Chemical Equilibrium

The equilibrium will shift to forward direction because according to second law of thermodynamics, the entropy must increase in the direction of spontaneous reaction.

The condition for equilibrium is $\mathrm{G}_{\mathrm{N}_2}+3 \mathrm{G}_{\mathrm{H}_2} \quad 2 \mathrm{G}_{\mathrm{NH}_3}$ where G is Gibbs free energy per mole of the gaseous species measured at that partial pressure. The condition of equilibrium is unaffected by the use of catalyst, which increases the rate of both the forward and backward reactions to the same extent.

The catalyst will increase the rate of forward reaction by and that of backward reaction by $\beta$.

Catalyst will not alter the rate of either of the reaction.