But pressure of the system increases. Because of this increase in pressure, wouldn't (according to Le Chatelier's principal) equilibrium shift towards the side with less moles of gas?
Addition of an inert gas at constant volume: When an inert gas is added to the system in equilibrium of constant volume though the total pressure exerted by the gases increases there is no shift in the equilibrium.
There is no shift in the equilibrium since there is no change in the molar concentrations(kept at constant volume) of each of the reacting components.
If an Inert Gas is added to a mixture kept at constant pressure there is a change in volume of overall mixture and hence the molar concentrations of the reacting components also decreases. Hence according to Le Chatelier’s Principle the reaction shift in direction of lower molar concentration.
Basically - ((Inert/Non Reacting) Gases)) do not affect the original concentrations and hence do not affect the equilibrium in case of constant volume situations