Answer to Question #106767 in Physical Chemistry for Bharti

Question

A binary liquid mixture is in equilibrium with its vapour at a temperature T=300K. The liquid mole fraction x1 of species 1 is 0.4 and the molar excess Gibbs energy is 200J/mol. the value of the universal gas constant is 8.314 J/mol/k and y1 denotes the liquid phase activity co-efficient of species.
1. If ln(y1)=0.09, find the value of ln(y2).

Answer 1

Excess molar Gibbs (G) energy of a binary liquid mixture is expressed as:

G = RT*(x₁*lny₁ + x₂*lny₂)

It is given that x₁ = 0.4, hence, x₂ = 0.6.

Thus,

lny₂ = (G/RT - x₁*lny₁)/x₂ = (200/8.314/300 - 0.4*0.09)/0.6 = 0.0735