PHYSICAL CHEMISTRY IN BRIEF

CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 193

7.5.4 Solid-vapour equilibrium

This subsection deals with the temperature-pressure dependence at sublimation (vapour de-
position) in the temperature region from 0 K to the triple point temperature. The Clausius-
Clapeyron equation (7.14) and its integrated forms (7.15) and (7.16), in which theenthalpy
ofsublimation∆subHacts in place of ∆vapH, usually provide an excellent approximation all
over this region. The Antoine equation (7.17) is also commonly used.

7.5.5 Solid-liquid equilibrium.

This subsection deals with the temperature-pressure dependence at melting (freezing). The
Clapeyron equation (7.13) is used in this case. Its integral form is

p 2 =p 1 +

∫T 2

T 1

∆Hm

T∆Vm

dT , (7.18)

where ∆Hm= ∆fusH≡Hm(l)−Hm(s)is theenthalpy of melting (fusion), ∆Vm= ∆fusV ≡
Vm(l)−Vm(s)is the change in volume at melting, andp 1 , p 2 are pressures at melting temperatures
T 1 , T 2. ∆fusH, ∆fusV can be mostly considered constants. Equation (7.18) may then be
simplified to

p 2 =p 1 +

∆fusH

∆fusV

ln

T 2

T 1

. (7.19)

Example

The normal melting temperature of water is 0◦C. At this temperature the enthalpy of melting

∆fusH= 6008 J mol−^1 , the molar volumes of liquid water and ice areVm(l)= 18cm^3 mol−^1 , and

Vm(s)= 19. 8 cm^3 mol−^1. Assuming that neither the enthalpy of melting nor the molar volumes

change with temperature, calculate the pressure at which the melting temperature of water is

− 1 ◦C.