One thing I have never got to grips with is Gibbs Free Energy. I can see the way to do chemical calculations using it but that doesn't tell you what it is. Every time I have come across it in thermodynamics, I have not understood what it is about. So I have been delving into the wonderful Great Physicists book which has the best account I've seen. I taught that Internal Energy U is the sum of the kinetic and potential energies of the particles. This can be affected by heat energy and mechanical work, which would increase the kinetic energy of the particles. I used to teach this as "hit it or heat it". But the potential energies can be affected by chemical reactions and the total number of particles will also affect the sum of kinetic and potential energies. The work on Gibbs Free Energy is going to lie in this area.
