1 00:00:17,500 --> 00:00:19,502 How is everyone doing today? 2 00:00:19,502 --> 00:00:22,271 [CHEERING] 3 00:00:22,271 --> 00:00:23,973 You know why there's a lot of excitement, 4 00:00:23,973 --> 00:00:26,108 and I saw the silent praise, because I 5 00:00:26,108 --> 00:00:31,313 know what this means, recently, and I'm doing more and more. 6 00:00:31,313 --> 00:00:34,517 You guys are excited, because we are celebrating something 7 00:00:34,517 --> 00:00:35,618 on Friday. 8 00:00:35,618 --> 00:00:41,957 We are celebrating knowledge, we are celebrating chemistry, 9 00:00:41,957 --> 00:00:45,494 and we are celebrating how much we've 10 00:00:45,494 --> 00:00:46,829 learned in the last month. 11 00:00:46,829 --> 00:00:48,497 It's called exam three. 12 00:00:48,497 --> 00:00:49,231 Woo. 13 00:00:49,231 --> 00:00:50,599 It's a midterm. 14 00:00:50,599 --> 00:00:51,534 Thank you for that. 15 00:00:58,574 --> 00:01:01,343 What I thought we'd do today instead of-- 16 00:01:01,343 --> 00:01:04,647 again, I mentioned this on Monday. 17 00:01:04,647 --> 00:01:08,250 You guys just had Thanksgiving, you're back, 18 00:01:08,250 --> 00:01:09,652 and now we've got a test. 19 00:01:09,652 --> 00:01:11,754 And I know you've got a lot of other stuff going on 20 00:01:11,754 --> 00:01:12,521 too at this time. 21 00:01:12,521 --> 00:01:14,623 So instead of throwing something in that we're not 22 00:01:14,623 --> 00:01:17,192 going to test you on, what I wanted to do with today 23 00:01:17,192 --> 00:01:21,896 was just to kind of feel our oneness with the concepts. 24 00:01:21,896 --> 00:01:22,831 All right? 25 00:01:22,831 --> 00:01:26,001 And so I want to go over the concepts that 26 00:01:26,001 --> 00:01:31,307 are going to be potentially on the exam on Friday, 27 00:01:31,307 --> 00:01:33,542 and I'll talk about those concepts, 28 00:01:33,542 --> 00:01:34,910 and we'll do a couple of problems 29 00:01:34,910 --> 00:01:36,545 here and there as we go. 30 00:01:36,545 --> 00:01:42,116 OK, so those are the metrics, the specs, for exam three. 31 00:01:46,221 --> 00:01:49,892 But on Monday, I finished with two minutes left, 32 00:01:49,892 --> 00:01:51,259 and I said, hey, there's one more 33 00:01:51,259 --> 00:01:52,995 kind of acid-base definition. 34 00:01:52,995 --> 00:01:55,197 You won't be tested on it, but it's the most general, 35 00:01:55,197 --> 00:01:57,032 and I've got to give Lewis his due. 36 00:01:57,032 --> 00:01:59,969 So I just wanted to just show you like that. 37 00:01:59,969 --> 00:02:02,938 You won't be tested on Lewis acids and bases, 38 00:02:02,938 --> 00:02:05,608 but I did throw this in there, and so 39 00:02:05,608 --> 00:02:09,211 I want to just, for one or two more minutes, talk about this. 40 00:02:09,211 --> 00:02:09,711 Right? 41 00:02:09,711 --> 00:02:11,914 These are the things you are responsible for knowing. 42 00:02:11,914 --> 00:02:13,682 So an Arrhenius acid-base-- 43 00:02:13,682 --> 00:02:14,783 OH, H plus. 44 00:02:14,783 --> 00:02:16,752 Bronsted-Lowry. 45 00:02:16,752 --> 00:02:19,488 It's proton transfer. 46 00:02:19,588 --> 00:02:21,390 And then there's Lewis, who broasted 47 00:02:21,390 --> 00:02:25,961 these guys, because he said, uh-uh, 48 00:02:25,961 --> 00:02:30,199 and this is the most general way to think about acids and bases. 49 00:02:30,199 --> 00:02:31,400 It is the most general. 50 00:02:31,400 --> 00:02:39,675 It is quite powerful, because you go back to say this one, 51 00:02:39,675 --> 00:02:42,811 and so if this is a-- 52 00:02:42,811 --> 00:02:46,815 what if we mix this with this? 53 00:02:46,815 --> 00:02:49,051 So here we have H. 54 00:02:49,051 --> 00:02:51,954 Now, remember, Lewis had all the dots all over the place. 55 00:02:51,954 --> 00:02:55,424 He loved dots, and so they're all over the place. 56 00:02:55,424 --> 00:03:00,195 And that's what if you had this, this is a Lewis acid, 57 00:03:00,195 --> 00:03:04,733 because it is ready to receive. 58 00:03:04,733 --> 00:03:06,435 What is it ready to receive? 59 00:03:06,435 --> 00:03:09,505 No more atoms, only electrons. 60 00:03:09,505 --> 00:03:12,641 It is the most general way to think about it. 61 00:03:12,641 --> 00:03:13,742 All right? 62 00:03:13,742 --> 00:03:17,246 And this would be a Lewis base, because it 63 00:03:17,246 --> 00:03:21,350 is ready to give a pair of electrons 64 00:03:21,350 --> 00:03:22,851 and form a bond together. 65 00:03:22,851 --> 00:03:26,588 And that's what they do, or that's what they can do. 66 00:03:26,588 --> 00:03:31,293 So a Lewis acid and a Lewis base is the most general form, 67 00:03:31,293 --> 00:03:32,795 and you really get rid of-- 68 00:03:32,795 --> 00:03:37,266 so for Lewis, it's all about electron transfer, 69 00:03:37,266 --> 00:03:43,204 electron pair transfer, pair transfer, or bonds if you're-- 70 00:03:43,204 --> 00:03:45,974 I'm just going to make it as general as possible. 71 00:03:45,974 --> 00:03:47,910 If you're going to mix an acid and a base, 72 00:03:47,910 --> 00:03:50,779 which I'll do in a second, it's a pair. 73 00:03:50,779 --> 00:03:54,650 Electron transfer is what it's all about, 74 00:03:54,650 --> 00:03:57,219 and what happens here? 75 00:03:57,219 --> 00:04:00,556 Well, you don't have any chemical identity, 76 00:04:00,556 --> 00:04:02,491 no more chemical identity. 77 00:04:05,861 --> 00:04:06,595 So it's full. 78 00:04:06,595 --> 00:04:08,163 You don't need the hydrogens anymore. 79 00:04:08,163 --> 00:04:09,898 You don't need the OH's. 80 00:04:09,898 --> 00:04:11,767 It's totally general. 81 00:04:11,767 --> 00:04:14,103 And this really opens it up, because now you 82 00:04:14,103 --> 00:04:17,206 can look at gases, liquid, solids, all forms of matter, 83 00:04:17,206 --> 00:04:19,641 all elements in the table, and you can think about them as 84 00:04:19,641 --> 00:04:21,810 whether they're going to have an acid-like 85 00:04:21,810 --> 00:04:24,780 or a base-like character in terms of electron transfer. 86 00:04:24,780 --> 00:04:29,451 So here's the general-- if you had a Lewis acid and a Lewis 87 00:04:29,451 --> 00:04:32,454 base, and you mix them together. 88 00:04:32,454 --> 00:04:36,358 Then, you can see that if you got an electron 89 00:04:36,358 --> 00:04:37,659 pair that could then go-- 90 00:04:37,659 --> 00:04:39,895 that one of them wants it, and the other can give it, 91 00:04:39,895 --> 00:04:42,464 and they can form a bond, then that 92 00:04:42,464 --> 00:04:45,267 would be how you think about mixing a Lewis acid and a Lewis 93 00:04:45,267 --> 00:04:45,768 base. 94 00:04:45,768 --> 00:04:48,971 And again, this won't be on the exam, 95 00:04:48,971 --> 00:04:52,707 but I just had to give Lewis his due. 96 00:04:52,707 --> 00:04:57,913 OK, Lewis acids and bases are all about the electrons. 97 00:04:57,913 --> 00:05:00,115 And then the other thing I didn't get to do on Monday 98 00:05:00,115 --> 00:05:02,184 was my Why This Matters, and so I want to do that. 99 00:05:02,184 --> 00:05:06,054 Now hair is very much affected by the softness of water. 100 00:05:08,891 --> 00:05:13,929 But instead of me showing you lots of pictures of hair 101 00:05:13,929 --> 00:05:19,401 that I found randomly on the internet, googling soft water, 102 00:05:19,401 --> 00:05:23,405 hard water, different forms of water, hair, 103 00:05:23,405 --> 00:05:26,642 I'm showing you pipes, because that's much more actually 104 00:05:26,642 --> 00:05:29,111 relevant in terms of like, for example, whether you can get 105 00:05:29,111 --> 00:05:31,513 water into your house at all. 106 00:05:31,513 --> 00:05:32,414 All right? 107 00:05:32,414 --> 00:05:35,150 And this is a real problem. 108 00:05:35,150 --> 00:05:36,985 If you have hard water what it means 109 00:05:36,985 --> 00:05:40,022 is you've got minerals in the water. 110 00:05:40,022 --> 00:05:40,756 Right? 111 00:05:40,756 --> 00:05:44,593 Things like magnesium and calcium ions are in the water. 112 00:05:44,593 --> 00:05:48,530 And what happens is, if you run that through pipes, they tend 113 00:05:48,530 --> 00:05:52,601 to react and form and deposit. 114 00:05:52,601 --> 00:05:55,170 And you get these deposits of very, very hard mineral 115 00:05:55,170 --> 00:05:58,373 deposits around the edges that eventually look like this. 116 00:05:58,373 --> 00:06:00,075 That's not a good thing. 117 00:06:00,075 --> 00:06:03,612 And so you need to soften the water, and that's something 118 00:06:03,612 --> 00:06:05,113 you may have heard of. 119 00:06:05,113 --> 00:06:07,516 But now you really know how to think about it, because you 120 00:06:07,516 --> 00:06:09,585 can think about it in terms of all of the things 121 00:06:09,585 --> 00:06:12,054 that you've learned. 122 00:06:12,054 --> 00:06:16,592 And just as an example, if one of those minerals 123 00:06:16,592 --> 00:06:18,627 that's a problem is calcium-- 124 00:06:18,627 --> 00:06:20,195 oh, it is, right? 125 00:06:20,195 --> 00:06:25,400 Magnesium is another one that can cause this in pipes. 126 00:06:25,400 --> 00:06:28,971 You've got to somehow take it out of the water 127 00:06:28,971 --> 00:06:33,842 or at least make it into a form that makes it like insoluble, 128 00:06:33,842 --> 00:06:36,311 so it'll just flow, and it won't have a chance 129 00:06:36,311 --> 00:06:41,617 to come around and deposit on the edge there of the pipe. 130 00:06:41,617 --> 00:06:42,718 And so what do you do? 131 00:06:42,718 --> 00:06:45,220 Well, you add, for example-- 132 00:06:45,220 --> 00:06:46,788 oh, we've done this before. 133 00:06:46,788 --> 00:06:47,289 Right? 134 00:06:47,289 --> 00:06:51,293 What if I add soda, something called soda ash? 135 00:06:51,293 --> 00:06:52,928 Oh, we know what that is. 136 00:06:52,928 --> 00:07:01,403 That's Na2CO3, and that will give me some ions. 137 00:07:01,403 --> 00:07:04,172 It'll give me some Na pluses, and it'll 138 00:07:04,172 --> 00:07:09,645 give me some CO3 2 minuses, and those are in aqueous. 139 00:07:09,645 --> 00:07:11,280 Now, this is all part of the stuff 140 00:07:11,280 --> 00:07:12,514 that we've been talking about. 141 00:07:12,514 --> 00:07:14,950 You're dissociating this to get ions in solution, 142 00:07:14,950 --> 00:07:18,287 but why do I want these ions? 143 00:07:18,287 --> 00:07:20,022 That's a water softener. 144 00:07:20,022 --> 00:07:20,589 Why? 145 00:07:20,589 --> 00:07:22,157 Because now you can see it. 146 00:07:22,157 --> 00:07:22,658 Right? 147 00:07:22,658 --> 00:07:26,061 Because this one here, this one here 148 00:07:26,061 --> 00:07:29,498 is going to remove the calcium. 149 00:07:29,498 --> 00:07:31,867 So if I've got these calcium, these minerals, 150 00:07:31,867 --> 00:07:35,904 in the water making it hard water which leads to that 151 00:07:35,904 --> 00:07:40,108 and wreaks havoc on your hair, then you 152 00:07:40,108 --> 00:07:41,909 get a little of this in there, and you're 153 00:07:41,909 --> 00:07:43,312 going to react with the calcium. 154 00:07:43,312 --> 00:07:43,812 Why? 155 00:07:43,812 --> 00:07:45,781 It's because of what we already saw. 156 00:07:45,781 --> 00:07:47,749 If I have this-- 157 00:07:47,749 --> 00:07:50,919 this is something we've already looked at-- if I have calcium 2 158 00:07:50,919 --> 00:07:54,056 plus, and I have some bicarbonate in there, 159 00:07:54,056 --> 00:08:00,562 CO3 minus, then we know that I can get precipitates, Ca-- 160 00:08:00,562 --> 00:08:03,065 this is just what we looked at in the goody bag, right-- 161 00:08:03,065 --> 00:08:07,469 plus CO2 plus H2O. 162 00:08:07,469 --> 00:08:10,973 That's the same kind of reaction that we looked at already. 163 00:08:10,973 --> 00:08:14,109 We have calcium carbonate, calcium carbonate. 164 00:08:14,109 --> 00:08:14,710 Why? 165 00:08:14,710 --> 00:08:18,246 Well, because this is going to give me these. 166 00:08:18,246 --> 00:08:23,485 This is a source for those which then eats up some calcium. 167 00:08:23,485 --> 00:08:28,156 And you think, well, now this can take the calcium ions out, 168 00:08:28,156 --> 00:08:30,525 so that it runs through. 169 00:08:30,525 --> 00:08:32,159 That's what you want to do here. 170 00:08:32,159 --> 00:08:34,229 That's how you soften water. 171 00:08:34,229 --> 00:08:38,100 Well, you can add lime which gives me a source of OH minus, 172 00:08:38,100 --> 00:08:40,501 and that takes out the magnesium. 173 00:08:40,501 --> 00:08:43,038 And these are ways to change the chemistry of water, 174 00:08:43,038 --> 00:08:46,008 so that you don't have as many ions, mineral, 175 00:08:46,008 --> 00:08:49,344 these calcium and magnesium ions floating around that cause 176 00:08:49,344 --> 00:08:50,712 problems. 177 00:08:50,712 --> 00:08:52,547 So that was my Why This Matters, and now we 178 00:08:52,547 --> 00:08:55,851 turn to what I started with which is exam three. 179 00:08:55,851 --> 00:08:58,553 Oh, look at that. 180 00:08:58,553 --> 00:09:01,556 I look at that, and that's just happiness. 181 00:09:01,556 --> 00:09:03,492 Look at all those topics-- 182 00:09:03,492 --> 00:09:10,799 X-rays XRD, defects, glasses, reaction rates, solubility, 183 00:09:10,799 --> 00:09:15,337 aqueous solutions, acids/bases. 184 00:09:15,337 --> 00:09:16,872 It's all there. 185 00:09:16,872 --> 00:09:23,078 It's all there, and it's all there in you, and if not, 186 00:09:23,078 --> 00:09:25,981 you've got two days. 187 00:09:25,981 --> 00:09:30,318 So please, make it be there. 188 00:09:30,318 --> 00:09:31,586 Let's go through this. 189 00:09:31,586 --> 00:09:32,521 Let's go through this. 190 00:09:32,521 --> 00:09:34,456 I'm going to go through this topic right there. 191 00:09:34,456 --> 00:09:36,491 So I'm going to tell you the concepts that I 192 00:09:36,491 --> 00:09:37,692 want to make sure you know. 193 00:09:41,096 --> 00:09:42,264 OK, so here's the first one. 194 00:09:42,264 --> 00:09:46,401 So it's X-rays, and XRD. 195 00:09:46,401 --> 00:09:48,603 So what do I want you to know? 196 00:09:48,603 --> 00:09:51,306 Well, for example, I want you to know 197 00:09:51,306 --> 00:09:57,879 about how you have characteristic, characteristic, 198 00:09:57,879 --> 00:10:04,419 characteristic X-rays, and remember this? 199 00:10:04,419 --> 00:10:06,221 This comes from those transitions. 200 00:10:06,221 --> 00:10:06,721 Right? 201 00:10:06,721 --> 00:10:13,028 So you get like the K and the L and the M. We say et cetera. 202 00:10:13,028 --> 00:10:15,263 We never really did et cetera, but we've 203 00:10:15,263 --> 00:10:22,804 got a lot of K and L lines we looked at, alpha, beta, 204 00:10:22,804 --> 00:10:24,773 but there's also the continuous. 205 00:10:24,773 --> 00:10:25,273 Right? 206 00:10:25,273 --> 00:10:26,441 So this was in-- 207 00:10:26,441 --> 00:10:31,012 if you want-- this would be in the topic of X-ray generation, 208 00:10:31,012 --> 00:10:40,255 and there's that Bremsstrahlung word that means breaking. 209 00:10:40,255 --> 00:10:42,491 Right? 210 00:10:42,491 --> 00:10:45,627 So if you just want to look at this, 211 00:10:45,627 --> 00:10:48,063 you might have a curve that looks-- 212 00:10:48,063 --> 00:10:49,564 OK, so we had things like this. 213 00:10:49,564 --> 00:10:50,365 Right? 214 00:10:50,365 --> 00:10:56,304 Oh, I'm going to try to make it not look too bad, 215 00:10:56,304 --> 00:11:00,242 and there's another one, and so on. 216 00:11:00,242 --> 00:11:06,815 And remember, so this would be like intensity, intensity, 217 00:11:06,815 --> 00:11:12,220 and this would be like maybe a lambda going that way or maybe 218 00:11:12,220 --> 00:11:15,924 energy going that way or frequency. 219 00:11:15,924 --> 00:11:16,424 Right? 220 00:11:16,424 --> 00:11:21,730 Those would be like the x-axis, and these are those lines. 221 00:11:21,730 --> 00:11:24,799 Those are the lines, and they come from the transitions 222 00:11:24,799 --> 00:11:28,904 that you get from like the K level to the L level 223 00:11:28,904 --> 00:11:29,804 to the M level. 224 00:11:29,804 --> 00:11:30,305 Right? 225 00:11:30,305 --> 00:11:35,911 Remember, if you get the energy high enough of an incident 226 00:11:35,911 --> 00:11:41,917 electron onto a target, metal, then you 227 00:11:41,917 --> 00:11:45,620 can knock out electrons from that 1s shell. 228 00:11:45,620 --> 00:11:47,322 And then something cascades down, 229 00:11:47,322 --> 00:11:49,257 and that emits these lines here. 230 00:11:49,257 --> 00:11:54,362 So that'd be like K alpha, K alpha, K beta, et cetera. 231 00:11:54,362 --> 00:11:57,199 But then, you also, even at lower energies, 232 00:11:57,199 --> 00:11:58,667 even if you don't have enough energy 233 00:11:58,667 --> 00:12:01,403 to knock out a 1s electron, you still 234 00:12:01,403 --> 00:12:05,106 can slow an electron down as it goes through a metal atom. 235 00:12:05,106 --> 00:12:08,843 And that's where you get this continuous spectrum 236 00:12:08,843 --> 00:12:13,381 and that limit of how much of that type of X-ray you get. 237 00:12:13,381 --> 00:12:15,784 And it just depends on the incident, 238 00:12:15,784 --> 00:12:19,321 on the voltage, on the maximum incident electron 239 00:12:19,321 --> 00:12:19,955 you fire at it. 240 00:12:19,955 --> 00:12:22,224 So that's those first two topics. 241 00:12:22,224 --> 00:12:24,426 OK? 242 00:12:24,426 --> 00:12:29,598 Well, oh, we also did X-ray diffraction. 243 00:12:29,598 --> 00:12:33,501 Oh, that's fun, diffraction. 244 00:12:33,501 --> 00:12:38,139 OK, and this involves understanding Bragg, 245 00:12:38,139 --> 00:12:43,511 the Bragg condition, and also selection rules. 246 00:12:47,549 --> 00:12:52,487 So let's just take a look at an example of the diffraction 247 00:12:52,487 --> 00:12:53,321 and selection rules. 248 00:12:53,321 --> 00:12:53,822 OK? 249 00:12:53,822 --> 00:12:55,056 So what would I want? 250 00:12:55,056 --> 00:12:56,825 So these are like the kind of concepts 251 00:12:56,825 --> 00:12:59,327 that I want you to know about. 252 00:12:59,327 --> 00:13:00,295 How might it play out? 253 00:13:00,295 --> 00:13:05,634 So like, OK, so here's like an example of a spectrum. 254 00:13:05,634 --> 00:13:13,241 Now, that's an X-ray spectrum for MgFeO4, magnesium ferrite, 255 00:13:13,241 --> 00:13:16,344 and it's a kind of steel. 256 00:13:16,344 --> 00:13:18,113 And you put it in, you make a powder of it, 257 00:13:18,113 --> 00:13:20,382 and and you throw some X-rays on it. 258 00:13:20,382 --> 00:13:24,219 Oh no, you throw just one type of X-ray on it. 259 00:13:24,219 --> 00:13:24,719 All right? 260 00:13:24,719 --> 00:13:26,821 So for these X-ray spectra, what happened? 261 00:13:26,821 --> 00:13:30,325 I threw some K alpha on it, I showed right there, you 262 00:13:30,325 --> 00:13:32,260 got to say what you got. 263 00:13:32,260 --> 00:13:33,395 All right? 264 00:13:33,395 --> 00:13:36,398 You've got to know at least the source of X-rays 265 00:13:36,398 --> 00:13:38,867 has this wavelength. 266 00:13:38,867 --> 00:13:39,934 Good. 267 00:13:39,934 --> 00:13:41,736 And if I have that spectrum, and say, 268 00:13:41,736 --> 00:13:44,572 what's the lattice constant? 269 00:13:44,572 --> 00:13:45,740 What's the structure? 270 00:13:45,740 --> 00:13:47,309 I can get that. 271 00:13:47,309 --> 00:13:48,176 How would I get that? 272 00:13:48,176 --> 00:13:49,044 How would I get that? 273 00:13:49,044 --> 00:13:54,749 So I would take this spectrum, and notice something 274 00:13:54,749 --> 00:13:59,888 is very much pointed out to me, a peak and a number, 35.5. 275 00:13:59,888 --> 00:14:00,388 Right? 276 00:14:00,388 --> 00:14:04,592 That's the 2 theta value for the 311 peak. 277 00:14:04,592 --> 00:14:06,695 Well, I think I'll take that as a hint. 278 00:14:06,695 --> 00:14:10,198 Maybe I should think about that number, and OK, so let's see. 279 00:14:10,198 --> 00:14:15,103 From Bragg, so from Bragg, you know 280 00:14:15,103 --> 00:14:23,778 that you got n lambda equals 2d sine theta, 281 00:14:23,778 --> 00:14:26,881 and remember that had to do with constructive and destructive 282 00:14:26,881 --> 00:14:29,918 interference of waves, the waves being the X-rays. 283 00:14:29,918 --> 00:14:35,023 And then we said, well, n is 1 in our class, so that's just 1 284 00:14:35,023 --> 00:14:35,757 in 3,091. 285 00:14:35,757 --> 00:14:36,958 It doesn't have to be. 286 00:14:36,958 --> 00:14:40,028 You could have interference off of two planes down, 287 00:14:40,028 --> 00:14:41,563 three planes down, but in this class, 288 00:14:41,563 --> 00:14:43,698 we're just doing the two planes next to each other. 289 00:14:43,698 --> 00:14:44,833 So n is 1. 290 00:14:44,833 --> 00:14:46,301 OK? 291 00:14:46,301 --> 00:14:50,138 Now, I'll take that angle, and I'll round it to 18 degrees. 292 00:14:50,138 --> 00:14:56,211 So I'm going to say for theta equals 18 degrees, then-- 293 00:14:56,211 --> 00:14:59,147 oh, wait, why is it 18? 294 00:14:59,147 --> 00:15:00,949 Because that's 2 theta. 295 00:15:00,949 --> 00:15:01,449 Right? 296 00:15:01,449 --> 00:15:04,018 Because remember, we take spectra in 2 theta, 297 00:15:04,018 --> 00:15:06,354 but the theta in Bragg is 1 theta. 298 00:15:06,354 --> 00:15:09,257 OK, that wasn't too hard. 299 00:15:09,257 --> 00:15:16,431 But now, I've got, let's see, sine theta is around 0.3, 300 00:15:16,431 --> 00:15:19,734 and oh, I got lambda. 301 00:15:19,734 --> 00:15:27,008 Lambda equals 1.54 nanometers, and so I can actually 302 00:15:27,008 --> 00:15:29,010 plug in now. 303 00:15:29,010 --> 00:15:31,012 I didn't even need the peak. 304 00:15:31,012 --> 00:15:37,385 I'm just plugging in the Bragg condition, and I've got d. 305 00:15:37,385 --> 00:15:43,324 d equals 2.52 Angstroms, so I'm done. 306 00:15:43,324 --> 00:15:44,559 No. 307 00:15:44,559 --> 00:15:46,895 No, I'm not done, because the question says, 308 00:15:46,895 --> 00:15:49,164 what's the lattice constant? 309 00:15:49,164 --> 00:15:50,331 What's the lattice constant? 310 00:15:50,331 --> 00:15:53,334 This d, I didn't say-- 311 00:15:53,334 --> 00:15:54,536 I did something very bad-- 312 00:15:54,536 --> 00:15:57,172 I didn't say what d-- 313 00:15:57,172 --> 00:15:59,841 d is in hkl. 314 00:15:59,841 --> 00:16:03,711 That's what an XRD does. 315 00:16:03,711 --> 00:16:07,782 XRD, that's a different than diffraction, but the d, 316 00:16:07,782 --> 00:16:11,986 in Bragg, is the distance between the mirror planes 317 00:16:11,986 --> 00:16:13,822 that are scattering. 318 00:16:13,822 --> 00:16:14,456 All right? 319 00:16:14,456 --> 00:16:18,293 And so that's some cuts in the crystal. 320 00:16:18,293 --> 00:16:23,131 That's some hkl, and we know from that era 321 00:16:23,131 --> 00:16:27,335 that there is an equation for cubic crystals 322 00:16:27,335 --> 00:16:30,805 that gives us hkl which is a divided 323 00:16:30,805 --> 00:16:38,813 by the square root of h squared plus k squared plus l squared. 324 00:16:38,813 --> 00:16:46,387 And that is the lattice constant of the crystal, 325 00:16:46,387 --> 00:16:49,724 and that would be the distance between any planes, 326 00:16:49,724 --> 00:16:51,893 any set of planes, in the crystal, 327 00:16:51,893 --> 00:16:53,194 and that's what we need. 328 00:16:53,194 --> 00:16:58,933 Now, I can use that, combine it with the d, 329 00:16:58,933 --> 00:17:03,938 and I can get that the lattice constant is 8.38 Angstroms. 330 00:17:03,938 --> 00:17:05,406 Good. 331 00:17:05,406 --> 00:17:08,041 But the second question is-- 332 00:17:08,041 --> 00:17:10,744 you don't even need to do any math to answer that-- 333 00:17:10,744 --> 00:17:13,515 what is the lattice structure? 334 00:17:13,515 --> 00:17:16,684 Here, we simply go to our selection rules, 335 00:17:16,684 --> 00:17:23,925 and we know from before if they're all even or all odd-- 336 00:17:23,925 --> 00:17:25,792 so here we have, let's see, all these peaks-- 337 00:17:25,792 --> 00:17:29,697 220, 311, 400. 338 00:17:29,697 --> 00:17:31,332 You can see, they're always all even, 339 00:17:31,332 --> 00:17:32,634 or they're always all odd. 340 00:17:32,634 --> 00:17:35,203 From our selection rules, what kind of crystal is that? 341 00:17:38,006 --> 00:17:40,208 It's got to be FCC. 342 00:17:40,208 --> 00:17:41,042 All right? 343 00:17:41,042 --> 00:17:42,810 It's got to be FCC. 344 00:17:42,810 --> 00:17:45,914 So that's the answer to that question, 345 00:17:45,914 --> 00:17:48,182 just from looking at the peaks that you get 346 00:17:48,182 --> 00:17:51,819 and matching them with the selection rules that you know, 347 00:17:51,819 --> 00:17:53,154 that we've already talked about. 348 00:17:55,823 --> 00:17:58,826 You could also, if you didn't have the planes-- 349 00:17:58,826 --> 00:18:01,996 so this is an example, where you're given all these planes. 350 00:18:01,996 --> 00:18:04,299 You're given all these hkls, but what if instead it's 351 00:18:04,299 --> 00:18:06,367 like the one we had in class? 352 00:18:06,367 --> 00:18:07,602 We went through this in class. 353 00:18:07,602 --> 00:18:08,903 Here, I'm not given the planes. 354 00:18:08,903 --> 00:18:13,641 I'm given instead just two theta values. 355 00:18:13,641 --> 00:18:17,912 Well now, you've got to go and use the procedure of XRD, 356 00:18:17,912 --> 00:18:19,380 and I'm not going to do that again. 357 00:18:19,380 --> 00:18:21,983 We've already done that pretty thoroughly, 358 00:18:21,983 --> 00:18:24,152 but that's what you would have to do here, 359 00:18:24,152 --> 00:18:26,187 where you create your columns. 360 00:18:26,187 --> 00:18:28,122 Remember the columns? 361 00:18:28,122 --> 00:18:29,824 All right? 362 00:18:29,824 --> 00:18:32,260 So you would simply make your columns, you make your sign, 363 00:18:32,260 --> 00:18:37,065 your thetas, your 2 theta theta sine squared thetas. 364 00:18:37,065 --> 00:18:41,035 And then you normalize, you take the lowest one, 365 00:18:41,035 --> 00:18:44,305 and you normalize to 1. 366 00:18:44,305 --> 00:18:47,408 Clear fractions, and then find the hkl combinations, 367 00:18:47,408 --> 00:18:50,645 and that's how you would go from this to getting, 368 00:18:50,645 --> 00:18:53,214 for example, the planes. 369 00:18:53,214 --> 00:18:55,550 So those are some examples of things 370 00:18:55,550 --> 00:18:59,153 I want you to be able to do with X-rays and XRD. 371 00:18:59,153 --> 00:19:00,888 Let's move on. 372 00:19:00,888 --> 00:19:02,023 Let's go to the next topic. 373 00:19:02,023 --> 00:19:04,058 Let's do defects. 374 00:19:04,058 --> 00:19:09,263 How about this, defects, because as we said, 375 00:19:09,263 --> 00:19:12,166 it's just like life, crystals, defects 376 00:19:12,166 --> 00:19:13,835 are what make them interesting. 377 00:19:13,835 --> 00:19:14,702 It's the same. 378 00:19:14,702 --> 00:19:16,704 Everything, it's all about defects, 379 00:19:16,704 --> 00:19:19,407 imperfections, those are the interesting and exciting 380 00:19:19,407 --> 00:19:22,877 things, so we've got to know about them in chemistry, 381 00:19:22,877 --> 00:19:25,747 of course. 382 00:19:25,747 --> 00:19:28,883 So we've talked about a bunch of different kinds of defects. 383 00:19:28,883 --> 00:19:31,052 The first one that we talked about 384 00:19:31,052 --> 00:19:39,127 were vacancies, vacancies, and these could be interstitial. 385 00:19:41,996 --> 00:19:47,635 These fall into the category of point defects, point defects, 386 00:19:47,635 --> 00:19:48,136 right? 387 00:19:51,039 --> 00:19:55,510 You could also have interstitial point defects, 388 00:19:55,510 --> 00:20:00,048 interstitial or substitutional. 389 00:20:03,184 --> 00:20:05,119 Those are the different kinds of defects we've 390 00:20:05,119 --> 00:20:07,355 talked about for point defects. 391 00:20:07,355 --> 00:20:11,492 Also, by the way, if it's an ionic point defect, ionic point 392 00:20:11,492 --> 00:20:17,999 defect, you need to make sure you 393 00:20:17,999 --> 00:20:25,973 have charge neutrality, charge neutrality, plus two types. 394 00:20:28,776 --> 00:20:31,079 There's Frenkel, and there's Schottky. 395 00:20:31,079 --> 00:20:36,050 You can think about Schottky, you remove, 396 00:20:36,050 --> 00:20:39,554 but you've got to remove them in a way that's charge-balanced. 397 00:20:39,554 --> 00:20:40,054 Right? 398 00:20:40,054 --> 00:20:42,390 So in Schottky, you remove. 399 00:20:42,390 --> 00:20:44,358 In an ionic crystal, you've got to keep charge. 400 00:20:44,358 --> 00:20:46,627 That's a new thing you've got to keep track of. 401 00:20:46,627 --> 00:20:47,729 And so if we had-- 402 00:20:47,729 --> 00:20:50,264 I'll go to this picture. 403 00:20:50,264 --> 00:20:52,166 Well, you should know this picture. 404 00:20:52,166 --> 00:20:53,367 This is an important picture. 405 00:20:53,367 --> 00:20:54,469 We showed it a lot-- 406 00:20:54,469 --> 00:20:57,538 vacancy, interstitial, self-interstitial, 407 00:20:57,538 --> 00:20:58,573 substitutional. 408 00:20:58,573 --> 00:21:00,641 And then if it's ionic, now all of a sudden, 409 00:21:00,641 --> 00:21:02,744 you've got charges in there, and so you've just 410 00:21:02,744 --> 00:21:05,680 got to make sure things remain neutral. 411 00:21:05,680 --> 00:21:06,581 Right? 412 00:21:06,581 --> 00:21:10,952 In Schottky, you would remove atoms to balance the charge, 413 00:21:10,952 --> 00:21:13,821 and in Frenkel, you move an atom. 414 00:21:16,524 --> 00:21:19,660 Schottky remove, Frenkel move. 415 00:21:19,660 --> 00:21:23,731 That just occurred to me, that that's the same word 416 00:21:23,731 --> 00:21:26,467 with just re in front of it. 417 00:21:26,467 --> 00:21:27,869 That's exciting. 418 00:21:27,869 --> 00:21:30,605 Well, so if I were to ask you, for example, if I were to 419 00:21:30,605 --> 00:21:31,873 ask you this. 420 00:21:31,873 --> 00:21:37,812 You diffuse chromium into one side of the ionic crystal 421 00:21:37,812 --> 00:21:41,415 alumina to make it red and titanium on the other. 422 00:21:41,415 --> 00:21:44,118 Would you expect oxygen vacancies, aluminum vacancies, 423 00:21:44,118 --> 00:21:48,489 or no vacancies in each case? 424 00:21:48,489 --> 00:21:54,962 Just follow the charge, follow the charge. 425 00:21:54,962 --> 00:22:00,034 So for example, if I had alumina, O3. 426 00:22:00,034 --> 00:22:03,905 Well, if I were Lewis, if I were Lewis 427 00:22:03,905 --> 00:22:10,311 I would see this as 2Al3 plus. 428 00:22:10,311 --> 00:22:10,812 Right? 429 00:22:10,812 --> 00:22:14,348 This is how he saw ionic bonds. 430 00:22:14,348 --> 00:22:21,522 Ah, I want to make sure this is clear. 431 00:22:21,522 --> 00:22:22,990 I'm going to start over. 432 00:22:22,990 --> 00:22:32,767 So I would have 2Al3 plus, and then I would have a 3O2 minus. 433 00:22:32,767 --> 00:22:37,371 Remember, O likes to be 2 minus, and so 434 00:22:37,371 --> 00:22:43,377 if I were to introduce something like Cr2O3, 435 00:22:43,377 --> 00:22:56,123 well, this is 2Cr3 plus, so this is 2Cr3 plus, and 3O2 minus. 436 00:22:56,123 --> 00:23:01,596 So if I substitute aluminum with chromium, 437 00:23:01,596 --> 00:23:03,965 then I'm charge-balanced. 438 00:23:03,965 --> 00:23:04,465 Right? 439 00:23:04,465 --> 00:23:05,166 I'm OK. 440 00:23:05,166 --> 00:23:16,944 But if I substitute titanium, TiO2 is Ti4 plus and 2O2 minus, 441 00:23:16,944 --> 00:23:18,746 you know this just from the formula. 442 00:23:18,746 --> 00:23:22,083 Because if oxygen is 2 minus, this thing's got to be neutral, 443 00:23:22,083 --> 00:23:24,719 and so that's Ti4 plus. 444 00:23:24,719 --> 00:23:27,355 But now, if I put a Ti in there, and I get one 445 00:23:27,355 --> 00:23:32,793 in for an aluminum, I've knocked the charge by 1. 446 00:23:32,793 --> 00:23:35,296 Right? 447 00:23:35,296 --> 00:23:43,337 So this gives us an extra charge, 448 00:23:43,337 --> 00:23:45,973 and that means you've got to create vacancies, 449 00:23:45,973 --> 00:23:49,343 create aluminum vacancies. 450 00:23:49,343 --> 00:23:51,779 It's the only way to do it. 451 00:23:51,779 --> 00:23:54,215 So for every three titanium atoms that I put in, 452 00:23:54,215 --> 00:23:55,917 I've got to take an aluminum one out. 453 00:23:55,917 --> 00:23:56,417 Right? 454 00:23:56,417 --> 00:23:59,320 Otherwise, I'm not going to have charge balance, 455 00:23:59,320 --> 00:24:00,688 not going to have charge balance. 456 00:24:00,688 --> 00:24:02,023 Right? 457 00:24:02,023 --> 00:24:06,427 So that would be an example of playing with an ionic crystal, 458 00:24:06,427 --> 00:24:09,163 but remember, we also had stress-strain curves. 459 00:24:09,163 --> 00:24:14,969 Because when we talked about line defects, 460 00:24:14,969 --> 00:24:18,839 we talked about how that's a way for metals and other materials 461 00:24:18,839 --> 00:24:20,241 to undergo deformation. 462 00:24:20,241 --> 00:24:21,943 And then we said, well, how are we 463 00:24:21,943 --> 00:24:26,380 going to conceptualize these things happening, 464 00:24:26,380 --> 00:24:28,115 and we did it with the stress-strain curve 465 00:24:28,115 --> 00:24:30,584 and the mechanical response of materials. 466 00:24:30,584 --> 00:24:32,787 So we learned about stress-strain curves 467 00:24:32,787 --> 00:24:42,129 and fracture points, fracture and plastic 468 00:24:42,129 --> 00:24:47,001 versus elastic regimes. 469 00:24:47,001 --> 00:24:50,504 OK, I'll give an example in a sec. 470 00:24:50,504 --> 00:24:51,005 OK? 471 00:24:53,841 --> 00:24:55,810 And finally, the last thing we did with defects 472 00:24:55,810 --> 00:24:57,945 is we talked about their activation. 473 00:24:57,945 --> 00:25:02,216 And so we know if something is thermally activated, 474 00:25:02,216 --> 00:25:07,688 as are point defects, vacancies are thermally activated, 475 00:25:07,688 --> 00:25:10,458 so are other types of point defects. 476 00:25:10,458 --> 00:25:13,661 And we said that we need an Arrhenius relationship, 477 00:25:13,661 --> 00:25:17,565 and that requires knowledge of an activation 478 00:25:17,565 --> 00:25:20,267 energy for the defect to form. 479 00:25:20,267 --> 00:25:23,304 So that was another really important concept 480 00:25:23,304 --> 00:25:24,071 that we covered. 481 00:25:24,071 --> 00:25:24,905 Right? 482 00:25:24,905 --> 00:25:29,443 So for example, here is like a defect formation energy 483 00:25:29,443 --> 00:25:29,944 question. 484 00:25:33,180 --> 00:25:38,819 So let me go over here, stay with this side, where I've got 485 00:25:38,819 --> 00:25:41,489 some defects. 486 00:25:41,489 --> 00:25:45,493 So one thing I want to make clear, 487 00:25:45,493 --> 00:25:47,294 the fraction of vacancies. 488 00:25:47,294 --> 00:25:48,162 We talked about this. 489 00:25:48,162 --> 00:25:50,631 We talked about an Arrhenius behavior, 490 00:25:50,631 --> 00:25:54,135 Arrhenius-like behavior, and the fraction of vacancies 491 00:25:54,135 --> 00:25:59,106 was the number of vacancies over the number of possible sites. 492 00:25:59,106 --> 00:26:00,641 That makes a lot of sense. 493 00:26:00,641 --> 00:26:02,376 Now, if it's Arrhenius, then this 494 00:26:02,376 --> 00:26:06,614 is some constant times e to the minus activation energy divided 495 00:26:06,614 --> 00:26:10,684 by KBT, where we use the Boltzmann constant 496 00:26:10,684 --> 00:26:12,920 if it's per atom. 497 00:26:12,920 --> 00:26:14,688 Right? 498 00:26:14,688 --> 00:26:18,993 So per vacancy, that activation energy would be per vacancy. 499 00:26:18,993 --> 00:26:23,431 But when I first introduced this, I simply let a be 1, 500 00:26:23,431 --> 00:26:25,666 but a is a constant. 501 00:26:25,666 --> 00:26:30,805 This is a constant, and it can be whatever. 502 00:26:30,805 --> 00:26:31,572 It's a constant. 503 00:26:31,572 --> 00:26:36,243 It's called the anthropic factor, 504 00:26:36,243 --> 00:26:39,547 and it's a constant related to as you would have 505 00:26:39,547 --> 00:26:42,149 in any Arrhenius-like behavior. 506 00:26:42,149 --> 00:26:43,384 Right? 507 00:26:43,384 --> 00:26:46,053 Remember how it's like a frequency factor, 508 00:26:46,053 --> 00:26:49,457 this is related to all sorts of complexities 509 00:26:49,457 --> 00:26:52,827 that we don't need to know about related to how vacancies form. 510 00:26:52,827 --> 00:26:54,962 It's a constant that's in there, and I let it be 1, 511 00:26:54,962 --> 00:26:57,431 but I want to make sure we put it in explicitly. 512 00:27:01,902 --> 00:27:04,672 This n is the number of possible sites. 513 00:27:04,672 --> 00:27:05,172 Right? 514 00:27:05,172 --> 00:27:09,710 So maybe it's the number of lattice sites in the crystal, 515 00:27:09,710 --> 00:27:11,011 number of possible sites. 516 00:27:11,011 --> 00:27:14,081 But you might get this could be related 517 00:27:14,081 --> 00:27:23,457 to, for example, or to or from, things like the grams 518 00:27:23,457 --> 00:27:29,530 that you have of something or maybe the volume 519 00:27:29,530 --> 00:27:30,564 or the moles, et cetera. 520 00:27:30,564 --> 00:27:31,065 Right? 521 00:27:31,065 --> 00:27:35,002 So these are the kinds of problems we've done. 522 00:27:35,002 --> 00:27:39,940 That gives you a sense of how many sites did you have. 523 00:27:39,940 --> 00:27:40,908 Right? 524 00:27:40,908 --> 00:27:43,511 It could be per centimeter cubed. 525 00:27:43,511 --> 00:27:45,746 It could be per moles. 526 00:27:45,746 --> 00:27:47,381 You go back and forth. 527 00:27:47,381 --> 00:27:49,783 How much stuff do I have? 528 00:27:49,783 --> 00:27:52,153 It's that kind of back and forth. 529 00:27:52,153 --> 00:27:56,157 If I had a problem like this, then I know I can set it up, 530 00:27:56,157 --> 00:27:58,993 because I've got two temperatures. 531 00:27:58,993 --> 00:28:01,795 You see the key here, the concentration of 10 532 00:28:01,795 --> 00:28:05,099 to the cubed per centimeter cubed, 533 00:28:05,099 --> 00:28:06,433 so don't let that throw you off. 534 00:28:06,433 --> 00:28:10,905 It's simply two equations, where a bunch of stuff cancels. 535 00:28:10,905 --> 00:28:11,906 Right? 536 00:28:11,906 --> 00:28:16,810 So the fraction of vacancies, fv1, 537 00:28:16,810 --> 00:28:21,515 would be 10 to the 3rd divided by fv2, 538 00:28:21,515 --> 00:28:26,053 and that's going to be 10 to the 3rd over 10 to the 16th, 539 00:28:26,053 --> 00:28:30,357 because the number of stuff cancels. 540 00:28:30,357 --> 00:28:30,858 Right? 541 00:28:30,858 --> 00:28:32,326 I didn't change that. 542 00:28:32,326 --> 00:28:34,662 But this pre-factor cancels too. 543 00:28:34,662 --> 00:28:43,003 You can put it there, A times e to the minus ea divided by KB 544 00:28:43,003 --> 00:28:46,774 times 300 Kelvin-- remember, so it was Kelvin-- 545 00:28:46,774 --> 00:28:55,683 divided by A times to the minus ea divided by KB times 546 00:28:55,683 --> 00:28:59,186 the other temperature, 900 Kelvin. 547 00:28:59,186 --> 00:28:59,920 Right? 548 00:28:59,920 --> 00:29:04,692 And so those cancel, the stuff related to n 549 00:29:04,692 --> 00:29:07,761 cancels, and I can just take the number of vacancies. 550 00:29:07,761 --> 00:29:08,429 Right? 551 00:29:08,429 --> 00:29:10,197 So that's what's nice about having something like this. 552 00:29:10,197 --> 00:29:12,499 You have two temperatures and a whole bunch of stuff 553 00:29:12,499 --> 00:29:17,605 can cancel, and you can figure out then the activation energy 554 00:29:17,605 --> 00:29:19,707 which doesn't change. 555 00:29:19,707 --> 00:29:23,510 The activation energy is simply the energy that you need, 556 00:29:23,510 --> 00:29:29,250 so you can now solve for ea, and I think you get something 557 00:29:29,250 --> 00:29:31,518 like 2.3 electron volts. 558 00:29:31,518 --> 00:29:33,921 Remember that you could also have plotted it. 559 00:29:33,921 --> 00:29:36,457 You'd know that in this equation, 560 00:29:36,457 --> 00:29:40,261 in the Arrhenius relationship, if you take the log, 561 00:29:40,261 --> 00:29:45,065 then you have the minus 1 over T relationship. 562 00:29:45,065 --> 00:29:46,734 So remember that? 563 00:29:46,734 --> 00:29:50,504 So if you take the T versus the log, 564 00:29:50,504 --> 00:29:52,606 then you're going to get that. 565 00:29:52,606 --> 00:29:54,875 Right? 566 00:29:54,875 --> 00:29:57,044 We like plots, when we think about Arrhenius, 567 00:29:57,044 --> 00:29:58,178 because it makes it easier. 568 00:29:58,178 --> 00:30:01,415 We can make it linear, where the slope of this 569 00:30:01,415 --> 00:30:09,323 is minus ea, the slope, minus ea over KB, in this case. 570 00:30:09,323 --> 00:30:09,823 Right? 571 00:30:09,823 --> 00:30:12,026 So we talked about these are all kinds of things 572 00:30:12,026 --> 00:30:13,060 that we talked about. 573 00:30:13,060 --> 00:30:14,862 And finally, getting to this stress-strain, 574 00:30:14,862 --> 00:30:16,697 what if we looked at this? 575 00:30:16,697 --> 00:30:20,000 This is the stress-strain, so now we're here. 576 00:30:20,000 --> 00:30:21,135 We just did this. 577 00:30:21,135 --> 00:30:22,036 We talked about that. 578 00:30:22,036 --> 00:30:24,405 We talked about this, so stress-strain. 579 00:30:24,405 --> 00:30:28,809 So if you were to be given plots like this, you should know 580 00:30:28,809 --> 00:30:30,344 which one is most brittle, which one 581 00:30:30,344 --> 00:30:33,280 is the stiffest, the most resistant to 582 00:30:33,280 --> 00:30:39,119 changing elastically, and which one is the most ductile? 583 00:30:39,119 --> 00:30:41,255 You can see that the stiffest one 584 00:30:41,255 --> 00:30:45,659 is going to be the one that's the most resistant to 585 00:30:45,659 --> 00:30:46,860 elastic deformation. 586 00:30:46,860 --> 00:30:49,330 That's that linear part, that first part. 587 00:30:49,330 --> 00:30:51,532 So there, it's going to be material 588 00:30:51,532 --> 00:30:56,236 A. It's going to be A, because it's got the highest slope. 589 00:30:56,236 --> 00:30:57,304 Right? 590 00:30:57,304 --> 00:30:58,839 OK. 591 00:30:58,839 --> 00:30:59,973 How about the most brittle? 592 00:30:59,973 --> 00:31:03,444 Well, that's the one that's going to break. 593 00:31:03,444 --> 00:31:05,045 So it sort of looks like-- 594 00:31:05,045 --> 00:31:08,449 without deforming, without being able to undergo defamation, 595 00:31:08,449 --> 00:31:10,417 that's brittleness. 596 00:31:10,417 --> 00:31:12,786 It's going to crack before doing anything. 597 00:31:12,786 --> 00:31:13,921 So that's B, right? 598 00:31:13,921 --> 00:31:15,389 That's B. 599 00:31:15,389 --> 00:31:18,325 And then the most ductile will be the one that has the most 600 00:31:18,325 --> 00:31:21,562 plastic deformation, because that's what ductility is, 601 00:31:21,562 --> 00:31:25,165 so that's going to be C. OK? 602 00:31:25,165 --> 00:31:26,667 So remember stress-strain curves. 603 00:31:26,667 --> 00:31:30,270 You've got this elastic part here, that's linear, 604 00:31:30,270 --> 00:31:34,274 and then if it's a material-- not all materials have 605 00:31:34,274 --> 00:31:37,010 plastic defamation. 606 00:31:37,010 --> 00:31:38,912 Some are going to break before they 607 00:31:38,912 --> 00:31:42,950 start deforming plastically, but if it can deform plastically, 608 00:31:42,950 --> 00:31:45,719 then it's going to have that yield point. 609 00:31:45,719 --> 00:31:46,220 Right? 610 00:31:46,220 --> 00:31:49,156 The yield stress, where then it starts becoming non-linear, 611 00:31:49,156 --> 00:31:54,161 and then finally, it fractures somewhere else. 612 00:31:54,161 --> 00:31:54,661 OK? 613 00:31:54,661 --> 00:31:56,930 So those are stress-strain curves. 614 00:31:56,930 --> 00:32:00,334 OK, let's move on. 615 00:32:00,334 --> 00:32:07,941 Now, oh, with the next topic-- 616 00:32:07,941 --> 00:32:11,945 oh boy, I'm going to run out of real estate-- 617 00:32:11,945 --> 00:32:21,054 we've got glasses, and here, the most important thing 618 00:32:21,054 --> 00:32:23,791 to know about is the curve. 619 00:32:23,791 --> 00:32:24,958 That's how it all started. 620 00:32:24,958 --> 00:32:25,459 Right? 621 00:32:25,459 --> 00:32:26,860 I'm calling it The Curve. 622 00:32:26,860 --> 00:32:30,931 Let's go all caps, because it's The Curve, 623 00:32:30,931 --> 00:32:34,101 and what I mean by The Curve is the volume 624 00:32:34,101 --> 00:32:40,474 per mole versus temperature. 625 00:32:40,474 --> 00:32:50,551 We also talked about the effects of cooling rate, 626 00:32:50,551 --> 00:32:59,460 and we also talked about the effects of modifiers, 627 00:32:59,460 --> 00:33:05,933 and in particular how the modifier changes the viscosity 628 00:33:05,933 --> 00:33:08,402 because it cuts the pasta. 629 00:33:08,402 --> 00:33:14,808 OK, so but the framing of these concepts was in The Curve, 630 00:33:14,808 --> 00:33:15,642 and that's this one. 631 00:33:15,642 --> 00:33:17,077 Oh, I have a picture of it. 632 00:33:17,077 --> 00:33:18,745 There it is. 633 00:33:18,745 --> 00:33:21,114 OK, they did specific-- we do volume per mole 634 00:33:21,114 --> 00:33:23,584 is how we're looking at it in this class, so volume per mole 635 00:33:23,584 --> 00:33:25,853 versus temperature. 636 00:33:25,853 --> 00:33:30,824 Now remember, if it's a crystal, where am I going to go? 637 00:33:30,824 --> 00:33:32,392 Let's go here. 638 00:33:32,392 --> 00:33:37,464 If it's a crystal, then you've got one melting point that 639 00:33:37,464 --> 00:33:41,735 only depends on the material. 640 00:33:41,735 --> 00:33:48,175 It only depends on the material, so that melting point is Tm, 641 00:33:48,175 --> 00:33:51,645 and it's going to have a big volume change as it goes 642 00:33:51,645 --> 00:33:55,215 from liquid to crystal solid. 643 00:33:55,215 --> 00:33:56,350 OK? 644 00:33:56,350 --> 00:34:01,722 And so for example, I'm just basically replotting it, 645 00:34:01,722 --> 00:34:04,591 but you would have something like this and something 646 00:34:04,591 --> 00:34:06,860 like this and something like this, 647 00:34:06,860 --> 00:34:10,230 and that's your melting point. 648 00:34:10,230 --> 00:34:13,166 This would be the liquid, and this would be the solid, 649 00:34:13,166 --> 00:34:15,636 and you know that, if it's going to undergo this big volume 650 00:34:15,636 --> 00:34:16,603 change. 651 00:34:16,603 --> 00:34:19,840 Then, it's the melting point and it's a crystal. 652 00:34:19,840 --> 00:34:22,576 But then we say, well, but if it can't find-- 653 00:34:22,576 --> 00:34:26,713 by crystal I mean in opposition to glass, which we know 654 00:34:26,713 --> 00:34:28,482 doesn't just mean your windows. 655 00:34:28,482 --> 00:34:32,351 It means any amorphous material, meaning it's not crystalline. 656 00:34:32,351 --> 00:34:34,888 It didn't find the lattice structure. 657 00:34:34,888 --> 00:34:37,724 Remember those three reasons, the musical chairs? 658 00:34:37,724 --> 00:34:39,560 Whatever you're trying to crystallize, atoms 659 00:34:39,560 --> 00:34:43,563 or molecules, they weren't able to find all the lattice sites, 660 00:34:43,563 --> 00:34:46,199 not even withstanding some defects here. 661 00:34:46,199 --> 00:34:49,303 They simply couldn't do it, and so it's amorphous, 662 00:34:49,303 --> 00:34:50,971 and it's a glass. 663 00:34:50,971 --> 00:34:54,206 And in that case, what happens is it 664 00:34:54,206 --> 00:35:02,583 super cools and then becomes a solid at something 665 00:35:02,583 --> 00:35:04,217 called the glass transition temperature. 666 00:35:04,217 --> 00:35:08,422 Which unlike the crystal can have different values, 667 00:35:08,422 --> 00:35:11,959 and those values can depend on things like the cooling rate. 668 00:35:11,959 --> 00:35:17,631 So if I cool it slower, if I cool it slower-- 669 00:35:17,631 --> 00:35:24,037 remember this is faster, faster, slower, and please, 670 00:35:24,037 --> 00:35:26,506 do not confuse time with this axis. 671 00:35:26,506 --> 00:35:28,175 This is just temperature. 672 00:35:28,175 --> 00:35:30,143 So we can use the same-- 673 00:35:30,143 --> 00:35:35,082 this is volume per mole-- we can use the same The Plot to think 674 00:35:35,082 --> 00:35:37,250 about modifiers as well. 675 00:35:37,250 --> 00:35:41,254 Because it's not-- this is just one plot, one curve 676 00:35:41,254 --> 00:35:42,255 and another. 677 00:35:42,255 --> 00:35:44,124 This happened to be cooled slower, 678 00:35:44,124 --> 00:35:46,960 so it was able to super cool more, 679 00:35:46,960 --> 00:35:49,129 before it locked in the disorder, 680 00:35:49,129 --> 00:35:50,764 and the other one's faster. 681 00:35:50,764 --> 00:35:53,600 You could also imagine if you cut the pasta, 682 00:35:53,600 --> 00:35:56,670 you change the viscosity. 683 00:35:56,670 --> 00:35:58,538 And so now you're changing something else 684 00:35:58,538 --> 00:36:00,674 about the glass using chemistry, and you're 685 00:36:00,674 --> 00:36:04,111 allowing it to find those lattice sites more easily. 686 00:36:04,111 --> 00:36:06,146 You're allowing it to try to become crystalline, 687 00:36:06,146 --> 00:36:08,882 to try to close pack just a little bit more. 688 00:36:08,882 --> 00:36:11,885 So you can also get this, by cutting the pasta you 689 00:36:11,885 --> 00:36:15,288 can get these kinds of changes. 690 00:36:15,288 --> 00:36:19,292 So those are the things we talked about with glass. 691 00:36:19,292 --> 00:36:26,033 Now, next, we talked about reactions. 692 00:36:26,033 --> 00:36:26,533 OK. 693 00:36:34,274 --> 00:36:41,715 What do we need to know about reactions, reaction rates? 694 00:36:41,715 --> 00:36:49,222 So we want to know the order of some general reaction, 695 00:36:49,222 --> 00:36:51,892 like aA plus bB-- 696 00:36:51,892 --> 00:36:55,629 remember this-- goes to cC plus dD. 697 00:36:58,832 --> 00:37:06,907 And we want to know the rate from-- 698 00:37:06,907 --> 00:37:09,609 basically, it's the mass conservation, 699 00:37:09,609 --> 00:37:13,046 so from the coefficients. 700 00:37:13,046 --> 00:37:15,415 OK, so that would be, for example, 701 00:37:15,415 --> 00:37:19,519 like minus 1 over a, d(A), dt-- 702 00:37:19,519 --> 00:37:25,959 that's a rate-- equals minus 1 over b d(B), dt, et cetera. 703 00:37:30,097 --> 00:37:32,165 Now, those come from the coefficients, 704 00:37:32,165 --> 00:37:38,071 but the rate law does not, the rate law does not. 705 00:37:38,071 --> 00:37:40,273 So these are simply instantaneous rates, 706 00:37:40,273 --> 00:37:43,110 but now I say, no, I want a rate law that 707 00:37:43,110 --> 00:37:50,083 gives me the dependence on these concentrations at any time. 708 00:37:53,854 --> 00:38:00,193 So the rate law would be, for example, 709 00:38:00,193 --> 00:38:09,336 like rate equals k times A to the m, B to the n. 710 00:38:09,336 --> 00:38:11,671 Now, here's the thing. 711 00:38:11,671 --> 00:38:16,243 These come from experiments. 712 00:38:21,481 --> 00:38:24,284 Very important distinction, right? 713 00:38:24,284 --> 00:38:27,120 Those come from experiments, and so you 714 00:38:27,120 --> 00:38:29,656 could get the rate with respect to A which would be-- 715 00:38:29,656 --> 00:38:30,257 I'm sorry. 716 00:38:30,257 --> 00:38:33,593 The order with respect to A would be m, 717 00:38:33,593 --> 00:38:35,762 the order with respect to B would be n, 718 00:38:35,762 --> 00:38:38,165 and the overall order of the reaction 719 00:38:38,165 --> 00:38:41,268 is m plus n, the overall order. 720 00:38:44,604 --> 00:38:48,942 And then, we had one more item here of conceptually 721 00:38:48,942 --> 00:38:52,212 what I want you to know about, which is that the rate also 722 00:38:52,212 --> 00:38:54,681 depends on temperature. 723 00:38:54,681 --> 00:38:59,686 Sorry, the rate constant, rate constant 724 00:38:59,686 --> 00:39:02,756 depends on temperature. 725 00:39:02,756 --> 00:39:04,991 So if I were to now say, well, OK, I 726 00:39:04,991 --> 00:39:07,294 want to know something about the order of a reaction, 727 00:39:07,294 --> 00:39:11,064 you might get a table like this, and we did this in class. 728 00:39:11,064 --> 00:39:12,833 You might get a table just like this. 729 00:39:12,833 --> 00:39:13,767 Here's a reaction. 730 00:39:13,767 --> 00:39:18,405 It's W and X and Y, and it goes to Z. 731 00:39:18,405 --> 00:39:21,942 Don't let the fact that you have three reactants throw you off. 732 00:39:21,942 --> 00:39:23,643 You've got a certain number of reactants, 733 00:39:23,643 --> 00:39:27,714 they've got their coefficients, and they go to some product. 734 00:39:27,714 --> 00:39:30,550 And now, you're given experimental data, so 735 00:39:30,550 --> 00:39:33,620 from this data, you can get the order 736 00:39:33,620 --> 00:39:36,823 of the reaction with respect to each one of these. 737 00:39:36,823 --> 00:39:37,757 Right? 738 00:39:37,757 --> 00:39:40,794 And that would then give you, of course, the overall order. 739 00:39:40,794 --> 00:39:41,494 So let's see. 740 00:39:41,494 --> 00:39:47,500 If we were to look at that data, then what would we get? 741 00:39:47,500 --> 00:39:54,808 So what you want to do in these kinds of situations is, 742 00:39:54,808 --> 00:39:57,210 first of all, don't panic. 743 00:39:57,210 --> 00:39:59,813 By the way, on an exam, in general, don't panic, 744 00:39:59,813 --> 00:40:02,015 and if you have a question, you can ask a question, 745 00:40:02,015 --> 00:40:04,985 but also show us what you know. 746 00:40:04,985 --> 00:40:07,888 We will give you-- as you I hope have seen already-- 747 00:40:07,888 --> 00:40:10,657 we will give you as much credit as we can for sharing 748 00:40:10,657 --> 00:40:11,258 what you know. 749 00:40:11,258 --> 00:40:14,794 You don't have to get everything right to get a lot of points. 750 00:40:14,794 --> 00:40:17,931 Please share your knowledge. 751 00:40:17,931 --> 00:40:19,900 So in this case, what would the knowledge be? 752 00:40:19,900 --> 00:40:21,868 Well, it would be that I want to compare stuff, 753 00:40:21,868 --> 00:40:23,370 like trial 1 and 2. 754 00:40:23,370 --> 00:40:27,974 And if I do that, you see, OK, trial 1, trial 2, then two 755 00:40:27,974 --> 00:40:31,111 of them stay constant, but W doubles. 756 00:40:31,111 --> 00:40:32,078 OK? 757 00:40:32,078 --> 00:40:44,090 So comparing 1 versus 2, you got W goes to 2 two times, 758 00:40:44,090 --> 00:40:48,662 but the rate is same, so you know 759 00:40:48,662 --> 00:40:58,471 the order is 0 with respect to W. But if I compare 1 versus 3, 760 00:40:58,471 --> 00:41:04,744 then you know that, let's see, x goes to 3x 761 00:41:04,744 --> 00:41:14,487 and the rate goes to 3x, and so the order is 1. 762 00:41:14,487 --> 00:41:16,623 And then finally, for Y-- 763 00:41:16,623 --> 00:41:18,625 I will just jump to it-- 764 00:41:18,625 --> 00:41:25,398 the order is 2, and you can do that just by find one 765 00:41:25,398 --> 00:41:27,634 where only Y changes. 766 00:41:27,634 --> 00:41:30,303 You don't have to necessarily find one 767 00:41:30,303 --> 00:41:31,638 where just one changes. 768 00:41:31,638 --> 00:41:33,640 Right? 769 00:41:33,640 --> 00:41:37,777 Because if you knew one is first order-- 770 00:41:37,777 --> 00:41:40,280 if you knew one, and then you had another one, and they both 771 00:41:40,280 --> 00:41:40,747 changed. 772 00:41:40,747 --> 00:41:42,148 But maybe the rate didn't change, 773 00:41:42,148 --> 00:41:44,551 then you know they must have both the same order, if they 774 00:41:44,551 --> 00:41:46,186 change in opposite ways. 775 00:41:46,186 --> 00:41:46,853 Right? 776 00:41:46,853 --> 00:41:48,621 So you can get into this in different ways, 777 00:41:48,621 --> 00:41:52,926 just looking at these changes from one to another 778 00:41:52,926 --> 00:41:55,328 and thinking about what must happen 779 00:41:55,328 --> 00:41:56,963 in terms of the rate law, in terms 780 00:41:56,963 --> 00:41:59,032 of what you wrote out here. 781 00:42:02,302 --> 00:42:07,707 But you could also ask questions like with reactions, 782 00:42:07,707 --> 00:42:09,242 OK, this is first order. 783 00:42:09,242 --> 00:42:11,011 What's the dependence of the concentration 784 00:42:11,011 --> 00:42:13,646 over time as a function of the rate constant? 785 00:42:13,646 --> 00:42:18,685 Well, that just goes back to our understanding of the integrated 786 00:42:18,685 --> 00:42:19,919 rate equation. 787 00:42:19,919 --> 00:42:20,653 Right? 788 00:42:20,653 --> 00:42:26,993 And so let's see, oh boy, now I need to find-- 789 00:42:26,993 --> 00:42:28,395 I'm going to go-- 790 00:42:28,395 --> 00:42:30,130 I hate to do this, XRD. 791 00:42:30,130 --> 00:42:38,705 I hate to do this, but sometimes being first carries 792 00:42:38,705 --> 00:42:39,506 a consequence. 793 00:42:42,742 --> 00:42:44,377 OK. 794 00:42:44,377 --> 00:42:45,612 So in this case-- 795 00:42:45,612 --> 00:42:47,514 first of all, by the way, you look at reaction 796 00:42:47,514 --> 00:42:49,749 like that, you're like, well OK, from the coefficients 797 00:42:49,749 --> 00:42:53,420 and the mass balance stuff, you know that the change in oxygen, 798 00:42:53,420 --> 00:42:55,622 for example, with time, the instantaneous 799 00:42:55,622 --> 00:43:03,396 rate would equal minus the change in MO2 with time. 800 00:43:03,396 --> 00:43:05,098 Well, that's not what the question asked. 801 00:43:05,098 --> 00:43:07,567 The question says it's first order. 802 00:43:07,567 --> 00:43:15,775 So that's enough, because this means that if I integrate 803 00:43:15,775 --> 00:43:20,080 the rate law then-- first of all, if it's first order-- 804 00:43:20,080 --> 00:43:25,318 then d of MO2 with respect to time 805 00:43:25,318 --> 00:43:31,558 must equal some constant times the concentration of MO2 806 00:43:31,558 --> 00:43:35,462 to the 1, first order. 807 00:43:35,462 --> 00:43:37,597 And so now, if I integrate this, I 808 00:43:37,597 --> 00:43:40,733 take this concentration over here, I put the dt over there. 809 00:43:40,733 --> 00:43:41,568 You integrate it. 810 00:43:41,568 --> 00:43:43,236 You've got all the integrated rate laws. 811 00:43:43,236 --> 00:43:44,804 We've gone through this already. 812 00:43:44,804 --> 00:43:48,641 You know that you get that the log-- 813 00:43:48,641 --> 00:43:50,310 oh, we do logs-- 814 00:43:50,310 --> 00:43:58,251 are this MO2 equals the log of some starting concentration 815 00:43:58,251 --> 00:44:00,086 minus Kt. 816 00:44:00,086 --> 00:44:02,088 OK? 817 00:44:02,088 --> 00:44:02,856 Why do we do that? 818 00:44:02,856 --> 00:44:05,325 Because we like plotting things, linear things. 819 00:44:05,325 --> 00:44:08,361 We love linear. 820 00:44:08,361 --> 00:44:10,263 So remember, we did this. 821 00:44:10,263 --> 00:44:12,165 We went from these integrated rate 822 00:44:12,165 --> 00:44:14,400 laws to plots and back and forth, 823 00:44:14,400 --> 00:44:17,036 and so that's also very important. 824 00:44:17,036 --> 00:44:18,304 OK. 825 00:44:18,304 --> 00:44:22,408 Now finally, so the last couple of things. 826 00:44:22,408 --> 00:44:25,545 And I'm purposely giving these last ones a little less time, 827 00:44:25,545 --> 00:44:28,181 because they're the ones that we've seen very recently, 828 00:44:28,181 --> 00:44:29,749 and these are the ones that we haven't 829 00:44:29,749 --> 00:44:31,885 seen for almost a month. 830 00:44:31,885 --> 00:44:33,520 Right? 831 00:44:33,520 --> 00:44:38,658 Yeah, but you still gotta know about solubility, 832 00:44:38,658 --> 00:44:42,162 and so for solubility, remember what we did is we did 833 00:44:42,162 --> 00:44:50,904 equilibrium and Le Chatelier, and we did the equilibrium 834 00:44:50,904 --> 00:44:54,040 constants, the K's. 835 00:44:54,040 --> 00:44:59,012 Like for example, Ksp is the solubility product, 836 00:44:59,012 --> 00:45:02,182 solubility product constant. 837 00:45:02,182 --> 00:45:03,383 Right? 838 00:45:03,383 --> 00:45:09,756 And then we also did ice tables, and then we 839 00:45:09,756 --> 00:45:11,124 talked about the common ion. 840 00:45:16,296 --> 00:45:18,765 And so as an example, if I were to tell you, 841 00:45:18,765 --> 00:45:21,568 well, OK, I'm going to take BaCl2. 842 00:45:21,568 --> 00:45:23,603 I might have done this one in class already. 843 00:45:23,603 --> 00:45:27,173 If I add BaCl2 to a saturated solution of BaSO4, 844 00:45:27,173 --> 00:45:31,110 why does it cause precipitation? 845 00:45:31,110 --> 00:45:32,779 Answer-- because of the common ion 846 00:45:32,779 --> 00:45:36,216 effect, but you could write these out. 847 00:45:36,216 --> 00:45:39,552 So you write out your saturated solution, 848 00:45:39,552 --> 00:45:43,122 so you write out your BaSO4, and you 849 00:45:43,122 --> 00:45:54,033 see that BaSO4 solid will go to Ba2 plus in solution 850 00:45:54,033 --> 00:45:57,937 plus SO4 2 minus in solution. 851 00:45:57,937 --> 00:46:00,773 And so the common ion effect tells you 852 00:46:00,773 --> 00:46:04,744 that if I now add something else that has something in common 853 00:46:04,744 --> 00:46:07,981 with one of these, that gives me an ion in common, 854 00:46:07,981 --> 00:46:09,482 then because of Le Chatelier, you're 855 00:46:09,482 --> 00:46:12,518 going to drive the reaction the other way. 856 00:46:12,518 --> 00:46:14,954 That precipitates, because it forms a solid BaSO4. 857 00:46:14,954 --> 00:46:15,888 So I've just done that. 858 00:46:15,888 --> 00:46:16,389 Right? 859 00:46:16,389 --> 00:46:20,226 I've given you BaCl2 which gives you a source of Ba2 plus, 860 00:46:20,226 --> 00:46:21,761 and how do you figure out if you were 861 00:46:21,761 --> 00:46:26,866 given amounts what happens, what the new equilibrium is? 862 00:46:26,866 --> 00:46:27,967 You use ICE. 863 00:46:27,967 --> 00:46:28,468 Right? 864 00:46:28,468 --> 00:46:31,471 You use the ICE tables. 865 00:46:31,471 --> 00:46:32,572 OK. 866 00:46:32,572 --> 00:46:38,211 And then finally, we talked about acids and bases. 867 00:46:38,211 --> 00:46:44,584 Oh, I really hate to erase defects, but here we go. 868 00:46:44,584 --> 00:46:45,518 Defects are gone. 869 00:46:45,518 --> 00:46:48,021 Arrhenius, I'm so sorry. 870 00:46:48,021 --> 00:46:50,056 That was painful. 871 00:46:50,056 --> 00:46:54,727 And the last topic here is acids and bases, 872 00:46:54,727 --> 00:47:02,168 and this is the most recent one, and so what do we have? 873 00:47:02,168 --> 00:47:06,906 Well, got the acid equilibrium constant, the base. 874 00:47:06,906 --> 00:47:09,375 We did water. 875 00:47:09,375 --> 00:47:10,977 We did pH. 876 00:47:10,977 --> 00:47:13,246 Oh, we did p anything. 877 00:47:13,246 --> 00:47:13,846 Right? 878 00:47:13,846 --> 00:47:19,886 p equals negative log of the thing, pKa, pKb. 879 00:47:23,056 --> 00:47:28,361 OK, and then we did, like for example, the definitions, 880 00:47:28,361 --> 00:47:37,103 so Arrhenius versus Bronsted-Lowry definitions. 881 00:47:37,103 --> 00:47:40,840 And so for example, if you're given a solution-- this is one, 882 00:47:40,840 --> 00:47:44,911 just a simple example of an acid-- 883 00:47:44,911 --> 00:47:46,913 and it's HOCN, and you're given the acid. 884 00:47:46,913 --> 00:47:50,116 And you know the pH, so you're given that. 885 00:47:50,116 --> 00:47:56,155 Then the pH from that information you can get that 886 00:47:56,155 --> 00:48:00,460 the concentration of H plus-- which is also a H3O plus-- 887 00:48:00,460 --> 00:48:06,265 is 1.7 times 10 to the minus 3 moles per liter. 888 00:48:06,265 --> 00:48:12,138 That's from the pH, and if you have that, 889 00:48:12,138 --> 00:48:17,243 then you can go to the Ka definition, which 890 00:48:17,243 --> 00:48:26,386 is H plus concentration OCN minus divided by the acid HOCN 891 00:48:26,386 --> 00:48:28,921 concentration, and you've got it all. 892 00:48:28,921 --> 00:48:32,759 Because if you're right the equilibrium equation, which 893 00:48:32,759 --> 00:48:38,331 is what Ka describes, the equilibrium of this acid 894 00:48:38,331 --> 00:48:42,368 dissociating into ions, dissociating 895 00:48:42,368 --> 00:48:45,338 into H plus and OCN minus, and so you can get Ka. 896 00:48:45,338 --> 00:48:45,838 OK. 897 00:48:45,838 --> 00:48:48,408 So what I hope is that this got us in the mood, 898 00:48:48,408 --> 00:48:50,943 that this got us all kind of on the right page with respect 899 00:48:50,943 --> 00:48:51,644 to these topics. 900 00:48:51,644 --> 00:48:53,012 You've got two days.