Acid dissociation constant - Wikipedia [PDF]

Acid dissociation constant An acid dissociation constant, K a, (also known as acidity constant, or acid-ionization constant) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid–base reactions.[note 1] In aqueous solution, the equilibrium of acid dissociation can be written symbolically as:

where HA is a generic acid that dissociates into A−, known as the conjugate base of the acid and a hydrogen ion which combines with a water molecule to make a hydronium ion. In the example shown in the figure, HA represents acetic acid, and A− represents the acetate ion, the conjugate base.

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.

The chemical species HA, A− and H3 O+ are said to be in equilibrium when their concentrations do not change with the passing of time. The dissociation constant is usually written as a quotient of the equilibrium concentrations (in mol/L), denoted by [HA], [A−] and [H3 O+]

In all but the most concentrated aqueous solutions of an acid, the concentration of water can be taken as constant and can be ignored. The definition can then be written more simply

This is the definition in common usage. For many practical purposes it is more convenient to discuss the logarithmic constant, pK a [note 2] The more positive the value of pK a, the smaller the extent of dissociation at any given pH (see Henderson–Hasselbalch equation)—that is, the weaker the acid. A weak acid has a pK a value in the approximate range −2 to 12 in water. Acids with a pK a value of less than about −2 are said to be strong acids; the dissociation of a strong acid is effectively complete such that concentration of the undissociated acid is too small to be measured. pK a values for strong acids can, however, be estimated by theoretical means. The definition can be extended to non-aqueous solvents, such as acetonitrile and dimethylsulfoxide. Denoting a solvent molecule by S

When the concentration of solvent molecules can be taken to be constant,

, as before.

Contents Theoretical background Definitions Equilibrium constant Monoprotic acids Polyprotic acids Isoelectric point Water self-ionization Protonation constants Amphoteric substances Bases and basicity Temperature dependence Acidity in nonaqueous solutions Mixed solvents Factors that affect pKa values Thermodynamics Experimental determination Micro-constants Applications and significance Values for common substances See also Notes References Further reading External links

Theoretical background The acid dissociation constant for an acid is a direct consequence of the underlying thermodynamics of the dissociation reaction; the pK a value is directly proportional to the standard Gibbs free energy change for the reaction. The value of the pK a changes with temperature and can be understood qualitatively based on Le Châtelier's principle: when the reaction is endothermic, K a increases and pK a decreases with increasing temperature; the opposite is true for exothermic reactions. The value of pK a also depends on molecular structure of the acid in many ways. For example, Pauling proposed two rules: one for successive pK a of polyprotic acids (see Polyprotic acids below), and one to estimate the pK a of oxyacids based on the number of =O and −OH groups (see Factors that affect pK a values below). Other structural factors that influence the magnitude of the acid dissociation constant include inductive effects, mesomeric effects, and hydrogen bonding. Hammett type equations have frequently been applied to the estimation of pK a.[1][2]

The quantitative behaviour of acids and bases in solution can be understood only if their pK a values are known. In particular, the pH of a solution can be predicted when the analytical concentration and pK a 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 pK a values, together with the water–octanol 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 chemical oceanography, where the acidity of water plays a fundamental role. In living organisms, acid–base homeostasis and enzyme kinetics are dependent on the pK a values of the many acids and bases present in the cell and in the body. In chemistry, a knowledge of pK a values is necessary for the preparation of buffer solutions and is also a prerequisite for a quantitative understanding of the interaction between acids or bases and metal ions to form complexes. Experimentally, pK a values can be determined by potentiometric (pH) titration, but for values of pK a less than about 2 or more than about 11, spectrophotometric or NMR measurements may be required due to practical difficulties with pH measurements.

Definitions According to Arrhenius's original definition, an acid is a substance that dissociates in aqueous solution, releasing the hydrogen ion H+ (a proton): [3]

HA A − + H +. The equilibrium constant for this dissociation reaction is known as a dissociation constant. The liberated proton combines with a water molecule to give a hydronium (or oxonium) ion H3 O+ (naked protons do not exist in solution), and so Arrhenius later proposed that the dissociation should be written as an acid–base reaction:

HA + H 2O A − + H 3O+. Brønsted and Lowry generalised this further to a proton exchange reaction: [4][5][6]

acid + base conjugate base + conjugate acid. 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 A− and the conjugate acid is the hydronium ion. The Brønsted–Lowry definition applies to other solvents, such as dimethyl sulfoxide: the solvent S acts as a base, accepting a proton and forming the conjugate acid SH+.

HA + S A − + SH +.

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.

In solution chemistry, it is common to use H+ as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution H+ denotes a solvated hydronium ion rather than a proton.[7][8] The designation of an acid or base as "conjugate" depends on the context. The conjugate acid BH+ of a base B dissociates according to

BH + + OH − B + H 2O which is the reverse of the equilibrium

H 2O (acid) + B (base) OH − (conjugate base) + BH + (conjugate acid). The hydroxide ion 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 hydrolysis, in which protons are produced by the splitting of water molecules. For example, boric acid (B(OH)3 ) produces H3 O+ as if it were a proton donor,[9] but it has been confirmed by Raman spectroscopy that this is due to the hydrolysis equilibrium: [10]

B(OH)3 + 2 H 2O B(OH) 4− + H 3O+. Similarly, metal ion hydrolysis causes ions such as [Al(H2 O)6 ]3+ to behave as weak acids: [11]

[Al(H 2O)6]3+ + H 2O [Al(H 2O)5(OH)]2+ + H 3O+. According to Lewis's original definition, an acid is a substance that accepts an electron pair to form a coordinate covalent bond.[12]

Equilibrium constant An acid dissociation constant is a particular example of an equilibrium constant. For the specific equilibrium between a monoprotic acid, HA and its conjugate base A−, in water,

HA + H 2O A − + H 3O+ can be defined by [13]

the thermodynamic equilibrium constant,

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

is 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 activity coefficient for a derivation of this expression. Since activity is the product of concentration and activity coefficient () the definition could also be written as

where [HA] represents the concentration of HA and is a quotient of activity coefficients. To avoid the complications involved in using activities, dissociation constants are determined, where possible, in a medium of high ionic strength, that is, under conditions in which can be assumed to be always constant.[13] For example, the medium might be a solution of 0.1 molar (M) sodium nitrate or 3 M potassium perchlorate. Furthermore, in all but the most concentrated by the constant terms and writing [H+] for the concentration of the

solutions it can be assumed that the concentration of water, [H2 O], is constant, approximately 55 M. On dividing

Variation of pK a of acetic acid with ionic strength.

hydronium ion the expression

is obtained. This is the definition in common use.[14] pK a is defined as −log 10 (K a). 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 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 specific ion theory (SIT) and other theories.[15] Using the equation as shown K a has dimensions of concentration, but the exact definition uses chemical activities, which can be dimensionless. Therefore, K a, as defined properly, is also dimensionless. But as defined here it is correct to quote a value with a dimension as, for example, "K a = 300 M".

Monoprotic acids After rearranging the expression defining K a, and putting pH = −log 10 [H+], one obtains[16]

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

−

[A ] At half-neutralization [HA] = 1; since log(1) = 0, the pH at half-neutralization is numerically equal to pK a. Conversely, when pH = pK a, the concentration of HA is equal to

Variation of the % formation of a monoprotic acid, AH, and its conjugate base, A −, with the difference between the pH and the pK a of the acid.

the concentration of A −.

−

[A ] 1 The buffer region extends over the approximate range pK a ± 2, though buffering is weak outside the range pK a ± 1. At pK a ± 1, [HA] = 10 or 10 .

If the pH is known, the ratio may be calculated. This ratio is independent of the analytical concentration of the acid. In water, measurable pK a values range from about −2 for a strong acid to about 12 for a very weak acid (or strong base). All acids with a pK a value of less than −2 are more than 99% dissociated at pH 0 (1 M acid). This is known as solvent leveling since all such acids are brought to the same level of being strong acids, regardless of their pK a values. Likewise, all bases with a pK a value larger than the upper limit are more than 99% protonated at all attainable pH values and are classified as strong bases.[5]

An example of a strong acid is hydrochloric acid, HCl, which has a pK a value, estimated from thermodynamic quantities, of −9.3 in water.[17] The concentration of undissociated acid in a 1 M solution will be less than 0.01% of the concentrations of the products of dissociation. Hydrochloric acid is said to be fully dissociated in aqueous solution because the amount of undissociated acid is imperceptible. When the pK a 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. A 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. The pK a of the acid must be less than two units different from the target pH.

Polyprotic acids Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as K a1 and the constants for dissociation of successive protons as K a2 , etc. Phosphoric acid, H3 PO4 , is an example of a polyprotic acid as it can lose three protons. pKa value[18]

Equilibrium H3PO4 H2PO−4 + H+

pK a1 = 2.14

+ H2PO−4 HPO2− 4 + H

pK a2 = 7.20

3− + HPO2− 4 PO4 + H

pK a3 = 12.37

When the difference between successive pK values is about four or more, as in this example, each species may be considered as an acid in its own right; [19] In fact salts of H2 PO−4 may be

Phosphoric acid speciation

crystallised from solution by adjustment of pH to about 5.5 and salts of HPO2− 4 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 5.5 and 10. When the difference between successive pK 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 2.5 to 7.5. According to Pauling's first rule, successive pK values of a given acid increase (pK a2 > pK a1 ).[20] For oxyacids with more than one ionizable hydrogen on the same atom, the pK a values often increase by about 5 units for each proton removed,[21][22] as in the example of phosphoric acid above. In the case of a diprotic acid, H2 A, the two equilibria are

H 2A HA − + H + HA− A 2− + H + it can be seen 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; that is the cause of the trend

% species formation calculated with the program HySS for a 10 millimolar solution of citric acid. pK a1 = 3.13, pK a2 = 4.76, pK a3 = 6.40.

noted above. Phosphoric acid values (above) illustrate this rule, as do the values for vanadic acid, H3 VO4 . When an exception to the rule is found it indicates that a major change in structure

is occurring. In the case of VO2 + (aq), the vanadium is octahedral, 6-coordinate, whereas vanadic acid is tetrahedral, 4-coordinate. This is the basis for an explanation of why pK a1 > pK a2 for vanadium(V) oxoacids. Equilibrium

pKa

[VO2(H2O)4] + H 3VO4 + H+ + 2H2O

pK a1 = 4.2

H3VO4 H2VO−4 + H+

pK a2 = 2.60

+ H2VO−4 HVO2− 4 + H

pK a3 = 7.92

3− + HVO2− 4 VO4 + H

pK a4 = 13.27

Isoelectric point For substances in solution the isoelectric point (pI) 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 pK values. Take the example of glycine, defined as AH. There are two dissociation equilibria to consider.

AH +2 AH + H +; [AH][H +] = K1[AH +2] AH A − + H +; [A−][H +] = K2[AH] Substitute the expression for [AH] into the first equation

[A−][H +]2 = K1K2[AH +2] At the isoelectric point the concentration of the positively charged species, AH2 +, is equal to the concentration of the negatively charged species, A−, so

[H +]2 = K1K2 Therefore, taking cologarithms, the pH is given by

pI values for amino acids are listed at Proteinogenic amino acid#Chemical properties. When more than two charged species are in equilibrium with each other a full speciation calculation may be needed.

Water self-ionization Water possesses both acidic and basic properties and is said to be amphiprotic. The ionization equilibrium can be written

H 2O OH − + H + where in aqueous solution H+ or H+(aq) denotes a solvated proton. Often this is written as the hydronium ion H3 O+, but this formula is not exact because in fact there is solvation by more than one water molecule and species such as H5 O2 +, H7 O3 + and H9 O4 + are also present.[23] The equilibrium constant is given by

When, as is usually the case, the concentration of water can be assumed to be constant, this expression may be replaced by

The self-ionization constant of water, K w, is thus just a special case of an acid dissociation constant. A logarithmic form analogous to pK a may also be defined

pK w values for pure water at various temperatures [24] T (°C)

0

5

10

15

20

25

30

35

40

45

50

pKw

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 fitted to a parabola with

pKw = 14.94 − 0.04209T + 0.0001718T2 From this equation, pK w = 14 at 24.87 °C. At that temperature both hydrogen and hydroxide ions have a concentration of 10 −7 M.

Protonation constants The dissociation of a monoprotic acid can also be described as the protonation of the conjugate base of the acid

A− + H + AH This leads to the definition of an association (protonation) constant, denoted here as Kassociation , as

The dissociation (deprotonation) constant definition can be written as

The definitions show that the values of the two constants are reciprocals of each other and

pKdissociation = log(Kassociation) The situation is a little more complicated with polybasic acids. For example, with phosphoric acid

pKa1 = log(Kassociation,3) pKa2 = log(Kassociation,2) pKa3 = log(Kassociation,1)

Amphoteric substances An amphoteric substance is one that can act as an acid or as a base, depending on pH. Water (above) is amphoteric. Another example of an amphoteric molecule is the bicarbonate ion HCO−3 that is the conjugate base of the carbonic acid molecule H2 CO3 in the equilibrium

H 2CO3 + H 2O HCO−3 + H 3O+ but also the conjugate acid of the carbonate ion CO2− 3 in (the reverse of) the equilibrium

HCO−3 + OH − CO2− 3 + H 2O. Carbonic acid equilibria are important for acid–base homeostasis in the human body. An 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 zwitterion.

NH 2CHRCO2H NH +3CHRCO−2 At pH less than about 5 both the carboxylate group and the amino group are protonated. As pH increases the acid dissociates according to

NH +3CHRCO2H NH +3CHRCO−2 + H + At high pH a second dissociation may take place.

NH +3CHRCO−2 NH 2CHRCO−2 + H + Thus the zwitterion, NH+3CHRCO−2, is amphoteric because it may either be protonated or deprotonated.

Bases and basicity The equilibrium constant K b for a base is usually defined as the association constant for protonation of the base, B, to form the conjugate acid, HB +.

B + H 2O HB + + OH − Using similar reasoning to that used before

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

Substitution of the expression for [OH−] into the expression for K b gives

When K a, K b and K w are determined under the same conditions of temperature and ionic strength, it follows, taking cologarithms, that pK b = pK w − pK a. In aqueous solutions at 25 °C, pK w is 13.9965,[25] so

with sufficient accuracy for most practical purposes. In effect there is no need to define pK b separately from pK a, but it is done here as often only pK b values can be found in the older literature. For metal hydroxides K b can also be defined as the dissociation constant for loss of a hydroxide ion: B(OH) B + + OH− or B(OH)2 B(OH) + + OH−.[26] This is the reciprocal of a stability constant for formation of the complex.

Temperature dependence All equilibrium constants vary with temperature according to the van 't Hoff equation [27]

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

, is negative) K decreases with temperature, but for endothermic reactions (

is positive) K increases

with temperature. The standard enthalpy change for a reaction is itself a function of temperature, according to Kirchhoff's law of thermochemistry:

where ΔC p is the heat capacity change at constant pressure. In practice

may be taken to be constant over a small temperature range.

Acidity in nonaqueous solutions A solvent will be more likely to promote ionization of a dissolved acidic molecule in the following circumstances: [28] 1. It is a protic solvent, capable of forming hydrogen bonds. 2. It has a high donor number, making it a strong Lewis base. 3. It has a high dielectric constant (relative permittivity), making it a good solvent for ionic species. pK a values of organic compounds are often obtained using the aprotic solvents dimethyl sulfoxide (DMSO)[28] and acetonitrile (ACN).[29] Solvent properties at 25 °C Donor number[28]

Dielectric constant[28]

Acetonitrile

14

37

Dimethylsulfoxide

30

47

Water

18

78

Solvent

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, hydrophobic substances more easily. It has a measurable pK a 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 pK a values at 25 °C for acetonitrile (ACN)[30][31][32] and dimethyl sulfoxide (DMSO)[33] are shown in the following tables. Values for water are included for comparison. pK a values of acids HA A − + H+

ACN

DMSO

Water

p-Toluenesulfonic acid

8.5

0.9

strong

2,4-Dinitrophenol

16.66

5.1

3.9

Benzoic acid

21.51

11.1

4.2

Acetic acid

23.51

12.6

4.756

Phenol

29.14

18.0

9.99

ACN

DMSO

Water

Pyrrolidine

19.56

10.8

11.4

Triethylamine

18.82

9.0

10.72

Proton sponge

18.62

7.5

12.1

Pyridine

12.53

3.4

5.2

Aniline

10.62

3.6

4.6

BH+ B + H +

Ionization of acids is less in an acidic solvent than in water. For example, hydrogen chloride is a weak acid when dissolved in acetic acid. This is because acetic acid is a much weaker base than water.

HCl + CH 3CO2H Cl − + CH 3C(OH)+2 acid + base conjugate base + conjugate acid Compare this reaction with what happens when acetic acid is dissolved in the more acidic solvent pure sulfuric acid [34]

H 2SO4 + CH 3CO2H HSO−4 + CH 3C(OH)+2 The unlikely geminal diol species CH3 C(OH)+2 is stable in these environments. For aqueous solutions the pH scale is the most convenient acidity function.[35] Other acidity functions have been proposed for non-aqueous media, the most notable being the Hammett acidity function, H0 , for superacid media and its modified version H− for superbasic media.[36]

In aprotic solvents, oligomers, such as the well-known acetic acid dimer, may be formed by hydrogen bonding. An acid may also form hydrogen bonds to its conjugate base. This process, known as homoconjugation, has the effect of enhancing the acidity of acids, lowering their effective pK a values, by stabilizing the conjugate base. Homoconjugation enhances the proton-donating power of toluenesulfonic acid in acetonitrile solution by a factor of nearly 800.[37] In aqueous solutions, homoconjugation does not occur, because water forms stronger hydrogen bonds to the conjugate base than does the acid.

Mixed solvents

Dimerization of a carboxylic acid.

When a compound has limited solubility in water it is common practice (in the pharmaceutical industry, for example) to determine pK a values in a solvent mixture such as water/dioxane or water/methanol, in which the compound is more soluble.[39] In the example shown at the right, the pK a value rises steeply with increasing percentage of dioxane as the dielectric constant of the mixture is decreasing. A pK a 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 9:1 is precisely that solvent mixture, with no added solutes. To obtain the pK a 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 pK a, but pK a values obtained in a given mixed solvent can be compared to each other, giving relative acid strengths. The same is true of pK a values obtained in a particular non-aqueous solvent such a DMSO. As of 2008, 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.

pK a of acetic acid in dioxane/water mixtures. Data at 25 °C from Pine et al. [38]

Factors that affect pKa values Pauling's second rule is that the value of the first pK a for acids of the formula XOm(OH)n 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 pK a are 8 for m = 0, 2 for m = 1, −3 for m = 2 and < −10 for m = 3.[20] Alternatively, various numerical formulas have been proposed including pK a = 8 − 5m (known as Bell's rule),[21][40]

pK a = 7 − 5m,[22][41] or pK a = 9 − 7m.[21] 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, pK a for HClO is 7.2, for HClO2 is 2.0, for HClO3 is −1 and HClO4 is a strong acid (pK a 0 ).[5] 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.[40] This rule

can help assign molecular structure: for example phosphorous acid (H3 PO3 ) has a pK a near 2 suggested that the structure is HPO(OH)2 , as later confirmed by NMR spectroscopy, and not P(OH)3 which would be expected to have a pK a near 8.[41]

With organic acids inductive effects and mesomeric effects affect the pK a 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 pK a values decrease in the series 4.7, 2.8, 1.4, and 0.7 when 0, 1, 2, or 3 chlorine atoms are present.[42] The Hammett equation, provides a general expression for the effect of substituents.[43]

Fumaric acid

0

log(Ka) = log(Ka) + . 0

K a is the dissociation constant of a substituted compound, K a is the dissociation constant when the substituent is hydrogen, is a property of the unsubstituted compound and has a particular value for each 0

substituent. A plot of log(K a) against is a straight line with intercept log(K a ) and slope . This is an example of a linear free energy relationship as log(K a) is proportional to the standard free energy change.

Hammett originally [44] formulated the relationship with data from benzoic acid with different substiuents 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 electron-withdrawing or electron-releasing power, and to distinguish between inductive and mesomeric effects.[45][46]

Maleic acid

Alcohols do not normally behave as acids in water, but the presence of a double bond adjacent to the OH group can substantially decrease the pK a by the mechanism of keto–enol tautomerism. Ascorbic acid is an example of this effect. The diketone 2,4-pentanedione (acetylacetone) is also a weak acid because of the keto–enol equilibrium. In aromatic compounds, such as phenol, which have an OH substituent, conjugation with the aromatic ring as a whole greatly increases the stability of the deprotonated form. Structural effects can also be important. The difference between fumaric acid and maleic acid is a classic example. Fumaric acid is (E)-1,4-but-2-enedioic acid, a trans 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 pK a values of approximately 3.0 and 4.5. By contrast, maleic acid has pK a 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 intramolecular hydrogen bond is formed with the nearby remaining carboxyl group. This

Proton sponge

favors the formation of the maleate H+, 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.[47] Proton sponge, 1,8-bis(dimethylamino)naphthalene, has a pK a 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.[48][49]

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, Me3 N > Me2 NH > MeNH2 > NH3 , is changed by water to Me2 NH > MeNH2 > Me3 N > NH3 . 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–OH2 . 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–OH2 bonding. Relative stabilization of methylammonium ions thus decreases with the number of methyl groups explaining the order of water basicity of methylamines.[2]

Thermodynamics An equilibrium constant is related to the standard Gibbs energy change for the reaction, so for an acid dissociation constant

. R is the gas constant and T is the absolute temperature. Note that pK a = −log(K a) and 2.303 » ln(10). At 25 °C, ΔG in kJ·mol −1 » 5.708 pK a (1 kJ·mol −1 = 1000 joules per mole). Free energy is made up of an enthalpy term and an entropy term.[9]

The standard enthalpy change can be determined by calorimetry or by using the 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 pK a and ΔH. The data were critically selected and refer to 25 °C and zero ionic strength, in water.[9]

Acids Compound

Equilibrium

pKa

ΔG (kJ·mol −1)

ΔH (kJ·mol −1)

−TΔS (kJ·mol −1)

HA = Acetic acid

HA H + + A −

4.756

27.147[a]

−0.41

27.56[b]

H2A + = GlycineH+

H2A + HA + H +

2.351

13.420

4.00

9.419

HA H + + A −

9.78

55.825

44.20

11.6

H2A HA − + H+

1.92

10.76

1.10

9.85

HA − H + + A 2−

6.27

35.79

−3.60

39.4

H3A H 2A − + H+

3.128

17.855

4.07

13.78

H2A − HA 2− + H+

4.76

27.176

2.23

24.9

HA 2− A 3− + H+

6.40

36.509

−3.38

39.9

H3A = Boric acid

H3A H 2A − + H+

9.237

52.725

13.80

38.92

H3A = Phosphoric acid

H3A H 2A − + H+

2.148

12.261

−8.00

20.26

H2A − HA 2− + H+

7.20

41.087

3.60

37.5

HA 2− A 3− + H+

12.35

80.49

16.00

54.49

HA − = Hydrogen sulfate

HA − A 2− + H+

1.99

11.36

−22.40

33.74

H2A = Oxalic acid

H2A HA − + H+

1.27

7.27

−3.90

11.15

HA − A 2− + H+

4.266

24.351

−7.00

31.35

H2A = Maleic acid

H3A = Citric acid

a. ΔG » 2.303RTpK a b. Computed here, from ΔH and ΔG values supplied in the citation, using −TΔS = ΔG − ΔH Conjugate acids of bases ΔH (kJ·mol −1)

−TΔS (kJ·mol −1)

9.245

51.95

0.8205

HB + B + H +

10.645

55.34

5.422

HB + B + H +

10.72

43.13

18.06

Equilibrium

pKa

B = Ammonia

HB + B + H +

B = Methylamine B = Triethylamine

Compound

The first point to note is that, when pK a 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 ΔH is negative TΔS is the dominant factor, which determines that ΔG is positive. Last, the entropy contribution is always unfavourable (ΔS < 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.[50] The ionization of a neutral acid involves formation of two ions so that the entropy decreases (ΔS < 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 chemical potentials of reactants and products are equal at equilibrium.

Experimental determination The experimental determination of pK a values is commonly performed by means of titrations, in a medium of high ionic strength and at constant temperature.[51] A typical procedure would be as follows. A solution of the compound in the medium is acidified with a strong acid to the point where the compound is fully protonated. The solution is then titrated with a strong base until all the protons have been removed. At each point in the titration pH is measured using a glass electrode and a pH meter. The equilibrium constants are found by fitting calculated pH values to the observed values, using the method of least squares.[52] 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 pK a remains invariant during the titration. A calculated titration curve for oxalic acid is shown at the right. Oxalic acid has pK a values of 1.27 and 4.27. Therefore, the buffer regions will be centered at about pH 1.3 and pH 4.3. The buffer regions carry the information necessary to get the pK a values as the concentrations of acid and conjugate base change along a buffer region. Between the two buffer regions there is an end-point, or equivalence point, at about pH 3. This end-point is not sharp and is typical of a diprotic acid whose buffer regions overlap by a small amount: pK a2 − pK a1 is about three in this example. (If the difference in pK values were about two or less, the end-point would not be noticeable.) The second end-point begins at

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

about pH 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 11 (pK w − 3), which is where self-ionization of water becomes important. It is very difficult to measure pH values of less than two in aqueous solution with a glass electrode, because the Nernst equation breaks down at such low pH values. To determine pK values of less than about 2 or more than about 11 spectrophotometric[53] [54] or NMR [14][55] 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.[31] These may involve absorbance or fluorescence measurements. In both cases the measured quantity is assumed to be proportional to the sum of contributions from each photo-active species; with absorbance measurements the Beer-Lambert law is assumed to apply. Aqueous solutions with normal water cannot be used for 1 H NMR measurements but heavy water, D2 O, must be used instead. 13 C NMR data, however, can be used with normal water and 1 H NMR spectra can be used with nonaqueous media. The quantities measured with NMR are time-averaged chemical shifts, as proton exchange is fast on the NMR time-scale. Other chemical shifts, such as those of 31 P can be measured.

Micro-constants A base such as spermine has a few different sites where protonation can occur. In this example the first proton can go on the terminal –NH2 group, or either of the internal –NH– groups. The pK a values for dissociation of spermine protonated at one or other of the sites are examples of micro-constants. They cannot be determined directly by means of pH, absorbance, fluorescence or NMR measurements. Nevertheless, the site of protonation is very important for biological function, so mathematical methods have been developed for the determination of micro-constants.[56]

Spermine

Applications and significance A knowledge of pK a values is important for the quantitative treatment of systems involving acid–base equilibria in solution. Many applications exist in biochemistry; for example, the pK a values of proteins and amino acid side chains are of major importance for the activity of enzymes and the stability of proteins.[57] Protein pK a 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; [58] the design of these solutions depends on a knowledge of the pK a values of their components. Important buffer solutions include MOPS, which provides a solution with pH 7.2, and tricine, which is used in gel electrophoresis.[59][60] Buffering is an essential part of acid base physiology including acid–base homeostasis,[61] and is key to understanding

disorders such as acid–base imbalance.[62][63][64] The isoelectric point of a given molecule is a function of its pK values, so different molecules have different isoelectric points. This permits a technique called isoelectric focusing,[65] which is used for separation of proteins by 2-D gel polyacrylamide gel electrophoresis. Buffer solutions also play a key role in 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 [66] of a simple buffer solution is largest when pH = pK a. In acid–base extraction, the efficiency of extraction of a compound into an organic phase, such as an 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.[67] A pH indicator is a weak acid or weak base that changes colour in the transition pH range, which is approximately pK a ± 1. The design of a universal indicator requires a mixture of indicators whose adjacent pK a values differ by about two, so that their transition pH ranges just overlap. In pharmacology, ionization of a compound alters its physical behaviour and macro properties such as solubility and lipophilicity, log p). For example, ionization of any compound will increase the solubility in water, but decrease the lipophilicity. This is exploited in drug development to increase the concentration of a compound in the blood by adjusting the pK a of an ionizable group.[68] Knowledge of pK a values is important for the understanding of coordination complexes, which are formed by the interaction of a metal ion, M m+, acting as a Lewis acid, with a 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

[M(H 2O)n]m+ + LH [M(H 2O)n−1L](m−1)+ + H 3O+ To determine the equilibrium constant for this reaction, in which the ligand loses a proton, the pK a of the protonated ligand must be known. In practice, the ligand may be polyprotic; for example EDTA4− can accept four protons; in that case, all pK a values must be known. In addition, the metal ion is subject to hydrolysis, that is, it behaves as a weak acid, so the pK values for the hydrolysis reactions must also be known.[69]

Assessing the hazard associated with an acid or base may require a knowledge of pK a values.[70] For example, hydrogen cyanide is a very toxic gas, because the cyanide ion inhibits the iron-containing enzyme cytochrome c oxidase. Hydrogen cyanide is a weak acid in aqueous solution with a pK a of 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 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 acid–base equilibria are important for lakes[71] and rivers; [72][73] for example, humic acids are important components of natural waters. Another example occurs in chemical oceanography: [74] in order to quantify the solubility of iron(III) in seawater at various salinities, the pK a values for the formation of the iron(III) hydrolysis products Fe(OH)2+, Fe(OH)+2 and Fe(OH)3 were determined, along with the solubility product of iron hydroxide.[75]

Values for common substances There are multiple techniques to determine the pK a 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 °C in water.[5][76] More values can be found in thermodynamics, above. Chemical

Equilibrium

pKa

BH B − + H+

4.17

BH+2 BH + H +

9.65

H3A H 2A − + H+

2.22

H2A − HA 2− + H+

6.98

HA 2− A 3− + H+

11.53

HA = Benzoic acid

HA H + + A −

4.204

HA = Butyric acid

HA H + + A −

4.82

H2A HA − + H+

0.98

HA − A 2− + H+

6.5

B = Codeine

BH+ B + H +

8.17

HA = Cresol

HA H + + A −

10.29

HA = Formic acid

HA H + + A −

3.751

HA = Hydrofluoric acid

HA H + + A −

3.17

HA = Hydrocyanic acid

HA H + + A −

9.21

HA = Hydrogen selenide

HA H + + A −

3.89

HA = Hydrogen peroxide (90%)

HA H + + A −

11.7

HA = Lactic acid

HA H + + A −

3.86

HA = Propionic acid

HA H + + A −

4.87

HA = Phenol

HA H + + A −

9.99

H2A HA − + H+

4.17

HA − A 2− + H+

11.57

BH = Adenine

H3A = Arsenic acid

H2A = Chromic acid

H2A = L-(+)-Ascorbic Acid

See also Acids in wine: tartaric, malic and citric are the principal acids in wine. Ocean acidification: dissolution of atmospheric carbon dioxide affects seawater pH. The reaction depends on total inorganic carbon and on solubility equilibria with solid carbonates such as limestone and dolomite. Grotthuss mechanism: how protons are transferred between hydronium ions and water molecules, accounting for the exceptionally high ionic mobility of the proton (animation). Predominance diagram: relates to equilibria involving polyoxyanions. pK a values are needed to construct these diagrams. Proton affinity: a measure of basicity in the gas phase. 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. Hammett acidity function: a measure of acidity that is used for very concentrated solutions of strong acids, including superacids. Acidosis Alkalosis Arterial blood gas Chemical equilibrium pCO2 pH

Notes 1. Some chemists maintain that a dissociation occurs when two or more ionic species separate from one another (such as occurs during dissolution of an ionic solid) but that the formation of one or more ions is properly an ionization process. Thus, sodium chloride solid dissociates in water whereas hydrogen chloride gas ionizes in water as the former already has an ionic structure whereas the later is a molecular substance with a covalent bond between the hydrogen and chlorine atoms and the gas does not consist of ions: NaCl(s) Õ Na+(aq) + Cl−(aq) HCl(g) + H2O Õ H3O+(aq) + Cl−(aq) From this perspective, K a is actually an acid ionization constant and not an acid dissociation constant, but for most practical purposes, the terms are used interchangeably. 2. pK a is sometimes referred to as an acid dissociation constant, but this is incorrect, strictly speaking, as the constant is K a whereas pK a is the logarithm of the reciprocal of that constant.

References 1. Perrin DD, Dempsey B, Serjeant EP (1981). "Chapter 3: Methods of pK a Prediction". pK a Prediction for Organic Acids and Bases. (secondary). London: Chapman & Hall. pp. 21–26. doi:10.1007/978-94-009-58838 (https://doi.org/10.1007%2F978-94-009-5883-8). ISBN 978-0-412-22190-3. 2. Fraczkiewicz R (2013). "In Silico Prediction of Ionization". In Reedijk J. Reference Module in Chemistry, Molecular Sciences and Chemical Engineering [Online]. (secondary). vol. 5. Amsterdam, The Netherlands: Elsevier. doi:10.1016/B978-0-12-409547-2.02610-X (https://doi.org/10.1016%2FB978-0-12-409547-2.02610-X). 3. Miessler, G. (1991). Inorganic Chemistry (2nd ed.). Prentice Hall. ISBN 0-13-465659-8. Chapter 6: Acid–Base and Donor–Acceptor Chemistry 4. Bell, R.P. (1973). The Proton in Chemistry (2nd ed.). London: Chapman & Hall. ISBN 0-8014-0803-2. Includes discussion of many organic Brønsted acids. 5. 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 6. Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chemistry (3rd ed.). Prentice Hall. ISBN 978-0131755536. Chapter 6: Acids, Bases and Ions in Aqueous Solution 7. Headrick, J.M.; Diken, E.G.; Walters, R. S.; Hammer, N. I.; Christie, R.A.; Cui, J.; Myshakin, E.M.; Duncan, M.A.; Johnson, M.A.; Jordan, K.D. (2005). "Spectral Signatures of Hydrated Proton Vibrations in Water Clusters". Science. 308 (5729): 1765–69. Bibcode:2005Sci...308.1765H (http://adsabs.harvard.edu/abs/2005Sci...308.1765H). doi:10.1126/science.1113094 (https://doi.org/10.1126%2Fscience.1113094). PMID 15961665 (https://www.ncbi.nlm.nih.gov/pubmed/15961665). 8. Smiechowski, M.; Stangret, J. (2006). "Proton hydration in aqueous solution: Fourier transform infrared studies of HDO spectra". J. Chem. Phys. 125 (20): 204508–204522. Bibcode:2006JChPh.125t4508S (http:// adsabs.harvard.edu/abs/2006JChPh.125t4508S). doi:10.1063/1.2374891 (https://doi.org/10.1063%2F1.2374891). PMID 17144716 (https://www.ncbi.nlm.nih.gov/pubmed/17144716). 9. Goldberg, R.; Kishore, N.; Lennen, R. (2002). "Thermodynamic Quantities for the Ionization Reactions of Buffers" (https://web.archive.org/web/20081006062140/https://www.nist.gov/data/PDFfiles/jpcrd615.pdf) (PDF). J. Phys. Chem. Ref. Data. 31 (2): 231–370. Bibcode:1999JPCRD..31..231G (http://adsabs.harvard.edu/abs/1999JPCRD..31..231G). doi:10.1063/1.1416902 (https://doi.org/10.1063%2F1.1416902). Archived from the original (https://www.nist.gov/data/PDFfiles/jpcrd615.pdf) (PDF) on 2008-10-06. 10. Jolly, William L. (1984). Modern Inorganic Chemistry. McGraw-Hill. p. 198. ISBN 978-0-07-032760-3. 11. Burgess, J. (1978). Metal Ions in Solution. Ellis Horwood. ISBN 0-85312-027-7. Section 9.1 "Acidity of Solvated Cations" lists many pK a values. 12. Petrucci, R.H.; Harwood, R.S.; Herring, F.G. (2002). General Chemistry (8th ed.). Prentice Hall. ISBN 0-13-014329-4. p.698 13. Rossotti, F.J.C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw–Hill. Chapter 2: Activity and Concentration Quotients 14. Popov, K.; Ronkkomaki, H.; Lajunen, L.H.J. (2006). "Guidelines for NMR Measurements for Determination of High and Low pK a Values" (http://media.iupac.org/publications/pac/2006/pdf/7803x0663.pdf) (PDF). Pure Appl. Chem. 78 (3): 663–675. doi:10.1351/pac200678030663 (https://doi.org/10.1351%2Fpac200678030663). 15. "Project: Ionic Strength Corrections for Stability Constants" (https://web.archive.org/web/20081029193538/http://www.iupac.org/web/ins/2000-003-1-500). International Union of Pure and Applied Chemistry. Archived from the original (http://www.iupac.org/web/ins/2000-003-1-500) on 29 October 2008. Retrieved 2008-11-23. 16. Mehta, Akul. "Henderson–Hasselbalch Equation: Derivation of pK a and pK b" (http://pharmaxchange.info/press/2012/10/henderson%E2%80%93hasselbalch-equation-derivation-of-pka-and-pkb/). PharmaXChange. Retrieved 16 November 2014. 17. Dasent, W.E. (1982). Inorganic Energetics: An Introduction. Cambridge University Press. ISBN 0-521-28406-6. Chapter 5 18. The values are for 25 °C and zero ionic strength — Powell, Kipton J.; Brown, Paul L.; Byrne, Robert H.; Gajda, Tamás; Hefter, Glenn; Sjöberg, Staffan; Wanner, Hans (2005). "Chemical speciation of 2− 2− 3− environmentally significant heavy metals with inorganic ligands. Part 1: The Hg2+ , Cl− , OH− , CO3 , SO4 , and PO4 aqueous systems". Pure Appl. Chem. 77 (4): 739–800. doi:10.1351/pac200577040739 (https: //doi.org/10.1351%2Fpac200577040739). 19. 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. 20. Greenwood, N.N.; Earnshaw, A. (1997). Chemistry of the Elements (2nd ed.). Oxford: Butterworth-Heinemann. p. 50. ISBN 0-7506-3365-4. 21. Miessler, Gary L.; Tarr Donald A. (1999). Inorganic Chemistry (2nd ed.). Prentice Hall. p. 164. ISBN 0-13-465659-8. 22. Huheey, James E. (1983). Inorganic Chemistry (3rd ed.). Harper & Row. p. 297. ISBN 0-06-042987-9. 23. Housecroft, C. E.; Sharpe, A. G. (2004). Inorganic Chemistry (2nd ed.). Prentice Hall. p. 163. ISBN 978-0130399137. 24. Harned, H.S.; Owen, B.B (1958). The Physical Chemistry of Electrolytic Solutions. New York: Reinhold Publishing Corp. pp. 634–649, 752–754. 25. Lide, D.R. (2004). CRC Handbook of Chemistry and Physics, Student Edition (84th ed.). CRC Press. ISBN 0-8493-0597-7. Section D–152 26. ChemBuddy dissociation constants pK a and pK b (http://www.chembuddy.com/?left=BATE&right=dissociation_constants) 27. Atkins, P.W.; de Paula, J. (2006). Physical Chemistry. Oxford University Press. ISBN 0-19-870072-5. Section 7.4: The Response of Equilibria to Temperature 28. Loudon, G. Marc (2005), Organic Chemistry (4th ed.), New York: Oxford University Press, pp. 317–318, ISBN 0-19-511999-1 29. March, J.; Smith, M. (2007). Advanced Organic Chemistry (6th ed.). New York: John Wiley & Sons. ISBN 978-0-471-72091-1. Chapter 8: Acids and Bases 30. 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.; Röschenthaler, G-V.; Koppel, I.A.; Kolomeitsev, A.A. (2008). "Pentakis(trifluoromethyl)phenyl, a Sterically Crowded and Electron-withdrawing Group: Synthesis and Acidity of Pentakis(trifluoromethyl)benzene, -toluene, -phenol, and aniline". J. Org. Chem. 73 (7): 2607–2620. doi:10.1021/jo702513w (https://doi.org/10.1021%2Fjo702513w). PMID 18324831 (https://www.ncbi.nlm.nih.gov/pubmed/18324831). 31. Kütt, A.; Leito, I.; Kaljurand, I.; Sooväli, L.; Vlasov, V.M.; Yagupolskii, L.M.; Koppel, I.A. (2006). "A Comprehensive Self-Consistent Spectrophotometric Acidity Scale of Neutral Brønsted Acids in Acetonitrile". J. Org. Chem. 71 (7): 2829–2838. doi:10.1021/jo060031y (https://doi.org/10.1021%2Fjo060031y). PMID 16555839 (https://www.ncbi.nlm.nih.gov/pubmed/16555839). 32. 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 Acetonitrile to a Full Span of 28 pKa Units: Unification of Different Basicity Scales". J. Org. Chem. 70 (3): 1019–1028. doi:10.1021/jo048252w (https://doi.org/10.1021%2Fjo048252w). PMID 15675863 (https://www.ncbi.nlm.nih.gov/pubmed/15675863). 33. "Bordwell pKa Table (Acidity in DMSO)" (https://web.archive.org/web/20081009060809/http://www.chem.wisc.edu/areas/reich/pkatable/). Archived from the original (http://www.chem.wisc.edu/areas/reich/pkatable/ ) on 9 October 2008. Retrieved 2008-11-02. 34. Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chemistry (3rd ed.). Prentice Hall. ISBN 978-0131755536. Chapter 8: Non-Aqueous Media 35. Rochester, C.H. (1970). Acidity Functions. Academic Press. ISBN 0-12-590850-4. 36. Olah, G.A; Prakash, S; Sommer, J (1985). Superacids. New York: Wiley Interscience. ISBN 0-471-88469-3. 37. Coetzee, J.F.; Padmanabhan, G.R. (1965). "Proton Acceptor Power and Homoconjugation of Mono- and Diamines". J. Am. Chem. Soc. 87 (22): 5005–5010. doi:10.1021/ja00950a006 (https://doi.org/10.1021%2Fja 00950a006). 38. Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). "Organic chemistry". McGraw–Hill: 203. ISBN 0-07-050115-7. 39. Box, K.J.; Völgyi, G.; Ruiz, R.; Comer, J.E.; Takács-Novák, K.; Bosch, E.; Ràfols, C.; Rosés, M. (2007). "Physicochemical Properties of a New Multicomponent Cosolvent System for the pKa Determination of Poorly Soluble Pharmaceutical Compounds". Helv. Chim. Acta. 90 (8): 1538–1553. doi:10.1002/hlca.200790161 (https://doi.org/10.1002%2Fhlca.200790161). 40. Housecroft, Catherine E.; Sharpe, Alan G. (2005). Inorganic chemistry (2nd ed.). Harlow, U.K.: Pearson Prentice Hall. pp. 170–171. ISBN 0130-39913-2. 41. 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 42. Pauling, L. (1960). The nature of the chemical bond and the structure of molecules and crystals; an introduction to modern structural chemistry (3rd ed.). Ithaca (NY): Cornell University Press. p. 277. ISBN 08014-0333-2. 43. Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). Organic Chemistry. McGraw–Hill. ISBN 0-07-050115-7. Section 13-3: Quantitative Correlations of Substituent Effects (Part B) – The Hammett Equation 44. Hammett, L.P. (1937). "The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives". J. Am. Chem. Soc. 59 (1): 96–103. doi:10.1021/ja01280a022 (https://doi.org/10.1021%2Fja01280 a022). 45. Hansch, C.; Leo, A.; Taft, R. W. (1991). "A Survey of Hammett Substituent Constants and Resonance and Field Parameters". Chem. Rev. 91 (2): 165–195. doi:10.1021/cr00002a004 (https://doi.org/10.1021%2Fcr 00002a004). 46. Shorter, J (1997). "Compilation and critical evaluation of structure-reactivity parameters and equations: Part 2. Extension of the Hammett scale through data for the ionization of substituted benzoic acids in aqueous solvents at 25 °C (Technical Report)". Pure and Applied Chemistry. 69 (12): 2497–2510. doi:10.1351/pac199769122497 (https://doi.org/10.1351%2Fpac199769122497). 47. 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 Acidity and Basicity 48. Alder, R.W.; Bowman, P.S.; Steele, W.R.S.; Winterman, D.R. (1968). "The Remarkable Basicity of 1,8-bis(dimethylamino)naphthalene". Chem. Commun. (13): 723–724. doi:10.1039/C19680000723 (https://doi.org/ 10.1039%2FC19680000723). 49. Alder, R.W. (1989). "Strain Effects on Amine Basicities". Chem. Rev. 89 (5): 1215–1223. doi:10.1021/cr00095a015 (https://doi.org/10.1021%2Fcr00095a015). 50. Atkins, Peter William; De Paula, Julio (2006). Atkins' physical chemistry. New York: W H Freeman. p. 94. ISBN 9780716774334. 51. Martell, A.E.; Motekaitis, R.J. (1992). Determination and Use of Stability Constants. Wiley. ISBN 0-471-18817-4. Chapter 4: Experimental Procedure for Potentiometric pH Measurement of Metal Complex Equilibria 52. Leggett, D.J. (1985). Computational Methods for the Determination of Formation Constants. Plenum. ISBN 0-306-41957-2. 53. Allen, R.I.; Box,K.J.; Comer, J.E.A.; Peake, C.; Tam, K.Y. (1998). "Multiwavelength Spectrophotometric Determination of Acid Dissociation Constants of Ionizable Drugs". J. Pharm. Biomed. Anal. 17 (4–5): 699– 712. doi:10.1016/S0731-7085(98)00010-7 (https://doi.org/10.1016%2FS0731-7085%2898%2900010-7). 54. 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-Wavelength UV and NMR pH Titrimetric Study of the MicroSpeciation of SKI-606". J. Pharm. Biomed. Anal. 47 (2): 303–311. doi:10.1016/j.jpba.2008.01.015 (https://doi.org/10.1016%2Fj.jpba.2008.01.015). PMID 18314291 (https://www.ncbi.nlm.nih.gov/pubmed/18314291). 55. Szakács, Z.; Hägele, G. (2004). "Accurate Determination of Low pK Values by 1H NMR Titration". Talanta. 62 (4): 819–825. doi:10.1016/j.talanta.2003.10.007 (https://doi.org/10.1016%2Fj.talanta.2003.10.007). PMID 18969368 (https://www.ncbi.nlm.nih.gov/pubmed/18969368). 56. Frassineti, C.; Alderighi, L; Gans, P; Sabatini, A; Vacca, A; Ghelli, S. (2003). "Determination of Protonation Constants of Some Fluorinated Polyamines by Means of 13C NMR Data Processed by the New Computer Program HypNMR2000. Protonation Sequence in Polyamines". Anal. Bioanal. Chem. 376 (7): 1041–1052. doi:10.1007/s00216-003-2020-0 (https://doi.org/10.1007%2Fs00216-003-2020-0). PMID 12845401 (https://www.ncbi.nlm.nih.gov/pubmed/12845401). 57. Onufriev, A.; Case, D.A; Ullmann G.M. (2001). "A Novel View of pH Titration in Biomolecules". Biochemistry. 40 (12): 3413–3419. doi:10.1021/bi002740q (https://doi.org/10.1021%2Fbi002740q). PMID 11297406 ( https://www.ncbi.nlm.nih.gov/pubmed/11297406). 58. Good, N.E.; Winget, G.D.; Winter, W.; Connolly, T.N.; Izawa, S.; Singh, R.M.M. (1966). "Hydrogen Ion Buffers for Biological Research". Biochemistry. 5 (2): 467–477. doi:10.1021/bi00866a011 (https://doi.org/10.1 021%2Fbi00866a011). PMID 5942950 (https://www.ncbi.nlm.nih.gov/pubmed/5942950). 59. Dunn, M.J. (1993). Gel Electrophoresis: Proteins. Bios Scientific Publishers. ISBN 1-872748-21-X. 60. Martin, R. (1996). Gel Electrophoresis: Nucleic Acids. Bios Scientific Publishers. ISBN 1-872748-28-7. 61. Brenner, B.M.; Stein, J.H., eds. (1979). Acid–Base and Potassium Homeostasis. Churchill Livingstone. ISBN 0-443-08017-8. 62. Scorpio, R. (2000). Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems. Kendall/Hunt Pub. Co. ISBN 0-7872-7374-0. 63. Beynon, R.J.; Easterby, J.S. (1996). Buffer Solutions: The Basics. Oxford: Oxford University Press. ISBN 0-19-963442-4. 64. Perrin, D.D.; Dempsey, B. (1974). Buffers for pH and Metal Ion Control. London: Chapman & Hall. ISBN 0-412-11700-2. 65. Garfin, D.; Ahuja, S., eds. (2005). Handbook of Isoelectric Focusing and Proteomics. 7. Elsevier. ISBN 0-12-088752-5. 66. Hulanicki, A. (1987). Reactions of Acids and Bases in Analytical Chemistry. Masson, M.R. (translation editor). Horwood. ISBN 0-85312-330-6. 67. Eyal, A.M (1997). "Acid Extraction by Acid–Base-Coupled Extractants". Ion Exchange and Solvent Extraction: A Series of Advances. 13: 31–94. 68. Avdeef, A. (2003). Absorption and Drug Development: Solubility, Permeability, and Charge State. New York: Wiley. ISBN 0-471-42365-3. 69. Beck, M.T.; Nagypál, I. (1990). Chemistry of Complex Equilibria. Horwood. ISBN 0-85312-143-5. 70. van Leeuwen, C.J.; Hermens, L. M. (1995). Risk Assessment of Chemicals: An Introduction. Springer. pp. 254–255. ISBN 0-7923-3740-9. 71. 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. Chapter 9-6: Acid Rain and the Buffer Capacity of Lakes 72. Stumm, W.; Morgan, J.J. (1996). Water Chemistry. New York: Wiley. ISBN 0-471-05196-9. 73. Snoeyink, V.L.; Jenkins, D. (1980). Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters. New York: Wiley. ISBN 0-471-51185-4. 74. Millero, F.J. (2006). Chemical Oceanography (3rd ed.). London: Taylor and Francis. ISBN 0-8493-2280-4. 75. Millero, F.J.; Liu, X. (2002). "The Solubility of Iron in Seawater". Marine chemistry. 77 (1): 43–54. doi:10.1016/S0304-4203(01)00074-3 (https://doi.org/10.1016%2FS0304-4203%2801%2900074-3). 76. Speight, J.G. (2005). Lange's Handbook of Chemistry (18th ed.). McGraw–Hill. ISBN 0-07-143220-5. Chapter 8

Further reading Albert, A.; Serjeant, E.P. (1971). The Determination of Ionization Constants: A Laboratory Manual. Chapman & Hall. ISBN 0-412-10300-1. (Previous edition published as Ionization constants of acids and bases. London (UK): Methuen. 1962.) Atkins, P.W.; Jones, L. (2008). Chemical Principles: The Quest for Insight (4th ed.). W.H. Freeman. ISBN 1-4292-0965-8. Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chemistry (3rd ed.). Prentice Hall. ISBN 978-0131755536. (Non-aqueous solvents) Hulanicki, A. (1987). Reactions of Acids and Bases in 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. Chapman & Hall. ISBN 0-412-22190-X. Reichardt, C. (2003). Solvents and Solvent Effects in Organic Chemistry (3rd ed.). Wiley-VCH. ISBN 3-527-30618-8. Chapter 4: Solvent Effects on the Position of Homogeneous Chemical Equilibria. 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.

External links Acidity–Basicity Data in Nonaqueous Solvents (http://tera.chem.ut.ee/~ivo/HA_UT/) Extensive bibliography of pK a values in DMSO, acetonitrile, THF, heptane, 1,2-dichloroethane, and in the gas phase Curtipot (http://www2.iq.usp.br/docente/gutz/Curtipot_.html) All-in-one freeware for pH and acid–base equilibrium calculations and for simulation and analysis of potentiometric titration curves with spreadsheets SPARC Physical/Chemical property calculator (https://web.archive.org/web/20070312045609/http://sparc.chem.uga.edu/) Includes a database with aqueous, non-aqueous, and gaseous phase pK a values than can be searched using SMILES or CAS registry numbers Aqueous-Equilibrium Constants (https://web.archive.org/web/20070205181504/http://jesuitnola.org/upload/clark/Refs/aqueous.htm) pK a values for various acid and bases. Includes a table of some solubility products Free guide to pK a and log p interpretation and measurement (http://www.raell.demon.co.uk/chem/logp/logppka.htm) Explanations of the relevance of these properties to pharmacology Free online prediction tool (Marvin) (https://web.archive.org/web/20090331121853/http://chemaxon.com/marvin/sketch/index.jsp) pK a, log p, log d etc. From ChemAxon Chemicalize.org:List of predicted structure based properties Evans pK a Chart [1] (http://evans.rc.fas.harvard.edu/pdf/evans_pKa_table.pdf) Retrieved from "https://en.wikipedia.org/w/index.php?title=Acid_dissociation_constant&oldid=838885971"

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