2025 Volume 74 Issue 7 Pages 133-141
In this study, we propose a method to efficiently estimate equilibrium constants for multiple reactions using titration curves of metal ion complexes. First, titration curves were measured, and candidate complex reactions were listed. An efficient numerical simulation method was then developed to compute titration curves parameterized by equilibrium constants. To estimate these constants, we formulated an optimization problem maximizing the likelihood between simulations and experiments, applying Bayesian estimation to reduce instability. Additionally, model selection based on Akaike’s information criterion （AIC） identified key complex reactions influencing pH changes. The method’s effectiveness was validated through two tests. First, simulated titration curves with artificial errors demonstrated accurate equilibrium constant estimation. Second, applying the method to aluminum hydroxide and aluminum fluoride titration curves, we identified eight major reactions from 21 candidates.
