# An Experimental Study of Glycerol Carbonate Synthesis over g-C\({}_{3}\)N\({}_{4}\) Catalysts
## 3 Results and Discussions
### Optimization of Catalyst Activity Through Experimental Design Methods  
The effectiveness of glycerol carboxylation with CO\({}_{2}\) using the MgPSCN catalyst was assessed by examining glycerol conversion and glycerol carbonate yield. This evaluation employed a Box-Behnken experimental design, which considered the three key independent variables of reaction temperature (X1), catalyst amount (X2), and reaction pressure (X3). The Box-Behnken design is a robust statistical method that has been successfully utilized in various studies to optimize complex chemical reactions. By systematically varying these factors researchers can identify the conditions for the maximization of the yield of the carboxylation process. This approach has proven to be valuable in enhancing the understanding and performance of catalytic systems in the literature [63; 64; 65]. The experimental design matrix corresponding to the Box-Behnken design consisted of a series of 15 experiments. The reaction time for these experiments was set to 4 h. The natural values as well as the coded factor values used in our experimental design matrix are given in Table 2.  
The impact of the factors on the responses was assessed using a polynomial model of the following form:  
\[ \begin{array}{ll}Y_{i}=&\beta_{0}+\beta_{1}\cdot X_{1}+\beta_{2}\cdot X_{2} +\beta_{3}\cdot X_{3}+\beta_{12}\cdot X_{1}\cdot X_{2}+\beta_{13}\cdot X_{1} \cdot X_{3}\\ &+\beta_{23}\cdot X_{2}\cdot X_{3}+\beta_{11}\cdot X_{1}^{2}+\beta_{22}\cdot X _{2}^{2}+\beta_{33}\cdot X_{3}^{2}\end{array}  \tag{2}\]  
The validation of the equations was performed using statistical methods, specifically analysis of variance (ANOVA). Additionally, response surface methodology (RSM) was employed to analyze the experimental design, utilizing the experimental values in Table 3. The Fisher test value (F-value) calculated for the model was compared with the theoretical Fisher test value (F(\(p-1\), \(n-p\))) at a 5% significance level. This comparison was made to assess the model's validity, taking into account the number of experiments conducted (\(n\) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multicolumn{6}{c}{**Value/Level**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Low**} & \multicolumn{2}{c}{**Medium**} & \multicolumn{2}{c}{**High**} \\ \cline{2-7}  & **Natural (Z)** & **Coded (X)** & **Natural (Z)** & **Coded (X)** & **Natural (Z)** & **Coded (X)** \\ \hline Reaction temperature (\({}^{\circ}\)C), X\({}_{1}\) & 150 & \(-1\) & 200 & 0 & 250 & +1 \\ Catalyst amount (\%), X\({}_{2}\) & 10 & \(-1\) & 30 & 0 & 50 & +1 \\ Operating pressure (bar), X\({}_{3}\) & 3 & \(-1\) & 7 & 0 & 10 & +1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical values assigned to the independent variables within the experimental design matrix. Figure 7: FTIR spectra of the CN, PSCN, MgPSCN, and LiPSCN. and the number of terms included in the model (_p_). By evaluating the F-value against the theoretical threshold, researchers can determine whether the model provides a statistically significant explanation of the observed data, ensuring the robustness and reliability of the experimental results [66]. In other words, as highlighted in the literature, the _p_-value for each parameter should be below 5% to ensure that each independent variable in the model significantly contributes to predicting the output. This threshold indicates that the variable's effect on the response is statistically significant, thereby validating its inclusion in the model [67]. The coefficients of the models, along with the ANOVA tests, were thoroughly evaluated using Design-Expert Version 8. Both glycerol conversion (Y1) and glycerol carbonate yield (Y2) were considered as dependent variables. To find the best operating conditions which ensure the highest glycerol conversion as well as glycerol carbonate yield, a polynomial model based on Equation (2) was developed.