## 3 Results and Discussion
### Practical Applications
It is evident from Figure 10a that for temperature T = 23 \({}^{\circ}\)C, after 24 h, and for the initial concentration at 5.5 ppm (i.e., 55 times higher than the recommended value in water), APC adsorbs 100% the Cr(VI) amount for pH values in the range 1-4 (acidic environment). After this value of pH the % adsorbed amount decreases and almost reaches 0% at pH = 8.0. For this reason, all kinetic experiments were carried out at pH = 3. As it is shown in Figure 10b for C\({}_{\text{init}}\) = 40 ppm, the experimental maximum adsorbed amount after 24 h of adsorption process is qmax(24 h) = 76 mgGv(VI)/gACC, while for C\({}_{\text{init}}\) = 53 ppm the experimental maximum adsorbed amount after 48 h of adsorption process is qmax(48 h) = 75 mgGv(VI)/gACC. This means that the maximum adsorbed amount is around 75 mgGv(VI)/gACC, if the initial Cr(VI) concentration is higher than 40 ppm, the temperature is 23 \({}^{\circ}\)C and the pH = 3. Moreover, the maximum adsorption capacity of APC as compared to the maximum adsorption capacity of PC is clearly higher for all cases of the Cr(VI) initial concentration. Figure 10: (**a**) Effect of pH on maximum uptake capacity for APC. (**b**) Effect of initial Cr(VI) concentration on Cr(VI) removed amount for pH = 3 and T = 23 \({}^{\circ}\)C after 24 h by PC and APC. It is also apparent from Figure 11 that APC exhibits superior adsorption rate and capacity properties compared to PC. For this reason, only the APC's kinetic data were interpreted in this work. Furthermore, for C\({}_{\text{init}}\) = 53 ppm, APC exhibits an experimental maximum adsorbed amount that is practically constant after 24 h of the adsorption process [i.e., q\({}_{\text{max}}\)(24 h) = 72 mg\({}_{\text{Cr(VI)}}\)/g\({}_{\text{AC}}\) and q\({}_{\text{max}}\)(48 h) = 75 mg\({}_{\text{Cr(VI)}}\)/g\({}_{\text{AC}}\)]. This essentially means that APC gets fully saturated after 24 h.  
As it is shown in Figure 12, four different kinetic models were used to quantify the adsorption kinetics in our work. The R\({}^{2}\) parameter of the Levenberg-Marquardt least-square fitting algorithm (Table 3) was the first tool for the evaluation of such models, in our case. The R\({}^{2}\) of the Pseudo First Order (PSO) model falls off as the initial concentration increases. This is reasonable because for C\({}_{\text{init}}\) = 5.5 ppm (the lower initial concentration), the occupation by Cr(VI) or other elements of the unoccupied sites in the pores is the controlling stage (PPO mechanism) [48] and the Cr(VI) was consumed totally before any saturation or transient phenomenon starts. But for higher initial concentrations, after the first steps, the occupation of the unoccupied sites stops to be the controlling stage. The R\({}^{2}\) trend of the pseudo second order (PSO) model is more stable as the initial concentration increases. This is an expected result because, for an increased initial concentration, a high percentage of the active sites of the pore surface were occupied quickly during initial time moments, but when this initial time pass, phenomena, such as transient adsorption, chemisorption, Van der Waals bonding, ion exchange and reactions, etc., start to exist in the pores. The PSO model was developed on the premise that chemisorption phenomena are the controlling mechanism [48]. This is the reason that the PSO model provides better fitting for increased initial Cr(VI) concentrations. The internal particle diffusion (IPD) R\({}^{2}\) values exhibited an increasing trend as the initial concentration increases. This is logical because the larger amounts of Cr(VI) in pores the lower the in-pore mobility of such species. This means that the intra particle diffusion (IPD) mechanism tends to be the controlling stage, but it is not accomplished. Nevertheless, the R\({}^{2}\) values for the IPD model are poor compared to the  
Figure 11: Kinetics and capacity comparison for various initial concentrations of PC and APC. respective values of the other three models.