PHYSICAL CHEMISTRY IN BRIEF

CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 191

is negligible compared to the volume of the gas. The equation is a good approximation when
describing the temperature-pressure dependence at boiling (condensation), and at sublimation
(vapour deposition), provided that the system pressure is not very high.

Note:In equation (7.14) we denote the saturated vapour pressure using the agreed symbol

ps, while in equation (7.13) we do not use any special symbol for equilibrium pressure

becausepcan denote the saturated vapour pressure as well as the melting pressure or the

pressure of a crystalline transformation.

7.5.3 Liquid-vapour equilibrium

This subsection deals with the temperature-pressure dependence at boiling, i.e. the relation be-
tween the boiling temperature and the saturated vapour pressure in the region of temperatures
at which the liquid exists (i.e. from the triple point to the critical point).
In the vicinity of the normal boiling point and at temperatures lower than TNBP, the
Clausius-Clapeyron equation (7.14) is an excellent approximation. Its integral form is

ln

ps(T 2 )

ps(T 1 )

=

1

R

∫T 2

T 1

∆Hm

T^2

dT , (7.15)

where ∆Hm = ∆vapH ≡Hm(g)−Hm(l)is theenthalpy of vaporization(older term heat of
vaporization), andps(T 2 ), ps(T 1 ) are the saturated vapour pressures at temperaturesT 2 , T 1.
To calculate the integral we need to know the temperature dependence of the enthalpy of
vaporization. In a small temperature range, the enthalpy of vaporization can be considered
constant, and equation (7.15) turns into

ln

ps(T 2 )

ps(T 1 )

=

∆vapH

R

( 1

T 1

−

1

T 2

)

. (7.16)

Example

The normal boiling temperature of butane isT = 272. 7 K, its enthalpy of vaporization at this

temperature is∆vapH= 22.4 kJ mol−^1. Find out whether butane would boil at Mount Everest

at− 30 ◦C, where the atmospheric pressure is 32 kPa. Assume that the enthalpy of vaporization

does not depend on temperature.