A Least-Squares Method for Computing Rate Constants of Reversible, First-Order, Triangular Network Reactions and Its Application to the Intermolecular Rearrangements of Acetylacetonatobis(4,4,4-trifluoro-1-phenyl-1,3-butanedionato)ruthenium(III)

A useful method for computing the rate constants of reversible, first-order, triangular network reactions (B1\ightleftarrowsB2, B2\ightleftarrowsB3, B3\ightleftarrowsB1) is developed. It gives the best-fit set of the rate constants from the experimental data of the equilibrium constants and the mole fraction-time curves through an iterative least-squares method. This type of reaction can be classified into three categories for different shapes of the mole fraction-time curves. The method was successfully applied to determining the rate constants of the rearrangement reactions among the three isomers of [Ru(acac)(tfpb)2] (acac−=acetylacetonate ion, tfpb−=4,4,4-trifluoro-1-phenyl-1,3-butanedionate ion) in N,N-dimethylformamide at 90 °C. The direct conversion between the de,fc-bis(tfpb) isomer and the cf,ed-bis(tfpb) isomer was forbidden. The twist mechanisms are incompatible with this fact.