# How to Use Raoult's Law to Calculate Vapor Pressure Change

This example problem demonstrates how to use Raoult's Law to calculate the change in vapor pressure by adding a nonvolatile liquid to a solvent.

### Problem

What is the change in vapor pressure when 164 g of glycerin (C3H8O3) is added to 338 mL of H2O at 39.8 °C.
The vapor pressure of pure H2O at 39.8 °C is 54.74 torr
The density of H2O at 39.8 °C is 0.992 g/mL.

### 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
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

### Determine the Mole Fraction of Solution

molar weightglycerin (C3H8O3) = 3(12)+8(1)+3(16) g/mol
molar weightglycerin = 36+8+48 g/mol
molar weightglycerin = 92 g/mol
molesglycerin = 164 g x 1 mol/92 g
molesglycerin = 1.78 mol
molar weightwater = 2(1)+16 g/mol
molar weightwater = 18 g/mol
densitywater = masswater/volumewater
masswater = densitywater x volumewater
masswater = 0.992 g/mL x 338 mL
masswater = 335.296 g
moleswater = 335.296 g x 1 mol/18 g
moleswater = 18.63 mol
Χsolution = nwater/(nwater + nglycerin)
Χsolution = 18.63/(18.63 + 1.78)
Χsolution = 18.63/20.36
Χsolution = 0.91

### Find the Vapor Pressure of the Solution

Psolution = ΧsolventP0solvent
Psolution = 0.91 x 54.74 torr
Psolution = 49.8 torr

### Find the Change in Vapor Pressure

Change in pressure is Pfinal - PO
Change = 49.8 torr - 54.74 torr
change = -4.94 torr