The role of a catalyst in a reversible reaction is to allow the equilibrium to be achieved quickly.
A catalyst increases the rate of forward and reverse reaction to equal extent. However, it does not affects the value of the equilibrium constant.

Explanation:

A catalyst is a substance that increases the rate of a chemical reaction by providing an alternative reaction pathway with lower activation energy. It does not undergo any net change during the reaction and is regenerated at the end of the reaction.

Effect of catalyst on equilibrium constant:

The equilibrium constant (K) is a measure of the extent of a reversible reaction at equilibrium. It is defined as the ratio of the concentration of the products to the concentration of the reactants, each raised to their respective stoichiometric coefficients.

When a catalyst is added to a reversible reaction at equilibrium, it speeds up both the forward and reverse reactions. However, it has no effect on the equilibrium position or the value of the equilibrium constant. This is because a catalyst does not change the concentrations of the reactants or products at equilibrium.

Key points:
- A catalyst increases the rate of both the forward and reverse reactions.
- A catalyst provides an alternative reaction pathway with lower activation energy.
- A catalyst does not undergo any net change during the reaction and is regenerated at the end.
- A catalyst does not affect the equilibrium position or the value of the equilibrium constant.
- The equilibrium constant is a measure of the extent of a reversible reaction at equilibrium.
- It is defined as the ratio of the concentration of the products to the concentration of the reactants, each raised to their respective stoichiometric coefficients.

Conclusion:
When a catalyst is added to a reversible reaction in the equilibrium state, the value of the equilibrium constant does not change. The catalyst only speeds up the reaction by providing an alternative pathway with lower activation energy, but it does not alter the equilibrium position or the ratio of product to reactant concentrations.