## 3 Results and Discussion  
### Experimental Density Data  
The densities of the CO\({}_{2}\)(1) + \(n\)-decane(2) mixtures with mole fractions of CO\({}_{2}\)\(x_{1}\) = 0, 0.2032, 0.4434, 0.7589, and 0.8947 were measured at temperatures ranging from 283 K to 363 K and pressures up to 100 MPa. The experimental data are listed in Table S1 in the Supplementary Materials. The deviations in the densities of the \(n\)-decane between the experimental data and values calculated using Equation (1) are shown in Figure 2. The information on density measurements taken for \(n\)-decane is summarized in Table 3. It can be noted that the relative deviations in the experimental data from the calculated values obtained from the modified Tait equations are mostly lower than 0.6%. The data from references [17; 18; 19; 20; 24; 32; 33; 34; 35; 36; 37] with relative deviations of within \(\pm\)0.6% are in satisfactory agreement with our correlation. These density data were obtained with a VTD. However, the larger deviations come from earlier literature [38; 39; 40; 41]. The experimental data obtained by [PERSON] et al. [38] and [PERSON] et al. [39] were measured through a volume measurement. [PERSON] et al. [40] and [PERSON] et al.'s experimental data [41] were obtained with a  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Chemical Name** & **Source** & **CAS No.** & **Molar Mass g/mol** & \begin{tabular}{c} **Stated Mass** \\ **Fraction Purity** \\ \end{tabular} & **Purification Method** \\ \hline CO\({}_{2}\) & \
\begin{tabular}{c} Jining Xieli Special \\ Gas \\ Aladdin \\ \end{tabular} & 124-38-9 & 44.01 & \(>\)0.99999 &
\begin{tabular}{c} Freeze-pump-thaw \\ cycle \\ none \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Specification of samples.  
Figure 1: Schematic diagram of density apparatus: PC, computer; TS, temperature sensor; PS, pressure sensor; PG, pressure gage; MC, motor controller; PP, piston pump; SM, stepping motor; MS, mixed sample vessel; N\({}_{2}\), nitrogen cylinder; SC, sample container; TB, thermostatic bath; VP, vacuum pump; V-1 to V-16, valve.  
Figure 3 shows the densities of CO\({}_{2}(1)+n\)-decane(2) mixtures at 283-363 K. It can be concluded that the density values of the mixtures smoothly increase with increasing pressure and mole fraction of CO\({}_{2}\) and decrease with increasing temperature. It is worth noting that the slopes of the density curve increase with increasing mole fraction of CO\({}_{2}\). The density curves for different mole fractions of CO\({}_{2}\) intersect under specific temperatures and pressures. For example, the liquid densities of the mixtures with a mole fraction of 0.2032 and 0.7589 are equal at 363 K and approximately 15 MPa. This intersection between the trends is largely due to the differences in molecular size, non-hydrogen atoms fraction, and critical temperature for mixture components [24].  
The deviations in density between the experimental data and the values calculated using Refprop 10.0 [43] are plotted in Figure 4. It is important to note that the deviations in the experimental data and the literature values are generally within \(\pm\)2.0%. The deviations in the data obtained by [PERSON] et al. [23] exhibit scattered deviations around the baseline within \(\pm\)1.5%. The deviations in the data obtained by [PERSON] et al. [17] and [PERSON] et al. [22] are within \(\pm\)1.6%. The deviations in the data obtained by [PERSON] et al. [24] are within \(\pm\)2.0%. The density data measured by [PERSON] et al. [11] have a maximum deviation of 2.2%. These results reveal that the measurement results are reasonably acceptable.