## 2 Materials and Methods
### Adsorption Kinetic Models
These loops indicate the presence of significant mesopores and macropores, which is consistent with the FESEM observations revealing macropores in the range of 10-20 \(\upmu\)m (>0.05 \(\upmu\)m) [39]. Additionally, the BjH pore size distribution, depicted in Figure 2c, confirms an average total pore diameter within the mesopore range (4-5 nm). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Surface Area (m\({}^{2}\)/g)** & **Pore Volume (cm\({}^{3}\)/g)** \\ \hline C-BP & 3.202 & 0.008 \\ \hline A-BP & 201.722 & 0.041 \\ \hline S-BP & 338.959 & 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The BET surface area and pore volume of the synthesized adsorbents. Figure 2: N\({}_{2}\) adsorption–desorption isotherm and BjH pore size distribution. The primary aim of this study is to explore potential applications in the food industry, with a particular focus on the banana chip sector. Consequently, sulfuric acid (H\({}_{2}\)SO\({}_{4}\)) was used solely for comparative purposes to highlight that acetic acid, a milder and food-safe alternative, can also effectively serve for activation. The results demonstrate that 5% acetic acid, commonly employed in food processing, significantly enhances the porosity of banana peel. For the final selection, this study primarily focuses on samples activated with acetic acid (A-BP) to ensure compatibility with edible palm oil. The data in Table 3 provide critical insights into the adsorption equilibrium characteristics for the removal of free fatty acids (%FFA) from used palm oil after adsorption, presenting the equilibrium concentration (Ce), adsorbed quantity (Q\({}_{\rm e}\)), and related parameters after 30 min of adsorption equilibrium time. The free fatty acid (FFA) content in the used palm oil prior to adsorption was determined to be 3.108%, indicating substantial degradation of the oil or prolonged usage (as FFA levels exceeding 2% are generally deemed unsuitable for consumption). At the highest initial concentration prior to dilution (C\({}_{\rm o}\) = 100% \(v/v\), 3631 mg/L), the FFA content decreased to 1.69%, representing a substantial reduction of approximately 54.38% compared to the initial FFA content. This reduction highlights the efficiency of the adsorbent in removing free fatty acids, achieved within a 30 min adsorption equilibrium period. The remaining diluted concentrations listed in Table 3 were used to evaluate the adsorption isotherms, facilitating the analysis of adsorption behavior of the Langmuir and Freundlich isotherm models, as illustrated in Figure 3a,b, respectively. The isotherm parameters obtained from both models are summarized in Table 4.  
The correlation coefficient (R\({}^{2}\) = 0.9115) of the linear Freundlich model demonstrates a superior fit to the adsorption data compared to the linear Langmuir model (R\({}^{2}\) = 0.1921). Furthermore, the maximum monolayer adsorption capacity (Q\({}_{\rm m}\)), calculated from the slope of the Langmuir plot, and the \(K_{L}\) parameter, obtained from its y-intercept, were found to exhibit negative values. These results suggest that the Langmuir monolayer adsorption model was not suitable for describing the adsorption behavior observed in this experiment. Moreover, the Freundlich parameter (\(1/n\)), referring to the intensity of adsorption with