JEE Main 2022 · 24 Jun · Shift 2, Chemistry question 83

$\mathrm{PCl_5}$ dissociates as
$$\mathrm{PCl_5(g)\rightleftharpoons PCl_3(g)+Cl_2(g)}$$
5 moles of $\mathrm{PCl_5}$ are placed in a 200 litre vessel which contains 2 moles of $\mathrm{N_2}$ and is maintained at 600 K. The equilibrium pressure is 2.46 atm. The equilibrium constant $K_p$ for the dissociation of $\mathrm{PCl_5}$ is ______ $\times10^{-3}$. (nearest integer)

(Given: $R=0.082\ \mathrm{L\,atm\,K^{-1}mol^{-1}}$; Assume ideal gas behaviour)