1 00:00:00,030 --> 00:00:02,400 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 00:00:20,912 --> 00:00:23,980 PROFESSOR: OK, OK, OK. 9 00:00:23,980 --> 00:00:26,220 Let's settle down. 10 00:00:26,220 --> 00:00:28,770 Weekend is over. 11 00:00:28,770 --> 00:00:31,160 Tomorrow, weekly quiz. 12 00:00:31,160 --> 00:00:33,080 Today I'll have office hours 3:00 to 4:00. 13 00:00:33,080 --> 00:00:35,180 I have to go down to Washington, so I've got to 14 00:00:35,180 --> 00:00:36,850 leave a little bit earlier than normal. 15 00:00:36,850 --> 00:00:42,420 So I will be available from 3:00 to 4:00 16 00:00:42,420 --> 00:00:45,070 The lecture has started and there's still way too much 17 00:00:45,070 --> 00:00:46,650 talking in here. 18 00:00:46,650 --> 00:00:47,430 Way too much. 19 00:00:47,430 --> 00:00:48,950 You know how much is too much? 20 00:00:48,950 --> 00:00:51,040 Any. 21 00:00:51,040 --> 00:00:52,290 Any. 22 00:00:58,200 --> 00:01:01,890 So last day, we started talking about oxide glasses, 23 00:01:01,890 --> 00:01:06,700 and we reasoned that we could have control of the properties 24 00:01:06,700 --> 00:01:10,420 by control of the composition. 25 00:01:10,420 --> 00:01:13,900 We started with a network former, which is some oxide 26 00:01:13,900 --> 00:01:16,505 that has the capacity for forming covalent bonds through 27 00:01:16,505 --> 00:01:18,160 a bridging oxygen. 28 00:01:18,160 --> 00:01:22,080 And then we wanted to drop the processing temperature, and we 29 00:01:22,080 --> 00:01:24,460 did so by adding modifiers. 30 00:01:24,460 --> 00:01:26,600 Intermediates, we haven't talked about and we're going 31 00:01:26,600 --> 00:01:28,570 to do that in just a moment. 32 00:01:28,570 --> 00:01:31,980 So if you look in the readings, this is from 33 00:01:31,980 --> 00:01:34,850 archival notes that were written by my predecessor, 34 00:01:34,850 --> 00:01:37,210 Professor Witt, these are compositions of 35 00:01:37,210 --> 00:01:38,870 some typical glasses. 36 00:01:38,870 --> 00:01:41,280 I don't expect you know these from memory, but I would 37 00:01:41,280 --> 00:01:45,370 expect you, if I gave you the composition, explain to me why 38 00:01:45,370 --> 00:01:46,920 the various constituents are there. 39 00:01:46,920 --> 00:01:49,060 So let's try few examples. 40 00:01:49,060 --> 00:01:51,210 The first one is soda-lime glass. 41 00:01:51,210 --> 00:01:53,740 And you see it contains silica, which 42 00:01:53,740 --> 00:01:55,150 is the network former. 43 00:01:55,150 --> 00:01:58,270 It contains sodium oxide, calcium oxide, 44 00:01:58,270 --> 00:01:59,710 and magnesium oxide. 45 00:01:59,710 --> 00:02:03,180 And these are alkaline earth oxides that are ionic, and so 46 00:02:03,180 --> 00:02:06,270 these are acting as network modifiers because they're 47 00:02:06,270 --> 00:02:10,240 donating oxide anions that go in and break 48 00:02:10,240 --> 00:02:12,670 the silicate chains. 49 00:02:12,670 --> 00:02:15,630 And then there's this Al203 and that's sort of halfway in 50 00:02:15,630 --> 00:02:16,490 between, isn't it? 51 00:02:16,490 --> 00:02:19,610 Silica is Group 4, or 14, if you want to 52 00:02:19,610 --> 00:02:21,500 use the modern notation. 53 00:02:21,500 --> 00:02:23,130 Sodium is Group 1. 54 00:02:23,130 --> 00:02:24,670 Calcium, magnesium, Group 2. 55 00:02:24,670 --> 00:02:28,160 Alumina is Group 3, and it's sort of halfway in between. 56 00:02:28,160 --> 00:02:29,030 It's amphoteric. 57 00:02:29,030 --> 00:02:31,680 It can either be a former or a modifier. 58 00:02:31,680 --> 00:02:34,140 And in these instances, depending on how much modifier 59 00:02:34,140 --> 00:02:39,150 is present, alumina can act as an intermediate. 60 00:02:39,150 --> 00:02:40,340 And what's an intermediate do? 61 00:02:40,340 --> 00:02:44,030 An intermediate is a covalent oxide. 62 00:02:44,030 --> 00:02:47,680 It's a covalent oxide, or an oxide that can act as both 63 00:02:47,680 --> 00:02:49,090 covalent and ionic. 64 00:02:49,090 --> 00:02:53,040 But in this instance, it's acting covalent oxide with a 65 00:02:53,040 --> 00:02:54,880 different coordination number. 66 00:02:59,200 --> 00:03:00,620 And what does that mean? 67 00:03:00,620 --> 00:03:02,670 Different coordination number? 68 00:03:02,670 --> 00:03:03,440 It coordinates-- 69 00:03:03,440 --> 00:03:06,070 remember last day I showed you B2O3? 70 00:03:06,070 --> 00:03:07,330 Borate glasses? 71 00:03:07,330 --> 00:03:09,790 So they have a coordination of three, whereas 72 00:03:09,790 --> 00:03:11,170 silicates have four. 73 00:03:11,170 --> 00:03:12,610 And what that means is that there's 74 00:03:12,610 --> 00:03:13,720 going to be a mismatch. 75 00:03:13,720 --> 00:03:16,640 There's still strong covalent bonds, but they don't fit 76 00:03:16,640 --> 00:03:17,510 quite right. 77 00:03:17,510 --> 00:03:20,190 And that's going to give even more free volume. 78 00:03:20,190 --> 00:03:24,190 And that excess free volume, through covalent bonds, gives 79 00:03:24,190 --> 00:03:26,950 you the ability to endure thermal shock. 80 00:03:26,950 --> 00:03:29,210 So if you want to impart thermal shock resistance in a 81 00:03:29,210 --> 00:03:33,290 glass, you give it lots of free volume so it can take the 82 00:03:33,290 --> 00:03:34,700 rapid change in temperature. 83 00:03:34,700 --> 00:03:40,810 So it's a covalent oxide with different coordination number. 84 00:03:40,810 --> 00:03:47,350 That is, nearest neighbors, in a covalent sense, from that of 85 00:03:47,350 --> 00:03:51,740 the network former. 86 00:03:51,740 --> 00:03:55,340 So you can add a borate or aluminate, what have you. 87 00:03:55,340 --> 00:03:58,090 And that'll give you thermal shock resistance. 88 00:03:58,090 --> 00:04:01,420 And so alumina here is acting as an intermediate. 89 00:04:01,420 --> 00:04:02,220 Let's go down here. 90 00:04:02,220 --> 00:04:03,960 There's borosilicate. 91 00:04:03,960 --> 00:04:06,650 borosilicate is the generic term for Pyrex. 92 00:04:06,650 --> 00:04:08,430 So Pyrex is a trade name. 93 00:04:08,430 --> 00:04:13,500 Pyrex was invented by Corning, and it contains silica as the 94 00:04:13,500 --> 00:04:14,620 network former. 95 00:04:14,620 --> 00:04:17,600 There's some sodium oxide, potassium oxide-- 96 00:04:17,600 --> 00:04:19,270 in rather small amounts. 97 00:04:19,270 --> 00:04:21,560 You can see this isn't a heavily modified network, but 98 00:04:21,560 --> 00:04:22,710 look at this. 99 00:04:22,710 --> 00:04:25,950 13% B2O3 and 2% alumina. 100 00:04:25,950 --> 00:04:27,220 That's the modifier. 101 00:04:27,220 --> 00:04:30,120 And what was the hallmark of Pyrex? 102 00:04:30,120 --> 00:04:32,120 It had thermal shock resistance. 103 00:04:32,120 --> 00:04:35,410 So you could take it out of the oven and put it under cold 104 00:04:35,410 --> 00:04:36,760 water and it didn't shatter. 105 00:04:36,760 --> 00:04:40,770 And we have the same analogous behavior for glass ware in the 106 00:04:40,770 --> 00:04:41,520 laboratory. 107 00:04:41,520 --> 00:04:44,420 For all room temperature and low temperature work in the 108 00:04:44,420 --> 00:04:48,630 laboratory, we use Pyrex that has this resistance to 109 00:04:48,630 --> 00:04:50,450 chemicals and resistance to heat. 110 00:04:50,450 --> 00:04:51,770 This is the big one, here. 111 00:04:51,770 --> 00:04:56,140 And that gave birth to functional crockery in the 112 00:04:56,140 --> 00:05:01,250 kitchen, where you could work in glass instead of in metal. 113 00:05:01,250 --> 00:05:04,570 And down here we see glass-- 114 00:05:04,570 --> 00:05:05,510 let's see, well, here's one. 115 00:05:05,510 --> 00:05:06,900 Light flint optical. 116 00:05:06,900 --> 00:05:08,220 See, that's 54%. 117 00:05:08,220 --> 00:05:11,150 It's down to 54% silica. 118 00:05:11,150 --> 00:05:14,160 And look at this-- boatloads of lead oxide. 119 00:05:14,160 --> 00:05:18,080 And the lead oxide is acting as a modifier and also changes 120 00:05:18,080 --> 00:05:19,850 the index of refraction. 121 00:05:19,850 --> 00:05:25,070 It modifies so much that we have almost down to the 122 00:05:25,070 --> 00:05:26,500 orthosilicate. 123 00:05:26,500 --> 00:05:30,390 So that the chains are modified to the point where 124 00:05:30,390 --> 00:05:32,770 they're almost all terminals. 125 00:05:32,770 --> 00:05:36,250 There's very little of this, and most of it is just 126 00:05:36,250 --> 00:05:37,710 terminal oxygens. 127 00:05:37,710 --> 00:05:40,960 And that means that it's more nearly crystalline, and 128 00:05:40,960 --> 00:05:41,990 therefore, you can cut it. 129 00:05:41,990 --> 00:05:45,760 And this is the lead crystal. 130 00:05:45,760 --> 00:05:48,000 Lead crystal has that high value. 131 00:05:48,000 --> 00:05:49,460 So you can see how that comes out. 132 00:05:49,460 --> 00:05:51,880 And this is also taken from the reading. 133 00:05:51,880 --> 00:05:55,140 It's a plot of viscosity versus temperature. 134 00:05:55,140 --> 00:05:56,580 Only it's a logarithmic plot. 135 00:05:56,580 --> 00:05:57,650 And what do you see? 136 00:05:57,650 --> 00:05:58,730 Here's pure silica. 137 00:05:58,730 --> 00:06:00,050 That's SiO2. 138 00:06:00,050 --> 00:06:03,560 And if I want to take it down to the point where, if the 139 00:06:03,560 --> 00:06:05,330 viscosity goes down, you have the ability to 140 00:06:05,330 --> 00:06:06,800 work with the glass. 141 00:06:06,800 --> 00:06:10,330 So if I want to melt silica, I've got to way, way up here. 142 00:06:10,330 --> 00:06:12,360 Over 2,000 Centigrade. 143 00:06:12,360 --> 00:06:15,890 So if I want to make bottles, if I want to make cookware, I 144 00:06:15,890 --> 00:06:17,990 don't want to run a lehr at this temperature. 145 00:06:17,990 --> 00:06:18,900 Lehr. 146 00:06:18,900 --> 00:06:19,950 L E H R. 147 00:06:19,950 --> 00:06:21,380 It's where you melt glass. 148 00:06:21,380 --> 00:06:24,040 Lehr. 149 00:06:24,040 --> 00:06:26,190 I don't want to run a lehr at this temperature. 150 00:06:26,190 --> 00:06:30,230 But you can see if I add modifier, the more modifier 151 00:06:30,230 --> 00:06:34,190 that I add, the more I break the network. 152 00:06:34,190 --> 00:06:37,190 So increasing modifier decreases network 153 00:06:37,190 --> 00:06:40,040 connectivity, and that means I can go to a lower temperature 154 00:06:40,040 --> 00:06:41,690 and get the same level of fluidity. 155 00:06:41,690 --> 00:06:44,250 So there's a whole bunch of definitions here that I'm not 156 00:06:44,250 --> 00:06:45,430 going to go over. 157 00:06:45,430 --> 00:06:46,470 You'll have this slide. 158 00:06:46,470 --> 00:06:50,430 But basically, it's just different points in 159 00:06:50,430 --> 00:06:51,610 processing. 160 00:06:51,610 --> 00:06:53,140 So if you go up here. 161 00:06:53,140 --> 00:06:54,260 Strain and annealing. 162 00:06:54,260 --> 00:06:56,060 I mean, these are very, very-- 163 00:06:56,060 --> 00:06:58,980 you're especially working with solid, whereas softening 164 00:06:58,980 --> 00:07:01,950 point, you start getting the glass to flow. 165 00:07:01,950 --> 00:07:05,390 And the working point, that's the viscosity that 166 00:07:05,390 --> 00:07:07,350 you have to get below. 167 00:07:07,350 --> 00:07:10,060 Otherwise, the glass is going to be to resistant to flow. 168 00:07:10,060 --> 00:07:12,740 You want to get the glass tacky so that you can put it 169 00:07:12,740 --> 00:07:16,390 into an injection mold, shape it, as they do with bottles. 170 00:07:16,390 --> 00:07:18,870 They take a blob of glass and boom, they just throw it into 171 00:07:18,870 --> 00:07:20,870 a mold and it sprays out. 172 00:07:20,870 --> 00:07:23,010 And if you've got the right mass and the right spinning, 173 00:07:23,010 --> 00:07:26,350 it makes the wall thickness proper. 174 00:07:26,350 --> 00:07:28,690 But you can imagine, if the glass is really, really 175 00:07:28,690 --> 00:07:31,470 viscous, it's not going to flow well enough. 176 00:07:31,470 --> 00:07:34,120 If it's too fluid, it'll drip all over. 177 00:07:34,120 --> 00:07:35,650 So there's an optimum in there. 178 00:07:35,650 --> 00:07:37,440 And this is telling you how to figure out what 179 00:07:37,440 --> 00:07:38,750 that optimum is. 180 00:07:38,750 --> 00:07:42,080 And you can see that as you change the composition, here's 181 00:07:42,080 --> 00:07:43,200 the working value. 182 00:07:43,200 --> 00:07:47,290 This is the viscosity that you have to get below which in 183 00:07:47,290 --> 00:07:48,160 order to work. 184 00:07:48,160 --> 00:07:50,550 And you can see that as you add more and more modifier, 185 00:07:50,550 --> 00:07:53,460 you can take the temperature and get it way, way down. 186 00:07:53,460 --> 00:07:56,330 So to work with silica you have to be about around 2,000. 187 00:07:56,330 --> 00:07:58,850 With soda-lime you can be down around 800. 188 00:07:58,850 --> 00:08:01,530 So that's going to cut your energy costs, isn't it? 189 00:08:01,530 --> 00:08:04,980 And it's going to make it easier to recycle. 190 00:08:04,980 --> 00:08:08,360 What's the point of recycling if you consume as much energy 191 00:08:08,360 --> 00:08:10,545 to recycle as if you started with virgin material? 192 00:08:10,545 --> 00:08:13,570 At least with virgin material you can guarantee the quality 193 00:08:13,570 --> 00:08:14,525 of the feeds stock. 194 00:08:14,525 --> 00:08:17,590 So there's got to be some big saving. 195 00:08:17,590 --> 00:08:18,440 All right. 196 00:08:18,440 --> 00:08:22,890 So that gives you a some sense as to what we can do 197 00:08:22,890 --> 00:08:24,335 technologically with glasses. 198 00:08:24,335 --> 00:08:28,340 I want to show you one last thing with glasses, and then 199 00:08:28,340 --> 00:08:30,610 we're going to move on to another topic. 200 00:08:30,610 --> 00:08:33,170 You know, new week, new day, new topic. 201 00:08:33,170 --> 00:08:35,160 So I want to go back to this curve. 202 00:08:35,160 --> 00:08:36,180 So what am I showing you here? 203 00:08:36,180 --> 00:08:40,210 I'm showing you that as we change the cooling rate, we 204 00:08:40,210 --> 00:08:43,060 change the amount of quenched-in excess volume. 205 00:08:43,060 --> 00:08:47,700 So fast cooling quenches in more of the liquid free volume 206 00:08:47,700 --> 00:08:48,950 than slow cooling does. 207 00:08:48,950 --> 00:08:52,520 That's why this V excess is small here, whereas V excess 208 00:08:52,520 --> 00:08:54,030 is large here for the other one. 209 00:08:54,030 --> 00:08:57,000 I'm going to use that in glass strengthening. 210 00:08:57,000 --> 00:08:58,250 So I want to strengthen. 211 00:09:00,720 --> 00:09:03,500 Strengthening glasses. 212 00:09:03,500 --> 00:09:06,170 We're talking about silicates or borates. 213 00:09:06,170 --> 00:09:08,210 Strengthening oxide glasses. 214 00:09:08,210 --> 00:09:10,030 Glass is a fantastic material. 215 00:09:10,030 --> 00:09:12,400 It's really good in compression, but it's no good 216 00:09:12,400 --> 00:09:13,400 in tensions. 217 00:09:13,400 --> 00:09:14,490 You know this. 218 00:09:14,490 --> 00:09:16,740 If you try to bend glass, it'll break. 219 00:09:16,740 --> 00:09:17,330 Why? 220 00:09:17,330 --> 00:09:19,170 Not because it doesn't have dislocations. 221 00:09:19,170 --> 00:09:21,350 It's got strong covalent bonds. 222 00:09:21,350 --> 00:09:24,300 But you know, suppose you want to strengthen the windshield 223 00:09:24,300 --> 00:09:26,200 of your car so that when a stone hits 224 00:09:26,200 --> 00:09:27,350 it, it doesn't shatter. 225 00:09:27,350 --> 00:09:30,280 What can we do to give it added strength? 226 00:09:30,280 --> 00:09:34,220 So I'm going to show you two ways, and both of them operate 227 00:09:34,220 --> 00:09:39,000 under this principle that the yield stress-- 228 00:09:39,000 --> 00:09:41,320 this is the stress that will break the glass, and I'm going 229 00:09:41,320 --> 00:09:43,390 to say the effective yield stress, what you 230 00:09:43,390 --> 00:09:45,320 experience in life-- 231 00:09:45,320 --> 00:09:51,510 is equal to the sum of what I'm going to call the natural 232 00:09:51,510 --> 00:09:54,660 yield stress, which is the basic property of the glass. 233 00:09:54,660 --> 00:09:59,000 Plus, I'm going to increase the surface stress. 234 00:09:59,000 --> 00:10:01,540 What I'm going to do is I'm going to modify the surface, 235 00:10:01,540 --> 00:10:04,840 and I'm going to put an additive stress at the 236 00:10:04,840 --> 00:10:08,950 surface, and that's going to be a compressive stress. 237 00:10:08,950 --> 00:10:12,920 So that means now the effective stress that I need 238 00:10:12,920 --> 00:10:15,390 to break the glass is going to be greater than it 239 00:10:15,390 --> 00:10:16,590 otherwise would be. 240 00:10:16,590 --> 00:10:21,350 So the whole gambit here is surface strengthening. 241 00:10:21,350 --> 00:10:25,232 Service strengthening, which means surface modification. 242 00:10:25,232 --> 00:10:28,250 And I'm going to show you two ways to modify the surface to 243 00:10:28,250 --> 00:10:30,310 bring the strength of the glass up. 244 00:10:30,310 --> 00:10:32,910 The first way is thermal. 245 00:10:32,910 --> 00:10:35,080 Thermal treatment. 246 00:10:35,080 --> 00:10:38,320 And the thermal treatment is to strengthen the glass. 247 00:10:38,320 --> 00:10:38,830 Well, let's see. 248 00:10:38,830 --> 00:10:42,050 Let's keep it in the context of the windshield. 249 00:10:42,050 --> 00:10:43,580 The technical term for this, the 250 00:10:43,580 --> 00:10:46,070 technological term is tempering. 251 00:10:46,070 --> 00:10:49,140 So what I'm going to show you was how we can look at that 252 00:10:49,140 --> 00:10:54,080 volume versus temperature curve and understand how we 253 00:10:54,080 --> 00:10:57,070 make tempered glass for windshields and so. 254 00:10:57,070 --> 00:10:59,400 So I'm going to show you a slab of glass. 255 00:10:59,400 --> 00:11:00,900 Here's a slab of glass. 256 00:11:00,900 --> 00:11:05,160 And we just got below the softening point-- so T just 257 00:11:05,160 --> 00:11:08,080 less than T softening. 258 00:11:08,080 --> 00:11:11,020 So now this thing's going to start, it's continuing to 259 00:11:11,020 --> 00:11:13,900 become more and more viscous and getting closer and closer 260 00:11:13,900 --> 00:11:15,580 to glass transition temperature. 261 00:11:15,580 --> 00:11:20,920 And what we're going to do is we're going to introduce air 262 00:11:20,920 --> 00:11:25,430 jets at the surface of the glass. 263 00:11:25,430 --> 00:11:27,750 What that's going to do is it's going to cause 264 00:11:27,750 --> 00:11:29,910 accelerated cooling at the surface. 265 00:11:29,910 --> 00:11:32,090 And the same thing happens on both surfaces, so I'm going to 266 00:11:32,090 --> 00:11:34,260 cut this piece of glass in half, and we're just going to 267 00:11:34,260 --> 00:11:35,125 look at the upper surface. 268 00:11:35,125 --> 00:11:36,800 The same thing happens in a lower surface. 269 00:11:36,800 --> 00:11:39,220 So let's now blow this up. 270 00:11:39,220 --> 00:11:41,630 I'm just going to look at the upper-half surface and I'm 271 00:11:41,630 --> 00:11:42,930 going to divide it into two zones. 272 00:11:45,530 --> 00:11:48,430 This is the first level, most primitive 273 00:11:48,430 --> 00:11:51,020 finite element analysis. 274 00:11:51,020 --> 00:11:54,150 Finite element analysis. 275 00:11:54,150 --> 00:11:56,300 I'm going to divide it in two, and I'm going to say, this has 276 00:11:56,300 --> 00:11:57,750 got two zones. 277 00:11:57,750 --> 00:12:00,260 Two cooling zones. 278 00:12:00,260 --> 00:12:03,490 Here is the zone of the center, OK? 279 00:12:03,490 --> 00:12:04,880 This is the center. 280 00:12:04,880 --> 00:12:09,170 And I'm going to call this the inner portion. 281 00:12:09,170 --> 00:12:10,430 And then there's the outer portion. 282 00:12:10,430 --> 00:12:13,090 Well, take a look at this curve here. 283 00:12:13,090 --> 00:12:15,340 Which is going to have slower cooling? 284 00:12:15,340 --> 00:12:17,895 In the center or near the free surface? 285 00:12:17,895 --> 00:12:21,030 The slower cooling is in the center and according to this 286 00:12:21,030 --> 00:12:25,800 graph, the slow cooling has a smaller residual volume. 287 00:12:25,800 --> 00:12:28,230 I've written, V-interior. 288 00:12:28,230 --> 00:12:29,890 That's the green line. 289 00:12:29,890 --> 00:12:32,610 And then the upper one is a yellow line. 290 00:12:32,610 --> 00:12:35,130 So the upper one where it's high cooling, it's going to 291 00:12:35,130 --> 00:12:36,210 have a higher volume. 292 00:12:36,210 --> 00:12:38,085 So this is the second piece of finite element. 293 00:12:38,085 --> 00:12:41,030 So I'm going to model this one like so. 294 00:12:41,030 --> 00:12:43,390 So this is outer. 295 00:12:43,390 --> 00:12:45,450 And the same thing happens on the other side, OK? 296 00:12:45,450 --> 00:12:47,340 So it's happening on the bottom as well. 297 00:12:47,340 --> 00:12:49,250 But we're just looking at the top because 298 00:12:49,250 --> 00:12:50,730 there's symmetry here. 299 00:12:50,730 --> 00:12:52,970 So you see what I've done? 300 00:12:52,970 --> 00:12:57,720 This is longer because that graph says it wants to be 301 00:12:57,720 --> 00:12:59,500 occupying a larger volume. 302 00:12:59,500 --> 00:13:02,160 Problem is the glass can't do this. 303 00:13:02,160 --> 00:13:04,970 I can do this with a piece of chalk, but the glass isn't 304 00:13:04,970 --> 00:13:06,030 going to look like that. 305 00:13:06,030 --> 00:13:08,250 The glass is going to have a flat edge. 306 00:13:08,250 --> 00:13:10,600 And how can it have a flat edge? 307 00:13:10,600 --> 00:13:13,880 Because the bottom, here-- this is not to scale, let's 308 00:13:13,880 --> 00:13:15,090 make it more to scale-- 309 00:13:15,090 --> 00:13:18,505 the top is a narrow zone and the bottom is a big, thick 310 00:13:18,505 --> 00:13:19,680 zone, isn't it? 311 00:13:19,680 --> 00:13:23,545 So this big, thick zone, which has a small volume, is going 312 00:13:23,545 --> 00:13:27,510 to pull on the thin upper zone, which has a large 313 00:13:27,510 --> 00:13:29,160 volume, and pull it in. 314 00:13:29,160 --> 00:13:30,010 Can you see that? 315 00:13:30,010 --> 00:13:32,110 And it's going to cause the introduction 316 00:13:32,110 --> 00:13:35,530 of compressive stresses. 317 00:13:35,530 --> 00:13:39,520 So we got to compressive stresses simply using that 318 00:13:39,520 --> 00:13:43,650 graph and a little bit of air. 319 00:13:43,650 --> 00:13:46,520 So you take that graph, put differential cooling, and now 320 00:13:46,520 --> 00:13:48,290 you've introduced compressive stress. 321 00:13:48,290 --> 00:13:50,570 And that's all tempered glass is. 322 00:13:50,570 --> 00:13:57,040 So the V-excess of the outer layer is greater than V-excess 323 00:13:57,040 --> 00:14:01,810 of the inner layer, or the interior, if you like. 324 00:14:01,810 --> 00:14:02,420 And why? 325 00:14:02,420 --> 00:14:06,070 Because the cooling rate, the change of temperature with 326 00:14:06,070 --> 00:14:13,400 time of the outer zone, is greater than the cooling rate 327 00:14:13,400 --> 00:14:18,000 of the inner or interior. 328 00:14:18,000 --> 00:14:19,950 And there it is. 329 00:14:19,950 --> 00:14:20,890 That's the beginning. 330 00:14:20,890 --> 00:14:25,140 And so now to fracture you have to apply a greater stress 331 00:14:25,140 --> 00:14:27,270 then you would have otherwise. 332 00:14:27,270 --> 00:14:29,980 So that's good, and that saves a lot of lives. 333 00:14:29,980 --> 00:14:31,260 There's another way. 334 00:14:31,260 --> 00:14:33,920 There's another way to surface strengthen, and that's a 335 00:14:33,920 --> 00:14:35,170 chemical treatment. 336 00:14:37,750 --> 00:14:39,030 And again, what am I trying to do? 337 00:14:39,030 --> 00:14:40,950 I'm trying to introduce a compressive stress, but I'm 338 00:14:40,950 --> 00:14:44,590 going to use a chemical means. 339 00:14:44,590 --> 00:14:49,050 And this one is called ion exchange. 340 00:14:49,050 --> 00:14:51,840 And this is used in technology, too. 341 00:14:51,840 --> 00:14:55,280 So now I'm going to take a piece of glass here. 342 00:14:55,280 --> 00:15:01,550 This is solid glass and let's put some components in here. 343 00:15:01,550 --> 00:15:05,720 So I'm going to put some silica as my network former. 344 00:15:05,720 --> 00:15:08,550 I'm going to put some sodium oxide. 345 00:15:08,550 --> 00:15:12,120 And I'm going to put some modifier, B2O3. 346 00:15:12,120 --> 00:15:13,510 So I got all three here. 347 00:15:13,510 --> 00:15:16,560 Former, modifier, intermediate. 348 00:15:16,560 --> 00:15:19,800 And just to put a little skin on the bones here, I want to 349 00:15:19,800 --> 00:15:23,050 show what the sodium oxide actually looks like. 350 00:15:23,050 --> 00:15:29,700 Sodium oxide goes in as sodium cations, and oxide anions. 351 00:15:29,700 --> 00:15:31,510 The oxide anions go in and they break some 352 00:15:31,510 --> 00:15:32,850 of the silica chains. 353 00:15:32,850 --> 00:15:34,870 But the sodiums don't get involved in that. 354 00:15:34,870 --> 00:15:37,560 They just sit around as spectators. 355 00:15:37,560 --> 00:15:39,270 Now what I'm going to do is I'm going to put this, I'm 356 00:15:39,270 --> 00:15:45,600 going to soak this in molten salt. 357 00:15:45,600 --> 00:15:46,900 Soak in molten salt. 358 00:15:46,900 --> 00:15:50,190 This is huge area of my own research. 359 00:15:50,190 --> 00:15:54,550 And the molten salt, one example might be I'm going to 360 00:15:54,550 --> 00:15:56,030 take potassium chloride. 361 00:15:56,030 --> 00:15:58,610 Remember, we talked about making aluminum or magnesium? 362 00:15:58,610 --> 00:16:00,235 This is one of the constituents of the melt in 363 00:16:00,235 --> 00:16:02,340 which we make electrolytic magnesium. 364 00:16:02,340 --> 00:16:03,480 Potassium chloride. 365 00:16:03,480 --> 00:16:08,560 And it exists as potassium cations and chloride anions. 366 00:16:12,040 --> 00:16:14,120 Chlorine is green, except we know-- 367 00:16:14,120 --> 00:16:15,900 you know, this is the way chemistry books write it, but 368 00:16:15,900 --> 00:16:19,020 that's stupid because this is isoelectronic with argon. 369 00:16:19,020 --> 00:16:20,200 And it's not green. 370 00:16:20,200 --> 00:16:20,510 I know. 371 00:16:20,510 --> 00:16:21,530 I've looked at this stuff. 372 00:16:21,530 --> 00:16:23,540 It's clear, colorless, and transparent. 373 00:16:23,540 --> 00:16:26,490 The chloride ion has to be clear and colorless. 374 00:16:26,490 --> 00:16:28,780 It's got a complete shell, but the chemistry books 375 00:16:28,780 --> 00:16:29,460 will make it green. 376 00:16:29,460 --> 00:16:32,900 Anyway, here's the potassium ion here. 377 00:16:32,900 --> 00:16:34,640 And there's a lot of potassium ion here. 378 00:16:34,640 --> 00:16:37,440 There's no potassium ion inside the glass. 379 00:16:37,440 --> 00:16:39,970 There's sodium ion in the glass, there's no sodium ion 380 00:16:39,970 --> 00:16:41,385 in the molten salt. 381 00:16:41,385 --> 00:16:45,970 But these are both media in which ions live. 382 00:16:45,970 --> 00:16:48,790 So can you see this is sort of like the perfume bottle? 383 00:16:48,790 --> 00:16:50,680 Things move from high concentration to low 384 00:16:50,680 --> 00:16:51,760 concentration. 385 00:16:51,760 --> 00:16:55,380 Some sodium wants to leave and enter the melt. 386 00:16:55,380 --> 00:16:58,770 And some potassium wants to leave the melt 387 00:16:58,770 --> 00:17:00,865 and enter the glass. 388 00:17:00,865 --> 00:17:02,840 And where's the potassium going to go? 389 00:17:02,840 --> 00:17:05,310 It has to go where there used to be sodium. 390 00:17:05,310 --> 00:17:07,440 What's the relative size of potassium ion 391 00:17:07,440 --> 00:17:08,840 versus sodium ion? 392 00:17:08,840 --> 00:17:10,590 Potassium ion is bigger. 393 00:17:10,590 --> 00:17:14,330 So potassium ion goes and occupies a site formerly 394 00:17:14,330 --> 00:17:19,500 occupied by sodium and causes compressive stress, because 395 00:17:19,500 --> 00:17:22,990 you get all these big ions jamming in there and that's 396 00:17:22,990 --> 00:17:27,400 going to lead to compressive stress through ion exchange. 397 00:17:27,400 --> 00:17:30,190 So through ion exchange we can raised the temp. 398 00:17:30,190 --> 00:17:34,240 Since r, the radius of potassium is greater than the 399 00:17:34,240 --> 00:17:39,030 radius of the sodium, we get a force fit, and this is how we 400 00:17:39,030 --> 00:17:42,360 got solution hardening. 401 00:17:42,360 --> 00:17:47,250 Hardening is the metallurgical term for raising the strength. 402 00:17:47,250 --> 00:17:50,730 Hardening is equal to strength going up. 403 00:17:50,730 --> 00:17:53,250 So we get hardening by solution. 404 00:17:53,250 --> 00:17:55,720 So this is solution hardening. 405 00:17:55,720 --> 00:17:59,350 Solution hardening because the potassium ion is in there. 406 00:17:59,350 --> 00:18:00,730 So we have surface. 407 00:18:00,730 --> 00:18:02,210 And this gives a lot of strength. 408 00:18:02,210 --> 00:18:05,400 We do the same thing metallurgically if you 409 00:18:05,400 --> 00:18:07,950 carburize the surface of a piece of steel. 410 00:18:07,950 --> 00:18:10,740 Tool steels, for example, surface carburized. 411 00:18:10,740 --> 00:18:13,630 So we get hard surfaces that can cut. 412 00:18:13,630 --> 00:18:15,630 You say, well, why don't you just put the carbon in all the 413 00:18:15,630 --> 00:18:16,170 way through? 414 00:18:16,170 --> 00:18:18,220 Well, then the tool bit will be brittle. 415 00:18:18,220 --> 00:18:21,060 So you want something that's got toughness in the center so 416 00:18:21,060 --> 00:18:23,460 it can take the impact, but it's got surface 417 00:18:23,460 --> 00:18:25,110 hardness so it'll cut. 418 00:18:25,110 --> 00:18:26,380 And that's an engineered material. 419 00:18:26,380 --> 00:18:29,330 We've got one set of properties at the surface, and 420 00:18:29,330 --> 00:18:31,440 we've got another set of properties in the bulk. 421 00:18:31,440 --> 00:18:36,240 And it's all brought to you by control of chemistry. 422 00:18:36,240 --> 00:18:38,990 And then that's also control of chemistry. 423 00:18:38,990 --> 00:18:39,880 OK. 424 00:18:39,880 --> 00:18:42,820 So I mean, I could talk more and more and more. 425 00:18:42,820 --> 00:18:45,030 Glasses are just fascinating things. 426 00:18:45,030 --> 00:18:47,090 But we've got to get moving. 427 00:18:47,090 --> 00:18:49,540 So we're going to move to a new topic. 428 00:18:49,540 --> 00:18:51,630 We're going to move to a new topic today. 429 00:18:51,630 --> 00:18:54,280 We're going to start talking about kinetics. 430 00:18:54,280 --> 00:18:55,530 Kinetics. 431 00:18:57,110 --> 00:18:58,280 And what is kinetics? 432 00:18:58,280 --> 00:19:02,790 Kinetics is the topic that we put into 3.091, because it's 433 00:19:02,790 --> 00:19:06,140 important, of course, but it's all about the study of 434 00:19:06,140 --> 00:19:08,240 reaction rates. 435 00:19:08,240 --> 00:19:14,235 It's the study of reaction rates and mechanism. 436 00:19:21,700 --> 00:19:23,210 So why do we study? 437 00:19:23,210 --> 00:19:27,250 Well, we study it because I think it belongs here. 438 00:19:27,250 --> 00:19:30,820 But first of all, kinetics is related to productivity and 439 00:19:30,820 --> 00:19:31,510 resource utilization. 440 00:19:31,510 --> 00:19:32,920 You've got two factories. 441 00:19:32,920 --> 00:19:37,060 One produces 200 units per time, the other produces 100 442 00:19:37,060 --> 00:19:37,860 units per time. 443 00:19:37,860 --> 00:19:40,410 The one that's producing 100 units per time probably isn't 444 00:19:40,410 --> 00:19:43,300 going to be in business that much longer. 445 00:19:43,300 --> 00:19:46,450 And it's all about understanding how to get more 446 00:19:46,450 --> 00:19:50,000 throughput per unit time, and that leads to competitiveness. 447 00:19:50,000 --> 00:19:53,010 So if you're interested in international competitiveness, 448 00:19:53,010 --> 00:19:54,640 you've got to know something about kinetics. 449 00:19:54,640 --> 00:19:56,290 The two go hand in glove. 450 00:19:56,290 --> 00:19:57,760 Second thing is energy and the environment. 451 00:19:57,760 --> 00:20:01,290 A number of you have come to talk to me after class, sent 452 00:20:01,290 --> 00:20:03,120 emails because you're interested in energy and the 453 00:20:03,120 --> 00:20:03,940 environment. 454 00:20:03,940 --> 00:20:07,740 Efficient use of energy involves understanding the 455 00:20:07,740 --> 00:20:11,160 kinetics so you can force chemical change with the least 456 00:20:11,160 --> 00:20:15,320 amount of energy utilization and do so in a way because its 457 00:20:15,320 --> 00:20:16,340 mechanism-- 458 00:20:16,340 --> 00:20:18,830 if there's two mechanisms that allow you to get to the same 459 00:20:18,830 --> 00:20:21,770 end product, choose the one that has the least toxic 460 00:20:21,770 --> 00:20:23,550 impact on the environment. 461 00:20:23,550 --> 00:20:27,010 Otherwise, you're going to have to spend money to avoid 462 00:20:27,010 --> 00:20:30,110 the effluents, which then gets you back up to number one. 463 00:20:30,110 --> 00:20:33,260 Your cost of doing business is higher than the other guy. 464 00:20:33,260 --> 00:20:34,090 Guess what? 465 00:20:34,090 --> 00:20:35,980 You're creamed in the marketplace. 466 00:20:35,980 --> 00:20:37,290 And lastly, societal. 467 00:20:37,290 --> 00:20:42,680 And this is one that excites me, is kinetics leads to 468 00:20:42,680 --> 00:20:45,440 productivity, which keeps factories open, which keeps 469 00:20:45,440 --> 00:20:46,800 people working. 470 00:20:46,800 --> 00:20:48,640 So through understanding kinetics. 471 00:20:48,640 --> 00:20:51,900 You go and you look at places in the United States where 472 00:20:51,900 --> 00:20:53,300 factories have closed. 473 00:20:53,300 --> 00:20:58,506 In many, many instances it was because the technology lagged. 474 00:20:58,506 --> 00:21:01,330 If you could just keep things going faster. 475 00:21:01,330 --> 00:21:02,835 You've got to make things-- you know how fast you've got 476 00:21:02,835 --> 00:21:03,740 to make them go? 477 00:21:03,740 --> 00:21:05,970 You've got to make them go so fast that even if the foreign 478 00:21:05,970 --> 00:21:08,560 workers are paid zero, you can still beat them in the 479 00:21:08,560 --> 00:21:09,490 marketplace. 480 00:21:09,490 --> 00:21:11,190 That's your standard. 481 00:21:11,190 --> 00:21:12,840 So that's how you design your processes. 482 00:21:12,840 --> 00:21:16,910 You design your processes so that you can produce at very, 483 00:21:16,910 --> 00:21:19,080 very low cost. 484 00:21:19,080 --> 00:21:21,810 And there's a huge range in reaction rates. 485 00:21:21,810 --> 00:21:25,980 You know, you can start the range of 486 00:21:25,980 --> 00:21:28,120 rates, rates of reaction. 487 00:21:28,120 --> 00:21:31,570 At the one that you have very, very slow. 488 00:21:31,570 --> 00:21:35,450 And way over here you have very, very fast, all right? 489 00:21:35,450 --> 00:21:36,970 So on the slow end, you have stuff that's 490 00:21:36,970 --> 00:21:39,740 sort of cosmic scale. 491 00:21:39,740 --> 00:21:40,990 Geological. 492 00:21:43,050 --> 00:21:44,320 And then over here, what do we have? 493 00:21:44,320 --> 00:21:45,570 We have explosions. 494 00:21:47,820 --> 00:21:50,190 You might say, well, explosions are usually bad, 495 00:21:50,190 --> 00:21:50,540 aren't they? 496 00:21:50,540 --> 00:21:51,360 Well, no. 497 00:21:51,360 --> 00:21:53,680 I can give you an example of where explosion is used to 498 00:21:53,680 --> 00:21:55,750 your advantage. 499 00:21:55,750 --> 00:21:57,230 The airbag in the automobile. 500 00:21:57,230 --> 00:22:00,570 There is no pump, no mechanical pump fast enough to 501 00:22:00,570 --> 00:22:03,320 inflate an airbag on demand. 502 00:22:03,320 --> 00:22:05,190 So how do we make those airbags work? 503 00:22:05,190 --> 00:22:08,370 And I hope none of us ever has to be present at the 504 00:22:08,370 --> 00:22:09,760 deployment of those airbags. 505 00:22:09,760 --> 00:22:12,460 But you know, just academically let's talk about 506 00:22:12,460 --> 00:22:13,470 how they work. 507 00:22:13,470 --> 00:22:19,550 There's like an explosion that occurs when you're driving. 508 00:22:19,550 --> 00:22:22,325 There's an accelerometer and this is a key piece. 509 00:22:22,325 --> 00:22:24,690 The accelerometer has to make a decision whether you're 510 00:22:24,690 --> 00:22:27,050 applying the brakes just because you've lost focus and 511 00:22:27,050 --> 00:22:28,390 you're, you know, whoops! 512 00:22:28,390 --> 00:22:29,650 You've had that jerky brake. 513 00:22:29,650 --> 00:22:33,090 Or maybe this is one of those holy-mackerel moments, and 514 00:22:33,090 --> 00:22:34,420 your jamming on the brakes, and we'd 515 00:22:34,420 --> 00:22:35,840 better deploy the airbags. 516 00:22:35,840 --> 00:22:40,390 Once the accelerometer decides that this is one of those holy 517 00:22:40,390 --> 00:22:43,410 you-know-what moments, it sends an electric current 518 00:22:43,410 --> 00:22:46,990 through a wire, which then raises the temperature to 300 519 00:22:46,990 --> 00:22:50,150 degrees C and causes this reaction to take place. 520 00:22:50,150 --> 00:22:52,970 When this reaction takes place, this is a solid, 521 00:22:52,970 --> 00:22:54,450 nitrogen is a gas. 522 00:22:54,450 --> 00:22:57,910 So the gas has a much, much higher volume than the solid 523 00:22:57,910 --> 00:23:00,400 and within milliseconds you get inflation. 524 00:23:00,400 --> 00:23:03,320 Well, that's good and that inflates the bag and prevents 525 00:23:03,320 --> 00:23:06,580 you from hitting the hard parts of the car. 526 00:23:06,580 --> 00:23:07,870 But you see the other byproduct? 527 00:23:07,870 --> 00:23:08,780 That's sodium. 528 00:23:08,780 --> 00:23:11,150 And if you look on your Periodic Table, elemental 529 00:23:11,150 --> 00:23:15,110 sodium is liquid above 98 degrees Celsius. 530 00:23:15,110 --> 00:23:16,580 So now you've got liquid sodium. 531 00:23:16,580 --> 00:23:19,430 There's no point preserving the safety of the occupants of 532 00:23:19,430 --> 00:23:21,810 the car just to cover them with liquid sodium. 533 00:23:21,810 --> 00:23:23,270 So we better do something about that. 534 00:23:23,270 --> 00:23:26,410 So being chemists, what we do is we add potassium nitrate 535 00:23:26,410 --> 00:23:28,060 inside the bag, as well. 536 00:23:28,060 --> 00:23:28,300 so. 537 00:23:28,300 --> 00:23:31,290 That that sodium is mopped up with potassium nitrate, which 538 00:23:31,290 --> 00:23:35,070 converts it to sodium oxide, potassium oxide, and a little 539 00:23:35,070 --> 00:23:35,593 more nitrogen. 540 00:23:35,593 --> 00:23:36,300 [BLOWING SOUND EFFECT] 541 00:23:36,300 --> 00:23:39,660 Keep the bag nice and firm. 542 00:23:39,660 --> 00:23:44,026 But now what happens when the Fires show up and they 543 00:23:44,026 --> 00:23:44,760 [SOUND EFFECT], 544 00:23:44,760 --> 00:23:46,670 you know, they start pouring water on it. 545 00:23:46,670 --> 00:23:48,440 This turns into caustic. 546 00:23:48,440 --> 00:23:52,072 So now you're going to get covered and wet lye. 547 00:23:52,072 --> 00:23:55,140 So that's probably not too good, either. 548 00:23:55,140 --> 00:23:58,540 Just remember, you've been physically saved from smashing 549 00:23:58,540 --> 00:24:01,470 your skull on the tempered windshield. 550 00:24:01,470 --> 00:24:04,680 So it's so far, so good. 551 00:24:04,680 --> 00:24:07,350 So now what? 552 00:24:07,350 --> 00:24:10,200 You want a mechanical, you want a Newtonian death? 553 00:24:10,200 --> 00:24:15,260 Or do you want a Coulombic death? 554 00:24:15,260 --> 00:24:17,210 I guess that's the question, here. 555 00:24:17,210 --> 00:24:19,500 And so we're going to keep doing some chemistry here and 556 00:24:19,500 --> 00:24:20,820 we're going to add silica. 557 00:24:20,820 --> 00:24:23,290 And what happens if we add silica to sodium oxide 558 00:24:23,290 --> 00:24:24,190 potassium oxide? 559 00:24:24,190 --> 00:24:26,870 Well that's a network former, these are network modifiers. 560 00:24:26,870 --> 00:24:29,370 We'll make an alkaline silicate glass and that's OK 561 00:24:29,370 --> 00:24:31,330 because we put food and beverages in 562 00:24:31,330 --> 00:24:33,040 alkaline silicate glasses. 563 00:24:33,040 --> 00:24:34,240 So everybody is happy. 564 00:24:34,240 --> 00:24:36,595 So that's all the chemistry that goes on inside an airbag. 565 00:24:36,595 --> 00:24:39,740 And we've got to understand the kinetics. 566 00:24:39,740 --> 00:24:42,400 So I hope I've whet your appetite. 567 00:24:42,400 --> 00:24:43,350 OK, that's enough of that. 568 00:24:43,350 --> 00:24:45,430 Now let's get to the real stuff. 569 00:24:45,430 --> 00:24:49,010 So let's write a general chemical reaction. 570 00:24:49,010 --> 00:24:50,090 The general reaction. 571 00:24:50,090 --> 00:24:53,740 What's the formalism if we want to set up the metrics? 572 00:24:53,740 --> 00:24:57,540 So I'm going to write just a plain, old equation. 573 00:24:57,540 --> 00:25:01,210 This is the classical P-Chem stuff. 574 00:25:01,210 --> 00:25:04,920 Little a moles of A, plus little b moles of B go to 575 00:25:04,920 --> 00:25:07,680 little c moles of C plus little d moles of D. 576 00:25:07,680 --> 00:25:09,590 So this could have been lecture two. 577 00:25:09,590 --> 00:25:11,520 Just a straight chemical reaction. 578 00:25:11,520 --> 00:25:13,400 Remember we were studying stoichiometry? 579 00:25:13,400 --> 00:25:16,885 So the constituents of the left side of the equation are 580 00:25:16,885 --> 00:25:19,480 called the reactants, whereas on the right side of the 581 00:25:19,480 --> 00:25:22,790 equation we have the products. 582 00:25:22,790 --> 00:25:28,190 And what kinetics gives us, kinetics tells us the rate of 583 00:25:28,190 --> 00:25:29,440 conversion. 584 00:25:31,380 --> 00:25:32,730 Or the rate of reaction. 585 00:25:32,730 --> 00:25:35,100 I'm using all these terms so you understand their 586 00:25:35,100 --> 00:25:36,860 equivalent. 587 00:25:36,860 --> 00:25:45,320 So we can write something like this where the conservation of 588 00:25:45,320 --> 00:25:46,130 mass kicks in. 589 00:25:46,130 --> 00:25:48,230 So I can't make products any faster 590 00:25:48,230 --> 00:25:49,920 than I consume reactants. 591 00:25:49,920 --> 00:25:51,750 There's no sources or sinks here. 592 00:25:51,750 --> 00:25:53,640 When I lose reactants, I make products. 593 00:25:53,640 --> 00:25:57,850 So I'm going to say, the rate of change of the total mass of 594 00:25:57,850 --> 00:25:59,710 the reactants-- this is summation sign-- 595 00:25:59,710 --> 00:26:03,510 I'm just saying the rate of change of the sum of all of 596 00:26:03,510 --> 00:26:06,530 the reactions must equal the rate of change. 597 00:26:06,530 --> 00:26:10,470 So the loss rate of reactants must equal the gain rate of 598 00:26:10,470 --> 00:26:12,680 all of the products. 599 00:26:12,680 --> 00:26:15,130 That's just simple stoichiometry. 600 00:26:15,130 --> 00:26:17,900 Or some people call this conservation of mass or Law of 601 00:26:17,900 --> 00:26:19,680 Mass Action, what have you. 602 00:26:19,680 --> 00:26:23,030 And then we count by concentration, usually. 603 00:26:26,440 --> 00:26:26,900 Just reminder. 604 00:26:26,900 --> 00:26:28,270 This is lowercase c. 605 00:26:28,270 --> 00:26:31,430 So this is the concentration of species i 606 00:26:31,430 --> 00:26:33,110 goes as the mole number. 607 00:26:33,110 --> 00:26:37,290 n is mole number divided by the volume of the reactor. 608 00:26:37,290 --> 00:26:42,330 So this would be in moles per meter cubed if 609 00:26:42,330 --> 00:26:43,770 we were in SI units. 610 00:26:43,770 --> 00:26:48,090 So therefore the rate of change, the ci by dt, is 611 00:26:48,090 --> 00:26:51,760 really the rate of change of mole number, isn't it? 612 00:26:51,760 --> 00:26:54,820 It's moles of i disappearing, but the volume 613 00:26:54,820 --> 00:26:56,900 doesn't change, typically. 614 00:26:56,900 --> 00:27:00,980 And then the last thing is we can use this idea up here that 615 00:27:00,980 --> 00:27:04,980 concentration of products can only equal the loss rate of 616 00:27:04,980 --> 00:27:06,140 the reactant. 617 00:27:06,140 --> 00:27:11,890 So I can write, term by term, the normalized rate loss of 618 00:27:11,890 --> 00:27:15,500 the concentration of a divided by its stoichiometric 619 00:27:15,500 --> 00:27:18,780 coefficient, for example, would equal the normalized 620 00:27:18,780 --> 00:27:23,210 weight gain, or pardon me, the concentration gain of the 621 00:27:23,210 --> 00:27:24,990 concentration of d. 622 00:27:24,990 --> 00:27:28,750 So this is just saying a disappears no faster than d 623 00:27:28,750 --> 00:27:32,490 appears, mediated by the stoichiometric coefficients. 624 00:27:32,490 --> 00:27:39,550 So this is just Law of Mass Action, which is stoichiometry 625 00:27:39,550 --> 00:27:41,290 in motion, isn't it? 626 00:27:41,290 --> 00:27:43,930 That's all it is. 627 00:27:43,930 --> 00:27:48,890 Now here comes the cool thing kinetic theory. 628 00:27:48,890 --> 00:27:51,670 We look at any reaction, I can tell you right now what it 629 00:27:51,670 --> 00:27:52,330 looks like. 630 00:27:52,330 --> 00:27:56,200 If I applied concentration of i as a function of time, I 631 00:27:56,200 --> 00:28:00,410 start off with some value c naught, some initial value, 632 00:28:00,410 --> 00:28:03,310 and it just attenuates. 633 00:28:03,310 --> 00:28:07,020 We know that's going to happen as we consume the-- it falls 634 00:28:07,020 --> 00:28:08,490 and there's some curvature here. 635 00:28:08,490 --> 00:28:11,990 What we're trying to do next is to give some mathematical 636 00:28:11,990 --> 00:28:13,780 representation to this. 637 00:28:13,780 --> 00:28:17,050 Can we come up with a mathematical formulation of 638 00:28:17,050 --> 00:28:18,490 the shape of that curve? 639 00:28:18,490 --> 00:28:21,660 And we can, and here's the central 640 00:28:21,660 --> 00:28:25,540 tenet kinetic of theory. 641 00:28:25,540 --> 00:28:36,640 Kinetic theory says that the reaction rate can be expressed 642 00:28:36,640 --> 00:28:38,187 in terms of a driving force. 643 00:28:46,020 --> 00:28:48,670 And that driving force is the instant concentration. 644 00:28:51,170 --> 00:28:51,420 OK. 645 00:28:51,420 --> 00:28:52,230 These are lofty words. 646 00:28:52,230 --> 00:28:54,745 I'll show you what it means with illustration. 647 00:28:57,970 --> 00:29:00,570 So that's the overall idea. 648 00:29:00,570 --> 00:29:06,250 So now let's say that the rate of change, the instant rate of 649 00:29:06,250 --> 00:29:14,190 change of concentration ci, is proportional to the instant 650 00:29:14,190 --> 00:29:16,410 value of the concentration. 651 00:29:16,410 --> 00:29:17,230 And you know, the concentration 652 00:29:17,230 --> 00:29:18,830 is changing, right? 653 00:29:18,830 --> 00:29:20,470 As the concentration decreases, the 654 00:29:20,470 --> 00:29:21,670 rate of change decreases. 655 00:29:21,670 --> 00:29:25,655 So just this alone, this idea alone would rationalize a 656 00:29:25,655 --> 00:29:27,460 curve like that. 657 00:29:27,460 --> 00:29:29,940 As the concentration falls, the rate of change falls, 658 00:29:29,940 --> 00:29:32,430 which means the concentration falls, which means-- 659 00:29:32,430 --> 00:29:35,640 and raised to some power-- 660 00:29:35,640 --> 00:29:37,120 it's not linear, necessarily-- 661 00:29:37,120 --> 00:29:40,770 raised to some power. 662 00:29:40,770 --> 00:29:43,250 There's a power law at work here. 663 00:29:43,250 --> 00:29:45,300 So now let's do this one more time. 664 00:29:45,300 --> 00:29:46,530 I'm going to write it mathematically. 665 00:29:46,530 --> 00:29:48,780 But I want you to first see the word, concepts. 666 00:29:48,780 --> 00:29:50,170 So let's write it mathematically. 667 00:29:50,170 --> 00:29:53,590 That means minus dci by dt-- 668 00:29:53,590 --> 00:29:57,260 so this is time rate a change of concentration i, the minus 669 00:29:57,260 --> 00:29:59,160 means it's falling-- 670 00:29:59,160 --> 00:30:05,160 is equal to the concentration of i raised to some power n. 671 00:30:05,160 --> 00:30:06,580 This is order reaction. 672 00:30:06,580 --> 00:30:08,060 It's not mole number over there. 673 00:30:08,060 --> 00:30:10,300 You've got to be pluralistic today. 674 00:30:10,300 --> 00:30:11,730 n is going to be used in different ways. 675 00:30:11,730 --> 00:30:18,510 So this is called order of reaction. 676 00:30:18,510 --> 00:30:19,825 And there's a constant. 677 00:30:19,825 --> 00:30:20,480 See up there? 678 00:30:20,480 --> 00:30:21,850 It's a proportionality. 679 00:30:21,850 --> 00:30:24,660 Here it's an equal sign, thanks to the constant. 680 00:30:24,660 --> 00:30:26,270 And this is called the rate constant. 681 00:30:30,980 --> 00:30:33,300 And this what all I need for plant design. 682 00:30:33,300 --> 00:30:37,300 Suppose I'm running a chemical plant and I'm taking a plus b 683 00:30:37,300 --> 00:30:39,590 and making c plus d and the management says, we want to 684 00:30:39,590 --> 00:30:41,000 double the rate of productivity. 685 00:30:41,000 --> 00:30:42,440 So you go, I know what to do. 686 00:30:42,440 --> 00:30:44,230 We'll increase the concentration. 687 00:30:44,230 --> 00:30:46,180 They say, by how much? 688 00:30:46,180 --> 00:30:49,230 Well, this allows you, if you know the value of k and n, you 689 00:30:49,230 --> 00:30:50,600 want to double this? 690 00:30:50,600 --> 00:30:53,090 Then you know what to do here. 691 00:30:53,090 --> 00:30:55,620 It's not necessarily double the concentration, Because 692 00:30:55,620 --> 00:30:57,710 this is a 1.5 power. 693 00:30:57,710 --> 00:30:59,720 By the way, this doesn't have to be an integer. 694 00:30:59,720 --> 00:31:00,760 Could be anything. 695 00:31:00,760 --> 00:31:11,180 Could be not necessarily integer and must be determined 696 00:31:11,180 --> 00:31:12,430 by experiment. 697 00:31:14,650 --> 00:31:17,030 You can't look at an equation and say, oh, that's going to 698 00:31:17,030 --> 00:31:17,980 be second order because there's a 699 00:31:17,980 --> 00:31:19,950 two in front of something. 700 00:31:19,950 --> 00:31:22,385 So here we are, plant designers. 701 00:31:22,385 --> 00:31:24,680 And the management wants to know, how do 702 00:31:24,680 --> 00:31:25,690 we make things happen? 703 00:31:25,690 --> 00:31:27,960 So I'm going to go back to that equation over there and 704 00:31:27,960 --> 00:31:32,890 I'll say that most generally, the rate of change of 705 00:31:32,890 --> 00:31:38,050 concentration of a will then go as rate constant times the 706 00:31:38,050 --> 00:31:39,370 concentration of a. 707 00:31:39,370 --> 00:31:41,860 See, the rate of change goes as something 708 00:31:41,860 --> 00:31:43,550 to the power alpha. 709 00:31:43,550 --> 00:31:47,470 But it could also be influenced by b. 710 00:31:47,470 --> 00:31:49,470 So I'm going to put-- this is the most general form. 711 00:31:49,470 --> 00:31:51,150 Then once you make your measurements, a lot 712 00:31:51,150 --> 00:31:52,570 of these fall out. 713 00:31:52,570 --> 00:31:56,120 I'm even going to put c I'm going to put d. 714 00:31:56,120 --> 00:31:58,900 Everything was in that equation. 715 00:31:58,900 --> 00:32:00,270 You might say, well, wait a minute. 716 00:32:00,270 --> 00:32:03,630 How can the rate of consumption of a be influenced 717 00:32:03,630 --> 00:32:05,350 by the concentration of d? 718 00:32:05,350 --> 00:32:07,090 d is a product. 719 00:32:07,090 --> 00:32:08,490 I'll give you two examples. 720 00:32:08,490 --> 00:32:13,070 One is that d, when I'm making d, d happens to have some 721 00:32:13,070 --> 00:32:15,350 catalytic value. 722 00:32:15,350 --> 00:32:19,740 So when I start making a convert to d, d catalyzes the 723 00:32:19,740 --> 00:32:22,810 reaction, which makes it go faster, which makes more d, 724 00:32:22,810 --> 00:32:27,060 which makes the reaction go faster, in which case this is 725 00:32:27,060 --> 00:32:28,810 going to have a profound effect. 726 00:32:28,810 --> 00:32:32,010 And unfortunately, there are some other situations where a 727 00:32:32,010 --> 00:32:35,790 converts to d and d retards the reaction. 728 00:32:35,790 --> 00:32:38,960 And so I start off with pretty decent conversion efficiency, 729 00:32:38,960 --> 00:32:43,120 but as I make more and more d, the d chokes the reaction, in 730 00:32:43,120 --> 00:32:47,070 which case the value here is going to have negative 731 00:32:47,070 --> 00:32:47,750 implications. 732 00:32:47,750 --> 00:32:49,980 So that's why you write it most generally, and then you 733 00:32:49,980 --> 00:32:51,795 go and you make some measurements in an experiment, 734 00:32:51,795 --> 00:32:53,300 and you figure out what these are. 735 00:32:53,300 --> 00:32:55,710 Some of them might be zeroes, and away you go. 736 00:32:55,710 --> 00:32:58,510 So I'll give you an example of one. 737 00:32:58,510 --> 00:32:58,980 Here's one. 738 00:32:58,980 --> 00:33:01,100 It's Monday after Halloween, so we'll get 739 00:33:01,100 --> 00:33:02,770 something kind of toxic. 740 00:33:02,770 --> 00:33:08,600 This was the manufacture of phosgene that was banned by 741 00:33:08,600 --> 00:33:10,220 international convention. 742 00:33:10,220 --> 00:33:13,110 It was used as one of the toxic gases for trench warfare 743 00:33:13,110 --> 00:33:14,700 in World War I. 744 00:33:14,700 --> 00:33:17,670 So it's made by the reaction of carbon 745 00:33:17,670 --> 00:33:19,880 monoxide and chlorine. 746 00:33:19,880 --> 00:33:21,010 COCL2. 747 00:33:21,010 --> 00:33:22,720 This is called phosgene. 748 00:33:22,720 --> 00:33:23,910 It's very bad stuff. 749 00:33:23,910 --> 00:33:25,430 I used it, actually, in my research. 750 00:33:25,430 --> 00:33:29,990 It has really good dehydration properties for salts. 751 00:33:29,990 --> 00:33:32,470 If you've got any moisture in potassium chloride, this'll go 752 00:33:32,470 --> 00:33:37,110 after it and turn the water into carbon dioxide and HCl. 753 00:33:37,110 --> 00:33:39,180 But you've got to be really, really careful with this. 754 00:33:39,180 --> 00:33:42,280 Gas leaks lead to a bad day at the lab. 755 00:33:42,280 --> 00:33:44,520 All right, this was banned. 756 00:33:44,520 --> 00:33:47,580 It's still use by tyrants throughout the world, and 757 00:33:47,580 --> 00:33:50,580 that's why we have international war tribunals. 758 00:33:50,580 --> 00:33:53,700 So here's the kinetics of it. 759 00:33:53,700 --> 00:33:54,820 Here's the kinetics of it. 760 00:33:54,820 --> 00:33:55,920 dc by dt. 761 00:33:55,920 --> 00:33:58,660 So this is the rate of consumption of carbon monoxide 762 00:33:58,660 --> 00:34:02,970 determined by experiment goes as the concentration of carbon 763 00:34:02,970 --> 00:34:06,850 monoxide and the concentration of chlorine raised 764 00:34:06,850 --> 00:34:08,730 to the power 3/2. 765 00:34:08,730 --> 00:34:13,340 So what I've done is mimic here. 766 00:34:13,340 --> 00:34:17,490 So in this case, gamma and delta are 0. 767 00:34:17,490 --> 00:34:23,790 Gamma equals delta equals 0, and it looks like beta equals 768 00:34:23,790 --> 00:34:26,600 1.5 and alpha equals 1. 769 00:34:26,600 --> 00:34:29,550 So I would say that this reaction is first order in 770 00:34:29,550 --> 00:34:34,650 carbon monoxide of order 1.5 in chlorine, or 771 00:34:34,650 --> 00:34:36,960 overall, of order 2.5. 772 00:34:36,960 --> 00:34:37,330 Because, right? 773 00:34:37,330 --> 00:34:39,340 This is the order of reaction. 774 00:34:39,340 --> 00:34:41,310 This is c to the power 1, isn't it? 775 00:34:41,310 --> 00:34:43,840 We don't write the 1. 776 00:34:43,840 --> 00:34:45,940 This is great. 777 00:34:45,940 --> 00:34:49,110 So we know, to increase the rate of reaction we increase 778 00:34:49,110 --> 00:34:50,080 the concentration. 779 00:34:50,080 --> 00:34:52,050 There's another way to increase the rate of reaction. 780 00:34:52,050 --> 00:34:53,865 What else can we do to increase the rate of reaction? 781 00:34:56,990 --> 00:34:58,290 Increase the temperature. 782 00:34:58,290 --> 00:35:00,270 Things go faster at higher temperatures. 783 00:35:00,270 --> 00:35:01,520 Again, how? 784 00:35:01,520 --> 00:35:02,480 How much? 785 00:35:02,480 --> 00:35:05,080 Suppose I said, I want to double the rate of reaction. 786 00:35:05,080 --> 00:35:07,270 Do I double the temperature? 787 00:35:07,270 --> 00:35:09,820 Do I raise the temperature by 10 degrees? 788 00:35:09,820 --> 00:35:11,750 How do I do that? 789 00:35:11,750 --> 00:35:20,130 So to increase rate of reaction, we can increase 790 00:35:20,130 --> 00:35:21,380 temperature. 791 00:35:23,600 --> 00:35:24,720 But how? 792 00:35:24,720 --> 00:35:27,290 And by the way, where is temperature here? 793 00:35:27,290 --> 00:35:29,090 I don't see temperature. 794 00:35:29,090 --> 00:35:31,550 I don't see temperature in this rate equation. 795 00:35:31,550 --> 00:35:33,130 You could say, well, if you increase the temperature 796 00:35:33,130 --> 00:35:34,470 you're going to increase the gas volume. 797 00:35:34,470 --> 00:35:36,550 But that's piddling effect, right? 798 00:35:36,550 --> 00:35:38,530 If I double the temperature, I double the gas volume. 799 00:35:38,530 --> 00:35:40,190 It doesn't change the mole number. 800 00:35:40,190 --> 00:35:42,020 The temperatures in here. 801 00:35:42,020 --> 00:35:45,160 That's where the temperature. 802 00:35:45,160 --> 00:35:46,980 Increase temperature, which then 803 00:35:46,980 --> 00:35:49,685 operates on the rate constant. 804 00:35:52,800 --> 00:35:55,540 That's the only place left in that formalism. 805 00:35:55,540 --> 00:35:57,420 But what's the quantitative value? 806 00:35:57,420 --> 00:36:02,530 Quantitative value was annunciated to us in 1889 by 807 00:36:02,530 --> 00:36:03,955 the Swedish chemist Arrhenius. 808 00:36:06,700 --> 00:36:11,730 And what Arrhenius found, he found that the rate constant 809 00:36:11,730 --> 00:36:14,080 varied with temperature in the following manner. 810 00:36:14,080 --> 00:36:20,730 Rate constant goes as the exponential of the ratio of 811 00:36:20,730 --> 00:36:24,730 minus some quantity call the activation energy e sub a-- 812 00:36:24,730 --> 00:36:26,750 I'm going to tell you what that means in a minute-- 813 00:36:26,750 --> 00:36:29,750 divided by the ratio of the product of the Boltzmann 814 00:36:29,750 --> 00:36:31,720 constant and temperature. 815 00:36:31,720 --> 00:36:35,220 And there's a constant of proportionality which we 816 00:36:35,220 --> 00:36:38,010 denote A in honor of Arrhenius. 817 00:36:38,010 --> 00:36:43,130 Or another way to write this is A times exponential-- 818 00:36:43,130 --> 00:36:44,460 are you familiar with this? 819 00:36:44,460 --> 00:36:47,570 Instead of writing e to the something, if there's a messy 820 00:36:47,570 --> 00:36:49,970 argument up here you can write it exp. 821 00:36:49,970 --> 00:36:55,860 This is the same as this minus ea over the ratio of Boltzmann 822 00:36:55,860 --> 00:36:58,520 constant and temperature. 823 00:36:58,520 --> 00:36:59,550 So what's in here? 824 00:36:59,550 --> 00:37:00,730 What's in here? 825 00:37:00,730 --> 00:37:02,180 Boltzmann constant temperature, 826 00:37:02,180 --> 00:37:03,520 we've seen that already. 827 00:37:03,520 --> 00:37:06,600 What's the Boltzmann constant temperature product? 828 00:37:06,600 --> 00:37:08,030 That's the environment. 829 00:37:08,030 --> 00:37:11,530 That's the energy of the environment. 830 00:37:11,530 --> 00:37:15,720 So this is the final environment. 831 00:37:18,640 --> 00:37:23,210 And this thing up on top, ea, is a barrier. 832 00:37:23,210 --> 00:37:24,260 It's a barrier. 833 00:37:24,260 --> 00:37:26,140 Remember we saw the band gap? 834 00:37:26,140 --> 00:37:27,090 Same idea. 835 00:37:27,090 --> 00:37:30,630 Those ideas go all through physical chemistry. 836 00:37:30,630 --> 00:37:33,860 You got thermal energy that allows you to do this 10 837 00:37:33,860 --> 00:37:35,180 trillion times a second. 838 00:37:35,180 --> 00:37:36,940 Everybody in this room is doing this 10 839 00:37:36,940 --> 00:37:39,830 trillion times a second. 840 00:37:39,830 --> 00:37:41,470 That's what kT is. 841 00:37:41,470 --> 00:37:43,390 And then there's a barrier energy. 842 00:37:43,390 --> 00:37:46,420 Every once in a while something happens. 843 00:37:46,420 --> 00:37:49,240 Sometimes one in a million, sometimes one in a billion. 844 00:37:49,240 --> 00:37:50,490 Whatever. 845 00:37:52,360 --> 00:37:56,170 What Arrhenius found was this relationship, which means we 846 00:37:56,170 --> 00:38:05,220 could plot the variation of the rate constant. 847 00:38:05,220 --> 00:38:06,130 This is a mess, right? 848 00:38:06,130 --> 00:38:07,980 This is an exponential-- 849 00:38:07,980 --> 00:38:10,740 look, the eye can only see straight lines. 850 00:38:10,740 --> 00:38:14,240 What if I show you this? 851 00:38:14,240 --> 00:38:14,930 What's that mean? 852 00:38:14,930 --> 00:38:16,640 I don't know. 853 00:38:16,640 --> 00:38:17,440 Is that first order? 854 00:38:17,440 --> 00:38:18,150 Second order? 855 00:38:18,150 --> 00:38:19,150 Is that Lagrangian? 856 00:38:19,150 --> 00:38:20,420 Is that exponential? 857 00:38:20,420 --> 00:38:21,730 I don't know. 858 00:38:21,730 --> 00:38:22,640 I know it's a curve. 859 00:38:22,640 --> 00:38:24,680 But what's this? 860 00:38:24,680 --> 00:38:26,640 I know what that is. 861 00:38:26,640 --> 00:38:27,990 And you know what that is. 862 00:38:27,990 --> 00:38:31,380 And you can tell goodness of fit. 863 00:38:31,380 --> 00:38:33,270 This is what science is all about. 864 00:38:33,270 --> 00:38:34,290 Forget all the other stuff. 865 00:38:34,290 --> 00:38:35,290 You know, all that UROP stuff. 866 00:38:35,290 --> 00:38:37,660 You're going to work in a lab and discover stuff. 867 00:38:37,660 --> 00:38:38,360 Forget that. 868 00:38:38,360 --> 00:38:39,980 This is what it's about. 869 00:38:39,980 --> 00:38:40,840 You got data. 870 00:38:40,840 --> 00:38:42,350 Data are all over the map. 871 00:38:42,350 --> 00:38:43,230 Here's the thing-- 872 00:38:43,230 --> 00:38:48,560 I need to come up with some f function here versus a g 873 00:38:48,560 --> 00:38:52,200 function here that linearize my data. 874 00:38:52,200 --> 00:38:54,120 That's all science is about. 875 00:38:54,120 --> 00:38:55,720 And how do I get to f and g? 876 00:38:55,720 --> 00:38:56,720 Well, there's two ways. 877 00:38:56,720 --> 00:38:58,040 One is trial and error. 878 00:38:58,040 --> 00:39:01,440 The other way is physical understanding. 879 00:39:01,440 --> 00:39:03,590 And this is what Arrhenius taught us. 880 00:39:03,590 --> 00:39:07,600 Arrhenius taught us that the f function for how k varies with 881 00:39:07,600 --> 00:39:09,630 temperature, right? 882 00:39:09,630 --> 00:39:12,610 The problem, I'm trying to say, k versus t. 883 00:39:12,610 --> 00:39:13,990 That's what I'm trying to do. 884 00:39:13,990 --> 00:39:16,730 And if I plot k versus t I get a curve. 885 00:39:16,730 --> 00:39:17,740 No good. 886 00:39:17,740 --> 00:39:24,650 Instead, if I plot some f of k versus g of t, I get a 887 00:39:24,650 --> 00:39:26,290 straight line. 888 00:39:26,290 --> 00:39:27,740 And this is all science. 889 00:39:27,740 --> 00:39:29,920 So what's f of k? 890 00:39:29,920 --> 00:39:31,870 The natural logarithm of k, right? 891 00:39:31,870 --> 00:39:34,860 If I've got k equals a exponential, I take the 892 00:39:34,860 --> 00:39:37,415 natural log of this, and the natural log of an exponential 893 00:39:37,415 --> 00:39:39,650 is just the argument. 894 00:39:39,650 --> 00:39:40,820 And what's in the argument? 895 00:39:40,820 --> 00:39:42,940 What's the T function? 896 00:39:42,940 --> 00:39:44,120 1 over T. 897 00:39:44,120 --> 00:39:48,750 So if I plot the natural log of k versus the reciprocal of 898 00:39:48,750 --> 00:39:51,910 the absolute temperature, I get a straight line and its 899 00:39:51,910 --> 00:39:59,020 slope is minus ea, forgive me, minus ea over k-Boltzmann. 900 00:39:59,020 --> 00:40:02,120 Minus ea over k-Boltzmann. 901 00:40:02,120 --> 00:40:05,440 So now it's linearized and I can look at that and within an 902 00:40:05,440 --> 00:40:08,330 instant, anybody in this room can look at and say, the data 903 00:40:08,330 --> 00:40:10,110 conform or they don't. 904 00:40:10,110 --> 00:40:11,360 They don't. 905 00:40:11,360 --> 00:40:13,290 So now let's think about this. 906 00:40:13,290 --> 00:40:19,650 We say well, what's the value of this barrier? 907 00:40:19,650 --> 00:40:21,560 It's called activation energy. 908 00:40:21,560 --> 00:40:24,820 This barrier energy is called activation energy. 909 00:40:24,820 --> 00:40:31,410 ea is called the activation energy. 910 00:40:31,410 --> 00:40:34,550 And it typically, it varies, but it has values-- 911 00:40:34,550 --> 00:40:37,990 just to give you a sense-- about 1 electron volt. 912 00:40:37,990 --> 00:40:41,500 1 electron volt, which you know now is about 100 913 00:40:41,500 --> 00:40:45,620 kilojoules per mole, isn't it? 914 00:40:45,620 --> 00:40:47,420 I hear the chorus of yesses. 915 00:40:47,420 --> 00:40:48,600 1 electron volt. 916 00:40:48,600 --> 00:40:49,750 What is thermal energy? 917 00:40:49,750 --> 00:40:51,410 What's kT? 918 00:40:51,410 --> 00:40:54,230 kT at room temperature, k-Boltzmann at room 919 00:40:54,230 --> 00:40:59,500 temperature is about 1/40 of an electron volt. 920 00:40:59,500 --> 00:41:01,910 Now, we are chemical machines. 921 00:41:01,910 --> 00:41:06,740 This conversation is occurring because all sorts of chemical 922 00:41:06,740 --> 00:41:10,460 processes are at work in me and you. 923 00:41:10,460 --> 00:41:12,770 And how's that happening? 924 00:41:12,770 --> 00:41:16,970 When all we've got to suck out of the environment is 1/40 of 925 00:41:16,970 --> 00:41:20,662 an electron volt and we need on the order one electron volt 926 00:41:20,662 --> 00:41:22,035 to drive certain processes. 927 00:41:24,990 --> 00:41:28,450 I guess we're all dead. 928 00:41:28,450 --> 00:41:29,700 Any ideas? 929 00:41:35,670 --> 00:41:38,520 Ay yay, yay. 930 00:41:38,520 --> 00:41:39,440 You guys need-- 931 00:41:39,440 --> 00:41:40,050 what's that thing? 932 00:41:40,050 --> 00:41:43,190 You've got to call your lifeline or something? 933 00:41:43,190 --> 00:41:44,260 Come on. 934 00:41:44,260 --> 00:41:45,110 How does anything happen? 935 00:41:45,110 --> 00:41:46,630 How do we get-- 936 00:41:46,630 --> 00:41:49,560 Why does anything happen in this world? 937 00:41:49,560 --> 00:41:53,160 Why should anything happen in a world with an environment of 938 00:41:53,160 --> 00:41:55,210 1/40 of an electron volt? 939 00:41:55,210 --> 00:41:56,365 AUDIENCE: Catalysts. 940 00:41:56,365 --> 00:41:58,500 PROFESSOR: Oh, catalysts. 941 00:41:58,500 --> 00:41:58,990 Catalysts. 942 00:41:58,990 --> 00:42:00,660 Yeah, yeah. 943 00:42:00,660 --> 00:42:04,810 I just went to the catalyst store and I got catalysts. 944 00:42:04,810 --> 00:42:06,402 Come on. 945 00:42:06,402 --> 00:42:07,740 AUDIENCE: Potential energy. 946 00:42:07,740 --> 00:42:08,550 PROFESSOR: Oh, potential energy. 947 00:42:08,550 --> 00:42:10,340 Jeez, this is good. 948 00:42:10,340 --> 00:42:12,130 Who can give me the wackiest answer? 949 00:42:12,130 --> 00:42:13,590 Can anybody give me the right answer? 950 00:42:13,590 --> 00:42:15,060 How come anything is happening? 951 00:42:18,600 --> 00:42:19,110 Over here. 952 00:42:19,110 --> 00:42:19,560 Again? 953 00:42:19,560 --> 00:42:20,850 AUDIENCE: Distribution of temperature. 954 00:42:20,850 --> 00:42:22,240 PROFESSOR: Thank you. 955 00:42:22,240 --> 00:42:23,500 Thank you. 956 00:42:23,500 --> 00:42:26,940 For a moment I thought we were all dead. 957 00:42:26,940 --> 00:42:31,460 At some level we were. 958 00:42:31,460 --> 00:42:33,320 So, yeah, it's Maxwell-Boltzmann. 959 00:42:33,320 --> 00:42:35,070 It's this, isn't it? 960 00:42:35,070 --> 00:42:37,260 And here's room temperature. 961 00:42:37,260 --> 00:42:39,940 And here is 1 electron volt. 962 00:42:39,940 --> 00:42:40,930 And this is it. 963 00:42:40,930 --> 00:42:43,600 And if you use this and you put it back to there, pretty 964 00:42:43,600 --> 00:42:45,660 soon you derive the Arrhenius equation. 965 00:42:45,660 --> 00:42:49,620 And if you increase the temperature 966 00:42:49,620 --> 00:42:50,480 you know what happens. 967 00:42:50,480 --> 00:42:53,530 After you increase the temperature, this. 968 00:42:53,530 --> 00:42:57,200 Time to use a hot color or chalk. 969 00:42:57,200 --> 00:43:01,810 So now this is T2 greater than T1. 970 00:43:01,810 --> 00:43:03,720 That's what's going on. 971 00:43:03,720 --> 00:43:04,600 That's what's going on. 972 00:43:04,600 --> 00:43:06,460 So now what is this activation energy? 973 00:43:06,460 --> 00:43:08,280 What is the meaning of it? 974 00:43:08,280 --> 00:43:09,940 You know, I've told you there's a barrier energy. 975 00:43:09,940 --> 00:43:10,870 What does it mean? 976 00:43:10,870 --> 00:43:15,160 Well, you go to the textbook, you see goofy stuff like this. 977 00:43:15,160 --> 00:43:17,000 And this is not a slam against the textbook. 978 00:43:17,000 --> 00:43:19,660 This is a slam against all chemistry textbooks, because 979 00:43:19,660 --> 00:43:21,000 they all write this stupid stuff. 980 00:43:21,000 --> 00:43:24,360 You see? a plus b goes c plus d, the energy falls and you 981 00:43:24,360 --> 00:43:26,640 have to go over this activated complex. 982 00:43:26,640 --> 00:43:29,470 You memorize it, and I ask you to repeat, it and we leave the 983 00:43:29,470 --> 00:43:31,970 room and we think, wow, we know physical chemistry. 984 00:43:31,970 --> 00:43:32,810 There's nothing here. 985 00:43:32,810 --> 00:43:33,405 This is nothing. 986 00:43:33,405 --> 00:43:35,230 This is stupid. 987 00:43:35,230 --> 00:43:36,960 Now this is a little bit better. 988 00:43:36,960 --> 00:43:38,070 Can you see this? 989 00:43:38,070 --> 00:43:39,030 This is the Maxwell-Boltzmann. 990 00:43:39,030 --> 00:43:42,260 This is actually a beautiful graph up to a point. 991 00:43:42,260 --> 00:43:43,840 See the Maxwell-Boltzmann? 992 00:43:43,840 --> 00:43:45,980 Low temperature, high temperature. 993 00:43:45,980 --> 00:43:48,110 Only they've turned this thing on its side. 994 00:43:48,110 --> 00:43:48,630 See? 995 00:43:48,630 --> 00:43:50,490 And there's the energy you need to get over 996 00:43:50,490 --> 00:43:51,620 the activated complex. 997 00:43:51,620 --> 00:43:53,350 You see what's wrong with this graph? 998 00:43:53,350 --> 00:43:54,040 What's wrong with it? 999 00:43:54,040 --> 00:43:55,486 AUDIENCE: The product. 1000 00:43:55,486 --> 00:43:57,160 PROFESSOR: Yeah, the product is at a higher 1001 00:43:57,160 --> 00:43:58,290 level than the reactants. 1002 00:43:58,290 --> 00:44:01,630 I looked at that and I thought, whoa! 1003 00:44:01,630 --> 00:44:03,580 I guess you'll activate them, but they won't go anywhere. 1004 00:44:03,580 --> 00:44:06,940 Anyway, so this is all stupid. 1005 00:44:06,940 --> 00:44:08,030 What can we do? 1006 00:44:08,030 --> 00:44:08,690 What can we do? 1007 00:44:08,690 --> 00:44:11,280 So I decided to give you a mechanical analogy. 1008 00:44:11,280 --> 00:44:12,970 So imagine this is the loudspeaker. 1009 00:44:12,970 --> 00:44:14,400 Can you say the x? 1010 00:44:14,400 --> 00:44:16,120 People in the back, can you see the x? 1011 00:44:16,120 --> 00:44:18,280 Give me a thumbs up. 1012 00:44:18,280 --> 00:44:19,120 Great eyes. 1013 00:44:19,120 --> 00:44:19,570 All right. 1014 00:44:19,570 --> 00:44:22,460 So what do we see here? 1015 00:44:22,460 --> 00:44:24,850 The center of mass, I've indicated here. 1016 00:44:24,850 --> 00:44:25,370 All right. 1017 00:44:25,370 --> 00:44:28,560 So this is in a certain energy state. 1018 00:44:28,560 --> 00:44:29,840 Let's get the right graph up there. 1019 00:44:29,840 --> 00:44:32,440 This is awful. 1020 00:44:32,440 --> 00:44:32,790 All right. 1021 00:44:32,790 --> 00:44:34,680 So this is a plus b. 1022 00:44:34,680 --> 00:44:36,420 Now this is c plus d. 1023 00:44:36,420 --> 00:44:38,630 You see, the center of mass fell. 1024 00:44:38,630 --> 00:44:39,170 It's lower. 1025 00:44:39,170 --> 00:44:42,310 It's closer to the table than it is here. 1026 00:44:42,310 --> 00:44:43,920 Can you see when I go like this, the photon goes? 1027 00:44:46,490 --> 00:44:47,740 Watch this. 1028 00:44:50,210 --> 00:44:51,520 Yeah, only I can see it. 1029 00:44:51,520 --> 00:44:53,990 Your eyes don't go to that end of the spectrum. 1030 00:44:53,990 --> 00:44:54,270 All right. 1031 00:44:54,270 --> 00:44:55,000 But what's wrong with it? 1032 00:44:55,000 --> 00:44:58,030 So why does the box not fall over? 1033 00:44:58,030 --> 00:44:58,930 Why does it not fall over? 1034 00:44:58,930 --> 00:45:01,790 We agreed that this is a lower energy state, and it is. 1035 00:45:01,790 --> 00:45:02,810 You're correct. 1036 00:45:02,810 --> 00:45:08,950 So why does the box manage to stay here and not fall over? 1037 00:45:08,950 --> 00:45:10,758 AUDIENCE: [INAUDIBLE PHRASE] 1038 00:45:10,758 --> 00:45:12,070 PROFESSOR: Exactly. 1039 00:45:12,070 --> 00:45:14,400 This is the box at 0 Kelvin. 1040 00:45:14,400 --> 00:45:16,940 Now we start raising the energy of the box, it starts 1041 00:45:16,940 --> 00:45:17,890 doing this. 1042 00:45:17,890 --> 00:45:20,860 Because above 0 Kelvin, it vibrates. 1043 00:45:20,860 --> 00:45:22,975 The higher the temperature, the greater the vibration. 1044 00:45:25,620 --> 00:45:28,640 But we're still in trouble here, you see, because you've 1045 00:45:28,640 --> 00:45:30,840 only got 1/40 of an electron volt. 1046 00:45:30,840 --> 00:45:33,150 So now we invoke distribution. 1047 00:45:33,150 --> 00:45:34,960 I don't know what's happening with any box. 1048 00:45:34,960 --> 00:45:36,140 Heisenberg tells me that. 1049 00:45:36,140 --> 00:45:37,870 I don't know what's happening to any box. 1050 00:45:37,870 --> 00:45:41,510 But if I take Avogadro's number of boxes I'll get this 1051 00:45:41,510 --> 00:45:42,990 distribution. 1052 00:45:42,990 --> 00:45:47,910 And some boxes will vibrate very little. 1053 00:45:47,910 --> 00:45:50,600 And some boxes will vibrate a lot. 1054 00:45:50,600 --> 00:45:53,170 And what's the critical level of vibration? 1055 00:45:53,170 --> 00:45:54,730 It's to get to here. 1056 00:45:54,730 --> 00:45:58,630 Because once it gets to here it's downhill all the way. 1057 00:45:58,630 --> 00:46:02,100 And that would be the activation energy. 1058 00:46:02,100 --> 00:46:05,620 And the fraction of boxes that get to the value of activation 1059 00:46:05,620 --> 00:46:09,200 energy tip over and then I restore the distribution, 1060 00:46:09,200 --> 00:46:11,990 because now this one's out of the game and now I distribute 1061 00:46:11,990 --> 00:46:13,800 that energy over the remaining ones. 1062 00:46:13,800 --> 00:46:16,550 And as I increase the temperature, the amplitude of 1063 00:46:16,550 --> 00:46:19,240 the vibration increases, the average increases, the 1064 00:46:19,240 --> 00:46:22,050 fraction in that red zone increases, and at some 1065 00:46:22,050 --> 00:46:27,040 temperature it's so, so hot that they actually do this, in 1066 00:46:27,040 --> 00:46:29,030 which case I have equilibrium. 1067 00:46:29,030 --> 00:46:31,640 The two states are in equilibrium. 1068 00:46:31,640 --> 00:46:32,940 So that's it. 1069 00:46:32,940 --> 00:46:33,810 This is what's going on. 1070 00:46:33,810 --> 00:46:36,390 So in three space, you can't go from here to here without 1071 00:46:36,390 --> 00:46:37,400 going to here. 1072 00:46:37,400 --> 00:46:40,390 You can try going this way so you-- no, you have to do this. 1073 00:46:40,390 --> 00:46:43,470 It still has to be mechanically activated so we 1074 00:46:43,470 --> 00:46:47,940 can show that this is what activation means. 1075 00:46:47,940 --> 00:46:49,020 So we can plot-- 1076 00:46:49,020 --> 00:46:52,550 this deserves it's own board-- 1077 00:46:52,550 --> 00:46:55,220 so we will plot something like this. 1078 00:46:55,220 --> 00:46:56,640 And now you'll see this. 1079 00:46:56,640 --> 00:46:58,930 Sometimes they write this in the books. 1080 00:46:58,930 --> 00:46:59,600 It's kind of goofy. 1081 00:46:59,600 --> 00:47:01,790 But they write stuff like this. 1082 00:47:01,790 --> 00:47:04,440 This is some kind of an energy coordinate. 1083 00:47:04,440 --> 00:47:05,820 This is an energy coordinate. 1084 00:47:05,820 --> 00:47:10,140 And this is called a reaction coordinate. 1085 00:47:10,140 --> 00:47:13,080 OR sometimes they write extent of reaction. 1086 00:47:13,080 --> 00:47:14,500 Again, some P-Chem term. 1087 00:47:14,500 --> 00:47:18,090 They usually use Greek C just to make it lofty, but it's 1088 00:47:18,090 --> 00:47:18,720 meaningless. 1089 00:47:18,720 --> 00:47:21,290 And then so you write like this-- reactants here, 1090 00:47:21,290 --> 00:47:26,880 products here, and this is exactly what we're seeing. 1091 00:47:26,880 --> 00:47:28,770 What do we see? 1092 00:47:28,770 --> 00:47:29,990 We see this. 1093 00:47:29,990 --> 00:47:35,190 Here we have the box sitting like so. 1094 00:47:35,190 --> 00:47:39,520 And then over here we have the box sitting like so. 1095 00:47:39,520 --> 00:47:43,285 And right here we have the box up like so. 1096 00:47:45,830 --> 00:47:48,640 And so now you have, here's the initial energy. 1097 00:47:48,640 --> 00:47:51,890 This is the energy of the reactants. 1098 00:47:51,890 --> 00:47:56,170 E of the reactants. 1099 00:47:56,170 --> 00:48:00,170 This is E of the products. 1100 00:48:00,170 --> 00:48:03,440 So then this distance here must be 1101 00:48:03,440 --> 00:48:04,695 delta E of the reaction. 1102 00:48:07,350 --> 00:48:10,510 And what's this? 1103 00:48:10,510 --> 00:48:12,090 That's the activation energy. 1104 00:48:12,090 --> 00:48:14,140 I have to come up with this; otherwise, I can't make the 1105 00:48:14,140 --> 00:48:15,440 box fall over. 1106 00:48:15,440 --> 00:48:19,740 So this is ea to go from here up onto the corner. 1107 00:48:19,740 --> 00:48:21,530 And now you understand what all this stuff means. 1108 00:48:21,530 --> 00:48:22,440 So that's here. 1109 00:48:22,440 --> 00:48:24,250 And this is the activated complex. 1110 00:48:27,030 --> 00:48:28,340 What's an activated complex? 1111 00:48:28,340 --> 00:48:30,390 It's a box on its edge ready to fall over. 1112 00:48:30,390 --> 00:48:31,820 That's what it is. 1113 00:48:31,820 --> 00:48:34,230 All right. 1114 00:48:34,230 --> 00:48:37,640 I think we're out of time, so let's cut to the end here. 1115 00:48:37,640 --> 00:48:39,190 What've we got. 1116 00:48:39,190 --> 00:48:39,910 Oh, just some plots. 1117 00:48:39,910 --> 00:48:41,390 We'll get to that next day. 1118 00:48:41,390 --> 00:48:42,950 All right. 1119 00:48:42,950 --> 00:48:43,890 So I want to show you a little bit 1120 00:48:43,890 --> 00:48:45,910 about first-order reactions. 1121 00:48:45,910 --> 00:48:48,280 This is radiocarbon dating. 1122 00:48:48,280 --> 00:48:49,630 n equals 1. 1123 00:48:49,630 --> 00:48:51,970 And strictly speaking, this is not a chemical reaction, but 1124 00:48:51,970 --> 00:48:53,320 it is first order. 1125 00:48:53,320 --> 00:48:54,600 So I'll lump it in here. 1126 00:48:54,600 --> 00:48:56,520 So this is a nuclear reaction. 1127 00:48:56,520 --> 00:48:58,220 And what happens in the upper atmosphere? 1128 00:48:58,220 --> 00:49:01,970 Radioactive carbon produced by cosmic rays, which generate 1129 00:49:01,970 --> 00:49:03,940 neutrons in the upper atmosphere and then those 1130 00:49:03,940 --> 00:49:07,040 neutrons attack nitrogen to make carbon 14. 1131 00:49:07,040 --> 00:49:08,650 That's the radioactive form of carbon. 1132 00:49:08,650 --> 00:49:08,870 Remember? 1133 00:49:08,870 --> 00:49:10,970 It's present in one part per trillion, if you look on your 1134 00:49:10,970 --> 00:49:13,280 Periodic Table for the isotopes. 1135 00:49:13,280 --> 00:49:15,760 Now carbon 14 enters the carbon cycle. 1136 00:49:15,760 --> 00:49:19,410 And so in all of us and in all living organisms the ratio of 1137 00:49:19,410 --> 00:49:22,790 carbon 14 to carbon 12 is one part per trillion. 1138 00:49:22,790 --> 00:49:24,760 And carbon 13 is also present. 1139 00:49:24,760 --> 00:49:25,140 I don't know. 1140 00:49:25,140 --> 00:49:25,420 What is it? 1141 00:49:25,420 --> 00:49:27,240 1 point something percent? 1142 00:49:27,240 --> 00:49:30,780 The thing is, the carbon 14 is radioactive. 1143 00:49:30,780 --> 00:49:32,470 And it decays. 1144 00:49:32,470 --> 00:49:33,840 Like this. 1145 00:49:33,840 --> 00:49:36,210 But what happens after somebody dies? 1146 00:49:36,210 --> 00:49:39,990 Well, they stop exchanging nutrients with the 1147 00:49:39,990 --> 00:49:40,550 surroundings. 1148 00:49:40,550 --> 00:49:43,810 They stop breathing, so their carbon level is pegged as it 1149 00:49:43,810 --> 00:49:45,870 was at the time of death. 1150 00:49:45,870 --> 00:49:47,410 And now it's a one0way street. 1151 00:49:47,410 --> 00:49:49,130 It's just carbon decay. 1152 00:49:49,130 --> 00:49:51,885 And it turns out you can measure the ratio of carbon 14 1153 00:49:51,885 --> 00:49:56,890 to carbon 12 to determine the age, which is given by 5,730 1154 00:49:56,890 --> 00:50:01,970 years, which is the inverse of the rate constant. 1155 00:50:01,970 --> 00:50:04,530 Now, you can't use this for crime scene investigations, 1156 00:50:04,530 --> 00:50:07,290 but certainly you can start dating things hundreds of 1157 00:50:07,290 --> 00:50:09,940 years old, not hundreds of minutes old. 1158 00:50:09,940 --> 00:50:12,090 So there's a whole bunch of other things that can be used, 1159 00:50:12,090 --> 00:50:12,860 not just carbon. 1160 00:50:12,860 --> 00:50:15,140 So this is radiochemical dating. 1161 00:50:15,140 --> 00:50:19,960 And these are used in trying to nail down art forgeries and 1162 00:50:19,960 --> 00:50:21,190 all sorts of things. 1163 00:50:21,190 --> 00:50:21,890 All right. 1164 00:50:21,890 --> 00:50:23,030 So here, you can see these. 1165 00:50:23,030 --> 00:50:25,020 These have all been radiocarbon dated. 1166 00:50:25,020 --> 00:50:27,270 You know, the Dead Sea Scrolls were radiocarbon dated and 1167 00:50:27,270 --> 00:50:29,290 they look like they're from about 2,000 years ago. 1168 00:50:29,290 --> 00:50:31,300 Makes sense. 1169 00:50:31,300 --> 00:50:32,970 You go out over here. 1170 00:50:32,970 --> 00:50:37,020 They they found these Indian sandals from Oregon, and then 1171 00:50:37,020 --> 00:50:40,250 they looked on an electron microscope, and they found 1172 00:50:40,250 --> 00:50:44,740 something on the sandals that looks a little bit like that. 1173 00:50:44,740 --> 00:50:46,030 That's a Nike swoosh. 1174 00:50:46,030 --> 00:50:46,630 I don't know. 1175 00:50:46,630 --> 00:50:48,320 You people are so-- 1176 00:50:48,320 --> 00:50:49,390 All right. 1177 00:50:49,390 --> 00:50:51,590 So now I want to show you the Shroud of Turin. 1178 00:50:51,590 --> 00:50:56,470 The Shroud of Turin, as you may know, for a long time was 1179 00:50:56,470 --> 00:50:59,510 reputed to be the burial shroud of Jesus Christ. And 1180 00:50:59,510 --> 00:51:01,960 this is taken from the National Geographic back in 1181 00:51:01,960 --> 00:51:04,050 the late '80s. 1182 00:51:04,050 --> 00:51:06,290 Back in the late '80s, they did a major study on it. 1183 00:51:06,290 --> 00:51:09,530 So this is the artist rendition of how the shroud 1184 00:51:09,530 --> 00:51:11,360 might have been wrapped around a body. 1185 00:51:11,360 --> 00:51:13,550 The question is, what's the date of this? 1186 00:51:13,550 --> 00:51:15,250 So we can use radiocarbon dating. 1187 00:51:15,250 --> 00:51:19,520 And so here's the formation of carbon 14. 1188 00:51:19,520 --> 00:51:23,200 Carbon 14 exchanges with carbon 12 in flax. 1189 00:51:23,200 --> 00:51:24,820 So it's got one part per trillion. 1190 00:51:24,820 --> 00:51:28,800 When the flax is harvested the carbon 14 starts to decay. 1191 00:51:28,800 --> 00:51:30,700 And then we look at the weaving of the 1192 00:51:30,700 --> 00:51:31,780 shroud and so on. 1193 00:51:31,780 --> 00:51:34,500 And they had three different labs, they took samples from 1194 00:51:34,500 --> 00:51:35,240 the shroud. 1195 00:51:35,240 --> 00:51:37,050 And they concluded that the shroud 1196 00:51:37,050 --> 00:51:38,040 dates from this period-- 1197 00:51:38,040 --> 00:51:39,900 1260 to 1390. 1198 00:51:39,900 --> 00:51:41,930 And the first time it was mentioned in the literature 1199 00:51:41,930 --> 00:51:43,010 was around 1354. 1200 00:51:43,010 --> 00:51:45,860 So everything seems to make sense that this is not the 1201 00:51:45,860 --> 00:51:49,470 burial shroud of Jesus Christ. It's something that has 1202 00:51:49,470 --> 00:51:54,010 importance to certain members of the Roman Church, but it's 1203 00:51:54,010 --> 00:51:55,460 scientifically not. 1204 00:51:55,460 --> 00:51:57,320 You know, this stirs up a lot of passion. 1205 00:51:57,320 --> 00:51:58,680 So people started saying, wait a minute. 1206 00:51:58,680 --> 00:51:59,440 Wait a minute. 1207 00:51:59,440 --> 00:52:03,910 There was a fire in 1532 and people repaired the shroud and 1208 00:52:03,910 --> 00:52:06,900 they were using candlelight and maybe the paraffin and 1209 00:52:06,900 --> 00:52:09,780 mold and so on covered the fibers. 1210 00:52:09,780 --> 00:52:12,100 So now, are we looking at the surface effect? 1211 00:52:12,100 --> 00:52:13,490 How do we know what really happened? 1212 00:52:13,490 --> 00:52:15,350 The only way to know is to take the whole shroud, put in 1213 00:52:15,350 --> 00:52:18,590 a big Cuisinart and break open the interior. 1214 00:52:18,590 --> 00:52:21,740 Well, in point of fact, what they did was take fibers and 1215 00:52:21,740 --> 00:52:22,450 look inside. 1216 00:52:22,450 --> 00:52:26,170 And I think as of the late '90s, the Roman Church says, 1217 00:52:26,170 --> 00:52:29,200 it's not the burial shroud of Jesus, but it is 1218 00:52:29,200 --> 00:52:30,330 an object of reverence. 1219 00:52:30,330 --> 00:52:32,160 And I think it's a good example of how science 1220 00:52:32,160 --> 00:52:35,940 sometimes comes up against spirituality, and we have to 1221 00:52:35,940 --> 00:52:37,844 be careful how we handle it. 1222 00:52:37,844 --> 00:52:40,360 It's a delicate matter.