Question 13.4.4: Calculate the vapor pressure of a solution. The vapor pressu......
Calculate the vapor pressure of a solution.
The vapor pressure of hexane (C_{6}H_{14}) at 50 °C is 399 mm Hg. What is the vapor pressure of a solution consisting of 70.0 g hexane and 0.100 mol of a solute that is a nonvolatile nonelectrolyte?
You are asked to calculate the vapor pressure of a solution.
You are given the vapor pressure of a solvent at a given temperature and the quantities of solute and solvent in the solution.
The vapor pressure of the solution is calculated using Raoult’s law.
P_{solution} = Pº_{hexane}χ_{hexane}i
The van’t Hoff factor is 1 because the solute is a nonelectrolyte. First calculate the mole fraction of hexane.
mol hexane = 70.0 g × \frac{1\text{ mol hexane}}{86.18\text{ g hexane}} = 0.812 mol
χ_{hexane} = \frac{\text{mol hexane}}{\text{mol hexane + mol solute}} =\frac{0.812}{0.812 + 0.100} = 0.980
Next, calculate the vapor pressure of the solvent in the solution.
P_{solution} = \left(399\text{ mm Hg}\right) \left(0.890\right) \left(1\right) = 355 mm Hg
Is your answer reasonable? A nonvolatile solute was added to the solvent, so the vapor pressure of the solution is less than the vapor pressure of the pure solvent.