Adsorption of basic red 9 onto activated carbon derived from immature cotton seeds: isotherm studies and error analysis

The activated carbon produced from immature cotton seeds via sulphuric acid activation was utilized for adsorption of the basic red 9 from the aqueous solution. Adsorbent possessed a larger surface area (495.96 m2/g), methylene blue number (42) and iodine number (510). The process parameters of the sorption system, such as pH of the solution (2–12), temperature (20–40°C) agitation time (1–5 h) and initial BR9 concentration (50–250 mg/l), were studied to understand their effects on BR9 removal. The optimized parameters are found to be pH: 12, temperature: 40°C, agitation time: 3 h and initial concentration: 150 mg/l. The experimental equilibrium data were analysed using a single-parameter model (Henry’s law), six two-parameter models (Langmuir, Freundlich, Temkin, Dubinin–Radushkevich, Smith, and Javanovic), eleven three-parameter models (Redlich–Peterson, Sips, Toth, Hill, Khan, Brunauer–Emmett–Teller (BET), Fritz–Schluender-III, Vieth–Sladek, Radke–Prausnitz, Brouers–Sotolongo, and Unilin), five four-parameter models (Baudu, Parker, Marczewski–Jaroniec, Fritz–Schlunder-IV and Weber–van Vliet) and a five-parameter model (Fritz–Schlunder-V). Non-linear regression analysis was employed to identify the best-fit isotherm based on the error functions: sum of the square error, derivative of hybrid fractional error function, derivative of Marquardt’s percentage standard deviation, average relative error, the sum of absolute errors and statistical comparison values: coefficient of determination (R2), root-mean-square error (RMSE) and non-linear chi-square test (χ2). Among the all adsorption isotherms considered, Fritz–Schlunder-V was found to be a perfect representation of the experimental equilibrium data (R2: 0.9998081, RMSE: 0.1018119, χ2: 0.0023423). The goodness of the models to explain the equilibrium data was in the order: Fritz–Schlunder-V ##xgt; Fritz–Schlunder-IV ##xgt; Brouers–Sotolongo ##xgt; Unilin ##xgt; Marczewski–Jaroniec ##xgt; Baudu ##xgt; Sips ##xgt; Hill ##xgt; Vieth–Sladek Fritz–Schluender-III ##xgt; Redlich–Peterson ##xgt; Khan ##xgt; Radke–Prausnitz ##xgt; BET ##xgt; Weber–van Vliet ##xgt; Langmuir ##xgt; Parker ##xgt; Jovanovic ##xgt; Freundlich.