Physical Chemistry Third Edition

286 6 The Thermodynamics of Solutions

segment, being richer in the higher-melting component than the original solid. The

lower-melting substance is “swept” to the end of the rod. This process is analogous to

distillation in a still with one theoretical plate. A second pass through the furnace can

lead to a further purification.

Exercise 6.28

By drawing a “staircase” in Figure 6.17, determine what composition will result from three

successive zone refining passes starting with a gold–copper solid solution of gold mole fraction

equal to 0.70. What would many successive zone refining passes lead to if the curves had a

maximum instead of a minimum?

Figure 6.18 shows the solid–liquid temperature–composition phase diagram of silver

and copper at 1.00 atm. There are two one-phase regions of limited solid solubility,

labeledαandβ. A tie line in the area between theαandβregions represents two

coexisting saturated solid solutions, one that is mostly silver and one that is mostly

copper. The tie line at 779◦C connects the points representing the two solid phases

and one liquid phase that can be at equilibrium with the two solid phases. The point

representing this liquid phase is called theeutectic point. If a liquid that has the same

composition as the eutectic is cooled, two solid phases will freeze out when it reaches

the eutectic temperature, with compositions represented by the ends of the tie line.

Exercise 6.29

For each one-phase region in the phase diagram of Figure 6.18, give the phase that can occur

and give the number of independent intensive variables (excluding the pressure, which is fixed

at 1 atm). For each two-phase (tie-line) region, give the phases that can be at equilibrium and

give the number of independent intensive variables, excluding the pressure.

9618 C

800

600

400

tC

/^8 C

Coexisting solid

phases

tie line area

two solid phases

Copper mole fraction

0 0.2 0.4 0.6 0.8 1.0

Solid

solution

Solid

solutionβ

Eutectic

Area of liquid states

Tie line

area

10838 C

7798 C

Figure 6.18 Solid–Liquid Temperature–Composition Phase Diagram of Silver and

Copper.From R. E. Dickerson,Molecular Thermodynamics, W. A. Benjamin, Inc., New York,

1969, p. 371.