Cato Maximilian Guldberg and Peter Waage — Norwegian chemists in Christiania (now Oslo) — published in 1864 what they called the law of mass action: at equilibrium, the ratio of product concentrations to reactant concentrations (each raised to its stoichiometric coefficient) is a constant at constant temperature. The paper was in Norwegian, ignored, republished in French in 1867, ignored again, and finally noticed in 1879. The equilibrium constant — K_eq — turned out to be the most useful single number in physical chemistry: a temperature-dependent property of a reaction that predicts where it will end up regardless of starting conditions. Le Châtelier's principle (1884) is qualitative; equilibrium constants are the quantitative version.
For a generic reversible reaction aA + bB ⇌ cC + dD, the equilibrium constant is K = ([C]^c · [D]^d) / ([A]^a · [B]^b), with brackets denoting concentrations at equilibrium. K depends only on temperature. K > 1 means products are favored; K < 1 means reactants are favored. The constant comes in several flavors depending on what you measure: Kc (concentrations), Kp (partial pressures), Ksp (solubility), Ka and Kb (acid and base ionization), Kw (water's autoionization, ≈ 10⁻¹⁴ at 25°C). The reaction quotient Q has the same form but uses current concentrations; comparing Q to K tells you which way the reaction will proceed. Connection to Gibbs free energy: ΔG° = −RT·ln(K). The equilibrium constant is the exponential of the negative standard free-energy change over RT — chemistry's most fundamental thermodynamic relation. Because of the exponential, catalysts (which don't change ΔG°) cannot change K. Temperature dependence follows the van't Hoff equation — d(ln K)/dT = ΔH°/RT²: endothermic reactions have K increasing with T, exothermic decreasing. Le Châtelier's principle reformulated: a system at equilibrium responds to a perturbation by shifting in the direction that partially undoes it — but K itself stays constant unless temperature changes. Equilibria are central in acid-base chemistry (Ka, pKa, buffers), solubility (Ksp), electrochemistry (the Nernst equation), biochemistry (every enzyme reaction, every metabolic pathway, every drug-receptor interaction), and atmospheric chemistry (ozone, CO₂ partitioning).
Industrial chemistry uses equilibrium calculations to set operating conditions: Haber-Bosch ammonia synthesis runs at high pressure and moderate temperature — chosen by Le Châtelier reasoning over K_eq — to maximize NH₃ yield. Geochemistry uses equilibrium constants to predict ocean pH, mineral solubility in groundwater, and isotope fractionation. Biochemistry is a study of interconnected equilibria: hemoglobin's oxygen affinity is one; ATP hydrolysis has a characteristic ΔG and K; every enzyme has a Michaelis constant. Drug-receptor binding is an equilibrium described by a dissociation constant Kd — typical drug Kd values are nanomolar. Climate models compute carbonate equilibria to predict ocean acidification. The Norwegian law of mass action is now quietly running in every chemical model anyone trusts.