Physical Chemistry , 1st ed.

which is one form of the Clausius-Clapeyron equation.This equation can also
be integrated between two sets of conditions, (p 1 ,T 1 ) and (p 2 ,T 2 ). If we as-
sume constant Hover the temperature range, we get

ln

p

p

1

2





R

H

(^) 
T

1

1



T

1

2

(^)  (6.14)
The Clausius-Clapeyron equation is very useful in considering gas-phase equi-
libria. For example, it helps predict equilibrium pressures at differing temper-
atures. Or it can predict what temperature is necessary to generate a particu-
lar pressure. Or pressure/temperature data can be used to determine the change
in enthalpy for the phase transition.
Example 6.7
All liquids have characteristic vapor pressuresthat vary with temperature. The
characteristic vapor pressure for pure water at 22.0°C is 19.827 mmHg and
at 30.0°C is 31.824 mmHg. Use these data to calculate the change in enthalpy
per mole for the vaporization process.
Solution
We must convert temperatures to kelvins, so those become 295.2 and 303.2 K.
Using equation 6.14:
ln

1

3

9

1

.

.

8

8

2

2

7

4

m

m

m

m

H

H

g

g

 

295

1

.2 K



303

1

.2 K

(^) 
Evaluating:
0.47317
8.31



4

H

J/mol

(8.938
10 ^5 )

H (

(

0

8

.4

.9

7

3

3

8

17

)(

1

8

0

.3



1

5

4

)

)J/mol 44,010 J/mol

The heat of vaporization,vapH, of water is 40.66 kJ/mol at its normal boil-

ing point of 100°C. At 25°C, it is 44.02 kJ/mol—very close to what is pre-

dicted by the Clausius-Clapeyron equation. (Note, however, that vapHvaries

by more than 3 kJ/mol over a temperature range of 75°, illustrating that

vapHdoes vary with temperature.)

Example 6.8

The vapor pressure of mercury at 536 K is 103 torr. Estimate the normal

boiling point of mercury, where the vapor pressure is 760 torr. The heat of

vaporization of mercury is 58.7 kJ/mol.

Solution

Using the Clausius-Clapeyron equation, we have

ln  1

7

0

6

3

0

t

t

o

o

r

r

r

r



8

5

.3

8

1

,7

4

00

J/K

J

^53

1

6K



T

1

BP

(^) 
where TBPrepresents the normal boiling point. Rearranging and canceling
the appropriate units, we get
0.000283 K^1 0.00187 K^1 
T

1

BP

H

8.314^ moJl^ K

6.5 The Clausius-Clapeyron Equation 153