Physical Chemistry Third Edition

298 6 The Thermodynamics of Solutions

Solution

Π(0.200 mol L−^1 )

(

1000 L

1m−^3

)(

8 .3145 J K−^1 mol−^1

)

(298.15 K)

 4. 96 × 105 Pa 4 .89 atm

Exercise 6.36

a.Verify Eq. (6.7-23).

b.Find the osmotic pressure of a solution of 5.00 g of glucose in 1.000 L of aqueous solution at

298.15 K.

c.Calculate the height of the solution required to give a hydrostatic pressure of this size. The

density of the solution is 1.002 g cm−^3.

PROBLEMS

Section 6.7: Colligative Properties

6.62 The normal melting temperature of phenanthrene is
96.3◦C. Its enthalpy change of fusion is 18.6 kJ mol−^1.
Find the solubility (maximum mole fraction) of
phenanthrene in a liquid solution with naphthalene at
82.0◦C. Assume that the liquid solution is ideal and that no
solid solubility occurs.

6.63 The melting temperature of TNT (2,4,6-trinitrotoluene)
is 80.83◦C, and its enthalpy change of fusion is
21.23 kJ mol−^1. Assume that TNT forms an ideal liquid
solution with nitrobenzene. Find the maximum solubility
(mole fraction of TNT in the liquid at equilibrium with
solid TNT) at 60◦C. Assume that the liquid solution is
ideal and that no solid solubility occurs. What can you say
about the maximum solubility of TNT in some other liquid
with which TNT forms an ideal solution?

6.64 a.Calculate the freezing temperature at 1.000 atm of a
solution of 5.00 g of sucrose in 95.00 g of water, using
Eq. (6.7-9).

b.Calculate the freezing temperature of the solution of

part a using Eq. (6.7-7).

c.Modify Eq. (6.7-7) by discontinuing the assumption

that the solution is dilute, including an activity

coefficient for the water. From the actual freezing point

depression of 0.29◦C, find the value of the activity

coefficient of water in the solution of part a.

6.65 Find the freezing point depression of a solution of 1.500 g

of KCl in 1.000 kg of water. Assume that the KCl

dissociates completely, so that 2 mol of dissolved ions

results from 1 mol of KCl.

6.66A sample of 1.000 g of a solute is dissolved in 15.00 mL of

benzene at 20◦C. The density of benzene at this

temperature is 0.8765 g mL−^1. The freezing temperature

depression was 3.04◦C. Find the molar mass of

the solute.

6.67 a.Calculate the boiling temperature of the solution of

Problem 6.64, using Eq. (6.7-14).

b.Repeat the calculation using Eq. (6.7-15) and calculate

the percent difference of the boiling point elevation

from that of part a.

c.Repeat the calculation using Eq. (6.7-16) and calculate

the difference of the boiling point elevation from that

of part a.

6.68 The density of ethylene glycol is 1.1088 g cm−^3 and its

melting temperature is equal to− 11. 5 ◦C. Calculate the

freezing temperature of a mixture of 0.500 L of ethylene

glycol and 9.500 L of water.

6.69A sample of myoglobin with mass 1.000 g is dissolved in

100.0 mL of aqueous solution. The osmotic pressure of the

solution is 11.0 torr at 25.00◦C. Find the molar mass of

myoglobin.