Chapter 4, Problem 4.10DQ

Interpretation Introduction

Interpretation:

The thermodynamic criterion for solution-vapour equailibrium has to be stated and justified.

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,

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

Gibb’s energy is an important factor which greatly affect the thermodynamic stability of a molecule or compound.

For example:  when state A is said to be more thermodynamically stable than state B of a chemical system, if the Gibbs energy of the change from A to B is positive.

The stable state of the chemical system is taken as its reference state.

The substance with lower molar Gibbs energy is more stable.