Development of a New Group Contribution Method Based on GCVOL

Article pubs.acs.org/IECR

Development of a New Group Contribution Method Based on GCVOL Model for the Estimation of Pure Ionic Liquid Density over a Wide Range of Temperature and Pressure Nathan S. Evangelista, Frederico R. do Carmo, Rílvia S. de Santiago-Aguiar, and Hosiberto B. de Sant’Ana* Grupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Universidade Federal do Ceará, Campus do Pici, Bloco 709, 60455-760 Fortaleza−CE, Brazil S Supporting Information *

ABSTRACT: A new group contribution method based on GCVOL model developed by Elbro et al. in 1991 [Elbro, H. S.; Fredenslund, A.; Rasmussen, P. Ind. Chem. Eng. Res. 1991, 30, 2576−2582] is proposed for the estimation of ionic liquids density over a wide range of temperature and pressure. A total of 102 new groups for ionic liquids were introduced to the already 60 existing groups revised and proposed in 2003 by Ihmels and Gmehling [Ihmels, E. C.; Gmehling, J. Ind. Chem. Eng. Res. 2003, 42, 408−412]. These groups were proposed based on a collection of density data from literature. The databank contains data of 864 different ionic liquids, including dicationic and tricationic species, and a total of 21 845 data points, covering a temperature range of 251.62−473.15 K and a pressure range of 0.1−300.0 MPa. An average absolute relative deviation (%AARD) of 0.83% was obtained, indicating that our model is able to predict densities of a great variety of ionic liquids accurately.

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INTRODUCTION For the past years, the properties of ionic liquids (ILs) have been the subject of considerable interest, especially because of their unique physicochemical properties, such as their almost null vapor pressure; high thermal and chemical stability; and, capability to dissolve polar, nonpolar, organic, and inorganic materials.1,2 The literature presents different academic and industrial applications for ionic liquids which include their usage as reaction media for catalysis reactions,3 as media for CO2 absorption,4−6 and also as solvents on liquid−liquid extraction operations.7−25 Among these physicochemical properties, the knowledge of volumetric properties of ILs play an important role, e.g., density is a crucial property for solving material and energy balances related to industrial processes.26 Furthermore, the pressure− volume-temperature (PVT) behavior is fundamental and very useful from a practical and theoretical point of view.27 Experimental measurement of fundamental properties for all the existing ILs is an exhaustive and expensive task. In addition, different selections of cations and anions may drastically change their properties. For this reason, accurate models capable to estimate ionic liquids properties could be extremely interesting. Several researchers have proposed models for estimating the density of ILs.1,26−31 In the next paragraphs, it will be present a brief review from the literature about some models based on group contribution. Ye and Shreeve29 proposed a method to estimate densities of ILs and salts. Jenkins et al. developed a procedure32 that was used to calculate the volumes of cations and anions. They have obtained reliable results, although the model is only applicable at room temperature. Gardas and Coutinho27 presented an extension of the previous method to estimate densities of ILs over a large range © 2014 American Chemical Society

of temperature (273.15−393.15 K) and pressure (0.1−100.0 MPa). The influence of temperature and pressure on density have been established by adding three universal constants that were obtained by using 788 experimental density data points for nine imidazolium-based ILs. These authors considered the density as a linear function of temperature and pressure. The method has been evaluated by predicting 1521 data points of pure imidazolium-based, pyridinium-based, pyrrolidiniumbased and phosphonium-based ionic liquids. The authors also predicted densities of binary mixtures of imidazolium-based ILs. Average absolute relative deviation (%AARD) analysis showed a range comprised between 0.45% to 1.49% for pure ILs. For binary mixtures, %AARD is in a range of 0.13%−2.63%, which indicates that the model is accurate for the specific ILs studied. Jacquemin et al.30,31 proposed a model for the estimation of the density of ILs at temperatures up to 423 K and pressures ranging from 0.1 MPa to 207.0 MPa. Temperature−pressure dependency has been evaluated by estimating parameters for each functional group. A quadratic effect of temperature was considered. Pressure effect on density has been performed by using a Tait-type equation with four adjustable parameters. Hence, seven adjustable parameters were estimated for each functional group proposed. A %AARD value of 0.36% between experimental and predicted data indicates that the model is able to predict the densities of 5089 experimental data accurately. Paduszyński and Domańska26 proposed a method able to predict densities of ILs based on a great variety of different cations and anions. Unlike the previous models, the authors Received: Revised: Accepted: Published: 9506

March 11, 2014 May 7, 2014 May 9, 2014 May 9, 2014 dx.doi.org/10.1021/ie501031r | Ind. Eng. Chem. Res. 2014, 53, 9506−9512

Industrial & Engineering Chemistry Research

Article

proposed functional groups capable to be extrapolated for a great variety of different ILs. For this reason, by comparing with previous methods, this model has a much wider range of applicability. The authors considered a linear relationship between molar volume and temperature at a reference pressure. A Tait-type equation (with temperature-dependent and independent parameters) was used to compute the density dependence of pressure. The authors emphasize that the adjustable parameters are universal coefficients, differently from the method proposed by Jacquemin et al.31 Over 16 800 density experimental data points were used in the model developed. Parameters estimation was based on 13 135 experimental data. Furthermore, 3695 experimental data points were used to model evaluation. Since a %AARD of 0.45% was obtained, the proposed model is reliable and capable to predict densities covering a temperature range of 253−473 K and a pressure range of 0.1−300 MPa. In this work, we propose an extension of the group contribution method GCVOL-OL-602, named GCVOL-IL. A total of 102 new groups for ILs were introduced to the already 60 existing groups revised and proposed by Ihmels and Gmehling.33 Among the groups added, 97 are charged and 5 are neutral. For detailed information, readers could consult the Supporting Information (SI), which describes how the functional groups were defined. For that, it has estimated IL densities at atmospheric pressure by using the model originally proposed by Elbro et al.34 Furthermore, a Tait-type equation has been used to predict density at pressures higher than atmospheric. A comprehensive database containing 21 845 density data points of 864 ionic liquids covering a wide range of temperature (251.62−473.15 K) and pressure (0.1−300.0 MPa) was used to develop the proposed model. The dataset was obtained from 534 different sources from literature. It is important to notice that the database used include monocationic, dicationic, and tricationic ILs.

Figure 1. Groups adopted for ionic liquids (ILs) based on the [C4mim] cation.

attached to atoms of the rings must be distinguished of the GCVOL-OL-60 groups, which were originally proposed to describe groups appearing on organic neutral molecules. These groups have been included in the “first level cation groups”. A second level has been proposed, named the “second level cation groups”, composed of groups directly attached to the “first level cation groups”, by using the original GCVOL-OL-60 groups. These two-level groups have been introduced because of the fact that most of the charged molecules are concentrated in the “first level cation groups”. Adopting this methodology, it will be possible to draw different cations and anions without increasing the number of functional groups. The same methodology was used to define the groups derived from the anions. It is important to mention that some of the largest anions were divided into smaller groups (namely, “first level anion groups”). The fragmentation procedure was based on the availability of density data of ILs containing anions derived of the same “first level anion group”. For example, Figure 2 shows how the “first level anion group” has been

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DEVELOPMENT OF THE NEW MODEL Functional Groups. As pointed out by Paduszyński and Domańska,26 the great majority of the methods reported in the literature is based on the division of the IL into cations and anions instead of smaller functional groups. Nowadays, there exists a wide variety of cations and anions, and new ionic liquids are synthesized for different industrial and academic applications. Consequently, a large number of new functional groups must be determined. Paduszyński and Domańska26 took special attention to the definition of functional groups, proposing that groups that are able to be extrapolated for different ionic liquids not be considered in the model development. Their methodology avoids “proximity effects” present on ionic liquids, by considering electronic charge distributions that occur when a group is attached or close to different atoms. By definition, a functional group should be the smallest entity into which a molecule is divided. In fact, it should be ensure geometry independency of the molecules present in a determinate group. In addition, it should also have the same net charge, ideally electroneutral.35 For this reason, in this paper, it has been set up functional groups in accordance to the restrictions proposed by Wu and Sandler,35 such as the maintenance of the group charge and geometry. In the definition of the groups derived from cations, it has been proposed a division into smaller and representative groups, as presented in Figure 1. Functional groups directly

Figure 2. Groups adopted for ILs based on the [NPFSO2F] anion.

defined. Following the same guideline, “second level anion groups” could be described by using the original GCVOL-OL60 groups. It is important to notice that some of the largest and all the smallest anions were taken as “first level anion groups”. For this reason, these groups have not been divided into smaller fragments. The same idea has been used previously by Paduszyński and Domańska26 and Gardas and Coutinho.27 The use of the methodology described above allow us to decrease the number of functional groups able to describe the variety of cations and anions present in the databank used in 9507

dx.doi.org/10.1021/ie501031r | Ind. Eng. Chem. Res. 2014, 53, 9506−9512


Article

constants are not computed by group contribution additions. This approach is in accordance with the fact that the density of approximately incompressible liquids does not vary significantly with variations in pressure. Coefficient D was considered as a linear function of temperature in order to consider the influence of this property on compressibility. The term (D + P0) ensures that, at the reference pressure (P0), the calculated density equals the value estimated by the GCVOL-IL method. A similar idea has already been applied by Paduszyński and Domańska.26 The term ρ(T,P0) is calculated by applying the GCVOL-IL method at a reference pressure (P0) of 0.1 MPa. Note that we set the term C of eq 1 at zero for all the groups here proposed, bceause of the fact that a linear influence of temperature on density is a satisfactory approach. The Model Parameters Estimation. The database used on this model development is presented in the SI. In addition, in the same spreadsheet, a schematic diagram is shown with a detailed description of each step followed during the development of the model proposed in this paper. To the databank created and provided by Paduszyński and Domańska,26 3124 new data points were added, including 83 new ILs, 24 new cations, and 4 new anions. First, GCVOL-IL parameters (namely, A and B) were determined for each group. In this step, we selected some of the data present on our databank to determinate density correlations. These correlations were further employed to determinate pseudo-experimental data points. The correlation dataset was selected after a critical statistical evaluation. We have not used dubious density data (in other words, data that showed large deviation in comparison to the other values reported by different researchers). It is important to mention that the dubious data removed in this estimation step have been included in the prediction dataset, as presented in the SI. A total of 384 density correlations for different compounds were obtained by fitting the 8699 evaluated data. These correlations were used to calculate pseudo-experimental data using 5-K steps in the temperature range. The temperatures of the pseudo-experimental data considered are within the melting and boiling points of the ionic liquids (ILs). These data were used for the estimation of the referred parameters for all 97 charged groups and 3 noncharged groups (−CF2OCHF−, −CF3OCHF−, and −CHF−). Although deviations between experimental and estimated data for compounds containing these three noncharged groups were low, the GCVOL-IL parameters for these groups should be determined using the density data of molecular compounds (that is, not of ILs). Unfortunately, for our knowledge, these data have not been found in the literature. The parameters for the remaining neutral groups (−CF2− and −aC−COOH) used in this work were obtained by using experimental data of molecular compounds taken from the literature.39,40 Furthermore, the pressure-related parameters (namely, d0, d1, and E) were determined by using 2411 experimental data of imidazoliumbased ILs. As previously mentioned, the values obtained for these coefficients are constant and should be extrapolated for all ILs. A computer tool developed in Visual Basic for Applications (VBA), involving MS-Access and MS-Excel, was employed to manipulate the great variety of data present in our databank. Furthermore, a code designed in Fortran 90 was used to perform the calculations. The estimation of the group parameters (A and B) was performed by using the Simplex

this paper, especially when compared to the methods present in literature, described previously. For example, unlike Paduszyński and Domańska’s paper,26 the same functional groups were employed to draw ILs containing pyrrolidinium, piperidinium, and azepanium. The GCVOL Method. The GCVOL method allows one to calculate saturated liquid densities accurately. The following equation was proposed by Elbro et al.:34 ρ=

MW MW = ∑ niΔvi V

(1)

where MW denotes the molecular weight (g/mol) and V is the molar volume (cm3/mol). The contributions of all group volume increments Δvi must be added for the calculation of the molar volume, and ni denotes the number of groups i present in the molecular structure of the compound. The temperature influence in the molar group volume is calculated using the following equation: Δvi = Ai + Bi T + CiT 2

(2) 3

whereby the units are K, cm /mol, cm /(mol K), and cm3/ (mol K2) for the temperature (T) and parameters A, B, and C, respectively. If the model will be used to predict densities of solvents, the temperature can vary between the melting point and the normal boiling point. For the prediction of densities of amorphous polymers, the temperature can vary between the glass-transition temperature and the degradation temperature.34 Elbro et al.34 proposed 36 functional groups, covering different chemical classes of compounds. The authors used density correlations presented in the DIPPR database36 to determine pseudo-experimental data points, covering temperatures from 200 K up to 500 K, spaced in 10-K steps, which were applied in the estimation of group parameters. Furthermore, Tsibanogiannis et al.37 proposed six functional groups, which allowed the density prediction of new classes of compounds by the original GCVOL method. Three of them are correction terms for allenes and cycloalkanes. The authors used density data from the DIPPR database36 to estimate parameters of each molar group. In 2003, Ihmels and Gmehling33 revised the original groups34,37 and proposed new groups, which broadened the applicability of the original model. The authors employed the DDB-Pure38 parameters to calculate the pseudoexperimental data used in the estimation of parameters for all molar groups. The temperatures of the data points were considered to vary from 200 K to 500 K in 10-K steps. After this extension, densities of tertiary alcohols, alkynes, carboxylic acids, allenes, cycloalkanes, fluorides, bromides, iodides, thiols, sulfides, sulfates, amines, nitriles, and nitro compounds were able to be predicted by using the GCVOL-OL-60 method. The Proposed Method. The prediction of density at various temperatures and pressures by the proposed method is based on the following Tait-type equation: ρ (T , P ) =

ρ(T , P0) ⎡ (D + P) ⎤ 1 − E ln⎢⎣ (D + P ) ⎥⎦ 0

3

(3)

where

D = d0 + d1T

(4)

whereby the units are MPa for the coefficients D and d0 and MPa/K for coefficient d1; coefficient E is dimensionless. Note that these parameters are universal for all ILs; that is, these 9508



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method proposed by Nelder and Mead.41 The following objective function (F) was minimized: F=

1 Np

Np

∑ i=1

|ρ(T , P0)pexp − ρ(T , P0)calc | ρ(T , P0)pexp

estimate the pressure-related parameters. The obtained values for these constants were d0 = 287.624 MPa, d1 = −0.444 MPa/ K, and E = 0.0711. As presented in Table 1, data from 11 different ILs have been used as the correlation dataset (that is, only these data were used to estimate these parameters). Furthermore, the reliability of these parameters was tested by predicting all density data at of ionic at pressures higher than atmospheric. The prediction data set consists of 10,242 experimental data points which were compared to each respective calculated value at pressures higher than 0.1 MPa and up to 300.0 MPa. The low value obtained of %AARD for this prediction (0.61%) ensures the reliability and universality of these parameters. Table 2 summarizes the evaluation process of the GCVOL-IL methodthat is, the method that is able to predict IL density

(5)

where ρ(T,P0) denotes the density calculated by using eq 1 and ρ(T,P0)pexp denotes the pseudo-experimental density value. The summation goes over all of the pseudo-experimental data (namely, Np) considered in the estimation. Similarly, the same numerical method was employed to minimize the following objective function, used in the estimation of coefficients d0, d1, and E: calc

F=

1 Ne

Ne

∑ i=1

|ρ(T , P)exp − ρ(T , P)calc | ρ(T , P)exp

(6)

Table 2. Summary of the Calculations Performed in the Model Validation

where ρ(T,P)calc denotes the density calculated according to eq 3 and ρ(T,P)exp denotes the experimental density value. The summation goes over all of the experimental data (Ne) considered in the estimation.

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RESULTS AND DISCUSSION In order to determine the accuracy of the proposed model, two statistical parameters have been used: the relative deviation (% RD) and the absolute average relative deviation (%AARD): %RD =

ρ(T , P)exp − ρ(T , P)calc ρ(T , P)exp

%AARD =

1 Ne

Ne

∑ i=1

(7)

|ρ(T , P)exp − ρ(T , P)calc | ρ(T , P)exp

(8)

The functional group parameters proposed by the GCVOLIL model are presented in the SI. As presented in this spreadsheet, the groups proposed are very simple and flexible; put another way, they can be used to draw new ILs with chains containing “first level cation/anion groups” and different groups present on the GCVOL-OL-60 group table. Table 1 presents the ILs, along with the number of data that have been used to

pressure range (MPa)

No. of data

AARD (%)

[C4mim][BF4] [C2mim][BF4] [C4mim][C(CN)3] [C2mim][NTf2] [C1−C1[2]C4im][NTf2] [C8mim][BF4] [C7mim][NTf2] [C8mim][NTf2] [C4mim][OTf] [C6mim][PF6] [C8mim][PF6] [C8mim][OcSO4] [C4mim][PF6] [C4mim][NTf2] [C2mim][EtSO4]

0.1−200 0.1−30 0.1−30 0.1−40 0.1−10 0.1−10 0.1−30 0.1−30 0.1−10 0.1−10 0.1−10 0.1−200 0.1−200 0.1−40 0.1−40

608 96 96 188 126 154 96 96 154 154 154 170 227 46 46

0.243 1.977 0.112 0.912 0.494 0.743 0.209 0.508 0.145 0.084 0.399 0.579 0.174 0.912 1.297

2411

0.450

total

No. of ionic liquids

data points used

AARD (%)

415 163 124 54 52 31 17 4 3 3 2

14518 2556 2210 607 1559 244 65 4 45 27 10

0.676 1.21 1.28 0.81 0.80 2.15 1.51 1.93 0.45 0.42 0.24

total

869

21845

0.83

at atmospheric pressure. The obtained %AARD values were low, which proves that the proposed model is accurate for all the presented ILs. Figure 3 illustrates the relative deviations between all experimental and predicted data (11 603 data points) at reference pressure (0.1 MPa). The values obtained of %RD are within a range of −20% and +14% and the %AARD value obtained for these points was 1.02%, which indicates that the model can accurately predict density at atmospheric

Table 1. Ionic Liquids Used To Estimate Parameters d0, d1, and E ionic liquid, IL

cation type imidazolium ammonium pyridinium pyrrolidinium phosphonium piperidinium morpholinium azepanium pyrazolium isoquinolinium quinolinium

Figure 3. Relative deviation (%) versus temperature (K) at P0 = 0.1 MPa. 9509



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pressure. For these points, high deviation values were observed for ILs based on cations containing the “carboxymethyl” group. The proximity effects occurring on this and other cations, such as “cholinium” may be the reason for this problem. The same effects occur on ionic liquids containing “serinate”, “L-Alanilate” and other anions. This may indicate further review on some groups. Unfortunately, because of the lack of density data for these compounds, we cannot ensure that this is a correct answer. Another possible reason for the higher deviation value may be related to uncertainties related to a few GCVOL-OL-60 groups. Figure 3, from the paper of Ihmels and Gmehling,33 shows that the deviations between pseudo-experimental and calculated data (by the GCVOL-OL-60 model) are approximately within a range of −10% to +10%. Although we cannot ensure this is the real cause of the problem, because the authors do not present a detailed analysis of the database used in the model validation. Figure 4 illustrates the deviation obtained by considering pressures higher than 0.1 and up to 300 MPa. The absolute

Figure 5. Distribution of relative deviation data (%), using 21 789 data points of our databank.

The densities of 48 dicationic and 14 tricationic ILs were predicted with elevated accuracy for the great majority of the data tested, as illustrated in the spreadsheet provided in the SI. Finally, we emphasize that the model is under constant development to include different types of ILs that are not able to be described by the proposed functional groups.

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CONCLUSION In this work, the group contribution method GCVOL-OL-602 was extended for the estimation of density of ionic liquid (IL) compounds at atmospheric pressure. A Tait-type equation was employed to estimate the density of ILs at pressures up to 300 MPa. The functional groups defined can easily be extrapolated to draw a wide variety of monocationic, dicationic, tricationic, and n-cationic ILs that have not been considered in this model development. The proposed method allows accurate estimation of the density of a great variety of ILs, since a very low value of average absolute deviation was obtained (%AARD = 0.83%). Although lower values of %AARD are reported for different group contribution methods that have been presented in the literature, we have used the largest available databank that contains density points to test the model reliability. The simplicity, reliability, and flexibility of the model encourage further use and development of the method proposed.

Figure 4. Relative deviation (%) versus temperature (K) at P0 > 0.1 MPa.

values of %RD at these pressures are below 8% and a value of % AARD obtained for these points was 0.61% was obtained for these points. The good results obtained for these data indicate the reliability of eqs 3 and 4. Furthermore, these results are in accordance to the fact that the compressibility of ILs is very limited. Figure 5 contains the relative deviation (%RD) distribution between experimental and calculated data for 99.7% of the data present on our databank (that is, for 21 789 data points). Therefore, only 56 data studied presented an absolute relative deviation above 10%. Paduszyński and Domańska26 performed an evaluation procedure to determine which experimental data would be used for correlation or prediction. This procedure was based on a statistical analysis of the databank. For ionic liquids data for a single temperature, the rejection process was based in the purity of the samples used by the authors that provided the data. After this process, Paduszyński and Domańska26 rejected 1898 data points which are still present on our databank and were used by us to test this model validity. This may explain higher values of %RD between calculated and experimental data points reported by one author and low values of %RD between calculated and experimental data reported by another author.

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ASSOCIATED CONTENT

S Supporting Information *

A MS-Excel spreadsheet containing the structural groups defined and details of the experimental database used in the model development are provided as Supporting Information. In addition, group assignments, data references, and GCVOL-OL60 parameters are presented. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +55-85-33669611. Fax: +55-85-33669610. E-mail: hbs@ ufc.br. Notes

The authors declare no competing financial interest. 9510



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Article

Butyl-3-Methylimidazolium Tetracyanoborate (3)}. J. Chem. Thermodyn. 2011, 43, 1672. (12) Mokhtarani, B.; Musavi, J.; Parvini, M.; Mafi, M.; Sharifi, A.; Mirzaei, M. Ternary (liquid−liquid) Equilibria of Nitrate Based Ionic Liquid + Alkane + Benzene at 298.15 K: Experiments and Correlation. Fluid Phase Equilib. 2013, 341, 35. (13) Hwang, I.-C.; Kim, J.-I.; Park, S.-J. Liquid−Liquid Equilibrium for Binary and Ternary Systems Containing Di-Isopropyl Ether (DIPE) and an Imidazolium-Based Ionic Liquid at Different Temperatures. Fluid Phase Equilib. 2010, 299, 294. (14) Rodríguez, H.; Francisco, M.; Soto, A.; Arce, A. Liquid−Liquid Equilibrium and Interfacial Tension of the Ternary System Heptane + Thiophene + 1-Ethyl-3-Methylimidazolium Bis(trifluoromethanesulfonyl)imide. Fluid Phase Equilib. 2010, 298, 240. (15) Seoane, R. G.; Gómez, E.; González, E. J.; Domínguez, Á . Liquid + Liquid) Equilibria for the Ternary Mixtures (Alkane + Toluene + Ionic Liquid) at T = 298.15 K: Influence of the Anion on the Phase Equilibria. J. Chem. Thermodyn. 2012, 47, 402. (16) González, E. J.; Calvar, N.; González, B.; Domínguez, Á . Liquid + Liquid) Equilibria for Ternary Mixtures of (Alkane + Benzene + [EMpy][ESO4]) at Several Temperatures and Atmospheric Pressure. J. Chem. Thermodyn. 2009, 41, 1215. (17) González, E. J.; Domínguez, I.; González, B.; Canosa, J. Liquid− Liquid Equilibria for Ternary Systems of {Cyclohexane + Aromatic Compounds + 1-Ethyl-3-Methylpyridinium Ethylsulfate}. Fluid Phase Equilib. 2010, 296, 213. (18) González, E. J.; Calvar, N.; González, B.; Domínguez, Á . Measurement and Correlation of Liquid−Liquid Equilibria for Ternary Systems {Cyclooctane + Aromatic Hydrocarbon + 1-Ethyl-3Methylpyridinium Ethylsulfate} at T=298.15K and Atmospheric Pressure. Fluid Phase Equilib. 2010, 291, 59. (19) González, E. J.; Calvar, N.; Gómez, E.; Domínguez, Á . Application of [EMim][ESO4] Ionic Liquid as Solvent in the Extraction of Toluene from Cycloalkanes: Study of Liquid−Liquid Equilibria at T = 298.15 K. Fluid Phase Equilib. 2011, 303, 174. (20) González, E. J.; Calvar, N.; Dominguez, I.; Domínguez, Á . Liquid + Liquid) Equilibrium Data for the Ternary Systems (Cycloalkane + Ethylbenzene + 1-Ethyl-3-Methylimidazolim Ethylsulfate) at T = 298.15 K and Atmospheric Pressure. J. Chem. Thermodyn. 2011, 43, 725. (21) González, E. J.; Calvar, N.; Domínguez, I.; Domínguez, Á . Extraction of Toluene from Aliphatic Compounds Using an Ionic Liquid as Solvent: Influence of the Alkane on the (Liquid + Liquid) Equilibrium. J. Chem. Thermodyn. 2011, 43, 562. (22) Jongmans, M. T. G.; Schuur, B.; de Haan, A. B. Binary and Ternary LLE Data of the System (Ethylbenzene + Styrene + 1-Ethyl-3Methylimidazolium Thiocyanate) and Binary VLE Data of the System (Styrene + 1-Ethyl-3-Methylimidazolium Thiocyanate). J. Chem. Thermodyn. 2012, 47, 234. (23) Heidari, M. R.; Mokhtarani, B.; Seghatoleslami, N.; Sharifi, A.; Mirzaei, M. Liquid−Liquid Extraction of Aromatics from Their Mixtures with Alkanes Using 1-Methyl 3-Octylimidazolium Thiocyanate Ionic Liquid. J. Chem. Thermodyn. 2012, 54, 310. (24) Corderí, S.; Calvar, N.; Gómez, E.; Domínguez, Á . Capacity of Ionic Liquids [EMim][NTf2] and [EMpy][NTf2] for Extraction of Toluene from Mixtures with Alkanes: Comparative Study of the Effect of the Cation. Fluid Phase Equilib. 2012, 315, 46. (25) González, E. J.; González, B.; Calvar, N.; Domínguez, Á . Study of [EMim][ESO4] Ionic Liquid as Solvent in the Liquid−Liquid Extraction of Xylenes from Their Mixtures with Hexane. Fluid Phase Equilib. 2011, 305, 227. (26) Paduszyński, K.; Domańska, U. A New Group Contribution Method For Prediction of Density of Pure Ionic Liquids over a Wide Range of Temperature and Pressure. Ind. Eng. Chem. Res. 2012, 51, 591. (27) Gardas, R. L.; Coutinho, J. A. P. Extension of the Ye and Shreeve Group Contribution Method for Density Estimation of Ionic Liquids in a Wide Range of Temperatures and Pressures. Fluid Phase Equilib. 2008, 263, 26.

ACKNOWLEDGMENTS The authors acknowledge the financial support provided by ́ CAPES (Coordenaçaõ de Aperfeiçoamento de Pessoal de Nivel Superior, Brazil).

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ABBREVIATIONS

Roman Letters

Ai, Bi, and Ci = GCVOL and GCVOL-IL parameters of the group i d0, d1, D, and E = Tait equation parameters F = objective function Np = number of pseudo-experimental data Ne = number of experimental data M = molar weight ni = number of appearances of group I P = absolute pressure T = absolute temperature V = volume Greek Letters

ρ = density Subscripts Superscripts

calc = calculated exp = experimental pexp = pseudo-experimental

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Development of a New Group Contribution Method Based on GCVOL

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