## 3 Results and Discussion
### Thermodynamic Parameters  
To study the nature of the adsorption process of Cd\({}^{2+}\) on YP, OPB, CH, CP and CCR, the free Gibbs energy \(\Delta G^{\circ}\) (KJ/mol), enthalpy \(\Delta H^{\circ}\) (KJ\({}^{\star}\)mol\({}^{-1}\)*K\({}^{-1}\)) and entropy \(\Delta S^{\circ}\) (KJ/mol) are determined according to Equations (3)-(5). The results of the thermodynamic adsorption parameters of Cd\({}^{2+}\) are shown in Table 6.  
According to these thermodynamic findings, the positive value of \(\Delta\)H\({}^{\circ}\) when using YP and CP indicates that the process of removing Cd\({}^{2+}\) on these bioadsorbents is endothermic and energy must be supplied to the system for the process to occur [5; 79]; however the ions adsorb best at intermediate and low temperature values as shown by the adsorption results. The negative values of enthalpy when using OPB, CH and CCR suggest that the adsorption process is exothermic and the system releases energy, which means energy savings when scaling up the process [39; 80]. Negative values of \(\Delta S^{\circ}\) when using YP, OPB and CCR suggest that the Cd\({}^{2+}\) biomass link is strong, the biosorbents have high affinity and selectivity for the metal ion studied and the randomness at the interface is lower, thus \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Biomaterial** & **Temperature (K)** & \(\Delta H^{\circ}\) (KJ\({}^{\star}\)mol\({}^{-1}\)*K\({}^{-1}\)) & \(\Delta S^{\circ}\) (KJ/mol) & \(\Delta G^{\circ}\) (KJ/mol) \\ \hline \multirow{3}{*}{YP} & 302.92 & \(4.34\) & \(-2.3\times 10^{-2}\) & \(5.01\) \\  & 328.15 & & & \(5.59\) \\  & 353.37 & & & \(6.16\) \\ \hline \multirow{3}{*}{OPB} & 302.92 & \(-11.29\) & \(-7.0\times 10^{-2}\) & \(-9.20\) \\  & 328.15 & & & \(-7.43\) \\  & 353.37 & & & \(-5.66\) \\ \hline \multirow{3}{*}{CH} & 302.92 & \(-14.73\) & \(5.4\times 10^{-2}\) & \(1.84\) \\  & 328.15 & & & \(3.22\) \\  & 353.37 & & & \(4.60\) \\ \hline \multirow{3}{*}{CP} & 302.92 & \(5.72\) & \(59.95\) & \(-3.08\) \\  & 328.15 & & & \(-2.78\) \\ \cline{1-1}  & 353.37 & & & \(-2.48\) \\ \hline \multirow{3}{*}{CCR} & 302.92 & \(-2.07\) & \(-2.4\times 10^{-2}\) & \(5.44\) \\ \cline{1-1}  & 328.15 & & & \(6.06\) \\ \cline{1-1} \cline{2-5}  & 353.37 & & & \(6.69\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Thermodynamic parameters of Cd\({}^{2+}\) adsorption on YP, OPB, CH, CP and CCR. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Isothermal Model** & **Parameters** & **YP** & **OBP** & **CH** & **CP** & **CCR** \\ \hline \multirow{4}{*}{Langmuir} & \(q_{max}\) & 32.02 & 178.18 & 426.28 & 107.01 & 126.93 \\  & B & 5.90 & 5.38 & 0.44 & 0.19 & 0.08 \\  & R\({}^{2}\) & 0.99 & 0.99 & 0.99 & 0.99 & 0.99 \\  & SS & 0.36 & 0.36 & 69.93 & 18.24 & 6.02 \\ \hline \multirow{4}{*}{Freundlich} & \(K_{f}\) & 26.70 & 19.47 & 20.62 & 13.72 & 6.28 \\  & \(1/n\) & 0.36 & 2.04 & 0.37 & 0.30 & 0.42 \\ \cline{1-1}  & B & 2.79 & 0.49 & 2.70 & 3.33 & 2.38 \\ \cline{1-1}  & R\({}^{2}\) & 0.98 & 0.98 & 0.99 & 0.98 & 0.99 \\ \cline{1-1}  & SS & 4.91 & 4.91 & 1.68 & 6.68 & 2.31 \\ \hline \multirow{4}{*}{Dubinin-Radushkevich} & qdr & 29.37 & 42.36 & 63.93 & 46.77 & 46.89 \\ \cline{1-1}  & K\({}_{\rm DR}\) & \(2.0\times 10^{-8}\) & \(1.9\times 10^{-7}\) & \(5.5\times 10^{-4}\) & \(3.7\times 10^{-4}\) & \(4.1\times 10^{-4}\) \\ \cline{1-1}  & E & 4.77 & 1.63 & 3.01 & 3.69 & 3.48 \\ \cline{1-1}  & SS & 2.96 & 2.83 & 12.45 & 11.56 & 13.78 \\ \cline{1-1}  & R\({}^{2}\) & 0.92 & 0.99 & 0.90 & 0.92 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Adsorption isotherm parameters of the [PERSON], [PERSON]’s models of Cd\({}^{2+}\) adsorption onto YP, OPB, CH, CP and CCR. obtaining a low possibility of reversibility, which implies that the adsorption process is energetically stable [38; 53].