Physical Chemistry Third Edition

6.7 Colligative Properties 299

Summary of the Chapter

For each component of an ideal solution, by definition

μi(T,P)μ∗i(T,P)+RTln(xi)

Each component of an ideal solution nearly obeys Raoult’s law,

PiPi∗xi

wherexiis the mole fraction of componentiin the solution. In a nonideal solution, the

partial vapor pressure of a sufficiently dilute solute is governed by Henry’s law:

Pikixi

The activityaiof substanceiin any state is defined by the relation

μiμ◦i+RTln(ai)

whereμ◦iis the chemical potential in some standard state. According to two different

mole fraction descriptions, called convention I and convention II, the activity is given

by

aiγixi

The activity of a solute in the molality description is given by

a(im)

γ(im)mi

m◦

The Debye–Hückel theory provides an accurate limiting law for the activity coefficients

of electrolyte solutes. A semi-empirical equation, the Davies equation, can provide

usable estimates of electrolyte activity coefficients at larger concentrations.

Two-component pressure–composition and temperature–composition phase dia-

grams give information about phases present at equilibrium. For a three-component

system, a composition–composition diagram at constant temperature and pressure is

plotted in an equilateral triangle.

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

elevation, vapor pressure lowering, and osmotic pressure. In each case, the magnitude

of the effect in a dilute solution is determined by the concentration of the solute but is

independent of its identity.