11.11 A system of s components, Al, A2, …As, consists of p phases in contact, so that components can pass between them. The Gibbs free energy of the system is given by

(11.178)

where the index α( = 1, 2, …p) labels the p phases of the system, Ni(α) is the number of molecules of component i in the

αth phase, and G(α) is the Gibbs free energy of this phase. By considering a change of the system at constant temperature and pressure in which dN molecules of component 1 pass from 368 phase 1 to phase 2, all other particle numbers Ni(α) remaining the same, show that in equilibrium the chemical potential of component 1 has the same value in phases 1 and 2. Hence write down the equilibrium conditions for the passage of any component between different phases.