Editing Acid dissociation constant (section)

== Experimental determination ==
{{See also|Determination of equilibrium constants}}
[[File:Oxalic acid titration grid.png|thumb|alt= The image shows the [[titration curve]] of oxalic acid, showing the pH of the solution as a function of added base. There is a small inflection point at about pH 3 and then a large jump from pH 5 to pH 11, followed by another region of slowly increasing pH.|A calculated [[titration curve]] of [[oxalic acid]] titrated with a solution of [[sodium hydroxide]]]]

The experimental determination of p''K''<sub>a</sub> values is commonly performed by means of [[titration]]s, in a medium of high ionic strength and at constant temperature.<ref>{{cite book
| title = Determination and Use of Stability Constants
| last = Martell
| first = A.E.
| author2 = Motekaitis, R.J.
| year = 1992
| publisher = Wiley
| isbn = 0-471-18817-4
}} Chapter 4: Experimental Procedure for Potentiometric [[pH]] Measurement of Metal Complex Equilibria</ref> A typical procedure would be as follows. A solution of the compound in the medium is acidified with a strong acid to the point where the compound is fully protonated. The solution is then titrated with a strong base until all the protons have been removed. At each point in the titration pH is measured using a [[glass electrode]] and a [[pH meter]]. The equilibrium constants are found by fitting calculated pH values to the observed values, using the method of [[least squares]].<ref>{{cite book
| last = Leggett
| first = D.J.
| title = Computational Methods for the Determination of Formation Constants
| publisher = Plenum
| year = 1985
| isbn = 0-306-41957-2
}}</ref>

The total volume of added strong base should be small compared to the initial volume of titrand solution in order to keep the ionic strength nearly constant. This will ensure that p''K''<sub>a</sub> remains invariant during the titration.

A calculated [[titration curve]] for oxalic acid is shown at the right. Oxalic acid has p''K''<sub>a</sub> values of 1.27 and 4.27. Therefore, the buffer regions will be centered at about pH&nbsp;1.3 and pH&nbsp;4.3. The buffer regions carry the information necessary to get the p''K''<sub>a</sub> values as the concentrations of acid and conjugate base change along a buffer region.

Between the two buffer regions there is an end-point, or [[equivalence point]], at about pH&nbsp;3. This end-point is not sharp and is typical of a diprotic acid whose buffer regions overlap by a small amount: p''K''<sub>a2</sub>&nbsp;−&nbsp;p''K''<sub>a1</sub> is about three in this example. (If the difference in p''K'' values were about two or less, the end-point would not be noticeable.) The second end-point begins at about pH&nbsp;6.3 and is sharp. This indicates that all the protons have been removed. When this is so, the solution is not buffered and the pH rises steeply on addition of a small amount of strong base. However, the pH does not continue to rise indefinitely. A new buffer region begins at about pH&nbsp;11 (p''K''<sub>w</sub>&nbsp;−&nbsp;3), which is where [[self-ionization of water]] becomes important.

It is very difficult to measure pH values of less than two in aqueous solution with a [[glass electrode#Range of a pH glass electrode|glass electrode]], because the [[Nernst equation]] breaks down at such low pH values. To determine p''K'' values of less than about 2 or more than about 11 [[Determination of equilibrium constants#Absorbance|spectrophotometric]]<ref>{{cite journal
| last = Allen
| first = R.I.
| author2 = Box, K.J.
| author3 = Comer, J.E.A.
| author4 = Peake, C.
| author5 = Tam, K.Y.
| year = 1998
| title = Multiwavelength Spectrophotometric Determination of Acid Dissociation Constants of Ionizable Drugs
| journal = J. Pharm. Biomed. Anal.
| volume = 17
| issue = 4–5
| pages = 699–712
| doi = 10.1016/S0731-7085(98)00010-7
| pmid = 9682153
}}</ref><ref>{{cite journal
| last = Box
| first = K.J.
| author2 = Donkor, R.E.
| author3 = Jupp, P.A.
| author4 = Leader, I.P.
| author5 = Trew, D.F.
| author6 = Turner, C.H.
| year = 2008
| title = The Chemistry of Multi-Protic Drugs Part 1: A Potentiometric, Multi-Wavelength UV and NMR pH Titrimetric Study of the Micro-Speciation of SKI-606
| journal = J. Pharm. Biomed. Anal.
| volume = 47
| issue = 2
| pages = 303–311
| doi = 10.1016/j.jpba.2008.01.015
| pmid = 18314291
}}</ref> or [[Determination of equilibrium constants#NMR chemical shift measurements|NMR]]<ref name=IUPAC-NMR>
{{cite journal
| last = Popov| first = K.
| author2 = Ronkkomaki, H.
| author3 = Lajunen, L.H.J.
| year = 2006
| title = Guidelines for NMR easurements for Determination of High and Low pK<sub>a</sub> Values
| url = http://media.iupac.org/publications/pac/2006/pdf/7803x0663.pdf
| journal = Pure Appl. Chem.
| volume = 78
| issue = 3
| pages = 663–675
| doi = 10.1351/pac200678030663
| s2cid = 4823180
}}</ref><ref>
{{cite journal
| last = Szakács
| first = Z.
| author2 = Hägele, G.
| year = 2004
| title = Accurate Determination of Low p''K'' Values by <sup>1</sup>H NMR Titration
| journal = Talanta
| volume = 62
| pages = 819–825
| doi = 10.1016/j.talanta.2003.10.007
| pmid = 18969368
| issue = 4
}}</ref> measurements may be used instead of, or combined with, pH measurements.

When the glass electrode cannot be employed, as with non-aqueous solutions, spectrophotometric methods are frequently used.<ref name=Ivo_AN /> These may involve [[absorbance]] or [[fluorescence]] measurements. In both cases the measured quantity is assumed to be proportional to the sum of contributions from each photo-active species; with absorbance measurements the [[Beer–Lambert law]] is assumed to apply.

[[Isothermal titration calorimetry]] (ITC) may be used to determine both a p''K'' value and the corresponding standard enthalpy for acid dissociation.<ref>{{cite journal |title=Methods in Enzymology|editor1-last=Feig |editor1-first=Andrew L. |journal=Calorimetry |date=2016 |volume=567 |pages=2–493 |publisher=Elsevier |issn=0076-6879}}</ref> Software to perform the calculations is supplied by the instrument manufacturers for simple systems.

Aqueous solutions with normal water cannot be used for <sup>1</sup>H NMR measurements but [[heavy water]], {{chem2|D2O}}, must be used instead. <sup>13</sup>C NMR data, however, can be used with normal water and <sup>1</sup>H NMR spectra can be used with non-aqueous media. The quantities measured with NMR are time-averaged [[chemical shift]]s, as proton exchange is fast on the NMR time-scale. Other chemical shifts, such as those of <sup>31</sup>P can be measured.

=== 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>