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, K can be defined by
where {A} is the activity of the chemical species A etc. K 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 Γ 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 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 (1 M = 1 mol·dm−3, a unit of molar concentration). Furthermore, in all but the most concentrated solutions it can be assumed that the concentration of water, is constant, approximately 55 mol·dm−3. On dividing K by the constant terms and writing for the concentration of the hydronium ion the expression
is obtained. 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, 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.
Although Ka appears to have the dimension of concentration it must in fact be dimensionless or it would not be possible to take its logarithm. The illusion is the result of omitting the constant term from the defining expression. Nevertheless it is not unusual, particularly in texts relating to biochemical equilibria, to see a value quoted with a dimension as, for example, "Ka = 300 M".
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