## 6 Adsorption Isotherms  
To analyze adsorption isotherms, the Langmuir and Freundlich models were employed (Table 2). Based on the adsorption isotherms results, the Langmuir model shows better adaptation for the RB dye on the surface of the CC biochars with a good regression coefficient (0.989-0.999) compared to the Freundlich model, where the R\({}^{2}\) values remained in the range of 0.327-0.827. According to the Langmuir model, RB dye adsorption behaviour on CC biochars is largely influenced by monolayer surface coverage (homogeneous surface), which involves physical and chemical adsorption processes. Previous studies on dye adsorption onto biochars derived from different biomass feedstocks confirm this observation [37; 43]. Furthermore, the Langmuir model assumes that a higher adsorption site is initially occupied and then the adsorption capacity of the adsorbent decreases with the increase in the coverage of the adsorption site [46]. The maximum adsorption capacitiesobtained by the Langmuir model for CCB500, CCB600, and CCB700 are equal to 39.37, 51.28, and 56.18 mg/g, respectively (Table 3). This is consistent with previous investigations, which show that the Langmuir isotherm is the best-fitting model, indicating homogeneous sites and monolayer adsorption [40]. K\({}_{\rm L}\) represents the equilibrium constant for the adsorption process, reflecting how strongly the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Pseudo-First-Order**} & \multicolumn{6}{c}{**Pseudo-Second-Order**} \\ \cline{2-9}  & **K\({}_{\rm 1}\)** & **q\({}_{\rm e}\) Experimental (mg/g)** & **q\({}_{\rm 1}\) Calculated (mg/g)** & **R\({}^{2}\)** & **K\({}_{\rm 2}\)** & **q\({}_{\rm e}\) Experimental (mg/g)** & **q\({}_{\rm e}\) Calculated (mg/g)** & **R\({}^{2}\)** \\ \hline CCB500 & 0.15 & 21.93 & 1.89 & 0.079 & 0.03 & 21.93 & 21.9 & 0.995 \\ \hline CCB600 & 0.12 & 23.33 & 0.128 & 0.005 & 0.05 & 23.33 & 23.3 & 0.993 \\ \hline CCB700 & 0.15 & 30.25 & 3.02 & 0.099 & 0.02 & 30.25 & 30.3 & 0.999 \\ \hline \end{tabular} (q\({}_{\rm e}\)) is the experimental adsorption capacity at equilibrium. (qe, I) is the calculated adsorption capacity at equilibrium by the pseudo-first-order model. (q\({}_{\rm e}\), II) is the calculated adsorption capacity at equilibrium by the pseudo-second-order model.  
\end{table} 
Table 2: Experimental and calculated equilibrium values and best-fit adsorption kinetic parameters. - dye molecules bind to the biochar surface [47; 48]. The calculated K\({}_{\rm L}\) parameter for CCB500, CCB600, and CCB700 is 0.07, 0.12, and 1.58, respectively. Higher K\({}_{\rm L}\) values indicate stronger interactions [49]. These results indicate that CCB700 presents a higher affinity for RB dye than CCB500 and CCB600, which is related to its high surface area, mineral composition, and high pore volume. Table 3 shows the favourability degree (R\({}_{\rm L}\)) values calculated for different initial concentrations of RB dye. It can be seen that R\({}_{\rm L}\) values range between 0 and 1 for CC biochars, and the lowest R\({}_{\rm L}\) value is obtained for CCB700, demonstrating the significantly greater adsorption efficiency of biochar produced at high temperatures. The favourability degree is generally linked to the irreversibility of the system, supplying a qualitative assessment of interactions between CCB- and RB dyemolecules. The degrees are between 0 and 1, which indicate a favorable adsorption process [50]. The findings for the physical characterization, kinetics, and isothermal modelling were used to infer the adsorption mechanism. As discussed above, the adsorption process of RB dye onto CC biochar seems to be mainly dominated by chemisorption. Thus, the sorption mechanism depends upon various factors, such as porosity, specific surface area, biochar functional groups, and pH value [3].