${\mathrm{N}}_2$and ${\mathrm{H}}_2$are taken in $1 : 3$molar ratio in a closed vessel to attained the following equilibrium,

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$  Find KP for reaction at total pressure of 2P if ${\mathrm{P}}_{{\mathrm{N}}_2}$ at equilibrium is $\frac{\mathrm{P}}{3}$

${\mathrm{N}}_2$and ${\mathrm{H}}_2$are taken in $1 : 3$molar ratio in a closed vessel to attained the following equilibrium, ${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$  The ${\mathrm{K}}_{\mathrm{P}}$for reaction at total pressure of 2P if ${\mathrm{P}}_{{\mathrm{N}}_2}$ at equilibrium is $\frac{\mathrm{P}}{3}$ is 

$2P=\frac{P}{3}+P+P_{{\mathrm{NH}}_3}$

$\Rightarrow P_{{\mathrm{NH}}_3}=\frac{2P}{3}$

$$\begin{gathered} K_P=\frac{P_{{\mathrm{NH}}_3}^2}{P_{{\mathrm{N}}_2}\times P_{{\mathrm{H}}_2^3}}=\frac{{\left(\frac{2P}{3}\right)}^2}{\frac{P}{3}\times P^3} \\ =\frac{4}{3P^2} \end{gathered}$$