CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 195
7.6 Liquid-vapour equilibrium in mixtures
This section deals with the relations between temperature, pressure, liquid composition and
vapour composition during the boiling and condensation of mixtures. These relations are needed
for the description of one of the major separation methods, distillation.
7.6.1 The concept of liquid-vapour equilibrium
Let us consider a multicomponent system formed by two coexisting phases (liquid and gaseous),
in the state of thermodynamic equilibrium. We usually speak about liquid-vapour equilibrium
(in contrast to liquid-gas equilibrium [see7.7]) when all components of the system are below
their critical temperatures at a given temperature.
7.6.2 Raoult’s law.
When ak−component mixture in the vapour phase behaves as an ideal gas and in the liquid
phase forms an ideal solution [see6.1.1], we can write for each component of the system
p yi=xipsi, i= 1. 2 ,... , k , (7.23)whereyiis the molar fraction of theithcomponent in the vapour phase, which is at pressure
pand temperatureT (psi =psi(T), see7.5.3) in equilibrium with the liquid phase in which
the molar fraction of theithcomponentxi. The condition for equilibrium between the liquid
and vapour phase written in this way is calledRaoult’s law. In order to find out at which
temperatures, pressures and compositions of both the vapour and liquid phase a system may
be in equilibrium, it is sufficient to know the temperature dependence of the saturated vapour
pressure for all components present in the system.
In order to determine the state of ak−component two-phase system, we need to determine
2 k[see7.3] values, i.e.T, p, x 1 ,... , xk− 1 , y 1 ,... , yk− 1. Since it is possible to writekequilibrium
conditions of the type (7.23), it is always necessary to specifykarbitrary quantities. For a binary
system obeying Raoult’s law, this situation is analyzed in the following table.