Fig shows graphically the abundance distributions of the
Fig. 3 shows, graphically, the abundance distributions of the ARD% of the investigated data with both the CPA-NRTL and CPA-UNIQUAC models, where ARD% is defined as,in which x and x are the experimental and calculated SO2 molar compositions in the liquid phase, respectively, and N is the total number of investigated data.
For even further investigations on both of the CPA-NRTL and CPA-UNIQUAC models, the values of infinite dilution activity coefficient, γ∞, Henry's constant, H, and enthalpy of absorption, ΔH, of SO2 in all of the investigated DESs were also calculated and presented in the Supporting Information as Table S2 for CPA-NRTL and Table S3 for CPA-UNIQUAC.
By considering the accumulation of the results above, it is concluded that the γ-ϕ approach is successful for modeling systems of SO2+DESs and both the CPA-NRTL and CPA-UNIQUAC can give reliable results.
As a further investigation to check the predictability of the proposed model, we studied whether it would be possible to obtain generalized correlations for the estimation of the adjustable parameters of NRTL (A, B, C and D of Eqs. (19), (20)) and UNIQUAC (A, B, C and D of Eqs. (35), (36)). To develop these correlations, molecular weight was considered as the independent parameter. Since the mentioned NRTL and UNIQUAC adjustable parameters are representatives of energy, then the choice of molecular weight which is also considered as an Pifithrin-μ parameter , and at the same time it is the most-readily available data of DESs, is quite suitable. Among all of the 14 investigated DESs in this study, the four DESs of 1 choline chloride+n-glycerol (where n=1, 2, 3, 4) are of the same family. Therefore, generalized correlations to estimate the NRTL and UNIQUAC adjustable parameters were developed for this family. The behavior of both the NRTL and UNIQUAC adjustable parameters with respect to molecular weight are shown, respectively, in Fig. 4, Fig. 5 for the homologous DESs of 1 choline chloride+n-glycerol (n=1, 2, 3, 4). The correlations are also presented on these figures.
Finally, the influence of using temperature-independent (Eqs. (13), (14), (33), (34)) or temperature-dependent (Eqs. (19), (20), (35), (36)) τ functions have been investigated on both the CPA-NRTL and CPA-UNIQUAC models. Table S5 of the Supplementary Information presents the results of these comparisons. It is concluded that temperature-dependent τ functions, in both the CPA-NRTL and CPA-UNIQUAC models, lead to great improvements in the final results.
Conclusions In this study, the thermodynamic modeling of SO2 solubility in 14 DESs was investigated over wide ranges of temperatures. This is the first literature study to model the solubility of SO2 in a variety of DESs of different nature. These are quite challenging systems to model, especially by considering the extraordinarily high molar solubility of SO2 in DESs, even reaching up to 0.7 in some cases. For this purpose, the γ−ϕ approach was employed. The CPA EoS was used for the vapor phase and the NRTL and UNIQUAC models were both investigated for the liquid phase. The binary parameters of NRTL and UNIQUAC were optimized based on the experimental values of SO2 solubility in the DESs. The results indicated that both of the CPA-NRTL and CPA-UNIQUAC models are reliable to estimate SO2 solubility in DESs. A total AARD% of 3.1% for the former and 2.9% for the latter suggest that CPA-UNIQUAC is slightly more accurate. Also, both models successfully follow the temperature behavior and trends of the experimental data. The values of infinite dilution activity coefficients, Henry's constants, and enthalpies of absorption of SO2 in all of the investigated DESs were also calculated by both models. In general, it is concluded that when high accuracy is a priority, CPA-UNIQUAC is the better choice, while in many cases where simplicity is preferred, the CPA-NRTL is suggested.
Acknowledgements The authors are grateful to Shiraz University for providing research facilities for this study.