Two complementary models of Lewis molecular acidity are introduced and tested in a wide series of 45 room temperature ionic liquids (RTIL). They are defined in the context of the conceptual density functional theory. The first one, which we tentatively call the excess electronic chemical potential, assesses the electron accepting power of the RTIL by relating the H-bond donor acidity with the charge transfer associated to the acidic H-atom migration at the cation of the RTIL considered as a HB-donor species. This global index accounts for the molecular acidity of the cation moiety of the ionic liquid that takes into account the perturbation of the anionic partner. The second index is defined in terms of the local charge capacity modeled through the maximum electronic charge that the cation, in its valence state, may accept from an unspecified environment. Each model is compared with the experimental HB-donor acidity parameter of the Kamlet Taft model. The best comparison is obtained for a combination of both the excess electronic chemical potential and the local charge capacity. As expected, the correlations with the Kamlet Taft alpha parameter do not lead to a universal model of HB-donor acidity. Reduced correlations for limited series of structurally related RTIL are obtained instead. Finally, we illustrate the reliability and usefulness of the proposed model of RTIL molecular acidity to explain the cation-dependent solvent effects on the reactivity trends for cycloaddition, Kemp elimination, and Menschutkin reactions, for which experimental rate coefficients are available from literature.