00:04:45.065 C6H12O6, 00:04:45.670 --> 00:04:47.840 and this is going to get us, 00:04:47.840 --> 00:04:52.840 we get 1.52 times 1,000 is equal to, 00:04:53.270 --> 00:04:56.200 this is the number of grams of glucose we have, 00:04:56.200 --> 00:05:01.200 and then we're going to divide by 180.16, 00:05:01.200 --> 00:05:05.570 divide by 180.16, 00:05:05.570 --> 00:05:07.400 gives us this number, 00:05:07.400 --> 00:05:09.640 and let's see, if we see significant figures, 00:05:09.640 --> 00:05:11.810 we have three significant figures here, 00:05:11.810 --> 00:05:14.440 we have five here so we wanna round it 00:05:14.440 --> 00:05:16.590 to three significant figures, 00:05:16.590 --> 00:05:19.920 so it will be 8.44 moles of glucose. 00:05:24.140 --> 00:05:28.770 So our kilograms cancel with our kilograms 00:05:28.770 --> 00:05:32.380 and then our grams of glucose 00:05:32.380 --> 00:05:35.310 cancel with our grams of glucose 00:05:35.310 --> 00:05:40.310 and we are left with 8.44 moles of glucose, 00:05:41.340 --> 00:05:43.713 moles of C6H12O6. 00:05:46.120 --> 00:05:48.083 And we are done.

How to reduce test prep anxiety: 3 tips from Sal Khan

https://www.youtube.com/watch?v=IZcbCnZsl5c

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WEBVTT Kind: captions Language: en 00:00:01.350 --> 00:00:03.860 - Here are my tips for reducing stress 00:00:03.860 --> 00:00:06.400 around taking important tests. 00:00:06.400 --> 00:00:10.260 Tip one, build a habit of practice. 00:00:10.260 --> 00:00:12.840 Building a habit of practice is super valuable. 00:00:12.840 --> 00:00:15.620 I know I'm guilty myself of sometimes I get so caught up 00:00:15.620 --> 00:00:18.380 with something, or I'm stressed about something, 00:00:18.380 --> 00:00:20.480 that I almost freeze. 00:00:20.480 --> 00:00:22.490 But it really should be the other way around. 00:00:22.490 --> 00:00:25.490 I try to remind myself that, Sal, 00:00:25.490 --> 00:00:28.560 if you put time in on a regular basis, 00:00:28.560 --> 00:00:31.950 if I use things like Official SAT Practice 00:00:31.950 --> 00:00:34.510 to take practice tests, understand my strengths 00:00:34.510 --> 00:00:37.120 and weaknesses, work on where my weaknesses are, 00:00:37.120 --> 00:00:38.770 and I do it on a regular basis, 00:00:38.770 --> 00:00:41.310 that's my best chance of actually improving. 00:00:41.310 --> 00:00:45.200 And we have studies that show there's a strong corelation 00:00:45.200 --> 00:00:48.710 between students who are able to put in even six hours 00:00:48.710 --> 00:00:51.520 and growing 50% more than expected. 00:00:51.520 --> 00:00:54.270 So I really encourage you don't get too obsessed 00:00:54.270 --> 00:00:56.810 with the outcome, but think about what can I do 00:00:56.810 --> 00:00:58.700 on a regular basis, not all at once, 00:00:58.700 --> 00:01:00.970 not binge-practicing, but what can I do 00:01:00.970 --> 00:01:02.760 on a regular basis, day in, day out, 00:01:02.760 --> 00:01:04.350 and you'll be really impressed 00:01:04.350 --> 00:01:06.640 how much the gains will accumulate. 00:01:06.640 --> 00:01:10.310 Tip two, share your feelings. 00:01:10.310 --> 00:01:13.330 One of the things that it's taken me many years 00:01:13.330 --> 00:01:16.880 to discover the wisdom of, and I hope to share it with you, 00:01:16.880 --> 00:01:19.530 is whatever is going on in your life 00:01:19.530 --> 00:01:22.330 that you think is unique to you, it's not. 00:01:22.330 --> 00:01:23.930 It's probably happening in the minds 00:01:23.930 --> 00:01:25.980 of everyone else around you, even those people 00:01:25.980 --> 00:01:27.660 who look perfect on social media 00:01:27.660 --> 00:01:29.380 and always seem to have their act together 00:01:29.380 --> 00:01:32.410 and their hair perfectly combed and great grades, 00:01:32.410 --> 00:01:35.430 they're feeling the same things, the same stresses, 00:01:35.430 --> 00:01:36.750 the same insecurities in their mind. 00:01:36.750 --> 00:01:39.530 They might even be feeling far more than what you are. 00:01:39.530 --> 00:01:42.750 And so do yourself a favor and do them a favor 00:01:42.750 --> 00:01:44.940 by being vulnerable and talking about it 00:01:44.940 --> 00:01:47.940 and talking about how you can actually support each other. 00:01:47.940 --> 00:01:50.110 I gotta tell you, even when I was a student like you, 00:01:50.110 --> 00:01:54.240 and even today, as I try to navigate my own life, 00:01:54.240 --> 00:01:56.840 by being able to have a support network, 00:01:56.840 --> 00:01:58.730 people who I can commiserate with, 00:01:58.730 --> 00:02:00.750 it really helps lower the stress. 00:02:00.750 --> 00:02:02.660 And that's just gonna make you a healthier person. 00:02:02.660 --> 00:02:05.420 But also, the more relaxed you are entering 00:02:05.420 --> 00:02:08.090 into these tests, the better you're going to perform. 00:02:08.090 --> 00:02:12.180 And tip three, keep a bigger perspective. 00:02:12.180 --> 00:02:15.060 One thing that some of us adults often forget 00:02:15.060 --> 00:02:20.060 is how sometimes stressful the stage of life you're in is. 00:02:20.810 --> 00:02:22.950 Us adults, we say, oh, I gotta pay bills. 00:02:22.950 --> 00:02:25.930 I gotta do this, I gotta pay the mortgage. 00:02:25.930 --> 00:02:28.650 But I can guess what's going on in your mind, 00:02:28.650 --> 00:02:30.550 'cause I went through it myself. 00:02:30.550 --> 00:02:32.150 You're saying, hey, I've gotta do really good 00:02:32.150 --> 00:02:34.490 on this test, because if I do good on this test, 00:02:34.490 --> 00:02:36.310 then I might be able to have that opportunity. 00:02:36.310 --> 00:02:37.750 If I do well with that opportunity, 00:02:37.750 --> 00:02:38.583 then I'll get that opportunity. 00:02:38.583 --> 00:02:40.550 And then my life will be perfect. 00:02:40.550 --> 00:02:41.830 But if I don't do well, 00:02:41.830 --> 00:02:43.850 well then that opportunity might not happen. 00:02:43.850 --> 00:02:45.180 And then that opportunity might not happen, 00:02:45.180 --> 00:02:47.310 and then what will I be? 00:02:47.310 --> 00:02:48.710 Who will I be? 00:02:48.710 --> 00:02:50.060 And what I'd like to tell you, 00:02:50.060 --> 00:02:53.070 and I'm literally, I'm not making this up, 00:02:53.070 --> 00:02:56.950 I have gotten rejected and I failed at far more things 00:02:56.950 --> 00:02:58.080 than you can imagine. 00:02:58.080 --> 00:02:59.540 And even though in the moment, 00:02:59.540 --> 00:03:01.850 I sometimes thought all was lost, 00:03:01.850 --> 00:03:05.070 a week later, six months later, a year later, 00:03:05.070 --> 00:03:07.340 I realize that actually it wasn't that big of a deal. 00:03:07.340 --> 00:03:08.910 And in some ways it was a blessing, 00:03:08.910 --> 00:03:10.950 'cause maybe that wasn't the thing for me. 00:03:10.950 --> 00:03:14.350 And so when you go into test-prep mode, 00:03:14.350 --> 00:03:16.840 yes, of course, you wanna do as well as you can, 00:03:16.840 --> 00:03:18.570 but that score isn't you. 00:03:18.570 --> 00:03:20.010 It doesn't define you. 00:03:20.010 --> 00:03:22.550 You are so much more than that one score. 00:03:22.550 --> 00:03:25.630 You are so much more than what school you get into. 00:03:25.630 --> 00:03:26.880 And I'll tell you a secret. 00:03:26.880 --> 00:03:31.440 And this is after being out in the real world 00:03:31.440 --> 00:03:33.480 for over 20 years. 00:03:33.480 --> 00:03:36.670 I've actually haven't seen a big correlation 00:03:36.670 --> 00:03:39.510 between where someone happened to go to school 00:03:39.510 --> 00:03:42.440 and how successful they might be. 00:03:42.440 --> 00:03:44.760 And I even did the successful in air quotes 00:03:44.760 --> 00:03:48.490 because what society calls successful, 00:03:48.490 --> 00:03:50.960 money, fame, all of that, I gotta tell you, 00:03:50.960 --> 00:03:53.550 also does not correlate with real happiness. 00:03:53.550 --> 00:03:55.820 Real happiness is knowing who you are, 00:03:55.820 --> 00:03:58.830 doing what you can, but not getting obsessed with outcomes, 00:03:58.830 --> 00:04:01.240 not coveting things, not coveting, I must do this, 00:04:01.240 --> 00:04:02.450 I must do that. 00:04:02.450 --> 00:04:04.080 Because no matter how much money you make, 00:04:04.080 --> 00:04:06.300 or how famous or accomplished you get, 00:04:06.300 --> 00:04:08.470 if you have that mindset, you'll never be happy. 00:04:08.470 --> 00:04:11.520 But if you say, look, I'm gonna be my best self. 00:04:11.520 --> 00:04:14.480 I'm gonna do right by myself and right by the world, 00:04:14.480 --> 00:04:17.900 and things will play out as they see fit, 00:04:17.900 --> 00:04:19.180 then you'll always be content. 00:04:19.180 --> 00:04:21.610 And you'll actually be far happier than most people 00:04:21.610 --> 00:04:22.800 on this planet. 00:04:22.800 --> 00:04:24.740 So those are my tips for reducing stress 00:04:24.740 --> 00:04:27.060 as you approach these types of tests 00:04:27.060 --> 00:04:29.620 and a little bit of general life advice too. 00:04:29.620 --> 00:04:30.690 I hope you take it to heart. 00:04:30.690 --> 00:04:32.410 Take it with a grain of salt too, 00:04:32.410 --> 00:04:35.833 but I believe that it might be really valuable.

Course Mastery Sal (intro only)

https://www.youtube.com/watch?v=qTMc5pmYHY4

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WEBVTT Kind: captions Language: en 00:00:00.400 --> 00:00:03.710 - Hi teachers, this is Sal Khan here from Khan Academy 00:00:03.710 --> 00:00:06.970 and welcome to Course Mastery. 00:00:06.970 --> 00:00:10.330 So back in 1984, famous education researcher 00:00:10.330 --> 00:00:13.960 Benjamin Bloom published the famous two-sigma study 00:00:13.960 --> 00:00:15.830 where he showed that a student who works 00:00:15.830 --> 00:00:18.150 in a mastery learning framework with a tutor, 00:00:18.150 --> 00:00:22.260 one-on-one can operate two standard deviations better. 00:00:22.260 --> 00:00:24.700 So the student who is operating in the 50th percentile 00:00:24.700 --> 00:00:27.200 can operate well into the 90th percentile, 00:00:27.200 --> 00:00:29.650 95th, 96th percentile. 00:00:29.650 --> 00:00:31.020 You fast forward to today, there have been 00:00:31.020 --> 00:00:34.870 over 200 studies that have backed up his claims. 00:00:34.870 --> 00:00:36.950 On top of that, you as an educator, 00:00:36.950 --> 00:00:39.110 know that your students enter your class 00:00:39.110 --> 00:00:40.830 at all different levels. 00:00:40.830 --> 00:00:43.330 You also know that differentiation has always been 00:00:43.330 --> 00:00:46.050 considered a best practice in education. 00:00:46.050 --> 00:00:48.870 The hard part, however, is how do you do that 00:00:48.870 --> 00:00:53.760 with 25, 30, 35 kids in the classroom? 00:00:53.760 --> 00:00:56.800 All of us at Khan Academy, we firmly believe 00:00:56.800 --> 00:00:58.840 that if we have to pick between an amazing teacher 00:00:58.840 --> 00:01:02.030 and an amazing technology, we'd pick you every time, 00:01:02.030 --> 00:01:03.540 the amazing teacher. 00:01:03.540 --> 00:01:05.730 Luckily, we don't have to make that trade-off, 00:01:05.730 --> 00:01:08.600 and so we're think about how can we empower you, 00:01:08.600 --> 00:01:12.450 an amazing teacher, with as powerful technology as possible? 00:01:12.450 --> 00:01:14.450 And that's what Course Mastery is. 00:01:14.450 --> 00:01:17.380 It's a way for you to set mastery goals 00:01:17.380 --> 00:01:20.440 for your students, and these goals are fairly large goals, 00:01:20.440 --> 00:01:22.650 so that they'd be appropriate for over a term 00:01:22.650 --> 00:01:25.300 or over a school year, and you set it once 00:01:25.300 --> 00:01:27.600 and then you can feel confident that over the rest 00:01:27.600 --> 00:01:29.310 of the year or the rest of the term, 00:01:29.310 --> 00:01:31.490 your students have things to work on 00:01:31.490 --> 00:01:33.150 the are appropriate for them. 00:01:33.150 --> 00:01:35.300 They'll be able to learn at their own time and pace, 00:01:35.300 --> 00:01:37.630 master concepts at their own time and pace, 00:01:37.630 --> 00:01:39.700 consistent with Benjamin Bloom's work, 00:01:39.700 --> 00:01:42.040 and remediate their gaps as necessary. 00:01:42.040 --> 00:01:44.640 And multiple studies have shown that when students 00:01:44.640 --> 00:01:47.530 on Khan Academy are able to engage in mastery learning, 00:01:47.530 --> 00:01:49.220 learn at their own time and pace, 00:01:49.220 --> 00:01:51.290 for even 30 minutes or more per week. 00:01:51.290 --> 00:01:54.510 So say 45 minutes a week, or one class period a week, 00:01:54.510 --> 00:01:56.080 they're able to accelerate their learning 00:01:56.080 --> 00:01:58.500 as measured by standardized benchmark exams 00:01:58.500 --> 00:02:00.913 by 20 or 30%.

Mastery Learning in Mr. Vandenberg’s Class

https://www.youtube.com/watch?v=1mL0FD7gnGQ

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en

WEBVTT Kind: captions Language: en 00:00:00.250 --> 00:00:03.980 - I Tim Vandenberg and I've been teaching for 25 years, 00:00:03.980 --> 00:00:06.680 17 years in Hesperia, California, 00:00:06.680 --> 00:00:09.560 sixth grade at Carmel Elementary School. 00:00:09.560 --> 00:00:13.800 And Hesperia is a lower socioeconomic status area, 00:00:13.800 --> 00:00:16.840 on average, especially among our student population. 00:00:16.840 --> 00:00:19.240 100% of our students at this school 00:00:19.240 --> 00:00:21.070 are on free reduced lunch. 00:00:21.070 --> 00:00:24.250 The traditional model among most schools 00:00:24.250 --> 00:00:26.940 is just moving kids along by age, 00:00:26.940 --> 00:00:28.860 whether they've mastered the skills or not. 00:00:28.860 --> 00:00:31.920 So by the time they come to me in sixth grade, 00:00:31.920 --> 00:00:34.240 they've got so many gaps in their learning 00:00:34.240 --> 00:00:38.070 because they haven't mastered the skills K through five. 00:00:38.070 --> 00:00:41.460 It's extremely difficult for most teachers, 00:00:41.460 --> 00:00:45.080 probably all teachers to really meet each kid 00:00:45.080 --> 00:00:47.940 at their individual mastery level. 00:00:47.940 --> 00:00:51.030 You're gonna have a third of the class tracking with you, 00:00:51.030 --> 00:00:53.420 a third of the class wishing you'd move faster, 00:00:53.420 --> 00:00:55.730 and a third of the class wishing you'd reteach 00:00:55.730 --> 00:00:57.090 that a few more times. 00:00:57.090 --> 00:00:59.650 My goals as a teacher using Khan Academy 00:00:59.650 --> 00:01:02.720 is for my students to master as much 00:01:02.720 --> 00:01:06.310 of the grade level specific skills as they can, 00:01:06.310 --> 00:01:08.040 truly master the skills. 00:01:08.040 --> 00:01:11.210 What I do is I assign to each student, 00:01:11.210 --> 00:01:13.260 the whole class, an entire unit. 00:01:13.260 --> 00:01:16.220 For example, expressions and variables. 00:01:16.220 --> 00:01:18.530 And then that next day in class, 00:01:18.530 --> 00:01:19.810 we'll have a class lecture. 00:01:19.810 --> 00:01:23.040 Students take notes in their math portfolios, 00:01:23.040 --> 00:01:26.780 and we teach the skill of expressions and variables. 00:01:26.780 --> 00:01:29.900 Then they dive right into Khan Academy, 00:01:29.900 --> 00:01:33.310 start the skills in that unit and work at their own pace. 00:01:33.310 --> 00:01:34.740 And those who need extra help, 00:01:34.740 --> 00:01:37.990 they have the Khan Academy videos and hints. 00:01:37.990 --> 00:01:39.790 And I also monitor the class. 00:01:39.790 --> 00:01:41.180 I rove around and help kids 00:01:41.180 --> 00:01:42.576 whenever they need help. 00:01:42.576 --> 00:01:43.409 (students chattering) 00:01:43.409 --> 00:01:45.810 When students master skills on Khan Academy, 00:01:45.810 --> 00:01:47.210 they're so excited. 00:01:47.210 --> 00:01:50.051 Their self-pride and self-confidence 00:01:50.051 --> 00:01:55.051 just overflows and they start to believe they can learn. 00:01:55.160 --> 00:01:57.760 It's so important in the learning model 00:01:57.760 --> 00:02:00.020 that students find out immediately 00:02:00.020 --> 00:02:03.230 if they are properly grasping a skill. 00:02:03.230 --> 00:02:04.670 Through Khan Academy they get 00:02:04.670 --> 00:02:08.260 that instant feedback after every single problem. 00:02:08.260 --> 00:02:10.250 Is a correct or not correct? 00:02:10.250 --> 00:02:12.260 And if they didn't get a correct, 00:02:12.260 --> 00:02:13.940 they get to find out immediately 00:02:13.940 --> 00:02:18.110 from the hints exactly where they might have misunderstood. 00:02:18.110 --> 00:02:19.970 It's so important for students 00:02:19.970 --> 00:02:22.080 in this day and age of technology, 00:02:22.080 --> 00:02:24.588 to learn to communicate and interact 00:02:24.588 --> 00:02:26.570 interpersonally with others. 00:02:26.570 --> 00:02:29.430 By using Khan Academy to teach students 00:02:29.430 --> 00:02:32.720 to support one another, instead of just being locked 00:02:32.720 --> 00:02:35.460 into a computer screen, they're actually interacting 00:02:35.460 --> 00:02:38.230 with their neighbors, their friends in class. 00:02:38.230 --> 00:02:41.810 They learn to interact with others in all of life. 00:02:41.810 --> 00:02:44.590 So as many good teachers love to do, 00:02:44.590 --> 00:02:48.730 they take their top successful students 00:02:48.730 --> 00:02:50.880 and spread them out in the class 00:02:50.880 --> 00:02:52.820 and give them two elbow buddies, 00:02:52.820 --> 00:02:54.120 one on each side of them. 00:02:54.120 --> 00:02:56.410 I'm monitoring, I'm encouraging first, 00:02:56.410 --> 00:02:57.650 students to help each other. 00:02:57.650 --> 00:03:01.620 It's so much better when students help each other first, 00:03:01.620 --> 00:03:04.460 because then they become so much more self-sufficient, 00:03:04.460 --> 00:03:07.000 self-motivated, self-rewarded. 00:03:07.000 --> 00:03:10.140 Plus, those peer helpers feel so special 00:03:10.140 --> 00:03:11.186 as they reward their friends 00:03:11.186 --> 00:03:13.300 with the help that they give. 00:03:13.300 --> 00:03:14.630 That really makes it possible 00:03:14.630 --> 00:03:18.780 to promote and increase teacher to student interaction, 00:03:18.780 --> 00:03:21.080 because now the teacher is spending their time 00:03:21.080 --> 00:03:23.720 where students really truly need the help, 00:03:23.720 --> 00:03:26.000 on 32 or more different levels 00:03:26.000 --> 00:03:28.230 in a class of that many students. 00:03:28.230 --> 00:03:30.170 I don't have one math class. 00:03:30.170 --> 00:03:33.120 I have 32 math classes. 00:03:33.120 --> 00:03:36.640 Every single student is working at their own pace. 00:03:36.640 --> 00:03:39.100 Now I can meet students where they're at, 00:03:39.100 --> 00:03:41.310 instead of where the middle of the class is at. 00:03:41.310 --> 00:03:44.600 Because the Khan Academy grade level skills 00:03:44.600 --> 00:03:49.420 are so well aligned with the Common Core standards for math, 00:03:49.420 --> 00:03:53.200 I can trust that if my students master those skills 00:03:53.200 --> 00:03:56.720 before the state test, they will do amazingly well. 00:03:56.720 --> 00:03:58.800 And they have for years now. 00:03:58.800 --> 00:04:00.410 After class, I always make sure 00:04:00.410 --> 00:04:04.330 to look at the data progress reports 00:04:04.330 --> 00:04:05.710 on the teacher dashboard. 00:04:05.710 --> 00:04:07.960 That really helps me know who is succeeding 00:04:07.960 --> 00:04:11.140 and who is really struggling and needs extra help. 00:04:11.140 --> 00:04:14.660 And then I set my pace and remediation 00:04:14.660 --> 00:04:17.490 and instructional support accordingly. 00:04:17.490 --> 00:04:21.250 There is no way I could have known to that great detail, 00:04:21.250 --> 00:04:22.530 who is really getting it 00:04:22.530 --> 00:04:25.507 and who's not without the help of Khan Academy. 00:04:25.507 --> 00:04:26.340 - [Students] Yes! 00:04:26.340 --> 00:04:28.030 - I love being a teacher because I love it 00:04:28.030 --> 00:04:31.090 when kids learn to love learning, 00:04:31.090 --> 00:04:32.730 and when they love learning, 00:04:32.730 --> 00:04:35.310 they don't need me for the rest of their life. 00:04:35.310 --> 00:04:37.300 So as they grow up and become adults 00:04:37.300 --> 00:04:38.930 pursuing their own interests, 00:04:38.930 --> 00:04:40.880 they've learned how to learn on their own 00:04:40.880 --> 00:04:43.023 and they have a passion and desire to.

Continuity and change in American society, 1754-1800

https://www.youtube.com/watch?v=wc3cDimF4a4

vtt

https://www.youtube.com/api/timedtext?v=wc3cDimF4a4&ei=cFiUZY-_HMPXxN8P_6qLwAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245984&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D9D0D10B02DAFC8FE90D3692937CBB554D86041D.69D6A43D2C4D7713343D137C0B593F1A59FF7B2D&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.490 --> 00:00:04.670 - [Instructor] In 1819, American author Washington Irving 00:00:04.670 --> 00:00:09.450 published a short story about a man named Rip Van Winkle. 00:00:09.450 --> 00:00:12.130 In the story, Rip lived in a sleepy village 00:00:12.130 --> 00:00:14.080 in the Catskill Mountains of New York, 00:00:14.080 --> 00:00:16.980 where he spent his days hanging around the local tavern, 00:00:16.980 --> 00:00:19.720 the King George, and avoiding his wife 00:00:19.720 --> 00:00:22.350 any time she asked him to do some work on their farm. 00:00:22.350 --> 00:00:25.190 One evening, Rip was walking in the mountains 00:00:25.190 --> 00:00:28.250 when he came upon a strange group of men 00:00:28.250 --> 00:00:29.910 who gave him some liquor to drink. 00:00:29.910 --> 00:00:33.320 He fell asleep, and when we woke up the next morning, 00:00:33.320 --> 00:00:35.110 he went back into town and found 00:00:35.110 --> 00:00:37.380 that everything had changed. 00:00:37.380 --> 00:00:40.860 Instead of a sleepy village, there was a bustling town, 00:00:40.860 --> 00:00:42.730 and the inhabitants all seemed 00:00:42.730 --> 00:00:45.700 to be loudly debating over an election. 00:00:45.700 --> 00:00:49.000 One person wanted to know if Rip favored the Federalists 00:00:49.000 --> 00:00:52.080 or the Republicans, groups that he had never heard of. 00:00:52.080 --> 00:00:54.850 The King George Tavern had transformed into something 00:00:54.850 --> 00:00:58.300 called the General Washington Tavern, and outside it, 00:00:58.300 --> 00:01:02.080 someone had put up an unfamiliar flag bearing stars 00:01:02.080 --> 00:01:03.160 and stripes. 00:01:03.160 --> 00:01:06.120 Gradually, Rip realized that he had been asleep not just 00:01:06.120 --> 00:01:09.250 for one night, but for 20 years, and that he had slept 00:01:09.250 --> 00:01:11.400 through the entire American Revolution. 00:01:11.400 --> 00:01:14.010 Now, this is just a story, and it's a pretty fun one, 00:01:14.010 --> 00:01:15.330 I can't do it justice here, 00:01:15.330 --> 00:01:17.410 but I highly recommend you read it. 00:01:17.410 --> 00:01:19.870 But this story reveals a lot about 00:01:19.870 --> 00:01:24.210 how Americans thought about the amount of social change 00:01:24.210 --> 00:01:26.700 that accompanied the American Revolution. 00:01:26.700 --> 00:01:29.310 If you, like Rip Van Winkle, 00:01:29.310 --> 00:01:31.430 fell asleep in the British colonies 00:01:31.430 --> 00:01:34.210 and woke up in the United States, 00:01:34.210 --> 00:01:36.850 which aspects of life would be familiar to you 00:01:36.850 --> 00:01:38.970 and which would be completely alien? 00:01:38.970 --> 00:01:41.640 In other words, how much did the American Revolution 00:01:41.640 --> 00:01:43.390 really affect society? 00:01:43.390 --> 00:01:46.780 If we set out to answer this question as historians, 00:01:46.780 --> 00:01:49.210 what we're really doing is exercising 00:01:49.210 --> 00:01:53.930 the historical thinking skill of continuity and change. 00:01:53.930 --> 00:01:56.710 What changed and what stayed the same 00:01:56.710 --> 00:01:59.950 from before the Revolution to after it? 00:01:59.950 --> 00:02:03.310 We know that the Revolution changed the political status 00:02:03.310 --> 00:02:05.640 of the British colonies in North America, 00:02:05.640 --> 00:02:07.890 which went from being part of the British Empire 00:02:07.890 --> 00:02:10.130 to being an independent nation, 00:02:10.130 --> 00:02:12.630 but how big of a deal was that, really? 00:02:12.630 --> 00:02:15.710 Was it not much more than erasing British colonies 00:02:15.710 --> 00:02:18.970 from the map and writing in United States instead, 00:02:18.970 --> 00:02:22.760 or did I actually lead to far-reaching changes in 00:02:22.760 --> 00:02:24.430 how people lived? 00:02:24.430 --> 00:02:26.190 If we're trying to answer this question, 00:02:26.190 --> 00:02:29.530 we really only have three options. 00:02:29.530 --> 00:02:32.370 First, things changed a lot. 00:02:32.370 --> 00:02:33.850 There was a great deal of change, 00:02:33.850 --> 00:02:36.040 and things were very different after the Revolution 00:02:36.040 --> 00:02:38.010 compared to beforehand. 00:02:38.010 --> 00:02:41.380 Second, things didn't change much at all. 00:02:41.380 --> 00:02:44.150 The Revolution was a revolution in name only, 00:02:44.150 --> 00:02:47.070 and most things were the same afterwards. 00:02:47.070 --> 00:02:49.950 Or third, some things changed 00:02:49.950 --> 00:02:52.120 but other things stayed the same. 00:02:52.120 --> 00:02:53.960 When we're asking what changed 00:02:53.960 --> 00:02:56.250 and what stayed the same over time, 00:02:56.250 --> 00:02:59.110 we need to be consistent about the aspects of society 00:02:59.110 --> 00:03:03.010 that we choose so that we're comparing apples to apples. 00:03:03.010 --> 00:03:05.280 So, let's decide which aspects we're going 00:03:05.280 --> 00:03:07.130 to compare over time. 00:03:07.130 --> 00:03:08.820 There are a lot that we could choose from, 00:03:08.820 --> 00:03:13.050 religion, slavery, gender roles, 00:03:13.050 --> 00:03:17.110 class and social structures, political institutions. 00:03:17.110 --> 00:03:19.300 It's a little like a choose your own adventure book 00:03:19.300 --> 00:03:20.540 for historians. 00:03:20.540 --> 00:03:24.550 All right, I'm gonna choose political institutions, 00:03:24.550 --> 00:03:27.960 social structures, and gender roles. 00:03:27.960 --> 00:03:29.740 Why am I choosing these? 00:03:29.740 --> 00:03:31.550 Well, I guess that I'm interested in 00:03:31.550 --> 00:03:34.300 how the ideas of the Revolution, 00:03:34.300 --> 00:03:36.010 that all men are created equal 00:03:36.010 --> 00:03:38.880 and that government should represent the will of the people, 00:03:38.880 --> 00:03:40.470 played out in reality. 00:03:40.470 --> 00:03:43.090 Did the Revolution really lead to more equality 00:03:43.090 --> 00:03:44.590 for men or for women? 00:03:44.590 --> 00:03:47.000 Did government really become more democratic? 00:03:47.000 --> 00:03:50.090 So, let's pretend that we're Rip Van Winkle, 00:03:50.090 --> 00:03:53.530 taking a gander at the society around us before 00:03:53.530 --> 00:03:55.130 and after the Revolution. 00:03:55.130 --> 00:03:57.470 I'm not gonna go into a whole lot of detail here, 00:03:57.470 --> 00:03:59.450 but if there's anything you're not familiar with, 00:03:59.450 --> 00:04:01.640 just jot it down and then you can look it up 00:04:01.640 --> 00:04:02.830 when you have a chance. 00:04:02.830 --> 00:04:07.000 So, what were political institutions, social structures, 00:04:07.000 --> 00:04:09.490 and gender roles like before the Revolution? 00:04:09.490 --> 00:04:12.650 Well, first of all, there were 13 separate colonies, 00:04:12.650 --> 00:04:14.560 not just one single nation. 00:04:14.560 --> 00:04:17.720 The colonies were ruled by a hereditary monarch, 00:04:17.720 --> 00:04:20.950 the King of England, and they had virtual representation 00:04:20.950 --> 00:04:21.830 in Parliament. 00:04:21.830 --> 00:04:24.640 Colonists considered themselves Englishmen 00:04:24.640 --> 00:04:27.200 who were entitled to the rights of Englishmen. 00:04:27.200 --> 00:04:29.440 Colonies had property requirements 00:04:29.440 --> 00:04:33.310 and usually also religious requirements for voters. 00:04:33.310 --> 00:04:35.130 Economically, things weren't too bad 00:04:35.130 --> 00:04:37.580 for your average white colonist in the North, 00:04:37.580 --> 00:04:39.940 although by the eve of the Revolution, 00:04:39.940 --> 00:04:42.120 there was a growing number of poor people 00:04:42.120 --> 00:04:43.630 as land become scarcer. 00:04:43.630 --> 00:04:47.030 American colonists were generally better off 00:04:47.030 --> 00:04:49.040 than the working class back in Britain. 00:04:49.040 --> 00:04:53.100 In the South, however, the planter aristocracy ruled, 00:04:53.100 --> 00:04:56.300 with a handful of wealthy white slave owners 00:04:56.300 --> 00:04:59.010 dominating society and politics. 00:04:59.010 --> 00:05:01.110 White indentured servants still existed 00:05:01.110 --> 00:05:03.120 in both the North and the South, 00:05:03.120 --> 00:05:05.960 although the practice was becoming a little less common. 00:05:05.960 --> 00:05:10.010 Most African Americans, excepting a few free people 00:05:10.010 --> 00:05:12.600 of color in the North, were enslaved 00:05:12.600 --> 00:05:16.510 and had no hope of social mobility, save for running away. 00:05:16.510 --> 00:05:19.630 Indigenous people were taking advantage 00:05:19.630 --> 00:05:23.030 of the dueling empires of Britain and France 00:05:23.030 --> 00:05:25.760 as best they could, but after the Seven Years' War, 00:05:25.760 --> 00:05:28.210 the departure of France meant that they were dealing 00:05:28.210 --> 00:05:29.550 with Britain alone. 00:05:29.550 --> 00:05:32.410 The British government tired to prevent more conflict 00:05:32.410 --> 00:05:35.100 between white settlers and indigenous people 00:05:35.100 --> 00:05:38.510 with the Proclamation of 1763, 00:05:38.510 --> 00:05:42.010 which stipulated that the colonists could not expand west 00:05:42.010 --> 00:05:43.970 past the Appalachian Mountains. 00:05:43.970 --> 00:05:47.690 Gender roles in the American colonies mimicked those 00:05:47.690 --> 00:05:49.800 of British society pretty closely. 00:05:49.800 --> 00:05:51.960 White men did farm labor. 00:05:51.960 --> 00:05:54.690 Women cared for the home and children. 00:05:54.690 --> 00:05:58.630 A woman had no political or legal identity 00:05:58.630 --> 00:06:01.960 apart from her husband in a practice called coverture, 00:06:01.960 --> 00:06:04.850 so a married woman couldn't own property or vote. 00:06:04.850 --> 00:06:09.527 Both enslaved men and enslaved women worked in the fields. 00:06:09.527 --> 00:06:11.930 (yawns) 00:06:11.930 --> 00:06:14.000 All this history has tired me out. 00:06:14.000 --> 00:06:15.520 Let's take a little rest and come back 00:06:15.520 --> 00:06:16.723 to our chart in a minute. 00:06:16.723 --> 00:06:19.008 (crickets chirping) 00:06:19.008 --> 00:06:20.410 Ah, that was a nice nap. 00:06:20.410 --> 00:06:21.500 Hang on, what year is it? 00:06:21.500 --> 00:06:23.710 Did we sleep through the whole American Revolution? 00:06:23.710 --> 00:06:25.610 Yikes, let's finish this chart quickly. 00:06:25.610 --> 00:06:28.320 How different were political institutions, 00:06:28.320 --> 00:06:31.930 social structures, and gender roles after the Revolution? 00:06:31.930 --> 00:06:35.040 In terms of politics, things had changed. 00:06:35.040 --> 00:06:38.180 Instead of 13 separate colonies ruled by a king 00:06:38.180 --> 00:06:40.730 and Parliament, there was one nation ruled 00:06:40.730 --> 00:06:42.660 by a three-branch government, 00:06:42.660 --> 00:06:45.930 where citizens were directly represented in Congress. 00:06:45.930 --> 00:06:48.250 Instead of the rights of Englishmen, 00:06:48.250 --> 00:06:52.510 people appealed to Enlightenment ideas of natural rights, 00:06:52.510 --> 00:06:55.090 with protections from government tyranny 00:06:55.090 --> 00:06:57.710 enshrined in a Bill of Rights. 00:06:57.710 --> 00:07:01.500 Many states reduced or eliminated property 00:07:01.500 --> 00:07:03.630 and religious requirements for voting, 00:07:03.630 --> 00:07:06.130 expanding the electorate among white men. 00:07:06.130 --> 00:07:08.920 Overall, social structures were pretty similar, 00:07:08.920 --> 00:07:11.140 with the exception that the institution 00:07:11.140 --> 00:07:14.690 of slavery was being phased out in northern states, 00:07:14.690 --> 00:07:18.180 and the indentured servitude of whites was being phased out 00:07:18.180 --> 00:07:19.210 pretty much everywhere. 00:07:19.210 --> 00:07:21.490 In the South, slavery continued. 00:07:21.490 --> 00:07:24.520 For indigenous people, American independence meant 00:07:24.520 --> 00:07:28.060 that that Proclamation line was no longer being enforced 00:07:28.060 --> 00:07:30.830 and white settlers saw western lands 00:07:30.830 --> 00:07:33.950 as one of the prizes of victory in the Revolution. 00:07:33.950 --> 00:07:37.880 Gender roles also looked pretty similar to before the war. 00:07:37.880 --> 00:07:41.930 Coverture remained, and men and women continued working 00:07:41.930 --> 00:07:45.210 at the same tasks that they had prior to independence. 00:07:45.210 --> 00:07:49.320 One minor difference was the elevation in the status 00:07:49.320 --> 00:07:52.940 of white women, who earned respect for their contributions 00:07:52.940 --> 00:07:55.400 to the war effort as Daughters of Liberty. 00:07:55.400 --> 00:07:57.500 After the Revolution, they took up roles 00:07:57.500 --> 00:08:01.410 as Republican mothers who instilled civic virtue 00:08:01.410 --> 00:08:04.690 in their sons and also required more education 00:08:04.690 --> 00:08:08.050 in order to properly inculcate those values. 00:08:08.050 --> 00:08:11.230 So, what do we make of these changes in continuities? 00:08:11.230 --> 00:08:13.340 The biggest area of change was going from 00:08:13.340 --> 00:08:15.740 hereditary monarchy to democracy, 00:08:15.740 --> 00:08:17.420 expanding the vote for white men. 00:08:17.420 --> 00:08:21.500 The ideas of liberty and equality had some impact 00:08:21.500 --> 00:08:23.740 on social structures and gender roles, 00:08:23.740 --> 00:08:27.370 leading to the gradual abolition of slavery in the North 00:08:27.370 --> 00:08:29.340 and some new opportunities for women. 00:08:29.340 --> 00:08:31.670 If I were to answer our question 00:08:31.670 --> 00:08:34.170 with one of those three options, 00:08:34.170 --> 00:08:38.810 I'd say some things changed and some things stayed the same. 00:08:38.810 --> 00:08:41.400 The Revolution changed the rhetoric of rights 00:08:41.400 --> 00:08:43.700 and expanded democracy for white men 00:08:43.700 --> 00:08:46.870 but didn't have much of a positive impact on the lives 00:08:46.870 --> 00:08:50.140 of women, enslaved people, or indigenous people. 00:08:50.140 --> 00:08:52.900 Now, you could choose totally different aspects 00:08:52.900 --> 00:08:54.810 of society to look at and come up 00:08:54.810 --> 00:08:56.850 with a completely different take than me. 00:08:56.850 --> 00:08:59.570 This is what being a historian is all about. 00:08:59.570 --> 00:09:01.860 If we take care to select aspects 00:09:01.860 --> 00:09:04.760 of society to compare across time, 00:09:04.760 --> 00:09:07.500 we can answer some tough questions about 00:09:07.500 --> 00:09:09.340 how society changed. 00:09:09.340 --> 00:09:10.173 Sleep tight.

The mole and Avogadro's number

https://www.youtube.com/watch?v=cvi4IJMZ13Q

vtt

https://www.youtube.com/api/timedtext?v=cvi4IJMZ13Q&ei=cViUZfeWELqfhcIP1-Od2AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245985&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=10EFF3CA20CE875426A46F16F68E6330DD4ED7E0.551F8D5D8572E60E88EDDD5B1A929744A1491E9A&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.800 --> 00:00:01.660 - [Instructor] In a previous video, 00:00:01.660 --> 00:00:06.660 we introduced ourselves to the idea of average atomic mass, 00:00:06.940 --> 00:00:09.900 which we began to realize could be a very useful way 00:00:09.900 --> 00:00:13.080 of thinking about a mass at an atomic level, 00:00:13.080 --> 00:00:15.370 or at a molecular level. 00:00:15.370 --> 00:00:16.930 But, what we're gonna do in this video 00:00:16.930 --> 00:00:19.950 is connect it to the masses that we might actually see 00:00:19.950 --> 00:00:20.783 in a chemistry lab. 00:00:20.783 --> 00:00:23.610 You're very unlikely to just be dealing with one atom, 00:00:23.610 --> 00:00:26.110 or just a few atoms, or just a few molecules. 00:00:26.110 --> 00:00:28.560 You're more likely to deal with several grams 00:00:28.560 --> 00:00:30.360 of an actual substance. 00:00:30.360 --> 00:00:33.840 So, how do we go from the masses at an atomic scale 00:00:33.840 --> 00:00:38.840 to the masses, masses of samples 00:00:39.110 --> 00:00:41.690 that you see in an actual chemistry lab, 00:00:41.690 --> 00:00:45.610 or in, I guess you could say, r-scale of the world. 00:00:45.610 --> 00:00:47.550 Well, the chemistry community has come up with 00:00:47.550 --> 00:00:49.060 a useful tool. 00:00:49.060 --> 00:00:51.360 They said, all right, let's think about a given element. 00:00:51.360 --> 00:00:52.330 So, say, lithium. 00:00:52.330 --> 00:00:55.683 We know its average atomic mass is 6.94, 00:00:55.683 --> 00:01:00.683 6.94 unified atomic mass units per atom, atom of lithium. 00:01:05.180 --> 00:01:09.370 What if there were a certain number of atoms of lithium 00:01:09.370 --> 00:01:12.370 such that if I have that number, 00:01:12.370 --> 00:01:17.370 so times certain, certain number of atoms, 00:01:19.210 --> 00:01:23.093 then I will actually end up with 6.94 grams, 00:01:25.900 --> 00:01:28.700 grams of lithium. 00:01:28.700 --> 00:01:32.017 And, this number of atoms is 6.02214076 00:01:36.600 --> 00:01:40.840 times 10 to the 23rd power. 00:01:40.840 --> 00:01:44.920 So, if you have a sample with this number of lithium atoms, 00:01:44.920 --> 00:01:49.170 that sample is going to have a mass of 6.94 grams. 00:01:49.170 --> 00:01:51.160 Whatever its average atomic mass is 00:01:51.160 --> 00:01:53.470 in terms of unified atomic mass units, 00:01:53.470 --> 00:01:56.870 if you have that number of the atom, 00:01:56.870 --> 00:02:01.870 you will have a mass of that same number in terms of grams. 00:02:02.420 --> 00:02:05.840 Now, you might be saying, is there a name for this number, 00:02:05.840 --> 00:02:07.670 and there is indeed a name, 00:02:07.670 --> 00:02:10.070 and it is called Avogadro's number, 00:02:10.070 --> 00:02:14.690 named in honor of the early 19th century Italian chemist, 00:02:14.690 --> 00:02:16.390 Amedeo Avogadro. 00:02:16.390 --> 00:02:20.030 And, in most contexts, because you're not normally 00:02:20.030 --> 00:02:23.220 dealing with data with this many significant digits, 00:02:23.220 --> 00:02:25.280 we will usually approximate it as 00:02:25.280 --> 00:02:30.280 6.022 times 10 to the 23rd power. 00:02:30.860 --> 00:02:33.950 Now, there's another word that it's very useful 00:02:33.950 --> 00:02:36.440 to familiarize yourself with in chemistry, 00:02:36.440 --> 00:02:40.360 and that's the idea of a mole. 00:02:40.360 --> 00:02:42.900 Now, what is a mole? 00:02:42.900 --> 00:02:44.800 It is not a little mark on your cheek. 00:02:44.800 --> 00:02:46.340 It is not a burrowing animal. 00:02:46.340 --> 00:02:48.220 Actually, it is both of those things, 00:02:48.220 --> 00:02:49.960 but, in a chemistry context, 00:02:49.960 --> 00:02:54.690 a mole is just saying you have this much of something. 00:02:54.690 --> 00:02:57.300 The word mole was first used by the German chemist 00:02:57.300 --> 00:03:00.870 Wilhelm Ostwald at the end of the 19th century, 00:03:00.870 --> 00:03:02.170 and he came up with the word 00:03:02.170 --> 00:03:05.030 because of its relation to molecule. 00:03:05.030 --> 00:03:06.760 Now, what does that mean? 00:03:06.760 --> 00:03:09.280 Well, think about the word dozen. 00:03:09.280 --> 00:03:12.300 If I say I've got a dozen of eggs, 00:03:12.300 --> 00:03:14.680 how many eggs do I have? 00:03:14.680 --> 00:03:16.370 Well, if I have a dozen of eggs, 00:03:16.370 --> 00:03:18.570 that means I have 12 eggs. 00:03:18.570 --> 00:03:22.240 So, if I say I have a mole of lithium atoms, 00:03:22.240 --> 00:03:24.800 how many lithium atoms do I have? 00:03:24.800 --> 00:03:27.770 That means that I have 6.02214076 00:03:29.690 --> 00:03:33.250 times 10 the to 23rd lithium atoms. 00:03:33.250 --> 00:03:36.510 Exact same idea, it's just that Avogadro's number 00:03:36.510 --> 00:03:40.103 is much hairier of a number than a dozen. 00:03:40.940 --> 00:03:45.230 So, let's use our new found powers of the mole 00:03:45.230 --> 00:03:49.380 and Avogadro's number to start doing some useful things. 00:03:49.380 --> 00:03:53.010 Let's say that someone were to walk up to you and say, 00:03:53.010 --> 00:03:58.010 hey, you, I have a 15.4 milligram sample of germanium. 00:04:02.120 --> 00:04:07.120 How many atoms of germanium am I dealing with? 00:04:08.050 --> 00:04:10.300 Pause this video and try to think about that. 00:04:11.780 --> 00:04:13.520 So, let me clear out some space 00:04:13.520 --> 00:04:16.423 the periodic table of elements was taking up. 00:04:17.490 --> 00:04:19.100 All right, so we started off 00:04:19.100 --> 00:04:24.100 with 15.4 milligrams of germanium. 00:04:24.690 --> 00:04:26.800 The first step might be hey, let's convert this 00:04:26.800 --> 00:04:29.210 to grams of germanium. 00:04:29.210 --> 00:04:32.460 And so, we can do a little bit of dimensional analysis. 00:04:32.460 --> 00:04:34.040 We can just multiply this, 00:04:34.040 --> 00:04:37.370 for every one gram of germanium 00:04:37.370 --> 00:04:41.130 that is equivalent to 1,000 milligrams, 00:04:41.130 --> 00:04:42.950 milligrams of germanium. 00:04:42.950 --> 00:04:46.010 And so, if you essentially multiply by one thousandth 00:04:46.010 --> 00:04:50.750 or divide by 1,000, we're gonna get the grams of germanium. 00:04:50.750 --> 00:04:52.720 And, you can see that in the dimensional analysis 00:04:52.720 --> 00:04:54.960 by seeing that that is going to cancel out with that 00:04:54.960 --> 00:04:58.020 leaving us with just the grams of germanium. 00:04:58.020 --> 00:05:01.130 And, now that we have an expression for grams of germanium, 00:05:01.130 --> 00:05:03.350 we can think about moles of germanium. 00:05:03.350 --> 00:05:05.350 So, how do we do that? 00:05:05.350 --> 00:05:07.940 Well, we're going to multiply by some quantity, 00:05:07.940 --> 00:05:09.710 and in the denominator we're going to want 00:05:09.710 --> 00:05:12.920 grams of germanium for the dimensional analysis to work out, 00:05:12.920 --> 00:05:16.190 grams of germanium, and in the numerator we want 00:05:16.190 --> 00:05:21.190 the new expression to be in terms of moles of germanium. 00:05:21.300 --> 00:05:24.270 So, one mole of germanium is equal to 00:05:24.270 --> 00:05:26.990 how many grams of germanium? 00:05:26.990 --> 00:05:28.650 Well, we see it right over here. 00:05:28.650 --> 00:05:33.650 Germanium's molar mass is 72.63 grams per mole. 00:05:33.780 --> 00:05:38.780 So, for every mole, we have 72.63 grams of germanium. 00:05:40.660 --> 00:05:42.780 And, you can see that the units work out. 00:05:42.780 --> 00:05:44.820 These grams of germanium are going to cancel 00:05:44.820 --> 00:05:46.350 with the grams of germanium 00:05:46.350 --> 00:05:50.080 just leaving us with moles of germanium. 00:05:50.080 --> 00:05:51.590 In an actual chemistry practice, 00:05:51.590 --> 00:05:53.710 finding out the moles of a substance 00:05:53.710 --> 00:05:56.440 might actually be the most useful thing, 00:05:56.440 --> 00:05:59.280 but if you wanted to find out the actual atoms of germanium 00:05:59.280 --> 00:06:01.710 that we're dealing with, we will just multiply by 00:06:01.710 --> 00:06:03.670 the number of atoms you have per mole. 00:06:03.670 --> 00:06:06.430 And, this is going to be true for any element. 00:06:06.430 --> 00:06:10.710 For every mole, you have Avogadro's number of atoms. 00:06:10.710 --> 00:06:12.550 And, we're going to approximate that as 00:06:12.550 --> 00:06:17.550 6.022 times 10 to the 23rd atoms, atoms of germanium, 00:06:20.620 --> 00:06:25.620 for every one mole, mole of germanium. 00:06:27.040 --> 00:06:29.370 And so, just to review what we just did, 00:06:29.370 --> 00:06:31.230 we had milligrams of germanium. 00:06:31.230 --> 00:06:32.820 You multiply these two together, 00:06:32.820 --> 00:06:34.910 you'll have grams of germanium, which makes sense, 00:06:34.910 --> 00:06:37.120 you're essentially just dividing by 1,000. 00:06:37.120 --> 00:06:39.570 If you were to multiply your grams of germanium 00:06:39.570 --> 00:06:42.100 times the moles per gram, 00:06:42.100 --> 00:06:43.480 which is really just the reciprocal 00:06:43.480 --> 00:06:45.110 of this molar mass we got here, 00:06:45.110 --> 00:06:47.360 and just to make sure where it makes sense, 00:06:47.360 --> 00:06:50.330 the units work out nice with the dimensional analysis, 00:06:50.330 --> 00:06:53.370 this right over here tells you your moles, 00:06:53.370 --> 00:06:55.940 moles of germanium. 00:06:55.940 --> 00:06:57.410 And then, if you take your moles 00:06:57.410 --> 00:07:00.050 and then you multiply it by Avogadro's number, 00:07:00.050 --> 00:07:02.020 it tells you how many atoms of germanium we have, 00:07:02.020 --> 00:07:02.853 and that makes sense. 00:07:02.853 --> 00:07:04.950 If I told you I had a certain number of dozen of eggs, 00:07:04.950 --> 00:07:06.470 if I wanted to know how many eggs that is 00:07:06.470 --> 00:07:08.480 I would multiply by 12. 00:07:08.480 --> 00:07:13.480 So, this whole expression is the number of atoms, 00:07:13.900 --> 00:07:16.960 atoms of germanium. 00:07:16.960 --> 00:07:21.490 So, we have 15.4 milligrams. 00:07:21.490 --> 00:07:23.510 If we wanna figure out how many grams we have, 00:07:23.510 --> 00:07:25.190 we then divide by 1,000, 00:07:25.190 --> 00:07:26.910 that's what our dimensional analysis tells us, 00:07:26.910 --> 00:07:28.810 and it also makes logical sense, 00:07:28.810 --> 00:07:30.650 divided by 1,000. 00:07:30.650 --> 00:07:33.600 So, this is how many grams we have. 00:07:33.600 --> 00:07:35.690 And then, if we wanna figure out how many moles, 00:07:35.690 --> 00:07:38.290 and it's going to be a small fraction of a mole 00:07:38.290 --> 00:07:41.790 because a mole is 72.63 grams per mole, 00:07:41.790 --> 00:07:44.230 we have a small fraction of a gram, 00:07:44.230 --> 00:07:46.320 much less 72.63 grams. 00:07:46.320 --> 00:07:48.070 And so, we saw from our analysis 00:07:48.070 --> 00:07:49.160 to figure out the number of moles, 00:07:49.160 --> 00:07:52.430 we're now going to essentially divide by 72.63, 00:07:52.430 --> 00:07:57.430 so divided by 72.63 is equal to, 00:07:57.810 --> 00:08:01.200 this is the number of moles of germanium we have. 00:08:01.200 --> 00:08:03.260 And, if we wanna figure out the number of atoms 00:08:03.260 --> 00:08:05.100 of germanium, we'll then multiply that 00:08:05.100 --> 00:08:06.640 times Avogadro's number. 00:08:06.640 --> 00:08:11.640 So, times 6.022 times 10 to the 23rd, 00:08:12.270 --> 00:08:15.900 and this EE button means times-10-to-the, 00:08:15.900 --> 00:08:19.750 EE 23rd power, so that's how you do it on a calculator. 00:08:19.750 --> 00:08:24.260 And then, that gives us this many atoms. 00:08:24.260 --> 00:08:27.670 And, let's see, just to get our significant digits here, 00:08:27.670 --> 00:08:29.960 our significant figures, out of all of the things 00:08:29.960 --> 00:08:33.290 we multiplied, see we had four significant digits here, 00:08:33.290 --> 00:08:34.370 four significant digits here, 00:08:34.370 --> 00:08:36.010 but we only had three over here, 00:08:36.010 --> 00:08:38.140 so I'm going to round to three significant digits. 00:08:38.140 --> 00:08:43.140 So, I'll go to 1.28 times 10 to the 20th atoms. 00:08:43.860 --> 00:08:46.270 So, we have approximately 00:08:46.270 --> 00:08:51.270 1.28 times 10 to the 20th atoms of germanium, 00:08:54.690 --> 00:08:55.643 which is a lot.

Average atomic mass

https://www.youtube.com/watch?v=YsqoF3hqdkg

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WEBVTT Kind: captions Language: en 00:00:00.890 --> 00:00:02.300 - [Instructor] The thing that I've always found 00:00:02.300 --> 00:00:04.300 amazing about chemistry, 00:00:04.300 --> 00:00:06.390 it's an entire field of science 00:00:06.390 --> 00:00:09.130 that we as human beings have developed 00:00:09.130 --> 00:00:11.950 to actually understand what is happening 00:00:11.950 --> 00:00:15.340 in an almost unimaginably small scale. 00:00:15.340 --> 00:00:17.970 In particular we're gonna be thinking about the atomic, 00:00:17.970 --> 00:00:20.930 and even the subatomic scale. 00:00:20.930 --> 00:00:24.920 And by looking at that scale we can then begin to understand 00:00:24.920 --> 00:00:26.890 the universe in which we live in, 00:00:26.890 --> 00:00:28.280 the scale in which we live in, 00:00:28.280 --> 00:00:32.160 and even be able to make predictions about what will happen, 00:00:32.160 --> 00:00:37.030 and make things that are useful for human beings. 00:00:37.030 --> 00:00:40.700 So if we're going to operate at this small of a scale, 00:00:40.700 --> 00:00:42.580 and we're gonna appreciate in a few seconds 00:00:42.580 --> 00:00:45.000 how small of a scale it is, 00:00:45.000 --> 00:00:48.010 we're going to have to have some units of measurement. 00:00:48.010 --> 00:00:51.960 And this video is going to focus on mass. 00:00:51.960 --> 00:00:55.670 How do we measure mass at such a small scale? 00:00:55.670 --> 00:00:58.290 Well to do that the chemistry community 00:00:58.290 --> 00:01:02.380 has historically used something called an atomic mass unit. 00:01:02.380 --> 00:01:07.380 I'll write it here, atomic, atomic mass unit, 00:01:08.900 --> 00:01:12.560 and it's historically denoted as AMU. 00:01:12.560 --> 00:01:14.260 And more recently, 00:01:14.260 --> 00:01:15.710 the more modern version of this 00:01:15.710 --> 00:01:18.000 is the unified atomic mass unit, 00:01:18.000 --> 00:01:22.890 that is denoted by just a U instead of an AMU. 00:01:22.890 --> 00:01:25.210 So how does a unified atomic mass unit 00:01:25.210 --> 00:01:26.910 connect to our units of mass 00:01:26.910 --> 00:01:28.570 that we might use on a larger scale 00:01:28.570 --> 00:01:31.740 like, say, grams or kilograms. 00:01:31.740 --> 00:01:36.733 Well, the unified atomic mass unit is defined as 00:01:36.733 --> 00:01:41.733 1.660540 times 10 00:01:42.560 --> 00:01:47.400 to the negative 27 kilograms. 00:01:47.400 --> 00:01:50.360 So when you see something like this, 00:01:50.360 --> 00:01:52.010 you might have a few reactions. 00:01:52.010 --> 00:01:55.220 Your first reaction, which would be an appropriate reaction, 00:01:55.220 --> 00:02:00.220 is that wow, 10 to the negative 27 power is very small. 00:02:00.710 --> 00:02:02.340 To appreciate it you could write it out, 00:02:02.340 --> 00:02:06.020 it would be zero point and then 26 zeros 00:02:06.020 --> 00:02:08.720 and then you would have one six six zero five four zero. 00:02:08.720 --> 00:02:11.920 So very, very, very small, really unimaginably small. 00:02:11.920 --> 00:02:15.700 We can only try to abstract it with things like mathematics. 00:02:15.700 --> 00:02:16.860 The other thing you might appreciate 00:02:16.860 --> 00:02:19.940 is this feels like a bit of a hairy number here, 00:02:19.940 --> 00:02:24.940 1.660540, why did they define it that way? 00:02:25.940 --> 00:02:28.300 And the answer to your question is, 00:02:28.300 --> 00:02:31.180 this definition makes it a lot cleaner 00:02:31.180 --> 00:02:34.660 when we think about the mass of whether it's an atom 00:02:34.660 --> 00:02:39.240 or the constituents of an atom like a proton or a neutron. 00:02:39.240 --> 00:02:42.750 Roughly speaking the mass of a proton 00:02:43.720 --> 00:02:48.350 is approximately one unified atomic mass unit. 00:02:48.350 --> 00:02:50.136 The mass of a neutron 00:02:50.136 --> 00:02:55.136 is approximately one unified atomic mass unit. 00:02:55.350 --> 00:02:56.880 It actually turns out that a proton's 00:02:56.880 --> 00:02:58.560 a little bit more than one, 00:02:58.560 --> 00:03:03.560 it's about 1.007 atomic mass units, 00:03:03.570 --> 00:03:05.290 but it's approximately one. 00:03:05.290 --> 00:03:07.070 And the neutron is actually a little bit more 00:03:07.070 --> 00:03:08.330 than even a proton, 00:03:08.330 --> 00:03:13.330 it's 1.008 approximately unified atomic mass units. 00:03:14.640 --> 00:03:16.950 Now an electron's mass is actually far smaller 00:03:16.950 --> 00:03:17.900 than either of these, 00:03:17.900 --> 00:03:19.810 it's actually almost one two thousandth 00:03:19.810 --> 00:03:21.260 of a proton or a neutron, 00:03:21.260 --> 00:03:23.080 and so you can imagine an atom 00:03:23.080 --> 00:03:24.390 which is made up of protons 00:03:24.390 --> 00:03:27.050 and usually neutrons and electrons as well, 00:03:27.050 --> 00:03:29.340 the mass is mainly going to be 00:03:29.340 --> 00:03:31.770 the protons and neutrons in the nucleus. 00:03:31.770 --> 00:03:34.190 And so if you know the number of protons 00:03:34.190 --> 00:03:35.840 and neutrons in the nucleus, 00:03:35.840 --> 00:03:37.500 you're going to have a pretty good sense 00:03:37.500 --> 00:03:39.780 of its atomic mass. 00:03:39.780 --> 00:03:41.720 And you can see that indicated 00:03:41.720 --> 00:03:46.080 on a periodic table of elements which we have here. 00:03:46.080 --> 00:03:48.300 And we will study the periodic table of elements 00:03:48.300 --> 00:03:51.100 in a lot more detail in other videos. 00:03:51.100 --> 00:03:53.070 But you can see a couple of interesting elements. 00:03:53.070 --> 00:03:54.990 One, you have the abbreviation of a given element, 00:03:54.990 --> 00:03:56.578 H represents hydrogen. 00:03:56.578 --> 00:03:58.830 The number on top on this periodic table, 00:03:58.830 --> 00:04:00.110 that's the atomic number, 00:04:00.110 --> 00:04:02.660 and that tells you how many protons it has. 00:04:02.660 --> 00:04:06.370 And an element is defined by the number of protons. 00:04:06.370 --> 00:04:10.260 So any atom that has exactly one proton in its nucleus 00:04:10.260 --> 00:04:13.070 is going to be hydrogen by definition. 00:04:13.070 --> 00:04:16.720 Any atom that has exactly 20 protons 00:04:16.720 --> 00:04:20.590 in its nucleus is going to be calcium by definition. 00:04:20.590 --> 00:04:23.760 Any atom that has exactly 36 protons in its nucleus 00:04:23.760 --> 00:04:27.620 is going to be krypton by definition. 00:04:27.620 --> 00:04:31.960 So what would you expect the mass of a hydrogen atom to be? 00:04:31.960 --> 00:04:34.070 Pause this video and think about it. 00:04:34.070 --> 00:04:36.520 Well we know that all hydrogen atoms 00:04:36.520 --> 00:04:39.840 by definition have one proton, 00:04:39.840 --> 00:04:40.710 but it actually turns out 00:04:40.710 --> 00:04:42.640 there's different versions of hydrogen 00:04:42.640 --> 00:04:45.460 that can have different numbers of neutrons. 00:04:45.460 --> 00:04:47.350 Most of the hydrogen in the universe 00:04:47.350 --> 00:04:51.430 actually has zero neutrons, zero neutrons. 00:04:51.430 --> 00:04:55.800 There are versions that have one or two neutrons, 00:04:55.800 --> 00:05:00.800 but most, 99.98% roughly, of hydrogen in the universe 00:05:01.686 --> 00:05:04.150 has one proton, zero neutrons, 00:05:04.150 --> 00:05:05.850 and if it's a neutral hydrogen 00:05:05.850 --> 00:05:08.010 it's going to have one electron. 00:05:08.010 --> 00:05:11.050 And when we talk about versions of a given element 00:05:11.050 --> 00:05:14.100 there's a fancy word for it, they're called isotopes. 00:05:14.100 --> 00:05:15.370 And the different isotopes, 00:05:15.370 --> 00:05:17.090 they'll all have the same number of protons 00:05:17.090 --> 00:05:18.960 'cause they're talking about the same element, 00:05:18.960 --> 00:05:22.130 but they'll have different numbers of neutrons. 00:05:22.130 --> 00:05:26.270 And so if this is the most common form of hydrogen. 00:05:26.270 --> 00:05:28.520 What do you think its mass is going to be? 00:05:28.520 --> 00:05:30.760 Well its mass is going to be essentially the mass 00:05:30.760 --> 00:05:32.520 of a proton plus an electron, 00:05:32.520 --> 00:05:35.140 and roughly speaking it's going to be the mass of a proton 00:05:35.140 --> 00:05:36.120 'cause the mass of a proton's 00:05:36.120 --> 00:05:38.460 going to be so much larger than the mass of an electron. 00:05:38.460 --> 00:05:40.020 And so you would expect 00:05:40.020 --> 00:05:45.020 that its mass is approximately one unified atomic mass unit. 00:05:45.770 --> 00:05:47.510 Now if you were to precisely look at 00:05:47.510 --> 00:05:51.370 the mass of a proton and a electron, 00:05:51.370 --> 00:05:53.730 if you add them together, you actually get something 00:05:53.730 --> 00:05:57.490 that's a little bit closer to 1.008. 00:05:57.490 --> 00:05:59.030 And you actually see that 00:05:59.030 --> 00:06:02.400 right over here on the periodic table of elements. 00:06:02.400 --> 00:06:06.530 Now this number, although it is pretty close 00:06:06.530 --> 00:06:09.660 to the mass of the version of hydrogen 00:06:09.660 --> 00:06:11.190 that I just described, 00:06:11.190 --> 00:06:12.995 it's actually a weighted average 00:06:12.995 --> 00:06:16.010 of the various versions of hydrogen. 00:06:16.010 --> 00:06:17.480 It's just close to this version 00:06:17.480 --> 00:06:20.550 because this version represents most of the hydrogen 00:06:20.550 --> 00:06:23.350 that we actually see around us. 00:06:23.350 --> 00:06:27.120 If for example you had two versions of an element, 00:06:27.120 --> 00:06:28.620 some hypothetical element, 00:06:28.620 --> 00:06:31.800 and let's say that 80% of the element 00:06:31.800 --> 00:06:34.130 that we see is version one 00:06:34.130 --> 00:06:35.970 and version one has a mass 00:06:35.970 --> 00:06:38.400 of let's call it five atomic mass units, 00:06:38.400 --> 00:06:41.970 and then version two, it's the remainder, 20%, 00:06:41.970 --> 00:06:43.710 of what we observe of that element, 00:06:43.710 --> 00:06:47.650 it has an atomic mass of six atomic mass units. 00:06:47.650 --> 00:06:49.370 You would get a weighted average here 00:06:49.370 --> 00:06:53.410 of 5.2 unified atomic mass units. 00:06:53.410 --> 00:06:57.800 And that's actually how these numbers are calculated. 00:06:57.800 --> 00:07:02.020 They are not just the mass of one type of that element, 00:07:02.020 --> 00:07:03.860 they're a weighted average mass 00:07:03.860 --> 00:07:06.670 of the various isotopes, of the various types. 00:07:06.670 --> 00:07:10.270 And so this number on a periodic table of elements 00:07:10.270 --> 00:07:14.340 is known as the average atomic mass, 00:07:14.340 --> 00:07:19.293 average, average atomic atomic mass. 00:07:21.470 --> 00:07:23.320 Now in older chemistry books, 00:07:23.320 --> 00:07:24.290 and this is actually the case 00:07:24.290 --> 00:07:25.740 when I first learned chemistry, 00:07:25.740 --> 00:07:28.320 they call this number atomic weight. 00:07:28.320 --> 00:07:29.940 And I've always complained about it 00:07:29.940 --> 00:07:32.270 because it's really talking about mass and not weight. 00:07:32.270 --> 00:07:33.160 If you don't know the difference 00:07:33.160 --> 00:07:35.240 you'll learn that at some point in the future, 00:07:35.240 --> 00:07:39.010 and it's really talking about average atomic mass. 00:07:39.010 --> 00:07:40.610 Now I'll give you one little detail 00:07:40.610 --> 00:07:41.960 that might be useful to you. 00:07:41.960 --> 00:07:45.370 Sometimes you'll hear something called relative atomic mass. 00:07:45.370 --> 00:07:47.940 It actually turns out this periodic table of elements, 00:07:47.940 --> 00:07:49.740 because it does not write a little U 00:07:49.740 --> 00:07:51.260 after each of these numbers, 00:07:51.260 --> 00:07:53.620 it's essentially these number are unitless, 00:07:53.620 --> 00:07:56.370 so it's really talking about relative atomic mass. 00:07:56.370 --> 00:07:59.900 So it's saying, hey on average, for example, 00:07:59.900 --> 00:08:01.959 the mass of a carbon atom 00:08:01.959 --> 00:08:04.533 is going to be roughly 12 times that of, 00:08:04.533 --> 00:08:08.540 on average, the mass of a hydrogen atom. 00:08:08.540 --> 00:08:10.567 If they put the units here, 00:08:10.567 --> 00:08:14.460 then that would actually truly be average atomic mass. 00:08:14.460 --> 00:08:17.160 But for our purposes, as we go into chemistry, 00:08:17.160 --> 00:08:18.930 you can look at these numbers, 00:08:18.930 --> 00:08:23.430 and say okay, if oxygen has a relative atomic mass of 16, 00:08:23.430 --> 00:08:25.180 it's average atomic mass 00:08:25.180 --> 00:08:30.050 is going to be 16 unified atomic mass units. 00:08:30.050 --> 00:08:32.280 And as we will see in the future, 00:08:32.280 --> 00:08:34.870 this understanding of average atomic mass 00:08:34.870 --> 00:08:37.603 will prove to be very, very useful.

Subtracting fractions with unlike denominators introduction

https://www.youtube.com/watch?v=SMshimc16LM

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WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.370 - [Instructor] Let's say we wanted to figure out 00:00:01.370 --> 00:00:05.750 what one half minus one third is equal to. 00:00:05.750 --> 00:00:08.980 And we can visualize each of these fractions. 00:00:08.980 --> 00:00:13.140 One half could look like that where if I take a whole 00:00:13.140 --> 00:00:15.590 and if I divide it into two equal sections, 00:00:15.590 --> 00:00:18.500 one of those two equal sections would be a half 00:00:18.500 --> 00:00:20.260 and you see that shaded in green here. 00:00:20.260 --> 00:00:23.440 And then from that, we're trying to subtract a third 00:00:23.440 --> 00:00:25.880 and we can visualize a third this way. 00:00:25.880 --> 00:00:27.900 That if this whole thing is a whole, 00:00:27.900 --> 00:00:29.620 I divide it into three equal sections 00:00:29.620 --> 00:00:33.460 and one of those three equal sections is a third. 00:00:33.460 --> 00:00:36.920 So what we wanna do is take away this gray box 00:00:36.920 --> 00:00:39.490 from this green box and figure out 00:00:39.490 --> 00:00:42.930 how we can mathematically say what is left over. 00:00:42.930 --> 00:00:46.170 So pause this video and see if you can have a go at this. 00:00:46.170 --> 00:00:48.910 And I'll give you a hint, it will be useful 00:00:48.910 --> 00:00:51.990 to be able to represent your halves and thirds 00:00:51.990 --> 00:00:54.313 in terms of a different denominator. 00:00:55.810 --> 00:00:59.170 All right, now let's work through this together. 00:00:59.170 --> 00:01:01.970 So the way that we can approach this is 00:01:01.970 --> 00:01:04.210 to get a common denominator. 00:01:04.210 --> 00:01:06.230 If I can express both fractions 00:01:06.230 --> 00:01:07.983 in terms of the same denominator, 00:01:07.983 --> 00:01:10.720 it's going to be a lot easier to subtract. 00:01:10.720 --> 00:01:13.420 And the common denominator that's most useful 00:01:13.420 --> 00:01:16.510 is to find the least common denominator. 00:01:16.510 --> 00:01:17.820 And the smallest number 00:01:17.820 --> 00:01:20.310 that is both a multiple of two and three 00:01:20.310 --> 00:01:22.850 is actually two times three, or six. 00:01:22.850 --> 00:01:25.160 So what if we were to write each of these numbers 00:01:25.160 --> 00:01:27.500 in terms of sixths. 00:01:27.500 --> 00:01:31.235 So how can we rewrite one half in terms of sixths? 00:01:31.235 --> 00:01:33.390 I always have trouble saying that. 00:01:33.390 --> 00:01:36.630 Well if I start with one half and if I multiply 00:01:36.630 --> 00:01:38.430 the denominator by three, 00:01:38.430 --> 00:01:40.050 that's going to get us to sixths 00:01:40.050 --> 00:01:42.060 and so I don't change the value of the fraction. 00:01:42.060 --> 00:01:44.430 I need to multiply the numerator by three as well. 00:01:44.430 --> 00:01:46.260 As long as I multiply both the numerator 00:01:46.260 --> 00:01:48.410 and the denominator by the same thing. 00:01:48.410 --> 00:01:51.360 Well, then that's still going to be equal to one half 00:01:51.360 --> 00:01:54.950 and you can visualize what that looks like. 00:01:54.950 --> 00:01:58.380 If you take each of these two equal sections 00:01:58.380 --> 00:02:01.320 and turn them into three equal sections, 00:02:01.320 --> 00:02:03.530 well then you're gonna have a total of six equal sections 00:02:03.530 --> 00:02:04.750 or sixths. 00:02:04.750 --> 00:02:06.430 Two times three in the denominator 00:02:06.430 --> 00:02:08.440 and the part that was shaded in in green 00:02:08.440 --> 00:02:09.820 which was just one of those sections 00:02:09.820 --> 00:02:12.680 is now three times as many sections. 00:02:12.680 --> 00:02:17.680 So your one half is now equal to three over six. 00:02:19.120 --> 00:02:21.630 And we can do the same thing over here. 00:02:21.630 --> 00:02:23.660 If we start with one third 00:02:23.660 --> 00:02:25.861 how do we express it in terms of sixths? 00:02:25.861 --> 00:02:30.830 Well to go from three to six I would multiply it by two, 00:02:30.830 --> 00:02:33.320 and so I also wanna do that in the numerator 00:02:33.320 --> 00:02:35.470 so that I don't change the value of the fraction 00:02:35.470 --> 00:02:37.690 and we can visualize that. 00:02:37.690 --> 00:02:39.885 Notice, if you take all three sections 00:02:39.885 --> 00:02:43.420 and you turn each of them into two sections 00:02:43.420 --> 00:02:45.610 you now have six equal sections. 00:02:45.610 --> 00:02:47.820 So you are now dealing with sixths, 00:02:47.820 --> 00:02:50.020 and that one section before 00:02:50.020 --> 00:02:52.660 is now going to become two sections. 00:02:52.660 --> 00:02:56.350 So this is now going to be equal to two sixths. 00:02:56.350 --> 00:02:59.460 So we can actually rewrite things as 00:02:59.460 --> 00:03:01.600 this is the same thing as 00:03:01.600 --> 00:03:06.600 three sixths minus, minus two sixths. 00:03:07.940 --> 00:03:10.710 And what do you think that is going to be? 00:03:10.710 --> 00:03:13.180 Well if I have three of something 00:03:13.180 --> 00:03:14.580 and I subtract two of them away 00:03:14.580 --> 00:03:17.103 I'm going to be left with one of that something. 00:03:17.103 --> 00:03:21.120 So I'm going to be left with one sixth in this case. 00:03:21.120 --> 00:03:23.800 And we can visualize it just the way 00:03:23.800 --> 00:03:25.520 we visualized everything else. 00:03:25.520 --> 00:03:27.790 If you take two of these gray bars 00:03:27.790 --> 00:03:30.880 or two of these sections from these three sections 00:03:30.880 --> 00:03:32.690 you're just going to be left with one of them. 00:03:32.690 --> 00:03:35.153 This is one of the six equal sections.

Worked example: Determining an empirical formula from percent composition data

https://www.youtube.com/watch?v=k9cxYojKI1I

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WEBVTT Kind: captions Language: en 00:00:00.940 --> 00:00:01.940 - [Instructor] Let's say that we have 00:00:01.940 --> 00:00:04.770 some type of a container that has 00:00:04.770 --> 00:00:08.410 some type of mystery molecule in it. 00:00:08.410 --> 00:00:10.350 So that's my mystery molecule there, 00:00:10.350 --> 00:00:12.930 and we're able to measure the composition 00:00:12.930 --> 00:00:15.510 of the mystery molecule by mass. 00:00:15.510 --> 00:00:20.510 We're able to see that it is 73% by mass mercury, 00:00:21.800 --> 00:00:25.933 and by mass it is 27% chlorine, 00:00:27.710 --> 00:00:30.970 so the remainder is chlorine by mass. 00:00:30.970 --> 00:00:33.910 So pause this video and see if you can come up with 00:00:36.263 --> 00:00:38.170 what is likely the empirical formula 00:00:38.170 --> 00:00:42.150 for our mystery molecule in here, 00:00:42.150 --> 00:00:43.550 and as a little bit of a hint, 00:00:43.550 --> 00:00:46.313 a periodic table of elements might be useful. 00:00:47.350 --> 00:00:50.890 All right, now let's work through this together, 00:00:50.890 --> 00:00:53.550 and to help us make things a little bit more tangible, 00:00:53.550 --> 00:00:57.100 I'm just going to assume a mass for this entire bag. 00:00:57.100 --> 00:01:00.910 Let's just assume it is, 00:01:00.910 --> 00:01:03.250 or this entire container is 100 grams. 00:01:03.250 --> 00:01:05.860 I could have assumed 1,000 grams or 5 grams, 00:01:05.860 --> 00:01:08.130 but 100 grams will make the math easy 00:01:08.130 --> 00:01:09.840 because our whole goal is to say, hey, 00:01:09.840 --> 00:01:13.020 what's the ratio between the number of moles we have 00:01:13.020 --> 00:01:15.810 of mercury and the number of the moles we have of chlorine 00:01:15.810 --> 00:01:19.180 and then that will inform the likely empirical formula. 00:01:19.180 --> 00:01:22.480 So if we assume 100 grams, well then we are dealing with 00:01:22.480 --> 00:01:27.480 a situation that our mercury, we have 73 grams of mercury, 00:01:29.300 --> 00:01:31.890 and we can figure out how many moles this is 00:01:31.890 --> 00:01:35.410 by looking at the average atomic mass of mercury. 00:01:35.410 --> 00:01:38.610 That's why that periodic table of elements is useful. 00:01:38.610 --> 00:01:43.610 We see that one mole of mercury is 200.59 grams on average, 00:01:44.460 --> 00:01:46.420 so we could multiply this times 00:01:46.420 --> 00:01:51.420 one over 200.59 moles per gram. 00:01:55.440 --> 00:01:59.060 So when we multiply this out, the grams will cancel out 00:01:59.060 --> 00:02:00.300 and we're just going to be left with 00:02:00.300 --> 00:02:02.750 a certain number of moles. 00:02:02.750 --> 00:02:05.750 So I'll take 73 and we're just going to divide it by 200.59, 00:02:07.802 --> 00:02:10.140 divided by 200.59 00:02:11.700 --> 00:02:16.700 is going to be equal to 0.36, and I'll just say 0.36 00:02:17.110 --> 00:02:18.250 because this is going to be a little bit 00:02:18.250 --> 00:02:20.820 of an estimation game, and significant digits, 00:02:20.820 --> 00:02:22.160 I only have two significant digits 00:02:22.160 --> 00:02:27.160 on the original mass of mercury, so 0.36 moles, roughly. 00:02:29.240 --> 00:02:31.100 I'll even say roughly right over there, 00:02:31.100 --> 00:02:33.810 and I can do the same thing with chlorine. 00:02:33.810 --> 00:02:37.990 Chlorine, if I have 27% by mass, 00:02:37.990 --> 00:02:42.000 27% of 100, which I'm assuming, is 27 grams. 00:02:42.000 --> 00:02:45.710 And then how many grams per mole? 00:02:45.710 --> 00:02:48.290 If I have one mole for chlorine, 00:02:48.290 --> 00:02:53.290 on average on earth the average atomic mass is 35.45 grams. 00:02:54.490 --> 00:02:58.120 And so this is going to approximate how many moles 00:02:58.120 --> 00:03:00.130 because the grams are going to cancel out, 00:03:00.130 --> 00:03:02.534 and it makes sense that this is going to be 00:03:02.534 --> 00:03:07.200 a fraction of a mole because 27 grams is less than 35.45. 00:03:07.200 --> 00:03:12.200 We take 27 divided by 35.45. 00:03:13.000 --> 00:03:17.933 It gets us to 0.76, roughly, 0.76. 00:03:19.990 --> 00:03:22.660 And remember, we're talking about moles. 00:03:22.660 --> 00:03:25.020 This is how many moles of chlorine we have, 00:03:25.020 --> 00:03:28.150 or this is how many moles of mercury, that's a number. 00:03:28.150 --> 00:03:31.080 You can view that as the number of atoms of mercury 00:03:31.080 --> 00:03:33.630 or the number of atoms of chlorine. 00:03:33.630 --> 00:03:37.890 Moles are just the quantity specified by Avogadro's number, 00:03:37.890 --> 00:03:42.467 so this is 0.76 times Avogadro's number of chlorine atoms. 00:03:46.040 --> 00:03:48.170 So what's the ratio here? 00:03:48.170 --> 00:03:51.200 Well, it looks like for every one mercury atom, 00:03:51.200 --> 00:03:53.450 there is roughly two chlorine atoms. 00:03:53.450 --> 00:03:58.260 If I take two times 0.36, it is 0.72, 00:03:58.260 --> 00:04:00.540 which is roughly close, it's not exact, 00:04:00.540 --> 00:04:02.800 but when you're doing this type of empirical analysis, 00:04:02.800 --> 00:04:04.320 you're not going to get exact results, 00:04:04.320 --> 00:04:07.290 and it's best to assume the simplest ratio 00:04:07.290 --> 00:04:09.340 that gets you pretty close. 00:04:09.340 --> 00:04:12.020 So if we assume a ratio of two chlorine atoms 00:04:12.020 --> 00:04:13.890 for every one mercury atom, 00:04:13.890 --> 00:04:16.580 the likely empirical formula is 00:04:16.580 --> 00:04:21.450 for every mercury atom we will have two chlorines. 00:04:21.450 --> 00:04:24.340 And so this could be the likely empirical formula. 00:04:24.340 --> 00:04:26.000 The name of this molecule happens to be 00:04:26.000 --> 00:04:28.170 mercury two chloride, and I won't go in depth 00:04:28.170 --> 00:04:30.810 why it's called mercury two chloride, 00:04:30.810 --> 00:04:33.963 but that's actually what we likely had in our container.

Adding fractions with unlike denominators introduction

https://www.youtube.com/watch?v=zkJ1gOrYhEg

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WEBVTT Kind: captions Language: en 00:00:00.450 --> 00:00:02.170 - [Instructor] In this video we're gonna try to figure out 00:00:02.170 --> 00:00:05.020 what 1/2 plus 1/3 is equal to. 00:00:05.020 --> 00:00:07.810 And like always, I encourage you to pause this video 00:00:07.810 --> 00:00:10.570 and try to figure it out on your own. 00:00:10.570 --> 00:00:12.620 All right, now let's work through this together. 00:00:12.620 --> 00:00:16.820 And it might be helpful to visualize 1/2 and 1/3. 00:00:16.820 --> 00:00:19.490 So this is a visualization of 1/2 00:00:19.490 --> 00:00:21.840 if you viewed this entire bar as whole, 00:00:21.840 --> 00:00:24.210 then we have shaded in half of it. 00:00:24.210 --> 00:00:28.150 And if you wanted to visualize 1/3 it looks like that. 00:00:28.150 --> 00:00:30.850 So you could view this as this half 00:00:30.850 --> 00:00:32.920 plus this gray third here, 00:00:32.920 --> 00:00:35.100 what is that going to be equal to? 00:00:35.100 --> 00:00:37.990 Now one of the difficult things is we know how to add 00:00:37.990 --> 00:00:39.420 if we have the same denominator. 00:00:39.420 --> 00:00:41.360 So if we had a certain number of halves here 00:00:41.360 --> 00:00:42.950 and a certain number of halves here, 00:00:42.950 --> 00:00:45.240 well then we would know how many halves we have here. 00:00:45.240 --> 00:00:47.990 But here we're trying to add halves to thirds. 00:00:47.990 --> 00:00:49.505 So how do we do that? 00:00:49.505 --> 00:00:54.160 Well we try to set up a common denominator. 00:00:54.160 --> 00:00:56.710 Now, what do we mean by a common denominator? 00:00:56.710 --> 00:01:00.170 Well what if we could express this quantity 00:01:00.170 --> 00:01:05.170 and this quantity in terms of some other denominator. 00:01:05.310 --> 00:01:07.290 And a good way to think about it is 00:01:07.290 --> 00:01:10.250 is there a multiple of two and three 00:01:10.250 --> 00:01:13.320 and it's simplest when you use the least common multiple 00:01:13.320 --> 00:01:17.660 and the least common multiple of two and three is six. 00:01:17.660 --> 00:01:21.450 So can we express 1/2 in terms of sixths 00:01:21.450 --> 00:01:24.870 and can we express 1/3 in terms of sixths? 00:01:24.870 --> 00:01:28.130 So we can just start with one over two 00:01:28.130 --> 00:01:30.680 and I made this little fraction bar a little bit longer 00:01:30.680 --> 00:01:32.340 'cause you'll see why in a second. 00:01:32.340 --> 00:01:34.350 Well if I wanna express it in terms of sixths, 00:01:34.350 --> 00:01:35.561 to go from halves to sixths, 00:01:35.561 --> 00:01:39.780 I would have to multiply the denominator by three. 00:01:39.780 --> 00:01:41.750 But if I want to multiply the denominator by three 00:01:41.750 --> 00:01:43.500 and not change the value of the fraction, 00:01:43.500 --> 00:01:47.100 I have to multiply the numerator by three as well. 00:01:47.100 --> 00:01:51.640 And to see why that makes sense, think about this. 00:01:51.640 --> 00:01:53.560 So this, what we have in green, 00:01:53.560 --> 00:01:56.240 is exactly what we had before but now 00:01:56.240 --> 00:01:59.640 if I multiply it the numerator and the denominator by three, 00:01:59.640 --> 00:02:01.910 I've expressed it into sixths. 00:02:01.910 --> 00:02:05.300 So notice, I have six times as many divisions 00:02:05.300 --> 00:02:06.620 of the whole bar. 00:02:06.620 --> 00:02:09.710 And the green part which you could view as the numerator, 00:02:09.710 --> 00:02:12.490 I now have three times as many. 00:02:12.490 --> 00:02:14.240 So these are now sixths. 00:02:14.240 --> 00:02:17.940 So I now have 3/6 instead of 1/2. 00:02:17.940 --> 00:02:21.170 So this is the same thing as three over six 00:02:21.170 --> 00:02:26.170 and I want to add that or if I want to add this to what? 00:02:26.320 --> 00:02:30.150 Well how do I express 1/3 in terms of sixths? 00:02:30.150 --> 00:02:34.040 Well the way that I could do that, it's one over three, 00:02:34.040 --> 00:02:35.570 I would want to take each of these thirds 00:02:35.570 --> 00:02:37.620 and make them into two sections. 00:02:37.620 --> 00:02:40.726 So to go from thirds to sixths I'd multiply the denominator 00:02:40.726 --> 00:02:44.610 by two but I'd also be multiplying the numerator by two. 00:02:44.610 --> 00:02:46.430 And to see why that makes sense, 00:02:46.430 --> 00:02:49.840 notice this shaded in gray part is exactly 00:02:49.840 --> 00:02:53.135 what we have here but now we took each of these sections 00:02:53.135 --> 00:02:55.790 and we made them into two sections. 00:02:55.790 --> 00:02:58.920 So you multiply the numerator and the denominator by two. 00:02:58.920 --> 00:03:01.760 Instead of thirds, instead of three equal sections, 00:03:01.760 --> 00:03:03.490 we now have six equal sections. 00:03:03.490 --> 00:03:05.391 That's what the denominator times two did. 00:03:05.391 --> 00:03:08.670 Instead of shading in just one of them, 00:03:08.670 --> 00:03:10.060 I now have shaded in two of them 00:03:10.060 --> 00:03:11.300 because that one thing that I shaded 00:03:11.300 --> 00:03:12.980 has now turned into two sections. 00:03:12.980 --> 00:03:15.710 And that's what multiplying the numerator by two does. 00:03:15.710 --> 00:03:17.848 And so this is the same thing as 3/6 00:03:17.848 --> 00:03:21.120 plus this is going to be 2/6. 00:03:21.120 --> 00:03:21.953 And you can see it here. 00:03:21.953 --> 00:03:26.014 This is 1/6, 2/6, and now that everything is in terms 00:03:26.014 --> 00:03:28.560 of sixths, what is it going to be? 00:03:28.560 --> 00:03:30.373 Well it's going to be a certain number of sixths. 00:03:30.373 --> 00:03:33.870 If I have three of something plus two of that something, 00:03:33.870 --> 00:03:35.350 well it's going to be five of that something. 00:03:35.350 --> 00:03:37.311 In this case, the something is sixths. 00:03:37.311 --> 00:03:39.860 So it's going to be 5/6. 00:03:39.860 --> 00:03:41.120 I have trouble saying that. 00:03:41.120 --> 00:03:43.870 And you can visualize it right over here. 00:03:43.870 --> 00:03:46.424 This is three of the sixths, one, two, three, 00:03:46.424 --> 00:03:50.250 plus two of the sixths, one, two, gets us to 5/6. 00:03:50.250 --> 00:03:52.130 But you could also view it as this green part 00:03:52.130 --> 00:03:54.610 was the original half and this gray part 00:03:54.610 --> 00:03:58.128 was the original 1/3, but to be able to compute it, 00:03:58.128 --> 00:04:01.223 we expressed both of them in terms of sixths.