Chapter 18, Problem 95QP

Interpretation Introduction

Interpretation:

The value of $\Delta S^o$, $\Delta H^o$, and $\Delta G^o$ for the given reaction are to be determined with the help of diagram.

Concept introduction:

All the energy available with the system, which is utilized in doing useful work, is called Gibbs free energy.

Entropy is the direct measurement of randomness or disorder. Entropy is an extensive property and a state function.

The enthalpy of the system is defined as the sum of the internal energy and the product of the pressure and the volume. It is a state function and an extensive property.

The relation between free energy change and standard free energy change is as follows:

$\Delta G=\Delta G^{\text{o}}+\text{R}T\ln Q$

Here, $\Delta G$ is free energy change, $\Delta G^o$ is standard free energy change, $Q$ is the reaction quotient, $\text{R}$ is the gas constant, and $T$ is the temperature.

At equilibrium the above equation is reduced to the expression: $\Delta G^{\text{o}}\text{=}-\text{R }T\text{lnK }$

The standard change in enthalpy for the given reaction is calculated by the expression:

$\begin{array}{c}\ln \frac{{\text{K}}_{\text{2}}}{{\text{K}}_{\text{1}}}=\frac{\Delta H^o}{R}\times \left(\frac{1}{T_1}-\frac{1}{T_2}\right)\\ =\frac{\Delta H^o}{\text{R}}\times \left(\frac{T_2-T_1}{T_1{T}_2}\right)\end{array}$

The Gibbs free energy change is calculated by using the expression as

$\Delta G=\Delta H-T\Delta S$

Here, $\Delta G$ is Gibbs free energy change, $\Delta H$ is the enthalpy change, $T$ is the temperature, and $\Delta S$ is the entropy change.