When a catalyst is added to a reaction then according to the intermediate complex theory it provides an alternative path to the reaction or the reaction mechanism by reducing its activation energy between the reactants and products and hence lowers the potential energy barrier. Consequently, the rate constant of the reaction increases thus increasing the rate of the reaction. but all this does not affect the enthalpy of the reaction as catalyst does not alter the Gibbs energy change or extent of the reaction.

For a reaction, A+B → C, graph will be,

As the initial and final point of the reaction is same therefore enthalpy of the reaction is constant.

Without catalyst,

lnK1 = lnA – Ea1/RT ……………………………..i)

lnK2 = lnA – Ea2/RT……………………………….ii)

by substituting value of lnA in eq i) from eqii)we get,

lnK2 – lnK1 = 1/RT(Ea1-Ea2)

log K2/K1 = (Ea1-Ea2)/2.303RT