Which among the following denotes the correct relationship between ${\mathrm{K}}_{\mathrm{p}}$ and ${\mathrm{K}}_{\mathrm{c}}$ for the reaction $2{\mathrm{A}}_{\left(\mathrm{g}\right)}\rightleftharpoons {\mathrm{B}}_{\left(\mathrm{g}\right)}+{\mathrm{C}}_{\left(\mathrm{g}\right)}$

Using the data provided, find the value of equilibrium constant for the following reaction at $298 \mathrm{K}$ and $1$ atm pressure. ${\mathrm{NO}}_{\left(\mathrm{g}\right)}+\frac{1}{2}{\mathrm{O}}_2( \mathrm{g})\rightleftharpoons {\mathrm{NO}}_2( \mathrm{g})$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_{\left(\mathrm{g}\right)}\right)=90.4\mathrm{kJ}.{\mathrm{mol}}^{-1}$

${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_2\left(\mathrm{g}\right)\right)=32.48\mathrm{kJ}\cdot {\mathrm{mol}}^{-1}$

${\mathrm{\Delta S}}^{\circ }\mathrm{at} 298\mathrm{K}=-70.8\mathrm{J}\cdot {\mathrm{K}}^{-1}\cdot {\mathrm{mol}}^{-1}$

$\mathrm{antilog}(0.50)=3162$