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Deriving the Equilibrium Constant Formula from Reaction Probabilities in Chemistry

The equilibrium constant expression is derived from probabilistic collision theory: for a reversible reaction, the probability of a forward or reverse reaction occurring within a small volume is proportional to the product of the reactant (or product) concentrations, each raised to its stoichiometric coefficient, times a temperature-dependent rate constant. Setting the forward and reverse reaction probabilities equal at equilibrium and combining the resulting rate constants yields the equilibrium constant (K) as the ratio of product concentrations (raised to their coefficients) to reactant concentrations (raised to their coefficients). This connects chemical kinetics and probability theory to equilibrium thermodynamics within general chemistry.