SIT theory was first proposed by Brønsted and was further developed by Guggenheim. Scatchard extended the theory to allow the interaction coefficients to vary with ionic strength. The theory was mainly of theoretical interest until 1945 because of the difficulty of determining equilibrium constants before the glass electrode was invented. Subsequently, Ciavatta developed the theory further.
The activity coefficient of the jth ion in solution is written as γ when concentrations are on the molal concentration scale and as y when concentrations are on the molar concentration scale. (The molality scale is preferred in thermodynamics because molal concentrations are independent of temperature). The basic idea of SIT theory is that the activity coefficient can be expressed as
: (molalities)
or
: (molar concentrations)
where z is the electrical charge on the ion, I is the ionic strength, ε and b are interaction coefficients and m and c are concentrations. The summation extends over the other ions present in solution, which includes the ions produced by the background electrolyte. The first term in these expressions comes from Debye–Hückel theory. The second term shows how the contributions from "interaction" are dependent on concentration. Thus, the interaction coefficients are used as corrections to Debye–Hückel theory when concentrations are higher than the region of validity of that theory.
The activity coefficient of a neutral species can be assumed to depend linearly on ionic strength, as in
where k is a Sechenov coefficient.
In the example of a monobasic acid HA, assuming that the background electrolyte is the salt NaNO, the interaction coefficients will be for interaction between H and NO, and between A and Na.