Le Châtelier's principle Knowledge-Based Study

Study notes

1. What is Dynamic Equilibrium?

   A reversible chemical reaction reaches dynamic equilibrium when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time, even though both reactions continue to occur simultaneously.

   The Principle Defined

   In 1884, French chemist Henri Louis Le Châtelier formulated a fundamental rule governing systems at dynamic equilibrium:

   Le Châtelier's Principle: If an external stress or change in conditions is applied to a system at dynamic equilibrium, the system adjusts in such a way as to partially counteract that change and establish a new equilibrium state.

   The common stresses that alter an equilibrium state include:

   • Changes in the concentration of reactants or products
   • Changes in pressure or volume (for gaseous systems)
   • Changes in temperature

   Adjusting Concentrations

   When the concentration of a substance in an equilibrium mixture is changed, the system shifts to consume part of the added species or replace part of the removed species.

   Consider the generalized reversible reaction:

   $$\text{A(aq)} + \text{B(aq)} ightleftharpoons \text{C(aq)} + \text{D(aq)}$$

   • Adding a reactant: Increasing the concentration of A causes the rate of the forward reaction to exceed the rate of the reverse reaction. The system shifts to the right (forward direction) to consume the excess A.
   • Removing a product: Decreasing the concentration of C shifts the equilibrium to the right to replenish the lost C.
   • Adding a product: Increasing the concentration of C shifts the equilibrium to the left (reverse direction) to consume the added C.
   • Removing a reactant: Decreasing the concentration of A shifts the equilibrium to the left to regenerate A.

   Note: Changing concentrations alters the individual equilibrium amounts, but the value of the equilibrium constant ($K_c$) remains completely unchanged at constant temperature.

   Pressure and Volume in Gaseous Equilibria

   According to Boyle's law, pressure and volume are inversely proportional at constant temperature. Therefore, decreasing the volume of a reaction vessel increases the total pressure, and increasing the volume decreases the total pressure.

   A system responds to pressure changes only if there is a difference between the total stoichiometric moles of gaseous reactants and gaseous products ($\Delta n_{\text{gas}} \neq 0$). Pure solids and liquids are essentially incompressible and are excluded from these mole counts.

   Consider the Haber-Bosch synthesis of ammonia:

   $$\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} ightleftharpoons 2\text{NH}_3\text{(g)}$$

   • Moles of gaseous reactants: $1 + 3 = 4\text{ mol}$
   • Moles of gaseous products: $2\text{ mol}$

   Effects of adjustments:

   • Increasing pressure (decreasing volume): The system shifts toward the side with fewer moles of gas to relieve the excess pressure. For this reaction, it shifts to the right.
   • Decreasing pressure (increasing volume): The system shifts toward the side with more moles of gas to restore pressure. For this reaction, it shifts to the left.
   • Equimolar systems ($\Delta n_{\text{gas}} = 0$): If both sides contain the same number of gaseous moles (e.g., $\text{H}_2\text{(g)} + \text{I}_2\text{(g)} ightleftharpoons 2\text{HI(g)}$), pressure or volume changes have no effect on the position of equilibrium.

   Temperature and the Equilibrium Constant

   Temperature is the only standard stress that changes the actual numerical value of the equilibrium constant ($K$). To predict the direction of the shift, treat heat as a chemical reactant or product.

   1. Exothermic Reactions ($\Delta H < 0$)

   $$\text{Reactants} ightleftharpoons \text{Products} + \text{Heat}$$

   • Increasing temperature: Heat is added, shifting the system to the left. As a result, product concentrations decrease, reactant concentrations increase, and the value of $K$ decreases.
   • Decreasing temperature: Heat is removed, shifting the system to the right. The value of $K$ increases.

   2. Endothermic Reactions ($\Delta H > 0$)

   $$\text{Reactants} + \text{Heat} ightleftharpoons \text{Products}$$

   • Increasing temperature: Heat is added, shifting the system to the right. Consequently, $K$ increases.
   • Decreasing temperature: Heat is removed, shifting the system to the left. Consequently, $K$ decreases.

   Common Misconceptions

   Role of a Catalyst

   A catalyst increases the rates of both the forward and reverse reactions equally by lowering the activation energy for both pathways. Therefore:

   • A catalyst allows a system to reach equilibrium faster.
   • A catalyst does not shift the position of equilibrium.
   • A catalyst does not change the value of $K$.

   Addition of an Inert Gas

   • At constant volume: Adding an unreactive gas (such as helium or argon) increases total pressure, but the partial pressures and molar concentrations of the reacting gases remain unchanged. Therefore, there is no shift in equilibrium.
   • At constant total pressure: Adding an inert gas expands the container volume, decreasing the partial pressures of all reacting gases. The system responds as it would to a volume increase, shifting toward the side with more moles of gas.