## 3 Results and Discussion
### Sorption Kinetics for Hexavalent Chromium
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Initial Cr(VI) Concentration (ppm)**} \\ \cline{2-6}  & **5.23** & **20.94** & **26.73** & **35.40** & **54.14** \\ \hline \multirow{6}{*}{**Pseudo 1 st**} & \(k_{1}\) & \multirow{2}{*}{1.3444} & \multirow{2}{*}{1.27414} & \multirow{2}{*}{1.1203} & \multirow{2}{*}{1.10482} & \multirow{2}{*}{1.0753} \\  & (**h\({}^{-1}\))** & & & & \\ \cline{2-6}  & **Std.Err.** & 0.2087 & 0.32308 & 0.18399 & 0.25478 & 0.19029 \\ \cline{2-6}  & \(q_{e}\) & \multirow{2}{*}{27.6321} & \multirow{2}{*}{67.51102} & \multirow{2}{*}{75.88982} & \multirow{2}{*}{84.64005} & \multirow{2}{*}{97.99323} \\  & (**mg/g**) & & & & \\ \cline{2-6}  & **Std.Err.** & 0.95304 & 3.88327 & 2.96895 & 4.67388 & 4.19475 \\ \cline{2-6}  & \(r_{i}\) & \multirow{2}{*}{37.1486} & \multirow{2}{*}{86.01849} & \multirow{2}{*}{85.01937} & \multirow{2}{*}{93.51202} & \multirow{2}{*}{105.37212} \\  & (**mg/(g h)**) & & & & \\ \cline{2-6}  & \(R^{2}\) & 0.962 & 0.90073 & 0.95637 & 0.91304 & 0.94961 \\ \cline{2-6}  & **Reduced Chi-Square** & & & & \\ \hline \multirow{6}{*}{**Pseudo 2 nd**} & \(k_{2}\) & \multirow{2}{*}{0.06913} & \multirow{2}{*}{0.02366} & \multirow{2}{*}{0.01884} & \multirow{2}{*}{0.0169} & \multirow{2}{*}{0.01368} \\  & (**g/(mg h)**) & & & & \\ \cline{2-6}  & **Std.Err.** & 0.00715 & 0.00585 & 0.00219 & 0.0035 & 0.00196 \\ \cline{2-6}  & \(q_{e}\) & \multirow{2}{*}{29.89882} & \multirow{2}{*}{74.37154} & \multirow{2}{*}{83.43419} & \multirow{2}{*}{93.05058} & \multirow{2}{*}{108.16824} \\  & (**mg/g**) & & & & \\ \cline{2-6}  & **Std.Err.** & 0.48902 & 3.08611 & 1.69007 & 3.35803 & 2.76546 \\ \cline{2-6}  & \(r_{i}\) & \multirow{2}{*}{61.79803} & \multirow{2}{*}{130.86644} & \multirow{2}{*}{131.15021} & \multirow{2}{*}{146.32714} & \multirow{2}{*}{160.06104} \\  & (**mg/(g h)**) & & & & \\ \cline{2-6}  & \(R^{2}\) & 0.99434 & 0.96616 & 0.99233 & 0.97546 & 0.98824 \\ \cline{2-6}  & **Reduced Chi-Square** & & & & \\ \hline \multirow{6}{*}{**Intraparticle Diffusion Model**} & \(K_{ID}\) (mg/g & \multirow{2}{*}{0.54307} & \multirow{2}{*}{20.14076} & \multirow{2}{*}{5.72074} & \multirow{2}{*}{22.58891} & \multirow{2}{*}{14.8523} \\  & **h\({}^{0.5}\))** & & & & \\ \cline{2-6}  & **Std.Err.** & 1.63303 & 3.3512 & 3.95221 & 4.21855 & 5.15192 \\ \cline{2-6}  & **C** & & & & \\ \cline{2-6}  & **(mg/g)** & & & & & \\ \cline{2-6}  & **Std.Err.** & 3.89454 & 7.9921 & 9.42542 & 10.06059 & 12.28655 \\ \cline{2-6}  & **\(R^{2}\)** & 0.53826 & 0.68655 & 0.65191 & 0.67888 & 0.65098 \\ \cline{2-6}  & **Reduced Chi-Square** & & & & & \\ \hline \multirow{6}{*}{**Diffusion- Chemisorption Model**} & \(K_{DC}\) & \multirow{2}{*}{44.30361} & \multirow{2}{*}{186.57304} & \multirow{2}{*}{259.49435} & \multirow{2}{*}{295.64733} & \multirow{2}{*}{440.94717} \\  & (**mg/(g h\({}^{0.5}\))**) & & & & \\ \cline{2-6}  & **Std.Err.** & 4.84763 & 4.76127 & 7.16302 & 4.2913 & 13.07894 \\ \cline{2-6}  & \(q_{e}\) & \multirow{2}{*}{35.52516} & \multirow{2}{*}{94.11232} & \multirow{2}{*}{104.76698} & \multirow{2}{*}{118.20737} & \multirow{2}{*}{137.06461} \\  & (**mg/g**) & & & & \\ \cline{2-6}  & **Std.Err.** & 1.47317 & 2.36586 & 3.77604 & 2.38653 & 7.6133 \\ \cline{2-6}  & **\(r_{i}\) & \multirow{2}{*}{60.33602} & \multirow{2}{*}{91.04585} & \multirow{2}{*}{94.69576} & \multirow{2}{*}{100.46845} & \multirow{2}{*}{110.53617} \\  & (**mg/(g h)**) & & & & \\ \cline{2-6}  & **\(R^{2}\)** & 0.98855 & 0.99651 & 0.9932 & 0.99788 & 0.9848 \\ \cline{2-6}  & **Reduced Chi-Square** & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Predicted parameters from the Cr(VI) uptake kinetic study. According to the literature [56], Table 3 values could be interpreted as follows:  
Although the pseudo-first model could not perfectly fit the experimental kinetic data, we could say that the initial adsorption rate \(r_{i}\) increased as the initial concentration increased, but not proportionally, as it was obvious by the reduction of the \(k_{1}\) values.