The exposition begins with a virial expansion of the excess Gibbs free energy
W is the mass of the water in kilograms, b, b ... are the molalities of the ions and I is the ionic strength. The first term, f(I) represents the Debye–Hückel limiting law. The quantities λ(I) represent the short-range interactions in the presence of solvent between solute particles i and j. This binary interaction parameter or second virial coefficient depends on ionic strength, on the particular species i and j and the temperature and pressure. The quantities μ represent the interactions between three particles. Higher terms may also be included in the virial expansion.
Next, the free energy is expressed as the sum of chemical potentials, or partial molal free energy, 
and an expression for the activity coefficient is obtained by differentiating the virial expansion with respect to a molality b.
For a simple electrolyte MX, at a concentration m, made up of ions M,  and 
are defined as
The term f is essentially the Debye–Hückel term. Terms involving  and  are not included as interactions between three ions of the same charge are unlikely to occur except in very concentrated solutions.
The B parameter was found empirically to show an ionic strength dependence (in the absence of ion-pairing) which could be expressed as
With these definitions, the expression for the osmotic coefficient becomes
A similar expression is obtained for the mean activity coefficient.
These equations were applied to an extensive range of experimental data at 25 °C with excellent agreement to about 6 mol kg for various types of electrolyte. The treatment can be extended to mixed electrolytes
and to include association equilibria. Values for the parameters &beta;, &beta; and C for inorganic and organic acids, bases and salts have been tabulated. Temperature and pressure variation is also discussed.
One area of application of Pitzer parameters is to describe the ionic strength variation of equilibrium constants measured as concentration quotients. Both SIT and Pitzer parameters have been used in this context, For example, both sets of parameters were calculated for some uranium complexes and were found to account equally well for the ionic strength dependence of the stability constants.
Pitzer parameters and SIT theory have been extensively compared. There are more parameters in the Pitzer equations  than in the SIT equations. Because of this the Pitzer equations provide for more precise modelling of mean activity coefficient data and equilibrium constants. However, the determination of the greater number of Pitzer parameters means that they are more difficult to determine.