Acid dissociation constant

Acetic acid, a weak acid, donates a proton (hydrogen ion, high-lighted in green) to water in an equilibrium reaction to give theacetate ion and the hydronium ion. Red: oxygen, black: carbon,white: hydrogen.

An acid dissociation constant, Kₐ, (also known asacidity constant, or acid-ionization constant) is aquantitativemeasure of the strength of an acid in solution.It is the equilibrium constant for a chemical reactionknown as dissociation in the context of acid-base reac-tions. In aqueous solution, the equilibrium of acid disso-ciation can be written symbolically as:

HA+ H2O ⇌ A− + H3O+

where HA is a generic acid that dissociates into A−,known as the conjugate base of the acid and a hydrogenion which combines with a water molecule to make anhydronium ion. In the example shown in the figure, HArepresents acetic acid, and A− represents the acetate ion,the conjugate base.The chemical species HA, A− and H3O+ are said to be inequilibriumwhen their concentrations do not change withthe passing of time. The dissociation constant is usuallywritten as a quotient of the equilibrium concentrations (inmol/L), denoted by [HA], [A−] and [H3O+]

Ka =[A−][H3O+]

[HA][H2O]In all but the most concentrated aqueous solutions of anacid the concentration of water can be taken as constantand can be ignored. The definition can then be writtenmore simply

HA ⇌ A− + H+ : Ka =[A−][H+]

[HA]This is the definition in common usage. For many prac-tical purposes it is more convenient to discuss the loga-rithmic constant, pKₐ

pKa = − log10 Ka

The larger the value of pKₐ, the smaller the extent of dis-sociation at any given pH (see Henderson–Hasselbalchequation)—that is, the weaker the acid. A weak acid hasa pKₐ value in the approximate range −2 to 12 in water.Acids with a pKₐ value of less than about −2 are said tobe strong acids; the dissociation of a strong acid is ef-fectively complete such that concentration of the undis-sociated acid is too small to be measured. pKₐ valuesfor strong acids can, however, be estimated by theoreti-cal means.pKₐ, is sometimes also (but incorrectly) referred to as anacid dissociation constant.The definition can be extended to non-aqueous solvents,such as acetonitrile and dimethylsulfoxide. Denoting asolvent molecule by S

HA+ S ⇌ A− + SH+;Ka =[A−][SH+]

[HA][S]

When the concentration of solventmolecules can be takento be constant,Ka =

[A−][H+][HA] , as before.

1 Theoretical background

The acid dissociation constant for an acid is a direct con-sequence of the underlying thermodynamics of the dis-sociation reaction; the pKₐ value is directly proportionalto the standard Gibbs energy change for the reaction.The value of the pKₐ changes with temperature and canbe understood qualitatively based on Le Chatelier’s prin-ciple: when the reaction is endothermic, the pKₐ de-creases with increasing temperature; the opposite is truefor exothermic reactions.The value of pKₐ also depends on molecular structure inmany ways. For example, Pauling proposed two rules:one for successive pKₐ of polyprotic acids (see Polyproticacids below), and one to estimate the pKₐ of oxyacidsbased on the number of =O and −OH groups (see Factorsthat affect pKₐ values below). Other structural factorsthat influence the magnitude of the acid dissociation con-stant include inductive effects, mesomeric effects, andhydrogen bonding.The quantitative behaviour of acids and bases in solutioncan be understood only if their pKₐ values are known. Inparticular, the pH of a solution can be predicted whenthe analytical concentration and pKₐ values of all acids

1

2 3 EQUILIBRIUM CONSTANT

and bases are known; conversely, it is possible to calcu-late the equilibrium concentration of the acids and basesin solution when the pH is known. These calculations findapplication in many different areas of chemistry, biology,medicine, and geology. For example, many compoundsused for medication are weak acids or bases, and a knowl-edge of the pKₐ values, together with the water–octanolpartition coefficient, can be used for estimating the extentto which the compound enters the blood stream. Aciddissociation constants are also essential in aquatic chem-istry and chemical oceanography, where the acidity ofwater plays a fundamental role. In living organisms, acid-base homeostasis and enzyme kinetics are dependent onthe pKₐ values of the many acids and bases present inthe cell and in the body. In chemistry, a knowledge ofpKₐ values is necessary for the preparation of buffer so-lutions and is also a prerequisite for a quantitative under-standing of the interaction between acids or bases andmetal ions to form complexes. Experimentally, pKₐ val-ues can be determined by potentiometric (pH) titration,but for values of pKₐ less than about 2 or more than about11, spectrophotometric or NMR measurements may berequired due to practical difficulties with pH measure-ments.

2 Definitions

According to Arrhenius's original definition, an acid is asubstance that dissociates in aqueous solution, releasingthe hydrogen ion H+ (a proton):[1]

HA A− + H+.

The equilibrium constant for this dissociation reaction isknown as a dissociation constant. The liberated protoncombines with a water molecule to give a hydronium (oroxonium) ion H3O+ (naked protons do not exist in solu-tion), and so Arrhenius later proposed that the dissocia-tion should be written as an acid–base reaction:

HA + H2O A− + H3O+.

Acetic acid, a weak acid, donates a proton (hydrogen ion, high-lighted in green) to water in an equilibrium reaction to give theacetate ion and the hydronium ion. Red: oxygen, black: carbon,white: hydrogen.

Brønsted and Lowry generalised this further to a protonexchange reaction:[2][3][4]

acid + base conjugate base + conjugate acid.

The acid loses a proton, leaving a conjugate base; the pro-ton is transferred to the base, creating a conjugate acid.For aqueous solutions of an acid HA, the base is water;the conjugate base is A− and the conjugate acid is the hy-dronium ion. The Brønsted–Lowry definition applies toother solvents, such as dimethyl sulfoxide: the solvent Sacts as a base, accepting a proton and forming the conju-gate acid SH+.

HA + S A− + SH+.

In solution chemistry, it is common to use H+ as an ab-breviation for the solvated hydrogen ion, regardless of thesolvent. In aqueous solution H+ denotes a solvated hydro-nium ion rather than a proton.[5][6]

The designation of an acid or base as “conjugate” dependson the context. The conjugate acid BH+ of a base B dis-sociates according to

BH+ + OH− B + H2O

which is the reverse of the equilibrium

H2O (acid) + B (base) OH− (conjugate base) +BH+ (conjugate acid).

The hydroxide ion OH−, a well known base, is here act-ing as the conjugate base of the acid water. Acids andbases are thus regarded simply as donors and acceptorsof protons respectively.A broader definition of acid dissociation includeshydrolysis, in which protons are produced by the splittingof water molecules. For example, boric acid (B(OH)3)produces H3O+ as if it were a proton donor,[7] but it hasbeen confirmed by Raman spectroscopy that this is dueto the hydrolysis equilibrium:[8]

B(OH)3 + 2 H2O B(OH)4− + H3O+.

Similarly, metal ion hydrolysis causes ions such as[Al(H2O)6]3+ to behave as weak acids:[9]

[Al(H2O)6]3+ +H2O [Al(H2O)5(OH)]2+ +H3O+.

According to Lewis's original definition, an acid is a sub-stance that accepts an electron pair to form a coordinatecovalent bond :[10]

3 Equilibrium constant

An acid dissociation constant is a particular example ofan equilibrium constant. For the specific equilibrium be-tween a monoprotic acid, HA and its conjugate base A−,in water,

3.1 Monoprotic acids 3

HA + H2O A− + H3O+

the thermodynamic equilibrium constant, K can bedefined by[11]

K⊖ ={A−}{H3O+}{HA}{H2O}

where {A} is the activity of the chemical species A etc.

K is dimensionless since activity is dimensionless. Ac-tivities of the products of dissociation are placed in thenumerator, activities of the reactants are placed in the de-nominator. See activity coefficient for a derivation of thisexpression.

Variation of pKa of acetic acid with ionic strength

Since activity is the product of concentration and activitycoefficient (γ) the definition could also be written as

K⊖ =[A−][H3O+]

[HA][H2O]×

γA− γH3O+

γHA γH2O=

[A−][H3O+]

[HA][H2O]×

where [HA] represents the concentration of HA and Γ isa quotient of activity coefficients.To avoid the complications involved in using activities,dissociation constants are determined, where possible, ina medium of high ionic strength, that is, under condi-tions in which Γ can be assumed to be always constant.[11]For example, the medium might be a solution of 0.1 Msodium nitrate or 3 M potassium perchlorate (1 M = 1mol·dm−3, a unit of molar concentration). Furthermore,in all but the most concentrated solutions it can be as-sumed that the concentration of water, [H2O], is constant,approximately 55 mol·dm−3. On dividing K by theconstant terms and writing [H+] for the concentration ofthe hydronium ion the expression

Ka =[A−][H+]

[HA]

is obtained. This is the definition in common use.[12] pKₐis defined as −log10 Kₐ. Note, however, that all pub-lished dissociation constant values refer to the specificionic medium used in their determination and that dif-ferent values are obtained with different conditions, asshown for acetic acid in the illustration above. When pub-lished constants refer to an ionic strength other than theone required for a particular application, they may be ad-justed by means of specific ion theory (SIT) and othertheories.[13]

Although Kₐ appears to have the dimension of concentra-tion, the exact definition uses chemical activities, whichare dimensionless. Therefore, Kₐ, as defined properly, isalso dimensionless. Nevertheless it is not unusual, par-ticularly in texts relating to biochemical equilibria, to seea value quoted with a dimension as, for example, "Kₐ =300 M”.

3.1 Monoprotic acids

See also: Acid § Monoprotic acidsAfter rearranging the expression defining Kₐ, and putting

−2 −1 0 210

50

100

% fo

rmat

ion

pH−pKa

AH A−

Variation of the % formation of a monoprotic acid, AH, and itsconjugate base, A−, with the difference between the pH and thepKa of the acid

pH = −log10[H+], one obtains[14]

pH = pKa + log [A−]

[HA]

This is a form of the Henderson–Hasselbalch equation,from which the following conclusions can be drawn.

4 3 EQUILIBRIUM CONSTANT

• At half-neutralization [A−]/[HA] = 1; since log(1)=0, the pH at half-neutralization is numericallyequal to pKₐ. Conversely, when pH = pKₐ, the con-centration of HA is equal to the concentration of A−.

• The buffer region extends over the approximaterange pKₐ ± 2, though buffering is weak outside therange pKₐ ± 1. At pKₐ ± 1, [A−]/[HA] = 10 or 1/10.

• If the pH is known, the ratio may be calculated. Thisratio is independent of the analytical concentrationof the acid.

In water, measurable pKₐ values range from about −2 fora strong acid to about 12 for a very weak acid (or strongbase). All acids with a pKₐ value of less than −2 are morethan 99% dissociated at pH 0 (1 M acid). This is knownas solvent leveling since all such acids are brought to thesame level of being strong acids, regardless of their pKₐvalues. Likewise, all bases with a pKₐ value larger thanthe upper limit are more than 99% protonated at all at-tainable pH values and are classified as strong bases.[3]

An example of a strong acid is hydrochloric acid, HCl,which has a pKₐ value, estimated from thermodynamicquantities, of −9.3 in water.[15] The concentration ofundissociated acid in a 1 mol·dm−3 solution will be lessthan 0.01% of the concentrations of the products of dis-sociation. Hydrochloric acid is said to be “fully dissoci-ated” in aqueous solution because the amount of undisso-ciated acid is imperceptible. When the pKₐ and analyticalconcentration of the acid are known, the extent of disso-ciation and pH of a solution of a monoprotic acid can beeasily calculated using an ICE table.A buffer solution of a desired pH can be prepared as amixture of a weak acid and its conjugate base. In practicethe mixture can be created by dissolving the acid in water,and adding the requisite amount of strong acid or base.The pKₐ of the acid must be less than two units differentfrom the target pH.

3.2 Polyprotic acids

Polyprotic acids are acids that can losemore than one pro-ton. The constant for dissociation of the first proton maybe denoted as Kₐ₁ and the constants for dissociation ofsuccessive protons as Kₐ₂, etc. Phosphoric acid, H3PO4,is an example of a polyprotic acid as it can lose three pro-tons.

When the difference between successive pK values isabout four or more, as in this example, each species maybe considered as an acid in its own right;[17] In fact saltsof H2PO4

− may be crystallised from solution by adjust-ment of pH to about 5.5 and salts of HPO4

2− may becrystallised from solution by adjustment of pH to about

Phosphoric acid speciation

10. The species distribution diagram shows that the con-centrations of the two ions are maximum at pH 5.5 and10.

% species formation calculated with the program HySS for a 10millimolar solution of citric acid. pKa1=3.13, pKa2 = 4.76,pKa3=6.40.

When the difference between successive pK values is lessthan about four there is overlap between the pH range ofexistence of the species in equilibrium. The smaller thedifference, the more the overlap. The case of citric acidis shown at the right; solutions of citric acid are bufferedover the whole range of pH 2.5 to 7.5.According to Pauling’s first rule, successive pK values ofa given acid increase (pKₐ₂ > pKₐ₁).[18] For oxyacids withmore than one ionizable hydrogen on the same atom, thepKₐ values often increase by about 5 units for each pro-

3.3 Water self-ionization 5

ton removed,[19][20] as in the example of phosphoric acidabove.In the case of a diprotic acid, H2A, the two equilibria are

H2A HA− + H+

HA− A2− + H+

it can be seen that the second proton is removed froma negatively charged species. Since the proton carriesa positive charge extra work is needed to remove it;that is the cause of the trend noted above. Phosphoricacid values (above) illustrate this rule, as do the valuesfor vanadic acid, H3VO4. When an exception to therule is found it indicates that a major change in struc-ture is occurring. In the case of VO2

+ (aq), the vana-dium is octahedral, 6-coordinate, whereas vanadic acid istetrahedral, 4-coordinate. This is the basis for an expla-nation of why pKₐ₁ > pKₐ₂ for vanadium(V) oxoacids.

3.2.1 Isoelectric point

Main article: isoelectric point

For substances in solution the isoelectric point (pI) is de-fined as the pH at which the sum, weighted by chargevalue, of concentrations of positively charged species isequal to the weighted sum of concentrations of negativelycharged species. In the case that there is one species ofeach type, the isoelectric point can be obtained directlyfrom the pK values. Take the example of glycine, definedas AH. There are two dissociation equilibria to consider.

AH2+ AH + H+; [AH][H+] = K1[AH2

+]AH A− + H+; [A−][H+] = K2[AH]

Substitute the expression for [AH] into the first equation

[A−][H+]2 = K1K2[AH2+]

At the isoelectric point the concentration of the positivelycharged species, AH2

+, is equal to the concentration ofthe negatively charged species, A−, so

[H+]2 = K1K2

Therefore, taking cologarithms, the pH is given by

pI =pK1 + pK2

2

pI values for amino acids are listed at Proteinogenicamino acid#Chemical properties. When more than twocharged species are in equilibrium with each other a fullspeciation calculation may be needed.

3.3 Water self-ionization

Main article: Self-ionization of water

Water possesses both acidic and basic properties. It isamphiprotic. The equilibrium constant for the equilib-rium

2 H2O OH− + H3O+

is given by

Ka =[H3O+][OH−]

[H2O]

When, as is usually the case, the concentration of watercan be assumed to be constant, this expression may bereplaced by

Kw = [H3O+][OH−]

The self-ionization constant of water, K , is thus just aspecial case of an acid dissociation constant.These data can be fitted to a parabola with

pK = 14.94 - 0.04209 T + 0.0001718 T2

From this equation, pK = 14 at 24.87 °C. At that tem-perature both hydrogen and hydroxide ions have a con-centration of 10−7 mol dm−3.

3.4 Amphoteric substances

An amphoteric substance is one that can act as an acidor as a base, depending on pH. Water (above) is ampho-teric. Another example of an amphoteric molecule is thebicarbonate ion HCO3

− that is the conjugate base of thecarbonic acid molecule H2CO3 in the equilibrium

H2CO3 + H2O HCO3− + H3O+

but also the conjugate acid of the carbonate ion CO32− in

(the reverse of) the equilibrium

HCO3− + OH− CO3

2− + H2O.

Carbonic acid equilibria are important for acid-basehomeostasis in the human body.An amino acid is also amphoteric with the added com-plication that the neutral molecule is subject to an inter-nal acid-base equilibrium in which the basic amino groupattracts and binds the proton from the acidic carboxylgroup, forming a zwitterion.

6 4 ACIDITY IN NONAQUEOUS SOLUTIONS

NH2CHRCO2H NH3+CHRCO2

−

At pH less than about 5 both the carboxylate group andthe amino group are protonated. As pH increases the aciddissociates according to

NH3+CHRCO2H NH3

+CHRCO2− + H+

At high pH a second dissociation may take place.

NH3+CHRCO2

− NH2CHRCO2− + H+

Thus the zwitter ion, NH3+CHRCO2

−, is amphoteric be-cause it may either be protonated or deprotonated.

3.5 Bases and basicity

Historically, the equilibrium constant K for a base hasbeen defined as the association constant for protonationof the base, B, to form the conjugate acid, HB+.

B + H2O HB+ + OH−

Using similar reasoning to that used before

Kb =[HB+][OH−]

[B]

K is related to Kₐ for the conjugate acid. In water,the concentration of the hydroxide ion, [OH−], is relatedto the concentration of the hydrogen ion by K = [H+][OH−], therefore

[OH−] =Kw[H+]

Substitution of the expression for [OH−] into the expres-sion for K gives

Kb =[HB+]Kw[B][H+]

=KwKa

When Kₐ, K and K are determined under the same con-ditions of temperature and ionic strength, it follows, tak-ing cologarithms, that pK or “basicity"= pK − pKₐ. Inaqueous solutions at 25 °C, pK is 13.9965,[22] so

pKb ≈ 14− pKa

with sufficient accuracy for most practical purposes. Ineffect there is no need to define pK separately from pKₐ,but it is done here as often only pK values can be foundin the older literature.

3.6 Temperature dependence

All equilibrium constants vary with temperature accord-ing to the van 't Hoff equation[23]

d lnKdT =

∆H⊖

RT 2

R is the gas constant and T is the absolute temperature. Thus, for exothermic reactions, (the standard enthalpy

change, ΔH , is negative) K decreases with tempera-

ture, but for endothermic reactions (ΔH is positive) Kincreases with temperature.

4 Acidity in nonaqueous solutions

A solvent will be more likely to promote ioniza-tion of a dissolved acidic molecule in the followingcircumstances:[24]

1. It is a protic solvent, capable of forming hydrogenbonds.

2. It has a high donor number, making it a strong Lewisbase.

3. It has a high dielectric constant (relative permittiv-ity), making it a good solvent for ionic species.

pKₐ values of organic compounds are often obtained us-ing the aprotic solvents dimethyl sulfoxide (DMSO)[24]and acetonitrile (ACN).[25]

DMSO is widely used as an alternative to water becauseit has a lower dielectric constant than water, and is lesspolar and so dissolves non-polar, hydrophobic substancesmore easily. It has a measurable pKₐ range of about 1to 30. Acetonitrile is less basic than DMSO, and, so,in general, acids are weaker and bases are stronger inthis solvent. Some pKₐ values at 25 °C for acetonitrile(ACN)[26][27][28] and dimethyl sulfoxide (DMSO)[29] areshown in the following tables. Values for water are in-cluded for comparison.Ionization of acids is less in an acidic solvent than in wa-ter. For example, hydrogen chloride is a weak acid whendissolved in acetic acid. This is because acetic acid is amuch weaker base than water.

HCl + CH3CO2H Cl− + CH3C(OH)2+

acid + base conjugate base + conjugate acid

Compare this reaction with what happens when aceticacid is dissolved in the more acidic solvent pure sulfuricacid[30]

7

H2SO4 + CH3CO2H HSO4− + CH3C(OH)2+

The unlikely geminal diol species CH3C(OH)2+ is sta-ble in these environments. For aqueous solutions the pHscale is the most convenient acidity function.[31] Otheracidity functions have been proposed for non-aqueousmedia, the most notable being the Hammett acidity func-tion, H0, for superacid media and its modified version H₋for superbasic media.[32]

Dimerization of a carboxylic acid

In aprotic solvents, oligomers, such as the well-knownacetic acid dimer, may be formed by hydrogen bonding.An acid may also form hydrogen bonds to its conjugatebase. This process, known as homoconjugation, has theeffect of enhancing the acidity of acids, lowering theireffective pKₐ values, by stabilizing the conjugate base.Homoconjugation enhances the proton-donating powerof toluenesulfonic acid in acetonitrile solution by a factorof nearly 800.[33] In aqueous solutions, homoconjugationdoes not occur, because water forms stronger hydrogenbonds to the conjugate base than does the acid.

4.1 Mixed solvents

pKa of acetic acid in dioxane/water mixtures. Data at 25 °Cfrom Pine et al.[34]

When a compound has limited solubility in water it iscommon practice (in the pharmaceutical industry, for ex-ample) to determine pKₐ values in a solvent mixture suchas water/dioxane or water/methanol, in which the com-pound is more soluble.[35] In the example shown at the

right, the pKₐ value rises steeply with increasing percent-age of dioxane as the dielectric constant of the mixture isdecreasing.A pKₐ value obtained in a mixed solvent cannot be useddirectly for aqueous solutions. The reason for this isthat when the solvent is in its standard state its activityis defined as one. For example, the standard state ofwater:dioxane 9:1 is precisely that solvent mixture, withno added solutes. To obtain the pKₐ value for use withaqueous solutions it has to be extrapolated to zero co-solvent concentration from values obtained from variousco-solvent mixtures.These facts are obscured by the omission of the solventfrom the expression that is normally used to define pKₐ,but pKₐ values obtained in a given mixed solvent can becompared to each other, giving relative acid strengths.The same is true of pKₐ values obtained in a particularnon-aqueous solvent such a DMSO.As of 2008, a universal, solvent-independent, scale foracid dissociation constants has not been developed, sincethere is no known way to compare the standard states oftwo different solvents.

5 Factors that affect pKₐ values

Pauling’s second rule is that the value of the first pKₐ foracids of the formula XO (OH) depends primarily on thenumber of oxo groups m, and is approximately indepen-dent of the number of hydroxy groups n, and also of thecentral atom X. Approximate values of pKₐ are 8 for m =0, 2 for m = 1, −3 for m = 2 and < −10 for m = 3.[18] Alter-natively, various numerical formulas have been proposedincluding pKₐ = 8 − 5n (known as Bell’s rule),[19][36] pKₐ= 7 − 5n,[20][37] or pKₐ = 9 − 7n.[19] The dependence onm correlates with the oxidation state of the central atom,X: the higher the oxidation state the stronger the oxyacid.For example, pKₐ for HClO is 7.2, for HClO2 is 2.0, forHClO3 is −1 and HClO4 is a strong acid (pKₐ << 0).[3]This rule can help assign molecular structure: for exam-ple phosphorous acid (H3PO3) has a pKₐ near 2 suggestedthat the structure is HPO(OH)2, as later confirmed byNMR spectroscopy, and not P(OH)3 which would be ex-pected to have a pKₐ near 8.[37]

With organic acids inductive effects and mesomeric ef-fects affect the pKₐ values. A simple example is pro-vided by the effect of replacing the hydrogen atoms inacetic acid by the more electronegative chlorine atom.The electron-withdrawing effect of the substituent makesionisation easier, so successive pKₐ values decrease in theseries 4.7, 2.8, 1.4 and 0.7 when 0,1, 2 or 3 chlorine atomsare present.[38] TheHammett equation, provides a generalexpression for the effect of substituents.[39]

log Kₐ = log Kₐ0 + ρσ.

8 5 FACTORS THAT AFFECT PKA VALUES

Fumaric acid

O

OH O

OH

Maleic acid

proton sponge

Kₐ is the dissociation constant of a substituted compound,Kₐ0 is the dissociation constant when the substituent ishydrogen, ρ is a property of the unsubstituted compoundand σ has a particular value for each substituent. A plotof log Kₐ against σ is a straight line with intercept logKₐ0 and slope ρ. This is an example of a linear free en-ergy relationship as log Kₐ is proportional to the standardfee energy change. Hammett originally[40] formulatedthe relationship with data from benzoic acid with differ-ent substiuents in the ortho- and para- positions: somenumerical values are in Hammett equation. This andother studies allowed substituents to be ordered accord-ing to their electron-withdrawing or electron-releasingpower, and to distinguish between inductive and me-

someric effects.[41][42]

Alcohols do not normally behave as acids in water, but thepresence of a double bond adjacent to the OH group cansubstantially decrease the pKₐ by the mechanism of keto-enol tautomerism. Ascorbic acid is an example of thiseffect. The diketone 2,4-pentanedione (acetylacetone) isalso a weak acid because of the keto-enol equilibrium. Inaromatic compounds, such as phenol, which have an OHsubstituent, conjugation with the aromatic ring as a wholegreatly increases the stability of the deprotonated form.Structural effects can also be important. The differencebetween fumaric acid and maleic acid is a classic ex-ample. Fumaric acid is (E)−1,4-but-2-enedioic acid, atrans isomer, whereas maleic acid is the correspondingcis isomer, i.e. (Z)−1,4-but-2-enedioic acid (see cis-trans isomerism). Fumaric acid has pKₐ values of ap-proximately 3.0 and 4.5. By contrast, maleic acid haspKₐ values of approximately 1.5 and 6.5. The reason forthis large difference is that when one proton is removedfrom the cis- isomer (maleic acid) a strong intramolecularhydrogen bond is formed with the nearby remaining car-boxyl group. This favors the formation of themaleate H+,and it opposes the removal of the second proton from thatspecies. In the trans isomer, the two carboxyl groups arealways far apart, so hydrogen bonding is not observed.[43]

Proton sponge, 1,8-bis(dimethylamino)naphthalene, hasa pKₐ value of 12.1. It is one of the strongest aminebases known. The high basicity is attributed to the reliefof strain upon protonation and strong internal hydrogenbonding.[44][45]

Effects of the solvent and solvation should be mentionedalso in this section. It turns out, these influences aremore subtle than that of a dielectric medium mentionedabove. For example, the expected (by electronic effectsof methyl substituents) and observed in gas phase order ofbasicity of methylamines, Me3N > Me2NH > MeNH2 >NH3, is changed by water to Me2NH >MeNH2 > Me3N> NH3. Neutral methylamine molecules are hydrogen-bonded to water molecules mailnly through one acceptor,N-HOH, interaction and only occasionally just one moredonor bond, NH-OH2. Hence, methylamines are stabi-lized to about the same extent by hydration, regardlessof the number of methyl groups. In stark contrast, cor-responding methylammonium cations always utilize allthe available protons for donor NH-OH2 bonding. Rela-tive stabilization ofmethylammonium ions thus decreaseswith the number of methyl groups explaining the order ofwater basicity of methylamines.[46]

5.1 Thermodynamics

An equilibrium constant is related to the standard Gibbsenergy change for the reaction, so for an acid dissociationconstant

9

ΔG = −RT ln Kₐ ≈ 2.303 RT pKₐ.

R is the gas constant and T is the absolute temperature.Note that pKₐ= −log Kₐ and 2.303 ≈ ln 10. At 25 °C

ΔG in kJ·mol−1 = 5.708 pKₐ (1 kJ·mol−1 = 1000 Joulesper mole). Free energy is made up of an enthalpy termand an entropy term.[7]

ΔG = ΔH − TΔS

The standard enthalpy change can be determined bycalorimetry or by using the van 't Hoff equation, thoughthe calorimetric method is preferable. When both thestandard enthalpy change and acid dissociation constanthave been determined, the standard entropy change iseasily calculated from the equation above. In the follow-ing table, the entropy terms are calculated from the ex-

perimental values of pKₐ and ΔH . The data were crit-ically selected and refer to 25 °C and zero ionic strength,in water.[7]

† ΔG = 2.303RT pKa‡ Computed here, fromΔH and ΔG values sup-

plied in the citation, using —TΔS = ΔG

—ΔH

The first point to note is that, when pKₐ is positive, thestandard free energy change for the dissociation reactionis also positive. Second, some reactions are exothermic

and some are endothermic, but, when ΔH is negative

−TΔS is the dominant factor, which determines thatΔG is positive. Last, the entropy contribution is al-

ways unfavourable (ΔS < 0) in these reactions. Ionsin aqueous solution tend to orient the surrounding watermolecules, which orders the solution and decreases theentropy. The contribution of an ion to the entropy is thepartial molar entropy which is often negative, especiallyfor small or highly charged ions.[47] The ionization of aneutral acid involves formation of two ions so that the en-tropy decreases (ΔS < 0). On the second ionization ofthe same acid, there are now three ions and the anion hasa charge, so the entropy again decreases.Note that the standard free energy change for the reac-tion is for the changes from the reactants in their standardstates to the products in their standard states. The freeenergy change at equilibrium is zero since the chemicalpotentials of reactants and products are equal at equilib-rium.

A calculated titration curve of oxalic acid titrated with a solutionof sodium hydroxide

6 Experimental determination

See also: Determination of equilibrium constants

The experimental determination of pKₐ values is com-monly performed by means of titrations, in a mediumof high ionic strength and at constant temperature.[48] Atypical procedure would be as follows. A solution of thecompound in the medium is acidified with a strong acidto the point where the compound is fully protonated. Thesolution is then titrated with a strong base until all the pro-tons have been removed. At each point in the titration pHis measured using a glass electrode and a pH meter. Theequilibrium constants are found by fitting calculated pHvalues to the observed values, using the method of leastsquares.[49]

The total volume of added strong base should be smallcompared to the initial volume of titrand solution in or-der to keep the ionic strength nearly constant. This willensure that pKₐ remains invariant during the titration.A calculated titration curve for oxalic acid is shown atthe right. Oxalic acid has pKₐ values of 1.27 and 4.27.Therefore the buffer regions will be centered at about pH1.3 and pH 4.3. The buffer regions carry the informationnecessary to get the pKₐ values as the concentrations ofacid and conjugate base change along a buffer region.Between the two buffer regions there is an end-point, orequivalence point, at about pH 3. This end-point is notsharp and is typical of a diprotic acid whose buffer re-gions overlap by a small amount: pKₐ₂ − pKₐ₁ is aboutthree in this example. (If the difference in pK valueswere about two or less, the end-point would not be no-ticeable.) The second end-point begins at about pH 6.3and is sharp. This indicates that all the protons have beenremoved. When this is so, the solution is not bufferedand the pH rises steeply on addition of a small amount ofstrong base. However, the pH does not continue to riseindefinitely. A new buffer region begins at about pH 11

10 7 APPLICATIONS AND SIGNIFICANCE

(pK − 3), which is where self-ionization of water be-comes important.It is very difficult to measure pH values of less than twoin aqueous solution with a glass electrode, because theNernst equation breaks down at such low pH values. Todetermine pK values of less than about 2 or more thanabout 11 spectrophotometric[50] [51] or NMR[12][52] mea-surements may be used instead of, or combined with, pHmeasurements.When the glass electrode cannot be employed, as withnon-aqueous solutions, spectrophotometric methods arefrequently used.[27] These may involve absorbance orfluorescence measurements. In both cases the mea-sured quantity is assumed to be proportional to the sumof contributions from each photo-active species; withabsorbance measurements the Beer-Lambert law is as-sumed to apply.Aqueous solutions with normal water cannot be used for1H NMR measurements but heavy water, D2O, must beused instead. 13C NMR data, however, can be used withnormal water and 1HNMR spectra can be used with non-aqueous media. The quantities measured with NMR aretime-averaged chemical shifts, as proton exchange is faston the NMR time-scale. Other chemical shifts, such asthose of 31P can be measured.

6.1 Micro-constants

H2N NH

HN NH2

spermine

A base such as spermine has a few different sites whereprotonation can occur. In this example the first proton cango on the terminal -NH2 group, or either of the internal-NH- groups. The pKₐ values for dissociation of sper-mine protonated at one or other of the sites are examplesof micro-constants. They cannot be determined directlyby means of pH, absorbance, fluorescence or NMR mea-surements. Nevertheless, the site of protonation is veryimportant for biological function, so mathematical meth-ods have been developed for the determination of micro-constants.[53]

7 Applications and significance

A knowledge of pKₐ values is important for the quanti-tative treatment of systems involving acid–base equilib-ria in solution. Many applications exist in biochemistry;for example, the pKₐ values of proteins and amino acidside chains are of major importance for the activity of en-zymes and the stability of proteins.[54] Protein pKa values

cannot always be measured directly, but may be calcu-lated using theoretical methods. Buffer solutions are usedextensively to provide solutions at or near the physiologi-cal pH for the study of biochemical reactions;[55] the de-sign of these solutions depends on a knowledge of the pKₐvalues of their components. Important buffer solutionsinclude MOPS, which provides a solution with pH 7.2,and tricine, which is used in gel electrophoresis.[56][57]Buffering is an essential part of acid base physiology in-cluding acid-base homeostasis,[58] and is key to under-standing disorders such as acid-base imbalance.[59][60][61]The isoelectric point of a given molecule is a function ofits pK values, so different molecules have different iso-electric points. This permits a technique called isoelectricfocusing,[62] which is used for separation of proteins by2-D gel polyacrylamide gel electrophoresis.Buffer solutions also play a key role in analytical chem-istry. They are used whenever there is a need to fix thepH of a solution at a particular value. Compared with anaqueous solution, the pH of a buffer solution is relativelyinsensitive to the addition of a small amount of strongacid or strong base. The buffer capacity[63] of a simplebuffer solution is largest when pH = pKₐ. In acid-base ex-traction, the efficiency of extraction of a compound intoan organic phase, such as an ether, can be optimised byadjusting the pH of the aqueous phase using an appropri-ate buffer. At the optimum pH, the concentration of theelectrically neutral species is maximised; such a speciesis more soluble in organic solvents having a low dielectricconstant than it is in water. This technique is used for thepurification of weak acids and bases.[64]

A pH indicator is a weak acid or weak base that changescolour in the transition pH range, which is approximatelypKₐ ± 1. The design of a universal indicator requires amixture of indicators whose adjacent pKₐ values differ byabout two, so that their transition pH ranges just overlap.In pharmacology ionization of a compound alters its phys-ical behaviour and macro properties such as solubility andlipophilicity (log p). For example ionization of any com-pound will increase the solubility in water, but decreasethe lipophilicity. This is exploited in drug developmentto increase the concentration of a compound in the bloodby adjusting the pKₐ of an ionizable group.[65]

Knowledge of pKₐ values is important for the understand-ing of coordination complexes, which are formed by theinteraction of a metal ion, Mm+, acting as a Lewis acid,with a ligand, L, acting as a Lewis base. However, theligand may also undergo protonation reactions, so the for-mation of a complex in aqueous solution could be repre-sented symbolically by the reaction

[M(H2O)n]m+ +LH[M(H2O)n₋₁L](m−1)+ + H3O+

To determine the equilibrium constant for this reaction,in which the ligand loses a proton, the pKₐ of the pro-tonated ligand must be known. In practice, the ligand

11

may be polyprotic; for example EDTA4− can accept fourprotons; in that case, all pKₐ values must be known. Inaddition, the metal ion is subject to hydrolysis, that is, itbehaves as a weak acid, so the pK values for the hydroly-sis reactions must also be known.[66] Assessing the hazardassociated with an acid or base may require a knowl-edge of pKₐ values.[67] For example, hydrogen cyanideis a very toxic gas, because the cyanide ion inhibits theiron-containing enzyme cytochrome c oxidase. Hydro-gen cyanide is a weak acid in aqueous solution with a pKₐof about 9. In strongly alkaline solutions, above pH 11,say, it follows that sodium cyanide is “fully dissociated”so the hazard due to the hydrogen cyanide gas is muchreduced. An acidic solution, on the other hand, is veryhazardous because all the cyanide is in its acid form. In-gestion of cyanide by mouth is potentially fatal, indepen-dently of pH, because of the reaction with cytochrome coxidase.In environmental science acid–base equilibria are impor-tant for lakes[68] and rivers;[69][70] for example, humicacids are important components of natural waters. An-other example occurs in chemical oceanography:[71] inorder to quantify the solubility of iron(III) in seawater atvarious salinities, the pKₐ values for the formation of theiron(III) hydrolysis products Fe(OH)2+, Fe(OH)2+ andFe(OH)3 were determined, along with the solubility prod-uct of iron hydroxide.[72]

8 Values for common substances

There are multiple techniques to determine the pKₐ of achemical, leading to some discrepancies between differ-ent sources. Well measured values are typically within0.1 units of each other. Data presented here were takenat 25 °C in water.[3][73] More values can be found inthermodynamics, above.

9 See also

• Acids in wine: tartaric, malic and citric are the prin-cipal acids in wine.

• Ocean acidification: dissolution of atmospheric car-bon dioxide affects seawater pH. The reaction de-pends on total inorganic carbon and on solubilityequilibria with solid carbonates such as limestoneand dolomite.

• Grotthuss mechanism: how protons are transferredbetween hydronium ions and water molecules, ac-counting for the exceptionally high ionic mobility ofthe proton (animation).

• Predominance diagram: relates to equilibria involv-ing polyoxyanions. pKₐ values are needed to con-struct these diagrams.

• Proton affinity: a measure of basicity in the gasphase.

• Stability constants of complexes: formation of acomplex can often be seen as a competition betweenproton and metal ion for a ligand, which is the prod-uct of dissociation of an acid.

• Hammett acidity function: a measure of acidity thatis used for very concentrated solutions of strongacids, including superacids.

• Acidosis

• Alkalosis

• Arterial blood gas

• Chemical equilibrium

• pCO2

• pH

10 References[1] Miessler, G. (1991). Inorganic Chemistry (2nd ed.). Pren-

tice Hall. ISBN 0-13-465659-8. Chapter 6: Acid-Baseand Donor-Acceptor Chemistry

[2] Bell, R.P. (1973). The Proton in Chemistry (2nd ed.).London: Chapman & Hall. ISBN 0-8014-0803-2. In-cludes discussion of many organic Brønsted acids.

[3] Shriver, D.F; Atkins, P.W. (1999). Inorganic Chemistry(3rd ed.). Oxford: Oxford University Press. ISBN 0-19-850331-8. Chapter 5: Acids and Bases

[4] Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chem-istry (3rd ed.). Prentice Hall. ISBN 978-0131755536.Chapter 6: Acids, Bases and Ions in Aqueous Solution

[5] Headrick, J.M.; Diken, E.G.; Walters, R. S.; Ham-mer, N. I.; Christie, R.A.; Cui, J.; Myshakin,E.M.; Duncan, M.A.; Johnson, M.A.; Jordan, K.D.(2005). “Spectral Signatures of Hydrated Pro-ton Vibrations in Water Clusters”. Science 308(5729): 1765–69. Bibcode:2005Sci...308.1765H.doi:10.1126/science.1113094. PMID 15961665.

[6] Smiechowski, M.; Stangret, J. (2006). “Proton hy-dration in aqueous solution: Fourier transform infraredstudies of HDO spectra”. J. Chem. Phys. 125(20): 204508–204522. Bibcode:2006JChPh.125t4508S.doi:10.1063/1.2374891. PMID 17144716.

[7] Goldberg, R.; Kishore, N.; Lennen, R. (2002).“Thermodynamic Quantities for the Ionization Reac-tions of Buffers” (PDF). J. Phys. Chem. Ref. Data31 (2): 231–370. Bibcode:1999JPCRD..31..231G.doi:10.1063/1.1416902.

[8] Jolly, William L. (1984). Modern Inorganic Chemistry.McGraw-Hill. p. 198. ISBN 978-0-07-032760-3.

12 10 REFERENCES

[9] Burgess, J. (1978). Metal Ions in Solution. Ellis Horwood.ISBN 0-85312-027-7. Section 9.1 “Acidity of SolvatedCations” lists many pKₐ values.

[10] Petrucci, R.H.; Harwood, R.S.; Herring, F.G. (2002).General Chemistry (8th ed.). Prentice Hall. ISBN 0-13-014329-4. p.698

[11] Rossotti, F.J.C.; Rossotti, H. (1961). The Determinationof Stability Constants. McGraw–Hill. Chapter 2: Activityand Concentration Quotients

[12] Popov, K.; Ronkkomaki, H.; Lajunen, L.H.J. (2006).“Guidelines for NMR Measurements for Determinationof High and Low pKₐ Values” (PDF). Pure Appl. Chem.78 (3): 663–675. doi:10.1351/pac200678030663.

[13] “Project: Ionic Strength Corrections for Stability Con-stants”. International Union of Pure and Applied Chem-istry. Archived from the original on 29 October 2008.Retrieved 2008-11-23.

[14] Mehta, Akul. “Henderson–Hasselbalch Equation:Derivation of pKa and pKb”. PharmaXChange.Retrieved 16 November 2014.

[15] Dasent, W.E. (1982). Inorganic Energetics: An Introduc-tion. Cambridge University Press. ISBN 0-521-28406-6.Chapter 5

[16] The values are for 25°C and zero ionic strength — Pow-ell, Kipton J.; Brown, Paul L.; Byrne, Robert H.; Gajda,Tamás; Hefter, Glenn; Sjöberg, Staffan; Wanner, Hans(2005). “Chemical speciation of environmentally sig-nificant heavy metals with inorganic ligands. Part 1:The Hg2+, Cl−, OH−, CO3

2−, SO42−, and PO4

3− aque-ous systems”. Pure Appl. Chem. 77 (4): 739–800.doi:10.1351/pac200577040739.

[17] Brown, T.E.; Lemay, H.E.; Bursten,B.E.; Murphy, C.;Woodward, P. (2008). Chemistry: The Central Science(11th ed.). New York: Prentice-Hall. p. 689. ISBN 0-13-600617-5.

[18] Greenwood, N.N.; Earnshaw, A. (1997). Chemistry of theElements (2nd ed.). Oxford: Butterworth-Heinemann. p.50. ISBN 0-7506-3365-4.

[19] Miessler, Gary L.; Tarr Donald A. (1999). InorganicChemistry (2nd ed.). Prentice Hall. p. 164. ISBN 0-13-465659-8.

[20] Huheey, James E. (1983). Inorganic Chemistry (3rd ed.).Harper & Row. p. 297. ISBN 0-06-042987-9.

[21] Harned, H.S.; Owen, B.B (1958). The Physical Chemistryof Electrolytic Solutions. New York: Reinhold PublishingCorp. pp. 634–649, 752–754.

[22] Lide, D.R. (2004). CRC Handbook of Chemistry andPhysics, Student Edition (84th ed.). CRC Press. ISBN0-8493-0597-7. Section D–152

[23] Atkins, P.W.; de Paula, J. (2006). Physical Chemistry.Oxford University Press. ISBN 0-19-870072-5. Section7.4: The Response of Equilibria to Temperature

[24] Loudon, G. Marc (2005), Organic Chemistry (4th ed.),New York: Oxford University Press, pp. 317–318, ISBN0-19-511999-1

[25] March, J.; Smith, M. (2007). Advanced Organic Chem-istry (6th ed.). New York: John Wiley & Sons. ISBN978-0-471-72091-1. Chapter 8: Acids and Bases

[26] Kütt, A.; Movchun, V.; Rodima, T,; Dansauer, T.;Rusanov, E.B. ; Leito, I.; Kaljurand, I.; Koppel, J.;Pihl, V.; Koppel, I.; Ovsjannikov, G.; Toom, L.;Mishima, M.; Medebielle, M.; Lork, E.; Röschen-thaler, G-V.; Koppel, I.A.; Kolomeitsev, A.A. (2008).“Pentakis(trifluoromethyl)phenyl, a Sterically Crowdedand Electron-withdrawing Group: Synthesis and Acidityof Pentakis(trifluoromethyl)benzene, -toluene, -phenol,and -aniline”. J. Org. Chem. 73 (7): 2607–2620.doi:10.1021/jo702513w. PMID 18324831.

[27] Kütt, A.; Leito, I.; Kaljurand, I.; Sooväli, L.; Vlasov,V.M.; Yagupolskii, L.M.; Koppel, I.A. (2006). “A Com-prehensive Self-Consistent Spectrophotometric AcidityScale of Neutral Brønsted Acids in Acetonitrile”. J. Org.Chem. 71 (7): 2829–2838. doi:10.1021/jo060031y.PMID 16555839.

[28] Kaljurand, I.; Kütt, A.; Sooväli, L.; Rodima, T.; Mäemets,V. Leito, I; Koppel, I.A. (2005). “Extension of the Self-Consistent Spectrophotometric Basicity Scale in Acetoni-trile to a Full Span of 28 pKa Units: Unification of Differ-ent Basicity Scales”. J. Org. Chem. 70 (3): 1019–1028.doi:10.1021/jo048252w. PMID 15675863.

[29] “Bordwell pKa Table (Acidity in DMSO)". Archivedfrom the original on 9 October 2008. Retrieved 2008-11-02.

[30] Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chem-istry (3rd ed.). Prentice Hall. ISBN 978-0131755536.Chapter 8: Non-Aqueous Media

[31] Rochester, C.H. (1970). Acidity Functions. AcademicPress. ISBN 0-12-590850-4.

[32] Olah, G.A; Prakash, S; Sommer, J (1985). Superacids.New York: Wiley Interscience. ISBN 0-471-88469-3.

[33] Coetzee, J.F.; Padmanabhan, G.R. (1965). “Proton Ac-ceptor Power and Homoconjugation of Mono- and Di-amines”. J. Amer. Chem. Soc. 87 (22): 5005–5010.doi:10.1021/ja00950a006.

[34] Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond,G.S. (1980). “Organic chemistry”. McGraw–Hill. p.203. ISBN 0-07-050115-7.

[35] Box, K.J.; Völgyi, G. Ruiz, R. Comer, J.E. Takács-Novák,K., Bosch, E. Ràfols, C. Rosés, M. (2007). “Physic-ochemical Properties of a New Multicomponent Cosol-vent System for the pKa Determination of Poorly SolublePharmaceutical Compounds”. Helv. Chim. Acta 90 (8):1538–1553. doi:10.1002/hlca.200790161.

[36] Housecroft, Catherine E.; Sharpe, Alan G. (2006). Inor-ganic chemistry (2. ed., [Nachdr.] ed.). Harlow [u.a.]:Prentice Hall. pp. 170–171. ISBN 0130-39913-2.

13

[37] Douglas B., McDaniel D.H. and Alexander J.J. Conceptsand Models of Inorganic Chemistry (2nd ed. Wiley 1983)p.526 ISBN 0-471-21984-3

[38] Pauling, L. (1960). The nature of the chemical bond andthe structure of molecules and crystals; an introduction tomodern structural chemistry (3rd ed.). Ithaca (NY): Cor-nell University Press. p. 277. ISBN 0-8014-0333-2.

[39] Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond,G.S. (1980). Organic Chemistry. McGraw–Hill. ISBN0-07-050115-7. Section 13-3: Quantitative Correlationsof Substituent Effects (Part B) – The Hammett Equation

[40] Hammett, L.P. (1937). “The Effect of Structure uponthe Reactions of Organic Compounds. Benzene Deriva-tives”. J. Amer. Chem. Soc. 59 (1): 96–103.doi:10.1021/ja01280a022.

[41] Hansch, C.; Leo, A.; Taft, R. W. (1991). “A Sur-vey of Hammett Substituent Constants and Resonanceand Field Parameters”. Chem. Rev. 91 (2): 165–195.doi:10.1021/cr00002a004.

[42] Shorter, J (1997). “Compilation and critical evaluationof structure-reactivity parameters and equations: Part 2.Extension of the Hammett σ scale through data for theionization of substituted benzoic acids in aqueous solventsat 25 C (Technical Report)". Pure and Applied Chemistry69 (12): 2497–2510. doi:10.1351/pac199769122497.

[43] Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond,G.S. (1980). Organic chemistry. McGraw–Hill. ISBN 0-07-050115-7. Section 6-2: Structural Effects on Acidityand Basicity

[44] Alder, R.W.; Bowman, P.S.; Steele, W.R.S.; Winter-man, D.R. (1968). “The Remarkable Basicity of 1,8-bis(dimethylamino)naphthalene”. Chem. Commun. (13):723–724. doi:10.1039/C19680000723.

[45] Alder, R.W. (1989). “Strain Effects on Amine Ba-sicities”. Chem. Rev. 89 (5): 1215–1223.doi:10.1021/cr00095a015.

[46] Fraczkiewicz, R (2013). “In Silico Prediction of Ion-ization”. In Reedijk, J. Reference Module in Chem-istry, Molecular Sciences and Chemical Engineering [On-line]. vol. 5. Amsterdam, The Netherlands: Elsevier.doi:10.1016/B978-0-12-409547-2.02610-X.

[47] Atkins, Peter William; De Paula, Julio (2006). Atkins’physical chemistry. New York: W H Freeman. p. 94.ISBN 9780716774334.

[48] Martell, A.E.; Motekaitis, R.J. (1992). Determination andUse of Stability Constants. Wiley. ISBN 0-471-18817-4. Chapter 4: Experimental Procedure for PotentiometricpH Measurement of Metal Complex Equilibria

[49] Leggett, D.J. (1985). Computational Methods for the De-termination of Formation Constants. Plenum. ISBN 0-306-41957-2.

[50] Allen, R.I.; Box,K.J.; Comer, J.E.A.; Peake, C.; Tam,K.Y. (1998). “Multiwavelength Spectrophotometric De-termination of Acid Dissociation Constants of IonizableDrugs”. J. Pharm. Biomed. Anal. 17 (4–5): 699–641.doi:10.1016/S0731-7085(98)00010-7.

[51] Box, K.J.; Donkor, R.E. Jupp, P.A. Leader, I.P. Trew,D.F. Turner, C.H. (2008). “The Chemistry of Multi-Protic Drugs Part 1: A Potentiometric, Multi-WavelengthUV and NMR pH Titrimetric Study of the Micro-Speciation of SKI-606”. J. Pharm. Biomed. Anal. 47(2): 303–311. doi:10.1016/j.jpba.2008.01.015. PMID18314291.

[52] Szakács, Z.; Hägele, G. (2004). “Accurate Determinationof Low pK Values by 1H NMR Titration”. Talanta 62(4): 819–825. doi:10.1016/j.talanta.2003.10.007. PMID18969368.

[53] Frassineti, C.; Alderighi, L; Gans, P; Sabatini, A;Vacca, A; Ghelli, S. (2003). “Determination of Pro-tonation Constants of Some Fluorinated Polyamines byMeans of 13C NMR Data Processed by the New Com-puter Program HypNMR2000. Protonation Sequencein Polyamines.”. Anal. Bioanal. Chem. 376 (7):1041–1052. doi:10.1007/s00216-003-2020-0. PMID12845401.

[54] Onufriev, A.; Case, D.A; Ullmann G.M. (2001). “ANovel View of pH Titration in Biomolecules”. Bio-chemistry 40 (12): 3413–3419. doi:10.1021/bi002740q.PMID 11297406.

[55] Good, N.E.; Winget, G.D.; Winter, W.; Connolly, T.N.;Izawa, S.; Singh, R.M.M. (1966). “Hydrogen Ion Buffersfor Biological Research”. Biochemistry 5 (2): 467–477.doi:10.1021/bi00866a011. PMID 5942950.

[56] Dunn, M.J. (1993). Gel Electrophoresis: Proteins. BiosScientific Publishers. ISBN 1-872748-21-X.

[57] Martin, R. (1996). Gel Electrophoresis: Nucleic Acids.Bios Scientific Publishers. ISBN 1-872748-28-7.

[58] Brenner, B.M. (Editor); Stein, J.H. (Editor) (1979). Acid–Base and Potassium Homeostasis. Churchill Livingstone.ISBN 0-443-08017-8.

[59] Scorpio, R. (2000). Fundamentals of Acids, Bases,Buffers & Their Application to Biochemical Systems.Kendall/Hunt Pub. Co. ISBN 0-7872-7374-0.

[60] Beynon, R.J.; Easterby, J.S. (1996). Buffer Solutions: TheBasics. Oxford: Oxford University Press. ISBN 0-19-963442-4.

[61] Perrin, D.D.; Dempsey, B. (1974). Buffers for pH andMetal Ion Control. London: Chapman & Hall. ISBN 0-412-11700-2.

[62] Garfin, D.(Editor); Ahuja, S. (Editor) (2005). Handbookof Isoelectric Focusing and Proteomics 7. Elsevier. ISBN0-12-088752-5.

[63] Hulanicki, A. (1987). Reactions of Acids and Bases inAnalytical Chemistry. Masson, M.R. (translation editor).Horwood. ISBN 0-85312-330-6.

[64] Eyal, A.M (1997). “Acid Extraction by Acid–Base-Coupled Extractants”. Ion Exchange and Solvent Extrac-tion: A Series of Advances 13: 31–94.

14 12 EXTERNAL LINKS

[65] Avdeef, A. (2003). Absorption and Drug Development:Solubility, Permeability, and Charge State. NewYork: Wi-ley. ISBN 0-471-42365-3.

[66] Beck, M.T.; Nagypál, I. (1990). Chemistry of ComplexEquilibria. Horwood. ISBN 0-85312-143-5.

[67] van Leeuwen, C.J.; Hermens, L. M. (1995). Risk Assess-ment of Chemicals: An Introduction. Springer. pp. 254–255. ISBN 0-7923-3740-9.

[68] Skoog, D.A; West, D.M.; Holler, J.F.; Crouch, S.R.(2004). Fundamentals of Analytical Chemistry (8th ed.).Thomson Brooks/Cole. ISBN 0-03-035523-0. Chapter9-6: Acid Rain and the Buffer Capacity of Lakes

[69] Stumm, W.; Morgan, J.J. (1996). Water Chemistry. NewYork: Wiley. ISBN 0-471-05196-9.

[70] Snoeyink, V.L.; Jenkins, D. (1980). Aquatic Chemistry:Chemical Equilibria and Rates in Natural Waters. NewYork: Wiley. ISBN 0-471-51185-4.

[71] Millero, F.J. (2006). Chemical Oceanography (3rd ed.).London: Taylor and Francis. ISBN 0-8493-2280-4.

[72] Millero, F.J.; Liu, X. (2002). “The Solubility ofIron in Seawater”. Marine chemistry 77 (1): 43–54.doi:10.1016/S0304-4203(01)00074-3.

[73] Speight, J.G. (2005). Lange’s Handbook of Chemistry(18th ed.). McGraw–Hill. ISBN 0-07-143220-5. Chap-ter 8

11 Further reading• Albert, A.; Serjeant, E.P. (1971). The Determina-tion of Ionization Constants: A Laboratory Manual.Chapman & Hall. ISBN 0-412-10300-1. (Previousedition published as Ionization constants of acids andbases. London (UK): Methuen. 1962.)

• Atkins, P.W.; Jones, L. (2008). Chemical Princi-ples: The Quest for Insight (4th ed.). W.H. Freeman.ISBN 1-4292-0965-8.

• Housecroft, C. E.; Sharpe, A. G. (2008). Inor-ganic Chemistry (3rd ed.). Prentice Hall. ISBN 978-0131755536. (Non-aqueous solvents)

• Hulanicki, A. (1987). Reactions of Acids and Basesin Analytical Chemistry. Horwood. ISBN 0-85312-330-6. (translation editor: Mary R. Masson)

• Perrin, D.D.; Dempsey, B.; Serjeant, E.P. (1981).pKa Prediction for Organic Acids and Bases. Chap-man & Hall. ISBN 0-412-22190-X.

• Reichardt, C. (2003). Solvents and Solvent Effectsin Organic Chemistry (3rd ed.). Wiley-VCH. ISBN3-527-30618-8. Chapter 4: Solvent Effects on thePosition of Homogeneous Chemical Equilibria.

• Skoog, D.A.; West, D.M.; Holler, J.F.; Crouch, S.R.(2004). Fundamentals of Analytical Chemistry (8thed.). Thomson Brooks/Cole. ISBN 0-03-035523-0.

12 External links• Acidity-Basicity Data in Nonaqueous Solvents Ex-tensive bibliography of pKₐ values in DMSO,acetonitrile, THF, heptane, 1,2-dichloroethane, andin the gas phase

• Curtipot All-in-one freeware for pH and acid-base equilibrium calculations and for simulationand analysis of potentiometric titration curves withspreadsheets

• SPARC Physical/Chemical property calculator In-cludes a database with aqueous, non-aqueous, andgaseous phase pKₐ values than can be searched us-ing SMILES or CAS registry numbers

• Aqueous-Equilibrium Constants pKₐ values for var-ious acid and bases. Includes a table of some solu-bility products

• Free guide to pKₐ and log p interpretation and mea-surement Explanations of the relevance of theseproperties to pharmacology

• Free online prediction tool (Marvin) pKₐ, logP, logDetc. From ChemAxon

• Chemicalize.org:List of predicted structure basedproperties

• Evans pKa Chart http://evans.harvard.edu/pdf/evans_pka_table.pdf

15

13 Text and image sources, contributors, and licenses

13.1 Text• Acid dissociation constant Source: https://en.wikipedia.org/wiki/Acid_dissociation_constant?oldid=666032945 Contributors: Derek

Ross, Bryan Derksen, Rmrf1024, Michael Hardy, ESnyder2, Kku, Charles Matthews, Altenmann, Nurg, Pifactorial, Diberri, David Gerard,Giftlite, Graeme Bartlett, Dratman, Michael Devore, Bensaccount, Eequor, Xwu, Brockert, Yath, H Padleckas, Filthybutter, Vsmith, Ben-der235, Konstantin~enwiki, Marx Gomes, ~K, Femto, Arcadian, KBi, Benjah-bmm27, EagleFalconn, Cburnett, TenOfAllTrades, GeneNygaard, Umbricht, LOL, The Wordsmith, Joerg Kurt Wegner, Graham87, V8rik, BD2412, Rjwilmsi, THE KING, Nihiltres, Shao, The-Sun, Physchim62, Sbrools, Krishnavedala, Bubbachuck, YurikBot, Borgx, Mushin, Postglock, AVM, Hellbus, Gaius Cornelius, A!eX,Derek.cashman, Tetracube, Eno-ja, Tsiaojian lee, Itub, Anthony Duff, SmackBot, Ashley thomas80, Cpdilkus, Edgar181, Robsomebody,DarkIye, Armeria, Chris the speller, Bluebot, Hichris, Analogue Kid, Lawrenceuniversity1, ShalomYechiel, OrphanBot, JonHarder, Garba-cie, Ctifumdope, Flyguy649, Fuhghettaboutit, Xcomradex, Smokefoot, Drphilharmonic, Mwtoews, DMacks, Clicketyclack, Euchiasmus,Olin, Smith609, Tac2z, Meco, SandyGeorgia, AdultSwim, Simon12, Cheesy Yeast, Twas Now, Eyehawk78, Conrad.Irwin, Fvasconcellos,A876, WillowW, Mike Christie, Skoddet, Rifleman 82, Dasfrpsl, Christian75, Chrislk02, Paddles, Headbomb, Trevyn, Raj76, AntiVan-dalBot, Jayron32, TimVickers, Litch, Turgidson, Magioladitis, Albmont, Think outside the box, Sns, KConWiki, Giggy, Causesobad,Dirac66, Talon Artaine, Ac44ck, Meduban, Bfesser, Nono64, Leyo, Slash, C.R.Selvakumar, Boghog, Derlay, Pisanidavid, L'Aquatique,Vicodin addict, Sd31415, Jorfer, Sanji Bhal, Almazi, Alex Allardyce, Gabby8228, Geometry guy, Proteins, Shanata, Temporaluser, Tneils,Hoopssheaffer, Petergans, Dguire, Graham Beards, WereSpielChequers, RJaguar3, Dsstman, Janopus, Mike2vil, Pinkadelica, Steveroon,Bob1960evens, Plastikspork, Spoladore, Unbuttered Parsnip, Ectomaniac, Niceguyedc, Thegeneralguy, 4zimuth, Peachypoh, Sdrtirs, KR-Morison, Addbot, DOI bot, Element16, Wickey-nl, Giants2008, Yobmod, Aboctok, Download, Favonian, Loupeter, Yobot, TaBOT-zerem,Aboalbiss, Raimundo Pastor, KDS4444, CyberScientist, Daniele Pugliesi, Citation bot, LilHelpa, BotPuppet, Arturkjakub, Dave3457, Re-tracc, FrescoBot, Citation bot 1, SUL, DrilBot, Spidey71, Double sharp, Trappist the monk, Oktanyum, Hmmwhatsthisdo, Quantumkinet-ics, Levoslashx, DASHBot, EmausBot, Erbrumar, Dcirovic, JSquish, Prayerfortheworld, Dmayank, Kittenono, Rmashhadi, Slowkow, Clue-Bot NG, Xinleiucd, Abk-sp3, MerlIwBot, Helpful Pixie Bot, Curb Chain, Bibcode Bot, Neeya The Great, LGreiner, Mark Arsten, Shadowintelligence, Stubcoffman, Blegat, Hieu nguyentrung12, Project Osprey, Ekips39, Kostaskal, Jewels Vern, Stamptrader, Avismith456 andAnonymous: 207

13.2 Images• File:Acetic-acid-dissociation-3D-balls.png Source: https://upload.wikimedia.org/wikipedia/commons/9/96/

Acetic-acid-dissociation-3D-balls.png License: Public domain Contributors: Own work Original artist: Ben Mills• File:Acetic_acid_pK_dioxane_water.png Source: https://upload.wikimedia.org/wikipedia/commons/a/a9/Acetic_acid_pK_dioxane_

water.png License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:QuiteUnusual usingCommonsHelper.Original artist: Original uploader was Petergans at en.wikipedia

• File:Carboxylic_acid_dimers.png Source: https://upload.wikimedia.org/wikipedia/commons/c/c9/Carboxylic_acid_dimers.png Li-cense: Public domain Contributors: ? Original artist: ?

• File:Citric_acid_speciation.png Source: https://upload.wikimedia.org/wikipedia/commons/3/39/Citric_acid_speciation.png License:Public domain Contributors: A species distribution diagram as described in Martell, A.E.; Motekaitis, R.J. (1992). Determination anduse of stability constants. Wiley. ISBN 0471188174. Section 2.4 Original artist: Petergans (talk)

• File:Fumaric-acid-2D-skeletal.png Source: https://upload.wikimedia.org/wikipedia/commons/1/13/Fumaric-acid-2D-skeletal.png Li-cense: Public domain Contributors: Own work Original artist: Ben Mills

• File:H3PO4_speciation.png Source: https://upload.wikimedia.org/wikipedia/commons/1/16/H3PO4_speciation.png License: CC BY-SA 4.0 Contributors: Own work Original artist: Petergans

• File:Maleic-acid-2D-skeletal-A.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/13/Maleic-acid-2D-skeletal-A.svgLicense: Public domain Contributors: Own work Original artist: Krishnavedala

• File:Oxalic_acid_titration_grid.png Source: https://upload.wikimedia.org/wikipedia/commons/e/e6/Oxalic_acid_titration_grid.pngLicense: CC-BY-SA-3.0 Contributors: Transferred from en.wikipedia to Commons. Original artist: JWSchmidt at English Wikipedia

• File:PK_acetic_acid.png Source: https://upload.wikimedia.org/wikipedia/commons/5/53/PK_acetic_acid.png License: Public domainContributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper.Original artist: PeterGans. Original uploader was Petergans at en.wikipedia

• File:Proton_sponge.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/06/Proton_sponge.svg License: Public domainContributors: Own work Original artist: User:Bryan Derksen

• File:Spermine.svg Source: https://upload.wikimedia.org/wikipedia/commons/d/db/Spermine.svg License: Public domain Contributors:Selfmade with ChemDraw. Original artist: Calvero.

• File:StrikeO.png Source: https://upload.wikimedia.org/wikipedia/commons/2/2d/StrikeO.png License: Public domain Contributors:Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper.Original artist: . Original uploader was Petergans at en.wikipedia

• File:Weak_acid_speciation.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/ab/Weak_acid_speciation.svg License:Public domain Contributors: Own work Original artist: Krishnavedala

13.3 Content license• Creative Commons Attribution-Share Alike 3.0