In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction HA <=> A^- + H^+ known as dissociation in the context of acid–base reactions. The chemical species HA is an acid that dissociates into , called the conjugate base of the acid, and a hydrogen ion, . 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.
The dissociation constant is defined by or by its logarithmic form
where quantities in square brackets represent the molar concentrations of the species at equilibrium. For example, a hypothetical weak acid having Ka = 10−5, the value of log Ka is the exponent (−5), giving pKa = 5. For acetic acid, Ka = 1.8 x 10−5, so pKa is 4.7. A lower Ka corresponds to a weaker acid (an acid that is less dissociated at equilibrium). The form pKa is often used because it provides a convenient logarithmic scale, and a lower pKa corresponds to a stronger acid.
Theoretical background
The acid dissociation constant for an acid is a direct consequence of the underlying thermodynamics of the dissociation reaction; the pKa value is directly proportional to the standard Gibbs free energy change for the reaction. The value of the pKa changes with temperature and can be understood qualitatively based on Le Chatelier's principle: when the reaction is endothermic, Ka increases and pKa decreases with increasing temperature; the opposite is true for exothermic reactions.
The value of pKa also depends on molecular structure of the acid in many ways. For example, Linus Pauling proposed two rules: one for successive pKa of polyprotic acids (see Polyprotic acids below), and one to estimate the pKa of oxyacids based on the number of =O and −OH groups (see Factors that affect pKa 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 pKa.
The quantitative behaviour of acids and bases in solution can be understood only if their pKa values are known. In particular, the pH of a solution can be predicted when the analytical concentration and pKa 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 pKa values, together with the octanol-water 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 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. Experimentally, pKa values can be determined by potentiometric (pH) titration, but for values of pKa 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 molecular definition, an acid is a substance that dissociates in aqueous solution, releasing the hydrogen ion (a proton): Chapter 6: Acid–Base and Donor–Acceptor Chemistry 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 (naked protons do not exist in solution), and so Arrhenius later proposed that the dissociation should be written as an acid–base reaction: HA + H2O <=> A- + H3O+
Brønsted and Lowry generalised this further to a proton exchange reaction: Includes discussion of many organic Brønsted acids. Chapter 5: Acids and Bases Chapter 6: Acids, Bases and Ions in Aqueous Solution
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 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 . HA + S <=> A- + SH+
In solution chemistry, it is common to use as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution denotes a solvated hydronium ion rather than a proton.
The designation of an acid or base as "conjugate" depends on the context. The conjugate acid of a base B dissociates according to BH+ + OH- <=> B + H2O
which is the reverse of the equilibrium
The hydroxide ion , 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 () produces as if it were a proton donor, but it has been confirmed by Raman spectroscopy that this is due to the hydrolysis equilibrium: B(OH)3 + 2 H2O <=> B(OH)4- + H3O+
Similarly, metal ion hydrolysis causes ions such as to behave as weak acids: Section 9.1 "Acidity of Solvated Cations" lists many pKa values. [Al(H2O)6]^3+ + H2O <=> [Al(H2O)5(OH)]^2+ + H3O+
According to Lewis's original definition, an acid is a substance that accepts an electron pair to form a coordinate covalent bond. p.698
Equilibrium constant An acid dissociation constant is a particular example of an equilibrium constant. The dissociation of a monoprotic acid, HA, in dilute solution can be written as HA <=> A- + H+
The thermodynamic equilibrium constant can be defined by Chapter 2: Activity and Concentration Quotients pp 5-10
where represents the activity, at equilibrium, of the chemical species X. 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 (γ) the definition could also be written as
where 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. For example, the medium might be a solution of 0.1 molar (M) sodium nitrate or 3 M potassium perchlorate. With this assumption,
is obtained. 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.
Cumulative and stepwise constants A cumulative equilibrium constant, denoted by is related to the product of stepwise constants, denoted by For a dibasic acid the relationship between stepwise and overall constants is as follows H2A <=> A^2- + 2H+
Note that in the context of metal-ligand complex formation, the equilibrium constants for the formation of metal complexes are usually defined as association constants. In that case, the equilibrium constants for ligand protonation are also defined as association constants. The numbering of association constants is the reverse of the numbering of dissociation constants; in this example
Association and dissociation constants When discussing the properties of acids it is usual to specify equilibrium constants as acid dissociation constants, denoted by Ka, with numerical values given the symbol pKa.
On the other hand, association constants are used for bases.
However, general purpose computer programs that are used to derive equilibrium constant values from experimental data use association constants for both acids and bases. Because stability constants for a metal-ligand complex are always specified as association constants, ligand protonation must also be specified as an association reaction. The definitions show that the value of an acid dissociation constant is the reciprocal of the value of the corresponding association constant:
Notes For a given acid or base in water, , the self-ionization constant of water. The association constant for the formation of a supramolecular complex may be denoted as Ka; in such cases "a" stands for "association", not "acid". For polyprotic acids, the numbering of stepwise association constants is the reverse of the numbering of the dissociation constants. For example, for phosphoric acid (details in the polyprotic acids section below):
Temperature dependence All equilibrium constants vary with temperature according to the van 't Hoff equation Section 7.4: The Response of Equilibria to Temperature
is the gas constant and is the absolute temperature. Thus, for exothermic reactions, the standard enthalpy change, , is negative and K decreases with temperature. For endothermic reactions, is positive and 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 is the heat capacity change at constant pressure. In practice may be taken to be constant over a small temperature range.
Dimensionality In the equation
Ka appears to have dimensions of concentration. However, since , the equilibrium constant, , cannot have a physical dimension. This apparent paradox can be resolved in various ways. Assume that the quotient of activity coefficients has a numerical value of 1, so that has the same numerical value as the thermodynamic equilibrium constant . Express each concentration value as the ratio c/c0, where c0 is the concentration in a [hypothetical] standard state, with a numerical value of 1, by definition. Express the concentrations on the mole fraction scale. Since mole fraction has no dimension, the quotient of concentrations will, by definition, be a pure number.
The first and second options above give identical numerical values for an equilibrium constant. Furthermore, since a concentration is simply proportional to mole fraction and density :
and since the molar mass is a constant in dilute solutions, an equilibrium constant value determined using the third option will simply be proportional to the values obtained with the first two.
It is common practice in biochemistry to quote a value with a dimension as, for example, "Ka = 30 mM" in order to indicate the scale, millimolar (mM) or micromolar (μM) of the concentration values used for its calculation.
Strong acids and bases