Chapter 18, Problem 81AP

Interpretation Introduction

Interpretation:

The standard free energy change and the equilibrium constant at constant pressure for the given equilibrium reaction at ${\text{25}}^{\circ }\text{C}$ are to be determined.

Concept introduction:

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

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

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

The relation between equilibrium constant and standard free energy is as follows:

${\text{lnK}}_{\text{P}}\text{=}\frac{-\Delta {\text{G}}^{\circ }}{R\text{T}}$

Here, $\Delta G^o$ is standard free energy change, $K_P$ is equilibrium constant at constant pressure, $\text{R}$ is universal gas constant, and $T$ is the absolute temperature.