Definitions

# Acid dissociation constant

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 $rightleftharpoons$ A + H+, Ka is defined, subject to certain conditions, as

$K_a = mathrm\left\{frac\left\{\left[A^-\right]\left[H^+\right]\right\}\left\{\left[HA\right]\right\}\right\}$
where [HA], [A] and [H+] 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.

## Definitions

According to Arrhenius's original definition, an acid is a substance which dissociates in aqueous solution, releasing the hydrogen ion.
HA $rightleftharpoons$ 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 $rightleftharpoons$ A + H3O+
Brønsted and Lowry generalized this definition as a proton exchange reaction, as follows.
acid + base $rightleftharpoons$ 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 $rightleftharpoons$ B + H2O

For example:

H2CO3 + H2O $rightleftharpoons$ HCO3 + H3O+
The bicarbonate ion is the conjugate base of carbonic acid.
HCO3 + OH $rightleftharpoons$ 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 $rightleftharpoons$ 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 to behave as weak acids.

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

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 $rightleftharpoons$ A + H3O+
the thermodynamic equilibrium constant, Kt can be defined by
$K^mbox\left\{t\right\}=mathrm\left\{frac \left\{\left\{H_3O^+\right\}\right\}\right\} \left\{\left\{H_2O\right\}\right\}\right\}\right\}$
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.

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

$K^mbox\left\{t\right\} = mathrm\left\{frac\left\{\left[A^-\right]\left[H_3O^+\right]\right\}\left\{\left[HA\right]\left[H_2O\right]\right\}times frac\left\{gamma_\left\{A^-\right\}gamma_\left\{H_3O^+\right\}\right\}\left\{gamma_\left\{HA\right\}gamma_\left\{H_2O\right\}\right\} =mathrm\left\{frac\left\{\left[A^-\right]\left[H_3O^+\right]\right\}\left\{\left[HA\right]\left[H_2O\right]\right\}\right\}timesGamma\right\}$
where [HA] 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. For example, the medium might be a solution of 0.1 M sodium nitrate or 3 M potassium perchlorate. Furthermore, in all but the most concentrated solutions it can be assumed that the concentration of water, [H2O], 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.

$K_a = mathrm\left\{frac\left\{\left[A^-\right]\left[H^+\right]\right\}\left\{\left[HA\right]\right\}\right\}$
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.

#### Monoprotic acids

After rearranging the expression defining Ka, and putting pH = −log10[H+], one obtains
pH = pKa – log ([AH]/[A] )
This is a form of the Henderson–Hasselbalch equation, from which the following conclusions can be drawn.

• At half-neutralization [AH]/[A] = 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 [AH]/[A]=10 or 1/10.
• if the pH is known the ratio [AH]:[A] 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

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 $rightleftharpoons$ HA + H+
HA $rightleftharpoons$ 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+$rightleftharpoons$ H3VO4 + H+ pKa1 = 4.2
H3PO4 $rightleftharpoons$ H2PO4 + H+ pKa1 = 2.15 H3VO4 $rightleftharpoons$ H2VO4 + H+ pKa2 = 2.60
H2PO4 $rightleftharpoons$ HPO42− + H+ pKa2 = 7.20 H2VO4 $rightleftharpoons$ HVO42− + H+ pKa3 = 7.92
HPO42− $rightleftharpoons$ PO43− + H+ pKa3 = 12.37 HVO42− $rightleftharpoons$ VO43− + H+ pKa4 = 13.27

### Water self-ionization

Water has both acidic and basic properties. The equilibrium constant for the equilibrium
H2O + H2O $rightleftharpoons$ OH + H3O+
is given by
$K_a=mathrm\left\{frac\left\{\left[H^+\right]\left[OH^-\right]\right\}\left\{\left[H_2O\right]^2\right\}\right\}$
Since the concentration of water can be assumed to be constant, this expression simplifies to

$K_w =\left[H^+\right]\left[OH^-\right],$

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

### Bases

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 $rightleftharpoons$ HB+ + OH
Using similar reasoning to that used before
$K_b = mathrm\left\{frac\left\{\left[HB^+\right]\left[OH^-\right]\right\}\left\{\left[B\right]\right\}\right\}$
In water, the concentration of the hydroxide ion, [OH], is related to the concentration of the hydrogen ion by Kw = [H+][OH], therefore
$mathrm\left\{\left[OH^-\right] = frac\left\{mathit\left\{K\right\}_w\right\}\left\{\left[H^+\right]\right\}\right\}$
Substitution of the expression for [OH] into the expression for Kb gives
$mathrm\left\{mathit\left\{K\right\}_b = frac\left\{\left[HB^+\right]mathit\left\{K\right\}_w\right\}\left\{\left[B\right] \left[H^+\right]\right\} = frac\left\{mathit\left\{K\right\}_w\right\}\left\{mathit\left\{K\right\}_a\right\}\right\}$
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

All equilibrium constants vary with temperature according to the van 't Hoff equation
$frac \left\{operatorname\left\{d\right\} ln mathit\left\{K\right\}\right\} \left\{operatorname\left\{d\right\}T\right\} = frac\left\{\left\{Delta mathit\left\{H\right\}_m\right\}^\left\{ominus\right\}\right\} \left\{RT^2\right\}$
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 if:

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.

Solvents can be polar, protic, donor or non-polar. The data in the following table refer to a temperature at or near 25 °C, unless stated otherwise.

Compound Solvent Class Dielectric constant
1,4-Dioxane Non-polar, Donor 2.2
Hexane Non-polar 1.9
Carbon tetrachloride Non-polar 2.2
Benzene Non-polar 2.3
Diethyl ether Non-polar, Donor 4.3
Acetic acid Protic donor 6.1
Tetrahydrofuran Donor 7.6
Acetone Polar donor 21
Liquid ammonia Polar donor 25 at 195 K
Acetonitrile Polar donor 37
Dimethylsulfoxide Polar donor 47
Water Polar protic donor 78
Formamide Polar protic donor 111
Sulphuric acid Polar protic 110

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 $rightleftharpoons$ Cl + CH3C(OH)2+
acid + base $rightleftharpoons$ 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 $rightleftharpoons$ HSO4 + CH3C(OH)2+
The apparently unlikely geminal diol species CH3C(OH)2+ is stable in these environments.

pKa values of organic compounds are often obtained using solvents other than water, such as dimethyl sulfoxide (DMSO) and acetonitrile. Water is more basic than DMSO so most acids dissociate to a lesser extent in DMSO than in water. DMSO is widely used as an alternative to water in evaluating acids and bases because it has a lower dielectric constant than water, it is less polar and so dissolves non-polar, hydrophobic substances more easily.

Below is a table of selected pKa values at 25 °C in acetonitrile (AN) and dimethyl sulfoxide (DMSO). Values for water are included for comparison.

HA $rightleftharpoons$ 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+ $rightleftharpoons$ 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

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

In aprotic solvents, oligomers 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 and prevents the oligomers from forming.

### Mixed solvents

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. However, 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.

## 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.

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, 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.
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 = ΔHOTΔSO
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 ΔH0 /kJ mol−1 TΔS0 /kJ mol−1
HA = Acetic acid HA $rightleftharpoons$ H+ + A 4.756 −0.41 27.56
H2A+ = GlycineH+ H2A+ $rightleftharpoons$ HA + H+ 2.351 4.00 9.419
HA $rightleftharpoons$ H+ + A 9.78 44.20 11.6
H2A = Maleic acid H2A $rightleftharpoons$ HA + H+ 1.92 1.10 9.85
HA $rightleftharpoons$ H+ + A2− 6.27 −3.60 39.4
H3A = Citric acid H3A $rightleftharpoons$ H2A + H+ 3.128 4.07 13.78
H2A $rightleftharpoons$ HA2− + H+ 4.76 2.23 24.9
HA2− $rightleftharpoons$ A3− + H+ 6.40 −3.38 39.9
HA = Boric acid HA $rightleftharpoons$ H+ + A 9.237 13.80 38.92
H3A = Phosphoric acid H3A $rightleftharpoons$ H2A + H+ 2.148 −8.00 20.26
H2A $rightleftharpoons$ HA2− + H+ 7.20 3.60 37.5
HA2− $rightleftharpoons$ A3− + H+ 12.35 16.00 54.49
HA = Hydrogen sulphate HA $rightleftharpoons$ A2− + H+ 1.99 −22.40 33.74
H2A = Oxalic acid H2A $rightleftharpoons$ HA + H+ 1.27 −3.90 11.15
HA $rightleftharpoons$ A2− + H+ 4.266 7.00 31.35

Conjugate acid of bases
Compound Equilibrium pKa ΔH0 /kJ mol−1 TΔS0 /kJ mol−1
B = Ammonia HB+ $rightleftharpoons$ B + H+ 9.245 51.95 0.8205
B = Methylamine HB+ $rightleftharpoons$ B + H+ 10.645 55.34 5.422
B = Triethylamine HB+ $rightleftharpoons$ 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

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 or NMR measurements may be used instead of, or combined with pH measurements.

## Importance of pKa values

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

• Biochemistry

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. The reaction that converts adenosine triphosphate to adenosine diphosphate is very pH sensistive.

• Buffer solutions

A buffer solution is made up of a mixture of an acid and its conjugate base, or a base and its conjugate acid. 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 of a simple buffer solution (illustrative diagram) is largest when pH = pKa.
Buffer solutions are used extensively in biochemistry to provide solutions at or near the physiological pH for the study of biochemical reactions. For example, MOPS provides a solution with pH 7.2; others are listed in buffer solutions and Good's buffers. Buffers such as tricine are used in Gel electrophoresis. Isoelectric focussing is a technique used for separation of proteins by 2-D gel polyacrylamide gel electrophoresis. Buffering is essential in Acid base physiology including Acid-base homeostasis and disorders such as Acid-base imbalance.

• Coordination compounds

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(H2O)n]m+ +LH $rightleftharpoons$ [M(H2O)n−1L](m−1)+ + H3O+
To determine the equilibrium constant for this reaction, in which the ligand loses a proton, the pKa of the 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.

• Solvent extraction

In solvent extraction, the efficiency of extraction of a compound into an organic phase, such as ether, can be optimized by adjusting the pH of the aqueous phase using an appropriate buffer. At the optimum pH, the concentration of the electrically neutral species is maximized; 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.

• Natural waters

Acid-base equilibria are important for rivers and lakes, and in chemical oceanography.

• Pharmacology

Ionization of a compound alters its physical behavior 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 pKa of an ionizable group.

• pH indicators

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+ $rightleftharpoons$ BH+ + H+ 4.17
BH+ $rightleftharpoons$ B + H+ 9.65
H3A = Arsenic acid H3A $rightleftharpoons$ H2A + H+ 2.22
H2A $rightleftharpoons$ HA2− + H+ 6.98
HA2− $rightleftharpoons$ A3− + H+ 11.53
HA = Benzoic acid HA $rightleftharpoons$ H+ + A 4.204
HA = Butanoic acid HA $rightleftharpoons$ H+ + A 4.82
H2A = Chromic acid H2A $rightleftharpoons$ HA + H+ 0.98
HA $rightleftharpoons$ A2− + H+ 6.5
B = Codeine BH+ $rightleftharpoons$ B + H+ 8.17
HA = Cresol HA $rightleftharpoons$ H+ + A 10.29
HA = Formic acid HA $rightleftharpoons$ H+ + A 3.751
HA = Hydrofluoric acid HA $rightleftharpoons$ H+ + A 3.17
HA = Hydrocyanic acid HA $rightleftharpoons$ H+ + A 9.21
HA = Hydrogen selenide HA $rightleftharpoons$ H+ + A 3.89
HA = Hydrogen peroxide (90%) HA $rightleftharpoons$ H+ + A 11.7
HA = Lactic acid HA $rightleftharpoons$ H+ + A 3.86
HA = Propanoic acid HA $rightleftharpoons$ H+ + A 4.87
HA = Phenol HA $rightleftharpoons$ H+ + A 9.99
H2A = L-(+)-Ascorbic Acid H2A $rightleftharpoons$ HA + H+ 4.17
HA $rightleftharpoons$ A2− + H+ 11.57