The need for this theory arises from  the need to derive activity coefficients of solutes when their concentrations are too high to be predicted accurately by Debye–Hückel theory. These activity coefficients are needed because an equilibrium constant is defined in thermodynamics as a quotient of activities but is usually measured using concentrations. The protonation of a monobasic acid will be used to simplify the exposition. The equilibrium for protonation of the conjugate base, A of the acid, may be written as 
for which
where {HA} signifies an activity of the chemical species HA etc.. The role of water in the equilibrium has been ignored as in all but the most concentrated solutions the activity of water is a constant. K is defined here as an association constant, the reciprocal of an acid dissociation constant.
Each activity term can be expressed as the product of a concentration and an activity coefficient. For example,
where the square brackets signify a concentration and γ is an activity coefficient. Thus the equilibrium constant can be expressed as a product of a concentration quotient and an activity coefficient quotient.
Taking logarithms.
K is the hypothetical value that the equilibrium constant would have if the solution of the acid were so dilute that the activity coefficients were all equal to one.
It is common practise to determine equilibrium constants in solutions containing an electrolyte at high ionic strength  such that the activity coefficients are effectively constant. However, when the ionic strength is changed the measured equilibrium constant will also change, so there is a need to estimate individual (single ion) activity coefficients. Debye–Huckel theory provides a means to do this, but it is accurate only at very low concentrations. Hence the need for an extension to Debye–Hückel theory. Two main approaches have been used. SIT theory, discussed here and Pitzer equations.