## 3 Results and Discussion
\(1.12\cdot 10^{-1}\) & L.II. \(10.1\) & L.IV. \(2.75\) & L.IV. \(7.85\cdot 10^{-3}\) \\ \hline \multirow{8}{*}{\(15\,\mathrm{\SIUnitSymbolDegree}\)C} & \multirow{8}{*}{\(1.0\,\,\mathrm{\SIUnitSymbolDegree}\)} & 0.5 & L.I. \(4.96\cdot 10^{-5}\) & L.I. \(7.38\cdot 10^{-2}\) & L.II. \(19.1\) & L.I. \(6.00\) & L.I. \(5.17\cdot 10^{-3}\) \\ \cline{2-7}  & 1.0 & L.IV. \(3.13\cdot 10^{-4}\) & L.IV. \(6.87\cdot 10^{-2}\) & L.II. \(6.97\) & L.IV. \(2.12\) & L.IV. \(4.81\cdot 10^{-3}\) \\ \cline{2-7}  & 2.0 & L.III. \(3.76\cdot 10^{-4}\) & L.III. \(6.36\cdot 10^{-2}\) & L.I. \(5.95\) & L.III. \(11.3\) & L.III. \(4.45\cdot 10^{-3}\) \\ \cline{2-7}  & 0.5 & L.I. \(3.45\cdot 10^{-5}\) & L.I. \(6.46\cdot 10^{-2}\) & L.II. \(18.9\) & L.I. \(9.13\) & L.I. \(4.52\cdot 10^{-3}\) \\ \cline{2-7}  & 1.0 & L.IV. \(6.12\cdot 10^{-5}\) & L.II. \(1.75\cdot 10^{-2}\) & L.II. \(3.85\) & L.IV. \(1.89\) & L.II. \(1.22\cdot 10^{-3}\) \\ \cline{2-7}  & 2.0 & L.IV. \(3.66\cdot 10^{-4}\) & L.II. \(5.59\cdot 10^{-2}\) & L.II. \(5.91\) & L.IV. \(4.10\) & L.II. \(3.91\cdot 10^{-3}\) \\ \cline{2-7}  & 2.0 & L.I. \(5.76\cdot 10^{-5}\) & L.I. \(5.52\cdot 10^{-2}\) & L.II. \(11.1\) & L.I. \(3.71\) & L.I. \(3.86\cdot 10^{-3}\) \\ \cline{2-7}  & 2.0-5.0 & L.IV. \(1.13\cdot 10^{-4}\) & L.II. \(2.87\cdot 10^{-2}\) & L.II. \(4.77\) & L.II. \(3.23\) & L.II. \(2.01\cdot 10^{-3}\) \\ \cline{2-7}  & 2.0 & L.IV. \(1.59\cdot 10^{-4}\) & L.II. \(2.29\cdot 10^{-2}\) & L.II. \(3.13\) & L.IV. \(3.96\) & L.IV. \(1.60\cdot 10^{-3}\) \\ \hline \multirow{8}{*}{\(20\,\mathrm{\SIUnitSymbolDegree}\)C} & \multirow{8}{*}{\(1.0\,\mathrm{\SIUnitSymbolDegree}\)} & 0.5 & L.III. \(9.77\cdot 10^{-5}\) & L.III. \(4.35\cdot 10^{-2}\) & L.I. \(9.70\) & L.III. \(16.4\) & L.III. \(3.05\cdot 10^{-3}\) \\ \cline{2-7}  & 1.0 & L.IV. \(9.48\cdot 10^{-4}\) & L.IV. \(1.81\cdot 10^{-1}\) & L.II. \(11.1\) & L.IV. \(2.84\) & L.IV. \(1.27\cdot 10^{-2}\) \\ \cline{2-7}  & 2.0 & L.III. \(3.92\cdot 10^{-4  
when the value is as high as possible. Analyzing all the fits together with the typical and commonly used R\({}^{2}\) is an excellent way of selecting the best fit for the results and thus, determining the correct values of K\({}_{\rm L}\), q\({}_{\rm max}\), and R\({}_{\rm L}\). However, listing any fit in the table as the best fit should not be misleading since, for ESRQ, one would have to accept results with a multiplier of no more than \(10^{-5}\), with multipliers for HYBRD, ARE, [PERSON]'s test, and the Chi-square test being less than \(5\cdot 10^{-2}\), less than 10, more significant than 5, and under \(5\cdot 10^{-3}\), respectively. In the thermodynamic analysis, we used q\({}_{\rm max}\) and C\({}_{0}\) to calculate K\({}_{\rm d}\), followed by functional graphs lnK\({}_{\rm d}\) = f(1/T). Example relationships for granulations of 1.0-1.6 mm and 2.0-5.0 mm and initial phosphate concentrations in solution of 0.5 and 1.0 mg/L are shown in Figure 11.  
The directional coefficients and ordinates of the vertical axis intersection were used as the basis for calculating standard entropy (\(\Delta\)S), standard enthalpy (\(\Delta\)H), and standard free energy (\(\Delta\)G). A summary of the results is shown in Table 4.  
The results in the \(\Delta\)G column are given for the range of temperatures tested. The first number corresponds to 5 \({}^{\circ}\)C and the second to 25 \({}^{\circ}\)C, and inside the range are values for intermediate temperatures. Positive entropy values indicate that some structural changes are taking place on the adsorbent's surface and reveal random interferences at the solid-liquid interface. They confirm an increase in the degree of disordered particles and energy dissipation throughout the temperature range. Negative enthalpy values indicate that sorption is exothermic.