2SO2(g) + O2(g) 2SO3(g)
a) Effect of catalyst: A catalyst increases the rate of forward and the backward reaction to the same extent. This is due to the fact that it decreases the energy of activation of the forward as well as backward reaction to the same extent. Hence a catalyst has no effect on the final state of equilibrium. A catalyst, however, enables the system to reach a state of equilibrium much quickly.
b) Addition of inert gas at constant pressure : The addition of inert gas at constant pressure will increase the total volume. Hence, at equilibrium the molar concentration of reactants and products decrease and the equilibrium will shift in a direction in which number of moles increase. Therefore, in above reaction, equilibrium shifts towards left.