Effect of Inert Gas Addition

The Core Idea: Inert Gas Addition at Constant Volume

When an inert gas — a gas that does not participate in the reaction — is added to a system at equilibrium while the volume is kept constant, the equilibrium position does not shift. This is a direct consequence of how the reaction quotient $Q$ is defined for gaseous equilibria.

The key is to understand what the addition of an inert gas actually changes inside the container. At constant volume, adding more gas particles increases the total pressure inside the container. However, the partial pressures of the reactants and products — the gases that actually appear in the equilibrium expression — remain unchanged.

Why? Because partial pressure depends on the number of moles of that specific gas and the total volume. Since the volume is fixed and no reactant or product gas is added or removed, the molar concentrations $[ \ ] = n/V$ of each reacting species stay exactly the same. Consequently, their partial pressures $p_i = (n_i RT)/V$ also remain the same.

Since $Q$ is calculated using these partial pressures or concentrations, and none of them change, $Q$ remains equal to $K$. The equilibrium is undisturbed.

The Quantitative Reasoning

Let's make this precise. Consider a general gaseous reaction at equilibrium:

The equilibrium constant in terms of partial pressures is:

Now, suppose we add an inert gas (e.g., argon, helium) at constant volume $V$. The partial pressure of each reacting gas $i$ is given by the ideal gas law:

Since $V$, $T$, and $n_i$ (the number of moles of that specific gas) are all unchanged, $p_i$ for every reactant and product remains exactly the same. Therefore, the value of $K_p$ — and the reaction quotient $Q$ — is unchanged. The system remains at equilibrium.

The Only Exception: When the Inert Gas Is a Reactant or Product …