Molar Gibbs free energy ($G_m$)

The molar Gibbs free energy is the Gibbs free energy per amount of substance, $G_m=G/n$, with units $\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}$. For a homogeneous pure substance, extensivity gives $G=n\mu$, so $G_m$ equals its chemical potential $\mu$.

For a mixture, $G/n$ is an average over the components; the separate chemical potentials are the partial derivatives ${\mu }_i=(\partial G/\partial n_i{)}_{T,p,n_{j\ne i}}$. Equality of a component's chemical potential in two phases is a condition for phase equilibrium. This explains why comparing molar free energies predicts which phase of a pure substance is stable at specified temperature and pressure.