Thermodynamic Behavior of (2-Propanol + 1,8-Cineole) Mixtures: Isothermal Vapor–Liquid Equilibria, Densities, Enthalpies of Mixing, and Modeling

Vapor pressures and other thermodynamic properties of liquids, such as density and enthalpy of mixtures, are the key parameters in chemical engineering for designing new process units, and are also essential for understanding the physical chemistry, macroscopic and molecular behavior of fluid systems. In this work, vapor pressures between 278.15 and 323.15 K, densities and enthalpies of mixtures between 288.15 and 318.15 K for the binary mixture (2-propanol + 1,8-cineole) have been measured. From the vapor pressure data, activity coefficients and excess Gibbs energies were calculated via the Barker’s method and the Wilson equation. Excess molar volumes and excess molar enthalpies were also obtained from the density and calorimetric measurements. Thermodynamic consistency test between excess molar Gibbs energies and excess molar enthalpies has been carried out using the Gibbs–Helmholtz equation. Robinson–Mathias, and Peng–Robinson–Stryjek–Vera together with volume translation of Peneloux equations of state (EoS) are considered, as well as the statistical associating fluid theory that offers a molecular vision quite suitable for systems having highly non-spherical or associated molecules. Of these three models, the first two fit the experimental vapor pressure results quite adequately; in contrast, only the last one approaches the volumetric behavior of the system. A brief comparison of the thermodynamic excess molar functions for binary mixtures of short-chain alcohol + 1,8-cineole (cyclic ether), or +di-n-propylether (lineal ether) is also included.


Introduction
Vapor pressures and other thermodynamic properties of pure liquid and mixtures are physical properties of great importance for not only being necessary for the daily challenges in chemical engineering but also from a theoretical point of view as they help to develop and improve representative models of the liquid state.
Within this context, the mixture (2-propanol + 1,8-cineole) is of particular interest due to the nature of the molecules it comprises, and because of its potential applications, as described below. In this work, an experimental study of vapor-liquid equilibria (VLE), densities, and enthalpies of mixing for the mixture (2-propanol + 1, 8-cineole), together with some current models to fit them, are addressed.
1,3,3-Trimethyl-2-oxabicyclo [2.2.2]octane is a cyclic ether usually known as 1,8-cineole, or more commonly as eucalyptol because it is the main component of essential oil obtained improve the results when considering systems with polar substances, by the introduction of a polar parameter in the temperature depending on the attractive term of the EoS. On the other hand, the Stryjek and Vera modification [45] to the Peng-Robinson equation is considered. In this version, an adjustable parameter for pure components is introduced together with a modification of the polynomial for the acentric parameters.
Finally, as previously indicated, experimental results are compared with that of SAFT. The development and success of this model was due to the progress in the statistical mechanics methods, especially the perturbation theory and the valuable contribution of Wertheim [47,48] for chain and association effects. It provided a reasonably simple and accurate [49] general formulation which is accepted as the basis of the SAFT free energy model. This theoretical approach was derived by Chapman et al. [50,51], resulting in a well-grounded EoS, especially in the case of chain-like molecules and when effect of association is remarkable. In fact, the model may simulate the behavior of a wide range of systems having molecules ranging from nearly spherical non-associating to non-spherical associated ones, passing through the intermediate structural configurations. This third situation becomes the case of the system considered in this work, for which molecules are not very far from a spherical shape and one of the components is markedly associated while the other is not. Thus, for our intermediate system, it is interesting to compare the results of this particular SAFT molecular association model with those of the Van der Waals Modified Cubic EoS PRM, and PRSV previously mentioned. A number of user-friendly reviews on the derivation and applications of the SAFT model and the cubic EoS can be found in the literature [39,[52][53][54][55][56][57].
It has been for the purpose of enhancing the vision of the models and the molecular interactions, that in addition to the measurements of P, the experimental determination of ρ and heats of mixture were carried out. In fact, the corresponding thermodynamic properties, V E m , and H E m , are very sensitive to the spatial effects derived from molecular geometry and the detail of intermolecular forces, which complements information provided by other thermophysical quantities [35,58,59]. Furthermore, the present work is also a part of a comprehensive study conducted by our group using 1.8-cineole as cyclic ether and a short-chain alcohol as the second component [32][33][34][35][36][37]60,61]. Likewise, in previous years, we also carried out a similar study with di-n-propylether as linear ether, and an alcohol as the second component of a series that also included the same short-chain alcohols [62,63]. Hence, we include a brief comparison of the different thermodynamic behavior of both sets of systems in the Discussion section.

Pure Components
The molar volumes of the pure components, V 0 , used in the Barker analysis, together with the experimental vapor pressures, P 0 , which are compared with the values in the literature are gathered in Table 1.
Experimental P 0 data of 2-propanol at ten temperatures between (278.15 K and 323.15 K) were fitted to an Antoine equation (Equation (1) The standard deviation of the experimental pressures with respect to that calculated are obtained according to Equation (2):  [36]. Some new experimental vapor pressure data of this liquid have been published in recent years and they are shown in Figure 1 along with our data. The interval of temperature selected in Figure 1 allows for a better comparison between the data from different authors. Table 1. Molar volumes, V 0 , and vapor pressures, P 0 , of pure liquids used in the Barker analysis a , and data taken from the literature. 1101 a Standard uncertainty u is u(T) = 0.01 K and the combined expanded uncertainty Uc is Uc(P) = 0.1% with a 0.95 level of confidence (k = 2). b Used in the Barker analysis. c Ref. [64]. d Ref. [65]. e Ref. [35]. f Ref. [66]. g Ref. [31]. h Ref. [67].

2-Propanol 1,8-Cineole
Experimental P 0 data of 2-propanol at ten temperatures between (278.15 K and 323.15 K) were fitted to an Antoine equation (Equation (1) The standard deviation of the experimental pressures with respect to that calculated are obtained according to Equation (2): X and Xcalc correspond to the experimental pressures and calculated values, respectively, N is the number of experimental data and n is the number of adjusted parameters. Standard deviation results in a value of 25 Pa, 15 Pa being the maximum deviation at 298.15 K. The corresponding Antoine equation for 1,8-cineole was published previously [36]. Some new experimental vapor pressure data of this liquid have been published in recent years and they are shown in Figure 1 along with our data. The interval of temperature selected in Figure 1 allows for a better comparison between the data from different authors.  [66]; ▲, Štejfa et al. [31]; and □, Guetachew et al. [67]. , Stull et al. [66]; , Štejfa et al. [31]; and , Guetachew et al. [67].

Vapor Pressures and Derived Thermodynamic Parameters
The activity coefficients are obtained through the appropriate differentiation of Equation (4). with: where the subscripts 1 and 2 stand for 2-propanol and 1,8-cineole, respectively. V 0 is the molar volume and λ's are the interaction constants between the molecules designated in the subscripts. The vapor pressure is then given by, and the non-ideality of the vapor phase is taken into account with the following corrections (Equations (9) and (10)): where y 1 and y 2 are the vapor phase mole fractions of 1-propanol and 1,8-cineole, respectively and δ 12 is defined by the following equation: For every liquid mixture, the vapor pressure is measured at different temperatures from 278.15 to 323.15 K, so a slight modification of the true initial liquid mole fraction can be detected in Table 2, because of the variation in the amount and composition of the vapor phase.
These differences point to a stronger energy of interaction of 2-propanol-1,8-cineole than 2-propanol-di-n-propylether and also a stronger energy of interaction of 1,8-cineole-1,8-cineole than di-n-propylether-di-n-propylether, taking into account that the calculated numerical values are relative and also the approximate nature of the Wilson model.

Excess Molar Enthalpies and Densities
Experimental excess molar enthalpies and densities at four temperatures are gathered in Tables 4 and 5, respectively.  Graphical representations of experimental densities as function of composition at the four temperatures considered appears in Figure 4.
Excess molar volumes were calculated using Equation (11): where ρ stands for experimental density of the mixture and subscripts 1 and 2 for 2-propanol and 1,8-cineole, respectively. The values of the excess molar properties, H E m and V E m , have been fitted via least squares to a Redlich-Kister polynomial: where Q E m denotes H E m or V E m , x 1 and x 2 represent the mole fraction of 2-propanol and 1,8-cineole, respectively. Graphical representations of experimental densities as function of composition at the four temperatures considered appears in Figure 4. Excess molar volumes were calculated using Equation (11): where stands for experimental density of the mixture and subscripts 1 and 2 for 2-propanol and 1,8-cineole, respectively. The values of the excess molar properties, and , have been fitted via least squares to a Redlich-Kister polynomial: where denotes or , x1 and x2 represent the mole fraction of 2-propanol and 1,8cineole, respectively.
The coefficients of Equation (13) are collected in Table 6 beside the standard deviation obtained from Equation (2).  The coefficients of Equation (13) are collected in Table 6 beside the standard deviation s Q E m obtained from Equation (2). Graphical representations of both excess molar properties, and , are plotted in Figures 5 and 6, respectively. Both excess molar properties increase with temperature and in the case of excess molar enthalpies that increase at molar fraction around 0.5 is almost lineal, so we can calculate a value of , 7.6 J · mol K .    Figures 5 and 6, respectively. Both excess molar properties increase with temperature and in the case of excess molar enthalpies that increase at molar fraction around 0.5 is almost lineal, so we can calculate a value of , 7.6 J · mol K .   the Gibbs-Duhem relation to test the thermodynamic consistency of the vapor pressure measurements. However, we can test the consistency of the and values via the Gibbs-Helmholtz equation. The values calculated at T = 298.15 K are shown as curves in Figure 7, together with our experimental data. The match can be considered satisfactory although considerable uncertainty is implied by the quantitative evaluation of from vapor pressures [72]. In the same figure and for the same temperature, curves, obtained from = − , are also plotted.

A Comparative Discussion of the Thermodynamic Excess Functions for Short-Chain Alcohol + 1,8-Cineol, or +di-n-Propylether
For comparative purposes, and in order to highlight the particularities of our binary mixture, the thermodynamic excess molar functions at T = 298.15 K and x = 0.5 of the shortchain alcohol + 1,8-cineole (cyclic ether) or +di-n-propylether (lineal ether) or +n-hexane (an inert solvent) are summarized in Table 7.  [73,74]. c This work. d Refs. [75,76]. e Ref. [77]. f Ref. [63]. g Ref. [62]. h Ref. [78]. i Ref. [79]. j G E -55 value calculated at 303.15 k from vapor pressures data taken from Barraza and Edwards [80]. k Ref. [81]. Table 7, the low values of and for alcohol + 1,8-cineol mixtures stand out when comparing with those corresponding to the mixture of alcohol with di-n-propylether or with n-hexane. Such behavior can be qualitatively interpreted in terms of the type of interactions between the molecules that constitute the
Among the reported values in Table 7, the low values of H E m and V E m for alcohol + 1,8-cineol mixtures stand out when comparing with those corresponding to the mixture of alcohol with di-n-propylether or with n-hexane. Such behavior can be qualitatively interpreted in terms of the type of interactions between the molecules that constitute the mixture, and the molecular shapes. Unlike what happens in the (alcohol + n-hexane) mixtures, where the most important contribution to the excess molar enthalpy is the breaking of hydrogen bonds in alcohol (endothermic contribution), in alcohol mixtures with both ethers we would also consider the breaking interactions of polar type in ether (endothermic contribution) and also the formation of alcohol-ether interactions (exothermic contribution). In the case of mixtures of alcohol with 1,8-cineole, we have to take into account that this molecule has a larger molar volume and a larger dipole moment than the corresponding di-n-propylether. For that reason, one would expect greater endothermic contributions to the excess molar enthalpy. However, experimental excess molar enthalpies are considerably lower in mixtures with 1,8-cineole than the corresponding ones with di-n-propylether. To justify this experimental behavior, we should consider that the alcohol-1,8-cineole (cyclic ether) interaction is stronger than the alcohol-di-n-propylether (linear ether) one. This justification is consistent with both the more negative values of the excess molar entropy and the excess molar volume of alcohol + 1,8-cineole mixtures, as shown in Table 7, as well as from the relative values of λ ij interaction energies between 2-propanol-1,8-cineole and 2-propanol-di-n-propylether obtained from the vapor pressure data using Wilson's model, as indicated above.
The negative value of V E m and the low value of H E m for alcohol-cineol mixtures probably also has to do with the slightly curled shape of the ether molecule, which can favor the formation of alcohol-ether complexes, thanks to a good spatial coupling of the molecules. ethers we would also consider the breaking interactions of polar type in ether (endothermic contribution) and also the formation of alcohol-ether interactions (exothermic contribution). In the case of mixtures of alcohol with 1,8-cineole, we have to take into account that this molecule has a larger molar volume and a larger dipole moment than the corresponding di-n-propylether. For that reason, one would expect greater endothermic contributions to the excess molar enthalpy. However, experimental excess molar enthalpies are considerably lower in mixtures with 1,8-cineole than the corresponding ones with din-propylether. To justify this experimental behavior, we should consider that the alcohol-1,8-cineole (cyclic ether) interaction is stronger than the alcohol-di-n-propylether (linear ether) one. This justification is consistent with both the more negative values of the excess molar entropy and the excess molar volume of alcohol + 1,8-cineole mixtures, as shown in Table 7, as well as from the relative values of λij interaction energies between 2-propanol-1,8-cineole and 2-propanol-di-n-propylether obtained from the vapor pressure data using Wilson's model, as indicated above.
The negative value of and the low value of for alcohol-cineol mixtures probably also has to do with the slightly curled shape of the ether molecule, which can favor the formation of alcohol-ether complexes, thanks to a good spatial coupling of the molecules. A sketch of the possible coupling between molecules of 1,8-cineole and 2-propanol is represented in Figure 8  The greater strength of the alcohol-cyclic ether interaction with respect to that existing in the case of the linear ether could be also caused by an increase in electron density of the oxygen atom in the cyclic molecule (ring strain), as pointed out by other authors [82,83]. To confirm the validity of this hypothesis, we calculated the electron density around the oxygen atom in both the molecules, 1,8-cineole and di-n-propylether, obtaining the values of 5.12 and 4.98 electrons, respectively, which it is consistent with previous arguments. The calculations of electron density have been carried out at the B3LYP/6-31** level of theory [84][85][86] and the analysis of the electron-pairing was conducted using the Electron Localization Function (ELF) methodology as implemented in the Topmod program [87]. The greater strength of the alcohol-cyclic ether interaction with respect to that existing in the case of the linear ether could be also caused by an increase in electron density of the oxygen atom in the cyclic molecule (ring strain), as pointed out by other authors [82,83]. To confirm the validity of this hypothesis, we calculated the electron density around the oxygen atom in both the molecules, 1,8-cineole and di-n-propylether, obtaining the values of 5.12 and 4.98 electrons, respectively, which it is consistent with previous arguments. The calculations of electron density have been carried out at the B3LYP/6-31** level of theory [84][85][86] and the analysis of the electron-pairing was conducted using the Electron Localization Function (ELF) methodology as implemented in the Topmod program [87].
In the discussion above, we are assuming that the main contribution to the alcoholether interaction is the hydrogen bond formation between the lone pair of the oxygen atom in the ether and the hydrogen atom of the OH group in the alcohol. This has been established by numerous authors, among which we could cite a recent article by Patel et al. on binary systems 1,8-cineol + cresol [88].
Focusing on the comparison between 2-propanol and the other alcohols included in Table 8, we can see that mixtures including 2-propanol show greater positive value of H E m and appreciably less negative value of V E m than mixtures where 2-propanol is replaced by one of the other alcohols. Only excess molar entropy in mixture 1,8-cineole with 2-propanol are quite similar to that of mixture with 1-propanol. The extra increase in the excess molar functions has been attributed to cyclic multimers formation in the case of branched alcohols in low polarity solvents [89]. Table 8 shows the properties of the pure compounds used in this work in order to describe both the phase equilibrium and the volumetric behavior of 1-propanol (1) + 1,8-cineole (2) mixtures via the PRM, PRSV and SAFT models.

Equations of State (EoS)
Equations for calculation are described in detail in Appendix A1 (EoS Implemented in PE) of the work of Pfohl, Petkov and Brunner [90].
The cubic PRM and PRSV EoS parameters for 2-propanol were calculated from the correlation of vapor pressure and saturation properties. The SAFT parameters for 2propanol were taken from the literature [39]. The cubic PRM and PRSV EoS parameters, and SAFT parameters corresponding to 1,8-cineole were calculated in a previous paper [35].   [32]. b Ref. [91]. c Ref. [35]. d This work. e Ref. [39].
The van der Waals one-fluid mixing rules [43] were used to determine the PρT behavior of the mixtures. Classical quadratic combining rules for the cross-terms [43] were selected in all cases. A quadratic dependence between the interaction parameter, k ij , and the temperature was found in the experimental range considered.
The k ij interaction parameter has been set to our VLE data, showing a quadratic dependence on temperature. The fitted parameters for the equation, k ij = a + b·T/K + c·T 2 /K 2 (14) appear in Table 9 together with the regression coefficients.  Figure 9 shows the experimental VLE at three temperatures together with the obtained results using the selected EoS. It should be noted that bubble curves corresponding to the three models appear well separated for the temperatures of 278.15 and 323.15 K, but not at 298.15 K, where the bubble curves for PRM and PRSV models appear to be almost overlapping. A similar behavior is displayed in the dew curves for these two same models at 298.15 K. The dew curves corresponding to the PRM and SAFT models at 278.15 K and those of the PRM and PRSV ones at 323.15 K are also practically coincident. The best results for the correlations of the experimental data of the mixture under study were achieved with PRSV-VT and PRM-VT. The absolute average percentage deviation values (ADD) for these models were 9.27% and 10.99%, respectively. The ADD obtained for SAFT was 19.30%. Figure 9 shows the experimental VLE at three temperatures together with the obtained results using the selected EoS. It should be noted that bubble curves corresponding to the three models appear well separated for the temperatures of 278.15 and 323.15 K, but not at 298.15 K, where the bubble curves for PRM and PRSV models appear to be almost overlapping. A similar behavior is displayed in the dew curves for these two same models at 298.15 K. The dew curves corresponding to the PRM and SAFT models at 278.15 K and those of the PRM and PRSV ones at 323.15 K are also practically coincident. The best results for the correlations of the experimental data of the mixture under study were achieved with PRSV-VT and PRM-VT. The absolute average percentage deviation values (ADD) for these models were 9.27% and 10.99%, respectively. The ADD obtained for SAFT was 19.30 %. The major or minor capacity of the three EoS to reproduce the volumetric behavior of the system was also tested at 298.15 K. Figure 10 shows our experimental data for the excess molar volume at that temperature, together with the predictions of the three EoS tested. The major or minor capacity of the three EoS to reproduce the volumetric behavior of the system was also tested at 298.15 K. Figure 10 shows our experimental data for the excess molar volume at that temperature, together with the predictions of the three EoS tested. As it can be observed, only the SAFT model correctly reproduces the sign of , and even approaches the values of the volumetric behavior of the system quite well, something that the other two EoS cannot satisfy even when the refinement of the volume translation is used in them.

Chemicals
2-Propanol and 1,8-cineole were supplied by Aldrich, Seelze, Germany (mass fraction As it can be observed, only the SAFT model correctly reproduces the sign of V E m , and even approaches the values of the volumetric behavior of the system quite well, something that the other two EoS cannot satisfy even when the refinement of the volume translation is used in them.

Chemicals
2-Propanol and 1,8-cineole were supplied by Aldrich, Seelze, Germany (mass fraction purity > 0.999 and >0.990, respectively). All the chemicals were low water content, stored over molecular sieve (4 Å), and used without further purification. The mass fraction purity was checked via gas chromatography and found to be 0.9999 for 2-propanol, and 0.9970 for 1,8-cineole.

Apparatus and Procedures
Vapor pressure measurements were carried out according a static method, using an apparatus similar to that of Marsh [92], but with the incorporation of some different details. The device and operating method have been thoroughly described previously [93]. Several important points should be noted here. The undesirable effects of condensation on the mercury meniscus were avoided by circulating the thermostat water at ±0.1 K to maintain the manometer temperature at 325 K. In the same way, most vapor phase was maintained at that temperature, T = 325 K. Liquid sample temperature was measured using Beckmann thermometers, calibrated against vapor-liquid equilibria (VLE) of pure benzene (Merck mole fraction > 0.999 and distilled twice), along with Ambrose's equation [94] relating temperature with pressure by means of a sum of Chebyshev polynomials up to the sixth degree. Thus, the accuracy in the temperature measurements was estimated to be ±0.01 K. The volume of the cell containing the liquid mixture was about 12 cm 3 , and (8 to 10) cm 3 of liquid were used in each experiment. Previously, to be successively added by gravity into the cell immersed in liquid nitrogen, the liquids were degassed via magnetic stirring, with the (air plus vapor) phase being pumped away periodically. Masses of both components were determined by weighing with a precision electronic balance (0.0001 g). Caution was taken to prevent evaporation. Conversion to molar quantities was based on the relative atomic mass table issued by IUPAC, leading to an uncertainty in the mole fraction estimated to be less than ±0.0003. The vapor pressures, P, obtained from the difference in heights of the mercury meniscus in the two columns of the manometer, were calculated using the specific weight of that element for the value of gravitational acceleration at the laboratory where the measurements were performed. Manometer readings were performed using a Wild KM-305 cathetometer within ±0.01 mm, and pressure reproducibility was estimated to be better than 13 Pa. The uncertainty in the vapor pressure is estimated to be less than 0.1%.
Advantages and limitations of the static (isothermal) measurements method used in this work have been previously detailed by Smith and Menzies [95], together with the more general sources of error involved in steam pressure measurement, and particular reference to the individual sources of error in both the static and dynamic methods. Despite their greater laboriousness, compared to dynamic measurements, the main advantages of the static ones are not having to resort to physical or chemical analysis of the phases, directly providing the value of the Gibbs energy at each of the measured temperatures and avoiding inaccuracies derived from the accumulation of impurities throughout the measurement process. Regarding the more general sources of error involved in any of the measurement methods, both static and dynamic, those authors have highlighted deficiencies in (i) the stability, distribution and precise determination of temperature, (ii) the measurement and corrections for pressure measurements, and (iii) the presence of impurities in the chemical species used as components. In our work, we tried to minimize these deficiencies through methodological details such as those indicated above. Finally, and from the point of view of thermodynamic consistence compliance based on the Gibbs-Duhem equation, the static (isothermal) measurements are also more adequate than the dynamic (isobaric) ones.
A vibrating tube densimeter DMA 5000, Anton Paar GmbH, Graz, Austria was used for density measurements on the pure liquids and mixtures. The sample density is calculated from the vibration period with an uncertainty of ±0.04 kg·m −3 . The composition of the binary mixtures was determined by weighing the vapor pressure mixtures preparation in a similar way. From the experimental densities, the excess molar volumes were calculated. The uncertainty in excess molar volumes is estimated to be ±2 × 10 −9 m 3 ·mol −1 .
A Thermometric 2277 Thermal Activity Monitor, American Laboratory Trading, San Diego, (CA, USA) together with two Shimadzu (model LC-10ADVP HPLC), Shimadzu Europe GmbH, Duisburg, Germany variable speed piston pumps, was used to determine excess enthalpies at the different temperatures. The pumps were programmed in order to be able to measure the excess molar enthalpies at the selected molar fractions of mixture and they were previously calibrated. The uncertainty in mole fraction is estimated to be ±0.001, and the uncertainty in H E m measurements is better than 2%, as verified by comparing the results for a standard system with those of the reference system [96]. Some additional details can be found in a previous paper [97].

Conclusions
New isothermal vapor-liquid equilibrium data at three temperatures, from 278.15 K to 323.15 K, and over the entire composition range for the binary mixture 2-propanol + 1,8-cineole are presented. Vapor pressures have been measured via a static method. From these data, activity coefficients and excess Gibbs energies have been calculated using Barker's method and the Wilson equation. The consistency of the obtained vapor pressure data is substantiated by the close values of excess molar enthalpies calculated from the vapor pressures by applying the Gibbs-Helmholtz equation to those experimental values obtained in the present work. Although the system is far from an ideal behavior, showing a large positive deviation from Raoult's law, azeotrope do not appear within the considered temperature interval.
On the other hand, excess molar volumes for this system at temperatures between 288.15 and 318.15 K have been calculated from the densities that were experimentally obtained.
A brief comparison is presented between the thermodynamic behavior of short-chain alcohol + 1,8-cineol binary mixtures and those where the cyclic ether has been replaced by a linear ether, di-n-propylether or inert solvent, n hexane. This comparison allowed us to attribute a higher OH-O interaction energy in the alcohol + cyclic ether mixture than that corresponding to the mixture with linear ether. This effect is probably due to an increase in the electronic density of the oxygen atom in the cyclic ether (which is associated with the ring strain) together with a steric effect derived from the possibility of a closer coupling between the alcohol molecule and the cyclic ether molecule.
Both experimental vapor-liquid equilibrium (VLE) and volumetric data were correlated using three different thermodynamic models, namely PRSV-VT, PRM-VT and SAFT. The best results for the correlations of the experimental VLE data are achieved when the first two models are used. This is probably due to the regression flexibility conferred in the cases of the modified PR models by considering the binary interaction parameter k ij as an adjustable coefficient. On the contrary, only the SAFT model approaches the volumetric behavior of the real system better than the other EoS, even using the volume translation correction in them. The detail of the localized interactions between the areas of higher electron charge densities that SAFT considers could be responsible for that improvement. The approximations reported, as provided by the two considered versions of the Robinson-Stokes equation for VLE, and the one provided by SAFT for excess enthalpy, are within a very reasonable range.
Because of the special characteristics of the chemicals involved in this study, the results obtained in this work can be a good database in the development of advanced theoretical models such as molecular dynamics and direct simulation Monte Carlo. From an application point of view, these results, together with others of a more industrial type, can contribute to the development of biorefineries. More concretely, the values of parameters, as well as the reported experimental data, can be potentially suitable for simulation and for designing separation processes to obtain the interesting chemical 1,8-cineole.