How does adding an inert gas at constant volume affect equilibrium?

Adding an inert gas at constant volume does not affect the position of equilibrium in a reaction.

In a chemical reaction, the equilibrium position is determined by the relative rates of the forward and reverse reactions. When an inert gas is added to a system at constant volume, it increases the total pressure of the system. However, it does not change the partial pressures of the reactants or products, which are the factors that directly influence the equilibrium position.

The equilibrium constant (K) for a reaction is given by the ratio of the concentrations (or pressures) of the products to the reactants, each raised to the power of their stoichiometric coefficients. Since the addition of an inert gas does not change the concentrations or partial pressures of the reactants or products, it does not change the value of K, and hence does not shift the equilibrium position.

This can be understood in terms of Le Chatelier's Principle, which states that if a system at equilibrium is subjected to a change, the system will adjust itself to counteract that change. In this case, the addition of an inert gas increases the total pressure of the system, but since the volume is constant, the system cannot counteract this change by expanding. Therefore, the only way the system can counteract the change is by shifting the equilibrium position. However, since the inert gas does not participate in the reaction, it does not affect the relative rates of the forward and reverse reactions, and hence does not cause a shift in the equilibrium position.

In conclusion, while the addition of an inert gas at constant volume increases the total pressure of the system, it does not change the partial pressures or concentrations of the reactants or products, and hence does not affect the equilibrium position. This is a key concept in physical chemistry and is important for understanding the behaviour of gases and the principles of chemical equilibrium.