1 00:00:00,000 --> 00:00:00,880 2 00:00:00,880 --> 00:00:03,649 Let's say we wanted to figure out the equilibrium constant 3 00:00:03,649 --> 00:00:10,550 for the reaction boron trifluoride in the gaseous 4 00:00:10,550 --> 00:00:14,839 plus 3-- so for every mole of this, we're going to have 3 5 00:00:14,839 --> 00:00:20,570 moles of H2O in the liquid state-- and that's in 6 00:00:20,570 --> 00:00:21,036 equilibrium. 7 00:00:21,036 --> 00:00:27,060 It's going forward and backwards with 3 moles of 8 00:00:27,059 --> 00:00:32,060 hydrofluoric acid, so it's in the aqueous state. 9 00:00:32,060 --> 00:00:33,760 It's been dissolved in the water. 10 00:00:33,759 --> 00:00:36,000 If it wasn't dissolved, if it was in the solid state, you 11 00:00:36,000 --> 00:00:37,539 would call this hydrogen fluoride. 12 00:00:37,539 --> 00:00:40,030 Once it's in water, you call it hydrofluoric acid, and 13 00:00:40,030 --> 00:00:42,820 we'll talk more about naming in the future, hopefully. 14 00:00:42,820 --> 00:00:50,030 Plus 1 mole of boric acid, also in the aqueous state. 15 00:00:50,030 --> 00:00:52,820 It's dissolved in the water. 16 00:00:52,820 --> 00:00:58,679 H3BO3 in the aqueous state. 17 00:00:58,679 --> 00:01:04,000 So what would the expression for the equilibrium constant 18 00:01:04,000 --> 00:01:06,180 look like in this situation? 19 00:01:06,180 --> 00:01:10,370 So you might be tempted say, OK, that's easy enough, Sal. 20 00:01:10,370 --> 00:01:12,700 So the equilibrium constant, you just take 21 00:01:12,700 --> 00:01:14,299 the right-hand side. 22 00:01:14,299 --> 00:01:16,280 That's just the convention. 23 00:01:16,280 --> 00:01:17,109 There's symmetry here. 24 00:01:17,109 --> 00:01:19,150 I could've rewritten it either way, but let's just say you 25 00:01:19,150 --> 00:01:22,370 take the right-hand side and say, OK, this is dependent on 26 00:01:22,370 --> 00:01:27,070 the concentration of the hydrofluoric acid, the 27 00:01:27,069 --> 00:01:31,919 concentration of the HF, or the molarity of the HF, to the 28 00:01:31,920 --> 00:01:35,680 third power, times the concentration of the boric 29 00:01:35,680 --> 00:01:37,840 acid, H3BO3. 30 00:01:37,840 --> 00:01:40,725 31 00:01:40,724 --> 00:01:43,354 And remember, this intuition of why you're taking this to 32 00:01:43,355 --> 00:01:45,760 the third power is what's the probability-- because in order 33 00:01:45,760 --> 00:01:50,300 for the reaction to go this way, you need to have 3 34 00:01:50,299 --> 00:01:53,810 molecules of hydrofluoric acid being very close to 1 molecule 35 00:01:53,810 --> 00:01:55,299 of the boric acid. 36 00:01:55,299 --> 00:01:58,649 So if you watched the last video I just made about the 37 00:01:58,650 --> 00:02:03,270 intuition behind the equilibrium constant, this is 38 00:02:03,269 --> 00:02:06,819 indicative of the probability of this reaction happening or 39 00:02:06,819 --> 00:02:08,668 the probability of finding all of these 40 00:02:08,669 --> 00:02:10,600 molecules in the same place. 41 00:02:10,599 --> 00:02:12,449 Of course, you can adjust it with a constant and that's 42 00:02:12,449 --> 00:02:13,769 essentially what that does. 43 00:02:13,770 --> 00:02:16,490 But that's on the product side, or the reactant, 44 00:02:16,490 --> 00:02:19,510 depending on what direction you're viewing this equation, 45 00:02:19,509 --> 00:02:31,149 divided by the molarity of the boron trifluoride times-- and 46 00:02:31,150 --> 00:02:36,360 I'll do this in a different color-- the molarity of the 47 00:02:36,360 --> 00:02:41,230 H2O to the third power. 48 00:02:41,229 --> 00:02:43,699 And that's, of course, the H2O liquid. 49 00:02:43,699 --> 00:02:44,409 So there you go. 50 00:02:44,409 --> 00:02:45,579 We'll just figure this out. 51 00:02:45,580 --> 00:02:51,200 And my rebuttal to you is I want you to figure out the 52 00:02:51,199 --> 00:02:52,589 molarity of the water. 53 00:02:52,590 --> 00:02:54,580 What is the concentration of the water? 54 00:02:54,580 --> 00:02:58,810 Remember, the concentration is moles per volume, but in this 55 00:02:58,810 --> 00:02:59,960 case, what's happening? 56 00:02:59,960 --> 00:03:03,030 I'm putting some boron trifluoride gas essentially 57 00:03:03,030 --> 00:03:07,090 into some water, and it's creating these aqueous acids. 58 00:03:07,090 --> 00:03:09,120 These other molecules are dissolved 59 00:03:09,120 --> 00:03:10,700 completely in the water. 60 00:03:10,699 --> 00:03:12,599 So what's the solvent here? 61 00:03:12,599 --> 00:03:13,849 The solvent is H2O. 62 00:03:13,849 --> 00:03:18,250 63 00:03:18,250 --> 00:03:20,979 This might be how the reaction happens, but pretty much, 64 00:03:20,979 --> 00:03:22,149 there's water everywhere. 65 00:03:22,150 --> 00:03:24,000 The water is in surplus. 66 00:03:24,000 --> 00:03:27,629 So if you were to really figure out the concentration 67 00:03:27,629 --> 00:03:31,150 of water, it's everywhere. 68 00:03:31,150 --> 00:03:32,860 I mean, you could say everything but the boron 69 00:03:32,860 --> 00:03:35,820 trifluoride, but it's a very high number. 70 00:03:35,819 --> 00:03:37,900 And if you think about it from the probability point of view, 71 00:03:37,900 --> 00:03:40,670 if you say, OK, in order for this reaction to happen 72 00:03:40,669 --> 00:03:43,679 forward, I need to figure out the probability of finding a 73 00:03:43,680 --> 00:03:47,710 boron trifluoride atom or molecule-- actually, 74 00:03:47,710 --> 00:03:50,650 molecule-- in a certain volume, and it also needs 3 75 00:03:50,650 --> 00:03:52,760 moles of water in that certain volume. 76 00:03:52,759 --> 00:03:54,310 But you say, hey, there's water everywhere. 77 00:03:54,310 --> 00:03:56,140 This is the solvent. 78 00:03:56,139 --> 00:03:58,739 There's water everywhere, so I really just need to worry 79 00:03:58,740 --> 00:04:01,360 about the concentration of the boron trifluoride. 80 00:04:01,360 --> 00:04:09,880 So you could say the forward reaction rate, rate forward, 81 00:04:09,879 --> 00:04:14,199 is going to be dependent on some forward constant times 82 00:04:14,199 --> 00:04:17,569 just the concentration of the boron trifluoride. 83 00:04:17,569 --> 00:04:19,509 The water's everywhere, so you don't have to multiply it 84 00:04:19,509 --> 00:04:21,810 times the concentration of water, whatever that means, 85 00:04:21,810 --> 00:04:23,649 because the water's everywhere. 86 00:04:23,649 --> 00:04:28,039 So the denominator here, you do not put the solvent. 87 00:04:28,040 --> 00:04:31,430 So the correct answer for this one is you only put whatever 88 00:04:31,430 --> 00:04:34,889 is actually dissolved in the solution. 89 00:04:34,889 --> 00:04:36,709 Because frankly, the concentration doesn't actually 90 00:04:36,709 --> 00:04:38,254 makes sense for everything else, and if you think about 91 00:04:38,254 --> 00:04:40,850 it from the probability point of view, that also makes 92 00:04:40,850 --> 00:04:42,290 sense, because there's always water around. 93 00:04:42,290 --> 00:04:45,700 If you said, OK, what's the probability of finding water 94 00:04:45,699 --> 00:04:48,939 at any small volume of our fluid, it's going to be 1, so 95 00:04:48,939 --> 00:04:50,819 you could just multiply it by a 1 there, but that doesn't 96 00:04:50,819 --> 00:04:52,269 make a difference. 97 00:04:52,269 --> 00:04:54,719 Now, what about the following reaction? 98 00:04:54,720 --> 00:04:57,650 99 00:04:57,649 --> 00:05:00,409 Any equilibrium where you have different states of matter is 100 00:05:00,410 --> 00:05:02,020 called a heterogeneous equilibrium. 101 00:05:02,019 --> 00:05:12,419 102 00:05:12,420 --> 00:05:16,610 And so let me write another heterogeneous equilibrium. 103 00:05:16,610 --> 00:05:21,810 So let's say I have H2O in the gaseous state and that's 104 00:05:21,810 --> 00:05:23,829 essentially steam-- so it's not going to be the solvent 105 00:05:23,829 --> 00:05:28,639 this time-- plus carbon in the solid state. 106 00:05:28,639 --> 00:05:32,120 And let's say that that's an equilibrium with hydrogen in 107 00:05:32,120 --> 00:05:36,939 the gas state plus carbon dioxide in the gaseous state. 108 00:05:36,939 --> 00:05:40,060 This is a heterogeneous equilibrium because you have 109 00:05:40,060 --> 00:05:42,610 things in the gaseous and the solid state. 110 00:05:42,610 --> 00:05:44,970 And solid state, by definition, it can't be 111 00:05:44,970 --> 00:05:48,840 dissolved either into the gas or into the-- when we talk 112 00:05:48,839 --> 00:05:53,489 about solutions, we talked about colloids and suspensions 113 00:05:53,490 --> 00:05:56,170 and mixtures before, but we're talking about solutions. 114 00:05:56,170 --> 00:05:57,689 By definition, if this is in the solid 115 00:05:57,689 --> 00:05:59,620 state, it's not dissolved. 116 00:05:59,620 --> 00:06:02,129 If this was dissolved, we would write an aq here. 117 00:06:02,129 --> 00:06:04,170 It would be the aqueous state. 118 00:06:04,170 --> 00:06:06,840 So if you talk about the forward reaction, what's the 119 00:06:06,839 --> 00:06:09,799 forward reaction going to be dependent on? 120 00:06:09,800 --> 00:06:15,670 So the rate forward, well, the solid, there's a big block of 121 00:06:15,670 --> 00:06:17,129 carbon sitting there. 122 00:06:17,129 --> 00:06:21,879 There's a big cube of carbon there, and there's steam, 123 00:06:21,879 --> 00:06:26,019 there's water gas all around it. 124 00:06:26,019 --> 00:06:28,599 So if you pick any volume, especially if you pick some 125 00:06:28,600 --> 00:06:31,760 volume near the boundary of the carbon, you're always 126 00:06:31,759 --> 00:06:33,289 going to have carbon around. 127 00:06:33,290 --> 00:06:35,330 It's just what matters is the concentration 128 00:06:35,329 --> 00:06:37,579 of the water gas. 129 00:06:37,579 --> 00:06:40,180 That's what's going to drive the forward rate, so the 130 00:06:40,180 --> 00:06:43,150 forward rate is going to be dependent on some constant 131 00:06:43,149 --> 00:06:49,299 times the concentration of the water gas. 132 00:06:49,300 --> 00:06:53,340 And, of course, the backwards rate, so you need to get some 133 00:06:53,339 --> 00:06:59,060 H2, some molecules of-- let me draw it like that, because it 134 00:06:59,060 --> 00:07:04,230 has 2 hydrogen molecules plus a carbon dioxide, so maybe a 135 00:07:04,230 --> 00:07:07,170 carbon dioxide looks like that. 136 00:07:07,170 --> 00:07:12,210 So the reverse reaction, so rate, let's call that reverse, 137 00:07:12,209 --> 00:07:14,099 is going to be equal to some constant times the probability 138 00:07:14,100 --> 00:07:16,980 of finding both of these molecules in the same place. 139 00:07:16,980 --> 00:07:20,340 And, of course, the probability is related to or 140 00:07:20,339 --> 00:07:22,719 it's on a first-level approximation, depending on 141 00:07:22,720 --> 00:07:24,590 the concentration. 142 00:07:24,589 --> 00:07:29,774 So it's concentration of H2 times the concentration-- and 143 00:07:29,774 --> 00:07:31,639 to find both of them, you multiply the probability, 144 00:07:31,639 --> 00:07:35,329 because you need this and that-- times the 145 00:07:35,329 --> 00:07:37,519 concentration of CO. 146 00:07:37,519 --> 00:07:42,029 So when a reaction is in equilibrium, these two equal 147 00:07:42,029 --> 00:07:44,639 each other-- this is an r right here-- so this is going 148 00:07:44,639 --> 00:07:49,879 to be equal to the reverse rate of reaction H2 times 149 00:07:49,879 --> 00:07:51,389 carbon dioxide. 150 00:07:51,389 --> 00:07:55,539 Divide both sides by the K's, both sides by the H2O, and you 151 00:07:55,540 --> 00:08:01,020 get the forward coefficient or constant or whatever you want 152 00:08:01,019 --> 00:08:04,459 to call that, divided by the reverse constant-- I'm just 153 00:08:04,459 --> 00:08:09,439 dividing both sides by that-- is equal to this-- let me just 154 00:08:09,439 --> 00:08:15,480 copy and paste that-- is equal to that divided by this. 155 00:08:15,480 --> 00:08:20,700 156 00:08:20,699 --> 00:08:22,930 You take that and you divide it by that. 157 00:08:22,930 --> 00:08:26,439 158 00:08:26,439 --> 00:08:28,875 And so if we call this the equilibrium constant, because 159 00:08:28,875 --> 00:08:30,949 it's just two arbitrary constants, so we can just call 160 00:08:30,949 --> 00:08:33,360 this the equilibrium constant, you see that it actually makes 161 00:08:33,360 --> 00:08:36,710 a lot of sense to ignore the solid state in your 162 00:08:36,710 --> 00:08:37,759 equilibrium reaction. 163 00:08:37,759 --> 00:08:39,769 So the two takeaways here is when you're trying to 164 00:08:39,769 --> 00:08:42,689 calculate an equilibrium constant, you should ignore-- 165 00:08:42,690 --> 00:08:46,360 especially when it's in a heterogeneous equilibrium-- 166 00:08:46,360 --> 00:08:51,250 you should ignore the 167 00:08:51,250 --> 00:08:53,970 solution-- or not the solution. 168 00:08:53,970 --> 00:08:57,370 Ignore the solvent in that first example, where I did it 169 00:08:57,370 --> 00:09:00,250 with boron trifluoride with water. 170 00:09:00,250 --> 00:09:01,889 Water was the solvent, so I ignored it. 171 00:09:01,889 --> 00:09:04,009 Because water is everywhere, and you also 172 00:09:04,009 --> 00:09:06,220 ignore the solid state. 173 00:09:06,220 --> 00:09:09,330 Ignore the solid. 174 00:09:09,330 --> 00:09:13,173 Anyway, we'll probably use these in future things where 175 00:09:13,173 --> 00:09:15,879 we actually calculate the equilibrium constant. 176 00:09:15,879 --> 00:09:17,889 See you in the next video where we'll learn about Le 177 00:09:17,889 --> 00:09:20,259 Chatelier's principle. 178 00:09:20,259 --> 00:09:21,004