At $473 \ K$,the equilibrium constant $K_{c}$ for the decomposition of phosphorus pentachloride is $8.3 \times 10^{-3}$. If the decomposition is depicted as:
$PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)} \quad \Delta_{r}H^{\circ} = 124.0 \ kJ \ mol^{-1}$
$(a)$ 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?

(B) The expression for $K_{c}$ is: $K_{c} = \frac{[PCl_{3(g)}][Cl_{2(g)}]}{[PCl_{5(g)}]}$
$(b)$ The value of $K_{c}$ for the reverse reaction is the reciprocal of the forward reaction: $K_{c}^{\prime} = \frac{1}{K_{c}} = \frac{1}{8.3 \times 10^{-3}} \approx 120.48$
$(c)$ $(i)$ $K_{c}$ remains unchanged because $K_{c}$ depends only on temperature.
$(ii)$ $K_{c}$ remains unchanged as it is independent of pressure at a constant temperature.
$(iii)$ Since the reaction is endothermic $(\Delta_{r}H^{\circ} > 0)$,the value of $K_{c}$ increases with an increase in temperature.