## 3 Results and Discussion
### Cu\({}^{2+}\) Removal Performance of the Biochar Sample  
Figure 4 shows the adsorption kinetics of Cu\({}^{2+}\) into the studied biochar samples. The three BCs presented saturation at different experimental times and before the final 1440 min. The order of the efficacy of Cu\({}^{2+}\) removal at 1440 min of adsorption time was BC450 (119.9 mg g\({}^{-1}\)) > BC600 (101.9 mg g\({}^{-1}\)) > BC300 (71.91 mg g\({}^{-1}\)). This may be explained by the higher surface area and pore volume of BC450 and BC600 compared with BC300. In addition, BC450 had a higher cation exchange capacity, which would favor the adsorption compared with the other biochar samples. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Linear Parameters** & **BC300** & **BC450** & **BC600** \\ \hline Langmuir & & & \\ \(q_{m}\) (mg g\({}^{-1}\)) & 49.24 & 58.00 & 93.55 \\ \(k_{L}\) (L mg\({}^{-1}\)) & 23.50 & 10.91 & 0.372 \\ \(R_{L}\) & 0.0003978 & 0.0003377 & 0.0002094 \\ \(R^{2}\) & 0.994 & 0.999 & 0.998 \\ Freundlich & & & \\ \(k_{F}\) (mg g\({}^{-1}\)) & 24.78 & 24.89 & 23.20 \\ \(n^{-1}\) (mg L\({}^{-1}\)) & 0.2364 & 0.1933 & 0.4417 \\ \(R^{2}\) & 0.963 & 0.919 & 0.952 \\ Dubinin–Radushkevich C & & & \\ \(q_{m}\) (mg g\({}^{-1}\)) & 139.22 & 222.20 & 637.08 \\ \(K\) (\(\times 10^{-9}\) mol\({}^{2}\)/k\(\mid\)\({}^{2}\)) & 1.25 & 1.57 & 2.41 \\ \(E\) (kd mol\({}^{-1}\)) & 19.99 & 17.83 & 14.4 \\ \(R^{2}\) & 0.967 & 0.938 & 0.970 \\ Tempkin & & & \\ \(b_{T}\) (J g mol\({}^{-1}\) mg\({}^{-1}\)) & 575.0 & 333.0 & 124.2 \\ \(a_{T}\) (L mg\({}^{-1}\)) & 479.0 & 92.99 & 3.705 \\ \(R^{2}\) & 0.850 & 0.934 & 0.991 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Adsorption isotherm parameters of the Langmuir, Freundlich, Dubinin–Radushkevich, and Temkin models determined for the biochar samples from _Macocystis pyrifera_ under study. Figure 4: Cu\({}^{2+}\) removal kinetics of biochar samples under study (BC300, BC450, and BC600). To better understand the type of Cu\({}^{2+}\) adsorption involved in the process with respect to the time and different biochar samples applied, we used a linearized form of pseudo-first-order (Equation (8)) and pseudo-second-order (Equation (9)) [53] models (Figure 5A,B and Table 5). The equations are as follows:  
\[\log(q_{e}-q_{t})\ =\ \log(q_{e})-\frac{k_{1}\ t}{2.303} \tag{8}\]  
\[\frac{t}{q_{t}}\ =\ \frac{1}{k_{2}q_{e}^{2}}+\frac{\mathrm{t}}{q_{e}} \tag{9}\]  
where \(q_{t}\) (mg g\({}^{-1}\)) is the amount of Cu\({}^{2+}\) adsorbed at time \(t\), \(q_{e}\) is the amount of Cu\({}^{2+}\) adsorbed at equilibrium time (1440 min), \(k_{1}\) (min\({}^{-1}\)) is the pseudo-first-order constant, and \(k_{2}\) (g mg\({}^{-1}\) min\({}^{-1}\)) is the pseudo-second-order reaction rate constant. The results showed that the kinetics of the BC300 sample better fit the pseudo-second-order model (R\({}^{2}\) = 0.995), whereas the experimental amount of Cu\({}^{2+}\) adsorbed at equilibrium (\(q_{e}\), _exp_) presented a similar value with the calculated \(q_{e}\), which is indicative of chemical adsorption [53] (Figure 5B, Table 5). This result was corroborated when calculating the adsorption energies according to the Dubinin-Radushkevich (D-R) model and the most appropriate fit obtained for the Langmuir model (Table 4). In contrast, we observed a linear adjustment with R\({}^{2}\) values of 0.933 and 0.960 for the BC450 and BC600 samples, respectively, to the pseudo-first-order model (Table 5; Figure 5A). Additionally, the calculated \(q_{e}\) is close to \(q_{e}\), _exp_ (Table 5), showing that BC450 and BC600 can be represented by a pseudo-first-order kinetic model. These results may be a consequence of the structural properties of biochar samples, because BC450 and BC600 exhibited a BET surface area two times higher than that of BC300, a higher porosity, and more binding sites available for copper adsorption.