The equilibrium constant for the reaction

${\mathrm{N}}_2\left(\mathrm{g}\right) + {\mathrm{O}}_2\left(\mathrm{g}\right) \rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right)$is $4 \times {10}^{-4}$ at 200 K. In the presence of a catalyst the equilibrium is attained 10 times faster. Therefore the equilibrium constant in presence of the catalyst at 200 K is