Physical Chemistry Third Edition

292 6 The Thermodynamics of Solutions

H 2 O

Li 2 SO 4

Li 2 SO 4

Li 2 SO 4 H 2 O

(NH 4 ) 2 SO 4

(NH 4 ) 2 SO 4

Figure 6.25 Concentration–Concentration Phase Diagram

of Lithium Sulfate, Ammonium Sulfate, and Water at 30◦C

and 1.000 atm.Pure lithium sulfate and ammonium sulfate are

solid at this temperature.

b.Repeat part a for a mole fraction of lanthanum equal to

0.53.

6.59 Sketch the titanium–nickel temperature–composition
phase diagram. The melting temperature of nickel is equal
to 1453◦C and that of titanium is equal to 1675◦C. There
are three compounds, TiNi 3 , melting near 1370◦C, TiNi,
melting near 1300◦C, and Ti 2 Ni, which melts

incongruently near 990◦C. There are fairly sizable regions

of solid solubility except that nothing dissolves in TiNi 3.

The three eutectics, in order of increasing titanium mole

fraction, are near 1300◦C, 1110◦C, and 940◦C. The

incongruent melting of Ti 2 Ni gives a solid solution that is

mostly TiNi and a solution that has a titanium mole

fraction near 0.70. Label each area with the phase or

phases present and the number of independent intensive

variables.

6.60 Figure 6.25 shows a phase diagram of lithium sulfate,

ammonium sulfate, and water at constant temperature and

pressure. For each area in the diagram, tell what phase or

phases are present and give the number of independent

intensive variables.

6.61 Consider a hypothetical pair of substances denoted by A

and B. Substance A melts at 650◦C and substance B melts

at 575◦C. The two substances form two compounds in the

solid state, A 2 B and AB 2 , but mix in all proportions in the

liquid phase. A 2 B melts congruently at 550◦C. AB 2 melts

incongruently to give pure A and a solution with

xA 0 .40. Sketch the phase diagram. Label each area

with the

phases present and the value off, the number of degrees

of freedom, or number of independent intensive

variables.

6.7 Colligative Properties

Colligative properties are properties that depend on the concentration of a solute but not

on its identity. The name comes from a Latin word meaning “tied together” and is used

because of the common dependence that these properties have on solute concentration.

The four principal colligative properties are freezing point depression, boiling point

elevation, vapor pressure lowering, and osmotic pressure.

Freezing Point Depression

Consider a solid solute that is soluble in a liquid solvent but insoluble in the solid

solvent. Assume that the pure solid solvent (component number 1) is at equilibrium

with a liquid solution containing the dilute solute. From the fundamental fact of phase

equilibrium,

μ(liq) 1 μ∗ 1 (solid) (6.7-1)