Chapter 4, Problem 4C.2ST

Interpretation Introduction

Interpretation:

The change in chemical potential when the partial pressure is decreased from 100 kPa to 50 kPa at 298 K has to be evaluated.

Concept introduction:

Chemical potential:

The chemical potential tell us how the Gibbs Free energy will vary with the number of moles $n_i$ of component i holding temperature, pressure, and the number of moles of all other components constant. For a pure substance, the chemical potential is equal to its molar Gibbs Free energy.

${\text{μ}}_{\text{i}}\text{=}{\left(\frac{\partial \text{G}}{\partial {\text{n}}_{\text{i}}}\right)}_{{\text{T,P,n}}_{\text{i,j}}}\boxed{\begin{array}{l}\text{where,}\\ {\text{μ}}_{\text{i}}\text{Chemical}\text{potential}\\ \text{G}\text{Gibbs}\text{free}\text{energy}\\ \text{T}\text{Temperature}\\ \text{P}\text{Pressure}\end{array}}$

If the partial pressure of a perfect gas in a mixture changes from $P_{J,i}to{P}_{J,f}$, then the change in its chemical potential can be calculated using the following equation as shown below,

$\Delta {\mu }_J=RT\ln \frac{P_{J,f}}{P_{J,i}}$