Physical Chemistry Third Edition

5.3 Phase Equilibria in One-Component Systems 213

LetP 1 be the vapor pressure whenP′P 1 ′and letP 2 be the vapor pressure when

P′P 2 ′. We assume the vapor phase to be ideal and assume the liquid to have a fixed

volume. Using Eqs. (4.4-14) and (4.4-4) we can write

∆Gm(liq)Vm(liq)(P 2 ′−P 1 ′)∆Gm(gas)RTln(P 2 /P 1 ) (5.3-17)

P 2 P 1 exp

(

Vm(liq)(P 2 ′−P 1 ′)

RT

)

(5.3-18)

EXAMPLE 5.7

At 298.15 K, the vapor pressure of water is equal to 23.756 torr if no other substance is

present. Calculate the vapor pressure of water if enough air is present in the vapor phase to

give a total pressure of 1.000 atm 760 .0 torr.

Solution

The molar volume of water at this temperature is 18.05 cm^3 mol−^1  18. 05 × 10 −^6 m^3

mol−^1.

Vm(liq)(P 2 ′−P 1 ′)

RT



(18. 05 × 10 −^6 m^3 mol−^1 )(760.0 torr− 23 .756 torr)

(8.3145 J K−^1 mol−^1 )(298.15 K)

(

101325 Pa

760 .0 torr

)

 7. 14 × 10 −^4

P(23.756 torr)e^7.^14 ×^10

− 4

 23 .772 torr

For many purposes, this increase in the vapor pressure due to atmospheric pressure is

negligible.

Exercise 5.10

Find the total pressure necessary to change the vapor pressure of water by 1.00 torr at 100. 0 ◦C.

PROBLEMS

Section 5.3: Phase Equilibria
in One-Component Systems

5.9Estimate the pressure at which diamond and graphite coexist

at equilibrium at 298.15 K. The density of

diamond is 3.52 g mL−^1 , and that of graphite is

2 .25 g mL−^1. The molar Gibbs energy of diamond is

higher than that of graphite by 2.90 kJ mol−^1 at

298 .15 K. Assume that each phase has constant

density. How accurate do you think this

assumption is?

5.10 The density of rhombic sulfur at 20◦Cis2.07 g cm−^3 ,

and the density of monoclinic sulfur at 20◦Cis

1 .957 g cm−^3. Assume that you can use these values at

25 ◦C. The Gibbs energy of formation of monoclinic

sulfur is 0.096 kJ mol−^1 , and the Gibbs energy of formation

of rhombic sulfur is equal to zero by

definition.

a. Estimate∆Gfor producing 1.000 mol of monoclinic

sulfur from rhombic sulfur at 101.0 bar and 298.15 K.

Assume that∆Vmis independent of pressure.