5518
Ind. Eng. Chem. Res. 2006, 45, 5518-5523
Solubilities in Ionic Liquids and Molten Salts from a Simple Perturbed-Hard-Sphere Theory Yuan Qin and John M. Prausnitz* Department of Chemical Engineering, UniVersity of California, Berkeley, and Chemical Sciences DiVision, Lawrence Berkeley National Laboratory, Berkeley, California 94720
In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are the hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent’s density and the solute’s polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for 20 solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry’s constants) agree with experiment to within roughly ( 70%. As more reliable experimental data become available, modifications in the characteristic parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation might be useful for solvent screening in engineering design. 1. Introduction Although ionic liquids have been known for a long time, they have attracted significant attention only during the past 5-10 years. For most practical purposes, ionic liquids are electrolytes with melting points near or below 25 °C. At normal temperatures, these liquids have high dielectric constants; densities somewhat larger than that of water; and most important, negligible vapor pressures. Because they are nonvolatile at normal temperatures, ionic liquids might be useful as “green” solvents that do not pollute the atmosphere.1,2 Numerous reviews of ionic-liquid properties are now available, notably those by Heintz3 and by Poole.4 An increasing number of authors have reported experimental data for Henry’s constants of gases and for infinite-dilution activity coefficients of nonelectrolytes in ionic liquids.5-22 Toward the interpretation and correlation of solubility data, in addition to molecular simulations,23,24 Eike et al.25 have used quantitative structure-property relationships (QSPRs), and Diedenhofen et al.26 have used quantum-mechanical calculations (COSMO-RS) to correlate such data. In this work, we report an initial correlation of Henry’s constants for ordinary solutes in ionic liquids based on a perturbed-hard-sphere theory. A main advantage of our theory is its simplicity. Because it is based on several simplifying assumptions, it provides only approximate results. Nevertheless, these approximate results might be useful for engineering calculations, in particular, for screening possible ionic-liquid solvents for specific applications. As more reliable experimental solubility data become available, it is likely that modifications in our theory will improve its accuracy. 2. Theoretical Framework Numerous authors, notably Pierotti,27 have used perturbedhard-sphere theory for correlating solubilities in nonelectrolyte * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: (510) 642-3592. Fax: (510) 6424778.
systems. Consistent with these earlier studies, we postulate that introducing a solute molecule into an ionic-liquid solvent consists of two steps: (1) creation of a cavity of solute size in the solvent and (2) charging of the cavity to the appropriate potential. As discussed elsewhere,27 the Henry’s constant H can be expressed as
ln(HVm/RT) ) Ghs/RT + Gi/RT
(1)
where R is the gas constant, T is the temperature, Vm is the molar volume of the solvent, Ghs is the molar hard-sphere cavityformation energy, and Gi is the molar solute-solvent interaction energy. The ionic liquid consists of cation c and anion a. The hardsphere diameters of the cation, anion, and solute are σc, σa, and σs, respectively. Ghs is given by scaled-particle theory23
3ξ2 Ghs σ + ) -ln(1 - ξ3) + RT 1 - ξ3 s
[
( )]
3ξ1 9 ξ2 + 1 - ξ 3 2 1 - ξ3
2
σs2 +
3
P πσs kBT 6
(2)
where ξi is given by
π ξi ) (Fcσci + Faσai) 6
for i ) 0, 1, 2, and 3
(3)
Here, Fc is the number density of the cation, Fa is the number density of the anion, kB is the Boltzmann constant, and P is the hard-sphere pressure of the ionic liquid28
P)
[
3ξ1ξ2 3ξ23 6kBT ξ0 + + π 1 - ξ3 (1 - ξ )2 (1 - ξ )3 3
3
]
(4)
In the original scaled-particle theory, Pierotti27 assumed that P is the experimental pressure of the solvent; that assumption
10.1021/ie051090p CCC: $33.50 © 2006 American Chemical Society Published on Web 01/26/2006
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5519
makes the last term in eq 2 negligible. However, on the basis of molecular simulations, Hu et al.29 reported that, when eq 4 is used with a more reasonable radial distribution function for the solvent, eq 2 gives better results. In this work, we use eqs 2 and 4. As used here, the hard-sphere theory considers the ionic liquid as an assembly of independent ions. An alternative view is to consider the ionic liquid as an assembly of ion pairs, as suggested by electrical conductivity measurements.30 The solvent molecule is polarizable and might have a dipole and/or quadrupole moment. Therefore Gi consists of four parts, reflecting contributions from dispersion, induction, dipolecharge interactions, and quadrupole-charge interactions
Gi ) Gdispersion + Ginduction + Gdipole + Gquadrupole
The solute molecule might have a dipole moment µ and/or a quadrupole moment Q. When a dipole or quadrupole is placed into a continuum dielectric, the potentials are31,32
φdipole ) -
∑ NA∫σ j)c,a
+∞ dis Γjs (r) js
gjs(r)Fj4πr2dr
Γjsdis(r) ) 4xjs
[( ) ( ) ] σjs r
12
-
σjs r
6
r > σjs
a)
σs ξ31/3
(8)
where ξ3, given by eq 3, is the packing fraction of the solvent. Embedded in the dielectric continuum, the solute experiences a fluctuating electrical field e32 given by
〈e2〉 )
6(D - 1)
kBT (2D + 1)(a/2)3
(9)
The induction energy is given by
1 Ginduction ) - NARs〈e2〉 2 where Rs is the polarizability of the solute.
(10)
(3D + 2)(a/2)5
Q
(12)
2(D - 1) µ2 ) -NA (2D + 1)(a/2)3
(13)
Gquadrupole ) NAφquadrupoleQ (D - 1) Q2 ) -NA (3D + 2)(a/2)5
(14)
Recent work by Wakai et al.33 suggests that dielectric constants for typical ionic liquids are in the range 9-15. Substituting eqs 2, 5, 9, 13, and 14 into eq 1 and using the simplification D . 1, we obtain an expression for Henry’s constant
ln(HVm/RT) ) - ln(1 - ξ3) + 9
( )] ξ2
2 1 - ξ3
where j and s are dispersion-energy parameters of ion j and solute s, respectively. To calculate the electrostatic contributions, we consider the solvent as a dielectric continuum with dielectric constant D and the solute in a cavity of diameter a in the dielectric continuum.31,32 This continuum theory differs from that using a summation of particle-particle interactions as given in eqs 2 and 6 to calculate the hard-sphere and dispersion contributions. Diameter a is not necessarily the same as the diameter of the solute; in general, a is somewhat larger than σs. Following Onsager’s31,32 suggestion for a cavity in a pure fluid, we use
(D - 1)
(11)
Gdipole ) NAφdipoleµ
(6)
(7)
µ
Contributions of the dipole-charge and quadrupole-charge interactions to Gi are given by
(5)
where r is the molecular center-to-center distance, Γjsdis(r) is the potential between ion and solute, gjs(r) is the radial distribution function of ions j around the solute, σjs ) (σj + σs)/2 is the collision diameter of ion j and solute s, and NA is Avogadro’s number. For our approximate data-correlation purposes, we use the van der Waals simplification gjs(r) )1 for r > σjs. For the dispersion potential between ion and solute, we assume
(2D + 1)(a/2)3
φquadrupole ) -
The dispersion interaction between solute and solvent is given by
Gdispersion )
2(D - 1)
32π
∑
9kBT j)c,a
2
σs + 2
[
ξ0
1 - ξ3
Fjσjs3xjs -
1
+
[
3ξ2
σs +
1 - ξ3
3ξ1ξ2 (1 - ξ3)
3kBTRsξ3
kBT 2(σ /2)3 s
+ 2
+
[
3ξ1
+
1 - ξ3 3ξ23
(1 - ξ3)
3
µ2ξ3 (σs/2)3
+
]
σs3 -
Q2ξ35/3 3(σs/2)5
]
(15) 3. Data Correlation In eq 15, Henry’s constant depends on temperature T and on solvent molar volume Vm. The solvent is characterized by two ionic diameters, σc and σa, and two dispersion-energy parameters, c and a. The solute is characterized by diameter σs, dispersion-energy parameter s, and polarizability Rs. For polar solute molecules, we also need the dipole moment µ and quadrupole moment Q. For high-temperature molten salts, we use ion diameters given by Pauling.34 For ionic liquids, each ion diameter is estimated according to the ion’s structure1 and then slightly adjusted as dictated by an overall examination of the solubility data. The densities of ionic liquids are from refs 16, 17, and 35-37, and those of molten salts are from the CRC Handbook of Chemistry and Physics.38 Solute polarizabilities, dipole moments, and some of the quadrupole moments are from Gray and Gubbins39 and the CRC Handbook of Chemistry and Physics.38 The quadrupole moments of relatively complex molecules are estimated from molecular structure. Because quadrupole data are not available for 1-pentene, 1-hexene, 1-heptene, and toluene, we assume that these liquids have the same quadrupole moment as ethylene and that toluene has the same quadrupole moment as benzene. The diameter of the solute, the dispersion-energy parameter of
5520
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
Figure 1. Henry’s constants for some gases at very high temperatures in (a) molten NaCl and (b) molten RbCl. Experimental data: b, Ar; 9, CO2; 2, HCl. Lines: Perturbed-hard-sphere theory.
Figure 3. Henry’s constants for some gases in (a) [BMIM][PF6] and (b) [BMIM][BF4]. Experimental data: ×, hydrogen; *, nitrogen; +, oxygen. Lines: Perturbed-hard-sphere theory.
Figure 2. Henry’s constants for some gases in [BMIM][PF6]. Experimental data: b, argon; 0, methane; 0, ethane; O, ethylene; 9, carbon dioxide. Lines: Perturbed-hard-sphere theory.
Figure 4. Henry’s constants for some solutes in [MMIM][(CF3SO2)2N]. Experimental data: b, n-pentane; 9, 1-pentene; 0, cyclopentane; 0, benzene; 0, toluene. Lines: Perturbed-hard-sphere theory.
the solute, and the dispersion-energy parameters of the ions are used as adjustable parameters to correlate Henry’s constants. For solutes that are liquids at ordinary temperatures, we obtain experimental Henry’s constants from experimental data for γ∞, the activity coefficient at infinite dilution
H ) Psφsγ∞
(16)
where Ps and φs are the saturation pressure and saturation fugacity coefficient of the pure solute, respectively. Ps and φs of the solutes are given by Krummen et al.16 We correlate Henry’s constants of gases at high temperatures in two molten salts, NaCl and RbCl, and at ordinary temperatures in two ionic liquids, [BMIM][PF6] and [BMIM][BF4]. We also correlate Henry’s constants of organic solutes in 10 ionic liquids. Because we require numerous parameters, we adjust the parameters by trial and error to achieve global agreement with experimental data. Results are given in Figures 1-4 and in Tables 1-10. Tables 11 and 12 give parameters for ions and for solutes. Table 13 gives sources for experimental solubility data.
Table 1. Henry’s Constants (bar) for Solutes in [MMIM][(CF3SO2)2N] at 30 and 60 °C 30 °C n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene
60 °C
calc
Expt
calc
expt
14.6 7.79 4.80 5.82 2.94 9.36 4.95 2.91 0.151 0.0843
18.2 9.77 5.13 6.93 3.64 10.2 5.13 2.64 0.211 0.0977
33.3 19.7 13.4 14.1 7.92 21.9 12.9 8.41 0.537 0.331
37.8 23.1 13.8 15.6 9.12 22.6 13.0 7.50 0.701 0.380
In many cases, experimental Henry’s constants for gases are subject to considerable uncertainty, especially for those gases whose solubilities are very small. In some cases, for the same system, different laboratories report appreciably different experimental results. Nevertheless, calculated Henry’s constants are in reasonable agreement with experiment. Although our results for hydrogen do not show the reported minimum near 314 K, we do not know whether the experimentally observed weak minimum is real.
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5521 Table 2. Henry’s Constants (bar) for Solutes in [EMIM][(CF3SO2)2N] at 20 and 50 °C
Table 6. Henry’s Constants (bar) for Solutes in [MMIM][CH3OC2H4SO4] at 50 and 60 °C
20 °C n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene acetone
50 °C
50 °C
calc
expt
calc
expt
7.60 3.85 2.25 3.16 1.52 4.95 2.51 1.39 0.0742 0.0431 0.0580
10.2 4.81 2.26 3.65 1.74 5.75 2.60 1.22 0.117 0.0526 0.0974
18.6 10.6 6.88 8.19 4.44 12.5 7.06 4.39 0.291 0.185 0.224
23.2 12.7 6.90 9.13 4.80 14.0 7.37 3.98 0.431 0.220 0.332
Table 3. Henry’s Constants (bar) for Solutes in [BMIM][(CF3SO2)2N] at 20 and 50 °C
expt
103 62.8 45.3 36.2 20.6 62.5 37.4 25.6 1.21 0.629 1.03
103 89.0 70.2 44.1 37.7 56.3 46.0 36.2 1.53 1.21 1.72
134 85.1 63.4 48.2 28.5 82.4 51.0 36.3 1.82 0.978 1.53
123 119 100 57.0 50.7 70.4 58.1 46.5 2.13 1.72 2.42
30 °C
expt
calc
expt
4.97 2.53 1.46 2.27 1.11 3.37 1.72 0.950 0.0565 0.0379
5.65 2.41 1.04 2.12 0.941 3.50 1.49 0.652 0.0868 0.0353
12.0 6.82 4.36 5.77 3.15 8.34 4.75 2.92 0.216 0.156
13.1 6.65 3.39 5.45 2.75 8.91 4.35 2.18 0.321 0.156
30 °C
60 °C
calc
expt
calc
expt
25.9 16.8 16.1 8.28 15.3 9.43 0.447 0.200
17.6 14.8 9.10 9.09 14.4 8.74 0.430 0.260
70.9 51.6 41.6 24.1 42.9 29.8 1.66 0.846
52.9 39.9 31.2 21.2 32.9 22.2 1.45 1.00
Table 5. Henry’s Constants (bar) for Solutes in [MMIM][CH3SO4] at 30 and 60 °C 30 °C n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene
calc
50 °C
calc
Table 4. Henry’s Constants (bar) for solutes in [EMIM][C2H5SO4] at 30 and 60 °C
n-hexane n-heptane cyclopentane cyclohexane 1-hexene 1-heptene benzene toluene
expt
Table 7. Henry’s Constants (bar) for Solutes in [MMIM][(CH3)2PO4] at 30 and 60 °C
20 °C n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene
n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene acetone
60 °C
calc
60 °C
calc
expt
calc
expt
55.3 27.7 16.8 15.6 7.22 29.6 15.1 8.62 0.491 0.119
36.4 27.7 23.3 28.6 22.5 36.2 29.3 22.2 1.15 0.836
152 88.1 61.2 46.1 24.6 88.4 49.4 32.3 2.05 0.611
60.5 53.7 49.2 41.9 44.9 62.8 55.4 47.4 3.03 2.30
The results reported in Figures 1-4 and Tables 1-10 suggest that calculated Henry’s constants agree with experiment within about (70%. This uncertainty is similar to that observed when Henry’s constants for ordinary systems are correlated with perturbed-hard-sphere theory. 4. Conclusion The correlation presented here is necessarily preliminary because, as yet, the experimental database is small. Further, there is considerable uncertainty in the measured Henry’s constants for gases. As more reliable experimental data become available,
cyclohexane 1-heptene benzene toluene
60 °C
calc
expt
calc
expt
7.69 8.68 0.474 0.178
7.78 8.98 0.559 0.353
23.4 28.9 1.81 0.791
22.3 28.1 1.87 1.34
Table 8. Henry’s Constants (bar) for Solutes in [PY][C2H5OC2H4SO4] at 30 and 60 °C 30 °C n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene benzene toluene
60 °C
calc
expt
calc
expt
12.0 7.21 8.31 4.00 14.4 7.28 0.252 0.0978
11.1 8.59 8.04 5.86 7.67 5.88 0.600 0.338
34.3 23.2 22.3 12.1 37.4 21.3 0.968 0.432
28.1 23.3 18.2 14.9 13.7 11.3 1.92 1.02
Table 9. Henry’s Constants (bar) for Solutes in [EPY][(CF3SO2)2N] at 30 and 60 °C 30 °C n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene acetone
60 °C
calc
expt
calc
expt
13.8 7.48 4.66 5.76 2.97 9.00 4.86 2.89 0.151 0.0956 0.114
17.1 8.33 4.14 5.78 2.98 8.79 4.30 2.25 0.199 0.0904 0.170
31.3 18.9 13.0 13.8 7.93 21.0 12.5 8.29 0.533 0.365 0.398
37.2 20.4 11.4 13.1 7.50 19.2 11.0 6.63 0.716 0.377 0.530
Table 10. Henry’s Constants (bar) for Solutes in [BMPY][BF4] at 40 and 60 °C 40 °C n-hexane n-heptane cyclohexane benzene toluene acetone
60 °C
calc
expt
calc
expt
19.1 12.4 7.07 0.463 0.240 0.386
22.0 10.5 7.04 0.395 0.206 0.496
36.0 25.1 13.8 1.05 0.590 0.868
40.1 21.0 12.6 0.843 0.488 1.01
some of the parameters reported in Tables 11 and 12 will require revision. Nevertheless, the promising initial correlation results reported here suggest that our simple perturbed-hard-sphere theory might be useful for estimating solubilities of volatile nonelectrolytes in ionic liquids.
5522
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006
Table 11. Parameters for Ionsa
Na+ Rb+ [MMIM+ [EMIM]+ [BMIM]+ [PY]+ [EPY]+ [BMPY]+
108σc (cm)
c/kB (K)
1.71 3.11 5.00 5.25 5.70 4.80 5.18 5.81
250 230 380 380 380 458 350 525
Cl[BF4][PF6][(CF3SO2)2N][(CH3)2PO4][CH3SO4][C2H5SO4][CH3OC2H4SO4][C2H5OC2H4SO4]-
108σa (cm)
a/kB (K)
3.35 4.40 4.76 6.05 5.03 4.70 5.05 5.34 5.50
250 250 205 500 455 565 450 440 430
a k is Boltzmann’s constant. [MMIM]+, 1-methyl-3-methylimidazolium; B [EMIM]+, 1-ethyl-3-methylimidazolium; [BMIM]+, 1-butyl-3-methylimidazolium; [PY]+, pyridinium; [EPY]+, N-ethyl-pyridinium; and [BMPY]+, 4-methyl-N-butyl-pyridinium.
Table 12. Parameters for Solutes
argon hydrogen oxygen nitrogen carbon dioxide hydrogen chloride methane ethane ethylene n-pentane n-hexane n-heptane cyclopentane cyclohexane 1-pentene 1-hexene 1-heptene benzene toluene acetone
108σs (cm)
s/kB (K)
1024Rs (cm3)
1018µ (esu cm)
1026Q (esu cm2)
3.60 3.00 3.80 3.90 3.81 3.50 3.95 4.32 4.28 5.10 5.31 5.54 4.90 5.10 5.00 5.20 5.44 4.80 5.00 4.62
120 25 130 130 280 335 180 300 350 450 505 550 510 570 465 525 575 410 720 250
1.64 0.806 1.58 1.74 2.64 2.63 2.60 4.50 4.25 9.99 11.9 13.6 9.15 11.0 9.65 11.65 13.51 10.6 12.3 6.42
0 0 0 0 0 1.11 0 0 0 0 0 0 0 0 0.4 0.3 0.3 0 0.37 2.88
0 0.637 0.4 1.4 4.30 0 0 0.65 1.50 0 0 0 0 0 1.50 1.50 1.50 8.69 8.69 0
Table 13. Data Sources for Experimental Solubilities and for Ionic-Liquid Densities
gases in NaCl gases in RbCl gases in [BMIM][PF6] gases in [BMIM][BF4] solutes in [MMIM][CH3SO4] solutes in [MMIM][CH3OC2H4SO4] solutes in [MMIM][(CH3)2PO4] solutes in [MMIM][(CF3SO2)2N] solutes in [EMIM][(CF3SO2)2N] solutes in [EMIM][C2H5SO4] solutes in [BMIM][(CF3SO2)2N] solutes in [PY][C2H5OC2H4SO4] solutes in [EPY][(CF3SO2)2N] solutes in [BMPY][BF4]
solubility
density
40 40 5 and 7a 6 and 7a 17 17 17 16 16 and 14 16 16 17 17 9
38 38 36 37 17 17 17 16 16 16 16 17 17 35
a For gases with low solubilities, ref 7 gives Henry’s constants that are more accurate than those in ref 5 and ref 6.
Acknowledgment We thank Philip Geissler for helpful discussions and Margarida Costa Gomes for providing experimental data before publication. For financial support, we are grateful to the Office for Basic Sciences of the U.S. Department of Energy. Nomenclature a ) diameter of cavity in the dielectric continuum D ) dielectric constant e ) electric field
Ghs ) molar hard-sphere cavity-formation energy Gi ) molar solute-solvent interaction energy g ) radial distribution function H ) Henry’s constant kB ) Boltzmann constant NA ) Avogadro’s number P ) pressure Q ) quadrupole moment R ) gas constant T ) temperature Vm ) molar volume of ionic liquid Subscripts a ) anion c ) cation s ) solute Greek Letters R ) polarizability Γ ) dispersion potential between ion and solute ) dispersion-energy parameter µ ) dipole moment ξi ) scaled-particle-theory parameter Fi ) number density of ion i σi ) diameter of ion i or solute i Literature Cited (1) Rogers, R. D., Seddon, K. R., Eds. Ionic Liquids: Industrial Applications to Green Chemistry; American Chemical Society: Washington, DC, 2002. (2) Rogers, R. D., Seddon, K. R., Eds. Ionic Liquids as Green SolVents; American Chemical Society: Washington, DC, 2003. (3) Heintz, A. Recent developments in thermodynamics and thermophysics of nonaqueous mixtures containing ionic liquids. A review J. Chem. Thermodyn. 2005, 37, 525. (4) Poole, C. F. Chromatographic and spectroscopic methods for the determination of solvent properties of room-temperature ionic liquids. J. Chromatogr. A 2004, 1037, 49. (5) Anthony, J. L.; Maginn, E. J.; Brennecke, J. F. Solubilities and thermodynamic properties of gases in the ionic liquid 1-n-butyl-3methylimidazolium hexafluorophosphate. J. Phys. Chem. B 2002, 106, 7315. (6) Anthony, J. L.; Anderson, J. L.; Maginn, E. J.; Brennecke, J. F. Anion effects on gas solubility in ionic liquids. J. Phys. Chem. B 2005, 109, 6366. (7) Gomes, M. C. Private communication. (8) Kumelan, J.; Kamps, A. P. S.; Urukova, I.; Tuma, D.; Maurer, G. Solubility of oxygen in the ionic liquid [bmim][PF6]: Experimental and molecular simulation results. J. Chem. Thermodyn. 2005, 37, 595. (9) Heintz, A.; Kulikov, D. V.; Verevkin, S. P. Thermodynamic properties of mixtures containing ionic liquids. 1. Activity coefficients at infinite dilution of alkanes, alkenes, and alkylbenzenes in 4-methyl-nbutylpyridinium tetrafluoroborate using gas-liquid chromatography. J. Chem. Eng. Data 2001, 46, 1526. (10) Heintz, A.; Kulikov, D. V.; Verevkin, S. P. Thermodynamic properties of mixtures containing ionic liquids. Activity coefficients at infinite dilution of polar solutes in 4-methyl-N-butyl-pyridinium tetrafluoroborate using gas-liquid chromatography. J. Chem. Thermodyn. 2002, 34, 1341. (11) David, W.; Letcher, T. M.; Ramjugernath, D.; Raal, J. D. Activity coefficients of hydrocarbon solutes at infinite dilution in the ionic liquid, 1-methyl-3-octyl-imidazolium chloride from gas-liquid chromatography. J. Chem. Thermodyn. 2003, 35, 1335. (12) Letcher, T. M.; Soko, B.; Ramjugernath, D.; Deenadayalu, N.; Nevines, A.; Naicker, P. K. Activity coefficients at infinite dilution of organic solutes in 1-hexyl-3-methylimidazolium hexafluorophosphate from gas-liquid chromatography. J. Chem. Eng. Data 2003, 48, 708. (13) Letcher, T. M.; Soko, B.; Reddy, P.; Deenadayalu, N. Determination of activity coefficients at infinite dilution of solutes in the ionic liquid 1-hexyl-3-methylimidazolium tetrafluoroborate using gas-liquid chromatography at the temperatures 298.15 and 323.15 K. J. Chem. Eng. Data 2003, 48, 1587.
Ind. Eng. Chem. Res., Vol. 45, No. 16, 2006 5523 (14) Deenadayalu, N.; Letcher, T. M.; Reddy, P. Determination of activity coefficients at infinite dilution of polar and nonpolar solutes in the ionic liquid 1-ethyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl) imidate using gas-liquid chromatography at the temperature 303.15 or 318.15 K. J. Chem. Eng. Data 2005, 50, 105. (15) Letcher, T. M.; Domanska, U.; Marciniak, M.; Marciniak, A. Activity coefficients at infinite dilution measurements for organic solutes in the ionic liquid 1-butyl-3-methyl-imidazolium 2-(2-methoxyethoxy)ethyl sulfate using GLC at T ) (298.15, 303.15, and 308.15) K. J. Chem. Thermodyn. 2005, 37, 587. (16) Krummen, M.; Wasserscheid, P.; Gmehling, J. Measurement of activity coefficients at infinite dilution in ionic liquids using the dilutor technique. J. Chem. Eng. Data 2002, 47, 1411. (17) Kato, R.; Gmehling, J. Activity coefficients at infinite dilution of various solutes in the ionic liquids [MMIM]+[CH3SO4]-, [MMIM]+[CH3OC2H4SO4]-, [MMIM]+[(CH3)2PO4]-, [C5H5NC2H5]+[(CF3SO2)2N]and [C5H5NH]+[C2H5OC2H4OSO3]-. Fluid Phase Equilib. 2004, 226, 37. (18) Shariati, A.; Perters, C. J. High-pressure phase behavior of systems with ionic liquids: measurements and modeling of the binary system fluoroform + 1-ethyl-3-methylimidazolium hexafluorophosphate. J. Supercrit. Fluids 2003, 25, 109. (19) Shariati, A.; Perters, C. J. High-pressure phase behavior of systems with ionic liquidssPart III. The binary system carbon dioxide + 1-hexyl3-methylimidazolium hexafluorophosphate J. Supercrit. Fluids 2004, 30, 139. (20) Costantini, M.; Toussaint, V. A.; Shariati, A.; Peters, C. J.; Kikic, I. High-pressure phase behavior of systems with ionic liquids: measurements and modeling of the binary system fluoroform + 1-ethyl-3-methylimidazolium hexafluorophosphate. J. Chem. Eng. Data 2005, 50, 52. (21) Shariati, A.; Peters, C. J. High-pressure phase equilibria of systems with ionic liquids. J. Supercrit. Fluids 2005, 34, 171. (22) Shariati, A.; Gutkowski, K.; Peters, C. J. Comparison of the phase behavior of some selected binary systems with ionic liquids. AIChE J. 2005, 51, 1532. (23) Urukova, I.; Vorholz, J.; Maurer, G. Solubility of CO2, CO, and H2 in the ionic liquid [bmim][PF6] from Monte Carlo simulations. J. Phys. Chem. B 2005, 109, 12154. (24) Cadena, C.; Anthony, J. L.; Shah, J. K.; Morrow, T. I.; Brennecke, J. F.; Maginn, E. J. Why is CO2 so soluble in imidazolium-based ionic liquids? J. Am. Chem. Soc. 2004, 126, 5300. (25) Eike, D. M.; Brennecke, J. F.; Maginn, E. J. Predicting infinitedilution activity coefficients of organic solutes in ionic liquids. Ind. Eng. Chem. Res. 2004, 43, 1039.
(26) Diedenhofen, M.; Eckert, F.; Klamt, A. Prediction of infinite dilution activity coefficients of organic compounds in ionic liquids using COSMORS. J. Chem. Eng. Data 2003, 48, 475. (27) Pierotti, R. A. Scaled particle theory for aqueous and nonaqueous solutions. Chem. ReV. 1976, 76, 717. (28) Lebowitz, J. L.; Helfand, E.; Praestgaard, E. Scaled particle theory of fluid mitxures. J. Chem. Phys. 1965, 43, 774. (29) Hu, Y.; Xu, Y. N.; Prausnitz, J. M. Molecular thermodynamics of gas solubility. Fluid Phase Equilib. 1985, 23, 15. (30) Widegren, J. A.; Saurer, E. M.; Marsh, K. N.; Magee, J. W. Electrolytic conductivity of four imidazolium-based room-temperature ionic liquids and the effect of a water impurity. J. Chem. Thermodyn. 2005, 37, 569. (31) Bo¨ttcher B. K. P. Theory of Electric Polarisation; Elsevier Publishing Company: Amsterdam, The Netherlands, 1952. (32) Scaife, B. K. P. Principles of Dielectrics; Clarendon Press: Oxford, U.K., 1989. (33) Wakai, C.; Oleinikova, A.; Ott, M.; Weingartner, H. How polar are ionic liquids? Determination of the static dielectric constant of an imidazolium-based ionic liquid by microwave dielectric spectroscopy. J. Phys. Chem. B 2005, 109, 17028. (34) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. (35) Heintz, A.; Klasen, D.; Lehmann, J. K. Excess molar volumes and viscosities of binary mixtures of methanol and the ionic liquid 4-methylN-butylpyridinium tetrafluoroborate at 25, 40, and 50 °C. J. Solut. Chem. 2002, 31, 467. (36) Gu, Z. Y.; Brennecke, J. F. Volume expansivities and isothermal compressibilities of imidazolium and pyridinium-based ionic liquids. J. Chem. Eng. Data 2002, 47, 339. (37) Fredlake, C. P.; Crosthwaite, J. M.; Hert, J. M.; Aki, S. N. V. K.; Brennecke, J. F. Thermophysical properties of imidazolium-based ionic liquids. J. Chem. Eng. Data 2004, 49, 954. (38) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press: Boca Raton, FL, 2004. (39) Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids; Oxford University Press: New York, 1984. (40) Tomkins, R. P. T.; Bansal N. P., Eds. Solubility Data Series: Gases in Molten Salts; Pergamon Press: Oxford, U.K., 1991.
ReceiVed for reView September 29, 2005 ReVised manuscript receiVed November 28, 2005 Accepted November 29, 2005 IE051090P
