## 3 Results and Discussion
### Adsorption Kinetics and Isotherms  
The kinetic model is essential for gaining a detailed understanding of the adsorption process of MB dye on BCA-Mag/AB and for identifying the rate-controlling step that explains the adsorption of these dyes. To achieve this goal, the nonlinear expressions of the most commonly used kinetic models, particularly the pseudo-first-order (PFO), pseudo-second-order (PSO), and Elovich models, are presented in Equations (5)-(7), respectively [29]. \[\mathrm{q_{t}}=\mathrm{q_{e}}\left(1-\mathrm{e^{-k_{1}t}}\right) \tag{5}\]  
\[\mathrm{q_{t}}=\left(\mathrm{k_{2}q_{e}^{2}t}\right)/\left(1+\mathrm{k_{2}q_{ e}t}\right) \tag{6}\]  
\[\mathrm{q_{t}}=(1/\beta)\mathrm{ln}(\alpha\beta t+1) \tag{7}\]  
In these expressions, \(\mathrm{k_{1}}\) represents the pseudo-first-order rate constant (1/min), \(\mathrm{k_{2}}\) indicates the pseudo-second-order rate constant (g/mg min), \(\alpha\) denotes the initial adsorption rate (mg g\({}^{-1}\) min\({}^{-1}\)), and \(\beta\) corresponds to the desorption constant related to the extent of surface coverage (g mg\({}^{-1}\)). Nonlinear plots (C\({}_{\mathrm{e}}\) vs. q\({}_{\mathrm{e}}\)) for the adsorption of MB dye are shown in Figure 5a. Moreover, the kinetic parameters for MB adsorption are summarized in Table 6. According to the findings presented in Table 6, the adsorption of MB dye onto BCA-Mag/AB aligns well with the pseudo-first-order (PFO) model. This finding is demonstrated by the high R\({}^{2}\) values and the close correlation between the experimental (q\({}_{\mathrm{e}}\), exp) and calculated (q\({}_{\mathrm{e}}\), cal) values when compared to the pseudo-second-order (PSO) and Elovich models. This indicates that physical adsorption is a more dominant mechanism than chemical adsorption [30]. Figure 5: (**a**) Nonlinear kinetics models; (**b**) nonlinear isotherm models. adsorption isotherm studies explain the interaction of MB dye with BCA-Mag/AB. As a result, the most commonly used isotherms, such as Langmuir, Freundlich, and Temkin, were applied to determine the adsorption capacity of BCA-Mag/AB and to evaluate the adsorption equilibrium statistics. The nonlinear expressions of Langmuir, Temkin, and Freundlich are presented in Equations (8)-(10), respectively [31]. \[\mathrm{q_{e}}=\mathrm{q_{m}K_{L}C_{e}/(1+K_{L}C_{e})} \tag{8}\]  
\[\mathrm{q_{e}}=\mathrm{B_{T}ln(A_{T}C_{e})} \tag{9}\]  
\[\mathrm{q_{e}}=\mathrm{K_{F}C_{e}^{\frac{1}{2}}} \tag{10}\]  
In these expressions, \(\mathrm{K_{L}}\) represents the Langmuir constant (L/mg), \(\mathrm{q_{m}}\) denotes the monolayer capacity (mg/g), \(\mathrm{K_{F}}\) signifies the Freundlich constant (mg/g) (L/mg), n indicates the adsorption intensity, \(\mathrm{A_{T}}\) is the Temkin constant (L/mg), and \(\mathrm{B_{T}}\) corresponds to the heat of adsorption (J/mol). Nonlinear plots (\(\mathrm{C_{e}}\) vs. \(\mathrm{q_{e}}\)) for the adsorption of MB dye are presented in Figure 5b. Additionally, the values of the isotherm parameters for MB adsorption are summarized in Table 7. The relevant values (Table 7) indicate a relatively high R\({}^{2}\) compared to the Freundlich, Langmuir, and Temkin isotherms, suggesting that the adsorption behavior of MB by BCA-Mag/AB implies a multilayer adsorption on the heterogeneous surface of BCA-Mag/AB. Therefore, it is clear that MAG has potential as an effective and economical adsorbent for the purification process of hazardous pollutants from water.