## 3 Results and Discussion
### Heavy Metals
#### 3.2.2 Equilibrium Tests
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter/Material**} & \multicolumn{6}{c}{\(K_{L}\) (\(R^{2}\))} & \multicolumn{6}{c}{**AG\({}^{0}\) dB/mol**} & \multirow{2}{*}{\(\Delta S^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} & \multirow{2}{*}{\(\Delta H^{0}\) (\(\mathbf{J}\)/mol-\(\mathbf{K}\))} \\ \cline{2-2} \cline{5-12} \multicolumn{1}{c}{} & \multicolumn{1}{c}{3 °C} & \multicolumn{1}{c}{**10 °C**} & \multicolumn{1}{c}{**22 °C**} & \multicolumn{1}{c}{**40 °C**} & \multicolumn{1}{c}{**3 °C**} & \multicolumn{1}{c}{**10 °C**} & \multicolumn{1}{c}{**22 °C**} & \multicolumn{1}{c}{**40 °C**} & \multicolumn{1}{c}{**40 °C**} & \\ \hline \multicolumn{12}{c}{**Ca**} \\ Diatomite & 0.79\% (0.999) & 0.925 (0.997) & 1.119 (0.998) & 1.837 (0.989) & -34.02 & -35.29 & -37.47 & -40.73 & 181.25 & 16.03 & 0.978 \\ Zeolite & 0.491 (0.989) & 0.591 (0.986) & 0.719 (0.963) & 0.943 (0.799) & -33.04 & -34.19 & -36.17 & -39.13 & 164.56 & 12.40 & 0.994 \\ Activated carbon & 0.701 (0.942) & 1.212 (0.997) & 8.197 (0.999) & 0.701 (0.415) & -33.94 & -37.01 & -3.59 & -42.25 & 457.43 & 86.85 & 0.996 \\ Limestone sand & 0.224 (0.952) & 0.493 (0.985) & 0.910 (0.995) & 0.929 (0.994) & -31.90 & -33.37 & -35.89 & -39.67 & 210.01 & 26.09 & 0.763 \\ Halloysite & 0.588 (0.988) & 1.495 (0.995) & 1.648 (0.987) & 2.370 (0.991) & -34.13 & -35.58 & -38.06 & -41.79 & 207.10 & 23.06 & 0.761 \\ \multicolumn{12}{c}{**Zn**} \\ Diatomite & 0.190 (0.970) & 0.361 (0.987) & 0.763 (0.994) & 1.153 (0.996) & -31.28 & -32.95 & -35.80 & -40.09 & 238.06 & 34.46 & 0.936 \\ Zeolite & 0.221 (0.955) & 0.441 (0.988) & 0.609 (0.954) & 2.238 (0.975) & -31.32 & -33.19 & -36.40 & -41.21 & 267.17 & 42.46 & 0.967 \\ Activated carbon & 0.611 (0.998) & 0.739 (0.996) & 0.878 (0.996) & 2.375 (0.997) & -33.31 & -34.81 & -37.38 & -41.22 & 213.85 & 25.74 & 0.913 \\ Halloysite & 0.219 (0.932) & 0.312 (0.974) & 0.578 (0.977) & 1.613 (0.992) & -31.08 & -32.86 & -35.90 & -40.46 & 253.36 & 38.88 & 0.996 \\ \multicolumn{12}{c}{**NH\({}_{\mathbf{t}}\)N**} \\ Diatomite & 0.414 (0.982) & 1.698 (0.995) & 4.725 (0.998) & - & -30.14 & -33.04 & -38.01 & - & 414.28 & 84.27 & 0.950 \\ Zeolite & 0.128 (0.771) & 0.239 (0.833) & 0.240 (0.781) & - & -27.36 & -28.57 & -30.64 & - & 172.76 & 20.35 & 0.640 \\ Activated carbon & 1.526 (0.994) & 1.931 (0.999) & 2.315 (0.996) & - & -32.76 & -33.96 & -36.01 & - & 170.97 & 14.45 & 0.958 \\ Limestone sand & 0.468 (0.996) & 0.7262 (0.994) & 1.262 (0.997) & - & -30.03 & -31.68 & -4.51 & - & 235.86 & 35.10 & 0.995 \\ Halloysite & 0.522 (0.992) & 0.952 (0.997) & 1.270 (0.999) & - & -30.47 & -32.01 & -34.65 & - & 220.06 & 30.30 & 0.899 \\ \multicolumn{12}{c}{**PO\({}_{\mathbf{t}}\)P**} \\ Diatomite & 0.048 (0.983) & 0.062 (0.976) & 0.082 (0.983) & - & -28.61 & -29.82 & -31.88 & - & 172.00 & 18.88 & 0.990 \\ Zeolite & 0.037 (0.548) & 0.071 (0.725) & 0.119 (0.838) & - & -28.15 & -29.89 & -32.88 & - & 249.15 & 40.65 & 0.958 \\ Activated carbon & 0.103 (0.830) & 0.231 (0.928) & 0.246 (0.953) & - & -30.76 & -32.26 & -34.83 & - & 213.97 & 28.32 & 0.688 \\ Limestone sand & 0.107 (0.961) & 0.168 (0.951) & 0.294 (0.986) & - & -30.47 & -32.15 & -35.02 & - & 29.29 & 35.61 & 0.996 \\ Halloysite & 0.051 (0.783) & 0.113 (0.872) & 0.182 (0.951) & - & -28.98 & -30.82 & -33.99 & - & 263.72 & 43.85 & 0.924 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Constants of the Langmuir equilibrium constant \(K_{L}\) and thermodynamic parameters.