Pentane and Hexane Mole Fraction Calculation

Pentane (C₅H₁₂) and hexane (C₆H₁₄) form an ideal solution

At 25ᵒC the vapor pressures of pentane and hexane are 511 and 150 torr, respectively. A solution is prepared by mixing 25 mL pentane (density, 0.63 g/mL) with 45mL hexane (density, 0.66 g/mL).

What is the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution?

Final answer: The composition by mole fraction of pentane in the vapor that is in equilibrium with this solution is 0.68, calculated using Raoult's law and the mole fraction of pentane and hexane in the mixture.

Explanation: The composition by mole fraction of pentane in the vapor that is in equilibrium with the solution of pentane and hexane can be determined using Raoult's law and the formula of the mole fraction.

Raoult's law states that the partial vapor pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture. First, we find the number of moles of each substance.

For pentane: moles = mass / molar mass = (volume × density) / molar mass = (25mL × 0.63g/mL) / (72.15g/mol) ≈ 0.218 moles. For hexane: moles = (45mL × 0.66g/mL) / (86.18g/mol) ≈ 0.345 moles. The total moles = 0.218 + 0.345 = 0.563 moles.

The mole fraction of pentane, XPentane = moles_pentane / total moles = 0.218 / 0.563 = 0.387. The mole fraction of hexane, XHexane = 1 - XPentane = 0.613.

According to Raoult's law, the partial pressure of each substance is the product of its mole fraction and its vapor pressure. Thus, PPentane = XPentane × P°_Pentane = 0.387 × 511 torr ≈ 198 torr, and PHexane = XHexane × P°_Hexane = 0.613 × 150 torr ≈ 92 torr.

The total pressure over the solution, PTotal = PPentane + PHexane = 198 torr + 92 torr = 290 torr. Thus, the mole fraction of pentane in the vapor phase, YPentane = PPentane / PTotal = 198 torr / 290 torr = 0.68.

Therefore, the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution is 0.68.