When liquid and vapour phase of multi-component system are in equilibrium (at a given temperature and pressure), then chemical potential of each component is

For thermodynamic equilibrium to satisfy by a system the system should satisfies three conditions
I. Temperature should be same between the phases.
II. Pressure should be same between the phases.(actually the system should not include in any of the work with the surroundings not only in expansion work).
III. Chemical potential between the phases should be same which ensures the equilibrium in mass transfer between the phases.