What is the difference between adding inert gas at constant volume and adding inert gas at constant pressure?

At equilibrium,

 

When an inert gas is added at constant volume, the pressure increases. But the ratio of the moles of reactants and products to the volume does not change.

Hence, there will nit be any effect on the equilibrium of the reaction.

 

When the inert gas is added at constant pressure, the total volume will increase. Thus, the number of moles of the reactants and products per unit volume will  drcrease. That means the concentration of the reactants and products will be changed. Hence, the equilibrium will shift towards the direction where there is an increase in the number of moles of gases.

 

Example:

2NH₃(g) ↔ N₂(g) + 3H₂(g) 

In the above case, addition of inert gas at constant pressure, will shift the equilibrium towards product side as the total number of moles of the products is more.