Raoult's Law Example Problem - Vapor Pressure Change

Calculating Vapor Pressure Change

Raoult's Law is used to calculate vapor pressure.
Raoult's Law is used to calculate vapor pressure. Shawn Henning

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

Step 1 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

Step 2 - Find the vapor pressure of the solution

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

Step 3 - 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.