WEBVTT 00:00:00.000 --> 00:00:02.435 align:middle line:90% [SQUEAKING] 00:00:02.435 --> 00:00:04.383 align:middle line:90% [RUSTLING] 00:00:04.383 --> 00:00:05.844 align:middle line:90% [CLICKING] 00:00:05.844 --> 00:00:14.568 align:middle line:90% 00:00:14.568 --> 00:00:16.110 align:middle line:84% RAFAEL JARAMILLO: All right, so today 00:00:16.110 --> 00:00:19.860 align:middle line:84% is the last lecture of new material. 00:00:19.860 --> 00:00:30.510 align:middle line:84% We're going to talk about reactions between gases 00:00:30.510 --> 00:00:31.860 align:middle line:90% and condensed phases. 00:00:31.860 --> 00:00:37.670 align:middle line:90% 00:00:37.670 --> 00:00:39.550 align:middle line:84% So we're going to talk about that, 00:00:39.550 --> 00:00:41.860 align:middle line:84% and then, we'll make it specific to oxidation. 00:00:41.860 --> 00:00:47.110 align:middle line:84% And then, on Friday, I'll do an extended practice problem, 00:00:47.110 --> 00:00:51.230 align:middle line:84% I suppose, on reactions between gases and condensed phases. 00:00:51.230 --> 00:00:57.630 align:middle line:90% So in general, some reaction-- 00:00:57.630 --> 00:01:00.030 align:middle line:84% I'm going to write this really generally. aA 00:01:00.030 --> 00:01:05.850 align:middle line:90% plus bB going to cC plus dD. 00:01:05.850 --> 00:01:14.760 align:middle line:84% And these are not just for ideal gases. 00:01:14.760 --> 00:01:19.710 align:middle line:84% So the last time we've seen reaction like this in 020, 00:01:19.710 --> 00:01:21.600 align:middle line:84% it's been for ideal gases reacting. 00:01:21.600 --> 00:01:23.640 align:middle line:84% And we're going to move away from that 00:01:23.640 --> 00:01:25.080 align:middle line:90% and do this more generally. 00:01:25.080 --> 00:01:27.090 align:middle line:84% So let me just quickly remind you 00:01:27.090 --> 00:01:32.250 align:middle line:84% of how we get to the action coefficient. 00:01:32.250 --> 00:01:35.130 align:middle line:84% We have a general expression for the change in Gibbs 00:01:35.130 --> 00:01:37.170 align:middle line:84% free energy with these unconstrained internal 00:01:37.170 --> 00:01:46.290 align:middle line:84% variables, and we can re-express this in terms of the reaction 00:01:46.290 --> 00:01:49.710 align:middle line:84% extent, remembering that DNI over 00:01:49.710 --> 00:01:55.307 align:middle line:84% mu I is a constant for all I reaction extent. 00:01:55.307 --> 00:01:56.640 align:middle line:90% I don't need to have an I there. 00:01:56.640 --> 00:01:59.100 align:middle line:90% Just xe. 00:01:59.100 --> 00:02:02.430 align:middle line:84% And reminding us that mu of I, the chemical potential 00:02:02.430 --> 00:02:06.420 align:middle line:84% of a given species is its reference chemical potential 00:02:06.420 --> 00:02:10.850 align:middle line:90% plus [INAUDIBLE] activity. 00:02:10.850 --> 00:02:13.370 align:middle line:84% So this is still completely general. 00:02:13.370 --> 00:02:22.300 align:middle line:84% We take that expression and we write d of g equals-- 00:02:22.300 --> 00:02:35.710 align:middle line:84% let's see, mu of I not mu of I plus rt log a of I 00:02:35.710 --> 00:02:41.740 align:middle line:84% to the power mu of I. And this is all times dt. 00:02:41.740 --> 00:02:56.380 align:middle line:84% And this is d G0 plus RT log product a of I mu of I. Again, 00:02:56.380 --> 00:02:59.020 align:middle line:90% whole thing times dt. 00:02:59.020 --> 00:03:05.170 align:middle line:84% And of course, this is 0 at equilibrium, 00:03:05.170 --> 00:03:08.260 align:middle line:84% because at equilibrium, Gibbs free energy is optimized. 00:03:08.260 --> 00:03:16.740 align:middle line:84% So the coefficient is 0, and we get, at equilibrium, 00:03:16.740 --> 00:03:22.680 align:middle line:84% this product, a of I mu of I, which 00:03:22.680 --> 00:03:26.640 align:middle line:84% we call the equilibrium constant, equals e to the minus 00:03:26.640 --> 00:03:29.520 align:middle line:90% delta G0 over RT. 00:03:29.520 --> 00:03:32.100 align:middle line:90% So that's just a reminder. 00:03:32.100 --> 00:03:36.510 align:middle line:84% But this is why I wanted to take three minutes for that 00:03:36.510 --> 00:03:39.390 align:middle line:84% because we're going to make this specific to metal oxidation. 00:03:39.390 --> 00:03:40.920 align:middle line:90% That's what we're doing. 00:03:40.920 --> 00:03:48.915 align:middle line:84% So equilibrium constant for metal. 00:03:48.915 --> 00:03:53.220 align:middle line:90% 00:03:53.220 --> 00:03:56.435 align:middle line:84% And what you're going to find is that it simplifies a lot. 00:03:56.435 --> 00:03:57.060 align:middle line:90% So that's good. 00:03:57.060 --> 00:03:58.470 align:middle line:90% Metal oxidation. 00:03:58.470 --> 00:04:01.890 align:middle line:84% As we started the last lecture, we 00:04:01.890 --> 00:04:05.820 align:middle line:84% have some metal reacting with a modal of oxygen gas 00:04:05.820 --> 00:04:07.475 align:middle line:90% going to MzO2. 00:04:07.475 --> 00:04:12.216 align:middle line:90% 00:04:12.216 --> 00:04:15.190 align:middle line:84% Remember, z here has to do with the fact 00:04:15.190 --> 00:04:18.510 align:middle line:84% that we don't know what the oxidation state of that metal 00:04:18.510 --> 00:04:19.010 align:middle line:90% is. 00:04:19.010 --> 00:04:21.500 align:middle line:84% So potassium would be 1, iron has a couple 00:04:21.500 --> 00:04:24.350 align:middle line:90% of different oxidation states. 00:04:24.350 --> 00:04:25.897 align:middle line:90% Copper would be 1 or 2-- 00:04:25.897 --> 00:04:27.480 align:middle line:84% so there's different oxidation states. 00:04:27.480 --> 00:04:29.690 align:middle line:90% So this is to do this generally. 00:04:29.690 --> 00:04:33.470 align:middle line:84% So all right, now, we're going to write the equilibrium 00:04:33.470 --> 00:04:37.800 align:middle line:90% constant for this reaction. 00:04:37.800 --> 00:04:44.865 align:middle line:84% So we have the activity of the oxide MzO2. 00:04:44.865 --> 00:04:48.960 align:middle line:90% 00:04:48.960 --> 00:04:51.810 align:middle line:84% Sorry, the writing is getting a little bit small there. 00:04:51.810 --> 00:04:54.480 align:middle line:84% The activity of the oxide over the activity 00:04:54.480 --> 00:04:59.460 align:middle line:84% of the metal to the power of z times 00:04:59.460 --> 00:05:02.505 align:middle line:90% is the activity of O2 gas. 00:05:02.505 --> 00:05:10.350 align:middle line:90% 00:05:10.350 --> 00:05:15.090 align:middle line:84% The products of the numerator, reactants, and the denominator. 00:05:15.090 --> 00:05:16.920 align:middle line:90% The metal is z modal of metal. 00:05:16.920 --> 00:05:20.753 align:middle line:84% So we have that activity to the power of z. 00:05:20.753 --> 00:05:22.170 align:middle line:84% And straightforward to write down. 00:05:22.170 --> 00:05:24.690 align:middle line:90% 00:05:24.690 --> 00:05:25.770 align:middle line:90% Everyone with me so far? 00:05:25.770 --> 00:05:40.770 align:middle line:90% 00:05:40.770 --> 00:05:45.605 align:middle line:84% All right, this oxidation reaction at equilibrium. 00:05:45.605 --> 00:05:46.980 align:middle line:84% We're going to come back to that. 00:05:46.980 --> 00:05:54.020 align:middle line:84% This is the metal and oxygen and the oxide all coexisting 00:05:54.020 --> 00:05:55.010 align:middle line:90% at equilibrium. 00:05:55.010 --> 00:05:58.940 align:middle line:90% 00:05:58.940 --> 00:06:00.340 align:middle line:90% And now come the approximations. 00:06:00.340 --> 00:06:05.640 align:middle line:84% We're going to treat O2 as-- how are we 00:06:05.640 --> 00:06:07.500 align:middle line:90% going to treat oxygen, anybody? 00:06:07.500 --> 00:06:10.240 align:middle line:90% 00:06:10.240 --> 00:06:13.096 align:middle line:90% How will we model oxygen? 00:06:13.096 --> 00:06:14.770 align:middle line:90% AUDIENCE: Constant pressure? 00:06:14.770 --> 00:06:16.060 align:middle line:90% [INAUDIBLE] question. 00:06:16.060 --> 00:06:19.160 align:middle line:84% RAFAEL JARAMILLO: Not constant pressure, but we have a-- 00:06:19.160 --> 00:06:20.380 align:middle line:90% AUDIENCE: It's a gas. 00:06:20.380 --> 00:06:21.670 align:middle line:84% RAFAEL JARAMILLO: --as a-- what kind of gas? 00:06:21.670 --> 00:06:22.660 align:middle line:90% AUDIENCE: Ideal gas. 00:06:22.660 --> 00:06:23.470 align:middle line:90% Ideal? 00:06:23.470 --> 00:06:26.012 align:middle line:84% RAFAEL JARAMILLO: Yeah, because it's the only model for gases 00:06:26.012 --> 00:06:26.770 align:middle line:90% that we know. 00:06:26.770 --> 00:06:31.930 align:middle line:84% [INAUDIBLE] So an ideal gas-- the activity of an ideal gas 00:06:31.930 --> 00:06:37.330 align:middle line:84% is just as partial pressure by atmosphere for 1 atmosphere 00:06:37.330 --> 00:06:39.100 align:middle line:90% reference statement. 00:06:39.100 --> 00:06:39.600 align:middle line:90% Good. 00:06:39.600 --> 00:06:41.340 align:middle line:90% That's easy. 00:06:41.340 --> 00:06:54.210 align:middle line:84% And we're going to assume that condensed phases are pure. 00:06:54.210 --> 00:06:57.500 align:middle line:90% 00:06:57.500 --> 00:06:58.000 align:middle line:90% That's big. 00:06:58.000 --> 00:07:00.600 align:middle line:90% 00:07:00.600 --> 00:07:05.790 align:middle line:84% If we assume the condensed phases are pure, that's 00:07:05.790 --> 00:07:12.520 align:middle line:84% equivalent to saying that their composition is unchanging, 00:07:12.520 --> 00:07:13.020 align:middle line:90% all right? 00:07:13.020 --> 00:07:21.360 align:middle line:84% That's saying that this metal does not dissolve any oxygen, 00:07:21.360 --> 00:07:24.780 align:middle line:84% and it's saying that this oxide is what? 00:07:24.780 --> 00:07:28.923 align:middle line:84% What kind of a compound is always at fixed stoichiometry? 00:07:28.923 --> 00:07:39.070 align:middle line:90% 00:07:39.070 --> 00:07:41.470 align:middle line:90% AUDIENCE: Like, perfect crystal? 00:07:41.470 --> 00:07:42.490 align:middle line:90% RAFAEL JARAMILLO: Sorry? 00:07:42.490 --> 00:07:44.153 align:middle line:90% AUDIENCE: The perfect crystal? 00:07:44.153 --> 00:07:45.820 align:middle line:84% RAFAEL JARAMILLO: No, well, not perfect. 00:07:45.820 --> 00:07:48.320 align:middle line:84% No, not a perfect crystal, actually. 00:07:48.320 --> 00:07:49.180 align:middle line:90% Be something else. 00:07:49.180 --> 00:07:51.460 align:middle line:84% We learned this just two days ago. 00:07:51.460 --> 00:08:09.460 align:middle line:90% 00:08:09.460 --> 00:08:10.490 align:middle line:90% AUDIENCE: [INAUDIBLE] ? 00:08:10.490 --> 00:08:11.680 align:middle line:90% RAFAEL JARAMILLO: Mm, yes. 00:08:11.680 --> 00:08:17.880 align:middle line:90% 00:08:17.880 --> 00:08:24.180 align:middle line:84% It's a pure oxide, meaning that stoichiometry is ideal. 00:08:24.180 --> 00:08:25.260 align:middle line:90% It's a line compound. 00:08:25.260 --> 00:08:26.800 align:middle line:90% It doesn't deviate from that. 00:08:26.800 --> 00:08:29.280 align:middle line:84% So if we can assume the condensed phases are pure, 00:08:29.280 --> 00:08:30.960 align:middle line:84% what is the activity of a pure phase? 00:08:30.960 --> 00:08:36.320 align:middle line:90% 00:08:36.320 --> 00:08:37.490 align:middle line:90% We've got to think back. 00:08:37.490 --> 00:08:41.090 align:middle line:84% What's the activity of a component in its reference 00:08:41.090 --> 00:08:41.937 align:middle line:90% statement? 00:08:41.937 --> 00:08:46.510 align:middle line:90% 00:08:46.510 --> 00:08:49.250 align:middle line:90% AUDIENCE: 1? 00:08:49.250 --> 00:08:50.810 align:middle line:90% RAFAEL JARAMILLO: Right. 00:08:50.810 --> 00:08:52.877 align:middle line:84% Thanks, that's recalling material 00:08:52.877 --> 00:08:55.460 align:middle line:84% from the middle of the semester, so it goes back a little bit, 00:08:55.460 --> 00:09:01.370 align:middle line:84% but the activity of the material in its reference date is 1. 00:09:01.370 --> 00:09:04.940 align:middle line:84% So now, I have some really handy approximations. 00:09:04.940 --> 00:09:06.350 align:middle line:90% The activity of oxygen gas. 00:09:06.350 --> 00:09:08.580 align:middle line:84% We're treating it like an ideal gas, 00:09:08.580 --> 00:09:11.060 align:middle line:90% so it's just Po2 by atmosphere. 00:09:11.060 --> 00:09:14.270 align:middle line:84% And the activity of the metal and the activity of the oxide 00:09:14.270 --> 00:09:17.300 align:middle line:90% are both 1. 00:09:17.300 --> 00:09:19.880 align:middle line:84% So it's equivalent to assuming that there's vanishing oxygen 00:09:19.880 --> 00:09:24.060 align:middle line:84% solubility in the metal and that the oxide is a line compound. 00:09:24.060 --> 00:09:29.520 align:middle line:84% So with those approximations, we have the equilibrium 00:09:29.520 --> 00:09:35.000 align:middle line:84% constant is Po2 by atmosphere, so minus 1, 00:09:35.000 --> 00:09:41.440 align:middle line:84% and this is going to be equal to the E minus delta G0 over RT. 00:09:41.440 --> 00:09:44.920 align:middle line:84% So you see this simplified quite a lot. 00:09:44.920 --> 00:09:46.060 align:middle line:90% Simplified quite a lot. 00:09:46.060 --> 00:09:49.610 align:middle line:90% 00:09:49.610 --> 00:09:52.550 align:middle line:84% All right, I want to share some slides on binary metal oxygen 00:09:52.550 --> 00:09:55.220 align:middle line:84% systems to convince you that they do 00:09:55.220 --> 00:09:58.680 align:middle line:90% tend to be pair of materials. 00:09:58.680 --> 00:10:00.668 align:middle line:90% So let's look here. 00:10:00.668 --> 00:10:01.460 align:middle line:90% I grabbed a couple. 00:10:01.460 --> 00:10:04.690 align:middle line:90% 00:10:04.690 --> 00:10:08.540 align:middle line:84% OK, so here's the tin oxygen system. 00:10:08.540 --> 00:10:11.600 align:middle line:84% And you could see that an oxygen-- 00:10:11.600 --> 00:10:14.120 align:middle line:90% well, it's just a gas here. 00:10:14.120 --> 00:10:24.920 align:middle line:84% Tin down here is a metal until it becomes a liquid. 00:10:24.920 --> 00:10:28.490 align:middle line:84% In the liquid phase, it dissolves some oxygen. 00:10:28.490 --> 00:10:30.620 align:middle line:84% You can see that the liquid phase here 00:10:30.620 --> 00:10:32.910 align:middle line:90% has a solution region. 00:10:32.910 --> 00:10:34.760 align:middle line:84% So you can dissolve oxygen in liquid tin, 00:10:34.760 --> 00:10:36.140 align:middle line:90% but what about in solid tin? 00:10:36.140 --> 00:10:41.420 align:middle line:90% 00:10:41.420 --> 00:10:43.040 align:middle line:90% I know oxygen is off. 00:10:43.040 --> 00:10:47.840 align:middle line:84% So you see solid tin will just coexist with this line compound 00:10:47.840 --> 00:10:49.220 align:middle line:90% tin oxide. 00:10:49.220 --> 00:10:50.720 align:middle line:84% So this is what we're talking about, 00:10:50.720 --> 00:10:53.240 align:middle line:84% a line compound of an oxide and a metal 00:10:53.240 --> 00:10:54.870 align:middle line:84% that doesn't dissolve any oxygen. 00:10:54.870 --> 00:10:59.860 align:middle line:84% Here's another example, copper oxygen. Again, copper. 00:10:59.860 --> 00:11:01.750 align:middle line:84% It's written here as a parentheses 00:11:01.750 --> 00:11:04.570 align:middle line:84% as if it's a solid solution, but really, there's 00:11:04.570 --> 00:11:07.300 align:middle line:84% vanishingly small oxygen dissolution and copper. 00:11:07.300 --> 00:11:08.470 align:middle line:90% There's some. 00:11:08.470 --> 00:11:11.710 align:middle line:84% There's some, but it's so small as to be 00:11:11.710 --> 00:11:13.808 align:middle line:90% invisible on this part. 00:11:13.808 --> 00:11:15.850 align:middle line:84% I'll tell you that when you're making a component 00:11:15.850 --> 00:11:18.340 align:middle line:84% for cryogenics or for space applications, 00:11:18.340 --> 00:11:20.380 align:middle line:90% you want oxygen-free copper. 00:11:20.380 --> 00:11:23.410 align:middle line:84% You can buy it from McMaster, and you want it, 00:11:23.410 --> 00:11:25.660 align:middle line:84% because oxygen is magnetic when it freezes, 00:11:25.660 --> 00:11:28.997 align:middle line:84% and so a lot of times you want non-magnetic copper. 00:11:28.997 --> 00:11:30.580 align:middle line:84% So you have to get oxygen-free copper, 00:11:30.580 --> 00:11:32.710 align:middle line:84% but it's there at the parts per million level. 00:11:32.710 --> 00:11:34.900 align:middle line:84% It doesn't show up at all on the spot. 00:11:34.900 --> 00:11:39.430 align:middle line:84% So again, oxygen not dissolving in copper and these 00:11:39.430 --> 00:11:41.620 align:middle line:90% oxides being line compounds. 00:11:41.620 --> 00:11:42.590 align:middle line:90% Here's more examples. 00:11:42.590 --> 00:11:44.590 align:middle line:84% This is a little counter example. 00:11:44.590 --> 00:11:45.340 align:middle line:90% This is manganese. 00:11:45.340 --> 00:11:47.215 align:middle line:84% Manganese actually does dissolve some oxygen. 00:11:47.215 --> 00:11:50.973 align:middle line:84% So you see it dissolves 1% or 2% of oxygen. 00:11:50.973 --> 00:11:52.390 align:middle line:84% So maybe the activity of manganese 00:11:52.390 --> 00:11:54.400 align:middle line:90% should be not quite 1. 00:11:54.400 --> 00:11:58.300 align:middle line:90% Maybe it should be 0.99. 00:11:58.300 --> 00:12:01.120 align:middle line:84% And making these oxide similarly to not quite long compounds. 00:12:01.120 --> 00:12:03.740 align:middle line:84% They have some solid solution region, 00:12:03.740 --> 00:12:05.350 align:middle line:90% so that's a counterexample. 00:12:05.350 --> 00:12:08.720 align:middle line:90% 00:12:08.720 --> 00:12:11.480 align:middle line:84% Another example a titanium oxide oxygen 00:12:11.480 --> 00:12:16.350 align:middle line:84% system is titanium dissolves a lot of oxygen. 00:12:16.350 --> 00:12:18.320 align:middle line:84% So this is an even counter counterexample. 00:12:18.320 --> 00:12:20.180 align:middle line:84% This is a titanium, so funny system. 00:12:20.180 --> 00:12:23.780 align:middle line:84% It dissolves a lot of oxygen into solid titanium, 00:12:23.780 --> 00:12:27.940 align:middle line:84% but its oxides here are line compounds. 00:12:27.940 --> 00:12:33.230 align:middle line:90% So what to make of it? 00:12:33.230 --> 00:12:36.088 align:middle line:84% It's good to understand where the approximations are 00:12:36.088 --> 00:12:37.130 align:middle line:90% and where they might not. 00:12:37.130 --> 00:12:39.885 align:middle line:90% 00:12:39.885 --> 00:12:41.260 align:middle line:84% Questions on these faith diagrams 00:12:41.260 --> 00:12:44.000 align:middle line:90% before I go back to the board? 00:12:44.000 --> 00:12:46.280 align:middle line:84% AUDIENCE: Does this dissolving all 00:12:46.280 --> 00:12:49.085 align:middle line:84% owe to the molecule or just oxygen in general? 00:12:49.085 --> 00:12:50.960 align:middle line:84% RAFAEL JARAMILLO: I'm sorry, I didn't quite-- 00:12:50.960 --> 00:12:52.490 align:middle line:90% could you repeat? 00:12:52.490 --> 00:12:54.200 align:middle line:84% AUDIENCE: Going back to the solution, 00:12:54.200 --> 00:12:58.010 align:middle line:84% is this like dissolving oxygen as auto form 00:12:58.010 --> 00:13:00.440 align:middle line:90% or other forms of oxygen? 00:13:00.440 --> 00:13:03.310 align:middle line:84% RAFAEL JARAMILLO: It almost certainly disassociate. 00:13:03.310 --> 00:13:06.030 align:middle line:84% So this would be dissolving oxygen atoms. 00:13:06.030 --> 00:13:09.560 align:middle line:84% Well, I mean, how do you dissolve oxygen atoms? 00:13:09.560 --> 00:13:12.560 align:middle line:84% You expose the material to oxygen gas, 00:13:12.560 --> 00:13:15.980 align:middle line:84% and there's some catalytic process by which the oxygen 00:13:15.980 --> 00:13:19.400 align:middle line:84% gas splits into oxygen atoms at the surface and the oxygen 00:13:19.400 --> 00:13:21.680 align:middle line:90% atoms diffuse into the metal. 00:13:21.680 --> 00:13:26.680 align:middle line:84% It's almost certainly not dissolving O2 molecules. 00:13:26.680 --> 00:13:29.380 align:middle line:84% Metals that do dissolve oxygen are 00:13:29.380 --> 00:13:34.540 align:middle line:84% the basis for a lot of interesting technologies, 00:13:34.540 --> 00:13:36.320 align:middle line:90% but we won't have time for that. 00:13:36.320 --> 00:13:39.072 align:middle line:90% So let's move back to-- 00:13:39.072 --> 00:13:40.780 align:middle line:84% sorry, any other questions on these phase 00:13:40.780 --> 00:13:43.750 align:middle line:84% diagrams and interpreting them or applications 00:13:43.750 --> 00:13:45.220 align:middle line:90% and so forth before I move back? 00:13:45.220 --> 00:13:47.730 align:middle line:90% 00:13:47.730 --> 00:13:50.310 align:middle line:84% All right, so we have this really simple expression 00:13:50.310 --> 00:13:52.350 align:middle line:84% for the equilibrium constant, and now we 00:13:52.350 --> 00:14:02.200 align:middle line:84% want to evaluate delta G0 equals delta H0 minus T delta 00:14:02.200 --> 00:14:05.320 align:middle line:90% S0 for metal oxidation. 00:14:05.320 --> 00:14:10.477 align:middle line:90% 00:14:10.477 --> 00:14:11.810 align:middle line:90% So we're going to evaluate that. 00:14:11.810 --> 00:14:13.393 align:middle line:84% So we're going to start with enthalpy. 00:14:13.393 --> 00:14:18.490 align:middle line:90% 00:14:18.490 --> 00:14:23.860 align:middle line:84% Enthalpy delta H0 equals delta H0-- 00:14:23.860 --> 00:14:32.290 align:middle line:84% let's say 298 plus 298 temperature D-- 00:14:32.290 --> 00:14:35.780 align:middle line:84% temperature and you can have a delta Cp for the reaction. 00:14:35.780 --> 00:14:39.042 align:middle line:84% So this is general, but here's the-- 00:14:39.042 --> 00:14:41.000 align:middle line:84% and you know what's coming is an approximation. 00:14:41.000 --> 00:14:53.270 align:middle line:84% So I'm going to tell you for most metal oxides, delta H0-- 00:14:53.270 --> 00:14:57.190 align:middle line:90% let's say 298-- is large. 00:14:57.190 --> 00:14:59.710 align:middle line:90% 00:14:59.710 --> 00:15:02.080 align:middle line:90% These are energetic reactions. 00:15:02.080 --> 00:15:06.670 align:middle line:84% Why would the enthalpy of formation of an oxide be large? 00:15:06.670 --> 00:15:09.430 align:middle line:84% Does somebody have the sense for why that should be? 00:15:09.430 --> 00:15:11.905 align:middle line:90% 00:15:11.905 --> 00:15:12.780 align:middle line:90% I'll give you a hint. 00:15:12.780 --> 00:15:15.290 align:middle line:90% It's large negative. 00:15:15.290 --> 00:15:17.851 align:middle line:84% It's large in the negative direction. 00:15:17.851 --> 00:15:22.930 align:middle line:90% 00:15:22.930 --> 00:15:24.780 align:middle line:84% What reaction are we talking about here? 00:15:24.780 --> 00:15:28.550 align:middle line:90% 00:15:28.550 --> 00:15:29.383 align:middle line:90% AUDIENCE: Oxidation? 00:15:29.383 --> 00:15:30.550 align:middle line:90% RAFAEL JARAMILLO: Oxidation. 00:15:30.550 --> 00:15:32.870 align:middle line:84% So what kind of reaction is an oxidation reaction other 00:15:32.870 --> 00:15:35.078 align:middle line:84% than just-- you could say it's an oxidation reaction, 00:15:35.078 --> 00:15:36.350 align:middle line:90% but what's actually happening? 00:15:36.350 --> 00:15:38.540 align:middle line:84% Maybe somebody who hasn't replied yet today. 00:15:38.540 --> 00:15:40.760 align:middle line:84% What's happening on the atomic level 00:15:40.760 --> 00:15:42.230 align:middle line:90% during an oxidation reaction? 00:15:42.230 --> 00:15:45.040 align:middle line:90% 00:15:45.040 --> 00:15:47.350 align:middle line:84% AUDIENCE: Does it include a favorable transfer 00:15:47.350 --> 00:15:48.222 align:middle line:90% of electrons? 00:15:48.222 --> 00:15:49.180 align:middle line:90% RAFAEL JARAMILLO: Yeah. 00:15:49.180 --> 00:15:52.180 align:middle line:90% Yeah, this is due to-- 00:15:52.180 --> 00:15:53.710 align:middle line:90% so thank you to the two of you. 00:15:53.710 --> 00:16:14.880 align:middle line:84% Due to exothermic nature of electron transfer during metal 00:16:14.880 --> 00:16:17.940 align:middle line:90% oxygen bond formation. 00:16:17.940 --> 00:16:22.420 align:middle line:90% 00:16:22.420 --> 00:16:24.750 align:middle line:90% And I could-- 00:16:24.750 --> 00:16:26.440 align:middle line:90% I get to ionic. 00:16:26.440 --> 00:16:28.180 align:middle line:90% So it's an ionic bond formation. 00:16:28.180 --> 00:16:30.110 align:middle line:84% You have very electronegative element, 00:16:30.110 --> 00:16:32.800 align:middle line:84% and that's oxygen, and less electronegative elements, 00:16:32.800 --> 00:16:33.790 align:middle line:90% those are metals. 00:16:33.790 --> 00:16:38.230 align:middle line:84% And that bonding mechanism is electron transfer, 00:16:38.230 --> 00:16:40.120 align:middle line:90% and it's very exothermic. 00:16:40.120 --> 00:16:43.990 align:middle line:84% So as a result, delta H's tend to be very large and negative. 00:16:43.990 --> 00:16:49.820 align:middle line:84% And this allows us to neglect temp dependence. 00:16:49.820 --> 00:16:55.440 align:middle line:90% 00:16:55.440 --> 00:16:56.790 align:middle line:90% Neglect temp dependence. 00:16:56.790 --> 00:17:02.900 align:middle line:90% 00:17:02.900 --> 00:17:05.630 align:middle line:84% We'll just say that it's whatever 00:17:05.630 --> 00:17:09.349 align:middle line:84% it is at 298, because that's a convenient reference point. 00:17:09.349 --> 00:17:10.520 align:middle line:90% And these are tabulated. 00:17:10.520 --> 00:17:12.890 align:middle line:84% The enthalpy of oxidation reactions 00:17:12.890 --> 00:17:16.650 align:middle line:84% at standard condition, those are tabulated. 00:17:16.650 --> 00:17:19.176 align:middle line:84% So that takes care of the enthalpy. 00:17:19.176 --> 00:17:20.134 align:middle line:90% What about the entropy? 00:17:20.134 --> 00:17:27.130 align:middle line:90% 00:17:27.130 --> 00:17:34.920 align:middle line:84% Entropy delta S is delta S at some reference temperature, 00:17:34.920 --> 00:17:37.205 align:middle line:90% 298 plus integral. 00:17:37.205 --> 00:17:45.710 align:middle line:90% 00:17:45.710 --> 00:17:48.350 align:middle line:84% OK, so who knows-- who has a guess on what 00:17:48.350 --> 00:17:49.100 align:middle line:90% we're going to do? 00:17:49.100 --> 00:17:51.190 align:middle line:84% We're going to approximate this as what? 00:17:51.190 --> 00:17:56.135 align:middle line:90% 00:17:56.135 --> 00:17:57.210 align:middle line:90% What am I looking for? 00:17:57.210 --> 00:18:00.790 align:middle line:84% I want to justify what approximation. 00:18:00.790 --> 00:18:03.460 align:middle line:84% AUDIENCE: Aren't entropy values usually much smaller? 00:18:03.460 --> 00:18:06.900 align:middle line:84% So if the enthalpy is already so big, we could assume entropy 00:18:06.900 --> 00:18:08.490 align:middle line:90% is 0? 00:18:08.490 --> 00:18:09.520 align:middle line:90% RAFAEL JARAMILLO: I see. 00:18:09.520 --> 00:18:14.180 align:middle line:84% So you're right that entropy values tend to be much smaller, 00:18:14.180 --> 00:18:16.498 align:middle line:84% but the thing is they're multiplied by temperature. 00:18:16.498 --> 00:18:19.040 align:middle line:84% So they do matter quite a lot, because the temperature number 00:18:19.040 --> 00:18:21.040 align:middle line:90% can get large. 00:18:21.040 --> 00:18:24.550 align:middle line:84% So we're not we're not going to neglect it completely, 00:18:24.550 --> 00:18:25.960 align:middle line:90% but I'll tell you-- 00:18:25.960 --> 00:18:27.110 align:middle line:90% I'm sorry? 00:18:27.110 --> 00:18:29.110 align:middle line:84% AUDIENCE: Neglecting its temperature dependence? 00:18:29.110 --> 00:18:29.680 align:middle line:84% RAFAEL JARAMILLO: Yeah, we're going 00:18:29.680 --> 00:18:31.600 align:middle line:84% to neglect its temperature dependence. 00:18:31.600 --> 00:18:36.620 align:middle line:84% So I'm going to write this before I write this. 00:18:36.620 --> 00:18:38.430 align:middle line:84% It's just the why we get to do that. 00:18:38.430 --> 00:18:43.940 align:middle line:84% So let me write neglect the temperature dependence, 00:18:43.940 --> 00:18:46.820 align:middle line:84% and now, somebody please tell me why 00:18:46.820 --> 00:18:50.005 align:middle line:90% we might be able to do this? 00:18:50.005 --> 00:18:52.630 align:middle line:84% And it's not just that we really like to make our lives easier. 00:18:52.630 --> 00:18:55.810 align:middle line:84% It turns out to be a really good approximation in many cases. 00:18:55.810 --> 00:18:57.655 align:middle line:84% What about this oxidation reaction? 00:18:57.655 --> 00:19:00.270 align:middle line:90% 00:19:00.270 --> 00:19:02.625 align:middle line:84% What's the dominant entropy change? 00:19:02.625 --> 00:19:05.950 align:middle line:90% 00:19:05.950 --> 00:19:12.483 align:middle line:84% What's the dominant contribution to delta S? 00:19:12.483 --> 00:19:14.650 align:middle line:84% AUDIENCE: Could it be when the phase change happens? 00:19:14.650 --> 00:19:17.112 align:middle line:84% So when the temperature is constant? 00:19:17.112 --> 00:19:19.320 align:middle line:84% RAFAEL JARAMILLO: The phase change meaning from metal 00:19:19.320 --> 00:19:21.300 align:middle line:90% to metal oxide? 00:19:21.300 --> 00:19:22.683 align:middle line:90% AUDIENCE: Yeah. 00:19:22.683 --> 00:19:24.350 align:middle line:84% RAFAEL JARAMILLO: That's true, but maybe 00:19:24.350 --> 00:19:26.360 align:middle line:90% tell me what part of that? 00:19:26.360 --> 00:19:31.420 align:middle line:90% 00:19:31.420 --> 00:19:33.375 align:middle line:84% AUDIENCE: [INAUDIBLE] condense it? 00:19:33.375 --> 00:19:34.750 align:middle line:84% RAFAEL JARAMILLO: Yes, thank you. 00:19:34.750 --> 00:19:36.220 align:middle line:90% That's what I'm looking for. 00:19:36.220 --> 00:19:38.937 align:middle line:84% The reaction entropy is dominated by-- 00:19:38.937 --> 00:19:41.020 align:middle line:84% I didn't see who said that, but thank you so much. 00:19:41.020 --> 00:19:51.890 align:middle line:84% By condensation of O2 from the gas. 00:19:51.890 --> 00:19:52.790 align:middle line:90% That's it. 00:19:52.790 --> 00:19:55.310 align:middle line:90% So here's metal. 00:19:55.310 --> 00:20:04.640 align:middle line:84% There's a chunk of metal, and then I have O2 gas. 00:20:04.640 --> 00:20:08.120 align:middle line:84% Gas is very high entropy, as you know. 00:20:08.120 --> 00:20:09.890 align:middle line:90% O2. 00:20:09.890 --> 00:20:15.470 align:middle line:84% And this reaction pulls the oxygen out of the gas 00:20:15.470 --> 00:20:19.520 align:middle line:90% and makes a metal oxide. 00:20:19.520 --> 00:20:23.480 align:middle line:84% So the reactants have much, much higher entropy 00:20:23.480 --> 00:20:25.730 align:middle line:84% than the products, simply due to the fact 00:20:25.730 --> 00:20:27.890 align:middle line:84% that the reactants included a mode of gas 00:20:27.890 --> 00:20:31.040 align:middle line:84% and the products don't include any gas. 00:20:31.040 --> 00:20:35.890 align:middle line:84% And in almost all cases, that change 00:20:35.890 --> 00:20:39.370 align:middle line:90% dominates the reaction entropy. 00:20:39.370 --> 00:20:45.650 align:middle line:84% And since we're modeling oxygen as an ideal gas, 00:20:45.650 --> 00:20:48.110 align:middle line:84% the entropy of this gas is temperature independent. 00:20:48.110 --> 00:20:50.580 align:middle line:90% It's configuration entropy. 00:20:50.580 --> 00:20:52.880 align:middle line:84% It's the thing we've been talking 00:20:52.880 --> 00:20:55.130 align:middle line:84% about pretty much the whole semester, which 00:20:55.130 --> 00:21:00.680 align:middle line:84% is the entropy of randomly configured gas molecules. 00:21:00.680 --> 00:21:01.180 align:middle line:90% Good. 00:21:01.180 --> 00:21:01.680 align:middle line:90% Thank you. 00:21:01.680 --> 00:21:04.390 align:middle line:84% So now we have waved our hands, although we've 00:21:04.390 --> 00:21:05.437 align:middle line:90% done it scientifically. 00:21:05.437 --> 00:21:07.270 align:middle line:84% Scientifically waving of hands has happened, 00:21:07.270 --> 00:21:09.730 align:middle line:84% and we figured out that we can neglect the temperature 00:21:09.730 --> 00:21:12.520 align:middle line:84% dependence of the enthalpy and we can neglect the temperature 00:21:12.520 --> 00:21:14.170 align:middle line:84% dependence of the entropy, and this 00:21:14.170 --> 00:21:17.530 align:middle line:84% is going to make our lives even easier than they already were. 00:21:17.530 --> 00:21:22.080 align:middle line:90% We can solve for this thing. 00:21:22.080 --> 00:21:25.290 align:middle line:84% We can solve for that oxygen partial pressure. 00:21:25.290 --> 00:21:35.280 align:middle line:84% PO2 by atmosphere equals e the delta H0 over RT. 00:21:35.280 --> 00:21:40.240 align:middle line:84% e the minus delta S0 over R. This 00:21:40.240 --> 00:22:00.600 align:middle line:84% is the oxygen pressure at which a metal and its oxide 00:22:00.600 --> 00:22:05.621 align:middle line:90% coexist at equilibrium. 00:22:05.621 --> 00:22:13.510 align:middle line:90% 00:22:13.510 --> 00:22:14.885 align:middle line:84% All right, so you've got a metal. 00:22:14.885 --> 00:22:18.470 align:middle line:90% 00:22:18.470 --> 00:22:24.400 align:middle line:84% They've got it's oxide, and this is the oxygen partial pressure, 00:22:24.400 --> 00:22:25.620 align:middle line:90% so there's some oxygen here. 00:22:25.620 --> 00:22:31.420 align:middle line:90% 00:22:31.420 --> 00:22:32.980 align:middle line:84% This is the oxygen partial pressure 00:22:32.980 --> 00:22:38.220 align:middle line:84% at which this kind of situation is that equilibrium. 00:22:38.220 --> 00:22:48.800 align:middle line:90% 00:22:48.800 --> 00:22:52.460 align:middle line:84% What happens if the oxygen partial pressure is higher 00:22:52.460 --> 00:22:53.730 align:middle line:90% than the equilibrium value? 00:22:53.730 --> 00:22:59.360 align:middle line:84% What do you think happens spontaneously in this system? 00:22:59.360 --> 00:23:01.012 align:middle line:90% Think Le Chatelier's principle. 00:23:01.012 --> 00:23:02.720 align:middle line:84% I have the system in equilibrium and then 00:23:02.720 --> 00:23:04.280 align:middle line:90% I shove more oxygen gas in. 00:23:04.280 --> 00:23:06.350 align:middle line:84% I increase the oxygen partial pressure. 00:23:06.350 --> 00:23:07.640 align:middle line:90% What do you expect to happen? 00:23:07.640 --> 00:23:10.780 align:middle line:90% How will the system respond? 00:23:10.780 --> 00:23:12.737 align:middle line:84% AUDIENCE: Spontaneously oxidized? 00:23:12.737 --> 00:23:14.070 align:middle line:90% RAFAEL JARAMILLO: One more time. 00:23:14.070 --> 00:23:14.960 align:middle line:84% I'm sorry, I didn't quite hear that. 00:23:14.960 --> 00:23:16.520 align:middle line:84% AUDIENCE: Spontaneously oxidized? 00:23:16.520 --> 00:23:17.900 align:middle line:84% RAFAEL JARAMILLO: Yes, fantastic. 00:23:17.900 --> 00:23:21.360 align:middle line:90% Metal spontaneously. 00:23:21.360 --> 00:23:28.380 align:middle line:90% 00:23:28.380 --> 00:23:31.370 align:middle line:84% So you're going to have spontaneous conversion of more 00:23:31.370 --> 00:23:32.720 align:middle line:90% metal into oxide. 00:23:32.720 --> 00:23:35.780 align:middle line:84% We've already established that the oxygen can't 00:23:35.780 --> 00:23:37.313 align:middle line:84% dissolve in the metal and the oxygen 00:23:37.313 --> 00:23:38.480 align:middle line:90% can't dissolve in the oxide. 00:23:38.480 --> 00:23:40.490 align:middle line:84% They're pure components, so all we can do 00:23:40.490 --> 00:23:44.090 align:middle line:84% is convert metal to oxide, metal to oxide, metal to oxide. 00:23:44.090 --> 00:23:44.690 align:middle line:90% Excellent. 00:23:44.690 --> 00:23:45.230 align:middle line:90% Thank you. 00:23:45.230 --> 00:23:46.706 align:middle line:90% What about at lower? 00:23:46.706 --> 00:23:50.087 align:middle line:90% 00:23:50.087 --> 00:23:52.160 align:middle line:84% At lower oxygen pressure pressure? 00:23:52.160 --> 00:23:54.680 align:middle line:84% If we're below this value, what do we 00:23:54.680 --> 00:23:58.062 align:middle line:90% expect to happen spontaneously? 00:23:58.062 --> 00:24:00.270 align:middle line:84% AUDIENCE: We will see the reverse reaction happening. 00:24:00.270 --> 00:24:03.062 align:middle line:90% So more O2 gas will form? 00:24:03.062 --> 00:24:06.030 align:middle line:84% RAFAEL JARAMILLO: How does it form? 00:24:06.030 --> 00:24:09.000 align:middle line:84% AUDIENCE: Through the oxide decomposing back 00:24:09.000 --> 00:24:11.598 align:middle line:90% into a metal and O2 gas. 00:24:11.598 --> 00:24:13.140 align:middle line:84% RAFAEL JARAMILLO: Exactly, thank you. 00:24:13.140 --> 00:24:15.140 align:middle line:84% I'm going to use this term the oxide is reduced, 00:24:15.140 --> 00:24:18.720 align:middle line:84% but your expression of spontaneously decomposing 00:24:18.720 --> 00:24:20.830 align:middle line:90% is exactly the right thing. 00:24:20.830 --> 00:24:25.350 align:middle line:84% So if we pull down the oxygen pressure below the equilibrium 00:24:25.350 --> 00:24:28.860 align:middle line:84% value, the system will respond by converting oxide 00:24:28.860 --> 00:24:30.790 align:middle line:90% into metal and oxygen gas. 00:24:30.790 --> 00:24:33.120 align:middle line:84% And you can think of this in terms of Le Chatelier. 00:24:33.120 --> 00:24:35.250 align:middle line:84% If I add more oxygen, the system will 00:24:35.250 --> 00:24:39.900 align:middle line:84% try to counteract that by condensing the oxygen into more 00:24:39.900 --> 00:24:43.230 align:middle line:84% oxide, so it'll take more metal, convert it into oxide 00:24:43.230 --> 00:24:48.360 align:middle line:84% by pulling some of my extra oxygen out of the atmosphere. 00:24:48.360 --> 00:24:50.880 align:middle line:84% If I pull down the oxygen pressure, 00:24:50.880 --> 00:24:54.060 align:middle line:84% the system will try to counteract that by giving off 00:24:54.060 --> 00:24:56.190 align:middle line:90% more oxygen gas from the oxide. 00:24:56.190 --> 00:25:00.990 align:middle line:84% The oxide will decompose into more oxygen gas and more metal. 00:25:00.990 --> 00:25:03.750 align:middle line:90% That's right. 00:25:03.750 --> 00:25:05.650 align:middle line:90% So that's what happens. 00:25:05.650 --> 00:25:09.560 align:middle line:84% So for example, let's imagine Ti oxidizing. 00:25:09.560 --> 00:25:12.750 align:middle line:90% 00:25:12.750 --> 00:25:14.730 align:middle line:90% That's a nice reaction. 00:25:14.730 --> 00:25:19.700 align:middle line:90% At 298 Kelvin, I looked it up. 00:25:19.700 --> 00:25:23.300 align:middle line:90% The PO2 at this equilibrium is-- 00:25:23.300 --> 00:25:25.220 align:middle line:90% anybody have a guess? 00:25:25.220 --> 00:25:26.120 align:middle line:90% Forget the guess. 00:25:26.120 --> 00:25:28.610 align:middle line:90% It's completely naive. 00:25:28.610 --> 00:25:34.720 align:middle line:90% 10 to the minus 150 atmospheres. 00:25:34.720 --> 00:25:39.370 align:middle line:84% A completely silly, make believe number. 00:25:39.370 --> 00:25:40.360 align:middle line:90% It's 0. 00:25:40.360 --> 00:25:40.860 align:middle line:90% It's 0. 00:25:40.860 --> 00:25:42.237 align:middle line:90% It might as well be 0. 00:25:42.237 --> 00:25:43.945 align:middle line:84% What does that mean about titanium metal? 00:25:43.945 --> 00:25:48.420 align:middle line:90% 00:25:48.420 --> 00:25:50.782 align:middle line:84% AUDIENCE: It's very favorable for it to oxidize. 00:25:50.782 --> 00:25:52.740 align:middle line:84% RAFAEL JARAMILLO: Very favorable with oxidized. 00:25:52.740 --> 00:25:55.710 align:middle line:84% Titanium metal, if you see it in the air, 00:25:55.710 --> 00:25:59.010 align:middle line:84% will actually be titanium metal with a thin layer 00:25:59.010 --> 00:26:01.950 align:middle line:84% of its own native oxide on top of it. 00:26:01.950 --> 00:26:03.810 align:middle line:84% Because if you were to remove the oxide 00:26:03.810 --> 00:26:06.060 align:middle line:84% and wait a split second, the oxide 00:26:06.060 --> 00:26:09.920 align:middle line:90% would spontaneously reform. 00:26:09.920 --> 00:26:13.330 align:middle line:84% And so this spontaneous oxide formation process 00:26:13.330 --> 00:26:16.670 align:middle line:84% is really important for a lot of reasons. 00:26:16.670 --> 00:26:18.520 align:middle line:84% It's important for microelectronics, 00:26:18.520 --> 00:26:20.350 align:middle line:84% it's important for stainless steel. 00:26:20.350 --> 00:26:22.630 align:middle line:84% That's how stainless steel remains stainless. 00:26:22.630 --> 00:26:25.570 align:middle line:84% You have spontaneous formation of a passive rating, 00:26:25.570 --> 00:26:28.150 align:middle line:84% or you can think of it as a protecting oxide 00:26:28.150 --> 00:26:32.410 align:middle line:84% layer and the engineering of those materials continues. 00:26:32.410 --> 00:26:34.030 align:middle line:90% It's all interesting stuff. 00:26:34.030 --> 00:26:38.855 align:middle line:84% All right, so that is enough to take us to Richardson Ellingham 00:26:38.855 --> 00:26:39.355 align:middle line:90% diagrams. 00:26:39.355 --> 00:26:52.560 align:middle line:90% 00:26:52.560 --> 00:26:54.733 align:middle line:90% So we're going to do this. 00:26:54.733 --> 00:26:56.400 align:middle line:84% I can't really motivate this, because it 00:26:56.400 --> 00:26:58.350 align:middle line:84% sounds kind of random what we're going to do. 00:26:58.350 --> 00:27:00.848 align:middle line:84% So I'm just going to tell you what it is, and at the end 00:27:00.848 --> 00:27:01.890 align:middle line:90% tell you why it's useful. 00:27:01.890 --> 00:27:06.410 align:middle line:90% 00:27:06.410 --> 00:27:09.190 align:middle line:84% We're going to plot delta G0 as a function of temperature 00:27:09.190 --> 00:27:11.110 align:middle line:90% for metal oxidation reactions. 00:27:11.110 --> 00:27:15.200 align:middle line:90% 00:27:15.200 --> 00:27:17.280 align:middle line:90% As you know, it's like this. 00:27:17.280 --> 00:27:20.010 align:middle line:84% And so this is a pretty simple thing. 00:27:20.010 --> 00:27:28.620 align:middle line:84% This is a line with slope minus delta S0 and intercept delta 00:27:28.620 --> 00:27:30.710 align:middle line:90% H0. 00:27:30.710 --> 00:27:36.945 align:middle line:84% This is a really, really simple line. 00:27:36.945 --> 00:27:39.880 align:middle line:90% 00:27:39.880 --> 00:27:40.930 align:middle line:90% So here's is temperature. 00:27:40.930 --> 00:27:42.290 align:middle line:90% Let's see in Kelvin. 00:27:42.290 --> 00:27:44.380 align:middle line:90% Here's 0, here's 0. 00:27:44.380 --> 00:27:49.790 align:middle line:84% Here's delta G0, and we have line. 00:27:49.790 --> 00:27:55.770 align:middle line:84% We have a line, the slope, and an intercept. 00:27:55.770 --> 00:28:00.120 align:middle line:90% Slope, intercept. 00:28:00.120 --> 00:28:02.830 align:middle line:90% 00:28:02.830 --> 00:28:06.760 align:middle line:84% That is a Richardson Ellingham diagram. 00:28:06.760 --> 00:28:09.610 align:middle line:90% Now, why did we do that? 00:28:09.610 --> 00:28:11.930 align:middle line:90% A couple of reasons. 00:28:11.930 --> 00:28:18.280 align:middle line:84% Let's start by talking about the PO2 scale. 00:28:18.280 --> 00:28:19.540 align:middle line:90% What's that? 00:28:19.540 --> 00:28:27.400 align:middle line:84% The equilibrium constant is PO2 by atmosphere to the minus 1, 00:28:27.400 --> 00:28:32.080 align:middle line:84% which is equal to e to the minus G0 over RT. 00:28:32.080 --> 00:28:37.180 align:middle line:84% So I'm just going to rearrange that and write delta G0 equals 00:28:37.180 --> 00:28:42.670 align:middle line:90% RT log PO2 by atmosphere. 00:28:42.670 --> 00:28:45.590 align:middle line:90% 00:28:45.590 --> 00:28:59.110 align:middle line:84% This is a line on delta G0 by t plot with slope 00:28:59.110 --> 00:29:06.970 align:middle line:90% our log, PO2 and 0 intercepts. 00:29:06.970 --> 00:29:16.570 align:middle line:90% 00:29:16.570 --> 00:29:17.690 align:middle line:90% Let's draw that. 00:29:17.690 --> 00:29:24.650 align:middle line:90% 00:29:24.650 --> 00:29:28.160 align:middle line:84% All right, here is temperature in Kelvin. 00:29:28.160 --> 00:29:30.200 align:middle line:90% 0 is 0. 00:29:30.200 --> 00:29:33.260 align:middle line:90% Here's delta G0. 00:29:33.260 --> 00:29:43.080 align:middle line:84% I'll draw the oxidation of a given metal 00:29:43.080 --> 00:29:47.920 align:middle line:90% just to have something on there. 00:29:47.920 --> 00:29:51.520 align:middle line:84% And now, I'm going to draw these two contours, right? 00:29:51.520 --> 00:29:54.550 align:middle line:84% Delta G0 equals RT log PO2 over atmosphere. 00:29:54.550 --> 00:29:56.560 align:middle line:84% So I'm going to draw a series of lines 00:29:56.560 --> 00:29:58.960 align:middle line:84% all with 0 intercepts in varying slope. 00:29:58.960 --> 00:30:10.210 align:middle line:90% 00:30:10.210 --> 00:30:12.900 align:middle line:84% So there's a series of lines with 0 intercept and varying 00:30:12.900 --> 00:30:13.890 align:middle line:90% slope. 00:30:13.890 --> 00:30:23.045 align:middle line:84% And as I move in this direction, I'm increasing PO2. 00:30:23.045 --> 00:30:26.850 align:middle line:90% 00:30:26.850 --> 00:30:30.500 align:middle line:84% So that's what a Richardson Ellingham plot is. 00:30:30.500 --> 00:30:32.780 align:middle line:84% Now, I get to tell you why it's useful. 00:30:32.780 --> 00:30:35.180 align:middle line:84% All right, so if I rush through the explanation what 00:30:35.180 --> 00:30:37.430 align:middle line:84% it is, because it's just like, I have to tell you what it is. 00:30:37.430 --> 00:30:39.097 align:middle line:84% But now, I can show you why it's useful. 00:30:39.097 --> 00:30:42.060 align:middle line:90% 00:30:42.060 --> 00:30:48.780 align:middle line:90% So why is this useful? 00:30:48.780 --> 00:30:53.170 align:middle line:90% 00:30:53.170 --> 00:30:55.980 align:middle line:84% It's useful for materials processing. 00:30:55.980 --> 00:31:03.460 align:middle line:90% 00:31:03.460 --> 00:31:05.460 align:middle line:90% Let me illustrate that. 00:31:05.460 --> 00:31:13.460 align:middle line:84% Let's consider two metals, and I pick these 00:31:13.460 --> 00:31:16.580 align:middle line:84% just because they appear nicely separate on the plot. 00:31:16.580 --> 00:31:22.050 align:middle line:90% Let's consider tin in manganese. 00:31:22.050 --> 00:31:24.930 align:middle line:90% 00:31:24.930 --> 00:31:28.650 align:middle line:84% If I look up the Richard Ellingham 00:31:28.650 --> 00:31:31.660 align:middle line:84% diagram for tin and manganese, I could do that, 00:31:31.660 --> 00:31:36.570 align:middle line:84% but I'll just draw qualitatively what it looks like. 00:31:36.570 --> 00:31:39.300 align:middle line:90% It's temperature in Kelvin. 00:31:39.300 --> 00:31:41.400 align:middle line:90% It's delta G0. 00:31:41.400 --> 00:31:53.380 align:middle line:84% And I'm just here to tell you that the tin line sits well 00:31:53.380 --> 00:31:58.430 align:middle line:90% above the manganese line. 00:31:58.430 --> 00:32:02.570 align:middle line:84% So that's just a fact about these metals. 00:32:02.570 --> 00:32:10.730 align:middle line:84% This here is tin plus O2 going to tin O2. 00:32:10.730 --> 00:32:19.130 align:middle line:84% That's what that is, and this is 2 manganese plus O2 00:32:19.130 --> 00:32:21.830 align:middle line:90% going to 2 manganese oxide. 00:32:21.830 --> 00:32:26.050 align:middle line:90% 00:32:26.050 --> 00:32:29.050 align:middle line:90% And here are my PO2 contours. 00:32:29.050 --> 00:32:37.940 align:middle line:90% 00:32:37.940 --> 00:32:41.340 align:middle line:90% What is this plot telling me? 00:32:41.340 --> 00:32:45.765 align:middle line:84% It's telling me that, at a given-- 00:32:45.765 --> 00:32:55.750 align:middle line:90% 00:32:55.750 --> 00:32:58.360 align:middle line:84% I have a typo on my scan lecture notes, I'm sorry. 00:32:58.360 --> 00:33:03.410 align:middle line:84% At a given temp at any given temperature, 00:33:03.410 --> 00:33:13.470 align:middle line:84% PO2 for the manganese oxidation reaction 00:33:13.470 --> 00:33:22.970 align:middle line:84% is lower than for the tin oxidation reaction. 00:33:22.970 --> 00:33:29.740 align:middle line:90% 00:33:29.740 --> 00:33:31.690 align:middle line:90% That's a useful fact. 00:33:31.690 --> 00:33:32.530 align:middle line:90% How do I see that? 00:33:32.530 --> 00:33:42.530 align:middle line:84% Let's say at a given temperature, 00:33:42.530 --> 00:33:46.260 align:middle line:90% let's see that temperature here. 00:33:46.260 --> 00:33:50.340 align:middle line:84% I have this point on the tin oxidation line. 00:33:50.340 --> 00:33:53.760 align:middle line:90% 00:33:53.760 --> 00:34:00.070 align:middle line:84% And this point on the manganese oxidation line. 00:34:00.070 --> 00:34:09.320 align:middle line:84% Well, the PO2 contour that runs through the manganese oxidation 00:34:09.320 --> 00:34:12.260 align:middle line:84% line intercepting of that temperature 00:34:12.260 --> 00:34:14.750 align:middle line:84% corresponds to a lower partial pressure 00:34:14.750 --> 00:34:18.650 align:middle line:84% than the PO2 contour that runs through the tin oxidation line 00:34:18.650 --> 00:34:20.840 align:middle line:90% for that given temperature. 00:34:20.840 --> 00:34:27.440 align:middle line:84% Again, at its given temperature, the PO2 partial pressure 00:34:27.440 --> 00:34:33.260 align:middle line:84% contour for manganese oxidation is a lower partial pressure 00:34:33.260 --> 00:34:35.510 align:middle line:84% than the contour for tin oxidation. 00:34:35.510 --> 00:34:39.100 align:middle line:90% 00:34:39.100 --> 00:34:40.880 align:middle line:90% What does that mean? 00:34:40.880 --> 00:34:50.139 align:middle line:84% Manganese metal will reduce tin oxide. 00:34:50.139 --> 00:34:51.630 align:middle line:84% So if you were to put tin oxide-- 00:34:51.630 --> 00:34:54.750 align:middle line:84% let's say an ore into a furnace in the presence 00:34:54.750 --> 00:34:59.870 align:middle line:84% of manganese metal and heat it up, 00:34:59.870 --> 00:35:03.620 align:middle line:84% the manganese will convert to manganese oxide 00:35:03.620 --> 00:35:06.950 align:middle line:84% and then tin oxide will convert to tin metal. 00:35:06.950 --> 00:35:08.390 align:middle line:90% Why is that? 00:35:08.390 --> 00:35:25.680 align:middle line:84% Manganese has higher affinity for oxygen than does tin. 00:35:25.680 --> 00:35:31.820 align:middle line:84% Or saying the same thing, the enthalpy of oxidation 00:35:31.820 --> 00:35:43.110 align:middle line:84% is more negative for manganese oxidation 00:35:43.110 --> 00:35:47.100 align:middle line:90% than for tin oxidation. 00:35:47.100 --> 00:35:50.520 align:middle line:90% 00:35:50.520 --> 00:35:53.880 align:middle line:84% So you can see that from the plots. 00:35:53.880 --> 00:35:56.790 align:middle line:84% The intercept of these plots is delta H. So 00:35:56.790 --> 00:35:59.810 align:middle line:84% you can see the intercepts for the manganese oxidation-- 00:35:59.810 --> 00:36:02.250 align:middle line:90% that's at this point down here-- 00:36:02.250 --> 00:36:03.510 align:middle line:90% is lower. 00:36:03.510 --> 00:36:04.620 align:middle line:90% Let me extend these lines. 00:36:04.620 --> 00:36:11.968 align:middle line:90% 00:36:11.968 --> 00:36:14.010 align:middle line:84% The intercept of the manganese oxidation reaction 00:36:14.010 --> 00:36:16.427 align:middle line:84% is lower than the intercept of the tin oxidation reaction. 00:36:16.427 --> 00:36:19.780 align:middle line:90% 00:36:19.780 --> 00:36:23.530 align:middle line:84% The enthalpy of manganese oxidation is more negative. 00:36:23.530 --> 00:36:27.100 align:middle line:84% Or if we are speaking a little bit colloquially, 00:36:27.100 --> 00:36:33.710 align:middle line:90% manganese metal pulls-- 00:36:33.710 --> 00:36:42.295 align:middle line:84% in quotation marks-- oxygen out of tin oxide. 00:36:42.295 --> 00:36:47.610 align:middle line:90% 00:36:47.610 --> 00:36:50.460 align:middle line:84% So everything I just wrote, these 00:36:50.460 --> 00:37:02.765 align:middle line:84% are all saying the same thing about metal oxygen bonds. 00:37:02.765 --> 00:37:06.180 align:middle line:90% 00:37:06.180 --> 00:37:09.150 align:middle line:84% All right, these are all equivalent statements. 00:37:09.150 --> 00:37:12.510 align:middle line:84% They're just ways of interpreting metal oxygen 00:37:12.510 --> 00:37:17.730 align:middle line:84% bonding and the implications of that for materials processing. 00:37:17.730 --> 00:37:19.680 align:middle line:84% If you're going to be processing manganese 00:37:19.680 --> 00:37:22.230 align:middle line:84% in the presence of tin, you need to know 00:37:22.230 --> 00:37:25.710 align:middle line:84% which one is going to have a higher PO2 at equilibrium 00:37:25.710 --> 00:37:29.290 align:middle line:84% for oxidation, because it's going to determine your process 00:37:29.290 --> 00:37:29.790 align:middle line:90% outcome. 00:37:29.790 --> 00:37:35.990 align:middle line:90% 00:37:35.990 --> 00:37:40.050 align:middle line:84% I want to share with you some pictures of Ellingham diagrams. 00:37:40.050 --> 00:37:44.040 align:middle line:84% So there's lots of Ellingham diagrams out there. 00:37:44.040 --> 00:37:47.870 align:middle line:84% Here is one representation that's a little busy, 00:37:47.870 --> 00:37:49.520 align:middle line:84% but you can see lots of things here. 00:37:49.520 --> 00:37:53.120 align:middle line:84% You can see many metals which are all represented. 00:37:53.120 --> 00:37:54.620 align:middle line:90% Let me grab my laser pointer. 00:37:54.620 --> 00:37:56.780 align:middle line:84% Sometimes the laser pointer is stubborn. 00:37:56.780 --> 00:37:57.935 align:middle line:90% So here's iron. 00:37:57.935 --> 00:38:00.470 align:middle line:90% 00:38:00.470 --> 00:38:03.440 align:middle line:84% Oxidation reaction is a nickel reaction copper. 00:38:03.440 --> 00:38:08.820 align:middle line:84% As you move down, you're going to metals that have 00:38:08.820 --> 00:38:10.740 align:middle line:90% higher affinity for oxygen. 00:38:10.740 --> 00:38:15.450 align:middle line:84% So copper is sometimes considered noble. 00:38:15.450 --> 00:38:18.590 align:middle line:84% So it doesn't readily form an oxide. 00:38:18.590 --> 00:38:20.630 align:middle line:84% You remember we talked about roof flashing. 00:38:20.630 --> 00:38:23.210 align:middle line:84% It takes a long time for it to turn green. 00:38:23.210 --> 00:38:24.445 align:middle line:90% As opposed to calcium, right? 00:38:24.445 --> 00:38:25.820 align:middle line:84% If you have calcium metal around, 00:38:25.820 --> 00:38:27.320 align:middle line:84% you should look out, because it's 00:38:27.320 --> 00:38:30.290 align:middle line:90% going to explosively oxidize. 00:38:30.290 --> 00:38:32.630 align:middle line:84% So down here, you have calcium, magnesium. 00:38:32.630 --> 00:38:33.470 align:middle line:90% Aluminum. 00:38:33.470 --> 00:38:36.500 align:middle line:84% Aluminum is a very energetic oxidation reaction, 00:38:36.500 --> 00:38:38.907 align:middle line:84% but we know it forms a passivating oxide. 00:38:38.907 --> 00:38:41.240 align:middle line:84% So you don't have exploding aluminum all over the place. 00:38:41.240 --> 00:38:44.120 align:middle line:84% You have almost instantaneous formation 00:38:44.120 --> 00:38:46.610 align:middle line:84% of aluminum oxide on the surface of aluminum. 00:38:46.610 --> 00:38:48.530 align:middle line:84% Titanium silicon manganese chromium. 00:38:48.530 --> 00:38:53.990 align:middle line:84% So this is a limited Richardson diagram, Ellingham diagram, 00:38:53.990 --> 00:38:57.200 align:middle line:84% because it only shows about a dozen or so metals. 00:38:57.200 --> 00:39:00.200 align:middle line:84% Of course, you can get very, very busy plots. 00:39:00.200 --> 00:39:06.320 align:middle line:84% I want to point out one more thing, which is the PO2 scale. 00:39:06.320 --> 00:39:08.890 align:middle line:90% PO2. 00:39:08.890 --> 00:39:11.260 align:middle line:84% And you see it's a series of numbers 00:39:11.260 --> 00:39:19.750 align:middle line:84% running from 1 atmosphere to 0 to the minus 200 atmospheres. 00:39:19.750 --> 00:39:22.390 align:middle line:84% And each of these numbers has a little tick mark, 00:39:22.390 --> 00:39:25.270 align:middle line:84% and the tick marks all point towards the origin. 00:39:25.270 --> 00:39:28.990 align:middle line:84% You see these tick marks, they're at different angles. 00:39:28.990 --> 00:39:30.310 align:middle line:90% Why is that? 00:39:30.310 --> 00:39:32.350 align:middle line:84% Because it's asking you to imagine 00:39:32.350 --> 00:39:35.710 align:middle line:84% a series of straight lines connecting the origin to those 00:39:35.710 --> 00:39:37.580 align:middle line:90% values. 00:39:37.580 --> 00:39:40.980 align:middle line:84% Those series of straight lines connecting the origin to-- 00:39:40.980 --> 00:39:42.590 align:middle line:90% I've never done this before. 00:39:42.590 --> 00:39:43.740 align:middle line:90% I draw the line. 00:39:43.740 --> 00:39:45.370 align:middle line:90% So here is-- oh, there we go. 00:39:45.370 --> 00:39:45.930 align:middle line:90% Look at that. 00:39:45.930 --> 00:39:49.880 align:middle line:84% So this would be a line of 10 to the minus 50 atmospheres 00:39:49.880 --> 00:39:53.590 align:middle line:84% of oxygen. So for example, you might 00:39:53.590 --> 00:40:03.480 align:middle line:84% say that zinc and its oxide are equilibrium at 400 degrees 00:40:03.480 --> 00:40:08.253 align:middle line:84% C and 10 to the minus 50 atmospheres of oxygen. 00:40:08.253 --> 00:40:09.920 align:middle line:84% That would be one way to read this plot. 00:40:09.920 --> 00:40:15.950 align:middle line:90% 00:40:15.950 --> 00:40:18.550 align:middle line:84% And you also see that the delta H of formation 00:40:18.550 --> 00:40:21.250 align:middle line:84% here is correlated to the electronegativity. 00:40:21.250 --> 00:40:25.060 align:middle line:84% So this idea that metal oxygen bond formation is energetic, 00:40:25.060 --> 00:40:29.700 align:middle line:84% well, we know that, but it's more energetic for less 00:40:29.700 --> 00:40:30.705 align:middle line:90% electronegative metals. 00:40:30.705 --> 00:40:33.830 align:middle line:90% 00:40:33.830 --> 00:40:38.690 align:middle line:84% So we expect noble metals like silver and copper 00:40:38.690 --> 00:40:40.670 align:middle line:90% to be fairly electronegative. 00:40:40.670 --> 00:40:44.240 align:middle line:84% They like their electrons, 1.9, 1.93. 00:40:44.240 --> 00:40:47.330 align:middle line:84% And we expect alkaline, alkaline Earth metals-- 00:40:47.330 --> 00:40:50.060 align:middle line:90% let's say alkaline earth-- 00:40:50.060 --> 00:40:51.110 align:middle line:90% alkali metals. 00:40:51.110 --> 00:40:53.790 align:middle line:84% Alkaline Earth metals like magnesium, right? 00:40:53.790 --> 00:40:56.840 align:middle line:84% They are happy to give up their electrons to oxygen. 00:40:56.840 --> 00:40:59.090 align:middle line:84% And that has a lower electronegativity 00:40:59.090 --> 00:41:00.275 align:middle line:90% calcium is down here at 1. 00:41:00.275 --> 00:41:03.030 align:middle line:90% 00:41:03.030 --> 00:41:05.042 align:middle line:84% So there's some solid chemistry here. 00:41:05.042 --> 00:41:06.750 align:middle line:84% There's one more thing I want to tell you 00:41:06.750 --> 00:41:14.470 align:middle line:84% about Ellingham diagrams, and that is the effect 00:41:14.470 --> 00:41:15.610 align:middle line:90% of phase transitions. 00:41:15.610 --> 00:41:26.520 align:middle line:90% 00:41:26.520 --> 00:41:37.590 align:middle line:84% So let's consider melting of metal or its oxide. 00:41:37.590 --> 00:41:42.420 align:middle line:84% Metal's metal-- oxide's also metal-- 00:41:42.420 --> 00:41:57.040 align:middle line:84% causes-- it causes discrete jumps in those values. 00:41:57.040 --> 00:42:06.080 align:middle line:84% So for example, let's consider solid metal 00:42:06.080 --> 00:42:12.390 align:middle line:90% plus O2 going to MO2 solid. 00:42:12.390 --> 00:42:13.860 align:middle line:90% Reaction one. 00:42:13.860 --> 00:42:18.220 align:middle line:90% This says standard entropy 1. 00:42:18.220 --> 00:42:18.920 align:middle line:90% It's negative. 00:42:18.920 --> 00:42:22.180 align:middle line:84% It's negative, because we're pulling oxygen gas out 00:42:22.180 --> 00:42:24.760 align:middle line:90% of the gas, right? 00:42:24.760 --> 00:42:26.240 align:middle line:90% Solids. 00:42:26.240 --> 00:42:26.740 align:middle line:90% Solids. 00:42:26.740 --> 00:42:29.560 align:middle line:90% 00:42:29.560 --> 00:42:47.720 align:middle line:84% Now, consider case where metal melts at lower temp than MO2. 00:42:47.720 --> 00:42:49.290 align:middle line:84% So metals have a lower melting point, 00:42:49.290 --> 00:42:52.520 align:middle line:84% which is true for most but all oxides. 00:42:52.520 --> 00:43:02.910 align:middle line:84% And raise the temp until then the metal solid 00:43:02.910 --> 00:43:04.055 align:middle line:90% becomes liquid metal. 00:43:04.055 --> 00:43:05.430 align:middle line:84% So that's what we're going to do. 00:43:05.430 --> 00:43:08.160 align:middle line:84% We're going to consider that, and now we're 00:43:08.160 --> 00:43:12.090 align:middle line:84% going to consider the oxidation again, except now we're 00:43:12.090 --> 00:43:13.410 align:middle line:90% oxidizing liquid metal. 00:43:13.410 --> 00:43:17.760 align:middle line:90% 00:43:17.760 --> 00:43:22.140 align:middle line:84% So the oxide is still solid but the metal is now liquid. 00:43:22.140 --> 00:43:30.780 align:middle line:84% And we'll call this reaction to have delta S02 Well, we 00:43:30.780 --> 00:43:39.640 align:middle line:84% know that the liquid metal has higher 00:43:39.640 --> 00:43:45.280 align:middle line:90% entropy than solid metal. 00:43:45.280 --> 00:43:48.680 align:middle line:90% 00:43:48.680 --> 00:43:50.460 align:middle line:90% We know that. 00:43:50.460 --> 00:43:56.350 align:middle line:84% So what that means is that delta S02 is 00:43:56.350 --> 00:44:01.030 align:middle line:84% going to be smaller than delta S01, 00:44:01.030 --> 00:44:02.380 align:middle line:90% and they're all less than 0. 00:44:02.380 --> 00:44:05.750 align:middle line:90% 00:44:05.750 --> 00:44:10.840 align:middle line:84% In other words, it's going to be even more negative. 00:44:10.840 --> 00:44:21.000 align:middle line:90% 00:44:21.000 --> 00:44:23.220 align:middle line:84% On a plot, it looks like as follows. 00:44:23.220 --> 00:44:30.880 align:middle line:90% 00:44:30.880 --> 00:44:32.830 align:middle line:90% There's temperature. 00:44:32.830 --> 00:44:41.520 align:middle line:84% This is delta G0, and we have a kink in the plot. 00:44:41.520 --> 00:44:44.410 align:middle line:84% The kink happens at the melting point. 00:44:44.410 --> 00:44:53.103 align:middle line:84% So here is metal melting at that temperature. 00:44:53.103 --> 00:45:00.500 align:middle line:90% 00:45:00.500 --> 00:45:04.150 align:middle line:84% The lower curve is a solid oxidation reaction-- 00:45:04.150 --> 00:45:10.920 align:middle line:90% 00:45:10.920 --> 00:45:14.730 align:middle line:90% solid metal oxidation. 00:45:14.730 --> 00:45:16.860 align:middle line:84% The upward curve is liquid metal oxidation. 00:45:16.860 --> 00:45:29.260 align:middle line:90% 00:45:29.260 --> 00:45:37.410 align:middle line:84% This intercept is delta H0 for solid metal oxidation, 00:45:37.410 --> 00:45:43.960 align:middle line:84% and this intercept is delta H0 for liquid metal oxidation. 00:45:43.960 --> 00:45:51.430 align:middle line:90% 00:45:51.430 --> 00:45:53.790 align:middle line:84% So let's go back to some real plots. 00:45:53.790 --> 00:45:57.190 align:middle line:90% 00:45:57.190 --> 00:45:59.080 align:middle line:84% So now we can understand why there 00:45:59.080 --> 00:46:01.480 align:middle line:90% are break points in these. 00:46:01.480 --> 00:46:04.300 align:middle line:84% There are break points in these curves, 00:46:04.300 --> 00:46:11.550 align:middle line:84% because at these transition points, the standard enthalpy 00:46:11.550 --> 00:46:14.820 align:middle line:84% and entropy of these reactions changes. 00:46:14.820 --> 00:46:18.230 align:middle line:84% So this melting point here of aluminum, 00:46:18.230 --> 00:46:19.800 align:middle line:84% it changes the slope very slightly. 00:46:19.800 --> 00:46:21.180 align:middle line:90% You can't really see it. 00:46:21.180 --> 00:46:23.400 align:middle line:84% You can't really see it, but there is a slope change. 00:46:23.400 --> 00:46:26.870 align:middle line:84% Then up here, the aluminum boils. 00:46:26.870 --> 00:46:32.290 align:middle line:84% So there's another break in the slope. 00:46:32.290 --> 00:46:33.355 align:middle line:90% Here, manganese melts. 00:46:33.355 --> 00:46:36.570 align:middle line:90% 00:46:36.570 --> 00:46:38.880 align:middle line:90% Here, the manganese melts. 00:46:38.880 --> 00:46:44.120 align:middle line:90% Here, zinc melts and zinc boils. 00:46:44.120 --> 00:46:45.270 align:middle line:90% So forth and so on. 00:46:45.270 --> 00:46:50.150 align:middle line:84% And if you want to really lose your mind, 00:46:50.150 --> 00:46:58.440 align:middle line:84% you can look at more complete Ellingham diagrams. 00:46:58.440 --> 00:47:01.140 align:middle line:84% So this is posted on the website. 00:47:01.140 --> 00:47:05.100 align:middle line:84% And this is a very, very, very thorough Ellingham diagram 00:47:05.100 --> 00:47:08.040 align:middle line:84% now with so many elements and melting 00:47:08.040 --> 00:47:10.740 align:middle line:84% points and boiling points and so forth. 00:47:10.740 --> 00:47:12.270 align:middle line:84% And you can start to look at these 00:47:12.270 --> 00:47:14.670 align:middle line:84% and learn what the melting points and the boiling points 00:47:14.670 --> 00:47:16.410 align:middle line:84% of the metals and the oxides are, 00:47:16.410 --> 00:47:19.080 align:middle line:84% and you can see how they change the slope of these curves. 00:47:19.080 --> 00:47:21.900 align:middle line:84% There are cases where the slope actually dips downward 00:47:21.900 --> 00:47:23.130 align:middle line:90% for a little while. 00:47:23.130 --> 00:47:28.990 align:middle line:84% That's typically a melting point of an oxide and so forth. 00:47:28.990 --> 00:47:32.713 align:middle line:84% And if you really like to explore this a little more, 00:47:32.713 --> 00:47:33.880 align:middle line:90% which I encourage you to do. 00:47:33.880 --> 00:47:36.030 align:middle line:90% It's a nice way to learn. 00:47:36.030 --> 00:47:41.102 align:middle line:84% Go to DoITPoMS page with Ellingham diagrams. 00:47:41.102 --> 00:47:42.810 align:middle line:84% For those of you who don't know DoITPoMS, 00:47:42.810 --> 00:47:43.920 align:middle line:90% you should know DoITPoMS. 00:47:43.920 --> 00:47:49.750 align:middle line:84% It's a really excellent resource for learning material science 00:47:49.750 --> 00:47:50.500 align:middle line:90% concepts. 00:47:50.500 --> 00:47:55.500 align:middle line:84% It's maintained by University of Cambridge, 00:47:55.500 --> 00:47:57.000 align:middle line:84% and it's a nice complement to things 00:47:57.000 --> 00:47:59.400 align:middle line:90% like OpenCourseWare and MIT. 00:47:59.400 --> 00:48:01.980 align:middle line:90% 00:48:01.980 --> 00:48:03.930 align:middle line:84% Let me share that just to show you 00:48:03.930 --> 00:48:11.440 align:middle line:84% where you might go to play with this a little more, 00:48:11.440 --> 00:48:12.880 align:middle line:90% get a feel for it. 00:48:12.880 --> 00:48:20.770 align:middle line:84% So here is the DoITPoMS page for Ellingham diagrams, 00:48:20.770 --> 00:48:24.630 align:middle line:84% and if you click on oxides, there's 00:48:24.630 --> 00:48:25.630 align:middle line:90% a whole bunch of oxides. 00:48:25.630 --> 00:48:28.255 align:middle line:84% And so let's go at random cobalt oxide. 00:48:28.255 --> 00:48:29.990 align:middle line:90% See Ellingham diagram. 00:48:29.990 --> 00:48:35.320 align:middle line:84% So it now shows you Ellingham diagrams for cobalt for its two 00:48:35.320 --> 00:48:37.120 align:middle line:90% different oxidation states. 00:48:37.120 --> 00:48:41.500 align:middle line:84% And it will give you data, you can mouse around, 00:48:41.500 --> 00:48:43.932 align:middle line:90% get the actual numbers. 00:48:43.932 --> 00:48:44.890 align:middle line:90% Change the temperature. 00:48:44.890 --> 00:48:47.530 align:middle line:84% It gives you free energy information, and so forth. 00:48:47.530 --> 00:48:50.110 align:middle line:90% And it's a nice learning tool. 00:48:50.110 --> 00:48:56.460 align:middle line:84% So now I will call it a day and stop recording. 00:48:56.460 --> 00:49:05.000 align:middle line:90%