Chapter 17.2, Problem 1RQ

Interpretation Introduction

Interpretation:

The equilibrium constant expression for the given reaction is to be written.

Concept introduction:

The Equilibrium constant is the ratio of the amount of the product to that of the reactants, containing each concentration term was raised to a power equal to its coefficient in a given balanced chemical equation at the constant temperature.

Answer to Problem 1RQ

The equilibrium expression is given as:

  $\text{K}\text{=}\frac{{\left[{\text{NO}}_{\text{2}}\right]}^{\text{2}}}{\left[{\text{O}}_{\text{2}}\right]{\left[\text{NO}\right]}^{\text{2}}}$

Explanation of Solution

The given reaction is

  $\text{2NO}\left(\text{g}\right)\text{+}{\text{O}}_{\text{2}}\left(\text{g}\right)\rightleftharpoons {\text{2NO}}_{\text{2}}\left(\text{g}\right)$

According to the law of mass action,

  $\begin{array}{l}\text{rate}\text{of}\text{forward}\text{reaction}\propto {\left[\text{NO}\right]}^{\text{2}}\left[\text{O}\right]\\ \text{=}{\text{K}}_{\text{f}}{\left[\text{NO}\right]}^{\text{2}}\left[\text{O}\right]\end{array}$

Similarly, the backward reaction is

  ${\text{2NO}}_{\text{2}}\left(\text{g}\right)\rightleftharpoons \text{2NO}\left(\text{g}\right)\text{+}\text{O}\left(\text{g}\right)$

  $\begin{array}{l}\text{rate}\text{of}\text{backward}\text{reaction}\propto {\left[{\text{NO}}_{\text{2}}\right]}^{\text{2}}\\ \text{=}{\text{K}}_{\text{b}}{\left[{\text{NO}}_{\text{2}}\right]}^{\text{2}}\end{array}$

At equilibrium, the rate of forwarding and reverse reactions is equal

  $\begin{array}{l}{\text{K}}_{\text{f}}{\left[\text{NO}\right]}^{\text{2}}\left[\text{O}\right]\text{=}{\text{K}}_{\text{b}}{\left[{\text{NO}}_{\text{2}}\right]}^{\text{2}}\\ \frac{{\text{K}}_{\text{f}}}{{\text{K}}_{\text{b}}}\text{=}\frac{{\left[{\text{NO}}_{\text{2}}\right]}^{\text{2}}}{{\left[\text{NO}\right]}^{\text{2}}\left[\text{O}\right]}\\ \text{K}\text{=}\frac{{\left[{\text{NO}}_{\text{2}}\right]}^{\text{2}}}{{\left[\text{NO}\right]}^{\text{2}}\left[\text{O}\right]}\end{array}$

Conclusion

The equilibrium expression is the ratio of the equilibrium constant for the forward reaction to that of the reverse reaction.