At 25°C the vapour pressure of pure pentane is 511 torr and that of hexane is 150. torr.
What is the mole fraction of pentane in a pentane-hexane solution that has a vapour pressure of 383 torr at 25°C?

ANSWER IS 6.45×10-1

QUESTION: What is the mole fraction of hexane in the vapour that is in equilibrium with this solution?
(Assume ideal gas behaviour.)

Respuesta :

Based on the vapor pressure of the pure substances, the mole fraction of pentane is 0.45 and mole fraction of hexane at equilibrium is 0.60.

What is vapor pressure of a liquid?

Vapor pressure of of a liquid is the pressure that is excreted on the walls of a sealed vessel by the molecules of the liquid that have been converted to gaseous phase.

TO determine the mole fraction of pentane in the solution, we use the vapor pressure of the pure substances.

Let the mole fraction of pentane in the mixture be X.

The mole fraction of hexane will be 1 - X

  • The vapor pressure of the solution = (mole fraction of pentane × vapor pressure of pentane) + (mole fraction of hexane × vapor pressure of hexane)

Vapor pressure of solution = 383 torr

(mole fraction of pentane × vapor pressure of pentane) + (mole fraction of hexane × vapor pressure of hexane) = 383 torr

X × 511 + (1 - X) × 150 = 383

511X - 150X + 150 = 383

511X = 233

X = 0.45

Also , at equilibrium, the vapor pressure of pentane = 0.45 × 511 = 230 torr

mole fraction of hexane in the vapor that is in equilibrium with this solution = 230/383

mole fraction of hexane at equilibrium = 0.60

Therefore, the mole fraction of pentane is 0.45 and mole fraction of hexane at equilibrium is 0.60.

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