Ion association in a 1-3 electrolyte is studied using an asymmetrically charged soft-sphere model. The ions in this model have identical size, and the aqueous solvent is treated as a structureless dielectric continuum. The fraction of monomers, dimers, and trimers in the electrolyte are predicted by an extension of Wertheim’s associating liquids integral equation theory. Over the range of concentrations from 0.002 to 1.5M, the predictions for the thermodynamic quantities such as the reduced excess energy and the osmotic coefficient, are compared with existing molecular dynamics simulations of a "hard-core" model of 1-3 electrolytes. The influence of charge asymmetry on ion association is examined by comparing the 1-3 predictions with those for 1-1, 1-2, and 2-2 model electrolytes with the same Debye screening length.