The Gibbs-Helmholtz equation has several forms -- I prefer the following:
[∂(∆G/T)/∂(1/T)]P = ∆H
We can use this equation, as was done in class, to calculate ∆G at a new temperature as long as we know its value at another temperature, along with ∆H. We can also easily predict, by the sign of ∆H, which direction to take the temperature to increase or decrease ∆G.
Missing from all of our previous work this quarter has been allowing n, the number of moles, to vary. In developing these ideas that are central to chemistry, we define the notion of a partial molar function (in terms of any extensive variable Y) as [∂Y/∂ni]T,P,nj=Yi. In other words, how does Y respond to changes in ni, while every other variable is constant.
A particularly valuable partial molar function is the partial molar gibbs energy, which is usually called the chemical potential µi. We demonstrated how matter spontaneously moves from high to low chemical potential until material equilibrium is established, at which points the chemical potentials are equal. This last point will lead the way to developing a framework for quantifying chemical equilibria.