Using response surface methodology to optimize the operating parameters on the sorption of cadmium and surface area of the adsorbent

Abstract In this study, the adsorption of cadmium ions from aqueous solutions onto hydroxyapatite was investigated. A series of apatite powders were synthesized under varying conditions of reaction time, reaction temperature and calcination temperature. In addition, the specific surface area ( S BET ) of the synthetized powders was measured. To model and optimize both cadmium adsorption efficiency and the surface area, response surface methodology (RSM) was employed. Three variables were considered: reaction time (time: 1–96 h), reaction temperature ( T Sol : 20–70 °C) and calcination temperature ( T Cal : 45–655 °C), while the reaction pH was initially fixed at 9. The developed regression models showed good agreement with the experimental data, as indicated by high coefficients of determination (R 2 ), confirming the adequacy of the fitted models. The optimal conditions determined using the desirability function, yielded a specific surface area of approximately 96.897 m 2 /g and a cadmium efficiency of 97.948 % at a calcination temperature of 329 °C, a synthesis temperature of 42 °C and a reaction time of 49.9 h. In the second step, a new parameter such as reaction pH, was introduced to study its effect on cadmium removal. The results indicated that when the pH exceeded 9.3, the removal efficiency decreased, while the maximum adsorption was observed at pH = 9.3. Equilibrium and kinetic studies were also conducted, revealing that cadmium adsorption follows the Langmuir isotherm model and pseudo-second order kinetics.