Adsorption isotherm models and error analysis for single and binary adsorption of Cd(II) and Zn(II) using leonardite as adsorbent

Leonardite, a by-product from coal mines, was applied to adsorb Cd(II) and Zn(II) from aqueous solutions. Individual and simultaneous adsorptions of the two metal ions were investigated. In a single-component adsorption system, Langmuir and Freundlich isotherms were fitted to the adsorption data. Linear and nonlinear regression methods were used for the assessment of the optimum adsorption isotherm. Error functions including root-mean-square error, sum of the squares of the errors, mean absolute percentage error, Marquardt’s percent standard deviation (MPSD), and Chi-square were applied in the nonlinear regression. The most suitable model for the adsorption of Cd(II) and Zn(II) in the single system is the Freundlich isotherm. The isotherm parameters calculated by MPSD provided the lowest sum of normalized error (SNE) value. The adsorption capacity was found to be 23.89 mg/g for Cd(II) and 16.86 mg/g for Zn(II). It was observed that the adsorption of Cd(II) on leonardite is greater than that of Zn(II). For binary component adsorption systems, Cd(II) and Zn(II) showed antagonistic behavior. The presence of the other metal ions could decrease the amount of metal adsorbed. Binary adsorption of Cd(II) and Zn(II) was tested with regard to four multi-component isotherms: Extended Langmuir, Modified Langmuir, Sheindorf–Rebuhn–Sheintuch, and Extended Freundlich. The Extended Freundlich isotherm proved to be a good fit for the experimental data.