Answer:
mole fraction benzene = 0.62
mole fraction toluene = 0.38
Step-by-step 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