Precise measurements on electrical conductance (Lambda) of solutions of an ionic liquid (IL) tetrabutylphosphonium tetrafluoroborate in acetonitrile (ACN), tetrahydrofuran (THF), and 1,3-dioxolane (1,3-DO) and their binary mixtures have been reported at 298.15 K. The conductance data have been analyzed by the Fuoss conductance equation (1978) in terms of the limiting molar conductance (Lambda(o)), the association constant (K-A), and the association diameter (R) for ion-pair formation. The Walden product is obtained and discussed. However, the deviation of the conductometric curves (Lambda versus root c) from linearity for the electrolyte in THF and 1,3-DO and their binary mixtures indicated triple-ion formation and therefore the corresponding conductance data have been analyzed by the Fuoss-Kraus theory of triple ions. The limiting ionic conductances (gamma(+/-)(o)) have been estimated from the appropriate division of the limiting molar conductivity value of tetrabutylammonium tetraphenylborate [Bu4NBPh4] as the "reference electrolyte" method along with a numerical evaluation of ion-pair and triple-ion formation constants (K-p approximate to K-A and K-T). The results have been discussed in terms of solvent properties and configurational theory. Ionic association in the limiting molar conductances as well as the single-ion conductivity values have been determined for the electrolyte in the solvent media.