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

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