Le Châtelier's Principle -- from Eric Weisstein's World of Physics

This entry contributed by David Rovnyak

A qualitative version of le Châtelier's principle states that, if some external change is imposed on a system in reactive equilibrium, the system will establish a new equilibrium which counteracts the external change. This principle was first stated by Henri Le Châtelier Eric Weisstein's World of Biography in 1884, and more fully developed in an 1888 paper.

Le Châtelier's principle can be illustrated by considering an equilibrium state of a gas-phase decomposition in which a reactant molecule may decompose into two molecules, and vice versa. If this process takes place in a cylinder with a movable piston and the pressure of the system is forcibly increased by compressing the piston, then le Châtelier's principle predicts that the equilibrium will shift to the reactants, since this reduces the number of gas molecules and will decrease the pressure. Let be the equilibrium value of advancement of reaction, be the Gibbs free energy at equilibrium, the heat of reaction for forward process (i.e., reactants to products), the change in volume, T the temperature, and P the pressure. The change in the advancement of a reaction with pressure at constant temperature is then

This equation can be interpreted by examining the signs of the various processes. Consider again a gas-phase reaction in which the products have twice the volume of the reactant. In the above equation, the sign of the right-hand side depends on the volume change for the forward reaction. In this case, the change in volume is positive, so the entire right-hand side becomes negative. Then an increase (positive change) in pressure requires a negative advancement to make the left-hand side negative as well. Thus, the equilibrium shifts toward the reactants, in agreement with the qualitative prediction.

Another illustration is provided by considering an aqueous reaction which is exothermic for the forward process. If the temperature of the system is decreased, then the equilibrium will shift in favor of the products, since this will evolve heat and raise the temperature of the system. The change in the advancement of a reaction with temperature, while keeping pressure constant, is

Here, the right-hand side depends on the sign of the heat of reaction. Taking the heat of reaction to be negative, the entire right-hand side becomes negative. If the temperature is decreased, then the advancement must be positive to make the left-hand side be negative. Thus, the equilibrium will shift to the products, again confirming the qualitative prediction.

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