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

Vapor pressure release

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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

Answer

The vapor pressure of the water is reduced by 4.94 torr with the addition of the glycerin.