# Adsorption of Hexavalent Chromium Ions Using Pine Sawdust Cellulose Fibres
## 3 Results and Discussion
### Adsorption Studies
#### 3.8.5 Effect of Temperature
Moreover, the R\({}_{\rm L}\) value implies that the total light power absorbed by the sample does not follow a linear relationship with the incident light intensity. This suggests that the incident irradiance influences the absorption coefficient, and multiple absorption mechanisms are at play, leading to nonlinear absorption behaviour. These various absorption mechanisms contribute to the nonlinear results observed in the study, supporting the findings obtained from the nonlinear analysis [59]. The Table 5 results offer essential insights into the adsorption behaviour and fitting parameters of the linear and nonlinear Freundlich isotherm models. The parameter \"n\" in the Freundlich equation signifies the adsorbent surface heterogeneity. In the linear Freundlich model, \"n\" has a relatively high value (12.136), indicating significant heterogeneity on the adsorbent surface. This implies that a wide range of binding energies influenced the adsorption process. In contrast, in the nonlinear Freundlich model (Figure 16b), \"n\" has a significantly lower value (3.95 \(\times\) 10\({}^{-2}\)), suggesting a reduced degree of heterogeneity. These findings suggest that the nonlinear Freundlich model better fit the experimental data compared to the linear model. Additionally, since the value of \"n\" is more significant than 1 in the nonlinear Freundlich model, the adsorption isotherm becomes increasingly nonlinear, deviating from ideal behaviour and leading to physisorption. Physical adsorption is facilitated by van der Waals forces between atoms or molecules on the adsorbent surface and the adsorbate [60; 61]. The parameter k\({}_{\rm F}\) in the Freundlich equation represents the adsorption capacity of the adsorbent. In both the linear and nonlinear models, the k\({}_{\rm F}\) value is approximately 10, \begin{table}
\begin{tabular}{c c c c} \hline  & & **Linear** & **Nonlinear** \\ \hline
**adsorption Isotherm** & **Parameters** & **Cr (VI)** & **Cr (VI)** \\ \hline Langmuir isotherm & q= (mg g\({}^{-1}\)) & 8.2782 & 9.838 \\  & k\({}_{\rm L}\) (min\({}^{-1}\)) & 0.0029 & 171.589 \\  & R\({}_{\rm L}\) & 0.476 & 0.09 \\  & R\({}^{2}\) & 0.9958 & 0.9991 \\ Freundlich isotherm & n (L g\({}^{-1}\)) & 12.136 & 0.0395 \\  & k\({}_{\rm F}\) (L mg\({}^{-1}\)) & 10.127 & 10.1817 \\  & R\({}^{2}\) & 0.8854 & 0.9988 \\ \hline \end{tabular}
\end{table} 
Table 5: Isotherm models for the adsorption of hexavalent chromium ions on cellulose fibres (CF) at 299 K.  
indicating a moderate adsorption capacity. The high \(\rm k_{F}\) values implies a significant uptake of chromium ions onto the absorbent surface [62]. The coefficient of determination (R\({}^{2}\)) evaluates the model's good fit to the experimental data. For the linear Freundlich model, the R\({}^{2}\) value is 0.8854, indicating a reasonable fit between the model and the experimental data. However, in the case of the nonlinear Freundlich model, the R\({}^{2}\) value is substantially higher (0.9988), which signified an excellent fit between the model and the experimental data. Therefore, the higher R\({}^{2}\) value indicates a closer agreement between the model and the observed data.