View source for Chemistry:Acid dissociation constant

{{short description|Measure of an acid's strength in solution}}

{{Acids and bases}}

In [[Chemistry:Chemistry|chemistry]], an '''acid dissociation constant''' (also known as '''acidity constant''', or '''acid-ionization constant'''; denoted {{tmath|K_a}}) is a quantitative measure of the [[Chemistry:Acid strength|strength]] of an [[Chemistry:Acid|acid]] in [[Chemistry:Solution|solution]]. It is the [[Chemistry:Equilibrium constant|equilibrium constant]] for a [[Chemistry:Chemical reaction|chemical reaction]]
:<chem>HA <=> A^- + H^+</chem>
known as [[Chemistry:Dissociation|dissociation]] in the context of [[Chemistry:Acid–base reaction|acid–base reaction]]s. The [[Chemistry:Chemical species|chemical species]] HA is an [[Chemistry:Acid|acid]] that dissociates into {{chem2|A-}}, the conjugate base of the acid and a [[Chemistry:Hydron|hydrogen ion]], {{chem2|H+}}.{{efn|The hydrogen ion does not exist as such in solution. It combines with a solvent molecule; when the solvent is water a [[Chemistry:Hydronium|hydronium]] ion is formed: {{chem2|H+ + H2O -> H3O+}}. This reaction is quantitative and hence can be ignored in the context of chemical equilibrium.}} The system is said to be in [[Chemistry:Chemical equilibrium|equilibrium]] when the concentrations of its components will not change over time, because both forward and backward reactions are occurring at the same rate.<ref>{{cite book| last1= Whitten |first1= Kenneth W.| last2= Gailey| first2= Kenneth D.| last3= Davis| first3= Raymond E.| date= 1992| title= General Chemistry| url= https://archive.org/details/generalchemistry00whit_0 | url-access= registration | edition = 4th| page= [https://archive.org/details/generalchemistry00whit_0/page/660 660]| publisher = Saunders College Publishing| isbn= 0-03-072373-6}}</ref>

The dissociation constant is defined by{{efn|1=It is common practice to quote p''K'' values rather than ''K'' values. {{nowrap|1=p''K'' = −log<sub>10</sub> ''K''}}. p''K''<sub>a</sub> is often referred to as an acid dissociation constant, but this is, strictly speaking, incorrect as p''K''<sub>a</sub> is the [[Cologarithm|cologarithm]] of the dissociation constant.}}
:<math>K_\text{a} = \mathrm{\frac{[A^-] [H^+]}{[HA]}},</math> or
:<math chem>\mathrm{p}K_\ce{a} = - \log_{10} K_\text{a} = \log_{10}\frac{\ce{[HA]}}{[\ce{A^-}][\ce{H+}]}</math>

where quantities in square brackets represent the [[Chemistry:Concentration|concentration]]s of the species at equilibrium.{{efn|It is implicit in this definition that the quotient of activity coefficients, <math> \frac{\gamma_{AH}}{\gamma_{A^-} \gamma_{H^+}},</math> is a constant with a value of 1 under a given set of experimental conditions.}}<ref>{{cite book| last1= Petrucci| first1= Ralph H.| last2= Harwood| first2= William S.| last3= Herring| first3= F. Geoffrey| date= 2002| title= General Chemistry| url= https://archive.org/details/generalchemistry00hill| url-access= registration| edition= 8th| pages= [https://archive.org/details/generalchemistry00hill/page/667 667–8]| publisher = Prentice Hall| isbn= 0-13-014329-4}}</ref> As a simple example for a weak acid with ''K''<sub>a</sub>&nbsp;=&nbsp;10<sup>−5</sup>, log ''K''<sub>a</sub> is the exponent which is -5, so that p''K''<sub>a</sub>&nbsp;=&nbsp;5. And for acetic acid with ''K''<sub>a</sub>&nbsp;=&nbsp;1.8&nbsp;x&nbsp;10<sup>−5</sup>, p''K''<sub>a</sub> is close to 5. A higher ''K''<sub>a</sub> corresponds to a stronger acid which is more dissociated at equilibrium. For the more convenient [[Logarithmic scale|logarithmic scale]], a lower p''K''<sub>a</sub> means a stronger acid.

== Theoretical background ==

The acid dissociation constant for an acid is a direct consequence of the underlying [[Chemistry:Chemical thermodynamics|thermodynamics]] of the dissociation reaction; the p''K''<sub>a</sub> value is directly proportional to the standard [[Physics:Gibbs free energy|Gibbs free energy]] change for the reaction. The value of the p''K''<sub>a</sub> changes with temperature and can be understood qualitatively based on Le Châtelier's principle: when the reaction is endothermic, ''K''<sub>a</sub> increases and p''K''<sub>a</sub> decreases with increasing temperature; the opposite is true for exothermic reactions.

The value of p''K''<sub>a</sub> also depends on molecular structure of the acid in many ways. For example, [[Biography:Linus Pauling|Pauling]] proposed two rules: one for successive p''K''<sub>a</sub> of polyprotic acids (see [[Chemistry:Acid dissociation constant#Polyprotic acids|Polyprotic acids]] below), and one to estimate the p''K''<sub>a</sub> of oxyacids based on the number of =O and −OH groups (see [[Chemistry:Acid dissociation constant#Factors that affect pKa values|Factors that affect p''K''<sub>a</sub> values]] below). Other structural factors that influence the magnitude of the acid dissociation constant include [[Chemistry:Inductive effect|inductive effect]]s, [[Chemistry:Mesomeric effect|mesomeric effect]]s, and hydrogen bonding. [[Hammett equation|Hammett type equations]] have frequently been applied to the estimation of p''K''<sub>a</sub>.<ref name="Perrin">{{cite book
| last1 = Perrin
| first1 = DD
| last2 = Dempsey
| first2 = B
| last3 = Serjeant
| first3 = EP
| name-list-style = vanc
| title = p''K''<sub>a</sub> Prediction for Organic Acids and Bases
| publisher = Chapman & Hall
| year = 1981
| location = London
| isbn = 978-0-412-22190-3
| doi = 10.1007/978-94-009-5883-8
| chapter = Chapter 3: Methods of p''K''<sub>a</sub> Prediction
| pages = 21–26
| department = (secondary)
}}</ref><ref name="RMC_2013">{{cite encyclopedia
| last = Fraczkiewicz
| first = R
| title = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering
| name-list-style = vanc
| chapter = In Silico Prediction of Ionization
| encyclopedia = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering [Online]
| editor-last = Reedijk
| editor-first = J
| volume = 5
| publisher = Elsevier
| location = Amsterdam, the Netherlands
| year = 2013
| doi = 10.1016/B978-0-12-409547-2.02610-X
| isbn = 9780124095472
| department = (secondary)
}}</ref>

The quantitative behaviour of acids and bases in solution can be understood only if their p''K''<sub>a</sub> values are known. In particular, the [[Chemistry:PH|pH]] of a solution can be predicted when the analytical concentration and p''K''<sub>a</sub> values of all acids and bases are known; conversely, it is possible to calculate the equilibrium concentration of the acids and bases in solution when the pH is known. These calculations find application in many different areas of chemistry, biology, medicine, and geology. For example, many compounds used for medication are weak acids or bases, and a knowledge of the p''K''<sub>a</sub> values, together with the [[Physics:Octanol-water partition coefficient|octanol-water partition coefficient]], can be used for estimating the extent to which the compound enters the blood stream. Acid dissociation constants are also essential in aquatic chemistry and [[Chemistry:Chemical oceanography|chemical oceanography]], where the acidity of water plays a fundamental role. In living organisms, [[Chemistry:Acid–base homeostasis|acid–base homeostasis]] and [[Chemistry:Enzyme kinetics|enzyme kinetics]] are dependent on the p''K''<sub>a</sub> values of the many acids and bases present in the cell and in the body. In chemistry, a knowledge of p''K''<sub>a</sub> values is necessary for the preparation of [[Chemistry:Buffer solution|buffer solution]]s and is also a prerequisite for a quantitative understanding of the interaction between acids or bases and metal ions to form [[Chemistry:Stability constants of complexes|complexes]]. Experimentally, p''K''<sub>a</sub> values can be determined by potentiometric (pH) [[Chemistry:Titration|titration]], but for values of p''K''<sub>a</sub> less than about 2 or more than about 11, [[Physics:Spectrophotometry|spectrophotometric]] or [[Physics:Nuclear magnetic resonance|NMR]] measurements may be required due to practical difficulties with pH measurements.

== Definitions ==
According to [[Biography:Svante Arrhenius|Arrhenius]]'s [[Chemistry:Acid–base reaction#Arrhenius definition|original molecular definition]], an acid is a substance that [[Chemistry:Dissociation|dissociates]] in aqueous solution, releasing the hydrogen ion {{chem2|H+}} (a proton):<ref name=Miessler>{{cite book
| title = Inorganic Chemistry
| last1 = Miessler
| first1 = Gary L.
| last2 = Tarr
| first2 = Donald A.
| year = 1991
| publisher = Prentice Hall
| isbn = 0-13-465659-8
| edition = 2nd
}} Chapter 6: Acid–Base and Donor–Acceptor Chemistry</ref>
: <chem>HA <=> A- + H+</chem>

The equilibrium constant for this dissociation reaction is known as a [[Chemistry:Dissociation constant|dissociation constant]]. The liberated proton combines with a water molecule to give a hydronium (or oxonium) ion {{chem2|H3O+}} (naked protons do not exist in solution), and so Arrhenius later proposed that the dissociation should be written as an [[Chemistry:Acid–base reaction|acid–base reaction]]:
:<chem>HA + H2O <=> A- + H3O+</chem>

[[File:Acetic-acid-dissociation-3D-balls.png|thumb|upright=1.5|alt=Acetic acid, {{chem2|CH3COOH}}, is composed of a methyl group, {{chem2|CH3}}, bound chemically to a carboxylate group, COOH. The carboxylate group can lose a proton and donate it to a water molecule, {{chem2|H2O}}, leaving behind an acetate anion {{chem2|CH3COO-}} and creating a hydronium cation {{chem2|H3O}}. This is an equilibrium reaction, so the reverse process can also take place.|Acetic acid, a weak acid, donates a proton (hydrogen ion, highlighted in green) to water in an equilibrium reaction to give the acetate ion and the hydronium ion. Red: oxygen, black: carbon, white: hydrogen.]]
[[Chemistry:Brønsted–Lowry acid–base theory|Brønsted and Lowry]] generalised this further to a proton exchange reaction:<ref name = Bell>{{cite book
 |last = Bell
 |first = R.P.
 |title = The Proton in Chemistry
 |publisher = Chapman & Hall
 |location = London
 |year = 1973
 |edition = 2nd
 |isbn = 0-8014-0803-2
 |url-access = registration
 |url = https://archive.org/details/protoninchemistr0000bell
}} Includes discussion of many organic Brønsted acids.</ref><ref name=SA>
{{cite book
| last = Shriver
| first = D.F
| author2 = Atkins, P.W.
| title = Inorganic Chemistry
| edition = 3rd
| year = 1999
| publisher = Oxford University Press
| location = Oxford
| isbn = 0-19-850331-8
}} Chapter 5: Acids and Bases</ref><ref>{{Housecroft3rd}} Chapter 6: Acids, Bases and Ions in Aqueous Solution</ref>
: <math chem>\text{acid} + \text{base } \ce{<=>} \text{ conjugate base} + \text{conjugate acid}</math>

The acid loses a proton, leaving a conjugate base; the proton is transferred to the base, creating a conjugate acid. For aqueous solutions of an acid HA, the base is water; the conjugate base is {{chem2|A-}} and the conjugate acid is the hydronium ion. The Brønsted–Lowry definition applies to other solvents, such as [[Chemistry:Dimethyl sulfoxide|dimethyl sulfoxide]]: the solvent S acts as a base, accepting a proton and forming the conjugate acid {{chem2|SH+}}.
:<chem>HA + S <=> A- + SH+</chem>

In solution chemistry, it is common to use {{chem2|H+}} as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution {{chem2|H+}} denotes a [[Chemistry:Hydronium#Solvation|solvated hydronium ion]] rather than a proton.<ref name=Headrick>
{{cite journal
| last = Headrick
| first = J.M.
| author2 = Diken, E.G.
| author3 = Walters, R. S.
| author4 = Hammer, N. I.
| author5 = Christie, R.A.
| author6 = Cui, J.
| author7 = Myshakin, E.M.
| author8 = Duncan, M.A.
| author9 = Johnson, M.A.|author10= Jordan, K.D.
| year = 2005
| title = Spectral Signatures of Hydrated Proton Vibrations in Water Clusters
| journal = Science
| volume = 308
| pages = 1765–69
| doi = 10.1126/science.1113094
| pmid = 15961665
| issue = 5729
| bibcode = 2005Sci...308.1765H
| s2cid = 40852810
}}</ref><ref name=Smiechowski>
{{cite journal
| last = Smiechowski
| first = M.
| author2 = Stangret, J.
| year = 2006
| title = Proton hydration in aqueous solution: Fourier transform infrared studies of HDO spectra
| journal = J. Chem. Phys.
| volume = 125
| pages = 204508–204522
| doi = 10.1063/1.2374891
| pmid = 17144716
| issue = 20
| bibcode = 2006JChPh.125t4508S
}}</ref>

The designation of an acid or base as "conjugate" depends on the context. The conjugate acid {{chem2|BH+}} of a base B dissociates according to
:<chem>BH+ + OH- <=> B + H2O</chem>

which is the reverse of the equilibrium
:<math chem>\ce{H2O}\text{ (acid)} + \ce{B}\text{ (base) } \ce{<=> OH-}\text{ (conjugate base)} + \ce{BH+}\text{ (conjugate acid)}</math>

The [[Chemistry:Hydroxide ion|hydroxide ion]] {{chem2|OH-}}, a well known base, is here acting as the conjugate base of the acid water. Acids and bases are thus regarded simply as donors and acceptors of protons respectively.

A broader definition of acid dissociation includes [[Chemistry:Hydrolysis|hydrolysis]], in which protons are produced by the splitting of water molecules. For example, [[Chemistry:Boric acid|boric acid]] ({{chem2|B(OH)3}}) produces {{chem2|H3O+}} as if it were a proton donor,<ref name="Goldmine" /> but it has been confirmed by [[Physics:Raman spectroscopy|Raman spectroscopy]] that this is due to the hydrolysis equilibrium:<ref>{{cite book
| title = Modern Inorganic Chemistry
| last = Jolly
| first = William L.
| year = 1984
| pages = [https://archive.org/details/trent_0116300649799/page/198 198]
| publisher = McGraw-Hill
| isbn = 978-0-07-032760-3
| url = https://archive.org/details/trent_0116300649799/page/198
}}</ref>
:<chem>B(OH)3 + 2 H2O <=> B(OH)4- + H3O+</chem>

Similarly, [[Chemistry:Hydrolysis#Hydrolysis of metal aqua ions|metal ion hydrolysis]] causes ions such as {{chem2|[Al(H2O)6](3+)}} to behave as weak acids:<ref name=Burgess>
{{cite book
| title = Metal Ions in Solution
| last = Burgess
| first = J.
| year = 1978
| publisher = Ellis Horwood
| isbn = 0-85312-027-7
}} Section 9.1 "Acidity of Solvated Cations" lists many p''K''<sub>a</sub> values.</ref>
: <chem>[Al(H2O)6]^3+ + H2O <=> [Al(H2O)5(OH)]^2+ + H3O+</chem>

According to [[Chemistry:Acid–base reaction#Lewis definition|Lewis]]'s original definition, an acid is a substance that accepts an [[Physics:Electron pair|electron pair]] to form a [[Chemistry:Coordinate covalent bond|coordinate covalent bond]].<ref name=Petrucci>
{{cite book
| last = Petrucci
| first = R.H.
| author2 = Harwood, R.S.
| author3 = Herring, F.G.
| title = General Chemistry
| url = https://archive.org/details/generalchemistry00hill
| url-access = registration
| edition = 8th
| year = 2002
| publisher = Prentice Hall
| isbn = 0-13-014329-4
}} p.698</ref>

== Equilibrium constant ==
An acid dissociation constant is a particular example of an [[Chemistry:Equilibrium constant|equilibrium constant]]. The dissociation of a monoprotic acid, HA, in dilute solution can be written as
: <chem>HA <=> A- + H+</chem>

The thermodynamic equilibrium constant {{tmath|K^\ominus}} can be defined by<ref name=rr>{{cite book| title= The Determination of Stability Constants| last= Rossotti| first= F.J.C.| author2= Rossotti, H.| year= 1961| publisher = McGraw–Hill}} Chapter 2: Activity and Concentration Quotients</ref>
:<math chem>K^\ominus = \frac{\{\ce{A^-}\} \{\ce{H+}\}}{\ce{\{HA\} }}</math>

where {{math|{X} }} represents the activity, at equilibrium, of the chemical species X. {{tmath|K^\ominus}} is [[Physics:Dimensionless|dimensionless]] since activity is dimensionless. Activities of the products of dissociation are placed in the numerator, activities of the reactants are placed in the denominator. See [[Chemistry:Activity coefficient|activity coefficient]] for a derivation of this expression.

[[File:PK acetic acid.png|thumb|200px|alt=Illustration of the effect of ionic strength on the p K A of an acid. In this figure, the p K A of acetic acid decreases with increasing ionic strength, dropping from 4.8 in pure water (zero ionic strength) and becoming roughly constant at 4.45 for ionic strengths above 1 molar sodium nitrate, N A N O 3.|Variation of p''K''<sub>a</sub> of acetic acid with ionic strength.]]

Since activity is the product of [[Chemistry:Concentration|concentration]] and [[Chemistry:Activity coefficient|activity coefficient]] (''γ'') the definition could also be written as
:<math chem>K^\ominus = {\frac{[\ce{A^-}] [\ce{H+}]}\ce{[HA] }\Gamma}, \quad \Gamma=\frac{\gamma_\ce{A^-} \ \gamma_\ce{H+}}{\gamma_\ce{HA} \ } </math>
where {{tmath|[\text{HA}]}} represents the concentration of HA and {{tmath|\Gamma}} is a quotient of activity coefficients.

To avoid the complications involved in using activities, dissociation constants are [[Chemistry:Determination of equilibrium constants|determined]], where possible, in a medium of high [[Chemistry:Ionic strength|ionic strength]], that is, under conditions in which {{tmath|\Gamma}} can be assumed to be always constant.<ref name=rr /> For example, the medium might be a solution of 0.1&nbsp;molar (M) [[Chemistry:Sodium nitrate|sodium nitrate]] or 3&nbsp;M [[Chemistry:Potassium perchlorate|potassium perchlorate]]. With this assumption,
:<math>K_\text{a} = \frac{K^\ominus}{\Gamma} = \mathrm{\frac{[A^-] [H^+]}{[HA]}}</math>
:<math chem>\mathrm{p}K_\ce{a} = -\log_{10}\frac{[\ce{A^-}][\ce{H^+}]}{[\ce{HA}]} = \log_{10}\frac{\ce{[HA]}}{[\ce{A^-}][\ce{H+}]}</math>
is obtained.<!-- <ref name=IUPAC-NMR>{{cite journal | last = Popov| first = K.| author2 = Ronkkomaki, H.| author3 = Lajunen, L.H.J.| year = 2006| title = Guidelines for NMR measurements for Determination of High and Low p''K''<sub>a</sub> Values| url = http://media.iupac.org/publications/pac/2006/pdf/7803x0663.pdf | format = PDF | journal = Pure Appl. Chem. | volume = 78 | issue = 3 | pages = 663–675 | doi = 10.1351/pac200678030663}}</ref> Irrelevant in this context--> Note, however, that all published dissociation constant values refer to the specific ionic medium used in their determination and that different values are obtained with different conditions, as shown for [[Chemistry:Acetic acid|acetic acid]] in the illustration above. When published constants refer to an ionic strength other than the one required for a particular application, they may be adjusted by means of [[Physics:Specific ion interaction theory|specific ion theory]] (SIT) and other theories.<ref>{{cite web | url= https://iupac.org/projects/project-details/?project_nr=2000-003-1-500 | title= Project: Ionic Strength Corrections for Stability Constants | publisher = International Union of Pure and Applied Chemistry | access-date = 2019-03-28}}</ref>

===Cumulative and stepwise constants===
A cumulative equilibrium constant, denoted by {{tmath|\mathrm \beta ,}} is related to the product of stepwise constants, denoted by {{tmath|\mathrm K .}} For a dibasic acid the relationship between stepwise and overall constants is as follows
:<chem>H2A <=> A^2- + 2H+</chem>
:<math chem>\beta_2 = \frac{\ce{[H2A]}}{[\ce{A^2-}][\ce{H+}]^2}</math>
:<math chem>\log \beta_2 = \mathrm{p}K_\ce{a1} + \mathrm{p}K_\ce{a2}</math>

Note that in the context of metal-ligand complex formation, the equilibrium constants for the formation of metal complexes are usually defined as ''association'' constants. In that case, the equilibrium constants for ligand protonation are also defined as association constants. The numbering of association constants is the reverse of the numbering of dissociation constants; in this example <math chem>\log \beta_1 = \mathrm{p}K_\ce{a2}</math>

=== 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+]}}: \mathrm{p}K_\text{b} = -\log K_\text{assoc}</math>

However, [[Chemistry: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 metal-ligand complex are always specified as association constants, ligand protonation must also be specified as an association reaction.<ref name=rr /> 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} = \log K_\text{assoc}</math>

Notes
# For a given acid or base {{nowrap|1=p''K''<sub>a</sub> + p''K''<sub>b</sub> = p''K''<sub>w</sub>}}, the [[Physics:Self-ionization of water|self-ionization constant of water]].
# The association constant for the formation of a [[Chemistry: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 [[Chemistry:Phosphoric acid|phosphoric acid]] (details in #polyprotic acids, 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>

=== Temperature dependence ===
All equilibrium constants vary with [[Physics:Temperature|temperature]] according to the [[Van 't Hoff equation|van 't Hoff equation]]<ref>
{{cite book
| title = Physical Chemistry
| last1 = Atkins
| first1 = P.W.
| last2 = de Paula
| first2 = J.
| year = 2006
| publisher = Oxford University Press
| isbn = 0-19-870072-5
}} Section 7.4: The Response of Equilibria to Temperature</ref>
:<math alt="The derivative of the natural logarithm of any equilibrium constant K with respect to the [[Physics:Absolute temperature|absolute temperature]] T equals the standard enthalpy change for the reaction divided by the product R times T squared. Here R represents the gas constant, which equals the thermal energy per mole per kelvin. The standard enthalpy is written as Delta H with a superscript plimsoll mark represented by the image strikeO. This equation follows from the definition of the Gibbs energy Delta G equals R times T times the natural logarithm of K.">
 \frac{\mathrm{d} \ln\left(K\right)}{\mathrm{d}T} = \frac{\Delta H^\ominus}{RT^2}
</math>

{{tmath|R}} is the [[Physics:Gas constant|gas constant]] and {{tmath|T}} is the [[Kelvin|absolute temperature]]. Thus, for exothermic reactions, the standard enthalpy change, {{tmath|\Delta H^\ominus}}, is negative and ''K'' decreases with temperature. For endothermic reactions, {{tmath|\Delta H^\ominus}} is positive and ''K'' increases with temperature.

The standard enthalpy change for a reaction is itself a function of temperature, according to [[Biography:Gustav Kirchhoff#Kirchhoff's law of thermochemistry|Kirchhoff's law of thermochemistry]]:
:<math>\left(\frac{\partial\Delta H}{\partial T}\right)_p = \Delta C_p</math>
where {{tmath|\Delta C_p}} is the [[Physics:Specific heat capacity|heat capacity]] change at constant pressure. In practice {{tmath|\Delta H^\ominus}} may be taken to be constant over a small temperature range.

===Dimensionality===
In the equation
:<math>K_\mathrm{a} = \mathrm{\frac{[A^-] [H^+]}{[HA]}},</math>

''K''<sub>a</sub> appears to have [[Dimensional analysis|dimensions]] of concentration. However, since <math>\Delta G = -RT\ln K</math>, the equilibrium constant, {{tmath|K}}, ''cannot'' have a physical dimension. This apparent paradox can be resolved in various ways. 
# Assume that the quotient of activity coefficients has a numerical value of 1, so that {{tmath|K}} has the same numerical value as the thermodynamic equilibrium constant <math>K^\ominus</math>.
# Express each concentration value as the ratio c/c<sup>0</sup>, where c<sup>0</sup> is the concentration in a [hypothetical] standard state, with a numerical value of 1, by definition.<ref>{{cite book |last1 = Petrucci |first1 = Ralph H. |last2 = Harwood |first2 = William S. |last3 = Herring |first3 = F. Geoffrey |date=2002 |title = General chemistry: principles and modern applications |url = https://archive.org/details/generalchemistry00hill |url-access = registration |edition=8th |page=[https://archive.org/details/generalchemistry00hill/page/633 633] |quote=Are you wondering... How using activities makes the equilibrium constant dimensionless? |publisher=Prentice Hall |isbn = 0-13-014329-4}}</ref> 
# Express the concentrations on the [[Chemistry:Mole fraction|mole fraction]] scale. Since mole fraction has no dimension, the quotient of concentrations will, by definition, be a pure number.

The procedures, (1) and (2), give identical numerical values for an equilibrium constant. Furthermore, since a concentration {{tmath|c_i}} is simply proportional to mole fraction {{tmath|x_i}} and density {{tmath|\rho}}:
:<math>c_i = \frac{x_i\rho}{M} </math>
and since the molar mass {{tmath|M}} is a constant in dilute solutions, an equilibrium constant value determined using (3) will be simply proportional to the values obtained with (1) and (2).

It is common practice in [[Biology:Biochemistry|biochemistry]] to quote a value with a dimension as, for example, "''K''<sub>a</sub> = 30&nbsp;mM" in order to indicate the scale, millimolar (mM) or micromolar (μM) of the [[Chemistry:Concentration|concentration]] values used for its calculation.

== Strong acids and bases ==
An acid is classified as "strong" when the concentration of its undissociated species is too low to be measured.<ref name="Bell" /> Any aqueous acid with a p''K''<sub>a</sub> value of less than 0 is almost completely deprotonated and is considered a ''strong acid''.<ref name=SA5.1c>{{cite book |last = Shriver |first = D.F |author2 = Atkins, P.W. |title = Inorganic Chemistry |edition = 3rd |year = 1999 |publisher = Oxford University Press |isbn = 0-19-850331-8}} Sec. 5.1c Strong and weak acids and bases</ref> All such acids transfer their protons to water and form the solvent cation species (H<sub>3</sub>O<sup>+</sup> in aqueous solution) so that they all have essentially the same acidity, a phenomenon known as [[Chemistry:Leveling effect|solvent leveling]].<ref>{{cite book| title = Inorganic Chemistry| last = Porterfield| first = William W.| year = 1984| publisher = Addison-Wesley| page=260| isbn = 0-201-05660-7}}</ref><ref name=SA5.2>{{cite book |last = Shriver |first = D.F |author2 = Atkins, P.W. |title = Inorganic Chemistry |edition = 3rd |year = 1999 |publisher = Oxford University Press |isbn = 0-19-850331-8}} Sec. 5.2 Solvent leveling</ref> They are said to be ''fully dissociated'' in aqueous solution because the amount of undissociated acid, in equilibrium with the dissociation products, is below the [[Chemistry:Detection limit|detection limit]].<!-- {{efn|1= In dilute solution [[Chemistry:Nitric acid|nitric acid]] (p''K''<sub>a</sub> = −1.4<ref>{{Citation |last=Bell |first=R. P. |title=The Proton in Chemistry |edition=2nd |publisher=Cornell University Press |location=Ithaca, NY |year=1973 }}</ref>) behaves as a strong acid. When the ratio of water molecules to acid molecules in a solution of an acid is too small to fully solvate the dissociation products, dissociation is not complete, for example, with extremely concentrated solutions of [[Chemistry:Sulfuric acid|sulfuric acid]] and [[Chemistry:Hydrochloric acid|hydrochloric acid]].}}.
 --> Likewise, any aqueous base with an [[Chemistry:Acid dissociation constant#Bases and basicity|association constant]] p''K''<sub>b</sub> less than about 0, corresponding to p''K''<sub>a</sub> greater than about 14, is leveled to OH<sup>−</sup> and is considered a ''strong base''.<ref name=SA5.2/>

[[Chemistry:Nitric acid|Nitric acid]], with a p''K'' value of around −1.7, behaves as a strong acid in aqueous solutions with a pH greater than 1.<ref>{{cite journal |title=Dissociation constant of nitric acid|journal=Russian Journal of Physical Chemistry A|volume=91|issue=7|pages=1221–1228|doi=10.1134/S0036024417070196|year=2017|last1=Levanov|first1=A. V.|last2=Isaikina|first2=O. Ya.|last3=Lunin|first3=V. V.|bibcode=2017RJPCA..91.1221L|s2cid=104093297}}</ref> At lower pH values it behaves as a weak acid.

p''K''<sub>a</sub> values for strong acids have been estimated by theoretical means.<ref>{{cite journal |title=Acidity of Strong Acids in Water and Dimethyl Sulfoxide|journal=The Journal of Physical Chemistry A|volume=120|issue=20|pages=3663–3669|doi=10.1021/acs.jpca.6b02253|pmid=27115918|year=2016|last1=Trummal|first1=Aleksander|last2=Lipping|first2=Lauri|last3=Kaljurand|first3=Ivari|last4=Koppel|first4=Ilmar A.|last5=Leito|first5=Ivo|bibcode=2016JPCA..120.3663T|s2cid=29697201 }}</ref> For example, the p''K''<sub>a</sub> value of aqueous [[Chemistry:Hydrochloric acid|HCl]] has been estimated as −9.3.

== Monoprotic acids ==
[[File:Weak acid speciation.svg|thumb|200px|right|alt=This figure plots the relative fractions of the protonated form A H of an acid to its deprotonated form, A minus, as the solution p H is varied about the value of the acid's p K A. When the p H equals the p K a, the amounts of the protonated and deprotonated forms are equal. When the p H is one unit higher than the p K A, the ratio of concentrations of protonated to deprotonated forms is 10 to 1. When the p H is two units higher that ratio is 100 to 1. Conversely, when the p H is one or two unit lower than the p K A, the ratio is 1 to ten or 1 to 100. The exact percentage of each form may be determined from the Henderson–Hasselbalch equation.|Variation of the % formation of a monoprotic acid, AH, and its conjugate base, A<sup>−</sup>, with the difference between the pH and the p''K''<sub>a</sub> of the acid.]]
After rearranging the expression defining ''K''<sub>a</sub>, and putting {{nowrap|pH {{=}} −log<sub>10</sub>[H<sup>+</sup>]}}, one obtains<ref>{{cite web | last1= Mehta| first1= Akul| title= Henderson–Hasselbalch Equation: Derivation of p''K''<sub>a</sub> and p''K''<sub>b</sub>| url= http://pharmaxchange.info/press/2012/10/henderson%E2%80%93hasselbalch-equation-derivation-of-pka-and-pkb/| website = PharmaXChange| date= 22 October 2012| access-date = 16 November 2014}}</ref>

:<math alt="p H equals p K A plus the logarithm (base ten) of a ratio of chemical concentrations, namely the concentration of the protonated form A H divided by that of the deprotonated form A minus." >
 \mathrm{pH} = \mathrm{p}K_\text{a} + \log\mathrm{\frac{[A^-]}{[HA]}}
</math>

This is the [[Henderson–Hasselbalch equation]], from which the following conclusions can be drawn.
* At half-neutralization the ratio {{nowrap|{{sfrac|[A<sup>−</sup>]|[HA]}} {{=}} 1}}; since {{nowrap|log(1) {{=}} 0}}, the pH at half-neutralization is numerically equal to p''K''<sub>a</sub>. Conversely, when {{nowrap|pH {{=}} p''K''<sub>a</sub>}}, the concentration of HA is equal to the concentration of A<sup>−</sup>.
* The [[Chemistry:Buffer solution|buffer region]] extends over the approximate range p''K''<sub>a</sub>&nbsp;±&nbsp;2. Buffering is weak outside the range p''K''<sub>a</sub>&nbsp;±&nbsp;1. At pH ≤ p''K''<sub>a</sub> − 2 the substance is said to be fully protonated and at pH ≥ p''K''<sub>a</sub> + 2 it is fully dissociated (deprotonated).
* If the pH is known, the ratio may be calculated. This ratio is independent of the analytical concentration of the acid.

In water, measurable p''K''<sub>a</sub> values range from about −2 for a strong acid to about 12 for a very weak acid (or strong base).

A [[Chemistry:Buffer solution|buffer solution]] of a desired pH can be prepared as a mixture of a weak acid and its conjugate base. In practice, the mixture can be created by dissolving the acid in water, and adding the requisite amount of strong acid or base. When the p''K''<sub>a</sub> and analytical concentration of the acid are known, the extent of dissociation and pH of a solution of a monoprotic acid can be easily calculated using an ICE table.

== Polyprotic acids ==
[[File:H3PO4 speciation.png|thumb|200px|alt=Acids with more than one ionizable hydrogen atoms are called polyprotic acids, and have multiple deprotonation states, also called species. This image plots the relative percentages of the different protonation species of phosphoric acid H 3 P O 4 as a function of solution p H. Phosphoric acid has three ionizable hydrogen atoms whose p K A's are roughly 2, 7 and 12. Below p H 2, the triply protonated species H 3 P O 4 predominates; the double protonated species H 2 P O 4 minus predominates near p H 5; the singly protonated species H P O 4 2 minus predominates near p H 9 and the unprotonated species P O 4 3 minus predominates above p H 12|Phosphoric acid speciation]]
A polyprotic acid is a compound which may lose more than 1 proton. Stepwise dissociation constants are each defined for the loss of a single proton. The constant for dissociation of the first proton may be denoted as ''K''<sub>a1</sub> and the constants for dissociation of successive protons as ''K''<sub>a2</sub>, etc. [[Chemistry:Phosphoric acid|Phosphoric acid]], {{chem2|H3PO4}}, is an example of a polyprotic acid as it can lose three protons.
:{| class="wikitable"
! Equilibrium
! p''K'' definition and value<ref>The values are for 25{{nbsp}}°C and 0 ionic strength – {{cite journal| last1=Powell| first1=Kipton J.| last2=Brown| first2=Paul L.| last3=Byrne| first3=Robert H.| last4=Gajda| first4=Tamás| last5=Hefter| first5=Glenn| last6=Sjöberg| first6=Staffan| last7=Wanner| first7=Hans| title=Chemical speciation of environmentally significant heavy metals with inorganic ligands. Part 1: The Hg<sup>2+</sup> – Cl<sup>−</sup>, OH<sup>−</sup>, CO<sub>3</sub><sup>2-</sup>, SO<sub>4</sub><sup>2-</sup>, and PO<sub>4</sub><sup>3-</sup> aqueous systems|journal=Pure Appl. Chem. |date=2005 |volume=77 |issue=4 |pages=739–800 |doi=10.1351/pac200577040739| doi-access=free}}</ref>
|-
| <chem>H3PO4 <=> H2PO4- + H+</chem>
| <math chem="">\mathrm{p}K_\ce{a1} = \log_{10} \frac{[\ce{H_3PO_4}]}{[\ce{H_2PO_4^{-}}][\ce{H^+}]} = 2.14</math>
|-
| <chem>H2PO4- <=> HPO4^2- + H+</chem>
| <math chem="">\mathrm{p}K_\ce{a2} = \log_{10} \frac{[\ce{H_2PO_4^{-}}]}{[\ce{HPO_4^{2-}}][\ce{H^+}]} = 7.2 </math>
|-
| <chem>HPO4^2- <=> PO4^3- + H+</chem>
| <math chem="">\mathrm{p}K_\ce{a3} = \log_{10} \frac{[\ce{HPO4^2-}]}{[\ce{PO4^3-}][\ce{H+}]} = 12.37 </math>
|}

When the difference between successive p''K'' values is about four or more, as in this example, each species may be considered as an acid in its own right;<ref>{{cite book| last= Brown| first= T.E.| author2= Lemay, H.E.| author3= Bursten, B.E.| author4= Murphy, C.| author5= Woodward, P.| year= 2008| title= Chemistry: The Central Science| edition= 11th| location = New York| publisher = Prentice-Hall| isbn= 978-0-13-600617-6| page= 689}}</ref> In fact salts of {{chem|H|2|PO|4|−}} may be crystallised from solution by adjustment of pH to about 5.5 and salts of {{chem2|HPO4(2-)}} may be crystallised from solution by adjustment of pH to about 10. The species distribution diagram shows that the concentrations of the two ions are maximum at pH&nbsp;5.5 and 10.

[[File:Citric acid speciation.png|thumb|200 px|alt=This image plots the relative percentages of the protonation species of citric acid as a function of p H. Citric acid has three ionizable hydrogen atoms and thus three p K A values. Below the lowest p K A, the triply protonated species prevails; between the lowest and middle p K A, the doubly protonated form prevails; between the middle and highest p K A, the singly protonated form prevails; and above the highest p K A, the unprotonated form of citric acid is predominant.|% species formation calculated with the program HySS for a 10 millimolar solution of citric acid. p''K''<sub>a1</sub>&nbsp;=&nbsp;3.13, p''K''<sub>a2</sub>&nbsp;=&nbsp;4.76, p''K''<sub>a3</sub>&nbsp;=&nbsp;6.40.]]
When the difference between successive p''K'' values is less than about four there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. The case of citric acid is shown at the right; solutions of citric acid are buffered over the whole range of pH&nbsp;2.5 to 7.5.

According to Pauling's first rule, successive p''K'' values of a given acid increase {{nowrap|(p''K''<sub>a2</sub> > p''K''<sub>a1</sub>)}}.<ref name="pauling">{{cite book| last= Greenwood| first= N.N.| author2= Earnshaw, A.| year = 1997| title= Chemistry of the Elements| edition= 2nd| location = Oxford| publisher = Butterworth-Heinemann| isbn= 0-7506-3365-4| page= 50}}</ref> For oxyacids with more than one ionizable hydrogen on the same atom, the p''K''<sub>a</sub> values often increase by about 5 units for each proton removed,<ref name=Miessler2ed>{{cite book| title= Inorganic Chemistry| last= Miessler| first= Gary L.| author2= Tarr Donald A.| year= 1999| publisher = Prentice Hall| isbn= 0-13-465659-8| edition = 2nd| page= 164}}</ref><ref name="Huheey">{{cite book| last= Huheey| first= James E.| year= 1983| title= Inorganic Chemistry| edition= 3rd| publisher = Harper & Row| isbn= 0-06-042987-9| page= 297}}</ref> as in the example of phosphoric acid above.

It can be seen in the table above that the second proton is removed from a negatively charged species. Since the proton carries a positive charge extra work is needed to remove it, which is why p''K''<sub>a2</sub> is greater than p''K''<sub>a1</sub>. p''K''<sub>a3</sub> is greater than p''K''<sub>a2</sub> because there is further charge separation. When an exception to Pauling's rule is found, it indicates that a major change in structure is also occurring. In the case of {{chem2|VO2+}}(aq), the vanadium is [[Physics:Octahedral molecular geometry|octahedral]], 6-coordinate, whereas vanadic acid is [[Physics:Tetrahedral molecular geometry|tetrahedral]], 4-coordinate. This means that four "particles" are released with the first dissociation, but only two "particles" are released with the other dissociations, resulting in a much greater entropy contribution to the standard [[Physics:Gibbs free energy|Gibbs free energy]] change for the first reaction than for the others.
:{| class="wikitable"
! Equilibrium
! p''K''<sub>a</sub>
|-
| <chem>[VO2(H2O)4]+ <=> H3VO4 + H+ + 2H2O</chem>
|<math chem>\mathrm{p}K_{a_1} = 4.2</math>
|-
| <chem>H3VO4 <=> H2VO4- + H+</chem>
|<math chem>\mathrm{p}K_{a_2} = 2.60</math>
|-
| <chem>H2VO4- <=> HVO4^2- + H+</chem>
| <math chem>\mathrm{p}K_{a_3} = 7.92</math>
|-
| <chem>HVO4^2- <=> VO4^3- + H+</chem>
| <math chem>\mathrm{p}K_{a_4} = 13.27</math>
|}

=== Isoelectric point ===
{{Main|Biology:Isoelectric point}}
For substances in solution, the isoelectric point (p''I'') is defined as the pH at which the sum, weighted by charge value, of concentrations of positively charged species is equal to the weighted sum of concentrations of negatively charged species. In the case that there is one species of each type, the isoelectric point can be obtained directly from the p''K'' values. Take the example of [[Chemistry:Glycine|glycine]], defined as AH. There are two dissociation equilibria to consider.
: <chem>AH2+ <=> AH~+ H+ \qquad [AH][H+] = \mathit{K}_1 [AH2+]</chem>
: <chem>AH <=> A^-~+H+ \qquad [A^- ][H+] = \mathit{K}_2 [AH]</chem>

Substitute the expression for [AH] from the second equation into the first equation
: <chem>[A^- ][H+]^2 = \mathit{K}_1 \mathit{K}_2 [AH2+]</chem>

At the isoelectric point the concentration of the positively charged species, {{chem2|AH2+}}, is equal to the concentration of the negatively charged species, {{chem2|A-}}, so
: <math chem>[\ce{H+}]^2 = K_1 K_2</math>

Therefore, taking [[Cologarithm|cologarithm]]s, the pH is given by
: <math>\mathrm{p}I = \frac{\mathrm{p}K_1 + \mathrm{p}K_2}{2}</math>

p''I'' values for amino acids are listed at [[Chemistry:Proteinogenic amino acid#Chemical properties|proteinogenic amino acid]]. When more than two charged species are in equilibrium with each other a full speciation calculation may be needed.

== Bases and basicity ==
The equilibrium constant ''K''<sub>b</sub> for a base is usually defined as the ''association'' constant for protonation of the base, B, to form the conjugate acid, {{chem2|HB+}}.
: <chem>B + H2O <=> HB+ + OH-</chem>

Using similar reasoning to that used before
: <math alt="The base association constant K b equals the concentration of the protonated form H B +, times the concentration of the hydroxyl anion O H minus, all divided by the concentration of the base B. The base power of disassociation constant p K b is defined in terms of the base association constant K b" >
\begin{align}
K_\text{b} &= \mathrm{\frac{[HB^+] [OH^-]}{[B]}} \\
\mathrm{p}K_\text{b} &= - \log_{10}\left(K_\text{b}\right)
\end{align}</math>

''K''<sub>b</sub> is related to ''K''<sub>a</sub> for the conjugate acid. In water, the concentration of the [[Chemistry:Hydroxide|hydroxide]] ion, {{chem2|[OH-]}}, is related to the concentration of the hydrogen ion by {{chem2|1=''K''_{w} = [H+][OH-]}}, therefore
: <math alt="The concentration of the hydroxyl anion O H minus equals the ionization constant of water K w divided by the concentration of H +, by the definition of K w." >
\mathrm{[OH^-]} = \frac{K_\mathrm{w}}{\mathrm{[H^+]}}
</math>

Substitution of the expression for {{chem2|[OH-]}} into the expression for ''K''<sub>b</sub> gives
: <math alt="K b can be written as a ratio of four terms. The numerator holds the concentration of the protonated base H B + times the ionization constant of water K w. The denominator holds the concentration of the base B times that of H +. Using the definition for K A, K b equals K w divided by K A." >
 K_\text{b} = \frac{[\mathrm{HB^+}]K_\text{w}}{\mathrm{[B] [H^+]}} = \frac{K_\text{w}}{K_\text{a}}
</math>

When ''K''<sub>a</sub>, ''K''<sub>b</sub> and ''K''<sub>w</sub> are determined under the same conditions of temperature and ionic strength, it follows, taking [[Cologarithm|cologarithm]]s, that p''K''<sub>b</sub>&nbsp;=&nbsp;p''K''<sub>w</sub>&nbsp;−&nbsp;p''K''<sub>a</sub>. In aqueous solutions at 25&nbsp;°C, p''K''<sub>w</sub> is 13.9965,<ref name=crc>{{cite book
| title = CRC Handbook of Chemistry and Physics, Student Edition
| last = Lide
| first = D.R.
| year = 2004
| publisher = CRC Press
| edition = 84th
| isbn = 0-8493-0597-7
}} Section D–152</ref> so
:<math>\mathrm{p}K_\text{b} \approx 14 - \mathrm{p}K_\text{a}</math>

with sufficient accuracy for most practical purposes. In effect there is no need to define p''K''<sub>b</sub> separately from p''K''<sub>a</sub>,<ref name=Skoog>{{cite book |last1=Skoog |first1=Douglas A. |last2=West |first2=Donald M. |last3=Holler |first3=F. James |last4=Crouch |first4=Stanley R. |title=Fundamentals of Analytical Chemistry |date=2014 |publisher=Brooks/Cole |isbn=978-0-495-55828-6 |pages=212 |edition=9th}}</ref> but it is done here as often only p''K''<sub>b</sub> values can be found in the older literature.

For an hydrolyzed metal ion, ''K''<sub>b</sub> can also be defined as a stepwise ''dissociation'' constant
: <math chem>\mathrm{M}_p(\ce{OH})_q \leftrightharpoons \mathrm{M}_p(\ce{OH})^{+}_{q-1} + \ce{OH-}</math>
: <math chem>K_\mathrm{b} = \frac{[\mathrm{M}_p(\ce{OH})^{+}_{q-1}] [\ce{OH-}]}{[\mathrm{M}_p(\ce{OH})_q]}</math>

This is the reciprocal of an [[Chemistry:Stability constants of complexes|association constant]] for formation of the complex.

=== Basicity expressed as dissociation constant of conjugate acid ===
Because the relationship p''K''<sub>b</sub>&nbsp;=&nbsp;p''K''<sub>w</sub>&nbsp;−&nbsp;p''K''<sub>a</sub> holds only in aqueous solutions (though analogous relationships apply for other amphoteric solvents), subdisciplines of chemistry like [[Chemistry:Organic chemistry|organic chemistry]] that usually deal with nonaqueous solutions generally do not use p''K''<sub>b</sub> as a measure of basicity. Instead, the p''K''<sub>a</sub> of the conjugate acid, denoted by p''K''<sub>aH</sub>, is quoted when basicity needs to be quantified. For base B and its conjugate acid BH<sup>+</sup> in equilibrium, this is defined as
: <math chem>\mathrm{p}K_\mathrm{aH}(\mathrm{B})=\mathrm{p}K_\mathrm{a}(\ce{BH+})=-\log_{10}\Big(\frac{[\ce{B}][\ce{H+}]}{[\ce{BH+}]}\Big)</math>

A higher value for p''K''<sub>aH</sub> corresponds to a stronger base. For example, the values {{chem2|1=p''K''_{aH} (C5H5N) = 5.25}} and {{chem2|1=p''K''_{aH} ((CH3CH2)3N) = 10.75}} indicate that {{chem2|(CH3CH2)3N}} (triethylamine) is a stronger base than {{chem2|C5H5N}} (pyridine).

== Amphoteric substances ==
An amphoteric substance is one that can act as an acid or as a base, depending on pH. Water (below) is amphoteric. Another example of an amphoteric molecule is the [[Chemistry:Bicarbonate|bicarbonate]] ion {{chem2|HCO3-}} that is the conjugate base of the [[Chemistry:Carbonic acid|carbonic acid]] molecule H2CO3 in the equilibrium
:<chem>H2CO3 + H2O <=> HCO3- + H3O+</chem>

but also the conjugate acid of the [[Chemistry:Carbonate|carbonate]] ion {{chem2|CO3(2-)}} in (the reverse of) the equilibrium
:<chem>HCO3- + OH- <=> CO3^2- + H2O</chem>
[[Chemistry:Carbonic acid|Carbonic acid]] equilibria are important for [[Chemistry:Acid–base homeostasis|acid–base homeostasis]] in the human body.

An [[Chemistry:Amino acid|amino acid]] is also amphoteric with the added complication that the neutral molecule is subject to an internal acid–base equilibrium in which the basic amino group attracts and binds the proton from the acidic carboxyl group, forming a [[Physics:Zwitterion|zwitterion]].
: <chem>NH2CHRCO2H <=> NH3+CHRCO2-</chem>

At pH less than about 5 both the carboxylate group and the amino group are protonated. As pH increases the acid dissociates according to
: <chem>NH3+CHRCO2H <=> NH3+CHRCO2- + H+</chem>

At high pH a second dissociation may take place.
: <chem>NH3+CHRCO2- <=> NH2CHRCO2- + H+</chem>

Thus the amino acid molecule is amphoteric because it may either be protonated or deprotonated.

=== Water self-ionization ===
{{Main|Physics:Self-ionization of water}}
The water molecule may either gain or lose a proton. It is said to be amphiprotic. The ionization equilibrium can be written
: <chem>H2O <=> OH- + H+</chem>

where in aqueous solution {{chem2|H+}} denotes a [[Chemistry:Solvation|solvated]] proton. Often this is written as the [[Chemistry:Hydronium|hydronium]] ion {{chem2|H3O+}}, but this formula is not exact because in fact there is solvation by more than one water molecule and species such as {{chem2|H5O2+}}, {{chem2|H7O3+}}, and {{chem2|H9O4+}} are also present.<ref>{{Housecroft2nd|page=163}}</ref>

The equilibrium constant is given by
:<math alt="The acidity constant K A for water equals the concentration of H + times that of O H minus divided by the concentration of water, H 2 O." >
 K_\text{a} = \mathrm{\frac{[H^+] [OH^-]}{[H_2O]}}
</math>

With solutions in which the solute concentrations are not very high, the concentration {{chem2|[H2O]}} can be assumed to be constant, regardless of solute(s); this expression may then be replaced by
:<math alt="The ionization constant of water K w equals the concentration of H + times the concentration of O H minus." >
 K_\text{w} = [\mathrm{H}^+] [\mathrm{OH}^-]\,
</math>

The [[Physics:Self-ionization of water|self-ionization]] constant of water, ''K''<sub>w</sub>, is thus just a special case of an acid dissociation constant. A logarithmic form analogous to p''K''<sub>a</sub> may also be defined
:<math>\mathrm{p}K_\text{w} = - \log_{10}\left(K_\text{w}\right)</math>

{| class="wikitable" style="text-align:center"
|+ p''K''<sub>w</sub> values for pure water at various temperatures<ref>{{cite book
| last1 = Harned
| first1 = H.S.
| last2 = Owen
| first2 = B.B
| title = The Physical Chemistry of Electrolytic Solutions
| url = https://archive.org/details/physicalchemistr0003harn
| url-access = registration
| year = 1958
| publisher = Reinhold Publishing Corp.
| location = New York
| pages = [https://archive.org/details/physicalchemistr0003harn/page/634 634]–649, 752–754
}}</ref>
|-
! scope="row" | ''T'' (°C)
| 0 || 5 || 10 || 15 || 20 || 25 || 30 || 35 || 40 || 45 || 50
|-
! scope="row" | p''K''<sub>w</sub>
| 14.943 || 14.734 || 14.535 || 14.346 || 14.167 || 13.997 || 13.830 || 13.680 || 13.535 || 13.396 || 13.262
|}

These data can be modelled by a [[Parabola|parabola]] with
: <math>\mathrm p K_\mathrm w = 14.94 - 0.04209\ T + 0.0001718\ T^2</math>

From this equation, p''K''<sub>w</sub>&nbsp;=&nbsp;14 at 24.87&nbsp;°C. At that temperature both hydrogen and hydroxide ions have a concentration of 10<sup>−7</sup>&nbsp;M.

== Acidity in nonaqueous solutions ==
A solvent will be more likely to promote ionization of a dissolved acidic molecule in the following circumstances:<ref name=loudon>{{citation
| last = Loudon
| first = G. Marc
| title = Organic Chemistry
| edition = 4th
| year = 2005
| publisher = Oxford University Press
| location = New York
| isbn = 0-19-511999-1
| pages = 317–318
}}</ref>
# It is a [[Chemistry:Protic solvent|protic solvent]], capable of forming hydrogen bonds.
# It has a high [[Chemistry:Donor number|donor number]], making it a strong Lewis base.
# It has a high dielectric constant (relative permittivity), making it a good solvent for ionic species.
p''K''<sub>a</sub> values of organic compounds are often obtained using the aprotic solvents [[Chemistry:Dimethyl sulfoxide|dimethyl sulfoxide]] (DMSO)<ref name=loudon /> and [[Chemistry:Acetonitrile|acetonitrile]] (ACN).<ref>{{cite book
| title = Advanced Organic Chemistry
| last = March
| first = J.
| author2 = Smith, M.
| year = 2007
| publisher = John Wiley & Sons
| location = New York
| isbn = 978-0-471-72091-1
| edition = 6th
}} Chapter 8: Acids and Bases</ref>

{| class="wikitable"
|+ Solvent properties at 25&nbsp;°C
|-
! Solvent !! Donor number<ref name=loudon /> !! Dielectric constant<ref name=loudon />
|-
| Acetonitrile || 14 || 37
|-
| Dimethylsulfoxide || 30 || 47
|-
| Water || 18 || 78
|}

DMSO is widely used as an alternative to water because it has a lower dielectric constant than water, and is less polar and so dissolves non-polar, [[Chemistry:Hydrophobic|hydrophobic]] substances more easily. It has a measurable p''K''<sub>a</sub> range of about 1 to 30. Acetonitrile is less basic than DMSO, and, so, in general, acids are weaker and bases are stronger in this solvent. Some p''K''<sub>a</sub> values at 25&nbsp;°C for acetonitrile (ACN)<ref>{{cite journal
| last = Kütt
| first = A.
| author2 = Movchun, V.
| author3 = Rodima, T
| author4 = Dansauer, T.
| author5 = Rusanov, E.B.
| author6 = Leito, I.
| author7 = Kaljurand, I.
| author8 = Koppel, J.
| author9 = Pihl, V.
| author10 = Koppel, I.
| author11 = Ovsjannikov, G.
| author12 = Toom, L.
| author13 = Mishima, M.
| author14 = Medebielle, M.
| author15 = Lork, E.
| author16 = Röschenthaler, G-V.
| author17 = Koppel, I.A.
| author18 = Kolomeitsev, A.A.
| year = 2008
| title = Pentakis(trifluoromethyl)phenyl, a Sterically Crowded and Electron-withdrawing Group: Synthesis and Acidity of Pentakis(trifluoromethyl)benzene, -toluene, -phenol, and -aniline
| journal = J. Org. Chem.
| volume = 73
| issue = 7
| pages = 2607–2620
| doi = 10.1021/jo702513w
| pmid = 18324831
}}</ref><ref name=Ivo_AN>{{cite journal
| last = Kütt
| first = A.
| author2 = Leito, I.
| author3 = Kaljurand, I.
| author4 = Sooväli, L.
| author5 = Vlasov, V.M.
| author6 = Yagupolskii, L.M.
| author7 = Koppel, I.A.
| year = 2006
| title = A Comprehensive Self-Consistent Spectrophotometric Acidity Scale of Neutral Brønsted Acids in Acetonitrile
| journal = J. Org. Chem.
| volume = 71
| issue = 7
| pages = 2829–2838
| doi = 10.1021/jo060031y
| pmid = 16555839
| s2cid = 8596886
}}</ref><ref>{{cite journal
| last = Kaljurand
| first = I.
| author2 = Kütt, A.
| author3 = Sooväli, L.
| author4 = Rodima, T.
| author5 = Mäemets, V.
| author6 = Leito, I
| author7 = Koppel, I.A.
| year = 2005
| title = Extension of the Self-Consistent Spectrophotometric Basicity Scale in Acetonitrile to a Full Span of 28 pKa Units: Unification of Different Basicity Scales
| journal = J. Org. Chem.
| volume = 70
| issue = 3
| pages = 1019–1028
| doi = 10.1021/jo048252w
| pmid = 15675863
}}</ref> and dimethyl sulfoxide (DMSO).<ref>{{cite web
| url = http://www.chem.wisc.edu/areas/reich/pkatable/
| title = Bordwell pKa Table (Acidity in DMSO)
| access-date = 2008-11-02
| archive-url = https://web.archive.org/web/20081009060809/http://www.chem.wisc.edu/areas/reich/pkatable/
| archive-date = 9 October 2008
| url-status = dead
}}</ref> are shown in the following tables. Values for water are included for comparison.

{| class="wikitable"
|+ p''K''<sub>a</sub> values of acids
|-
! HA {{Eqm}} A{{sup|−}} + H{{sup|+}} !! ACN !! DMSO !! Water
|-
| [[Chemistry:P-Toluenesulfonic acid|''p''-Toluenesulfonic acid]] || 8.5 || 0.9 || ''Strong''
|-
| [[Chemistry:2,4-Dinitrophenol|2,4-Dinitrophenol]] || 16.66 || 5.1 || 3.9
|-
| [[Chemistry:Benzoic acid|Benzoic acid]] || 21.51 || 11.1 || 4.2
|-
| [[Chemistry:Acetic acid|Acetic acid]] || 23.51 || 12.6 || 4.756
|-
| [[Chemistry:Phenol|Phenol]] || 29.14 || 18.0 || 9.99
|-
<!--
|}

{| class="wikitable" align="center"
|+ p''K''<sub>a</sub> values of acids conjugate to bases
|-
-->
! BH{{sup|+}} {{Eqm}} B + H{{sup|+}} !! ACN !! DMSO !! Water
|-
| [[Chemistry:Pyrrolidine|Pyrrolidine]] || 19.56 || 10.8 || 11.4
|-
| [[Chemistry:Triethylamine|Triethylamine]] || 18.82 || 9.0 || 10.72
|-
| Proton sponge{{nbsp|11}} || 18.62 || 7.5 || 12.1
|-
| [[Chemistry:Pyridine|Pyridine]] || 12.53 || 3.4 || 5.2
|-
| [[Chemistry:Aniline|Aniline]] || 10.62 || 3.6 || 4.6
|}

Ionization of acids is less in an acidic solvent than in water. For example, [[Chemistry:Hydrogen chloride|hydrogen chloride]] is a weak acid when dissolved in [[Chemistry:Acetic acid|acetic acid]]. This is because acetic acid is a much weaker base than water.
: <chem>HCl + CH3CO2H <=> Cl- + CH3C(OH)2+</chem>
: <math chem>\text{acid} + \text{base } \ce{<=>} \text{ conjugate base} + \text{conjugate acid}</math>

Compare this reaction with what happens when acetic acid is dissolved in the more acidic solvent pure sulfuric acid:<ref>{{Housecroft3rd}} Chapter 8: Non-Aqueous Media</ref>
:<chem>H2SO4 + CH3CO2H <=> HSO4- + CH3C(OH)2+</chem>

[[File:Carboxylic acid dimers.png|thumb|upright=0.65|alt=This image illustrates how two carboxylic acids, C O O H, can associate through mutual hydrogen bonds. The hydroxyl portion O H of each molecule forms a hydrogen bond to the carbonyl portion C O of the other.|Dimerization of a carboxylic acid.]]
The unlikely [[Chemistry:Diol|geminal diol]] species {{chem2|CH3C(OH)2+}} is stable in these environments. For aqueous solutions the [[Chemistry:PH|pH]] scale is the most convenient [[Chemistry:Acidity function|acidity function]].<ref>{{cite book
| title = Acidity Functions
| last = Rochester
| first = C.H.
| year = 1970
| publisher = Academic Press
| isbn = 0-12-590850-4
}}</ref> Other acidity functions have been proposed for non-aqueous media, the most notable being the [[Chemistry:Hammett acidity function|Hammett acidity function]], ''H''<sub>0</sub>, for [[Chemistry:Superacid|superacid]] media and its modified version ''H''<sub>−</sub> for [[Chemistry:Superbase|superbasic]] media.<ref>{{cite book
| last = Olah
| first = G.A
| author2 = Prakash, S
| author3 = Sommer, J
| title = Superacids
| publisher = Wiley Interscience
| location = New York
| year = 1985
| isbn = 0-471-88469-3
}}</ref>

In aprotic solvents, [[Chemistry:Oligomer|oligomer]]s, such as the well-known acetic acid [[Chemistry:Dimer|dimer]], may be formed by hydrogen bonding. An acid may also form hydrogen bonds to its conjugate base. This process, known as [[Chemistry:Homoassociation|homoconjugation]], has the effect of enhancing the acidity of acids, lowering their effective p''K''<sub>a</sub> values, by stabilizing the conjugate base. Homoconjugation enhances the proton-donating power of toluenesulfonic acid in acetonitrile solution by a factor of nearly 800.<ref>{{cite journal
| last = Coetzee
| first = J.F.
| author2 = Padmanabhan, G.R.
| title = Proton Acceptor Power and Homoconjugation of Mono- and Diamines
| journal = J. Am. Chem. Soc.
| year = 1965
| volume = 87
| issue = 22
| pages = 5005–5010
| doi = 10.1021/ja00950a006
}}</ref>

In aqueous solutions, homoconjugation does not occur, because water forms stronger hydrogen bonds to the conjugate base than does the acid.

=== Mixed solvents ===
[[File:Acetic acid pK dioxane water.png|thumb|alt=The p K A of acetic acid in the mixed solvent dioxane/water. p K A increases as the proportion of dioxane increases, primarily because the dielectric constant of the mixture decreases with increasing doxane content. A lower dielectric constant disfavors the dissociation of the uncharged acid into the charged ions, H + and C H 3 C O O minus, shifting the equilibrium to favor the uncharged protonated form C H 3 C O O H. Since the protonated form is the reactant not the product of the dissociation, this shift decreases the equilibrium constant K A, and increases P K A, its negative logarithm.|p''K''<sub>a</sub> of acetic acid in dioxane/water mixtures. Data at 25&nbsp;°C from Pine ''et al.''<ref>{{cite book
| title = Organic chemistry
| last = Pine
| first = S.H.
| author2 = Hendrickson, J.B.
| author3 = Cram, D.J.
| author4 = Hammond, G.S.
| year = 1980
| publisher = McGraw–Hill
| isbn = 0-07-050115-7
| page = 203
}}</ref>]]

When a compound has limited solubility in water it is common practice (in the pharmaceutical industry, for example) to determine p''K''<sub>a</sub> values in a solvent mixture such as water/dioxane or water/[[Chemistry:Methanol|methanol]], in which the compound is more soluble.<ref>{{cite journal
| last = Box
| first = K.J.
| author2 = Völgyi, G.
| author3 = Ruiz, R.
| author4 = Comer, J.E.
| author5 = Takács-Novák, K.
| author6 = Bosch, E.
| author7 = Ràfols, C.
| author8 = Rosés, M.
| year = 2007
| title = Physicochemical Properties of a New Multicomponent Cosolvent System for the pKa Determination of Poorly Soluble Pharmaceutical Compounds
| journal = Helv. Chim. Acta
| volume = 90
| issue = 8
| pages = 1538–1553
| doi = 10.1002/hlca.200790161
}}</ref> In the example shown at the right, the p''K''<sub>a</sub> value rises steeply with increasing percentage of dioxane as the dielectric constant of the mixture is decreasing.

A p''K''<sub>a</sub> value obtained in a mixed solvent cannot be used directly for aqueous solutions. The reason for this is that when the solvent is in its standard state its activity is ''defined'' as one. For example, the standard state of water:dioxane mixture with 9:1 [[Chemistry:Mixing ratio|mixing ratio]] is precisely that solvent mixture, with no added solutes. To obtain the p''K''<sub>a</sub> value for use with aqueous solutions it has to be extrapolated to zero co-solvent concentration from values obtained from various co-solvent mixtures.

These facts are obscured by the omission of the solvent from the expression that is normally used to define p''K''<sub>a</sub>, but p''K''<sub>a</sub> values obtained in a ''given'' mixed solvent can be compared to each other, giving relative acid strengths. The same is true of p''K''<sub>a</sub> values obtained in a particular non-aqueous solvent such a DMSO.

A universal, solvent-independent, scale for acid dissociation constants has not been developed, since there is no known way to compare the standard states of two different solvents.

== Factors that affect p''K''<sub>a</sub> values ==
Pauling's second rule is that the value of the first p''K''<sub>a</sub> for acids of the formula XO<sub>''m''</sub>(OH)<sub>''n''</sub> depends primarily on the number of oxo groups ''m'', and is approximately independent of the number of hydroxy groups ''n'', and also of the central atom X. Approximate values of p''K''<sub>a</sub> are 8 for ''m''&nbsp;=&nbsp;0, 2 for ''m''&nbsp;=&nbsp;1, −3 for ''m''&nbsp;=&nbsp;2 and <&nbsp;−10 for ''m''&nbsp;=&nbsp;3.<ref name="pauling" /> Alternatively, various numerical formulas have been proposed including p''K''<sub>a</sub>&nbsp;=&nbsp;8&nbsp;−&nbsp;5''m'' (known as Bell's rule),<ref name=Miessler2ed /><ref name=House2>{{cite book
| last1 = Housecroft
| first1 = Catherine E.
| last2 = Sharpe
| first2 = Alan G.
| title = Inorganic chemistry
| date = 2005
| publisher = Pearson Prentice Hall
| location = Harlow, U.K.
| isbn = 0-13-039913-2
| pages = 170–171
| edition = 2nd
}}</ref> p''K''<sub>a</sub>&nbsp;=&nbsp;7&nbsp;−&nbsp;5''m'',<ref name=Huheey /><ref name=Douglas>Douglas B., McDaniel D.H. and Alexander J.J. ''Concepts and Models of Inorganic Chemistry'' (2nd ed. Wiley 1983) p.526 {{ISBN|0-471-21984-3}}</ref> or p''K''<sub>a</sub>&nbsp;=&nbsp;9&nbsp;−&nbsp;7''m''.<ref name=Miessler2ed /> The dependence on ''m'' correlates with the oxidation state of the central atom, X: the higher the oxidation state the stronger the oxyacid.

For example, p''K''<sub>a</sub> for HClO is 7.2, for HClO<sub>2</sub> is 2.0, for HClO<sub>3</sub> is −1 and HClO<sub>4</sub> is a strong acid ({{nowrap|p''K''<sub>a</sub> ≪ 0}}).<ref name="SA" /> The increased acidity on adding an oxo group is due to stabilization of the conjugate base by delocalization of its negative charge over an additional oxygen atom.<ref name="House2" /> This rule can help assign molecular structure: for example, [[Chemistry:Phosphorous acid|phosphorous acid]], having molecular formula H<sub>3</sub>PO<sub>3</sub>, has a p''K''<sub>a</sub> near 2, which suggested that the structure is HPO(OH)<sub>2</sub>, as later confirmed by [[Physics:Nuclear magnetic resonance spectroscopy|NMR spectroscopy]], and not P(OH)<sub>3</sub>, which would be expected to have a p''K''<sub>a</sub> near 8.<ref name="Douglas" />

[[File:Chloroacetic pka.png|thumb|300x300px|pKa values for acetic, chloroacetic, dichloroacetic and trichloroacetic acids.]]

Inductive effects and [[Chemistry:Mesomeric effect|mesomeric effect]]s affect the p''K''<sub>a</sub> values. A simple example is provided by the effect of replacing the hydrogen atoms in acetic acid by the more electronegative chlorine atom. The electron-withdrawing effect of the substituent makes ionisation easier, so successive p''K''<sub>a</sub> values decrease in the series 4.7, 2.8, 1.4, and 0.7 when 0, 1, 2, or 3 chlorine atoms are present.<ref>{{cite book
| last = Pauling
| first = L.
| title = The nature of the chemical bond and the structure of molecules and crystals; an introduction to modern structural chemistry
| url = https://archive.org/details/natureofchemical00paul
| url-access = registration
| publisher = Cornell University Press
| location = Ithaca (NY)
| year = 1960
| edition = 3rd
| page = [https://archive.org/details/natureofchemical00paul/page/277 277]
| isbn = 0-8014-0333-2
}}</ref> The [[Hammett equation]], provides a general expression for the effect of substituents.<ref>{{cite book
| title = Organic Chemistry
| last = Pine
| first = S.H.
| author2 = Hendrickson, J.B.
| author3 = Cram, D.J.
| author4 = Hammond, G.S.
| year = 1980
| publisher = McGraw–Hill
| isbn = 0-07-050115-7
}} Section 13-3: Quantitative Correlations of Substituent Effects (Part B) – The Hammett Equation</ref>
: log(''K''<sub>a</sub>)&nbsp;=&nbsp;log(''K''{{su|b=a|p=0}})&nbsp;+&nbsp;ρσ.

''K''<sub>a</sub> is the dissociation constant of a substituted compound, ''K''{{su|b=a|p=0}} is the dissociation constant when the substituent is hydrogen, ρ is a property of the unsubstituted compound and σ has a particular value for each substituent. A plot of log(''K''<sub>a</sub>) against σ is a straight line with [[Y-intercept|intercept]] log(''K''{{su|b=a|p=0}}) and [[Slope|slope]] ρ. This is an example of a linear free energy relationship as log(''K''<sub>a</sub>) is proportional to the standard free energy change. Hammett originally<ref>{{cite journal
| last = Hammett
| first = L.P.
| title = The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives
| journal = J. Am. Chem. Soc.
| volume = 59
| issue = 1
| pages = 96–103
| doi = 10.1021/ja01280a022
| year = 1937
}}</ref> formulated the relationship with data from [[Chemistry:Benzoic acid|benzoic acid]] with different substituents in the ''ortho-'' and ''para-'' positions: some numerical values are in [[Hammett equation]]. This and other studies allowed substituents to be ordered according to their [[Chemistry:Inductive effect|electron-withdrawing]] or [[Chemistry:Inductive effect|electron-releasing]] power, and to distinguish between inductive and mesomeric effects.<ref>{{cite journal
| last = Hansch
| first = C.
| author2 = Leo, A.
| author3 = Taft, R. W.
| year = 1991
| title = A Survey of Hammett Substituent Constants and Resonance and Field Parameters
| journal = Chem. Rev.
| volume = 91
| issue = 2
| pages = 165–195
| doi = 10.1021/cr00002a004
| s2cid = 97583278
}}</ref><ref>{{cite journal
| last = Shorter
| first = J
| year = 1997
| title = Compilation and critical evaluation of structure-reactivity parameters and equations: Part 2. Extension of the Hammett σ scale through data for the ionization of substituted benzoic acids in aqueous solvents at 25&nbsp;°C (Technical Report)
| volume = 69
| issue = 12
| pages = 2497–2510
| doi = 10.1351/pac199769122497
| journal = Pure and Applied Chemistry
| s2cid = 98814841
| doi-access= free
}}</ref>

[[Chemistry:Alcohol|Alcohol]]s do not normally behave as acids in water, but the presence of a double bond adjacent to the OH group can substantially decrease the p''K''<sub>a</sub> by the mechanism of [[Chemistry:Keto–enol tautomerism|keto–enol tautomerism]]. [[Chemistry:Ascorbic acid|Ascorbic acid]] is an example of this effect. The diketone 2,4-pentanedione ([[Chemistry:Acetylacetone|acetylacetone]]) is also a weak acid because of the keto–enol equilibrium. In aromatic compounds, such as [[Chemistry:Phenol|phenol]], which have an OH substituent, [[Chemistry:Conjugated system|conjugation]] with the aromatic ring as a whole greatly increases the stability of the deprotonated form.

{{Multiple image
| direction         = vertical
| image1            = Fumaric-acid-2D-skeletal.png
| caption1          = [[Chemistry:Fumaric acid|Fumaric acid]]
| image2            = Maleic-acid-2D-skeletal-A.svg
| caption2          = [[Chemistry:Maleic acid|Maleic acid]]
}}

Structural effects can also be important. The difference between [[Chemistry:Fumaric acid|fumaric acid]] and [[Chemistry:Maleic acid|maleic acid]] is a classic example. Fumaric acid is (E)-1,4-but-2-enedioic acid, a ''trans'' [[Chemistry:Isomer|isomer]], whereas maleic acid is the corresponding ''cis'' isomer, i.e. (Z)-1,4-but-2-enedioic acid (see cis-trans isomerism). Fumaric acid has p''K''<sub>a</sub> values of approximately 3.0 and 4.5. By contrast, maleic acid has p''K''<sub>a</sub> values of approximately 1.5 and 6.5. The reason for this large difference is that when one proton is removed from the ''cis'' isomer (maleic acid) a strong [[Chemistry:Intramolecular force|intramolecular]] [[Chemistry:Hydrogen bond|hydrogen bond]] is formed with the nearby remaining carboxyl group. This favors the formation of the maleate H<sup>+</sup>, and it opposes the removal of the second proton from that species. In the ''trans'' isomer, the two carboxyl groups are always far apart, so hydrogen bonding is not observed.<ref>{{cite book
| title = Organic chemistry
| last = Pine
| first = S.H.
| author2 = Hendrickson, J.B.
| author3 = Cram, D.J.
| author4 = Hammond, G.S.
| year = 1980
| publisher = McGraw–Hill
| isbn = 0-07-050115-7
}} Section 6-2: Structural Effects on Acidity and Basicity</ref>[[File:Proton sponge.svg|thumb|upright=0.65|alt=Proton sponge is a derivative of naphthalene with dimethylamino groups in the one and ten positions. This brings the two dimethyl amino groups into close proximity to each other.|Proton sponge]]Proton sponge, 1,8-bis(dimethylamino)naphthalene, has a p''K''<sub>a</sub> value of 12.1. It is one of the strongest amine bases known. The high basicity is attributed to the relief of strain upon protonation and strong internal hydrogen bonding.<ref>{{cite journal
| last = Alder
| first = R.W.
| author2 = Bowman, P.S.
| author3 = Steele, W.R.S.
| author4 = Winterman, D.R.
| journal = Chem. Commun.
| issue = 13
| year = 1968
| doi = 10.1039/C19680000723
| title = The Remarkable Basicity of 1,8-bis(dimethylamino)naphthalene
| pages = 723–724
}}</ref><ref>{{cite journal
| last = Alder
| first = R.W.
| journal = Chem. Rev.
| year = 1989
| volume = 89
| issue = 5
| pages = 1215–1223
| doi = 10.1021/cr00095a015
| title = Strain Effects on Amine Basicities
}}</ref>

Effects of the solvent and solvation should be mentioned also in this section. It turns out, these influences are more subtle than that of a dielectric medium mentioned above. For example, the expected (by electronic effects of methyl substituents) and observed in gas phase order of basicity of methylamines, Me<sub>3</sub>N > Me<sub>2</sub>NH > MeNH<sub>2</sub> > NH<sub>3</sub>, is changed by water to Me<sub>2</sub>NH > MeNH<sub>2</sub> > Me<sub>3</sub>N > NH<sub>3</sub>. Neutral methylamine molecules are hydrogen-bonded to water molecules mainly through one acceptor, N–HOH, interaction and only occasionally just one more donor bond, NH–OH<sub>2</sub>. Hence, methylamines are stabilized to about the same extent by hydration, regardless of the number of methyl groups. In stark contrast, corresponding methylammonium cations always utilize '''all''' the available protons for donor NH–OH<sub>2</sub> bonding. Relative stabilization of methylammonium ions thus decreases with the number of methyl groups explaining the order of water basicity of methylamines.<ref name="RMC_2013" />

=== Thermodynamics ===
An equilibrium constant is related to the standard [[Physics:Gibbs free energy|Gibbs energy]] change for the reaction, so for an acid dissociation constant
: <math>\Delta G^\ominus = -RT \ln K_\text{a} \approx 2.303 RT\ \mathrm{p}K_\text{a}</math>.

''R'' is the [[Physics:Gas constant|gas constant]] and ''T'' is the [[Kelvin|absolute temperature]]. Note that {{nowrap|p''K''<sub>a</sub> {{=}} −log(''K''<sub>a</sub>)}} and {{nowrap|2.303 ≈ [[Natural logarithm|ln]](10)}}. At 25&nbsp;°C, Δ''G''{{sup|⊖}} in kJ·mol<sup>−1</sup> ≈ 5.708 p''K''<sub>a</sub> (1 kJ·mol<sup>−1</sup> = 1000 [[Joule|joule]]s per [[Mole (unit)|mole]]). Free energy is made up of an [[Physics:Enthalpy|enthalpy]] term and an [[Physics:Entropy|entropy]] term.<ref name=Goldmine />
:<math>\Delta G^\ominus = \Delta H^\ominus - T \Delta S^\ominus</math>

The standard enthalpy change can be determined by [[Physics:Calorimetry|calorimetry]] or by using the [[Van 't Hoff equation|van 't Hoff equation]], though the calorimetric method is preferable. When both the standard enthalpy change and acid dissociation constant have been determined, the standard entropy change is easily calculated from the equation above. In the following table, the entropy terms are calculated from the experimental values of p''K''<sub>a</sub> and Δ''H''{{sup|⊖}}. The data were critically selected and refer to 25&nbsp;°C and zero ionic strength, in water.<ref name="Goldmine">{{cite journal
| title = Thermodynamic Quantities for the Ionization Reactions of Buffers
| last = Goldberg
| first = R.
| author2 = Kishore, N.
| author3 = Lennen, R.
| journal = J. Phys. Chem. Ref. Data
| volume = 31
| issue = 2
| pages = 231–370
| year = 2002
| url = https://www.nist.gov/data/PDFfiles/jpcrd615.pdf
| doi = 10.1063/1.1416902
| bibcode = 2002JPCRD..31..231G
| url-status = dead
| archive-url = https://web.archive.org/web/20081006062140/https://www.nist.gov/data/PDFfiles/jpcrd615.pdf
| archive-date = 2008-10-06
}}</ref>

{| class="wikitable" style="text-align:center;"
|+ Acids
! Compound
! Equilibrium
! p''K''<sub>a</sub>
! Δ''G''{{sup|⊖}} (kJ·mol{{sup|−1}}){{efn|{{nowrap|Δ''G''{{sup|⊖}} ≈ 2.303''RT''p''K''{{sub|a}}}}}}
! Δ''H''{{sup|⊖}} (kJ·mol{{sup|−1}})
! −''T''Δ''S''{{sup|⊖}} (kJ·mol{{sup|−1}}){{efn|Computed here, from Δ''H'' and Δ''G'' values supplied in the citation, using {{nowrap|−''T''Δ''S''{{sup|⊖}} {{=}} Δ''G''{{sup|⊖}} − Δ''H''{{sup|⊖}}}}}}
|-
| style="text-align:left;" | HA = [[Chemistry:Acetic acid|Acetic acid]]
| style="text-align:left;" | HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
|  4.756
| 27.147
| −0.41
| 27.56
|-
| style="text-align:left;" | H<sub>2</sub>A<sup>+</sup> = [[Chemistry:Glycine|Glycine]]H<sup>+</sup>
| style="text-align:left;" | H<sub>2</sub>A<sup>+</sup> {{eqm}} HA + H<sup>+</sup>
|  2.351
| 13.420
|  4.00
|  9.419
|-
| style="text-align:left;" |
| style="text-align:left;" | HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 9.78
| 55.825
| 44.20
| 11.6
|-
| style="text-align:left;" | H<sub>2</sub>A = [[Chemistry:Maleic acid|Maleic acid]]
| style="text-align:left;" | H<sub>2</sub>A {{eqm}} HA<sup>−</sup> + H<sup>+</sup>
|  1.92
| 10.76
|  1.10
|  9.85
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>−</sup> {{eqm}} H<sup>+</sup> + A<sup>2−</sup>
|  6.27
| 35.79
| −3.60
| 39.4
|-
| style="text-align:left;" | H<sub>3</sub>A = [[Chemistry:Citric acid|Citric acid]]
| style="text-align:left;" | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
|  3.128
| 17.855
|  4.07
| 13.78
|-
|
| style="text-align:left;" | H<sub>2</sub>A<sup>−</sup> {{eqm}} HA<sup>2−</sup> + H<sup>+</sup>
|  4.76
| 27.176
|  2.23
|  24.9
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>2−</sup> {{eqm}} A<sup>3−</sup> + H<sup>+</sup>
|  6.40
| 36.509
| −3.38
| 39.9
|-
| style="text-align:left;" | H<sub>3</sub>A = [[Chemistry:Boric acid|Boric acid]]
| style="text-align:left;" | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
| 9.237
| 52.725
| 13.80
| 38.92
|-
| style="text-align:left;" | H<sub>3</sub>A = [[Chemistry:Phosphoric acid|Phosphoric acid]]
| style="text-align:left;" | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
|  2.148
| 12.261
| −8.00
| 20.26
|-
| style="text-align:left;" |
| style="text-align:left;" | H<sub>2</sub>A<sup>−</sup> {{eqm}} HA<sup>2−</sup> + H<sup>+</sup>
|  7.20
| 41.087
|  3.60
|  37.5
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>2−</sup> {{eqm}} A<sup>3−</sup> + H<sup>+</sup>
| 12.35
| 80.49
| 16.00
| 54.49
|-
| style="text-align:left;" | HA<sup>−</sup> = Hydrogen sulfate
| style="text-align:left;" | HA<sup>−</sup> {{eqm}} A<sup>2−</sup> + H<sup>+</sup>
|   1.99
|  11.36
| −22.40
|  33.74
|-
| style="text-align:left;" | H<sub>2</sub>A = [[Chemistry:Oxalic acid|Oxalic acid]]
| style="text-align:left;" | H<sub>2</sub>A {{eqm}} HA<sup>−</sup> + H<sup>+</sup>
|   1.27
|   7.27
|  −3.90
| 11.15
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>−</sup> {{eqm}} A<sup>2−</sup> + H<sup>+</sup>
|  4.266
| 24.351
| −7.00
| 31.35
|}
{{noteslist}}

{| class="wikitable"
|+ Conjugate acids of bases
! Compound
! Equilibrium
! p''K''<sub>a</sub>
! ΔH{{sup|⊖}} (kJ·mol{{sup|−1}})
! −''T''Δ''S''{{sup|⊖}} (kJ·mol{{sup|−1}})
|-
| style="text-align:left;" | B = [[Chemistry:Ammonia|Ammonia]]
| style="text-align:left;" | HB<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 9.245
| 51.95
| 0.8205
|-
| style="text-align:left;" | B = [[Chemistry:Methylamine|Methylamine]]
| style="text-align:left;" | HB<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 10.645
| 55.34
| 5.422
|-
| style="text-align:left;" | B = [[Chemistry:Triethylamine|Triethylamine]]
| style="text-align:left;" | HB<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 10.72
| 43.13
| 18.06
|}

The first point to note is that, when p''K''<sub>a</sub> is positive, the standard free energy change for the dissociation reaction is also positive. Second, some reactions are exothermic and some are endothermic, but, when Δ''H''{{sup|⊖}} is negative ''T''ΔS{{sup|⊖}} is the dominant factor, which determines that Δ''G''{{sup|⊖}} is positive. Last, the entropy contribution is always unfavourable ({{nowrap|Δ''S''{{sup|⊖}} < 0}}) in these reactions. Ions in aqueous solution tend to orient the surrounding water molecules, which orders the solution and decreases the entropy. The contribution of an ion to the entropy is the partial molar entropy which is often negative, especially for small or highly charged ions.<ref>{{cite book
| last1 = Atkins
| first1 = Peter William
| last2 = De Paula
| first2 = Julio
| title = Atkins' physical chemistry.
| url = https://archive.org/details/atkinsphysicalch00pwat
| url-access = registration
| date = 2006
| publisher = W H Freeman
| location = New York
| isbn = 978-0-7167-7433-4
| page = [https://archive.org/details/atkinsphysicalch00pwat/page/94 94]
}}</ref> The ionization of a neutral acid involves formation of two ions so that the entropy decreases ({{nowrap|Δ''S''{{sup|⊖}} < 0}}). On the second ionization of the same acid, there are now three ions and the anion has a charge, so the entropy again decreases.

Note that the ''standard'' free energy change for the reaction is for the changes ''from'' the reactants in their standard states ''to'' the products in their standard states. The free energy change ''at'' equilibrium is zero since the [[Chemistry:Chemical potential|chemical potential]]s of reactants and products are equal at equilibrium.

== Experimental determination ==
[[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 [[Chemistry:Titration|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 [[Chemistry:PH|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 [[Physics:Glass electrode|glass electrode]] and a [[Chemistry:PH meter|pH meter]]. The equilibrium constants are found by fitting calculated pH values to the observed values, using the method of [[Least squares|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 [[Chemistry:Titration curve|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 [[Chemistry:Equivalence point|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 [[Physics:Self-ionization of water|self-ionization of water]] becomes important.

It is very difficult to measure pH values of less than two in aqueous solution with a [[Physics:Glass electrode#Range of a pH glass electrode|glass electrode]], because the [[Physics:Nernst equation|Nernst equation]] breaks down at such low pH values. To determine p''K'' values of less than about 2 or more than about 11 [[Chemistry: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 [[Chemistry: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 [[Physics:Absorbance|absorbance]] or [[Biology:Fluorescence|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 [[Physics:Beer–Lambert law|Beer–Lambert law]] is assumed to apply.

[[Biology:Isothermal titration calorimetry|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 [[Chemistry:Heavy water|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 [[Physics:Chemical shift|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">{{cite encyclopedia
| last = Fraczkiewicz
| first = R
| title = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering
| name-list-style = vanc
| chapter = In Silico Prediction of Ionization
| encyclopedia = Reference Module in Chemistry, Molecular Sciences and Chemical Engineering [Online]
| editor-last = Reedijk
| editor-first = J
| volume = 5
| publisher = Elsevier
| location = Amsterdam, the Netherlands
| year = 2013
| doi = 10.1016/B978-0-12-409547-2.02610-X
| isbn = 9780124095472
| department = (secondary)
}}</ref> and the observed macroscopic equilibrium constant or macroconstant is a combination of [[Chemistry:Equilibrium constant#Micro-constants|microconstant]]s involving distinct species. When one reactant forms two products in parallel, the macroconstant is a sum of two microconstants, <math>K = K_X + K_Y.</math> This is true for example for the deprotonation of the [[Chemistry:Amino acid|amino acid]] [[Chemistry:Cysteine|cysteine]], which exists in solution as a neutral [[Physics:Zwitterion|zwitterion]] {{chem2|HS\sCH2\sCH(NH3+)\sCOO-}}. The two microconstants represent deprotonation either at sulphur or at nitrogen, and the macroconstant 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 [[Chemistry:Spermine|spermine]] has more than one site where protonation can occur. For example, monoprotonation 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 [[Chemistry: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 macroconstant <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 macroconstant 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 macroconstant for the combined reaction is the product of the microconstant for the two steps. For example, the abovementioned cysteine zwitterion can lose two protons, one from sulphur and one from nitrogen, and the overall macroconstant 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>

== Applications and significance ==
A knowledge of p''K''<sub>a</sub> values is important for the quantitative treatment of systems involving acid–base equilibria in solution. Many applications exist in [[Biology:Biochemistry|biochemistry]]; for example, the p''K''<sub>a</sub> values of proteins and [[Chemistry:Amino acid|amino acid]] side chains are of major importance for the activity of enzymes and the stability of proteins.<ref>{{cite journal
| last = Onufriev
| first = A.
| author2 = Case, D.A
| author3 = Ullmann G.M.
| year = 2001
| title = A Novel View of pH Titration in Biomolecules
| journal = Biochemistry
| volume = 40
| pages = 3413–3419
| doi = 10.1021/bi002740q
| pmid = 11297406
| issue = 12
}}</ref> [[Biology:Protein pKa calculations|Protein p''K''<sub>a</sub> values]] cannot always be measured directly, but may be calculated using theoretical methods. Buffer solutions are used extensively to provide solutions at or near the physiological pH for the study of biochemical reactions;<ref>{{cite journal
| last = Good
| first = N.E.
| author2 = Winget, G.D.
| author3 = Winter, W.
| author4 = Connolly, T.N.
| author5 = Izawa, S.
| author6 = Singh, R.M.M.
| title = Hydrogen Ion Buffers for Biological Research
| year = 1966
| journal = Biochemistry
| volume = 5
| issue = 2
| pages = 467–477
| doi = 10.1021/bi00866a011
| pmid = 5942950
}}</ref> the design of these solutions depends on a knowledge of the p''K''<sub>a</sub> values of their components. Important buffer solutions include [[Chemistry:MOPS|MOPS]], which provides a solution with pH&nbsp;7.2, and [[Chemistry:Tricine|tricine]], which is used in [[Biology:Gel electrophoresis|gel electrophoresis]].<ref>{{cite book
| title = Gel Electrophoresis: Proteins
| last = Dunn
| first = M.J.
| year = 1993
| publisher = Bios Scientific Publishers
| isbn = 1-872748-21-X
| url-access = registration
| url = https://archive.org/details/gelelectrophores0000dunn
}}</ref><ref>{{cite book
| title = Gel Electrophoresis: Nucleic Acids
| last = Martin
| first = R.
| year = 1996
| publisher = Bios Scientific Publishers
| isbn = 1-872748-28-7
}}</ref> Buffering is an essential part of acid base physiology including [[Chemistry:Acid–base homeostasis|acid–base homeostasis]],<ref>{{cite book
 |title = Acid–Base and Potassium Homeostasis
 |editor-last = Brenner
 |editor-first = B.M.
 |editor2 = Stein, J.H.
 |year = 1979
 |publisher = Churchill Livingstone
 |isbn = 0-443-08017-8
 |url-access = registration
 |url = https://archive.org/details/acidbasepotassiu0002unse
}}</ref> and is key to understanding disorders such as [[Medicine:Acid–base disorder|acid–base disorder]].<ref>{{cite book
 | title = Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems
 | last = Scorpio
 | first = R.
 | year = 2000
 | publisher = Kendall/Hunt Pub. Co.
 | isbn = 0-7872-7374-0
}}</ref><ref>{{cite book
 |title = Buffer Solutions: The Basics
 |last = Beynon
 |first = R.J.
 |author2 = Easterby, J.S.
 |year = 1996
 |publisher = Oxford University Press
 |location = Oxford
 |isbn = 0-19-963442-4
 |url-access = registration
 |url = https://archive.org/details/buffersolutions0000beyn
}}</ref><ref>{{cite book
| title = Buffers for pH and Metal Ion Control
| last = Perrin
| first = D.D.
| author2 = Dempsey, B.
| year = 1974
| publisher = Chapman & Hall
| location = London
| isbn = 0-412-11700-2
}}</ref> The [[Biology:Isoelectric point|isoelectric point]] of a given molecule is a function of its p''K'' values, so different molecules have different isoelectric points. This permits a technique called [[Biology:Isoelectric focusing|isoelectric focusing]],<ref>{{cite book
| editor-last = [[Biology:QPNC-PAGE|Garfin]]
| editor-first = D.
| editor2 = Ahuja, S.
| title = Handbook of Isoelectric Focusing and Proteomics
| publisher = Elsevier
| year = 2005
| volume = 7
| isbn = 0-12-088752-5
}}</ref> which is used for separation of proteins by [[Biology:Two-dimensional gel electrophoresis|2-D gel polyacrylamide gel electrophoresis]].

Buffer solutions also play a key role in [[Chemistry:Analytical chemistry|analytical chemistry]]. They are used whenever there is a need to fix the pH of a solution at a particular value. Compared with an aqueous solution, the pH of a buffer solution is relatively insensitive to the addition of a small amount of strong acid or strong base. The buffer capacity<ref>{{cite book
 | last = Hulanicki
 | first = A.
 | title = Reactions of Acids and Bases in Analytical Chemistry
 | publisher = Horwood
 | year = 1987
 | isbn = 0-85312-330-6
 | others = Masson, M.R. (translation editor)
}}</ref> of a simple buffer solution is largest when pH&nbsp;=&nbsp;p''K''<sub>a</sub>. In [[Acid–base extraction|acid–base extraction]], the efficiency of extraction of a compound into an organic phase, such as an [[Chemistry:Ether|ether]], can be optimised by adjusting the pH of the aqueous phase using an appropriate buffer. At the optimum pH, the concentration of the electrically neutral species is maximised; such a species is more soluble in organic solvents having a low dielectric constant than it is in water. This technique is used for the purification of weak acids and bases.<ref>{{cite journal
 | last = Eyal
 | first = A.M
 | year = 1997
 | title = Acid Extraction by Acid–Base-Coupled Extractants
 | journal = Ion Exchange and Solvent Extraction: A Series of Advances
 | volume = 13
 | pages = 31–94
}}</ref>

A [[Chemistry:PH indicator|pH indicator]] is a weak acid or weak base that changes colour in the transition pH range, which is approximately p''K''<sub>a</sub>&nbsp;±&nbsp;1. The design of a [[Chemistry:Universal indicator|universal indicator]] requires a mixture of indicators whose adjacent p''K''<sub>a</sub> values differ by about two, so that their transition pH ranges just overlap.

In [[Biology:Pharmacology|pharmacology]], ionization of a compound alters its physical behaviour and macro properties such as solubility and [[Physics:Partition coefficient|lipophilicity]], log&nbsp;''p''). For example, ionization of any compound will increase the solubility in water, but decrease the lipophilicity. This is exploited in [[Medicine:Drug development|drug development]] to increase the concentration of a compound in the blood by adjusting the p''K''<sub>a</sub> of an ionizable group.<ref name=avdeef>{{cite book
| title = Absorption and Drug Development: Solubility, Permeability, and Charge State
| last = Avdeef
| first = A.
| year = 2003
| publisher = Wiley
| location = New York
| isbn = 0-471-42365-3
}}</ref>

Knowledge of p''K''<sub>a</sub> values is important for the understanding of [[Chemistry:Complex|coordination complexes]], which are formed by the interaction of a metal ion, M<sup>m+</sup>, acting as a [[Chemistry:Lewis acid|Lewis acid]], with a [[Chemistry:Ligand|ligand]], L, acting as a Lewis base. However, the ligand may also undergo protonation reactions, so the formation of a complex in aqueous solution could be represented symbolically by the reaction
:<math chem>[\ce{M(H2O)_\mathit{n}}]^{m+} + \ce{LH <=> } \ [\ce{M(H2O)}_{n - 1} \ce{L}]^{(m - 1)+} + \ce{H3O+}</math>

To determine the equilibrium constant for this reaction, in which the ligand loses a proton, the p''K''<sub>a</sub> of the protonated ligand must be known. In practice, the ligand may be polyprotic; for example [[Chemistry:EDTA|EDTA]]<sup>4−</sup> can accept four protons; in that case, all p''K''<sub>a</sub> values must be known. In addition, the metal ion is subject to [[Chemistry:Hydrolysis#Hydrolysis of metal aqua ions|hydrolysis]], that is, it behaves as a weak acid, so the p''K'' values for the hydrolysis reactions must also be known.<ref>{{cite book
| title = Chemistry of Complex Equilibria
| last = Beck
| first = M.T.
| author2 = Nagypál, I.
| year = 1990
| publisher = Horwood
| isbn = 0-85312-143-5
}}</ref>

Assessing the [[Risk assessment|hazard]] associated with an acid or base may require a knowledge of p''K''<sub>a</sub> values.<ref>{{cite book
| title = Risk Assessment of Chemicals: An Introduction
| last = van Leeuwen
| first = C.J.
| author2 = Hermens, L. M.
| year = 1995
| publisher = Springer
| isbn = 0-7923-3740-9
| pages = 254–255
}}</ref> For example, [[Chemistry:Hydrogen cyanide|hydrogen cyanide]] is a very toxic gas, because the [[Chemistry:Cyanide#Toxicity|cyanide ion]] inhibits the iron-containing enzyme [[Biology:Cytochrome c oxidase|cytochrome c oxidase]]. Hydrogen cyanide is a weak acid in aqueous solution with a p''K''<sub>a</sub> of about 9. In strongly alkaline solutions, above pH&nbsp;11, say, it follows that sodium cyanide is "fully dissociated" so the hazard due to the hydrogen cyanide gas is much reduced. An acidic solution, on the other hand, is very hazardous because all the cyanide is in its acid form. Ingestion of cyanide by mouth is potentially fatal, independently of pH, because of the reaction with cytochrome c oxidase.

In [[Environmental science|environmental science]] acid–base equilibria are important for lakes<ref>{{cite book
| last = Skoog
| first = D.A
| author2 = West, D.M.
| author3 = Holler, J.F.
| author4 = Crouch, S.R.
| title = Fundamentals of Analytical Chemistry
| publisher = Thomson Brooks/Cole
| year = 2004
| edition = 8th
| isbn = 0-03-035523-0
}} Chapter 9-6: Acid Rain and the Buffer Capacity of Lakes</ref> and rivers;<ref name=stumm_morgan>{{cite book
 |title = Water Chemistry
 |last = Stumm
 |first = W.
 |author2 = Morgan, J.J.
 |year = 1996
 |publisher = Wiley
 |location = New York
 |isbn = 0-471-05196-9
 |url = https://archive.org/details/waterchemistry00snoerich
}}</ref><ref name=aquatic>{{cite book
| title = Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters
| last = Snoeyink
| first = V.L.
| author2 = Jenkins, D.
| year = 1980
| publisher = Wiley
| location = New York
| isbn = 0-471-51185-4
}}</ref> for example, humic acids are important components of natural waters. Another example occurs in [[Chemistry:Chemical oceanography|chemical oceanography]]:<ref>{{cite book
| title = Chemical Oceanography
| last = Millero
| first = F.J.
| edition = 3rd
| year = 2006
| publisher = Taylor and Francis
| location = London
| isbn = 0-8493-2280-4
}}</ref> in order to quantify the solubility of iron(III) in seawater at various [[Earth:Salinity|salinities]], the p''K''<sub>a</sub> values for the formation of the iron(III) hydrolysis products {{chem2|Fe(OH)(2+)}}, {{chem2|Fe(OH)2+}} and {{chem2|Fe(OH)3}} were determined, along with the solubility product of iron hydroxide.<ref>{{cite journal
| last = Millero
| first = F.J.
| author2 = Liu, X.
| year = 2002
| title = The Solubility of Iron in Seawater
| journal = Marine Chemistry
| volume = 77
| issue = 1
| pages = 43–54
| doi = 10.1016/S0304-4203(01)00074-3
| bibcode = 2002MarCh..77...43L
}}</ref>

== Values for common substances ==
There are multiple techniques to determine the p''K''<sub>a</sub> of a chemical, leading to some discrepancies between different sources. Well measured values are typically within 0.1 units of each other. Data presented here were taken at 25&nbsp;°C in water.<ref name=SA /><ref name=Lange>{{cite book
| title = Lange's Handbook of Chemistry
| last = Speight
| first = J.G.
| year = 2005
| publisher = McGraw–Hill
| edition = 18th
| isbn = 0-07-143220-5
| url-access = registration
| url = https://archive.org/details/langeshandbookof70edlang
}} Chapter 8</ref> More values can be found in the Thermodynamics section, above. A table of p''K''<sub>a</sub> of carbon acids, measured in DMSO, can be found on the page on [[Chemistry:Carbanion|carbanion]]s.

{| class="wikitable sortable"
|-
! class="unsortable"| Chemical
! class="unsortable"| Equilibrium
! p''K''<sub>a</sub>
|-
| rowspan=2 | BH = [[Chemistry:Adenine|Adenine]]
| BH {{eqm}} B<sup>−</sup> + H<sup>+</sup>
| 4.17
|-
| {{chem|BH|2|+}} {{eqm}} BH + H<sup>+</sup>
| 9.65
|-
| rowspan=3 | H<sub>3</sub>A = [[Chemistry:Arsenic acid|Arsenic acid]]
| H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
| 2.22
|-
| H<sub>2</sub>A<sup>−</sup> {{eqm}} HA<sup>2−</sup> + H<sup>+</sup>
| 6.98
|-
| HA<sup>2−</sup> {{eqm}} A<sup>3−</sup> + H<sup>+</sup>
| 11.53
|-
| HA = [[Chemistry:Benzoic acid|Benzoic acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 4.204
|-
| HA = [[Chemistry:Butyric acid|Butyric acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 4.82
|-
| rowspan=2 | H<sub>2</sub>A = [[Chemistry:Chromic acid|Chromic acid]]
| H<sub>2</sub>A {{eqm}} HA<sup>−</sup> + H<sup>+</sup>
| 0.98
|-
| HA<sup>−</sup> {{eqm}} A<sup>2−</sup> + H<sup>+</sup>
| 6.5
|-
| B = [[Chemistry:Codeine|Codeine]]
| BH<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 8.17
|-
| HA = [[Chemistry:Cresol|Cresol]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 10.29
|-
| HA = [[Chemistry:Formic acid|Formic acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 3.751
|-
| HA = [[Chemistry:Hydrofluoric acid|Hydrofluoric acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 3.17
|-
| HA = [[Chemistry:Hydrocyanic acid|Hydrocyanic acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 9.21
|-
| HA = [[Chemistry:Hydrogen selenide|Hydrogen selenide]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 3.89
|-
| HA = [[Chemistry:Hydrogen peroxide|Hydrogen peroxide]] (90%)
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 11.7
|-
| HA = [[Chemistry:Lactic acid|Lactic acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 3.86
|-
| HA = [[Chemistry:Propionic acid|Propionic acid]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 4.87
|-
| HA = [[Chemistry:Phenol|Phenol]]
| HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 9.99
|-
| rowspan=2 | H<sub>2</sub>A = [[Biology:Vitamin C|<small>L</small>-(+)-Ascorbic Acid]]
| H<sub>2</sub>A {{eqm}} HA<sup>−</sup> + H<sup>+</sup>
| 4.17
|-
| HA<sup>−</sup> {{eqm}} A<sup>2−</sup> + H<sup>+</sup>
| 11.57
|}

== See also ==
* Acidosis
* [[Chemistry:Acids in wine|Acids in wine]]: [[Chemistry:Tartaric acid|tartaric]], [[Chemistry:Malic acid|malic]] and [[Chemistry:Citric acid|citric]] are the principal acids in wine.
* Alkalosis
* Arterial blood gas
* [[Chemistry:Chemical equilibrium|Chemical equilibrium]]
* [[Physics:Conductivity (electrolytic)|Conductivity (electrolytic)]]
* [[Chemistry:Grotthuss mechanism|Grotthuss mechanism]]: how protons are transferred between hydronium ions and water molecules, accounting for the exceptionally high ionic mobility of the proton (animation).
* [[Chemistry:Hammett acidity function|Hammett acidity function]]: a measure of acidity that is used for very concentrated solutions of strong acids, including superacids.
* [[Chemistry:Ion transport number|Ion transport number]]
* [[Biology:Ocean acidification|Ocean acidification]]: dissolution of atmospheric carbon dioxide affects [[Chemistry:PH#Seawater|seawater pH]]. The reaction depends on [[Chemistry:Total inorganic carbon|total inorganic carbon]] and on solubility equilibria with solid carbonates such as [[Earth:Limestone|limestone]] and [[Chemistry:Dolomite (mineral)|dolomite]].
* [[Physics:Law of dilution|Law of dilution]]
* [[Chemistry:PCO2|pCO2]]
* [[Chemistry:PH|pH]]
* [[Chemistry:Predominance diagram|Predominance diagram]]: relates to equilibria involving [[Chemistry:Oxyanion|polyoxyanions]]. p''K''<sub>a</sub> values are needed to construct these diagrams.
* [[Chemistry:Proton affinity|Proton affinity]]: a measure of basicity in the gas phase.
* [[Chemistry:Stability constants of complexes|Stability constants of complexes]]: formation of a complex can often be seen as a competition between proton and metal ion for a ligand, which is the product of dissociation of an acid.

== Notes ==
{{notelist}}
{{reflist|group=note}}

== References ==
{{Reflist|30em}}

== Further reading ==
* {{cite book
| last = Albert
| first = A.
| author2 = Serjeant, E.P.
| title = The Determination of Ionization Constants: A Laboratory Manual
| publisher = Chapman & Hall
| year = 1971
| isbn = 0-412-10300-1
| url = https://archive.org/details/determinationofi0000albe
}} (Previous edition published as {{cite book
| title = Ionization constants of acids and bases
| location = London (UK)
| publisher = Methuen
| year = 1962
}})
* {{cite book
| title = Chemical Principles: The Quest for Insight
| last = Atkins
| first = P.W.
| author2 = Jones, L.
| year = 2008
| edition = 4th
| publisher = W.H. Freeman
| isbn = 978-1-4292-0965-6
| url-access = registration
| url = https://archive.org/details/chemicalprincipl0004unse
}}
* {{Housecroft3rd}} (Non-aqueous solvents)
* {{cite book
| last = Hulanicki
| first = A.
| title = Reactions of Acids and Bases in Analytical Chemistry
| publisher = Horwood
| year = 1987
| isbn = 0-85312-330-6
}} (translation editor: Mary R. Masson)
* {{cite book
| last = Perrin
| first = D.D.
| author2 = Dempsey, B.
| author3 = Serjeant, E.P.
| title = pKa Prediction for Organic Acids and Bases
| publisher = Chapman & Hall
| year = 1981
| isbn = 0-412-22190-X
}}
* {{cite book
| last = Reichardt
| first = C.
| title = Solvents and Solvent Effects in Organic Chemistry
| publisher = Wiley-VCH
| year = 2003
| edition = 3rd
| isbn = 3-527-30618-8
}} Chapter 4: Solvent Effects on the Position of Homogeneous Chemical Equilibria.
* {{cite book
| last = Skoog
| first = D.A.
| author2 = West, D.M.
| author3 = Holler, J.F.
| author4 = Crouch, S.R.
| title = Fundamentals of Analytical Chemistry
| publisher = Thomson Brooks/Cole
| year = 2004
| edition = 8th
| isbn = 0-03-035523-0
}}

== External links ==
* [http://tera.chem.ut.ee/~ivo/HA_UT/ Acidity–Basicity Data in Nonaqueous Solvents] Extensive bibliography of p''K''<sub>a</sub> values in [[Chemistry:Dimethyl sulfoxide|DMSO]], [[Chemistry:Acetonitrile|acetonitrile]], THF, [[Chemistry:Heptane|heptane]], 1,2-dichloroethane, and in the gas phase
* [http://www2.iq.usp.br/docente/gutz/Curtipot_.html Curtipot] All-in-one freeware for pH and acid–base equilibrium calculations and for simulation and analysis of [[Chemistry:Potentiometric titration|potentiometric titration]] curves with spreadsheets
* [https://web.archive.org/web/20070312045609/http://sparc.chem.uga.edu/ SPARC Physical/Chemical property calculator] Includes a database with aqueous, non-aqueous, and gaseous phase p''K''<sub>a</sub> values than can be searched using SMILES or CAS registry numbers
* [https://web.archive.org/web/20070205181504/http://jesuitnola.org/upload/clark/Refs/aqueous.htm Aqueous-Equilibrium Constants] p''K''<sub>a</sub> values for various acid and bases. Includes a table of some solubility products
* [http://www.raell.demon.co.uk/chem/logp/logppka.htm Free guide to p''K''<sub>a</sub> and log ''p'' interpretation and measurement] {{Webarchive|url=https://web.archive.org/web/20160810120341/http://www.raell.demon.co.uk/chem/logp/logppka.htm |date=2016-08-10 }} Explanations of the relevance of these properties to [[Biology:Pharmacology|pharmacology]]
* [https://web.archive.org/web/20090331121853/http://chemaxon.com/marvin/sketch/index.jsp Free online prediction tool (Marvin)] p''K''<sub>a</sub>, log ''p'', log ''d'' etc. From [[Company:Chemaxon|ChemAxon]]
* Chemicalize.org:List of predicted structure based properties
* p''K''<sub>a</sub> Chart [http://ccc.chem.pitt.edu/wipf/MechOMs/evans_pKa_table.pdf] by David A. Evans

{{Chemical equilibria}}
{{Chemical solutions}}

[[Category:Equilibrium chemistry]]
[[Category:Acids]]
[[Category:Bases (chemistry)]]
[[Category:Analytical chemistry]]
[[Category:Physical chemistry]]

{{Sourceattribution|Acid dissociation constant}}