Physical Chemistry Third Edition

5.3 Phase Equilibria in One-Component Systems 205

PROBLEMS

Section 5.2: The Gibbs Phase Rule

5.5Give the number of independent intensive variables for

each of the following systems at equilibrium:

a.SO 2 ,SO 3 , and O 2 in a one-phase gaseous system, with

the chemical reaction among these substances at

equilibrium and with each substance added

separately.

b. The same substances as in part a, but with the system

produced by placing only SO 3 in the container.

c.N 2 ,H 2 , and NH 3 in a one-phase gaseous system, with

each substance added separately and allowed to come

to chemical equilibrium by the equation

N 2 (g)+3H 2 (g)
2NH 3 (g)

d.NH 3 (g) placed in a container and allowed to come to

chemical equilibrium according to the equation of the

previous part.

e.Ice VI, ice VII, and ice VIII.

5.6Give the number of independent intensive variables for

each of the following systems at equilibrium:

a.Ice and liquid water.

b. Ice and water vapor.

c.CO, O 2 , and CO 2 in a single gas phase, with no catalyst

present so that the chemical reaction cannot equilibrate,

and with each substance added separately.

d.The system as in part c, but with a catalyst so that the

chemical reaction can equilibrate.

e.The system as in part c, but with the system prepared

by adding only CO 2.

5.7 Give the number of components and the number of

independent intensive variables for each of the following

systems at equilibrium:

a.H 2 ,I 2 , and HI in a single gas phase at a temperature

such that the following equilibrium can be

established:

H 2 +I 2 
2HI

b.CaCO 3 (s), CaO(s), and CO 2 (g) at a temperature such

that the following equilibrium can be established:

CaCO 3 (s)
CaO(s)+CO 2 (g)

c.An aqueous solution of acetic acid. Make a list of the

major species present in the solution.

5.8A researcher exhibits a photo showing four phases, which

he claims are ice I, ice II, liquid water, and water vapor.

What is your comment?

5.3 Phase Equilibria in One-Component Systems

In a phase diagram such as that of Figure 1.4, the temperature is plotted on the hori-

zontal axis and the pressure is plotted on the vertical axis. An open area represents

a single phase. For a one-component one-phase system the number of independent

intensive variables at equilibrium is

f 1 − 1 + 2 2 (one component, one phase)

The temperature and pressure can both be independent, and any point in the area can

represent a possible intensive state of the system. For one component and two phases,

the number of independent intensive variables at equilibrium is

f 1 − 2 + 2 1 (one component, two phases)

The pressure must be a function of the temperature:

PP(T)(c1,p2) (5.3-1)