Chapter 13, Problem 13.62P

Interpretation Introduction

Interpretation:

To derive the expression for $H^E$

To show that the implied excess heat capacity is necessarily positive

Concept introduction:

The excess property relation is given as

  $\frac{H^E}{RT}=-T{\left[\frac{\partial (G^E/RT}{\partial T}\right]}_{P,x}$

By Wilson equation,

  $\frac{G^E}{RT}=-x_1\ln (x_1+x_2{\Lambda }_{12})+x_2\ln (x_2+x_1{\Lambda }_{21})$

  ${\Lambda }_{ij}=\frac{V_j}{V_i}exp\left(\frac{-a_{ij}}{RT}\right)$

  $C_P^E=\frac{d{H}^E}{dT}$

  $\frac{G^E}{RT}$ = Excess Gibbs Energy

x₁ = Mole fraction of species 1

x₂ = Mole fraction of species 2

R = Universal Gas Constant

T = Temperature

V_i = Molar volume of Species (1)

V_j = Molar volume of Species (2)