Calculate the mole fraction of pentane in the vapor above the solution

Question

A solution initially contains 2.0 mol of pentane (C₅H₁₂) and 12.0 mol of octane (C₈H₁₈) at 25 C. The vapor pressures of pure pentane and pure octane at 25 C are 510 torr and 11 torr, respectively. Calculate the mole fraction of pentane in the vapor above the solution

Answer 1

Just to clarify above: Partial pressure of pentane=(Total pressure of solution)(mole fraction of pentane). So 72.88=82.31(mole fraction of pentane), and follow calculation above.

Answer 2

Total moles of solution = 2.0 mol pentane + 12.0 mol octane = 14.0 mols

Mole fraction of pentane = 2.0 / 14.0 = 0.1429

Mole fraction octane = 12.0 / 14.0 = 0.8571

Vapor pressure pentane = 0.1429 x 510 torr = 72.88 torr

Vapor pressure octane = 0.8571 x 11 torr = 9.428 torr

Total vapor pressure of solution = 72.88 torr + 9.428 torr = 82.31 torr

Mole fraction pentane in the vapor phase = 72.88 torr / 82.31 torr = 0.88