1 00:00:00,030 --> 00:00:02,400 SPEAKER: The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,830 Commons License. 3 00:00:03,830 --> 00:00:06,840 Your support will help MIT OpenCourseWare continue to 4 00:00:06,840 --> 00:00:10,510 offer high-quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,490 hundreds of MIT courses visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:21,410 --> 00:00:21,960 PROFESSOR: OK. 9 00:00:21,960 --> 00:00:22,220 OK. 10 00:00:22,220 --> 00:00:23,890 Settle down. 11 00:00:23,890 --> 00:00:25,680 Settle down. 12 00:00:25,680 --> 00:00:26,450 Settle down. 13 00:00:26,450 --> 00:00:32,940 So the weekend doesn't begin until after the 3.091 lecture. 14 00:00:32,940 --> 00:00:33,270 OK. 15 00:00:33,270 --> 00:00:34,240 A couple of announcements. 16 00:00:34,240 --> 00:00:38,110 Tuesday, Quiz 3 based on Homework 3. 17 00:00:38,110 --> 00:00:41,260 The final exam has been scheduled. 18 00:00:41,260 --> 00:00:45,080 In fact, all the finals are scheduled now, so please 19 00:00:45,080 --> 00:00:47,990 consult the Registrar's listing. 20 00:00:47,990 --> 00:00:51,260 The celebration of celebrations, the 3.091 final 21 00:00:51,260 --> 00:00:55,430 exam, will be Tuesday, 15th of December in the morning, 9:00 22 00:00:55,430 --> 00:00:59,190 am to 12:00 noon over in the Johnson Athletic Center. 23 00:00:59,190 --> 00:01:03,640 So I urge you to go through the final exam schedule and 24 00:01:03,640 --> 00:01:06,810 then make your travel plans when you know what your last 25 00:01:06,810 --> 00:01:07,630 obligation is. 26 00:01:07,630 --> 00:01:11,010 And book them soon, because we've got about a quarter of a 27 00:01:11,010 --> 00:01:15,660 million students in the Boston area and the semesters all 28 00:01:15,660 --> 00:01:18,550 come to a close within a very narrow time window, and 29 00:01:18,550 --> 00:01:21,030 everybody's trying to get through a wormhole called 30 00:01:21,030 --> 00:01:22,060 Logan Airport. 31 00:01:22,060 --> 00:01:24,950 So you want to be ready. 32 00:01:24,950 --> 00:01:27,290 Do not try to leave town before you've met all of your 33 00:01:27,290 --> 00:01:27,940 obligations. 34 00:01:27,940 --> 00:01:30,160 You can't leave before you've finished all of your finals. 35 00:01:30,160 --> 00:01:35,620 But you know what they are now, so call your travel agent 36 00:01:35,620 --> 00:01:36,870 or make your internet booking. 37 00:01:36,870 --> 00:01:41,890 And an announcement for Professor Paul's section. 38 00:01:41,890 --> 00:01:44,280 Owing to the holiday on Monday, he's going to have 39 00:01:44,280 --> 00:01:47,910 office hours from noon to 1:30 today. 40 00:01:47,910 --> 00:01:50,620 So if you're in Professor Paul's section, you'd like to 41 00:01:50,620 --> 00:01:54,470 catch up with him, noon till 1:30 today. 42 00:01:54,470 --> 00:01:54,800 All right. 43 00:01:54,800 --> 00:01:56,210 Let's get to the lesson. 44 00:01:56,210 --> 00:02:00,070 The last day we started looking at octet stability, 45 00:02:00,070 --> 00:02:04,450 and we looked at octet stability and what it means in 46 00:02:04,450 --> 00:02:09,940 terms of shell filling and some sweet spot in energy with 47 00:02:09,940 --> 00:02:12,420 respect to reactivity. 48 00:02:12,420 --> 00:02:16,200 And a filled shell leaves us with this electron 49 00:02:16,200 --> 00:02:20,290 configuration, ns2np6 for n greater than 1. 50 00:02:20,290 --> 00:02:24,480 In the case of n equals 1, there's just ns2 for helium. 51 00:02:24,480 --> 00:02:26,420 Otherwise, ns2np6. 52 00:02:26,420 --> 00:02:27,400 2 plus 6 is 8. 53 00:02:27,400 --> 00:02:29,160 There's the octet stability. 54 00:02:29,160 --> 00:02:32,070 It's observed trivially in noble gases. 55 00:02:32,070 --> 00:02:34,250 And then we saw that it can also be 56 00:02:34,250 --> 00:02:36,350 observed in certain ions. 57 00:02:36,350 --> 00:02:39,110 And how do we get to octet stability? 58 00:02:39,110 --> 00:02:40,330 Electron transfer. 59 00:02:40,330 --> 00:02:42,350 And here's the prototypical reaction. 60 00:02:42,350 --> 00:02:43,150 I like this. 61 00:02:43,150 --> 00:02:44,750 This is very iconic. 62 00:02:44,750 --> 00:02:49,850 It puts it in broad terms. The marriage of an electron donor 63 00:02:49,850 --> 00:02:53,640 with an electron acceptor leads to the formation of a 64 00:02:53,640 --> 00:02:57,120 cation and an anion, thanks to electron transfer from the 65 00:02:57,120 --> 00:03:00,400 donor to the acceptor. 66 00:03:00,400 --> 00:03:01,430 It doesn't end there, though. 67 00:03:01,430 --> 00:03:04,720 You have cations and anions in the gas phase and they're 68 00:03:04,720 --> 00:03:07,990 attracted to one another by coulombic forces, or 69 00:03:07,990 --> 00:03:12,050 electrostatic forces, and that leads to ionic bonding. 70 00:03:12,050 --> 00:03:15,560 And today I want to go deeper into it and study the 71 00:03:15,560 --> 00:03:18,370 energetics of ion-pair formation. 72 00:03:18,370 --> 00:03:20,100 So let's do it. 73 00:03:20,100 --> 00:03:24,810 And what I'm going to do is study this with reference to 74 00:03:24,810 --> 00:03:27,530 an example of sodium chloride. 75 00:03:27,530 --> 00:03:36,520 So we will go through the energetics of sodium chloride, 76 00:03:36,520 --> 00:03:38,290 which we know is going to exist as 77 00:03:38,290 --> 00:03:40,550 Na plus and Cl minus-- 78 00:03:40,550 --> 00:03:44,350 sodium being the electron donor and chlorine being the 79 00:03:44,350 --> 00:03:45,430 electron acceptor. 80 00:03:45,430 --> 00:03:49,500 So what I'm going to do is show you a plot of energy as a 81 00:03:49,500 --> 00:03:51,200 function of separation. 82 00:03:51,200 --> 00:03:55,570 So you're going to have to be pluralistic 83 00:03:55,570 --> 00:03:56,650 here in your ideas. 84 00:03:56,650 --> 00:03:59,780 So, for example, if I wrote this word by itself you don't 85 00:03:59,780 --> 00:04:03,760 know if I'm saying lead or I'm talking about the metal lead. 86 00:04:03,760 --> 00:04:05,920 The only way you know is in context. 87 00:04:05,920 --> 00:04:07,450 And so you have to know in context here. 88 00:04:07,450 --> 00:04:10,720 So r is not the radius of the atom. 89 00:04:10,720 --> 00:04:12,730 In this case it's the symbol. 90 00:04:12,730 --> 00:04:14,580 And I'm using this symbol not to confuse you. 91 00:04:14,580 --> 00:04:16,080 This is what professionals use. 92 00:04:16,080 --> 00:04:19,170 So if you go to the text and the literature you'll see r. 93 00:04:19,170 --> 00:04:26,220 This is the interionic separation, and it's 94 00:04:26,220 --> 00:04:30,170 determined nucleus to nucleus. 95 00:04:30,170 --> 00:04:35,920 So I'm going to put a sodium ion at the origin. 96 00:04:35,920 --> 00:04:36,940 This is the origin. 97 00:04:36,940 --> 00:04:40,140 Energy is on the ordinate. 98 00:04:40,140 --> 00:04:42,725 So I'm going to model this as a hard sphere. 99 00:04:42,725 --> 00:04:47,210 So this is sodium ion, Na plus, and it's 100 00:04:47,210 --> 00:04:49,780 got some finite radius. 101 00:04:49,780 --> 00:04:52,750 And its radius, I'm going to call it r-plus. 102 00:04:52,750 --> 00:04:54,660 That's the radius of the cation. 103 00:04:54,660 --> 00:04:58,530 And next to sodium I'm going to put the chloride anion. 104 00:04:58,530 --> 00:05:01,170 And it's bigger. 105 00:05:01,170 --> 00:05:02,650 It's bigger. 106 00:05:02,650 --> 00:05:04,130 It's not to scale, but it's bigger. 107 00:05:04,130 --> 00:05:08,200 So this is chloride, the Cl minus, and it has 108 00:05:08,200 --> 00:05:13,440 its radius, rCL minus. 109 00:05:13,440 --> 00:05:18,050 And then the interionic separation is measured from 110 00:05:18,050 --> 00:05:21,670 the sodium nucleus to the chloride nucleus, and it's 111 00:05:21,670 --> 00:05:22,920 given the symbol r0. 112 00:05:25,500 --> 00:05:27,370 That's the interionic separation. 113 00:05:27,370 --> 00:05:34,460 And we could we write that r0, in fact, is strictly r-plus 114 00:05:34,460 --> 00:05:37,020 plus r-minus because we're using a hard sphere model. 115 00:05:37,020 --> 00:05:40,490 So there's no shrinkage when the two touch. 116 00:05:40,490 --> 00:05:41,300 So that makes sense. 117 00:05:41,300 --> 00:05:44,040 Now what I want to do is calculate the energy here. 118 00:05:44,040 --> 00:05:47,030 The only energy that we have here is electrostatic. 119 00:05:47,030 --> 00:05:49,320 So we're going to start and say, imagine if we had these 120 00:05:49,320 --> 00:05:53,890 two ions separated by infinite distance and we brought them 121 00:05:53,890 --> 00:05:56,410 to a separation of r0. 122 00:05:56,410 --> 00:05:59,510 How much electrostatic energy would be stored there? 123 00:05:59,510 --> 00:06:04,680 So I can write that as E, and I'm going to call it 124 00:06:04,680 --> 00:06:05,300 attractive. 125 00:06:05,300 --> 00:06:09,280 There's a force that attracts these two ions together, and 126 00:06:09,280 --> 00:06:11,540 that's given by Coulomb's Law. 127 00:06:11,540 --> 00:06:16,940 So that's the product q1 q2 over 4 pi 128 00:06:16,940 --> 00:06:20,940 epsilon0r, in general. 129 00:06:20,940 --> 00:06:23,670 I'm making this as a function of r and then we're going to 130 00:06:23,670 --> 00:06:24,920 figure out how to get to r0. 131 00:06:27,820 --> 00:06:29,710 Let's put a little ledge in here. 132 00:06:29,710 --> 00:06:32,890 So q1, I'm going to make that the sodium just 133 00:06:32,890 --> 00:06:33,860 for grins and chuckles. 134 00:06:33,860 --> 00:06:43,090 So q1 is equal to the z, the valence on the sodium, times 135 00:06:43,090 --> 00:06:44,900 the charge, the elementary charge. 136 00:06:44,900 --> 00:06:48,960 So the charge on the sodium is plus 1-- so it's plus 1e-- 137 00:06:48,960 --> 00:06:52,220 and q2 is going to equal the charge on the 138 00:06:52,220 --> 00:06:54,120 chloride times e. 139 00:06:54,120 --> 00:06:57,620 And in this case the chloride ion is negative 1, so q2 is 140 00:06:57,620 --> 00:06:59,720 minus e, q1 is plus e. 141 00:06:59,720 --> 00:07:02,720 Now if instead I were doing magnesium oxide, magnesium 142 00:07:02,720 --> 00:07:06,760 would be plus 2, oxide would be minus 2. 143 00:07:06,760 --> 00:07:10,940 So that's where the charge on the ion comes into play. 144 00:07:10,940 --> 00:07:16,350 So we can put that in here and will make this z-plus times e, 145 00:07:16,350 --> 00:07:18,520 z-minus times e. 146 00:07:18,520 --> 00:07:23,870 So there's q1 q2 over 4 pi epsilon0 r. 147 00:07:23,870 --> 00:07:28,910 And in this case, for sodium chloride, this is plus 1 times 148 00:07:28,910 --> 00:07:36,640 minus 1 is minus 1 e squared over 4 pi epsilon0 r. 149 00:07:36,640 --> 00:07:38,300 So this is a function of r. 150 00:07:38,300 --> 00:07:39,950 This e is 1/r. 151 00:07:39,950 --> 00:07:45,450 That's the hyperbole, and I can draw that here. 152 00:07:45,450 --> 00:07:47,690 So it's going to look something like this. 153 00:07:47,690 --> 00:07:48,600 All right? 154 00:07:48,600 --> 00:07:53,400 It's going to be a right like this. 155 00:07:53,400 --> 00:07:53,890 Good. 156 00:07:53,890 --> 00:07:57,540 So that's the attractive force. 157 00:07:57,540 --> 00:08:03,490 Now how do we avoid the ions just blending together? 158 00:08:03,490 --> 00:08:05,150 Why do they stop at r0? 159 00:08:05,150 --> 00:08:08,180 What puts the brakes on the coulombic force? 160 00:08:08,180 --> 00:08:08,460 Ah! 161 00:08:08,460 --> 00:08:11,790 For that we have to look at the fine structure of sodium. 162 00:08:11,790 --> 00:08:14,580 So let's look at the fine structure of sodium. 163 00:08:14,580 --> 00:08:17,750 So sodium is net charge plus 1. 164 00:08:17,750 --> 00:08:20,960 But sodium more properly, if I go to the next level of 165 00:08:20,960 --> 00:08:25,310 structure, is really 11 protons in the nucleus and 166 00:08:25,310 --> 00:08:28,300 it's got electrons around it-- 167 00:08:28,300 --> 00:08:30,520 in total, 10 electrons. 168 00:08:30,520 --> 00:08:35,610 So it's net charge is plus 1, all right? 169 00:08:35,610 --> 00:08:41,680 Now if I'm way over here and I look at sodium I just see 170 00:08:41,680 --> 00:08:43,980 something of charge plus 1. 171 00:08:43,980 --> 00:08:48,640 And, in fact, I could model sodium as just a point charge, 172 00:08:48,640 --> 00:08:52,060 a plus 1, and do all the electrostatics and I would be 173 00:08:52,060 --> 00:08:55,010 perfectly accurate in my estimation. 174 00:08:55,010 --> 00:08:59,450 But as I get closer I see there's fine structure. 175 00:08:59,450 --> 00:09:00,780 It's like so many other things in life. 176 00:09:00,780 --> 00:09:02,885 You know, from a distance it looks really good, and you get 177 00:09:02,885 --> 00:09:05,190 up close you go, eww. 178 00:09:05,190 --> 00:09:06,360 [LAUGHTER] 179 00:09:06,360 --> 00:09:07,960 PROFESSOR: I'm not going to mention any names, all right? 180 00:09:07,960 --> 00:09:10,380 But it's Friday. 181 00:09:10,380 --> 00:09:10,920 Be careful. 182 00:09:10,920 --> 00:09:16,150 So as I get up closer I realize that it's plus 1, but 183 00:09:16,150 --> 00:09:21,660 the plus 1 is plus 11 mediated by minus 10. 184 00:09:21,660 --> 00:09:26,710 So when things start getting close together this exterior 185 00:09:26,710 --> 00:09:30,350 of negative charge becomes manifest, palpable. 186 00:09:30,350 --> 00:09:32,090 So let's look at the chlorine. 187 00:09:32,090 --> 00:09:34,660 The chlorine's coming, sees plus 1, plus 1. 188 00:09:34,660 --> 00:09:36,180 It starts getting closer and closer. 189 00:09:36,180 --> 00:09:37,680 And now what happens? 190 00:09:37,680 --> 00:09:41,360 The negative electronic configuration on the outside 191 00:09:41,360 --> 00:09:45,190 of sodium is interacting with the negative electronic 192 00:09:45,190 --> 00:09:48,270 configuration on chlorine, and the result is you have 193 00:09:48,270 --> 00:09:50,540 electron-electron repulsion. 194 00:09:50,540 --> 00:09:55,200 And we've got an equation for that, and that's given by E 195 00:09:55,200 --> 00:10:02,240 repulsion is equal to some constant b over r to the n. 196 00:10:02,240 --> 00:10:07,890 And this n is called the Born exponent. 197 00:10:07,890 --> 00:10:09,630 It's not the quantum number. 198 00:10:09,630 --> 00:10:12,680 So r today means interionic separation, 199 00:10:12,680 --> 00:10:14,450 n means Born exponent. 200 00:10:14,450 --> 00:10:17,800 And you have to determine it by experiment and the value 201 00:10:17,800 --> 00:10:22,760 lies between 6 and 12. 202 00:10:22,760 --> 00:10:25,210 And we have to determine b by experiment. 203 00:10:25,210 --> 00:10:26,750 So let's say this thing's got a-- pick a 204 00:10:26,750 --> 00:10:27,410 number in the middle. 205 00:10:27,410 --> 00:10:29,520 Say it's 8. 206 00:10:29,520 --> 00:10:33,610 So let's plot r to the eighth. 207 00:10:33,610 --> 00:10:37,680 So that's going to hug the abscissa, and it's going to 208 00:10:37,680 --> 00:10:39,890 come in really, really close. 209 00:10:39,890 --> 00:10:44,570 And then somewhere around this distance here, where the 210 00:10:44,570 --> 00:10:47,580 electron-electron repulsion starts to be felt, 211 00:10:47,580 --> 00:10:49,000 this thing takes off. 212 00:10:49,000 --> 00:10:52,870 But 1 over r to the 8 goes way, way up fast. So instead 213 00:10:52,870 --> 00:10:54,890 of being a gentle curve it's more like a 214 00:10:54,890 --> 00:10:56,900 hockey stick shape here. 215 00:10:56,900 --> 00:11:00,770 And so now the net energy is the sum of the negative 216 00:11:00,770 --> 00:11:04,080 attractive energy and the positive repulsive energy. 217 00:11:04,080 --> 00:11:08,840 And if we sum the two what are we going to get? 218 00:11:08,840 --> 00:11:12,780 Well, way out here 1 over r to the 8 is negligible. 219 00:11:12,780 --> 00:11:14,550 And the net value-- 220 00:11:14,550 --> 00:11:17,960 so E net, in red-- 221 00:11:17,960 --> 00:11:20,430 is essentially equal to E attractive. 222 00:11:20,430 --> 00:11:25,820 And at very, very low values of r, r to the 8 dominates r. 223 00:11:25,820 --> 00:11:28,770 So we have this as the net value. 224 00:11:28,770 --> 00:11:30,840 And the two sum-- 225 00:11:30,840 --> 00:11:33,650 and I can't quite do it because of the way this is 226 00:11:33,650 --> 00:11:35,460 drawn, but I think you can see. 227 00:11:35,460 --> 00:11:38,780 These two eventually equilibrate and 228 00:11:38,780 --> 00:11:39,850 go through a minimum. 229 00:11:39,850 --> 00:11:42,410 So I'm going to cheat a little bit here and I'm going to add 230 00:11:42,410 --> 00:11:45,900 these two in such a way as to go through a minimum value of 231 00:11:45,900 --> 00:11:50,790 energy at r equals r0, which is the sum of E attractive and 232 00:11:50,790 --> 00:11:52,500 E repulsive. 233 00:11:52,500 --> 00:12:00,730 So we can sum those two and let's see what we get. 234 00:12:00,730 --> 00:12:12,980 At r equals r0, E net is equal to its minimum value. 235 00:12:12,980 --> 00:12:15,070 So how do you find a minimum in a function? 236 00:12:15,070 --> 00:12:16,650 You take the derivative. 237 00:12:16,650 --> 00:12:18,180 I'm going to put some math to work here. 238 00:12:18,180 --> 00:12:23,890 So we'll take dE by dr and set it equal to 0. 239 00:12:23,890 --> 00:12:30,820 And the value of r at which it equals 0 is termed r0. 240 00:12:30,820 --> 00:12:31,500 OK? 241 00:12:31,500 --> 00:12:34,020 So we'll just go through and take the 242 00:12:34,020 --> 00:12:35,450 derivative of that thing. 243 00:12:35,450 --> 00:12:37,940 And I'm not going to go through all the math but just 244 00:12:37,940 --> 00:12:39,120 show you the set-up here. 245 00:12:39,120 --> 00:12:40,830 What's the other thing that we know? 246 00:12:40,830 --> 00:12:43,200 dE by dr represents what? 247 00:12:43,200 --> 00:12:44,700 That's force. 248 00:12:44,700 --> 00:12:50,520 So I could say that at r equals r0 the net force is 0, 249 00:12:50,520 --> 00:12:51,540 which is what you'd expect. 250 00:12:51,540 --> 00:12:54,390 Because if the net force isn't 0 it's going to either push 251 00:12:54,390 --> 00:12:57,240 the ions farther apart or draw them closer together. 252 00:12:57,240 --> 00:13:00,060 So this is mathematics imitating reality. 253 00:13:00,060 --> 00:13:01,300 What a concept. 254 00:13:01,300 --> 00:13:04,610 Math working for you instead of you working for math. 255 00:13:04,610 --> 00:13:06,070 So what do I have? 256 00:13:06,070 --> 00:13:08,270 I have everything in these equations except 257 00:13:08,270 --> 00:13:09,540 the value of b. 258 00:13:09,540 --> 00:13:12,400 I'm assuming we know the value of n from experiment. 259 00:13:12,400 --> 00:13:13,860 We don't know the value of b. 260 00:13:13,860 --> 00:13:20,420 And so you can solve to get the value of b, and once 261 00:13:20,420 --> 00:13:23,500 you've got that you can put everything together and give 262 00:13:23,500 --> 00:13:28,350 an expression for the energy of the system at r equals r0. 263 00:13:28,350 --> 00:13:32,920 When you plug everything in you get this: z-plus, which is 264 00:13:32,920 --> 00:13:36,465 the net charge on the cation, times z-minus, which is the 265 00:13:36,465 --> 00:13:42,890 net charge on anion, divided by 4 pi epsilon0 r0. 266 00:13:42,890 --> 00:13:47,310 1 minus 1/n, where n is the Born exponent. 267 00:13:47,310 --> 00:13:50,060 And this is valid at r equals r0 only. 268 00:13:54,870 --> 00:13:58,850 If you're not at r equals r0 then you can get the value of 269 00:13:58,850 --> 00:14:02,460 b and then put it into this expression, where E net will 270 00:14:02,460 --> 00:14:05,630 equal E attractive plus E repulsive. 271 00:14:05,630 --> 00:14:06,890 So there it is. 272 00:14:06,890 --> 00:14:08,150 And so this represents-- 273 00:14:08,150 --> 00:14:16,370 this is the energy of a single ionic bond, because that's all 274 00:14:16,370 --> 00:14:17,320 the energy that's there. 275 00:14:17,320 --> 00:14:18,840 It's the single ionic bond. 276 00:14:18,840 --> 00:14:25,360 And the second thing that we realize is plus times minus is 277 00:14:25,360 --> 00:14:29,080 net minus, so this means that it's negative quantity, 278 00:14:29,080 --> 00:14:29,980 as it should be. 279 00:14:29,980 --> 00:14:32,790 It has to be a negative quantity. 280 00:14:32,790 --> 00:14:33,080 All right. 281 00:14:33,080 --> 00:14:34,020 So what do we have here? 282 00:14:34,020 --> 00:14:36,800 What we've seen by going through this derivation is the 283 00:14:36,800 --> 00:14:42,880 recognition that the ionic bond is electrostatic 284 00:14:42,880 --> 00:14:46,980 attraction mediated by electronic repulsion. 285 00:14:46,980 --> 00:14:48,800 It's the balance of the two. 286 00:14:48,800 --> 00:14:50,745 And those words sound so good to me that I'm going 287 00:14:50,745 --> 00:14:52,070 to write them down. 288 00:14:52,070 --> 00:14:59,140 Electrostatic attraction mediated-- 289 00:14:59,140 --> 00:15:00,420 another lovely word-- 290 00:15:00,420 --> 00:15:06,170 mediated by electronic repulsion. 291 00:15:10,750 --> 00:15:16,040 So that's how you get to the final setting here of the 292 00:15:16,040 --> 00:15:18,410 interionic separation. 293 00:15:18,410 --> 00:15:20,110 So what are the characteristics? 294 00:15:20,110 --> 00:15:22,380 What does this lead to in terms of 295 00:15:22,380 --> 00:15:25,280 characteristics of this bond? 296 00:15:25,280 --> 00:15:31,020 Characteristics of the ionic bond. 297 00:15:31,020 --> 00:15:32,750 First of all, it's omnidirectional. 298 00:15:39,100 --> 00:15:41,270 This is a concept based on the fact that the electric field 299 00:15:41,270 --> 00:15:43,950 radiates in all directions uniformly. 300 00:15:43,950 --> 00:15:48,060 So the negative field coming from the chloride ion is 301 00:15:48,060 --> 00:15:49,630 uniform in all directions. 302 00:15:49,630 --> 00:15:52,200 There's no preferred direction. 303 00:15:52,200 --> 00:15:53,660 Omnidirectional. 304 00:15:53,660 --> 00:15:54,470 OK? 305 00:15:54,470 --> 00:15:56,160 E field-- 306 00:15:56,160 --> 00:15:57,170 oh, I better not say that. 307 00:15:57,170 --> 00:16:07,230 Electric field, not the energy field, radiates in all 308 00:16:07,230 --> 00:16:10,380 directions uniformly. 309 00:16:17,740 --> 00:16:19,180 And that's going to have consequences. 310 00:16:19,180 --> 00:16:20,640 I'm not just telling you this because we 311 00:16:20,640 --> 00:16:22,600 like cataloguing things. 312 00:16:22,600 --> 00:16:25,070 This isn't a bookkeeping class. 313 00:16:25,070 --> 00:16:27,820 So we're going to come back, use this fact. 314 00:16:27,820 --> 00:16:33,720 And the second thing is that the bond is unsaturated, which 315 00:16:33,720 --> 00:16:38,110 is a chemical way of saying that a given ion can bond to 316 00:16:38,110 --> 00:16:40,510 more than one other ion. 317 00:16:40,510 --> 00:16:43,430 In other types of bonds that's not the case. 318 00:16:43,430 --> 00:16:47,430 A given atom can only bond once and then it's done. 319 00:16:47,430 --> 00:16:52,050 Whereas in this case the ion can bond to a plurality of 320 00:16:52,050 --> 00:16:53,240 other ions. 321 00:16:53,240 --> 00:16:58,440 So ions bond to more than one. 322 00:17:02,460 --> 00:17:03,000 OK? 323 00:17:03,000 --> 00:17:05,560 Plurality of bonds is formed. 324 00:17:05,560 --> 00:17:09,300 They're polygamous, if you like. 325 00:17:09,300 --> 00:17:11,000 So what does that mean? 326 00:17:11,000 --> 00:17:14,270 That means that here is what happens. 327 00:17:14,270 --> 00:17:17,600 We've got the blues as the sodiums, and for any given 328 00:17:17,600 --> 00:17:22,240 sodium it forms bonds without limit until the number of 329 00:17:22,240 --> 00:17:27,800 bonds is stopped by physical limitations-- 330 00:17:27,800 --> 00:17:30,020 not because the E field was saturated. 331 00:17:30,020 --> 00:17:31,310 It's unsaturated. 332 00:17:31,310 --> 00:17:35,140 You just can't jam any more chlorides physically around 333 00:17:35,140 --> 00:17:35,740 the sodium. 334 00:17:35,740 --> 00:17:38,930 That's why the sodium is only bonding to the number of 335 00:17:38,930 --> 00:17:40,205 chlorides that it bonds to. 336 00:17:40,205 --> 00:17:42,605 There's no intrinsic limitation. 337 00:17:46,930 --> 00:17:51,140 So what happens when you get to this situation where you 338 00:17:51,140 --> 00:17:56,090 have omnidirectional forces, unsaturated bonds, and ions 339 00:17:56,090 --> 00:18:00,280 that you can model as hard spheres of constant radius? 340 00:18:00,280 --> 00:18:03,190 All the sodiums have the same radius, all the chlorides have 341 00:18:03,190 --> 00:18:03,950 the same radius. 342 00:18:03,950 --> 00:18:08,270 You make a 3-dimensional ordered array. 343 00:18:08,270 --> 00:18:19,500 So you can make an infinite atomic ordered array, which we 344 00:18:19,500 --> 00:18:21,650 use the simple Anglo-Saxon word last day 345 00:18:21,650 --> 00:18:23,145 to describe: crystal. 346 00:18:23,145 --> 00:18:25,670 You form a crystal. 347 00:18:25,670 --> 00:18:33,650 And as a result ionics have to be solid at room temperature, 348 00:18:33,650 --> 00:18:38,240 because if you've got thousands and thousands of 349 00:18:38,240 --> 00:18:40,490 atoms together in one aggregate they're 350 00:18:40,490 --> 00:18:41,560 not going to float. 351 00:18:41,560 --> 00:18:42,980 They're going to settle. 352 00:18:42,980 --> 00:18:45,690 Put another way, the strength of the bond, the amount of 353 00:18:45,690 --> 00:18:48,900 energy in here, is so great that the thermal energy of the 354 00:18:48,900 --> 00:18:52,763 room isn't great enough to disrupt this bond. 355 00:18:52,763 --> 00:18:57,420 It's a combination of unsaturated, omnidirectional, 356 00:18:57,420 --> 00:18:59,310 and high energy. 357 00:18:59,310 --> 00:19:02,470 So we form solids at room temperature. 358 00:19:02,470 --> 00:19:03,470 OK. 359 00:19:03,470 --> 00:19:05,860 Now I want to show the energetics of that one because 360 00:19:05,860 --> 00:19:06,850 this is good. 361 00:19:06,850 --> 00:19:09,320 You know, I promised you I wouldn't do derivations, so 362 00:19:09,320 --> 00:19:11,300 I'm not going in detail on this. 363 00:19:11,300 --> 00:19:13,710 I'm giving you just enough so that I can introduce the 364 00:19:13,710 --> 00:19:15,040 characters here. 365 00:19:15,040 --> 00:19:16,100 You know, how else am I going to 366 00:19:16,100 --> 00:19:17,860 introduce the Born exponent? 367 00:19:17,860 --> 00:19:20,510 Am I'm just going to say, there's this exponent n, the 368 00:19:20,510 --> 00:19:21,330 Born exponent. 369 00:19:21,330 --> 00:19:22,850 We're going to introduce it in context. 370 00:19:22,850 --> 00:19:24,630 So now you know what the energetics are. 371 00:19:24,630 --> 00:19:27,980 So now I want to prove to you energetically along this line 372 00:19:27,980 --> 00:19:29,830 that crystals will form. 373 00:19:32,540 --> 00:19:35,010 So let's imagine-- 374 00:19:35,010 --> 00:19:36,520 we're going to do this thought experiment. 375 00:19:36,520 --> 00:19:47,100 We're going to take three ion-pairs of sodium chloride. 376 00:19:47,100 --> 00:19:50,090 So here's three ion-pairs of sodium chloride. 377 00:19:50,090 --> 00:19:52,850 And I want to compare these three ion-pairs. 378 00:19:52,850 --> 00:19:57,240 So this is an ion gas. 379 00:19:57,240 --> 00:20:03,430 And the distance between ion-pairs is great enough that 380 00:20:03,430 --> 00:20:05,100 one pair doesn't affect the other. 381 00:20:05,100 --> 00:20:08,350 The electrostatics are only strong within the pair. 382 00:20:08,350 --> 00:20:12,530 So we'll just label this infinity with quotation 383 00:20:12,530 --> 00:20:13,690 marks around it. 384 00:20:13,690 --> 00:20:15,260 They're very far apart. 385 00:20:15,260 --> 00:20:18,860 When a physicist says they're very far apart, very is code 386 00:20:18,860 --> 00:20:20,370 for infinity. 387 00:20:20,370 --> 00:20:22,820 So this one doesn't interact with this one, which doesn't 388 00:20:22,820 --> 00:20:23,900 interact with this one. 389 00:20:23,900 --> 00:20:27,530 And I want to compare the energetic state of the ion 390 00:20:27,530 --> 00:20:33,820 dispersion to what would happen if I were to put all of 391 00:20:33,820 --> 00:20:37,600 those in a single line. 392 00:20:37,600 --> 00:20:40,830 Plus, minus, plus, minus, plus, minus. 393 00:20:40,830 --> 00:20:43,320 So then this has a certain energy state, it's the energy 394 00:20:43,320 --> 00:20:44,642 of the ion line. 395 00:20:44,642 --> 00:20:49,300 And I want to show you that there's an energy decrease in 396 00:20:49,300 --> 00:20:54,312 collecting all of these and ordering them into a line. 397 00:20:54,312 --> 00:20:56,250 So there's more energy in a line dance 398 00:20:56,250 --> 00:20:57,520 than in ballroom dancing. 399 00:20:57,520 --> 00:20:59,150 That's what we're going to say ultimately. 400 00:20:59,150 --> 00:20:59,450 OK? 401 00:20:59,450 --> 00:21:01,300 So let's compare the energies. 402 00:21:01,300 --> 00:21:02,930 That's all we're going to do. 403 00:21:02,930 --> 00:21:05,060 So what's the energy of this? 404 00:21:05,060 --> 00:21:08,720 Well, we're not going to do 3 versus 3 Let's think big. 405 00:21:08,720 --> 00:21:09,170 It's Friday. 406 00:21:09,170 --> 00:21:12,690 So let's take Avogadro's number of pairs, shall we? 407 00:21:12,690 --> 00:21:22,350 So the energy of the ion dispersion would then equal-- 408 00:21:22,350 --> 00:21:25,610 that's the energy of one pair, and they're infinite distance 409 00:21:25,610 --> 00:21:28,450 apart, so there's nothing to be gained by putting them in 410 00:21:28,450 --> 00:21:31,220 the same chamber. 411 00:21:31,220 --> 00:21:33,330 So it's just going to be N Avogadro, if that's the 412 00:21:33,330 --> 00:21:38,100 number, times the energy evaluated at r equals r0. 413 00:21:38,100 --> 00:21:39,160 So we're done. 414 00:21:39,160 --> 00:21:40,550 And we know what that is. 415 00:21:40,550 --> 00:21:42,300 I don't have to rewrite it for you. 416 00:21:42,300 --> 00:21:42,620 OK. 417 00:21:42,620 --> 00:21:46,640 So now what I have to do is get an estimate of the energy 418 00:21:46,640 --> 00:21:49,040 of the line and show you that the line is at a 419 00:21:49,040 --> 00:21:50,165 lower energy state. 420 00:21:50,165 --> 00:21:52,420 Well, let's see. 421 00:21:52,420 --> 00:21:56,240 Jocelyn, take the top one and the middle one, please, but 422 00:21:56,240 --> 00:21:57,360 not the bottom one. 423 00:21:57,360 --> 00:21:58,090 Thanks. 424 00:21:58,090 --> 00:21:58,380 OK. 425 00:21:58,380 --> 00:22:00,960 So now let's look at the energy of a line. 426 00:22:00,960 --> 00:22:03,270 So we're going to do-- here's my line. 427 00:22:03,270 --> 00:22:06,950 I'm going to get the colored chalk. 428 00:22:06,950 --> 00:22:08,720 Green and blue. 429 00:22:08,720 --> 00:22:10,880 You know, some people think being a professor is so cool 430 00:22:10,880 --> 00:22:14,540 because you get to travel, you get to research, and so on. 431 00:22:14,540 --> 00:22:15,580 It's the colored chalk. 432 00:22:15,580 --> 00:22:16,855 [LAUGHTER] 433 00:22:16,855 --> 00:22:19,280 PROFESSOR: It's the colored chalk. 434 00:22:19,280 --> 00:22:20,400 All right. 435 00:22:20,400 --> 00:22:22,100 So there's a sodium. 436 00:22:22,100 --> 00:22:24,860 And on each side of the sodium we'll put a chloride. 437 00:22:24,860 --> 00:22:25,470 All right? 438 00:22:25,470 --> 00:22:27,450 And I'm going to just keep going this way. 439 00:22:27,450 --> 00:22:30,690 Here's a sodium and here's a chloride. 440 00:22:30,690 --> 00:22:31,530 All right. 441 00:22:31,530 --> 00:22:33,960 And now what I'm going to do, I'm going to start here at 442 00:22:33,960 --> 00:22:38,120 this sodium and I'm going to count the energy, 443 00:22:38,120 --> 00:22:41,610 electrostatic energy, that's in this system. 444 00:22:41,610 --> 00:22:44,090 So we're going to count to the left, we're going to count to 445 00:22:44,090 --> 00:22:46,060 the right, and then we're going to multiply it by the 446 00:22:46,060 --> 00:22:47,780 total number of ion-pairs. 447 00:22:47,780 --> 00:22:50,540 And I know that the ones on the end aren't the same, but 448 00:22:50,540 --> 00:22:53,650 the number of ends over N Avogadro, that's peanuts. 449 00:22:53,650 --> 00:22:56,390 The edge effects are negligible because there's 450 00:22:56,390 --> 00:22:57,670 such a giant middle. 451 00:22:57,670 --> 00:22:58,760 That's how you model this stuff. 452 00:22:58,760 --> 00:23:01,960 You don't obsess over the fact that the last ion doesn't see 453 00:23:01,960 --> 00:23:03,080 anything on that side. 454 00:23:03,080 --> 00:23:05,960 You just do it and forget about it, because you know you 455 00:23:05,960 --> 00:23:07,060 wouldn't do it for 5. 456 00:23:07,060 --> 00:23:08,300 This would be a big problem. 457 00:23:08,300 --> 00:23:12,130 But if you have Avogadro's number, who cares? 458 00:23:12,130 --> 00:23:13,280 It's called risk assessment. 459 00:23:13,280 --> 00:23:13,610 All right. 460 00:23:13,610 --> 00:23:17,050 So let's look at the energetics here. 461 00:23:17,050 --> 00:23:24,820 So what we've got is the energy of the ion line. 462 00:23:24,820 --> 00:23:25,470 OK? 463 00:23:25,470 --> 00:23:27,970 So let's start with this central one. 464 00:23:27,970 --> 00:23:32,380 And separated by distance r0 is the chloride, and there's 465 00:23:32,380 --> 00:23:33,950 an attractive energy here. 466 00:23:33,950 --> 00:23:38,190 So that's going to equal minus e squared over 467 00:23:38,190 --> 00:23:42,400 4 pi epsilon0 r0. 468 00:23:42,400 --> 00:23:44,290 Now I'm going to keep going, because the field is 469 00:23:44,290 --> 00:23:46,710 unsaturated and goes in all directions. 470 00:23:46,710 --> 00:23:51,490 So this sodium, that's a distance 2r0 away. 471 00:23:51,490 --> 00:23:55,920 It's got a repulsive force exerted on this sodium. 472 00:23:55,920 --> 00:23:56,920 So let's add that. 473 00:23:56,920 --> 00:23:58,040 So that's going to be plus. 474 00:23:58,040 --> 00:24:01,020 A repulsive force raises the energy of a system. 475 00:24:01,020 --> 00:24:07,180 That's e squared over 4pi epsilon0 times 2r0. 476 00:24:07,180 --> 00:24:08,620 And let's keep going. 477 00:24:08,620 --> 00:24:10,940 So now let's go 3r0 away. 478 00:24:10,940 --> 00:24:15,330 So 3 times r0, that gets me out to the chloride over here. 479 00:24:15,330 --> 00:24:17,040 Let's put 3r0. 480 00:24:17,040 --> 00:24:20,570 Now that will take me from the center of the sodium to the 481 00:24:20,570 --> 00:24:22,610 center of the next chloride. 482 00:24:22,610 --> 00:24:24,540 And that's going to be attractive. 483 00:24:24,540 --> 00:24:30,180 So that'll be minus e squared over 4pi epsilon0 times 3r0 484 00:24:30,180 --> 00:24:31,180 plus, et cetera. 485 00:24:31,180 --> 00:24:32,820 So you see how this goes. 486 00:24:32,820 --> 00:24:34,560 So you go all the way out, you add them all up, and you go 487 00:24:34,560 --> 00:24:35,610 the other way. 488 00:24:35,610 --> 00:24:37,670 And so on and so forth. 489 00:24:37,670 --> 00:24:39,400 So that's how the derivation goes. 490 00:24:39,400 --> 00:24:40,370 You might say, hey wait a minute. 491 00:24:40,370 --> 00:24:43,520 What happened to the Born exponent and the repulsive 492 00:24:43,520 --> 00:24:44,870 energy term? 493 00:24:44,870 --> 00:24:48,190 Well, where's the repulsive energy term going to be felt? 494 00:24:48,190 --> 00:24:51,960 It's called electron-electron repulsion. 495 00:24:51,960 --> 00:24:54,980 Axiomatically, the electrons here are 496 00:24:54,980 --> 00:24:56,980 nowhere near these electrons. 497 00:24:56,980 --> 00:25:00,130 See, you only have to count it for the nearest neighbor. 498 00:25:00,130 --> 00:25:02,530 So we can patch that in at the end. 499 00:25:02,530 --> 00:25:04,130 And we do. 500 00:25:04,130 --> 00:25:05,610 I haven't forgotten. 501 00:25:05,610 --> 00:25:08,390 But I'm not going to spend a whole day trying to derive 502 00:25:08,390 --> 00:25:08,940 this thing. 503 00:25:08,940 --> 00:25:10,720 I'll show you how it starts to evolve. 504 00:25:10,720 --> 00:25:12,290 At some point you end up with something 505 00:25:12,290 --> 00:25:13,490 that looks like this. 506 00:25:13,490 --> 00:25:15,450 e squared over-- 507 00:25:15,450 --> 00:25:17,310 in fact, I'll put the minus sign up here. 508 00:25:17,310 --> 00:25:22,210 Minus e squared over 4 pi epsilon0 r0. 509 00:25:22,210 --> 00:25:24,450 And you're going to double it, because you're going to go one 510 00:25:24,450 --> 00:25:26,710 side and the other side, and you're going to get a series 511 00:25:26,710 --> 00:25:33,830 that looks like this: 1 minus 1/2 plus 1/3 minus 1/4 plus 512 00:25:33,830 --> 00:25:35,150 blah, blah, blah. 513 00:25:35,150 --> 00:25:36,090 Yeah. 514 00:25:36,090 --> 00:25:36,760 OK. 515 00:25:36,760 --> 00:25:39,800 So what does this look like? 516 00:25:39,800 --> 00:25:44,660 I've really broken this into two pieces. 517 00:25:44,660 --> 00:25:49,570 So this coefficient out in front here, you should now be 518 00:25:49,570 --> 00:25:52,500 able to repeat this in your sleep: e squared over 4 pi 519 00:25:52,500 --> 00:25:53,740 epsilon0 r. 520 00:25:53,740 --> 00:25:58,170 This is electrostatics, isn't it? 521 00:25:58,170 --> 00:25:59,000 Electrostatics. 522 00:25:59,000 --> 00:26:01,580 This is the consequence of Coulomb's law. 523 00:26:01,580 --> 00:26:03,830 What's this second term here? 524 00:26:03,830 --> 00:26:06,000 What's this all about? 525 00:26:06,000 --> 00:26:07,440 Geometry. 526 00:26:07,440 --> 00:26:10,450 This is dictated by atomic arrangement. 527 00:26:17,060 --> 00:26:20,810 So I could calculate this if I took, instead of a line, what 528 00:26:20,810 --> 00:26:24,960 if I put them in a sheet subject to the constraints of 529 00:26:24,960 --> 00:26:28,400 those sizes and plus 1 and minus 1? 530 00:26:28,400 --> 00:26:29,150 So what would be? 531 00:26:29,150 --> 00:26:31,900 I'd start at the sodium and count how many chlorides? 532 00:26:31,900 --> 00:26:35,710 If I'm on a plane there'd be one, two, three, four. 533 00:26:35,710 --> 00:26:36,820 And then how many sodiums? 534 00:26:36,820 --> 00:26:38,810 Well, they'd be on the backside 535 00:26:38,810 --> 00:26:40,090 of each of the chlorides. 536 00:26:40,090 --> 00:26:43,430 And I'd add them all up in 2-space and I'd end up with 537 00:26:43,430 --> 00:26:45,045 another coefficient here. 538 00:26:45,045 --> 00:26:46,070 All right? 539 00:26:46,070 --> 00:26:50,490 And we compress all of this into a coefficient which we 540 00:26:50,490 --> 00:26:52,170 call the Madelung constant. 541 00:26:55,700 --> 00:26:57,890 And it's a function of the atomic arrangements. 542 00:26:57,890 --> 00:27:00,320 So different crystal structures have different 543 00:27:00,320 --> 00:27:02,450 Madelung constants. 544 00:27:02,450 --> 00:27:06,302 It's named after a German professor, Madelung. 545 00:27:06,302 --> 00:27:10,630 In 1910, he published calculations for the energy of 546 00:27:10,630 --> 00:27:12,230 a system of point charges-- 547 00:27:12,230 --> 00:27:14,510 just abstract theoretical paper. 548 00:27:14,510 --> 00:27:18,925 And then about 10 years later another German professor by 549 00:27:18,925 --> 00:27:20,970 the name of Paul Ewald-- 550 00:27:20,970 --> 00:27:22,970 he did his PhD for Sommerfeld-- 551 00:27:22,970 --> 00:27:25,770 he published a paper in which he actually made the 552 00:27:25,770 --> 00:27:30,310 calculation for ion crystals, and he came 553 00:27:30,310 --> 00:27:31,390 up with this constant. 554 00:27:31,390 --> 00:27:34,380 And to show you the class of the guy, instead of naming the 555 00:27:34,380 --> 00:27:37,790 constant after himself he named it after Madelung. 556 00:27:37,790 --> 00:27:38,870 Now that's class. 557 00:27:38,870 --> 00:27:42,190 So Madelung did the first calculation so he gets named. 558 00:27:42,190 --> 00:27:45,620 So now what we're going to do is we're going to multiply by 559 00:27:45,620 --> 00:27:48,970 the N Avogadro, because I've got N Avogadro of these 560 00:27:48,970 --> 00:27:52,510 things, and we're going to put in the Born exponent 561 00:27:52,510 --> 00:27:53,690 patch and so on. 562 00:27:53,690 --> 00:27:56,260 And here's what the final expression looks 563 00:27:56,260 --> 00:27:59,220 like for the line. 564 00:27:59,220 --> 00:28:02,620 There are a few algebraic tricks that I'm not willing to 565 00:28:02,620 --> 00:28:05,140 do in class because I don't think that's a profitable use 566 00:28:05,140 --> 00:28:06,930 of our time in a chemistry class. 567 00:28:06,930 --> 00:28:08,940 But if you want to try the derivation I have it in full 568 00:28:08,940 --> 00:28:10,450 and we can compare notes. 569 00:28:10,450 --> 00:28:13,350 So once we get the patch in it's going to look like this. 570 00:28:13,350 --> 00:28:14,490 It'll be minus. 571 00:28:14,490 --> 00:28:17,060 There'll be the Madelung constant times 572 00:28:17,060 --> 00:28:19,750 N Avogadro e squared-- 573 00:28:19,750 --> 00:28:22,020 and this is already assuming it's plus 1, minus 1. 574 00:28:22,020 --> 00:28:25,100 If this were magnesium oxide there'd be a 4 in here. 575 00:28:25,100 --> 00:28:32,170 4 pi epsilon0 r0 times 1 minus 1/n, where 576 00:28:32,170 --> 00:28:33,870 n is the Born exponent. 577 00:28:33,870 --> 00:28:38,730 So compare this to this one here. 578 00:28:38,730 --> 00:28:40,060 What's the only difference? 579 00:28:40,060 --> 00:28:42,870 The only difference is the Madelung constant, right? 580 00:28:42,870 --> 00:28:44,160 It's the only difference. 581 00:28:44,160 --> 00:28:56,480 So E of the pair dispersion is really equal to E of the line 582 00:28:56,480 --> 00:28:58,240 divided by the Madelung constant. 583 00:28:58,240 --> 00:29:01,670 So what I'm trying to prove to you is that E line is more 584 00:29:01,670 --> 00:29:03,860 negative than E of the dispersion. 585 00:29:03,860 --> 00:29:06,140 So it all hinges on the magnitude of M. 586 00:29:06,140 --> 00:29:08,240 If M is greater than 1 we win. 587 00:29:08,240 --> 00:29:12,050 If M is less than 1 I've just proved to you that water runs 588 00:29:12,050 --> 00:29:13,390 uphill, so that's a bad day. 589 00:29:13,390 --> 00:29:14,240 All right? 590 00:29:14,240 --> 00:29:16,600 So let's calculate the value of M. 591 00:29:16,600 --> 00:29:21,020 And you can go to your algebra books. 592 00:29:21,020 --> 00:29:24,680 And you've got this series natural log-- and engineers 593 00:29:24,680 --> 00:29:27,160 write natural log "ln." I know the mathematicians write 594 00:29:27,160 --> 00:29:28,770 "log." Uh-uh. 595 00:29:28,770 --> 00:29:29,650 Engineers-- 596 00:29:29,650 --> 00:29:30,320 uh. 597 00:29:30,320 --> 00:29:31,620 That's 1 plus x. 598 00:29:31,620 --> 00:29:32,240 OK? 599 00:29:32,240 --> 00:29:34,070 Natural log, 1 plus x. 600 00:29:34,070 --> 00:29:43,120 You can expand this as x minus x squared over 2 plus x cubed 601 00:29:43,120 --> 00:29:44,510 over 3, dah, dah, dah, dah. 602 00:29:44,510 --> 00:29:46,080 You know, look that one up. 603 00:29:46,080 --> 00:29:50,250 Set x equal to 1, which is what we've got, right? 604 00:29:50,250 --> 00:29:54,510 Because we've got 1 minus 1/2, 1/3, dah, dah, dah, dah. 605 00:29:54,510 --> 00:29:57,920 Go through it and you'll get the value that M, according to 606 00:29:57,920 --> 00:30:01,740 this, will give you 2 times the natural logarithm of 2, 607 00:30:01,740 --> 00:30:03,990 which is 1.386-- 608 00:30:03,990 --> 00:30:06,330 which is greater than 1. 609 00:30:06,330 --> 00:30:08,170 And so we're golden. 610 00:30:08,170 --> 00:30:12,840 That means that the energy of the line is lower, more 611 00:30:12,840 --> 00:30:15,800 negative, than the energy of the dispersion. 612 00:30:15,800 --> 00:30:17,400 So I'm going to do this pictorially. 613 00:30:17,400 --> 00:30:19,780 Let's make an energy level diagram. 614 00:30:19,780 --> 00:30:22,370 And the energy level diagram will look like this. 615 00:30:22,370 --> 00:30:28,010 So up here the energy is 0 and everything is negative. 616 00:30:28,010 --> 00:30:31,595 So if I put this as minus 1 unit. 617 00:30:31,595 --> 00:30:32,340 All right? 618 00:30:32,340 --> 00:30:35,980 These are all negative values increasing in this direction. 619 00:30:35,980 --> 00:30:45,370 So this is the dispersion of ion-pairs. 620 00:30:45,370 --> 00:30:47,070 So all we've done is take a cation and 621 00:30:47,070 --> 00:30:48,270 put it to the anion. 622 00:30:48,270 --> 00:30:52,670 We've just seen that if we do the calculation for the line 623 00:30:52,670 --> 00:30:56,580 it's 1.386 times whatever this is. 624 00:30:56,580 --> 00:31:01,695 So that gives us-- this is for the ion line, which I'm going 625 00:31:01,695 --> 00:31:05,650 to take the liberty of calling a 1-dimensional crystal. 626 00:31:05,650 --> 00:31:07,250 It's a 1-dimensional ordered array. 627 00:31:09,750 --> 00:31:15,580 And what I can do is go to the 3-dimensional array, start at 628 00:31:15,580 --> 00:31:18,690 the lower right-hand corner with that chloride. 629 00:31:18,690 --> 00:31:21,630 Calculate the distance to each of the nearest neighbor 630 00:31:21,630 --> 00:31:23,860 sodiums. Go through the geometry. 631 00:31:23,860 --> 00:31:26,440 The next nearest neighbor chlorides, the next nearest 632 00:31:26,440 --> 00:31:29,570 neighbor sodiums. And you'll build an infinite series and 633 00:31:29,570 --> 00:31:30,570 you'll evaluate it. 634 00:31:30,570 --> 00:31:33,880 And in three dimensions it's even lower. 635 00:31:33,880 --> 00:31:38,140 It's 1.7476. 636 00:31:38,140 --> 00:31:41,230 So this is for the 3-dimensional crystal. 637 00:31:41,230 --> 00:31:44,760 This is for the ionic crystal. 638 00:31:44,760 --> 00:31:45,410 All right? 639 00:31:45,410 --> 00:31:48,390 3-D crystal. 640 00:31:48,390 --> 00:31:52,400 So what this is showing is that the system keeps making 641 00:31:52,400 --> 00:31:53,660 more and more bonds. 642 00:31:53,660 --> 00:31:55,110 Why does it make bonds? 643 00:31:55,110 --> 00:31:58,590 Because the more nearest neighbors it has the lower the 644 00:31:58,590 --> 00:32:01,510 energy goes. 645 00:32:01,510 --> 00:32:03,630 So making a 3-dimensional crystal is 646 00:32:03,630 --> 00:32:04,820 energetically favored. 647 00:32:04,820 --> 00:32:07,400 Now there are different Madelung constants for 648 00:32:07,400 --> 00:32:08,550 different crystal structures. 649 00:32:08,550 --> 00:32:09,340 You say, well wait a minute. 650 00:32:09,340 --> 00:32:11,020 How do you get different crystal structures? 651 00:32:11,020 --> 00:32:13,780 Suppose instead of sodium it's potassium. 652 00:32:13,780 --> 00:32:14,850 What's the only difference? 653 00:32:14,850 --> 00:32:16,940 Potassium is plus 1. 654 00:32:16,940 --> 00:32:18,300 What's the difference? 655 00:32:18,300 --> 00:32:19,650 Size. 656 00:32:19,650 --> 00:32:21,080 Potassium is larger. 657 00:32:21,080 --> 00:32:24,470 They're not going to pack quite the same. 658 00:32:24,470 --> 00:32:26,800 And so depending on the relative ion sizes-- 659 00:32:26,800 --> 00:32:31,440 I mean what if I have something like silver iodide? 660 00:32:31,440 --> 00:32:33,000 Iodide is huge. 661 00:32:33,000 --> 00:32:37,630 Silver is so small it'll fit into the interstices between 662 00:32:37,630 --> 00:32:39,980 touching iodines. 663 00:32:39,980 --> 00:32:41,720 So it's going to have a different crystal structure, 664 00:32:41,720 --> 00:32:43,860 and the different crystal structure will give us a 665 00:32:43,860 --> 00:32:46,370 different Madelung constant. 666 00:32:46,370 --> 00:32:48,130 And there it is. 667 00:32:48,130 --> 00:32:52,210 So we've come a long way with that little assumption of 668 00:32:52,210 --> 00:32:53,660 octet stability. 669 00:32:53,660 --> 00:32:56,490 So now let's take a look at what the properties are of 670 00:32:56,490 --> 00:32:57,540 these things. 671 00:32:57,540 --> 00:32:59,400 They're solid at room temperature because we've got 672 00:32:59,400 --> 00:33:01,070 strong bonds. 673 00:33:01,070 --> 00:33:02,400 High melting points. 674 00:33:02,400 --> 00:33:05,390 Bonding is related to melting point. 675 00:33:05,390 --> 00:33:07,640 Now think point is dictated by bonding, because now you're 676 00:33:07,640 --> 00:33:11,240 comparing thermal energy versus the cohesive energy of 677 00:33:11,240 --> 00:33:12,180 the crystal. 678 00:33:12,180 --> 00:33:15,720 So tightly bonded substances melt at high temperatures, 679 00:33:15,720 --> 00:33:18,710 weakly bonded substances melt at low temperatures. 680 00:33:18,710 --> 00:33:21,010 Transparent to visible light. 681 00:33:21,010 --> 00:33:23,690 How do I know that? 682 00:33:23,690 --> 00:33:24,970 Because I'm the professor. 683 00:33:24,970 --> 00:33:25,570 No. 684 00:33:25,570 --> 00:33:26,840 How do I know that? 685 00:33:26,840 --> 00:33:28,970 How do we think about it when someone says to you is 686 00:33:28,970 --> 00:33:32,490 something transparent, in this case to visible light. 687 00:33:32,490 --> 00:33:37,310 Well, what I do is I say, here's the solid. 688 00:33:37,310 --> 00:33:41,780 This is the ionic solid and here is visible light, h nu. 689 00:33:41,780 --> 00:33:46,700 And I'm going to write 2 to 3 electron volts per photon. 690 00:33:46,700 --> 00:33:49,730 And what happens when I want to decide whether this is 691 00:33:49,730 --> 00:33:51,000 transparent to visible light? 692 00:33:51,000 --> 00:33:52,690 Now look at the modeling here. 693 00:33:52,690 --> 00:33:54,140 Photon is a squiggle. 694 00:33:54,140 --> 00:33:55,960 I don't know if that's Cartesian space. 695 00:33:55,960 --> 00:33:58,425 This is like a crystal, right? 696 00:33:58,425 --> 00:33:59,700 I'm speaking California. 697 00:33:59,700 --> 00:34:00,860 It's like a crystal. 698 00:34:00,860 --> 00:34:05,080 So now if I go inside I want to make the energy diagram. 699 00:34:05,080 --> 00:34:07,360 So what's the energy diagram look like? 700 00:34:07,360 --> 00:34:09,260 All right? 701 00:34:09,260 --> 00:34:12,270 So now the question is how does-- 702 00:34:12,270 --> 00:34:17,510 if this is the energy diagram of the crystal and I make this 703 00:34:17,510 --> 00:34:21,960 the energy of the photon of visible light, I'm going to 704 00:34:21,960 --> 00:34:25,460 compare how much energy the photon has versus how much 705 00:34:25,460 --> 00:34:28,780 energy it takes to excite electrons all the 706 00:34:28,780 --> 00:34:30,710 way to a new state. 707 00:34:30,710 --> 00:34:31,980 Because if you don't excite them all the 708 00:34:31,980 --> 00:34:33,140 way to a new state-- 709 00:34:33,140 --> 00:34:35,720 they can't go part way, so nothing happens. 710 00:34:35,720 --> 00:34:38,270 And if nothing happens the photon goes through and that's 711 00:34:38,270 --> 00:34:40,440 transparent. 712 00:34:40,440 --> 00:34:43,830 Now what do I know about the binding energy and the energy 713 00:34:43,830 --> 00:34:46,240 level diagram of Na plus? 714 00:34:46,240 --> 00:34:49,560 Well, it's isoelectronic with neon. 715 00:34:49,560 --> 00:34:51,960 And I know that neon has an average valence electron 716 00:34:51,960 --> 00:34:55,490 energy of about 20 electron volts. 717 00:34:55,490 --> 00:34:57,660 So my guess is the visible light is 718 00:34:57,660 --> 00:34:59,550 not going to do anything. 719 00:34:59,550 --> 00:35:03,160 And so it just passes right on through. 720 00:35:03,160 --> 00:35:04,940 See, we got all that. 721 00:35:04,940 --> 00:35:06,090 Electrical insulator. 722 00:35:06,090 --> 00:35:06,840 How do I know that? 723 00:35:06,840 --> 00:35:09,160 Well, all that glitters is not gold, but it 724 00:35:09,160 --> 00:35:11,040 must have free electrons. 725 00:35:11,040 --> 00:35:13,510 And these electrons are all bound, and 726 00:35:13,510 --> 00:35:16,490 they're tightly bound. 727 00:35:16,490 --> 00:35:18,532 Hard and brittle. 728 00:35:18,532 --> 00:35:22,350 If it's going to be ductile the atoms need to be able to 729 00:35:22,350 --> 00:35:24,260 slide over one another. 730 00:35:24,260 --> 00:35:26,890 Well, there's no way these can slide over one another because 731 00:35:26,890 --> 00:35:29,900 to slide over one another requires that at some point 732 00:35:29,900 --> 00:35:32,160 the two sodiums are going to be nearest neighbors, and the 733 00:35:32,160 --> 00:35:35,570 repulsive forces are so high the crystal fractures. 734 00:35:35,570 --> 00:35:39,890 So if you try to deform an ionic solid you will get it 735 00:35:39,890 --> 00:35:43,660 moving in accordance to the elasticity. 736 00:35:43,660 --> 00:35:46,790 So force will be proportional to the extension-- 737 00:35:46,790 --> 00:35:49,270 Hooke's Law-- but if you try to plastically deform 738 00:35:49,270 --> 00:35:52,270 it, you shear it. 739 00:35:52,270 --> 00:35:53,170 Soluble in water. 740 00:35:53,170 --> 00:35:54,580 We'll come back to that later. 741 00:35:54,580 --> 00:35:56,530 Melt to form ionic liquids. 742 00:35:56,530 --> 00:36:00,150 And good for electrolytic extraction of metals. 743 00:36:00,150 --> 00:36:01,580 I showed you magnesium last day. 744 00:36:01,580 --> 00:36:04,700 Today I'll talk a little bit about aluminum. 745 00:36:04,700 --> 00:36:06,640 But that comes later. 746 00:36:06,640 --> 00:36:07,120 OK. 747 00:36:07,120 --> 00:36:11,520 So where do we find elements that are going 748 00:36:11,520 --> 00:36:13,510 to form ionic solids? 749 00:36:13,510 --> 00:36:14,920 Well, you go back to the beginning of the lecture. 750 00:36:14,920 --> 00:36:15,930 What do you look for? 751 00:36:15,930 --> 00:36:19,580 You've got to find the box of really good electron donors 752 00:36:19,580 --> 00:36:22,130 and the box of really good electron acceptors. 753 00:36:22,130 --> 00:36:24,220 That's where you go. 754 00:36:24,220 --> 00:36:28,340 So the good electron donors are at the left side and the 755 00:36:28,340 --> 00:36:30,990 good electron acceptors are at the right side. 756 00:36:30,990 --> 00:36:33,220 So if you take sodium plus chlorine 757 00:36:33,220 --> 00:36:34,360 you get sodium chloride. 758 00:36:34,360 --> 00:36:36,750 If you get calcium plus fluorine, calcium fluoride. 759 00:36:36,750 --> 00:36:39,332 Magnesium plus oxygen, and so on. 760 00:36:39,332 --> 00:36:41,300 OK? 761 00:36:41,300 --> 00:36:43,330 Yeah, this shows. 762 00:36:43,330 --> 00:36:45,030 Yeah. 763 00:36:45,030 --> 00:36:48,850 Aluminum plus oxygen, yeah. 764 00:36:48,850 --> 00:36:50,780 There's Max Born. 765 00:36:50,780 --> 00:36:54,180 Max Born, he got a Nobel Prize. 766 00:36:54,180 --> 00:36:56,070 And so did Fritz Haber, but we're going to 767 00:36:56,070 --> 00:36:57,420 come to him in a minute. 768 00:36:57,420 --> 00:36:57,770 All right. 769 00:36:57,770 --> 00:37:04,820 So now I want to do this energetic calculation one more 770 00:37:04,820 --> 00:37:08,340 way, because right now we've been operating with ion gas 771 00:37:08,340 --> 00:37:11,130 but sodium isn't found normally in the 772 00:37:11,130 --> 00:37:12,250 form of an ion gas. 773 00:37:12,250 --> 00:37:15,320 So let's do something that starts with 774 00:37:15,320 --> 00:37:16,810 elements found in nature. 775 00:37:16,810 --> 00:37:26,670 So we want to form an ionic crystal from elements in their 776 00:37:26,670 --> 00:37:27,920 natural state. 777 00:37:31,060 --> 00:37:33,660 And what's going to happen is en route we're going to be 778 00:37:33,660 --> 00:37:36,870 able to define a few more terms. So that's going to make 779 00:37:36,870 --> 00:37:39,090 everybody happy because we get more definitions. 780 00:37:39,090 --> 00:37:44,900 And this is called the Born-Haber Cycle, named after 781 00:37:44,900 --> 00:37:48,070 Born and Haber. 782 00:37:48,070 --> 00:37:50,880 And what we're going to do is we're going to-- 783 00:37:50,880 --> 00:37:53,360 pardon me, there's a C in there-- we're going to invoke 784 00:37:53,360 --> 00:37:56,570 Hess's Law. 785 00:37:56,570 --> 00:37:59,710 And Hess's Law is sort of like Kirchhoff's law 786 00:37:59,710 --> 00:38:00,740 for electric circuits. 787 00:38:00,740 --> 00:38:05,050 Hess's law says that the energy of a chemical change is 788 00:38:05,050 --> 00:38:06,650 path independent. 789 00:38:06,650 --> 00:38:18,380 So energy change in a chemical reaction is path independent. 790 00:38:18,380 --> 00:38:23,950 It's sort of like potential energy in Newtonian mechanics. 791 00:38:23,950 --> 00:38:26,090 It doesn't matter if you take the elevator to the top of the 792 00:38:26,090 --> 00:38:29,420 Hancock Tower or if you walk up the stairs, the change in 793 00:38:29,420 --> 00:38:33,320 potential energy is the same when you express it from the 794 00:38:33,320 --> 00:38:36,850 top of the Hancock Tower, although you might be somewhat 795 00:38:36,850 --> 00:38:39,920 more exhausted having walked the steps instead of taking 796 00:38:39,920 --> 00:38:40,720 the elevator. 797 00:38:40,720 --> 00:38:42,240 But you don't get any credit in terms of 798 00:38:42,240 --> 00:38:45,000 the potential energy. 799 00:38:45,000 --> 00:38:52,070 So let's use Hess's Law in order to describe the 800 00:38:52,070 --> 00:38:53,250 formation of sodium chloride. 801 00:38:53,250 --> 00:38:56,940 So I'm going to start with sodium as it's found in 802 00:38:56,940 --> 00:38:58,980 nature, and I'm going to talk about room temperature. 803 00:38:58,980 --> 00:39:02,480 So sodium is a solid at room temperature, and I'm going to 804 00:39:02,480 --> 00:39:07,010 react it with chlorine gas. 805 00:39:07,010 --> 00:39:08,755 Chlorine's a gas at room temperature and it's a 806 00:39:08,755 --> 00:39:11,090 diatomic molecule. 807 00:39:11,090 --> 00:39:16,640 And we're going to react it to form sodium chloride, which is 808 00:39:16,640 --> 00:39:18,810 a solid and a crystal. 809 00:39:18,810 --> 00:39:20,590 Now you might say, well isn't that kind of redundant? 810 00:39:20,590 --> 00:39:23,230 No, because later on I'm going to teach you about a form of 811 00:39:23,230 --> 00:39:26,980 solid matter that does not consist of atoms 812 00:39:26,980 --> 00:39:28,310 in a regular array-- 813 00:39:28,310 --> 00:39:29,580 disordered solids. 814 00:39:29,580 --> 00:39:33,300 So we're specifying, I want to form crystal and solid sodium 815 00:39:33,300 --> 00:39:35,775 chloride, because that's the reaction that would occur if 816 00:39:35,775 --> 00:39:37,540 we were to do it in the lab. 817 00:39:37,540 --> 00:39:39,700 And what have we calculated so far? 818 00:39:39,700 --> 00:39:42,490 What we've calculated so far is this. 819 00:39:42,490 --> 00:39:48,630 We've calculated chloride ion in the gas phase plus sodium 820 00:39:48,630 --> 00:39:52,560 ion in the gas phase reacting to form the crystal. 821 00:39:52,560 --> 00:39:57,720 And we've called this the energy of crystallization. 822 00:39:57,720 --> 00:39:59,960 That's this Madelung stuff. 823 00:39:59,960 --> 00:40:01,860 This is the Madelung energy here. 824 00:40:01,860 --> 00:40:02,430 All right? 825 00:40:02,430 --> 00:40:04,370 I'll even put M here. 826 00:40:04,370 --> 00:40:05,280 Madelung energy. 827 00:40:05,280 --> 00:40:06,320 And why am I using H? 828 00:40:06,320 --> 00:40:07,850 Because that's what the books use. 829 00:40:07,850 --> 00:40:10,580 H is enthalpy, and for condensed matter the 830 00:40:10,580 --> 00:40:12,060 difference between enthalpy and energy 831 00:40:12,060 --> 00:40:13,660 doesn't amount to much. 832 00:40:13,660 --> 00:40:17,870 So H, just for the record, is enthalpy. 833 00:40:17,870 --> 00:40:20,750 And we've been operating with E as energy. 834 00:40:20,750 --> 00:40:24,930 It's almost equal to E, which is energy 835 00:40:24,930 --> 00:40:26,250 for condensed matter. 836 00:40:29,590 --> 00:40:31,090 For the gas phase it gets hairy. 837 00:40:35,630 --> 00:40:36,710 OK. 838 00:40:36,710 --> 00:40:41,320 So I want to get us from sodium solid, chloride solid 839 00:40:41,320 --> 00:40:42,440 over to here. 840 00:40:42,440 --> 00:40:43,410 So how am I going to do that? 841 00:40:43,410 --> 00:40:47,090 Well, first of all, I know how to make sodium ion gas. 842 00:40:47,090 --> 00:40:52,630 I start with sodium gas and then by ionization I make the 843 00:40:52,630 --> 00:40:55,280 electron plus sodium ion. 844 00:40:55,280 --> 00:40:58,730 So this is called the ionization energy, isn't it? 845 00:40:58,730 --> 00:41:00,170 This is the ionization energy. 846 00:41:00,170 --> 00:41:02,060 Sodium gas goes to that. 847 00:41:02,060 --> 00:41:04,090 And now how do I get sodium gas from sodium? 848 00:41:04,090 --> 00:41:06,310 Well that's just called sublimation. 849 00:41:06,310 --> 00:41:09,050 So this I'm going to need delta H of sublimation. 850 00:41:09,050 --> 00:41:12,560 Sublimation is the conversion of solid to vapor. 851 00:41:12,560 --> 00:41:16,640 And you can look that up on the Periodic Table. 852 00:41:16,640 --> 00:41:18,310 I'll show you how to get that in a second. 853 00:41:18,310 --> 00:41:19,780 And now how do I get chloride gas? 854 00:41:19,780 --> 00:41:23,370 Well chloride gas is going to start with atomic chlorine 855 00:41:23,370 --> 00:41:27,320 gas, but instead of losing an electron I've got to acquire 856 00:41:27,320 --> 00:41:29,420 an electron. 857 00:41:29,420 --> 00:41:33,720 And this action of adding an electron is sort of an inverse 858 00:41:33,720 --> 00:41:38,860 ionization, and this is called electron affinity. 859 00:41:38,860 --> 00:41:41,230 And there are tables of electron affinity. 860 00:41:41,230 --> 00:41:44,620 So each element has the ability to lose an electron, 861 00:41:44,620 --> 00:41:45,950 it has the ability to gain an electron. 862 00:41:45,950 --> 00:41:48,485 Losing an electron is ionization energy, acquiring 863 00:41:48,485 --> 00:41:50,000 an electron is electron affinity. 864 00:41:50,000 --> 00:41:53,100 And just as with ionization energies, if you have multiple 865 00:41:53,100 --> 00:41:55,730 electrons you have a first electron affinity, second 866 00:41:55,730 --> 00:41:57,580 electron affinity, and so on. 867 00:41:57,580 --> 00:42:00,270 And now how do I get to atomic chlorine? 868 00:42:00,270 --> 00:42:02,760 I've got to dissociate diatomic chlorine. 869 00:42:02,760 --> 00:42:04,120 So this is called dissociation. 870 00:42:07,820 --> 00:42:08,790 So that's the whole thing. 871 00:42:08,790 --> 00:42:11,000 And I'm going to now put some numbers on here. 872 00:42:11,000 --> 00:42:11,200 Let's see. 873 00:42:11,200 --> 00:42:16,120 I'm going to call sublimation step one, dissociation step 874 00:42:16,120 --> 00:42:22,280 two, ionization I've got here is step three, electron 875 00:42:22,280 --> 00:42:25,810 affinity is step four, and crystallization or 876 00:42:25,810 --> 00:42:27,630 Madelung is step five. 877 00:42:27,630 --> 00:42:32,390 And so working off of Hess's law we can say that the total 878 00:42:32,390 --> 00:42:36,380 energy required for the formation of the crystal-- 879 00:42:36,380 --> 00:42:38,930 delta H for the reaction. 880 00:42:38,930 --> 00:42:39,560 What's the reaction? 881 00:42:39,560 --> 00:42:41,260 The reaction of sodium plus chlorine 882 00:42:41,260 --> 00:42:42,470 to make sodium chloride-- 883 00:42:42,470 --> 00:42:47,210 is going to be the sum of all of the constituent components. 884 00:42:47,210 --> 00:42:49,870 The sum of all the delta's H. 885 00:42:49,870 --> 00:42:51,160 Not delta H's. 886 00:42:51,160 --> 00:42:52,990 delta's H, like attorneys general. 887 00:42:52,990 --> 00:42:53,660 All right? 888 00:42:53,660 --> 00:42:54,850 So now let's add these up. 889 00:42:54,850 --> 00:42:56,500 So we go number one. 890 00:42:56,500 --> 00:43:01,120 Number one I can look up on the Periodic Table. 891 00:43:01,120 --> 00:43:01,510 Where is it? 892 00:43:01,510 --> 00:43:03,810 There's Fritz Haber. 893 00:43:03,810 --> 00:43:05,310 So that's given here. 894 00:43:05,310 --> 00:43:06,630 If you look on the Periodic Table that'll 895 00:43:06,630 --> 00:43:07,770 give you the number. 896 00:43:07,770 --> 00:43:12,640 And for sodium it's 108 kilojoules per mole. 897 00:43:12,640 --> 00:43:14,990 Number two, get that from tables. 898 00:43:14,990 --> 00:43:16,660 It's 122. 899 00:43:16,660 --> 00:43:20,310 Number three is just the first ionization energy. 900 00:43:20,310 --> 00:43:22,250 You look it up on the Periodic Table. 901 00:43:22,250 --> 00:43:25,220 First ionization energy of sodium is about 5.3 electron 902 00:43:25,220 --> 00:43:29,320 volts, which turns out to be 496 kilojoules per mole. 903 00:43:29,320 --> 00:43:31,230 But look, these are all positive energies and we're 904 00:43:31,230 --> 00:43:33,140 trying to make a net negative energy. 905 00:43:33,140 --> 00:43:35,340 So these three steps are all raising the 906 00:43:35,340 --> 00:43:36,600 energy of the system. 907 00:43:36,600 --> 00:43:40,820 Finally, acquiring an electron by chlorine is going to 908 00:43:40,820 --> 00:43:43,190 decrease the energy of the system, because chlorine is a 909 00:43:43,190 --> 00:43:44,655 good electron acceptor. 910 00:43:44,655 --> 00:43:46,430 So that's minus 349. 911 00:43:46,430 --> 00:43:47,900 But watch this people. 912 00:43:47,900 --> 00:43:51,550 The energy in forming the crystal from the discrete 913 00:43:51,550 --> 00:43:57,220 ion-pairs is 787 kilojoules per mole, which gives us a net 914 00:43:57,220 --> 00:44:02,690 value of minus 410 kilojoules per mole. 915 00:44:02,690 --> 00:44:05,580 So what this is showing you is what the relative 916 00:44:05,580 --> 00:44:07,830 contributions are of the different 917 00:44:07,830 --> 00:44:10,630 components of that thing. 918 00:44:10,630 --> 00:44:12,450 So here it is in graphical form. 919 00:44:12,450 --> 00:44:15,350 There's the vaporization of sodium. 920 00:44:15,350 --> 00:44:18,390 This is the dissociation of chlorine. 921 00:44:18,390 --> 00:44:20,500 This is the ionization of sodium. 922 00:44:20,500 --> 00:44:21,810 All positive energies. 923 00:44:21,810 --> 00:44:23,110 And now electron affinity. 924 00:44:23,110 --> 00:44:25,870 And look at this contribution from the Madelung energy. 925 00:44:25,870 --> 00:44:28,970 So when things crystallize a lot of heat's given off. 926 00:44:28,970 --> 00:44:35,160 In fact, we can use that in cooling and moderating climate 927 00:44:35,160 --> 00:44:36,700 if we're clever about it. 928 00:44:36,700 --> 00:44:37,400 All right. 929 00:44:37,400 --> 00:44:41,960 Now just to show you what the different values are here that 930 00:44:41,960 --> 00:44:44,500 you're going to go in and get the lattice energies, you need 931 00:44:44,500 --> 00:44:47,750 to know the various r values, you see. 932 00:44:47,750 --> 00:44:50,970 The r0 is simply going to be the r-plus and the r-minus. 933 00:44:50,970 --> 00:44:53,440 So lithium fluoride, there it is. 934 00:44:53,440 --> 00:44:57,600 There's the lattice energy and it's based on the combination 935 00:44:57,600 --> 00:45:00,090 of lithium cation and fluoride anion. 936 00:45:00,090 --> 00:45:02,710 So they've gone through and calculated these values. 937 00:45:02,710 --> 00:45:05,090 So there's sodium chloride is 787. 938 00:45:05,090 --> 00:45:07,020 And, you know, you even get things like the boiling 939 00:45:07,020 --> 00:45:08,020 points, melting points. 940 00:45:08,020 --> 00:45:11,920 So sodium chloride, for example, melts at about 800 941 00:45:11,920 --> 00:45:13,290 degrees Celsius. 942 00:45:13,290 --> 00:45:17,310 Now if you take magnesium oxide, magnesium oxide is, 943 00:45:17,310 --> 00:45:19,860 look, 3,700 versus 700. 944 00:45:19,860 --> 00:45:22,170 And the melting point of magnesium oxide is 945 00:45:22,170 --> 00:45:24,480 2,800 degrees C. 946 00:45:24,480 --> 00:45:25,250 Look at aluminum. 947 00:45:25,250 --> 00:45:29,340 Aluminum plus oxygen, look at the end binding energy there. 948 00:45:29,340 --> 00:45:33,200 It's phenomenal, which means it might be useful for-- 949 00:45:33,200 --> 00:45:34,820 I'm standing underneath the shuttle here. 950 00:45:34,820 --> 00:45:37,800 This is the tiles underneath the shuttle, and they're made 951 00:45:37,800 --> 00:45:40,730 of aluminum oxide because the Madelung energy is so high so 952 00:45:40,730 --> 00:45:43,120 it's got the thermal shock resistance. 953 00:45:43,120 --> 00:45:46,810 So now you know how to go and design things for thermal 954 00:45:46,810 --> 00:45:48,340 ablation resistance. 955 00:45:48,340 --> 00:45:49,990 All you need is this table. 956 00:45:49,990 --> 00:45:50,800 That's all. 957 00:45:50,800 --> 00:45:52,650 No, you need a little more than that, but this is a good 958 00:45:52,650 --> 00:45:53,740 place to start. 959 00:45:53,740 --> 00:45:56,320 If you don't understand this table I don't want you working 960 00:45:56,320 --> 00:45:57,080 on the project. 961 00:45:57,080 --> 00:45:58,980 OK? 962 00:45:58,980 --> 00:45:59,700 What else? 963 00:45:59,700 --> 00:46:01,850 All this shows you-- yeah, we're going skip that. 964 00:46:01,850 --> 00:46:02,160 All right. 965 00:46:02,160 --> 00:46:03,390 So now we've got a few minutes here. 966 00:46:03,390 --> 00:46:06,360 What I want to do is last day I talked about magnesium, 967 00:46:06,360 --> 00:46:08,020 today I want to talk about aluminum. 968 00:46:08,020 --> 00:46:11,510 And it is also made in an electrochemical process. 969 00:46:11,510 --> 00:46:14,370 In this case the electrodes are horizontal. 970 00:46:14,370 --> 00:46:16,980 We feed aluminum oxide in and we pass current-- 971 00:46:16,980 --> 00:46:17,870 and huge currents. 972 00:46:17,870 --> 00:46:22,615 This thing typically runs at 300,000, 400,000 amperes and 973 00:46:22,615 --> 00:46:24,770 about 4 volts. 974 00:46:24,770 --> 00:46:27,250 So with the cathode we are running-- remember, we're 975 00:46:27,250 --> 00:46:28,910 running nature in reverse. 976 00:46:28,910 --> 00:46:31,720 Instead of the electron donor that aluminum is, we're 977 00:46:31,720 --> 00:46:34,370 shoving electrons onto aluminum ion and converting it 978 00:46:34,370 --> 00:46:35,460 back to aluminum. 979 00:46:35,460 --> 00:46:39,090 Unfortunately, on the anode side we have to use carbon, 980 00:46:39,090 --> 00:46:41,330 and the carbon itself is consumed. 981 00:46:41,330 --> 00:46:43,320 So we consume about a half a ton of carbon to 982 00:46:43,320 --> 00:46:44,910 make a ton of aluminum. 983 00:46:44,910 --> 00:46:47,820 So aluminum smelters generate a lot of greenhouse gases. 984 00:46:50,640 --> 00:46:53,730 So you can see this is like a drafting pencil: it's 985 00:46:53,730 --> 00:46:54,810 constantly being fed. 986 00:46:54,810 --> 00:46:56,340 And to give you a sense of scale this is probably about 987 00:46:56,340 --> 00:47:00,520 10 feet across, and this gap is about 2 inches, and this is 988 00:47:00,520 --> 00:47:02,780 about, I don't know, a foot and a half deep. 989 00:47:02,780 --> 00:47:04,720 It's going to get about 1,000 degrees Centigrade-- 990 00:47:04,720 --> 00:47:07,710 liquid aluminum and liquid salt. 991 00:47:07,710 --> 00:47:09,660 So this is what a smelter looks like. 992 00:47:09,660 --> 00:47:13,232 What's the sound of electric current? 993 00:47:13,232 --> 00:47:13,650 Yeah. 994 00:47:13,650 --> 00:47:16,810 The only sound you hear is the fans on the top that keep the 995 00:47:16,810 --> 00:47:17,470 place clean. 996 00:47:17,470 --> 00:47:19,450 There's the busbars that are bringing in the current. 997 00:47:19,450 --> 00:47:23,410 And all of these various posts are these things. 998 00:47:23,410 --> 00:47:25,710 So all of the magic is occurring 999 00:47:25,710 --> 00:47:26,940 below the floor here. 1000 00:47:26,940 --> 00:47:29,780 It was invented simultaneously in the United States by 1001 00:47:29,780 --> 00:47:32,700 Charles Martin Hall and in France by Paul Heroult. 1002 00:47:32,700 --> 00:47:35,390 In the same year they filed patents independently and 1003 00:47:35,390 --> 00:47:38,080 eventually crossed license when they collided at the 1004 00:47:38,080 --> 00:47:40,260 World Court. 1005 00:47:40,260 --> 00:47:41,450 So this is what happens. 1006 00:47:41,450 --> 00:47:44,820 We dissolve aluminum oxide in a molten fluoride called 1007 00:47:44,820 --> 00:47:48,000 cryolite, which originally came from Greenland, make 1008 00:47:48,000 --> 00:47:49,530 liquid aluminum carbon dioxide. 1009 00:47:49,530 --> 00:47:52,330 Now if we wanted to make this truly green, we want to 1010 00:47:52,330 --> 00:47:55,100 eliminate greenhouse gas emissions, you need to find an 1011 00:47:55,100 --> 00:47:56,490 inert anode. 1012 00:47:56,490 --> 00:47:59,970 So on an inert anode aluminum oxide would be converted into 1013 00:47:59,970 --> 00:48:01,560 aluminum and oxygen. 1014 00:48:01,560 --> 00:48:06,540 So not only would you not produce greenhouse gases but 1015 00:48:06,540 --> 00:48:10,760 you'd produce tonnage oxygen, which is marketable. 1016 00:48:10,760 --> 00:48:14,520 So some of the work that goes on in my lab is in advanced 1017 00:48:14,520 --> 00:48:18,380 materials with a view to trying to find an inert anode 1018 00:48:18,380 --> 00:48:21,660 that would then make this process very, very clean and 1019 00:48:21,660 --> 00:48:25,700 justify substituting aluminum for steel in cars. 1020 00:48:25,700 --> 00:48:32,680 By the way, when you have the field, even though it's a DC 1021 00:48:32,680 --> 00:48:34,980 current it's a divergent field. 1022 00:48:34,980 --> 00:48:39,580 And this is me in a magnesium smelter just in Utah. 1023 00:48:39,580 --> 00:48:41,690 There is the busbar for the magnesium cell. 1024 00:48:41,690 --> 00:48:44,360 So I'm about, oh, two meters away from 1025 00:48:44,360 --> 00:48:46,240 the edge of the busbars. 1026 00:48:46,240 --> 00:48:49,180 The magnetic field is so high I've got one, two, three, 1027 00:48:49,180 --> 00:48:54,560 four, five paper clips standing against gravity. 1028 00:48:54,560 --> 00:48:57,720 And I asked them for paper clips and there 1029 00:48:57,720 --> 00:48:58,560 was no office there. 1030 00:48:58,560 --> 00:48:59,920 They managed to find a few. 1031 00:48:59,920 --> 00:49:01,540 I wanted to see how many would go. 1032 00:49:01,540 --> 00:49:04,520 I'm willing to bet I could probably have about seven or 1033 00:49:04,520 --> 00:49:07,510 eight paper clips up before the gravity would cause them 1034 00:49:07,510 --> 00:49:07,970 to collapse. 1035 00:49:07,970 --> 00:49:09,290 That's the intensity of magnetic 1036 00:49:09,290 --> 00:49:10,770 fields in these smelters. 1037 00:49:10,770 --> 00:49:14,230 So when you drive up to the smelter for the tour you park 1038 00:49:14,230 --> 00:49:16,940 a fair distance away, you leave your wallet with the 1039 00:49:16,940 --> 00:49:19,940 credit cards in it, because this is the biggest bulk 1040 00:49:19,940 --> 00:49:22,410 demagnetizer you can imagine. 1041 00:49:22,410 --> 00:49:25,630 If you've got a watch that's got hands that move they're 1042 00:49:25,630 --> 00:49:26,655 going to be going like this. 1043 00:49:26,655 --> 00:49:28,590 [GESTURING] 1044 00:49:28,590 --> 00:49:30,640 PROFESSOR: Yeah. 1045 00:49:30,640 --> 00:49:32,430 This is the shuttle. 1046 00:49:32,430 --> 00:49:34,870 This is forged aluminum wheels. 1047 00:49:34,870 --> 00:49:37,410 The shuttle lands on Centerline racing wheels. 1048 00:49:37,410 --> 00:49:39,140 They're forged at a place in California. 1049 00:49:39,140 --> 00:49:40,810 They're made of aluminum alloy. 1050 00:49:40,810 --> 00:49:42,870 And I don't know if you can read on the side here, it's a 1051 00:49:42,870 --> 00:49:45,340 little bit light, but these are special tires. 1052 00:49:45,340 --> 00:49:48,800 They're made by Michelin 1053 00:49:48,800 --> 00:49:54,880 So, anyways, the whole message here is learn the lessons here 1054 00:49:54,880 --> 00:49:59,760 in 3.091 and then we can work together to make metal in an 1055 00:49:59,760 --> 00:50:01,230 environmentally acceptable way. 1056 00:50:01,230 --> 00:50:04,050 And just before I send you on your way for the weekend I 1057 00:50:04,050 --> 00:50:06,890 thought I'd tell a little joke related to 1058 00:50:06,890 --> 00:50:08,400 the uncertainty principle. 1059 00:50:08,400 --> 00:50:09,380 So the joke goes like this. 1060 00:50:09,380 --> 00:50:13,740 Heisenberg is racing down the Autobahn and he gets pulled 1061 00:50:13,740 --> 00:50:18,410 over by the state trooper who comes to the car and says, 1062 00:50:18,410 --> 00:50:20,610 where's the fire buddy? 1063 00:50:20,610 --> 00:50:22,560 Do you know how fast you were going? 1064 00:50:22,560 --> 00:50:25,860 And Heisenberg looks at him he says, no, but I 1065 00:50:25,860 --> 00:50:27,122 know where I am. 1066 00:50:27,122 --> 00:50:28,300 [LAUGHTER] 1067 00:50:28,300 --> 00:50:28,670 PROFESSOR: All right. 1068 00:50:28,670 --> 00:50:29,270 Get out of here. 1069 00:50:29,270 --> 00:50:30,890 Have a good weekend.