Raoult's Law Example Problem - Volatile Mixture

This example problem demonstrates how to use Raoult's Law to calculate the vapor pressure of two volatile solutions mixed together.

Raoult's Law Example

What is the expected vapor pressure when 58.9 g of hexane (C₆H₁₄) is mixed with 44.0 g of benzene (C₆H₆) at 60.0 °C?
Given:
Vapor pressure of pure hexane at 60 °C is 573 torr.
Vapor pressure of pure benzene at 60 °C is 391 torr.

Solution

Raoult's Law can be used to express the vapor pressure relationships of solutions containing both volatile and nonvolatile solvents.

Raoult's Law is expressed by the vapor pressure equation:
P_solution = Χ_solventP⁰_solvent
where
P_solution is the vapor pressure of the solution
Χ_solvent is mole fraction of the solvent
P⁰_solvent is the vapor pressure of the pure solvent
When two or more volatile solutions are mixed, each pressure component of the mixed solution is added together to find the total vapor pressure.
P_Total = P_{solution A} + P_{solution B} + ...
Step 1 - Determine the number of moles of each solution in order to be able to calculate the mole fraction of the components.
From the periodic table, the atomic masses of the carbon and hydrogen atoms in hexane and benzene are:
C = 12 g/mol
H = 1 g/mol

Use the molecular weights to find the number of moles of each component:
molar weight

of hexane = 6(12) + 14(1) g/mol
molar weight of hexane = 72 + 14 g/mol
molar weight of hexane = 86 g/mol
n_hexane = 58.9 g x 1 mol/86 g
n_hexane = 0.685 mol
molar weight of benzene = 6(12) + 6(1) g/mol
molar weight of benzene = 72 + 6 g/mol
molar weight of benzene = 78 g/mol
n_benzene = 44.0 g x 1 mol/78 g
n_benzene = 0.564 mol
Step 2 - Find mole fraction of each solution. It doesn't matter which component you use to perform the calculation. In fact, a good way to check your work is to do the calculation for both hexane and benzene and then make sure they add up to 1.
Χ_hexane = n_hexane/(n_hexane + n_benzene)
Χ_hexane = 0.685/(0.685 + 0.564)
Χ_hexane = 0.685/1.249
Χ_hexane = 0.548
Since there are only two solutions present and the total mole fraction is equal to one:
Χ_benzene = 1 - Χ_hexane
Χ_benzene = 1 - 0.548
Χ_benzene = 0.452
Step 3 - Find the total vapor pressure by plugging the values into the equation:
P_Total = Χ_hexaneP⁰_hexane + Χ_benzeneP⁰_benzene
P_Total = 0.548 x 573 torr + 0.452 x 391 torr
P_Total = 314 + 177 torr
P_Total = 491 torr

Answer:

The vapor pressure of this solution of hexane and benzene at 60 °C is 491 torr.