Physical Chemistry Third Edition

6.1 Ideal Solutions 247

Equilibrium

solution

compositions

Super-

saturated P*(I)(supercooled)

Naph

P*(s)

Naph

xsaturated

xNaph

0 1

P

Super-

Equilibriumsaturated

solution

compositions

m*(I)(supercooled)

Naph

m*(s)

Naph

xsaturated

xNaph

0 1

Naph

(a) (b)

Figure 6.8 Naphthalene in an Ideal Solution (Schematic).(a) The vapor pressure as

a function of composition. (b) The chemical potential as a function of composition.

to besaturated. If a metastable solution occurs with a greater mole fraction of

naphthalene than this, it is called asupersaturated solution. The maximum solubility

of a solid such as naphthalene in a liquid solvent is independent of the identity of the

liquid solvent if the two substances form an ideal solution and are insoluble in the solid

phases.

Area of

vapor states

Tie line areas

3500

3000

2500

2000

T/K

1500

1000

500

0 0.2 0.4

Mole fraction of Si

0.6 0.8 10

Area of

liquid states

Area of

solid states

Figure 6.7 The Solid–Liquid and

Liquid–Vapor Phase Diagram of Sili-

con and Germanium (Schematic).

PROBLEMS

Section 6.1: Ideal Solutions

6.1Derive Eq. (6.1-25).

6.2Show that an ideal solution obeys the Gibbs–Duhem

relation.

6.3A bulb contains an ideal solution of a nonvolatile substance

A and a volatile substance S. This bulb is connected to

another bulb containing a solution of another nonvolatile

substance B and S so that the two solutions can equilibrate

with the same vapor phase. After equilibration, it is found

that for any set of compositions, the mole fraction of S in

the first bulb is proportional to the mole fraction of S in the

second bulb. Prove that the solution of B in S is also ideal.

6.4Find∆Smix,∆Gmix,∆Hmix, and∆Vmixif 125.0 g of

benzene and 25.0 g of naphthalene are mixed at 60.0◦C.

State any assumptions.

6.5A solution is made from 2.50 mol of benzene and 1.50 mol

of deuterobenzene at 25◦C and 1.00 atm. Find∆Smix,

∆Gmix,∆Hmix,∆Umix, and∆Vmix.

6.6Assume that carbon tetrachloride and 1,1,1-trichloroethane

(methyl chloroform) form an ideal solution. Look up the

vapor pressures of the pure compounds at 25◦C and plot a

pressure–composition phase diagram for this temperature

(four points besides the end points should give an adequate

plot).

6.7Assume that toluene and ethyl benzene form a nearly ideal

liquid solution.

a. Construct an accurate graph of the entropy of mixing of

a solution of these two substances as a function ofxif

1.000 mol of toluene andxmol of ethyl benzene are

mixed at a constant temperature of 25◦C.

b. Construct an accurate graph of the Gibbs energy of

mixing of the solution of part a as a function ofx.

6.8 Benzene and toluene form a nearly ideal solution.

a.At 25. 00 ◦C, the vapor pressure of benzene is 73.0 torr,

and that of toluene is 27.0 torr. Calculate the total vapor

pressure and the mole fraction of benzene in the vapor

phase that is at equilibrium at 25.00◦C with a solution

of benzene and toluene having a mole fraction of

benzene equal to 0.500.

b. Calculate the Gibbs energy of mixing, the enthalpy

of mixing, the volume change of mixing, and the

entropy of mixing of the solution in part c if the total

amount of substances in the solution is equal to

3.500 mol.