Application of a Group Contribution Equation of State for the

Apr 23, 2010 - María Dolores Bermejo, David Méndez and Ángel Martín*. High Pressure Processes Group, Department of Chemical Engineering and ...
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Ind. Eng. Chem. Res. 2010, 49, 4966–4973

Application of a Group Contribution Equation of State for the Thermodynamic Modeling of Gas + Ionic Liquid Mixtures ´ ngel Martı´n* Marı´a Dolores Bermejo, David Me´ndez, and A High Pressure Processes Group, Department of Chemical Engineering and EnVironmental Technology, UniVersity of Valladolid, Prado de la Magdalena s/n 47011 Valladolid, Spain

The group contribution equation of state (GC-EoS) is used to describe the phase behavior of gas + ionic liquid mixtures. With this equation, by application of the group contribution concept, if the parameters of the characteristic functional group of a family of ionic liquids are calculated using experimental data of a reduced number of ionic liquids of the family, then the phase behavior of all ionic liquids of the same family can be predicted. With this work, the parameter table of the GC-EoS is extended to systems that are comprised of an ionic liquid of the methylimidazolium bis[(trifluoromethyl)sulfonyl]imide family [-mim][Tf2N] and a gas (H2, CO, C2H4, O2, SO2, CH3OH, N2O, or Xe). Furthermore, a compilation of all GC-EoS parameters for gas + ionic liquid systems currently available in the literature is presented. 1. Introduction Ionic liquids (ILs) are substances that are composed entirely of ions that are liquid at ambient or close-to-ambient temperatures. Their low vapor pressure and excellent solvating properties have generated enormous interest in using these substances to replace conventional organic solvents. Most ionic liquids are nonflammable, which reduces the fire and explosion hazards. A wide liquid range and good thermal stability are other favorable properties of ILs.1 By appropriate selection of the anion and cation, the properties of the resulting IL can be modified. The determination of the physical properties of an ionic liquid often is a lengthy and costly process. Considering the large number of ILs that can be prepared, it would be advantageous to have methods to predict the physical properties of potential ionic liquids, which could be used for a preliminary selection of suitable ILs for a certain application.2 In particular, predictive methods of phase equilibrium parameters of systems with ILs would be very useful, because these parameters must be known in many separation and reaction applications. Several authors have developed models to calculate the phase behavior of systems with ILs. Here, some of the most representative works in this field are mentioned. Methods using molecular simulation3-6 were developed to explain and predict phase equilibrium and properties of ILs. Excess Gibbs energy models such as NRTL and UNIQUAC7 were developed for describing both liquid-liquid (LL) and liquid-vapor (LV) equilibrium. Cubic equations of state (EoSs) have also been tested,8,9 and although they certainly are not the most suitable way to describe these systems, they are able to model the solubility of gases and supercritical fluids in ILs satisfactorily and to predict the solubility of ILs in supercritical CHF3 qualitatively. To describe the behavior of the CO2 + IL system at high pressure, the tPC SAFT10,11 and the soft-SAFT12 were used. Other authors used different EoSs that incorporate the “group contribution concept”: if the parameters of the characteristic functional group of a family of ILs are fitted using data of a reduced number of ILs of the family, then the phase behavior of all the ILs of the same family can be predicted.13-16 * To whom correspondence should be addressed. E-mail: [email protected].

Breure et al.17 described the capability of the group contribution equation of state (GC-EoS) originally developed by SkjoldJørgensen18 to represent the phase behavior of systems consisting of carbon dioxide (CO2) and the previously commonly used ionic liquids 3-methylimidazolium tetrafluoroborate ([-mim][BF4]) and 3-methylimidazolium hexafluorophosphate 1-substituted ([-mim][PF6]). One of the main advantages of this method is that it relies on the group contribution concept. Bermejo et al.19 used the same methodology to describe the phase behavior of ILs based on the 3-methylimidazolium nitrate 1-substituted [-mim][NO3] functional group. Ku¨hne et al.20 applied this model to describe some ternary (CO2 + organic + IL) mixtures. Schilderman et al.21 used this model to calculate the solubility of CO2 in 3-methylimidazolium bis[(trifluomethyl)sulfonyl]imide 1-substituted ([-mim][Tf2N]) ILs. Martı´n et al.22 extended the parameter table of the GC-EoS to systems that are comprised of ILs with a Tf2N anion and 1-alkyl-2,3dimethyl imidazolium ([-dmim]), 1-alkyl-3-methyl-pyridinium ([-mpy]), and 1-alkyl-1-methyl-pyrrolidinium ([-mpyrr]) cations as well as different gases (CO2, SO2, and O2). In this case, the groups admit substituents in position 1 of the respective cycles of the cation. The objective of this work is to extend the GC EoS to systems that contain ILs of the family [-mim][Tf2N] with several gases as H2, CO, C2H4, O2 SO2, CH3OH, N2O, and Xe. To do so, pure group parameters for the Xe and N2O not previously available in the literature were calculated. In addition, and to apply the equation to ILs with fluorinated substituents, pure and binary interaction parameters of the groups CF3 and CF2 were calculated. To do so, new pure group parameters and binary interaction parameters for the new functional groups were estimated based on experimental information about the ILs of this family that was found in the literature. Moreover, a compilation of all available parameters for application of the GC-EoS to the IL + gas systems is presented. 2. GC-EoS Model The GC-EoS was proposed by Skjold-Jørgensen18 to calculate vapor-liquid (VL) equilibria of nonideal mixtures at pressures up to 30 MPa. It is based on the generalized van der Waals function, combined with the local composition principle. It is expressed in terms of the residual Helmholtz energy (AR) as

10.1021/ie901989f  2010 American Chemical Society Published on Web 04/23/2010

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Table 1. Systems Studied in This Work: Bibliographic Sources and Comparison between Experimental and Calculated Equilibrium Pressures system

ref

CO + [hmim][Tf2N] C2H4 + [bmim][Tf2N] O2 + [bmim][Tf2N] N2O + [hmim][Tf2N] SO2 + [hmim][Tf2N] CH3OH + [bmim][Tf2N] CH3OH + [emim][Tf2N] CH3OH + [hmim][Tf2N] Xe + [hmim][Tf2N] H2 + [hmim][Tf2N] CO2 + [C6H4F9mim][Tf2N]

23

Peters Anthony et al.24 Anthony et al.24 Anthony et al.24 Anderson et al.25 Verevkin et al.26 Kato et al.7 Kato et al.7 Kumelan et al.27 Kumelan et al.28 Muldoon et al.29

pressure range

temperature range (K)

AAPD %

Max PD %

4-12 MPa 0.1-1.3 MPa 0.1-1.3 MPa 0.1-1.3 MPa 50-350 kPa 0-40 kPa 10-150 kPa 10-150 kPa 2-10 MPa 1.5-10 MPa 0.1-10 MPa

300-420 283-323 283-323 283-323 298-333 298-313 353 353 293-413 294-413 298-333

0.4 5.5 17 6.9 6.5 3.6 11 19 5.5 6.1 7.8

1.9 34 68 20 35 12 19 42 15 17.5 27

the sum of an attractive term (denoted by the subscript “att”) and a free-volume contribution (denoted by the subscript “fv”):

( ) AR RT

)

T,V,n

( ) ( ) AR RT

AR RT

+

att

(1)

fv

where V is total volume, n the total number of moles, R the gas constant, and T temperature. The free-volume term (denoted by the subscript “fv”) can be described by the Mansoori and Leland expression for hard spheres:

( ) AR RT

T,V,n

)3

( )

( )

λ1λ2 λ23 2 (Y - 1) + (Y - Y - ln Y) + λ3 λ32 n ln Y(2)

NC

∑nd

k j j

(3)

(

)

-1

(4)

where n is the total number of moles, NC the number of components, V the total volume, and d the hard sphere diameter per mole. The hard-sphere diameter d is assumed to be a function of the temperature:

( )]

[

2Tc d ) 1.065655dc 1 - 0.12 exp 3T

( ) AR RT

att

z )2

()

NG

∑ ∑ ni

(5)

i)1

NG

Vijqj

j)1

∑ θ (g qτ k

kj

kj /RTV)

k)1 NG

(6)

∑θτ

l lj

l)1

where θk )

( )∑ qk q

NC

i)1

NC

niVjkq )

)

(8) (9)

In eq 6, z is the number of nearest neighbors to any segment (set equal to 10), Vji the number of groups j in component i, qj the number of segments assigned to group j, θk the surface fraction of group k, q the total number of segments, gij the attractive energy parameter for interactions between segments j and i, and Rij the corresponding nonrandomness parameter. The interactions between unlike segments are defined by gji ) kji(giigjj)1/2

(10)

NG

∑ ∑Vq

i j j

ni

i)1

[

( [

j)1

)

( )]

T T - 1 + gii′′ ln T*i T*i

kij ) k*ij 1 + kij′ ln

( )] T T*ij

(11) (12)

where Tij* ) 0.5(Ti*+ Tj*) and Ti* is an arbitrary (but fixed) reference temperature for group i. 3. Parameterization

where dc is the value of the hard-sphere diameter at the critical temperature Tc of the pure component. The attractive part of AR is a group contribution version of a density-dependent NRTL type of expression. With the group contribution approach, the molecule is decomposed in a combination of segments, with each segment corresponding to some atoms or functional groups of the molecule, and it is assumed that a certain segment behaves similarly in different molecules. Interactions are considered to occur through the segment surfaces, rather than through the surfaces of parent molecules. This reduces the number of different interaction energies that are required to describe a large number of mixtures. NC

Rkj∆gkjq RTV

∆gkj ) gkj - gjj

gii ) g*ii 1 + gii′

j

πλ3 Y) 16V

(

where kji is a binary interaction parameter. Temperature dependence assumed for the attractive energy parameter and the binary interaction parameter are shown in eqs 11 and 12:

where λk )

τkj ) exp

(7)

In this work, binary interaction parameters for the functional group methylimidazolium trifluoromethyl sulfonyl imide ([-mim][Tf2N]) with H2, CO, C2H4, O2, SO2, CH3OH, N2O, and Xe were calculated. These parameters were calculated by correlation of LV equilibrium data found in the literature. Bibliographic sources of experimental data used in this work are described in Table 1.7,23-28 In addition, pure and binary interaction parameters corresponding to groups Xe, N2O, CF3, and CF2 were calculated to apply the model to obtain the phase behavior of ionic liquids containing these groups, such as, for example, 1-methyl-3-(3,3,4,4,5,5,6,6,6-nonafluorohexyl)-imidazolium [Tf2N] ([C6H4F9mim][Tf2N]).29 3.1. Ionic Liquid Functional Groups. To apply the GCEoS, pure components must be decomposed into separate functional groups. H2, CO, C2H4, O2 SO2, CH3OH, N2O, and Xe are functional groups themselves. ILs were decomposed into separate functional groups according to the methodology of Breure et al.,17 as shown in Figure 1. According to this methodology, the anion and part of cation are considered as a single group that is characteristic of a certain family of ILs. The two ions are included together in a single group, because if they were considered as two separated groups, it would be necessary to explicitly represent the ionic interactions between these two groups with the EoS model, which is beyond the capabilities of the GC EoS and most modern equations of state.

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rium data.7,23-29 Group parameters of Xe and N2O were calculated using PVT and vapor pressure data of the pure components retrieved from NIST,35 and interaction parameters of these groups with alkane groups CH2 and CH3 were calculated by correlation of the literature data of the solubility of these gases in alkanes.36 Similarly, parameters of groups CF3 and CF2 and interaction parameters of these groups with alkane groups were correlated using literature data.37 In all cases, the correlation was performed by minimization of the average absolute deviation (AAD) between experimental measurements and model results, defined in eq 13, where Y is the magnitude used for the correlation (e.g., bubble point pressure, density, vapor pressure). 100 AAD ) ndata

ndata

exp

∑ |Y i)1

- Ycalc | Yexp

(13)

All group and interaction parameters obtained in this work are presented in the recopilation of parameters presented in Tables 2-4. 4. Results and Discussion

Figure 1. Group decomposition of some ionic liquids (ILs) considered in this work: (a) [bmim][Tf2N] and (b) [C6H4F9mim][Tf2N].

On the other hand, if the two ions are considered together in a single group, ionic interactions are represented through the parameters of this group, which considerably simplifies calculations, although increases the number of groups that must be considered to describe several IL families. 3.2. Free-Volume Term. The free-volume term of the residual Helmholtz energy depends on only one characteristic parameter: the critical hard sphere diameter (dc). Results obtained with the GC-EoS are very sensitive to the value of dc. Moreover, energy interaction parameters of the GC-EoS can show correlation with the dc parameter. Therefore, accurate estimations of dc are important. Values for dc are usually calculated from critical properties, or by fitting the equation to vapor pressure data. One of the main characteristics of ILs is their negligible vapor pressure. Therefore, for most ILs, this information is not available or only rough estimations of the vapor pressure are known.30 In this work, dc was calculated using the correlation developed by Espinosa et al.31 between the critical diameter dc and the normalized van der Waals molecular volume (Rw) of highmolecular-weight compounds. Rw was calculated by the method of Bondi.32 3.3. Attractive Term. The following parameters are required to calculate the attractive term of the GC-EoS: • Pure group constants: Ti*, qi. • Pure group energy parameters: gii*, gii′ , gii′′. • Group-group interaction parameters: k*, kij′ , Rij, Rji. Group parameters of [-mim][Tf2N] were taken from Schilderman et al.21 Group parameters of H2, CH3, CH2, and CO2 were taken from Skjold-Jørgensen.18 Binary parameters for interactions between CO2 and the paraffin groups were taken from Espinosa et al.33 Those for H2, CH3OH, CO, C2H4, O2, and SO2 were taken from Fornari.34 The remaining parameters required for application of the model were calculated in this work. The binary interaction parameters (kij and Rij) between the group [-mim][Tf2N] and groups H2, CO, C2H4, O2, SO2, CH3OH, N2O, Xe, CF3, and CF2 were obtained by correlation of the literature LV equilib-

A list of the gas + IL systems modeled in this work with the GC-EoS is presented in Table 1. This table also shows the average absolute deviation (AAD) between experimental and calculated bubble point pressures, defined according to eq 13, as well as the maximum deviation observed. Figure 2 shows graphical comparisons between experimental and calculated vapor liquid equilibrium properties of several gas + IL systems. The GC-EoS parameters required for these calculations are shown in Tables 2-4. Critical temperatures of the ionic liquids, presented in Table 3, were estimates using the method developed by Valderrama and Robles.38 The critical diameter (dc) shown in Table 3 is characteristic of the molecular size of the compound. Therefore, it is expected to increase when the length of the alkyl substituents is increased, as it occurs in parameters presented in Table 3. It can also be observed that the dc value of the IL [C6H4F9mim][Tf2N] is higher than the dc value of all other ILs with [TF2N] anion reported in Table 3, as expected, because of the size of the [C6H4F9mim] cation. Similarly, Tc is expected to increase when the size of the cation or the length of the alkyl chains in the cation increases, as is observed with the parameters of Table 3. On the other hand, values of the pure group energy parameter gii* reported in the literature usually are in the range of 300 000-500 000 for nonpolar groups such as paraffins, and above 1 000 000 in the case of polar groups such as water.18 In the case of ILs, gii* is expected to have a value between these two limits. Table 3 shows that correlated gii* parameters have values in this range. Larger g*ii values were obtained in the case of ILs with anions PF6, BF4, and NO3 than in ILs with the Tf2N anion. Indeed, ILs with BF4 and NO3 anions generally are highly miscible with polar fluids such as water and only partially miscible with nonpolar solvents, while ILs with the Tf2N anion are less miscible with water which is a sign of lower polarity. In the case of the pure group energy parameter g′ii values reported in the literature when gii′′ ) 0 generally are negative,18 as is the case in the IL group parameters presented in Table 3. With respect to interaction parameters, interaction parameters between IL groups and nonpolar groups such as CH3, CH2, and CO2 generally are expected to be k*ij < 1, because of the differences between these groups and particularly the differences in their polarity.17 This is the case of most interaction parameters reported in Table 4. For the same reason, nonrandomness

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Figure 2. Comparison of experimental bubble point of gas + IL systems with GC-EoS calculations with the parameters obtained in this work. Symbols represent experimental data and continuous lines model results.

parameters can have rather large values that are generally expected to be in the range -20 < Rij, Rji < 20. Figure 2 and Table 1 demonstrate that the GC-EoS is capable of correlating the vapor-liquid equilibrium of several gas + IL systems with good accuracy. The average deviation between experimental and calculated bubble point pressures is in the range of 3%-6% in most cases. The only exceptions in which a higher deviation is observed are the systems O2 + [bmim][Tf2N], CH3OH + [emim][Tf2N], and CH3OH + [hmim][Tf2N]. In the case of the O2 + [bmim][Tf2N] system,

the high value of the mean average deviation (17%) is due to the high dispersion of experimental data, which is apparent in Figure 2. In the case of the systems [emim][Tf2N] and CH3OH + [hmim][Tf2N], the data of Kato et al.7 show almost no influence of a variation in the substituents of the methyl imidazolim cation in the equilibrium pressure, while the GCEoS calculates a higher equilibrim pressure for the CH3OH + [emim][Tf2N] system than for the CH3OH + [hmim][Tf2N] system. Figure 2 also shows that the GC-EoS model correctly predicts the variations of equilibrium pressure with variations

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Table 2. Group Parameters for Calculation of Phase Equilibrium of Systems with Ionic Liquids Using the GC-EoS group [-mim][PF6] [-mim][BF4] [-mim][NO3] [-mim][Tf2N] [-dmim][Tf2N] [-mpyrr][Tf2N] [-mpy][Tf2N] -CF3 -CF2N2O Xe

source 17

Breure et al. Breure et al.17 Bermejo et al.19 Schilderman et al.21 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 this work this work this work this work

T* (K)

Rw

q

g*

g′

g′′

600 600 600 600 600 600 600 600 600 455.3 289.65

4.179 6.549 4.676 8.921 9.822 9.752 9.658

4.891 1.098 3.731 7.260 7.800 8.032 7.738 1.380 1.000 0.888 1.13

954500 1013000 1332740 824000 425160 630060 319550 362680 389910 1138590 759300

-0.5931 -1.5857 -0.1775 -0.1980 -0.6620 -0.4101 -0.4409 -0.1144 1.5848 -0.4710 -0.2432

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.025 0.000 0.000

Table 3. Molecular Parameters of Ionic Liquids for Application of the GC-EoS

a

ionic liquid

source

critical temperature, Tc (K)

critical hard sphere diameter, dc (cm/mol)

[emim][PF6] [bmim][PF6] [hmim][PF6] [bmim][BF4] [hmim][BF4] [omim][BF4] [bmim][NO3] [HOpmim][NO3] [emim][Tf2N] [bmim][Tf2N] [hmim][Tf2N] [omim][Tf2N] [edmim][Tf2N] [hdmim][Tf2N] [bmpyrr][Tf2N] [hmpy][Tf2N] [C6H4F9mim][Tf2N]

Breure et al.17 Breure et al.17 Breure et al.17 Breure et al.17 Breure et al.17 Breure et al.17 Bemejo et al.19 Bemejo et al.19 Schilderman et al.21 Schilderman et al.21 Schilderman et al.21 Schilderman et al.21 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 this work

1150 1100 1050 1150 1100 1050 950 1000 1200 1100 1000 1300 1250 1100 1210 1260 1210

6.177 6.581 6.953 6.585 6.989 7.360 6.070a 6.424a 6.836a 7.240a 7.630a 7.855a 7.103 7.754 7.738 7.399 7.891

The parameter dc is calculated via correlation of experimental VLE data.

Figure 3. Present status of the GC-EoS parameter table for systems with ILs.

in temperature and composition, with the exception of the H2 + [hmim][Tf2N] system, in which the model is not able to reproduce the equilibrium isotherm at the highest temperature

studied in experiments (413.2 K). On the other hand, in most cases, the maximum deviations reported in Table 1 are observed in the comparison of the data point with the lowest equilibrium

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Table 4. Interaction Parameters of the GC-EoS for Systems with Ionic Liquids group i

group j

k* ij

kij′

Rij

Rji

ref

[vmim][PF6] [-mim][PF6] [-mim][PF6] [-mim][BF4] [-mim][BF4] [-mim][BF4] [-mim][BF4] [-mim][BF4] [-mim][BF4] [-mim][BF4] [-mim][NO3] [-mim][NO3] [-mim][NO3] [-mim][NO3] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-mim][Tf2N] [-dmim][Tf2N] [-dmim][Tf2N] [-dmim][Tf2N] [-mpyrr][Tf2N] [-mpyrr][Tf2N] [-mpyrr][Tf2N] [-mpyrr][Tf2N] [-mpy][Tf2N] [-mpy][Tf2N] [-mpy][Tf2N] [-mpy][Tf2N] N2O N 2O Xe Xe CF3 CF3 CF3 CF2 CF2 CF2

CH3 CH2 CO2 CH3 CH2 CO2 ACH AC CH3CO CHOH CH3 CH2 CO2 CH2OH CH3 CH2 CO2 CF3 CF2 CO SO2 C2H4 CH3OH O2 N2O Xe H2 CH3 CH2 CO2 CH3 CH2 CO2 SO2 CH3 CH2 CO2 O2 CH3 CH2 CH3 CH2 CH3 CH2 CO2 CH3 CH2 CO2

0.8710 0.8710 0.8850 0.7910 0.7910 0.6010 0.5548 0.5548 1.9084 2.2153 0.6500 0.6500 0.0824 1.1093 0.7500 0.7500 0.9460 1.1871 1.1871 1.2620 1.7463 1.0730 0.9543 1.1339 0.9314 0.9016 1.5386 1.0000 1.0000 0.9201 1.0000 1.0000 0.9781 1.1811 1.0000 1.0000 0.9268 1.0360 1.0000 1.0000 1.0124 1.0124 0.7769 0.7510 1.4136 1.0000 0.9670 1.4136

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3420 0.0000 0.0000 0.9036 0.6740 0.1113 0.0020 1.7479 0.0000 0.0000 2.2847 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6290 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

-3.8260 -3.8260 -5.6560 -1.0020 -1.0020 0.4710 0.1977 0.1977 0.0999 -0.0151 0.0000 0.0000 -0.0033 0.0000 2.0000 2.0000 -2.1820 -0.0037 -0.0037 -10.8941 -4.3573 -7.2795 -0.1127 1.8628 0.0000 0.0000 15.2300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0039 0.0000 0.0000 0.0039

-0.8570 -0.8570 0.8330 -1.0010 -1.0010 11.0680 0.1977 0.1977 0.0999 -0.0151 0.0000 0.0000 -0.0033 0.0000 1.3000 1.3000 4.8240 0.0053 0.0053 0.7310 -7.5553 -0.1609 0.1436 0.0005 0.0000 0.0000 15.2300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -2.6527 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0032 0.0000 0.0000 0.0032

Breure et al.17 Breure et al.17 Breure et al.17 Breure et al.17 Breure et al.17 Breure et al.17 Ku¨hne et al.20 Ku¨hne et al.20 Ku¨hne et al.20 Ku¨hne et al.20 Bermejo et al.19 Bermejo et al.19 Bermejo et al.19 Bermejo et al.19 Schilderman et al.21 Schilderman et al.21 Schilderman et al.21 this work this work this work this work this work this work this work this work this work this work Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 Martı´n et al.22 this work this work this work this work this work this work this work this work this work this work

pressure and the highest temperature, conditions in which a small deviation between experiments and calculations in absolute terms results in a large relative deviation. The only exceptions are the systems H2 + [hmim][Tf2N] and Xe + [hmim][Tf2N], in which the highest deviations are observed at the point with the highest equilibrium pressure. Results presented in Table 1 and Figure 2 show the versatility of the GC-EoS, which is capable of correlating the solubility of several gases in ILs at high pressure. With the objective of compiling all the parameters available for application of the GC-EoS to systems with ILs, which are already numerous and are dispersed in several articles, Tables 2-4 show a recopilation of all currently available parameters. Table 2 show group parameters of IL characteristic groups. It can be seen that parameters included in this table cover many of the most frequently used ILs, with alkyl methyl imidazolim [-mim], 1-alkyl-2,3-dimethyl imidazolium [-dmim], 1-alkyl1-methyl pyrrolidinium [-mpyrr], and 1-alkyl-3-methyl pyridinium [-mpy] cations, and hexafluorophosphate [PF6], tetrafluoroborate[BF4],nitrate[NO3]andbis[(trifluoromethyl)sulfonyl]imide [Tf2N] anions. In addition to the parameters of these IL characteristic groups, Table 2 also shows the parameters of the

CF3, CF2, N2O, and Xe groups obtained in this work. These parameters are required for calculating the solubility of Xe and N2O in ILs, or for calculations for ILs with fluorinated substituents. The molecular parameters of all ILs modeled with the GC-EoS until now are presented in Table 3. The current status of the calculation of interaction parameters for application of the GC-EoS is summarized in Figure 3. It can be seen that, for all the ILs studied, the interaction parameters with alkyl groups CH3 and CH2 are available, because these are the most common substituents in IL cations. Interaction parameters with CO2 are also available in all cases, which enables calculation of the solubility of CO2 in all studied ILs. On the other hand, interaction parameters required for the calculation of the solubility of other gases are more scarce, and, currently, they are available mostly for ILs of the [-mim][Tf2N] family, which have been intensively studied recently. The limiting factor for calculating interaction parameters with other gas + IL families is the lack of experimental information. Values of interaction parameters, together with the bibliographic source from which they have been taken, are reported in Table 4.

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5. Conclusions Experimental bubble points of 11 binary gas + ionic liquid (IL) systems of the [-mim][Tf2N] family were adjusted using the group contribution equation of state (GC EoS). Binary interaction parameters (k and R) of the characteristic group of the [-mim][Tf2N] family of ILs with the gases, as well as pure and binary interaction parameters with the CF3 and CF2 groups, were correlated using literature phase equilibrium data. For most systems, the average deviations between model results and experiments under pressure are