Explain the effect of a catalyst on chemical equilibrium with examples.

(N/A) catalyst is used to increase or decrease the rate of a chemical reaction. It does not affect the equilibrium position or the value of the equilibrium constant $K$. The catalyst does not appear in the balanced chemical equation or the expression for the equilibrium constant.
Effect of catalyst:
$(i)$ $A$ catalyst increases the rate of the chemical reaction by providing a new,lower-energy pathway for the conversion of reactants to products.
$(ii)$ It increases the rates of both forward and reverse reactions equally,thus not shifting the equilibrium.
$(iii)$ $A$ catalyst lowers the activation energy for both forward and reverse reactions by the same amount.
Example $1$: The Haber process for the synthesis of $NH_{3}$ from $N_{2}$ and $H_{2}$:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
This reaction is exothermic. At low temperatures,the reaction rate is very slow. Fritz Haber discovered that an iron catalyst allows the reaction to occur at a satisfactory rate at $500 \ ^\circ C$,where the equilibrium concentration of $NH_{3}$ is favorable.
Example $2$: The contact process for the manufacture of sulphuric acid:
$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,$K_{c} = 1.7 \times 10^{26}$
Although the large $K_{c}$ value suggests the reaction goes to completion,the oxidation of $SO_{2}$ to $SO_{3}$ is very slow. Therefore,platinum or vanadium$(V)$ oxide $(V_{2}O_{5})$ is used as a catalyst to increase the reaction rate.