1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,060 Your support will help MIT OpenCourseWare 4 00:00:06,060 --> 00:00:10,150 continue to offer high-quality educational resources for free. 5 00:00:10,150 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:16,435 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,435 --> 00:00:17,060 at ocw.mit.edu. 8 00:00:33,252 --> 00:00:34,460 CATHERINE DRENNAN: All right. 9 00:00:34,460 --> 00:00:36,190 Let's just do 10 more seconds. 10 00:00:53,690 --> 00:00:54,190 All right. 11 00:00:54,190 --> 00:01:01,181 Does someone want to tell me up here-- hello everyone up here-- 12 00:01:01,181 --> 00:01:02,430 how they got the right answer? 13 00:01:06,570 --> 00:01:09,160 Over-- everyone over there, I guess. 14 00:01:09,160 --> 00:01:10,640 OK, I'm coming over there. 15 00:01:10,640 --> 00:01:15,080 So for the answer we have an MIT chemistry bag. 16 00:01:15,080 --> 00:01:15,960 That's quite special. 17 00:01:23,620 --> 00:01:26,320 AUDIENCE: Well, since your delta H value 18 00:01:26,320 --> 00:01:28,990 acts as the y-intercept, you know that it's negative 19 00:01:28,990 --> 00:01:31,030 because it's negatively. 20 00:01:31,030 --> 00:01:33,700 And then you also see that you're ascending positively, 21 00:01:33,700 --> 00:01:37,010 so that you know your slope is positive. 22 00:01:37,010 --> 00:01:41,770 And so delta S also has to be negative to make it positive. 23 00:01:41,770 --> 00:01:43,150 CATHERINE DRENNAN: Interesting. 24 00:01:43,150 --> 00:01:45,370 That was a different answer than I would have given, 25 00:01:45,370 --> 00:01:47,350 but that works really well, which 26 00:01:47,350 --> 00:01:48,950 is always great to ask people. 27 00:01:48,950 --> 00:01:52,720 So you could also think about this in terms of your going 28 00:01:52,720 --> 00:01:56,459 from a situation with a negative delta G to a positive value. 29 00:01:56,459 --> 00:01:58,000 So you know that temperature is going 30 00:01:58,000 --> 00:01:59,870 to make a difference there. 31 00:01:59,870 --> 00:02:05,006 And so that would also tell you how the temperature changes 32 00:02:05,006 --> 00:02:06,880 is also going to tell you the answer to that. 33 00:02:06,880 --> 00:02:08,631 So that's great. 34 00:02:08,631 --> 00:02:09,130 All right. 35 00:02:09,130 --> 00:02:11,080 So a couple of announcements. 36 00:02:11,080 --> 00:02:18,400 As you can see, see what I am wearing on my legs. 37 00:02:18,400 --> 00:02:23,200 So I was pleased with the performance on exam 2. 38 00:02:23,200 --> 00:02:29,110 The average was 84.7, not quite as celebratory 39 00:02:29,110 --> 00:02:33,610 as 87.4, which was the average on exam 1. 40 00:02:33,610 --> 00:02:34,944 Yeah, those are real numbers. 41 00:02:34,944 --> 00:02:35,860 That's a little weird. 42 00:02:35,860 --> 00:02:39,400 But anyway, I was still very happy with the performance 43 00:02:39,400 --> 00:02:40,690 on the exam. 44 00:02:40,690 --> 00:02:43,420 I would like for exam 3 for the average 45 00:02:43,420 --> 00:02:45,110 to be back at 87, though. 46 00:02:45,110 --> 00:02:49,930 I like it to be very close to 90 because I want everyone 47 00:02:49,930 --> 00:02:53,380 to have an average around 90 in the class 48 00:02:53,380 --> 00:02:55,730 to demonstrate excellent knowledge of chemistry. 49 00:02:55,730 --> 00:02:57,490 So I try to write an exam where I 50 00:02:57,490 --> 00:03:00,040 feel like if you have excellent knowledge of chemistry, 51 00:03:00,040 --> 00:03:02,420 you can get a 90% or above. 52 00:03:02,420 --> 00:03:04,000 So this is my goal. 53 00:03:04,000 --> 00:03:07,060 I all want you to have this fundamental knowledge 54 00:03:07,060 --> 00:03:10,300 of chemistry that you can go out and solve the energy problem, 55 00:03:10,300 --> 00:03:13,030 that you can go out and be ready to tackle 56 00:03:13,030 --> 00:03:15,850 the next great challenge in health. 57 00:03:15,850 --> 00:03:17,680 There's so many challenges facing us, 58 00:03:17,680 --> 00:03:20,000 and we don't even know what they are right now. 59 00:03:20,000 --> 00:03:24,770 So the Ebola situation, I think, is a real case in point, 60 00:03:24,770 --> 00:03:27,370 that we don't know what the next challenge facing us 61 00:03:27,370 --> 00:03:28,270 is going to be. 62 00:03:28,270 --> 00:03:31,111 So we need to be ready with our chemistry knowledge. 63 00:03:31,111 --> 00:03:33,610 The only thing I can tell you about the challenges facing us 64 00:03:33,610 --> 00:03:35,110 is that knowing chemistry is going 65 00:03:35,110 --> 00:03:37,630 to be really important in tackling those problems. 66 00:03:37,630 --> 00:03:40,280 So everyone needs to have an excellent understanding 67 00:03:40,280 --> 00:03:43,930 of chemistry to go on and do well and solve 68 00:03:43,930 --> 00:03:45,310 the problems of the world. 69 00:03:45,310 --> 00:03:49,030 So 84.7, really good. 70 00:03:49,030 --> 00:03:50,100 You're getting there. 71 00:03:50,100 --> 00:03:51,350 Awesome. 72 00:03:51,350 --> 00:03:53,752 So celebratory tights, or leggings. 73 00:03:53,752 --> 00:03:56,210 Not really sure the difference between tights and leggings. 74 00:03:56,210 --> 00:03:58,690 Anyway, I was very pleased. 75 00:03:58,690 --> 00:04:04,660 But next unit, next exam, has thermodynamics, chemical 76 00:04:04,660 --> 00:04:06,550 equilibrium, and acid-base. 77 00:04:06,550 --> 00:04:08,960 We're already done with thermodynamics and moving on. 78 00:04:08,960 --> 00:04:11,260 So it's just for the rest of the semester, 79 00:04:11,260 --> 00:04:15,110 we're about halfway there, the rate seems to accelerate. 80 00:04:15,110 --> 00:04:17,589 So problem set 5, thermodynamics. 81 00:04:17,589 --> 00:04:20,134 It's a little shorter because you have fewer days to do it. 82 00:04:20,134 --> 00:04:21,550 So we wanted to make sure that you 83 00:04:21,550 --> 00:04:24,619 would be able to get it done by Friday at noon. 84 00:04:24,619 --> 00:04:25,660 But that's when it's due. 85 00:04:25,660 --> 00:04:26,950 It's all thermodynamics. 86 00:04:26,950 --> 00:04:29,440 We've already covered all the material on the problem set. 87 00:04:29,440 --> 00:04:33,100 You can do it already right away. 88 00:04:33,100 --> 00:04:33,600 All right. 89 00:04:33,600 --> 00:04:37,210 So also in my wardrobe-- I'm commenting a lot on my wardrobe 90 00:04:37,210 --> 00:04:40,157 today-- you'll notice maybe that I've worn this shirt once 91 00:04:40,157 --> 00:04:42,490 before, and my goal was really to have a different shirt 92 00:04:42,490 --> 00:04:43,270 every time. 93 00:04:43,270 --> 00:04:46,390 Now, this shirt is appropriate for today's lecture. 94 00:04:46,390 --> 00:04:48,040 But I just wanted to say that I did 95 00:04:48,040 --> 00:04:50,470 try to get a different shirt. 96 00:04:50,470 --> 00:04:54,550 And I ordered new shirts on thermodynamics and chemical 97 00:04:54,550 --> 00:04:57,850 equilibrium this year, and one of the shirts 98 00:04:57,850 --> 00:04:59,087 had to do with entropy. 99 00:04:59,087 --> 00:05:01,170 And I just thought I would share with you briefly, 100 00:05:01,170 --> 00:05:03,220 because it's a good review of thermodynamics, 101 00:05:03,220 --> 00:05:06,620 what happens when you do things related to entropy. 102 00:05:06,620 --> 00:05:09,100 So just to sort of show you what happened. 103 00:05:09,100 --> 00:05:11,320 In September, I was super organized. 104 00:05:11,320 --> 00:05:12,370 I ordered my shirts. 105 00:05:12,370 --> 00:05:15,130 And on October 3, they shipped. 106 00:05:15,130 --> 00:05:18,430 They went through Indianapolis to Massachusetts 107 00:05:18,430 --> 00:05:20,320 and to Newton Highlands about somewhere 108 00:05:20,320 --> 00:05:22,180 around October 8 or 9. 109 00:05:22,180 --> 00:05:24,640 That's where I live, so that's really good. 110 00:05:24,640 --> 00:05:27,580 But the shirts were about entropy, 111 00:05:27,580 --> 00:05:28,930 and then look what happened. 112 00:05:28,930 --> 00:05:32,320 Wait-- rerouted for delivery to a new address. 113 00:05:32,320 --> 00:05:37,990 Jersey City, Cincinnati, Ohio, Warrendale, Pennsylvania. 114 00:05:37,990 --> 00:05:41,890 And then yesterday they were in Springfield, Massachusetts, 115 00:05:41,890 --> 00:05:43,970 to which I say, entropy! 116 00:05:47,780 --> 00:05:51,560 This does not happen when you order T-shirts about kinetics. 117 00:05:51,560 --> 00:05:52,940 That's all I'm saying. 118 00:05:52,940 --> 00:05:55,257 Those arrive record time. 119 00:05:58,460 --> 00:06:01,160 Thermodynamics is not always your friend, 120 00:06:01,160 --> 00:06:02,420 but you can embrace it. 121 00:06:02,420 --> 00:06:05,150 And I'm going to try to calm myself down 122 00:06:05,150 --> 00:06:09,200 because we should be at equilibrium today. 123 00:06:09,200 --> 00:06:12,890 Today, the topic is chemical equilibrium. 124 00:06:12,890 --> 00:06:16,970 It's the calm part of thermodynamics. 125 00:06:16,970 --> 00:06:18,620 We'll get back to entropy. 126 00:06:18,620 --> 00:06:20,690 There will be some mention of entropy. 127 00:06:20,690 --> 00:06:22,220 But I'm going to try to calm down. 128 00:06:22,220 --> 00:06:23,990 I'm going to remember my reaction 129 00:06:23,990 --> 00:06:26,570 quotients and my equilibrium constants 130 00:06:26,570 --> 00:06:29,300 and think about chemical equilibrium 131 00:06:29,300 --> 00:06:31,310 and embrace the T-shirt I am wearing. 132 00:06:31,310 --> 00:06:35,600 Because I feel powerful in this T-shirt, like I can control 133 00:06:35,600 --> 00:06:39,350 thermodynamics with the power of the Green Lantern, 134 00:06:39,350 --> 00:06:41,660 with chemistry knowledge at my fingertips, 135 00:06:41,660 --> 00:06:44,130 and I will move forward. 136 00:06:44,130 --> 00:06:47,330 So chemical equilibrium is calming, 137 00:06:47,330 --> 00:06:49,250 but it's also a dynamic process. 138 00:06:49,250 --> 00:06:53,570 We can't forget that the reactions have not stopped. 139 00:06:53,570 --> 00:06:56,150 It's just the rate of the forward reaction 140 00:06:56,150 --> 00:06:59,640 is equal to the rate of the reverse reaction. 141 00:06:59,640 --> 00:07:02,810 So there's no net change, but the dynamic process 142 00:07:02,810 --> 00:07:05,580 is still happening. 143 00:07:05,580 --> 00:07:10,910 So my goal in life is to have equilibrium in my life. 144 00:07:10,910 --> 00:07:15,590 The amount of work-- the rate at which work comes into my office 145 00:07:15,590 --> 00:07:18,350 equals the rate at which I complete the work 146 00:07:18,350 --> 00:07:20,450 and it leaves my office. 147 00:07:20,450 --> 00:07:22,550 Most of you should also have this goal. 148 00:07:22,550 --> 00:07:25,160 The rate at which problem sets come in 149 00:07:25,160 --> 00:07:28,330 equals the rate at which you complete the problem sets 150 00:07:28,330 --> 00:07:30,470 and the problem sets get turned in. 151 00:07:30,470 --> 00:07:32,390 You don't want to get yourself in a situation 152 00:07:32,390 --> 00:07:34,480 where that equilibrium is messed up, 153 00:07:34,480 --> 00:07:36,470 where the rate of things coming in 154 00:07:36,470 --> 00:07:39,350 is just nowhere at all equal to the rate at which things 155 00:07:39,350 --> 00:07:41,180 are completed and going out. 156 00:07:41,180 --> 00:07:43,260 So goal-- chemical equilibrium. 157 00:07:43,260 --> 00:07:47,340 We want to be at this calm place where we're still working hard. 158 00:07:47,340 --> 00:07:49,550 It's still dynamic. 159 00:07:49,550 --> 00:07:51,490 But the net change is good. 160 00:07:51,490 --> 00:07:52,580 It's in our favor. 161 00:07:52,580 --> 00:07:55,640 The amount of work we're doing equals the work coming in. 162 00:07:55,640 --> 00:07:57,380 So I like chemical equilibrium. 163 00:07:57,380 --> 00:08:01,280 I feel like it brings hope to thermodynamics. 164 00:08:01,280 --> 00:08:04,300 So let's look at an example of a reaction, 165 00:08:04,300 --> 00:08:06,920 and we're going to talk a lot about this reaction in chemical 166 00:08:06,920 --> 00:08:08,160 equilibrium. 167 00:08:08,160 --> 00:08:12,650 So we have N2, nitrogen, H2, hydrogen coming together 168 00:08:12,650 --> 00:08:15,620 to form ammonia, and it has a delta G0 169 00:08:15,620 --> 00:08:19,710 of minus 32.9 kilojoules per mole. 170 00:08:19,710 --> 00:08:21,260 So let's think about what's happening 171 00:08:21,260 --> 00:08:23,343 in the beginning of this reaction, when we're just 172 00:08:23,343 --> 00:08:25,260 starting this reaction. 173 00:08:25,260 --> 00:08:30,810 So we can plot concentration on one axis, 174 00:08:30,810 --> 00:08:34,419 and we can have time on our other axis, 175 00:08:34,419 --> 00:08:36,724 so time increasing over here. 176 00:08:36,724 --> 00:08:38,390 And we can think about what happens when 177 00:08:38,390 --> 00:08:39,556 we're starting our reaction. 178 00:08:43,309 --> 00:08:45,860 We can have hydrogen starting out. 179 00:08:45,860 --> 00:08:48,920 We have some hydrogen in a certain concentration, 180 00:08:48,920 --> 00:08:51,350 and it's going to come down and level out. 181 00:08:51,350 --> 00:08:53,270 So that's our H2. 182 00:08:53,270 --> 00:08:56,720 We'll also have nitrogen as a reactant. 183 00:08:56,720 --> 00:09:00,320 It comes down, levels out. 184 00:09:00,320 --> 00:09:02,570 And we're starting with our product. 185 00:09:02,570 --> 00:09:03,650 We have no product. 186 00:09:03,650 --> 00:09:06,200 We're just starting the reaction with the reactants. 187 00:09:06,200 --> 00:09:10,002 So product increases and then levels out. 188 00:09:13,160 --> 00:09:15,860 So we're decreasing our reactants, 189 00:09:15,860 --> 00:09:18,470 increasing our product, but the lines go flat. 190 00:09:18,470 --> 00:09:20,335 The reaction is still happening. 191 00:09:20,335 --> 00:09:22,460 The reaction in the forward direction is happening, 192 00:09:22,460 --> 00:09:25,140 and then in the reverse direction is happening. 193 00:09:25,140 --> 00:09:27,434 But there's no net change at equilibrium 194 00:09:27,434 --> 00:09:28,850 because it's reached a state where 195 00:09:28,850 --> 00:09:31,550 the rate of the forward reaction equals the rate 196 00:09:31,550 --> 00:09:34,940 of the reverse reaction. 197 00:09:34,940 --> 00:09:37,910 And let me also just point out some arrows 198 00:09:37,910 --> 00:09:39,710 and some nomenclature here. 199 00:09:39,710 --> 00:09:41,360 So we have this double arrow, and you 200 00:09:41,360 --> 00:09:43,370 can see this a couple of different ways. 201 00:09:43,370 --> 00:09:46,370 But this indicates the reaction's going forward, 202 00:09:46,370 --> 00:09:48,380 and the reaction is going back. 203 00:09:48,380 --> 00:09:50,630 And that's necessary if you're at equilibrium. 204 00:09:50,630 --> 00:09:52,520 The definition of equilibrium-- rate 205 00:09:52,520 --> 00:09:55,070 forward equals rate back at equilibrium. 206 00:09:55,070 --> 00:09:56,970 So you'll be seeing those arrows a lot. 207 00:09:56,970 --> 00:09:57,470 All right. 208 00:09:57,470 --> 00:10:00,350 So let's think about delta G now in terms 209 00:10:00,350 --> 00:10:03,690 of what's happening at different times in this reaction. 210 00:10:03,690 --> 00:10:06,560 So if we're just starting out this reaction, 211 00:10:06,560 --> 00:10:08,120 and you don't have a lot of products, 212 00:10:08,120 --> 00:10:11,194 so you're in this case of pure reactants. 213 00:10:11,194 --> 00:10:12,860 At this point, you're going to be moving 214 00:10:12,860 --> 00:10:13,901 in the forward direction. 215 00:10:13,901 --> 00:10:15,830 You need to make products. 216 00:10:15,830 --> 00:10:18,440 And so at this point, the forward direction is negative. 217 00:10:18,440 --> 00:10:19,490 It's spontaneous. 218 00:10:19,490 --> 00:10:21,380 You're spontaneously making your products. 219 00:10:21,380 --> 00:10:23,630 You don't have any at this point. 220 00:10:23,630 --> 00:10:26,100 And so your delta G is going to be negative. 221 00:10:26,100 --> 00:10:30,300 So up here with pure reactants, your delta G is negative. 222 00:10:30,300 --> 00:10:32,090 Now, if you started with pure products-- 223 00:10:32,090 --> 00:10:36,350 you could do that as well-- the NH3 will dissociate and form 224 00:10:36,350 --> 00:10:38,010 the reactants. 225 00:10:38,010 --> 00:10:40,700 And so that would be over here. 226 00:10:40,700 --> 00:10:43,670 And so when you have excess products, 227 00:10:43,670 --> 00:10:46,280 now the forward direction is positive. 228 00:10:46,280 --> 00:10:49,610 It's not spontaneous because it's the reverse direction that 229 00:10:49,610 --> 00:10:51,140 is spontaneous. 230 00:10:51,140 --> 00:10:54,020 So over in this part of the graph over here, 231 00:10:54,020 --> 00:10:56,850 our delta G is positive. 232 00:10:56,850 --> 00:10:59,390 So if you have pure reactants, you spontaneously 233 00:10:59,390 --> 00:11:00,290 go to products. 234 00:11:00,290 --> 00:11:05,560 If you have pure products, you're going toward reactants. 235 00:11:05,560 --> 00:11:08,490 And when you have the right amount of reactants 236 00:11:08,490 --> 00:11:11,830 to products, the right ratio for equilibrium, 237 00:11:11,830 --> 00:11:18,190 then you get to equilibrium and delta G equals 0 at that point. 238 00:11:18,190 --> 00:11:20,560 So delta G is going to change depending 239 00:11:20,560 --> 00:11:22,608 on your ratio of products to reactants. 240 00:11:26,200 --> 00:11:29,890 So delta G changes as the proportion 241 00:11:29,890 --> 00:11:31,390 of the reactants and the products 242 00:11:31,390 --> 00:11:36,740 change, and there's an equation to describe that. 243 00:11:36,740 --> 00:11:39,070 So we're back now to having a few more 244 00:11:39,070 --> 00:11:40,670 equations in this unit. 245 00:11:40,670 --> 00:11:44,510 We noted a lot of people forgot to bring calculators to exam 2. 246 00:11:44,510 --> 00:11:46,840 There weren't so many calculations. 247 00:11:46,840 --> 00:11:49,630 We're back to more calculations again. 248 00:11:49,630 --> 00:11:55,660 So delta G equals delta G0 plus RT natural log of Q. 249 00:11:55,660 --> 00:11:57,040 So let's think about these terms. 250 00:11:57,040 --> 00:12:01,960 So delta G is Gibbs free energy at some particular point, 251 00:12:01,960 --> 00:12:05,470 at some ratio of product to reactant. 252 00:12:05,470 --> 00:12:10,900 Delta G0 is Gibb's free energy under standard conditions, 253 00:12:10,900 --> 00:12:13,030 in their standard state. 254 00:12:13,030 --> 00:12:17,620 Q is our reaction quotient, products over reactants. 255 00:12:17,620 --> 00:12:22,210 And R is the universal gas constant, and T is temperature. 256 00:12:22,210 --> 00:12:26,140 So this equation describes how delta G 257 00:12:26,140 --> 00:12:29,050 will compare to delta G0 at a particular condition, 258 00:12:29,050 --> 00:12:33,340 a particular ratio, of products and reactants. 259 00:12:33,340 --> 00:12:34,780 So let's talk about this reaction 260 00:12:34,780 --> 00:12:41,870 quotient Q. So let's look at a made-up reaction-- 261 00:12:41,870 --> 00:12:47,090 A plus B goes to C plus D. And think about that reaction 262 00:12:47,090 --> 00:12:48,450 in the gas phase. 263 00:12:48,450 --> 00:12:50,930 When we think about that reaction in the gas phase, 264 00:12:50,930 --> 00:12:55,190 we're going to be talking about partial pressures. 265 00:12:55,190 --> 00:13:01,040 And so Q over here is products over reactants, 266 00:13:01,040 --> 00:13:05,450 but here we're writing it out in a more complicated long way. 267 00:13:05,450 --> 00:13:07,190 So let's go through this. 268 00:13:07,190 --> 00:13:10,640 So we have this P sub C. Well, what is that? 269 00:13:10,640 --> 00:13:12,500 That is partial pressure. 270 00:13:12,500 --> 00:13:15,800 So partial pressure of gas X, and this 271 00:13:15,800 --> 00:13:20,240 is partial pressure of gas C, and C is a product 272 00:13:20,240 --> 00:13:21,380 and D is a product. 273 00:13:21,380 --> 00:13:23,750 So we have products over reactants. 274 00:13:23,750 --> 00:13:28,010 Partial pressure of gas C over P reference, 275 00:13:28,010 --> 00:13:31,040 partial pressure reference, which is 1 bar. 276 00:13:31,040 --> 00:13:34,400 The reference is 1 bar, so we're dividing that by 1. 277 00:13:34,400 --> 00:13:37,460 And this is raised to the little c, 278 00:13:37,460 --> 00:13:41,210 which has to do with the coefficients of the reaction. 279 00:13:41,210 --> 00:13:43,210 Then we have partial pressure of gas D 280 00:13:43,210 --> 00:13:46,520 over our reference raised to the small d-- those 281 00:13:46,520 --> 00:13:49,030 are our products, products are C and D-- 282 00:13:49,030 --> 00:13:51,200 over reactants-- partial pressure 283 00:13:51,200 --> 00:13:54,470 of gas A over reference raised to little a, 284 00:13:54,470 --> 00:13:59,300 partial pressure of gas B over reference raised to little b. 285 00:13:59,300 --> 00:14:04,910 But 1, the number 1, the reference is 1. 286 00:14:04,910 --> 00:14:09,350 So most of the time you'll see the following expression-- Q, 287 00:14:09,350 --> 00:14:12,040 our reaction quotient, partial pressure of gas 288 00:14:12,040 --> 00:14:16,595 C to the stoichiometry little c partial pressure of gas 289 00:14:16,595 --> 00:14:20,780 D raised to the stoichiometry d, over reactants, 290 00:14:20,780 --> 00:14:25,690 partial pressure of A little a partial pressure of B little b. 291 00:14:25,690 --> 00:14:30,320 And you will note that because we had 1 bar 292 00:14:30,320 --> 00:14:34,070 and these are in bars, our units are going to cancel here. 293 00:14:34,070 --> 00:14:37,220 So Q does not have units. 294 00:14:37,220 --> 00:14:39,665 I knew this should be very exciting for you. 295 00:14:39,665 --> 00:14:43,490 You won't be losing one point for lack of units with Q. 296 00:14:43,490 --> 00:14:44,600 There are no units. 297 00:14:44,600 --> 00:14:46,640 So this is very exciting. 298 00:14:46,640 --> 00:14:50,645 So there's the expression that you'll mostly see for Q. 299 00:14:50,645 --> 00:14:54,140 And now we can kind of forget that the reference is there. 300 00:14:54,140 --> 00:14:55,490 We can ignore the reference. 301 00:14:55,490 --> 00:14:58,910 You just don't freak out later if you have no units. 302 00:14:58,910 --> 00:15:00,710 It's OK. 303 00:15:00,710 --> 00:15:01,210 All right. 304 00:15:01,210 --> 00:15:04,880 So we also could be talking about solution, 305 00:15:04,880 --> 00:15:07,142 and here we're going to talk about concentrations. 306 00:15:07,142 --> 00:15:08,600 In a lot of these problems, they're 307 00:15:08,600 --> 00:15:10,070 talking about things in the gas phase, 308 00:15:10,070 --> 00:15:11,570 and they're giving you concentrations. 309 00:15:11,570 --> 00:15:12,460 Don't worry about it. 310 00:15:12,460 --> 00:15:14,180 It's all OK. 311 00:15:14,180 --> 00:15:17,900 So here our concentration reference, C for concentration, 312 00:15:17,900 --> 00:15:19,490 is 1 molar. 313 00:15:19,490 --> 00:15:22,220 And you'll see this term-- C in brackets. 314 00:15:22,220 --> 00:15:25,070 That means concentration of. 315 00:15:25,070 --> 00:15:28,430 And so if you see that like this, you 316 00:15:28,430 --> 00:15:32,750 would express this in words as the concentration of C-- again, 317 00:15:32,750 --> 00:15:35,232 that's a product-- over the reference-- we'll get rid 318 00:15:35,232 --> 00:15:37,190 of the reference in a minute, but we'll keep it 319 00:15:37,190 --> 00:15:42,110 for now-- raised to the little c, concentration of product D 320 00:15:42,110 --> 00:15:45,530 over this concentration reference of 1 molar 321 00:15:45,530 --> 00:15:49,820 to the little d, concentration of reactant A 322 00:15:49,820 --> 00:15:52,010 over this concentration reference 323 00:15:52,010 --> 00:15:55,400 raised to the little a, concentration of other reactant 324 00:15:55,400 --> 00:15:59,330 B over our concentration reference of 1 molar raised 325 00:15:59,330 --> 00:16:00,620 to the little b. 326 00:16:00,620 --> 00:16:04,640 And then, again, this is concentration. 327 00:16:04,640 --> 00:16:06,620 And we can get this expression, which 328 00:16:06,620 --> 00:16:10,790 is usually the one you see, of just products over reactants. 329 00:16:10,790 --> 00:16:14,120 But I will make one point here, that you 330 00:16:14,120 --> 00:16:16,370 need to know how to balance equations 331 00:16:16,370 --> 00:16:18,110 to be able to do these. 332 00:16:18,110 --> 00:16:21,020 So in the beginning of the book there 333 00:16:21,020 --> 00:16:23,660 was something about balancing, limiting reagents, 334 00:16:23,660 --> 00:16:25,250 stuff like that. 335 00:16:25,250 --> 00:16:27,020 If you feel like you did not master that, 336 00:16:27,020 --> 00:16:27,994 you want to go over it. 337 00:16:27,994 --> 00:16:29,285 You need to be able to balance. 338 00:16:29,285 --> 00:16:30,710 And in a lot of these problems you 339 00:16:30,710 --> 00:16:33,771 may be thinking about limiting reagents again. 340 00:16:33,771 --> 00:16:34,270 All right. 341 00:16:34,270 --> 00:16:37,569 So that's Q. You can see it as partial pressure-- 342 00:16:37,569 --> 00:16:39,610 and I'm going to do a little partial pressure gas 343 00:16:39,610 --> 00:16:42,760 review on Friday-- or concentrations 344 00:16:42,760 --> 00:16:45,940 with these brackets. 345 00:16:45,940 --> 00:16:51,820 So at equilibrium, delta G equals 0. 346 00:16:51,820 --> 00:16:54,280 And it's a dynamic process-- rate 347 00:16:54,280 --> 00:16:58,000 of the forward reaction equals rate of the reverse reaction. 348 00:16:58,000 --> 00:17:01,630 Q now is the equilibrium constant, 349 00:17:01,630 --> 00:17:05,170 because the ratio of products to reactants at equilibrium 350 00:17:05,170 --> 00:17:09,859 is the definition of the equilibrium constant. 351 00:17:09,859 --> 00:17:13,359 So when delta G equals 0, Q equals K. 352 00:17:13,359 --> 00:17:17,890 So we now can go back to this expression that we had 353 00:17:17,890 --> 00:17:20,829 and rewrite this for the situation 354 00:17:20,829 --> 00:17:24,510 at equilibrium, when delta G equals 0. 355 00:17:24,510 --> 00:17:27,329 So when delta G equals 0, this is 0 356 00:17:27,329 --> 00:17:33,030 and Q is K. K is products over reactants at equilibrium. 357 00:17:33,030 --> 00:17:36,300 And we can rewrite this or rearrange it now-- 358 00:17:36,300 --> 00:17:42,560 delta G0 equals minus RT natural log of K. 359 00:17:42,560 --> 00:17:44,560 And that's a very important equation that you'll 360 00:17:44,560 --> 00:17:46,590 be using a lot in these units. 361 00:17:46,590 --> 00:17:51,400 So it relates delta G0 with our equilibrium constant K, 362 00:17:51,400 --> 00:17:55,031 and it depends on temperature. 363 00:17:55,031 --> 00:17:55,530 All right. 364 00:17:55,530 --> 00:18:01,510 So K-- same expression as Q, except for something 365 00:18:01,510 --> 00:18:04,540 very important, which is that the concentrations are 366 00:18:04,540 --> 00:18:07,480 the concentrations at equilibrium. 367 00:18:07,480 --> 00:18:10,320 So it has the same form as Q, but it's 368 00:18:10,320 --> 00:18:13,790 only the amount of products and reactants at equilibrium. 369 00:18:13,790 --> 00:18:15,880 So in the gas phase, we would write 370 00:18:15,880 --> 00:18:18,670 K in terms of our partial pressures. 371 00:18:18,670 --> 00:18:22,120 And again, this is this little symbol to remind you 372 00:18:22,120 --> 00:18:25,490 these are the concentrations at equilibrium. 373 00:18:25,490 --> 00:18:27,550 And in solution it would be expressed 374 00:18:27,550 --> 00:18:29,390 in molar or something else. 375 00:18:29,390 --> 00:18:32,790 So K is, again, products over reactants, 376 00:18:32,790 --> 00:18:35,140 but only those concentrations at equilibrium. 377 00:18:35,140 --> 00:18:38,590 Whereas Q is at any point, any concentrations 378 00:18:38,590 --> 00:18:41,740 of products over reactants for Q. For K, 379 00:18:41,740 --> 00:18:45,895 it's those concentrations at equilibrium. 380 00:18:45,895 --> 00:18:46,690 All right. 381 00:18:46,690 --> 00:18:53,070 So now let's think about Q and K together. 382 00:18:53,070 --> 00:18:55,530 So we can rewrite this expression again. 383 00:18:55,530 --> 00:19:01,290 We just derived a new expression for delta G0, 384 00:19:01,290 --> 00:19:04,800 and that was minus RT natural log of K. 385 00:19:04,800 --> 00:19:07,900 So we can say delta G equals, and now 386 00:19:07,900 --> 00:19:10,180 have this other expression, minus RT 387 00:19:10,180 --> 00:19:15,445 natural log of K plus RT again-- gas constant 388 00:19:15,445 --> 00:19:19,090 and temperature-- natural log of Q. 389 00:19:19,090 --> 00:19:24,030 And we can simplify it, bring out the RTs, 390 00:19:24,030 --> 00:19:30,130 and now we have delta G equals RT natural log of Q/K. 391 00:19:30,130 --> 00:19:33,860 And this is, again, a very important expression 392 00:19:33,860 --> 00:19:35,260 that you'll use a lot. 393 00:19:35,260 --> 00:19:39,460 Because it tells you about delta G, 394 00:19:39,460 --> 00:19:41,890 whether the reaction is going to be spontaneous 395 00:19:41,890 --> 00:19:44,510 in the forward direction or the reverse direction, 396 00:19:44,510 --> 00:19:48,670 depending on the ratio of Q and K. 397 00:19:48,670 --> 00:19:50,820 This is a very important equation 398 00:19:50,820 --> 00:19:53,040 for chemical equilibrium. 399 00:19:53,040 --> 00:19:57,640 So let's think about what this means, what comes out of this. 400 00:19:57,640 --> 00:20:07,750 So the relationship between Q and K, if Q is less than K, 401 00:20:07,750 --> 00:20:12,420 what is the sign of delta G? 402 00:20:12,420 --> 00:20:14,012 You can just yell it out. 403 00:20:14,012 --> 00:20:14,904 AUDIENCE: Negative. 404 00:20:14,904 --> 00:20:16,352 CATHERINE DRENNAN: Yep. 405 00:20:16,352 --> 00:20:17,560 So it's going to be negative. 406 00:20:17,560 --> 00:20:20,585 Just mathematically, you can look at that expression. 407 00:20:20,585 --> 00:20:21,460 So it'll be negative. 408 00:20:21,460 --> 00:20:23,140 And again, we give you all the equations 409 00:20:23,140 --> 00:20:24,130 on the equation sheet. 410 00:20:24,130 --> 00:20:24,921 That will be there. 411 00:20:24,921 --> 00:20:27,570 So you just need to know how to think about it. 412 00:20:27,570 --> 00:20:29,960 And so the forward reaction will occur. 413 00:20:29,960 --> 00:20:31,720 And so if we think about this, it's 414 00:20:31,720 --> 00:20:33,580 going to mean that at equilibrium there 415 00:20:33,580 --> 00:20:37,390 are more products than there are at this time for Q. 416 00:20:37,390 --> 00:20:39,790 There's less products in the Q expression. 417 00:20:39,790 --> 00:20:43,690 K is greater than Q. So we need to make more products. 418 00:20:43,690 --> 00:20:46,590 So delta G will be negative, and the forward reaction 419 00:20:46,590 --> 00:20:48,800 will occur. 420 00:20:48,800 --> 00:20:53,890 So when Q is greater than K, delta G is positive. 421 00:20:53,890 --> 00:20:55,660 And so when Q is greater than K, that 422 00:20:55,660 --> 00:20:58,900 means there's more products now in Q 423 00:20:58,900 --> 00:21:02,110 than there are at equilibrium, too many products. 424 00:21:02,110 --> 00:21:05,170 So we need to shift it in the reverse direction. 425 00:21:05,170 --> 00:21:07,190 So delta G will be positive. 426 00:21:07,190 --> 00:21:10,270 So again, thinking about the ratio of Q and K 427 00:21:10,270 --> 00:21:13,450 tells you about what direction is going to be spontaneous. 428 00:21:13,450 --> 00:21:18,070 Is it spontaneous in the forward direction or in the reverse? 429 00:21:18,070 --> 00:21:18,880 OK. 430 00:21:18,880 --> 00:21:23,960 So let's continue doing a little example. 431 00:21:23,960 --> 00:21:25,900 We can do a little calculation here 432 00:21:25,900 --> 00:21:28,480 on the board for the same reaction. 433 00:21:28,480 --> 00:21:31,960 We're given a value of K. And now 434 00:21:31,960 --> 00:21:35,710 we're told some partial pressures of these gases 435 00:21:35,710 --> 00:21:38,410 and asked which direction the reaction will go. 436 00:21:38,410 --> 00:21:41,665 So let's write the expression for Q. 437 00:21:41,665 --> 00:21:45,190 So Q, again, is going to be equal to products 438 00:21:45,190 --> 00:21:51,400 over reactants, and our product here is our NH3. 439 00:21:51,400 --> 00:21:55,020 So we're going to be talking about the partial pressure 440 00:21:55,020 --> 00:21:58,320 because it's a gas of NH3. 441 00:21:58,320 --> 00:22:01,050 And am I done with the top part of this expression? 442 00:22:01,050 --> 00:22:01,592 AUDIENCE: No. 443 00:22:01,592 --> 00:22:02,508 CATHERINE DRENNAN: No. 444 00:22:02,508 --> 00:22:03,448 What do I need? 445 00:22:03,448 --> 00:22:04,364 AUDIENCE: [INAUDIBLE]. 446 00:22:04,364 --> 00:22:05,440 CATHERINE DRENNAN: Yep. 447 00:22:05,440 --> 00:22:09,500 Again, you need to remember the stoichiometry of the reaction. 448 00:22:09,500 --> 00:22:14,330 So now we have the partial pressure of N2 on the bottom, 449 00:22:14,330 --> 00:22:18,540 and I'm good, and the partial pressure of H2. 450 00:22:18,540 --> 00:22:22,720 And again, I have to remember that there are three 451 00:22:22,720 --> 00:22:25,610 H2s in this balanced reaction. 452 00:22:25,610 --> 00:22:29,740 So we have the partial pressure of H2 to the third. 453 00:22:29,740 --> 00:22:31,910 I can put in my numbers. 454 00:22:31,910 --> 00:22:44,140 1.1 squared over 5.5 over 2.2-- these numbers may be made up, 455 00:22:44,140 --> 00:22:52,750 that's OK-- equals 2.1 times 10 to the minus 2. 456 00:22:52,750 --> 00:22:56,110 And we're back to thinking about significant figures 457 00:22:56,110 --> 00:22:58,370 a lot again in this unit. 458 00:22:58,370 --> 00:23:02,380 So I have two there, so I'm going to have these two here, 459 00:23:02,380 --> 00:23:03,810 and I'm good. 460 00:23:03,810 --> 00:23:07,270 But now this is the value of Q. And I 461 00:23:07,270 --> 00:23:10,530 want you to tell me with a clicker question, what 462 00:23:10,530 --> 00:23:12,761 direction is this reaction going to go? 463 00:23:39,141 --> 00:23:39,640 All right. 464 00:23:39,640 --> 00:23:41,098 Let's just take 10 more seconds. 465 00:23:57,620 --> 00:23:58,380 All right? 466 00:23:58,380 --> 00:24:02,770 So recognized, for the most part, 467 00:24:02,770 --> 00:24:04,780 that yeah, most of these numbers, 468 00:24:04,780 --> 00:24:07,620 that Q is a bigger number than K. 469 00:24:07,620 --> 00:24:10,780 And so then you have to think about what that means. 470 00:24:10,780 --> 00:24:15,670 And so when Q is greater than K, then you're 471 00:24:15,670 --> 00:24:18,100 going to go toward reactants. 472 00:24:21,360 --> 00:24:25,060 And so you're going to dissociate the product 473 00:24:25,060 --> 00:24:27,550 until you achieve equilibrium again. 474 00:24:27,550 --> 00:24:30,180 And so this means when you have a big Q number, 475 00:24:30,180 --> 00:24:34,060 you have too many products compared to the equilibrium 476 00:24:34,060 --> 00:24:37,540 state, and you want to dissociate your products. 477 00:24:37,540 --> 00:24:40,510 So you're going to go spontaneously 478 00:24:40,510 --> 00:24:42,280 in the reverse direction. 479 00:24:42,280 --> 00:24:46,846 Now, I just want to mention one point. 480 00:24:46,846 --> 00:24:48,220 For the first part of the course, 481 00:24:48,220 --> 00:24:50,747 I only taught that material once before. 482 00:24:50,747 --> 00:24:52,330 But the second part I've taught a lot. 483 00:24:52,330 --> 00:24:54,580 So I have lots of years of experience 484 00:24:54,580 --> 00:24:57,220 of what people do wrong on exams on this part, 485 00:24:57,220 --> 00:24:59,500 and I will share one thing. 486 00:24:59,500 --> 00:25:02,740 A lot of students-- and faculty too, 487 00:25:02,740 --> 00:25:06,460 I'm this way-- right-left challenged. 488 00:25:06,460 --> 00:25:09,510 So they write left when they mean right. 489 00:25:09,510 --> 00:25:12,730 They write right when they mean left. 490 00:25:12,730 --> 00:25:18,050 And so for those of you who are like me and have this issue, 491 00:25:18,050 --> 00:25:20,200 draw an arrow. 492 00:25:20,200 --> 00:25:23,130 When people draw an arrow, they always draw it in the direction 493 00:25:23,130 --> 00:25:26,680 that they mean, or they say toward reactants 494 00:25:26,680 --> 00:25:28,570 or toward products. 495 00:25:28,570 --> 00:25:30,550 And so I've seen so many times on the test 496 00:25:30,550 --> 00:25:35,110 they'd explain the answer beautifully, and then 497 00:25:35,110 --> 00:25:38,210 write the wrong direction down. 498 00:25:38,210 --> 00:25:41,110 So if you are right-left challenged, 499 00:25:41,110 --> 00:25:45,550 try toward reactants or toward products or draw an arrow. 500 00:25:45,550 --> 00:25:48,880 So that is my suggestion to you, as someone 501 00:25:48,880 --> 00:25:52,510 who's also very bad with saying the right direction, 502 00:25:52,510 --> 00:25:55,110 left or right, when I mean that direction. 503 00:25:55,110 --> 00:25:56,110 OK. 504 00:25:56,110 --> 00:25:57,432 So what does K tell us? 505 00:26:00,160 --> 00:26:04,660 So K tells us about the ratio of products 506 00:26:04,660 --> 00:26:07,560 to reactants at equilibrium. 507 00:26:07,560 --> 00:26:11,090 And if you have a very big number for K, 508 00:26:11,090 --> 00:26:13,850 it's going to tell you something about the ratio 509 00:26:13,850 --> 00:26:16,310 of those products to the reactants, 510 00:26:16,310 --> 00:26:18,950 and there'll be a lot of products for reactants. 511 00:26:18,950 --> 00:26:21,600 So let's just think about this for a minute. 512 00:26:21,600 --> 00:26:26,840 So when K is greater than 1-- K is 513 00:26:26,840 --> 00:26:29,990 products over reactants at equilibrium-- 514 00:26:29,990 --> 00:26:33,170 that's going to mean high products. 515 00:26:33,170 --> 00:26:35,950 So you'll have a higher number there. 516 00:26:35,950 --> 00:26:40,580 But if you have a small value for K, 517 00:26:40,580 --> 00:26:43,760 then you're going to have low products at equilibrium. 518 00:26:43,760 --> 00:26:47,005 So this is a good thing just to think about and check yourself 519 00:26:47,005 --> 00:26:48,380 when you're doing these problems. 520 00:26:48,380 --> 00:26:50,810 Does my answer actually make sense? 521 00:26:50,810 --> 00:26:53,780 And if you see a big value for K, you're like, great. 522 00:26:53,780 --> 00:26:57,110 If I want products, I want a big value for the equilibrium 523 00:26:57,110 --> 00:26:59,200 constant, means that this reaction 524 00:26:59,200 --> 00:27:01,010 is going to give me a lot of what I want, 525 00:27:01,010 --> 00:27:02,380 a lot of my products. 526 00:27:02,380 --> 00:27:07,380 Because again, K is products over reactants at equilibrium. 527 00:27:07,380 --> 00:27:08,120 All right. 528 00:27:08,120 --> 00:27:10,680 So let's do an example here. 529 00:27:10,680 --> 00:27:13,900 So here is an example where K is greater than 1. 530 00:27:13,900 --> 00:27:16,450 It's actually 6.84 at room temperature. 531 00:27:16,450 --> 00:27:21,590 We have a delta G0 of minus 4.76 kilojoules per mole. 532 00:27:21,590 --> 00:27:23,870 Two NO2 molecules going to N2O4. 533 00:27:26,930 --> 00:27:30,740 So we're going to start with 1 bar of our reactants 534 00:27:30,740 --> 00:27:32,680 and no products. 535 00:27:32,680 --> 00:27:34,520 So we can look at what that's going 536 00:27:34,520 --> 00:27:38,380 to look like in our plot of concentration versus time. 537 00:27:38,380 --> 00:27:40,430 And here the concentration is indicated 538 00:27:40,430 --> 00:27:44,270 as partial pressure, which is one type of concentration. 539 00:27:44,270 --> 00:27:46,490 So we're starting only with our reactants. 540 00:27:46,490 --> 00:27:48,130 It will go down. 541 00:27:48,130 --> 00:27:50,030 We'll have no products in the beginning. 542 00:27:50,030 --> 00:27:52,880 At time 0, no products, and that will grow up. 543 00:27:52,880 --> 00:27:56,180 The curves will level off as you reach the equilibrium. 544 00:27:56,180 --> 00:27:58,040 Again, the reaction's still going 545 00:27:58,040 --> 00:27:59,680 in the forward and reverse directions, 546 00:27:59,680 --> 00:28:01,430 but the rates are equal so there's 547 00:28:01,430 --> 00:28:06,300 no net change in the concentrations then. 548 00:28:06,300 --> 00:28:08,790 So now we can actually do some math 549 00:28:08,790 --> 00:28:12,600 and figure out how this changes. 550 00:28:12,600 --> 00:28:15,300 And so this is one way that you can set up 551 00:28:15,300 --> 00:28:16,880 these kinds of problems. 552 00:28:16,880 --> 00:28:18,910 And we will be doing these types of problems 553 00:28:18,910 --> 00:28:21,930 in chemical equilibrium, acid-base equilibrium. 554 00:28:21,930 --> 00:28:23,580 There'll be many examples, so it's 555 00:28:23,580 --> 00:28:25,000 good to become familiar with them 556 00:28:25,000 --> 00:28:27,030 if you haven't seen it before. 557 00:28:27,030 --> 00:28:28,980 So we can calculate the partial pressures 558 00:28:28,980 --> 00:28:32,230 at equilibrium using this information. 559 00:28:32,230 --> 00:28:35,120 So when we started, we only had our reactant. 560 00:28:35,120 --> 00:28:40,050 We had 1 bar, 1.000 bar, to be specific, 561 00:28:40,050 --> 00:28:41,610 and we had no product. 562 00:28:41,610 --> 00:28:44,610 As the reaction goes, we will form product, 563 00:28:44,610 --> 00:28:47,856 so it's plus X. Some amount of product is going to be formed. 564 00:28:50,630 --> 00:28:53,120 What is the change in partial pressure 565 00:28:53,120 --> 00:28:55,590 as you go to equilibrium? 566 00:28:55,590 --> 00:28:56,880 What happens to this? 567 00:28:56,880 --> 00:28:57,810 What changes? 568 00:28:57,810 --> 00:29:00,544 What do I put in this area? 569 00:29:00,544 --> 00:29:01,460 AUDIENCE: [INAUDIBLE]. 570 00:29:01,460 --> 00:29:02,460 CATHERINE DRENNAN: What? 571 00:29:02,460 --> 00:29:03,446 AUDIENCE: [INAUDIBLE] 572 00:29:03,446 --> 00:29:04,862 CATHERINE DRENNAN: I heard minus-- 573 00:29:04,862 --> 00:29:06,812 AUDIENCE: [INAUDIBLE]. 574 00:29:06,812 --> 00:29:09,270 CATHERINE DRENNAN: So I heard minus X. I heard somebody say 575 00:29:09,270 --> 00:29:09,770 [INAUDIBLE]. 576 00:29:09,770 --> 00:29:13,380 It's minus 2X because you have to remember the stoichiometry 577 00:29:13,380 --> 00:29:14,930 of the reaction. 578 00:29:14,930 --> 00:29:18,120 And so we have two of these going to one of those, 579 00:29:18,120 --> 00:29:21,060 so it's minus 2X. 580 00:29:21,060 --> 00:29:28,230 And then at equilibrium, we have 1.000 minus 2X is 581 00:29:28,230 --> 00:29:31,380 our concentration of our reactant, 582 00:29:31,380 --> 00:29:36,120 and our concentration of product is plus X. 583 00:29:36,120 --> 00:29:38,370 So now we're going to solve for this, 584 00:29:38,370 --> 00:29:41,970 and we need to write an expression for the equilibrium 585 00:29:41,970 --> 00:29:42,970 constant. 586 00:29:42,970 --> 00:29:44,586 So why don't you write that for me. 587 00:30:04,660 --> 00:30:05,160 All right. 588 00:30:05,160 --> 00:30:06,026 10 more seconds. 589 00:30:16,570 --> 00:30:17,340 I'd like 90%. 590 00:30:20,710 --> 00:30:24,290 Oh, so close. 591 00:30:24,290 --> 00:30:24,980 OK. 592 00:30:24,980 --> 00:30:28,390 So again, the trick here, you have products over reactants, 593 00:30:28,390 --> 00:30:31,550 and you have to remember the stoichiometry. 594 00:30:31,550 --> 00:30:33,360 So we can go back over here. 595 00:30:33,360 --> 00:30:36,190 So we have partial pressure of our product 596 00:30:36,190 --> 00:30:39,160 over partial pressure of our reactant. 597 00:30:39,160 --> 00:30:42,890 And we have the stoichiometry there, 598 00:30:42,890 --> 00:30:45,530 and now we can continue to plug in. 599 00:30:45,530 --> 00:30:48,650 So the concentration, the partial pressure, 600 00:30:48,650 --> 00:30:52,340 of our product is X at equilibrium. 601 00:30:52,340 --> 00:30:57,400 The partial pressure of our reactant is 1 minus 2X, 602 00:30:57,400 --> 00:31:00,532 and that whole term is raised to the 2. 603 00:31:00,532 --> 00:31:04,210 So it's all that whole term is squared. 604 00:31:04,210 --> 00:31:12,910 And if you solve for X, you will get 0.38 bar. 605 00:31:12,910 --> 00:31:15,830 So you definitely want to remember calculators and things 606 00:31:15,830 --> 00:31:18,190 on this exam. 607 00:31:18,190 --> 00:31:21,210 And that value, then, is our product. 608 00:31:21,210 --> 00:31:23,950 So that's the answer to the partial pressure of the product 609 00:31:23,950 --> 00:31:25,660 because that's what X is. 610 00:31:25,660 --> 00:31:27,460 Another thing that I've seen on exams 611 00:31:27,460 --> 00:31:30,130 is that people solve for X. They're happy to solve for X. 612 00:31:30,130 --> 00:31:32,200 But then they don't remember what X was. 613 00:31:32,200 --> 00:31:36,640 So keep track of what things belong to what. 614 00:31:36,640 --> 00:31:39,400 So then we want to also find the partial pressure 615 00:31:39,400 --> 00:31:40,690 of our reactant. 616 00:31:40,690 --> 00:31:43,790 That was 1 minus 2X. 617 00:31:43,790 --> 00:31:48,080 So here we have 1 minus 2 times X. 618 00:31:48,080 --> 00:31:50,780 And you can see the significant figure fun 619 00:31:50,780 --> 00:31:56,510 that one can have in this because we have multiplication, 620 00:31:56,510 --> 00:32:00,020 division, subtraction, and pretty soon we're going to have 621 00:32:00,020 --> 00:32:02,650 log significant figure rules. 622 00:32:02,650 --> 00:32:05,060 So there's going to be a lot of fun. 623 00:32:05,060 --> 00:32:08,580 And of course, then this is our reactant over here. 624 00:32:08,580 --> 00:32:11,060 So let's just go back to the diagram, which 625 00:32:11,060 --> 00:32:15,530 is up above in your notes, on the same page in your notes, 626 00:32:15,530 --> 00:32:18,450 and plug these in and think about what this means. 627 00:32:18,450 --> 00:32:20,440 So we've done the math. 628 00:32:20,440 --> 00:32:27,700 And we see that our reactant at equilibrium is 0.238 bar, 629 00:32:27,700 --> 00:32:32,360 and our product at equilibrium is 0.381 bar. 630 00:32:32,360 --> 00:32:35,920 So K is greater than 1, more products, 631 00:32:35,920 --> 00:32:38,240 and you see that that works out. 632 00:32:38,240 --> 00:32:41,570 So if you were asked just to explain what you expected, 633 00:32:41,570 --> 00:32:43,480 you could say K is greater than 1. 634 00:32:43,480 --> 00:32:45,020 I expect more products. 635 00:32:45,020 --> 00:32:47,410 But if you do the math, and you'll often do the math, 636 00:32:47,410 --> 00:32:50,090 you can calculate what the partial pressures 637 00:32:50,090 --> 00:32:56,211 are at equilibrium of the reactants and of the products. 638 00:32:56,211 --> 00:32:56,710 All right. 639 00:32:56,710 --> 00:33:00,590 So now let's think about the relationship, again, 640 00:33:00,590 --> 00:33:07,580 between delta G0 and K. So here is 641 00:33:07,580 --> 00:33:10,150 our expression we saw before. 642 00:33:10,150 --> 00:33:14,630 We can also rewrite this to solve for K. 643 00:33:14,630 --> 00:33:18,460 So sometimes you will be given information about delta G0 644 00:33:18,460 --> 00:33:23,330 and asked to calculate a K at a particular temperature. 645 00:33:23,330 --> 00:33:26,650 But we can also think about what we would expect. 646 00:33:26,650 --> 00:33:31,880 So if K is large, what is going to be true about delta G0? 647 00:33:31,880 --> 00:33:34,352 And so why don't you tell me what you think. 648 00:33:55,950 --> 00:33:56,450 All right. 649 00:33:56,450 --> 00:33:57,980 Let's just do 10 more seconds. 650 00:34:16,080 --> 00:34:20,340 So it would be a large negative number. 651 00:34:20,340 --> 00:34:24,989 And we can think about this, that if you really 652 00:34:24,989 --> 00:34:28,650 are lying on the side of products in your reaction, 653 00:34:28,650 --> 00:34:31,530 then that would be consistent with a bigger 654 00:34:31,530 --> 00:34:33,510 value and a negative value. 655 00:34:33,510 --> 00:34:35,219 So you can think about-- again, we 656 00:34:35,219 --> 00:34:37,560 talked about in terms of formation, 657 00:34:37,560 --> 00:34:41,489 is the thing that's being formed more or less stable compared 658 00:34:41,489 --> 00:34:44,100 to its elements, the same sort of idea. 659 00:34:44,100 --> 00:34:46,920 You can think about the relative stability 660 00:34:46,920 --> 00:34:49,650 and whether you'd expect more products or more reactants 661 00:34:49,650 --> 00:34:53,980 at equilibrium based on these values. 662 00:34:53,980 --> 00:34:57,280 So let's do an example and prove that this is true. 663 00:34:57,280 --> 00:35:00,240 So let's consider baking soda again. 664 00:35:00,240 --> 00:35:03,750 Baking soda works really well for this unit on thermodynamics 665 00:35:03,750 --> 00:35:05,730 and chemical equilibrium. 666 00:35:05,730 --> 00:35:08,340 So again, we have our baking soda 667 00:35:08,340 --> 00:35:13,800 going to CO2, which is very important, the CO2 gas, which 668 00:35:13,800 --> 00:35:16,020 helps our bread rise. 669 00:35:16,020 --> 00:35:20,160 And we calculated last week that the delta G0 670 00:35:20,160 --> 00:35:22,110 at room temperature for this process 671 00:35:22,110 --> 00:35:25,660 was plus 36 kilojoules per mole. 672 00:35:25,660 --> 00:35:27,930 And that would mean that it's not 673 00:35:27,930 --> 00:35:30,210 spontaneous in the forward direction, which 674 00:35:30,210 --> 00:35:33,390 is really bad for our bread, because we need the CO2 675 00:35:33,390 --> 00:35:35,430 gas to cause it to rise. 676 00:35:35,430 --> 00:35:37,770 But the good news was that if we remember 677 00:35:37,770 --> 00:35:40,200 to turn on the oven in baking bread 678 00:35:40,200 --> 00:35:43,380 and put it at a normal temperature in the oven, 679 00:35:43,380 --> 00:35:47,500 that the delta G0 is minus 15 kilojoules per mole. 680 00:35:47,500 --> 00:35:50,460 So then it becomes a spontaneous reaction. 681 00:35:50,460 --> 00:35:52,620 Now we can think about this in terms 682 00:35:52,620 --> 00:35:57,540 of our equilibrium constant K. So if we do the math here, 683 00:35:57,540 --> 00:36:03,540 at room temperature K would be 4.9 times 10 to the minus 7. 684 00:36:03,540 --> 00:36:06,300 That is a small number. 685 00:36:06,300 --> 00:36:11,100 That means that there is very little product at equilibrium 686 00:36:11,100 --> 00:36:12,450 at this temperature. 687 00:36:12,450 --> 00:36:17,070 Very little CO2 gas to be able to be used to make our bread 688 00:36:17,070 --> 00:36:18,060 rise. 689 00:36:18,060 --> 00:36:21,150 But now if we calculate K at this value, 690 00:36:21,150 --> 00:36:27,510 at a negative number for delta G, K is now 55. 691 00:36:27,510 --> 00:36:30,210 So we have quite a lot of product 692 00:36:30,210 --> 00:36:32,640 then to be used to make the bread rise. 693 00:36:32,640 --> 00:36:34,410 So you can think about things in terms 694 00:36:34,410 --> 00:36:36,390 of delta G's and whether something's 695 00:36:36,390 --> 00:36:39,510 going to be spontaneous and give you the product you want. 696 00:36:39,510 --> 00:36:41,670 But the equilibrium constant gives you 697 00:36:41,670 --> 00:36:43,410 that information as well. 698 00:36:43,410 --> 00:36:46,344 If it's a very small number, you have very little product. 699 00:36:46,344 --> 00:36:47,760 And if you want product, if you're 700 00:36:47,760 --> 00:36:50,100 trying to industrially make something, 701 00:36:50,100 --> 00:36:52,260 that's a very bad thing. 702 00:36:52,260 --> 00:36:58,200 But if you have a big value for K and this negative delta G0 703 00:36:58,200 --> 00:37:00,560 value, then that's good if you want a lot 704 00:37:00,560 --> 00:37:03,390 of the product at equilibrium. 705 00:37:03,390 --> 00:37:06,030 So equilibrium doesn't just matter 706 00:37:06,030 --> 00:37:11,940 for things like baking soda or forming ammonia from nitrogen 707 00:37:11,940 --> 00:37:14,820 and hydrogen. Chemical equilibrium 708 00:37:14,820 --> 00:37:17,830 applies to large molecules as well, 709 00:37:17,830 --> 00:37:21,810 such as enzymes in your body that are catalyzing reactions. 710 00:37:21,810 --> 00:37:25,230 So I'm going to share with you an In Their Own Words. 711 00:37:25,230 --> 00:37:29,700 And this is Nozomi Ando, who I will just 712 00:37:29,700 --> 00:37:33,460 mention is an MIT undergraduate-- was 713 00:37:33,460 --> 00:37:38,040 a graduate of MIT, was an undergraduate here in physics, 714 00:37:38,040 --> 00:37:39,840 majored in physics. 715 00:37:39,840 --> 00:37:43,637 And she is now a professor of-- do you want to guess? 716 00:37:43,637 --> 00:37:44,470 AUDIENCE: Chemistry. 717 00:37:44,470 --> 00:37:46,261 CATHERINE DRENNAN: Chemistry, that's right. 718 00:37:46,261 --> 00:37:49,140 She's a professor of chemistry at Princeton University. 719 00:37:49,140 --> 00:37:53,340 So here is a good example of what can happen. 720 00:37:53,340 --> 00:37:55,980 And she was very happy-- actually, 721 00:37:55,980 --> 00:37:58,380 I think 5.111 didn't exist then. 722 00:37:58,380 --> 00:38:00,420 I think it was 5.11 when she was here. 723 00:38:00,420 --> 00:38:03,150 But nonetheless, so here in her words 724 00:38:03,150 --> 00:38:06,534 about chemical equilibrium and the proteins she studies. 725 00:38:06,534 --> 00:38:07,200 [VIDEO PLAYBACK] 726 00:38:07,200 --> 00:38:09,995 -My name is Nozomi Ando, and I study 727 00:38:09,995 --> 00:38:14,760 a protein called Ribonucleotide Reductase, or RNR for short. 728 00:38:14,760 --> 00:38:19,440 It catalyzes the reaction of converting ribonucleotides, 729 00:38:19,440 --> 00:38:23,490 or the building blocks of RNA, into deoxyribonucleotides, 730 00:38:23,490 --> 00:38:25,970 or the building blocks of DNA. 731 00:38:25,970 --> 00:38:28,890 It's the only means of getting those letters for DNA, 732 00:38:28,890 --> 00:38:32,880 so it's important for DNA synthesis and repair 733 00:38:32,880 --> 00:38:34,320 and replication. 734 00:38:34,320 --> 00:38:37,620 It knows, for example, when there's 735 00:38:37,620 --> 00:38:43,440 an imbalance in the pools of the letters for DNA 736 00:38:43,440 --> 00:38:48,480 or if there's a lot of letters of the RNA. 737 00:38:48,480 --> 00:38:54,600 And this controls the sort of state that RNR is in. 738 00:38:54,600 --> 00:38:58,890 And RNR can be in an equilibrium of active and inactive states 739 00:38:58,890 --> 00:39:03,030 that are sort of regulated by the alphabet soup in the cell. 740 00:39:03,030 --> 00:39:05,070 When it's active, it's very compact, 741 00:39:05,070 --> 00:39:07,800 but then it has to make a really dramatic structural change 742 00:39:07,800 --> 00:39:10,500 to go into an inactive state. 743 00:39:10,500 --> 00:39:12,870 I have this imagery of Transformers 744 00:39:12,870 --> 00:39:14,230 because it's just so dramatic. 745 00:39:14,230 --> 00:39:16,740 So when it's active, it's compact, like when 746 00:39:16,740 --> 00:39:18,330 a Transformer's a car. 747 00:39:18,330 --> 00:39:22,080 And when it's inactive and it makes a sound, che, che, che, 748 00:39:22,080 --> 00:39:26,360 che, and then it expands into a robot. 749 00:39:26,360 --> 00:39:30,980 The letter A, or adenosine, pushes this equilibrium 750 00:39:30,980 --> 00:39:33,050 from the active to inactive state. 751 00:39:33,050 --> 00:39:36,680 And it tells RNR, OK, we have enough of the DNA letters, 752 00:39:36,680 --> 00:39:37,760 so stop. 753 00:39:37,760 --> 00:39:40,280 For humans, it's really important to study RNR 754 00:39:40,280 --> 00:39:46,220 because it's the protein that is essential for making letters 755 00:39:46,220 --> 00:39:46,790 of DNA. 756 00:39:46,790 --> 00:39:50,390 So it's essential for DNA replication, which is 757 00:39:50,390 --> 00:39:54,500 essential for cells to divide. 758 00:39:54,500 --> 00:39:59,330 And we want RNR to function normally for our health. 759 00:39:59,330 --> 00:40:03,360 But in cells that are dividing too quickly, 760 00:40:03,360 --> 00:40:06,740 such as tumor cells, we want to slow it down. 761 00:40:06,740 --> 00:40:10,490 So actually, RNR is a really important target 762 00:40:10,490 --> 00:40:13,530 for anti-cancer drugs. 763 00:40:13,530 --> 00:40:17,570 But also, because RNR exists in every organism, 764 00:40:17,570 --> 00:40:20,000 we can start looking at differences 765 00:40:20,000 --> 00:40:22,620 between different species. 766 00:40:22,620 --> 00:40:27,193 So for example, it could be anti-bacterial and not just 767 00:40:27,193 --> 00:40:27,693 anti-cancer. 768 00:40:30,431 --> 00:40:31,014 [END PLAYBACK] 769 00:40:31,014 --> 00:40:32,990 CATHERINE DRENNAN: So that's an example 770 00:40:32,990 --> 00:40:36,350 of how you have a shift between two 771 00:40:36,350 --> 00:40:39,130 states, an inactive and active state, 772 00:40:39,130 --> 00:40:41,810 that it's just a chemical equilibrium. 773 00:40:41,810 --> 00:40:44,480 And binding one thing shifts the equilibrium one way. 774 00:40:44,480 --> 00:40:46,190 Binding something else shifts it back. 775 00:40:46,190 --> 00:40:47,990 So chemical equilibrium-- a lot of nature 776 00:40:47,990 --> 00:40:51,500 works by just suddenly shifting the equilibrium 777 00:40:51,500 --> 00:40:53,060 between different states. 778 00:40:53,060 --> 00:40:54,770 So understanding chemical equilibrium 779 00:40:54,770 --> 00:40:56,191 is pretty important. 780 00:40:56,191 --> 00:40:56,690 All right. 781 00:40:56,690 --> 00:41:02,300 So now we're going to apply stress to our chemical 782 00:41:02,300 --> 00:41:07,180 equilibrium, and we're going to talk about the principle of Le 783 00:41:07,180 --> 00:41:09,630 Chatelier. 784 00:41:09,630 --> 00:41:15,650 So here, a system in equilibrium that's subject to stress 785 00:41:15,650 --> 00:41:23,750 will react in a way that tends to minimize that stress. 786 00:41:23,750 --> 00:41:26,240 And whenever I talk to MIT students about this, 787 00:41:26,240 --> 00:41:30,410 I feel like I need to really emphasize this point. 788 00:41:30,410 --> 00:41:34,040 MIT students experience a lot of stress, 789 00:41:34,040 --> 00:41:37,040 but often do not tend to react in a way 790 00:41:37,040 --> 00:41:39,920 to minimize that stress. 791 00:41:39,920 --> 00:41:43,850 They say, all right, I am just struggling with this double 792 00:41:43,850 --> 00:41:44,360 major. 793 00:41:44,360 --> 00:41:45,660 I don't know what to do. 794 00:41:45,660 --> 00:41:46,890 It's just so much work. 795 00:41:46,890 --> 00:41:50,003 So maybe I should triple major instead. 796 00:41:50,003 --> 00:41:50,502 No. 797 00:41:50,502 --> 00:41:53,160 [LAUGHTER] 798 00:41:53,160 --> 00:41:55,830 Ask yourself, what would Le Chatelier do? 799 00:41:55,830 --> 00:41:56,600 Minimize. 800 00:41:56,600 --> 00:42:00,860 Double major, single major. 801 00:42:00,860 --> 00:42:04,010 So this is a principle that can apply to your life. 802 00:42:04,010 --> 00:42:08,942 And I recently saw a chemistry major, and we had lunch. 803 00:42:08,942 --> 00:42:10,650 He was a former MIT student, and now he's 804 00:42:10,650 --> 00:42:13,580 a CEO of a company, small company, in Cambridge 805 00:42:13,580 --> 00:42:18,050 that's designing computer software platforms. 806 00:42:18,050 --> 00:42:21,260 He was a chemistry major, and he's doing software design 807 00:42:21,260 --> 00:42:24,620 and building like little computer tablet 808 00:42:24,620 --> 00:42:26,010 things for restaurants. 809 00:42:26,010 --> 00:42:28,780 So I said, would you use your chemistry at all? 810 00:42:28,780 --> 00:42:31,490 And he goes, oh, I use some things all the time, especially 811 00:42:31,490 --> 00:42:33,080 Le Chatelier's principle. 812 00:42:33,080 --> 00:42:35,510 I'm all about minimizing the stress. 813 00:42:35,510 --> 00:42:38,090 So that was one thing that he really 814 00:42:38,090 --> 00:42:40,430 grabbed onto in chemistry. 815 00:42:40,430 --> 00:42:43,220 So again, if you think about this, 816 00:42:43,220 --> 00:42:47,240 about minimizing the stress, you can predict 817 00:42:47,240 --> 00:42:48,515 the direction of the reaction. 818 00:42:48,515 --> 00:42:51,140 And in nature, this really works pretty well. 819 00:42:51,140 --> 00:42:53,090 So Le Chatelier's principle gives us 820 00:42:53,090 --> 00:42:56,210 a way to predict the direction the reaction will 821 00:42:56,210 --> 00:43:03,530 go if you ask, which direction will minimize the stress? 822 00:43:03,530 --> 00:43:05,760 So let's look at an example. 823 00:43:05,760 --> 00:43:09,680 We're back to N2 and H2 making ammonia. 824 00:43:09,680 --> 00:43:12,890 So here's a slightly different plot than I drew over here. 825 00:43:12,890 --> 00:43:15,350 Now, this is a reaction sensitive to temperature, 826 00:43:15,350 --> 00:43:16,850 so the equilibrium constant's going 827 00:43:16,850 --> 00:43:18,030 to change with temperature. 828 00:43:18,030 --> 00:43:20,488 So every plot of this may look a little different depending 829 00:43:20,488 --> 00:43:22,580 on what temperature it's at. 830 00:43:22,580 --> 00:43:24,364 But some things are the same. 831 00:43:24,364 --> 00:43:26,030 If you start with hydrogen and nitrogen, 832 00:43:26,030 --> 00:43:27,980 you'll have some of those to begin with. 833 00:43:27,980 --> 00:43:29,750 They will be above 0. 834 00:43:29,750 --> 00:43:32,630 But ammonia will start-- if you had no product, 835 00:43:32,630 --> 00:43:34,984 you'll have ammonia at 0 and it'll rise in. 836 00:43:34,984 --> 00:43:36,650 The other thing that should look similar 837 00:43:36,650 --> 00:43:39,470 is that as the reaction runs for long enough it'll 838 00:43:39,470 --> 00:43:43,820 reach equilibrium, and you'll have the lines level out. 839 00:43:43,820 --> 00:43:45,860 You'll reach an equilibrium state. 840 00:43:45,860 --> 00:43:49,950 Now what happens if you stress that equilibrium state? 841 00:43:49,950 --> 00:43:54,340 So say you add hydrogen. And so this line adds the hydrogen, 842 00:43:54,340 --> 00:43:56,030 then it goes down. 843 00:43:56,030 --> 00:43:59,840 Then you're also going to use up some nitrogen as you're 844 00:43:59,840 --> 00:44:01,790 using up the hydrogen. You're going 845 00:44:01,790 --> 00:44:05,300 to shift it to make more product. 846 00:44:05,300 --> 00:44:08,570 Now, say, you make product. 847 00:44:08,570 --> 00:44:11,600 You add product-- sorry, you're adding product. 848 00:44:11,600 --> 00:44:16,880 It's going to shift to minimize the stress, use up the product, 849 00:44:16,880 --> 00:44:21,020 have the product dissociate, and make more hydrogen and more 850 00:44:21,020 --> 00:44:22,800 nitrogen. 851 00:44:22,800 --> 00:44:25,230 So here's the plot. 852 00:44:25,230 --> 00:44:28,500 Now, let's just think about what's happening at each step. 853 00:44:28,500 --> 00:44:31,400 So if we're adding more reactant, 854 00:44:31,400 --> 00:44:32,360 you have more reactant. 855 00:44:32,360 --> 00:44:34,580 You have too much reactant. 856 00:44:34,580 --> 00:44:39,800 Shift to minimize the stress, and you will shift 857 00:44:39,800 --> 00:44:41,390 the reaction toward product. 858 00:44:41,390 --> 00:44:43,760 Get rid of the reactant, use up the reactant. 859 00:44:43,760 --> 00:44:46,780 Let's get back to the equilibrium condition, 860 00:44:46,780 --> 00:44:49,220 minimize the stress. 861 00:44:49,220 --> 00:44:54,126 Now, we can think about this in terms of Q and K again. 862 00:44:57,030 --> 00:45:01,580 So when you have reactants added, 863 00:45:01,580 --> 00:45:05,850 then Q is going to fall below K momentarily. 864 00:45:05,850 --> 00:45:09,620 And so that means-- if you think about our equation over here, 865 00:45:09,620 --> 00:45:13,130 recall this equation, this important equation. 866 00:45:13,130 --> 00:45:18,170 So with Q less than K, you get a negative delta G, 867 00:45:18,170 --> 00:45:21,200 and that's going to be spontaneous toward the right, 868 00:45:21,200 --> 00:45:22,440 toward products. 869 00:45:22,440 --> 00:45:26,240 So again, you respond by making more products. 870 00:45:26,240 --> 00:45:29,720 You shift to the right. 871 00:45:29,720 --> 00:45:31,390 And you saw that over here. 872 00:45:31,390 --> 00:45:33,890 It's shifting toward products. 873 00:45:33,890 --> 00:45:37,040 You're using up the hydrogen. You're using up the nitrogen. 874 00:45:37,040 --> 00:45:41,390 You're trying to return to an equilibrium condition. 875 00:45:41,390 --> 00:45:47,360 Now what happens if we add more product? 876 00:45:47,360 --> 00:45:51,230 And so when you're adding more product, Q is greater than K 877 00:45:51,230 --> 00:45:51,890 momentarily. 878 00:45:51,890 --> 00:45:55,910 You have too many products now compared to equilibrium. 879 00:45:55,910 --> 00:46:02,360 And when Q is greater than K, you get a positive delta G. 880 00:46:02,360 --> 00:46:04,250 And that means that it's spontaneous 881 00:46:04,250 --> 00:46:06,680 in the reverse direction, or non-spontaneous 882 00:46:06,680 --> 00:46:08,160 in the forward direction. 883 00:46:08,160 --> 00:46:09,710 So you shift toward reactants. 884 00:46:09,710 --> 00:46:11,910 You shift to the left. 885 00:46:11,910 --> 00:46:13,460 So again, you can use this equation 886 00:46:13,460 --> 00:46:17,550 to think about what direction is now going to be favorable. 887 00:46:17,550 --> 00:46:19,610 And so here you added product. 888 00:46:19,610 --> 00:46:21,140 The product gets used up. 889 00:46:21,140 --> 00:46:23,210 It's shifting toward reactants, and you're 890 00:46:23,210 --> 00:46:27,590 making more reactants until you reach equilibrium again. 891 00:46:27,590 --> 00:46:32,060 And we have one minute left for a last clicker question. 892 00:46:32,060 --> 00:46:33,990 What happens when you remove products? 893 00:46:54,631 --> 00:46:55,130 All right. 894 00:46:55,130 --> 00:46:56,795 So let's just take 10 more seconds. 895 00:47:08,670 --> 00:47:11,130 All right. 896 00:47:11,130 --> 00:47:13,540 So we'll just put it up over here. 897 00:47:13,540 --> 00:47:15,690 So that means that delta G is going 898 00:47:15,690 --> 00:47:19,580 to be negative in that case because you remove products. 899 00:47:19,580 --> 00:47:22,710 So Q is less than K, and so the reaction 900 00:47:22,710 --> 00:47:25,170 is going to be spontaneous in the forward direction. 901 00:47:25,170 --> 00:47:26,910 Delta G will be negative, and you'll 902 00:47:26,910 --> 00:47:28,710 move to make more products. 903 00:47:28,710 --> 00:47:30,870 Again, minimize the stress. 904 00:47:30,870 --> 00:47:32,080 You took away products. 905 00:47:32,080 --> 00:47:33,780 You need to make more. 906 00:47:33,780 --> 00:47:36,620 Minimize the stress. 907 00:47:36,620 --> 00:47:40,650 Do problem set 5 and minimize your stress.