1 00:00:00,000 --> 00:00:01,080 2 00:00:01,080 --> 00:00:03,600 All of the reactions we've looked at so far have been of 3 00:00:03,600 --> 00:00:10,890 the form lowercase a moles of the molecule uppercase A, plus 4 00:00:10,890 --> 00:00:15,190 lowercase b moles of a molecule uppercase B. 5 00:00:15,189 --> 00:00:18,870 They react to form the product or the products. 6 00:00:18,870 --> 00:00:20,380 Let's just say they have a couple of products. 7 00:00:20,379 --> 00:00:22,140 I could have had as many molecules here as I wanted. 8 00:00:22,140 --> 00:00:28,070 Let's say c moles of the molecule C plus d moles of the 9 00:00:28,070 --> 00:00:30,480 molecule capital D. 10 00:00:30,480 --> 00:00:33,070 And the idea here is that they went in one direction. 11 00:00:33,070 --> 00:00:36,090 And if we did a little energy diagram, just going off of the 12 00:00:36,090 --> 00:00:43,900 kinematics video we just did, if that's the reaction, or how 13 00:00:43,899 --> 00:00:47,259 the reaction progresses, you could imagine that here you 14 00:00:47,259 --> 00:00:49,100 have it at a higher energy state. 15 00:00:49,100 --> 00:00:54,640 You have lowercase a moles of capital A molecule, plus 16 00:00:54,640 --> 00:00:57,500 lowercase b moles of capital B molecule, and you have some 17 00:00:57,500 --> 00:00:58,780 activation energy. 18 00:00:58,780 --> 00:01:01,450 And then you get to a more stable state or a lower energy 19 00:01:01,450 --> 00:01:05,650 level here, where it's lowercase c moles of C 20 00:01:05,650 --> 00:01:08,300 molecule plus lowercase d moles of the D moles, and of 21 00:01:08,299 --> 00:01:09,649 course, you had some activation energy. 22 00:01:09,650 --> 00:01:10,980 It only goes in this direction. 23 00:01:10,980 --> 00:01:13,549 Once you get here, it's very hard to go back. 24 00:01:13,549 --> 00:01:15,359 So that if you came back and looked at this-- if you get 25 00:01:15,359 --> 00:01:18,625 enough of A and B-- you'll just be sitting with molecules 26 00:01:18,625 --> 00:01:19,689 of C and D. 27 00:01:19,689 --> 00:01:20,870 It'll only go in this direction. 28 00:01:20,870 --> 00:01:23,570 But that's not how it happens in reality. 29 00:01:23,569 --> 00:01:26,179 In reality-- well, it sometimes happens like this in 30 00:01:26,180 --> 00:01:28,670 reality where the reaction can only go in one direction. 31 00:01:28,670 --> 00:01:31,180 But in a lot of cases, the reaction can actually go in 32 00:01:31,180 --> 00:01:32,840 both directions. 33 00:01:32,840 --> 00:01:35,439 So we could write, instead of this one-way reaction, we 34 00:01:35,439 --> 00:01:38,810 could write a two-way reaction like this. 35 00:01:38,810 --> 00:01:44,930 And not to confuse you too much, these are the number of 36 00:01:44,930 --> 00:01:49,290 moles or the ratios of the molecules I'm adding up, and 37 00:01:49,290 --> 00:01:51,080 they become relevant in a second. 38 00:01:51,079 --> 00:01:54,370 So let's say I have lowercase a moles of this molecule plus 39 00:01:54,370 --> 00:01:58,480 lowercase b moles of this molecule, and then they react 40 00:01:58,480 --> 00:02:02,680 to form lowercase c moles of this molecule plus lowercase d 41 00:02:02,680 --> 00:02:04,680 moles of that molecule. 42 00:02:04,680 --> 00:02:07,020 Sometimes the reaction can go in both directions. 43 00:02:07,019 --> 00:02:11,590 And to do that, to just show an equilibrium reaction, you 44 00:02:11,590 --> 00:02:13,860 do these arrows that go in both directions. 45 00:02:13,860 --> 00:02:16,610 That means that, hey, some of this is going to start forming 46 00:02:16,610 --> 00:02:17,520 into some of this. 47 00:02:17,520 --> 00:02:20,240 But at the same time, some of this might start forming into 48 00:02:20,240 --> 00:02:21,080 some of this. 49 00:02:21,080 --> 00:02:23,680 And at some point, I'm going to be reaching an equilibrium. 50 00:02:23,680 --> 00:02:27,370 When the rate of reaction of molecules going in that 51 00:02:27,370 --> 00:02:30,120 direction is equal to the number of molecules going in 52 00:02:30,120 --> 00:02:32,640 the other direction, then I'm going to reach some type of 53 00:02:32,639 --> 00:02:33,889 equilibrium. 54 00:02:33,889 --> 00:02:41,419 55 00:02:41,419 --> 00:02:43,669 Now, why would this happen as opposed to that? 56 00:02:43,669 --> 00:02:45,609 And I can think of one situation. 57 00:02:45,610 --> 00:02:48,880 If we draw this energy diagram again. 58 00:02:48,879 --> 00:02:51,609 Maybe both of these have similar or not so different 59 00:02:51,610 --> 00:02:53,960 energy states. 60 00:02:53,960 --> 00:02:55,930 There could be other reasons, but this is the one that comes 61 00:02:55,930 --> 00:02:58,670 to my mind. 62 00:02:58,669 --> 00:03:00,699 Maybe the energy states look something like this. 63 00:03:00,699 --> 00:03:04,869 On this side, you have the A plus B, and then you need some 64 00:03:04,870 --> 00:03:05,870 activation energy. 65 00:03:05,870 --> 00:03:08,890 And then maybe the C plus D, maybe it's a little bit of a 66 00:03:08,889 --> 00:03:11,869 lower potential, but it's not that much lower. 67 00:03:11,870 --> 00:03:14,770 So maybe they're favored to go in this direction, because 68 00:03:14,770 --> 00:03:15,880 this is a more stable state. 69 00:03:15,879 --> 00:03:19,650 So this is the A plus B, but here you have the C plus D. 70 00:03:19,650 --> 00:03:22,010 But it's not ridiculous to go this way either. 71 00:03:22,009 --> 00:03:23,840 So most of it might go that way, but some of it 72 00:03:23,840 --> 00:03:24,890 might go this way. 73 00:03:24,889 --> 00:03:28,509 If some of these molecules just have the right amount of 74 00:03:28,509 --> 00:03:31,569 kinetic energy, they can surmount this activation 75 00:03:31,569 --> 00:03:35,400 energy and then go backwards to that side of it. 76 00:03:35,400 --> 00:03:38,090 And the study of this is called equilibrium, where 77 00:03:38,090 --> 00:03:39,710 you're looking at the concentrations of the 78 00:03:39,710 --> 00:03:40,590 different molecules. 79 00:03:40,590 --> 00:03:43,330 And just to compare that to kinetics, kinetics was how 80 00:03:43,330 --> 00:03:44,790 fast is this is going to happen? 81 00:03:44,789 --> 00:03:48,259 Or what can I do to change the activation, this hump here? 82 00:03:48,259 --> 00:03:53,859 Equilibrium is studying what will be the concentrations of 83 00:03:53,860 --> 00:03:57,650 the different molecules that end up, once the rate going in 84 00:03:57,650 --> 00:04:00,289 this direction is equal to the rate going in that direction. 85 00:04:00,289 --> 00:04:01,199 And I want to be clear. 86 00:04:01,199 --> 00:04:04,459 Equilibrium is where the rate going in the forward direction 87 00:04:04,460 --> 00:04:07,469 is equal to the rate going in the reverse direction. 88 00:04:07,469 --> 00:04:10,530 It doesn't mean that the concentrations of the two 89 00:04:10,530 --> 00:04:11,169 things are equal. 90 00:04:11,169 --> 00:04:15,719 You might end up with 25% of your eventual solution's 91 00:04:15,719 --> 00:04:19,189 concentration to be A and B and 75% here. 92 00:04:19,189 --> 00:04:21,449 All we know is that at some point, you've reached an-- 93 00:04:21,449 --> 00:04:23,759 equilibrium just means that those concentrations won't 94 00:04:23,759 --> 00:04:25,289 change anymore. 95 00:04:25,290 --> 00:04:28,590 And just to give you an example what I mean here, I 96 00:04:28,589 --> 00:04:30,759 could have written-- let's see, this is actually the 97 00:04:30,759 --> 00:04:31,719 Haber process. 98 00:04:31,720 --> 00:04:37,520 I could write nitrogen gas plus 3 hydrogen gases. 99 00:04:37,519 --> 00:04:39,729 These are all in gas form, so I can put a little g in 100 00:04:39,730 --> 00:04:40,980 parentheses. 101 00:04:40,980 --> 00:04:43,030 102 00:04:43,029 --> 00:04:49,679 Actually, it's an equilibrium reaction, and it produces 2 103 00:04:49,680 --> 00:04:52,000 moles of ammonia. 104 00:04:52,000 --> 00:04:53,220 It's called the Haber process. 105 00:04:53,220 --> 00:04:56,000 We could talk about that in another video. 106 00:04:56,000 --> 00:05:01,990 So in this case, we could say a is just 1, this lowercase a. 107 00:05:01,990 --> 00:05:05,040 Capital A is the nitrogen molecule. 108 00:05:05,040 --> 00:05:08,710 Lowercase b is 3. 109 00:05:08,709 --> 00:05:10,719 Uppercase B is the hydrogen molecule. 110 00:05:10,720 --> 00:05:14,910 And then lowercase c is the number of moles of ammonia and 111 00:05:14,910 --> 00:05:17,230 uppercase C is the ammonia molecule itself. 112 00:05:17,230 --> 00:05:20,600 I just want you to realize this is just an abstract way 113 00:05:20,600 --> 00:05:22,950 of describing a whole set of equations. 114 00:05:22,949 --> 00:05:25,949 Now, what's interesting in equilibrium reactions is that 115 00:05:25,949 --> 00:05:27,759 you can define a constant called 116 00:05:27,759 --> 00:05:29,254 the equilibrium constant. 117 00:05:29,254 --> 00:05:32,259 118 00:05:32,259 --> 00:05:35,779 It's defined as the constant of equilibrium. 119 00:05:35,779 --> 00:05:36,859 Let me switch colors. 120 00:05:36,860 --> 00:05:39,020 I'm using this light blue too much. 121 00:05:39,019 --> 00:05:44,649 The equilibrium constant is defined as you take the 122 00:05:44,649 --> 00:05:49,319 products, or the right-hand side-- but if it goes in both 123 00:05:49,319 --> 00:05:51,639 directions, you can obviously go in either direction. 124 00:05:51,639 --> 00:05:53,789 But let's say that this is the forward direction going from A 125 00:05:53,790 --> 00:05:54,990 plus B to C plus D. 126 00:05:54,990 --> 00:05:59,300 So you take the products, you take the concentration of each 127 00:05:59,300 --> 00:06:04,819 of the products, and you multiply them by each other, 128 00:06:04,819 --> 00:06:08,699 and you raise them to the mole ratios that you're taking. 129 00:06:08,699 --> 00:06:11,599 So in this case, it would be the concentration of big C 130 00:06:11,600 --> 00:06:15,050 raised to the lowercase c power and the concentration of 131 00:06:15,050 --> 00:06:17,550 big D raised to the lowercase d power. 132 00:06:17,550 --> 00:06:21,819 And when I say concentration, they usually-- especially what 133 00:06:21,819 --> 00:06:24,980 you see in your intro chemistry classes, the 134 00:06:24,980 --> 00:06:31,790 concentration is going to be measured in molarity, which, 135 00:06:31,790 --> 00:06:36,270 just as a review, is moles per liter. 136 00:06:36,269 --> 00:06:39,649 A couple of videos ago, when I taught you what molarity was, 137 00:06:39,649 --> 00:06:41,829 I said, you know, moles per liter--- I don't like it so 138 00:06:41,829 --> 00:06:46,550 much because the volume of your fluid or your gas you're 139 00:06:46,550 --> 00:06:47,870 dealing with is dependent on temperature. 140 00:06:47,870 --> 00:06:49,449 So I didn't like using molarity. 141 00:06:49,449 --> 00:06:52,139 But in this case, it's kind of OK. 142 00:06:52,139 --> 00:06:55,995 Because this equilibrium constant is also only true for 143 00:06:55,995 --> 00:06:57,030 a given temperature. 144 00:06:57,029 --> 00:06:59,219 We assume it for a given temperature, and I'll show you 145 00:06:59,220 --> 00:07:00,200 how we use it in a second. 146 00:07:00,199 --> 00:07:04,899 But it's defined as the concentrations of the products 147 00:07:04,899 --> 00:07:06,269 to the powers. 148 00:07:06,269 --> 00:07:07,842 And also, if I have time, maybe I'll do 149 00:07:07,843 --> 00:07:08,850 it in the next video. 150 00:07:08,850 --> 00:07:11,370 The intuition why you're raising it to the power 151 00:07:11,370 --> 00:07:17,819 divided by the concentrations of the reactants, or the 152 00:07:17,819 --> 00:07:21,579 things on the left-hand side of the equilibrium reaction. 153 00:07:21,579 --> 00:07:27,609 So capital A to the lowercase a divided by capital B to the 154 00:07:27,610 --> 00:07:28,920 lowercase B. 155 00:07:28,920 --> 00:07:31,220 And what's interesting about this, and this is a bit of a 156 00:07:31,220 --> 00:07:32,640 simplification, because this doesn't 157 00:07:32,639 --> 00:07:33,979 apply to all reactions. 158 00:07:33,980 --> 00:07:36,920 But to most things that you're going to encounter in an intro 159 00:07:36,920 --> 00:07:40,160 chemistry class, this is true, that once you establish this 160 00:07:40,160 --> 00:07:42,580 equilibrium constant for a certain temperature-- it's 161 00:07:42,579 --> 00:07:45,089 only true for a certain temperature-- then you can 162 00:07:45,089 --> 00:07:48,529 change the concentrations and then be able to predict what 163 00:07:48,529 --> 00:07:50,759 the resulting concentrations are going to be. 164 00:07:50,759 --> 00:07:52,449 Let me give you an example. 165 00:07:52,449 --> 00:07:55,229 So let's say that after you did this equilibrium 166 00:07:55,230 --> 00:07:59,770 reaction-- and actually, just to make things hit home a 167 00:07:59,769 --> 00:08:02,109 little bit, let me take this Haber process reaction and 168 00:08:02,110 --> 00:08:03,090 write it in the same form. 169 00:08:03,089 --> 00:08:05,339 So if I wanted to write the equilibrium constant for the 170 00:08:05,339 --> 00:08:09,799 Haber reaction, or if I wanted to calculate it, I would let 171 00:08:09,800 --> 00:08:11,990 this reaction go at some temperature. 172 00:08:11,990 --> 00:08:14,319 So this is only true at-- let's say we're doing it at 25 173 00:08:14,319 --> 00:08:16,540 Celsius, which is roughly room temperature. 174 00:08:16,540 --> 00:08:19,550 So what I would do is I would take the products. 175 00:08:19,550 --> 00:08:23,790 So the only product is ammonia, NH3. 176 00:08:23,790 --> 00:08:26,280 I raise it to the power of the number of moles that's 177 00:08:26,279 --> 00:08:29,649 produced for every 1 mole of nitrogen gas 178 00:08:29,649 --> 00:08:31,029 and 3 moles of hydrogen. 179 00:08:31,029 --> 00:08:32,879 So I raise it to the power of 2. 180 00:08:32,879 --> 00:08:34,350 So that's what that gets me. 181 00:08:34,350 --> 00:08:37,990 And I divide it by the reactants. 182 00:08:37,990 --> 00:08:41,399 So 1 mole of nitrogen, so I would just put the 183 00:08:41,399 --> 00:08:46,860 concentration of the nitrogen, plus 3 moles of 184 00:08:46,860 --> 00:08:47,830 hydrogen-- oh, no, no. 185 00:08:47,830 --> 00:08:48,759 I shouldn't write a plus there. 186 00:08:48,759 --> 00:08:49,889 It's multiplied. 187 00:08:49,889 --> 00:08:55,199 So times the hydrogen, and I raise it to the third power, 188 00:08:55,200 --> 00:08:59,090 because for every 1 mole of nitrogen, I have 3 moles of 189 00:08:59,090 --> 00:09:01,780 hydrogen and then 2 moles of ammonia. 190 00:09:01,779 --> 00:09:04,059 And if I were to calculate this, remember, when I put 191 00:09:04,059 --> 00:09:05,879 these in brackets, I'm figuring out the 192 00:09:05,879 --> 00:09:06,730 concentration. 193 00:09:06,730 --> 00:09:09,430 So I would have to figure out the moles per liter. 194 00:09:09,429 --> 00:09:14,169 Or sometimes they say, the molarity of each of these 195 00:09:14,169 --> 00:09:15,429 things, and it'll get me some constant. 196 00:09:15,429 --> 00:09:17,629 If I change it, I can go and calculate the rest, so let me 197 00:09:17,629 --> 00:09:19,909 just do an example right now. 198 00:09:19,909 --> 00:09:29,480 So let's say I have 1 mole of molecule A plus 2 moles of 199 00:09:29,480 --> 00:09:40,710 molecule B are in equilibrium with 3 moles of molecule C. 200 00:09:40,710 --> 00:09:44,690 And let's say that once we're in equilibrium, we go and we 201 00:09:44,690 --> 00:09:47,820 measure the concentrations, and we figure out that the 202 00:09:47,820 --> 00:09:55,100 concentration of A is 1 molar, which is equal 203 00:09:55,100 --> 00:09:59,519 to 1 mole per liter. 204 00:09:59,519 --> 00:10:01,360 That's the concentration of A. 205 00:10:01,360 --> 00:10:03,990 We figure out that once we're in equilibrium, the 206 00:10:03,990 --> 00:10:17,480 concentration of B is equal to 3 molar, which 207 00:10:17,480 --> 00:10:21,680 means 3 moles per liter. 208 00:10:21,679 --> 00:10:23,750 And let's say that once we're in that equilibrium, the 209 00:10:23,750 --> 00:10:35,100 concentration of C is equal to point-- well, I don't want to 210 00:10:35,100 --> 00:10:37,779 do something too-- let's say it's equal to 1 molar as well. 211 00:10:37,779 --> 00:10:39,740 I should get rid of that point there, because I don't want to 212 00:10:39,740 --> 00:10:42,200 say 0.1 molar, so it's just 1 molar. 213 00:10:42,200 --> 00:10:45,410 So if we wanted to calculate the equilibrium constant for 214 00:10:45,409 --> 00:10:53,000 this reaction, we just take C, the concentration of C over 215 00:10:53,000 --> 00:10:53,769 here, so let's see. 216 00:10:53,769 --> 00:11:00,970 The equilibrium constant is equal to the concentration of 217 00:11:00,970 --> 00:11:12,639 C to the third power divided by the concentration of A to 218 00:11:12,639 --> 00:11:15,740 the first power-- because there's only 1 mole of A for 219 00:11:15,740 --> 00:11:20,480 every 3 of C and 2 of B-- times the concentration of-- 220 00:11:20,480 --> 00:11:25,639 I'll do it in that color-- B to the third power. 221 00:11:25,639 --> 00:11:29,819 So if we needed to calculate this, concentration of C is 1 222 00:11:29,820 --> 00:11:35,129 molar, and we're raising it to the third power, divided by 223 00:11:35,129 --> 00:11:39,950 concentration of A is 1 molar times the concentration of B, 224 00:11:39,950 --> 00:11:44,280 which is 3 molars, to the third power. 225 00:11:44,279 --> 00:11:51,299 So this is equal to 1/27. 226 00:11:51,299 --> 00:11:52,939 There's a couple of things we can think about. 227 00:11:52,940 --> 00:11:57,800 The fact that this is less than 1, what does that mean? 228 00:11:57,799 --> 00:12:05,319 Well, that means that our concentration of our reactants 229 00:12:05,320 --> 00:12:07,660 is much larger than the concentration of the products, 230 00:12:07,659 --> 00:12:09,600 where we view just the products as whatever's on the 231 00:12:09,600 --> 00:12:11,050 right-hand side of the equation. 232 00:12:11,049 --> 00:12:14,490 So once this reaction goes to equilibrium, we're still left 233 00:12:14,490 --> 00:12:18,960 with a lot more of this than this. 234 00:12:18,960 --> 00:12:21,860 And because we're left with a lot more of that, our 235 00:12:21,860 --> 00:12:25,870 equilibrium constant is less than 1, which means that the 236 00:12:25,870 --> 00:12:27,919 reaction favors this direction. 237 00:12:27,919 --> 00:12:29,454 It favors the backward direction. 238 00:12:29,455 --> 00:12:32,770 239 00:12:32,769 --> 00:12:35,250 Think about it. 240 00:12:35,250 --> 00:12:38,720 Because there's more of this, this must be happening more 241 00:12:38,720 --> 00:12:42,700 than the left-to-right reaction. 242 00:12:42,700 --> 00:12:45,100 The left to right might be a small direction like this, 243 00:12:45,100 --> 00:12:46,899 while more is happening there, and that's why we're finding 244 00:12:46,899 --> 00:12:49,649 more reaction here, and that causes the equilibrium 245 00:12:49,649 --> 00:12:51,149 constant to be less than 1. 246 00:12:51,149 --> 00:12:55,269 On the other hand, if the equilibrium constant was 247 00:12:55,269 --> 00:12:58,470 greater than 1, that means that this numerator is greater 248 00:12:58,470 --> 00:12:59,800 than this denominator. 249 00:12:59,799 --> 00:13:02,729 Which would imply that you have more concentration-- once 250 00:13:02,730 --> 00:13:04,560 you're in equilibrium, you end up with a lot more of the 251 00:13:04,559 --> 00:13:06,529 stuff on the right than you end up with the stuff on the 252 00:13:06,529 --> 00:13:09,029 left, so then that means the reaction would be going in the 253 00:13:09,029 --> 00:13:11,199 forward direction. 254 00:13:11,200 --> 00:13:13,340 The other interesting thing is you can then figure out, well, 255 00:13:13,340 --> 00:13:19,420 what happens if I add another mole of A to the reaction? 256 00:13:19,419 --> 00:13:21,370 So let's say I throw some A into the reaction. 257 00:13:21,370 --> 00:13:24,629 258 00:13:24,629 --> 00:13:26,299 I add some concentration of A. 259 00:13:26,299 --> 00:13:37,109 So now my new A is equal to 2. 260 00:13:37,110 --> 00:13:39,070 Let's say my new A is equal to 2. 261 00:13:39,070 --> 00:13:45,170 Let's say my new B, let's say that I want to-- well, 262 00:13:45,169 --> 00:13:49,819 actually, we can figure out the relation between the-- 263 00:13:49,820 --> 00:13:51,760 actually, instead of going into this situation where I 264 00:13:51,759 --> 00:13:54,149 change the concentration, let me do that in the next video, 265 00:13:54,149 --> 00:13:56,549 because I just realized that I'm running very low on time. 266 00:13:56,549 --> 00:13:59,699 But hopefully, you got a good sense of what the equilibrium 267 00:13:59,700 --> 00:14:01,280 constant is all about and how it's 268 00:14:01,279 --> 00:14:03,129 measured or how it's defined. 269 00:14:03,129 --> 00:14:04,889 And in the next video, we're going to talk a little bit 270 00:14:04,889 --> 00:14:07,069 about how else it could be useful. 271 00:14:07,070 --> 00:14:09,540 In this video, you just said, oh, if it's less than 1, that 272 00:14:09,539 --> 00:14:11,730 means that the backward reaction is favored. 273 00:14:11,730 --> 00:14:14,090 If it's greater than 1, the forward reaction is favored. 274 00:14:14,090 --> 00:14:16,110 In the next video, we'll get a little intuition, hopefully, 275 00:14:16,110 --> 00:14:21,800 on why it is defined this way as opposed to, say, this way. 276 00:14:21,799 --> 00:14:26,479 My intuition said, hey, why isn't it three times the 277 00:14:26,480 --> 00:14:30,620 concentration of C divided by one times the concentration of 278 00:14:30,620 --> 00:14:33,810 A plus three times the concentration of B? 279 00:14:33,809 --> 00:14:35,509 This might have been more intuitive to me, but this 280 00:14:35,509 --> 00:14:36,460 isn't the case. 281 00:14:36,460 --> 00:14:39,139 This is what actually is constant, regardless of how 282 00:14:39,139 --> 00:14:42,819 you change the concentrations of the various reactants. 283 00:14:42,820 --> 00:14:47,879 So maybe we'll talk a little bit about why this is true and 284 00:14:47,879 --> 00:14:50,570 not necessarily this.