## 3 Results and Discussion
### Equilibrium Isotherm  
In general, a sorption equilibrium isotherm test can be utilized to optimize the design of an adsorption system for the removal of a target contaminant from the solution. Several types of isotherm equations were widely employed to predict the adsorption processes and behaviors, such as generalized, Temkin [45], Toth [46], [PERSON] [47], Dubinin-Radushkevich [48] and two sorption equilibrium models, Langmuir [49] and Freundlich [50]. In principle, the Langmuir isotherm assumes that sorption takes place at a specific site and no further adsorption occurs after the sorption is complete, while the Freundlich isotherm occurs at infinite sorption on a heterogeneous surface through a multilayer.  
The Langmuir and Freundlich equations are given in Equations (4) and (5), respectively, and both can be transformed to linear equations, as shown in Equations (6) and (7), respectively.  
\[\text{Langmuir: }q_{e}=\frac{QbC_{e}}{1+bC_{e}} \tag{4}\]  
\[\text{Freundlich: }q_{e}=k_{f}C_{e}^{1/n} \tag{5}\]  
\[\text{Linear Langmuir: }\frac{C_{e}}{q_{e}}=\frac{1}{Qb}+\frac{1}{Q}C_{e} \tag{6}\]  
\[\text{Linear Freundlich: }lnq_{e}=lnk_{f}+\frac{1}{n}lnC_{e} \tag{7}\]  
where, \(C_{e}\) is the equilibrium concentrations (mg/L) of Cu(II) or phosphate in solution and \(q_{e}\) is the amount of Cu(II) or phosphate adsorbed per unit mass of FHO-A (mg/g), \(Q\) is the maximum uptake  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **k** & **R\({}^{2}\)** & **C** & **q-exp. (\({}^{1}\))** & **q-cal. (\({}^{2}\))** \\ \hline Pseudo & Cu(II) & 0.0174 & 0.926 & 3.29 & 26.8 & 84.8 \\
1 st & Phosphate & 0.0169 & 0.962 & 3.88 & 48.4 & 48.6 \\ \hline Pseudo & Cu(II) & 0.0107 & 0.999 & 0.0378 & 93.5 & 84.8 \\
2 nd & Phosphate & 0.0581 & 0.986 & 1.27 & 17.2 & 48.6 \\ \hline Intraparticle & Cu(II) & 0.9124 & 0.822 & 76.5 & - & - \\  & Phosphate & 2.1118 & 0.980 & 12.5 & - & - \\ \hline \end{tabular} (1) Experimental q value. (2) Calculated q value.  
\end{table}
Table 2: Pseudo 1 st and 2 nd order and intraparticle kinetic parameters.  
per unit mass of FHO-A (mg/g), and \(b\) is the Langmuir constant related to the adsorption energy (L/mg), \(k_{f}\) is the Freundlich constant related to the adsorption capacity, \(n\) is the empirical parameter representing the energetic heterogeneity of the adsorption sites (dimensionless). Therefore, the higher b and \(k_{f}\) value represents higher affinity for adsorbate toward the adsorbent [41]. The value of \(n\) from Freundlich can be utilized to differentiate between the alternate adsorption pathways, where \(n>1\) is indicative of a physical process and \(n<1\) is points to a chemical process [51].  
Figure 5 showed the fitted adsorption isotherms and the calculated parameters are found in Table 3. According to the values in Table 3, the parameters obtained by [PERSON] for Cu(II) were not consistent and showed that no plateau was observed in Figure 5. This indicates that the sorption isotherm is not complete. The saturation of the sorbent is not achieved. In addition, the maximum uptake of Cu(II) was calculated to be 487 and 350 mg/g for the non-linear and linear equations, respectively. The correlation coefficients (R\({}^{2}\)) of 0.966 and 0.704, respectively, were noted and not comparable with other studies for the removal of Cu(II) [52]. This suggests that the Freundlich equation is more appropriate for fitting an isotherm profile for Cu(II). However, a comparison of the other model and the parameters for Cu(II) and phosphate can be done. Based on the values of \(b\), \(k_{f}\), and \(n\), phosphate has a higher affinity and more favorable adsorption than Cu(II), verifying that the interaction between FHO and phosphate is stronger than that between alginate and Cu(II).