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Heavy metals are one of deadly contaminants in ground water across the globe. Thus, herein, this data set comprises experimental and modelled data on the removal of heavy metals from ground water using melanin synthesized by the marine bacteria Pseudomonas stutzeri. Characterization of biosynthesized melanin and modelling of the kinetic and the thermodynamic study on adsorption of heavy metals such as mercury (Hg(II)), lead (Pb(II)), chromium (Cr(VI)), and copper (Cu(II)) are included in this article. Apart from the study of parameters involved in adsorption such as pH, temperature, concentration and time; the data from these studies are modelled to analyze the nature and characteristic of heavy metals adsorbing to melanin nanoparticles. The figures from models, results from models as tables, characterization and analytical figures are depicted in this work.