A quantity of ${\mathrm{PCl}}_5$ was heated in a 10 litre vessel at ${250}^0\mathrm{C};$   ${\text{PCl}}_5\left(\mathrm{g}\right) \rightleftharpoons {\mathrm{PCl}}_3\left(\mathrm{g}\right) + {\mathrm{Cl}}_2\left(\mathrm{g}\right).$ At equilibrium the vessel contains 0.1 mole of ${\mathrm{PCl}}_5$, 0.20 mole of ${\mathrm{PCl}}_3$ and 0.2 more of ${\mathrm{Cl}}_2$. The equilibrium constant of the reaction is