Limited ionicity in poor protic ionic liquids: Association Gibbs energies

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 ΔG_A (and thus the association constants K_A) as functions of three fundamental properties: the acid/base mixing ratio (n = x_A/x_B), the HA-to-B proton-transfer strength (ΔpK_a,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 ΔG_A functions were then used to predict ΔG_ioniz values for the net ion-generating (autoionization) equilibrium in carboxylic acid/amine mixtures: 2B(HA)_n⇄B(HA)_n-dHB⁺+A(HA)_n+d-1 ^-, where n = x_A/x_B and d = degree of disproportionation. The agreement with experiment was excellent, demonstrating that these equations could have useful predictive power.