Reactions at Equilibrium and the Equilibrium Constant

The equilibrium constant K is the ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients in the balanced equation. It can also be expressed as the ratio of the forward reaction rate constant to the reverse reaction rate constant. K quantifies the relative tendency of a reaction to form products or reactants at equilibrium.

The reaction quotient Q has the same mathematical form as K but applies to any point in the reaction, not necessarily at equilibrium. Q helps assess the system's current state and direction. When Q equals K, the system is at equilibrium and concentrations remain constant over time.

The standard Gibbs free energy change ΔrG° and equilibrium constant K are related by the equation ΔrG° = –RT ln K. At equilibrium, ΔrG equals zero. This relationship links thermodynamic favorability with equilibrium composition, allowing prediction of reaction direction based on energy values.

When K is much greater than one, ΔrG° is negative, indicating the reaction is thermodynamically favorable and proceeds toward product formation. The equilibrium mixture contains predominantly products with minimal reactants remaining, showing the reaction strongly favors the forward direction and will proceed to completion.

When K is much less than one, ΔrG° is positive, meaning the reaction is not thermodynamically feasible under standard conditions. The equilibrium mixture predominantly consists of reactants with minimal product formation, indicating the reverse reaction is strongly favored and the forward reaction will not proceed significantly.

When K equals one, ΔrG° is approximately zero, indicating neither products nor reactants are strongly favored thermodynamically. The equilibrium mixture contains substantial quantities of both reactants and products in comparable amounts, representing a balanced system where forward and reverse reactions occur at equal rates.

This equation relates Gibbs free energy under current conditions to standard conditions through the reaction quotient Q. By comparing Q to K, you can determine whether the reaction will shift forward or reverse to reach equilibrium. Understanding the response of equilibria to the conditions allows prediction of spontaneous reaction direction.