Chapter 17, Problem 67A

(a)

Interpretation Introduction

Interpretation:

The equilibrium expression of the given heterogeneous equilibria has to be written.

Concept Introduction:

At chemical equilibrium, the rate of forward reaction and that of backward reaction becomes equal. The chemical reaction follows the law of mass action. The law of mass action states that the rate of a chemical reaction is directly proportional to the product of active masses of the reactants.

  $aA+bB\rightleftharpoons cC+dD$

  $Rateoftheforwardreaction{r}_f=k_f{[A]}^a{[B]}^b$

  $Rateofthebackwardreaction{r}_b=k_b{[C]}^c{[D]}^d$

  $k_{f}and{k}_{b}aretherateconstantsofforwardandbackwardreactionrespectively$

  $Atequilibriumtherateoftheforwardreaction=therateofthebackwardreaction$

  $k_f{[A]}^a{[B]}^b=k_b{[C]}^c{[D]}^d$

  $\frac{k_f}{k_b}=K_{eq}=\frac{{[C]}^c{[D]}^d}{{[A]}^a{[B]}^b}$

  $K_{eq}istheequilibriumconstantofthereaction.$

Answer to Problem 67A

  $K_{eq}=\frac{1}{{[O_2]}^3}$

Explanation of Solution

The given chemical equation is-

  $\begin{array}{l}4Al(s)+3O_2(g)\rightleftharpoons 2A{l}_2{O}_3(s)\\ EquilibriumConstant{K}_{eq}=\frac{{[A{l}_2{O}_3]}^2}{{[Al]}^4{[O_2]}^3}\\ Theactivityofsolidcomponentsisequalto1.\\ [A{l}_2{O}_3]=[Al]=1\\ K_{eq}=\frac{1}{{[O_2]}^3}\end{array}$