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Process Calculations
Vapor-Liquid Equilibrium
GATE 2013
Hard

The vapor liquid equilibrium relation for an ideal binary system is given by y*A=αAB·xA/[1+(αAB−1)xA]. Here xA and y*A are the mole fractions of species A in the liquid and vapor, respectively. The relative volatility (αAB) is greater than unity. The liquid mole fraction xA at which the maximum difference between the equilibrium vapor mole fraction and liquid mole fraction occurs is

  • 1/(1+√αAB)
  • B0.75/(1+√αAB)
  • C0.5/(√αAB+1)
  • D0.75/(√αAB+1)

Explanation

Let β=αAB−1. y*−x=βx(1−x)/(1+βx). Setting d(y*−x)/dx=0 and simplifying gives βx²+2x−1=0, so x=(√(1+β)−1)/β=(√αAB−1)/(αAB−1)=(√αAB−1)/[(√αAB−1)(√αAB+1)]=1/(√αAB+1).

Source: GATE CH 2013 (2013)

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