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Raoult's Law

Key Concepts

  • 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:

    Pa = XaPao
    Pa = vapor pressure of the solution
    Pao = vapor pressure of pure solvent
    Xa = mole fraction of the solvent

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

    Xb = (Pao - Pa) ÷ Pao
    Pa = vapor pressure of the solution
    Pao = vapor pressure of pure solvent
    Xb = 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, C6H8O2N2S, is dissolved in 10.0g of acetone, C3H6O.
The vapor pressure of pure acetone at the same temperature is 400 mmHg.
Calculate the vapor pressure of the solution.

  1. Calculate moles of solute: n (C6H8O2N2S) = mass ÷ MM
    n(C6H8O2N2S) = 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

  2. Calculate moles of solvent: n(C3H6O) = mass ÷ MM
    n(C3H6O) = 10.0g ÷ (3 x 12 + 6 x 1 + 16) g/mol
                  = 10.0 ÷ 58 = 0.172 mol

  3. Calculate the mole fraction of the solvent: Xsolvent = nsolvent ÷ (nsolute + nsolvent)
    Xa = n(C3H6O) ÷ [n(C3H6O) + n(C6H8O2N2S)]
        = 0.172 ÷ [0.172 + 0.0058] = 0.967

  4. Calculate the vapor pressure: Pa = XaPao
    Pa = 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 30oC.
The vapor pressure of the solution was measured and found to be 31.20 Torr.
The vapor pressure of pure water at 30oC is 31.82 Torr.
Calculate the molecular mass (formula weight) of the unknown solute.

  1. Calculate the mole fraction of the solute: Xb = (Pao - Pa) ÷ Pao
    Xb = (31.82 - 31.2) ÷ 31.82 = 0.0195

  2. Calculate moles of solvent: n(H2O) = mass ÷ molecular mass
    n(H2O) = 100g ÷ (2 x 1 + 16)g/mol = 5.556mol

  3. Calculate moles of solute: Xsolute = nsolute ÷ (nsolute + nsolvent)
    0.0195 = nsolute ÷ (nsolute + 5.556)
    0.0195(nsolute + 5.556) = nsolute
    0.0195(nsolute) + 0.108 = nsolute
    0.108 = nsolute - 0.0195(nsolute)
    0.108 = 0.9805(nsolute)
    (nsolute) = 0.108 ÷ 0.9805 = 0.11 mol

  4. Calculate molecular mass (formula weight) of solute: MM = mass ÷ moles
    MM = 5.00g ÷ 0.11 mol = 45.45 g/mol


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