Physical Chemistry Third Edition

200 5 Phase Equilibrium

5.1 The Fundamental Fact of Phase Equilibrium

The principal business of this chapter is to establish the thermodynamic relations obeyed

by two or more phases that are at equilibrium with each other. Aphaseis a portion

of a system (or an entire system) inside which intensive properties do not change

abruptly as a function of position. The principal kinds of phases are solids, liquids,

and gases, although plasmas (ionized gases), liquid crystals, and glasses are sometimes

considered to be separate types of phases. Solid and liquid phases are calledcondensed

phasesand a gas phase is often called avapor phase.Several elements such as carbon

exhibit solid-phaseallotropy. That is, there is more than one kind of solid phase of the

element. For example, diamond and graphite are both solid carbon, but have different

crystal structures and different physical properties. With compounds, this phenomenon

is calledpolymorphisminstead of allotropy. Most pure substances have only one liquid

phase, but helium exhibits allotropy in the liquid phase.

In a multicomponent system there can often be several solid phases or several liquid

phases at equilibrium. For example, if one equilibrates mercury, a mineral oil, a methyl

silicone oil, water, benzyl alcohol, and a perfluoro compound such as perfluoro (N-ethyl

piperidine) at room temperature, one can obtain six coexisting liquid phases.^1 Each of

these phases consists of a large amount of one substance with small amounts of the

other substances dissolved in it. Under ordinary conditions, a system can exhibit only

a single gas phase. However, if certain gaseous mixtures are brought to supercritical

temperatures and pressures, where the distinction between gas and liquid disappears,

two fluid phases can form without first making a gas–liquid phase transition.

Equilibrium between Phases

An equilibrium two-phase simple system containing several substances is depicted

schematically in Figure 5.1. This system is closed to the surroundings, but each phase

is open to the other and both phases are at the same temperature and pressure. If the

contribution of the surface area between the phases is negligible (a good approximation

in most cases), the Gibbs energy of the system is the sum of the Gibbs energies of the

two phases:

GG(I)+G(II) (5.1-1)

where we denote the two phases by the superscripts (I) and (II).

Piston to exert

external pressure

Phase II

Phase I

Figure 5.1 A Two-Phase Simple
System.

The substances in the system whose amounts can be varied independently are called

components. We denote the number of components byc. Since the system is closed, if

component numberimoves out of one phase it must move into the other phase:

dn(I)i −dn(II)i (5.1-2)

For an infinitesimal change of state involving changes inTandPand a transfer of

matter from one phase to the other,

dGdG(I)+dG(II)

−S(I)dT+V(I)dP+

∑c

i 1

μ(I)i dn(I)i −S(II)dT+V(II)dP+

∑c

i 1

μ(II)i dn(II)i

(5.1-3)

(^1) J. Kochansky,J. Chem. Educ., 68 , 653 (1991).