Chapter 4, Problem 4.10P

Interpretation Introduction

Interpretation:

Derivation of the expression $\boxed{\Delta G=nRT\left\{X_A\ln X_A+X_B\ln X_B\right\}}$ has to be done. 

Concept Introduction:

The Gibbs energy of a gas can be interpreted in terms of chemical potential as follows,

$G=n\mu =n\left\{{\mu }^{\Theta }+RT\ln \left(\frac{p}{p^{\Theta }}\right)\right\}$

Where,

$n=$ No. of moles

$\mu =$ Chemical potential

${\mu }^{\Theta }=$ Standard chemical potential

$R=$ Universal gas constant

$T=$ Absolute temperature

$p=$ Final pressure

$p^{\Theta }=$ Initial pressure

  $\Delta G_{mix}=G_{final}-G_{initial}$

Mole fraction:

  $X=\frac{n}{n_{total}}$