Thermodynamic and Kinetic Studies on the Conversion of Solvent-Shared to Contact Ion Pairs in Sparingly Soluble MF 2 (M = Mg 2+ and Ca 2+ ) Aqueous Solutions: Implications for Understanding Supersaturated Behavior and Association Constant Determination.

The thermodynamic and kinetic behaviors of Mg 2+ -F - ion pairing in aqueous solution are investigated theoretically and experimentally and are contrasted to those of Ca 2+ -F - . Thermodynamically, similar to CaF x (H 2 O) 14 2- x ( x = 1 and 2), MgF(H 2 O) y + ( y = 14-20) contact ion pairs (CIPs) are more stable than their solvent-shared ion pairs (SSIPs), whereas the CIPs and SSIPs of MF 2 (H 2 O) y are almost isoenergetic. However, in kinetics, the conversion of SSIPs to CIPs for M 2+ -F - (M = Mg 2+ and Ca 2+ ) ion pairing must overcome a high energy barrier due to the strong hydration of Mg 2+ and F - . The kinetics dominate after the thermodynamics and kinetics are balanced, which hinders the formation of M 2+ -F - CIPs in practical MF 2 aqueous solutions (less than or equal to saturated concentrations). This result is also supported by the 19 F nuclear magnetic resonance spectra of saturated MF 2 solutions. Although the interaction between Mg 2+ and F - is slightly stronger than that between Ca 2+ and F - due to the smaller radius of Mg 2+ , the formation of Mg 2+ -F - CIPs needs to go through two rate-limiting steps, the dehydration and entrance of F - (i.e., via exchange mode) with a higher energy barrier, due to the ability of strongly bound water molecules and rigorous octahedral coordinated configuration of Mg 2+ , while the formation of Ca 2+ -F - CIPs only goes through a single rate-limiting step, the entrance of F - (i.e., via swinging mode) with a lower energy barrier, due to the flexible coordination configuration of Ca 2+ . This is responsible for precipitation in MgF 2 aqueous solution requiring a larger supersaturation degree and a lower precipitation rate than in CaF 2 . These kinetic factors lead to the association constants previously reported for MF + determined by a fluoride ion-selective electrode (ISE) combined with the titration method, where the MF 2 solutions were always unsaturated at the titration end point, which actually corresponds to those of the ligand process going from completely free M 2+ and F - to their SSIPs. A possible strategy to accurately determine the association constants of MF + and MF 2 (aq) CIPs by fluoride ISEs is proposed. The present results suggest that judging the formation of M 2+ -F - CIPs in practical solutions from a theoretical calculation perspective requires significant consideration of the kinetic factors, except for the thermodynamic factors.