Physical Chemistry Third Edition

280 6 The Thermodynamics of Solutions

EXAMPLE6.17

The following are values for ethanol at 298.15 K:

∆fH◦/kJ mol−^1 ∆fG◦/kJ mol−^1

liquid − 277. 69 − 174. 78

ao − 288. 3 − 181. 64

a.Find the value of the differential heat of solution in the standard state.

b.Find the value ofμ◦ 2 (m)−G∗m,2(liq) for ethanol in H 2 O at 298.15 K.

Solution

a.Call ethanol component number 2:

∆Hdiff,2◦Hm,2◦(m◦)−Hm,2∗ (liq)∆fH

◦

(2,ao)−∆fH

◦

2 (liq)

− 288 .3kJmol−^1 −(− 277 .69 kJ mol−^1 )− 10 .6kJmol−^1

Note the difference in value between this quantity and the integral heat of solution in

Example 6.16.

b. μ 2 ◦(m)−G∗m,2(liq)∆fG◦(2,ao)−∆fG◦(2,liq)

− 181 .64 kJ mol−^1 −(− 174 .78 kJ mol−^1 )− 6 .86 kJ mol−^1

PROBLEMS

Section 6.5: Thermodynamic Functions of Nonideal
Solutions

6.39 At 35.2◦C, the vapor pressure of pure acetone is equal to
344.5 torr, and that of pure chloroform is equal to 293 torr.
At this temperature, a solution of 0.7090 mol of acetone
and 0.2910 mol of chloroform has a total vapor pressure of
286 torr and a mole fraction of acetone in the vapor of
0.8062.
a.Using convention I, find the activity and activity
coefficient of each component.
b.Find the Gibbs energy change of mixing and the excess
Gibbs energy for the solution.
c.The Henry’s law constant for chloroform in acetone at
this temperature is equal to 145 torr. Considering
acetone to be the solvent, find the activity and activity
coefficient for each component according to
convention II.

6.40 A solution of acetone (substance 2) and diethyl ether
(substance 1) hasx 2  0 .500. At 30◦C, this solution is at
equilibrium with a vapor phase that has partial pressures
P 2 168 torr andP 1 391 torr. The vapor pressures of

the pure substances at this temperature areP∗ 2 283 torr

andP 1 ∗646 torr.

a.Using convention I, find the activity and activity

coefficient of each substance.

b. Find∆Gmixfor a solution containing 1.000 mol of

acetone and 1.000 mol of diethyl ether.

6.41At 35.2◦C, the equilibrium vapor pressure of chloroform is

293 torr and that of acetone is 344.5 torr. A liquid solution

with acetone mole fraction equal to 0.5061 has an

equilibrium total vapor pressure of 255 torr and an acetone

mole fraction in the vapor of 0.5625. Assume the vapor to

be an ideal gas mixture.

a.Using convention I, find the activity and activity

coefficient of each substance.

b. Find the Gibbs energy change of mixing for 1.000 mol

of solution (that is, 0.4939 mol of chloroform and

0.5061 mol of acetone).

6.42At 298.15 K, the equilibrium vapor pressure of water is

23.756 torr, and that ofn-propanol is 21.76 torr. The

Henry’s law constant forn-propanol in water at this