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• Single-layered 2D nanosheets of α-ZrP were obtained through exfoliation. • Free amine groups were covalently attached to the single-layered α-ZrP nanosheets. • AF-ZrP shows an extraordinarily high adsorption capacity for Pb2+ and Congo red dye. • Non-linear regression methods are more accurate compared to linear methods. This paper reports a facile route for preparing single-layered and crystalline 2D nanosheets of α-zirconium phosphate (α-ZrP), which were further functionalized through covalent attachment of amino organosilane on its exfoliated surfaces (AF-ZrP) to enhance their sorption capacity for Pb2+ and Congo red removal. Two possible surface arrangements of NH 2 groups were observed: one as free amine groups without bonding and the other as protonated or hydrogen-bonded amine groups. AF-ZrP exhibits extraordinary adsorption capacities of 1640 and 1213 mg g−1 for removing Pb2+ ions and CR dye. Further, linear and non-linear regression methods have been studied and compared for fitting four adsorption isotherm models and two kinetics models. Non-linear Freundlich isotherm and non-linear pseudo-second order kinetic models prove the most suitable. The high adsorption capacity, easy regeneration, and reusability rendered AF-ZrP a suitable adsorbent for removing Pb2+ ions and Congo red (CR) dye at industrial scale. [ABSTRACT FROM AUTHOR]