Physical Chemistry Third Edition

6.1 Ideal Solutions 245

If the pressure is taken as an independent variable, the mole fractions in the two phases,

represented by the ends of the tie line, are dependent variables.

Temperature–Composition Phase Diagrams

In this type of phase diagram the pressure is held fixed. For two components the mole

fraction of one component is plotted on the horizontal axis and the temperature is plot-

ted on the vertical axis. Figure 6.3 shows the liquid–vapor temperature–composition

diagram of benzene and toluene at 1.000 atm. The upper curve gives the boiling tem-

perature at the given pressure as a function of the mole fraction of benzene in the vapor

phase, and the lower curve gives the boiling temperature at the given pressure as a func-

tion of the mole fraction of benzene in the liquid phase. The tie lines drawn between

the two curves connect values of the mole fraction in the two phases at equilibrium

with each other, giving the composition of one phase as a function of the composition

of the other phase at the temperature given by the height of the tie line. Each tie line

in this diagram must be the same as the tie line in a pressure–composition diagram

corresponding to the temperature of this diagram.

Area of

vapor states

400

390

380

370

360

350

340

0 0.2 0.4 0.6 0.8 10

Mole fraction of benzene

T/

K

Area of

liquid states Tie

line

area

Points

representing

coexisting

phases

Figure 6.3 The Liquid–Vapor Tem-

perature–Composition Phase Dia-

gram of Benzene and Toluene at 1.000

atm.Drawn from data of M. A. Rosanoff,

C. W. Bacon, and F. W. Schulze,J. Am.

Chem. Soc., 36 , 1993 (1914).

In order to represent the full equilibrium pressure-temperature-composition behav-

ior of a two-component system, a three-dimensional graph is required, as schematically

represented in Figure 6.4 for a nearly ideal liquid solution. There are two surfaces in this

diagram, and they coincide at the edges of the graph. A pressure–composition diagram

is created by passing a plane of constant temperature through the three-dimensional

Pressure at

constantT

Temperature

at constant P

Tie lines Plane of

constant

P

Plane of

constant

T

Region of

vapor states

X T

2

P

Figure 6.4 Perspective View of the Three-Dimensional Liquid–Vapor Phase Diagram

for an Ideal Solution (Schematic).