Raoult's Law Example Problem - Volatile Mixture

Calculating Vapor Pressure of Volatile Solutions

Raoult's Law can determine vapor pressure when mixing volatile solutions.
Raoult's Law can determine vapor pressure when mixing volatile solutions. Lumina Imaging, Getty Images

This example problem demonstrates how to use Raoult's Law to calculate the of 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:

Psolution = ΧsolventP0solvent

where

Psolution is the vapor pressure of the solution
Χsolvent is mole fraction of the solvent
P0solvent 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.

PTotal = Psolution A + Psolution 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

nhexane = 58.9 g x 1 mol/86 g
nhexane = 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

nbenzene = 44.0 g x 1 mol/78 g
nbenzene = 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.

Χhexane = nhexane/(nhexane + nbenzene)
Χhexane = 0.685/(0.685 + 0.564)
Χhexane = 0.685/1.249
Χhexane = 0.548

Since there are only two solutions present and the total mole fraction is equal to one:

Χbenzene = 1 - Χhexane
Χbenzene = 1 - 0.548
Χbenzene = 0.452

Step 3 - Find the total vapor pressure by plugging the values into the equation:

PTotal = ΧhexaneP0hexane + ΧbenzeneP0benzene
PTotal = 0.548 x 573 torr + 0.452 x 391 torr
PTotal = 314 + 177 torr
PTotal = 491 torr

Answer:

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