Equilibrium Constants
- Guldberg and Waage's law of mass actionnot yet tested
- K expression, Q vs K, and the K flavorsnot yet tested
- ΔG° = −RT·ln(K) and temperature dependencenot yet tested
- Haber-Bosch, buffers, and drug-receptor Kdnot yet tested
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).