WEBVTT 00:00:00.030 --> 00:00:02.400 The following content is provided under a Creative 00:00:02.400 --> 00:00:03.830 Commons license. 00:00:03.830 --> 00:00:06.840 Your support will help MIT OpenCourseWare continue to 00:00:06.840 --> 00:00:10.510 offer high-quality educational resources for free. 00:00:10.510 --> 00:00:13.390 To make a donation or view additional materials from 00:00:13.390 --> 00:00:17.490 hundreds of MIT courses, visit MIT OpenCourseWare at 00:00:17.490 --> 00:00:18.740 ocw.mit.edu. 00:00:20.912 --> 00:00:23.980 PROFESSOR: OK, OK, OK. 00:00:23.980 --> 00:00:26.220 Let's settle down. 00:00:26.220 --> 00:00:28.770 Weekend is over. 00:00:28.770 --> 00:00:31.160 Tomorrow, weekly quiz. 00:00:31.160 --> 00:00:33.080 Today I'll have office hours 3:00 to 4:00. 00:00:33.080 --> 00:00:35.180 I have to go down to Washington, so I've got to 00:00:35.180 --> 00:00:36.850 leave a little bit earlier than normal. 00:00:36.850 --> 00:00:42.420 So I will be available from 3:00 to 4:00 00:00:42.420 --> 00:00:45.070 The lecture has started and there's still way too much 00:00:45.070 --> 00:00:46.650 talking in here. 00:00:46.650 --> 00:00:47.430 Way too much. 00:00:47.430 --> 00:00:48.950 You know how much is too much? 00:00:48.950 --> 00:00:51.040 Any. 00:00:51.040 --> 00:00:52.290 Any. 00:00:58.200 --> 00:01:01.890 So last day, we started talking about oxide glasses, 00:01:01.890 --> 00:01:06.700 and we reasoned that we could have control of the properties 00:01:06.700 --> 00:01:10.420 by control of the composition. 00:01:10.420 --> 00:01:13.900 We started with a network former, which is some oxide 00:01:13.900 --> 00:01:16.505 that has the capacity for forming covalent bonds through 00:01:16.505 --> 00:01:18.160 a bridging oxygen. 00:01:18.160 --> 00:01:22.080 And then we wanted to drop the processing temperature, and we 00:01:22.080 --> 00:01:24.460 did so by adding modifiers. 00:01:24.460 --> 00:01:26.600 Intermediates, we haven't talked about and we're going 00:01:26.600 --> 00:01:28.570 to do that in just a moment. 00:01:28.570 --> 00:01:31.980 So if you look in the readings, this is from 00:01:31.980 --> 00:01:34.850 archival notes that were written by my predecessor, 00:01:34.850 --> 00:01:37.210 Professor Witt, these are compositions of 00:01:37.210 --> 00:01:38.870 some typical glasses. 00:01:38.870 --> 00:01:41.280 I don't expect you know these from memory, but I would 00:01:41.280 --> 00:01:45.370 expect you, if I gave you the composition, explain to me why 00:01:45.370 --> 00:01:46.920 the various constituents are there. 00:01:46.920 --> 00:01:49.060 So let's try few examples. 00:01:49.060 --> 00:01:51.210 The first one is soda-lime glass. 00:01:51.210 --> 00:01:53.740 And you see it contains silica, which 00:01:53.740 --> 00:01:55.150 is the network former. 00:01:55.150 --> 00:01:58.270 It contains sodium oxide, calcium oxide, 00:01:58.270 --> 00:01:59.710 and magnesium oxide. 00:01:59.710 --> 00:02:03.180 And these are alkaline earth oxides that are ionic, and so 00:02:03.180 --> 00:02:06.270 these are acting as network modifiers because they're 00:02:06.270 --> 00:02:10.240 donating oxide anions that go in and break 00:02:10.240 --> 00:02:12.670 the silicate chains. 00:02:12.670 --> 00:02:15.630 And then there's this Al203 and that's sort of halfway in 00:02:15.630 --> 00:02:16.490 between, isn't it? 00:02:16.490 --> 00:02:19.610 Silica is Group 4, or 14, if you want to 00:02:19.610 --> 00:02:21.500 use the modern notation. 00:02:21.500 --> 00:02:23.130 Sodium is Group 1. 00:02:23.130 --> 00:02:24.670 Calcium, magnesium, Group 2. 00:02:24.670 --> 00:02:28.160 Alumina is Group 3, and it's sort of halfway in between. 00:02:28.160 --> 00:02:29.030 It's amphoteric. 00:02:29.030 --> 00:02:31.680 It can either be a former or a modifier. 00:02:31.680 --> 00:02:34.140 And in these instances, depending on how much modifier 00:02:34.140 --> 00:02:39.150 is present, alumina can act as an intermediate. 00:02:39.150 --> 00:02:40.340 And what's an intermediate do? 00:02:40.340 --> 00:02:44.030 An intermediate is a covalent oxide. 00:02:44.030 --> 00:02:47.680 It's a covalent oxide, or an oxide that can act as both 00:02:47.680 --> 00:02:49.090 covalent and ionic. 00:02:49.090 --> 00:02:53.040 But in this instance, it's acting covalent oxide with a 00:02:53.040 --> 00:02:54.880 different coordination number. 00:02:59.200 --> 00:03:00.620 And what does that mean? 00:03:00.620 --> 00:03:02.670 Different coordination number? 00:03:02.670 --> 00:03:03.440 It coordinates-- 00:03:03.440 --> 00:03:06.070 remember last day I showed you B2O3? 00:03:06.070 --> 00:03:07.330 Borate glasses? 00:03:07.330 --> 00:03:09.790 So they have a coordination of three, whereas 00:03:09.790 --> 00:03:11.170 silicates have four. 00:03:11.170 --> 00:03:12.610 And what that means is that there's 00:03:12.610 --> 00:03:13.720 going to be a mismatch. 00:03:13.720 --> 00:03:16.640 There's still strong covalent bonds, but they don't fit 00:03:16.640 --> 00:03:17.510 quite right. 00:03:17.510 --> 00:03:20.190 And that's going to give even more free volume. 00:03:20.190 --> 00:03:24.190 And that excess free volume, through covalent bonds, gives 00:03:24.190 --> 00:03:26.950 you the ability to endure thermal shock. 00:03:26.950 --> 00:03:29.210 So if you want to impart thermal shock resistance in a 00:03:29.210 --> 00:03:33.290 glass, you give it lots of free volume so it can take the 00:03:33.290 --> 00:03:34.700 rapid change in temperature. 00:03:34.700 --> 00:03:40.810 So it's a covalent oxide with different coordination number. 00:03:40.810 --> 00:03:47.350 That is, nearest neighbors, in a covalent sense, from that of 00:03:47.350 --> 00:03:51.740 the network former. 00:03:51.740 --> 00:03:55.340 So you can add a borate or aluminate, what have you. 00:03:55.340 --> 00:03:58.090 And that'll give you thermal shock resistance. 00:03:58.090 --> 00:04:01.420 And so alumina here is acting as an intermediate. 00:04:01.420 --> 00:04:02.220 Let's go down here. 00:04:02.220 --> 00:04:03.960 There's borosilicate. 00:04:03.960 --> 00:04:06.650 borosilicate is the generic term for Pyrex. 00:04:06.650 --> 00:04:08.430 So Pyrex is a trade name. 00:04:08.430 --> 00:04:13.500 Pyrex was invented by Corning, and it contains silica as the 00:04:13.500 --> 00:04:14.620 network former. 00:04:14.620 --> 00:04:17.600 There's some sodium oxide, potassium oxide-- 00:04:17.600 --> 00:04:19.270 in rather small amounts. 00:04:19.270 --> 00:04:21.560 You can see this isn't a heavily modified network, but 00:04:21.560 --> 00:04:22.710 look at this. 00:04:22.710 --> 00:04:25.950 13% B2O3 and 2% alumina. 00:04:25.950 --> 00:04:27.220 That's the modifier. 00:04:27.220 --> 00:04:30.120 And what was the hallmark of Pyrex? 00:04:30.120 --> 00:04:32.120 It had thermal shock resistance. 00:04:32.120 --> 00:04:35.410 So you could take it out of the oven and put it under cold 00:04:35.410 --> 00:04:36.760 water and it didn't shatter. 00:04:36.760 --> 00:04:40.770 And we have the same analogous behavior for glass ware in the 00:04:40.770 --> 00:04:41.520 laboratory. 00:04:41.520 --> 00:04:44.420 For all room temperature and low temperature work in the 00:04:44.420 --> 00:04:48.630 laboratory, we use Pyrex that has this resistance to 00:04:48.630 --> 00:04:50.450 chemicals and resistance to heat. 00:04:50.450 --> 00:04:51.770 This is the big one, here. 00:04:51.770 --> 00:04:56.140 And that gave birth to functional crockery in the 00:04:56.140 --> 00:05:01.250 kitchen, where you could work in glass instead of in metal. 00:05:01.250 --> 00:05:04.570 And down here we see glass-- 00:05:04.570 --> 00:05:05.510 let's see, well, here's one. 00:05:05.510 --> 00:05:06.900 Light flint optical. 00:05:06.900 --> 00:05:08.220 See, that's 54%. 00:05:08.220 --> 00:05:11.150 It's down to 54% silica. 00:05:11.150 --> 00:05:14.160 And look at this-- boatloads of lead oxide. 00:05:14.160 --> 00:05:18.080 And the lead oxide is acting as a modifier and also changes 00:05:18.080 --> 00:05:19.850 the index of refraction. 00:05:19.850 --> 00:05:25.070 It modifies so much that we have almost down to the 00:05:25.070 --> 00:05:26.500 orthosilicate. 00:05:26.500 --> 00:05:30.390 So that the chains are modified to the point where 00:05:30.390 --> 00:05:32.770 they're almost all terminals. 00:05:32.770 --> 00:05:36.250 There's very little of this, and most of it is just 00:05:36.250 --> 00:05:37.710 terminal oxygens. 00:05:37.710 --> 00:05:40.960 And that means that it's more nearly crystalline, and 00:05:40.960 --> 00:05:41.990 therefore, you can cut it. 00:05:41.990 --> 00:05:45.760 And this is the lead crystal. 00:05:45.760 --> 00:05:48.000 Lead crystal has that high value. 00:05:48.000 --> 00:05:49.460 So you can see how that comes out. 00:05:49.460 --> 00:05:51.880 And this is also taken from the reading. 00:05:51.880 --> 00:05:55.140 It's a plot of viscosity versus temperature. 00:05:55.140 --> 00:05:56.580 Only it's a logarithmic plot. 00:05:56.580 --> 00:05:57.650 And what do you see? 00:05:57.650 --> 00:05:58.730 Here's pure silica. 00:05:58.730 --> 00:06:00.050 That's SiO2. 00:06:00.050 --> 00:06:03.560 And if I want to take it down to the point where, if the 00:06:03.560 --> 00:06:05.330 viscosity goes down, you have the ability to 00:06:05.330 --> 00:06:06.800 work with the glass. 00:06:06.800 --> 00:06:10.330 So if I want to melt silica, I've got to way, way up here. 00:06:10.330 --> 00:06:12.360 Over 2,000 Centigrade. 00:06:12.360 --> 00:06:15.890 So if I want to make bottles, if I want to make cookware, I 00:06:15.890 --> 00:06:17.990 don't want to run a lehr at this temperature. 00:06:17.990 --> 00:06:18.900 Lehr. 00:06:18.900 --> 00:06:19.950 L E H R. 00:06:19.950 --> 00:06:21.380 It's where you melt glass. 00:06:21.380 --> 00:06:24.040 Lehr. 00:06:24.040 --> 00:06:26.190 I don't want to run a lehr at this temperature. 00:06:26.190 --> 00:06:30.230 But you can see if I add modifier, the more modifier 00:06:30.230 --> 00:06:34.190 that I add, the more I break the network. 00:06:34.190 --> 00:06:37.190 So increasing modifier decreases network 00:06:37.190 --> 00:06:40.040 connectivity, and that means I can go to a lower temperature 00:06:40.040 --> 00:06:41.690 and get the same level of fluidity. 00:06:41.690 --> 00:06:44.250 So there's a whole bunch of definitions here that I'm not 00:06:44.250 --> 00:06:45.430 going to go over. 00:06:45.430 --> 00:06:46.470 You'll have this slide. 00:06:46.470 --> 00:06:50.430 But basically, it's just different points in 00:06:50.430 --> 00:06:51.610 processing. 00:06:51.610 --> 00:06:53.140 So if you go up here. 00:06:53.140 --> 00:06:54.260 Strain and annealing. 00:06:54.260 --> 00:06:56.060 I mean, these are very, very-- 00:06:56.060 --> 00:06:58.980 you're especially working with solid, whereas softening 00:06:58.980 --> 00:07:01.950 point, you start getting the glass to flow. 00:07:01.950 --> 00:07:05.390 And the working point, that's the viscosity that 00:07:05.390 --> 00:07:07.350 you have to get below. 00:07:07.350 --> 00:07:10.060 Otherwise, the glass is going to be to resistant to flow. 00:07:10.060 --> 00:07:12.740 You want to get the glass tacky so that you can put it 00:07:12.740 --> 00:07:16.390 into an injection mold, shape it, as they do with bottles. 00:07:16.390 --> 00:07:18.870 They take a blob of glass and boom, they just throw it into 00:07:18.870 --> 00:07:20.870 a mold and it sprays out. 00:07:20.870 --> 00:07:23.010 And if you've got the right mass and the right spinning, 00:07:23.010 --> 00:07:26.350 it makes the wall thickness proper. 00:07:26.350 --> 00:07:28.690 But you can imagine, if the glass is really, really 00:07:28.690 --> 00:07:31.470 viscous, it's not going to flow well enough. 00:07:31.470 --> 00:07:34.120 If it's too fluid, it'll drip all over. 00:07:34.120 --> 00:07:35.650 So there's an optimum in there. 00:07:35.650 --> 00:07:37.440 And this is telling you how to figure out what 00:07:37.440 --> 00:07:38.750 that optimum is. 00:07:38.750 --> 00:07:42.080 And you can see that as you change the composition, here's 00:07:42.080 --> 00:07:43.200 the working value. 00:07:43.200 --> 00:07:47.290 This is the viscosity that you have to get below which in 00:07:47.290 --> 00:07:48.160 order to work. 00:07:48.160 --> 00:07:50.550 And you can see that as you add more and more modifier, 00:07:50.550 --> 00:07:53.460 you can take the temperature and get it way, way down. 00:07:53.460 --> 00:07:56.330 So to work with silica you have to be about around 2,000. 00:07:56.330 --> 00:07:58.850 With soda-lime you can be down around 800. 00:07:58.850 --> 00:08:01.530 So that's going to cut your energy costs, isn't it? 00:08:01.530 --> 00:08:04.980 And it's going to make it easier to recycle. 00:08:04.980 --> 00:08:08.360 What's the point of recycling if you consume as much energy 00:08:08.360 --> 00:08:10.545 to recycle as if you started with virgin material? 00:08:10.545 --> 00:08:13.570 At least with virgin material you can guarantee the quality 00:08:13.570 --> 00:08:14.525 of the feeds stock. 00:08:14.525 --> 00:08:17.590 So there's got to be some big saving. 00:08:17.590 --> 00:08:18.440 All right. 00:08:18.440 --> 00:08:22.890 So that gives you a some sense as to what we can do 00:08:22.890 --> 00:08:24.335 technologically with glasses. 00:08:24.335 --> 00:08:28.340 I want to show you one last thing with glasses, and then 00:08:28.340 --> 00:08:30.610 we're going to move on to another topic. 00:08:30.610 --> 00:08:33.170 You know, new week, new day, new topic. 00:08:33.170 --> 00:08:35.160 So I want to go back to this curve. 00:08:35.160 --> 00:08:36.180 So what am I showing you here? 00:08:36.180 --> 00:08:40.210 I'm showing you that as we change the cooling rate, we 00:08:40.210 --> 00:08:43.060 change the amount of quenched-in excess volume. 00:08:43.060 --> 00:08:47.700 So fast cooling quenches in more of the liquid free volume 00:08:47.700 --> 00:08:48.950 than slow cooling does. 00:08:48.950 --> 00:08:52.520 That's why this V excess is small here, whereas V excess 00:08:52.520 --> 00:08:54.030 is large here for the other one. 00:08:54.030 --> 00:08:57.000 I'm going to use that in glass strengthening. 00:08:57.000 --> 00:08:58.250 So I want to strengthen. 00:09:00.720 --> 00:09:03.500 Strengthening glasses. 00:09:03.500 --> 00:09:06.170 We're talking about silicates or borates. 00:09:06.170 --> 00:09:08.210 Strengthening oxide glasses. 00:09:08.210 --> 00:09:10.030 Glass is a fantastic material. 00:09:10.030 --> 00:09:12.400 It's really good in compression, but it's no good 00:09:12.400 --> 00:09:13.400 in tensions. 00:09:13.400 --> 00:09:14.490 You know this. 00:09:14.490 --> 00:09:16.740 If you try to bend glass, it'll break. 00:09:16.740 --> 00:09:17.330 Why? 00:09:17.330 --> 00:09:19.170 Not because it doesn't have dislocations. 00:09:19.170 --> 00:09:21.350 It's got strong covalent bonds. 00:09:21.350 --> 00:09:24.300 But you know, suppose you want to strengthen the windshield 00:09:24.300 --> 00:09:26.200 of your car so that when a stone hits 00:09:26.200 --> 00:09:27.350 it, it doesn't shatter. 00:09:27.350 --> 00:09:30.280 What can we do to give it added strength? 00:09:30.280 --> 00:09:34.220 So I'm going to show you two ways, and both of them operate 00:09:34.220 --> 00:09:39.000 under this principle that the yield stress-- 00:09:39.000 --> 00:09:41.320 this is the stress that will break the glass, and I'm going 00:09:41.320 --> 00:09:43.390 to say the effective yield stress, what you 00:09:43.390 --> 00:09:45.320 experience in life-- 00:09:45.320 --> 00:09:51.510 is equal to the sum of what I'm going to call the natural 00:09:51.510 --> 00:09:54.660 yield stress, which is the basic property of the glass. 00:09:54.660 --> 00:09:59.000 Plus, I'm going to increase the surface stress. 00:09:59.000 --> 00:10:01.540 What I'm going to do is I'm going to modify the surface, 00:10:01.540 --> 00:10:04.840 and I'm going to put an additive stress at the 00:10:04.840 --> 00:10:08.950 surface, and that's going to be a compressive stress. 00:10:08.950 --> 00:10:12.920 So that means now the effective stress that I need 00:10:12.920 --> 00:10:15.390 to break the glass is going to be greater than it 00:10:15.390 --> 00:10:16.590 otherwise would be. 00:10:16.590 --> 00:10:21.350 So the whole gambit here is surface strengthening. 00:10:21.350 --> 00:10:25.232 Service strengthening, which means surface modification. 00:10:25.232 --> 00:10:28.250 And I'm going to show you two ways to modify the surface to 00:10:28.250 --> 00:10:30.310 bring the strength of the glass up. 00:10:30.310 --> 00:10:32.910 The first way is thermal. 00:10:32.910 --> 00:10:35.080 Thermal treatment. 00:10:35.080 --> 00:10:38.320 And the thermal treatment is to strengthen the glass. 00:10:38.320 --> 00:10:38.830 Well, let's see. 00:10:38.830 --> 00:10:42.050 Let's keep it in the context of the windshield. 00:10:42.050 --> 00:10:43.580 The technical term for this, the 00:10:43.580 --> 00:10:46.070 technological term is tempering. 00:10:46.070 --> 00:10:49.140 So what I'm going to show you was how we can look at that 00:10:49.140 --> 00:10:54.080 volume versus temperature curve and understand how we 00:10:54.080 --> 00:10:57.070 make tempered glass for windshields and so. 00:10:57.070 --> 00:10:59.400 So I'm going to show you a slab of glass. 00:10:59.400 --> 00:11:00.900 Here's a slab of glass. 00:11:00.900 --> 00:11:05.160 And we just got below the softening point-- so T just 00:11:05.160 --> 00:11:08.080 less than T softening. 00:11:08.080 --> 00:11:11.020 So now this thing's going to start, it's continuing to 00:11:11.020 --> 00:11:13.900 become more and more viscous and getting closer and closer 00:11:13.900 --> 00:11:15.580 to glass transition temperature. 00:11:15.580 --> 00:11:20.920 And what we're going to do is we're going to introduce air 00:11:20.920 --> 00:11:25.430 jets at the surface of the glass. 00:11:25.430 --> 00:11:27.750 What that's going to do is it's going to cause 00:11:27.750 --> 00:11:29.910 accelerated cooling at the surface. 00:11:29.910 --> 00:11:32.090 And the same thing happens on both surfaces, so I'm going to 00:11:32.090 --> 00:11:34.260 cut this piece of glass in half, and we're just going to 00:11:34.260 --> 00:11:35.125 look at the upper surface. 00:11:35.125 --> 00:11:36.800 The same thing happens in a lower surface. 00:11:36.800 --> 00:11:39.220 So let's now blow this up. 00:11:39.220 --> 00:11:41.630 I'm just going to look at the upper-half surface and I'm 00:11:41.630 --> 00:11:42.930 going to divide it into two zones. 00:11:45.530 --> 00:11:48.430 This is the first level, most primitive 00:11:48.430 --> 00:11:51.020 finite element analysis. 00:11:51.020 --> 00:11:54.150 Finite element analysis. 00:11:54.150 --> 00:11:56.300 I'm going to divide it in two, and I'm going to say, this has 00:11:56.300 --> 00:11:57.750 got two zones. 00:11:57.750 --> 00:12:00.260 Two cooling zones. 00:12:00.260 --> 00:12:03.490 Here is the zone of the center, OK? 00:12:03.490 --> 00:12:04.880 This is the center. 00:12:04.880 --> 00:12:09.170 And I'm going to call this the inner portion. 00:12:09.170 --> 00:12:10.430 And then there's the outer portion. 00:12:10.430 --> 00:12:13.090 Well, take a look at this curve here. 00:12:13.090 --> 00:12:15.340 Which is going to have slower cooling? 00:12:15.340 --> 00:12:17.895 In the center or near the free surface? 00:12:17.895 --> 00:12:21.030 The slower cooling is in the center and according to this 00:12:21.030 --> 00:12:25.800 graph, the slow cooling has a smaller residual volume. 00:12:25.800 --> 00:12:28.230 I've written, V-interior. 00:12:28.230 --> 00:12:29.890 That's the green line. 00:12:29.890 --> 00:12:32.610 And then the upper one is a yellow line. 00:12:32.610 --> 00:12:35.130 So the upper one where it's high cooling, it's going to 00:12:35.130 --> 00:12:36.210 have a higher volume. 00:12:36.210 --> 00:12:38.085 So this is the second piece of finite element. 00:12:38.085 --> 00:12:41.030 So I'm going to model this one like so. 00:12:41.030 --> 00:12:43.390 So this is outer. 00:12:43.390 --> 00:12:45.450 And the same thing happens on the other side, OK? 00:12:45.450 --> 00:12:47.340 So it's happening on the bottom as well. 00:12:47.340 --> 00:12:49.250 But we're just looking at the top because 00:12:49.250 --> 00:12:50.730 there's symmetry here. 00:12:50.730 --> 00:12:52.970 So you see what I've done? 00:12:52.970 --> 00:12:57.720 This is longer because that graph says it wants to be 00:12:57.720 --> 00:12:59.500 occupying a larger volume. 00:12:59.500 --> 00:13:02.160 Problem is the glass can't do this. 00:13:02.160 --> 00:13:04.970 I can do this with a piece of chalk, but the glass isn't 00:13:04.970 --> 00:13:06.030 going to look like that. 00:13:06.030 --> 00:13:08.250 The glass is going to have a flat edge. 00:13:08.250 --> 00:13:10.600 And how can it have a flat edge? 00:13:10.600 --> 00:13:13.880 Because the bottom, here-- this is not to scale, let's 00:13:13.880 --> 00:13:15.090 make it more to scale-- 00:13:15.090 --> 00:13:18.505 the top is a narrow zone and the bottom is a big, thick 00:13:18.505 --> 00:13:19.680 zone, isn't it? 00:13:19.680 --> 00:13:23.545 So this big, thick zone, which has a small volume, is going 00:13:23.545 --> 00:13:27.510 to pull on the thin upper zone, which has a large 00:13:27.510 --> 00:13:29.160 volume, and pull it in. 00:13:29.160 --> 00:13:30.010 Can you see that? 00:13:30.010 --> 00:13:32.110 And it's going to cause the introduction 00:13:32.110 --> 00:13:35.530 of compressive stresses. 00:13:35.530 --> 00:13:39.520 So we got to compressive stresses simply using that 00:13:39.520 --> 00:13:43.650 graph and a little bit of air. 00:13:43.650 --> 00:13:46.520 So you take that graph, put differential cooling, and now 00:13:46.520 --> 00:13:48.290 you've introduced compressive stress. 00:13:48.290 --> 00:13:50.570 And that's all tempered glass is. 00:13:50.570 --> 00:13:57.040 So the V-excess of the outer layer is greater than V-excess 00:13:57.040 --> 00:14:01.810 of the inner layer, or the interior, if you like. 00:14:01.810 --> 00:14:02.420 And why? 00:14:02.420 --> 00:14:06.070 Because the cooling rate, the change of temperature with 00:14:06.070 --> 00:14:13.400 time of the outer zone, is greater than the cooling rate 00:14:13.400 --> 00:14:18.000 of the inner or interior. 00:14:18.000 --> 00:14:19.950 And there it is. 00:14:19.950 --> 00:14:20.890 That's the beginning. 00:14:20.890 --> 00:14:25.140 And so now to fracture you have to apply a greater stress 00:14:25.140 --> 00:14:27.270 then you would have otherwise. 00:14:27.270 --> 00:14:29.980 So that's good, and that saves a lot of lives. 00:14:29.980 --> 00:14:31.260 There's another way. 00:14:31.260 --> 00:14:33.920 There's another way to surface strengthen, and that's a 00:14:33.920 --> 00:14:35.170 chemical treatment. 00:14:37.750 --> 00:14:39.030 And again, what am I trying to do? 00:14:39.030 --> 00:14:40.950 I'm trying to introduce a compressive stress, but I'm 00:14:40.950 --> 00:14:44.590 going to use a chemical means. 00:14:44.590 --> 00:14:49.050 And this one is called ion exchange. 00:14:49.050 --> 00:14:51.840 And this is used in technology, too. 00:14:51.840 --> 00:14:55.280 So now I'm going to take a piece of glass here. 00:14:55.280 --> 00:15:01.550 This is solid glass and let's put some components in here. 00:15:01.550 --> 00:15:05.720 So I'm going to put some silica as my network former. 00:15:05.720 --> 00:15:08.550 I'm going to put some sodium oxide. 00:15:08.550 --> 00:15:12.120 And I'm going to put some modifier, B2O3. 00:15:12.120 --> 00:15:13.510 So I got all three here. 00:15:13.510 --> 00:15:16.560 Former, modifier, intermediate. 00:15:16.560 --> 00:15:19.800 And just to put a little skin on the bones here, I want to 00:15:19.800 --> 00:15:23.050 show what the sodium oxide actually looks like. 00:15:23.050 --> 00:15:29.700 Sodium oxide goes in as sodium cations, and oxide anions. 00:15:29.700 --> 00:15:31.510 The oxide anions go in and they break some 00:15:31.510 --> 00:15:32.850 of the silica chains. 00:15:32.850 --> 00:15:34.870 But the sodiums don't get involved in that. 00:15:34.870 --> 00:15:37.560 They just sit around as spectators. 00:15:37.560 --> 00:15:39.270 Now what I'm going to do is I'm going to put this, I'm 00:15:39.270 --> 00:15:45.600 going to soak this in molten salt. 00:15:45.600 --> 00:15:46.900 Soak in molten salt. 00:15:46.900 --> 00:15:50.190 This is huge area of my own research. 00:15:50.190 --> 00:15:54.550 And the molten salt, one example might be I'm going to 00:15:54.550 --> 00:15:56.030 take potassium chloride. 00:15:56.030 --> 00:15:58.610 Remember, we talked about making aluminum or magnesium? 00:15:58.610 --> 00:16:00.235 This is one of the constituents of the melt in 00:16:00.235 --> 00:16:02.340 which we make electrolytic magnesium. 00:16:02.340 --> 00:16:03.480 Potassium chloride. 00:16:03.480 --> 00:16:08.560 And it exists as potassium cations and chloride anions. 00:16:12.040 --> 00:16:14.120 Chlorine is green, except we know-- 00:16:14.120 --> 00:16:15.900 you know, this is the way chemistry books write it, but 00:16:15.900 --> 00:16:19.020 that's stupid because this is isoelectronic with argon. 00:16:19.020 --> 00:16:20.200 And it's not green. 00:16:20.200 --> 00:16:20.510 I know. 00:16:20.510 --> 00:16:21.530 I've looked at this stuff. 00:16:21.530 --> 00:16:23.540 It's clear, colorless, and transparent. 00:16:23.540 --> 00:16:26.490 The chloride ion has to be clear and colorless. 00:16:26.490 --> 00:16:28.780 It's got a complete shell, but the chemistry books 00:16:28.780 --> 00:16:29.460 will make it green. 00:16:29.460 --> 00:16:32.900 Anyway, here's the potassium ion here. 00:16:32.900 --> 00:16:34.640 And there's a lot of potassium ion here. 00:16:34.640 --> 00:16:37.440 There's no potassium ion inside the glass. 00:16:37.440 --> 00:16:39.970 There's sodium ion in the glass, there's no sodium ion 00:16:39.970 --> 00:16:41.385 in the molten salt. 00:16:41.385 --> 00:16:45.970 But these are both media in which ions live. 00:16:45.970 --> 00:16:48.790 So can you see this is sort of like the perfume bottle? 00:16:48.790 --> 00:16:50.680 Things move from high concentration to low 00:16:50.680 --> 00:16:51.760 concentration. 00:16:51.760 --> 00:16:55.380 Some sodium wants to leave and enter the melt. 00:16:55.380 --> 00:16:58.770 And some potassium wants to leave the melt 00:16:58.770 --> 00:17:00.865 and enter the glass. 00:17:00.865 --> 00:17:02.840 And where's the potassium going to go? 00:17:02.840 --> 00:17:05.310 It has to go where there used to be sodium. 00:17:05.310 --> 00:17:07.440 What's the relative size of potassium ion 00:17:07.440 --> 00:17:08.840 versus sodium ion? 00:17:08.840 --> 00:17:10.590 Potassium ion is bigger. 00:17:10.590 --> 00:17:14.330 So potassium ion goes and occupies a site formerly 00:17:14.330 --> 00:17:19.500 occupied by sodium and causes compressive stress, because 00:17:19.500 --> 00:17:22.990 you get all these big ions jamming in there and that's 00:17:22.990 --> 00:17:27.400 going to lead to compressive stress through ion exchange. 00:17:27.400 --> 00:17:30.190 So through ion exchange we can raised the temp. 00:17:30.190 --> 00:17:34.240 Since r, the radius of potassium is greater than the 00:17:34.240 --> 00:17:39.030 radius of the sodium, we get a force fit, and this is how we 00:17:39.030 --> 00:17:42.360 got solution hardening. 00:17:42.360 --> 00:17:47.250 Hardening is the metallurgical term for raising the strength. 00:17:47.250 --> 00:17:50.730 Hardening is equal to strength going up. 00:17:50.730 --> 00:17:53.250 So we get hardening by solution. 00:17:53.250 --> 00:17:55.720 So this is solution hardening. 00:17:55.720 --> 00:17:59.350 Solution hardening because the potassium ion is in there. 00:17:59.350 --> 00:18:00.730 So we have surface. 00:18:00.730 --> 00:18:02.210 And this gives a lot of strength. 00:18:02.210 --> 00:18:05.400 We do the same thing metallurgically if you 00:18:05.400 --> 00:18:07.950 carburize the surface of a piece of steel. 00:18:07.950 --> 00:18:10.740 Tool steels, for example, surface carburized. 00:18:10.740 --> 00:18:13.630 So we get hard surfaces that can cut. 00:18:13.630 --> 00:18:15.630 You say, well, why don't you just put the carbon in all the 00:18:15.630 --> 00:18:16.170 way through? 00:18:16.170 --> 00:18:18.220 Well, then the tool bit will be brittle. 00:18:18.220 --> 00:18:21.060 So you want something that's got toughness in the center so 00:18:21.060 --> 00:18:23.460 it can take the impact, but it's got surface 00:18:23.460 --> 00:18:25.110 hardness so it'll cut. 00:18:25.110 --> 00:18:26.380 And that's an engineered material. 00:18:26.380 --> 00:18:29.330 We've got one set of properties at the surface, and 00:18:29.330 --> 00:18:31.440 we've got another set of properties in the bulk. 00:18:31.440 --> 00:18:36.240 And it's all brought to you by control of chemistry. 00:18:36.240 --> 00:18:38.990 And then that's also control of chemistry. 00:18:38.990 --> 00:18:39.880 OK. 00:18:39.880 --> 00:18:42.820 So I mean, I could talk more and more and more. 00:18:42.820 --> 00:18:45.030 Glasses are just fascinating things. 00:18:45.030 --> 00:18:47.090 But we've got to get moving. 00:18:47.090 --> 00:18:49.540 So we're going to move to a new topic. 00:18:49.540 --> 00:18:51.630 We're going to move to a new topic today. 00:18:51.630 --> 00:18:54.280 We're going to start talking about kinetics. 00:18:54.280 --> 00:18:55.530 Kinetics. 00:18:57.110 --> 00:18:58.280 And what is kinetics? 00:18:58.280 --> 00:19:02.790 Kinetics is the topic that we put into 3.091, because it's 00:19:02.790 --> 00:19:06.140 important, of course, but it's all about the study of 00:19:06.140 --> 00:19:08.240 reaction rates. 00:19:08.240 --> 00:19:14.235 It's the study of reaction rates and mechanism. 00:19:21.700 --> 00:19:23.210 So why do we study? 00:19:23.210 --> 00:19:27.250 Well, we study it because I think it belongs here. 00:19:27.250 --> 00:19:30.820 But first of all, kinetics is related to productivity and 00:19:30.820 --> 00:19:31.510 resource utilization. 00:19:31.510 --> 00:19:32.920 You've got two factories. 00:19:32.920 --> 00:19:37.060 One produces 200 units per time, the other produces 100 00:19:37.060 --> 00:19:37.860 units per time. 00:19:37.860 --> 00:19:40.410 The one that's producing 100 units per time probably isn't 00:19:40.410 --> 00:19:43.300 going to be in business that much longer. 00:19:43.300 --> 00:19:46.450 And it's all about understanding how to get more 00:19:46.450 --> 00:19:50.000 throughput per unit time, and that leads to competitiveness. 00:19:50.000 --> 00:19:53.010 So if you're interested in international competitiveness, 00:19:53.010 --> 00:19:54.640 you've got to know something about kinetics. 00:19:54.640 --> 00:19:56.290 The two go hand in glove. 00:19:56.290 --> 00:19:57.760 Second thing is energy and the environment. 00:19:57.760 --> 00:20:01.290 A number of you have come to talk to me after class, sent 00:20:01.290 --> 00:20:03.120 emails because you're interested in energy and the 00:20:03.120 --> 00:20:03.940 environment. 00:20:03.940 --> 00:20:07.740 Efficient use of energy involves understanding the 00:20:07.740 --> 00:20:11.160 kinetics so you can force chemical change with the least 00:20:11.160 --> 00:20:15.320 amount of energy utilization and do so in a way because its 00:20:15.320 --> 00:20:16.340 mechanism-- 00:20:16.340 --> 00:20:18.830 if there's two mechanisms that allow you to get to the same 00:20:18.830 --> 00:20:21.770 end product, choose the one that has the least toxic 00:20:21.770 --> 00:20:23.550 impact on the environment. 00:20:23.550 --> 00:20:27.010 Otherwise, you're going to have to spend money to avoid 00:20:27.010 --> 00:20:30.110 the effluents, which then gets you back up to number one. 00:20:30.110 --> 00:20:33.260 Your cost of doing business is higher than the other guy. 00:20:33.260 --> 00:20:34.090 Guess what? 00:20:34.090 --> 00:20:35.980 You're creamed in the marketplace. 00:20:35.980 --> 00:20:37.290 And lastly, societal. 00:20:37.290 --> 00:20:42.680 And this is one that excites me, is kinetics leads to 00:20:42.680 --> 00:20:45.440 productivity, which keeps factories open, which keeps 00:20:45.440 --> 00:20:46.800 people working. 00:20:46.800 --> 00:20:48.640 So through understanding kinetics. 00:20:48.640 --> 00:20:51.900 You go and you look at places in the United States where 00:20:51.900 --> 00:20:53.300 factories have closed. 00:20:53.300 --> 00:20:58.506 In many, many instances it was because the technology lagged. 00:20:58.506 --> 00:21:01.330 If you could just keep things going faster. 00:21:01.330 --> 00:21:02.835 You've got to make things-- you know how fast you've got 00:21:02.835 --> 00:21:03.740 to make them go? 00:21:03.740 --> 00:21:05.970 You've got to make them go so fast that even if the foreign 00:21:05.970 --> 00:21:08.560 workers are paid zero, you can still beat them in the 00:21:08.560 --> 00:21:09.490 marketplace. 00:21:09.490 --> 00:21:11.190 That's your standard. 00:21:11.190 --> 00:21:12.840 So that's how you design your processes. 00:21:12.840 --> 00:21:16.910 You design your processes so that you can produce at very, 00:21:16.910 --> 00:21:19.080 very low cost. 00:21:19.080 --> 00:21:21.810 And there's a huge range in reaction rates. 00:21:21.810 --> 00:21:25.980 You know, you can start the range of 00:21:25.980 --> 00:21:28.120 rates, rates of reaction. 00:21:28.120 --> 00:21:31.570 At the one that you have very, very slow. 00:21:31.570 --> 00:21:35.450 And way over here you have very, very fast, all right? 00:21:35.450 --> 00:21:36.970 So on the slow end, you have stuff that's 00:21:36.970 --> 00:21:39.740 sort of cosmic scale. 00:21:39.740 --> 00:21:40.990 Geological. 00:21:43.050 --> 00:21:44.320 And then over here, what do we have? 00:21:44.320 --> 00:21:45.570 We have explosions. 00:21:47.820 --> 00:21:50.190 You might say, well, explosions are usually bad, 00:21:50.190 --> 00:21:50.540 aren't they? 00:21:50.540 --> 00:21:51.360 Well, no. 00:21:51.360 --> 00:21:53.680 I can give you an example of where explosion is used to 00:21:53.680 --> 00:21:55.750 your advantage. 00:21:55.750 --> 00:21:57.230 The airbag in the automobile. 00:21:57.230 --> 00:22:00.570 There is no pump, no mechanical pump fast enough to 00:22:00.570 --> 00:22:03.320 inflate an airbag on demand. 00:22:03.320 --> 00:22:05.190 So how do we make those airbags work? 00:22:05.190 --> 00:22:08.370 And I hope none of us ever has to be present at the 00:22:08.370 --> 00:22:09.760 deployment of those airbags. 00:22:09.760 --> 00:22:12.460 But you know, just academically let's talk about 00:22:12.460 --> 00:22:13.470 how they work. 00:22:13.470 --> 00:22:19.550 There's like an explosion that occurs when you're driving. 00:22:19.550 --> 00:22:22.325 There's an accelerometer and this is a key piece. 00:22:22.325 --> 00:22:24.690 The accelerometer has to make a decision whether you're 00:22:24.690 --> 00:22:27.050 applying the brakes just because you've lost focus and 00:22:27.050 --> 00:22:28.390 you're, you know, whoops! 00:22:28.390 --> 00:22:29.650 You've had that jerky brake. 00:22:29.650 --> 00:22:33.090 Or maybe this is one of those holy-mackerel moments, and 00:22:33.090 --> 00:22:34.420 your jamming on the brakes, and we'd 00:22:34.420 --> 00:22:35.840 better deploy the airbags. 00:22:35.840 --> 00:22:40.390 Once the accelerometer decides that this is one of those holy 00:22:40.390 --> 00:22:43.410 you-know-what moments, it sends an electric current 00:22:43.410 --> 00:22:46.990 through a wire, which then raises the temperature to 300 00:22:46.990 --> 00:22:50.150 degrees C and causes this reaction to take place. 00:22:50.150 --> 00:22:52.970 When this reaction takes place, this is a solid, 00:22:52.970 --> 00:22:54.450 nitrogen is a gas. 00:22:54.450 --> 00:22:57.910 So the gas has a much, much higher volume than the solid 00:22:57.910 --> 00:23:00.400 and within milliseconds you get inflation. 00:23:00.400 --> 00:23:03.320 Well, that's good and that inflates the bag and prevents 00:23:03.320 --> 00:23:06.580 you from hitting the hard parts of the car. 00:23:06.580 --> 00:23:07.870 But you see the other byproduct? 00:23:07.870 --> 00:23:08.780 That's sodium. 00:23:08.780 --> 00:23:11.150 And if you look on your Periodic Table, elemental 00:23:11.150 --> 00:23:15.110 sodium is liquid above 98 degrees Celsius. 00:23:15.110 --> 00:23:16.580 So now you've got liquid sodium. 00:23:16.580 --> 00:23:19.430 There's no point preserving the safety of the occupants of 00:23:19.430 --> 00:23:21.810 the car just to cover them with liquid sodium. 00:23:21.810 --> 00:23:23.270 So we better do something about that. 00:23:23.270 --> 00:23:26.410 So being chemists, what we do is we add potassium nitrate 00:23:26.410 --> 00:23:28.060 inside the bag, as well. 00:23:28.060 --> 00:23:28.300 so. 00:23:28.300 --> 00:23:31.290 That that sodium is mopped up with potassium nitrate, which 00:23:31.290 --> 00:23:35.070 converts it to sodium oxide, potassium oxide, and a little 00:23:35.070 --> 00:23:35.593 more nitrogen. 00:23:35.593 --> 00:23:36.300 [BLOWING SOUND EFFECT] 00:23:36.300 --> 00:23:39.660 Keep the bag nice and firm. 00:23:39.660 --> 00:23:44.026 But now what happens when the Fires show up and they 00:23:44.026 --> 00:23:44.760 [SOUND EFFECT], 00:23:44.760 --> 00:23:46.670 you know, they start pouring water on it. 00:23:46.670 --> 00:23:48.440 This turns into caustic. 00:23:48.440 --> 00:23:52.072 So now you're going to get covered and wet lye. 00:23:52.072 --> 00:23:55.140 So that's probably not too good, either. 00:23:55.140 --> 00:23:58.540 Just remember, you've been physically saved from smashing 00:23:58.540 --> 00:24:01.470 your skull on the tempered windshield. 00:24:01.470 --> 00:24:04.680 So it's so far, so good. 00:24:04.680 --> 00:24:07.350 So now what? 00:24:07.350 --> 00:24:10.200 You want a mechanical, you want a Newtonian death? 00:24:10.200 --> 00:24:15.260 Or do you want a Coulombic death? 00:24:15.260 --> 00:24:17.210 I guess that's the question, here. 00:24:17.210 --> 00:24:19.500 And so we're going to keep doing some chemistry here and 00:24:19.500 --> 00:24:20.820 we're going to add silica. 00:24:20.820 --> 00:24:23.290 And what happens if we add silica to sodium oxide 00:24:23.290 --> 00:24:24.190 potassium oxide? 00:24:24.190 --> 00:24:26.870 Well that's a network former, these are network modifiers. 00:24:26.870 --> 00:24:29.370 We'll make an alkaline silicate glass and that's OK 00:24:29.370 --> 00:24:31.330 because we put food and beverages in 00:24:31.330 --> 00:24:33.040 alkaline silicate glasses. 00:24:33.040 --> 00:24:34.240 So everybody is happy. 00:24:34.240 --> 00:24:36.595 So that's all the chemistry that goes on inside an airbag. 00:24:36.595 --> 00:24:39.740 And we've got to understand the kinetics. 00:24:39.740 --> 00:24:42.400 So I hope I've whet your appetite. 00:24:42.400 --> 00:24:43.350 OK, that's enough of that. 00:24:43.350 --> 00:24:45.430 Now let's get to the real stuff. 00:24:45.430 --> 00:24:49.010 So let's write a general chemical reaction. 00:24:49.010 --> 00:24:50.090 The general reaction. 00:24:50.090 --> 00:24:53.740 What's the formalism if we want to set up the metrics? 00:24:53.740 --> 00:24:57.540 So I'm going to write just a plain, old equation. 00:24:57.540 --> 00:25:01.210 This is the classical P-Chem stuff. 00:25:01.210 --> 00:25:04.920 Little a moles of A, plus little b moles of B go to 00:25:04.920 --> 00:25:07.680 little c moles of C plus little d moles of D. 00:25:07.680 --> 00:25:09.590 So this could have been lecture two. 00:25:09.590 --> 00:25:11.520 Just a straight chemical reaction. 00:25:11.520 --> 00:25:13.400 Remember we were studying stoichiometry? 00:25:13.400 --> 00:25:16.885 So the constituents of the left side of the equation are 00:25:16.885 --> 00:25:19.480 called the reactants, whereas on the right side of the 00:25:19.480 --> 00:25:22.790 equation we have the products. 00:25:22.790 --> 00:25:28.190 And what kinetics gives us, kinetics tells us the rate of 00:25:28.190 --> 00:25:29.440 conversion. 00:25:31.380 --> 00:25:32.730 Or the rate of reaction. 00:25:32.730 --> 00:25:35.100 I'm using all these terms so you understand their 00:25:35.100 --> 00:25:36.860 equivalent. 00:25:36.860 --> 00:25:45.320 So we can write something like this where the conservation of 00:25:45.320 --> 00:25:46.130 mass kicks in. 00:25:46.130 --> 00:25:48.230 So I can't make products any faster 00:25:48.230 --> 00:25:49.920 than I consume reactants. 00:25:49.920 --> 00:25:51.750 There's no sources or sinks here. 00:25:51.750 --> 00:25:53.640 When I lose reactants, I make products. 00:25:53.640 --> 00:25:57.850 So I'm going to say, the rate of change of the total mass of 00:25:57.850 --> 00:25:59.710 the reactants-- this is summation sign-- 00:25:59.710 --> 00:26:03.510 I'm just saying the rate of change of the sum of all of 00:26:03.510 --> 00:26:06.530 the reactions must equal the rate of change. 00:26:06.530 --> 00:26:10.470 So the loss rate of reactants must equal the gain rate of 00:26:10.470 --> 00:26:12.680 all of the products. 00:26:12.680 --> 00:26:15.130 That's just simple stoichiometry. 00:26:15.130 --> 00:26:17.900 Or some people call this conservation of mass or Law of 00:26:17.900 --> 00:26:19.680 Mass Action, what have you. 00:26:19.680 --> 00:26:23.030 And then we count by concentration, usually. 00:26:26.440 --> 00:26:26.900 Just reminder. 00:26:26.900 --> 00:26:28.270 This is lowercase c. 00:26:28.270 --> 00:26:31.430 So this is the concentration of species i 00:26:31.430 --> 00:26:33.110 goes as the mole number. 00:26:33.110 --> 00:26:37.290 n is mole number divided by the volume of the reactor. 00:26:37.290 --> 00:26:42.330 So this would be in moles per meter cubed if 00:26:42.330 --> 00:26:43.770 we were in SI units. 00:26:43.770 --> 00:26:48.090 So therefore the rate of change, the ci by dt, is 00:26:48.090 --> 00:26:51.760 really the rate of change of mole number, isn't it? 00:26:51.760 --> 00:26:54.820 It's moles of i disappearing, but the volume 00:26:54.820 --> 00:26:56.900 doesn't change, typically. 00:26:56.900 --> 00:27:00.980 And then the last thing is we can use this idea up here that 00:27:00.980 --> 00:27:04.980 concentration of products can only equal the loss rate of 00:27:04.980 --> 00:27:06.140 the reactant. 00:27:06.140 --> 00:27:11.890 So I can write, term by term, the normalized rate loss of 00:27:11.890 --> 00:27:15.500 the concentration of a divided by its stoichiometric 00:27:15.500 --> 00:27:18.780 coefficient, for example, would equal the normalized 00:27:18.780 --> 00:27:23.210 weight gain, or pardon me, the concentration gain of the 00:27:23.210 --> 00:27:24.990 concentration of d. 00:27:24.990 --> 00:27:28.750 So this is just saying a disappears no faster than d 00:27:28.750 --> 00:27:32.490 appears, mediated by the stoichiometric coefficients. 00:27:32.490 --> 00:27:39.550 So this is just Law of Mass Action, which is stoichiometry 00:27:39.550 --> 00:27:41.290 in motion, isn't it? 00:27:41.290 --> 00:27:43.930 That's all it is. 00:27:43.930 --> 00:27:48.890 Now here comes the cool thing kinetic theory. 00:27:48.890 --> 00:27:51.670 We look at any reaction, I can tell you right now what it 00:27:51.670 --> 00:27:52.330 looks like. 00:27:52.330 --> 00:27:56.200 If I applied concentration of i as a function of time, I 00:27:56.200 --> 00:28:00.410 start off with some value c naught, some initial value, 00:28:00.410 --> 00:28:03.310 and it just attenuates. 00:28:03.310 --> 00:28:07.020 We know that's going to happen as we consume the-- it falls 00:28:07.020 --> 00:28:08.490 and there's some curvature here. 00:28:08.490 --> 00:28:11.990 What we're trying to do next is to give some mathematical 00:28:11.990 --> 00:28:13.780 representation to this. 00:28:13.780 --> 00:28:17.050 Can we come up with a mathematical formulation of 00:28:17.050 --> 00:28:18.490 the shape of that curve? 00:28:18.490 --> 00:28:21.660 And we can, and here's the central 00:28:21.660 --> 00:28:25.540 tenet kinetic of theory. 00:28:25.540 --> 00:28:36.640 Kinetic theory says that the reaction rate can be expressed 00:28:36.640 --> 00:28:38.187 in terms of a driving force. 00:28:46.020 --> 00:28:48.670 And that driving force is the instant concentration. 00:28:51.170 --> 00:28:51.420 OK. 00:28:51.420 --> 00:28:52.230 These are lofty words. 00:28:52.230 --> 00:28:54.745 I'll show you what it means with illustration. 00:28:57.970 --> 00:29:00.570 So that's the overall idea. 00:29:00.570 --> 00:29:06.250 So now let's say that the rate of change, the instant rate of 00:29:06.250 --> 00:29:14.190 change of concentration ci, is proportional to the instant 00:29:14.190 --> 00:29:16.410 value of the concentration. 00:29:16.410 --> 00:29:17.230 And you know, the concentration 00:29:17.230 --> 00:29:18.830 is changing, right? 00:29:18.830 --> 00:29:20.470 As the concentration decreases, the 00:29:20.470 --> 00:29:21.670 rate of change decreases. 00:29:21.670 --> 00:29:25.655 So just this alone, this idea alone would rationalize a 00:29:25.655 --> 00:29:27.460 curve like that. 00:29:27.460 --> 00:29:29.940 As the concentration falls, the rate of change falls, 00:29:29.940 --> 00:29:32.430 which means the concentration falls, which means-- 00:29:32.430 --> 00:29:35.640 and raised to some power-- 00:29:35.640 --> 00:29:37.120 it's not linear, necessarily-- 00:29:37.120 --> 00:29:40.770 raised to some power. 00:29:40.770 --> 00:29:43.250 There's a power law at work here. 00:29:43.250 --> 00:29:45.300 So now let's do this one more time. 00:29:45.300 --> 00:29:46.530 I'm going to write it mathematically. 00:29:46.530 --> 00:29:48.780 But I want you to first see the word, concepts. 00:29:48.780 --> 00:29:50.170 So let's write it mathematically. 00:29:50.170 --> 00:29:53.590 That means minus dci by dt-- 00:29:53.590 --> 00:29:57.260 so this is time rate a change of concentration i, the minus 00:29:57.260 --> 00:29:59.160 means it's falling-- 00:29:59.160 --> 00:30:05.160 is equal to the concentration of i raised to some power n. 00:30:05.160 --> 00:30:06.580 This is order reaction. 00:30:06.580 --> 00:30:08.060 It's not mole number over there. 00:30:08.060 --> 00:30:10.300 You've got to be pluralistic today. 00:30:10.300 --> 00:30:11.730 n is going to be used in different ways. 00:30:11.730 --> 00:30:18.510 So this is called order of reaction. 00:30:18.510 --> 00:30:19.825 And there's a constant. 00:30:19.825 --> 00:30:20.480 See up there? 00:30:20.480 --> 00:30:21.850 It's a proportionality. 00:30:21.850 --> 00:30:24.660 Here it's an equal sign, thanks to the constant. 00:30:24.660 --> 00:30:26.270 And this is called the rate constant. 00:30:30.980 --> 00:30:33.300 And this what all I need for plant design. 00:30:33.300 --> 00:30:37.300 Suppose I'm running a chemical plant and I'm taking a plus b 00:30:37.300 --> 00:30:39.590 and making c plus d and the management says, we want to 00:30:39.590 --> 00:30:41.000 double the rate of productivity. 00:30:41.000 --> 00:30:42.440 So you go, I know what to do. 00:30:42.440 --> 00:30:44.230 We'll increase the concentration. 00:30:44.230 --> 00:30:46.180 They say, by how much? 00:30:46.180 --> 00:30:49.230 Well, this allows you, if you know the value of k and n, you 00:30:49.230 --> 00:30:50.600 want to double this? 00:30:50.600 --> 00:30:53.090 Then you know what to do here. 00:30:53.090 --> 00:30:55.620 It's not necessarily double the concentration, Because 00:30:55.620 --> 00:30:57.710 this is a 1.5 power. 00:30:57.710 --> 00:30:59.720 By the way, this doesn't have to be an integer. 00:30:59.720 --> 00:31:00.760 Could be anything. 00:31:00.760 --> 00:31:11.180 Could be not necessarily integer and must be determined 00:31:11.180 --> 00:31:12.430 by experiment. 00:31:14.650 --> 00:31:17.030 You can't look at an equation and say, oh, that's going to 00:31:17.030 --> 00:31:17.980 be second order because there's a 00:31:17.980 --> 00:31:19.950 two in front of something. 00:31:19.950 --> 00:31:22.385 So here we are, plant designers. 00:31:22.385 --> 00:31:24.680 And the management wants to know, how do 00:31:24.680 --> 00:31:25.690 we make things happen? 00:31:25.690 --> 00:31:27.960 So I'm going to go back to that equation over there and 00:31:27.960 --> 00:31:32.890 I'll say that most generally, the rate of change of 00:31:32.890 --> 00:31:38.050 concentration of a will then go as rate constant times the 00:31:38.050 --> 00:31:39.370 concentration of a. 00:31:39.370 --> 00:31:41.860 See, the rate of change goes as something 00:31:41.860 --> 00:31:43.550 to the power alpha. 00:31:43.550 --> 00:31:47.470 But it could also be influenced by b. 00:31:47.470 --> 00:31:49.470 So I'm going to put-- this is the most general form. 00:31:49.470 --> 00:31:51.150 Then once you make your measurements, a lot 00:31:51.150 --> 00:31:52.570 of these fall out. 00:31:52.570 --> 00:31:56.120 I'm even going to put c I'm going to put d. 00:31:56.120 --> 00:31:58.900 Everything was in that equation. 00:31:58.900 --> 00:32:00.270 You might say, well, wait a minute. 00:32:00.270 --> 00:32:03.630 How can the rate of consumption of a be influenced 00:32:03.630 --> 00:32:05.350 by the concentration of d? 00:32:05.350 --> 00:32:07.090 d is a product. 00:32:07.090 --> 00:32:08.490 I'll give you two examples. 00:32:08.490 --> 00:32:13.070 One is that d, when I'm making d, d happens to have some 00:32:13.070 --> 00:32:15.350 catalytic value. 00:32:15.350 --> 00:32:19.740 So when I start making a convert to d, d catalyzes the 00:32:19.740 --> 00:32:22.810 reaction, which makes it go faster, which makes more d, 00:32:22.810 --> 00:32:27.060 which makes the reaction go faster, in which case this is 00:32:27.060 --> 00:32:28.810 going to have a profound effect. 00:32:28.810 --> 00:32:32.010 And unfortunately, there are some other situations where a 00:32:32.010 --> 00:32:35.790 converts to d and d retards the reaction. 00:32:35.790 --> 00:32:38.960 And so I start off with pretty decent conversion efficiency, 00:32:38.960 --> 00:32:43.120 but as I make more and more d, the d chokes the reaction, in 00:32:43.120 --> 00:32:47.070 which case the value here is going to have negative 00:32:47.070 --> 00:32:47.750 implications. 00:32:47.750 --> 00:32:49.980 So that's why you write it most generally, and then you 00:32:49.980 --> 00:32:51.795 go and you make some measurements in an experiment, 00:32:51.795 --> 00:32:53.300 and you figure out what these are. 00:32:53.300 --> 00:32:55.710 Some of them might be zeroes, and away you go. 00:32:55.710 --> 00:32:58.510 So I'll give you an example of one. 00:32:58.510 --> 00:32:58.980 Here's one. 00:32:58.980 --> 00:33:01.100 It's Monday after Halloween, so we'll get 00:33:01.100 --> 00:33:02.770 something kind of toxic. 00:33:02.770 --> 00:33:08.600 This was the manufacture of phosgene that was banned by 00:33:08.600 --> 00:33:10.220 international convention. 00:33:10.220 --> 00:33:13.110 It was used as one of the toxic gases for trench warfare 00:33:13.110 --> 00:33:14.700 in World War I. 00:33:14.700 --> 00:33:17.670 So it's made by the reaction of carbon 00:33:17.670 --> 00:33:19.880 monoxide and chlorine. 00:33:19.880 --> 00:33:21.010 COCL2. 00:33:21.010 --> 00:33:22.720 This is called phosgene. 00:33:22.720 --> 00:33:23.910 It's very bad stuff. 00:33:23.910 --> 00:33:25.430 I used it, actually, in my research. 00:33:25.430 --> 00:33:29.990 It has really good dehydration properties for salts. 00:33:29.990 --> 00:33:32.470 If you've got any moisture in potassium chloride, this'll go 00:33:32.470 --> 00:33:37.110 after it and turn the water into carbon dioxide and HCl. 00:33:37.110 --> 00:33:39.180 But you've got to be really, really careful with this. 00:33:39.180 --> 00:33:42.280 Gas leaks lead to a bad day at the lab. 00:33:42.280 --> 00:33:44.520 All right, this was banned. 00:33:44.520 --> 00:33:47.580 It's still use by tyrants throughout the world, and 00:33:47.580 --> 00:33:50.580 that's why we have international war tribunals. 00:33:50.580 --> 00:33:53.700 So here's the kinetics of it. 00:33:53.700 --> 00:33:54.820 Here's the kinetics of it. 00:33:54.820 --> 00:33:55.920 dc by dt. 00:33:55.920 --> 00:33:58.660 So this is the rate of consumption of carbon monoxide 00:33:58.660 --> 00:34:02.970 determined by experiment goes as the concentration of carbon 00:34:02.970 --> 00:34:06.850 monoxide and the concentration of chlorine raised 00:34:06.850 --> 00:34:08.730 to the power 3/2. 00:34:08.730 --> 00:34:13.340 So what I've done is mimic here. 00:34:13.340 --> 00:34:17.490 So in this case, gamma and delta are 0. 00:34:17.490 --> 00:34:23.790 Gamma equals delta equals 0, and it looks like beta equals 00:34:23.790 --> 00:34:26.600 1.5 and alpha equals 1. 00:34:26.600 --> 00:34:29.550 So I would say that this reaction is first order in 00:34:29.550 --> 00:34:34.650 carbon monoxide of order 1.5 in chlorine, or 00:34:34.650 --> 00:34:36.960 overall, of order 2.5. 00:34:36.960 --> 00:34:37.330 Because, right? 00:34:37.330 --> 00:34:39.340 This is the order of reaction. 00:34:39.340 --> 00:34:41.310 This is c to the power 1, isn't it? 00:34:41.310 --> 00:34:43.840 We don't write the 1. 00:34:43.840 --> 00:34:45.940 This is great. 00:34:45.940 --> 00:34:49.110 So we know, to increase the rate of reaction we increase 00:34:49.110 --> 00:34:50.080 the concentration. 00:34:50.080 --> 00:34:52.050 There's another way to increase the rate of reaction. 00:34:52.050 --> 00:34:53.865 What else can we do to increase the rate of reaction? 00:34:56.990 --> 00:34:58.290 Increase the temperature. 00:34:58.290 --> 00:35:00.270 Things go faster at higher temperatures. 00:35:00.270 --> 00:35:01.520 Again, how? 00:35:01.520 --> 00:35:02.480 How much? 00:35:02.480 --> 00:35:05.080 Suppose I said, I want to double the rate of reaction. 00:35:05.080 --> 00:35:07.270 Do I double the temperature? 00:35:07.270 --> 00:35:09.820 Do I raise the temperature by 10 degrees? 00:35:09.820 --> 00:35:11.750 How do I do that? 00:35:11.750 --> 00:35:20.130 So to increase rate of reaction, we can increase 00:35:20.130 --> 00:35:21.380 temperature. 00:35:23.600 --> 00:35:24.720 But how? 00:35:24.720 --> 00:35:27.290 And by the way, where is temperature here? 00:35:27.290 --> 00:35:29.090 I don't see temperature. 00:35:29.090 --> 00:35:31.550 I don't see temperature in this rate equation. 00:35:31.550 --> 00:35:33.130 You could say, well, if you increase the temperature 00:35:33.130 --> 00:35:34.470 you're going to increase the gas volume. 00:35:34.470 --> 00:35:36.550 But that's piddling effect, right? 00:35:36.550 --> 00:35:38.530 If I double the temperature, I double the gas volume. 00:35:38.530 --> 00:35:40.190 It doesn't change the mole number. 00:35:40.190 --> 00:35:42.020 The temperatures in here. 00:35:42.020 --> 00:35:45.160 That's where the temperature. 00:35:45.160 --> 00:35:46.980 Increase temperature, which then 00:35:46.980 --> 00:35:49.685 operates on the rate constant. 00:35:52.800 --> 00:35:55.540 That's the only place left in that formalism. 00:35:55.540 --> 00:35:57.420 But what's the quantitative value? 00:35:57.420 --> 00:36:02.530 Quantitative value was annunciated to us in 1889 by 00:36:02.530 --> 00:36:03.955 the Swedish chemist Arrhenius. 00:36:06.700 --> 00:36:11.730 And what Arrhenius found, he found that the rate constant 00:36:11.730 --> 00:36:14.080 varied with temperature in the following manner. 00:36:14.080 --> 00:36:20.730 Rate constant goes as the exponential of the ratio of 00:36:20.730 --> 00:36:24.730 minus some quantity call the activation energy e sub a-- 00:36:24.730 --> 00:36:26.750 I'm going to tell you what that means in a minute-- 00:36:26.750 --> 00:36:29.750 divided by the ratio of the product of the Boltzmann 00:36:29.750 --> 00:36:31.720 constant and temperature. 00:36:31.720 --> 00:36:35.220 And there's a constant of proportionality which we 00:36:35.220 --> 00:36:38.010 denote A in honor of Arrhenius. 00:36:38.010 --> 00:36:43.130 Or another way to write this is A times exponential-- 00:36:43.130 --> 00:36:44.460 are you familiar with this? 00:36:44.460 --> 00:36:47.570 Instead of writing e to the something, if there's a messy 00:36:47.570 --> 00:36:49.970 argument up here you can write it exp. 00:36:49.970 --> 00:36:55.860 This is the same as this minus ea over the ratio of Boltzmann 00:36:55.860 --> 00:36:58.520 constant and temperature. 00:36:58.520 --> 00:36:59.550 So what's in here? 00:36:59.550 --> 00:37:00.730 What's in here? 00:37:00.730 --> 00:37:02.180 Boltzmann constant temperature, 00:37:02.180 --> 00:37:03.520 we've seen that already. 00:37:03.520 --> 00:37:06.600 What's the Boltzmann constant temperature product? 00:37:06.600 --> 00:37:08.030 That's the environment. 00:37:08.030 --> 00:37:11.530 That's the energy of the environment. 00:37:11.530 --> 00:37:15.720 So this is the final environment. 00:37:18.640 --> 00:37:23.210 And this thing up on top, ea, is a barrier. 00:37:23.210 --> 00:37:24.260 It's a barrier. 00:37:24.260 --> 00:37:26.140 Remember we saw the band gap? 00:37:26.140 --> 00:37:27.090 Same idea. 00:37:27.090 --> 00:37:30.630 Those ideas go all through physical chemistry. 00:37:30.630 --> 00:37:33.860 You got thermal energy that allows you to do this 10 00:37:33.860 --> 00:37:35.180 trillion times a second. 00:37:35.180 --> 00:37:36.940 Everybody in this room is doing this 10 00:37:36.940 --> 00:37:39.830 trillion times a second. 00:37:39.830 --> 00:37:41.470 That's what kT is. 00:37:41.470 --> 00:37:43.390 And then there's a barrier energy. 00:37:43.390 --> 00:37:46.420 Every once in a while something happens. 00:37:46.420 --> 00:37:49.240 Sometimes one in a million, sometimes one in a billion. 00:37:49.240 --> 00:37:50.490 Whatever. 00:37:52.360 --> 00:37:56.170 What Arrhenius found was this relationship, which means we 00:37:56.170 --> 00:38:05.220 could plot the variation of the rate constant. 00:38:05.220 --> 00:38:06.130 This is a mess, right? 00:38:06.130 --> 00:38:07.980 This is an exponential-- 00:38:07.980 --> 00:38:10.740 look, the eye can only see straight lines. 00:38:10.740 --> 00:38:14.240 What if I show you this? 00:38:14.240 --> 00:38:14.930 What's that mean? 00:38:14.930 --> 00:38:16.640 I don't know. 00:38:16.640 --> 00:38:17.440 Is that first order? 00:38:17.440 --> 00:38:18.150 Second order? 00:38:18.150 --> 00:38:19.150 Is that Lagrangian? 00:38:19.150 --> 00:38:20.420 Is that exponential? 00:38:20.420 --> 00:38:21.730 I don't know. 00:38:21.730 --> 00:38:22.640 I know it's a curve. 00:38:22.640 --> 00:38:24.680 But what's this? 00:38:24.680 --> 00:38:26.640 I know what that is. 00:38:26.640 --> 00:38:27.990 And you know what that is. 00:38:27.990 --> 00:38:31.380 And you can tell goodness of fit. 00:38:31.380 --> 00:38:33.270 This is what science is all about. 00:38:33.270 --> 00:38:34.290 Forget all the other stuff. 00:38:34.290 --> 00:38:35.290 You know, all that UROP stuff. 00:38:35.290 --> 00:38:37.660 You're going to work in a lab and discover stuff. 00:38:37.660 --> 00:38:38.360 Forget that. 00:38:38.360 --> 00:38:39.980 This is what it's about. 00:38:39.980 --> 00:38:40.840 You got data. 00:38:40.840 --> 00:38:42.350 Data are all over the map. 00:38:42.350 --> 00:38:43.230 Here's the thing-- 00:38:43.230 --> 00:38:48.560 I need to come up with some f function here versus a g 00:38:48.560 --> 00:38:52.200 function here that linearize my data. 00:38:52.200 --> 00:38:54.120 That's all science is about. 00:38:54.120 --> 00:38:55.720 And how do I get to f and g? 00:38:55.720 --> 00:38:56.720 Well, there's two ways. 00:38:56.720 --> 00:38:58.040 One is trial and error. 00:38:58.040 --> 00:39:01.440 The other way is physical understanding. 00:39:01.440 --> 00:39:03.590 And this is what Arrhenius taught us. 00:39:03.590 --> 00:39:07.600 Arrhenius taught us that the f function for how k varies with 00:39:07.600 --> 00:39:09.630 temperature, right? 00:39:09.630 --> 00:39:12.610 The problem, I'm trying to say, k versus t. 00:39:12.610 --> 00:39:13.990 That's what I'm trying to do. 00:39:13.990 --> 00:39:16.730 And if I plot k versus t I get a curve. 00:39:16.730 --> 00:39:17.740 No good. 00:39:17.740 --> 00:39:24.650 Instead, if I plot some f of k versus g of t, I get a 00:39:24.650 --> 00:39:26.290 straight line. 00:39:26.290 --> 00:39:27.740 And this is all science. 00:39:27.740 --> 00:39:29.920 So what's f of k? 00:39:29.920 --> 00:39:31.870 The natural logarithm of k, right? 00:39:31.870 --> 00:39:34.860 If I've got k equals a exponential, I take the 00:39:34.860 --> 00:39:37.415 natural log of this, and the natural log of an exponential 00:39:37.415 --> 00:39:39.650 is just the argument. 00:39:39.650 --> 00:39:40.820 And what's in the argument? 00:39:40.820 --> 00:39:42.940 What's the T function? 00:39:42.940 --> 00:39:44.120 1 over T. 00:39:44.120 --> 00:39:48.750 So if I plot the natural log of k versus the reciprocal of 00:39:48.750 --> 00:39:51.910 the absolute temperature, I get a straight line and its 00:39:51.910 --> 00:39:59.020 slope is minus ea, forgive me, minus ea over k-Boltzmann. 00:39:59.020 --> 00:40:02.120 Minus ea over k-Boltzmann. 00:40:02.120 --> 00:40:05.440 So now it's linearized and I can look at that and within an 00:40:05.440 --> 00:40:08.330 instant, anybody in this room can look at and say, the data 00:40:08.330 --> 00:40:10.110 conform or they don't. 00:40:10.110 --> 00:40:11.360 They don't. 00:40:11.360 --> 00:40:13.290 So now let's think about this. 00:40:13.290 --> 00:40:19.650 We say well, what's the value of this barrier? 00:40:19.650 --> 00:40:21.560 It's called activation energy. 00:40:21.560 --> 00:40:24.820 This barrier energy is called activation energy. 00:40:24.820 --> 00:40:31.410 ea is called the activation energy. 00:40:31.410 --> 00:40:34.550 And it typically, it varies, but it has values-- 00:40:34.550 --> 00:40:37.990 just to give you a sense-- about 1 electron volt. 00:40:37.990 --> 00:40:41.500 1 electron volt, which you know now is about 100 00:40:41.500 --> 00:40:45.620 kilojoules per mole, isn't it? 00:40:45.620 --> 00:40:47.420 I hear the chorus of yesses. 00:40:47.420 --> 00:40:48.600 1 electron volt. 00:40:48.600 --> 00:40:49.750 What is thermal energy? 00:40:49.750 --> 00:40:51.410 What's kT? 00:40:51.410 --> 00:40:54.230 kT at room temperature, k-Boltzmann at room 00:40:54.230 --> 00:40:59.500 temperature is about 1/40 of an electron volt. 00:40:59.500 --> 00:41:01.910 Now, we are chemical machines. 00:41:01.910 --> 00:41:06.740 This conversation is occurring because all sorts of chemical 00:41:06.740 --> 00:41:10.460 processes are at work in me and you. 00:41:10.460 --> 00:41:12.770 And how's that happening? 00:41:12.770 --> 00:41:16.970 When all we've got to suck out of the environment is 1/40 of 00:41:16.970 --> 00:41:20.662 an electron volt and we need on the order one electron volt 00:41:20.662 --> 00:41:22.035 to drive certain processes. 00:41:24.990 --> 00:41:28.450 I guess we're all dead. 00:41:28.450 --> 00:41:29.700 Any ideas? 00:41:35.670 --> 00:41:38.520 Ay yay, yay. 00:41:38.520 --> 00:41:39.440 You guys need-- 00:41:39.440 --> 00:41:40.050 what's that thing? 00:41:40.050 --> 00:41:43.190 You've got to call your lifeline or something? 00:41:43.190 --> 00:41:44.260 Come on. 00:41:44.260 --> 00:41:45.110 How does anything happen? 00:41:45.110 --> 00:41:46.630 How do we get-- 00:41:46.630 --> 00:41:49.560 Why does anything happen in this world? 00:41:49.560 --> 00:41:53.160 Why should anything happen in a world with an environment of 00:41:53.160 --> 00:41:55.210 1/40 of an electron volt? 00:41:55.210 --> 00:41:56.365 AUDIENCE: Catalysts. 00:41:56.365 --> 00:41:58.500 PROFESSOR: Oh, catalysts. 00:41:58.500 --> 00:41:58.990 Catalysts. 00:41:58.990 --> 00:42:00.660 Yeah, yeah. 00:42:00.660 --> 00:42:04.810 I just went to the catalyst store and I got catalysts. 00:42:04.810 --> 00:42:06.402 Come on. 00:42:06.402 --> 00:42:07.740 AUDIENCE: Potential energy. 00:42:07.740 --> 00:42:08.550 PROFESSOR: Oh, potential energy. 00:42:08.550 --> 00:42:10.340 Jeez, this is good. 00:42:10.340 --> 00:42:12.130 Who can give me the wackiest answer? 00:42:12.130 --> 00:42:13.590 Can anybody give me the right answer? 00:42:13.590 --> 00:42:15.060 How come anything is happening? 00:42:18.600 --> 00:42:19.110 Over here. 00:42:19.110 --> 00:42:19.560 Again? 00:42:19.560 --> 00:42:20.850 AUDIENCE: Distribution of temperature. 00:42:20.850 --> 00:42:22.240 PROFESSOR: Thank you. 00:42:22.240 --> 00:42:23.500 Thank you. 00:42:23.500 --> 00:42:26.940 For a moment I thought we were all dead. 00:42:26.940 --> 00:42:31.460 At some level we were. 00:42:31.460 --> 00:42:33.320 So, yeah, it's Maxwell-Boltzmann. 00:42:33.320 --> 00:42:35.070 It's this, isn't it? 00:42:35.070 --> 00:42:37.260 And here's room temperature. 00:42:37.260 --> 00:42:39.940 And here is 1 electron volt. 00:42:39.940 --> 00:42:40.930 And this is it. 00:42:40.930 --> 00:42:43.600 And if you use this and you put it back to there, pretty 00:42:43.600 --> 00:42:45.660 soon you derive the Arrhenius equation. 00:42:45.660 --> 00:42:49.620 And if you increase the temperature 00:42:49.620 --> 00:42:50.480 you know what happens. 00:42:50.480 --> 00:42:53.530 After you increase the temperature, this. 00:42:53.530 --> 00:42:57.200 Time to use a hot color or chalk. 00:42:57.200 --> 00:43:01.810 So now this is T2 greater than T1. 00:43:01.810 --> 00:43:03.720 That's what's going on. 00:43:03.720 --> 00:43:04.600 That's what's going on. 00:43:04.600 --> 00:43:06.460 So now what is this activation energy? 00:43:06.460 --> 00:43:08.280 What is the meaning of it? 00:43:08.280 --> 00:43:09.940 You know, I've told you there's a barrier energy. 00:43:09.940 --> 00:43:10.870 What does it mean? 00:43:10.870 --> 00:43:15.160 Well, you go to the textbook, you see goofy stuff like this. 00:43:15.160 --> 00:43:17.000 And this is not a slam against the textbook. 00:43:17.000 --> 00:43:19.660 This is a slam against all chemistry textbooks, because 00:43:19.660 --> 00:43:21.000 they all write this stupid stuff. 00:43:21.000 --> 00:43:24.360 You see? a plus b goes c plus d, the energy falls and you 00:43:24.360 --> 00:43:26.640 have to go over this activated complex. 00:43:26.640 --> 00:43:29.470 You memorize it, and I ask you to repeat, it and we leave the 00:43:29.470 --> 00:43:31.970 room and we think, wow, we know physical chemistry. 00:43:31.970 --> 00:43:32.810 There's nothing here. 00:43:32.810 --> 00:43:33.405 This is nothing. 00:43:33.405 --> 00:43:35.230 This is stupid. 00:43:35.230 --> 00:43:36.960 Now this is a little bit better. 00:43:36.960 --> 00:43:38.070 Can you see this? 00:43:38.070 --> 00:43:39.030 This is the Maxwell-Boltzmann. 00:43:39.030 --> 00:43:42.260 This is actually a beautiful graph up to a point. 00:43:42.260 --> 00:43:43.840 See the Maxwell-Boltzmann? 00:43:43.840 --> 00:43:45.980 Low temperature, high temperature. 00:43:45.980 --> 00:43:48.110 Only they've turned this thing on its side. 00:43:48.110 --> 00:43:48.630 See? 00:43:48.630 --> 00:43:50.490 And there's the energy you need to get over 00:43:50.490 --> 00:43:51.620 the activated complex. 00:43:51.620 --> 00:43:53.350 You see what's wrong with this graph? 00:43:53.350 --> 00:43:54.040 What's wrong with it? 00:43:54.040 --> 00:43:55.486 AUDIENCE: The product. 00:43:55.486 --> 00:43:57.160 PROFESSOR: Yeah, the product is at a higher 00:43:57.160 --> 00:43:58.290 level than the reactants. 00:43:58.290 --> 00:44:01.630 I looked at that and I thought, whoa! 00:44:01.630 --> 00:44:03.580 I guess you'll activate them, but they won't go anywhere. 00:44:03.580 --> 00:44:06.940 Anyway, so this is all stupid. 00:44:06.940 --> 00:44:08.030 What can we do? 00:44:08.030 --> 00:44:08.690 What can we do? 00:44:08.690 --> 00:44:11.280 So I decided to give you a mechanical analogy. 00:44:11.280 --> 00:44:12.970 So imagine this is the loudspeaker. 00:44:12.970 --> 00:44:14.400 Can you say the x? 00:44:14.400 --> 00:44:16.120 People in the back, can you see the x? 00:44:16.120 --> 00:44:18.280 Give me a thumbs up. 00:44:18.280 --> 00:44:19.120 Great eyes. 00:44:19.120 --> 00:44:19.570 All right. 00:44:19.570 --> 00:44:22.460 So what do we see here? 00:44:22.460 --> 00:44:24.850 The center of mass, I've indicated here. 00:44:24.850 --> 00:44:25.370 All right. 00:44:25.370 --> 00:44:28.560 So this is in a certain energy state. 00:44:28.560 --> 00:44:29.840 Let's get the right graph up there. 00:44:29.840 --> 00:44:32.440 This is awful. 00:44:32.440 --> 00:44:32.790 All right. 00:44:32.790 --> 00:44:34.680 So this is a plus b. 00:44:34.680 --> 00:44:36.420 Now this is c plus d. 00:44:36.420 --> 00:44:38.630 You see, the center of mass fell. 00:44:38.630 --> 00:44:39.170 It's lower. 00:44:39.170 --> 00:44:42.310 It's closer to the table than it is here. 00:44:42.310 --> 00:44:43.920 Can you see when I go like this, the photon goes? 00:44:46.490 --> 00:44:47.740 Watch this. 00:44:50.210 --> 00:44:51.520 Yeah, only I can see it. 00:44:51.520 --> 00:44:53.990 Your eyes don't go to that end of the spectrum. 00:44:53.990 --> 00:44:54.270 All right. 00:44:54.270 --> 00:44:55.000 But what's wrong with it? 00:44:55.000 --> 00:44:58.030 So why does the box not fall over? 00:44:58.030 --> 00:44:58.930 Why does it not fall over? 00:44:58.930 --> 00:45:01.790 We agreed that this is a lower energy state, and it is. 00:45:01.790 --> 00:45:02.810 You're correct. 00:45:02.810 --> 00:45:08.950 So why does the box manage to stay here and not fall over? 00:45:08.950 --> 00:45:10.758 AUDIENCE: [INAUDIBLE PHRASE] 00:45:10.758 --> 00:45:12.070 PROFESSOR: Exactly. 00:45:12.070 --> 00:45:14.400 This is the box at 0 Kelvin. 00:45:14.400 --> 00:45:16.940 Now we start raising the energy of the box, it starts 00:45:16.940 --> 00:45:17.890 doing this. 00:45:17.890 --> 00:45:20.860 Because above 0 Kelvin, it vibrates. 00:45:20.860 --> 00:45:22.975 The higher the temperature, the greater the vibration. 00:45:25.620 --> 00:45:28.640 But we're still in trouble here, you see, because you've 00:45:28.640 --> 00:45:30.840 only got 1/40 of an electron volt. 00:45:30.840 --> 00:45:33.150 So now we invoke distribution. 00:45:33.150 --> 00:45:34.960 I don't know what's happening with any box. 00:45:34.960 --> 00:45:36.140 Heisenberg tells me that. 00:45:36.140 --> 00:45:37.870 I don't know what's happening to any box. 00:45:37.870 --> 00:45:41.510 But if I take Avogadro's number of boxes I'll get this 00:45:41.510 --> 00:45:42.990 distribution. 00:45:42.990 --> 00:45:47.910 And some boxes will vibrate very little. 00:45:47.910 --> 00:45:50.600 And some boxes will vibrate a lot. 00:45:50.600 --> 00:45:53.170 And what's the critical level of vibration? 00:45:53.170 --> 00:45:54.730 It's to get to here. 00:45:54.730 --> 00:45:58.630 Because once it gets to here it's downhill all the way. 00:45:58.630 --> 00:46:02.100 And that would be the activation energy. 00:46:02.100 --> 00:46:05.620 And the fraction of boxes that get to the value of activation 00:46:05.620 --> 00:46:09.200 energy tip over and then I restore the distribution, 00:46:09.200 --> 00:46:11.990 because now this one's out of the game and now I distribute 00:46:11.990 --> 00:46:13.800 that energy over the remaining ones. 00:46:13.800 --> 00:46:16.550 And as I increase the temperature, the amplitude of 00:46:16.550 --> 00:46:19.240 the vibration increases, the average increases, the 00:46:19.240 --> 00:46:22.050 fraction in that red zone increases, and at some 00:46:22.050 --> 00:46:27.040 temperature it's so, so hot that they actually do this, in 00:46:27.040 --> 00:46:29.030 which case I have equilibrium. 00:46:29.030 --> 00:46:31.640 The two states are in equilibrium. 00:46:31.640 --> 00:46:32.940 So that's it. 00:46:32.940 --> 00:46:33.810 This is what's going on. 00:46:33.810 --> 00:46:36.390 So in three space, you can't go from here to here without 00:46:36.390 --> 00:46:37.400 going to here. 00:46:37.400 --> 00:46:40.390 You can try going this way so you-- no, you have to do this. 00:46:40.390 --> 00:46:43.470 It still has to be mechanically activated so we 00:46:43.470 --> 00:46:47.940 can show that this is what activation means. 00:46:47.940 --> 00:46:49.020 So we can plot-- 00:46:49.020 --> 00:46:52.550 this deserves it's own board-- 00:46:52.550 --> 00:46:55.220 so we will plot something like this. 00:46:55.220 --> 00:46:56.640 And now you'll see this. 00:46:56.640 --> 00:46:58.930 Sometimes they write this in the books. 00:46:58.930 --> 00:46:59.600 It's kind of goofy. 00:46:59.600 --> 00:47:01.790 But they write stuff like this. 00:47:01.790 --> 00:47:04.440 This is some kind of an energy coordinate. 00:47:04.440 --> 00:47:05.820 This is an energy coordinate. 00:47:05.820 --> 00:47:10.140 And this is called a reaction coordinate. 00:47:10.140 --> 00:47:13.080 OR sometimes they write extent of reaction. 00:47:13.080 --> 00:47:14.500 Again, some P-Chem term. 00:47:14.500 --> 00:47:18.090 They usually use Greek C just to make it lofty, but it's 00:47:18.090 --> 00:47:18.720 meaningless. 00:47:18.720 --> 00:47:21.290 And then so you write like this-- reactants here, 00:47:21.290 --> 00:47:26.880 products here, and this is exactly what we're seeing. 00:47:26.880 --> 00:47:28.770 What do we see? 00:47:28.770 --> 00:47:29.990 We see this. 00:47:29.990 --> 00:47:35.190 Here we have the box sitting like so. 00:47:35.190 --> 00:47:39.520 And then over here we have the box sitting like so. 00:47:39.520 --> 00:47:43.285 And right here we have the box up like so. 00:47:45.830 --> 00:47:48.640 And so now you have, here's the initial energy. 00:47:48.640 --> 00:47:51.890 This is the energy of the reactants. 00:47:51.890 --> 00:47:56.170 E of the reactants. 00:47:56.170 --> 00:48:00.170 This is E of the products. 00:48:00.170 --> 00:48:03.440 So then this distance here must be 00:48:03.440 --> 00:48:04.695 delta E of the reaction. 00:48:07.350 --> 00:48:10.510 And what's this? 00:48:10.510 --> 00:48:12.090 That's the activation energy. 00:48:12.090 --> 00:48:14.140 I have to come up with this; otherwise, I can't make the 00:48:14.140 --> 00:48:15.440 box fall over. 00:48:15.440 --> 00:48:19.740 So this is ea to go from here up onto the corner. 00:48:19.740 --> 00:48:21.530 And now you understand what all this stuff means. 00:48:21.530 --> 00:48:22.440 So that's here. 00:48:22.440 --> 00:48:24.250 And this is the activated complex. 00:48:27.030 --> 00:48:28.340 What's an activated complex? 00:48:28.340 --> 00:48:30.390 It's a box on its edge ready to fall over. 00:48:30.390 --> 00:48:31.820 That's what it is. 00:48:31.820 --> 00:48:34.230 All right. 00:48:34.230 --> 00:48:37.640 I think we're out of time, so let's cut to the end here. 00:48:37.640 --> 00:48:39.190 What've we got. 00:48:39.190 --> 00:48:39.910 Oh, just some plots. 00:48:39.910 --> 00:48:41.390 We'll get to that next day. 00:48:41.390 --> 00:48:42.950 All right. 00:48:42.950 --> 00:48:43.890 So I want to show you a little bit 00:48:43.890 --> 00:48:45.910 about first-order reactions. 00:48:45.910 --> 00:48:48.280 This is radiocarbon dating. 00:48:48.280 --> 00:48:49.630 n equals 1. 00:48:49.630 --> 00:48:51.970 And strictly speaking, this is not a chemical reaction, but 00:48:51.970 --> 00:48:53.320 it is first order. 00:48:53.320 --> 00:48:54.600 So I'll lump it in here. 00:48:54.600 --> 00:48:56.520 So this is a nuclear reaction. 00:48:56.520 --> 00:48:58.220 And what happens in the upper atmosphere? 00:48:58.220 --> 00:49:01.970 Radioactive carbon produced by cosmic rays, which generate 00:49:01.970 --> 00:49:03.940 neutrons in the upper atmosphere and then those 00:49:03.940 --> 00:49:07.040 neutrons attack nitrogen to make carbon 14. 00:49:07.040 --> 00:49:08.650 That's the radioactive form of carbon. 00:49:08.650 --> 00:49:08.870 Remember? 00:49:08.870 --> 00:49:10.970 It's present in one part per trillion, if you look on your 00:49:10.970 --> 00:49:13.280 Periodic Table for the isotopes. 00:49:13.280 --> 00:49:15.760 Now carbon 14 enters the carbon cycle. 00:49:15.760 --> 00:49:19.410 And so in all of us and in all living organisms the ratio of 00:49:19.410 --> 00:49:22.790 carbon 14 to carbon 12 is one part per trillion. 00:49:22.790 --> 00:49:24.760 And carbon 13 is also present. 00:49:24.760 --> 00:49:25.140 I don't know. 00:49:25.140 --> 00:49:25.420 What is it? 00:49:25.420 --> 00:49:27.240 1 point something percent? 00:49:27.240 --> 00:49:30.780 The thing is, the carbon 14 is radioactive. 00:49:30.780 --> 00:49:32.470 And it decays. 00:49:32.470 --> 00:49:33.840 Like this. 00:49:33.840 --> 00:49:36.210 But what happens after somebody dies? 00:49:36.210 --> 00:49:39.990 Well, they stop exchanging nutrients with the 00:49:39.990 --> 00:49:40.550 surroundings. 00:49:40.550 --> 00:49:43.810 They stop breathing, so their carbon level is pegged as it 00:49:43.810 --> 00:49:45.870 was at the time of death. 00:49:45.870 --> 00:49:47.410 And now it's a one0way street. 00:49:47.410 --> 00:49:49.130 It's just carbon decay. 00:49:49.130 --> 00:49:51.885 And it turns out you can measure the ratio of carbon 14 00:49:51.885 --> 00:49:56.890 to carbon 12 to determine the age, which is given by 5,730 00:49:56.890 --> 00:50:01.970 years, which is the inverse of the rate constant. 00:50:01.970 --> 00:50:04.530 Now, you can't use this for crime scene investigations, 00:50:04.530 --> 00:50:07.290 but certainly you can start dating things hundreds of 00:50:07.290 --> 00:50:09.940 years old, not hundreds of minutes old. 00:50:09.940 --> 00:50:12.090 So there's a whole bunch of other things that can be used, 00:50:12.090 --> 00:50:12.860 not just carbon. 00:50:12.860 --> 00:50:15.140 So this is radiochemical dating. 00:50:15.140 --> 00:50:19.960 And these are used in trying to nail down art forgeries and 00:50:19.960 --> 00:50:21.190 all sorts of things. 00:50:21.190 --> 00:50:21.890 All right. 00:50:21.890 --> 00:50:23.030 So here, you can see these. 00:50:23.030 --> 00:50:25.020 These have all been radiocarbon dated. 00:50:25.020 --> 00:50:27.270 You know, the Dead Sea Scrolls were radiocarbon dated and 00:50:27.270 --> 00:50:29.290 they look like they're from about 2,000 years ago. 00:50:29.290 --> 00:50:31.300 Makes sense. 00:50:31.300 --> 00:50:32.970 You go out over here. 00:50:32.970 --> 00:50:37.020 They they found these Indian sandals from Oregon, and then 00:50:37.020 --> 00:50:40.250 they looked on an electron microscope, and they found 00:50:40.250 --> 00:50:44.740 something on the sandals that looks a little bit like that. 00:50:44.740 --> 00:50:46.030 That's a Nike swoosh. 00:50:46.030 --> 00:50:46.630 I don't know. 00:50:46.630 --> 00:50:48.320 You people are so-- 00:50:48.320 --> 00:50:49.390 All right. 00:50:49.390 --> 00:50:51.590 So now I want to show you the Shroud of Turin. 00:50:51.590 --> 00:50:56.470 The Shroud of Turin, as you may know, for a long time was 00:50:56.470 --> 00:50:59.510 reputed to be the burial shroud of Jesus Christ. And 00:50:59.510 --> 00:51:01.960 this is taken from the National Geographic back in 00:51:01.960 --> 00:51:04.050 the late '80s. 00:51:04.050 --> 00:51:06.290 Back in the late '80s, they did a major study on it. 00:51:06.290 --> 00:51:09.530 So this is the artist rendition of how the shroud 00:51:09.530 --> 00:51:11.360 might have been wrapped around a body. 00:51:11.360 --> 00:51:13.550 The question is, what's the date of this? 00:51:13.550 --> 00:51:15.250 So we can use radiocarbon dating. 00:51:15.250 --> 00:51:19.520 And so here's the formation of carbon 14. 00:51:19.520 --> 00:51:23.200 Carbon 14 exchanges with carbon 12 in flax. 00:51:23.200 --> 00:51:24.820 So it's got one part per trillion. 00:51:24.820 --> 00:51:28.800 When the flax is harvested the carbon 14 starts to decay. 00:51:28.800 --> 00:51:30.700 And then we look at the weaving of the 00:51:30.700 --> 00:51:31.780 shroud and so on. 00:51:31.780 --> 00:51:34.500 And they had three different labs, they took samples from 00:51:34.500 --> 00:51:35.240 the shroud. 00:51:35.240 --> 00:51:37.050 And they concluded that the shroud 00:51:37.050 --> 00:51:38.040 dates from this period-- 00:51:38.040 --> 00:51:39.900 1260 to 1390. 00:51:39.900 --> 00:51:41.930 And the first time it was mentioned in the literature 00:51:41.930 --> 00:51:43.010 was around 1354. 00:51:43.010 --> 00:51:45.860 So everything seems to make sense that this is not the 00:51:45.860 --> 00:51:49.470 burial shroud of Jesus Christ. It's something that has 00:51:49.470 --> 00:51:54.010 importance to certain members of the Roman Church, but it's 00:51:54.010 --> 00:51:55.460 scientifically not. 00:51:55.460 --> 00:51:57.320 You know, this stirs up a lot of passion. 00:51:57.320 --> 00:51:58.680 So people started saying, wait a minute. 00:51:58.680 --> 00:51:59.440 Wait a minute. 00:51:59.440 --> 00:52:03.910 There was a fire in 1532 and people repaired the shroud and 00:52:03.910 --> 00:52:06.900 they were using candlelight and maybe the paraffin and 00:52:06.900 --> 00:52:09.780 mold and so on covered the fibers. 00:52:09.780 --> 00:52:12.100 So now, are we looking at the surface effect? 00:52:12.100 --> 00:52:13.490 How do we know what really happened? 00:52:13.490 --> 00:52:15.350 The only way to know is to take the whole shroud, put in 00:52:15.350 --> 00:52:18.590 a big Cuisinart and break open the interior. 00:52:18.590 --> 00:52:21.740 Well, in point of fact, what they did was take fibers and 00:52:21.740 --> 00:52:22.450 look inside. 00:52:22.450 --> 00:52:26.170 And I think as of the late '90s, the Roman Church says, 00:52:26.170 --> 00:52:29.200 it's not the burial shroud of Jesus, but it is 00:52:29.200 --> 00:52:30.330 an object of reverence. 00:52:30.330 --> 00:52:32.160 And I think it's a good example of how science 00:52:32.160 --> 00:52:35.940 sometimes comes up against spirituality, and we have to 00:52:35.940 --> 00:52:37.844 be careful how we handle it. 00:52:37.844 --> 00:52:40.360 It's a delicate matter.