Reactions at Equilibrium and the Equilibrium Constant

Reactions at equilibrium are characterized by equal rates of forward and reverse reactions. This state of equilibrium does not mean that the reactions have stopped, but rather that they are occurring at identical rates. As a result, the concentrations of reactants and products remain constant over time.

The equilibrium constant, denoted as 'K', is a key factor in understanding this state of equilibrium. 'K' is the ratio of the rate constant of the forward reaction to the rate constant of the reverse reaction. This provides a quantitative measure of the relative speed of the forward and reverse reactions.

Beyond this, 'K' can also be calculated using the concentrations of the components of the reaction. It's determined by the ratio of the concentration of products to the concentration of reactants, with each concentration raised to a power that matches its stoichiometric coefficient in the balanced chemical equation.

Additionally, for any point in the reaction (not necessarily at equilibrium), the reaction quotient Q represents the ratio of product to reactant concentrations in the same stoichiometric manner. At equilibrium, Q equals K.

The relationship between Gibbs free energy and the reaction composition is given by the equation:

Δ_rG = Δ_rG° + RT ln Q

where Δ_rG refers to the Gibbs energy change under the current conditions of the system, Δ_rG° is the standard Gibbs energy change only under standard conditions (1 M concentration, 1 atm pressure), R is the gas constant, and T is the temperature in Kelvin. At equilibrium, where Q = K, this equation simplifies to:

0 = Δ_rG° + RT ln K

This equation links thermodynamic favorability with equilibrium composition.

The values of 'K' and Δ_rG° can provide insights into the feasibility and direction of a reaction. If 'K' is greater than one and Δ_rG° is negative, the reaction is thermodynamically favorable and will proceed towards the formation of products. Conversely, if 'K' is less than one and Δ_rG° is positive, the reaction is not feasible, and the equilibrium mixture will predominantly consist of reactants. If 'K' equals one, this indicates that the equilibrium mixture has substantial quantities of both reactants and products.