Beyond the basic chemical equilibrium context, to understand Gibbs free energy you need to understand thermodynamics in a "ground up" fashion. The thing is, I'm not sure even I understand thermodynamics in a ground up fashion. This was part of my motivation to start blogging on it: To keep me thinking about the concepts such that they might eventually click.
The thermodynamic approach I was taught started with quantum mechanics, moved into statistical mechanics, and ended on thermodynamics. What's nice, from a chemist's perspective, about this approach is that the quantum model of the atom elucidates a lot of qualitative understanding of the atom you pick up in earlier courses, such as bond strengths, aromaticity, and IR spectra (or spectroscopy in general). Then statistical mechanics utilizes the energy levels found in quantum mechanics to make macroscopic predictions from the quantum model through statistics (ergo: statistical mechanics).
However, when approaching thermodynamics, then, outside of the basic chemical approach linked to equilibrium, I found the study to be very odd. I have been acquainted with explaining macroscopic observations through microscopic models, so it was hard to think "Macroscopically", even though the mathematics was simpler. So, in approaching general thermodynamics I think it's important to remember what it is thermodynamics is trying to describe, as that is where I lost a conceptual foot-hold in the race (and resorted to math to get me through, as opposed to understanding the concept behind the math)
Literally, thermodynamics is describing the movement of heat. But more is involved than heat: there is also work. So the name isn't exactly the best. What helped me was in emphasizing the macroscopic nature of thermodynamics. It models a large system of particles within some kind of surrounding environment. We are free to define the system, so the system is chosen such that something interesting can be measured or for conveniences sake.
In this case, the system is a beaker with a piston. The little green dots are supposed to be particles of gas floating around inside the beaker. The system stops where the beaker begins, and the surroundings begin just after the system stops. This allows measurements of the gaseous behavior alone to be recorded.
Thermodynamically speaking, there are three quantities that define this system: Pressure, Temperature, and Volume. Of these three, you only need know two to know the third as they are related through the ideal gas law. (Note: There are more "equations of state", as they are called, than the ideal gas law. But it's the simplest and gets the point across)
However, the ideal gas law isn't enough. That just defines the "State" of the system. It doesn't tell us very much about how much energy is transferred from or to the system in going from one state to another. And that, I think, is the best way to think about thermodynamics: the amount of energy transferred in moving from one state to another in a macroscopic system. Macroscopic states can be defined by the three variables of P, V, and T, and the movement between these states requires energy to enter or leave the system. How much energy enters or leaves depends upon the way in which one moves from one state to another.
That leads to the first law of thermodynamics. There are many ways of stating this law, but when trying to understanding how much energy passes into or out of a system due to a process the following is used:
ΔU = W + q
Where "U" is the "Internal Energy", W is work, and q is heat. Internal energy, to me, is a weird concept. It's this energy that's.... there?... inside the system 'n stuff? Yes. That's exactly it. Personally, I'm still wrapping my head around the concept -- the best I can do is to say that it represents every shred of energy that is within the system, from the vibration of bonds, the momentum of molecules, the mass of the atoms, the potentials of fields, EVERY source of energy that happens to be within the system. That.... I think is it. And, frankly, we don't even care about the total internal energy, but rather the changes in internal energy, because those are much easier to measure than absolute internal energies. (ergo: Δ)
So, changes occur in internal energy, and those changes are equal to work and heat. These are the processes by which energy is removed from or added to a system. They both transfer energy, but they do so in different ways. For now it is enough to understand that the changes in internal energy occur through the two processes (or mechanism, or "How-to", if that makes more sense?) of work and heat. What those processes encompass I'll blog about later.