Thermodynamics and Chemistry

CHAPTER 13 THE PHASE RULE AND PHASE DIAGRAMS

13.2 PHASEDIAGRAMS: BINARYSYSTEMS 432

g + l

liquidus

vaporus

liquid

gas

0

0:2

0:4

0:6

0:8

0 0:2 0:4 0:6 0:8 1:0

benzene zA toluene

(a)

p=

bar

g + l

liquidus

gas vaporus

liquid

350

360

370

380

390

0 0:2 0:4 0:6 0:8 1:0

benzene zA toluene

(b)

T=

K

Figure 13.6 Phase diagrams for the binary system of toluene (A) and benzene (B).

The curves are calculated from Eqs.13.2.6and13.2.7and the saturation vapor pres-

sures of the pure liquids.

(a) Pressure–composition diagram atTD 340 K.

(b) Temperature–composition diagram atpD 1 bar.

pressures of the pure liquids to generate the liquidus and vaporus curves of the pressure–
composition and temperature–composition phase diagram. The results are shown in Fig.
13.6. The composition variablezAis the overall mole fraction of component A (toluene).
The equations needed to generate the curves can be derived as follows. Consider a
binary liquid mixture of components A and B and mole fraction compositionxAthat obeys
Raoult’s law for partial pressure (Eq.9.4.2):

pADxApA pBD.1xA/pB (13.2.3)

Strictly speaking, Raoult’s law applies to a liquid–gas system maintained at a constant pres-
sure by means of a third gaseous component, andpAandpBare the vapor pressures of
the pure liquid components at this pressure and the temperature of the system. However,
when a liquid phase is equilibrated with a gas phase, the partial pressure of a constituent of
the liquid is practically independent of the total pressure (Sec.12.8.1), so that it is a good
approximation to apply the equations to abinaryliquid–gas system and treatpAandpBas
functions only ofT.
When the binary system contains a liquid phase and a gas phase in equilibrium, the
pressure is the sum ofpAandpB, which from Eq.13.2.3is given by

pDxApAC.1xA/pB

DpBC.pApB/xA (13.2.4)

(CD 2 , ideal liquid mixture)

wherexAis the mole fraction of A in the liquid phase. Equation13.2.4shows that in the
two-phase system,phas a value betweenpAandpB, and that ifTis constant,pis a linear