# Effect of Hydrogen Ion Presence in Adsorbent and Solution to Enhance Phosphate Adsorption
## 3 Results and Discussion
### Isotherm Tests
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**pH**} & \multirow{2}{*}{**Condition**} & \multicolumn{8}{c}{**Langmuir**} & \multicolumn{3}{c}{**Freundlich**} \\ \cline{3-10}  & & \(Q_{\text{max}}\) & \(b\) & \(\Delta G^{\circ}\) & \(R^{2}\) & \(k_{f}\) & \(1/n\) & \(n\) & \(R^{2}\) \\  & & **(mg/g)** & **(L/mg)** & **(kJ/mol)** & & & & & & \\ \hline \multirow{2}{*}{4} & \multirow{2}{*}{GAC-wo} & 3.36 & 0.419 & \multirow{2}{*}{\(-25.8\)} & 0.979 & 1.10 & 0.329 & \multirow{2}{*}{3.04} & \multirow{2}{*}{0.976} \\  & & (0.196) * & (0.107) & & & (0.130) & (0.0401) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GAC-w} & 3.94 & 0.134 & \multirow{2}{*}{\(-23.0\)} & 0.967 & 0.722 & 0.446 & \multirow{2}{*}{2.24} & \multirow{2}{*}{0.972} \\  & & (0.457) & (0.0461) & & & (0.127) & (0.0583) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GACA-wo} & 1.53 & 0.598 & \multirow{2}{*}{\(-26.7\)} & 0.955 & 0.643 & 0.244 & \multirow{2}{*}{4.10} & \multirow{2}{*}{0.848} \\  & & (0.109) & (0.217) & & & (0.164) & (0.0843) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GACA-w} & 1.7 & 0.438 & \multirow{2}{*}{\(-25.9\)} & 0.963 & 0.640 & 0.268 & \multirow{2}{*}{3.73} & \multirow{2}{*}{0.853} \\  & & (0.118) & (0.141) & & & (0.173) & (0.0893) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GAC-wo} & 3.59 & 0.0732 & \multirow{2}{*}{\(-21.6\)} & 0.946 & 0.401 & 0.539 & \multirow{2}{*}{1.86} & \multirow{2}{*}{0.964} \\  & & (0.715) & (0.0353) & & & (0.0994) & (0.0783) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GAC-w} & 3.00 & 0.296 & \multirow{2}{*}{\(-25.0\)} & 0.986 & 0.790 & 0.407 & \multirow{2}{*}{2.46} & \multirow{2}{*}{0.969} \\  & & (0.172) & (0.0367) & & & (0.130) & (0.0606) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GACA-wo} & 3.71 & 0.237 & \multirow{2}{*}{\(-24.4\)} & 0.911 & 0.857 & 0.420 & \multirow{2}{*}{2.38} & \multirow{2}{*}{0.959} \\  & & (0.566) & (0.136) & & & (0.172) & (0.0671) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GACA-w} & 3.77 & 0.398 & \multirow{2}{*}{\(-25.7\)} & 0.993 & 1.23 & 0.328 & \multirow{2}{*}{3.04} & \multirow{2}{*}{0.955} \\  & & (0.129) & (0.0564) & & & (0.192) & (0.0543) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GAC-wo} & 1.29 & 0.406 & \multirow{2}{*}{\(-25.8\)} & 0.783 & 0.441 & 0.301 & \multirow{2}{*}{3.33} & \multirow{2}{*}{0.736} \\  & & (0.240) & (0.341) & & & (0.190) & (0.139) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GAC-w} & 1.46 & 0.284 & \multirow{2}{*}{\(-24.9\)} & 0.804 & 0.385 & 0.373 & \multirow{2}{*}{2.68} & \multirow{2}{*}{0.815} \\  & & (0.284) & (0.227) & & & (0.163) & (0.134) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GACA-wo} & 3.96 & 0.291 & \multirow{2}{*}{\(-24.9\)} & 0.991 & 1.11 & 0.363 & \multirow{2}{*}{2.75} & \multirow{2}{*}{0.954} \\  & & (0.173) & (0.0476) & & & (0.192) & (0.0597) & & \\ \multirow{4}{*}{} & \multirow{2}{*}{GACA-w} & 2.59 & 0.543 & \multirow{2}{*}{\(-26.5\)} & 0.970 & 0.972 & 0.284 & \multirow{2}{*}{3.52} & \multirow{2}{*}{0.891} \\  & & (0.159) & (0.148) & & & (0.214) & (0.0749) & & \\ \hline \hline \end{tabular}  
* \({}^{*}\)indicate stand error using SigmaPlot 12.5.  
\end{table} 
Table 3: Values of the Langmuir and Freundlich parameters for nonlinear equations.