Chapter 18, Problem 42QP

Interpretation Introduction

Interpretation:

The standard free energy changefor the auto ionization of water 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 moleculeson 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 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 $\Delta \text{G}$ for a reaction to be spontaneous, must be negative.

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

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