the Gibbs free energy
/ gibz /
Real chemistry and everyday phase changes happen not at fixed volume but out in the open, at the fixed temperature and pressure of the lab bench. The Gibbs free energy is the master potential for exactly those conditions: a system held at constant T and p spontaneously slides toward lower G and settles at its minimum. If G would decrease, the change happens by itself; if not, it will not.
It is defined as G = U - T S + p V = H - T S = F + p V, with natural variables temperature T, pressure p and particle number N, and differential dG = -S dT + V dp + sum mu_i dN_i. It is the double Legendre transform of U that trades entropy for temperature and volume for pressure. A key identity for a single pure substance is G = mu N, so the chemical potential is just the Gibbs energy per particle.
You meet G whenever equilibrium or spontaneity at constant T and p is the question: a reaction proceeds while sum nu_i mu_i < 0 and stops at chemical equilibrium; two phases coexist when their molar Gibbs energies (chemical potentials) are equal, which is the starting point for the Clausius-Clapeyron equation. Caveat: 'spontaneous' here means thermodynamically allowed, not fast — kinetics (activation barriers) can make a G-lowering change take geological time.
At 1 atm, ice and liquid water have equal molar Gibbs energies exactly at 273.15 K — that is why they coexist there. Just above it, liquid has the lower G and ice melts; just below, solid wins and water freezes. The phase you observe at given T and p is always the one with the smallest Gibbs free energy.
The equilibrium phase is the one that minimizes G at the given T and p.
delta G < 0 signals a thermodynamically favourable process at constant T and p, but says nothing about rate; diamond is metastable relative to graphite yet does not visibly convert.