Page 134 - Modern physical chemistry

6.10 Variation of Vapor Pressure with Concentration 125

Here IlP is the excess pressure on a condensed phase with molar volume V(l) while IlPA
is the resulting increase in vapor pressure P A'

Example 6.5
Determine the partial pressure of water in a gas saturated with water vapor at 6.00
atm and 25 C. At this temperature the vapor pressure of pure water is 23.8 torr.
0
The change in total pressure is

IlP == 6.00 atm - 23.8 torr == 5.969 atm.
760 torr atm- 1
Solve (6.47) for IlPA and insert the data together with the value of R from equation (3.31):

1 23 8
5 969
IlPA == ~lfAIlP == (0.0181 mol- X . torrX . atm) == 0.10 torr.
RT (0.082061 atm K- 1 mol- 1 X298.15 K)
The final vapor pressure is
PA == 23.8 torr + 0.10 torr == 23.9 torr.

6. 10 Variation of Vapor Pressure with Concentration
When two phases are in equilibrium, the various molecules leaving one phase per unit
time balance those leaving the other phase and entering the first phase per unit time. For
a solution of A and B in a condensed phase interacting with a gaseous phase, we have
the equilibria
A(c) ( ) A(g) [6.48]
and
B(c) ( ) B(g) [6.49]
Here c identifies the condensed phase and g the gaseous phase.
Decreasing the rate of either process (6.48) or (6.49) to the right decreases the bal-
ancing rate to the left. But the latter decrease implies a decrease in the corresponding
vapor pressure. In our discussion, let us keep the temperature T constant and neglect
the effect of changing the total pressure on either vapor pressure.
If the average interactions between neighboring A molecules, neighboring B mole-
cules, and neighboring A and B molecules are effectively the same and if A and B mole-
cules occupy similar cross sections at the surface of the condensed phase, a molecule
of A would exhibit the same tendency to leave as it would at the surface of pure con-
densed A Furthermore, the number of Ks per unit area of surface would be proportional
to the mole fractionX A in the condensed phase. So the resulting partial pressure P A would
be proportional to X B • But since the vapor pressure of pure A is P AO, the constant of pro-
portionality equals this number.
Raoult's law
[6.50]