Question

The following equilibrium are given:
$N_2+3H_2\rightleftharpoons 2{NH}_3$ $K_1$
$N_2+O_2\rightleftharpoons 2NO$ $K_2$
$H_2+\frac{1}{2}{O}_2\rightleftharpoons H_{2}O$ $K_3$
The equilibrium constant of the reaction
$2{NH}_3+\frac{5}{2}{O}_2\rightleftharpoons 2NO+3H_{2}O$ 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 $\frac{K_2{K}_3^3}{K_1}$

$\left(I\right)N_2+3H_2\rightleftharpoons 2{NH}_3$; $K_1=\frac{{\left[{NH}_3\right]}^2}{\left[N_2\right]{\left[H_2\right]}^3}$

$\left(II\right)N_2{O}_2\rightleftharpoons 2NO$; $K_2=\frac{{\left[NO\right]}^2}{\left[N_2\right]\left[O_2\right]}$

$\left(III\right)H_{2}1/2O_2\rightleftharpoons H_{2}O$; $K_3=\frac{\left[H_{2}O\right]}{\left[H_2\right]{\left[O_2\right]}^{1/2}}$

$\left(IV\right)2{NH}_3+5/2O_2\rightleftharpoons 2NO+3H_{2}O$; $K_c=\frac{{\left[NO\right]}^2{\left[H_{2}O\right]}^3}{{\left[{NH}_3\right]}^2{\left[O_2\right]}^{5/2}}=\frac{K_2{K}_3^3}{K_1}$

Hence, option C is correct.