Editing Equilibrium constant (section)

== Basic definitions and properties ==
For a system undergoing a [[reversible reaction]] described by the general [[chemical equation]]
: <math>\alpha\,\mathrm{A} + \beta\,\mathrm{B} + \cdots \rightleftharpoons \rho\,\mathrm{R} + \sigma\,\mathrm{S} + \cdots</math>
a thermodynamic equilibrium constant, denoted by <math>K^\ominus</math>, is defined to be the value of the [[reaction quotient]] ''Q<sub>t</sub>'' when forward and reverse reactions occur at the same rate. At [[chemical equilibrium]], the chemical composition of the mixture does not change with time, and the [[Gibbs free energy]] change <math>\Delta G</math> for the reaction is zero. If the composition of a mixture at equilibrium is changed by addition of some reagent, a new equilibrium position will be reached, given enough time. An equilibrium constant is related to the composition of the mixture at equilibrium by
<ref>[https://goldbook.iupac.org/html/S/S05915.html IUPAC Gold Book].</ref><ref>{{cite book |title=The Determination of Stability Constants |last1=Rossotti |first1=F. J. C. |last2=Rossotti |first2=H. |date=1961 |publisher=McGraw-Hill |page=5}}</ref>

: <math>K^\ominus = \frac{{\mathrm{\{R\}}^\rho \mathrm{\{S\}}^\sigma...}}{{\mathrm{\{A\}}^\alpha \mathrm{\{B\}}^\beta...}}
= \frac{{{[\mathrm{R}]}}^\rho {{[\mathrm{S}]}}^\sigma ... } {{{[\mathrm{A}]}}^\alpha {{[\mathrm{B}]}}^\beta ...} \times \Gamma,
</math>
: <math>\Gamma= \frac{\gamma_R^\rho \gamma_S^\sigma...}{\gamma_A^\alpha \gamma_B^\beta...},</math>

where {X} denotes the [[thermodynamic activity]] of reagent X at equilibrium, [X] the numerical value <ref name="Atkins7th">Atkins, P.; Jones, L.; Laverman, L. (2016).''Chemical Principles'', 7th edition, pp. 399 & 461. Freeman.  ISBN 978-1-4641-8395-9</ref> of the corresponding [[Molar concentration|concentration in moles per liter]], and γ the corresponding [[activity coefficient]]. If X is a gas, instead of [X] the numerical value of the [[partial pressure]] <math>P_X</math> in bar is used.<ref name="Atkins7th" /> If it can be assumed that the quotient of activity coefficients, <math>\Gamma</math>, is constant over a range of experimental conditions, such as pH, then an equilibrium constant can be derived as a quotient of concentrations.
: <math>K_c = K^\ominus/\Gamma = \frac{[\mathrm{R}]^\rho [\mathrm{S}]^\sigma ...}{[\mathrm{A}]^\alpha [\mathrm{B}]^\beta ...}.</math>

An equilibrium constant is related to the standard [[Gibbs free energy]] change of reaction <math>\Delta G^\ominus</math> by 
: <math>\Delta G^\ominus = -RT \ln K^\ominus,</math>
where ''R'' is the [[Gas constant|universal gas constant]], ''T'' is the [[Thermodynamic temperature|absolute temperature]] (in [[kelvin]]s<!-- pluralized – see Kelvin#Usage conventions -->), and {{math|ln}} is the [[natural logarithm]]. This expression implies that <math>K^\ominus</math> must be a pure number and cannot have a dimension, since [[logarithm]]s can only be taken of pure numbers. <math>K_c</math> must also be a pure number. On the other hand, the [[reaction quotient]] at equilibrium

: <math>\frac{[\mathrm{R}]^\rho [\mathrm{S}]^\sigma ...}{[\mathrm{A}]^\alpha [\mathrm{B}]^\beta ...}\ \text{(eq)}</math>
    
does have the dimension of concentration raised to some power (see {{slink||Dimensionality}}, below). Such reaction quotients are often referred to, in the biochemical literature, as equilibrium constants.

For an equilibrium mixture of gases, an equilibrium constant can be defined in terms of [[partial pressure]] or [[fugacity]].

An equilibrium constant is related to the forward and backward [[Reaction rate constant|rate constants]], ''k''<sub>f</sub> and ''k''<sub>r</sub> of the reactions involved in reaching equilibrium:

: <math>K^\ominus = \frac{k_\text{f}}{k_\text{r}}.</math>