$N_2 + 3H_2 \rightleftharpoons 2NH_3 \,;$ $K_1$
$N_2 + O_2 \rightleftharpoons 2NO\,;$ $K_2$
$H_2 + 2 O_2 \rightleftharpoons H_2O\,;$ $K_3$
The equilibrium constant $(K)$ of the reaction :
$2NH_3 + \frac{5}{2} \overset K \leftrightarrows 2NO + 3H_2O$
$\mathrm{N}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO} \quad \mathrm{K}_{2}\dots (2)$
$\mathrm{H}_{2}+\frac{1}{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O} \quad \mathrm{K}_{3} \dots (3)$
For reaction $2 \mathrm{NH}_{3}+\frac{5}{2} \mathrm{O}_{2} \stackrel{\mathrm{k}}{\rightleftharpoons} 2 \mathrm{NO}+3 \mathrm{H}_{2} \mathrm{O} \dots (4)$
equation $( 4) =$ equation $(2)+3 \times$ equation $(3)-$ equation $( 1)$
$\Rightarrow \mathrm{K}=\frac{\mathrm{K}_{2} \mathrm{K}_{3}^{3}}{\mathrm{K}_{1}},$
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