Chemical reactions that proceed in both a forward and reverse direction eventually reach chemical equilibrium. This is a dynamic state where the rate of the forward reaction exactly equals the rate of the reverse reaction. The relative amounts of reactants and products present are governed by the equilibrium constant, \(K_{eq}\). The numerical value of the equilibrium constant changes with temperature, a fact rooted in its thermodynamic basis.
Defining the Equilibrium Constant
The equilibrium constant (\(K_{eq}\)) provides a single, quantitative value describing the composition of a reversible reaction at equilibrium. It is calculated as the ratio of product concentrations to reactant concentrations, each raised to its stoichiometric coefficient. This ratio remains fixed for a specific reaction under a specific set of conditions. A large \(K_{eq}\) (greater than one) signifies that products are favored, meaning the reaction lies heavily toward the product side. Conversely, a small \(K_{eq}\) (less than one) indicates that reactants are favored. This constant is a thermodynamic property derived from the standard change in Gibbs free energy (\(\Delta G^\circ\)). The equilibrium constant is fixed only when the temperature is held constant; other factors that shift the position of equilibrium will not alter the numerical value of \(K_{eq}\) itself.
Qualitative Shifts Using Le Chatelier’s Principle
Temperature is unique because changing it affects the stability of the entire system, leading to a new value for \(K_{eq}\). We predict the direction of this change using Le Chatelier’s Principle, which states that a system at equilibrium will shift to counteract any applied stress. Heat is treated as either a reactant or a product, depending on the reaction’s energy profile.
Endothermic Reactions
In an endothermic reaction, which absorbs heat from its surroundings (represented by a positive change in enthalpy, \(\Delta H > 0\)), heat is conceptually a reactant. Increasing the temperature shifts the equilibrium toward the products, increasing the product-to-reactant ratio and causing \(K_{eq}\) to increase.
Exothermic Reactions
In an exothermic reaction, which releases heat into the surroundings (a negative change in enthalpy, \(\Delta H < 0[/latex]), heat is conceptually a product. If the temperature is raised, the system consumes the excess heat by shifting the equilibrium toward the reactants. This movement decreases the product-to-reactant ratio, resulting in a decrease in [latex]K_{eq}[/latex].
Quantifying the Temperature Dependence
While Le Chatelier’s Principle predicts the direction of the shift, the Van’t Hoff equation provides the quantitative relationship between temperature change and the magnitude of the [latex]K_{eq}\) change. This relationship shows that the degree to which \(K_{eq}\) is altered is directly proportional to the standard enthalpy change (\(\Delta H^\circ\)) of the reaction. Reactions with a large absolute value of \(\Delta H^\circ\) are inherently more sensitive to temperature fluctuations than reactions with a small \(\Delta H^\circ\).
Temperature changes affect the rates of the forward and reverse reactions differently because each direction possesses a distinct activation energy. The equilibrium constant is mathematically defined as the ratio of the forward rate constant (\(k_f\)) to the reverse rate constant (\(k_r\)). Since the rate constants are exponentially dependent on temperature, a change in temperature alters \(k_f\) and \(k_r\) by differing amounts, leading to a new, unique ratio for \(K_{eq}\).
Factors That Do Not Influence the Constant
Unlike temperature, several common factors influence the position of equilibrium without changing the numerical value of \(K_{eq}\). Changes in the concentration of reactants or products cause the system to shift, but the final concentration ratio always restores the original \(K_{eq}\). Altering the pressure or volume of a gaseous system shifts the equilibrium position toward the side with fewer or more moles of gas, but does not change the constant itself. The addition of a catalyst also leaves \(K_{eq}\) untouched, as it speeds up the rate at which equilibrium is reached by lowering the activation energy for both the forward and reverse reactions equally. These factors alter the composition of the equilibrium mixture, not the underlying thermodynamic ratio.