WEBVTT 00:00:00.000 --> 00:00:02.970 align:middle line:90% [SQUEAKING] 00:00:02.970 --> 00:00:04.455 align:middle line:90% [RUSTLING] 00:00:04.455 --> 00:00:07.425 align:middle line:90% [CLICKING] 00:00:07.425 --> 00:00:12.375 align:middle line:90% 00:00:12.375 --> 00:00:17.238 align:middle line:84% RAFAEL JARAMILLO: OK, so today we are starting a new topic. 00:00:17.238 --> 00:00:18.780 align:middle line:84% We're done with unary phase diagrams. 00:00:18.780 --> 00:00:24.510 align:middle line:84% We are going to start reacting gas systems. 00:00:24.510 --> 00:00:29.250 align:middle line:84% And it's useful, not just because it's useful 00:00:29.250 --> 00:00:34.450 align:middle line:84% and it's all right, but because it's an entree for solutions. 00:00:34.450 --> 00:00:43.500 align:middle line:84% So just a bit of topic here, we have start, 00:00:43.500 --> 00:00:49.400 align:middle line:84% and then we went to-- we did some heat engines. 00:00:49.400 --> 00:00:55.760 align:middle line:84% We did a little bit of heat engines, a little bit. 00:00:55.760 --> 00:00:59.770 align:middle line:90% And this is where the course-- 00:00:59.770 --> 00:01:01.520 align:middle line:84% this is where the course do people get off 00:01:01.520 --> 00:01:03.140 align:middle line:90% the bus, at the engines. 00:01:03.140 --> 00:01:05.630 align:middle line:84% But we stayed on the bus, and then we're 00:01:05.630 --> 00:01:12.620 align:middle line:84% going to do a little bit of reacting gas reacting gases. 00:01:12.620 --> 00:01:15.690 align:middle line:84% We're going to do a little bit of that. 00:01:15.690 --> 00:01:19.750 align:middle line:84% And after this, this is where the course 10 people 00:01:19.750 --> 00:01:21.160 align:middle line:90% get off the bus. 00:01:21.160 --> 00:01:24.310 align:middle line:84% They get off the bus here, but we stay on the bus. 00:01:24.310 --> 00:01:26.800 align:middle line:84% And reacting gases-- we're doing it 00:01:26.800 --> 00:01:29.830 align:middle line:84% because in addition to being useful, 00:01:29.830 --> 00:01:33.820 align:middle line:90% it sets us up for solutions. 00:01:33.820 --> 00:01:36.640 align:middle line:84% And I mean mixtures, not answers. 00:01:36.640 --> 00:01:39.100 align:middle line:90% So this is where this goes. 00:01:39.100 --> 00:01:42.640 align:middle line:84% And I find this interesting because thermo 00:01:42.640 --> 00:01:44.950 align:middle line:84% is a weird topic in that it's taught by, 00:01:44.950 --> 00:01:49.200 align:middle line:84% like seven or eight different courses at MIT. 00:01:49.200 --> 00:01:51.322 align:middle line:84% You don't have that with multivariable calculus. 00:01:51.322 --> 00:01:53.280 align:middle line:84% You don't have seven different classes teaching 00:01:53.280 --> 00:01:55.810 align:middle line:90% their all multi and others. 00:01:55.810 --> 00:01:58.110 align:middle line:84% But thermo is really unique in that we 00:01:58.110 --> 00:02:01.350 align:middle line:84% have so many different disciplines teaching thermo, 00:02:01.350 --> 00:02:02.800 align:middle line:90% and we each have our own flavor. 00:02:02.800 --> 00:02:04.020 align:middle line:90% So that's that. 00:02:04.020 --> 00:02:06.270 align:middle line:90% So anyway, let's get started. 00:02:06.270 --> 00:02:15.560 align:middle line:84% Gas mixtures-- and what do I mean? 00:02:15.560 --> 00:02:23.580 align:middle line:84% Homogeneous now, homogeneous multi component. 00:02:23.580 --> 00:02:28.300 align:middle line:90% 00:02:28.300 --> 00:02:30.320 align:middle line:84% So this is a complement of what we just did. 00:02:30.320 --> 00:02:31.300 align:middle line:90% We did unary. 00:02:31.300 --> 00:02:35.170 align:middle line:84% Unary was one component, multiple phases. 00:02:35.170 --> 00:02:40.480 align:middle line:84% Now, we have multiple components, one phase. 00:02:40.480 --> 00:02:42.490 align:middle line:84% So let's get that clear in our head. 00:02:42.490 --> 00:02:44.920 align:middle line:90% So let's talk about air. 00:02:44.920 --> 00:02:47.960 align:middle line:90% 00:02:47.960 --> 00:02:51.350 align:middle line:90% Air, what's in air? 00:02:51.350 --> 00:02:53.060 align:middle line:90% Here's my bucket of air. 00:02:53.060 --> 00:02:54.320 align:middle line:90% What's in my bucket of air? 00:02:54.320 --> 00:02:58.980 align:middle line:90% 00:02:58.980 --> 00:03:01.590 align:middle line:84% AUDIENCE: Primarily oxygen, then nitrogen. 00:03:01.590 --> 00:03:04.110 align:middle line:84% RAFAEL JARAMILLO: Primarily nitrogen-- 00:03:04.110 --> 00:03:09.843 align:middle line:84% about 80% by mole than oxygen. So it's a mixture of those. 00:03:09.843 --> 00:03:10.760 align:middle line:90% What else is in there? 00:03:10.760 --> 00:03:15.370 align:middle line:84% Just kind of curiosity, what else do you know to be in air? 00:03:15.370 --> 00:03:18.000 align:middle line:84% What's the third dominant component? 00:03:18.000 --> 00:03:19.640 align:middle line:90% AUDIENCE: Argon maybe. 00:03:19.640 --> 00:03:20.640 align:middle line:90% RAFAEL JARAMILLO: Sorry? 00:03:20.640 --> 00:03:22.642 align:middle line:90% AUDIENCE: Argon. 00:03:22.642 --> 00:03:23.850 align:middle line:90% RAFAEL JARAMILLO: Argon, yes. 00:03:23.850 --> 00:03:26.433 align:middle line:84% Yeah, sorry, I had a hard time understanding you for a minute. 00:03:26.433 --> 00:03:28.980 align:middle line:84% Yeah, argon is the third major-- the third-- 00:03:28.980 --> 00:03:32.040 align:middle line:84% it's not a principal component because 1% or something. 00:03:32.040 --> 00:03:35.910 align:middle line:84% But it's, I think, the third most prevalent component. 00:03:35.910 --> 00:03:37.770 align:middle line:90% H2O, we know H2O is in air. 00:03:37.770 --> 00:03:39.210 align:middle line:90% We talked all about humid air. 00:03:39.210 --> 00:03:42.640 align:middle line:90% 00:03:42.640 --> 00:03:44.930 align:middle line:90% CO2, of course, is in there. 00:03:44.930 --> 00:03:46.400 align:middle line:90% And there are others. 00:03:46.400 --> 00:03:48.370 align:middle line:90% So let's say that that's air. 00:03:48.370 --> 00:03:50.890 align:middle line:84% So there we have our bucket of air. 00:03:50.890 --> 00:03:55.175 align:middle line:90% So the phase is gas. 00:03:55.175 --> 00:03:58.130 align:middle line:90% 00:03:58.130 --> 00:04:04.610 align:middle line:84% The components-- the components are what we just mentioned. 00:04:04.610 --> 00:04:09.860 align:middle line:84% There's nitrogen. There's oxygen. There's argon. 00:04:09.860 --> 00:04:11.540 align:middle line:90% There's water. 00:04:11.540 --> 00:04:14.820 align:middle line:84% There's carbon dioxide and so forth. 00:04:14.820 --> 00:04:15.890 align:middle line:90% Those are the components. 00:04:15.890 --> 00:04:24.020 align:middle line:84% And the components are not to be confused with elements, OK 00:04:24.020 --> 00:04:30.320 align:middle line:84% elements are nitrogen, oxygen, argon, hydrogen, carbon, OK, 00:04:30.320 --> 00:04:32.257 align:middle line:84% so don't confuse elements and components, 00:04:32.257 --> 00:04:33.590 align:middle line:90% although sometimes they overlap. 00:04:33.590 --> 00:04:40.587 align:middle line:90% 00:04:40.587 --> 00:04:42.420 align:middle line:84% All right, let's get right into Dalton's law 00:04:42.420 --> 00:04:43.990 align:middle line:90% because this is important. 00:04:43.990 --> 00:04:46.140 align:middle line:84% We've talked about it in the previous lecture. 00:04:46.140 --> 00:04:47.790 align:middle line:84% This is a little bit of a preview. 00:04:47.790 --> 00:04:50.410 align:middle line:84% Apparently Professor Carter has been talking about it. 00:04:50.410 --> 00:04:52.630 align:middle line:90% So it's in the air. 00:04:52.630 --> 00:04:53.130 align:middle line:90% Get it? 00:04:53.130 --> 00:04:54.800 align:middle line:90% That was an air pun. 00:04:54.800 --> 00:04:56.580 align:middle line:84% Darton's law of partial pressures-- 00:04:56.580 --> 00:05:01.350 align:middle line:90% 00:05:01.350 --> 00:05:03.210 align:middle line:84% Dalton's law of partial pressures. 00:05:03.210 --> 00:05:05.130 align:middle line:84% All right, so I'm just going to write it out. 00:05:05.130 --> 00:05:06.780 align:middle line:90% In a gas mixture-- 00:05:06.780 --> 00:05:11.250 align:middle line:90% 00:05:11.250 --> 00:05:32.560 align:middle line:84% so gas mixture-- each component contributes a partial pressure 00:05:32.560 --> 00:05:40.525 align:middle line:84% in proportion to its mole fraction. 00:05:40.525 --> 00:05:45.910 align:middle line:90% 00:05:45.910 --> 00:05:50.220 align:middle line:84% All right, so this is full of thermodynamics terms here. 00:05:50.220 --> 00:05:53.730 align:middle line:84% Let's highlight on component, mole fraction, 00:05:53.730 --> 00:05:54.570 align:middle line:90% partial pressure. 00:05:54.570 --> 00:05:57.460 align:middle line:90% 00:05:57.460 --> 00:05:59.100 align:middle line:90% It's also a mixture. 00:05:59.100 --> 00:06:00.800 align:middle line:84% It's full of thermal concepts in here. 00:06:00.800 --> 00:06:03.300 align:middle line:84% And I won't circle gas because that's not really new for us. 00:06:03.300 --> 00:06:06.680 align:middle line:84% But, all right, so what does that mean? 00:06:06.680 --> 00:06:13.760 align:middle line:84% So, for example, if I have two components, 00:06:13.760 --> 00:06:14.890 align:middle line:90% this is how we label it. 00:06:14.890 --> 00:06:18.820 align:middle line:84% The pressure of the system equals pressure 1 00:06:18.820 --> 00:06:23.410 align:middle line:84% plus pressure 2 I think you'll remember that we 00:06:23.410 --> 00:06:32.260 align:middle line:90% use subscripts for components. 00:06:32.260 --> 00:06:36.570 align:middle line:90% 00:06:36.570 --> 00:06:38.250 align:middle line:90% Subscripts are for components. 00:06:38.250 --> 00:06:42.480 align:middle line:90% 00:06:42.480 --> 00:06:45.240 align:middle line:84% We won't have any phase labels here because it's one phase. 00:06:45.240 --> 00:06:45.910 align:middle line:90% It's only gas. 00:06:45.910 --> 00:06:47.785 align:middle line:84% So we don't have to worry about phase labels, 00:06:47.785 --> 00:06:51.100 align:middle line:84% but we do have subscripts for components. 00:06:51.100 --> 00:06:55.284 align:middle line:84% And in order to find the partial pressure for component i, 00:06:55.284 --> 00:07:01.270 align:middle line:84% you take the total pressure, and you multiply by the moles of i 00:07:01.270 --> 00:07:06.310 align:middle line:84% over the total moles of gas in the system. 00:07:06.310 --> 00:07:10.030 align:middle line:84% And we already have seen that we have a symbol. 00:07:10.030 --> 00:07:15.830 align:middle line:90% We use X for the mole fraction-- 00:07:15.830 --> 00:07:24.270 align:middle line:90% 00:07:24.270 --> 00:07:25.155 align:middle line:90% mole fraction sub i. 00:07:25.155 --> 00:07:29.420 align:middle line:90% 00:07:29.420 --> 00:07:33.410 align:middle line:84% All right, so there's a lot here actually. 00:07:33.410 --> 00:07:34.295 align:middle line:90% It may look simple. 00:07:34.295 --> 00:07:37.500 align:middle line:90% 00:07:37.500 --> 00:07:39.780 align:middle line:84% That's sort of a deceptively simple question. 00:07:39.780 --> 00:07:42.840 align:middle line:90% Are partial pressure real? 00:07:42.840 --> 00:07:47.100 align:middle line:84% Are these real measurable things or are these concepts 00:07:47.100 --> 00:07:49.692 align:middle line:84% that we just use out of convenience? 00:07:49.692 --> 00:07:51.400 align:middle line:84% AUDIENCE: Aren't partial pressure is just 00:07:51.400 --> 00:07:53.500 align:middle line:84% like different pressures at different places 00:07:53.500 --> 00:07:57.087 align:middle line:90% within like a material? 00:07:57.087 --> 00:07:59.420 align:middle line:84% RAFAEL JARAMILLO: So we're assuming that the pressure is 00:07:59.420 --> 00:08:00.215 align:middle line:90% everywhere uniform. 00:08:00.215 --> 00:08:02.990 align:middle line:90% 00:08:02.990 --> 00:08:07.050 align:middle line:84% So it can't be different places, not exactly. 00:08:07.050 --> 00:08:09.972 align:middle line:84% But maybe you're on to something. 00:08:09.972 --> 00:08:11.570 align:middle line:84% AUDIENCE: I think I've have seen, 00:08:11.570 --> 00:08:13.880 align:middle line:84% like the pressure is uniform, which is 00:08:13.880 --> 00:08:16.140 align:middle line:90% kind of like force over area. 00:08:16.140 --> 00:08:20.450 align:middle line:84% So if we take any random area since like very small fraction 00:08:20.450 --> 00:08:24.230 align:middle line:84% like 50% or like 80% is nitrogen, 00:08:24.230 --> 00:08:27.470 align:middle line:84% 80% of the like momentum heading that area 00:08:27.470 --> 00:08:30.240 align:middle line:90% is from nitrogen molecules. 00:08:30.240 --> 00:08:32.809 align:middle line:84% So it's kind of like having 80% contribution 00:08:32.809 --> 00:08:34.760 align:middle line:90% to the total pressure. 00:08:34.760 --> 00:08:36.809 align:middle line:84% But it's because of a small fraction. 00:08:36.809 --> 00:08:39.380 align:middle line:84% Maybe like we have a chemical reaction that's only permitting 00:08:39.380 --> 00:08:42.350 align:middle line:84% one, it would only work as a spare 00:08:42.350 --> 00:08:49.450 align:middle line:84% as, like 80% pressure of the nitrogen that penetrate. 00:08:49.450 --> 00:08:52.360 align:middle line:84% RAFAEL JARAMILLO: OK, that's good. 00:08:52.360 --> 00:08:55.930 align:middle line:84% So here's a gas mixture, red and green. 00:08:55.930 --> 00:08:57.700 align:middle line:90% And those gases're in a box. 00:08:57.700 --> 00:09:03.690 align:middle line:84% So one thing you can think is pressure is forced by area. 00:09:03.690 --> 00:09:08.000 align:middle line:84% So these gases-- the molecules hit the side of the box, 00:09:08.000 --> 00:09:09.590 align:middle line:90% and they bounce off. 00:09:09.590 --> 00:09:13.280 align:middle line:84% And maybe 80% of the force experienced by any given 00:09:13.280 --> 00:09:19.230 align:middle line:84% patch of the wall comes from nitrogen 00:09:19.230 --> 00:09:23.460 align:middle line:84% and 20% comes from oxygen. If it's air, 80 20. 00:09:23.460 --> 00:09:26.580 align:middle line:84% So that's a good way of thinking about it. 00:09:26.580 --> 00:09:31.110 align:middle line:84% Or you could say 80% of all the molecules 00:09:31.110 --> 00:09:36.150 align:middle line:84% that hit the wall are nitrogen and 20% are air. 00:09:36.150 --> 00:09:38.400 align:middle line:84% So the pressure is proportional to the mole fraction. 00:09:38.400 --> 00:09:40.950 align:middle line:84% That's exactly what we're saying, that-- 00:09:40.950 --> 00:09:46.478 align:middle line:84% but that-- that's the right way to think about it. 00:09:46.478 --> 00:09:48.270 align:middle line:84% But you can really go down the rabbit hole. 00:09:48.270 --> 00:09:56.340 align:middle line:84% Because if you have a force transducer, it measures force. 00:09:56.340 --> 00:09:59.040 align:middle line:90% It doesn't measure chemistry. 00:09:59.040 --> 00:10:01.230 align:middle line:84% It doesn't know whether what hit it was a nitrogen 00:10:01.230 --> 00:10:05.190 align:middle line:90% molecule or an oxygen molecule. 00:10:05.190 --> 00:10:06.800 align:middle line:84% So you can really head down this path. 00:10:06.800 --> 00:10:10.160 align:middle line:84% And you can convince yourself that partial pressure-- 00:10:10.160 --> 00:10:14.270 align:middle line:84% although it's very adjacent to a lot of measurable things, 00:10:14.270 --> 00:10:16.838 align:middle line:84% and it's very, very adjacent to electrochemistry-- 00:10:16.838 --> 00:10:19.130 align:middle line:84% it may not seem that we're close to electric chemistry. 00:10:19.130 --> 00:10:19.760 align:middle line:90% We really are. 00:10:19.760 --> 00:10:22.640 align:middle line:84% We're very close to electric chemistry. 00:10:22.640 --> 00:10:26.278 align:middle line:84% Itself is kind of an immeasurable concept. 00:10:26.278 --> 00:10:28.320 align:middle line:84% Anyway, I don't want to go down that rabbit hole, 00:10:28.320 --> 00:10:29.680 align:middle line:90% but it's worth thinking about. 00:10:29.680 --> 00:10:30.924 align:middle line:90% It's interesting. 00:10:30.924 --> 00:10:34.170 align:middle line:90% 00:10:34.170 --> 00:10:39.660 align:middle line:84% So let's move on with foundational concepts here. 00:10:39.660 --> 00:10:41.310 align:middle line:90% We did partial pressure. 00:10:41.310 --> 00:10:42.870 align:middle line:90% Let's talk about reactions. 00:10:42.870 --> 00:10:47.900 align:middle line:90% 00:10:47.900 --> 00:10:49.265 align:middle line:90% Reactions can change. 00:10:49.265 --> 00:10:54.210 align:middle line:90% 00:10:54.210 --> 00:10:55.700 align:middle line:90% They can change components. 00:10:55.700 --> 00:10:59.350 align:middle line:90% 00:10:59.350 --> 00:11:10.510 align:middle line:84% Or they can change phases or both, but not elements. 00:11:10.510 --> 00:11:16.510 align:middle line:90% 00:11:16.510 --> 00:11:22.245 align:middle line:84% So right now, we're doing multi component unary. 00:11:22.245 --> 00:11:25.190 align:middle line:90% 00:11:25.190 --> 00:11:27.170 align:middle line:84% So now, we're dealing with reactions 00:11:27.170 --> 00:11:29.120 align:middle line:84% that can change components, but everything 00:11:29.120 --> 00:11:32.160 align:middle line:90% is remaining in the gas phase. 00:11:32.160 --> 00:11:36.530 align:middle line:90% So phases, that's later. 00:11:36.530 --> 00:11:38.090 align:middle line:84% I mean, we actually did that already 00:11:38.090 --> 00:11:39.545 align:middle line:84% when we did unary transformations, 00:11:39.545 --> 00:11:41.420 align:middle line:84% but we didn't talk about them like reactions. 00:11:41.420 --> 00:11:41.990 align:middle line:90% But you can. 00:11:41.990 --> 00:11:43.430 align:middle line:90% It's fine. 00:11:43.430 --> 00:11:47.330 align:middle line:90% And this is course 22. 00:11:47.330 --> 00:11:52.190 align:middle line:84% So if you're changing the elements, go to course 22. 00:11:52.190 --> 00:11:53.545 align:middle line:90% But the formulism is the same. 00:11:53.545 --> 00:11:54.170 align:middle line:90% It actually is. 00:11:54.170 --> 00:11:55.640 align:middle line:90% It's just-- all right. 00:11:55.640 --> 00:11:59.500 align:middle line:84% So reactions can change components and phase. 00:11:59.500 --> 00:12:00.610 align:middle line:90% So here's an example. 00:12:00.610 --> 00:12:02.790 align:middle line:90% Let's see, here's an example-- 00:12:02.790 --> 00:12:19.670 align:middle line:84% a reaction that changes components but not phase. 00:12:19.670 --> 00:12:22.910 align:middle line:84% Reaction that can change its components but not phase. 00:12:22.910 --> 00:12:26.840 align:middle line:90% 1/2 nitrogen gas-- 00:12:26.840 --> 00:12:31.393 align:middle line:84% I'll carry the phase labels here just in a simple way just for-- 00:12:31.393 --> 00:12:32.810 align:middle line:84% since we're just getting started-- 00:12:32.810 --> 00:12:40.520 align:middle line:90% 1/2 oxygen gas equals NO2 gas. 00:12:40.520 --> 00:12:44.500 align:middle line:84% So same phase-- this is a mixture 00:12:44.500 --> 00:12:47.780 align:middle line:84% changed components, but not the phase. 00:12:47.780 --> 00:12:50.140 align:middle line:84% Here's another example-- a reaction 00:12:50.140 --> 00:12:56.825 align:middle line:84% that changes components and phase. 00:12:56.825 --> 00:13:04.110 align:middle line:90% 00:13:04.110 --> 00:13:06.090 align:middle line:84% A reaction that changes components and phase. 00:13:06.090 --> 00:13:17.770 align:middle line:84% You can have H2 gas plus 1/2 O2 gas go to H2O liquid. 00:13:17.770 --> 00:13:22.020 align:middle line:90% So that's a common reaction. 00:13:22.020 --> 00:13:28.350 align:middle line:84% We're not going to deal with reacting heterogeneous systems 00:13:28.350 --> 00:13:29.582 align:middle line:90% for weeks and weeks. 00:13:29.582 --> 00:13:31.290 align:middle line:84% So we're not going to deal with that yet, 00:13:31.290 --> 00:13:32.970 align:middle line:84% but I just wanted to let you know 00:13:32.970 --> 00:13:34.890 align:middle line:84% that everything we're writing down 00:13:34.890 --> 00:13:36.630 align:middle line:84% here-- the formalism for reactions-- 00:13:36.630 --> 00:13:39.480 align:middle line:84% will apply to more complicated situations. 00:13:39.480 --> 00:13:45.350 align:middle line:84% Now, before I move on, I want to-- 00:13:45.350 --> 00:13:46.690 align:middle line:90% the attendance is low today. 00:13:46.690 --> 00:13:51.090 align:middle line:84% So if there are reasons for that that I should know, 00:13:51.090 --> 00:13:53.575 align:middle line:90% please tell me. 00:13:53.575 --> 00:13:54.700 align:middle line:90% You won't hurt my feelings. 00:13:54.700 --> 00:13:57.000 align:middle line:90% I'm really curious. 00:13:57.000 --> 00:13:58.230 align:middle line:90% Why do I bring that up now? 00:13:58.230 --> 00:14:01.080 align:middle line:84% I want to remind you, those who are here today, 00:14:01.080 --> 00:14:08.052 align:middle line:84% that the reading for today and on Monday is in Denbigh. 00:14:08.052 --> 00:14:10.430 align:middle line:90% So the PDF is on the website. 00:14:10.430 --> 00:14:13.360 align:middle line:84% So we're changing books because Denbigh 00:14:13.360 --> 00:14:17.633 align:middle line:84% treats reacting chemical systems much better than DeHoff. 00:14:17.633 --> 00:14:18.925 align:middle line:90% Denbigh is a chemical engineer. 00:14:18.925 --> 00:14:23.360 align:middle line:90% 00:14:23.360 --> 00:14:27.330 align:middle line:84% This is an exceptionally well-written text. 00:14:27.330 --> 00:14:32.737 align:middle line:84% So don't be put off by the fact that it's got some years on it. 00:14:32.737 --> 00:14:34.070 align:middle line:90% It's exceptionally well written. 00:14:34.070 --> 00:14:35.490 align:middle line:84% And as with the rest of the class, 00:14:35.490 --> 00:14:37.940 align:middle line:84% if you're not doing the reading associated with lecture, 00:14:37.940 --> 00:14:40.015 align:middle line:84% if you're not doing the reading ahead of time, 00:14:40.015 --> 00:14:42.140 align:middle line:84% and if you're not working the problems in the text, 00:14:42.140 --> 00:14:43.723 align:middle line:84% you're not getting your money's worth. 00:14:43.723 --> 00:14:46.100 align:middle line:84% So please do keep up with the reading, 00:14:46.100 --> 00:14:49.100 align:middle line:84% especially on a topic like this where it's a little bit-- it's 00:14:49.100 --> 00:14:52.520 align:middle line:84% just a little bit outside of the mainstream of material science. 00:14:52.520 --> 00:14:54.350 align:middle line:90% It's not just covered in DeHoff. 00:14:54.350 --> 00:14:56.635 align:middle line:84% And there are so many textbooks on this topic, 00:14:56.635 --> 00:14:58.010 align:middle line:84% and I picked the one that I think 00:14:58.010 --> 00:14:59.750 align:middle line:84% is just the most elegantly written, 00:14:59.750 --> 00:15:02.010 align:middle line:84% really intellectually very clear. 00:15:02.010 --> 00:15:05.515 align:middle line:84% So I hope that you find the same. 00:15:05.515 --> 00:15:07.140 align:middle line:84% Also, some of the problems on the p set 00:15:07.140 --> 00:15:08.307 align:middle line:90% are straight out of Denbigh. 00:15:08.307 --> 00:15:09.930 align:middle line:90% So there's that too. 00:15:09.930 --> 00:15:14.935 align:middle line:84% All right, so let us move on, more really foundational 00:15:14.935 --> 00:15:15.435 align:middle line:90% concepts. 00:15:15.435 --> 00:15:20.450 align:middle line:90% 00:15:20.450 --> 00:15:36.950 align:middle line:84% Ideal gas mixtures-- and throughout this course, 00:15:36.950 --> 00:15:39.720 align:middle line:84% I often use mixtures or solutions interchangeably. 00:15:39.720 --> 00:15:41.570 align:middle line:84% They're always going to mean the same thing. 00:15:41.570 --> 00:15:45.982 align:middle line:90% 00:15:45.982 --> 00:15:47.440 align:middle line:84% All right, so we're going to set up 00:15:47.440 --> 00:15:49.440 align:middle line:84% a little bit of a toy problem, sort of a thought 00:15:49.440 --> 00:15:51.210 align:middle line:90% experiment here. 00:15:51.210 --> 00:15:52.460 align:middle line:90% Here's the thought experiment. 00:15:52.460 --> 00:15:53.502 align:middle line:90% It's a really simple one. 00:15:53.502 --> 00:16:02.040 align:middle line:90% 00:16:02.040 --> 00:16:04.260 align:middle line:90% We've got a box. 00:16:04.260 --> 00:16:06.240 align:middle line:84% And as so often happens in thermodynamics, 00:16:06.240 --> 00:16:09.730 align:middle line:84% we find ourselves with the box that's been partitioned. 00:16:09.730 --> 00:16:17.250 align:middle line:84% And we have now two components in their pure state, not mixed. 00:16:17.250 --> 00:16:21.390 align:middle line:90% Let's call this pure number 1. 00:16:21.390 --> 00:16:23.640 align:middle line:84% You can think of this as a nitrogen, pure nitrogen gas 00:16:23.640 --> 00:16:24.990 align:middle line:90% if you like. 00:16:24.990 --> 00:16:28.110 align:middle line:84% It's at some-- it's at a temperature. 00:16:28.110 --> 00:16:30.290 align:middle line:90% It's at a pressure. 00:16:30.290 --> 00:16:34.490 align:middle line:84% And it is at a volume, and I'm using that tag there 00:16:34.490 --> 00:16:36.570 align:middle line:84% for an extensive quantity of volume. 00:16:36.570 --> 00:16:37.940 align:middle line:90% So there's pure number one. 00:16:37.940 --> 00:16:47.570 align:middle line:84% And then we've got in the other part, pure number 2. 00:16:47.570 --> 00:16:50.380 align:middle line:90% 00:16:50.380 --> 00:16:52.898 align:middle line:90% It's orange and green. 00:16:52.898 --> 00:16:54.940 align:middle line:84% I'm like three days delayed for St Patrick's Day, 00:16:54.940 --> 00:16:56.470 align:middle line:90% but I got there. 00:16:56.470 --> 00:17:01.120 align:middle line:84% All right, temperature, pressure, and volume. 00:17:01.120 --> 00:17:03.520 align:middle line:84% And although it may not look like it in my drawing, 00:17:03.520 --> 00:17:06.250 align:middle line:84% I intended for those volumes to be equal. 00:17:06.250 --> 00:17:08.130 align:middle line:84% So here's a very simple situation. 00:17:08.130 --> 00:17:13.329 align:middle line:84% And this really brings us back to the baby book almost. 00:17:13.329 --> 00:17:19.621 align:middle line:84% We've got these gases, and we're going to mix them. 00:17:19.621 --> 00:17:21.579 align:middle line:84% Are there any other national flags that combine 00:17:21.579 --> 00:17:23.970 align:middle line:90% orange and green? 00:17:23.970 --> 00:17:27.970 align:middle line:84% Those colors have nice contrast, orange and green. 00:17:27.970 --> 00:17:29.200 align:middle line:90% AUDIENCE: Ireland, I think. 00:17:29.200 --> 00:17:30.575 align:middle line:84% RAFAEL JARAMILLO: I think there's 00:17:30.575 --> 00:17:31.858 align:middle line:90% orange in the Indian flag. 00:17:31.858 --> 00:17:34.150 align:middle line:84% AUDIENCE: This-- yeah, I think some country too called, 00:17:34.150 --> 00:17:36.460 align:middle line:84% like the Ivory Coast that's basically 00:17:36.460 --> 00:17:39.130 align:middle line:90% just the Irish flag reversed. 00:17:39.130 --> 00:17:44.680 align:middle line:84% RAFAEL JARAMILLO: OK, OK, all right. 00:17:44.680 --> 00:17:47.180 align:middle line:90% Any others? 00:17:47.180 --> 00:17:49.790 align:middle line:84% Ivory Coast, I think India had the orange and green 00:17:49.790 --> 00:17:51.770 align:middle line:90% in the flag, Ireland. 00:17:51.770 --> 00:17:56.550 align:middle line:90% 00:17:56.550 --> 00:18:00.700 align:middle line:84% Anyway, all right, so now we've got a mixture of these things. 00:18:00.700 --> 00:18:01.320 align:middle line:90% So they mixed. 00:18:01.320 --> 00:18:03.880 align:middle line:90% 00:18:03.880 --> 00:18:05.790 align:middle line:90% There we go. 00:18:05.790 --> 00:18:10.880 align:middle line:84% And so we have a mixture of 1 and 2. 00:18:10.880 --> 00:18:13.860 align:middle line:90% 00:18:13.860 --> 00:18:17.820 align:middle line:84% I'll claim or just postulate for this model system 00:18:17.820 --> 00:18:20.100 align:middle line:90% that temperature didn't change. 00:18:20.100 --> 00:18:22.380 align:middle line:90% The pressure didn't change. 00:18:22.380 --> 00:18:26.530 align:middle line:90% And we have twice the volume. 00:18:26.530 --> 00:18:31.277 align:middle line:84% And if you don't believe me, it's PV equals nRT. 00:18:31.277 --> 00:18:32.610 align:middle line:90% You solve for the moles of this. 00:18:32.610 --> 00:18:33.943 align:middle line:90% You solve for the moles of this. 00:18:33.943 --> 00:18:39.290 align:middle line:84% You add them together, a very simple situation. 00:18:39.290 --> 00:18:43.280 align:middle line:90% 00:18:43.280 --> 00:18:45.940 align:middle line:90% Why is it so simple? 00:18:45.940 --> 00:18:53.277 align:middle line:84% It's because ideal gas molecules don't interact. 00:18:53.277 --> 00:18:54.360 align:middle line:90% That's why it's so simple. 00:18:54.360 --> 00:18:57.760 align:middle line:90% 00:18:57.760 --> 00:19:00.510 align:middle line:90% They don't interact. 00:19:00.510 --> 00:19:14.770 align:middle line:84% Each component behaves as if it undergoes-- 00:19:14.770 --> 00:19:18.300 align:middle line:90% 00:19:18.300 --> 00:19:21.135 align:middle line:84% and here is kind of the less intuitive part. 00:19:21.135 --> 00:19:30.190 align:middle line:90% 00:19:30.190 --> 00:19:32.500 align:middle line:84% Each component behaves as if it's undergoing 00:19:32.500 --> 00:19:36.360 align:middle line:90% an isothermal expansion. 00:19:36.360 --> 00:19:38.760 align:middle line:84% And you could either choose to believe this 00:19:38.760 --> 00:19:39.960 align:middle line:90% or disbelieve this. 00:19:39.960 --> 00:19:41.647 align:middle line:90% It may or may not make sense. 00:19:41.647 --> 00:19:43.230 align:middle line:84% If it doesn't make sense, that's fine. 00:19:43.230 --> 00:19:44.490 align:middle line:90% Just treat it as a model. 00:19:44.490 --> 00:19:45.600 align:middle line:90% I'm showing you a model. 00:19:45.600 --> 00:19:46.320 align:middle line:90% It may apply. 00:19:46.320 --> 00:19:48.550 align:middle line:90% It may not. 00:19:48.550 --> 00:19:52.690 align:middle line:84% All right, so we know how to treat that. 00:19:52.690 --> 00:20:10.160 align:middle line:84% Delta G of component i equals nI RT log its partial pressure 00:20:10.160 --> 00:20:11.105 align:middle line:90% over the pressure. 00:20:11.105 --> 00:20:16.360 align:middle line:90% 00:20:16.360 --> 00:20:18.850 align:middle line:84% This is a really critical equation that 00:20:18.850 --> 00:20:21.310 align:middle line:90% comes from this assumption. 00:20:21.310 --> 00:20:23.200 align:middle line:84% We're using an expression for delta G 00:20:23.200 --> 00:20:26.240 align:middle line:84% for an isothermal process and ideal gas. 00:20:26.240 --> 00:20:29.630 align:middle line:84% And we are modeling that as an expansion from pressure 00:20:29.630 --> 00:20:34.310 align:middle line:90% P to partial pressure P sub i. 00:20:34.310 --> 00:20:40.090 align:middle line:90% 00:20:40.090 --> 00:20:47.640 align:middle line:84% So the Gibbs free energy is its starting value 00:20:47.640 --> 00:21:11.340 align:middle line:84% plus the change where Gi have 0nP 00:21:11.340 --> 00:21:14.610 align:middle line:84% because it's some standard state, however it started off. 00:21:14.610 --> 00:21:22.620 align:middle line:90% 00:21:22.620 --> 00:21:24.465 align:middle line:84% So they started off in a standard state. 00:21:24.465 --> 00:21:31.310 align:middle line:90% 00:21:31.310 --> 00:21:33.230 align:middle line:84% And they started off in a standard state. 00:21:33.230 --> 00:21:41.310 align:middle line:90% 00:21:41.310 --> 00:21:43.620 align:middle line:90% So this slide here-- 00:21:43.620 --> 00:21:46.590 align:middle line:84% this board-- there's a lot of intellectual content here. 00:21:46.590 --> 00:21:50.378 align:middle line:90% 00:21:50.378 --> 00:21:52.420 align:middle line:84% The equation might look simple, but there's a lot 00:21:52.420 --> 00:21:53.710 align:middle line:90% of intellectual content here. 00:21:53.710 --> 00:21:55.960 align:middle line:84% So it's going to take a little while and some practice 00:21:55.960 --> 00:21:58.870 align:middle line:90% to understand this fully. 00:21:58.870 --> 00:22:00.790 align:middle line:84% But I'll restate the assumption here. 00:22:00.790 --> 00:22:03.760 align:middle line:84% This model is that each component behaves as if it 00:22:03.760 --> 00:22:05.450 align:middle line:90% undergoes isothermal expansion. 00:22:05.450 --> 00:22:09.820 align:middle line:84% And if you buy that, then you can use the apparatus which 00:22:09.820 --> 00:22:11.800 align:middle line:84% we've already established, which is calculating 00:22:11.800 --> 00:22:15.730 align:middle line:84% the change in Gibbs free energy for an isothermal process 00:22:15.730 --> 00:22:19.990 align:middle line:84% as each gas expands from initial pressure P 00:22:19.990 --> 00:22:22.640 align:middle line:90% to partial pressure P sub i. 00:22:22.640 --> 00:22:27.883 align:middle line:90% 00:22:27.883 --> 00:22:29.300 align:middle line:84% To follow up on my earlier comment 00:22:29.300 --> 00:22:32.870 align:middle line:84% that we're really close to electrochemistry-- 00:22:32.870 --> 00:22:36.320 align:middle line:84% and for those of you who have seen the Nernst equation 00:22:36.320 --> 00:22:39.230 align:middle line:84% or done any batteries research, this 00:22:39.230 --> 00:22:42.110 align:middle line:84% looks a lot like the Nernst equation actually. 00:22:42.110 --> 00:22:46.140 align:middle line:90% 00:22:46.140 --> 00:22:48.810 align:middle line:84% And it's just a hop, skip-- it's a little bit of a stutter 00:22:48.810 --> 00:22:52.320 align:middle line:84% step from here to get to talking about electrochemistry. 00:22:52.320 --> 00:22:54.660 align:middle line:84% So if you don't care about electric chemistry 00:22:54.660 --> 00:22:57.215 align:middle line:84% or haven't been exposed to that yet, don't worry about it. 00:22:57.215 --> 00:22:58.590 align:middle line:84% But I think those connections are 00:22:58.590 --> 00:23:01.147 align:middle line:84% kind of neat for those of you who have been exposed to that. 00:23:01.147 --> 00:23:03.105 align:middle line:84% So now, let's talk a little bit about notation. 00:23:03.105 --> 00:23:10.650 align:middle line:90% 00:23:10.650 --> 00:23:13.400 align:middle line:84% To remind you here, this is a reminder. 00:23:13.400 --> 00:23:30.470 align:middle line:84% G of i prime is an extensive property of component i. 00:23:30.470 --> 00:23:32.720 align:middle line:84% That is the total Gibbs free energy 00:23:32.720 --> 00:23:37.080 align:middle line:90% of all the stuff in component i. 00:23:37.080 --> 00:23:46.260 align:middle line:84% G sub i without the prime is a molar intensive property. 00:23:46.260 --> 00:23:49.830 align:middle line:90% 00:23:49.830 --> 00:23:54.892 align:middle line:84% That is Gibbs free energy of i per moles of i. 00:23:54.892 --> 00:24:03.570 align:middle line:90% 00:24:03.570 --> 00:24:05.950 align:middle line:84% So you could read that Gibbs per mole of i. 00:24:05.950 --> 00:24:10.130 align:middle line:90% 00:24:10.130 --> 00:24:11.390 align:middle line:90% Here's a new concept-- 00:24:11.390 --> 00:24:31.210 align:middle line:84% G of i 0 molar Gibbs free energy of component i 00:24:31.210 --> 00:24:32.620 align:middle line:90% in its standard state. 00:24:32.620 --> 00:24:47.808 align:middle line:90% 00:24:47.808 --> 00:24:48.350 align:middle line:90% What is that? 00:24:48.350 --> 00:24:50.810 align:middle line:84% I'm going to define it for gases-- 00:24:50.810 --> 00:24:56.256 align:middle line:90% standard state for gases. 00:24:56.256 --> 00:25:00.000 align:middle line:90% 00:25:00.000 --> 00:25:09.180 align:middle line:84% It's a pure gas that's unmixed at standard pressure-- 00:25:09.180 --> 00:25:18.840 align:middle line:90% 00:25:18.840 --> 00:25:22.250 align:middle line:90% 1 got its one bar-- 00:25:22.250 --> 00:25:38.230 align:middle line:84% and same temp as the solution or mixture in question. 00:25:38.230 --> 00:25:41.100 align:middle line:90% 00:25:41.100 --> 00:25:45.630 align:middle line:84% So concept, concept, concept, concept-- 00:25:45.630 --> 00:25:49.470 align:middle line:84% these two are not new to you today. 00:25:49.470 --> 00:25:50.860 align:middle line:84% They are-- they can be confusing, 00:25:50.860 --> 00:25:51.943 align:middle line:90% but they're not new today. 00:25:51.943 --> 00:25:55.530 align:middle line:84% And all of this is consistent with DeHoff. 00:25:55.530 --> 00:25:56.760 align:middle line:90% This is new today. 00:25:56.760 --> 00:25:59.490 align:middle line:84% We're introducing standard states. 00:25:59.490 --> 00:26:03.240 align:middle line:84% And standard states are defined somewhat differently than you 00:26:03.240 --> 00:26:05.680 align:middle line:90% might have seen than before. 00:26:05.680 --> 00:26:11.480 align:middle line:84% Standard states for gases, to be specific for today, 00:26:11.480 --> 00:26:16.770 align:middle line:84% is the pure gas non mixed at one pressure 00:26:16.770 --> 00:26:20.890 align:middle line:84% but at whatever temperature the problem you're analyzing is. 00:26:20.890 --> 00:26:22.660 align:middle line:84% So it's not the same thing as STP. 00:26:22.660 --> 00:26:24.460 align:middle line:84% It's not standard temperature and pressure. 00:26:24.460 --> 00:26:29.120 align:middle line:84% It's not one bar 25 degrees C. It's whatever you have 00:26:29.120 --> 00:26:30.365 align:middle line:90% before you make the mixture. 00:26:30.365 --> 00:26:33.793 align:middle line:90% 00:26:33.793 --> 00:26:35.210 align:middle line:84% And the process of making mixtures 00:26:35.210 --> 00:26:37.850 align:middle line:84% is so central to material science, 00:26:37.850 --> 00:26:40.310 align:middle line:84% I'm going to slide backwards here. 00:26:40.310 --> 00:26:44.270 align:middle line:84% We have a pure gas and another pure gas, a pure substance 00:26:44.270 --> 00:26:45.410 align:middle line:90% and another pure substance. 00:26:45.410 --> 00:26:47.090 align:middle line:84% They're both at the same temperature. 00:26:47.090 --> 00:26:48.410 align:middle line:84% I don't know what temperature that is. 00:26:48.410 --> 00:26:49.827 align:middle line:84% It's just a parameter, but they're 00:26:49.827 --> 00:26:51.176 align:middle line:90% at the same temperature. 00:26:51.176 --> 00:26:54.370 align:middle line:90% 00:26:54.370 --> 00:26:57.400 align:middle line:84% The standard state of pure component 1 00:26:57.400 --> 00:27:00.880 align:middle line:90% is this temperature and one bar. 00:27:00.880 --> 00:27:02.620 align:middle line:84% The standard state of pure component 2 00:27:02.620 --> 00:27:06.960 align:middle line:90% is this temperature and one bar. 00:27:06.960 --> 00:27:09.540 align:middle line:84% And those are standards because it's what you have 00:27:09.540 --> 00:27:11.340 align:middle line:90% before you make the mixture. 00:27:11.340 --> 00:27:15.960 align:middle line:90% 00:27:15.960 --> 00:27:19.020 align:middle line:84% So I'll use this analogy often in this course. 00:27:19.020 --> 00:27:22.500 align:middle line:84% You imagine you have a beaker of A and a beaker of B. 00:27:22.500 --> 00:27:24.023 align:middle line:84% And you're at whatever temperature 00:27:24.023 --> 00:27:25.440 align:middle line:84% you want to make your solution at, 00:27:25.440 --> 00:27:27.960 align:middle line:84% whatever temperature you're processing your material at. 00:27:27.960 --> 00:27:30.630 align:middle line:84% Beaker of A beaker of B-- they're at temperature. 00:27:30.630 --> 00:27:33.510 align:middle line:84% And you mix them, stir it around. 00:27:33.510 --> 00:27:36.390 align:middle line:90% That's material science. 00:27:36.390 --> 00:27:38.310 align:middle line:84% The standard state of a substance 00:27:38.310 --> 00:27:42.330 align:middle line:84% is however it's found when it's pure at one 00:27:42.330 --> 00:27:44.400 align:middle line:84% bar at the temperature that you're 00:27:44.400 --> 00:27:45.450 align:middle line:90% doing your solution form. 00:27:45.450 --> 00:27:51.568 align:middle line:90% 00:27:51.568 --> 00:27:52.610 align:middle line:90% All right, let's move on. 00:27:52.610 --> 00:27:55.800 align:middle line:90% 00:27:55.800 --> 00:28:05.430 align:middle line:84% Chemical potential-- chemical potential 00:28:05.430 --> 00:28:08.340 align:middle line:90% and ideal gas mixtures. 00:28:08.340 --> 00:28:13.120 align:middle line:90% 00:28:13.120 --> 00:28:21.690 align:middle line:84% So we know that for any sort of change of temperature, 00:28:21.690 --> 00:28:29.710 align:middle line:84% and pressure, and mole number, this 00:28:29.710 --> 00:28:34.610 align:middle line:84% is the change in chemical potential. 00:28:34.610 --> 00:28:38.050 align:middle line:84% So mu i-- and we've been here before-- 00:28:38.050 --> 00:28:43.930 align:middle line:84% equals dG Eni at fixed temperature, fixed pressure, 00:28:43.930 --> 00:28:47.890 align:middle line:84% and fixed moles of everything else. 00:28:47.890 --> 00:28:52.390 align:middle line:90% 00:28:52.390 --> 00:28:55.180 align:middle line:90% All right, this is now. 00:28:55.180 --> 00:29:13.840 align:middle line:84% From before we have mu of i equals mu i 0 plus RT log 00:29:13.840 --> 00:29:16.455 align:middle line:90% P of i over P0. 00:29:16.455 --> 00:29:22.900 align:middle line:90% 00:29:22.900 --> 00:29:25.780 align:middle line:84% So chemical potential is molar Gibbs free energy. 00:29:25.780 --> 00:29:29.170 align:middle line:84% We calculated the change in Gibbs free energy 00:29:29.170 --> 00:29:31.630 align:middle line:90% for the mixture process. 00:29:31.630 --> 00:29:35.810 align:middle line:90% 00:29:35.810 --> 00:29:37.570 align:middle line:84% And so we can write an analogous equation 00:29:37.570 --> 00:29:38.960 align:middle line:90% for chemical potential. 00:29:38.960 --> 00:29:41.410 align:middle line:90% So again, how to read this. 00:29:41.410 --> 00:29:48.405 align:middle line:84% Chemical potential of component i-- 00:29:48.405 --> 00:29:52.980 align:middle line:90% 00:29:52.980 --> 00:29:55.900 align:middle line:84% chemical potential of component i dot dot 00:29:55.900 --> 00:30:11.760 align:middle line:84% dot relative to its standard state dot dot 00:30:11.760 --> 00:30:20.045 align:middle line:90% dot at temp T and partial-- 00:30:20.045 --> 00:30:27.782 align:middle line:90% 00:30:27.782 --> 00:30:29.240 align:middle line:84% so the chemical potential component 00:30:29.240 --> 00:30:31.970 align:middle line:84% i relative to its standard state at temperature T 00:30:31.970 --> 00:30:33.900 align:middle line:90% and partial pressure Pi. 00:30:33.900 --> 00:30:34.900 align:middle line:90% That's how to read that. 00:30:34.900 --> 00:30:38.530 align:middle line:90% 00:30:38.530 --> 00:30:40.780 align:middle line:84% And we're going to use this so very, very much. 00:30:40.780 --> 00:30:42.520 align:middle line:84% I think it deserves a purple square. 00:30:42.520 --> 00:30:55.463 align:middle line:90% 00:30:55.463 --> 00:30:57.380 align:middle line:84% I'm going a little fast through this material, 00:30:57.380 --> 00:31:01.880 align:middle line:84% so I remind you to please interrupt me with questions. 00:31:01.880 --> 00:31:10.480 align:middle line:90% 00:31:10.480 --> 00:31:13.450 align:middle line:90% Here, let's get a question. 00:31:13.450 --> 00:31:21.780 align:middle line:84% Do ideal gases mix spontaneously? 00:31:21.780 --> 00:31:29.110 align:middle line:90% 00:31:29.110 --> 00:31:31.140 align:middle line:84% Right, do ideal gases mix spontaneously? 00:31:31.140 --> 00:31:35.310 align:middle line:90% Here's my setup from lecture 1. 00:31:35.310 --> 00:31:48.170 align:middle line:90% 00:31:48.170 --> 00:31:50.170 align:middle line:84% These are ideal gases, two different components. 00:31:50.170 --> 00:31:51.712 align:middle line:84% Are they going to make spontaneously? 00:31:51.712 --> 00:32:01.680 align:middle line:90% 00:32:01.680 --> 00:32:03.470 align:middle line:90% AUDIENCE: Yes. 00:32:03.470 --> 00:32:04.880 align:middle line:90% RAFAEL JARAMILLO: Yes. 00:32:04.880 --> 00:32:06.800 align:middle line:90% Yes, they do. 00:32:06.800 --> 00:32:11.470 align:middle line:84% OK, so that you knew on day one, I think. 00:32:11.470 --> 00:32:15.010 align:middle line:84% Most of you sort of got that on day one. 00:32:15.010 --> 00:32:18.270 align:middle line:90% 00:32:18.270 --> 00:32:20.830 align:middle line:84% But now, we can answer this question. 00:32:20.830 --> 00:32:22.780 align:middle line:90% Why? 00:32:22.780 --> 00:32:27.085 align:middle line:90% What is the driving force? 00:32:27.085 --> 00:32:33.780 align:middle line:90% 00:32:33.780 --> 00:32:36.390 align:middle line:84% On day one, we talked about randomness and entropy, 00:32:36.390 --> 00:32:39.480 align:middle line:84% and it just sort of seemed like what would happen. 00:32:39.480 --> 00:32:43.180 align:middle line:84% And we said oh, this is going to be an entropy-driven process, 00:32:43.180 --> 00:32:44.560 align:middle line:90% which is true. 00:32:44.560 --> 00:32:45.090 align:middle line:90% That's true. 00:32:45.090 --> 00:32:48.270 align:middle line:90% 00:32:48.270 --> 00:32:52.170 align:middle line:84% But now we have a more useful way 00:32:52.170 --> 00:32:56.630 align:middle line:84% of analyzing this problem in general, which 00:32:56.630 --> 00:33:01.000 align:middle line:90% is what is the driving force? 00:33:01.000 --> 00:33:13.930 align:middle line:84% At fixed T and P, the driving force 00:33:13.930 --> 00:33:21.930 align:middle line:84% is to lower the Gibbs free energy, the total Gibbs 00:33:21.930 --> 00:33:22.430 align:middle line:90% free energy. 00:33:22.430 --> 00:33:25.020 align:middle line:90% 00:33:25.020 --> 00:33:32.440 align:middle line:84% So Gibbs free energy equals the sum of the molar Gibbs 00:33:32.440 --> 00:33:33.340 align:middle line:90% free energies-- 00:33:33.340 --> 00:33:36.470 align:middle line:90% 00:33:36.470 --> 00:33:41.840 align:middle line:84% and the molar Gibbs free energies are their reference 00:33:41.840 --> 00:33:44.690 align:middle line:90% values plus the change. 00:33:44.690 --> 00:33:55.550 align:middle line:90% 00:33:55.550 --> 00:33:59.450 align:middle line:84% I can combine these, and I find that the Gibbs free energy 00:33:59.450 --> 00:34:05.320 align:middle line:84% is the Gibbs free energy before mixing plus delta 00:34:05.320 --> 00:34:15.150 align:middle line:84% G due to mixing and delta G due to mixing the change of Gibbs 00:34:15.150 --> 00:34:18.030 align:middle line:84% free energy when this spontaneous process happens. 00:34:18.030 --> 00:34:20.370 align:middle line:90% And you can plug and chug here. 00:34:20.370 --> 00:34:34.409 align:middle line:84% It's i ni RT log Pi over P. And here's the kicker-- 00:34:34.409 --> 00:34:36.350 align:middle line:90% positive or negative? 00:34:36.350 --> 00:34:37.159 align:middle line:90% What should it be? 00:34:37.159 --> 00:34:38.630 align:middle line:90% Without-- forget the math. 00:34:38.630 --> 00:34:39.469 align:middle line:90% What should it be? 00:34:39.469 --> 00:34:40.969 align:middle line:84% Should this be positive or negative? 00:34:40.969 --> 00:34:45.429 align:middle line:84% The process will happen spontaneously. 00:34:45.429 --> 00:34:46.760 align:middle line:90% AUDIENCE: Negative. 00:34:46.760 --> 00:34:49.030 align:middle line:84% RAFAEL JARAMILLO: Got to be negative. 00:34:49.030 --> 00:34:50.949 align:middle line:84% If a process happens spontaneously 00:34:50.949 --> 00:34:52.510 align:middle line:84% at fixed temperature and pressure, 00:34:52.510 --> 00:34:55.210 align:middle line:84% the driving force is lowering the Gibbs free energy. 00:34:55.210 --> 00:34:57.430 align:middle line:84% The change of Gibbs for that process 00:34:57.430 --> 00:35:02.020 align:middle line:84% must be negative if it is to be spontaneous. 00:35:02.020 --> 00:35:03.820 align:middle line:90% Does the math work out? 00:35:03.820 --> 00:35:04.960 align:middle line:90% This is strictly positive. 00:35:04.960 --> 00:35:06.043 align:middle line:90% This is strictly positive. 00:35:06.043 --> 00:35:07.270 align:middle line:90% This is strictly positive. 00:35:07.270 --> 00:35:10.715 align:middle line:90% 00:35:10.715 --> 00:35:12.090 align:middle line:84% What about the partial pressures? 00:35:12.090 --> 00:35:14.830 align:middle line:90% 00:35:14.830 --> 00:35:16.900 align:middle line:84% AUDIENCE: The i is strictly lower than P, 00:35:16.900 --> 00:35:18.550 align:middle line:90% so it's like a negative mole. 00:35:18.550 --> 00:35:23.950 align:middle line:84% RAFAEL JARAMILLO: Pi equals Xi P. Xi is less than 00:35:23.950 --> 00:35:25.480 align:middle line:90% or equal to 1 by definition. 00:35:25.480 --> 00:35:28.520 align:middle line:84% You can't have a mole fraction greater than 1. 00:35:28.520 --> 00:35:39.100 align:middle line:84% Therefore, Pi's are less than or equal to P. So log Pi over P 00:35:39.100 --> 00:35:41.500 align:middle line:90% is less than or equal to 0. 00:35:41.500 --> 00:35:46.440 align:middle line:90% 00:35:46.440 --> 00:35:48.300 align:middle line:84% This is our driving force for mixing. 00:35:48.300 --> 00:35:49.920 align:middle line:84% The driving force for wave mixing 00:35:49.920 --> 00:35:54.660 align:middle line:84% is that the chemical potential of each and every component 00:35:54.660 --> 00:35:56.745 align:middle line:90% is lowered by mixing. 00:35:56.745 --> 00:36:00.820 align:middle line:90% 00:36:00.820 --> 00:36:05.170 align:middle line:84% So we're just a little more than 30 days 00:36:05.170 --> 00:36:06.520 align:middle line:90% past the start of the semester. 00:36:06.520 --> 00:36:07.895 align:middle line:84% And at the start of the semester, 00:36:07.895 --> 00:36:10.960 align:middle line:84% you knew this would happen, and you sort of-- 00:36:10.960 --> 00:36:15.730 align:middle line:84% we were able to discuss why it would happen in a hand way 00:36:15.730 --> 00:36:16.930 align:middle line:90% to be an intuitive way. 00:36:16.930 --> 00:36:19.150 align:middle line:84% And now, a little under five weeks 00:36:19.150 --> 00:36:22.820 align:middle line:84% later, we now see the same result. 00:36:22.820 --> 00:36:25.690 align:middle line:84% But we have a formalism attached to it. 00:36:25.690 --> 00:36:28.880 align:middle line:84% We can calculate the change of strategy for this process, 00:36:28.880 --> 00:36:30.500 align:middle line:84% and we can see that it's negative. 00:36:30.500 --> 00:36:33.530 align:middle line:84% And we can quantify and count things. 00:36:33.530 --> 00:36:36.310 align:middle line:84% So I guess you could say we've come full circle. 00:36:36.310 --> 00:36:41.780 align:middle line:90% 00:36:41.780 --> 00:36:45.330 align:middle line:84% All right, for the remaining 10 minutes or so or eight minutes, 00:36:45.330 --> 00:36:47.240 align:middle line:84% I'm going to talk about balancing chemical 00:36:47.240 --> 00:36:50.335 align:middle line:90% reactions, which gets back to-- 00:36:50.335 --> 00:36:52.460 align:middle line:84% for those of you who took chemistry in high school, 00:36:52.460 --> 00:36:54.252 align:middle line:84% it would be high school chemistry. 00:36:54.252 --> 00:36:56.460 align:middle line:84% And I'm just going to remind you of some basic facts. 00:36:56.460 --> 00:36:59.780 align:middle line:84% So this is probably the most opportune time 00:36:59.780 --> 00:37:03.680 align:middle line:84% for questions on this mixing process 00:37:03.680 --> 00:37:07.950 align:middle line:84% and the thermodynamics of mixing ideal gases. 00:37:07.950 --> 00:37:09.815 align:middle line:90% Now there's a chat. 00:37:09.815 --> 00:37:11.440 align:middle line:84% Again, I'm very slow on the uptake when 00:37:11.440 --> 00:37:13.420 align:middle line:84% it comes to chats when I'm lecturing-- 00:37:13.420 --> 00:37:14.930 align:middle line:90% so much work in this circle. 00:37:14.930 --> 00:37:16.360 align:middle line:90% Well, it took five weeks. 00:37:16.360 --> 00:37:20.560 align:middle line:90% 00:37:20.560 --> 00:37:22.350 align:middle line:84% If not, then let's remind ourselves 00:37:22.350 --> 00:37:26.702 align:middle line:84% about how to balance chemical reactions. 00:37:26.702 --> 00:37:27.660 align:middle line:90% All right, here we go-- 00:37:27.660 --> 00:37:41.790 align:middle line:90% 00:37:41.790 --> 00:37:46.860 align:middle line:90% balancing chemical reactions. 00:37:46.860 --> 00:37:51.020 align:middle line:90% So, for example, a gas-- 00:37:51.020 --> 00:37:57.730 align:middle line:90% 00:37:57.730 --> 00:38:00.830 align:middle line:90% sorry, give me one second. 00:38:00.830 --> 00:38:02.740 align:middle line:84% I want to remind you of something. 00:38:02.740 --> 00:38:06.220 align:middle line:84% Not a reminder, it's a public service announcement. 00:38:06.220 --> 00:38:08.890 align:middle line:90% Here's a PSA. 00:38:08.890 --> 00:38:25.790 align:middle line:84% PSA-- can ignore fugacity in Denbigh. 00:38:25.790 --> 00:38:31.020 align:middle line:90% 00:38:31.020 --> 00:38:32.910 align:middle line:84% It's the only count against using 00:38:32.910 --> 00:38:34.830 align:middle line:84% Denbigh at this point in this class 00:38:34.830 --> 00:38:37.770 align:middle line:84% is that Denbigh admits to the existence of something called 00:38:37.770 --> 00:38:39.840 align:middle line:90% fugacity. 00:38:39.840 --> 00:38:42.990 align:middle line:84% Fugacity is the same as activity. 00:38:42.990 --> 00:38:44.940 align:middle line:90% We haven't gotten there yet. 00:38:44.940 --> 00:38:46.875 align:middle line:84% Fugacity is a chemical engineer's term. 00:38:46.875 --> 00:38:49.470 align:middle line:90% 00:38:49.470 --> 00:38:52.260 align:middle line:84% Activity is a material scientist's term. 00:38:52.260 --> 00:38:54.580 align:middle line:90% They have the same meaning. 00:38:54.580 --> 00:38:57.320 align:middle line:84% And as I said, we haven't gotten there yet. 00:38:57.320 --> 00:38:59.860 align:middle line:84% And you can completely ignore the discussion of fugacity 00:38:59.860 --> 00:39:02.050 align:middle line:84% in that relevant chapter of Denbigh. 00:39:02.050 --> 00:39:03.280 align:middle line:90% Don't let it trip you up. 00:39:03.280 --> 00:39:06.240 align:middle line:90% Don't sweat it. 00:39:06.240 --> 00:39:07.613 align:middle line:90% And you got to remember-- 00:39:07.613 --> 00:39:08.780 align:middle line:90% public service announcement. 00:39:08.780 --> 00:39:11.310 align:middle line:84% OK, back to balancing chemical reactions. 00:39:11.310 --> 00:39:17.240 align:middle line:84% So let's have a gas phase reaction A plus B equals 2C. 00:39:17.240 --> 00:39:18.950 align:middle line:90% Everything's gases. 00:39:18.950 --> 00:39:27.970 align:middle line:84% So the reaction balance can be written in another way. 00:39:27.970 --> 00:39:38.690 align:middle line:84% 0 equals 2C minus A minus B. And so this is pretty familiar. 00:39:38.690 --> 00:39:41.570 align:middle line:84% The only-- here's something new, but it's not that new. 00:39:41.570 --> 00:39:45.380 align:middle line:84% We're going to use stoichiometric coefficients. 00:39:45.380 --> 00:39:48.020 align:middle line:90% We're going to define them here. 00:39:48.020 --> 00:40:09.595 align:middle line:84% Plus, this defines stoichiometry coefficients U sub i. 00:40:09.595 --> 00:40:10.970 align:middle line:84% So maybe you've seen this before. 00:40:10.970 --> 00:40:13.137 align:middle line:84% Maybe you haven't, but it's a pretty simple concept. 00:40:13.137 --> 00:40:16.490 align:middle line:90% This way we can just generalize. 00:40:16.490 --> 00:40:20.470 align:middle line:84% So we have these stoichiometric coefficients U sub i. 00:40:20.470 --> 00:40:27.190 align:middle line:84% The U sub i's, they come from conservation of atoms, 00:40:27.190 --> 00:40:30.380 align:middle line:90% balancing chemical reactions. 00:40:30.380 --> 00:40:34.910 align:middle line:84% Conservation of atoms-- and by convention, 00:40:34.910 --> 00:40:39.050 align:middle line:84% U sub i's are less than 0 for reactants 00:40:39.050 --> 00:40:41.460 align:middle line:90% because they're consumed. 00:40:41.460 --> 00:40:45.940 align:middle line:84% And U sub i is greater than 0 for products 00:40:45.940 --> 00:40:46.940 align:middle line:90% because they're created. 00:40:46.940 --> 00:40:55.700 align:middle line:90% 00:40:55.700 --> 00:40:58.880 align:middle line:84% So that's balancing chemical reactions. 00:40:58.880 --> 00:41:02.300 align:middle line:90% And I want to just remind us. 00:41:02.300 --> 00:41:09.075 align:middle line:84% When we see this, this is what we should think. 00:41:09.075 --> 00:41:12.220 align:middle line:90% 00:41:12.220 --> 00:41:18.370 align:middle line:84% We should think-- well, let me not use a bunch of different 00:41:18.370 --> 00:41:19.660 align:middle line:90% colors-- 00:41:19.660 --> 00:41:23.320 align:middle line:84% we should think of at some fixed temperature 00:41:23.320 --> 00:41:32.230 align:middle line:84% and pressure of volume of A, A, A, A, A, A, B, B, B, B, B, C, 00:41:32.230 --> 00:41:39.520 align:middle line:84% C, C. This is meant to be more gas molecules in a box. 00:41:39.520 --> 00:41:45.490 align:middle line:84% This isn't I took A and B, and it went totally to C. 00:41:45.490 --> 00:41:49.630 align:middle line:84% We'll actually see that never happens, except in 0 Kelvin. 00:41:49.630 --> 00:41:52.837 align:middle line:84% Instead, it's a system that's fluctuating back and forth. 00:41:52.837 --> 00:41:53.920 align:middle line:90% Reactions go to the right. 00:41:53.920 --> 00:41:54.970 align:middle line:90% Reactions go to the left. 00:41:54.970 --> 00:41:59.210 align:middle line:84% Nature doesn't care what you wrote in the left-hand side. 00:41:59.210 --> 00:42:00.850 align:middle line:84% You could have easily written 2C equals 00:42:00.850 --> 00:42:02.440 align:middle line:90% A plus B. Nature doesn't care. 00:42:02.440 --> 00:42:09.750 align:middle line:84% It's a reacting mixture of gases and, in our case, 00:42:09.750 --> 00:42:13.040 align:middle line:84% at a fixed temperature and pressure. 00:42:13.040 --> 00:42:15.612 align:middle line:84% So that's a little bit about balancing chemical reactions. 00:42:15.612 --> 00:42:16.320 align:middle line:90% Let's keep going. 00:42:16.320 --> 00:42:18.880 align:middle line:90% 00:42:18.880 --> 00:42:29.830 align:middle line:84% We have constraints on the d ni's. 00:42:29.830 --> 00:42:38.010 align:middle line:84% If you remember, dG at fixed temperature and pressure 00:42:38.010 --> 00:42:41.520 align:middle line:90% equals mu i d ni. 00:42:41.520 --> 00:42:43.770 align:middle line:84% The total-- all the changing in Gibbs free energy 00:42:43.770 --> 00:42:46.660 align:middle line:84% at fixed temperature pressure comes 00:42:46.660 --> 00:42:49.400 align:middle line:90% from changing of mole numbers. 00:42:49.400 --> 00:42:51.710 align:middle line:84% It's going to come from these reactions 00:42:51.710 --> 00:42:54.498 align:middle line:84% as some components are produced and other components 00:42:54.498 --> 00:42:55.040 align:middle line:90% are consumed. 00:42:55.040 --> 00:42:59.090 align:middle line:90% 00:42:59.090 --> 00:43:02.710 align:middle line:84% So we want to figure out what are constraints on the d ni's. 00:43:02.710 --> 00:43:05.080 align:middle line:84% And I'll just write this down for the reaction, which 00:43:05.080 --> 00:43:06.580 align:middle line:90% we saw in the previous slide-- 00:43:06.580 --> 00:43:13.830 align:middle line:84% d na-- it's not meant to be DNA, like dinucleic acid. 00:43:13.830 --> 00:43:16.050 align:middle line:90% It's just d na. 00:43:16.050 --> 00:43:28.770 align:middle line:84% Here is dn V nu V equals dn C over nu C. 00:43:28.770 --> 00:43:33.610 align:middle line:84% So this is just true in general for any chemical reaction. 00:43:33.610 --> 00:43:37.730 align:middle line:90% 00:43:37.730 --> 00:43:41.435 align:middle line:84% The term d ni over nu i are constant. 00:43:41.435 --> 00:43:44.140 align:middle line:90% 00:43:44.140 --> 00:43:48.570 align:middle line:84% And this defines for us a new variable. 00:43:48.570 --> 00:43:56.275 align:middle line:84% It's just C, which is the reaction extent. 00:43:56.275 --> 00:43:59.280 align:middle line:90% 00:43:59.280 --> 00:44:01.820 align:middle line:84% So it's a unitless, generalized parameter 00:44:01.820 --> 00:44:05.210 align:middle line:84% to describe whether the reaction runs a little bit to the left 00:44:05.210 --> 00:44:06.707 align:middle line:90% or a little bit to the right. 00:44:06.707 --> 00:44:08.540 align:middle line:84% And maybe some of you have seen this before, 00:44:08.540 --> 00:44:10.310 align:middle line:84% and probably most of you have not. 00:44:10.310 --> 00:44:13.870 align:middle line:90% 00:44:13.870 --> 00:44:27.170 align:middle line:84% So this is a series of M minus 1 equations in M variables. 00:44:27.170 --> 00:44:29.920 align:middle line:84% M here is a number of components in the reaction-- 00:44:29.920 --> 00:44:34.140 align:middle line:90% A, B, C, three components. 00:44:34.140 --> 00:44:35.340 align:middle line:90% How many equal signs? 00:44:35.340 --> 00:44:36.650 align:middle line:90% 1, 2. 00:44:36.650 --> 00:44:40.620 align:middle line:84% M minus 1 equations in M variables-- 00:44:40.620 --> 00:44:41.640 align:middle line:90% what does that mean? 00:44:41.640 --> 00:44:47.550 align:middle line:84% If I have M minus 1 independent linear equations and M 00:44:47.550 --> 00:44:51.570 align:middle line:84% variables, how many independent variables do I have? 00:44:51.570 --> 00:45:09.750 align:middle line:84% Linear algebra again-- how many independent variables 00:45:09.750 --> 00:45:15.710 align:middle line:84% do I have describing the change in moles as this reaction 00:45:15.710 --> 00:45:18.000 align:middle line:90% proceeds? 00:45:18.000 --> 00:45:19.425 align:middle line:90% AUDIENCE: One. 00:45:19.425 --> 00:45:20.850 align:middle line:90% RAFAEL JARAMILLO: One. 00:45:20.850 --> 00:45:23.370 align:middle line:84% One independent variable, that's right. 00:45:23.370 --> 00:45:26.220 align:middle line:84% So instead of having to sum a bunch of different d ni's 00:45:26.220 --> 00:45:28.590 align:middle line:84% on the right-hand side of my expression for dG, 00:45:28.590 --> 00:45:31.103 align:middle line:84% I can simplify and have only one. 00:45:31.103 --> 00:45:33.270 align:middle line:84% And I think you probably have an intuition for that. 00:45:33.270 --> 00:45:39.100 align:middle line:84% If I have a reaction, it can go to the right. 00:45:39.100 --> 00:45:41.330 align:middle line:90% It can go to the left. 00:45:41.330 --> 00:45:42.590 align:middle line:90% It's like one variable. 00:45:42.590 --> 00:45:45.350 align:middle line:84% There's sort of one variable that tells you what's changing. 00:45:45.350 --> 00:45:46.640 align:middle line:90% It can go to the right. 00:45:46.640 --> 00:45:49.850 align:middle line:90% It can go to the left. 00:45:49.850 --> 00:45:51.640 align:middle line:84% So that comes out in the analysis, 00:45:51.640 --> 00:45:53.240 align:middle line:90% one independent variable. 00:45:53.240 --> 00:46:03.340 align:middle line:84% So, for example, I can express d na as nu a over nu C d nC. 00:46:03.340 --> 00:46:11.950 align:middle line:84% And I can express d nB equals nu B over nu C d nC 00:46:11.950 --> 00:46:23.410 align:middle line:84% and write dG totally with respect to d nC. 00:46:23.410 --> 00:46:24.470 align:middle line:90% That's just an example. 00:46:24.470 --> 00:46:28.420 align:middle line:84% I can eliminate nA and nB and write 00:46:28.420 --> 00:46:30.610 align:middle line:84% the differential of Gibbs free energy 00:46:30.610 --> 00:46:33.172 align:middle line:84% totally with respect for one independent variable. 00:46:33.172 --> 00:46:35.380 align:middle line:84% So again we're back to counting independent variables 00:46:35.380 --> 00:46:36.520 align:middle line:90% to set up problems. 00:46:36.520 --> 00:46:43.130 align:middle line:84% All right, another concept from introductory chemistry-- 00:46:43.130 --> 00:46:44.440 align:middle line:90% coupled reactions. 00:46:44.440 --> 00:46:49.160 align:middle line:90% 00:46:49.160 --> 00:46:53.530 align:middle line:84% Coupled reactions-- so, for example, 4 ammonias 00:46:53.530 --> 00:47:06.310 align:middle line:84% is plus 5 oxygens can turn into 4 nitrous oxides plus 6 waters. 00:47:06.310 --> 00:47:08.970 align:middle line:84% I'm going to call that reaction 1. 00:47:08.970 --> 00:47:19.100 align:middle line:84% And that is the same thing as 4 ammonias splitting 00:47:19.100 --> 00:47:26.570 align:middle line:84% into nitrogen and hydrogen. I'll call that reaction 2. 00:47:26.570 --> 00:47:35.990 align:middle line:84% 2 nitrogens plus 3 oxygens becoming 4 N0 molecules. 00:47:35.990 --> 00:47:40.580 align:middle line:90% I'll call that reaction 3. 00:47:40.580 --> 00:47:47.500 align:middle line:90% 6 hydrogens plus 3 oxygens-- 00:47:47.500 --> 00:47:51.370 align:middle line:84% did I get my numbers right here or did I not-- 00:47:51.370 --> 00:47:54.280 align:middle line:90% becoming 6 waters. 00:47:54.280 --> 00:47:57.700 align:middle line:90% And that is reaction 4. 00:47:57.700 --> 00:48:06.370 align:middle line:84% And reaction 1 is simply the sum of reaction 2, reaction 3, 00:48:06.370 --> 00:48:08.340 align:middle line:90% and reaction 4. 00:48:08.340 --> 00:48:11.790 align:middle line:84% This is a reminder of how you can break down 00:48:11.790 --> 00:48:14.490 align:middle line:84% chemical reactions into subordinate reactions. 00:48:14.490 --> 00:48:17.540 align:middle line:90% 00:48:17.540 --> 00:48:18.830 align:middle line:90% Why am I telling you this? 00:48:18.830 --> 00:48:22.310 align:middle line:84% I'm telling you this because of thermodynamics, of course. 00:48:22.310 --> 00:48:37.640 align:middle line:84% The overall change in state variables 00:48:37.640 --> 00:48:52.090 align:middle line:84% is the sum of changes between intermediate states. 00:48:52.090 --> 00:48:52.965 align:middle line:90% This is super useful. 00:48:52.965 --> 00:48:56.760 align:middle line:90% 00:48:56.760 --> 00:48:58.620 align:middle line:84% And, again, it's introductory chemistry, 00:48:58.620 --> 00:49:00.940 align:middle line:90% so this hopefully is a reminder. 00:49:00.940 --> 00:49:05.370 align:middle line:84% So, for example, delta G for equation 1-- 00:49:05.370 --> 00:49:06.990 align:middle line:90% reaction 1, I should say-- 00:49:06.990 --> 00:49:11.640 align:middle line:84% is the same as delta G for reaction 2 00:49:11.640 --> 00:49:18.375 align:middle line:84% plus delta G for reaction 3 plus delta G for reaction 4. 00:49:18.375 --> 00:49:22.140 align:middle line:90% 00:49:22.140 --> 00:49:24.570 align:middle line:84% And this is something that you'll use on the p set. 00:49:24.570 --> 00:49:26.760 align:middle line:90% And preview for next time-- 00:49:26.760 --> 00:49:40.385 align:middle line:84% each reaction obeys its own equilibrium balance. 00:49:40.385 --> 00:49:47.880 align:middle line:90% 00:49:47.880 --> 00:49:51.250 align:middle line:84% And we will talk about equilibrium balance on Monday. 00:49:51.250 --> 00:49:53.900 align:middle line:90% So that's it for today. 00:49:53.900 --> 00:49:56.000 align:middle line:90%