Chapter 4, Problem 4A.5E

Interpretation Introduction

Interpretation:

Change in molar Gibbs energy in a sample of water vapor at ${200}^{o}C$ is compressed isothermally from $350c{m}^{3}to120c{m}^3$ has to be determined.

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.

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

Molal Gibbs free energy can be determined using the following formula as show below,

$\Delta G=RT\ln \frac{V_1}{V_2}\boxed{\begin{array}{l}Where,\\ \Delta G:ChangeinGibbsfreeenergy\\ R:Gascons\tan t\\ T:Temperature\\ V_1:Initialvolume\\ V_2:Finalvolume\end{array}}$