Explanation:

When a reversible reaction is carried out in the presence of a catalyst, the equilibrium constant of the reaction remains unaffected.

Equilibrium Constant:

The equilibrium constant (K) is a measure of the extent to which a reaction proceeds to form products. It is defined as the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium, with each concentration raised to the power of its stoichiometric coefficient. The equilibrium constant is a constant value at a given temperature.

Effect of Catalyst:

A catalyst is a substance that speeds up the rate of a reaction by providing an alternative reaction pathway with a lower activation energy. It does not participate in the reaction and is not consumed or changed in the reaction. The presence of a catalyst does not alter the position of equilibrium or the equilibrium constant of a reaction.

Reasoning:

The equilibrium constant is determined solely by the stoichiometry of the reaction and the temperature at which it is carried out. It is independent of the presence of a catalyst because the catalyst only affects the rate at which the reaction reaches equilibrium, not the position of equilibrium itself. The catalyst provides an alternative pathway with a lower activation energy, allowing the reaction to proceed faster in both the forward and reverse directions. This means that the catalyst speeds up the approach to equilibrium, but does not affect the final composition of the equilibrium mixture.

Example:

Consider the reversible reaction:
A + B ⇌ C + D

The equilibrium constant for this reaction is given by:
K = [C][D] / [A][B]

If a catalyst is introduced to the reaction, it may increase the rate at which products C and D are formed, as well as the rate at which reactants A and B are reformed. However, the equilibrium constant K remains unchanged because the ratio of product concentrations to reactant concentrations at equilibrium is still the same.

Therefore, the equilibrium constant remains unaffected when a reversible reaction is carried out in the presence of a catalyst.