Equilibria, kinetics, and boron isotope partitioning in the aqueous boric acid–hydrofluoric acid system

The aqueous boric, hydrofluoric, and fluoroboric acid systems are key to a variety of applications, including boron measurements in marine carbonates for CO₂ system reconstructions, chemical analysis and synthesis, polymer science, sandstone acidizing, fluoroborate salt manufacturing, and more. Here we present a comprehensive study of chemical equilibria and boron isotope partitioning in the aqueous boric acid–hydrofluoric acid system. We work out the chemical speciation of the various dissolved compounds over a wide range of pH, total fluorine (F_T), and total boron (B_T) concentrations. We show that at low pH (0 ≤ pH ≤ 4) and F_T ≫ B_T, the dominant aqueous species is BF₄⁻, a result relevant to recent advances in high precision measurements of boron concentration and isotopic composition. Using experimental data on kinetic rate constants, we provide estimates for the equilibration time of the slowest reaction in the system as a function of pH and [HF], assuming F_T ≫ B_T. Furthermore, we present the first quantum-chemical (QC) computations to determine boron isotope fractionation in the fluoroboric acid system. Our calculations suggest that the equilibrium boron isotope fractionation between BF₃ and BF₄⁻ is slightly smaller than that calculated between B(OH)₃ and B(OH)₄⁻. Based on the QC methods X3LYP/6-311+G(d,p) (X3LYP+) and MP2/aug-cc-pVTZ (MP2TZ),  α_{(BF3−BF4⁻)} ≃ 1.030 and 1.025, respectively. However, BF₄⁻ is enriched in ¹¹B relative to B(OH)₄⁻, i.e., α_{(BF4⁻−B(OH)4⁻)} ≃ 1.010 (X3LYP+) and 1.020 (MP2TZ), respectively. Selection of the QC method (level of theory and basis set) represents the largest uncertainty in the calculations. The effect of hydration on the calculated boron isotope fractionation turned out to be minor in most cases, except for BF₄⁻ and B(OH)₃. Finally, we provide suggestions on best practice for boric acid–hydrofluoric acid applications in geochemical boron analyses.