Acid dissociation constant

[a] The system is said to be in equilibrium when the concentrations of its components do not change over time, because both forward and backward reactions are occurring at the same rate.

[1] The dissociation constant is defined by[b] where quantities in square brackets represent the molar concentrations of the species at equilibrium.

In living organisms, acid–base homeostasis and enzyme kinetics are dependent on the pKa values of the many acids and bases present in the cell and in the body.

In chemistry, a knowledge of pKa 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.

A broader definition of acid dissociation includes hydrolysis, in which protons are produced by the splitting of water molecules.

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 ⁠

[28] For oxyacids with more than one ionizable hydrogen on the same atom, the pKa values often increase by about 5 units for each proton removed,[29][30] as in the example of phosphoric acid above.

Substitute the expression for [AH] from the second equation into the first equation At the isoelectric point the concentration of the positively charged species, AH+2, is equal to the concentration of the negatively charged species, A−, so Therefore, taking cologarithms, the pH is given by pI values for amino acids are listed at proteinogenic amino acid.

In water, the concentration of the hydroxide ion, [OH−], is related to the concentration of the hydrogen ion by Kw = [H+][OH−], therefore Substitution of the expression for [OH−] into the expression for Kb gives When Ka, Kb and Kw are determined under the same conditions of temperature and ionic strength, it follows, taking cologarithms, that pKb = pKw − pKa.

Because the relationship pKb = pKw − pKa holds only in aqueous solutions (though analogous relationships apply for other amphoteric solvents), subdisciplines of chemistry like organic chemistry that usually deal with nonaqueous solutions generally do not use pKb as a measure of basicity.

Often this is written as the hydronium ion H3O+, but this formula is not exact because in fact there is solvation by more than one water molecule and species such as H5O+2, H7O+3, and H9O+4 are also present.

[44] In aqueous solutions, homoconjugation does not occur, because water forms stronger hydrogen bonds to the conjugate base than does the acid.

[46] 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 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.

[7] 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.

The electron-withdrawing effect of the substituent makes ionisation easier, so successive pKa values decrease in the series 4.7, 2.8, 1.4, and 0.7 when 0, 1, 2, or 3 chlorine atoms are present.

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.

[52][53] 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 pKa by the mechanism of keto–enol tautomerism.

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.

For example, the expected (by electronic effects of methyl substituents) and observed in gas phase order of basicity of methylamines, Me3N > Me2NH > MeNH2 > NH3, is changed by water to Me2NH > MeNH2 > Me3N > NH3.

Relative stabilization of methylammonium ions thus decreases with the number of methyl groups explaining the order of water basicity of methylamines.

[11] The standard enthalpy change can be determined by calorimetry or by using the van 't Hoff equation, though the calorimetric method is preferable.

The experimental determination of pKa values is commonly performed by means of titrations, in a medium of high ionic strength and at constant temperature.

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.

When this is so, the solution is not buffered and the pH rises steeply on addition of a small amount of strong base.

Isothermal titration calorimetry (ITC) may be used to determine both a pK value and the corresponding standard enthalpy for acid dissociation.

For some polyprotic acids, dissociation (or association) occurs at more than one nonequivalent site,[4] and the observed macroscopic equilibrium constant, or macro-constant, is a combination of micro-constants involving distinct species.

[65] For example, the abovementioned equilibrium for spermine may be considered in terms of Ka values of two tautomeric conjugate acids, with macro-constant In this case

In pharmacology, ionization of a compound alters its physical behaviour and macro properties such as solubility and lipophilicity, log p).

This is exploited in drug development to increase the concentration of a compound in the blood by adjusting the pKa of an ionizable group.

Acetic acid, CH3COOH, is composed of a methyl group, CH3, bound chemically to a carboxylate group, COOH. The carboxylate group can lose a proton and donate it to a water molecule, H2O, leaving behind an acetate anion CH3COO− and creating a hydronium cation H3O. This is an equilibrium reaction, so the reverse process can also take place.
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.
Illustration of the effect of ionic strength on the p K A of an acid. In this figure, the p K A of acetic acid decreases with increasing ionic strength, dropping from 4.8 in pure water (zero ionic strength) and becoming roughly constant at 4.45 for ionic strengths above 1 molar sodium nitrate, N A N O 3.
Variation of p K a of acetic acid with ionic strength.
This figure plots the relative fractions of the protonated form A H of an acid to its deprotonated form, A minus, as the solution p H is varied about the value of the acid's p K A. When the p H equals the p K a, the amounts of the protonated and deprotonated forms are equal. When the p H is one unit higher than the p K A, the ratio of concentrations of protonated to deprotonated forms is 10 to 1. When the p H is two units higher that ratio is 100 to 1. Conversely, when the p H is one or two unit lower than the p K A, the ratio is 1 to ten or 1 to 100. The exact percentage of each form may be determined from the Henderson–Hasselbalch equation.
Variation of the % formation of a monoprotic acid, AH, and its conjugate base, A − , with the difference between the pH and the p K a of the acid.
Acids with more than one ionizable hydrogen atoms are called polyprotic acids, and have multiple deprotonation states, also called species. This image plots the relative percentages of the different protonation species of phosphoric acid H 3 P O 4 as a function of solution p H. Phosphoric acid has three ionizable hydrogen atoms whose p K A's are roughly 2, 7 and 12. Below p H 2, the triply protonated species H 3 P O 4 predominates; the double protonated species H 2 P O 4 minus predominates near p H 5; the singly protonated species H P O 4 2 minus predominates near p H 9 and the unprotonated species P O 4 3 minus predominates above p H 12
Phosphoric acid speciation
This image plots the relative percentages of the protonation species of citric acid as a function of p H. Citric acid has three ionizable hydrogen atoms and thus three p K A values. Below the lowest p K A, the triply protonated species prevails; between the lowest and middle p K A, the doubly protonated form prevails; between the middle and highest p K A, the singly protonated form prevails; and above the highest p K A, the unprotonated form of citric acid is predominant.
% species formation calculated with the program HySS for a 10 millimolar solution of citric acid. p K a1 = 3.13, p K a2 = 4.76, p K a3 = 6.40.
This image illustrates how two carboxylic acids, C O O H, can associate through mutual hydrogen bonds. The hydroxyl portion O H of each molecule forms a hydrogen bond to the carbonyl portion C O of the other.
Dimerization of a carboxylic acid.
The p K A of acetic acid in the mixed solvent dioxane/water. p K A increases as the proportion of dioxane increases, primarily because the dielectric constant of the mixture decreases with increasing doxane content. A lower dielectric constant disfavors the dissociation of the uncharged acid into the charged ions, H + and C H 3 C O O minus, shifting the equilibrium to favor the uncharged protonated form C H 3 C O O H. Since the protonated form is the reactant not the product of the dissociation, this shift decreases the equilibrium constant K A, and increases P K A, its negative logarithm.
p K a of acetic acid in dioxane/water mixtures. Data at 25 °C from Pine et al. [ 45 ]
pKa values for acetic, chloroacetic, dichloroacetic and trichloroacetic acids.
Proton sponge is a derivative of naphthalene with dimethylamino groups in the one and ten positions. This brings the two dimethyl amino groups into close proximity to each other.
Proton sponge
The image shows the titration curve of oxalic acid, showing the pH of the solution as a function of added base. There is a small inflection point at about pH 3 and then a large jump from pH 5 to pH 11, followed by another region of slowly increasing pH.
A calculated titration curve of oxalic acid titrated with a solution of sodium hydroxide
Cysteine
Spermine is a long, symmetrical molecule capped at both ends with amino groups N H 2. It has two N H groups symmetrically placed within the molecule, separated from each other by four methylene groups C H 2, and from the amino ends by three methylene groups. Thus, the full molecular formula is N H 2 C H 2 C H 2 C H 2 N H C H 2 C H 2 C H 2 C H 2 N H C H 2 C H 2 C H 2 N H 2.
Spermine