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Acid dissociation constant
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=== Association and dissociation constants === When discussing the properties of acids it is usual to specify equilibrium constants as acid dissociation constants, denoted by ''K''<sub>a</sub>, with numerical values given the symbol p''K''<sub>a</sub>. :<math chem>K_\text{dissoc} = \frac{ \ce{[A- ][H+]}}{\ce{[HA]}}: \mathrm{p}K_\text{a} = -\log K_\text{dissoc} </math> On the other hand, association constants are used for bases. :<math chem="">K_\text{assoc} = \frac{\ce{[HA]}}{\ce{[A- ][H+]}} </math> However, [[Determination of equilibrium constants#Implementations|general purpose computer programs]] that are used to derive equilibrium constant values from experimental data use association constants for both acids and bases. Because stability constants for a [[Coordination complex|metal-ligand complex]] are always specified as association constants, ligand protonation must also be specified as an association reaction.<ref>{{Cite book |last1=Rossotti |first1=Francis J. C |url=https://books.google.com/books?id=zY8zAAAAIAAJ&q=The%20determination%20of%20stability%20constants%20:%20and%20other%20equilibrium%20constants%20in%20solution |title=The determination of stability constants : and other equilibrium constants in solution |last2=Rozotti |first2=Hazel |publisher=McGraw-Hill |year=1961 |isbn=9781013909146 |location=New York |pages=5{{--}}10 |language=en |archive-url=https://archive.org/details/determinationofs0000ross/page/10/mode/2up |archive-date=7 February 2020}}</ref> The definitions show that the value of an acid dissociation constant is the reciprocal of the value of the corresponding association constant: : <math>K_\text{dissoc} = \frac{1}{K_\text{assoc}}</math> : <math>\log K_\text{dissoc} = - \log K_\text{assoc}</math> : <math>\mathrm{p}K_\text{dissoc} = - \mathrm{p}K_\text{assoc}</math> Notes # For a given acid or base in water, {{nowrap|1=p''K''<sub>a</sub> + p''K''<sub>b</sub> = p''K''<sub>w</sub>}}, the [[self-ionization of water|self-ionization constant of water]]. # The association constant for the formation of a [[Supramolecular chemistry|supramolecular]] complex may be denoted as K<sub>a</sub>; in such cases "a" stands for "association", not "acid". # For polyprotic acids, the numbering of stepwise association constants is the reverse of the numbering of the dissociation constants. For example, for [[phosphoric acid]] (details in the [[#polyprotic acids|polyprotic acids]] section below): ::<math>\begin{align} \log K_{\text{assoc},1} &= \mathrm{p}K_{\text{dissoc},3} \\ \log K_{\text{assoc},2} &= \mathrm{p}K_{\text{dissoc},2} \\ \log K_{\text{assoc},3} &= \mathrm{p}K_{\text{dissoc},1} \end{align}</math>
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