Physical Chemistry Third Edition

234 5 Phase Equilibrium

surface areas act asheterogeneous catalyststhat allow adsorbed reactants to react on

their surfaces.

PROBLEMS

Section 5.6: Surfaces in Multicomponent Systems

5.48 The following measurements of the surface tension of
aqueous sodium chloride solutions at 25. 0 ◦C were taken
by a student in a physical chemistry laboratory:

c/mol L−^10. 00 1. 00 2. 00 3. 00 4. 00

γ/N m−^10 .0720 0.0809 0.0821 0.0841 0. 0904

Using Eq. (5.6-16), find the surface concentration of

sodium chloride at 1.00 mol L−^1 and at 2.00 mol−^1.

What does the sign of this quantity tell you?

5.49 The following measurements of the surface tension of

aqueous 1-butanol solutions at 25. 0 ◦C were taken by a

student in a physical chemistry laboratory:

c/mol L−^10. 00 0. 110 0. 140 0. 190

γ/Nm−^10 .0720 0.0595 0.0574 0. 0515

c/mol L−^10. 250 0. 450 0. 600

γ/Nm−^10 .0475 0.0412 0. 0354

Using Eq. (5.6-15), find the surface concentration of

1-butanol at 0.100 mol L−^1 and at 0.200 mol L−^1. What

does the sign of this quantity tell you? Calculate the

surface area per molecule of 1-butanol for each of these

two molar concentrations.

Summary of the Chapter

The fundamental fact of phase equilibrium is that at equilibrium

μ

(α)

i μ

(β)

i

where the subscriptidenotes the substance and the superscriptsαandβdenote two

different phases.

The Gibbs phase rule is

fc−p+ 2

wherefis the number of independent intensive variables,cis the number of com-

ponents, andpis the number of phases. The fundamental fact of phase equilibrium

and the Gibbs phase rule can be used to understand phase diagrams and the exper-

imental facts related to a given phase equilibrium. There are several kinds of phase

transitions, including first-order phase transitions, second-order phase transitions, and

lambda transitions. Their properties were discussed using the fundamental fact of phase

equilibrium.

The Clapeyron equation governs the curves in one-component pressure–temperature

phase diagrams:

dP

dT



∆Sm

∆Vm

wherePis the pressure at which two phases can coexist at equilibrium,∆Smis the

molar entropy change of the phase transition, and∆Vmis the molar volume change of

the transition.