CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS
12.8 LIQUID–GASEQUILIBRIA 404
possible because both fugacity curves have two inflection points instead of the usual one.
Other types of unusual nonideal behavior are possible.^13
12.8.3 The Duhem–Margules equation
When we divide both sides of Eq.12.8.6by dxA, we obtain theDuhem–Margules equa-
tion:
xA
fA
dfA
dxA
D
xB
fB
dfB
dxA
(12.8.18)
(binary liquid mixture equilibrated
with gas, constantTandp)
If we assume the gas mixture is ideal, the fugacities are the same as the partial pressures,
and the Duhem–Margules equation then becomes
xA
pA
dpA
dxA
D
xB
pB
dpB
dxA
(12.8.19)
(binary liquid mixture equilibrated
with ideal gas, constantTandp)
Solving Eq.12.8.19for dpB=dxA, we obtain
dpB
dxA
D
xApB
xBpA
dpA
dxA
(12.8.20)
To a good approximation, by assuming an ideal gas mixture and neglecting the effect
of total pressure on fugacity, we can apply Eq.12.8.20to a liquid–gas system in which the
total pressure isnotconstant, but instead is the sum ofpAandpB. Under these conditions,
we obtain the following expression for the rate at which the total pressure changes with the
liquid composition at constantT:
dp
dxA
D
d.pACpB/
dxA
D
dpA
dxA