Thermodynamic and Kinetic Studies on the Conversion of Solvent-Shared to Contact Ion Pairs in Sparingly Soluble MF2 (M = Mg2+ and Ca2+) Aqueous Solutions: Implications for Understanding Supersaturated Behavior and Association Constant Determination

The thermodynamic and kinetic behaviors of Mg2+F- ion pairing in aqueous solution are investigated theoretically and experimentally and are contrasted to those of Ca2+-F-. Thermodynamically, similar to CaFx(H2O)142-x (x = 1 and 2), MgF(H2O)y+ (y = 14-20) contact ion pairs (CIPs) are more stable than their solvent-shared ion pairs (SSIPs), whereas the CIPs and SSIPs of MF2(H2O)y are almost isoenergetic. However, in kinetics, the conversion of SSIPs to CIPs for M2+-F- (M = Mg2+ and Ca2+) ion pairing must overcome a high energy barrier due to the strong hydration of Mg2+ and F-. The kinetics dominate after the thermodynamics and kinetics are balanced, which hinders the formation of M2+-F- CIPs in practical MF2 aqueous solutions (less than or equal to saturated concentrations). This result is also supported by the 19F nuclear magnetic resonance spectra of saturated MF2 solutions. Although the interaction between Mg2+ and F- is slightly stronger than that between Ca2+ and F- due to the smaller radius of Mg2+, the formation of Mg2+-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 Mg2+, while the formation of Ca2+-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 Ca2+. This is responsible for precipitation in MgF2 aqueous solution requiring a larger supersaturation degree and a lower precipitation rate than in CaF2. 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 MF2 solutions were always unsaturated at the titration end point, which actually corresponds to those of the ligand process going from completely free M2+ and F- to their SSIPs. A possible strategy to accurately determine the association constants of MF+ and MF2(aq) CIPs by fluoride ISEs is proposed. The present results suggest that judging the formation of M2+-F- CIPs in practical solutions from a theoretical calculation perspective requires significant consideration of the kinetic factors, except for the thermodynamic factors.

Automated summary

The thermodynamic and kinetic behaviors of Mg2+-F- and Ca2+-F- ion pairing in aqueous solution were investigated. The results showed that the formation of ion pairs in the presence of water molecules is influenced by the hydration of the ions. The kinetic process of ion pairing for Mg2+-F- and Ca2+-F- involves multiple rate-limiting steps, and the formation of Mg2+-F- ion pairs requires overcoming a higher energy barrier. These findings are important for accurately determining the formation of ion pairs in practical solutions.