The Gibbs Phase Rule: What Happens When Some Phases Lack Some Components?

Abstract

The derivation for the Gibbs phase rule, provided in physical chemistry text books, often assumes that all the components are present in all the phases coexisting at equilibrium. However, very often we have situations where all the phases at equilibrium do not have all the components, the binary eutectic system being a classic example. The melt (miscible solution of A and B) coexists with pure solid A and pure solid B at the eutectic point. The solid phases are one-component phases, whereas the system itself is binary. How does the phase rule, derived under the above-mentioned assumption, apply to the eutectic point? Using a simple example, we demonstrate that all the components need not be present in all the phases to arrive at the phase rule.

Liquid–Liquid Demonstrations: Phase Equilibria and the Lever Rule

“…One especially challenging concept concerns the equilibrium state of a two-component system when two phases α and β are present. According to the Gibbs phase rule, − such a system has no degrees of freedom under isothermal and isobaric conditions: the compositions of α and β remain unchanged even as one or the other pure component is added to the system (provided the system remains in two phases). Instead, only the extensive amounts of α and β change.…”