Chapter 15.5, Problem 47PP

Interpretation Introduction

Interpretation:

The lowest temperature at which the given reaction becomes spontaneous needs to be determined.

Concept introduction:

A reaction is spontaneous if its Gibbs free energy change is negative. Gibbs free energy change is given by:

$\begin{array}{l}\Delta G=\Delta H-T\Delta S\\ where\\ \Delta GischangeinGibbsfreeenergy\\ \Delta Hischangeinenthalpy\\ \Delta Sischangeinentropy\\ TisTemperatureofreaction\end{array}$

Answer to Problem 47PP

The reaction will be spontaneous above $3913.04K$ temperature.

Explanation of Solution

For a reaction to be spontaneous:

$\begin{array}{l}\Delta G\le 0\\ Weknow\\ \Delta G=\Delta H-T\Delta S\\ \therefore \Delta H-T\Delta S\le 0\\ or\\ T\ge \frac{\Delta H}{\Delta S}\end{array}$

Information given:

$\begin{array}{c}\Delta H=-144kJ\\ \Delta S=-36.8J/K\\ =-0.0368kJ/K\end{array}$

Putting the values into the formula:

$\begin{array}{l}T\ge \frac{\Delta H}{\Delta S}\\ T\ge \frac{-144}{-0.0368}\\ T\ge 3913.04K\end{array}$

At the temperature above than $3913.04K$, the reaction will be spontaneous.