Adsorptive Removal of Heavy Metals from Industrial Wastewater Using Modified Agricultural Waste-Derived Biochar: An Isotherm, Kinetic and Thermodynamic Modelling Study

Abstract

Agricultural residues converted to biochar are among the most frequently proposed low-cost adsorbents for heavy metal removal, but the parameters reported for them are difficult to compare because model selection is often made on the coefficient of determination of a linearised transform, which is known to distort the error structure of the underlying data. This article applies a consistent non-linear fitting protocol to a declared synthetic dataset representing phosphoric-acid-modified rice husk biochar in contact with lead, cadmium and copper. Equilibrium data were generated from a Langmuir surface with stated capacities and affinity constants and 3 % multiplicative dispersion, then fitted by the Langmuir, Freundlich, Temkin and Dubinin–Radushkevich models without linearisation. The Langmuir model was preferred for all three metals, returning monolayer capacities of 108.9, 78.1 and 63.1 mg g⁻¹ for lead, cadmium and copper at coefficients of determination of 0.9976, 0.9929 and 0.9925, against Freundlich values of 0.9045, 0.9538 and 0.9620. Dubinin–Radushkevich mean sorption energies of 13.46, 11.66 and 10.53 kJ mol⁻¹ place all three systems in the chemisorption regime. Kinetic data generated from a pseudo-second-order process were fitted by both the pseudo-first-order and pseudo-second-order forms; the latter was preferred throughout, with coefficients of determination of 0.9855 to 0.9976 against 0.9040 to 0.9641. Van 't Hoff analysis returned an enthalpy of 18.5 kJ mol⁻¹ with free energies from −19.9 to −27.3 kJ mol⁻¹, indicating a spontaneous, endothermic and entropy-driven process.