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October 28th, 2008

“pKa” redirects here. For other uses, see pKa (disambiguation).

The weak acid acetic acid donates a proton to water in an equilibrium reaction to give the acetate ion and the hydronium ion. Key: Hydrogen is white, oxygen is red, carbon is gray. Lines are chemical bonds.

An acid dissociation constant, Ka, (aka acidity constant, acid-ionization constant) is a quantitative measure of the strength of an acid in solution: the larger the value the stronger the acid and the more the acid is dissociated, at a given concentration, into its conjugate base and the hydrogen ion.

Ka is an equilibrium constant. For an equilibrium between a generic acid, HA, and its conjugate base, A−, HA A− + H+, Ka is defined, subject to certain conditions, as

where are equilibrium concentrations of the reactants.

The term acid dissociation constant is also used for pKa, which is equal to −log10 Ka. As Ka increases pKa decreases. In aqueous solution, acids that release a single proton are partially dissociated to an appreciable extent in the pH range pKa ± 2. The actual extent of the dissociation can be calculated if the acid concentration and pH are known.

The term pKb is used in relation to bases, though pKb has faded from modern use due to the easy relationship available between pKb and pKa, the strength of its conjugate acid. Though discussions of this topic typically assume water as the solvent, particularly at introductory levels, the Brønsted–Lowry acid-base theory is versatile enough that acidic behavior can now be characterized even in non-aqueous solutions.

A knowledge of pKa values is essential for the understanding of the behaviour of acids and bases in solution. For example, many compounds used for medication are weak acids or bases, so a knowledge of the pKa and log p values is essential for an understanding of how the compound enters (or does not enter) the blood stream. Other applications include aquatic chemistry, chemical oceanography, buffer solutions, acid-base homeostasis and certain kinds of enzyme kinetics, such as Michaelis–Menten kinetics, which involve a pre-equilibrium step. Also, knowledge of pKa values is a prerequisite for a quantitative understanding of the interaction between acids or bases and metal ions to form complexes in solution.

Acids and bases:

Acid dissociation constant
Acid-base extraction
Acid-base reaction
Acid-base catalysis
Acid-base physiology
Acid-base homeostasis
Acidity function
Buffer solution
Dissociation constant
Non-nucleophilic base
pH
Proton affinity
Self-ionization of water

  Lewis acid/base
  Mineral acid/base
  Organic acid/base
  Weak acid/base
  Strong acid/base
  Super acid/base

Contents

1 Definitions
2 Equilibrium Constant
3 Acidity in nonaqueous solutions
- 3.1 Mixed solvents
4 Factors that determine the relative strengths of acids
- 4.1 Thermodynamics
5 Experimental determination of pKa values
6 Importance of pKa values
7 pKa of some common substances
8 See also
9 References
10 Further reading
11 External links

Definitions

Concepts in
Chemical Equilibria

Acid dissociation constant

Binding constant

Buffer solution

Chemical equilibrium

Chemical stability

Dissociation constant

Distribution coefficient

Distribution ratio

Equilibrium constant

Equilibrium unfolding

Equilibrium stage

Liquid-liquid extraction

Phase diagram

Phase rule

Reaction quotient

Relative volatility

Solubility equilibrium

Stability constant

Thermodynamic equilibrium

Theoretical plate

Vapor-liquid equilibrium

edit

According to Arrhenius’s original definition, an acid is a substance which dissociates in aqueous solution, releasing the hydrogen ion.

HA A− + H+

The equilibrium constant for this “dissociation” reaction is known as a dissociation constant. However, since the liberated proton combines with a water molecule to give an hydronium ion, Arrhenius proposed that the “dissociation” reaction should be written as an acid-base reaction.

HA + H2O A− + H3O+

Brønsted and Lowry generalized this definition as a proton exchange reaction, as follows.

acid + base conjugate base + conjugate acid

The acid donates a proton to the base. The conjugate base is what is left after the acid has lost a proton and the conjugate acid is created when the base gains a proton. For aqueous solutions an acid, HA, reacts with the base, water, donating a proton to it, creating the conjugate base, A−, and the conjugate acid, the hydronium ion. The Brønsted–Lowry definition is particularly useful when the solvent is a substance other than water, such as dimethyl sulfoxide; in that case the solvent, S, acts as a base, accepting a proton and forming the conjugate acid SH+. It also puts acids and bases on the same footing as being, respectively, donors or acceptors of protons. The conjugate acid of a base, B, “dissociates” according to

BH+ + OH− B + H2O

For example:

H2CO3 + H2O HCO3− + H3O+

The bicarbonate ion is the conjugate base of carbonic acid.

HCO3− + OH− CO32− + H2O

and the bicarbonate ion is also the conjugate acid of the base, the carbonate ion. In fact the bicarbonate ion is amphiprotic. These reactions are important for acid-base homeostasis in the human body (see carbonic acid).

Any compound subject to an hydrolysis equilibrium can also be classed as a weak acid since, in hydrolysis, protons are produced by the splitting of water molecules. For example, the equilibrium

B(OH)3 + 2 H2O B(OH)4- + H3O+

shows why boric acid behaves as a weak acid even though it is not, itself, a proton donor. In a similar way, metal ion hydrolysis causes ions such as

It is important to note that, in the context of solution chemistry, a “proton” is understood to mean a solvated hydrogen ion. In aqueous solution the “proton” is a solvated hydronium ion.

Equilibrium Constant

Main article: 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 + H2O A− + H3O+

the thermodynamic equilibrium constant, Kt can be defined by

where {A} is the activity of the chemical species A etc (activity is a dimensionless quantity). Activities of the products are placed in the numerator, activities of the reactants are placed in the denominator. See Chemical equilibrium for a derivation of this expression.

Variation of pKa of acetic acid with ionic strength

Since activity is the product of concentration and activity coefficient the definition could also be written as

where represents the concentration of HA and Γ is a quotient of activity coefficients.

In order 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 Γ can be assumed to be always constant., is constant, approximately 55 mol dm−3, and that the hydration of the proton can also be assumed to be constant.

Leaving out the constant terms, the acid dissociation constant can be defined as a concentration quotient.

This is the definition in common use. pKa is defined as −log10 Ka. 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.

When operating under the assumption that Γ is constant, the equilibrium constant does not change upon the addition of other chemicals to the solution. This assumption holds true when the concentration of spectator ions is low relative to the concentrations of other ions in the system. This allows, for example, for the behaviour of various ions to be explored at various pH values without worry that the equilibrium constant will also change. By exploiting this property, it is possible to obtain very complicated buffer solutions composed of many protonations of the same anion. This is accomplished with the addition of a strong acid to a solution of the anion. The conjugate base of the strong acid will act as a spectator ion, and the weak-base anion will be free to react with the proton as the equilibrium constant dictates.

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

Monoprotic acids

After rearranging the expression defining Ka, and putting pH = −log10, one obtains

pH = pKa – log ( )

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

At half-neutralization = 1; since log(1) =0 , the pH at half neutralization is numerically equal to pKa.
The buffer region extends over the approximate range pKa ± 2, though buffering is weak outside the range pKa ± 1. At pKa ± 1 =10 or 1/10.
if the pH is known the ratio may be calculated. This ratio is independent of the analytical concentration of the acid.

In water, measurable pKa values range from about –2 for a strong acid to about 12 for a very weak acid (or strong base). Any acid with a pKa value of less than -2 is more than 99% dissociated at pH 0 (1M acid). Any base with a pKa value larger than the upper limit is “fully” de-protonated at all attainable pH values. This is known as solvent leveling.

An example of a strong acid is hydrochloric acid, HCl, which has a pKa value, estimated from thermodynamic quantities, of –9.3 in water. The concentration of undissociated acid in a 1 mol dm-3 solution, will be less than 10-4 mol dm-3. In common parlance this is known as complete dissociation.

The extent of dissociation and pH of a solution of a monoprotic acid can be easily calculated when the pKa and analytical concentration of the acid are known. See ICE table for details.

Polyprotic acids

% species’ formation as a function of pH

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

Polyprotic acids are acids which can lose more than one proton. The constant for dissociation of the first proton may be denoted as Ka1 and the constants for dissociation of successive protons as Ka2, etc.

When the difference between successive pK values is about four or more, each species may be considered as an acid in its own right; the pH range of existence of each species is about pK± 2, so there is very little overlap between the ranges for successive species. The case of phosphoric acid illustrates this point. In fact salts of either H2PO4− or HPO42− may be crystallized from solution by adjustment of pH to either 4 or 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.

It is generally true that successive pK values increase (Pauling’s first rule). For example, for a diprotic acid, H2A, the two equilibria are

H2A HA− + H+
HA− A2− + 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 noted above. Phosphoric acid, H3PO4, (values below), illustrates this rule, as does vanadic acid. 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 all the other species are tetrahedral, 4-coordinate. This explains why pKa1 > pKa2 for vanadium(V) oxoacids.

VO2+ H3VO4 + H+
pKa1 = 4.2

H3PO4 H2PO4− + H+
pKa1 = 2.15
H3VO4 H2VO4− + H+
pKa2 = 2.60

H2PO4− HPO42− + H+
pKa2 = 7.20
H2VO4− HVO42− + H+
pKa3 = 7.92

HPO42− PO43− + H+
pKa3 = 12.37
HVO42− VO43− + H+
pKa4 = 13.27

Water self-ionization

Main article: Self-ionization of water

Water has both acidic and basic properties. The equilibrium constant for the equilibrium

H2O + H2O OH− + H3O+

is given by

Since the concentration of water can be assumed to be constant, this expression simplifies to

The self-ionization constant of water, Kw, can thus be seen as a special case of an acid dissociation constant.

Bases

Main article: Base (chemistry)

Historically the equilibrium constant Kb for a base was defined as the association constant for protonation of the base, B, to form the conjugate acid, HB+.

B + H2O HB+ + OH−

Using similar reasoning to that used before

In water, the concentration of the hydroxide ion, , therefore

Substitution of the expression for into the expression for Kb gives

It follows, taking cologarithms, that pKb = pKw – pKa. In aqueous solutions at 25 °C, pKw is 13.9965, so pKb ~ 14 – pKa.

In effect there is no need to define pKb separately from pKa, but it is done here because pKb values can be found in the older literature.

Temperature dependence

Main article: Van ‘t Hoff equation

All equilibrium constants vary with temperature according to the van ‘t Hoff equation

R is the gas constant and T is the temperature /Kelvin. Thus, for exothermic reactions, (ΔHo is negative) K decreases with temperature, but for endothermic reactions (ΔHo is positive) K increases with temperature.

Acidity in nonaqueous solutions

A solvent will be more likely to promote ionization of a dissolved acidic molecule in the following circumstances.

It is a protic solvent, capable of forming hydrogen bonds.
It has a high donor number, making it a strong Lewis base.
it has a high dielectric constant (relative permittivity), making it a good solvent for ionic species.

pKa values of organic compounds are often obtained using the aprotic sovents dimethyl sulfoxide (DMSO) Methanol may be used when a protic solvent is preferable.

Solvent properties at 25oC

Solvent
Donor number
Dielectric constant

Acetonitrile
14
37

Dimethylsulfoxide
30
47

Water
18
78

DMSO is widely used as an alternative to water because it has a lower dielectric constant than water, it is less polar and so dissolves non-polar, hydrophobic substances more easily. It has a measurable pKa range of about 1 to 30. Acetonitrile is less basic than DMSO and so acids are generally weaker and bases are generally stronger in this solvent. Some pKa values at 25oC for acetonitrile (AN) are shown in the following tables. Values for water are included for comparison.

HA A− + H+
AN
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

BH+ B + H+
AN
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
9.4

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 + CH3CO2H Cl− + CH3C(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 sulphuric acid

H2SO4 + CH3CO2H HSO4− + CH3C(OH)2+

The apparently unlikely geminal diol species CH3C(OH)2+ is stable in these environments.

In solvents of low dielectric constant ions tend to associate forming ion pairs and clusters, which complicates the interpretation of pKa values.

dimerization of a carboxylic acid

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 is known as homoconjugation. Homoconjugation has the effect of enhancing the acidity of acids, lowering their effective pKa values, by stabilizing the conjugate base. Due to homoconjugation, the proton-donating power of toluenesulfonic acid in acetonitrile solution is enhanced by a factor of nearly 800.

Homoconjugation does not occur in aqueous solutions because water forms stronger hydrogen bonds to the conjugate base than does the acid.

Mixed solvents

Data at 25oC from

When a compound has limited solubility in water it is common practice (in the pharmaceutical industry, for example) to determine pKa values in a solvent mixture such as water/dioxane or water/methanol, in which the compound is more soluble. In the example shown at the right, the pKa value rises steeply with increasing percentage of dioxane as the dielectric constant of the mixture is decreasing.

A pKa 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 pKa 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 which is normally used to define pKa, but pKa values obtained in a given mixed solvent can be compared to each other, giving relative acid strengths. The same is true of pKa values obtained in a particular non-aqueous solvent such a DMSO.

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

^ a b Miessler, G. (1991). Inorganic Chemistry, 2nd edition, Prentice Hall, 165. ISBN 0134656598.
^ Burgess, J. (1978). Metal ions in solution. Ellis Horwood. ISBN 0853120277. Section 9.1, “Acidity of solvated cations”, lists many pKa values.
^ Headrick, Jeffrey M.; Eric G. Diken, Richard S. Walters, Nathan I. Hammer, Richard A. Christie, Jun Cui, Evgeniy M. Myshakin, Michael A. Duncan,* Mark A. Johnson, Kenneth D. Jordan (2005). “Spectral Signatures of Hydrated Proton Vibrations in Water Clusters”. Science 308: 1765 - 1769. DOI: 10.1126/science.1113094
^ Smiechowski, M.; Stangret J. (2006). “Proton hydration in aqueous solution: Fourier transform infrared studies of HDO spectra”. J. Chem. Phys.: 204508-204522. DOI:10.1063/1.2374891
^ a b Rossotti, F.J.C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw-Hill.
^ Shriver, D.F; Atkins, P.W. (1999). Inorganic Chemistry, third edition, Oxford: Oxford University Press. ISBN 0198503318. Section 5.2
^ Dasent, W.E. (1982). Inorganic energetics : an introduction. Cambridge University Press. ISBN 0521284066.
^ Brown, T.E.; Lemay, H.E.; Bursten, B.E. (2009). Chemistry The Central Science, 11th Edition, Pearson Publications. ISBN 0131096869. p. 689
^ Greenwood, Norman N.; Earnshaw, A. (1997). Chemistry of the Elements, 2nd Edition, Oxford: Butterworth-Heinemann. ISBN 0-7506-3365-4. p. 50
^ Lide, D.R. (2004). CRC Handbook of Chemistry and Physics, Student Edition, 84th. ed., CRC press. ISBN 0849305977.
^ Atkins, P.W.; de Paula, J. (2006). Physical chemistry. Oxford University Press. ISBN 0198700725. p 212
^ a b c d Loudon, G.M. (2005). Organic Chemistry, 4th Edition, New York: Oxford University Press. ISBN 0-19-511999-1. p. 317–318
^ March, J.; Smith, M. (2007). Advanced Organic Chemistry, 6th edition, New York: J. Wiley and Sons. ISBN 978-0-471-72091-1.
^ Kütt, Agnes; Valeria Movchun, Toomas Rodima, Timo Dansauer, Eduard B. Rusanov, Ivo Leito, Ivari Kaljurand, Juta Koppel, Viljar Pihl, Ivar Koppel, Gea Ovsjannikov, Lauri Toom, Masaaki Mishima, Maurice Medebielle, Enno Lork, Gerd-Volker Röschenthaler, Ilmar A. Koppel, and Alexander A. Kolomeitsev (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
^ Kütt, Agnes; Ivo Leito, Ivari Kaljurand, Lilli Sooväli, Vladislav M. Vlasov, Lev M. Yagupolskii, and Ilmar A. Koppel (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
^ 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
^ Bordwell pKa Table in DMSO
^ Housecroft, C.E.; Sharpe, A.G. (2008). Inorganic chemistry, 3rd. ed., Prentice Hall. ISBN 0131755536. Chapter 8
^ Coetzee, J. F. and Padmanabhan, G. R. (1965). “Proton Acceptor Power and Homoconjugation of Mono- and Diamines”. J. Amer. Chem. Soc. 87: 5005–5010. doi:10.1021/ja00950a006.
^ Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). Organic chemistry. McGraw Hill. ISBN 0070501157. p 203
^ 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.

Factors that determine the relative strengths of acids

Pauling’s second rule states that the value of the first pKa for acids of the formula XOm(OH) n is approximately independent of n and X and is approximately 8 for m = 0, 2 for m = 1, −3 for m = 2 and < −10 for m = 3. This 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, for HClO3 is −1 and HClO4 is a strong acid.

fumaric acid

maleic acid

With organic acids inductive effects and mesomeric effects affect the pK’a values. The effects are summarised in the Hammett equation and subsequent extensions.

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 pKa values of approximately 3.5 and 4.5. By contrast, maleic acid has pKa 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 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.

proton sponge

Proton sponge, 1,8-Bis(dimethylamino)naphthalene, has a pKa 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.

Thermodynamics

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

ΔGo = 2.303 RT pKa.

R is the gas constant and T is the temperature /Kelvin. Note that pKa= –log Ka. At 25 °C ΔGo /kJ mol-1 = 5.708 pKa. Free energy is made up of an enthalpy term and an entropy term.

ΔGo = ΔHo – TΔSo

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 pKa and ΔHo. The data were critically selected and refer to 25 °C and zero ionic strength, in water.

Acids

Compound
Equilibrium
pKa
ΔHo /kJ mol−1
–TΔSo /kJ mol−1

HA = Acetic acid
HA H+ + A−
4.756
−0.41
27.56

H2A+ = GlycineH+
H2A+ HA + H+
2.351
4.00
9.419

HA H+ + A−
9.78
44.20
11.6

H2A = Maleic acid
H2A HA− + H+
1.92
1.10
9.85

HA− H+ + A2−
6.27
−3.60
39.4

H3A = Citric acid
H3A H2A− + H+
3.128
4.07
13.78

H2A− HA2− + H+
4.76
2.23
24.9

HA2− A3− + H+
6.40
−3.38
39.9

HA = Boric acid
HA H+ + A−
9.237
13.80
38.92

H3A = Phosphoric acid
H3A H2A− + H+
2.148
−8.00
20.26

H2A− HA2− + H+
7.20
3.60
37.5

HA2− A3− + H+
12.35
16.00
54.49

HA− = Hydrogen sulphate
HA− A2− + H+
1.99
−22.40
33.74

H2A = Oxalic acid
H2A HA− + H+
1.27
−3.90
11.15

HA− A2− + H+
4.266
7.00
31.35

Conjugate acid of bases

Compound
Equilibrium
pKa
ΔHo /kJ mol−1
–TΔSo /kJ mol−1

B = Ammonia
HB+ B + H+
9.245
51.95
0.8205

B = Methylamine
HB+ B + H+
10.645
55.34
5.422

B = Triethylamine
HB+ B + H+
10.72
43.13
18.06

The first point to note is that when pKa is positive, the standard free energy change for the dissociation reaction is also positive, that is, dissociation of a weak acid is not a spontaneous process. Secondly some reactions are exothermic and some are endothermic, but when ΔHo is negative –TΔSo is the dominant factor which determines that ΔGo is positive. Lastly, the entropy contribution is always unfavourable in these reactions.

Note. 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 of pKa values

Main article: Determination of equilibrium constants

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

pKa values are commonly determined by means of titrations, in a medium of high ionic strength and at constant temperature. 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 pH meter. The equilibrium constants are found by fitting calculated pH values to the observed values, using the method of least squares.

The total volume of added strong base should be small compared to the initial volume of to keep the ionic strength nearly constant. This will ensure that pKa remains invariant during the titration.

A calculated titration curve for oxalic acid is shown at the right. Oxalic acid has pKa 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 pKa 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, where the pH rises by about two units. This end-point is not sharp and is typical of a diprotic acid whose buffer regions overlap by a small amount: pKa2 – pKa1 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 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 (pKw – 3), which is where self-ionization of water becomes important.

It is very difficult to measure pH values of less than two 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

Importance of pKa values

A knowledge of pKa values is important for the quantitative treatment of systems involving acid-base equilibria in solution.

In biochemistry, the pKa values of proteins and amino acid side chains are of major importance for the activity of enzymes and the stability of proteins.

In analytical chemistry buffer solutions 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

A coordination complex is formed by interaction of a metal ion, Mm+, 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−1)+ + H3O+

To determine the equilibrium constant for this reaction, in which the ligand loses a proton, the pKa 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 pKa 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.

Knowledge of pKa may be very important in assessing the hazard associated with an acid or base. 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 pKa 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 rivers and lakes,

The transition range of a pH indicator is about pKa ± 1. This is the range over which the color is intermediate between the colors of the acidic and basic forms of the indicator. Universal indicator is a mixture of indicators whose adjacent pKa values differ by about two.

pKa of some common substances

There are multiple techniques to determine the pKa of a chemical causing some discrepancy between different sources. Well measured values are typically are within 0.1 units of each other. Data presented here was taken at 25 °C in water. More values can be found in thermodynamics, above.

Chemical Name
Equilibrium
pKa

B = Adenine
BH22+ BH+ + H+
4.17

BH+ B + H+
9.65

H3A = Arsenic acid
H3A H2A− + H+
2.22

H2A− HA2− + H+
6.98

HA2− A3− + H+
11.53

HA = Benzoic acid
HA H+ + A−
4.204

HA = Butanoic acid
HA H+ + A−
4.82

H2A = Chromic acid
H2A HA− + H+
0.98

HA− A2− + 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 = Propanoic acid
HA H+ + A−
4.87

HA = Phenol
HA H+ + A−
9.99

H2A = L-(+)-Ascorbic Acid
H2A HA− + H+
4.17

HA− A2− + H+
11.57

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