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When an inert gas is added to the system, it doesn't participate in the reaction at all, and the reacting gases will retain their same volume and remain unchanged. That's why when we have inert gases we can pretty much disregard it.
Introducing an inert gas in a chemical equilibrium will change the volume and the pressure of the vessel that the reactants and products occupy. However, the inert gas will not change the concentration/partial pressure of the reactants and products and therefore will not affect the chemical equilibrium between the reactants and products. The pressure of the reactants and products will only change if the volume is through compression with a piston.
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