Question

The following equilibrium are given
$N_2+3H_2\rightleftharpoons 2N{H}_2$ ---------------$K_1$
$N_2+O_2\rightleftharpoons 2NO$ ---------------$K_2$
$H_2+\frac{1}{2}{O}_2\rightleftharpoons H_{2}O$ ---------------$K_3$
The equilibrium constant of the reaction
$2N{H}_3+\frac{5}{2}{O}_2\rightleftharpoons 2NO+3H_{2}O$ in terms of $K_1,K_2$ and $K_3$ is:

• A. $\frac{K_1{K}_2}{K_3}$
• B. $\frac{K_1{K}_3}{K_2}$
• C. $\frac{K_2{K_3}^3}{K_1}$
• D. $K_1{K}_2{K}_3$

Answer 1

The correct option is C $\frac{K_2{K_3}^3}{K_1}$

$N_2+3H_2\rightleftharpoons 2{NH}_3$ So, $K_1=\frac{{\left[{NH}_3\right]}^2}{\left[N_2\right].{\left[H_2\right]}^3}$

$N_2+O_2\rightleftharpoons 2NO$ So, $K_2=\frac{{\left[NO\right]}^2}{\left[N_2\right]\left[O_2\right]}$

$H_2+\frac{1}{2}{O}_2\rightleftharpoons H_{2}O$ So, $K_3=\frac{\left[H_{2}O\right]}{\left[H_2\right]\times {\left[O_2\right]}^{1/2}}$

$2M\frac{1}{3}+\frac{5}{2}{O}_2\rightleftharpoons 2NO+3H_{2}O$

$K_{eq}=\frac{{\left[NO\right]}^2\times {\left[H_{2}O\right]}^3}{{\left[{NH}_3\right]}^2{\left[O_2\right]}^{5/2}}$

$=\frac{{\left[NO\right]}^2}{\left[N_2\right]\left[O_2\right]}\times {\left(\frac{\left[H_{2}O\right]}{\left[H_2\right]{\left[O_2\right]}^{1/2}}\right)}^3\times \left(\frac{\left[N_2\right]{\left[H_2\right]}^3}{{\left[{nH}_3\right]}^2}\right)$

$=K_2\times K_3^3\times K_1^{-1}$

$=\frac{K_2\times K_3^3}{K_1}$