Chapter 15, Problem 100A

Interpretation Introduction

Interpretation:

Temperature at which ${\text{ΔG}}_{\text{system}}=0$ is to be calculated.

Concept introduction:: Free energy change, ${\text{ΔG}}_{\text{system}}$ is the difference between the system’s change in enthalpy ( ${\text{ΔH}}_{\text{system}}$ ) and the product of the kelvin temperature and the change in entropy ( ${\text{TΔS}}_{\text{system}}$ ). That is,

${\text{ΔG}}_{\text{system}}\text{=}{\text{ΔH}}_{\text{system}}-{\text{TΔS}}_{\text{system}}$

.

Answer to Problem 100A

Temperature at which ${\text{ΔG}}_{\text{system}}=0$ is 86.95K.

Explanation of Solution

Given information,

$\begin{array}{l}{\text{ΔG}}_{\text{system}}=0\\ {\text{ΔH}}_{\text{system}}=\text{4}\text{.88kJ}\\ {\text{ΔS}}_{\text{system}}=\text{55}\text{.2J/K}\\ {\text{ΔS}}_{\text{system}}=\text{0}\text{.0552kJ/L}\text{(converted}\text{J}\text{to}\text{kJ)}\end{array}$

Since,

$\begin{array}{c}{\text{ΔG}}_{\text{system}}\text{=}{\text{ΔH}}_{\text{system}}{\text{-TΔS}}_{\text{system}}\\ \text{0}=\text{4}\text{.8-T(0}\text{.0552)}\\ \text{0}\text{.0552T}=\text{4}\text{.8}-\text{0}\\ \text{T}=\frac{\text{4}\text{.8}}{\text{0}\text{.0552}}\\ \text{T}=\text{86}\text{.95K}\end{array}$

Conclusion

In order to calculate Gibbs free energy( $\text{ΔG}$ ), it is usually necessary to convert units because $\text{ΔS}$ is usually expressed in $\text{j/K}$, whereas $\text{ΔH}$ is expressed in $\text{kJ}$.