Calculate the vapor pressure of a solution of 45.0 g of glycerol (c3h8o3) in 500.0 g of water at 25 c. the vapor pressure of water at 25 c is 23.76 torr.

The vapour pressure of the glycerol solution is 23.35 torr.

Use Raoult’s Law to calculate the vapour pressure:

p_1 = χ_1p_1°

where

χ_1 = the mole fraction of the solvent

p_1 and p_1° are the vapour pressures of the solution and of the pure solvent

The formula for vapour pressure lowering Δp is

Δp = p_1° - p_1

Δp = p_1° - χ_1p_1° = p_1°(1 - χ_1) = χ_2p_1°

where χ_2 is the mole fraction of the solute.

Step 1. Calculate the mole fraction of glycerol

n_2 = 45.0 g gly × (1 moL gly/92.08 gly) = 0.4887 mol gly

n_1 = 500.0 g H_2O × (1 mol H_2O/18.02 g H_2O) = 27.75 mol H_2O

χ_2 = n_2/(n_1 + n_2) = 0.4887/(0.4887 + 27.75) = 0.4887/28.24 = 0.017 31

Step 2. Calculate the vapour pressure lowering

Δp = χ_2p_1° = 0.017 31 × 23.76 torr = 0.4112 torr

Step 3. Calculate the vapour pressure

p_1 = p_1° - Δp = 23.76 torr – 0.4112 torr = 23.35 torr

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