Physical Chemistry Third Edition

282 6 The Thermodynamics of Solutions

6.6 Phase Diagrams of Nonideal Mixtures

A complete two-component phase diagram requires three dimensions to plotT,P,

and the mole fraction of one component, as depicted in Figure 6.4. Two-dimensional

phase diagrams are produced by passing planes of constantTor constantPthrough

the diagram.

400

300

200

100

Mole fraction of ethanol

Tie line area

Area of

liquid states

Coexisting states

of two phases

Area of

vapor states

0 0.2 0.4 0.6 0.8 10

0

P

/torr

Figure 6.11 Pressure–Composition
Phase Diagram for Diethyl Ether–
Ethanol at 20◦C. The lower curve
shows the pressure as a function of
mole fraction in the vapor, and the upper
curve shows the pressure as a function
of mole fraction in the liquid. Drawn
from data in J. Timmermans,Physico-
chemical Constants of Binary Systems,
Vol. 2, Interscience Publishers, New
York, 1959, p. 401.

Liquid–Vapor Phase Diagrams

Figure 6.11 shows a pressure–composition liquid–vapor phase diagram of ethanol and

diethyl ether for a fixed temperature of 20◦C. Compare Figure 6.11 with Figure 6.2,

which represents the nearly ideal mixture of benzene and toluene. Figure 6.12 shows

the temperature–composition phase diagram of the same mixture for a fixed pressure of

1.84 atm. Compare this figure with Figure 6.3. This system exhibits positive deviation

from Raoult’s law. The vapor pressure is larger than it would be if the solution were

ideal, and the solution boils at a lower temperature than if it were an ideal solution.

Figure 6.13 shows the pressure–composition phase diagram of ethanol and benzene.

There is such a large positive deviation from Raoult’s law that there is a maximum

in the vapor pressure curve. Figure 6.14 shows the temperature–composition phase

diagram of acetone and chloroform, which corresponds to a large negative deviation

from Raoult’s law. Either a maximum or minimum point in a phase diagram is called an

azeotrope. The two curves representing liquid and vapor compositions must be tangent

at an azeotrope, so that the two phases have the same composition. This assertion is

proved in Appendix D.

120

110

100

90

80

70

tc

/^8

C

Ethanol mole fraction

Tie line area

Area of

liquid states

Coexisting

states of

two phases

Area of

vapor states

0

0

0.2 0.4 0.6 0.8 1

Figure 6.12 Temperature–Composition Phase Diagram for Diethyl Ether–Ethanol at

1.84 atm.The lower curve represents the temperature as a function of mole fraction in the

liquid, and the upper curve represents the temperature as a function of mole fraction in the

vapor. Drawn from data in J. Timmermans,Physicochemical Constants of Binary Systems,

Vol. 2, Interscience Publishers, New York, 1959, p. 401.