At 473 K, equilibrium constant $K_c$ for decomposition of phosphorus pentachloride, ${PCl}_5$ is $8.3\times {10}^{-3}$. If decomposition is depicted as,
${PCl}_5\left(g\right)\rightleftharpoons {PCl}_3\left(g\right)+{Cl}_2\left(g\right)$ ${\Delta }_r{H}^{\ominus }=124.0kJ{mol}^{-1}$
(a) Write an expression for $K_c$ for the reaction.
(b) What is the value of $K_c$ for the reverse reaction at the same temperature?
(c) What would be the effect on $K_c$ if (i) more ${PCl}_5$ is added (ii) pressure is increased (iii) the temperature is increased ?

(a) The equilibrium constant expression is
$K_c=\frac{[PC{l}_3][C{l}_2]}{[PC{l}_5]}$
(b) The equilibrium constant expression for the reverse reaction is
$K_c(reverse)=\frac{1}{8.3\times 10^{-3}}=120.48$
(c) (i) When more $PC{l}_5$ is added, the direction of equilibrium is affected but the value of equilibrium constant is unaffected as $K_c$ is constant at a given temperature.
(ii) When pressure is increased, the value of the equilibrium constant remains unaffected.
(iii) When temperature is increased, the value of equilibrium constant is increased. The reaction is endothermic. When temperature is increased, $K_f$ is increased. Hence, $K_c=\frac{K_f}{K_r}$ is also increased.