 So it gets boring if we can only compare things with theoretical equations. We need a way to relate these free energies to experiments. The problem is that I can measure energy in terms of how much heat, for instance, I'm putting into a system, but there is no trivial way of directly getting the free energy on a meter. But it turns out to be easier to get them anyway. So assuming that I have two systems or a system that can be divided, this could be concentrations in A versus concentration in B, or pretty much anything you can count. It could be membrane proteins inserting or in a membrane, or the ones that don't insert in a membrane. And I would like to compare these two states. So if I have a state A and a B, I could then say that the probability in being in A relative to the probability of being in B, you know that. You're going to use the Boltzmann distribution. That corresponds E raised to minus G A divided by RT. We're going to be chemists today. Raise to E raised to minus G B divided by RT, which we can write as E raised to minus delta G when going from B to A divided by RT. That doesn't look like a simplification, but it is because in the next time I can now solve this for delta G. And that means that delta G going from B to A equals minus RT L m P A divided by P B. The point here is that the P A's and the P B's are the stuff we can get from experiments. This can be concentrations in this class, but it could also be anything you can count. The second you have something you can compare, take the quotient, the logarithm, and then you will get the free energy from it. So this allows us to get delta G where we previously only had concentrations or counts. We are going to use that for a couple of simple cases. So let's start with a simple hydrocarbon. Why do we want to start with a simple hydrocarbon? Well, if I take something like a protein here, very small protein, just two alanine molecules. We have these side chains. We have the backbone and we're going to look into that in great detail in lecture 5. But the backbone is the same for all amino acids. What I'm interested in here are the things that differ from one residue to another and that's going to be the side chain. In this case, it's alanine that has a CH3 group as a side chain. So let's tear off that side chain. And when I add a hydrogen to it, and voila, what I have is no longer a side chain but a methane molecule. So the properties of methane is a very good, even outstanding approximation of the properties of the side chain on alanine. And this turns out to be the case for virtually all amino acid side chains. There is a corresponding small molecule analog that we can study as a pure compound and then understand the properties of that side chain. And in particular, that means that we should start by studying the solubility of simple hydrocarbons in water and see if we can use that to get at these free energies.