Physical Chemistry , 1st ed.

Solution

There are three distinct phases in this equilibrium, a solid ferric sulfate phase,

a solid ferric oxide phase, and a gaseous phase. Therefore,P3. As with the

H 2 O dissociation, there are only two independent components in this equi-

librium. (The amount of the third component can be determined from the

stoichiometry of the reaction.) Therefore C2. Using the Gibbs phase rule,

F 2  3  2

F 1

7.3 Two Components: Liquid/Liquid Systems

An understanding of the Gibbs phase rule for multicomponent systems al-

lows us to consider specific multicomponent systems. We will focus on two-

component systems for illustration, although the concepts are applicable to

systems with more than two components.

Let us consider a binarysolution that is composed of two liquid compo-

nents that are not interacting chemically. If the volume of the liquid is equal

to the size of the system, then we have only one phase and two components,

so the Gibbs phase rule says that we have F 2  1  2 3 degrees of free-

dom. We can specify temperature, pressure, and mole fraction of one compo-

nent to completely define our system. Recall from equation 3.22 that the mole

fraction of a component equals the moles of some component i,ni,divided by

the total number of moles of all components in the system,ntot:

mole fraction of component ixi

n

n

to

i

t

 (7.4)

The sum of all of the mole fractions for a phase in a system equals exactly 1.

Mathematically,



i

xi 1 (7.5)

This is why we need specify only one mole fraction in our binary solution. The

other mole fraction can be determined by subtraction.

If, however, the volume of liquid is less than the volume of the system, then

there is some “empty” space in the system. This space is not empty but filled

with the vapors of the liquid components. In all systems where the liquid vol-

ume is less than the system volume,the remaining space will be filled with each

component in the gas phase,as shown in Figure 7.2.* If the system has a single

component, then the partial pressure of the gas phase is characteristic of only

two things: the identity of the liquid phase, and the temperature. This equilib-

rium gas-phase pressure is called the vapor pressureof the pure liquid. In a two-

component liquid solution in equilibrium with its vapor, the chemical poten-

tial for each component in the gas phase must be equal to the chemical potential

in the liquid phase:

i() i(g) for i1, 2

ni





all i

ni

7.3 Two Components: Liquid/Liquid Systems 169

*In many cases, the same statement applies if the system has a solid phase that does not

completely fill the system. “Freezer burn” is one example of this happening to solid H 2 O.

System

H 2 O (g)



C 2 H 5 OH (g)

H 2 O ( )



C 2 H 5 OH ( )

Figure 7.2 Systems with more volume than
condensed phase will always have a vapor phase
in equilibrium with that condensed phase.
Although we usually picture liquid in equilib-
rium with vapor, in many cases solid phases also
exist in equilibrium with a vapor phase.