6.2 Henry’s Law and Dilute Nonelectrolyte Solutions 257
which is the same asμ 1 (x 1 )μ∗ 1 +RTln(x 1 ) (6.2-24b)where we drop the prime symbol (′)onx 1. This is the same as Eq. (6.1-1), which leads
to Raoult’s law as in Section 6.1. If a dilute solution contains several solutes that all
obey Henry’s law, the solvent obeys Raoult’s law just as in the case of one solute. The
proof of this assertion is assigned in Problem 6.20.PROBLEMS
Section 6.2: Henry’s Law and Dilute Nonelectrolyte
Solutions
6.13A certain volatile solvent has a vapor pressure of 300.0 torr
when pure at 298.15 K. When 6.40 g of a solute is
dissolved in 1.000 mol of the solvent, the partial vapor
pressure of the solvent at 298.15 K is 285.7 torr. Assuming
that the solute obeys Henry’s law and that the solvent
obeys Raoult’s law, find the molar mass of the solute.
6.14 Deep-sea divers can suffer a condition known as the
“bends” if they breathe ordinary air at a pressure equal
to the ambient hydrostatic pressure, because nitrogen gas
dissolves in blood at high pressure and is released as
bubbles in the bloodstream when the diver
decompresses.
a.Calculate the amount of nitrogen dissolved in 5.000 L
of blood (roughly the volume in an adult human) at
equilibrium with air (78 mol% nitrogen) at a depth of
200 m, assuming that Henry’s law constant for nitrogen
in blood is equal to 7. 56 × 104 atm, the value for
nitrogen in water at 20.0◦C.
b. Calculate the volume of this amount of nitrogen as a
gas at 1.000 atm and 20. 0 ◦C.
6.15 a.Find the value of the distribution coefficient for iodine
between water and carbon tetrachloride at 25◦C, using
the concentration description. The density of carbon
tetrachloride is 1.59 g cm−^3.
b.Iodine is equilibrated between water and carbon
tetrachloride at 25◦C. The final concentration of
iodine in the carbon tetrachloride phase is equal to
0.0734 mol L−^1. Find the volume of a sodium
thiosulfate solution with 0.0100 mol L−^1 required to
titrate 25.00 mL of the aqueous phase. (2 mol of
thiosulfate is required to react with 1 mol of I 2 .)6.16 Find the value of the distribution coefficient for iodine
between water and carbon tetrachloride at 25◦C, using the
molality description.6.17 From the value of the Henry’s law constant for ethanol in
benzene at 40◦C, calculate the value of the Henry’s law
constant for ethanol in benzene at this temperature if mass
fractions are used instead of mole fractions to describe the
system.
6.18 When water is saturated with air at sea level and 298 K,
there are 8.3 ppm (parts per million) of oxygen by mass
dissolved. Find the equilibrium mole fraction of oxygen
dissolved in water at 298 K if the partial pressure of
oxygen is equal to 10.0 atm.6.19At 25◦C, the Henry’s law constant for nitrogen in water is
8. 68 × 109 Pa and the Henry’s law constant for nitrogen in
benzene is 0. 239 × 109 Pa. A solution of nitrogen in water
at 25◦C with 6.00 ppm (parts per million) of nitrogen by
mass is at equilibrium with a solution of nitrogen in
benzene. Find the mole fraction of nitrogen in the benzene
solution.6.20 Show that the solvent in a solution of several solutes obeys
Raoult’s law at a certain composition if all solutes obey
Henry’s law for all compositions between this composition
and the pure solvent.Hint:Carry out the integration for
fixed proportions of solutes, so that the mole fractions of
the solutes remain proportional to each other.
6.21 Find the activity of water in a 0.0250 mol kg−^1 solution of
sucrose in water at 298.15 K. Assume dilute solution
behavior.6.22 The Henry’s law constant for methane in benzene is
equal to 481 atm. Find the molality of methane
dissolved in benzene if the equilibrium partial pressure
of methane is 0.250 atm.