## 3 Results and Discussion
### Sorption Kinetics for Hexavalent Chromium  
The kinetic behavior for the adsorption process of Cr(VI) on AC@SCF, for different Cr(VI) initial concentrations and pH = 3, is depicted in Figure 5a. Solutions of 100 mL each, which contained 18 mg of AC@SCF and five different Cr(VI) initial concentrations (i.e., 5.23, 20.94, 26.73, 35.40, and 54.14 ppm), were used to carry out 24-h adsorption experiments. Figure 4: Effect of the initial pH (**a**) and the initial concentration of hexavalent chromium (Cr(VI)) (**b**) on the uptake capacity of AC@SCF. Figure 5: (**a**) Kinetic behavior of Cr(VI) removal via adsorption on AC@SCF activated carbon. The 24-h experiments at pH = 3 for different Cr(VI) initial concentrations (5.23, 20.94, 26.73, 35.40, and 54.14 ppm). Best fit of four kinetic models on adsorption process experimental data for initial concentrations of (**b**) 5.23 ppm, (**c**) 20.94 ppm, (**d**) 26.73 ppm, (**e**) 35.40 ppm, (**f**) 54.14 ppm. As can be seen from the same figure, apart from the 5.23 ppm initial concentration, all the other Cr(VI) initial concentrations were enough for AC@SCF to almost reach the intraparticle saturation stage after 24 h of adsorption activity. Nevertheless, this data set, in combination with the other four data sets, is useful for the interpretation of the kinetic behaviour of the process and the evaluation of the influence of the initial concentration on kinetic parameters for different kinetic models. For the study of the complete adsorption process as to the chemical equilibrium stage and for the prediction of the maximum uptake capacity of AC@SCF, an initial concentration beyond 20 ppm Cr(VI) in combination with 1.8 gAC@SCF/L was required. The main criterion which was used for the choice of the most appropriate kinetic model for the adsorption process was the goodness of fitting of the model over the experimental data. Figure 5b-f and the values of the correlation coefficient \(R^{2}\), which are presented in Table 3, showed that the diffusion-chemisorption (DC) model provided the most accurate estimations. It was also obvious that the intraparticle diffusion (ID) model provided the worst estimations and the worst fitting. The pseudo-second model also provided good enough estimations with \(R^{2}\) values quite close to these of the DC model. Moreover, in the case of the 5.23 ppm initial Cr(VI) concentration, the \(R^{2}\) value was better. But in this case, no equilibrium stage was reached. For this reason, reduced chi values are also presented in Table 3. The bigger the difference between q\({}_{t}\) values, experimental and predicted by a model, the bigger the reduced chi-squared values. In theory, if the observed (experimental) and expected (theoretical) values were identical, then chi-square would be zero. It is also obvious from Table 3, that apart from the case of 5.23 ppm, the DC model was superior to the pseudo-second model. The values in Table 3 were achieved using the OriginPro 2015 software of OriginLab Corporation. Moreover, the IBM SPSS Statistics software, version 26, was deployed to statistically investigate the hypothesis further that the diffusion-chemisorption model is the most appropriate kinetic model. The Akaike and Bayesian criteria showed that the diffusion-chemisorption model was the preferred model with \(K_{DC}\) = 46-123 mg/(g h\({}^{0.5}\)). Moreover, the predicted uptake capacity of AC@SCF at the equilibrium stage was higher than the experimental maximum adsorbed amount (\(q_{max}\)) for 24 h and fell in the range of \(q_{e}\) = 35-137 mgCr(VI)/gAC@SCF. This is presented in Figure 6a, which was based on the predictions of the DC model. This figure showed that, for temperature 21 \({}^{\circ}\)C and pH 3, the maximum uptake of Cr(VI) on AC@SCF activated carbon at the equilibrium stage was obtained for the initial concentration of 54.14 ppm and it was around 137 mgCr(VI)/gAC@SCF. It was also obvious from this figure that a sharp trend existed for increased \(q_{e}\) in cases of increased initial concentrations.