PCl_5 dissociates as PCl_5( g ) ⇌ PCl_3( g )+ Cl_2( g ) 5 moles of PCl_5 are placed in a 200 litre vessel which contains 2 moles of N_2 and is…

$\displaystyle \mathrm{PCl}_5$ dissociates as $$\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g}) $$ $\displaystyle 5$ moles of $\displaystyle \mathrm{PCl}_5$ are placed in a $\displaystyle 200$ litre vessel which contains $\displaystyle 2$ moles of $\displaystyle \mathrm{N}_2$ and is maintained at $\displaystyle 600$ K . The equilibrium pressure is $\displaystyle 2.46$ atm . The equilibrium constant $\displaystyle \mathrm{K}_{\mathrm{p}}$ for the dissociation of $\displaystyle \mathrm{PCl}_5$ is \_\_\_\_ $\displaystyle \times 10^{-3}$. (nearest integer) (Given: $\displaystyle \mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$; Assume ideal gas behaviour)