Computational and solubility equilibrium experimental insight into Ca2+-fluoride complexation and their dissociation behaviors in aqueous solutions: implication for the association constant measured using fluoride ion selective electrodes

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 CaF_x(H₂O)₁₄^2-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.