The thermodynamic equilibrium constant, K, for the equilibrium
can be defined as
where {ML} is the activity of the chemical species ML etc. K is dimensionless since activity is dimensionless. Activities of the products 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 [ML] represents the concentration of ML and Γ is a quotient of activity coefficients. This expression can be generalized as
To avoid the complications involved in using activities, stability constants are determined, where possible, in a medium consisting of a solution of a background electrolyte at 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 mol dm sodium nitrate or 3 mol dm sodium perchlorate. When Γ is constant it may be ignored and the general expression in theory, above, is obtained.
All published stability constant values refer to the specific ionic medium used in their determination and different values are obtained with different conditions, as illustrated for the complex CuL (L = glycinate). Furthermore, stability constant values depend on the specific electrolyte used as the value of Γ is different for different electrolytes, even at the same ionic strength. There does not need to be any chemical interaction between the species in equilibrium and the background electrolyte, but such interactions might occur in particular cases. For example, phosphates form weak complexes with alkali metals, so, when determining stability constants involving phosphates, such as ATP, the background electrolyte used will be, for example, a tetralkylammonium salt. Another example involves iron(III) which forms weak complexes with halide and other anions, but not with perchlorate ions.
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.