## 3 Results and Discussion
### Kinetic Test  
Figure 4 shows Cu(II) and phosphate adsorption rates at 2 mM of Fe. Initially, both contaminants show a rapid initial uptake, followed by a slower uptake that gradually reaches equilibrium due to the increased concentration gradient resulting in a high driving force from the solution to the surface. Cu(II) sorption equilibrium was achieved within 60 min and over 90% sorption was observed rapidly,  
Figure 3: A schematic illustration of Cu(II) and phosphate removal on FHO-A. Figure 2: Cu(II) and phosphate removal efficiency (%) at (**a**) different Fe concentrations (1 mM and 2 mM) and 120 mg/L of alginate solution, (**b**) different alginate concentrations (0, 60, 120, 180 mg/L), and (**c**) the relation between Cu(II) removal efficiency (%) and alginate amount (g). requiring only a few minutes. The sorption rate is comparable with [PERSON] [35] who obtained \(\sim\)90% of removal efficiency using the alginate solution within 10 min, regardless of the initial amounts of alginate introduced. In comparison with the granule type alginate (average particle size of 3.5 mm), a previous study required at least 24 h to reach the sorption equilibrium [2]. This indicates that the removal of Cu(II) is occurring on the surface of FHO-A and within the pore structures, as is observed in similar nanoparticle systems. The noted trends in phosphate removal are clearly different than Cu(II). Only 50% of phosphate was removed in 10 min and the removal efficiency gradually increased over the course of 6 h. This is several times longer than previous studies using other iron-based adsorbents [36]. [PERSON] et al. [37] prepared FHO on the pore of an anion exchange resin and reported that most phosphate can be removed within 60 min. The use of powdered adsorbent (average size: 10-30 \(\upmu\)m) required less than 10 min to reach equilibrium, which was attributed to the same phenomena as the Cu(II) removal in our current study [38]. As suggested by the data presented in Figure 3 and Section 3.2, the longer equilibrium time for phosphate would be due phosphate penetrating the alginate polymer layer on the surface of FHO. In addition, the substantially faster kinetics for Cu(II) sorption supports the assertion that the alginate on the surface of FHO was responsible for the removal of Cu(II). In order to clarify transient behavior of Cu(II) and phosphate, linearized forms for pseudo 1 st and 2 nd order models were used to fit the experiment data based on Equations (1) and (2), respectively:  
\[\ln(q_{e}-q_{t})=lnq_{e}-k_{1}t \tag{1}\]  
\[t/q_{t}=(\frac{1}{k_{2}q_{e}^{2}})+\left(\frac{1}{q_{e}}\right)t \tag{2}\]  
where \(q_{e}\) and \(q_{t}\) are the uptake of the Cu(II) and phosphate per unit weight (mg/g) of FHO at equilibrium and at any time (t), respectively, \(k_{1}\) (1/min) and \(k_{2}\) (g/mg-min) are the rate constants of pseudo 1 st and 2 nd sorption, respectively. The value of \(k_{1}\) and \(k_{2}\) can be used to obtain the slope and the intercept of linearized Equations (1) and (2), respectively. Figure S1a,b shows the linearized pseudo 1 st and 2 nd order sorption model and the parameters used are found in Table 2. The results show that the pseudo 2 nd order plot is a better fit to the data than pseudo 1 st order, based on R\({}^{2}\) values. Furthermore, the pseudo 1 st and pseudo 2 nd order plots exhibited a strong correlation between the calculated and experimental \(q_{e}\) values for phosphate and Cu(II), respectively. A previous study [39] on metal removal using alginate confirmed that theoretical and experimental kinetics were well matched with a 2 nd order kinetic analysis. The fact  
Figure 4: Kinetic test of FHO-A at 2 mM Fe and 120 mg/L alginate. that the 2 nd order is more strongly correlated than the 1 st order suggests that the rate-limiting step for Cu(II) adsorption on the FHO-A is chemical adsorption but not mass transport limitations [40; 41]. In conjunction with this, the phosphate adsorption would be more affected by the mass transport due to the alginate layer.