Physical Chemistry Third Edition

212 5 Phase Equilibrium

Exercise 5.8

The normal boiling temperature of ethanol is equal to 78. 5 ◦C and the molar enthalpy change of

vaporization is equal to 40.5 kJ mol−^1. Estimate the vapor pressure of ethanol at 100. 0 ◦C.

If the enthalpy change of a particular substance is not known, and one wishes to

estimate the vapor pressure of a liquid at one temperature from knowledge of the vapor

pressure at another temperature, Trouton’s rule (see Section 3.4) can be used as an

approximation.

EXAMPLE 5.6

The normal boiling temperature of chloroform is 61. 7 ◦C. Estimate the vapor pressure of

chloroform at 50. 0 ◦C, using Trouton’s rule to estimate∆vapHm.

Solution

∆vapHmT∆vapSm≈(334.8 K)(88 J K−^1 mol−^1 ) 2. 95 × 104 J mol−^1

ln

(

P 2

P 1

)

≈

∆vapHm

R

(

1

T 2

−

1

T 1

)

ln

(

P 2

1 .00 atm

)

≈−

29500 J mol−^1

8 .3145 J K−^1 mol−^1

(

1

323 .15 K

−

1

334 .8K

)

≈− 0. 382

P 2 (1.000 atm)e−^0.^382  0 .68 atm520 torr69 kPa

Exercise 5.9

Estimate the vapor pressure of chloroform at 50. 0 ◦C, using the experimental value of the enthalpy

change of vaporization, 31.38 kJ mol−^1.

A modified version of the Clausius–Clapeyron equation can be derived using the

assumption that∆CP, mis constant:

∆Hm(T)∆Hm(T 1 )+∆CP, m(T−T 1 )

The derivation of this equation is assigned in Problem 5.27.

The Effect of Total Pressure on the Vapor Pressure

The vapor pressure that we have discussed thus far is measured with no other substances

present. We are often interested in the vapor pressure of a liquid that is open to the

atmosphere. The other gases in the atmosphere exert an additional pressure on the liquid

that modifies its vapor pressure. Small amounts of the other gases dissolve in the liquid,

but we neglect these impurities in the liquid. Denote the vapor pressure corresponding

to a total pressure ofP′byP. From the fundamental fact of phase equilibrium for a

one-component system,

Gm(liq)Gm(gas) (5.3-16)