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# The CPA parameters of SO were calculated based on Eq

The CPA parameters of SO2 were calculated based on Eq. (11) using the vapor pressure and saturated liquid density data of SO2 over the reduced temperature range of 0.55 to 0.9. All of the data used were taken from the NIST database [53]. The resulting CPA parameters of SO2 are presented in Table S1 of the Supporting Information. With the obtained CPA parameters of SO2, the vapor phase fugacity was then calculated at different conditions. In the next step involving the calculation of the liquid fugacity, the successful approach of considering a DES as a pseudo-component was adopted [54], [55], [56]. In this PRIMA-1 way, all of the investigated systems in this study are considered to be a binary mixture of SO2 and the DES pseudo-component. Following this procedure, some physical properties of the DES pseudo-components are required. The critical properties and acentric factors were calculated by the modified Lydersen-Joback-Reid method, as proposed by Valderrama and Rojas [57] together with the Lee-Kesler mixing rules for the various HBD to HBA ratios as recommended by Knapp et al. [58], [59]. Table 2 presents the values of the critical properties, acentric factors, and molecular weights of all of the investigated DESs [60], [61]. The detailed equations and calculation steps corresponding to this table are presented as Supplementary Material. Following this, the NRTL and UNIQUAC models were used to calculate liquid fugacity. With the aid of the newly proposed equations for τ (Eqs. (19), (20)), and based on Eq. (21) as objective function, the NRTL binary parameters were obtained. The optimized binary NRTL parameters for SO2 and the DES pseudo-components are reported in Table 3 for all of the investigated DESs. A similar procedure is followed for UNIQUAC, for the newly proposed equations (Eqs. (35), (36)). Table 4 presents the optimized binary UNIQUAC parameters of SO2 and the DES pseudo-components. The UNIQUAC parameters of r, q and q′ for each component must also be determined. For the DES pseudo-components, these parameters were calculated based on Eqs. (29), (30), (31), (32). The required critical properties of DESs for the modified Racket model (Eqs. (31), (32)) were taken from Table 2. The resulting values of the parameters of r, q and q′ are reported in Table 5. After calculating all of the required parameters for vapor-liquid equilibrium modeling, the solubility of SO2 was calculated in all of the investigated DESs. In order to have an evaluation of the two models of NRTL-CPA and UNIQUAC-CPA, the statistical error parameter of AARD% is defined as Eq. (42).where x and x are the experimental and calculated SO2 liquid phase molar compositions, respectively, and N is the total number of investigated data. Table 6 presents the values of AARD% for both of the CPA-NRTL and CPA-UNIQUAC models. In addition to the quantitative comparison of the errors of the two models, Fig. 1, Fig. 2 evaluate the behavior and trend of SO2 solubility in DESs as a function of temperature. Fig. 1 shows the CPA-NRTL and CPA-UNIQUAC model trends with respect to experimental data for four similar DESs with the same HBD to HBA molar ratio, in which levulinic acid is the HBD, but different HBAs are considered, consisting of tetraethylammonium chloride (TEAC), tetraethylammonium bromide (TEAB), tetrabutylammonium chloride (TBAC) and tetrabutylammonium bromide (TBAB). It is clear from this figure that both models show the reliable decreasing SO2 solubility behavior and trend with respect to temperature. Fig. 2 shows the temperature trend of SO2 solubility for four other DESs. The four investigated DESs of this figure have the same HBD and HBA molecules, but at different HBD to HBA molar ratios. The systems consist of choline chloride and glycerol at molar ratios of 1:1, 1:2, 1:3 and 1:4. Also in this figure, it is observed that both CPA-NRTL and CPA-UNIQUAC succeed to reliably model the decreasing SO2 solubility-temperature trends. Furthermore, SO2 solubility decreases as the molar ratio of glycerol increases in the investigated DESs and both models were able to correctly estimate this behavior without intersections over the temperature range.