Physical Chemistry Third Edition

6.6 Phase Diagrams of Nonideal Mixtures 285

97.9◦C connects three points representing the compositions of two liquid phases and

one gas phase that can coexist at equilibrium. By the Gibbs phase rule, only one

intensive variable is independent in a system of two components and three phases.

Since the pressure is fixed for this diagram, the compositions of all three phases and

the temperature are fixed.

To purify furfural by the process ofsteam distillation, water is added to impure

furfural and the two-phase mixture is boiled. If the impurities do not change the boiling

temperature very much, the two-phase mixture boils near 97.9◦C at 1.000 atm. The

vapor has a furfural mole fraction equal to 0.092. The vapor is condensed to two liquid

phases, and the furfural layer is recovered and dried. At 20◦C, this layer has a furfural

mole fraction of 0.78 before drying. The advantage of steam distillation is that it can be

carried out at a lower temperature than an ordinary distillation. The higher temperature

of an ordinary distillation might decompose the organic substance.

Solid–Liquid Phase Diagrams

Figure 6.6 depicted the temperature–composition phase diagram of silicon and ger-

manium, which form a nearly ideal solid solution. Figure 6.17 shows the solid–liquid

temperature–composition phase diagram of gold and copper, which are completely

miscible in both the solid and liquid phases, but which do not form an ideal solid

solution. The lower area represents temperatures and compositions of a one-phase

system (a solid solution). The tie-line areas contain tie lines connecting the composi-

tion of a solid solution and the composition of the liquid solution at equilibrium with

that solid solution. The area above the tie-line region represents a liquid solution.

Just as liquids are purified by distillation, solids are sometimes purified byzone

refining, in which a rod-shaped piece of the solid is gradually pulled through a ring-

shaped furnace. A zone of the solid melts as it moves into the furnace and freezes

as it moves out of the furnace. This process is analogous to the vaporization and

recondensation of a liquid in distillation, except that the melting process gives a liquid

of the same composition as the solid, making the initial process correspond to a vertical

line segment in the diagram. In many cases the solid that freezes out approximates the

equilibrium composition at the other end of the tie line at the end of the vertical line

1100

1000

900

800

700

600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 0

tC

/
C

Area of solid states

Area of liquid states

Tie line

areas

889 
C

1063 
C

Gold mole fraction

1083 
C

Figure 6.17 Solid–Liquid Temperature–Composition Phase Diagram of Gold and

Copper.From M. Hansen,The Constitution of Binary Alloys, McGraw-Hill, New York,

1958, p. 199.