 So we've seen that we can calculate a pressure-based equilibrium from the Gibbs free energy change for a chemical reaction. So now that we've introduced the Gibbs free energy, let's see what that can tell us about the temperature dependence of the equilibrium constant. And in particular, that'll lead to something called the Van Tof equation. So to start with, let me write down, instead of this pressure-based equilibrium constant, which has some units of pressure, one over pressure, pressure raised to some coefficient for, depending on the reaction, there's units of pressure raised to some coefficient. For the moment, I'd rather deal with a unit-less equilibrium constant. So let's imagine we've converted this pressure-based equilibrium constant to a Kn, Kbn, Kln, Kx, for example, one of the equilibrium constants that doesn't have units. So I can either literally just drop the units from this expression and get rid of them and this is a unit-less quantity. I can instead think of, for example, if I want a Kx, that would be the Kp divided by a pressure raised to the delta nu. So that's going to end up cancelling these units of pressure, for example. But by whichever way we want to think about it, this K, whether it's a Kx or Kn or something, is either e to the minus delta g over RT, or it's e to the minus delta g over RT times some multiplicative constant. So if we use this unit-less equilibrium constant, we're going to be interested in temperature dependence of this quantity. But to make it a little more convenient, I'm going to take the natural log of it. So on the right side, I don't have e to the minus delta g over RT. I just have, and I'm going to write that as delta g over t, and then the 1 over R dependence separately. Because next what I want to do to talk about how those quantities change when I change the temperature is I'll take the temperature derivative. So on the left, I'm taking the temperature derivative of log K. On the right, the reason I pulled the 1 over R out separately is they don't depend on temperature. And then I need the temperature derivative of this quantity delta g over t. That quantity, temperature derivative of g over temperature, might look familiar, should look familiar. That's something that we understand using the Gibbs-Helmholtz relation. The Gibbs-Helmholtz equation tells us that the derivative of a Gibbs free energy over temperature is an enthalpy over t squared with a minus sign. So that's, I've only taken the result of the temperature derivative. I now have to multiply by negative 1 over R. So let me just write the negative becomes a positive, negative 1 over R becomes positive 1 over R delta h over t squared. So that's what I've got on the right side. The left side is still derivative of log of K with respect to temperature. So Gibbs-Helmholtz is what led us to this result. This result itself is called the van Tof equation. That's given us the beginnings of what we were after when I said we were interested in the temperature dependence of the equilibrium constant. It tells us when I change the temperature, the rate at which the log of the equilibrium constant is changing with temperature is proportional to the enthalpy, inversely proportional to the temperature squared with this proportionality constant of 1 over R. So I'm going to leave the results at this point, but we do add some more things to say about the van Tof equation. In particular, what I'll show you in the next video is an alternate way of arriving at the same van Tof equation result as well as why this equation is useful and how we can use it to tell us about how equilibrium constants change as we change the temperature.