Chapter 15, Problem 95A

Interpretation Introduction

Interpretation:

The circumstances for an endothermic chemical reaction with negative change in entropy to become spontaneous needs to be explained.

Concept introduction:

Any physical or chemical change that oncebegun, occurs with no outside intervention is a spontaneous process.

Answer to Problem 95A

Anendothermic chemical reaction can be spontaneous only at high temperature when $-\text{TΔS}>\Delta \text{H}\text{.}$

Explanation of Solution

A chemical reaction is said to be spontaneous if the Gibbs free energy associated with it is negative.

$\text{ΔG=}\text{ΔH-TΔS}\text{(for}\text{spontaneity,}\text{ΔG<0)}$

For an endothermic chemical reaction to be spontaneous in which the entropy of the system increases, the following condition should be followed:

$-\text{TΔS}>\Delta \text{H}\text{.}$

This is because change in entropy is negative and due to endothermic reaction, change in enthalpy is positive. To get negative change in Gibbs free energy, temperature should be high.

Conclusion

Thus, an endothermic chemical reaction can be spontaneous only at high temperature when $-\text{TΔS}>\Delta \text{H}\text{.}$