The following equilibrium constants are given:
$\mathrm{N_2 + 3H_2 \rightleftharpoons 2NH_3}$; K$_1$
$\mathrm{N_2 + O_2 \rightleftharpoons 2NO}$; K$_2$
$\mathrm{H_2 + \frac{1}{2}O_2 \rightleftharpoons H_2O}$; K$_3$

The equilibrium constant for the oxidation of 2 moles of NH$_3$ by oxygen to give NO is: