Total vapor pressure: Calculate from mole fraction in vapor

Practice question

Question

A solution of two volatile liquids has vapor pressures of 300 mm Hg and 400 mm Hg for pure components. If the mole fraction of the second component in the vapor phase is 0.6, what is the total vapor pressure?

Options

Choose one · Correct answer highlighted

350 mm Hg 352.96 mm Hg Correct 360 mm Hg 340 mm Hg

Explanation

Vapor phase: y₂ = (P₂⁰ · x₂/Ptotal) . 0.6 = (400 · x₂/Ptotal) . Liquid phase: Ptotal = 300 (1 - x₂) + 400 x₂ . Substitute: 0.6 Ptotal = 400 x₂ , Ptotal = 300 + 100 x₂ . 0.6 (300 + 100 x₂) = 400 x₂ , 180 + 60 x₂ = 400 x₂ , 340 x₂ = 180 , x₂ = (180/340) ≈ 0.5294 . Ptotal = 300 (1 - 0.5294) + 400 × 0.5294 ≈ 352.96 mm Hg .

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