Page 132 - Modern physical chemistry

6.8 Variation of Vapor Pressure with Thmperature 123

From (6.30), we obtain the fonnula

dT= TAV dP.
L
During the small change here, the coefficient of dP is approximately constant. So we have

AT= TAV AP.
L
In applying this fonnula, the energy units in L and in A V AP must be the same. From
example 3.3, the number of joules in 1 cm 3 atm is 0.101325. But 760 torr is 1 atm. So here

AP = -755.4 torr 0.101325 J cm-3 atm-l = -0.100712 J cm-3.
760 torr atm- l

Substituting into the fonnula now gives

(273.15 KX-0.0906 cm g-lX-O.100712 J cm-3)
3
AT = = 0.0075 K.
333.5 J g-l

6.8 Variation of Vapor Pressure with Temperature
Below the pertinent critical point, transition from a condensed phase to vapor is first
order. The Clapeyron equation then applies, with P the vapor pressure, T the tempera-
ture, L the heat of transition and V the volume for the given amount of pure substance.
Here this amount is taken to be 1 mole.
To integrate equation (6.30), one needs the dependence of AV and L on T. As an
approximation, we neglect the volume of 1 mole in the condensed phase:

[6.39]

Furthennore, we consider the vapor to be an ideal gas:
RT
\(2) ~p. [6.40]

These two approximations transfonn (6.30) to the fonn

dP LP
-=--, [6.41 ]
dT RT2
which is called the Clausius - Clapeyron equation. Let us rearrange equation (6.41),

dP LdT
[6.42]
p= RT2 '
and introduce a third approximation, that L be constant. Integration then leads to the
fonnula
lnP=- L ..!.+c. [6.43]
RT
Thus, a plot of the logarithm of the vapor pressure P against the reciprocal of the
absolute temperature liT is apprOximately linear with the slope -LIR.