An equilibrium constant is a quantity that characterizes the composition of a chemical reaction at chemical equilibrium. It equals a specified product-to-reactant ratio, with each constituent raised to a power determined by the reaction equation. The rigorous thermodynamic form uses activities rather than uncorrected concentrations or pressures. Its value depends on the reaction as written, temperature, and the chosen standard-state conventions; it describes equilibrium composition, not reaction speed. (goldbook.iupac.org)
Definition and reaction expression
For a balanced chemical equation
[ \alpha A+\beta B\rightleftharpoons\gamma C+\delta D, ]
the dimensionless standard equilibrium constant is
[ K^\circ= \left. \frac{a_C^\gamma a_D^\delta} {a_A^\alpha a_B^\beta} \right|_{\mathrm{equilibrium}}, ]
where (a_i) denotes the thermodynamic activity of constituent (i). More generally,
[ K^\circ=\prod_i a_i^{\nu_i}, ]
with stoichiometric numbers (\nu_i) positive for products and negative for reactants. Activities express chemical behavior relative to a specified standard state, making (K^\circ) dimensionless. Equilibrium constants defined directly using dimensional concentrations or pressures are distinct quantities and may carry units. (goldbook.iupac.org)
For a dilute solution under a concentration-based convention,
[ a_i=\gamma_i\frac{c_i}{c^\circ}, ]
where (c_i) is molar concentration, (c^\circ) is the reference concentration, and (\gamma_i) is an activity coefficient. For a gas under the usual ideal-gas standard convention, (a_i=f_i/p^\circ), where fugacity (f_i) approaches partial pressure in the low-pressure limit. These corrections distinguish real mixtures from idealized ones. (goldbook.iupac.org)
Concentration and pressure forms
Introductory treatments commonly use
[ K_c=\frac{[C]^\gamma[D]^\delta} {[A]^\alpha[B]^\beta}, ]
or, for gaseous constituents,
[ K_p=\frac{p_C^\gamma p_D^\delta} {p_A^\alpha p_B^\beta}. ]
Brackets denote equilibrium concentrations, while (p_i) denotes partial pressure. For an ideal-gas mixture, the unnormalized dimensional forms satisfy
[ K_p=K_c(RT)^{\Delta n_g}, ]
where (R) is the gas constant and (\Delta n_g) is the sum of gaseous product coefficients minus that of gaseous reactant coefficients. Units and normalization conventions must therefore accompany reported values. (openstax.org)
For example, the synthesis of ammonia from nitrogen and hydrogen,
[ \mathrm{N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g)}, ]
has (K_p=p_{\mathrm{NH_3}}^2/(p_{\mathrm{N_2}}p_{\mathrm{H_2}}^3)), using the dimensional pressure convention. This equilibrium underlies the Haber process. (openstax.org)
Pure solids and pure liquids are assigned unit activity in the usual introductory approximation, so their factors disappear from equilibrium expressions. This does not mean that these phases are chemically inactive: their presence determines which heterogeneous equilibrium can be established. Changing the amount of a pure solid does not change its activity while that phase remains present. (openstax.org)
Reaction direction and thermodynamic meaning
The reaction quotient (Q) has the same mathematical form as the equilibrium expression but uses the mixture’s current composition. At equilibrium, (Q=K^\circ). Under constant temperature and pressure, the reaction Gibbs energy satisfies
[ \Delta_rG=\Delta_rG^\circ+RT\ln Q. ]
Consequently,
[ \Delta_rG^\circ=-RT\ln K^\circ, \qquad \Delta_rG=RT\ln(Q/K^\circ). ]
These relations connect equilibrium composition to thermodynamics. If (Q<K^\circ), the forward reaction is thermodynamically favored; if (Q>K^\circ), the reverse reaction is favored. At equilibrium, (\Delta_rG=0), although (\Delta_rG^\circ) need not be zero. (goldbook.iupac.org)
A large (K^\circ) indicates a product-favored activity ratio, whereas a small value indicates a reactant-favored ratio. Neither value alone specifies every equilibrium concentration: composition also depends on starting amounts, volume, and other constraints. A value near unity does not imply equal concentrations because the expression includes stoichiometric powers. (openstax.org)
Temperature, perturbations, and kinetics
With fixed standard-state conventions, temperature changes generally change (K^\circ). Increasing temperature favors the endothermic direction: the equilibrium constant increases for an endothermic forward reaction and decreases for an exothermic one. This behavior is related to the reaction’s enthalpy change. (openstax.org)
Changing concentrations or compressing an ideal-gas mixture at fixed temperature can change (Q) and shift equilibrium composition without changing the equilibrium constant. Such responses are commonly described by Le Châtelier’s principle. In nonideal systems, concentration-based apparent constants can vary as activity coefficients change, even when the underlying thermodynamic constant remains fixed. (openstax.org)
A catalyst accelerates approach to equilibrium but does not alter its position or equilibrium constant. Chemical kinetics determines the timescale of equilibration; a thermodynamically favorable reaction can nevertheless proceed slowly. For a reversible elementary reaction obeying compatible mass-action rate laws, the concentration equilibrium constant equals the ratio of forward and reverse rate constants. This relationship cannot be applied indiscriminately to an overall multistep reaction. (openstax.org)
Reaction transformations and applications
Reversing a reaction replaces its equilibrium constant by (1/K). Multiplying all coefficients by a factor (m) gives (K^m). Adding reaction equations gives an overall constant equal to the product of their constants, provided temperature and conventions are consistent. Thus a quoted constant is meaningful only alongside its reaction equation. (openstax.org)
Specialized equilibrium constants include acid-dissociation constants for acid–base reactions, solubility products for dissolution of sparingly soluble solids, and association constants for reversible binding. The same framework also connects equilibrium constants to standard cell potentials in electrochemistry. (openstax.org)
Experimentally, constants are obtained by measuring equilibrium composition and substituting the resulting concentrations, pressures, or activities into the appropriate expression. Conversely, known constants are combined with material balances to calculate equilibrium compositions. Such calculations require consistent units and an explicit statement of any ideal-mixture approximations. (openstax.org)