Chapter 18, Problem 88AP

Interpretation Introduction

Interpretation:

The two ways that determine $\Delta G^{\circ }$ of a reaction are to be described.

Concept introduction:

The quantity that predicts the spontaneity of a process is called the Gibbs free energy. The mathematical equation is as follows:

$\Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }$

Here, $\Delta G^{\circ }$ is the change in standard Gibbs free energy, $\Delta H^{\circ }$ is the standardenthalpy change of a system, and $\Delta S^{\circ }$ is the standard entropy change of the system.

Entropy is a thermodynamic function. Entropy is a measure of randomness or disorder of the system. The unit of entropy is $\text{J/K}\text{.mol}$.

The reaction is spontaneous if $\Delta G^{\circ }$ is negative.

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

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

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: $\Delta G^{\text{o}}\text{=}-\text{R }T\text{lnK }$

An equilibrium process is the state at which the rate of the backward reaction is equal to the rate of the forward reaction.

$\Delta \text{G}\text{<}\text{0}$ (negative), the reaction is spontaneous.

$\Delta \text{G}>\text{0}$ (positive), the reaction is non-spontaneous.

$\Delta \text{G}=\text{0}$ (zero), the system is at equilibrium.