Thermodynamics and Chemistry

CHAPTER 13 THE PHASE RULE AND PHASE DIAGRAMS

13.2 PHASEDIAGRAMS: BINARYSYSTEMS 433

function ofxA. The mole fraction composition of the gas in the two-phase system is given
by

yAD

pA

p

D

xApA

pBC.pApB/xA

(13.2.5)

A binary two-phase system has two degrees of freedom. At a givenTandp, each phase
must have a fixed composition. We can calculate the liquid composition by rearranging Eq.
13.2.4:

xAD

ppB

pApB

(13.2.6)

(CD 2 , ideal liquid mixture)

The gas composition is then given by

yAD

pA

p

D

xApA

p

D



ppB

pApB



pA

p

(13.2.7)

(CD 2 , ideal liquid mixture)

If we knowpAandpBas functions ofT, we can use Eqs.13.2.6and13.2.7to calculate the
compositions for any combination ofTandpat which the liquid and gas phases can coexist,
and thus construct a pressure–composition or temperature–composition phase diagram.
In Fig.13.6(a), the liquidus curve shows the relation betweenpandxAfor equilibrated
liquid and gas phases at constantT, and the vaporus curve shows the relation betweenp
andyAunder these conditions. We see thatpis a linear function ofxAbut not ofyA.
In a similar fashion, the liquidus curve in Fig.13.6(b) shows the relation betweenTand
xA, and the vaporus curve shows the relation betweenTandyA, for equilibrated liquid and
gas phases at constantp. Neither curve is linear.
A liquidus curve is also called abubble-pointcurve or aboiling-pointcurve. Other
names for a vaporus curve aredew-pointcurve andcondensationcurve. These curves are
actually cross-sections of liquidus and vaporussurfacesin a three-dimensionalT–p–zA
phase diagram, as shown in Fig.13.7on the next page. In this figure, the liquidus surface is
in view at the front and the vaporus surface is hidden behind it.

13.2.5 Liquid–gas systems with nonideal liquid mixtures

Most binary liquid mixtures do not behave ideally. The most common situation ispositive
deviations from Raoult’s law.^5 Some mixtures, however, have specific A–B interactions,
such as solvation or molecular association, that prevent random mixing of the molecules
of A and B, and the result is thennegativedeviations from Raoult’s law. If the deviations
from Raoult’s law, either positive or negative, are large enough, the constant-temperature
liquidus curve exhibits a maximum or minimum andazeotropicbehavior results.
Figure13.8on page 435 shows the azeotropic behavior of the binary methanol-benzene
system at constant temperature. In Fig.13.8(a), the experimental partial pressures in a

(^5) In the molecular model of Sec.11.1.5, positive deviations correspond to a less negative value ofkABthan the
average ofkAAandkBB.