A catalyst is a substance that increases the rate of a chemical reaction by lowering the activation energy without being consumed in the reaction. It does not affect the equilibrium position of the reaction or the equilibrium constant Kc . The catalyst only speeds up the time it takes for the reaction to reach equilibrium.Let's consider a hypothetical reaction with unequal numbers of gaseous reactants and gaseous products:aA g + bB g cC g + dD g where A and B are reactants, C and D are products, and a, b, c, and d are their respective stoichiometric coefficients.The equilibrium constant Kc for this reaction is given by:Kc = [C]^c * [D]^d / [A]â * [B]^b where [A], [B], [C], and [D] represent the equilibrium concentrations of the respective species.Now, let's assume we have the initial concentrations of the reactants and products as [A]0, [B]0, [C]0, and [D]0. When the reaction reaches equilibrium, the concentrations will change as follows:[A] = [A]0 - ax[B] = [B]0 - bx[C] = [C]0 + cx[D] = [D]0 + dxwhere x is the extent of reaction at equilibrium.When a catalyst is introduced, the reaction rate increases, but the equilibrium position remains the same. Therefore, the equilibrium concentrations of the reactants and products will not change, and the value of Kc will also remain the same.In summary, introducing a catalyst to a reaction with unequal numbers of gaseous reactants and gaseous products will only affect the rate at which the reaction reaches equilibrium, but it will not change the equilibrium position, the equilibrium concentrations of the reactants and products, or the value of Kc.