## 3 Results and Discussion
### Effect of Reaction Temperature on the LA Esterification
#### 3.4.2 Activation Energy of LA Esterification with \(n\)-Butanol  
The activation energy of LA esterification with \(n\)-butanol, calculated from the experimental data, subjected to the Arrhenius equation (Figure 12), is summarized in Table 4. The activation energy of LA esterification without a catalyst was 71.3 \(\pm\) 5.0 kJ/mol. HUSY insignificantly decreased the activation energy to 66.2 \(\pm\) 8.4 kJ/mol, while the activation energy of LA esterification over HMS-SO3H (0.4) was 65.2 \(\pm\) 9.7 kJ/mol. As mentioned above, this was a result of unsuitable physicochemical properties, which traded off between porosity and hydrophobicity. The presence of NRHMS-SO3H (0.4) remarkably decreased the activation energy to 58.2 \(\pm\) 7.1 kJ/mol, lower than that reported by [PERSON] et al. (71.1 kJ/mol) [55], which used nano core-shell magnetic materials based on the Keggin-heteropolyacids catalyst, possibly due to different reaction conditions and the esterification mechanism.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Catalyst**} & \multirow{2}{*}{**Alcohol**} & **Temperature** & **Rate of Reaction** & \multirow{2}{*}{**k (h\({}^{-1}\))**} \\  & & (\({}^{\circ}\)**C)** & **(mmol ALE/h)** & \\ \hline \multirow{6}{*}{Blank} & ethanol & 80 & 0.165 \(\pm\) 0.046 & 0.0065 \(\pm\) 0.0017 \\  & \(n\)-propanol & 80 & 0.163 \(\pm\) 0.023 & 0.0063 \(\pm\) 0.0006 \\  & \(n\)-butanol & 80 & 0.150 \(\pm\) 0.049 & 0.0052 \(\pm\) 0.0008 \\  & \(n\)-butanol & 100 & 0.521 \(\pm\) 0.084 & 0.0220 \(\pm\) 0.0037 \\  & \(n\)-butanol & 120 & 1.281 \(\pm\) 0.035 & 0.0671 \(\pm\) 0.0040 \\ \hline \multirow{6}{*}{HUSY} & ethanol & 80 & 0.242 \(\pm\) 0.058 & 0.0097 \(\pm\) 0.0023 \\  & \(n\)-propanol & 80 & 0.223 \(\pm\) 0.052 & 0.0085 \(\pm\) 0.0018 \\  & \(n\)-butanol & 80 & 0.184 \(\pm\) 0.052 & 0.0072 \(\pm\) 0.0021 \\  & \(n\)-butanol & 100 & 0.576 \(\pm\) 0.011 & 0.0246 \(\pm\) 0.0007 \\  & \(n\)-butanol & 120 & 1.481 \(\pm\) 0.100 & 0.0715 \(\pm\) 0.0065 \\ \hline \multirow{6}{*}{HMS-SO3H (0.4)} & ethanol & 80 & 0.344 \(\pm\) 0.151 & 0.0138 \(\pm\) 0.0059 \\  & \(n\)-propanol & 80 & 0.295 \(\pm\) 0.053 & 0.0117 \(\pm\) 0.0019 \\  & \(n\)-butanol & 80 & 0.241 \(\pm\) 0.093 & 0.0094 \(\pm\) 0.0034 \\  & \(n\)-butanol & 100 & 0.942 \(\pm\) 0.164 & 0.0406 \(\pm\) 0.0071 \\  & \(n\)-butanol & 120 & 1.860 \(\pm\) 0.269 & 0.0892 \(\pm\) 0.0137 \\ \hline \multirow{6}{*}{NRHMS-SO3H (0.4)} & ethanol & 80 & 0.512 \(\pm\) 0.214 & 0.0209 \(\pm\) 0.0089 \\  & \(n\)-propanol & 80 & 0.452 \(\pm\) 0.157 & 0.0185 \(\pm\) 0.0063 \\ \cline{1-1}  & \(n\)-butanol & 80 & 0.320 \(\pm\) 0.127 & 0.0129 \(\pm\) 0.0033 \\ \cline{1-1}  & \(n\)-butanol & 100 & 1.011 \(\pm\) 0.042 & 0.0444 \(\pm\) 0.0026 \\ \cline{1-1}  & \(n\)-butanol & 120 & 1.973 \(\pm\) 0.136 & 0.0971 \(\pm\) 0.0066 \\ \hline \hline \end{tabular} Reaction condition: Catalyst loading, 2.5 wt.% based on LA weight; LA-alcohol molar ratio, 1:5; reaction time, 5 h.  
\end{table}
Table 3: Alkyl levininate esters (ALEs) yield and kinetic parameters obtained from heterogeneously catalyzed LA esterification under different reaction conditions.