# Biosorption of Pb(II) Using Coffee Pulp as a Sustainable Alternative for Wastewater Treatment
## 3 Results and Discussion
### Kinetics and Adsorption Isotherm  
According to the kinetics models applied to the Pb(II) biosorption process (see Table 2), the best fit was the pseudo-second order model of [PERSON], with an equilibrium time of 105 min and a removal percentage of 86.45%, under the optimum conditions described in Section 3.2 (see Figure 3). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Order Kinetic** & **Kinetic Parameters** & **R\({}^{2}\)** \\ \hline
0 & Time (t) vs. Concentration Pb(II) (C) & 0.4725 \\ \hline
1 & t vs. Ln C & 0.6868 \\ \hline
2 & t vs. \(\frac{1}{k}\) & 0.8469 \\ \hline Pseudo-first order & t vs. Log (qe - qt) & 0.5112 \\ \hline Pseudo-second order & t vs. \(\frac{1}{qH}\) & 0.9997 \\ \hline \hline \end{tabular}  
qe: concentration of Pb(II) in the equilibrium; qt: concentration of Pb(II) in a specific time. The equations that were applied to the isotherm’s models were taken from [PERSON] et al. [43].  
\end{table} 
Table 2: Kinetic models applied to the biosorption process, parameters and R\({}^{2}\). Figure 2: Boxplot of optimum pH for removal of Pb(II) with CP obtained with XLSTAT software. Table 3 shows that the isotherm model that best fitted to the sorption of Pb(II) was the [PERSON]'s model (it was obtained applying \(\frac{dq}{dt}=K\left(qe-qt\right)^{2}\)), allowing to establish three hypotheses for the sorption phenomenon according to [PERSON] (1998) and [PERSON] (1998), both cited in [PERSON] (2002): (a) the first one indicates that the sorption of the Pb(II) pollutant occurs only on specific active sites--functional groups exposed in Section 3.1--located on the CP surface, (b) the second states that each metal adsorbs only on each active site (c) and the third assumption suggests that there is no interaction between adjacent adsorbed metals on the CP surface. For the sorption isotherm obtained (see Figure 4) under the conditions described earlier, the CP presented a capacity of maximum adsorption of 24.10 mg\(\cdot\)g\({}^{-1}\) for this metal without chemical modification. In relation to this value, we performed a bibliographic review to carry out a comparative analysis with wastes derived from crops of coffee (modified and not chemically modified) based on the capacity of maximum adsorption for the removal of Pb(II). In Tables 4 and 5, the respectively consolidated values are reported. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Lignocellulosic** \\ **Wastes Derived from** \\ **Coffee Crops** \\ \end{tabular} } & \multicolumn{2}{c}{**Biosorption Characteristics**} & \multirow{2}{*}{**Q max.**} & \multirow{2}{*}{**Reference**} \\ \cline{2-2} \cline{4-4}  & **pH Units** & & & \\ \cline{2-2} \cline{4-4}  & 4.5 & 66.30 & & [44] \\ \cline{2-2} \cline{4-4}  & 3.5 & 49.73 & & \\ \cline{2-2} \cline{4-4}  & 3.5 & 159.50 & & [45] \\ \cline{2-2} \cline{4-4}  & 4.0 & 158.70 & & [46] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Capacity of maximum adsorption in coffee wastes without chemical modification. Figure 3: Adsorption kinetics for Pb(II) with CP.