A catalyst increases the rate of the chemical reaction by making available a new low energy pathway for the conversion of reactants to products.
It increases the rate of forward and reverse reactions that pass through the same transition state and does not affect equilibrium. Catalyst lowers the activation energy for the forward and reverse reactions by exactly the same amount.
Catalyst does not affect the equilibrium composition of a reaction mixture. It does not appear in the balanced chemical equation or in the equilibrium constant expression.
Let us consider the formation of NH3 from dinitrogen and dihydrogen which is highly exothermic reaction and proceeds with decrease in total number of moles formed as compared to the reactants. Equilibrium constant decreases with increase in temperature.
At low temperature rate decreases and it takes long time to reach at equilibrium, whereas high temperatures give satisfactory rates but poor yields.
German chemist, Fritz Haber discovered that a catalyst consisting of iron catalyse the reaction to occur at a satisfactory rate at temperatures, where the equilibrium concentration of NH3 is reasonably favourable.
Since the number of moles formed in the reaction is less than those of reactants, the yield of NH3 can be improved by increasing the pressure.
Optimum conditions of temperature and pressure for the synthesis of NH3 using catalyst are around 500°C and 200 atm.
Similarly, in manufacture of sulphuric acid by contact process,
2SO2(g) + O2(g) ⇔ 2SO3(g); Kc = 1.7 × 1026
though the value of K is suggestive of reaction going to completion, but practically the oxidation of SO2 to SO3 is very slow. Thus, platinum or divanadium penta-oxide (V2O5) is used as catalyst to increase the rate of the reaction.
Note: If a reaction has an exceedingly small K, a catalyst would be of little help.