300 6 The Thermodynamics of SolutionsADDITIONAL PROBLEMS
6.70 a.The vapor pressure of pure water at 25◦C is equal to
23.756 torr if the total pressure on the liquid is just that
due to the vapor. Calculate the vapor pressure of water
at 25◦C if enough oxygen gas is added to the vapor to
give a total pressure of 1.000 atm. Neglect any oxygen
dissolved in the water.
b.Calculate the mole fraction of dissolved oxygen in the
water under the conditions of part a. The Henry’s law
constant is in Example 6.9. Calculate the effect of this
dissolved oxygen on the vapor pressure.
c.Repeat parts a and b with 100.00 atm total pressure
instead of 1.000 atm.
6.71The molar enthalpy change of fusion of ethylene glycol is
11.23 kJ mol−^1. Its density is 1.1088 g cm−^3. Find the
freezing temperature of a solution made from 0.500 L of
water and 9.500 L of ethylene glycol. State any assumptions.
6.72Assuming complete dissociation, and assuming that the
water activity coefficient equals unity, calculate the
osmotic pressure at 25.00◦C of a solution of 2.500 g of
KCl in 1.000 kg of water. The density of the solution is
equal to 1.002 g cm−^3.
6.73 a.Calculate the osmotic pressure at 20.00◦C of a solution
of 5.000 g of sucrose in 95.00 g of water, using
Eq. (6.7-23). The density of the solution is equal to
1.0194 g cm−^3. Calculate the height of a column of the
solution sufficient to equilibrate an osmometer like that
of Figure 6.26.
b.Repeat the calculation using the version of Eq. (6.7-22)
with the natural logarithm in it.
6.74 a.Find the osmotic pressure at 25.0◦C of a solution
containing 1.000 g of sucrose and 99.000 g of water.
The density of this solution is 1.0021 g cm−^3. Sucrose
is C 12 H 22 O 11 , with a molar mass of 342.3 g mol−^1.
b.Find the height of a column of this solution needed to
provide the hydrostatic pressure equal to the osmotic
pressure.
6.75The freezing temperature of CH 2 OHCH 2 OH, ethylene
glycol (the main ingredient of automobile antifreeze), is
− 11. 5 ◦C. Its density is 1.1088 g cm−^3 , and its enthalpy
change of fusion is 11.23 kJ mol−^1. Its molar mass is
62.058 g mol−^1. Assume that water is insoluble in solid
ethylene glycol and find the freezing temperature of a
solution containing 10.00 mol of ethylene glycol and
0.250 mol of water.
6.76A solution is made from 10.00 g of a certain protein and
enough water to make 1.000 L at 298.15 K. The osmotic
pressure is found to be 1.33 torr. What is the molar mass of
the protein?6.77Find the osmotic pressure at 298.15 K and the freezing
point depression of a solution of horse hemoglobin
(M68 kg mol−^1 ) if 1.000 L of solution contains 40.00 g
of hemoglobin and 968.00 g of water.6.78A solution is made from 5.000 g of glucose and 95.000 g of
water. At 20.0◦C the density of this solution is
1.0175 g cm−^3.a.Find the freezing temperature of this solution at
1.000 atm.b. Find the vapor pressure of this solution at 100.0◦C.c.Find the boiling temperature of this solution at
1.000 atm.d.Find the osmotic pressure of this solution at a
temperature of 20.0◦C.
6.79Identify each statement as true or false (if a statement is
true only under some special circumstance, count it as
false):a.For small enough concentration of a solute, its activity
according to convention I and its activity according to
convention II are nearly equal.
b. For small enough concentration of a solute, its activity
coefficient according to convention I and its activity
coefficient according to convention II are nearly equal.c.For small enough concentration of a solute, its activity
coefficient according to convention I and its molality
activity coefficient are nearly equal.d.For small enough concentration of a solute, its activity
coefficient according to convention II and its molality
activity coefficient are nearly equal.e.In a dilute solution, the mole fraction and the activity of
a solute are equal.f. In a dilute solution, the mole fraction and the activity of
the solvent are equal.g.In an ideal solution, the mole fraction of every
component is equal to its activity.