## 2 Materials and Methods
### Adsorption Kinetic Models  
Adsorption kinetic models are utilized to elucidate the underlying mechanisms and characteristics of the adsorption process. In this study, pseudo-first-order and pseudo-second-order kinetic models were employed to analyze the experimental data [34; 35]. The linearized expressions for these models are presented in Equations (8) and (9) below:  
* Pseudo-first-order kinetic model: \[\log\left({\rm{Q}}_{\rm{e}}-{\rm{Q}}_{t}\right)=\] log Q  
ysis reveals important details about their surface morphology and porous structure. As illustrated in Figure 1a,b, the surface morphology of the C-BP sample prepared without chemical activation exhibited a dense and fibrous structure that closely resembled its natural form. This characteristic results in low porosity, thereby reducing its effectiveness for adsorption applications. The S-BP sample underwent significant changes due to the strong acid treatment. This treatment broke down the dense lignocellulosic structure, creating a rough surface with visible layers and sharp edges, as shown in Figure 1c,d. The effect of the sulfuric acid was intensified during calcination, which removed organic material and exposed the inorganic phases. As a result, the surface developed many voids and pores, increasing its porosity and adsorption capacity compared to the untreated sample. This study aimed to employ mild conditions and straightforward chemical treatments. To achieve this, the banana peel was activated using acetic acid from commercial vinegar (5% concentration). The FESEM images of the A-BP sample, presented in Figure 1e,f, demonstrate a distinct honeycomb-like structure characterized by large, well-defined pores approximately 10-20 \(\upmu\)m in size. The surface morphology appears more organized and less fragmented compared to that of S-BP, indicative of the gentler impact of the acetic acid treatment. As a weak acid, acetic acid facilitates a controlled interaction with the lignocellulosic components of banana peel, including cellulose, hemicellulose, and lignin [36]. This interaction preserves the natural framework of the material, yielding a uniform and interconnected porous structure while minimizing excessive degradation. The resulting chemical modification effectively enhances the porosity and stability of A-BP, making it a viable material for adsorption applications. The untreated C-BP sample demonstrated the lowest BET surface area (3.202 m\({}^{2}\)/g) and pore volume (0.008 cm\({}^{3}\)/g), as detailed in Table 2. This finding aligns with the dense  
Figure 1: FESEM images of (**a,b**) C-BP, (**c,d**) S-BP, and (**e,f**) A-BP captured at magnifications of 1000\(\times\) and 3000\(\times\), respectively. and compact morphology observed in the FESEM images. Consequently, the material exhibited limited porosity and a reduced surface area, rendering C-BP unsuitable for applications requiring high adsorption capacities. To further investigate the surface properties, N\({}_{2}\) adsorption-desorption isotherms for the C-BP sample were generated and are shown in Figure 2a. The isotherm exhibited a profile typical of an IUPAC Type II isotherm [37], commonly associated with non-porous materials. The BjH pore size distribution plot presented in Figure 2c indicates an absence of well-defined pores, distinguishing it from the other samples analyzed in this study. In contrast, the sulfuric-acid-treated banana peel (S-BP) exhibited the highest BET surface area (338.959 m\({}^{2}\)/g) and pore volume (0.059 cm\({}^{3}\)/g) among the analyzed samples. This result is consistent with the highly porous and fragmented morphology observed in the FESEM images. Similarly, the banana peel treated with acetic acid (A-BP) showed a notable enhancement in the surface area (201.722 m\({}^{2}\)/g) and pore volume (0.041 cm\({}^{3}\)/g). As shown in Figure 2b, the adsorption-desorption isotherms of the S-BP and A-BP samples exhibited hysteresis loops typical of a Type IV isotherm with H3 slit-shaped pores [37; 38].