Question

The following equilibria are given :
$N_2+3H_2\rightleftharpoons 2N{H}_3$ $K_1$
$N_2+O_2\rightleftharpoons 2NO$ $K_2$
$H_2+\frac{1}{2}{O}_2\rightleftharpoons H_{2}O$ $K_3$
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. $\frac{K_1{K}_3^2}{K_2}$
• C. $\frac{K_2{K}_3^3}{K_1}$
• D. $K_1{K}_2{K}_3$

Answer 1

The correct option is C $\frac{K_2{K}_3^3}{K_1}$

(I)$N_2+3H_2\rightleftharpoons 2N{H}_3;K_1=\frac{[N{H}_3{]}^2}{\left[N_2\right][H_2{]}^3}$
(II)$N_2+O_2\rightleftharpoons 2NO:K_2=\frac{[NO{]}^2}{\left[N_2\right]\left[O_2\right]}$
(III)$H_2+1/2O_2\rightleftharpoons H_{2}O;K_3=\frac{\left[H_{2}O\right]}{\left[H_2\right][O_2{]}^{1/2}}$
(IV)$2N{H}_3+5/2O_2\rightleftharpoons 2NO+3H_{2}O;K_c=\frac{\left[NO{]}^2\right[H_{2}O{]}^3}{\left[N{H}_3{]}^2\right[O_2{]}^{5/2}}$
$\frac{K_2{K}_3^3}{K_1}$