Chapter 18, Problem 44QP

Interpretation Introduction

Interpretation:

The standard free energy changeand equilibrium constant at constant pressure $\text{(}{K}_{\text{P}})$ for the given equilibrium reaction, at ${\text{25}}^{\circ }\text{C}$, is to be determined.

Concept introduction:

The reaction quotient is the ratio of molar concentration of the ions or the partial pressure of the gaseous atoms or molecules on the product side to the molecules on the reactant side, raised to the power of their stoichiometric coefficient in the balanced chemical reaction.

For a general chemical reaction, $\text{aA + bB }\underset{}{\overset{}{\rightleftarrows }}\text{cC+dD}$, the reaction quotient will be represented as:

$Q=\frac{{\text{[C]}}^{\text{c}}{\text{[D]}}^{\text{d}}}{{\text{[A]}}^{\text{a}}{\text{[B]}}^{\text{b}}}$

The standard free energy change of the reaction is the difference of the sum of standard free energy change of products and the sum of the standard free energy change of reactants.

$\Delta {\text{G}}_{rxn}^{\circ }\text{=}{\displaystyle \sum \Delta {\text{G}}_{product}^{\circ }}-{\displaystyle \sum \Delta {\text{G}}_{reac\tan t}^{\circ }}$

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

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

Here, $\Delta G$ is the free energy change, $\Delta G^o$ is the standard free energy change, $Q$ is the reaction quotient, $\text{R}$ is the gas constant and $T$ is the temperature.

The value of $\Delta G$ for a reaction to be spontaneous, must be negative.

The value of $\Delta G$ for a reaction at equilibrium, must be zero.

The value of $\Delta G$ for a reaction to be non-spontaneous, must be positive.