Beyond Pseudo-Order Kinetics: Multireaction and Second-Order Models Reveal a Dose-Dependent Irreversible Chromium Retention Threshold on Nano Zero-valent Iron -Biochar

Abstract

Pseudo-first-order (PFO), pseudo-second-order (PSO), multireaction (MRM) and second-order (SOM) kinetic models were compared for Cr(VI) adsorption on nano zero-valent iron impregnated biochar (nZVIbiochar, 1:5) across three sorbent masses (0.5, 1 and 2 g in 50 mL) and two initial concentrations (20 and 100 mg L-¹). Adsorbed amounts were in the range ~0.15-4.8 mg g-¹; removal efficiencies (48-65% at 80 min) are consistent with the companion optimisation study, confirming mass conservation. All four models described the kinetics well at most conditions (R² = 0.63-0.998), with PSO and SOM giving the closest fits overall. PSO equilibrium capacities were physically bounded (qe,cal = 0.7-6.6 mg g-¹). MRM, fitted by the pooled approach with the reaction order fixed at the Freundlich 1/n, described the 100 mg L-¹ data closely (R² = 0.958-0.997) and the 20 mg L-¹ data less well (R² = 0.63-0.85). SOM, fitted per treatment with four parameters against six points, was over-parameterised (residual df = 2) and was retained only as a crosscheck. The one mechanistic inference the data support is a dose-dependent threshold for consecutive irreversible retention: the coefficient ks is statistically distinguishable from zero only at the 2 g dose (MRM ks = 0.0305 min-¹, 95% CI ≈ 0.008-0.053; SOM ks = 0.025 min-¹ in agreement and robust to the fixed Smax). This is tentatively consistent with Cr(III)-Fe coprecipitation at higher nZVI loading, as indicated spectroscopically in the companion study, but requires desorption/leaching validation. Residual diagnostics confirm random residuals except for MRM at 2 g/20 mg L-¹. Overall, MRM and SOM add a retention reversibility dimension that is not represented in the PFO and PSO functional forms, while the limited kinetic dataset constrains how far the additional parameters can be interpreted.