# Adsorption of Arsenic and Heavy Metals from Solutions by Unmodified Iron-Ore Sludge
## 3 Results and Discussion
### Batch Equilibrium Adsorption  
In this study, the adsorption isotherms for the single- and mixed-metal experiments show that the adsorption capacity decreased in the following order Pb > As > Mn > Cd > Zn (Figure 7). The [PERSON] (Equation (6)) and Freundlich (Equation (7)) models were employed to describe the adsorptive behavior of selected adsorbates onto the adsorbent. To minimize the respective error functions, the non-linear optimization technique was applied in calculating the adsorption parameters from these models:  
\[q_{e}=\frac{Q_{max}^{0}K_{L}C_{e}}{1+K_{L}C_{e}} \tag{6}\]  
\[q_{e}=K_{F}C_{e}^{\frac{1}{n}} \tag{7}\]  
where \(q_{e}\) and \(C_{e}\) are obtained from Equation (2); \(Q_{max}^{o}\) (mg/g) is the maximum saturated monolayer adsorption capacity of the adsorbent; \(K_{L}\) (L/mg) is the Langmuir constant related to the affinity between the adsorbent and adsorbate; \(K_{F}\) [(mg/g)/(mg/L)\({}^{n}\)] is the Freundlich constant, describing the intensity of adsorption; \(\frac{1}{n}\) (dimensionless; 0 < \(n\) < 10) is a Freundlich intensity parameter, implying the magnitude of the adsorption driving strength or surface heterogeneity. The parameters of the adsorption models are listed in Table 3. The \(R^{2}\) values of the Langmuir model (0.902-0.993) are higher than those of the Freundlich model (0.833-0.949), indicating that the adsorption characteristics of the contaminants in the adsorbent are adequately described by the Langmuir model. The data are consistent with the Langmuir adsorption model, suggesting that the adsorption sites were homogeneous with monolayer adsorption coverage [42]. Figure 7: Adsorption isotherm of As and heavy metals onto the adsorbent from (a) single-metal experiments and (b) mixed-metal experiments. The order of Langmuir maximum adsorption capacity for the single-metal experiments was Pb \(>\) As \(>\) Cd \(>\) Zn \(>\) Mn, with values of 1.305, 1.113, 0.771, 0.745, and 0.710 mg/g, respectively. Under the same experimental conditions, the \(Q^{o}_{max}\) values in the mixed-metal experiments exhibited the following order: Pb \(>\) Cd \(>\) Zn \(>\) Mn, with values of 1.059, 0.484, 0.447, and 0.370 mg/g, respectively. The order of adsorption capacities might reflect the ionic radius of heavy metals (Pb\({}^{2+}\), Cd\({}^{2+}\), Mn\({}^{2+}\), Zn\({}^{2+}\)), which affects the charge density of ions. The greater the cation radius, the smaller the charge density, and vice versa. The cation radius of the metals in the study are as follows: rPb(1.2 A) \(>\) rCd (0.97A) \(>\) rZn (0.74A) \(>\) rMn (0.67A) [45]. In addition, it is noted that the adsorption capacity of the heavy metals in the single-metal experiments is higher than that in the mixed-metal experiments, implying competition among heavy metals in the same solution [8]. The adsorption ability of heavy metals by SBC in this study can be explained by the specific surface area (BET), cation exchange capacity (CEC), presence of clay minerals (e.g., kaolinite and illite) [36], presence of large amounts of silica (Si-OH) [46,47] and O-H bending [46,48]. In addition, high contents of goethite (20%) may result in adsorption of As by the adsorbent [49,50]. The maximum Langmuir adsorption capacity (\(Q^{o}_{max}\)) of SBC is compared with that of other adsorbents in Table 4. The adsorption capacity of SBC was higher than that of laterite [34,51] and red mud [52] for As; laterite (OBY) for Pb [51]; and laterite (Tam Duong) for Zn, Cd, and Mn [34] (Table 4). However, the maximum adsorption capacity of SBC was lower than that of some clays and modified materials such as \(\delta\)-FeOOH [53], kaolinite [36], montmorillonite [54,55], glucose AC [56], activated carbon [57], and ICZ (iron-coated zeolite) [44] (Table 4). Of note, the modification of raw materials increases their adsorption capacity [10,15,58]. Therefore, suitable modification of SBC should be performed to increase its adsorption capacity.