Thermodynamic Principles of Phase Equilibria

The equilibrium conditions for phase equilibria can be derived in the simplest way using the Gibbs energy G. According to the second law of thermodynamics, the total Gibbs energy of a closed system at constant temperature and pressure is a minimum at equilibrium. If this condition is combined with the condition that the total number of moles of component i is constant in a closed system [Eq. (1), where is number of moles of component i in phase a], the equilibrium conditions given by Eq. (2) can easily be derived for a system of n phases and N components [7]. 

The chemical potential of component i in phase a is defined by Eq. (3), where g is the molar Gibbs energy. 

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