## 3 Results
### Physicochemical Characterization of Activated Allophane
#### 3.2.4 Superficial Area BET  
Allophane samples activated by the alkaline fusion method followed by hydrothermal treatment showed a BET surface area greater than 300 m\({}^{2}\)/g, which is within the range established by KAUFHOLD STEPHAN in activated samples 3, 6, 11, and 15. The other samples are outside the characteristic range of the allophane and at the same time of an FCC catalyst; for this reason, they were not considered in the following tests since the total surface area of the solid has an important effect on the reaction rate. The smaller the size of a catalyst particle, the greater the surface area.  
The results of the BET surface area of each sample are presented below, Table 11.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Activated Samples** & **\textless{}20 mm** & **20 mm** & **40 mm** & **60 mm** & **\textgreater{}80 mm** \\ \hline AA-5 & 0.03 & 1.10 & 5.85 & 13.21 & 79.81 \\ AA-6 & 0.03 & 1.19 & 6.34 & 14.11 & 78.33 \\ AA-7 & 0.04 & 1.28 & 7.00 & 15.61 & 76.08 \\ AA-8 & 0.03 & 1.07 & 5.82 & 13.38 & 79.70 \\ AA-9 & 0.03 & 1.00 & 5.32 & 12.30 & 81.35 \\ AA-10 & 0.03 & 0.94 & 4.72 & 10.94 & 83.37 \\ AA-11 & 0.02 & 0.69 & 3.47 & 8.00 & 87.82 \\ AA-12 & 0.01 & 0.39 & 1.93 & 4.34 & 93.33 \\ AA-13 & 0.00 & 0.06 & 0.32 & 0.74 & 98.88 \\ AA-14 & 0.00 & 0.05 & 0.27 & 0.64 & 99.04 \\ AA-15 & 0.00 & 0.05 & 0.23 & 0.59 & 99.13 \\ \hline \hline \end{tabular}
\end{table}
Table 10: _Cont_.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Samples** & **Essays** & \begin{tabular}{c} **Empty Cell** \\ **(g)** \\ \end{tabular} & \begin{tabular}{c} **Cell with** \\ **Sample BET (g)** \\ \end{tabular} & \begin{tabular}{c} **Area BET** \\ **(m\({}^{2}\)/g)** \\ \end{tabular} & \
\begin{tabular}{c} **Superficial** \\ **Area (m\({}^{2}\)/g)** \\ \end{tabular} &
\begin{tabular}{c} **Average of Superficial** \\ **Area (m\({}^{2}\)/g)** \\ \end{tabular} \\ \hline AA-1 & 1 & 10.0500 & 10.1662 & 33.94 & 292.08 & \\ AA-1 & 2 & 10.2000 & 10.3198 & 32.73 & 284.11 & 285.1324 \\  & 3 & 10.0500 & 10.1625 & 31.41 & 279.20 & \\ \hline AA-2 & 1 & 10.2024 & 10.3217 & 27.95 & 234.28 & \\ AA-2 & 2 & 10.2003 & 10.3234 & 27.94 & 226.97 & 228.9463 \\  & 3 & 10.0524 & 10.1634 & 25.04 & 225.59 & \\ \hline AA-3 & 1 & 10.0537 & 10.1701 & 35.12 & 301.72 & \\ AA-3 & 2 & 10.2060 & 10.3240 & 36.66 & 310.68 & 302.0292 \\  & 3 & 10.0462 & 10.1635 & 34.45 & 293.69 & \\ \hline AA-4 & 1 & 10.1998 & 10.3118 & 28.86 & 257.68 & \\ AA-4 & 2 & 10.0504 & 10.1553 & 30.3100 & 288.94 & 271.6072 \\  & 3 & 10.2028 & 10.2962 & 25.0500 & 268.20 & \\ \hline AA-5 & 1 & 10.0506 & 10.1757 & 24.87 & 198.00 & \\ AA-5 & 2 & 10.2029 & 10.3208 & 25 & 212.04 & 201.2320 \\  & 3 & 10.2022 & 10.3169 & 22.12 & 192.85 & \\ \hline AA-6 & 1 & 10.0504 & 10.1422 & 35.75 & 389.43 & \\ AA-6 & 2 & 10.0500 & 10.1603 & 45.47 & 412.24 & 402.6160 \\  & 3 & 10.2021 & 10.3106 & 44.07 & 406.18 & \\ \hline AA-7 & 1 & 10.2019 & 10.3228 & 13.27 & 109.76 & \\ AA-7 & 2 & 10.0503 & 10.1922 & 10.49 & 73.93 & 99.8721 \\  & 3 & 10.2019 & 10.3174 & 13.39 & 115.93 & \\ \hline AA-8 & 1 & 10.0492 & 10.161 & 20.22 & 180.86 & \\ AA-8 & 2 & 10.2014 & 10.3139 & 21.27 & 189.07 & 188.5667 \\  & 3 & 10.0500 & 10.1636 & 22.24 & 195.77 & \\ \hline \hline \end{tabular}
\end{table}
Table 11: Results of superficial area BET of activated allophane.