Chapter 15, Problem 1RE

RECALL Is there a connection between the free-energy change for a reaction and its equilibrium constant? If there is a connection, what is it?

Interpretation Introduction

Interpretation:

The relationship between free energy change and equilibrium constant is to be determined.

Concept introduction:

The equation for free energy change $\Delta G=\text{R}T\ln \left(\frac{Q}{K}\right)$ is used to find out whether the reaction proceeds in the forward direction or the backward direction.

Answer to Problem 1RE

Solution: Yes, there is a relation between Gibbs free energy change and equilibrium. The relation between free energy change and equilibrium constant is justified by the equation $\Delta G^{\text{°}}=-\text{R}T\ln K_{eq}$.

Explanation of Solution

Yes, there is a connection between free energy change and equilibrium constant. Free energy change, under the standard condition, is related to the equilibrium constant by an equation.

The equation by which they are related to each other is as follows:

$\Delta G^{\text{°}}=-\text{R}T\ln K_{eq}$

Here, $\Delta G^{\text{o}}$ is the standard free energy change; $\text{R}$ is the universal gas constant; $K$ is the equilibrium constant.

Conclusion

Yes, there is a relation between equilibrium constant and free energy change. The relationship is expressed by an equation represented above.