Protic ionic liquids (PILs), made from anhydrous mixtures of Bronsted acids HA and bases B (HA + B → BH+ + A), occasionally suffer from limited ionicity. In cases of “poor” PILs (<10% ionicity, e.g., using carboxylic acids), past simulations have hinted that ion-pair association, more than incomplete proton transfer, is at fault. To improve upon the Fuoss equation for predicting the degree of ion pairing, new electrostatic equations (including induced dipoles) are presented, for ion-pair and other associations that occur in anhydrous amine/carboxylic acid mixtures. The equations present the association Gibbs energies ΔGA (and thus the association constants KA) as functions of three fundamental properties: the acid/base mixing ratio (n = xA/xB), the HA-to-B proton-transfer strength (ΔpKa,ε=78), and the dielectric constant (relative permittivity) of the mixture (ε). Parameter values were obtained from fits to constant-dielectric quantum chemistry data (obtained and presented here). These ΔGA functions were then used to predict ΔGioniz values for the net ion-generating (autoionization) equilibrium in carboxylic acid/amine mixtures: 2B(HA)nB(HA)ndHB++A(HA)n+d1, where n = xA/xB and d = degree of disproportionation. The agreement with experiment was excellent, demonstrating that these equations could have useful predictive power.

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