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.
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.
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
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.
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.
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 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
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|
The self-ionization constant of water, Kw, can thus be seen as a special case of an acid dissociation constant.
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.
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|
|Diethyl ether||Non-polar, Donor||4.3|
|Acetic acid||Protic donor||6.1|
|Liquid ammonia||Polar donor||25 at 195 K|
|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.
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 A− + H+||AN||DMSO||water|
|BH+ B + H+||AN||DMSO||water|
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.
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.
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.
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.
|Compound||Equilibrium||pKa|| ΔH|| –TΔS|
|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|
|Compound||Equilibrium||pKa|| ΔH|| –TΔS|
|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|
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.
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.
|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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