CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 177
7.2 Thermodynamic conditions of equilibrium in multiphase systems.
7.2.0.1 Extensive and intensive criteria of phase equilibrium
In the state of phase equilibrium, the coexisting phases have the same temperature and pressure.
Hence, the following criterion is applied in the study of phase equilibria [see3.4.6]
dG= 0, [T, p]. (7.1)From this equation and from the definition of the chemical potential of a component in a
mixture (6.65) we have
μi(1)=μ(2)i =···=μ(if), i= 1, 2 ,... , k , [T, p], (7.2)whereμ(ij)is the chemical potential of componentiin phasej,fis the number of phases, and
kis the number of components in the system.
From (7.2) and from the definition of the fugacity of a component in a mixture (6.74) we
have
fi(1)=fi(2)=···=fi(f), i= 1. 2 ,... , k , [T, p], (7.3)
wherefi(j)is the fugacity of componentiin phasej.
If we choose the same standard state in all phases, we can rearrange equation (7.3) using
(6.89) to obtain
a(1)i =ai(2)= ··· =a(if), i= 1. 2 ,... , k , [T, p], (7.4)wherea(ij)is the activity of componentiin phasej.
Equation (7.1) is called theextensive criterion of phase equilibrium(it is written
for the extensive thermodynamic functionG). Equations (7.2), (7.3), and (7.4) are called the
intensive criteria of phase equilibria(they are written for the intensive thermodynamic
functionsμi,fi,ai).
Note: When studying the phase equilibria of pure substances, it is totally unimportant
which of the criteria (7.1) through (7.4) we use. When studying the equilibria of mixtures,
we choose intensive criteria which state the conditions of equilibrium for each component.
If one of the phases is gaseous, it is practicable to choose criterion (7.3), while criterion (7.2)
is chosen for the solid-liquid equilibria, and criterion (7.4) for the liquid-liquid equilibria.