Considering the Basis of Accounting for CO2 Mole Fractions in Ionic

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Considering the Basis of Accounting for CO2 Mole Fractions in Ionic Liquids and Its Influence on the Interpretation of Solution Nonideality Jason E. Bara* University of Alabama, Department of Chemical and Biological Engineering, Tuscaloosa, Alabama 35487-0203, United States ABSTRACT: Does the common use of a particular basis of accounting lead to an overstatement of the solubilities of CO2 and other gases in ionic liquids (ILs)? Consequently, is further discussion needed in judging the positive or negative deviations from ideality for CO2−IL solutions? Here, an alternative framework for mole fraction accounting previously proposed is more thoroughly considered. The results suggest that ILs tend to exhibit positive deviations from Raoult’s Law when the cation and anion are taken as distinct molecular entities. An analysis of the influence of the variables associated with calculating CO2 mole fractions in ILs is provided which illustrates the large effects of solvent molecular weight on the calculations leading to the judgment of deviation from Raoult’s Law.

1. INTRODUCTION As a convention in the field of measurement and reporting of mole fraction-based solubility data for gases in ionic liquids (ILs), the cation and anion that compose a given IL have been almost always treated as a single molecule for the purposes of calculating mole fractions of CO2 or Henry’s constants.1−48 However, Scovazzo49 initially stated that, according to Hildebrand and Scott, the “true mole fraction” of CO2 (or any solute) in an IL must account for all neutral and ionized species.50 Furthermore, Scovazzo showed that when the cation and anion were counted as individual species, positive deviations from Raoult’s Law were observed for CO2−IL mixtures. This is in distinct contrast to a more recent work from Carvalho and Coutinho that suggests that CO2−IL mixtures tend to exhibit negative deviations from Raoult’s Law.36 However, whether positive or negative deviations from ideality are observed may simply be a matter of accounting. Fundamentally, if charge neutrality is satisfied, then a cation cannot exist without an anion (and vice versa). For the vast majority of ILs reported in the literature, these cations and anions are large molecular species (e.g., triflate) rather than atomic point charges (e.g., chloride). Many of the individual ions that comprise ILs dwarf the mass of gaseous solutes for which ILs have been studied as solvents, and among these gases of interest, CO2 (44 g mol−1) is one of the larger species in terms of molecular weight (MW). Yet despite the large differences in MW (and molar volumes), both ILs and solutes are commonly given equal weighting in the calculation of solute mole fraction. The sheer size of the IL components relative to these gaseous solutes necessitates an analysis of the implications of counting cation−anion pairs as one molecule or two. Because these large MWs can lead to overstatements of the physical solubility of CO2 when comparing ILs to other solvents and polymers,3,51 several works have utilized units of moles of CO2 per volume or mass (e.g., molarity or molality) as a normalization that is comparable with any solvent/material and is more useful for the design of gas absorption processes.3,7,8,36,52−60 © 2013 American Chemical Society

The smallest imidazolium cations, such as 1-ethyl-3methylimidazolium ([C2mim]), exhibit MWs that begin at ∼100 g mol−1, and this mass only grows as the substituents are modified. Another cationic moiety used in ILs is the phosphonium center, where a commonly used derivative is trihexyltetradecylphosphonium ([P6,6,6,14]), with a MW = 483.86 g mol−1 or ∼11× the mass of a single CO2 molecule. Among anions, bistriflimide (known as [TFSI] or [Tf2N]) is broadly employed and has a MW = 280.15 g mol−1, which is roughly 6.5× the mass of a CO2 molecule. Other common anions include: dicyanamide ([N(CN)2], 66.04 g mol−1), tetrafluoroborate ([BF4], 86.81 g mol−1), hexafluorophosphate ([PF6], 144.96 g mol−1), and triflate ([OTf], 149.07 g mol−1). For the combined cation−anion pairs, even the smallest ILs begin to exceed 200 g mol−1 and many ILs of interest easily exceed 300−400 g mol−1, or approximately 8−10× the mass of a single CO2 molecule. This large disparity in MW between solvent and solute results in the observance of Henry’s constants which are often lower than those observed in conventional organic solvents, such as methanol, acetonitrile, acetone, etc., which have MWs much closer to that of CO2.3,51 While smaller Henry’s constants may be taken to imply greater solubility of CO2, this must be considered within an appropriate context. As the MWs of ILs are at least several times larger than common organic solvents, this can obfuscate the fact that, on a moles per volume basis, the solubility of CO2 in ILs is only ∼30−40% of that observed in polar solvents such as acetonitrile and acetone and is quite similar to that of nonpolar solvents such as hexane.3,51 In measuring the solubility of CO2 in progressively larger molecules with a propagating chemical structure (e.g., alkanes: hexane, heptane, octane, ...), the mole fraction of CO2 will continue to increase although the moles of CO2 per mass/ Received: Revised: Accepted: Published: 3522

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Figure 1. Example solvent systems which are identical in elemental composition and number of molecular entities: (a) 1:1 mixture of 1ethylimidazole and methyl acetate and (b) an IL, [emim][OAc].

volume of material will eventually approach a constant.3,36 Even at a partial pressure of 1 bar, the mole fraction of CO2 can approach unity in macromolecules and polymers,51 yet this seemingly high solubility provides little insight about the actual forces driving the affinity of the solvent/material for CO2.

Because the moles of CO2 dissolved in an IL (at a given temperature and pressure) are weighted against the moles of the much larger cation−anion pair, the relationship between the partial pressure of CO2 and the mole fraction of CO2 in solution will tend to present itself as a negative deviation from Raoult’s Law when the “1 + 1 = 1” method is applied (Figure 2).36

2. ANALYSIS OF THE ACCOUNTING METHOD FOR CO2 MOLE FRACTIONS IN ILS In Figure 1, two example solvents are presented which are identical in their elemental compositions and the number of molecular entities (neutral or ionic). Figure 1a shows a 1:1 (mol/mol) mixture of 1-ethylimidazole and methyl acetate, while Figure 1b depicts an analogous IL, 1-ethyl-3-methylimidazolium acetate ([emim][OAc]). The total number of molecules present in the first example (Figure 1a) would certainly be taken as the sum of the individual 1-ethylimidazole and methyl acetate (MeOAc) molecules. Yet, in the IL solvent (Figure 1b), the total number of molecules is commonly determined by taking the sum of imidazolium cations and acetate anions and dividing by two. In both solvents, the same number of discrete entities exists, yet if the IL is considered to be one molecule, then the shift of a methyl group from the ester to the imidazole has drastically altered the accounting basis for determining the mole fraction of CO2 (or other solutes). Suppose, at a given temperature and pressure, 10 solute molecules are dissolved in 90 mols of the 1:1 (mol/mol) 1ethylimidazole/MeOAc mixture. Clearly, the solute mole fraction would be reported as 0.10. If these same 10 solute molecules were introduced to 45 mols of [emim][OAc] (which has the same mass, elemental composition, and number of discrete entities as the mixture of neutral organics), the mole fraction would be reported as 0.1818. On the basis of these accounting principles, the dissolution of the solute in the IL is 1.818 times more favorable. Yet, the mole fraction solubilities are identical if the total number of entities in the IL system is considered. Furthermore, the mass fraction (or molality) of the solute is the same in both systems. The “1 cation + 1 anion = 1 molecule” method of accounting has been consistently applied in the majority of all experimental and computational work on gas solubility in ILs, which has been convenient for comparing CO2 solubility across different ILs. Yet, is the exclusive use of this methodology most appropriate for drawing conclusions as to the solution behaviors of CO2 in ILs to that of CO2 in neutral organic molecules? Here, the implications of a “1 anion + 1 cation = 2 molecules” approach initially discussed by Scovazzo will be given further consideration for the calculation of CO2 mole fractions in ILs.

Figure 2. Relationship between CO2 partial pressure and mole fraction of CO2 in various solvents and ILs at 313 K. Reprinted from ref 36. Copyright 2010 American Chemical Society. Raoult’s Law and Flory− Huggins models included for comparison.

As presented in Figure 2, the apparent negative deviations from Raoult’s Law in IL−CO2 systems would suggest favorable solute−solvent interactions. However, the relationship between CO2 partial pressure and mole fraction (Figure 2) does not reflect the relatively low solubility of CO2 in ILs on a basis of moles per IL mass or volume.3,36,51,61

3. INFLUENCE OF SOLVENT MW ON DEVIATION FROM RAOULT’S LAW Alternatively, if the moles of CO2 are compared to the total number of cations and anions (i.e., 2× the number of cation− anion pairs), the mole fraction of CO2 at given T and P conditions is essentially halved. This will lead to positive deviations from Raoult’s Law, indicative of weak solute−solvent interactions and thus better correlated to the low levels of CO2 solubility per IL mass or volume.3,36 At 313 K, the partial pressure of CO2 above a nonvolatile solvent that corresponds to Raoult’s Law can be determined from eq 1, the limiting case of Raoult’s Law with one volatile component used by Carvalho and Coutinho,36 3523

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Figure 3. (a−e) Comparison of solubility calculations to Raoult’s Law (solid black line) for CO2 in a nonvolatile solvent (313 K) for the “1 + 1 = 2” method (solid line, filled points) or the “1 + 1 = 1” method (dashed line, unfilled points) with SCO2 values of 0.700 (diamonds), 0.875 (triangles), and 1.050 (circles) mol CO2 (kg IL)−1 MPa−1 for a given IL MW: (a) 150 g mol−1, (b) 200 g mol−1, (c) 250 g mol−1, (d) 300 g mol−1, and (e) 400 g mol−1.

PCO2(MPa) = 8.94·xCO2

deviations from Raoult’s Law are observed for ILs in which CO2 would be equally soluble on a molality basis. Figure 3a−e illustrates the implications of the “1 + 1 = 2” accounting method by examining the apparent deviation from Raoult’s Law for ILs with MWs ranging from 150 to 400 g mol−1. In each example, CO2 solubilities in the IL are considered in terms of moles per mass of solvent (i.e.,

(1)

where PCO2 is the partial pressure of CO2 above the IL and xCO2 is the mole fraction of CO2 in the IL. As shown through Figures 3a−e and 4a,b, the accounting method by which xCO2 is defined and the MW of the IL influence whether positive or negative 3524

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Correspondingly, when the IL MWs are in the range of 150− 200 g mol−1, positive deviations from Raoult’s Law are still observed at partial pressures as low as 1 MPa, even if the “1 + 1 = 1” method that has been commonly used throughout the literature is applied. As stated earlier, although there are very few ILs that would have MWs this small while remaining molten at ambient conditions, species such as 1-ethyl-3methylimidazolium thiocyanate ([C2mim][SCN], MW = 169.25 and [C2mim][BF4], MW = 197.97) do fit this definition. Figure 4 considers cases where SCO2 is held constant and the MW of the IL is varied. The examples illustrate that, even if CO2 is observed to have the same solubility (in terms of molality per pressure) in ILs that differ only in MW, then different conclusions can be reached with respect to the manner in which they deviate from Raoult’s Law. The impact of the accounting method is also illustrated to show that if a “1 + 1 = 2” approach is used, then either positive or negative deviations can occur, while a “1 + 1 = 1” approach leads to the observance of primarily negative deviations. In both cases, the magnitude of these deviations is directly correlated to MW. In Figure 4a, where the solubility of CO2 is 0.70 mol CO2 (kg IL)−1 MPa−1, ILs with MWs up to 400 g mol−1 are observed to show positive deviations from Raoult’s Law at pressures 200 g mol−1. When the solvent MW is set to be equal to that of CO2 (Figure 5a), then the solubility of CO2 in the smaller solvent must be >2.45 mol CO2 (kg solvent)−1 MPa−1 (i.e., 2−3× the solubility (molality basis) of CO2 in ILs) before a negative deviation from Raoult’s Law would be observed.

(6a)

1 1+

2 SCO2·PCO2·k·MWCO2

(6b)

where k = MWIL/MWCO2, thus indicating that solvents with smaller MW (smaller values of k) will be more likely to exhibit positive deviations from Raoult’s Law for given values of SCO2 and PCO2. This influence of the ratio of solvent MW to CO2 MW is implied within Figure 2 as the alcohols are, on average, of smaller MWs (∼120−180 g mol−1) than the other solvents (>200 g mol−1), while ILs are typically larger than most of these other solvents, with the exception of the PEGs. Thus, if solvents with MWs much closer to that of CO2 are also 3526

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(6) Finotello, A.; Bara, J. E.; Camper, D.; Noble, R. D. Roomtemperature ionic liquids: Temperature dependence of gas solubility selectivity. Ind. Eng. Chem. Res. 2008, 47, 3453−3459. (7) Bara, J. E.; Gabriel, C. J.; Lessmann, S.; Carlisle, T. K.; Finotello, A.; Gin, D. L.; Noble, R. D. Enhanced CO2 separation selectivity in oligo(ethylene glycol) functionalized room-temperature ionic liquids. Ind. Eng. Chem. Res. 2007, 46, 5380−5386. (8) Camper, D.; Bara, J.; Koval, C.; Noble, R. Bulk-fluid solubility and membrane feasibility of Rmim-based room-temperature ionic liquids. Ind. Eng. Chem. Res. 2006, 45, 6279−6283. (9) Camper, D.; Becker, C.; Koval, C.; Noble, R. Diffusion and solubility measurements in room temperature ionic liquids. Ind. Eng. Chem. Res. 2006, 45, 445−450. (10) Koval, C.; Camper, D.; Finotello, A.; Noble, R. Properties of imidazolium-based room temperature ionic liquids that effect CO2 solubility and selectivity for CO2/N2 and CO2/CH4 gas separations. PMSE Prepr. 2006, 95, 266. (11) Camper, D.; Becker, C.; Koval, C.; Noble, R. Low pressure hydrocarbon solubility in room temperature ionic liquids containing imidazolium rings interpreted using regular solution theory. Ind. Eng. Chem. Res. 2005, 44, 1928−1933. (12) Camper, D.; Scovazzo, P.; Koval, C.; Noble, R. Gas solubilities in room-temperature ionic liquids. Ind. Eng. Chem. Res. 2004, 43, 3049−3054. (13) Condemarin, R.; Scovazzo, P. Gas permeabilities, solubilities, diffusivities, and diffusivity correlations for ammonium-based room temperature ionic liquids with comparison to imidazolium and phosphonium RTIL data. Chem. Eng. J. 2009, 147, 51−57. (14) Kilaru, P. K.; Condemarin, R. A.; Scovazzo, P. Correlations of low-pressure carbon dioxide and hydrocarbon solubilities in imidazolium-, phosphonium-, and ammonium-based room-temperature ionic liquids. Part 1. Using surface tension. Ind. Eng. Chem. Res. 2008, 47, 900−909. (15) Kilaru, P. K.; Scovazzo, P. Correlations of low-pressure carbon dioxide and hydrocarbon solubilities in imidazolium-, phosphonium-, and ammonium-based room-temperature ionic liquids. Part 2. Using activation energy of viscosity. Ind. Eng. Chem. Res. 2008, 47, 910−919. (16) Ferguson, L.; Scovazzo, P. Solubility, diffusivity, and permeability of gases in phosphonium-based room temperature ionic liquids: Data and correlations. Ind. Eng. Chem. Res. 2007, 46, 1369− 1374. (17) Kilaru, P.; Baker, G. A.; Scovazzo, P. Density and surface tension measurements of imidazolium-, quaternary phosphonium-, and ammonium-based room-temperature ionic liquids: Data and correlations. J. Chem. Eng. Data 2007, 52, 2306−2314. (18) Goodrich, B. F.; de la Fuente, J. C.; Gurkan, B. E.; Zadigian, D. J.; Price, E. A.; Huang, Y.; Brennecke, J. F. Experimental measurements of amine-functionalized anion-tethered ionic liquids with carbon dioxide. Ind. Eng. Chem. Res. 2010, 50, 111−118. (19) Gurkan, B. E.; de la Fuente, J. C.; Mindrup, E. M.; Ficke, L. E.; Goodrich, B. F.; Price, E. A.; Schneider, W. F.; Brennecke, J. F. Equimolar CO2 absorption by anion-functionalized ionic liquids. J. Am. Chem. Soc. 2010, 132, 2116−2117. (20) Gurkan, B.; Goodrich, B. F.; Mindrup, E. M.; Ficke, L. E.; Massel, M.; Seo, S.; Senftle, T. P.; Wu, H.; Glaser, M. F.; Shah, J. K.; Maginn, E. J.; Brennecke, J. F.; Schneider, W. F. Molecular design of high capacity, low viscosity, chemically tunable ionic liquids for CO2 capture. J. Phys. Chem. Lett. 2010, 1, 3494−3499. (21) Anderson, J. L.; Dixon, J. K.; Brennecke, J. F. Solubility of CO2, CH4, C2H6, C2H4, O2, and N2 in 1-hexyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide: Comparison to other ionic liquids. Acc. Chem. Res. 2007, 40, 1208−1216. (22) Muldoon, M. J.; Aki, S. N. V. K.; Anderson, J. L.; Dixon, J. K.; Brennecke, J. F. Improving carbon dioxide solubility in ionic liquids. J. Phys. Chem. B 2007, 111, 9001−9009. (23) 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, 6366−6374.

5. CONCLUSIONS Others have recognized this asymmetry in the size and shape between the CO2 solute and much larger solvents (e.g., ILs) and have rationalized the nonideality through entropic and free volume contributions.36 When considering ILs, a natural and logical division between cation and anion exists such that the”1 + 1 = 2” method of molecular accounting for ILs originally proposed by Scovazzo (based on the earlier work of Hildebrand and Scott)49,50 provides an alternative framework by which to interpret CO2 solubility in mole fraction terms. Although the separation of the IL cation and anion has been considered here due to their observations, this discussion is not advocating for large molecules such as alkanes, fatty acids, or liquid poly(ethylene glycols) (PEGs) to also be segmented to better represent small molecules so as to shift mole fractions within Figure 2. Clearly, better agreement between CO2 partial pressure and mole fraction in ILs is observed in Figure 2 for the Flory−Huggins model because it considers weighted volume fractions that take into account the relative sizes of the molecules.69−71 Across all examples in Figure 2, it appears that negative deviations from Raoult’s Law for ILs and other species tend to be observed when the molecular weight of the solvent of interest is >300 g mol−1. As the use of Raoult’s Law in Figure 2 is based on negligible solvent volatility, relatively large molecules will typically be required to satisfy this condition. Thus, the negative deviation from Raoult’s Law that has been associated with ILs is largely due to the contribution of their large MWs and the “1 + 1 = 1” method of accounting. Furthermore, when mole fraction solubilities are normalized to a basis that accounts for moles of CO2 per solvent mass (e.g., molality)36,52−54 or per solvent volume (e.g., cm3 (STP) (cm3 solvent)−1),3,51 the solubility of CO2 in ILs and other physical solvents with MWs several times that of the CO2 solute falls within a relatively narrow range regardless of molecular composition or charge.36

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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