CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 212
7.8.1 Conditions of equilibrium at constant temperature and pressure
The intensive criterion of equilibrium (7.4) betweenfliquid phases in ak−component system
may be written in the form
x(1)i γ(1)i =x(2)i γ(2)i =.. .=x(if)γi(f), i= 1, 2 ,... , k. (7.55)If we know the composition of one liquid phase and the activity coefficients, we may use
equations (7.55) to calculate the composition of the other liquid phases.
Note: Given that activity coefficients are non-linear functions of composition [see e.g.
(6.114)], it is necessary to solve a set of non-linear equations when calculating the compo-
sition of the coexisting phases.7.8.2 Two-component system containing two liquid phases
The course of the binodal line for these systems is usually illustrated in isobaric diagramsT−x 1
[see Figure 7.9]. The composition of the coexisting phases varies with temperature, and the tie
lines run parallel to the axisx. Point C represents theupper critical temperature, which is
the highest temperature at which a system may split into two phases. There are also systems
with alower critical temperature, or those with both upper and lower critical temperatures.
7.8.3 Two-component system containing two liquid phases and one gaseous phase
At constant pressure, this system does not have any degree of freedom [see7.3]. Temperature
does not change until one of the phases disappears.
- Heterogeneous azeotrope
If two liquid phases are in equilibrium with a gaseous phase the composition of which
isy 1 ∈(x( 1^1 ), x( 1^2 )), we speak about a heterogeneous azeotrope [see Figure7.2, where
(α) = (g), (β) = (1 ), and (γ) = (2 )].