Editing Acid dissociation constant (section)

=== Micro-constants ===
[[File:L-Cystein - L-Cysteine.svg|thumb|Cysteine]]
For some polyprotic acids, dissociation (or association) occurs at more than one nonequivalent site,<ref name="RMC_2013"/> and the observed macroscopic equilibrium constant, or macro-constant, is a combination of [[micro-constant]]s involving distinct species. When one reactant forms two products in parallel, the macro-constant is a sum of two micro-constants, <math>K = K_X + K_Y.</math> This is true for example for the deprotonation of the [[amino acid]] [[cysteine]], which exists in solution as a neutral [[zwitterion]] {{chem2|HS\sCH2\sCH(NH3+)\sCOO-}}. The two micro-constants represent deprotonation either at sulphur or at nitrogen, and the macro-constant sum here is the acid dissociation constant <math chem>K_\mathrm a = K_\mathrm a \ce{(-SH)} + K_\mathrm a \ce{(-NH3+)}.</math><ref name=Splittgerber>{{cite journal |last1=Splittgerber |first1=A. G. |last2=Chinander |first2=L.L. |title=The spectrum of a dissociation intermediate of cysteine: a biophysical chemistry experiment |journal=Journal of Chemical Education |date=1 February 1988 |volume=65 |issue=2 |page=167 |doi=10.1021/ed065p167 |bibcode=1988JChEd..65..167S }}</ref>

[[File:Spermine.svg|thumb|alt=Spermine is a long, symmetrical molecule capped at both ends with amino groups N H 2. It has two N H groups symmetrically placed within the molecule, separated from each other by four methylene groups C H 2, and from the amino ends by three methylene groups. Thus, the full molecular formula is N H 2 C H 2 C H 2 C H 2 N H C H 2 C H 2 C H 2 C H 2 N H C H 2 C H 2 C H 2 N H 2.|Spermine]]

Similarly, a base such as [[spermine]] has more than one site where protonation can occur. For example, mono-protonation can occur at a terminal {{chem2|\sNH2}} group or at internal {{chem2|\sNH\s}} groups. The ''K''<sub>b</sub> values for dissociation of spermine protonated at one or other of the sites are examples of [[equilibrium constant#Micro-constants|micro-constants]]. They cannot be determined directly by means of pH, absorbance, fluorescence or NMR measurements; a measured ''K''<sub>b</sub> value is the sum of the K values for the micro-reactions.
: <math>K_\text{b} = K_\text{terminal} + K_\text{internal}</math>

Nevertheless, the site of protonation is very important for biological function, so mathematical methods have been developed for the determination of micro-constants.<ref>{{cite journal
| last = Frassineti
| first = C.
| author2 = Alderighi, L
| author3 = Gans, P
| author4 = Sabatini, A
| author5 = Vacca, A
| author6 = Ghelli, S.
| year = 2003
| title = Determination of Protonation Constants of Some Fluorinated Polyamines by Means of <sup>13</sup>C NMR Data Processed by the New Computer Program HypNMR2000. Protonation Sequence in Polyamines.
| journal = Anal. Bioanal. Chem.
| volume = 376
| pages = 1041–1052
| doi = 10.1007/s00216-003-2020-0
| pmid = 12845401
| issue = 7
| s2cid = 14533024
}}</ref>

When two reactants form a single product in parallel, the macro-constant <math>1/K = 1/K_X + 1/K_Y .</math><ref name=Splittgerber/> For example, the abovementioned equilibrium for spermine may be considered in terms of ''K''<sub>a</sub> values of two [[tautomeric]] conjugate acids, with macro-constant In this case <math>1/K_\text{a} = 1/K_{\text{a},\text{terminal}} + 1/K_{\text{a},\text{internal}}.</math> This is equivalent to the preceding expression since <math>K_\mathrm{b}</math> is proportional to <math>1/K_\mathrm{a}.</math>

When a reactant undergoes two reactions in series, the macro-constant for the combined reaction is the product of the micro-constant for the two steps. For example, the abovementioned cysteine zwitterion can lose two protons, one from sulphur and one from nitrogen, and the overall macro-constant for losing two protons is the product of two dissociation constants <math chem>K = K_\mathrm a \ce{(-SH)} K_\mathrm a \ce{(-NH3+)}.</math><ref name=Splittgerber/> This can also be written in terms of logarithmic constants as <math chem>\mathrm p K = \mathrm p K_\mathrm a \ce{(-SH)} + \mathrm p K_\mathrm a \ce{(-NH3+)}.</math>