At 20 °C the vapor pressure of pure benzene (C6H6) is 75.0 torr, and that of toluene (C7H8) is 22.0 torr. Assume that benzene and toluene form ideal solutions. What is the mole fraction of benzene in a solution that has a (total) vapor pressure of 55.0 torr at 20 °C?

mole fraction benzene = 0.62

mole fraction toluene = 0.38

Explanation:

Raoults law for ideal solutions tells us that the totoal vapor pressure of the solution will be given by adding the partial pressures of the components of the solution and the partial pressures are simply given by the product of the component in solution times its pure vapor pressure at the temperature given:

p total = x₁ P⁰₁ + x₂ P⁰₂

where x1 and x2 for this solution denote the mole fractions of benzene and toluene and p⁰ ₁, p⁰₂ the vapor pressures of benzene and toluene respectively.

Solving the algebraic equation:

75 x₁ + 22 x₂ = 55

75 x₁ + 22 (1 - x₁) = 55 (since x₁ + x₂ = 1)

75 x₁ + 22 - 22 x₁ = 55

53 x₁ = 33

x₁ = 0.62

x₂ = 1 - 0.62 = 0.38