PHYSICAL CHEMISTRY IN BRIEF

CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 223

7.10 Gas-solid equilibrium in mixtures

This section deals with the relations between temperature, pressure, and the composition of
phases during sublimation and vapour deposition of mixtures.

7.10.1 General condition of equilibrium

From the intensive criterion of equilibrium (7.2)μ(g)i =μ(s)i we may derive

ln

fi(g)/fi•,(g)

γi(s)x(s)i

=

∫T

Ts,i

∆subHi

RT^2

dT−

∫p

psi

∆subVi

RT

dp. (7.69)

For integration we need to know the dependence of the volume change during sublimation on
pressure, and the dependence of the enthalpy of sublimation of a pureithcomponent ∆subHion
temperature.Ts,iis the temperature of sublimation of a pureithcomponent,psiis the respective
saturated vapour pressure.

7.10.2 Isobaric equilibrium in a two-component system

For a binary mixture whose components form an ideal gaseous mixture over the solid phase of
pure crystals of component 1, we have (provided that ∆subHiis independent of temperature)

−lny(g) 1 =

∆subH 1

R

(

1

T

−

1

Tf, 1

)

, (7.70)

whereTf, 1 is the melting temperature of a pure substance 1. The same relation applies to
the second component. The common solution of the equations for both components gives the
temperature and composition at point E, which is called theeutectic point of vapour. Figure
7.16ashows the dependence of the vapour phase composition on temperature for this case.

7.10.3 Isothermal equilibrium in a two-component system

Let us consider a mixture whose components form an ideal gaseous mixture and are immiscible
in the solid phase. Given that the volume of the solid phase is usually much smaller than that