In today's lecture, we showed how the chemical potential μi (aka the partial molar gibbs energy) naturally leads to the way we have written equilibrium constants since we first began studying chemistry. Along the way, we learned why solids and liquids are typically not included in the equilibrium expression [aka mass-action expression]: because their chemical potentials do not appreciably vary from their standard states, unless subjected to significant pressures.
A very important equation in chemical thermodynamics is ∆G=∆G° + RT lnQ, where Q is the reaction quotient. Recall from previous courses that this parameter tells us how far away from equilibrium we are and which direction a process will go to get there. This relationship is also a jumping off point for electrochemistry and kinetics, both of which we will examine in detail next quarter. Coupled with that is the equally important ∆G° =– RT lnK.
Treating real gases, using the van der Waals equation, in a brute-force mathematical way would have destroyed the elegance of our equilibrium constant, so, instead, a new function that captures the nonideality of gases was introduced: fugacity. We define the fugacity through the chemical potential: μ = μo + RT ln f. The fugacity can be calculated through methods outlined in class and, in principle, would replace the partial pressures in the equilibrium constant.
A note on the rest of the quarter: My plan is, before the last day, to get through Chapter 8, which is phase changes and diagrams, with one added half-lecturette on the Gibbs Phase Rule. Even though Chapter 9 is in the syllabus/schedule, we will cover that next quarter in Chem 352 (when we do solutions outright). This is, in fact, how I always teach this series, I had just forgotten that Chapter 9 was solutions.