 All right, so now it's time for a brief confession about what we've not been able to do in PKEM so far. So, if you've been watching these videos all the way through in order, you've watched hundreds of them at this point. We're a semester and a half into the course, and yet we've never really talked about chemical reactions at all. That doesn't sound very good for a chemistry class. We've talked about all sorts of different types of changes and processes. We've talked about changes in the state of a system, meaning if I change the temperature, if I change the pressure, if I change some other state variable, we can do a lot with thermodynamics in predicting the value of the energy or free energy or various other thermodynamic properties. We've talked a lot about phase changes, so solids can turn into liquids and gases. We understand a lot about the thermodynamics of that sort of process. That's almost a chemical reaction. I'm converting one physical state of a system to another physical state changing phase, but we have not talked about any bona fide chemical reactions. We haven't written reactions of the form molecule A turns into molecule B. The closest we've come has been molecule A in the solid phase turns into molecule A in the liquid phase, just changing phase without changing the chemical identity of the molecule. Like I said, that doesn't sound like a chemistry class if we can't talk about chemical reactions, but we have developed a pretty large collection of tools for dealing with physical chemistry problems, thermodynamics and chemical potential, statistical mechanics. Those are the sorts of tools we'll need to employ to be able to talk about chemical reactions and in particular chemical equilibrium reactions. Just to remind you what I mean by equilibrium, you probably know from some previous chemistry course something about an equilibrium constant. You'll remember that's something like amounts of products divided by amounts of reactants. That gives us an equilibrium constant. That's all still true, but when we think about that from a physical chemistry point of view, we'd like to know why is it that some reaction is an equilibrium reaction instead of going all the way to completion? If I write down a reaction, let's say a reaction between two gases, H2 and Br2, that's an equilibrium reaction. If I combine a mole of H2 and a mole of Br2 and I heat them up to a particular temperature, they're not going to react completely and form two moles of HBr. I'm going to react a portion of a mole of H2 and a portion of a mole of Br2 to generate twice as much HBr, but I'm still going to have some HBr, H2 and Br2 left when that reaction reaches equilibrium as determined by this equilibrium constant. Why does it experience an equilibrium rather than going to completion? Why is the equilibrium constant equal to some particular value? Those are all things we're going to be able to understand using physical chemistry and thermodynamics and statistical mechanics. We can already, at least qualitatively guess what physical chemistry has to say about this reaction, about why we have an equilibrium reaction and the reaction goes partway to completion. We can say using language we've developed in different portions of the course, surely the reason that the reaction only proceeds partway is because from a probabilistic point of view, that's more probable than any other outcome. Or if we want to phrase that in terms of thermodynamics, we have a couple of different ways of talking about that. We could say that that's the outcome that maximizes the entropy of the universe, or that's the outcome that minimizes the free energy of the system, or if we want to use chemical potential, we could say the chemical potential is equal for the products and the reactants when we reach equilibrium. If we want to depict that visually, the language, for example, of saying that a reaction experiences a minimum in its free energy when it's at equilibrium, we can say, for example, if the reaction doesn't proceed at all, it has some free energy. If it proceeds all the way to completion, so this axis, we'll talk more about what this axis is exactly coming up soon, but if the reaction doesn't proceed at all, it has some free energy. If it proceeds all the way to completion, it might have some different free energy, and at every point in between, it has some different value of the free energy. When the free energy is minimized at some value other than 0% or 100% completion for the reaction, then we say that the reaction reaches equilibrium at some intermediate extent of the reaction. In order to discuss this a little more quantitatively, we'll start to employ the tools that we've used to describe free energies like partition functions and other thermodynamic equations to help us determine exactly where that minimum in the free energy is, so we can start to make some quantitative predictions about when a reaction will reach equilibrium.