Physical Chemistry Third Edition

248 6 The Thermodynamics of Solutions

6.9Assume that carbon tetrachloride and 1,1,1-trichloroethane

form an ideal solution. Look up the normal boiling tem-

peratures and the enthalpy changes of vaporization of the

pure substances and plot a temperature–composition phase

diagram for 1.000 atm. (Four points besides the end points

should give an adequate plot.) Assume that the enthalpy

changes of vaporization are temperature-independent.

6.10 At 35.2◦C, the equilibrium vapor pressure of acetone is
25.9 kPa, and that of carbon disulfide is 68.3 kPa.
a.Assume that Raoult’s law is obeyed. Find the partial
vapor pressures of each substance at equilibrium with a
liquid solution that has a mole fraction of acetone equal
to 0.400.
b.The actual equilibrium partial pressure of acetone is
30.7 kPa and that of carbon disulfide is 56.7 kPa. Find
the activity and activity coefficient of each substance,
using convention I.

6.11 Calculate∆Sfor the process of mixing the following:

2.00 mol of an ideal solution of substance 1 and substance

2 withx 1  0 .500 plus 4.00 mol of an ideal solution of

substance 1 and substance 2 withx 1  0 .75 plus

1.00 mol of pure substance 1 plus 0.5 mol of pure

substance 2.

6.12Assume that toluene andortho-xylene form an ideal

solution at all compositions. At 298.15 K, the vapor

pressure of pure toluene is 26.987 torr and the vapor

pressure of pureo-xylene is 6.609 torr. A solution is

formed from 0.500 mol of toluene and a solution of

toluene ando-xylene containing 0.500 mol of each

substance.

a.Find∆S,∆G,∆H,∆V, and∆Ufor this process.

b. Find the total vapor pressure of the resulting solution

and the mole fraction of each substance in the vapor

phase at equilibrium with the solution.

6.2 Henry’s Law and Dilute Nonelectrolyte Solutions

Most solutions are not well described by Raoult’s law for all compositions. Figure 6.9

shows the partial vapor pressures and total vapor pressure of a liquid solution of diethyl

ether (component 1) and ethanol (component 2) at 20◦C. The partial vapor pressures

of both components are greater for all compositions than the prediction of Raoult’s

law, which is represented by broken lines. This behavior is calledpositive deviation

from Raoult’s law. It corresponds to greater repulsions and/or lesser attractions between

unlike molecules than between like molecules. In the case ofnegative deviation, the

vapor pressure is smaller than predicted by Raoult’s law. It is also possible (but less

likely) for the deviation to be positive for one component and negative for another, as

is the case with acetone and nitromethane at 318.5 K. However, it is not possible for

one component to have positive deviation and the other to have negative deviation over

the entire composition range.^1

Exercise 6.8

At 318.15 K, acetone (component 1) has a negative deviation from Raoult’s law in a solution

with nitromethane (component 2), and nitromethane has a positive deviation from Raoult’s law

over part of the range of compositions. What conclusions can you draw about 1-1, 1-2, and 2-2

molecular interactions?

There is a feature of Figure 6.9 that is typical of nonionic substances. For small

values ofx 1 the curve representingP 1 is nearly linear and for small values ofx 2 the

(^1) See M. L. McGlashan,J. Chem. Educ., 40 , 516 (1963).