One corollary to this equation gives the ratio of activity to mole fraction for the constituents of a binary system as the ratio of derivatives of activities with respect to mole fractions at constant pressure and temperature.
One corollary to this equation gives the ratio of activity to mole fraction for the constituents of a binary system as the ratio of derivatives of activities with respect to mole fractions at constant pressure and temperature. It can be derived by substituting the temperature and pressure Maxwell relations into the usual differential of the Gibbs function, then equating the differential of the definition of the Gibbs function as a sum over species only. It sets differential pressure time volume equal to entropy times differential temperature plus sum over species of particle number times differential chemical potential. For 10 points, name this equation used in the usual derivation of the rule that the number of species plus the number of degrees of freedom minus the number of phases equals two.
One corollary to this equation gives the ratio of activity to mole fraction for the constituents of a binary system as the ratio of derivatives of activities with respect to mole fractions at constant pressure and temperature.
Gibbs-Duhem equation [prompt on Gibbs' phase rule]