Chapter 17, Problem 17.6P

Interpretation Introduction

Interpretation:

Whether the value of Q for a given reaction at given temperature is constant or not has to be explained.

Concept Introduction:

Equilibrium constant$\left({\text{K}}_{\text{c}}\right)$:

Equilibrium constant $\left({\text{K}}_{\text{c}}\right)$ is the ratio of the rate constants of the forward and reverse reactions at a given temperature.  In other words it is the ratio of the concentrations of the products to concentrations of the reactants.  Each concentration term is raised to a power, which is same as the coefficients in the chemical reaction.

Consider the reaction where A reacts to give B.

    $\text{aA}\rightleftharpoons \text{bB}$

    $\begin{array}{l}\text{Rate of forward reaction = Rate of reverse reaction}\\ {\text{k}}_{\text{f}}{\left[\text{A}\right]}^{\text{a}}{\text{=k}}_{\text{r}}{\left[\text{B}\right]}^{\text{b}}\end{array}$

On rearranging,

    $\begin{array}{l}\frac{{\left[\text{B}\right]}^{\text{b}}}{{\left[\text{A}\right]}^{\text{a}}}\text{=}\frac{{\text{k}}_{\text{f}}}{{\text{k}}_{\text{r}}}{\text{=K}}_{\text{c}}\\ (\text{or)}\\ {\text{K}}_{\text{c}}\text{ = }\frac{\text{[products]}}{[\text{reactants]}}\end{array}$

Where,

    ${\text{k}}_{\text{f}}$ is the rate constant of the forward reaction.

    ${\text{k}}_{\text{r}}$ is the rate constant of the reverse reaction.

    ${\text{K}}_{\text{c}}$ is the equilibrium constant.

Reaction Quotient:

Reaction quotient, Q is the ratio between product of the product concentration to the product of the reactant concentration with each term raised to the power of its balancing coefficient.

Consider a general equation,

  $a\text{A +}b\text{A}\stackrel{}{\rightleftharpoons }c\text{C}+d\text{D}$

Where a, b, c and d are the stoichiometric coefficients.  The reaction quotient is,

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