Theoretical Estimation of Equilibrium Constants for Boron Isotopic Exchange Reactions in Ion-exchange Chromatography

The equilibrium constant K for isotopic exchange reactions between boric acid B(OH)₃ in the external solution and the main species of B(OH)₄^-，B₃O₃(OH)₅^2- and B₃O₃(OH)₄^- formed in an ion-exchange resin is one of the fundamental parameters in the study of boron isotopes separation by ion-exchange chromatography．Unfortunately， it is very difficult to determine the K value accurately from experiments．Density function theory（DFT）calculations were used to compute the vibrational frequencies of boron isotopomers of the gasphase B(OH)₃ and B(OH)₄^- at the B3LYP/6—31G level．The values of reduced partition function ratio（RPFR）of the four boron species，B(OH)₃, B(OH)₄^-, B₃O₃(OH)₅^2- and B₃O₃(OH)₄^-，were estimated following Urey’s model，using the calculated frequencies obtained from DFT calculation．The equilibrium constant K of isotopic exchange reactions were theoretically obtained as the ratio of the RPFRs of two boron species． The results implied that the isotopic effect between B(OH)₃ and B(OH)₄^- was remarkable with a calculated equilibrium constant K of 1.025 7 at 25 ℃. However, these K valcues for the reactions between B(OH)₃ with other two species，B₃O₃(OH)₅^2- and B₃O₃(OH)₄，were smaller around 1.017 2 and 1.008 4， respectively．