Chapter 14, Problem 14.21QA

Interpretation Introduction

To find:

The expressions for $K_c$ and $K_p$ for the given reactions

Answer to Problem 14.21QA

Solution:

The expressions for $K_c$ and $K_p$ for the given reactions are

a) For the reaction $N_2\left(g\right)+2O_2\left(g\right)\leftrightarrow N_2{O}_4\left(g\right)$,

$K_c=\frac{\left[N_2{O}_4\right]}{\left[N_2\right]{\left[O_2\right]}^2}$

$K_p=\frac{P_{N_2{O}_4}}{P_{N_2}·P_{O_2}^2}$

b) For the reaction $3NO\left(g\right)\leftrightarrow N{O}_2\left(g\right)+N_{2}O\left(g\right)$,

$K_c=\frac{\left[N{O}_2\right]\left[N_{2}O\right]}{{\left[NO\right]}^3}$

$K_p=\frac{P_{N{O}_2}·P_{N_{2}O}}{P_{N{O}_2}^3}$

c) For the reaction $2N_{2}O\left(g\right)\leftrightarrow 2N_2\left(g\right)+O_2\left(g\right)$,

$K_c=\frac{{\left[N_2\right]}^2·\left[O_2\right]}{{\left[N_{2}O\right]}^2}$

$K_p=\frac{P_{N_2}^2·P_{O_2}}{P_{N_{2}O}^3}$

Explanation of Solution

1) Concept:

The equilibrium constant for a reaction is usually written as the ratio of concentrations of products and reactants, each raised to a power equal to its coefficient in the balanced equation. For reactions in which the terms that appear in the equilibrium constant are only of gaseous species, the equilibrium constant can also be written in terms of their partial pressures. This is because the partial pressure and concentration of a gas are related through the ideal gas equation. The two forms are given below in the formula section.

a) For the reaction $N_2\left(g\right)+2O_2\left(g\right)\leftrightarrow N_2{O}_4\left(g\right)$,

$K_c=\frac{\left[N_2{O}_4\right]}{\left[N_2\right]{\left[O_2\right]}^2}$

$K_p=\frac{P_{N_2{O}_4}}{P_{N_2}·P_{O_2}^2}$

b) For the reaction $3NO\left(g\right)\leftrightarrow N{O}_2\left(g\right)+N_{2}O\left(g\right)$,

$K_c=\frac{\left[N{O}_2\right]\left[N_{2}O\right]}{{\left[NO\right]}^3}$

$K_p=\frac{P_{N{O}_2}·P_{N_{2}O}}{P_{N{O}_2}^3}$

c) For the reaction $2N_{2}O\left(g\right)\leftrightarrow 2N_2\left(g\right)+O_2\left(g\right)$,

$K_c=\frac{{\left[N_2\right]}^2·\left[O_2\right]}{{\left[N_{2}O\right]}^2}$

$K_p=\frac{P_{N_2}^2·P_{O_2}}{P_{N_{2}O}^3}$

2) Formula:

For a reaction $aA\left(g\right)+bB\left(g\right)\leftrightarrow cC\left(g\right)+dD\left(g\right)$, the equilibrium constants are given by

$K_c=\frac{{\left[C\right]}^c·{\left[D\right]}^d}{{\left[A\right]}^a·{\left[B\right]}^b}$

$K_p=\frac{P_C^c·P_D^D}{P_A^a·P_B^b}$

Conclusion:

The equilibrium constant for a reaction is written as the ratio of concentrations (or partial pressures for gases) of products and reactants, each raised to a power equal to its coefficient in the balanced equation.