WEBVTT 00:00:00.090 --> 00:00:02.430 The following content is provided under a Creative 00:00:02.430 --> 00:00:03.820 Commons license. 00:00:03.820 --> 00:00:06.060 Your support will help MIT OpenCourseWare 00:00:06.060 --> 00:00:10.150 continue to offer high-quality educational resources for free. 00:00:10.150 --> 00:00:12.690 To make a donation or to view additional materials 00:00:12.690 --> 00:00:16.435 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.435 --> 00:00:17.060 at ocw.mit.edu. 00:00:33.252 --> 00:00:34.460 CATHERINE DRENNAN: All right. 00:00:34.460 --> 00:00:36.190 Let's just do 10 more seconds. 00:00:53.690 --> 00:00:54.190 All right. 00:00:54.190 --> 00:01:01.181 Does someone want to tell me up here-- hello everyone up here-- 00:01:01.181 --> 00:01:02.430 how they got the right answer? 00:01:06.570 --> 00:01:09.160 Over-- everyone over there, I guess. 00:01:09.160 --> 00:01:10.640 OK, I'm coming over there. 00:01:10.640 --> 00:01:15.080 So for the answer we have an MIT chemistry bag. 00:01:15.080 --> 00:01:15.960 That's quite special. 00:01:23.620 --> 00:01:26.320 AUDIENCE: Well, since your delta H value 00:01:26.320 --> 00:01:28.990 acts as the y-intercept, you know that it's negative 00:01:28.990 --> 00:01:31.030 because it's negatively. 00:01:31.030 --> 00:01:33.700 And then you also see that you're ascending positively, 00:01:33.700 --> 00:01:37.010 so that you know your slope is positive. 00:01:37.010 --> 00:01:41.770 And so delta S also has to be negative to make it positive. 00:01:41.770 --> 00:01:43.150 CATHERINE DRENNAN: Interesting. 00:01:43.150 --> 00:01:45.370 That was a different answer than I would have given, 00:01:45.370 --> 00:01:47.350 but that works really well, which 00:01:47.350 --> 00:01:48.950 is always great to ask people. 00:01:48.950 --> 00:01:52.720 So you could also think about this in terms of your going 00:01:52.720 --> 00:01:56.459 from a situation with a negative delta G to a positive value. 00:01:56.459 --> 00:01:58.000 So you know that temperature is going 00:01:58.000 --> 00:01:59.870 to make a difference there. 00:01:59.870 --> 00:02:05.006 And so that would also tell you how the temperature changes 00:02:05.006 --> 00:02:06.880 is also going to tell you the answer to that. 00:02:06.880 --> 00:02:08.631 So that's great. 00:02:08.631 --> 00:02:09.130 All right. 00:02:09.130 --> 00:02:11.080 So a couple of announcements. 00:02:11.080 --> 00:02:18.400 As you can see, see what I am wearing on my legs. 00:02:18.400 --> 00:02:23.200 So I was pleased with the performance on exam 2. 00:02:23.200 --> 00:02:29.110 The average was 84.7, not quite as celebratory 00:02:29.110 --> 00:02:33.610 as 87.4, which was the average on exam 1. 00:02:33.610 --> 00:02:34.944 Yeah, those are real numbers. 00:02:34.944 --> 00:02:35.860 That's a little weird. 00:02:35.860 --> 00:02:39.400 But anyway, I was still very happy with the performance 00:02:39.400 --> 00:02:40.690 on the exam. 00:02:40.690 --> 00:02:43.420 I would like for exam 3 for the average 00:02:43.420 --> 00:02:45.110 to be back at 87, though. 00:02:45.110 --> 00:02:49.930 I like it to be very close to 90 because I want everyone 00:02:49.930 --> 00:02:53.380 to have an average around 90 in the class 00:02:53.380 --> 00:02:55.730 to demonstrate excellent knowledge of chemistry. 00:02:55.730 --> 00:02:57.490 So I try to write an exam where I 00:02:57.490 --> 00:03:00.040 feel like if you have excellent knowledge of chemistry, 00:03:00.040 --> 00:03:02.420 you can get a 90% or above. 00:03:02.420 --> 00:03:04.000 So this is my goal. 00:03:04.000 --> 00:03:07.060 I all want you to have this fundamental knowledge 00:03:07.060 --> 00:03:10.300 of chemistry that you can go out and solve the energy problem, 00:03:10.300 --> 00:03:13.030 that you can go out and be ready to tackle 00:03:13.030 --> 00:03:15.850 the next great challenge in health. 00:03:15.850 --> 00:03:17.680 There's so many challenges facing us, 00:03:17.680 --> 00:03:20.000 and we don't even know what they are right now. 00:03:20.000 --> 00:03:24.770 So the Ebola situation, I think, is a real case in point, 00:03:24.770 --> 00:03:27.370 that we don't know what the next challenge facing us 00:03:27.370 --> 00:03:28.270 is going to be. 00:03:28.270 --> 00:03:31.111 So we need to be ready with our chemistry knowledge. 00:03:31.111 --> 00:03:33.610 The only thing I can tell you about the challenges facing us 00:03:33.610 --> 00:03:35.110 is that knowing chemistry is going 00:03:35.110 --> 00:03:37.630 to be really important in tackling those problems. 00:03:37.630 --> 00:03:40.280 So everyone needs to have an excellent understanding 00:03:40.280 --> 00:03:43.930 of chemistry to go on and do well and solve 00:03:43.930 --> 00:03:45.310 the problems of the world. 00:03:45.310 --> 00:03:49.030 So 84.7, really good. 00:03:49.030 --> 00:03:50.100 You're getting there. 00:03:50.100 --> 00:03:51.350 Awesome. 00:03:51.350 --> 00:03:53.752 So celebratory tights, or leggings. 00:03:53.752 --> 00:03:56.210 Not really sure the difference between tights and leggings. 00:03:56.210 --> 00:03:58.690 Anyway, I was very pleased. 00:03:58.690 --> 00:04:04.660 But next unit, next exam, has thermodynamics, chemical 00:04:04.660 --> 00:04:06.550 equilibrium, and acid-base. 00:04:06.550 --> 00:04:08.960 We're already done with thermodynamics and moving on. 00:04:08.960 --> 00:04:11.260 So it's just for the rest of the semester, 00:04:11.260 --> 00:04:15.110 we're about halfway there, the rate seems to accelerate. 00:04:15.110 --> 00:04:17.589 So problem set 5, thermodynamics. 00:04:17.589 --> 00:04:20.134 It's a little shorter because you have fewer days to do it. 00:04:20.134 --> 00:04:21.550 So we wanted to make sure that you 00:04:21.550 --> 00:04:24.619 would be able to get it done by Friday at noon. 00:04:24.619 --> 00:04:25.660 But that's when it's due. 00:04:25.660 --> 00:04:26.950 It's all thermodynamics. 00:04:26.950 --> 00:04:29.440 We've already covered all the material on the problem set. 00:04:29.440 --> 00:04:33.100 You can do it already right away. 00:04:33.100 --> 00:04:33.600 All right. 00:04:33.600 --> 00:04:37.210 So also in my wardrobe-- I'm commenting a lot on my wardrobe 00:04:37.210 --> 00:04:40.157 today-- you'll notice maybe that I've worn this shirt once 00:04:40.157 --> 00:04:42.490 before, and my goal was really to have a different shirt 00:04:42.490 --> 00:04:43.270 every time. 00:04:43.270 --> 00:04:46.390 Now, this shirt is appropriate for today's lecture. 00:04:46.390 --> 00:04:48.040 But I just wanted to say that I did 00:04:48.040 --> 00:04:50.470 try to get a different shirt. 00:04:50.470 --> 00:04:54.550 And I ordered new shirts on thermodynamics and chemical 00:04:54.550 --> 00:04:57.850 equilibrium this year, and one of the shirts 00:04:57.850 --> 00:04:59.087 had to do with entropy. 00:04:59.087 --> 00:05:01.170 And I just thought I would share with you briefly, 00:05:01.170 --> 00:05:03.220 because it's a good review of thermodynamics, 00:05:03.220 --> 00:05:06.620 what happens when you do things related to entropy. 00:05:06.620 --> 00:05:09.100 So just to sort of show you what happened. 00:05:09.100 --> 00:05:11.320 In September, I was super organized. 00:05:11.320 --> 00:05:12.370 I ordered my shirts. 00:05:12.370 --> 00:05:15.130 And on October 3, they shipped. 00:05:15.130 --> 00:05:18.430 They went through Indianapolis to Massachusetts 00:05:18.430 --> 00:05:20.320 and to Newton Highlands about somewhere 00:05:20.320 --> 00:05:22.180 around October 8 or 9. 00:05:22.180 --> 00:05:24.640 That's where I live, so that's really good. 00:05:24.640 --> 00:05:27.580 But the shirts were about entropy, 00:05:27.580 --> 00:05:28.930 and then look what happened. 00:05:28.930 --> 00:05:32.320 Wait-- rerouted for delivery to a new address. 00:05:32.320 --> 00:05:37.990 Jersey City, Cincinnati, Ohio, Warrendale, Pennsylvania. 00:05:37.990 --> 00:05:41.890 And then yesterday they were in Springfield, Massachusetts, 00:05:41.890 --> 00:05:43.970 to which I say, entropy! 00:05:47.780 --> 00:05:51.560 This does not happen when you order T-shirts about kinetics. 00:05:51.560 --> 00:05:52.940 That's all I'm saying. 00:05:52.940 --> 00:05:55.257 Those arrive record time. 00:05:58.460 --> 00:06:01.160 Thermodynamics is not always your friend, 00:06:01.160 --> 00:06:02.420 but you can embrace it. 00:06:02.420 --> 00:06:05.150 And I'm going to try to calm myself down 00:06:05.150 --> 00:06:09.200 because we should be at equilibrium today. 00:06:09.200 --> 00:06:12.890 Today, the topic is chemical equilibrium. 00:06:12.890 --> 00:06:16.970 It's the calm part of thermodynamics. 00:06:16.970 --> 00:06:18.620 We'll get back to entropy. 00:06:18.620 --> 00:06:20.690 There will be some mention of entropy. 00:06:20.690 --> 00:06:22.220 But I'm going to try to calm down. 00:06:22.220 --> 00:06:23.990 I'm going to remember my reaction 00:06:23.990 --> 00:06:26.570 quotients and my equilibrium constants 00:06:26.570 --> 00:06:29.300 and think about chemical equilibrium 00:06:29.300 --> 00:06:31.310 and embrace the T-shirt I am wearing. 00:06:31.310 --> 00:06:35.600 Because I feel powerful in this T-shirt, like I can control 00:06:35.600 --> 00:06:39.350 thermodynamics with the power of the Green Lantern, 00:06:39.350 --> 00:06:41.660 with chemistry knowledge at my fingertips, 00:06:41.660 --> 00:06:44.130 and I will move forward. 00:06:44.130 --> 00:06:47.330 So chemical equilibrium is calming, 00:06:47.330 --> 00:06:49.250 but it's also a dynamic process. 00:06:49.250 --> 00:06:53.570 We can't forget that the reactions have not stopped. 00:06:53.570 --> 00:06:56.150 It's just the rate of the forward reaction 00:06:56.150 --> 00:06:59.640 is equal to the rate of the reverse reaction. 00:06:59.640 --> 00:07:02.810 So there's no net change, but the dynamic process 00:07:02.810 --> 00:07:05.580 is still happening. 00:07:05.580 --> 00:07:10.910 So my goal in life is to have equilibrium in my life. 00:07:10.910 --> 00:07:15.590 The amount of work-- the rate at which work comes into my office 00:07:15.590 --> 00:07:18.350 equals the rate at which I complete the work 00:07:18.350 --> 00:07:20.450 and it leaves my office. 00:07:20.450 --> 00:07:22.550 Most of you should also have this goal. 00:07:22.550 --> 00:07:25.160 The rate at which problem sets come in 00:07:25.160 --> 00:07:28.330 equals the rate at which you complete the problem sets 00:07:28.330 --> 00:07:30.470 and the problem sets get turned in. 00:07:30.470 --> 00:07:32.390 You don't want to get yourself in a situation 00:07:32.390 --> 00:07:34.480 where that equilibrium is messed up, 00:07:34.480 --> 00:07:36.470 where the rate of things coming in 00:07:36.470 --> 00:07:39.350 is just nowhere at all equal to the rate at which things 00:07:39.350 --> 00:07:41.180 are completed and going out. 00:07:41.180 --> 00:07:43.260 So goal-- chemical equilibrium. 00:07:43.260 --> 00:07:47.340 We want to be at this calm place where we're still working hard. 00:07:47.340 --> 00:07:49.550 It's still dynamic. 00:07:49.550 --> 00:07:51.490 But the net change is good. 00:07:51.490 --> 00:07:52.580 It's in our favor. 00:07:52.580 --> 00:07:55.640 The amount of work we're doing equals the work coming in. 00:07:55.640 --> 00:07:57.380 So I like chemical equilibrium. 00:07:57.380 --> 00:08:01.280 I feel like it brings hope to thermodynamics. 00:08:01.280 --> 00:08:04.300 So let's look at an example of a reaction, 00:08:04.300 --> 00:08:06.920 and we're going to talk a lot about this reaction in chemical 00:08:06.920 --> 00:08:08.160 equilibrium. 00:08:08.160 --> 00:08:12.650 So we have N2, nitrogen, H2, hydrogen coming together 00:08:12.650 --> 00:08:15.620 to form ammonia, and it has a delta G0 00:08:15.620 --> 00:08:19.710 of minus 32.9 kilojoules per mole. 00:08:19.710 --> 00:08:21.260 So let's think about what's happening 00:08:21.260 --> 00:08:23.343 in the beginning of this reaction, when we're just 00:08:23.343 --> 00:08:25.260 starting this reaction. 00:08:25.260 --> 00:08:30.810 So we can plot concentration on one axis, 00:08:30.810 --> 00:08:34.419 and we can have time on our other axis, 00:08:34.419 --> 00:08:36.724 so time increasing over here. 00:08:36.724 --> 00:08:38.390 And we can think about what happens when 00:08:38.390 --> 00:08:39.556 we're starting our reaction. 00:08:43.309 --> 00:08:45.860 We can have hydrogen starting out. 00:08:45.860 --> 00:08:48.920 We have some hydrogen in a certain concentration, 00:08:48.920 --> 00:08:51.350 and it's going to come down and level out. 00:08:51.350 --> 00:08:53.270 So that's our H2. 00:08:53.270 --> 00:08:56.720 We'll also have nitrogen as a reactant. 00:08:56.720 --> 00:09:00.320 It comes down, levels out. 00:09:00.320 --> 00:09:02.570 And we're starting with our product. 00:09:02.570 --> 00:09:03.650 We have no product. 00:09:03.650 --> 00:09:06.200 We're just starting the reaction with the reactants. 00:09:06.200 --> 00:09:10.002 So product increases and then levels out. 00:09:13.160 --> 00:09:15.860 So we're decreasing our reactants, 00:09:15.860 --> 00:09:18.470 increasing our product, but the lines go flat. 00:09:18.470 --> 00:09:20.335 The reaction is still happening. 00:09:20.335 --> 00:09:22.460 The reaction in the forward direction is happening, 00:09:22.460 --> 00:09:25.140 and then in the reverse direction is happening. 00:09:25.140 --> 00:09:27.434 But there's no net change at equilibrium 00:09:27.434 --> 00:09:28.850 because it's reached a state where 00:09:28.850 --> 00:09:31.550 the rate of the forward reaction equals the rate 00:09:31.550 --> 00:09:34.940 of the reverse reaction. 00:09:34.940 --> 00:09:37.910 And let me also just point out some arrows 00:09:37.910 --> 00:09:39.710 and some nomenclature here. 00:09:39.710 --> 00:09:41.360 So we have this double arrow, and you 00:09:41.360 --> 00:09:43.370 can see this a couple of different ways. 00:09:43.370 --> 00:09:46.370 But this indicates the reaction's going forward, 00:09:46.370 --> 00:09:48.380 and the reaction is going back. 00:09:48.380 --> 00:09:50.630 And that's necessary if you're at equilibrium. 00:09:50.630 --> 00:09:52.520 The definition of equilibrium-- rate 00:09:52.520 --> 00:09:55.070 forward equals rate back at equilibrium. 00:09:55.070 --> 00:09:56.970 So you'll be seeing those arrows a lot. 00:09:56.970 --> 00:09:57.470 All right. 00:09:57.470 --> 00:10:00.350 So let's think about delta G now in terms 00:10:00.350 --> 00:10:03.690 of what's happening at different times in this reaction. 00:10:03.690 --> 00:10:06.560 So if we're just starting out this reaction, 00:10:06.560 --> 00:10:08.120 and you don't have a lot of products, 00:10:08.120 --> 00:10:11.194 so you're in this case of pure reactants. 00:10:11.194 --> 00:10:12.860 At this point, you're going to be moving 00:10:12.860 --> 00:10:13.901 in the forward direction. 00:10:13.901 --> 00:10:15.830 You need to make products. 00:10:15.830 --> 00:10:18.440 And so at this point, the forward direction is negative. 00:10:18.440 --> 00:10:19.490 It's spontaneous. 00:10:19.490 --> 00:10:21.380 You're spontaneously making your products. 00:10:21.380 --> 00:10:23.630 You don't have any at this point. 00:10:23.630 --> 00:10:26.100 And so your delta G is going to be negative. 00:10:26.100 --> 00:10:30.300 So up here with pure reactants, your delta G is negative. 00:10:30.300 --> 00:10:32.090 Now, if you started with pure products-- 00:10:32.090 --> 00:10:36.350 you could do that as well-- the NH3 will dissociate and form 00:10:36.350 --> 00:10:38.010 the reactants. 00:10:38.010 --> 00:10:40.700 And so that would be over here. 00:10:40.700 --> 00:10:43.670 And so when you have excess products, 00:10:43.670 --> 00:10:46.280 now the forward direction is positive. 00:10:46.280 --> 00:10:49.610 It's not spontaneous because it's the reverse direction that 00:10:49.610 --> 00:10:51.140 is spontaneous. 00:10:51.140 --> 00:10:54.020 So over in this part of the graph over here, 00:10:54.020 --> 00:10:56.850 our delta G is positive. 00:10:56.850 --> 00:10:59.390 So if you have pure reactants, you spontaneously 00:10:59.390 --> 00:11:00.290 go to products. 00:11:00.290 --> 00:11:05.560 If you have pure products, you're going toward reactants. 00:11:05.560 --> 00:11:08.490 And when you have the right amount of reactants 00:11:08.490 --> 00:11:11.830 to products, the right ratio for equilibrium, 00:11:11.830 --> 00:11:18.190 then you get to equilibrium and delta G equals 0 at that point. 00:11:18.190 --> 00:11:20.560 So delta G is going to change depending 00:11:20.560 --> 00:11:22.608 on your ratio of products to reactants. 00:11:26.200 --> 00:11:29.890 So delta G changes as the proportion 00:11:29.890 --> 00:11:31.390 of the reactants and the products 00:11:31.390 --> 00:11:36.740 change, and there's an equation to describe that. 00:11:36.740 --> 00:11:39.070 So we're back now to having a few more 00:11:39.070 --> 00:11:40.670 equations in this unit. 00:11:40.670 --> 00:11:44.510 We noted a lot of people forgot to bring calculators to exam 2. 00:11:44.510 --> 00:11:46.840 There weren't so many calculations. 00:11:46.840 --> 00:11:49.630 We're back to more calculations again. 00:11:49.630 --> 00:11:55.660 So delta G equals delta G0 plus RT natural log of Q. 00:11:55.660 --> 00:11:57.040 So let's think about these terms. 00:11:57.040 --> 00:12:01.960 So delta G is Gibbs free energy at some particular point, 00:12:01.960 --> 00:12:05.470 at some ratio of product to reactant. 00:12:05.470 --> 00:12:10.900 Delta G0 is Gibb's free energy under standard conditions, 00:12:10.900 --> 00:12:13.030 in their standard state. 00:12:13.030 --> 00:12:17.620 Q is our reaction quotient, products over reactants. 00:12:17.620 --> 00:12:22.210 And R is the universal gas constant, and T is temperature. 00:12:22.210 --> 00:12:26.140 So this equation describes how delta G 00:12:26.140 --> 00:12:29.050 will compare to delta G0 at a particular condition, 00:12:29.050 --> 00:12:33.340 a particular ratio, of products and reactants. 00:12:33.340 --> 00:12:34.780 So let's talk about this reaction 00:12:34.780 --> 00:12:41.870 quotient Q. So let's look at a made-up reaction-- 00:12:41.870 --> 00:12:47.090 A plus B goes to C plus D. And think about that reaction 00:12:47.090 --> 00:12:48.450 in the gas phase. 00:12:48.450 --> 00:12:50.930 When we think about that reaction in the gas phase, 00:12:50.930 --> 00:12:55.190 we're going to be talking about partial pressures. 00:12:55.190 --> 00:13:01.040 And so Q over here is products over reactants, 00:13:01.040 --> 00:13:05.450 but here we're writing it out in a more complicated long way. 00:13:05.450 --> 00:13:07.190 So let's go through this. 00:13:07.190 --> 00:13:10.640 So we have this P sub C. Well, what is that? 00:13:10.640 --> 00:13:12.500 That is partial pressure. 00:13:12.500 --> 00:13:15.800 So partial pressure of gas X, and this 00:13:15.800 --> 00:13:20.240 is partial pressure of gas C, and C is a product 00:13:20.240 --> 00:13:21.380 and D is a product. 00:13:21.380 --> 00:13:23.750 So we have products over reactants. 00:13:23.750 --> 00:13:28.010 Partial pressure of gas C over P reference, 00:13:28.010 --> 00:13:31.040 partial pressure reference, which is 1 bar. 00:13:31.040 --> 00:13:34.400 The reference is 1 bar, so we're dividing that by 1. 00:13:34.400 --> 00:13:37.460 And this is raised to the little c, 00:13:37.460 --> 00:13:41.210 which has to do with the coefficients of the reaction. 00:13:41.210 --> 00:13:43.210 Then we have partial pressure of gas D 00:13:43.210 --> 00:13:46.520 over our reference raised to the small d-- those 00:13:46.520 --> 00:13:49.030 are our products, products are C and D-- 00:13:49.030 --> 00:13:51.200 over reactants-- partial pressure 00:13:51.200 --> 00:13:54.470 of gas A over reference raised to little a, 00:13:54.470 --> 00:13:59.300 partial pressure of gas B over reference raised to little b. 00:13:59.300 --> 00:14:04.910 But 1, the number 1, the reference is 1. 00:14:04.910 --> 00:14:09.350 So most of the time you'll see the following expression-- Q, 00:14:09.350 --> 00:14:12.040 our reaction quotient, partial pressure of gas 00:14:12.040 --> 00:14:16.595 C to the stoichiometry little c partial pressure of gas 00:14:16.595 --> 00:14:20.780 D raised to the stoichiometry d, over reactants, 00:14:20.780 --> 00:14:25.690 partial pressure of A little a partial pressure of B little b. 00:14:25.690 --> 00:14:30.320 And you will note that because we had 1 bar 00:14:30.320 --> 00:14:34.070 and these are in bars, our units are going to cancel here. 00:14:34.070 --> 00:14:37.220 So Q does not have units. 00:14:37.220 --> 00:14:39.665 I knew this should be very exciting for you. 00:14:39.665 --> 00:14:43.490 You won't be losing one point for lack of units with Q. 00:14:43.490 --> 00:14:44.600 There are no units. 00:14:44.600 --> 00:14:46.640 So this is very exciting. 00:14:46.640 --> 00:14:50.645 So there's the expression that you'll mostly see for Q. 00:14:50.645 --> 00:14:54.140 And now we can kind of forget that the reference is there. 00:14:54.140 --> 00:14:55.490 We can ignore the reference. 00:14:55.490 --> 00:14:58.910 You just don't freak out later if you have no units. 00:14:58.910 --> 00:15:00.710 It's OK. 00:15:00.710 --> 00:15:01.210 All right. 00:15:01.210 --> 00:15:04.880 So we also could be talking about solution, 00:15:04.880 --> 00:15:07.142 and here we're going to talk about concentrations. 00:15:07.142 --> 00:15:08.600 In a lot of these problems, they're 00:15:08.600 --> 00:15:10.070 talking about things in the gas phase, 00:15:10.070 --> 00:15:11.570 and they're giving you concentrations. 00:15:11.570 --> 00:15:12.460 Don't worry about it. 00:15:12.460 --> 00:15:14.180 It's all OK. 00:15:14.180 --> 00:15:17.900 So here our concentration reference, C for concentration, 00:15:17.900 --> 00:15:19.490 is 1 molar. 00:15:19.490 --> 00:15:22.220 And you'll see this term-- C in brackets. 00:15:22.220 --> 00:15:25.070 That means concentration of. 00:15:25.070 --> 00:15:28.430 And so if you see that like this, you 00:15:28.430 --> 00:15:32.750 would express this in words as the concentration of C-- again, 00:15:32.750 --> 00:15:35.232 that's a product-- over the reference-- we'll get rid 00:15:35.232 --> 00:15:37.190 of the reference in a minute, but we'll keep it 00:15:37.190 --> 00:15:42.110 for now-- raised to the little c, concentration of product D 00:15:42.110 --> 00:15:45.530 over this concentration reference of 1 molar 00:15:45.530 --> 00:15:49.820 to the little d, concentration of reactant A 00:15:49.820 --> 00:15:52.010 over this concentration reference 00:15:52.010 --> 00:15:55.400 raised to the little a, concentration of other reactant 00:15:55.400 --> 00:15:59.330 B over our concentration reference of 1 molar raised 00:15:59.330 --> 00:16:00.620 to the little b. 00:16:00.620 --> 00:16:04.640 And then, again, this is concentration. 00:16:04.640 --> 00:16:06.620 And we can get this expression, which 00:16:06.620 --> 00:16:10.790 is usually the one you see, of just products over reactants. 00:16:10.790 --> 00:16:14.120 But I will make one point here, that you 00:16:14.120 --> 00:16:16.370 need to know how to balance equations 00:16:16.370 --> 00:16:18.110 to be able to do these. 00:16:18.110 --> 00:16:21.020 So in the beginning of the book there 00:16:21.020 --> 00:16:23.660 was something about balancing, limiting reagents, 00:16:23.660 --> 00:16:25.250 stuff like that. 00:16:25.250 --> 00:16:27.020 If you feel like you did not master that, 00:16:27.020 --> 00:16:27.994 you want to go over it. 00:16:27.994 --> 00:16:29.285 You need to be able to balance. 00:16:29.285 --> 00:16:30.710 And in a lot of these problems you 00:16:30.710 --> 00:16:33.771 may be thinking about limiting reagents again. 00:16:33.771 --> 00:16:34.270 All right. 00:16:34.270 --> 00:16:37.569 So that's Q. You can see it as partial pressure-- 00:16:37.569 --> 00:16:39.610 and I'm going to do a little partial pressure gas 00:16:39.610 --> 00:16:42.760 review on Friday-- or concentrations 00:16:42.760 --> 00:16:45.940 with these brackets. 00:16:45.940 --> 00:16:51.820 So at equilibrium, delta G equals 0. 00:16:51.820 --> 00:16:54.280 And it's a dynamic process-- rate 00:16:54.280 --> 00:16:58.000 of the forward reaction equals rate of the reverse reaction. 00:16:58.000 --> 00:17:01.630 Q now is the equilibrium constant, 00:17:01.630 --> 00:17:05.170 because the ratio of products to reactants at equilibrium 00:17:05.170 --> 00:17:09.859 is the definition of the equilibrium constant. 00:17:09.859 --> 00:17:13.359 So when delta G equals 0, Q equals K. 00:17:13.359 --> 00:17:17.890 So we now can go back to this expression that we had 00:17:17.890 --> 00:17:20.829 and rewrite this for the situation 00:17:20.829 --> 00:17:24.510 at equilibrium, when delta G equals 0. 00:17:24.510 --> 00:17:27.329 So when delta G equals 0, this is 0 00:17:27.329 --> 00:17:33.030 and Q is K. K is products over reactants at equilibrium. 00:17:33.030 --> 00:17:36.300 And we can rewrite this or rearrange it now-- 00:17:36.300 --> 00:17:42.560 delta G0 equals minus RT natural log of K. 00:17:42.560 --> 00:17:44.560 And that's a very important equation that you'll 00:17:44.560 --> 00:17:46.590 be using a lot in these units. 00:17:46.590 --> 00:17:51.400 So it relates delta G0 with our equilibrium constant K, 00:17:51.400 --> 00:17:55.031 and it depends on temperature. 00:17:55.031 --> 00:17:55.530 All right. 00:17:55.530 --> 00:18:01.510 So K-- same expression as Q, except for something 00:18:01.510 --> 00:18:04.540 very important, which is that the concentrations are 00:18:04.540 --> 00:18:07.480 the concentrations at equilibrium. 00:18:07.480 --> 00:18:10.320 So it has the same form as Q, but it's 00:18:10.320 --> 00:18:13.790 only the amount of products and reactants at equilibrium. 00:18:13.790 --> 00:18:15.880 So in the gas phase, we would write 00:18:15.880 --> 00:18:18.670 K in terms of our partial pressures. 00:18:18.670 --> 00:18:22.120 And again, this is this little symbol to remind you 00:18:22.120 --> 00:18:25.490 these are the concentrations at equilibrium. 00:18:25.490 --> 00:18:27.550 And in solution it would be expressed 00:18:27.550 --> 00:18:29.390 in molar or something else. 00:18:29.390 --> 00:18:32.790 So K is, again, products over reactants, 00:18:32.790 --> 00:18:35.140 but only those concentrations at equilibrium. 00:18:35.140 --> 00:18:38.590 Whereas Q is at any point, any concentrations 00:18:38.590 --> 00:18:41.740 of products over reactants for Q. For K, 00:18:41.740 --> 00:18:45.895 it's those concentrations at equilibrium. 00:18:45.895 --> 00:18:46.690 All right. 00:18:46.690 --> 00:18:53.070 So now let's think about Q and K together. 00:18:53.070 --> 00:18:55.530 So we can rewrite this expression again. 00:18:55.530 --> 00:19:01.290 We just derived a new expression for delta G0, 00:19:01.290 --> 00:19:04.800 and that was minus RT natural log of K. 00:19:04.800 --> 00:19:07.900 So we can say delta G equals, and now 00:19:07.900 --> 00:19:10.180 have this other expression, minus RT 00:19:10.180 --> 00:19:15.445 natural log of K plus RT again-- gas constant 00:19:15.445 --> 00:19:19.090 and temperature-- natural log of Q. 00:19:19.090 --> 00:19:24.030 And we can simplify it, bring out the RTs, 00:19:24.030 --> 00:19:30.130 and now we have delta G equals RT natural log of Q/K. 00:19:30.130 --> 00:19:33.860 And this is, again, a very important expression 00:19:33.860 --> 00:19:35.260 that you'll use a lot. 00:19:35.260 --> 00:19:39.460 Because it tells you about delta G, 00:19:39.460 --> 00:19:41.890 whether the reaction is going to be spontaneous 00:19:41.890 --> 00:19:44.510 in the forward direction or the reverse direction, 00:19:44.510 --> 00:19:48.670 depending on the ratio of Q and K. 00:19:48.670 --> 00:19:50.820 This is a very important equation 00:19:50.820 --> 00:19:53.040 for chemical equilibrium. 00:19:53.040 --> 00:19:57.640 So let's think about what this means, what comes out of this. 00:19:57.640 --> 00:20:07.750 So the relationship between Q and K, if Q is less than K, 00:20:07.750 --> 00:20:12.420 what is the sign of delta G? 00:20:12.420 --> 00:20:14.012 You can just yell it out. 00:20:14.012 --> 00:20:14.904 AUDIENCE: Negative. 00:20:14.904 --> 00:20:16.352 CATHERINE DRENNAN: Yep. 00:20:16.352 --> 00:20:17.560 So it's going to be negative. 00:20:17.560 --> 00:20:20.585 Just mathematically, you can look at that expression. 00:20:20.585 --> 00:20:21.460 So it'll be negative. 00:20:21.460 --> 00:20:23.140 And again, we give you all the equations 00:20:23.140 --> 00:20:24.130 on the equation sheet. 00:20:24.130 --> 00:20:24.921 That will be there. 00:20:24.921 --> 00:20:27.570 So you just need to know how to think about it. 00:20:27.570 --> 00:20:29.960 And so the forward reaction will occur. 00:20:29.960 --> 00:20:31.720 And so if we think about this, it's 00:20:31.720 --> 00:20:33.580 going to mean that at equilibrium there 00:20:33.580 --> 00:20:37.390 are more products than there are at this time for Q. 00:20:37.390 --> 00:20:39.790 There's less products in the Q expression. 00:20:39.790 --> 00:20:43.690 K is greater than Q. So we need to make more products. 00:20:43.690 --> 00:20:46.590 So delta G will be negative, and the forward reaction 00:20:46.590 --> 00:20:48.800 will occur. 00:20:48.800 --> 00:20:53.890 So when Q is greater than K, delta G is positive. 00:20:53.890 --> 00:20:55.660 And so when Q is greater than K, that 00:20:55.660 --> 00:20:58.900 means there's more products now in Q 00:20:58.900 --> 00:21:02.110 than there are at equilibrium, too many products. 00:21:02.110 --> 00:21:05.170 So we need to shift it in the reverse direction. 00:21:05.170 --> 00:21:07.190 So delta G will be positive. 00:21:07.190 --> 00:21:10.270 So again, thinking about the ratio of Q and K 00:21:10.270 --> 00:21:13.450 tells you about what direction is going to be spontaneous. 00:21:13.450 --> 00:21:18.070 Is it spontaneous in the forward direction or in the reverse? 00:21:18.070 --> 00:21:18.880 OK. 00:21:18.880 --> 00:21:23.960 So let's continue doing a little example. 00:21:23.960 --> 00:21:25.900 We can do a little calculation here 00:21:25.900 --> 00:21:28.480 on the board for the same reaction. 00:21:28.480 --> 00:21:31.960 We're given a value of K. And now 00:21:31.960 --> 00:21:35.710 we're told some partial pressures of these gases 00:21:35.710 --> 00:21:38.410 and asked which direction the reaction will go. 00:21:38.410 --> 00:21:41.665 So let's write the expression for Q. 00:21:41.665 --> 00:21:45.190 So Q, again, is going to be equal to products 00:21:45.190 --> 00:21:51.400 over reactants, and our product here is our NH3. 00:21:51.400 --> 00:21:55.020 So we're going to be talking about the partial pressure 00:21:55.020 --> 00:21:58.320 because it's a gas of NH3. 00:21:58.320 --> 00:22:01.050 And am I done with the top part of this expression? 00:22:01.050 --> 00:22:01.592 AUDIENCE: No. 00:22:01.592 --> 00:22:02.508 CATHERINE DRENNAN: No. 00:22:02.508 --> 00:22:03.448 What do I need? 00:22:03.448 --> 00:22:04.364 AUDIENCE: [INAUDIBLE]. 00:22:04.364 --> 00:22:05.440 CATHERINE DRENNAN: Yep. 00:22:05.440 --> 00:22:09.500 Again, you need to remember the stoichiometry of the reaction. 00:22:09.500 --> 00:22:14.330 So now we have the partial pressure of N2 on the bottom, 00:22:14.330 --> 00:22:18.540 and I'm good, and the partial pressure of H2. 00:22:18.540 --> 00:22:22.720 And again, I have to remember that there are three 00:22:22.720 --> 00:22:25.610 H2s in this balanced reaction. 00:22:25.610 --> 00:22:29.740 So we have the partial pressure of H2 to the third. 00:22:29.740 --> 00:22:31.910 I can put in my numbers. 00:22:31.910 --> 00:22:44.140 1.1 squared over 5.5 over 2.2-- these numbers may be made up, 00:22:44.140 --> 00:22:52.750 that's OK-- equals 2.1 times 10 to the minus 2. 00:22:52.750 --> 00:22:56.110 And we're back to thinking about significant figures 00:22:56.110 --> 00:22:58.370 a lot again in this unit. 00:22:58.370 --> 00:23:02.380 So I have two there, so I'm going to have these two here, 00:23:02.380 --> 00:23:03.810 and I'm good. 00:23:03.810 --> 00:23:07.270 But now this is the value of Q. And I 00:23:07.270 --> 00:23:10.530 want you to tell me with a clicker question, what 00:23:10.530 --> 00:23:12.761 direction is this reaction going to go? 00:23:39.141 --> 00:23:39.640 All right. 00:23:39.640 --> 00:23:41.098 Let's just take 10 more seconds. 00:23:57.620 --> 00:23:58.380 All right? 00:23:58.380 --> 00:24:02.770 So recognized, for the most part, 00:24:02.770 --> 00:24:04.780 that yeah, most of these numbers, 00:24:04.780 --> 00:24:07.620 that Q is a bigger number than K. 00:24:07.620 --> 00:24:10.780 And so then you have to think about what that means. 00:24:10.780 --> 00:24:15.670 And so when Q is greater than K, then you're 00:24:15.670 --> 00:24:18.100 going to go toward reactants. 00:24:21.360 --> 00:24:25.060 And so you're going to dissociate the product 00:24:25.060 --> 00:24:27.550 until you achieve equilibrium again. 00:24:27.550 --> 00:24:30.180 And so this means when you have a big Q number, 00:24:30.180 --> 00:24:34.060 you have too many products compared to the equilibrium 00:24:34.060 --> 00:24:37.540 state, and you want to dissociate your products. 00:24:37.540 --> 00:24:40.510 So you're going to go spontaneously 00:24:40.510 --> 00:24:42.280 in the reverse direction. 00:24:42.280 --> 00:24:46.846 Now, I just want to mention one point. 00:24:46.846 --> 00:24:48.220 For the first part of the course, 00:24:48.220 --> 00:24:50.747 I only taught that material once before. 00:24:50.747 --> 00:24:52.330 But the second part I've taught a lot. 00:24:52.330 --> 00:24:54.580 So I have lots of years of experience 00:24:54.580 --> 00:24:57.220 of what people do wrong on exams on this part, 00:24:57.220 --> 00:24:59.500 and I will share one thing. 00:24:59.500 --> 00:25:02.740 A lot of students-- and faculty too, 00:25:02.740 --> 00:25:06.460 I'm this way-- right-left challenged. 00:25:06.460 --> 00:25:09.510 So they write left when they mean right. 00:25:09.510 --> 00:25:12.730 They write right when they mean left. 00:25:12.730 --> 00:25:18.050 And so for those of you who are like me and have this issue, 00:25:18.050 --> 00:25:20.200 draw an arrow. 00:25:20.200 --> 00:25:23.130 When people draw an arrow, they always draw it in the direction 00:25:23.130 --> 00:25:26.680 that they mean, or they say toward reactants 00:25:26.680 --> 00:25:28.570 or toward products. 00:25:28.570 --> 00:25:30.550 And so I've seen so many times on the test 00:25:30.550 --> 00:25:35.110 they'd explain the answer beautifully, and then 00:25:35.110 --> 00:25:38.210 write the wrong direction down. 00:25:38.210 --> 00:25:41.110 So if you are right-left challenged, 00:25:41.110 --> 00:25:45.550 try toward reactants or toward products or draw an arrow. 00:25:45.550 --> 00:25:48.880 So that is my suggestion to you, as someone 00:25:48.880 --> 00:25:52.510 who's also very bad with saying the right direction, 00:25:52.510 --> 00:25:55.110 left or right, when I mean that direction. 00:25:55.110 --> 00:25:56.110 OK. 00:25:56.110 --> 00:25:57.432 So what does K tell us? 00:26:00.160 --> 00:26:04.660 So K tells us about the ratio of products 00:26:04.660 --> 00:26:07.560 to reactants at equilibrium. 00:26:07.560 --> 00:26:11.090 And if you have a very big number for K, 00:26:11.090 --> 00:26:13.850 it's going to tell you something about the ratio 00:26:13.850 --> 00:26:16.310 of those products to the reactants, 00:26:16.310 --> 00:26:18.950 and there'll be a lot of products for reactants. 00:26:18.950 --> 00:26:21.600 So let's just think about this for a minute. 00:26:21.600 --> 00:26:26.840 So when K is greater than 1-- K is 00:26:26.840 --> 00:26:29.990 products over reactants at equilibrium-- 00:26:29.990 --> 00:26:33.170 that's going to mean high products. 00:26:33.170 --> 00:26:35.950 So you'll have a higher number there. 00:26:35.950 --> 00:26:40.580 But if you have a small value for K, 00:26:40.580 --> 00:26:43.760 then you're going to have low products at equilibrium. 00:26:43.760 --> 00:26:47.005 So this is a good thing just to think about and check yourself 00:26:47.005 --> 00:26:48.380 when you're doing these problems. 00:26:48.380 --> 00:26:50.810 Does my answer actually make sense? 00:26:50.810 --> 00:26:53.780 And if you see a big value for K, you're like, great. 00:26:53.780 --> 00:26:57.110 If I want products, I want a big value for the equilibrium 00:26:57.110 --> 00:26:59.200 constant, means that this reaction 00:26:59.200 --> 00:27:01.010 is going to give me a lot of what I want, 00:27:01.010 --> 00:27:02.380 a lot of my products. 00:27:02.380 --> 00:27:07.380 Because again, K is products over reactants at equilibrium. 00:27:07.380 --> 00:27:08.120 All right. 00:27:08.120 --> 00:27:10.680 So let's do an example here. 00:27:10.680 --> 00:27:13.900 So here is an example where K is greater than 1. 00:27:13.900 --> 00:27:16.450 It's actually 6.84 at room temperature. 00:27:16.450 --> 00:27:21.590 We have a delta G0 of minus 4.76 kilojoules per mole. 00:27:21.590 --> 00:27:23.870 Two NO2 molecules going to N2O4. 00:27:26.930 --> 00:27:30.740 So we're going to start with 1 bar of our reactants 00:27:30.740 --> 00:27:32.680 and no products. 00:27:32.680 --> 00:27:34.520 So we can look at what that's going 00:27:34.520 --> 00:27:38.380 to look like in our plot of concentration versus time. 00:27:38.380 --> 00:27:40.430 And here the concentration is indicated 00:27:40.430 --> 00:27:44.270 as partial pressure, which is one type of concentration. 00:27:44.270 --> 00:27:46.490 So we're starting only with our reactants. 00:27:46.490 --> 00:27:48.130 It will go down. 00:27:48.130 --> 00:27:50.030 We'll have no products in the beginning. 00:27:50.030 --> 00:27:52.880 At time 0, no products, and that will grow up. 00:27:52.880 --> 00:27:56.180 The curves will level off as you reach the equilibrium. 00:27:56.180 --> 00:27:58.040 Again, the reaction's still going 00:27:58.040 --> 00:27:59.680 in the forward and reverse directions, 00:27:59.680 --> 00:28:01.430 but the rates are equal so there's 00:28:01.430 --> 00:28:06.300 no net change in the concentrations then. 00:28:06.300 --> 00:28:08.790 So now we can actually do some math 00:28:08.790 --> 00:28:12.600 and figure out how this changes. 00:28:12.600 --> 00:28:15.300 And so this is one way that you can set up 00:28:15.300 --> 00:28:16.880 these kinds of problems. 00:28:16.880 --> 00:28:18.910 And we will be doing these types of problems 00:28:18.910 --> 00:28:21.930 in chemical equilibrium, acid-base equilibrium. 00:28:21.930 --> 00:28:23.580 There'll be many examples, so it's 00:28:23.580 --> 00:28:25.000 good to become familiar with them 00:28:25.000 --> 00:28:27.030 if you haven't seen it before. 00:28:27.030 --> 00:28:28.980 So we can calculate the partial pressures 00:28:28.980 --> 00:28:32.230 at equilibrium using this information. 00:28:32.230 --> 00:28:35.120 So when we started, we only had our reactant. 00:28:35.120 --> 00:28:40.050 We had 1 bar, 1.000 bar, to be specific, 00:28:40.050 --> 00:28:41.610 and we had no product. 00:28:41.610 --> 00:28:44.610 As the reaction goes, we will form product, 00:28:44.610 --> 00:28:47.856 so it's plus X. Some amount of product is going to be formed. 00:28:50.630 --> 00:28:53.120 What is the change in partial pressure 00:28:53.120 --> 00:28:55.590 as you go to equilibrium? 00:28:55.590 --> 00:28:56.880 What happens to this? 00:28:56.880 --> 00:28:57.810 What changes? 00:28:57.810 --> 00:29:00.544 What do I put in this area? 00:29:00.544 --> 00:29:01.460 AUDIENCE: [INAUDIBLE]. 00:29:01.460 --> 00:29:02.460 CATHERINE DRENNAN: What? 00:29:02.460 --> 00:29:03.446 AUDIENCE: [INAUDIBLE] 00:29:03.446 --> 00:29:04.862 CATHERINE DRENNAN: I heard minus-- 00:29:04.862 --> 00:29:06.812 AUDIENCE: [INAUDIBLE]. 00:29:06.812 --> 00:29:09.270 CATHERINE DRENNAN: So I heard minus X. I heard somebody say 00:29:09.270 --> 00:29:09.770 [INAUDIBLE]. 00:29:09.770 --> 00:29:13.380 It's minus 2X because you have to remember the stoichiometry 00:29:13.380 --> 00:29:14.930 of the reaction. 00:29:14.930 --> 00:29:18.120 And so we have two of these going to one of those, 00:29:18.120 --> 00:29:21.060 so it's minus 2X. 00:29:21.060 --> 00:29:28.230 And then at equilibrium, we have 1.000 minus 2X is 00:29:28.230 --> 00:29:31.380 our concentration of our reactant, 00:29:31.380 --> 00:29:36.120 and our concentration of product is plus X. 00:29:36.120 --> 00:29:38.370 So now we're going to solve for this, 00:29:38.370 --> 00:29:41.970 and we need to write an expression for the equilibrium 00:29:41.970 --> 00:29:42.970 constant. 00:29:42.970 --> 00:29:44.586 So why don't you write that for me. 00:30:04.660 --> 00:30:05.160 All right. 00:30:05.160 --> 00:30:06.026 10 more seconds. 00:30:16.570 --> 00:30:17.340 I'd like 90%. 00:30:20.710 --> 00:30:24.290 Oh, so close. 00:30:24.290 --> 00:30:24.980 OK. 00:30:24.980 --> 00:30:28.390 So again, the trick here, you have products over reactants, 00:30:28.390 --> 00:30:31.550 and you have to remember the stoichiometry. 00:30:31.550 --> 00:30:33.360 So we can go back over here. 00:30:33.360 --> 00:30:36.190 So we have partial pressure of our product 00:30:36.190 --> 00:30:39.160 over partial pressure of our reactant. 00:30:39.160 --> 00:30:42.890 And we have the stoichiometry there, 00:30:42.890 --> 00:30:45.530 and now we can continue to plug in. 00:30:45.530 --> 00:30:48.650 So the concentration, the partial pressure, 00:30:48.650 --> 00:30:52.340 of our product is X at equilibrium. 00:30:52.340 --> 00:30:57.400 The partial pressure of our reactant is 1 minus 2X, 00:30:57.400 --> 00:31:00.532 and that whole term is raised to the 2. 00:31:00.532 --> 00:31:04.210 So it's all that whole term is squared. 00:31:04.210 --> 00:31:12.910 And if you solve for X, you will get 0.38 bar. 00:31:12.910 --> 00:31:15.830 So you definitely want to remember calculators and things 00:31:15.830 --> 00:31:18.190 on this exam. 00:31:18.190 --> 00:31:21.210 And that value, then, is our product. 00:31:21.210 --> 00:31:23.950 So that's the answer to the partial pressure of the product 00:31:23.950 --> 00:31:25.660 because that's what X is. 00:31:25.660 --> 00:31:27.460 Another thing that I've seen on exams 00:31:27.460 --> 00:31:30.130 is that people solve for X. They're happy to solve for X. 00:31:30.130 --> 00:31:32.200 But then they don't remember what X was. 00:31:32.200 --> 00:31:36.640 So keep track of what things belong to what. 00:31:36.640 --> 00:31:39.400 So then we want to also find the partial pressure 00:31:39.400 --> 00:31:40.690 of our reactant. 00:31:40.690 --> 00:31:43.790 That was 1 minus 2X. 00:31:43.790 --> 00:31:48.080 So here we have 1 minus 2 times X. 00:31:48.080 --> 00:31:50.780 And you can see the significant figure fun 00:31:50.780 --> 00:31:56.510 that one can have in this because we have multiplication, 00:31:56.510 --> 00:32:00.020 division, subtraction, and pretty soon we're going to have 00:32:00.020 --> 00:32:02.650 log significant figure rules. 00:32:02.650 --> 00:32:05.060 So there's going to be a lot of fun. 00:32:05.060 --> 00:32:08.580 And of course, then this is our reactant over here. 00:32:08.580 --> 00:32:11.060 So let's just go back to the diagram, which 00:32:11.060 --> 00:32:15.530 is up above in your notes, on the same page in your notes, 00:32:15.530 --> 00:32:18.450 and plug these in and think about what this means. 00:32:18.450 --> 00:32:20.440 So we've done the math. 00:32:20.440 --> 00:32:27.700 And we see that our reactant at equilibrium is 0.238 bar, 00:32:27.700 --> 00:32:32.360 and our product at equilibrium is 0.381 bar. 00:32:32.360 --> 00:32:35.920 So K is greater than 1, more products, 00:32:35.920 --> 00:32:38.240 and you see that that works out. 00:32:38.240 --> 00:32:41.570 So if you were asked just to explain what you expected, 00:32:41.570 --> 00:32:43.480 you could say K is greater than 1. 00:32:43.480 --> 00:32:45.020 I expect more products. 00:32:45.020 --> 00:32:47.410 But if you do the math, and you'll often do the math, 00:32:47.410 --> 00:32:50.090 you can calculate what the partial pressures 00:32:50.090 --> 00:32:56.211 are at equilibrium of the reactants and of the products. 00:32:56.211 --> 00:32:56.710 All right. 00:32:56.710 --> 00:33:00.590 So now let's think about the relationship, again, 00:33:00.590 --> 00:33:07.580 between delta G0 and K. So here is 00:33:07.580 --> 00:33:10.150 our expression we saw before. 00:33:10.150 --> 00:33:14.630 We can also rewrite this to solve for K. 00:33:14.630 --> 00:33:18.460 So sometimes you will be given information about delta G0 00:33:18.460 --> 00:33:23.330 and asked to calculate a K at a particular temperature. 00:33:23.330 --> 00:33:26.650 But we can also think about what we would expect. 00:33:26.650 --> 00:33:31.880 So if K is large, what is going to be true about delta G0? 00:33:31.880 --> 00:33:34.352 And so why don't you tell me what you think. 00:33:55.950 --> 00:33:56.450 All right. 00:33:56.450 --> 00:33:57.980 Let's just do 10 more seconds. 00:34:16.080 --> 00:34:20.340 So it would be a large negative number. 00:34:20.340 --> 00:34:24.989 And we can think about this, that if you really 00:34:24.989 --> 00:34:28.650 are lying on the side of products in your reaction, 00:34:28.650 --> 00:34:31.530 then that would be consistent with a bigger 00:34:31.530 --> 00:34:33.510 value and a negative value. 00:34:33.510 --> 00:34:35.219 So you can think about-- again, we 00:34:35.219 --> 00:34:37.560 talked about in terms of formation, 00:34:37.560 --> 00:34:41.489 is the thing that's being formed more or less stable compared 00:34:41.489 --> 00:34:44.100 to its elements, the same sort of idea. 00:34:44.100 --> 00:34:46.920 You can think about the relative stability 00:34:46.920 --> 00:34:49.650 and whether you'd expect more products or more reactants 00:34:49.650 --> 00:34:53.980 at equilibrium based on these values. 00:34:53.980 --> 00:34:57.280 So let's do an example and prove that this is true. 00:34:57.280 --> 00:35:00.240 So let's consider baking soda again. 00:35:00.240 --> 00:35:03.750 Baking soda works really well for this unit on thermodynamics 00:35:03.750 --> 00:35:05.730 and chemical equilibrium. 00:35:05.730 --> 00:35:08.340 So again, we have our baking soda 00:35:08.340 --> 00:35:13.800 going to CO2, which is very important, the CO2 gas, which 00:35:13.800 --> 00:35:16.020 helps our bread rise. 00:35:16.020 --> 00:35:20.160 And we calculated last week that the delta G0 00:35:20.160 --> 00:35:22.110 at room temperature for this process 00:35:22.110 --> 00:35:25.660 was plus 36 kilojoules per mole. 00:35:25.660 --> 00:35:27.930 And that would mean that it's not 00:35:27.930 --> 00:35:30.210 spontaneous in the forward direction, which 00:35:30.210 --> 00:35:33.390 is really bad for our bread, because we need the CO2 00:35:33.390 --> 00:35:35.430 gas to cause it to rise. 00:35:35.430 --> 00:35:37.770 But the good news was that if we remember 00:35:37.770 --> 00:35:40.200 to turn on the oven in baking bread 00:35:40.200 --> 00:35:43.380 and put it at a normal temperature in the oven, 00:35:43.380 --> 00:35:47.500 that the delta G0 is minus 15 kilojoules per mole. 00:35:47.500 --> 00:35:50.460 So then it becomes a spontaneous reaction. 00:35:50.460 --> 00:35:52.620 Now we can think about this in terms 00:35:52.620 --> 00:35:57.540 of our equilibrium constant K. So if we do the math here, 00:35:57.540 --> 00:36:03.540 at room temperature K would be 4.9 times 10 to the minus 7. 00:36:03.540 --> 00:36:06.300 That is a small number. 00:36:06.300 --> 00:36:11.100 That means that there is very little product at equilibrium 00:36:11.100 --> 00:36:12.450 at this temperature. 00:36:12.450 --> 00:36:17.070 Very little CO2 gas to be able to be used to make our bread 00:36:17.070 --> 00:36:18.060 rise. 00:36:18.060 --> 00:36:21.150 But now if we calculate K at this value, 00:36:21.150 --> 00:36:27.510 at a negative number for delta G, K is now 55. 00:36:27.510 --> 00:36:30.210 So we have quite a lot of product 00:36:30.210 --> 00:36:32.640 then to be used to make the bread rise. 00:36:32.640 --> 00:36:34.410 So you can think about things in terms 00:36:34.410 --> 00:36:36.390 of delta G's and whether something's 00:36:36.390 --> 00:36:39.510 going to be spontaneous and give you the product you want. 00:36:39.510 --> 00:36:41.670 But the equilibrium constant gives you 00:36:41.670 --> 00:36:43.410 that information as well. 00:36:43.410 --> 00:36:46.344 If it's a very small number, you have very little product. 00:36:46.344 --> 00:36:47.760 And if you want product, if you're 00:36:47.760 --> 00:36:50.100 trying to industrially make something, 00:36:50.100 --> 00:36:52.260 that's a very bad thing. 00:36:52.260 --> 00:36:58.200 But if you have a big value for K and this negative delta G0 00:36:58.200 --> 00:37:00.560 value, then that's good if you want a lot 00:37:00.560 --> 00:37:03.390 of the product at equilibrium. 00:37:03.390 --> 00:37:06.030 So equilibrium doesn't just matter 00:37:06.030 --> 00:37:11.940 for things like baking soda or forming ammonia from nitrogen 00:37:11.940 --> 00:37:14.820 and hydrogen. Chemical equilibrium 00:37:14.820 --> 00:37:17.830 applies to large molecules as well, 00:37:17.830 --> 00:37:21.810 such as enzymes in your body that are catalyzing reactions. 00:37:21.810 --> 00:37:25.230 So I'm going to share with you an In Their Own Words. 00:37:25.230 --> 00:37:29.700 And this is Nozomi Ando, who I will just 00:37:29.700 --> 00:37:33.460 mention is an MIT undergraduate-- was 00:37:33.460 --> 00:37:38.040 a graduate of MIT, was an undergraduate here in physics, 00:37:38.040 --> 00:37:39.840 majored in physics. 00:37:39.840 --> 00:37:43.637 And she is now a professor of-- do you want to guess? 00:37:43.637 --> 00:37:44.470 AUDIENCE: Chemistry. 00:37:44.470 --> 00:37:46.261 CATHERINE DRENNAN: Chemistry, that's right. 00:37:46.261 --> 00:37:49.140 She's a professor of chemistry at Princeton University. 00:37:49.140 --> 00:37:53.340 So here is a good example of what can happen. 00:37:53.340 --> 00:37:55.980 And she was very happy-- actually, 00:37:55.980 --> 00:37:58.380 I think 5.111 didn't exist then. 00:37:58.380 --> 00:38:00.420 I think it was 5.11 when she was here. 00:38:00.420 --> 00:38:03.150 But nonetheless, so here in her words 00:38:03.150 --> 00:38:06.534 about chemical equilibrium and the proteins she studies. 00:38:06.534 --> 00:38:07.200 [VIDEO PLAYBACK] 00:38:07.200 --> 00:38:09.995 -My name is Nozomi Ando, and I study 00:38:09.995 --> 00:38:14.760 a protein called Ribonucleotide Reductase, or RNR for short. 00:38:14.760 --> 00:38:19.440 It catalyzes the reaction of converting ribonucleotides, 00:38:19.440 --> 00:38:23.490 or the building blocks of RNA, into deoxyribonucleotides, 00:38:23.490 --> 00:38:25.970 or the building blocks of DNA. 00:38:25.970 --> 00:38:28.890 It's the only means of getting those letters for DNA, 00:38:28.890 --> 00:38:32.880 so it's important for DNA synthesis and repair 00:38:32.880 --> 00:38:34.320 and replication. 00:38:34.320 --> 00:38:37.620 It knows, for example, when there's 00:38:37.620 --> 00:38:43.440 an imbalance in the pools of the letters for DNA 00:38:43.440 --> 00:38:48.480 or if there's a lot of letters of the RNA. 00:38:48.480 --> 00:38:54.600 And this controls the sort of state that RNR is in. 00:38:54.600 --> 00:38:58.890 And RNR can be in an equilibrium of active and inactive states 00:38:58.890 --> 00:39:03.030 that are sort of regulated by the alphabet soup in the cell. 00:39:03.030 --> 00:39:05.070 When it's active, it's very compact, 00:39:05.070 --> 00:39:07.800 but then it has to make a really dramatic structural change 00:39:07.800 --> 00:39:10.500 to go into an inactive state. 00:39:10.500 --> 00:39:12.870 I have this imagery of Transformers 00:39:12.870 --> 00:39:14.230 because it's just so dramatic. 00:39:14.230 --> 00:39:16.740 So when it's active, it's compact, like when 00:39:16.740 --> 00:39:18.330 a Transformer's a car. 00:39:18.330 --> 00:39:22.080 And when it's inactive and it makes a sound, che, che, che, 00:39:22.080 --> 00:39:26.360 che, and then it expands into a robot. 00:39:26.360 --> 00:39:30.980 The letter A, or adenosine, pushes this equilibrium 00:39:30.980 --> 00:39:33.050 from the active to inactive state. 00:39:33.050 --> 00:39:36.680 And it tells RNR, OK, we have enough of the DNA letters, 00:39:36.680 --> 00:39:37.760 so stop. 00:39:37.760 --> 00:39:40.280 For humans, it's really important to study RNR 00:39:40.280 --> 00:39:46.220 because it's the protein that is essential for making letters 00:39:46.220 --> 00:39:46.790 of DNA. 00:39:46.790 --> 00:39:50.390 So it's essential for DNA replication, which is 00:39:50.390 --> 00:39:54.500 essential for cells to divide. 00:39:54.500 --> 00:39:59.330 And we want RNR to function normally for our health. 00:39:59.330 --> 00:40:03.360 But in cells that are dividing too quickly, 00:40:03.360 --> 00:40:06.740 such as tumor cells, we want to slow it down. 00:40:06.740 --> 00:40:10.490 So actually, RNR is a really important target 00:40:10.490 --> 00:40:13.530 for anti-cancer drugs. 00:40:13.530 --> 00:40:17.570 But also, because RNR exists in every organism, 00:40:17.570 --> 00:40:20.000 we can start looking at differences 00:40:20.000 --> 00:40:22.620 between different species. 00:40:22.620 --> 00:40:27.193 So for example, it could be anti-bacterial and not just 00:40:27.193 --> 00:40:27.693 anti-cancer. 00:40:30.431 --> 00:40:31.014 [END PLAYBACK] 00:40:31.014 --> 00:40:32.990 CATHERINE DRENNAN: So that's an example 00:40:32.990 --> 00:40:36.350 of how you have a shift between two 00:40:36.350 --> 00:40:39.130 states, an inactive and active state, 00:40:39.130 --> 00:40:41.810 that it's just a chemical equilibrium. 00:40:41.810 --> 00:40:44.480 And binding one thing shifts the equilibrium one way. 00:40:44.480 --> 00:40:46.190 Binding something else shifts it back. 00:40:46.190 --> 00:40:47.990 So chemical equilibrium-- a lot of nature 00:40:47.990 --> 00:40:51.500 works by just suddenly shifting the equilibrium 00:40:51.500 --> 00:40:53.060 between different states. 00:40:53.060 --> 00:40:54.770 So understanding chemical equilibrium 00:40:54.770 --> 00:40:56.191 is pretty important. 00:40:56.191 --> 00:40:56.690 All right. 00:40:56.690 --> 00:41:02.300 So now we're going to apply stress to our chemical 00:41:02.300 --> 00:41:07.180 equilibrium, and we're going to talk about the principle of Le 00:41:07.180 --> 00:41:09.630 Chatelier. 00:41:09.630 --> 00:41:15.650 So here, a system in equilibrium that's subject to stress 00:41:15.650 --> 00:41:23.750 will react in a way that tends to minimize that stress. 00:41:23.750 --> 00:41:26.240 And whenever I talk to MIT students about this, 00:41:26.240 --> 00:41:30.410 I feel like I need to really emphasize this point. 00:41:30.410 --> 00:41:34.040 MIT students experience a lot of stress, 00:41:34.040 --> 00:41:37.040 but often do not tend to react in a way 00:41:37.040 --> 00:41:39.920 to minimize that stress. 00:41:39.920 --> 00:41:43.850 They say, all right, I am just struggling with this double 00:41:43.850 --> 00:41:44.360 major. 00:41:44.360 --> 00:41:45.660 I don't know what to do. 00:41:45.660 --> 00:41:46.890 It's just so much work. 00:41:46.890 --> 00:41:50.003 So maybe I should triple major instead. 00:41:50.003 --> 00:41:50.502 No. 00:41:50.502 --> 00:41:53.160 [LAUGHTER] 00:41:53.160 --> 00:41:55.830 Ask yourself, what would Le Chatelier do? 00:41:55.830 --> 00:41:56.600 Minimize. 00:41:56.600 --> 00:42:00.860 Double major, single major. 00:42:00.860 --> 00:42:04.010 So this is a principle that can apply to your life. 00:42:04.010 --> 00:42:08.942 And I recently saw a chemistry major, and we had lunch. 00:42:08.942 --> 00:42:10.650 He was a former MIT student, and now he's 00:42:10.650 --> 00:42:13.580 a CEO of a company, small company, in Cambridge 00:42:13.580 --> 00:42:18.050 that's designing computer software platforms. 00:42:18.050 --> 00:42:21.260 He was a chemistry major, and he's doing software design 00:42:21.260 --> 00:42:24.620 and building like little computer tablet 00:42:24.620 --> 00:42:26.010 things for restaurants. 00:42:26.010 --> 00:42:28.780 So I said, would you use your chemistry at all? 00:42:28.780 --> 00:42:31.490 And he goes, oh, I use some things all the time, especially 00:42:31.490 --> 00:42:33.080 Le Chatelier's principle. 00:42:33.080 --> 00:42:35.510 I'm all about minimizing the stress. 00:42:35.510 --> 00:42:38.090 So that was one thing that he really 00:42:38.090 --> 00:42:40.430 grabbed onto in chemistry. 00:42:40.430 --> 00:42:43.220 So again, if you think about this, 00:42:43.220 --> 00:42:47.240 about minimizing the stress, you can predict 00:42:47.240 --> 00:42:48.515 the direction of the reaction. 00:42:48.515 --> 00:42:51.140 And in nature, this really works pretty well. 00:42:51.140 --> 00:42:53.090 So Le Chatelier's principle gives us 00:42:53.090 --> 00:42:56.210 a way to predict the direction the reaction will 00:42:56.210 --> 00:43:03.530 go if you ask, which direction will minimize the stress? 00:43:03.530 --> 00:43:05.760 So let's look at an example. 00:43:05.760 --> 00:43:09.680 We're back to N2 and H2 making ammonia. 00:43:09.680 --> 00:43:12.890 So here's a slightly different plot than I drew over here. 00:43:12.890 --> 00:43:15.350 Now, this is a reaction sensitive to temperature, 00:43:15.350 --> 00:43:16.850 so the equilibrium constant's going 00:43:16.850 --> 00:43:18.030 to change with temperature. 00:43:18.030 --> 00:43:20.488 So every plot of this may look a little different depending 00:43:20.488 --> 00:43:22.580 on what temperature it's at. 00:43:22.580 --> 00:43:24.364 But some things are the same. 00:43:24.364 --> 00:43:26.030 If you start with hydrogen and nitrogen, 00:43:26.030 --> 00:43:27.980 you'll have some of those to begin with. 00:43:27.980 --> 00:43:29.750 They will be above 0. 00:43:29.750 --> 00:43:32.630 But ammonia will start-- if you had no product, 00:43:32.630 --> 00:43:34.984 you'll have ammonia at 0 and it'll rise in. 00:43:34.984 --> 00:43:36.650 The other thing that should look similar 00:43:36.650 --> 00:43:39.470 is that as the reaction runs for long enough it'll 00:43:39.470 --> 00:43:43.820 reach equilibrium, and you'll have the lines level out. 00:43:43.820 --> 00:43:45.860 You'll reach an equilibrium state. 00:43:45.860 --> 00:43:49.950 Now what happens if you stress that equilibrium state? 00:43:49.950 --> 00:43:54.340 So say you add hydrogen. And so this line adds the hydrogen, 00:43:54.340 --> 00:43:56.030 then it goes down. 00:43:56.030 --> 00:43:59.840 Then you're also going to use up some nitrogen as you're 00:43:59.840 --> 00:44:01.790 using up the hydrogen. You're going 00:44:01.790 --> 00:44:05.300 to shift it to make more product. 00:44:05.300 --> 00:44:08.570 Now, say, you make product. 00:44:08.570 --> 00:44:11.600 You add product-- sorry, you're adding product. 00:44:11.600 --> 00:44:16.880 It's going to shift to minimize the stress, use up the product, 00:44:16.880 --> 00:44:21.020 have the product dissociate, and make more hydrogen and more 00:44:21.020 --> 00:44:22.800 nitrogen. 00:44:22.800 --> 00:44:25.230 So here's the plot. 00:44:25.230 --> 00:44:28.500 Now, let's just think about what's happening at each step. 00:44:28.500 --> 00:44:31.400 So if we're adding more reactant, 00:44:31.400 --> 00:44:32.360 you have more reactant. 00:44:32.360 --> 00:44:34.580 You have too much reactant. 00:44:34.580 --> 00:44:39.800 Shift to minimize the stress, and you will shift 00:44:39.800 --> 00:44:41.390 the reaction toward product. 00:44:41.390 --> 00:44:43.760 Get rid of the reactant, use up the reactant. 00:44:43.760 --> 00:44:46.780 Let's get back to the equilibrium condition, 00:44:46.780 --> 00:44:49.220 minimize the stress. 00:44:49.220 --> 00:44:54.126 Now, we can think about this in terms of Q and K again. 00:44:57.030 --> 00:45:01.580 So when you have reactants added, 00:45:01.580 --> 00:45:05.850 then Q is going to fall below K momentarily. 00:45:05.850 --> 00:45:09.620 And so that means-- if you think about our equation over here, 00:45:09.620 --> 00:45:13.130 recall this equation, this important equation. 00:45:13.130 --> 00:45:18.170 So with Q less than K, you get a negative delta G, 00:45:18.170 --> 00:45:21.200 and that's going to be spontaneous toward the right, 00:45:21.200 --> 00:45:22.440 toward products. 00:45:22.440 --> 00:45:26.240 So again, you respond by making more products. 00:45:26.240 --> 00:45:29.720 You shift to the right. 00:45:29.720 --> 00:45:31.390 And you saw that over here. 00:45:31.390 --> 00:45:33.890 It's shifting toward products. 00:45:33.890 --> 00:45:37.040 You're using up the hydrogen. You're using up the nitrogen. 00:45:37.040 --> 00:45:41.390 You're trying to return to an equilibrium condition. 00:45:41.390 --> 00:45:47.360 Now what happens if we add more product? 00:45:47.360 --> 00:45:51.230 And so when you're adding more product, Q is greater than K 00:45:51.230 --> 00:45:51.890 momentarily. 00:45:51.890 --> 00:45:55.910 You have too many products now compared to equilibrium. 00:45:55.910 --> 00:46:02.360 And when Q is greater than K, you get a positive delta G. 00:46:02.360 --> 00:46:04.250 And that means that it's spontaneous 00:46:04.250 --> 00:46:06.680 in the reverse direction, or non-spontaneous 00:46:06.680 --> 00:46:08.160 in the forward direction. 00:46:08.160 --> 00:46:09.710 So you shift toward reactants. 00:46:09.710 --> 00:46:11.910 You shift to the left. 00:46:11.910 --> 00:46:13.460 So again, you can use this equation 00:46:13.460 --> 00:46:17.550 to think about what direction is now going to be favorable. 00:46:17.550 --> 00:46:19.610 And so here you added product. 00:46:19.610 --> 00:46:21.140 The product gets used up. 00:46:21.140 --> 00:46:23.210 It's shifting toward reactants, and you're 00:46:23.210 --> 00:46:27.590 making more reactants until you reach equilibrium again. 00:46:27.590 --> 00:46:32.060 And we have one minute left for a last clicker question. 00:46:32.060 --> 00:46:33.990 What happens when you remove products? 00:46:54.631 --> 00:46:55.130 All right. 00:46:55.130 --> 00:46:56.795 So let's just take 10 more seconds. 00:47:08.670 --> 00:47:11.130 All right. 00:47:11.130 --> 00:47:13.540 So we'll just put it up over here. 00:47:13.540 --> 00:47:15.690 So that means that delta G is going 00:47:15.690 --> 00:47:19.580 to be negative in that case because you remove products. 00:47:19.580 --> 00:47:22.710 So Q is less than K, and so the reaction 00:47:22.710 --> 00:47:25.170 is going to be spontaneous in the forward direction. 00:47:25.170 --> 00:47:26.910 Delta G will be negative, and you'll 00:47:26.910 --> 00:47:28.710 move to make more products. 00:47:28.710 --> 00:47:30.870 Again, minimize the stress. 00:47:30.870 --> 00:47:32.080 You took away products. 00:47:32.080 --> 00:47:33.780 You need to make more. 00:47:33.780 --> 00:47:36.620 Minimize the stress. 00:47:36.620 --> 00:47:40.650 Do problem set 5 and minimize your stress.