Consider the following gaseous equilibrium reactions $(I)$,$(II)$ and $(III)$ with equilibrium constants $K_1$,$K_2$ and $K_3$ respectively:
$I$) $\frac{1}{2} N_2 + \frac{3}{2} H_2 \rightleftharpoons NH_3$
$II$) $2 NO \rightleftharpoons N_2 + O_2$
$III$) $H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2 O$
The correct expression for the equilibrium constant for the gaseous equilibrium reaction $2 NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2 NO + 3 H_2 O$ is

• A
  $\frac{K_3^3}{K_1^2 \times K_2}$
• B
  $\frac{K_3^2}{K_1^2 \times K_2}$
• C
  $\frac{K_3^3}{K_1 \times K_2}$
• D
  $\frac{K_3^2}{K_1 \times K_2}$