1 mole of ${\mathrm{PCl}}_5$ taken in a lit vessel , it dissociates into ${\mathrm{PCl}}_5\text{ and }{\mathrm{Cl}}_2$ to an extent of 50% and  equilibrium pressure is at 5 atm then $K_P$ value of  ${\mathrm{PCl}}_{5\left(g\right)}\rightleftharpoons {\mathrm{PCl}}_{3\left(g\right)}+{\mathrm{Cl}}_2\left(g\right)$

$$\begin{gathered} {\mathrm{PCl}}_5\rightleftharpoons {\mathrm{PCl}}_3+{\mathrm{Cl}}_2 ; x=50\%=0.5 \\ \mathrm{Initial}: 1\mathrm{mol} 0 0 \\ \mathrm{at} \mathrm{equi}.: 1-0.5 0.5 0.5 \end{gathered}$$ 

Total no. of moles = 1.5

${\mathrm{K}}_{\mathrm{p}}=\frac{{\mathrm{P}}_{{\mathrm{PCl}}_3}\times {\mathrm{P}}_{{\mathrm{Cl}}_2}}{{\mathrm{P}}_{{\mathrm{PCl}}_5}}=\frac{{\displaystyle \frac{0.5}{1.5}}\mathrm{p}\times {\displaystyle \frac{0.5}{1.5}}\mathrm{p}}{\frac{0.5}{1.5}\mathrm{p}}=\frac{5}{3}=1.67$