Modeling Complexometric Titrations of Natural Water Samples

Complexometric titrations are the primary source of metal speciation data for aquatic systems, yet their interpretation in waters containing humic and fulvic acids remains problematic. In particular, the accuracy of inferred ambient free metal ion concentrations and parameters quantifying metal complexation by natural ligands has been challenged because of the difficulties inherent in calibrating common analytical methods and in modeling the diverse array of ligands present. This work tests and applies a new method of modeling titration data that combines calibration of analytical sensitivity (S) and estimation of concentrations and stability constants for discrete natural ligand classes ([L_i]_T and K_i) into a single step using nonlinear regression and a new analytical solution to the one-metal/two-ligand equilibrium problem. When applied to jointly model data from multiple titrations conducted at different analytical windows, it yields accurate estimates of S, [L_i]_T, K_i, and [Cu²⁺] plus Monte Carlo-based estimates of the uncertainty in [Cu²⁺]. Jointly modeling titration data at low- and high-analytical windows leads to an efficient adaptation of the recently proposed “overload” approach to calibrating ACSV/CLE measurements. Application of the method to published data sets yields model results with greater accuracy and precision than originally obtained. The discrete ligand-class model is also re-parametrized, using humic and fulvic acids, L₁ class (K₁ = 10¹³ M^-1), and strong ligands (L_S) with K_S ≫ K₁ as “natural components”. This approach suggests that Cu complexation in NW Mediterranean Sea water can be well represented as 0.8 ± 0.3/0.2 mg humic equiv/L, 13 ± 1 nM L₁, and 2.5 ± 0.1 nM L_S with [Cu]_T = 3 nM. In coastal seawater from Narragansett Bay, RI, Cu speciation can be modeled as 0.6 ± 0.1 mg humic equiv/L and 22 ± 1 nM L₁ or ∼12 nM L₁ and ∼9 nM L_S, with [Cu]_T = 13 nM. In both waters, the large excess (∼10 nM) of high-affinity, Cu-binding ligands over [Cu]_T results in low equilibrium [Cu²⁺] of 10^-14.5±0.2 M and 10^-13.3±0.4 M, respectively.