# 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 analysis of variance (ANOVA) for both models given in Table 4 proves that the adequacy of these models is in good agreement with the experimental data. The adequacy is supported by a _p_-value lower than 5%, a correlation coefficient (R2) above 0.95, as well as the shapes of the parity diagrams presented in Figure 8. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Independent Variable** & **Correlation Coefficient, R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **Calculated F-Value** & _p_**-Value** \\ \hline \(Y_{1}\) & 0.991 & 0.985 & 162.9 & \(<\)0.0001 \\ \(Y_{2}\) & 0.993 & 0.984 & 114.3 & \(<\)0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ANOVA parameters used to evaluate the suitability of the model. Figure 8: Parity diagrams for glycerol conversion (**A**) and glycerol carbonate yield (**B**). The thorough analysis of the values of residuals, providing the differences between the calculated and experimental values, is another justification regarding the model accuracy if these values are enough small (Figure 8). By considering the normal probability plot, one can evaluate the data's normal distribution. Figure 9 presents both the internally studentized residuals and the normal probability plot for glycerol conversion and GC yield. The estimated coefficients together with their confidence intervals are given by relation (2) for glycerol conversion and by relation (3) for GC yield. The effects of the main and binary interactions can be evaluated using the estimated coefficients. Coefficients that did not pass the statistical significance test (based on \(p\)-value) were removed, except for those necessary to maintain the model's hierarchy. The main interactions were significant for both dependent variables. Equations (3) and (4) are as follows:  
\[ \begin{array}{ll}Y_{1}=&40.21(1\pm 0.056)+13.87(1\pm 0.152)\cdot X_{1}+18.69(1 \pm 0.113)\cdot X_{2}+9.54(1\pm 0.221)\cdot X_{3}\\ &+10.76(1\pm 0.278)\cdot X_{1}\cdot X_{2}+8.13(1\pm 0.369)\cdot X_{1}\cdot X_{3}-14. 66(1\pm 0.0211)\cdot X_{1}^{2}\\ \\ Y_{2}=&27.99(1\pm 0.084)+8.91(1\pm 0.162)\cdot X_{1}+10.7(1\pm 0.135)\cdot X_{2}+7. 18(1\pm 0.203)\cdot X_{3}\\ &+6.25(1\pm 0.329)\cdot X_{1}\cdot X_{2}+6.9(1\pm 0.298)\cdot X_{2}\cdot X_{3}-6. 31(1\pm 0.339)\cdot X_{1}^{2}\\ &-3.81(1\pm 0.559)\cdot X_{2}^{2}-5.36(1\pm 0.397)\cdot X_{3}^{2}\\ \end{array}  \tag{4}\]  
Figure 9: Normal probability plot ((**A**)—glycerol conversion; (**C**)—GC yield) and internally studentized residuals ((**B**)—glycerol conversion, (**D**)—GC yield). A positive influence means that the parameter is increasing with the factor and a negative influence means that the parameter decreases with the factor. Given the coefficients in Equations (3) and (4) and plots in Figure 10, both glycerol conversion and GC yield are positively influenced by reaction temperature (X\({}_{1}\)), catalyst amount (X\({}_{2}\)), and reaction pressure (X\({}_{3}\)). The impact of the key factors on glycerol conversion and GC yield is illustrated in Figure 10. The ANOVA for the GC yield model is given in Table 5. Based on these values, an F-value 114.3 for the model suggests that this is significant, and \(p\)-values below 0.05 indicate that the model terms are significant. The experimental results given in Table 6 are determined using the optimal condition calculated based on the mathematical model, and the highest values for glycerol conversion as well as GC yield were for the MgPSCN catalyst. The optimal values of the factors obtained by maximizing both glycerol conversion and GC yield are \(X_{1}=0.83,\ X_{2}=1,\ \text{and}\ X_{3}=0.5\) that provides a glycerol conversion of 71% and a GC yield of 46%, values close to the experimental values presented in Table 6 for the same catalyst. The reusability of the MgPSCN catalyst in the synthesis of glycerol carbonate was investigated over four consecutive reaction cycles under optimal conditions.