CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS
12.8 LIQUID–GASEQUILIBRIA 403
fB
fA
0
10
20
30
40
0 0:2 0:4 0:6 0:8 1:0
xB
fA
=kPa and
fB
=kPa
Figure 12.11 Fugacities in a gas phase equilibrated with a binary liquid mixture of
chloroform (A) and ethanol (B) at 35 C (Ref. [ 149 ]).
WhenDis zero, this equation becomes xBdfB=fB DdxA. WhenDis positive, the
left side of the equation is less than xBdfB=fBand is equal to dxA, so that dxAis less
than xBdfB=fB. SinceDcannot be negative, Eq.12.8.14is equivalent to the following
relation:
xB
fB
dfBdxA (12.8.15)
A substitution from Eq.12.8.6gives us
xA
fA
dfAdxA or
dfA
fA
dxA
xA
(12.8.16)
We can integrate both sides of the second relation as follows:^12
ZfA 0
fA
dfA
fA
Zx (^0) A
1
dxA
xA
ln
fA^0
fA
lnxA^0 fAxAfA (12.8.17)
Thus,if the curve of fugacity versus mole fraction for one component of a binary liquid
mixture exhibits only positive deviations from Raoult’s law, with only one inflection point,
so also must the curve of the other component. In the water–ethanol system shown in
Fig.12.10, both curves have positive deviations from Raoult’s law, and both have a single
inflection point.
By the same method, we find that if the fugacity curve of one component has only
negativedeviations from Raoult’s law with a single inflection point, the same is true of the
other component.
Figure12.11illustrates the case of a binary mixture in which component B has only
positive deviations from Raoult’s law, whereas component A has both positive and negative
deviations (fAis slightly less thanxAfAforxBless than 0.3). This unusual behavior is
(^12) The equalities are the same as Eqs.12.8.10and12.8.11, with the difference that herexAis not restricted to
the ideal-dilute region.