On the Replicability of the Thermodynamic Modeling of Spectroscopic Titration Data in the Nickel(II) En System

Characterizing complicated solution phase systems in situ requires advanced modeling techniques to capture the intricate balances between the many chemical species. Due to the error inherent in any scientific measurement, a spectrophotometric titration experiment with nickel(II) and ethylenediamine (en) was repeated six times using an autotitrator to test the replicability of the data and the consistency of the resulting thermodynamic model. All six datasets could be modeled very tightly (R² > 99.9999%) with the following eight complexes: [Ni]²⁺, [Ni₂en]⁴⁺, [Nien]²⁺, [Ni₂en₃]⁴⁺, [Nien₂]²⁺, [Ni₂en₅]⁴⁺, [Nien₃]²⁺, and [Nien₆]²⁺. The logK values for the stepwise associative reactions agree with existing literature values for the majority species ([Nien_{n = 1–3}]²⁺) and matched expectations for the minority species; 95% confidence intervals for each logK value were determined via bootstrapping, which quantifies the variability in the binding constant value that is supported by a given dataset. The repeated experiments, which could not be successfully concatenated together, demonstrate that replication is crucial to capturing all the variability in the logK values. Conversely, bootstrapped confidence intervals across multiple experiments can be readily combined to generate an appropriate range for an experimentally determined binding constant.