# Effect of Hydrogen Ion Presence in Adsorbent and Solution to Enhance Phosphate Adsorption
## 3 Results and Discussion
### Isotherm Tests  
A series of batch isotherm tests were conducted at initial pH of 4, 7, and 9 with and without pH solution adjustment. Among several mathematical models to fit the experimental data of the adsorption isotherms, such as [PERSON] [24], [PERSON] [25], [PERSON] [13], and Freundlich [14], the [PERSON] and Freundlich isotherm equations are widely used and follow below. \[q_{e}=\frac{bQ_{m}C_{e}}{1+bC_{e}}, \tag{2}\]  
Figure 3: The removal efficiency of phosphate and final pH (**a**) and uptake and fraction of species of phosphate at initial pH of 3–9 (**b**). where \(q_{e}\) and \(Q_{m}\) are the equilibrium uptake (mg/g) and the maximum phosphate capacity (mg/g) in the solid phase, respectively. \(C_{e}\) is the equilibrium concentration of phosphate in the aqueous phase (mg/L), and \(b\) is the Langmuir affinity coefficient related to the sorption (binding) energy between the sorbent and sorbate. \[q_{e}=k_{f}C^{1/n}, \tag{3}\]  
where \(q_{e}\) is the \(C\) is the aqueous phosphate concentration at equilibrium, \(k_{f}\) is the adsorption capacity, and \(1/n\) is the sorption intensity. Briefly, certain concepts describe both adsorption isotherms. The shapes of the adsorption isotherms were classified into four main groups, such as L, S, H, and C [26]. According to the classification, all of the isotherms displayed the L-curve pattern that is called the Langmuir isotherm, indicating the flat adsorption of the molecules on the surface and lack of strong competition during the adsorption process [26,27]. As shown in Equations (2) and (3), the Freundlich equation is expressed by an exponential equation assuming that the uptake of the adsorbate increases with the increasing adsorbate concentration [27]. The assumption for Langmuir and Freundlich is the mono and multi-adsorption layer, and this shows better fit data at low and high experimental concentrations, respectively [28]. Figures 4 and 5 are the nonlinear Langmuir and Freundlich isotherm models, respectively, and the parameters calculated are listed in Table 3. Based on the coefficient of determination (R\({}^{2}\)), it is hard to determine which is a better fit for both isotherm equations. Among the three pH experiments, pH 7 shows less difference of the \(Q_{m}\) obtained to over 3 mg/g than those of pH 4 and 9 for both the GAC and the GACA, corresponding to approximately less pH shift around 6-7. However, the value of \(Q_{m}\) is clearly shown to be twice as high for the GAC at the acid condition and for the GACA at the base condition, respectively. This result has a similar tendency to that in Figure 3 at the base condition but is the opposite at the acid condition. This is because of sufficient concentration of the phosphate compared with Figure 3, describing that the removal efficiency does not show significant differences at the acid condition for the GAC and GACA. Additionally, the pH adjustment at the acid condition does not have a significant effect on the \(Q_{m}\) of phosphate for the GAC and GACA, whereas \(Q_{m}\) decreases from 3.96 to 2.59 mg/g (35% reduction) for the GACA at the base condition. With regard to the electrostatic force between the surface charge of the GAC and phosphate species at the acid condition, the higher \(Q_{m}\) for the GAC is estimated to be the shift species from H\({}_{2}\)PO\({}_{4}\)\({}^{-}\) to HPO\({}_{4}\)\({}^{2-}\), which is possible due to the Donna effect [29]. At a pH of 9, the higher \(Q_{m}\) for the GACA is attributed to the maintenance of the solution at a pH of approximately 7 during the experiment, while the pH increases to 8 and 9 for the GAC. The reduction from 3.96 to 2.56 mg/g will be explained in Section 3.5. The values of \(Q_{m}\) and \(k_{f}\) show the same trends in all of the experimental conditions. The value of \(n\) indicates the adsorption process as follows: (a) linear adsorption at \(n=1\) (b) chemical process \(n<1\), physical process \(n>1\)[30]. \(n\) within the range of 1-10 is considered to be good adsorption [31].