Effect of addition of Inert gas (Le Chatelier’s Principle)
Addition of inert gas can be done under two conditions. One, under constant volume and two, under constant pressure.
Addition of inert gas under constant volume
When an inert gas is added to an equilibrium mixture keeping volume of the system constant, total number of moles inside the system increases. As a result, the total pressure inside the system increases too. But it does not affect the partial pressures of substances involved in the reaction. Thus, there is no impact on the reaction quotient, (Q_p), of the reaction and it remains equal to the equilibrium constant (K_p).
(ce{Q_$p$ = {(P_{NH_3})^2 over {(P_{H_2})^3.(P_{N_2)}}}}) = (K_p), (Q_p) is independent of any other gases other than reacting ones.
Addition of inert gas under constant pressure
When inert gas is added to an equilibrium mixture under fixed pressure, the number of moles of gases increases inside the system. In order to maintain the constant pressure, the system needs to be expanded, (P = {nRT over V}). There is a increase in the volume, which decreases the partial pressure of the reactants and products and hence reaction quotient, (Q_p), changes. Thus, the reaction moves in a direction to counter the increase in the volume of the system.