The escaping tendency of a solvent is measured by its vapor pressure, which is dependent on temperature.

Vapor pressure measures the concentration of solvent molecules in the gas phase.

Assuming the solute is nonvolatile, the only particles in the gas phase are solvent molecules.

In a solution, fewer solvent molecules are at the surface compared to the pure solvent, so a smaller proportion of solvent molecules will be in the gas phase and the vapor pressure for the solution is lower than that for the pure solvent.

Raoult's Law states that for an ideal solution the partial vapor pressure of a component in solution is equal to the mole fraction of that component times its vapor pressure when pure:

P_{a} = X_{a}P_{a}^{o} P_{a} = vapor pressure of the solution
P_{a}^{o} = vapor pressure of pure solvent
X_{a} = mole fraction of the solvent

The fractional vapor pressure lowering is equal to the mole fraction of the solute:

X_{b} = (P_{a}^{o} - P_{a}) ÷ P_{a}^{o} P_{a} = vapor pressure of the solution
P_{a}^{o} = vapor pressure of pure solvent
X_{b} = mole fraction of the solute

Fractional vapor pressure lowering can be used to calculate molecular mass (formula weight) of a solute.

Example 1: Calculating the Vapor Pressure of a Solvent

1.00g of nonvolatile sulfanilamide, C_{6}H_{8}O_{2}N_{2}S, is dissolved in 10.0g of acetone, C_{3}H_{6}O.
The vapor pressure of pure acetone at the same temperature is 400 mmHg.
Calculate the vapor pressure of the solution.

Calculate moles of solute: n (C_{6}H_{8}O_{2}N_{2}S) = mass ÷ MM
n(C_{6}H_{8}O_{2}N_{2}S) = 1.00g ÷ (6 x 12 + 8 x 1 + 2 x 16 + 2 x 14 + 32.1) g/mol
= 1.00 ÷ 172.1 = 0.0058 mol

Calculate moles of solvent: n(C_{3}H_{6}O) = mass ÷ MM
n(C_{3}H_{6}O) = 10.0g ÷ (3 x 12 + 6 x 1 + 16) g/mol
= 10.0 ÷ 58 = 0.172 mol

Calculate the mole fraction of the solvent: X_{solvent} = n_{solvent} ÷ (n_{solute} + n_{solvent})
X_{a} = n(C_{3}H_{6}O) ÷ [n(C_{3}H_{6}O) + n(C_{6}H_{8}O_{2}N_{2}S)]
= 0.172 ÷ [0.172 + 0.0058] = 0.967

Calculate the vapor pressure: P_{a} = X_{a}P_{a}^{o} P_{a} = 0.967 x 400 mmHg = 386.8 mmHg = 387 mmHg

Example 2: Calculating the Molecular Mass (Formula Weight) of a Solute

5.00g of a nonvolatile compound was dissolved in 100g of water at 30^{o}C.
The vapor pressure of the solution was measured and found to be 31.20 Torr.
The vapor pressure of pure water at 30^{o}C is 31.82 Torr.
Calculate the molecular mass (formula weight) of the unknown solute.

Calculate the mole fraction of the solute: X_{b} = (P_{a}^{o} - P_{a}) ÷ P_{a}^{o} X_{b} = (31.82 - 31.2) ÷ 31.82 = 0.0195

Calculate moles of solvent: n(H_{2}O) = mass ÷ molecular mass
n(H_{2}O) = 100g ÷ (2 x 1 + 16)g/mol = 5.556mol

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