Reactions in equilibrium

All of the reactions we've looked at so far have been of the form lowercase a moles of the molecule uppercase A, plus lowercase b moles of a molecule uppercase B. They react to form the product or the products. Let's just say they have a couple of products. I could have had as many molecules here as I wanted. Let's say c moles of the molecule C plus d moles of the molecule capital D. And the idea here is that they went in one direction. And if we did a little energy diagram, just going off of the kinematics video we just did, if that's the reaction, or how the reaction progresses, you could imagine that here you have it at a higher energy state. You have lowercase a moles of capital A molecule, plus lowercase b moles of capital B molecule, and you have some activation energy. And then you get to a more stable state or a lower energy level here, where it's lowercase c moles of C molecule plus lowercase d moles of the D moles, and of course, you had some activation energy. It only goes in this direction. Once you get here, it's very hard to go back. So that if you came back and looked at this-- if you get enough of A and B-- you'll just be sitting with molecules of C and D. It'll only go in this direction. But that's not how it happens in reality. In reality-- well, it sometimes happens like this in reality where the reaction can only go in one direction. But in a lot of cases, the reaction can actually go in both directions. So we could write, instead of this one-way reaction, we could write a two-way reaction like this. And not to confuse you too much, these are the number of moles or the ratios of the molecules I'm adding up, and they become relevant in a second. So let's say I have lowercase a moles of this molecule plus lowercase b moles of this molecule, and then they react to form lowercase c moles of this molecule plus lowercase d moles of that molecule. Sometimes the reaction can go in both directions. And to do that, to just show an equilibrium reaction, you do these arrows that go in both directions. That means that, hey, some of this is going to start forming into some of this. But at the same time, some of this might start forming into some of this. And at some point, I'm going to be reaching an equilibrium. When the rate of reaction of molecules going in that direction is equal to the number of molecules going in the other direction, then I'm going to reach some type of equilibrium. Now, why would this happen as opposed to that? And I can think of one situation. If we draw this energy diagram again. Maybe both of these have similar or not so different energy states. There could be other reasons, but this is the one that comes to my mind. Maybe the energy states look something like this. On this side, you have the A plus B, and then you need some activation energy. And then maybe the C plus D, maybe it's a little bit of a lower potential, but it's not that much lower. So maybe they're favored to go in this direction, because this is a more stable state. So this is the A plus B, but here you have the C plus D. But it's not ridiculous to go this way either. So most of it might go that way, but some of it might go this way. If some of these molecules just have the right amount of kinetic energy, they can surmount this activation energy and then go backwards to that side of it. And the study of this is called equilibrium, where you're looking at the concentrations of the different molecules. And just to compare that to kinetics, kinetics was how fast is this is going to happen? Or what can I do to change the activation, this hump here? Equilibrium is studying what will be the concentrations of the different molecules that end up, once the rate going in this direction is equal to the rate going in that direction. And I want to be clear. Equilibrium is where the rate going in the forward direction is equal to the rate going in the reverse direction. It doesn't mean that the concentrations of the two things are equal. You might end up with 25% of your eventual solution's concentration to be A and B and 75% here. All we know is that at some point, you've reached an-- equilibrium just means that those concentrations won't change anymore. And just to give you an example what I mean here, I could have written-- let's see, this is actually the Haber process. I could write nitrogen gas plus 3 hydrogen gases. These are all in gas form, so I can put a little g in parentheses. Actually, it's an equilibrium reaction, and it produces 2 moles of ammonia. It's called the Haber process. We could talk about that in another video. So in this case, we could say a is just 1, this lowercase a. Capital A is the nitrogen molecule. Lowercase b is 3. Uppercase B is the hydrogen molecule. And then lowercase c is the number of moles of ammonia and uppercase C is the ammonia molecule itself. I just want you to realize this is just an abstract way of describing a whole set of equations. Now, what's interesting in equilibrium reactions is that you can define a constant called the equilibrium constant. It's defined as the constant of equilibrium. Let me switch colors. I'm using this light blue too much. The equilibrium constant is defined as you take the products, or the right-hand side-- but if it goes in both directions, you can obviously go in either direction. But let's say that this is the forward direction going from A plus B to C plus D. So you take the products, you take the concentration of each of the products, and you multiply them by each other, and you raise them to the mole ratios that you're taking. So in this case, it would be the concentration of big C raised to the lowercase c power and the concentration of big D raised to the lowercase d power. And when I say concentration, they usually-- especially what you see in your intro chemistry classes, the concentration is going to be measured in molarity, which, just as a review, is moles per liter. A couple of videos ago, when I taught you what molarity was, I said, you know, moles per liter--- I don't like it so much because the volume of your fluid or your gas you're dealing with is dependent on temperature. So I didn't like using molarity. But in this case, it's kind of OK. Because this equilibrium constant is also only true for a given temperature. We assume it for a given temperature, and I'll show you how we use it in a second. But it's defined as the concentrations of the products to the powers. And also, if I have time, maybe I'll do it in the next video. The intuition why you're raising it to the power divided by the concentrations of the reactants, or the things on the left-hand side of the equilibrium reaction. So capital A to the lowercase a divided by capital B to the lowercase B. And what's interesting about this, and this is a bit of a simplification, because this doesn't apply to all reactions. But to most things that you're going to encounter in an intro chemistry class, this is true, that once you establish this equilibrium constant for a certain temperature-- it's only true for a certain temperature-- then you can change the concentrations and then be able to predict what the resulting concentrations are going to be. Let me give you an example. So let's say that after you did this equilibrium reaction-- and actually, just to make things hit home a little bit, let me take this Haber process reaction and write it in the same form. So if I wanted to write the equilibrium constant for the Haber reaction, or if I wanted to calculate it, I would let this reaction go at some temperature. So this is only true at-- let's say we're doing it at 25 Celsius, which is roughly room temperature. So what I would do is I would take the products. So the only product is ammonia, NH3. I raise it to the power of the number of moles that's produced for every 1 mole of nitrogen gas and 3 moles of hydrogen. So I raise it to the power of 2. So that's what that gets me. And I divide it by the reactants. So 1 mole of nitrogen, so I would just put the concentration of the nitrogen, plus 3 moles of hydrogen-- oh, no, no. I shouldn't write a plus there. It's multiplied. So times the hydrogen, and I raise it to the third power, because for every 1 mole of nitrogen, I have 3 moles of hydrogen and then 2 moles of ammonia. And if I were to calculate this, remember, when I put these in brackets, I'm figuring out the concentration. So I would have to figure out the moles per liter. Or sometimes they say, the molarity of each of these things, and it'll get me some constant. If I change it, I can go and calculate the rest, so let me just do an example right now. So let's say I have 1 mole of molecule A plus 2 moles of molecule B are in equilibrium with 3 moles of molecule C. And let's say that once we're in equilibrium, we go and we measure the concentrations, and we figure out that the concentration of A is 1 molar, which is equal to 1 mole per liter. That's the concentration of A. We figure out that once we're in equilibrium, the concentration of B is equal to 3 molar, which means 3 moles per liter. And let's say that once we're in that equilibrium, the concentration of C is equal to point-- well, I don't want to do something too-- let's say it's equal to 1 molar as well. I should get rid of that point there, because I don't want to say 0.1 molar, so it's just 1 molar. So if we wanted to calculate the equilibrium constant for this reaction, we just take C, the concentration of C over here, so let's see. The equilibrium constant is equal to the concentration of C to the third power divided by the concentration of A to the first power-- because there's only 1 mole of A for every 3 of C and 2 of B-- times the concentration of-- I'll do it in that color-- B to the third power. So if we needed to calculate this, concentration of C is 1 molar, and we're raising it to the third power, divided by concentration of A is 1 molar times the concentration of B, which is 3 molars, to the third power. So this is equal to 1/27. There's a couple of things we can think about. The fact that this is less than 1, what does that mean? Well, that means that our concentration of our reactants is much larger than the concentration of the products, where we view just the products as whatever's on the right-hand side of the equation. So once this reaction goes to equilibrium, we're still left with a lot more of this than this. And because we're left with a lot more of that, our equilibrium constant is less than 1, which means that the reaction favors this direction. It favors the backward direction. Think about it. Because there's more of this, this must be happening more than the left-to-right reaction. The left to right might be a small direction like this, while more is happening there, and that's why we're finding more reaction here, and that causes the equilibrium constant to be less than 1. On the other hand, if the equilibrium constant was greater than 1, that means that this numerator is greater than this denominator. Which would imply that you have more concentration-- once you're in equilibrium, you end up with a lot more of the stuff on the right than you end up with the stuff on the left, so then that means the reaction would be going in the forward direction. The other interesting thing is you can then figure out, well, what happens if I add another mole of A to the reaction? So let's say I throw some A into the reaction. I add some concentration of A. So now my new A is equal to 2. Let's say my new A is equal to 2. Let's say my new B, let's say that I want to-- well, actually, we can figure out the relation between the-- actually, instead of going into this situation where I change the concentration, let me do that in the next video, because I just realized that I'm running very low on time. But hopefully, you got a good sense of what the equilibrium constant is all about and how it's measured or how it's defined. And in the next video, we're going to talk a little bit about how else it could be useful. In this video, you just said, oh, if it's less than 1, that means that the backward reaction is favored. If it's greater than 1, the forward reaction is favored. In the next video, we'll get a little intuition, hopefully, on why it is defined this way as opposed to, say, this way. My intuition said, hey, why isn't it three times the concentration of C divided by one times the concentration of A plus three times the concentration of B? This might have been more intuitive to me, but this isn't the case. This is what actually is constant, regardless of how you change the concentrations of the various reactants. So maybe we'll talk a little bit about why this is true and not necessarily this.