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Raoult's Law Example Problem

Calculating Vapor Pressure Change

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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

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.
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