Chemical Equilibrium

Consider the following gaseous equilibrium reactions (I), (II) and (III) with equilibrium constants $K_1, K_2$ and $K_3$ respectively

(I) $\frac{1}{2} \mathrm{~N}_2+\frac{3}{2} \mathrm{H}_2 \rightleftharpoons \mathrm{NH}_3$

(II) $2 \mathrm{NO} \rightleftharpoons \mathrm{N}_2+\mathrm{O}_2$

(III) $\mathrm{H}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{H}_2 \mathrm{O}$

The correct expression for the equilibrium constant for the gaseous equilibrium reaction

\(2 \mathrm{NH}_3+\frac{5}{2} \mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO}+3 \mathrm{H}_2 \mathrm{O} \text { is }\)