1 00:00:00,000 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,840 Your support will help MIT OpenCourseWare continue to 4 00:00:06,840 --> 00:00:10,520 offer high quality educational resources for free. 5 00:00:10,520 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,580 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,580 --> 00:00:20,350 ocw.mit.edu. 8 00:00:20,350 --> 00:00:27,250 PROFESSOR: I want to remind and clarify as needed the 9 00:00:27,250 --> 00:00:36,420 equilibrium constant Kp for gas phase reaction was the 10 00:00:36,420 --> 00:00:43,060 ratios of the partial pressures referenced to some 11 00:00:43,060 --> 00:00:47,110 reference pressure, which we usually take as one, one bar. 12 00:00:47,110 --> 00:00:54,952 To the stoichiometry , pD divided by p naught, to the mu 13 00:00:54,952 --> 00:00:57,910 D where species C and D are products. 14 00:00:57,910 --> 00:01:11,540 And the reactants are on the bottom. 15 00:01:11,540 --> 00:01:19,350 And usually we don't write p naught, but it's important to 16 00:01:19,350 --> 00:01:22,380 remember that it's there. 17 00:01:22,380 --> 00:01:26,360 And then we can also write this in terms of the Gibbs 18 00:01:26,360 --> 00:01:29,170 free energy for the reaction. 19 00:01:29,170 --> 00:01:32,920 The standard Gibbs free energy, minus delta G naught 20 00:01:32,920 --> 00:01:39,570 of the reaction, divided by RT. 21 00:01:39,570 --> 00:01:43,860 And what this tells us is that this is a number. 22 00:01:43,860 --> 00:01:45,930 This is a number, there's no pre-factor 23 00:01:45,930 --> 00:01:48,240 here that has units. 24 00:01:48,240 --> 00:01:52,640 That's a unitless number. 25 00:01:52,640 --> 00:02:04,410 And it doesn't depend on the total pressure. 26 00:02:04,410 --> 00:02:05,905 And the other thing to remember is that delta G 27 00:02:05,905 --> 00:02:10,080 naught for the reaction is the process of taking the 28 00:02:10,080 --> 00:02:12,760 reactants separated in separate boxes, separate 29 00:02:12,760 --> 00:02:19,090 containers, and the final product, the final step, is 30 00:02:19,090 --> 00:02:22,350 the products separated in individual containers. 31 00:02:22,350 --> 00:02:24,435 That's what we write when we write delta G 32 00:02:24,435 --> 00:02:30,190 naught for the reaction. 33 00:02:30,190 --> 00:02:35,340 We also looked at K in terms of mole fractions. 34 00:02:35,340 --> 00:02:38,020 So if you replace all the partial pressures with the 35 00:02:38,020 --> 00:02:40,360 mole fraction times the total pressure, you get an 36 00:02:40,360 --> 00:02:47,560 expression for K sub x, which we define as the mole fraction 37 00:02:47,560 --> 00:02:59,140 of the products to the stoichiometric powers. 38 00:02:59,140 --> 00:03:02,420 Which is also unitless. 39 00:03:02,420 --> 00:03:04,880 This is true, it's unitless. 40 00:03:04,880 --> 00:03:08,940 But, if you write it in terms of K sub p, the total pressure 41 00:03:08,940 --> 00:03:11,880 comes in here. p total, divided by the reference 42 00:03:11,880 --> 00:03:17,770 pressure to the minus delta nu, where this is the change 43 00:03:17,770 --> 00:03:21,010 in the number of moles, in going from 44 00:03:21,010 --> 00:03:23,330 reactants to products. 45 00:03:23,330 --> 00:03:25,810 And there's K sub p sitting here. 46 00:03:25,810 --> 00:03:28,620 So unlike K sub p, which doesn't depend on the total 47 00:03:28,620 --> 00:03:33,040 pressure, K sub x does depend on the total pressure through 48 00:03:33,040 --> 00:03:47,340 this term right here. 49 00:03:47,340 --> 00:03:49,970 So when we look at problems where we change the pressure, 50 00:03:49,970 --> 00:03:53,300 the total pressure of the system, this is 51 00:03:53,300 --> 00:03:54,400 going to stay the same. 52 00:03:54,400 --> 00:03:56,130 Because it only cares about delta G 53 00:03:56,130 --> 00:03:57,880 naught for the reaction. 54 00:03:57,880 --> 00:04:01,586 But this K sub x will depend on the total pressure. 55 00:04:01,586 --> 00:04:10,330 And that's often a source of confusion in doing problems. 56 00:04:10,330 --> 00:04:11,700 OK, any questions? 57 00:04:11,700 --> 00:04:13,060 We're going to do an example where we change 58 00:04:13,060 --> 00:04:16,600 the pressure first. 59 00:04:16,600 --> 00:04:19,340 So there are examples in the notes, and I'm going to skip 60 00:04:19,340 --> 00:04:20,470 the first one. 61 00:04:20,470 --> 00:04:22,930 I'm going to go to the second one, which is the effect of 62 00:04:22,930 --> 00:04:24,840 the total pressure on the reaction. 63 00:04:24,840 --> 00:04:31,840 And Le Chatelier's principle, for pressure. 64 00:04:31,840 --> 00:04:34,720 And the example we're going to take is a fairly standard 65 00:04:34,720 --> 00:04:37,040 example, also. 66 00:04:37,040 --> 00:04:46,450 Which is the reaction of N2O4, which is a gas, to 2 NO2, 67 00:04:46,450 --> 00:04:49,670 which is a gas, the kind of reaction that happens when you 68 00:04:49,670 --> 00:04:59,080 have smog and, fairly common in big cities. 69 00:04:59,080 --> 00:05:05,130 The question we're going to ask is, what happens when we 70 00:05:05,130 --> 00:05:08,690 change the total pressure in this reaction here. 71 00:05:08,690 --> 00:05:11,600 Which way does the equilibrium go? 72 00:05:11,600 --> 00:05:13,700 Does it go to the right, does it go to the left? 73 00:05:13,700 --> 00:05:15,650 Does it go to the products or the reactants. 74 00:05:15,650 --> 00:05:19,270 And so, in order to answer that question, we're going to 75 00:05:19,270 --> 00:05:20,970 ask a slightly different question. 76 00:05:20,970 --> 00:05:24,280 We're going to ask what is the molar ratio, what is the 77 00:05:24,280 --> 00:05:31,270 fraction, what is fraction of the reactant, 78 00:05:31,270 --> 00:05:39,920 the N2O4 that's reacted. 79 00:05:39,920 --> 00:05:43,120 That has reacted. 80 00:05:43,120 --> 00:05:47,800 And we're going to call that alpha. 81 00:05:47,800 --> 00:05:56,470 It's the number of moles that have reacted divided by number 82 00:05:56,470 --> 00:06:03,350 of moles initially. 83 00:06:03,350 --> 00:06:08,110 So we're going to need to find at equilibrium what is the 84 00:06:08,110 --> 00:06:13,950 number of moles of N2O4 that has reacted. 85 00:06:13,950 --> 00:06:16,640 So we have to set up the problem. 86 00:06:16,640 --> 00:06:21,180 And so the way that, the standard way of setting up the 87 00:06:21,180 --> 00:06:30,300 problem is to write the equilibrium, 2 NO2 gas. 88 00:06:30,300 --> 00:06:34,650 And then on this line here, we write the initial conditions 89 00:06:34,650 --> 00:06:36,490 before we set up the equilibrium. 90 00:06:36,490 --> 00:06:38,960 And let's say that we have n moles of N2O4 91 00:06:38,960 --> 00:06:39,880 initially in the box. 92 00:06:39,880 --> 00:06:43,550 And zero moles of the NO2. 93 00:06:43,550 --> 00:06:44,970 So we have n moles here. 94 00:06:44,970 --> 00:06:47,320 And zero moles here. 95 00:06:47,320 --> 00:06:50,170 At equilibrium, let's write the number of moles. 96 00:06:50,170 --> 00:06:52,640 A certain number of moles of N2O4 will have reacted, let's 97 00:06:52,640 --> 00:06:53,880 call that x. 98 00:06:53,880 --> 00:06:55,940 So n minus x moles left. 99 00:06:55,940 --> 00:06:59,970 For every x moles of N2O4 that's reacted, we create two 100 00:06:59,970 --> 00:07:01,820 moles of NO2. 101 00:07:01,820 --> 00:07:04,270 So we have 2x here. 102 00:07:04,270 --> 00:07:06,060 And then we're going to need the total number of moles, 103 00:07:06,060 --> 00:07:07,060 because we're going to be doing mole 104 00:07:07,060 --> 00:07:09,460 ratios, mole fractions. 105 00:07:09,460 --> 00:07:15,020 So the total number of moles at any time is the sum of 106 00:07:15,020 --> 00:07:17,130 these two, n minus x plus 2x. 107 00:07:17,130 --> 00:07:18,900 It's n plus x. 108 00:07:18,900 --> 00:07:21,020 So if we're going to be writing our equilibrium 109 00:07:21,020 --> 00:07:23,780 constant in terms of mole fractions, we're going to need 110 00:07:23,780 --> 00:07:27,180 mole fractions. 111 00:07:27,180 --> 00:07:31,010 So the mole fraction at any time is n minus x divided by 112 00:07:31,010 --> 00:07:33,290 the total number of moles, which we just 113 00:07:33,290 --> 00:07:36,110 calculated as n plus x. 114 00:07:36,110 --> 00:07:40,210 And this is 2x divided by the total number of 115 00:07:40,210 --> 00:07:43,610 moles, n plus x. 116 00:07:43,610 --> 00:07:49,640 And what we want is this ratio here. 117 00:07:49,640 --> 00:07:55,070 We want the ratio of the number of moles reacted, which 118 00:07:55,070 --> 00:08:01,010 is x, that's the number of moles that's gone. 119 00:08:01,010 --> 00:08:03,560 That have reacted. 120 00:08:03,560 --> 00:08:09,130 Divided by the number of moles initially, which is n. 121 00:08:09,130 --> 00:08:10,120 That's what we want. 122 00:08:10,120 --> 00:08:15,740 We want to see how that is going to change with pressure. 123 00:08:15,740 --> 00:08:18,160 So we're going to deal first with Kp, because Kp doesn't 124 00:08:18,160 --> 00:08:20,990 depend on total pressure. 125 00:08:20,990 --> 00:08:21,870 We're going to write that down. 126 00:08:21,870 --> 00:08:24,850 Then we're going to go to Kx, somehow. 127 00:08:24,850 --> 00:08:26,040 And that's going to depend on pressure. 128 00:08:26,040 --> 00:08:37,160 So let's see what Kp is here. 129 00:08:37,160 --> 00:08:41,020 So K sub p, you've got the products on top. 130 00:08:41,020 --> 00:08:45,490 So it's the partial pressure of NO2 to the second power, 131 00:08:45,490 --> 00:08:47,900 divided by the partial pressure of 132 00:08:47,900 --> 00:08:50,130 N2O4 to the one power. 133 00:08:50,130 --> 00:08:51,600 And everything is referenced to one bar, 134 00:08:51,600 --> 00:08:54,180 everything's in bar. 135 00:08:54,180 --> 00:08:57,060 And in terms of the molar fractions, it's the total 136 00:08:57,060 --> 00:09:04,380 pressure squared, times the mole fraction of NO2 squared, 137 00:09:04,380 --> 00:09:07,290 divided by the total pressure to the first power. 138 00:09:07,290 --> 00:09:09,680 So the square root on top gets divided by 139 00:09:09,680 --> 00:09:11,350 one factor of pressure. 140 00:09:11,350 --> 00:09:12,830 So we have total pressure in front. 141 00:09:12,830 --> 00:09:25,340 Divided by x to the N2O4, and that's p times Kx. 142 00:09:25,340 --> 00:09:27,950 So let's plug in what these mole fractions are from our 143 00:09:27,950 --> 00:09:30,950 table here. 144 00:09:30,950 --> 00:09:35,930 The mole fraction of NO2 is 2x divided by n plus x. 145 00:09:35,930 --> 00:09:39,040 2x divided by n plus x to the square power. 146 00:09:39,040 --> 00:09:43,650 Mole fraction of N2O4, n minus x over n plus x. n minus x 147 00:09:43,650 --> 00:09:46,560 over n plus x. 148 00:09:46,560 --> 00:09:50,270 Multiply, square the top, 4x squared. 149 00:09:50,270 --> 00:09:52,220 Divided by n plus x squared. 150 00:09:52,220 --> 00:09:54,900 Things sort of cancel out here. 151 00:09:54,900 --> 00:09:56,770 Rearrange. 152 00:09:56,770 --> 00:10:05,830 4x squared divided by n squared minus x squared. 153 00:10:05,830 --> 00:10:08,220 What we're really interested in is, we're not 154 00:10:08,220 --> 00:10:09,550 interested in x. 155 00:10:09,550 --> 00:10:12,690 We're interested in x divided by n. 156 00:10:12,690 --> 00:10:17,610 So let's divide both the top and the bottom by n squared. 157 00:10:17,610 --> 00:10:20,120 And we're going to get alpha come up. 158 00:10:20,120 --> 00:10:28,200 So this is then p times 4 alpha squared divided by one 159 00:10:28,200 --> 00:10:32,350 minus alpha squared. 160 00:10:32,350 --> 00:10:35,390 This is not, there's no total pressure here. 161 00:10:35,390 --> 00:10:39,310 The only way, the only place, where the total pressure comes 162 00:10:39,310 --> 00:10:42,500 in, is right here. 163 00:10:42,500 --> 00:10:44,655 This is just a number that doesn't care what the total 164 00:10:44,655 --> 00:10:45,250 pressure is. 165 00:10:45,250 --> 00:10:47,260 Which is why we're using it. 166 00:10:47,260 --> 00:10:51,810 And not K sub x, which cares what the total pressure is. 167 00:10:51,810 --> 00:10:54,590 So now we can solve for alpha. 168 00:10:54,590 --> 00:11:03,870 We can solve for alpha by rearranging this equation. 169 00:11:03,870 --> 00:11:07,140 This is just a number. 170 00:11:07,140 --> 00:11:11,290 And this is where the total pressure comes in. 171 00:11:11,290 --> 00:11:15,020 So you rearrange that, and you get alpha is equal to 1 plus 172 00:11:15,020 --> 00:11:22,050 4p divided by Kp, to the minus 1/2 power. 173 00:11:22,050 --> 00:11:25,080 And if I rewrite that slightly to make it a little bit easier 174 00:11:25,080 --> 00:11:28,880 to see what's going to happen, when I change the pressure, 1 175 00:11:28,880 --> 00:11:37,120 plus 4p divided by Kp, to the 1/2 power. 176 00:11:37,120 --> 00:11:41,530 And that's what I'm after. 177 00:11:41,530 --> 00:11:48,910 This tells me what happens at equilibrium to the amount of 178 00:11:48,910 --> 00:11:53,250 NO2 as I change the total pressure. 179 00:11:53,250 --> 00:11:54,780 This is the only place where it comes in. 180 00:11:54,780 --> 00:12:03,020 So now I can see that if I raise the pressure in my 181 00:12:03,020 --> 00:12:09,200 container, raise the pressure, this is in the denominator, so 182 00:12:09,200 --> 00:12:12,030 this fraction gets smaller. 183 00:12:12,030 --> 00:12:16,550 Alpha gets smaller. 184 00:12:16,550 --> 00:12:22,250 I raise the pressure, the fraction of material that 185 00:12:22,250 --> 00:12:24,170 reacts gets smaller. 186 00:12:24,170 --> 00:12:30,480 Therefore, the reaction goes towards the reactants. 187 00:12:30,480 --> 00:12:38,160 If I decrease the pressure, this is a smaller number here. 188 00:12:38,160 --> 00:12:40,500 The fraction gets bigger. 189 00:12:40,500 --> 00:12:40,990 Alpha goes up. 190 00:12:40,990 --> 00:12:47,210 If I decrease the pressure and I compare what happens to the 191 00:12:47,210 --> 00:12:51,320 number of moles of reactants that react, more of it reacts. 192 00:12:51,320 --> 00:12:55,140 Equilibrium shifts towards the product. 193 00:12:55,140 --> 00:13:02,680 And this is Le Chatelier that you already know. 194 00:13:02,680 --> 00:13:10,480 Le Chatelier's principle, for pressure. 195 00:13:10,480 --> 00:13:14,860 The way it works is that Le Chatelier's principle states 196 00:13:14,860 --> 00:13:23,050 that, this chemical system wants to stay as close to what 197 00:13:23,050 --> 00:13:23,820 it was before. 198 00:13:23,820 --> 00:13:24,620 It doesn't like change. 199 00:13:24,620 --> 00:13:28,030 It doesn't want to have any change happen. 200 00:13:28,030 --> 00:13:34,280 So if you increase the pressure, the chemical system 201 00:13:34,280 --> 00:13:37,320 says, hey, you know I'm not so happy that you're increasing 202 00:13:37,320 --> 00:13:38,860 the pressure on me. 203 00:13:38,860 --> 00:13:43,030 I'd like to go back to a smaller pressure. 204 00:13:43,030 --> 00:13:44,020 It doesn't like change. 205 00:13:44,020 --> 00:13:46,780 Very conservative. 206 00:13:46,780 --> 00:13:50,760 And the way to decrease the pressure is to decrease the 207 00:13:50,760 --> 00:13:53,230 number of moles in the container. 208 00:13:53,230 --> 00:13:55,140 How does it decrease the number of moles? 209 00:13:55,140 --> 00:13:56,590 Goes back to where there are fewer moles. 210 00:13:56,590 --> 00:14:03,870 And that's on the reactant side. 211 00:14:03,870 --> 00:14:06,450 How many of you know Lenz's law? 212 00:14:06,450 --> 00:14:07,980 In magnetism. 213 00:14:07,980 --> 00:14:11,070 The diamagnetic materials. 214 00:14:11,070 --> 00:14:11,830 Right. 215 00:14:11,830 --> 00:14:13,760 At least one person knows it. 216 00:14:13,760 --> 00:14:17,640 It's the same idea. 217 00:14:17,640 --> 00:14:20,880 You take a diamagnetic material in the absence of a 218 00:14:20,880 --> 00:14:24,820 magnetic field, and you slowly move it into a place where 219 00:14:24,820 --> 00:14:27,920 there's high magnetic field, what does the diamagnetic 220 00:14:27,920 --> 00:14:30,110 material do? 221 00:14:30,110 --> 00:14:33,680 It orients its magnetic moment to reverse the field. 222 00:14:33,680 --> 00:14:35,160 So that there's no field inside. 223 00:14:35,160 --> 00:14:36,740 It starts out with no field. 224 00:14:36,740 --> 00:14:38,640 Doesn't like change. 225 00:14:38,640 --> 00:14:42,590 So Lenz's law says it's going to do whatever it can so that 226 00:14:42,590 --> 00:14:44,450 it retains no field inside. 227 00:14:44,450 --> 00:14:47,790 Le Chatelier's principle is basically the same thing. 228 00:14:47,790 --> 00:14:50,100 Equilibrium systems are very unhappy if you 229 00:14:50,100 --> 00:14:52,330 try to change them. 230 00:14:52,330 --> 00:14:56,950 And that's what happens for Le Chatelier here with pressure. 231 00:14:56,950 --> 00:15:01,790 Any questions? 232 00:15:01,790 --> 00:15:04,660 So before we go to Le Chatelier's with temperature, 233 00:15:04,660 --> 00:15:06,570 and the van 't Hoff equation. 234 00:15:06,570 --> 00:15:11,290 Let's do a little detour here and talk about equilibrium in 235 00:15:11,290 --> 00:15:14,960 solution, which is really as important, or if not important 236 00:15:14,960 --> 00:15:20,430 for a lot of you, then gas phase equilibrium. 237 00:15:20,430 --> 00:15:23,320 Although gas phase equilibrium was where everything started. 238 00:15:23,320 --> 00:15:26,860 And still a huge deal. 239 00:15:26,860 --> 00:15:32,330 OK, so in equilibrium now, when we talk about equilibrium 240 00:15:32,330 --> 00:15:35,290 in solution, we still have to, still going to be 241 00:15:35,290 --> 00:15:36,870 the chemical potential. 242 00:15:36,870 --> 00:15:39,680 It's still going to be looking at how chemical potential 243 00:15:39,680 --> 00:15:41,530 likes to go downhill. 244 00:15:41,530 --> 00:15:46,730 And we're going to have to write chemical potential for a 245 00:15:46,730 --> 00:15:51,140 species, A, let's say, which is in solution. 246 00:15:51,140 --> 00:15:54,920 At some concentration c sub A in solution. 247 00:15:54,920 --> 00:16:03,860 And the concentration could be given in moles per liter. 248 00:16:03,860 --> 00:16:08,510 Or it could be in grams per liter. 249 00:16:08,510 --> 00:16:13,910 Or it could be in grams per 1000 grams. 250 00:16:13,910 --> 00:16:16,860 Whatever your favorite unit of concentration is. 251 00:16:16,860 --> 00:16:17,740 Use it. 252 00:16:17,740 --> 00:16:20,210 Stick to it. 253 00:16:20,210 --> 00:16:22,260 And in order to do equilibrium, we're going to 254 00:16:22,260 --> 00:16:28,360 have to reference it to, so this would be the species at 255 00:16:28,360 --> 00:16:30,280 some arbitrary concentration. 256 00:16:30,280 --> 00:16:33,110 We're going to have to reference it to some reference 257 00:16:33,110 --> 00:16:33,730 concentration. 258 00:16:33,730 --> 00:16:37,210 Just like we referenced everything to one bar before, 259 00:16:37,210 --> 00:16:39,920 as our standard pressure. 260 00:16:39,920 --> 00:16:41,860 And we're going to take, usually you take one mole per 261 00:16:41,860 --> 00:16:45,690 liter, or one gram per liter, or one whatever. 262 00:16:45,690 --> 00:16:47,750 One as your reference concentration. 263 00:16:47,750 --> 00:16:49,220 And the reference concentration is going to 264 00:16:49,220 --> 00:16:50,460 disappear from the equation. 265 00:16:50,460 --> 00:16:52,140 It's just like the reference pressure. 266 00:16:52,140 --> 00:16:54,100 Disappear from the equation. 267 00:16:54,100 --> 00:16:59,320 So we're going to reference this to some standard state 268 00:16:59,320 --> 00:17:01,580 chemical potential. 269 00:17:01,580 --> 00:17:06,390 Where the naught refers now to the standard concentration. 270 00:17:06,390 --> 00:17:12,245 And instead of having RT log p, now we're going 271 00:17:12,245 --> 00:17:16,500 to have RT log cA. 272 00:17:16,500 --> 00:17:19,390 It's kind of like considering the molecules in the solution 273 00:17:19,390 --> 00:17:26,240 to act like an ideal gas. 274 00:17:26,240 --> 00:17:28,730 Knowing fully well that behind, that underneath the 275 00:17:28,730 --> 00:17:33,280 cA, is this reference concentration of one. 276 00:17:33,280 --> 00:17:36,960 One whatever is your favorite units. 277 00:17:36,960 --> 00:17:39,230 Now, it's a little bit more complicated than 278 00:17:39,230 --> 00:17:41,420 for the ideal gas. 279 00:17:41,420 --> 00:17:48,550 Because your solution may contain other things than your 280 00:17:48,550 --> 00:17:50,740 reactants and your products. 281 00:17:50,740 --> 00:17:52,920 Especially if you're doing biology. 282 00:17:52,920 --> 00:17:54,430 It could be a buffer. 283 00:17:54,430 --> 00:17:56,390 It could be a buffer, it could have salt. 284 00:17:56,390 --> 00:18:00,160 It could have a pH that's not equal to seven, whatever. 285 00:18:00,160 --> 00:18:04,060 And so this reference, chemical potential, now needs 286 00:18:04,060 --> 00:18:12,380 to be referenced to a particular pH or salt 287 00:18:12,380 --> 00:18:13,120 concentration. 288 00:18:13,120 --> 00:18:20,280 Or whatever the properties of your solvent are. 289 00:18:20,280 --> 00:18:23,240 Or your solution are. 290 00:18:23,240 --> 00:18:25,660 And that's the big difference. 291 00:18:25,660 --> 00:18:26,980 In an ideal gas, it's 292 00:18:26,980 --> 00:18:28,870 reference to vacuum, basically. 293 00:18:28,870 --> 00:18:30,090 There's nothing there. 294 00:18:30,090 --> 00:18:32,340 In here, in solution you have all these molecules of 295 00:18:32,340 --> 00:18:38,000 solvent, molecules of salt, molecules of acid, or 296 00:18:38,000 --> 00:18:42,260 whatever, that are going to be around to buffer the pH. 297 00:18:42,260 --> 00:18:45,320 And that's going to change what the chemical potential of 298 00:18:45,320 --> 00:18:46,370 a species is. 299 00:18:46,370 --> 00:18:50,160 And if I change the pH and I've got a molecule that I'm 300 00:18:50,160 --> 00:18:54,500 interested in, it may not have an acidic moiety on it, but it 301 00:18:54,500 --> 00:18:59,660 could still care what the pH is, slightly. 302 00:18:59,660 --> 00:19:01,990 And that would change what the reference potential is, 303 00:19:01,990 --> 00:19:03,920 chemical potential is. 304 00:19:03,920 --> 00:19:05,540 So this is really important to remember. 305 00:19:05,540 --> 00:19:07,640 And there are textbooks that are written on how to do this 306 00:19:07,640 --> 00:19:09,090 the right way. 307 00:19:09,090 --> 00:19:10,110 We're not going to do that here. 308 00:19:10,110 --> 00:19:13,020 We're just going to remember this is, we're going to assume 309 00:19:13,020 --> 00:19:15,290 that this is done correctly. 310 00:19:15,290 --> 00:19:20,360 Once you take that as a given, that you have a way to have a 311 00:19:20,360 --> 00:19:23,630 reference chemical potential at a properly referenced pH 312 00:19:23,630 --> 00:19:25,520 and salt concentration, then you can go through the same 313 00:19:25,520 --> 00:19:29,740 analysis that we went to for partial pressures. 314 00:19:29,740 --> 00:19:34,590 This looks just like the ideal gas, where the concentration 315 00:19:34,590 --> 00:19:38,130 replaces the partial pressure. 316 00:19:38,130 --> 00:19:43,360 Or the pressure of chemical A. And you can go through, then 317 00:19:43,360 --> 00:19:52,440 the same argument, where you take your reaction. 318 00:19:52,440 --> 00:20:00,370 And you initially have some delta G for the reactants. 319 00:20:00,370 --> 00:20:05,420 And you have some delta G for the products. 320 00:20:05,420 --> 00:20:07,830 And the difference is the delta G for the reaction, 321 00:20:07,830 --> 00:20:17,110 delta G naught for the reaction, and then on this 322 00:20:17,110 --> 00:20:26,510 side here, you have a solution of A, so the reaction would be 323 00:20:26,510 --> 00:20:30,390 nu A times A, which is in a solution. 324 00:20:30,390 --> 00:20:31,980 Temperature and pressure. 325 00:20:31,980 --> 00:20:36,910 Plus nu B of reactant B, in a solution, 326 00:20:36,910 --> 00:20:38,340 temperature and pressure. 327 00:20:38,340 --> 00:20:44,330 Going to a nu C, C solution, temperature and pressure plus 328 00:20:44,330 --> 00:20:48,560 nu D, D in a solution, constant 329 00:20:48,560 --> 00:20:50,230 temperature and pressure. 330 00:20:50,230 --> 00:20:54,420 So this is taking a solution of A, in one container, a 331 00:20:54,420 --> 00:20:56,150 solution of B in another the container. 332 00:20:56,150 --> 00:20:57,360 That's the initial point. 333 00:20:57,360 --> 00:20:57,970 Mix them together. 334 00:20:57,970 --> 00:20:59,690 Let them react. 335 00:20:59,690 --> 00:21:01,580 Then you take the product, you put them in separate 336 00:21:01,580 --> 00:21:02,640 containers. 337 00:21:02,640 --> 00:21:06,770 And that gets you the stuff that you have the reaction. 338 00:21:06,770 --> 00:21:09,980 So when you mix A and B, you're going to have the same 339 00:21:09,980 --> 00:21:10,980 entropy of mixing. 340 00:21:10,980 --> 00:21:14,100 You're going to lower the delta G. Of the solution. 341 00:21:14,100 --> 00:21:16,640 And you're going to have the same curve that 342 00:21:16,640 --> 00:21:18,530 goes down like this. 343 00:21:18,530 --> 00:21:21,890 To the mixture of products. 344 00:21:21,890 --> 00:21:24,630 And just like for the gases, where we wanted to know what 345 00:21:24,630 --> 00:21:26,360 is the bottom of this curve which gives us the 346 00:21:26,360 --> 00:21:29,480 equilibrium, we can do the same thing. 347 00:21:29,480 --> 00:21:34,110 Exactly the same thing, for solutions. 348 00:21:34,110 --> 00:21:37,050 And so we start out with a mixture of the A and B in 349 00:21:37,050 --> 00:21:39,470 solution and C and D, reactants 350 00:21:39,470 --> 00:21:41,070 and products together. 351 00:21:41,070 --> 00:21:45,650 And we let the reaction proceed a little bit. 352 00:21:45,650 --> 00:21:53,030 And we look at the change in delta G, going from, say this 353 00:21:53,030 --> 00:21:56,130 point here through that point here. 354 00:21:56,130 --> 00:21:58,570 This will be delta G of epsilon. 355 00:21:58,570 --> 00:22:01,600 We ask, is this positive, negative, or zero. 356 00:22:01,600 --> 00:22:04,100 And if it's zero, that means that we're in equilibrium, 357 00:22:04,100 --> 00:22:07,150 that we're actually sitting down here. 358 00:22:07,150 --> 00:22:09,420 And that gives us the equilibrium constant. 359 00:22:09,420 --> 00:22:13,280 So, just for the sake of completeness, let me just 360 00:22:13,280 --> 00:22:15,730 write down what we would do. 361 00:22:15,730 --> 00:22:20,240 We would react it for a small amount. 362 00:22:20,240 --> 00:22:24,530 And then we'd end up with nu C. 363 00:22:24,530 --> 00:22:28,050 So you would have the chemical potentials of the products 364 00:22:28,050 --> 00:22:33,480 minus the chemical potentials of the reactants, nu C mu C, 365 00:22:33,480 --> 00:22:44,160 plus nu D mu D, minus nu A mu A, minus nu B mu B. And 366 00:22:44,160 --> 00:22:46,680 instead of these chemical potentials, you would write 367 00:22:46,680 --> 00:22:51,130 them in terms of the pure chemical potentials times 368 00:22:51,130 --> 00:22:55,630 their concentrations. 369 00:22:55,630 --> 00:23:01,470 And then you'd end up with epsilon times delta G naught 370 00:23:01,470 --> 00:23:10,360 of the reaction, plus RT log, and then the concentrations. 371 00:23:10,360 --> 00:23:12,450 And then you write them in a different way. 372 00:23:12,450 --> 00:23:15,380 So if it's moles per liter, you usually write that with 373 00:23:15,380 --> 00:23:18,240 these brackets here. 374 00:23:18,240 --> 00:23:21,940 That means concentration of A in moles per liter, I'd say. 375 00:23:21,940 --> 00:23:29,420 So C to the nu C power, D to the nu D power, A to the nu A 376 00:23:29,420 --> 00:23:34,110 power, and B to the nu B power, in these 377 00:23:34,110 --> 00:23:37,370 concentrations. 378 00:23:37,370 --> 00:23:41,420 Where this ratio of logs comes from expanding out the 379 00:23:41,420 --> 00:23:44,380 chemical potential here. 380 00:23:44,380 --> 00:23:46,750 And there's the log term here. 381 00:23:46,750 --> 00:23:48,670 Just like an ideal gas. 382 00:23:48,670 --> 00:23:51,070 Then at equilibrium, this is equal to zero, you're at the 383 00:23:51,070 --> 00:23:52,620 bottom of that curve. 384 00:23:52,620 --> 00:23:57,350 And you set these two things equal to each other. 385 00:23:57,350 --> 00:24:04,880 And you get the chemical, you get your equation 386 00:24:04,880 --> 00:24:06,200 that you know well. 387 00:24:06,200 --> 00:24:11,550 For the equilibrium constant. 388 00:24:11,550 --> 00:24:16,050 And this time it's not K sub p, it's just K. And that's 389 00:24:16,050 --> 00:24:19,700 what you know from doing solution equilibrium. 390 00:24:19,700 --> 00:24:23,390 And it's just like V. 391 00:24:23,390 --> 00:24:28,810 So the thing to remember, which is the slightly more 392 00:24:28,810 --> 00:24:32,520 advanced part, which you'll have to worry about at some 393 00:24:32,520 --> 00:24:37,820 point if you stay in some sort of biochemistry oriented 394 00:24:37,820 --> 00:24:41,060 field, is that you've got to reference your initial 395 00:24:41,060 --> 00:24:43,340 solution properly. 396 00:24:43,340 --> 00:24:48,150 To get to the right equilibrium constant. 397 00:24:48,150 --> 00:24:53,960 OK, any questions? 398 00:24:53,960 --> 00:24:57,260 Alright, then now we can do the temperature dependence of 399 00:24:57,260 --> 00:25:02,900 the equilibrium constant in a general way. 400 00:25:02,900 --> 00:25:05,260 Whether it be a gas or a solution. 401 00:25:05,260 --> 00:25:06,160 It doesn't matter. 402 00:25:06,160 --> 00:25:13,970 It's going to be the same thing. 403 00:25:13,970 --> 00:25:18,080 So the question that we ask now is, suppose that I change 404 00:25:18,080 --> 00:25:21,320 the temperature of my equilibrium, which way is the 405 00:25:21,320 --> 00:25:23,990 equilibrium going to shift? 406 00:25:23,990 --> 00:25:28,580 And you all know the answer already, probably. 407 00:25:28,580 --> 00:25:31,010 But let's derive it out. 408 00:25:31,010 --> 00:25:34,010 So we're going to want to know basically, we want to know 409 00:25:34,010 --> 00:25:35,260 what is dKp/dT. 410 00:25:38,060 --> 00:25:41,850 How does equilibrium constant, or dK/dT, if you're doing 411 00:25:41,850 --> 00:25:45,150 solution, how does the equilibrium change with 412 00:25:45,150 --> 00:25:46,230 temperature? 413 00:25:46,230 --> 00:25:46,880 What's the slope? 414 00:25:46,880 --> 00:25:49,090 Is it positive, negative? 415 00:25:49,090 --> 00:25:51,350 If we have this, we can integrate it out. 416 00:25:51,350 --> 00:25:53,560 We can do an integral over temperature. 417 00:25:53,560 --> 00:25:56,380 And get an actual change. 418 00:25:56,380 --> 00:25:58,540 So that's our goal. 419 00:25:58,540 --> 00:26:00,670 To find how the equilibrium constant changes with 420 00:26:00,670 --> 00:26:03,350 temperature. 421 00:26:03,350 --> 00:26:04,220 What do we know? 422 00:26:04,220 --> 00:26:11,640 Well, we know how Kp depends on temperature, through the 423 00:26:11,640 --> 00:26:14,740 Gibbs free energy of the reaction. 424 00:26:14,740 --> 00:26:16,780 The Gibbs free energy, delta G naught, has a temperature 425 00:26:16,780 --> 00:26:18,060 dependence. 426 00:26:18,060 --> 00:26:19,700 And then there's an RT sitting on the bottom. 427 00:26:19,700 --> 00:26:23,890 There's another temperature dependence here. 428 00:26:23,890 --> 00:26:27,000 Well, dKp/dT is sort of like, we could also ask 429 00:26:27,000 --> 00:26:28,990 what's d log Kp dT. 430 00:26:28,990 --> 00:26:30,500 That might be an easier question. 431 00:26:30,500 --> 00:26:32,810 It's basically the same question. 432 00:26:32,810 --> 00:26:35,010 Especially since we have something which is log K, is 433 00:26:35,010 --> 00:26:35,830 equal to something. 434 00:26:35,830 --> 00:26:38,320 So let's ask this question instead. 435 00:26:38,320 --> 00:26:42,580 Let's ask, what is d log Kp dT? 436 00:26:42,580 --> 00:26:48,380 Alright, so let's differentiate both sides. 437 00:26:48,380 --> 00:26:54,880 d/dT, d/dT here. 438 00:26:54,880 --> 00:26:56,950 Got to use the chain rule now. 439 00:26:56,950 --> 00:26:58,490 Because we've got temperature as part of 440 00:26:58,490 --> 00:27:04,270 delta G Write it out. 441 00:27:04,270 --> 00:27:05,930 So let's take the derivative with respect to the 442 00:27:05,930 --> 00:27:07,180 temperature on the bottom first. 443 00:27:07,180 --> 00:27:10,710 We have delta G naught, which is a function of temperature, 444 00:27:10,710 --> 00:27:14,100 divided by RT squared. 445 00:27:14,100 --> 00:27:17,250 The minus sign here disappears when you take the derivative 446 00:27:17,250 --> 00:27:18,960 on the bottom. 447 00:27:18,960 --> 00:27:30,160 Minus one over RT, d/dT of delta G naught. 448 00:27:30,160 --> 00:27:36,840 So this is a derivative of delta G, where zero 449 00:27:36,840 --> 00:27:38,370 means here one bar. 450 00:27:38,370 --> 00:27:39,210 Fixed at one bar. 451 00:27:39,210 --> 00:27:46,490 So really, d/dT, with delta G naught fixed on one bar, is 452 00:27:46,490 --> 00:27:50,130 the same thing as the partial derivative of delta G with 453 00:27:50,130 --> 00:27:53,605 respect to temperature, keeping p is equal to constant 454 00:27:53,605 --> 00:27:55,650 at one bar. 455 00:27:55,650 --> 00:28:01,620 It's the same thing, just different notation. 456 00:28:01,620 --> 00:28:05,530 And we know what this is. 457 00:28:05,530 --> 00:28:12,540 In terms of other things that we can find in books, like 458 00:28:12,540 --> 00:28:16,960 delta H, or delta S. Because we can go to 459 00:28:16,960 --> 00:28:18,900 the fundamental equations. 460 00:28:18,900 --> 00:28:27,370 To find out how delta G depends on temperature. 461 00:28:27,370 --> 00:28:31,170 And our goal is to get rid of delta G, which clearly has a 462 00:28:31,170 --> 00:28:33,790 nice temperature dependence through the entropy term. 463 00:28:33,790 --> 00:28:36,510 And to replace delta G with delta H, if we can. 464 00:28:36,510 --> 00:28:38,750 Because delta h is going to be much less sensitive to 465 00:28:38,750 --> 00:28:43,390 temperature and it's, delta H is going to be over small 466 00:28:43,390 --> 00:28:44,700 temperature ranges, is going to be independent of 467 00:28:44,700 --> 00:28:46,100 temperature. 468 00:28:46,100 --> 00:28:49,380 And we know the temperature dependence of delta H, because 469 00:28:49,380 --> 00:28:51,020 it's through the heat capacities. 470 00:28:51,020 --> 00:28:55,150 So our goal is to get rid of this delta G here. 471 00:28:55,150 --> 00:28:59,430 And to try to replace it with delta H, if at all possible. 472 00:28:59,430 --> 00:29:04,260 So we go to the fundamental equation for G, dG is equal to 473 00:29:04,260 --> 00:29:10,100 minus S dT plus V dp. 474 00:29:10,100 --> 00:29:17,800 And sitting right here is dG/dT at constant p. 475 00:29:17,800 --> 00:29:19,940 Which is what we have here. 476 00:29:19,940 --> 00:29:25,110 So we get rid of this derivative of G. And replace 477 00:29:25,110 --> 00:29:35,890 it with S. So now, now we have d log Kp dT, and I mentioned 478 00:29:35,890 --> 00:29:38,890 already that I want to get rid of G. Because it has a strong 479 00:29:38,890 --> 00:29:39,680 temperature dependence. 480 00:29:39,680 --> 00:29:42,490 And I want to somehow get H in there, which is not going to 481 00:29:42,490 --> 00:29:44,130 have a strong temperature dependence. 482 00:29:44,130 --> 00:29:47,625 And delta G naught, I can write in terms of H and S, and 483 00:29:47,625 --> 00:29:56,410 T. Delta H naught minus T delta S naught 484 00:29:56,410 --> 00:29:59,630 divided by RT squared. 485 00:29:59,630 --> 00:30:04,800 And then my derivative here, I have minus one over RT. 486 00:30:04,800 --> 00:30:08,890 Partial of G with respect to T. p is equal to one bar. 487 00:30:08,890 --> 00:30:13,080 Well, that's just delta S. p is equal to one bar, well, 488 00:30:13,080 --> 00:30:14,260 that's just delta S naught. 489 00:30:14,260 --> 00:30:20,660 Times delta S naught. 490 00:30:20,660 --> 00:30:23,800 And that's great, because now there's minus T 491 00:30:23,800 --> 00:30:24,920 divided by RT squared. 492 00:30:24,920 --> 00:30:27,080 That's one over RT. 493 00:30:27,080 --> 00:30:31,340 And somewhere I've lost a sign. 494 00:30:31,340 --> 00:30:33,300 And there's my sign that I lost, right there. 495 00:30:33,300 --> 00:30:40,580 This minus sign here. d/dT of delta G naught is minus S. It 496 00:30:40,580 --> 00:30:43,000 actually includes this minus sign right here. 497 00:30:43,000 --> 00:30:45,650 Which is great, because now things work out, because this 498 00:30:45,650 --> 00:30:49,090 becomes a plus sign. 499 00:30:49,090 --> 00:30:54,460 And this and this cancel out. 500 00:30:54,460 --> 00:31:03,380 And this becomes delta H naught over RT squared. 501 00:31:03,380 --> 00:31:04,300 Great, so we have what we want. 502 00:31:04,300 --> 00:31:07,320 We have how the equilibrium constant depends on 503 00:31:07,320 --> 00:31:10,050 temperature in a way which is very clear. 504 00:31:10,050 --> 00:31:13,110 Where the top part is only very weakly dependent on 505 00:31:13,110 --> 00:31:14,740 temperature, usually. 506 00:31:14,740 --> 00:31:23,160 And this is called the van 't Hoff equation. 507 00:31:23,160 --> 00:31:26,900 And this will tell us what happens to equilibrium when we 508 00:31:26,900 --> 00:31:30,340 change the temperature. 509 00:31:30,340 --> 00:31:34,710 So if you want to do a finite temperature change, now what 510 00:31:34,710 --> 00:31:52,700 you need to do is, you need to integrate. 511 00:31:52,700 --> 00:31:59,320 You integrate both sides here. 512 00:31:59,320 --> 00:32:02,520 From some T1 to T2. 513 00:32:02,520 --> 00:32:09,880 From T1 to T2, and that tells you, then, that the log of the 514 00:32:09,880 --> 00:32:13,480 equilibrium constant at the new temperature is equal to 515 00:32:13,480 --> 00:32:15,650 the log of the equilibrium constant of the old 516 00:32:15,650 --> 00:32:21,310 temperature, T1, plus the integral from T1 to T2 of 517 00:32:21,310 --> 00:32:28,180 delta H over RT delta H naught, over RT squared. 518 00:32:28,180 --> 00:32:31,690 And this could be slightly temperature dependent. dT. 519 00:32:31,690 --> 00:32:34,810 And this is the integrated van 't Hoff equation. 520 00:32:34,810 --> 00:32:39,480 And if you're going to be designing a chemical plant 521 00:32:39,480 --> 00:32:43,810 where you have high temperatures and high 522 00:32:43,810 --> 00:32:48,070 pressures around, you better use that. 523 00:32:48,070 --> 00:32:50,070 Because there is some temperature dependence in 524 00:32:50,070 --> 00:32:53,150 delta H, through the heat capacities of the reactants 525 00:32:53,150 --> 00:32:54,460 and the products. 526 00:32:54,460 --> 00:32:57,880 And that could make the difference between your plant 527 00:32:57,880 --> 00:33:00,750 running nice and smoothly or your plant exploding. 528 00:33:00,750 --> 00:33:04,210 And you don't want to have exploding plants around. 529 00:33:04,210 --> 00:33:10,160 So for heavy-duty uses of this equation, you've got to do the 530 00:33:10,160 --> 00:33:11,800 integral properly. 531 00:33:11,800 --> 00:33:14,830 But for most normal applications, like if you're 532 00:33:14,830 --> 00:33:17,030 doing biology, where the temperature changes by a few 533 00:33:17,030 --> 00:33:19,730 degrees, like today I have a little bit of a cold. 534 00:33:19,730 --> 00:33:22,500 I don't have a fever, but I could have a fever. 535 00:33:22,500 --> 00:33:25,050 So my biochemistry would change if I had a fever. 536 00:33:25,050 --> 00:33:27,420 The equilibrium constant of all my reactions would change 537 00:33:27,420 --> 00:33:28,820 a little bit. 538 00:33:28,820 --> 00:33:31,350 It's a small change in temperature. 539 00:33:31,350 --> 00:33:34,640 I'm not going to explode. 540 00:33:34,640 --> 00:33:37,330 And so you can then take the approximation. 541 00:33:37,330 --> 00:33:47,140 In that case, the delta H naught, is independent of T. 542 00:33:47,140 --> 00:33:53,960 And this is fine over small temperature ranges. 543 00:33:53,960 --> 00:33:55,940 And that's the one that you're most used to. 544 00:33:55,940 --> 00:33:57,770 Is this approximation here, this 545 00:33:57,770 --> 00:34:00,020 approximate van 't Hoff equation. 546 00:34:00,020 --> 00:34:02,860 Which is really fine for most cases that you're going to be 547 00:34:02,860 --> 00:34:05,870 dealing with. 548 00:34:05,870 --> 00:34:09,190 So then, if that's the case then you can take your delta 549 00:34:09,190 --> 00:34:12,830 H. Ignore the temperature dependence and take it outside 550 00:34:12,830 --> 00:34:14,210 of the integral. 551 00:34:14,210 --> 00:34:17,370 And now you can do the integral fine. 552 00:34:17,370 --> 00:34:21,190 And then you have an analytic expression for the change in 553 00:34:21,190 --> 00:34:23,600 the equilibrium constant with temperature. 554 00:34:23,600 --> 00:34:29,170 Log Kp at a new temperature, T2, is log Kp temperature T1. 555 00:34:29,170 --> 00:34:31,610 And I'm carrying this little p around everywhere. 556 00:34:31,610 --> 00:34:33,410 But really, it doesn't have to be there. 557 00:34:33,410 --> 00:34:35,180 This could be solution. 558 00:34:35,180 --> 00:34:38,450 I shouldn't really have written this for the specific 559 00:34:38,450 --> 00:34:40,240 case of partial pressures. 560 00:34:40,240 --> 00:34:43,090 But it's equally valid for solutions. 561 00:34:43,090 --> 00:34:46,970 Then we have delta H naught over R. And then we have the 562 00:34:46,970 --> 00:34:51,430 integral from T1 to T2, over one of RT squared. 563 00:34:51,430 --> 00:34:53,520 And if you do that the right way, you get T2 564 00:34:53,520 --> 00:34:57,610 minus T1 over T1 T2. 565 00:34:57,610 --> 00:35:00,020 And that gives you the 566 00:35:00,020 --> 00:35:04,280 approximate van 't Hoff equation. 567 00:35:04,280 --> 00:35:06,480 Which is fine. 568 00:35:06,480 --> 00:35:09,080 And you'll know that it's fine in problem sets or exam, 569 00:35:09,080 --> 00:35:11,450 because we'll say assume that delta H is temperature - yes. 570 00:35:11,450 --> 00:35:18,940 STUDENT: You said that the [INAUDIBLE] 571 00:35:18,940 --> 00:35:20,740 PROFESSOR: For K, if K is solution K. 572 00:35:20,740 --> 00:35:23,260 STUDENT: Right. 573 00:35:23,260 --> 00:35:23,770 PROFESSOR: Yeah. 574 00:35:23,770 --> 00:35:26,930 STUDENT: So then, can you also use Kx? 575 00:35:26,930 --> 00:35:28,450 PROFESSOR: Can you use Kx? 576 00:35:28,450 --> 00:35:33,140 Well, as long as you keep the pressure, the total pressure, 577 00:35:33,140 --> 00:35:38,720 constant, then you should be able to use Kx. 578 00:35:38,720 --> 00:35:43,920 Let me think about this. 579 00:35:43,920 --> 00:35:47,100 Yeah, here you would have p, you have a log c so, you can 580 00:35:47,100 --> 00:35:47,840 use Kx, fine. 581 00:35:47,840 --> 00:35:50,560 Because then you would have log p to the minus delta nu 582 00:35:50,560 --> 00:35:53,890 times Kx, log p to the delta nu minus Kx. 583 00:35:53,890 --> 00:35:56,770 And the log of the multiplication is 584 00:35:56,770 --> 00:35:58,380 the sum of the logs. 585 00:35:58,380 --> 00:35:59,440 And the logs will just fall out. 586 00:35:59,440 --> 00:36:01,460 So it could be any K that you want. 587 00:36:01,460 --> 00:36:04,080 Doesn't matter. 588 00:36:04,080 --> 00:36:06,190 As long as you keep the pressure constant. 589 00:36:06,190 --> 00:36:10,630 If you change the pressure, then you're in trouble. 590 00:36:10,630 --> 00:36:14,660 So now we can see what happens when you do change the 591 00:36:14,660 --> 00:36:18,280 temperature. 592 00:36:18,280 --> 00:36:25,420 If I have some equilibrium, and it's all going to depend 593 00:36:25,420 --> 00:36:28,020 on the sign of delta H. Whether the reaction is 594 00:36:28,020 --> 00:36:33,200 exothermic or endothermic. 595 00:36:33,200 --> 00:36:36,340 And it's the same thing as Le Chatelier's for pressure, or 596 00:36:36,340 --> 00:36:37,090 Lenz's law. 597 00:36:37,090 --> 00:36:40,300 The system doesn't want to have change happening. 598 00:36:40,300 --> 00:36:43,430 So if you have something that's, delta H is less than 599 00:36:43,430 --> 00:36:46,810 zero, it's exothermic. 600 00:36:46,810 --> 00:36:51,750 Exothermic, that means that it's putting out heat. it 601 00:36:51,750 --> 00:36:55,300 wants to heat up its environment. 602 00:36:55,300 --> 00:36:59,990 And if I take temperature and I raise the temperature, the 603 00:36:59,990 --> 00:37:02,130 system's not going to like that very much. 604 00:37:02,130 --> 00:37:06,540 It doesn't want to get hotter, and going from reactants to 605 00:37:06,540 --> 00:37:08,550 products makes things hotter. 606 00:37:08,550 --> 00:37:09,520 And if you go from products to 607 00:37:09,520 --> 00:37:10,980 reactants, that's the opposite. 608 00:37:10,980 --> 00:37:13,840 Go from reactants to products, that becomes endothermic. 609 00:37:13,840 --> 00:37:15,420 It sucks in heat. 610 00:37:15,420 --> 00:37:16,610 You raise the temperature. 611 00:37:16,610 --> 00:37:19,210 The system said no, no, no, I'm happy where I am at my 612 00:37:19,210 --> 00:37:20,450 original temperature. 613 00:37:20,450 --> 00:37:22,960 I'm going to start sucking in heat, to try to get the 614 00:37:22,960 --> 00:37:24,810 temperature down. 615 00:37:24,810 --> 00:37:26,630 And it's going to try to make more product. 616 00:37:26,630 --> 00:37:29,250 More reactants. 617 00:37:29,250 --> 00:37:40,170 So, equilibrium K is going to go down. and the reaction goes 618 00:37:40,170 --> 00:37:43,810 towards the reactants. 619 00:37:43,810 --> 00:37:46,090 And the opposite if you have something that's endothermic 620 00:37:46,090 --> 00:37:49,670 to begin with. 621 00:37:49,670 --> 00:37:51,230 OK, delta H is positive here. 622 00:37:51,230 --> 00:37:54,650 Delta H naught is positive. 623 00:37:54,650 --> 00:37:57,850 You raise the temperature, delta H naught is positive, 624 00:37:57,850 --> 00:37:58,590 T2's bigger. 625 00:37:58,590 --> 00:38:00,620 This is a positive number. 626 00:38:00,620 --> 00:38:06,910 K becomes larger at higher temperature. 627 00:38:06,910 --> 00:38:08,850 K goes up. 628 00:38:08,850 --> 00:38:10,900 The reaction goes to products. 629 00:38:10,900 --> 00:38:15,210 So if you think of it in terms of the system, the system is 630 00:38:15,210 --> 00:38:16,960 at some temperature. 631 00:38:16,960 --> 00:38:18,820 You raise the temperature. 632 00:38:18,820 --> 00:38:20,500 System doesn't like it. 633 00:38:20,500 --> 00:38:21,910 Says, I want to go back to my original 634 00:38:21,910 --> 00:38:24,520 temperature, what can I do. 635 00:38:24,520 --> 00:38:27,690 I can try to suck in heat that you're trying to put in the 636 00:38:27,690 --> 00:38:28,970 environment. 637 00:38:28,970 --> 00:38:31,630 That's great because if I make more products, that's 638 00:38:31,630 --> 00:38:32,730 endothermic. 639 00:38:32,730 --> 00:38:34,810 And I'm just going to make more products until I try to 640 00:38:34,810 --> 00:38:35,740 lower my temperature. 641 00:38:35,740 --> 00:38:41,740 So I move the equilibrium to the products. 642 00:38:41,740 --> 00:38:56,130 OK, Le Chatelier for temperature. 643 00:38:56,130 --> 00:38:59,910 Any questions? 644 00:38:59,910 --> 00:39:08,300 On equilibrium. 645 00:39:08,300 --> 00:39:09,970 OK, let's do a quick example. 646 00:39:09,970 --> 00:39:13,410 Because this was the example that we started out with, 647 00:39:13,410 --> 00:39:14,760 talking about, the Haber process. 648 00:39:14,760 --> 00:39:21,570 This important industrial reaction that started the 649 00:39:21,570 --> 00:39:23,670 chemical industry, essentially. 650 00:39:23,670 --> 00:39:27,860 That uses up 1%, or close to 1%, of the world's energy. 651 00:39:27,860 --> 00:39:29,740 If you think about it, that's an amazing number. 652 00:39:29,740 --> 00:39:31,960 1% of all energy produced in the 653 00:39:31,960 --> 00:39:35,110 world goes to one reaction. 654 00:39:35,110 --> 00:39:37,050 One industrial reaction. 655 00:39:37,050 --> 00:39:45,430 Just shows how important it is. 656 00:39:45,430 --> 00:39:47,210 OK, why does it take so much energy? 657 00:39:47,210 --> 00:39:48,260 We're going to find out. 658 00:39:48,260 --> 00:39:55,310 We're going to find out why it takes so much energy to run 659 00:39:55,310 --> 00:39:57,500 this here reaction. 660 00:39:57,500 --> 00:40:00,100 Alright, let's look at this Haber process. 661 00:40:00,100 --> 00:40:04,990 Take some nitrogen gas. 662 00:40:04,990 --> 00:40:11,270 Plus some hydrogen gas. 663 00:40:11,270 --> 00:40:14,380 And this is usually done over catalysts, like an iron oxide 664 00:40:14,380 --> 00:40:15,850 catalyst or something. 665 00:40:15,850 --> 00:40:17,090 To try to speed it up. 666 00:40:17,090 --> 00:40:18,330 It doesn't change the thermodynamics. 667 00:40:18,330 --> 00:40:22,070 As you know, and you'll hear again in this class, catalysts 668 00:40:22,070 --> 00:40:23,140 just affect the kinetics. 669 00:40:23,140 --> 00:40:25,330 They don't change the thermodynamics. 670 00:40:25,330 --> 00:40:27,950 So this is usually done over some catalyst to try to 671 00:40:27,950 --> 00:40:29,220 speed things up. 672 00:40:29,220 --> 00:40:30,450 To make ammonia. 673 00:40:30,450 --> 00:40:35,200 And ammonia becomes the feedstock for fertilizers, for 674 00:40:35,200 --> 00:40:37,310 almost anything that contains an amine in it, or 675 00:40:37,310 --> 00:40:38,680 a nitrogen in it. 676 00:40:38,680 --> 00:40:42,090 If you're going to make proteins or whatever. 677 00:40:42,090 --> 00:40:45,740 You've got to have ammonia somewhere in the process. 678 00:40:45,740 --> 00:40:48,470 OK, delta H naught of the reaction, we're given all 679 00:40:48,470 --> 00:40:50,210 these numbers. 680 00:40:50,210 --> 00:40:54,630 At 298 degrees Kelvin. 681 00:40:54,630 --> 00:40:57,080 And they're in your notes, so I'm not going to go through 682 00:40:57,080 --> 00:40:58,390 them in detail. 683 00:40:58,390 --> 00:40:59,890 Delta G naught for the reaction, 684 00:40:59,890 --> 00:41:01,940 we're given that number. 685 00:41:01,940 --> 00:41:06,810 At 298 degrees Kelvin, that's minus 16, roughly minus 16 686 00:41:06,810 --> 00:41:12,340 kilojoules per mole. 687 00:41:12,340 --> 00:41:16,500 And we want to know, what is the equilibrium constant. 688 00:41:16,500 --> 00:41:17,430 Room temperature. 689 00:41:17,430 --> 00:41:18,880 So you know how to calculate that. 690 00:41:18,880 --> 00:41:22,760 Minus RT log Kp, log K is equal to minus RT. 691 00:41:25,450 --> 00:41:28,110 Minus delta G naught over RT. 692 00:41:28,110 --> 00:41:30,340 So you put that in there. 693 00:41:30,340 --> 00:41:33,530 You get Kp is equal to 860. 694 00:41:33,530 --> 00:41:35,170 A number, no units. 695 00:41:35,170 --> 00:41:36,820 It's a big number. 696 00:41:36,820 --> 00:41:38,800 It's a big number, you've got the products 697 00:41:38,800 --> 00:41:40,500 divided by the reactants. 698 00:41:40,500 --> 00:41:42,450 It means that the products are favored. 699 00:41:42,450 --> 00:41:45,160 This is great. 700 00:41:45,160 --> 00:41:48,760 What a wonderful reaction. 701 00:41:48,760 --> 00:41:51,340 Shouldn't take energy to for us to do that, right? 702 00:41:51,340 --> 00:41:53,090 It's a room temperature reaction. 703 00:41:53,090 --> 00:41:55,560 Thermodynamics is great. 704 00:41:55,560 --> 00:41:59,570 But even over a catalyst, this is a really, really, really 705 00:41:59,570 --> 00:42:01,230 slow reaction. 706 00:42:01,230 --> 00:42:04,590 We'd still be waiting here for Mr. Haber to produce his first 707 00:42:04,590 --> 00:42:08,190 mole of amine, if you were doing it, or ammonia if we 708 00:42:08,190 --> 00:42:10,040 were doing it at room temperature. 709 00:42:10,040 --> 00:42:13,770 It's just so slow. 710 00:42:13,770 --> 00:42:16,380 Thus, not at all practical. 711 00:42:16,380 --> 00:42:18,620 We're not going to run the world on room temperature 712 00:42:18,620 --> 00:42:23,840 Haber process. 713 00:42:23,840 --> 00:42:27,710 But it turns out, if you raise the temperature, kinetics is 714 00:42:27,710 --> 00:42:29,240 wonderful in terms of the temperature dependence. 715 00:42:29,240 --> 00:42:31,180 It's exponential. 716 00:42:31,180 --> 00:42:32,620 Arrhenius rate law. 717 00:42:32,620 --> 00:42:34,970 Great thing, you raise the temperature by a little bit. 718 00:42:34,970 --> 00:42:37,190 Rates speed up, things go faster. 719 00:42:37,190 --> 00:42:39,750 So if you were to raise the temperature from 298 degrees 720 00:42:39,750 --> 00:42:49,050 Kelvin to 800 degrees Kelvin, the rate speeds up. 721 00:42:49,050 --> 00:42:50,540 You're going to need some energy. 722 00:42:50,540 --> 00:42:53,620 As input here, to feed that. 723 00:42:53,620 --> 00:42:57,510 Hence the 1% energy use. 724 00:42:57,510 --> 00:42:58,750 Rate speeds up, that's great. 725 00:42:58,750 --> 00:43:00,030 Things happen faster. 726 00:43:00,030 --> 00:43:00,930 It becomes practical. 727 00:43:00,930 --> 00:43:04,600 But, what happens if you raise the temperature? 728 00:43:04,600 --> 00:43:04,910 Let's see. 729 00:43:04,910 --> 00:43:09,380 This is an endothermic, or exothermic, negative sign. 730 00:43:09,380 --> 00:43:10,740 And negative sign's exothermic. 731 00:43:10,740 --> 00:43:12,780 I raise the temperature, K goes down. 732 00:43:12,780 --> 00:43:14,590 I know how to calculate it here. 733 00:43:14,590 --> 00:43:17,090 And if I want to be super careful, because it's a fairly 734 00:43:17,090 --> 00:43:20,420 large temperature range, I can even use the exact form of the 735 00:43:20,420 --> 00:43:21,280 van 't Hoff equation. 736 00:43:21,280 --> 00:43:27,110 And what I find, if I do that, and putting the heat 737 00:43:27,110 --> 00:43:30,190 capacities for all these gases, I find 738 00:43:30,190 --> 00:43:32,150 that Kp does go down. 739 00:43:32,150 --> 00:43:34,310 In fact, it goes down quite a bit. 740 00:43:34,310 --> 00:43:39,050 It becomes 0.0007. 741 00:43:39,050 --> 00:43:40,580 Two zero's. 742 00:43:40,580 --> 00:43:43,350 Still really small. 743 00:43:43,350 --> 00:43:45,560 That's not practical. 744 00:43:45,560 --> 00:43:48,510 Not practical at all. 745 00:43:48,510 --> 00:43:49,440 No good. 746 00:43:49,440 --> 00:43:53,810 We can't run an industrial plant with this kind of yield. 747 00:43:53,810 --> 00:43:56,290 There's just no way it's going to work. 748 00:43:56,290 --> 00:43:59,190 So, you're a chemical engineer. 749 00:43:59,190 --> 00:44:01,350 Or a chemist, like Haber and Bosch were. 750 00:44:01,350 --> 00:44:05,510 And you're trying, you know by Le Chatelier, you know that it 751 00:44:05,510 --> 00:44:07,310 went in the wrong direction for you here. 752 00:44:07,310 --> 00:44:10,070 And then you look at your reaction and you say, how many 753 00:44:10,070 --> 00:44:12,180 moles of reactants do I have? 754 00:44:12,180 --> 00:44:15,860 3/2 plus 1/2, that's two moles of reactants. 755 00:44:15,860 --> 00:44:18,040 And I've got one mole of product. 756 00:44:18,040 --> 00:44:20,600 Two moles reactants, one mole of product. 757 00:44:20,600 --> 00:44:21,720 Two moles reactant... 758 00:44:21,720 --> 00:44:25,060 What happens if I change the pressure? 759 00:44:25,060 --> 00:44:27,040 If I change the pressure, if I increase the pressure, the 760 00:44:27,040 --> 00:44:29,480 system is going to say, no, I don't want 761 00:44:29,480 --> 00:44:31,050 the pressure increased. 762 00:44:31,050 --> 00:44:33,520 It's going to go to where there's less moles. 763 00:44:33,520 --> 00:44:36,070 And the less moles in the product area. 764 00:44:36,070 --> 00:44:37,420 It's going to go to my product. 765 00:44:37,420 --> 00:44:38,020 That's great. 766 00:44:38,020 --> 00:44:39,710 I've got to increase the pressure. 767 00:44:39,710 --> 00:44:40,220 Wonderful. 768 00:44:40,220 --> 00:44:41,710 Let's start increasing the pressure. 769 00:44:41,710 --> 00:44:43,710 Again, we need some energy to do that. 770 00:44:43,710 --> 00:44:46,380 We're going to go from one bar to some higher pressure. 771 00:44:46,380 --> 00:44:48,020 It's going to make our lives more complicated. 772 00:44:48,020 --> 00:44:49,390 The plant might explode now. 773 00:44:49,390 --> 00:44:50,890 If the pressure's too high. 774 00:44:50,890 --> 00:44:53,230 All sorts of problems going to come into play. 775 00:44:53,230 --> 00:44:56,660 But, let's do it. 776 00:44:56,660 --> 00:44:59,790 Let's increase the pressure. 777 00:44:59,790 --> 00:45:10,280 So, you increase the pressure from one bar to 100 bar. 778 00:45:10,280 --> 00:45:18,160 And you calculate Kx. 779 00:45:18,160 --> 00:45:20,420 Which is really what you want. 780 00:45:20,420 --> 00:45:24,730 So Kx, in this case here, is equal to p times Kp. 781 00:45:24,730 --> 00:45:25,770 Kp doesn't change. 782 00:45:25,770 --> 00:45:27,590 Kp doesn't care what the total pressure is. 783 00:45:27,590 --> 00:45:29,190 It's Kx that cares. 784 00:45:29,190 --> 00:45:32,800 At one bar, Kx is equal Kp. 785 00:45:32,800 --> 00:45:35,050 Kx is p to the minus delta nu. 786 00:45:35,050 --> 00:45:40,130 Number of moles of products minus the number of reactants. 787 00:45:40,130 --> 00:45:47,950 If I go from one bar to 100 bars, Kx goes from 0.007 to 788 00:45:47,950 --> 00:45:53,320 100 times 0.007, which is equal to 0.7. 789 00:45:53,320 --> 00:45:55,970 That's a lot better. 790 00:45:55,970 --> 00:45:58,340 Kx is the mole fraction or the, of 791 00:45:58,340 --> 00:46:00,860 products divided by reactants. 792 00:46:00,860 --> 00:46:09,220 And if I go to p is equal to 300 bars, then Kx goes to 2.1. 793 00:46:09,220 --> 00:46:11,960 three times 0.7. 794 00:46:11,960 --> 00:46:12,870 This is great. 795 00:46:12,870 --> 00:46:14,630 Now I'm really starting to make good products. 796 00:46:14,630 --> 00:46:16,670 But I've got to go to 300 bar. 797 00:46:16,670 --> 00:46:22,300 I've got to go to 300 bar, and 800 degrees Kelvin. 798 00:46:22,300 --> 00:46:25,500 That is incredibly energy-intensive. 799 00:46:25,500 --> 00:46:27,330 But it works. 800 00:46:27,330 --> 00:46:29,170 That's why Haber and Bosch made this work. 801 00:46:29,170 --> 00:46:32,500 And why Germany stayed in the war longer than after 1916. 802 00:46:32,500 --> 00:46:35,180 The first world war. 803 00:46:35,180 --> 00:46:39,840 Ended in 1918. 804 00:46:39,840 --> 00:46:41,240 Nobel Prizes. 805 00:46:41,240 --> 00:46:44,910 Merck, Bayer, all these german companies. 806 00:46:44,910 --> 00:46:48,770 Because they figured how to do this at high pressure and high 807 00:46:48,770 --> 00:46:49,510 temperature. 808 00:46:49,510 --> 00:46:54,450 Without blowing everything up. 809 00:46:54,450 --> 00:46:55,910 OK. 810 00:46:55,910 --> 00:47:01,710 Any questions? 811 00:47:01,710 --> 00:47:02,000 Alright. 812 00:47:02,000 --> 00:47:07,560 The last topic is, so far we've seen equilibria where 813 00:47:07,560 --> 00:47:09,770 you had things that were well mixed. 814 00:47:09,770 --> 00:47:11,470 equilibria of ideal gases. 815 00:47:11,470 --> 00:47:14,730 Or in solutions, where your solutes, your solute molecules 816 00:47:14,730 --> 00:47:17,440 are mixing around. 817 00:47:17,440 --> 00:47:20,590 And the entropy of mixing was really super important. 818 00:47:20,590 --> 00:47:23,260 Our curve, our going down for delta G, was all because of 819 00:47:23,260 --> 00:47:24,440 the entropy of mixing. 820 00:47:24,440 --> 00:47:28,610 Now, suppose that I have a heterogeneous mixture. 821 00:47:28,610 --> 00:47:32,230 I've got some solids or some pure liquids that are refusing 822 00:47:32,230 --> 00:47:35,930 to share their environment. 823 00:47:35,930 --> 00:47:38,680 And staying as pure materials. 824 00:47:38,680 --> 00:47:43,870 So, for instance, if I have a beaker with some solid 825 00:47:43,870 --> 00:47:45,770 reactant on the bottom here. 826 00:47:45,770 --> 00:47:55,080 And the products are in solution. 827 00:47:55,080 --> 00:47:57,440 How do I deal with that equilibrium? 828 00:47:57,440 --> 00:48:00,030 Well, you know the answer, but let's just do it out again. 829 00:48:00,030 --> 00:48:04,470 So we're going to have nu A moles of A, of solid. 830 00:48:04,470 --> 00:48:06,270 Not mixed in the solution. 831 00:48:06,270 --> 00:48:08,400 Let's say we have multiple phases here. 832 00:48:08,400 --> 00:48:10,980 Nu B moles of B, which is a gas. 833 00:48:10,980 --> 00:48:13,760 Instead of a solution, let's do a gas phase reaction. 834 00:48:13,760 --> 00:48:18,540 Nu C moles of C, which is a pure liquid. 835 00:48:18,540 --> 00:48:22,020 And nu D moles of D, which is a gas. 836 00:48:22,020 --> 00:48:23,280 So these two gases can mix. 837 00:48:23,280 --> 00:48:26,580 But the pure solid and the pure liquid can't mix. 838 00:48:26,580 --> 00:48:28,650 So let's think again, where does the equilibrium 839 00:48:28,650 --> 00:48:29,460 constant come from? 840 00:48:29,460 --> 00:48:34,310 It comes from looking at this delta G of the mixture and 841 00:48:34,310 --> 00:48:36,210 letting it react a little bit more. 842 00:48:36,210 --> 00:48:39,905 And taking out these chemical potentials for the species and 843 00:48:39,905 --> 00:48:40,750 the mixture. 844 00:48:40,750 --> 00:48:46,460 Expanding it out in terms of log p or log concentration. 845 00:48:46,460 --> 00:48:48,360 So we need to have this delta G in. 846 00:48:48,360 --> 00:48:51,100 Let's take epsilon equal to one, to make our 847 00:48:51,100 --> 00:48:51,800 life simpler here. 848 00:48:51,800 --> 00:48:57,740 So now we have nu C mu C of the pure. 849 00:48:57,740 --> 00:48:59,350 The pure solid. 850 00:48:59,350 --> 00:49:04,740 Plus nu D mu C of the gas. 851 00:49:04,740 --> 00:49:07,150 Which is in the mixture. 852 00:49:07,150 --> 00:49:14,220 Minus nu A mu A of the pure liquid, minus nu 853 00:49:14,220 --> 00:49:17,860 B mu B of the gas. 854 00:49:17,860 --> 00:49:20,200 Which is in the mixture. 855 00:49:20,200 --> 00:49:24,190 That's what this delta G is, when we allow the reaction to 856 00:49:24,190 --> 00:49:27,380 proceed for a little bit more. 857 00:49:27,380 --> 00:49:29,300 We add a little bit of chemical 858 00:49:29,300 --> 00:49:30,890 potentials from the products. 859 00:49:30,890 --> 00:49:32,210 Subtract a little bit of chemical 860 00:49:32,210 --> 00:49:34,370 potential from the reactants. 861 00:49:34,370 --> 00:49:37,330 And then we expand it out in terms of the standard chemical 862 00:49:37,330 --> 00:49:39,950 potentials for everything being pure. 863 00:49:39,950 --> 00:49:41,720 Entropy of mixing comes in here. 864 00:49:41,720 --> 00:49:42,610 Comes in here. 865 00:49:42,610 --> 00:49:46,300 Delta G of mixing comes in here. 866 00:49:46,300 --> 00:49:54,860 And we end up with something that looks like nu C mu C 867 00:49:54,860 --> 00:50:02,760 naught, plus nu D mu D naught, minus nu A mu A naught, minus 868 00:50:02,760 --> 00:50:06,670 nu B mu B naught. 869 00:50:06,670 --> 00:50:11,730 Plus RT log, and the only place where we have these log 870 00:50:11,730 --> 00:50:14,590 p's, or log concentration coming in, is for those 871 00:50:14,590 --> 00:50:17,640 species that were not pure. 872 00:50:17,640 --> 00:50:19,930 And those are only these two guys here. 873 00:50:19,930 --> 00:50:22,340 The ones that are in the gas phase. 874 00:50:22,340 --> 00:50:26,820 D and B. So we end up with partial pressure of D to the 875 00:50:26,820 --> 00:50:27,770 nu D power. 876 00:50:27,770 --> 00:50:32,500 Partial pressure of B, to the nu B power. 877 00:50:32,500 --> 00:50:34,560 The other two species don't come in there. 878 00:50:34,560 --> 00:50:36,630 Because they started out as pure. 879 00:50:36,630 --> 00:50:39,360 There's no mixing going on. 880 00:50:39,360 --> 00:50:44,060 And there's no expansion of the log for them. 881 00:50:44,060 --> 00:50:49,985 And so now, when we look at the Q for the reaction, the 882 00:50:49,985 --> 00:50:52,010 reaction quotient, it doesn't contain 883 00:50:52,010 --> 00:50:53,050 any of the pure species. 884 00:50:53,050 --> 00:50:56,950 It only contains those species that are allowed to mix. 885 00:50:56,950 --> 00:51:00,440 Those that are in the gas phase or in solution. 886 00:51:00,440 --> 00:51:08,350 And so K, then, for this reaction only takes in those 887 00:51:08,350 --> 00:51:14,780 products like D. Or reactants like B, which 888 00:51:14,780 --> 00:51:16,380 are in the gas phase. 889 00:51:16,380 --> 00:51:18,170 The pure solids or pure liquids don't come in. 890 00:51:18,170 --> 00:51:19,640 They come in for delta G naught. 891 00:51:19,640 --> 00:51:23,090 There's delta G naught sitting right here. 892 00:51:23,090 --> 00:51:26,850 Delta G naught for the reaction is 893 00:51:26,850 --> 00:51:28,650 sitting right there. 894 00:51:28,650 --> 00:51:32,365 So when you write your log K is equal to minus delta G 895 00:51:32,365 --> 00:51:36,940 naught over RT, the delta G naught has everything in it. 896 00:51:36,940 --> 00:51:40,710 The pure stuff, the solution stuff, the gas phase stuff. 897 00:51:40,710 --> 00:51:44,570 But the K only has the gas phase and solution stuff. 898 00:51:44,570 --> 00:51:49,560 Alright, any questions? 899 00:51:49,560 --> 00:51:49,760 Good. 900 00:51:49,760 --> 00:51:51,900 Next time we'll do an example. 901 00:51:51,900 --> 00:51:54,130 And then we'll go on phase transitions.