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CHAPTER
12

Multicomponent

Phase Equilibrium

CHAPTER OUTLINE

12.1 Colligative Properties

12.2 Vapor-Pressure Lowering
One-component phase equilibrium was discussed in Chapter 7. We now consider mul- 12.3 Freezing-Point Depression
ticomponent phase equilibria, which have important applications in chemistry, chem- and Boiling-Point Elevation
ical engineering, materials science, and geology.
12.4 Osmotic Pressure
12.1 COLLIGATIVE PROPERTIES 12.5 Two-Component Phase
Diagrams
We begin with a group of interrelated properties of solutions that are called col-
ligative properties (from the Latin colligatus, meaning “bound together”). When a 12.6 Two-Component
solute is added to a pure solvent A, the A mole fraction decreases. The relation Liquid–Vapor Equilibrium
10m >0x 2 7 0 [Eq. (4.90)] shows that a decrease in x (dx 6 0) must decrease 12.7 Two-Component
A
A
A
A T,P,n i A
the chemical potential of A (dm 6 0). Therefore, addition of a solute at constant T
A Liquid–Liquid Equilibrium
and P lowers the solvent chemical potential m below m*. This change in solvent
A A
chemical potential changes the vapor pressure, the normal boiling point, and the nor- 12.8 Two-Component
mal freezing point and causes the phenomenon of osmotic pressure. These four prop- Solid–Liquid Equilibrium
erties are the colligative properties. Each involves an equilibrium between phases.
The chemical potential m is a measure of the escaping tendency of A from the 12.9 Structure of Phase Diagrams
A
solution, so the decrease in m means the vapor partial pressure P of the solution is
A A 12.10 Solubility
less than the vapor pressure P* of pure A. The next section discusses this vapor-
A
pressure lowering. 12.11 Computer Calculation of
Phase Diagrams
12.2 VAPOR-PRESSURE LOWERING 12.12 Three-Component Systems
Consider a solution of a nonvolatile solute in a solvent. A nonvolatile solute is one 12.13 Summary
whose contribution to the vapor pressure of the solution is negligible. This condition
will hold for most solid solutes but not for liquid or gaseous solutes. The solution’s
vapor pressure P is then due to the solvent A alone. For simplicity, we shall assume
pressures are low enough to treat all gases as ideal. If this is not so, pressures are to be
replaced by fugacities.
From Eq. (10.16) for nonelectrolyte solutions and Eq. (10.56) for electrolyte
solutions, the solution’s vapor pressure is

P P g x P* nonvolatile solute (12.1)
A A A
A
where the mole-fraction scale is used for the solvent activity coefficient g . The
A
change in vapor pressure P compared with pure A is P P P*. Use of (12.1)
A
gives
¢P 1g x 12P* nonvol. solute (12.2)
A A
A