A previous model, developed to describe the thermodynamic properties of associating electrolytes within the binding mean spherical approximation (BIMSA), is modified on the basis of a better representation of the pair. The ions are represented as charged hard spheres interacting through a sticky point potential, leading to the creation of pairs. In this version of the model, the species constituting the pair are allowed to have charges and sizes different from those of the free ions. New expressions for the osmotic and activity coefficients are proposed that account for these features. The equations were applied to fit the parameters in the model to osmotic data for a variety of aqueous solutions of inorganic acids, and for a base, NaOH, at 25 degreesC up to the highest concentrations for which data are available. In all cases, accurate representations could be obtained up to very high concentrations, such as 28 mol kg(-1) for nitric acid, 45 mol kg(-1) for hydrochloric acid, and 29 mol kg(-1) for NaOH. The case of sulfuric acid could be treated consistently in the concentration range 0-27.7 mol kg(-1) by considering the equilibrium between sulfate and bisulfate ions. In all cases, the new model represents an improvement over the previous BIMSA model.