Regular Solution Theory for Low Pressure Carbon Dioxide Solubility in RoomTemperature Ionic Liquids: Ionic Liquid Solubility Parameter from ActivationEnergy of Viscosity

Surya S. Moganty† and Ruth E. Baltus*

Department of Chemical and Biomolecular Engineering, Clarkson UniVersity, Potsdam, New York 13699-5705

The low pressure solubility of carbon dioxide in eight commercially available room temperature ionic liquidswas measured at 10, 25, and 40 °C using a transient thin liquid film technique. In this paper, carbon dioxidesolubility is reported as the Henry’s law constant for each system. Experimental results were interpretedusing regular solution theory where Eyring’s reaction rate theory was successfully applied to estimate thesolubility parameter of each ionic liquid from its activation energy of viscosity. Consistent with the regularsolution theory, the carbon dioxide solubility was found to be inversely proportional to the solubility parameterof the ionic liquid, and Henry’s law constants were successfully correlated with the square of the differencebetween ionic liquid and carbon dioxide solubility parameters.

Introduction

Room temperature ionic liquids (RTILs) are organic saltsconsisting of a bulky cation and an inorganic anion with meltingpoints below 100 °C. The large cation size allows for delocal-ization and screening of charges, resulting in a reduction in thelattice energy and thereby the melting or glass transitiontemperature. RTILs exhibit many interesting properties, whichmake them suitable for applications such as chemical synthesis,catalysis, electrochemical applications, and gas separations.

Knowledge of the solubilities of gases in different RTILs isimportant for the design and development of ionic liquid-basedreaction and separation processes as well as for understandinggas-liquid interactions that govern solubility. Among differentgases, carbon dioxide is the most widely studied because itsrelatively high solubility in many RTILs has focused attentionon RTIL-based separation processes for carbon capture fromflue gases generated in coal-fired power plants.1-5

A number of different techniques have been used to measuregas solubilities in RTILs. These include a gravimetric method,6-10

a quartz crystal microbalance method,11 and equilibrium pressureand volume techniques.12,13 In recent years, work in ourlaboratory has focused on measuring gas solubility and diffu-sivity in RTILs using a technique involving gas uptake into athin ionic liquid film.14-16

Efforts have also been directed toward the development ofthermodynamic models for predicting gas solubilities in RTILs.Shiflett and Yokozeki7,9,17,18 developed a Redlich-Kwong cubicequation of state as well as different activity coefficient modelsto describe NH3, CO2, and hydrofluorocarbon solubilities inRTILs. Quantitative structure-properties relationship modelshave also been developed for modeling solubilities in RTILs.19

However, these approaches require experimental data for eachRTIL-gas pair to determine the model parameters. This problemcan be avoided with regular solution theory (RST) becausemodel parameters involve only pure component properties. Shiand Maginn20 compared RST predictions with results frommolecular modeling simulations and concluded that RST was

the most useful predictive tool for correlating low pressure gassolubilities. Using different approaches to relate measurableproperties to RTIL solubility parameters, Noble and co-work-ers21-24 and Scovazzo and co-workers25-27 successfully appliedRST to interpret and predict the solubilities of a variety of gasesin different RTILs.

In this paper, we report results from measurements of thelow pressure solubility of CO2 in eight different RTILs at 10,25, and 40 °C. Results are interpreted using RST, where analternative approach for estimating the RTIL solubility param-eters is presented. In this approach, RTIL solubility parametersare estimated from activation energies of RTIL viscosity,building upon Eyring’s absolute reaction rate theory of the liquidstate, which relates the energy of vaporization to the activationenergy of viscosity.28 This approach is similar yet different thanthe approach used by Kilaru and Scovazzo27 for interpretingcarbon dioxide and hydrocarbon solubilities in RTILs. Theresulting expression allows one to estimate the Henry’s lawconstant for CO2 in an ionic liquid from viscosity measurementsat several different temperatures.

Regular Solution Theory

RST assumes that at constant temperature and pressure, theexcess entropy of mixing vanishes and that forces of attractionbetween molecules are primarily short-range dispersion forces.Low columbic interactions are expected for RTILs because thelarge cation size delocalizes the charge. Hence, it is reasonableto assume that RTIL solutions are dominated by short-rangeforces.

The vapor liquid equilibrium of carbon dioxide dissolved inan RTIL can be expressed in terms of the fugacity of carbondioxide:

Because RTILs are nonvolatile and only CO2 is introduced intothe experimental cell, the gas phase is pure CO2 and is assumedto be ideal. Therefore, the fugacity of CO2 can be assumed tobe equal to the gas pressure. The CO2 fugacity in the liquidphase can be written in terms of an activity coefficient:

* To whom correspondence should be addressed. E-mail: baltus@clarkson.edu.

† Present address: School of Chemical and Biomolecular Engineering,Cornell University, Ithaca, New York 14850.

fCO2

G ) fCO2

IL (1)

Ind. Eng. Chem. Res. 2010, 49, 5846–58535846

10.1021/ie901837k 2010 American Chemical SocietyPublished on Web 05/17/2010

where xCO2 is the mole fraction of carbon dioxide in the RTILsolution phase, γCO2 is the activity coefficient of carbon dioxidein the RTIL phase, and fCO2

0 is the fugacity of pure CO2 atstandard state, defined to be a hypothetical pure liquid at thesolution temperature. Rearranging eq 2 and applying logarithmsyields

According to the Scatchard-Hildebrand RST, the logarithm ofthe activity coefficient is proportional to the squared differencein solubility parameters between solute and solvent:29-31

where VCO2 is the molar volume of hypothetical liquid carbondioxide at the solution temperature and pressure, �IL is thevolume fraction of RTIL, and δILand δCO2 are the solubilityparameters for pure RTIL and pure CO2. Substituting eq 4 intoeq 3 yields

Applying Henry’s law (P ) HCO2xCO2), eq 5 can be rearrangedto:

where A and B are parameters that depend only on temperature.

RTIL Solubility Parameter

The applicability of RST to RTIL-gas systems requires anestimation of the solubility parameter of the RTIL. In theHildebrand treatment of RST, the solubility parameter is thesquare root of the cohesive energy density, which is defined asthe ratio of the energy of vaporization, ∆Uvap, to the molarvolume, V:

Because RTILs are nonvolatile, experimental measurement oftheir energy of vaporization is difficult. For this reason, reportsfrom experimental measurements of ∆Uvap have been verylimited.

Alternative approaches have been considered for relating thecohesive energy density to measurable parameters that charac-terize the intermolecular forces in RTILs. Assuming that theintermolecular forces that dictate melting point temperatures arerelated to the intermolecular forces that control vaporization,Camper et al.21 used RTIL melting temperatures to estimatethe δIL. However, this approach is limited because few RTILshave a melting point. Assuming that the lattice energy densitycharacterizes intermolecular interactions in ionic liquids, Camperet al.23 used the Kapustinskii equation to estimate the latticeenergy density of RTILs. In the Kapustinskii equation, the lattice

energy density for the ion pairs is estimated from the chargeand molar radii of the ions, ignoring ion polarizability.32 Leeand Lee33 report δIL values that were determined from intrinsicviscosity measurements performed with ionic liquid solutionsprepared with solvents of known δ. The RTIL solubilityparameter was assumed to be equal to the solubility parameterof the solvent that yielded the maximum intrinsic viscosity.Recently, Kilaru et al.27 estimated Hansen solubility parametersof RTILs from surface tension values. Similarly, Jin et al.34

estimated Hildebrand solubility parameters for ionic liquids fromsurface tension measurements using correlations developed forRTILs with measured values of ∆Uvap. In another approach,Kilaru and Scovazzo27 estimated RTIL solubility parametersfrom the free energy of activation of viscosity using Eyring’sabsolute reaction rate theory. The proportionality constantrelating the free energy of activation of viscosity to the energyof vaporization was estimated using the solubility parametervalues reported by Lee and Lee.33 It was found that a differentproportionality constant was needed for Tf2N-based RTILs andfor non-Tf2N-based RTILs.

As an alternative approach, we have examined estimation ofthe energy of vaporization of RTILs from the activation energyfor viscosity, which is also suggested by Eyring’s absolutereaction rate theory.35 Note that the activation energy forviscosity differs from the free energy of activation for viscosityby the entropy change that accompanies activation for viscousflow.28 Eyring and co-workers used reaction rate theory to modelthe liquid state and to develop equations for estimating transportproperties of liquids.28,35,36 In Eyring’s approach, the liquid isconsidered to be made up of “holes”, and the process of flow isassumed to be a unimolecular rate process. For a molecule totake part in flow, a suitable “hole” or vacant site must beavailable, but this “hole” is not necessarily of molecular size.Hence, the activation energy for viscous flow, Ea

vis, is assumedto be related to the work required to form a “hole” in the liquid.Similarly, the energy of vaporization is the work required toremove a molecule from the liquid phase, that is, to form amolecular size hole in the liquid. Therefore, Eyring argued thatthe activation energy of viscosity is related to, but a fractionof, the energy of vaporization. For nonspherical molecules,Eyring reported that ∆Uvap ) 4Ea

vis.36

Energy of vaporization values for a few RTILs have beenmeasured and reported by Armstrong et al.37 who used massspectrometry, by Santos et al.38 who used a vacuum micro-calorimeter, and by Luo et al.39 who used thermogravimetricanalysis. There is general agreement between values measuredusing these different techniques. Using literature values for RTILviscosity as a function of temperature, the activation energy ofviscosity was determined for the RTILs investigated in thevaporization studies. A plot of the energy of vaporization versusthe activation energy of viscosity was prepared and is shownin Figure 1. A linear regression fit yields a slope of 4.3. This isin very good agreement with the Eyring prediction that ∆Uvap

is a factor of 4 times larger than Eavis. We have opted to use

the Eyring factor of 4, recognizing that the difference in δIL

predicted with the two different proportionality factors is lessthan 3%. Using the Eyring relationship, the RTIL solubilityparameter can be estimated from the activation energy ofviscosity:

The solubility parameter for carbon dioxide at differenttemperatures can be estimated from the following correlation:40

P ) xCO2γCO2

fCO2

0 (2)

-ln xCO2) ln(fCO2

0

P ) + ln γCO2(3)

ln γCO2)

VCO2�IL

2

RT (δIL - δCO2)2 (4)

-ln xCO2) ln(fCO2

0

P ) +VCO2

�IL2

RT (δIL - δCO2)2 (5)

ln HCO2) ln fCO2

0 +VCO2

φIL2

RT (δIL - δCO2)2 )

A + B(δIL - δCO2)2 (6)

δ ) �∆Uvap

V(7)

δIL ) �4Eavis

VIL(8)

Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 5847

where T is in K. This expression predicts δCO2 ) 13.1 (J/cm3)1/2

at 10 °C, δCO2 ) 12.3 (J/cm3)1/2 at 25 °C, and δCO2 ) 11.5(J/cm3)1/2 at 40 °C.

Experimental Section

The experimental system used for solubility measurementsinvolves tracking the decrease in pressure that results followingthe introduction of target gas (CO2 in this work) into a smallclosed chamber containing a thin film of RTIL. The solubility,characterized using Henry’s law constant, H, and diffusivity,D, of the target gas are determined by fitting the pressure decayto a one-dimensional diffusion model of gas transport in theRTIL film. Details of the experimental setup and operatingprinciples for our measurements are described in detailelsewhere.14-16

By combining Fick’s law for diffusion in the RTIL film witha mass balance on gas above the liquid, the pressure decay canbe related to system parameters and gas properties by

where V is the volume of gas, VIL is the volume, FIL is thedensity, MWIL is the molecular weight, and L is the thicknessof the RTIL film. In developing eq 10, it is assumed that thephysical properties (i.e., density and viscosity) of the ionic liquidfilm do not change during the gas dissolution process. Math-ematical details of the derivation of eq 1 are presented in Houand Baltus.14 The final model includes two unknowns, H andD. Using a nonlinear least-squares method in the MATLABcurve fitting tool box, the experimental P vs time data were fitto eq 10 to determine H and D. In all cases, there was excellentagreement between experimentally measured pressure valuesand model predictions over the entire experimental time,supporting the assumption that the properties of the ionic liquidare constant throughout the process. In this paper, we focusexclusively on solubility values. Diffusion coefficient values willbe reported and discussed in a subsequent paper.41

Materials. Eight different ionic liquids were studied in thiswork: 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfo-nyl)imide (Emim Tf2N) (Solvent Innovation, 99% purity),1-ethyl-3-methylimidazolium bis(pentafluoroethylsufonyl)imide

(Emim BETI) (Covalent Associates, 99% purity), 1-ethyl-3-methylimidazolium trifluoromethylsulfonate (Emim TfO) (SigmaAldrich, 98% purity), 1-ethyl-3-methylimidazolium trifluoro-acetate (Emim TfA) (EMD Merck, 98% purity), 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (HmimTf2N) (EMD Merck, 99% purity), 1-hexyl-3-methylimidazoliumtetrafluoroborate (Hmim BF4) (Sigma Aldrich, 98% purity),1-octyl-3-methylimidazolium tetrafluoroborate (Omim BF4)(Solvent Innovation, 99% purity), and 1-butyl-3-methylpyri-dinium tetrafluoroborate (Bmpy BF4) (Sigma Aldrich, 97%purity). High-purity nitrogen (N2) and carbon dioxide (CO2)were obtained from Merriam-Graves Co. (Charlestown, NH)with purities of 99.998 and 99.995%, respectively. (Nitrogengas was used for RTIL regeneration following CO2 uptakemeasurements.15)

Results and Discussion

Carbon Dioxide Solubility. The values of the Henry’s lawconstant for CO2 in the RTILs are presented in Table 1. For alimited number of these RTILs, exact comparison with literaturereports of H for CO2 can be made. These comparisons aresummarized in Table 2, showing generally good agreementbetween Henry’s law constants measured in this work to valuesreported by others using different techniques.

The solubility of CO2 in each RTIL at 1 bar CO2 pressure islisted on both a mole fraction basis as well as in mol CO2/L ofRTIL in Table 3. When expressed as a mole fraction, acomparison of CO2 solubilities in the tested ionic liquids showssolubility in Hmim Tf2N > Emim Tf2N ∼ Emim BETI > EmimTfA ∼ Omim BF4 > Emim TfO > Hmim BF4 > Bmpy BF4. Acomparison of carbon dioxide solubilities in Hmim Tf2N andHmim BF4 clearly shows that CO2 is significantly more solublein Hmim Tf2N than in Hmim BF4. This is consistent withpreviously reported observations that CO2 solubility is higherin RTILs with Tf2N anion than in RTILs with BF4 anion.6 CO2

solubility in the Emim RTILs is highest in Emim Tf2N and

Figure 1. Comparison of the relationship between ∆Uvap and Eavis:

Experimental measurements vs best fit line with slope ) 4.3 (dashed) andEyring prediction36 with slope ) 4.0 (solid). Data were taken fromArmstrong et al.37 ((), Santos et al.38 (b), and Luo et al.39 (9).

δCO2) -0.0535T + 28.26 (9)

lnPP0

) 8

π2

VIL

V

FIL

MWIL

RTH

· ∑n)0

∞1

(2n + 1)2·

[exp(- (2n + 1)2π2Dt

4L2 ) - 1] (10)

Table 1. Experimentally Measured Henry’s Law Constants (H) forCarbon Dioxide in Ionic Liquidsa

H (bar)

RTIL 10 °C 25 °C 40 °C

Bmpy BF4 52 ( 4 60 ( 6 71 ( 14Omim BF4 32 ( 3 43 ( 5 56 ( 3Hmim BF4 42 ( 4 57 ( 4 75.5 ( 0.1Hmim Tf2N 23 ( 1 28.2 ( 0.6 42 ( 3Emim Tf2N 22 ( 1 31.3 ( 0.4 45 ( 6Emim BETI 25 ( 1 33 ( 3 46 ( 7Emim TfA 33 ( 5 43 ( 6 54 ( 3Emim TfO 40.1 ( 0.2 50 ( 12 68 ( 14

a Uncertainty limits represent 95% confidence limits.

Table 2. Comparison of Henry’s Law Constants for CO2 Measuredin This Study to Literature Reports from Others

H (bar)

RTIL T (°C) this work literature report ref

Hmim Tf2N 10 23 ( 1 24.2 6Hmim Tf2N 25 28.2 ( 0.6 31.6 6Hmim Tf2N 25 28.2 ( 0.6 34 49Hmim Tf2N 40 42 ( 3 45.6 6Hmim Tf2N 40 42 ( 3 43 49Emim Tf2N 10 22 ( 1 25.3 48Emim Tf2N 25 31.3 ( 0.4 35.6 48Emim Tf2N 25 31.3 ( 0.4 39 49Emim Tf2N 40 45 ( 6 50 49Emim TfA 25 43 ( 6 55 50Emim TfO 40 68 ( 14 70 22

5848 Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010

Emim BETI, with comparable H values in these ionic liquids.The poorest CO2 solubility among the Emim RTILs wasobserved in Emim TfO. The comparable H values determinedfor CO2 in Emim Tf2N and Emim BETI were counter toexpectations that the additional fluorines (and therefore elec-tronegativity) in the BETI anion would improve CO2 solubilityrelative to the Tf2N RTIL. The difference in CO2 solubilitybetween Emim TfA and Emim TfO was also unexpected, giventhe similar structure in these two anions. A comparison of CO2

solubility in Omim BF4 and Hmim BF4 supports previousobservations that CO2 solubility increases with an increase inthe alkyl chain length on the cation.6,42,43 It is speculated thatthis increase in solubility arises from an increase in free volumeintroduced with the longer alkyl chain.

When expressed as mol CO2/L, solubility is considerablyhigher in Emim Tf2N and Emim TfA when compared to theother ionic liquids. Solubility is lowest in the three ionic liquidswith BF4

- anion, consistent with the trends observed whensolubility is expressed on a mole fraction basis.

RST. To consider the application of RST (eq 6) to theobserved CO2 solubilities in RTILs, solubility parameter valuesfor RTILs were estimated using eq 8. Values for the activationenergy of viscosity were calculated from viscosity valuesreported in the literature and are listed in Table 4. RTIL molarvolume values from the literature were used in these calcula-tions, and these values are also listed in Table 4. In this analysis,we have included results for several other ionic liquids that wereexamined and previously reported by our group.14 The Hilde-brand solubility parameters were determined from these pa-rameters using eq 8 and are listed in Table 5. Examination ofthe values in Table 5 shows that the solubility parameters are

generally insensitive to temperature, consistent with the resultsfrom molecular simulations.44

As noted earlier, energy of vaporization values have beendetermined for several of the ionic liquids examined in thisstudy.37-39 Solubility parameters were calculated for these ionicliquids using reported ∆Uvap values and eq 7. Solubilityparameters have also been determined by Scovazzo and co-workers for selected ionic liquids from surface tension and freeenergy of activation for viscosity.26,27 These values are com-pared to values estimated using the approach that we propose(eq 8) in Table 6. There is generally very good agreementbetween δIL values calculated from ∆Uvap measurements andδIL values calculated in this work from activation energy ofviscosity values. Solubility parameter values estimated usingother approaches (surface tension and free energy of viscosity)are generally larger than the δIL values determined using ourapproach, with the largest values estimated from the free energyof viscosity, as reported by Kilaru and Scovazzo.27

CO2 solubility as a function of the RTIL solubility parameterat 25 °C is shown in Figure 2. When δIL < 25 (J/cm3)1/2, theobserved solubility is inversely proportional to the solubilityparameter. The observed trend can be explained by understand-ing the definition of the solubility parameter from a molecularlevel. Hildebrand defined the solubility parameter as the squareroot of the cohesive energy density, which is related tointermolecular interactions in the pure substance. Hence, CO2

solubility is expected to be a maximum in RTILs with cohesiveenergy density equal to that of CO2. Therefore, RTILs withsolubility parameters close to the solubility parameter for CO2

[12.3 (J/cm3)1/2] at 25 °C are expected to have high CO2

solubility.According to the RST, a semilog plot of Henry’s law constant

of carbon dioxide versus (δIL - δCO2)2 should yield a straight

line at each temperature (eq 7). Plots prepared using thesolubility data measured in this study with the predictions forδIL are shown in Figure 3 for data at 10, 25, and 40 °C. Aspredicted from RST (eq 7), generally, linear plots are observed,

Table 3. CO2 Solubility in Ionic Liquids at 1 bar CO2 Pressurea

mol CO2/mol IL mol CO2/L

RTIL 10 °C 25 °C 40 °C 10 °C 25 °C 40 °C

Bmpy BF4 0.019 ( 0.001 0.017 ( 0.002 0.014 ( 0.003 0.10 ( 0.01 0.089 ( 0.009 0.074 ( 0.014Omim BF4 0.031 ( 0.003 0.023 ( 0.003 0.018 ( 0.001 0.12 ( 0.01 0.093 ( 0.011 0.070 ( 0.003Hmim BF4 0.024 ( 0.002 0.018 ( 0.001 0.013 ( 0.001 0.11 ( 0.01 0.080 ( 0.006 0.060 ( 0.001Hmim Tf2N 0.043 ( 0.002 0.035 ( 0.001 0.024 ( 0.002 0.14 ( 0.01 0.11 ( 0.002 0.073 ( 0.005Emim Tf2N 0.045 ( 0.002 0.032 ( 0.001 0.022 ( 0.003 0.18 ( 0.01 0.13 ( 0.002 0.086 ( 0.011Emim BETI 0.040 ( 0.002 0.030 ( 0.003 0.022 ( 0.003 0.13 ( 0.01 0.099 ( 0.009 0.071 ( 0.011Emim TfA 0.030 ( 0.004 0.023 ( 0.003 0.019 ( 0.001 0.18 ( 0.03 0.14 ( 0.02 0.11 ( 0.006Emim TfO 0.025 ( 0.001 0.020 ( 0.005 0.015 ( 0.003 0.13 ( 0.01 0.11 ( 0.02 0.077 ( 0.016

a Uncertainty limits represent 95% confidence limits.

Table 4. Activation Energy of Viscosity and Molar Volumes for theRTILs Examined in This Studya

VIL (cm3/mol)

RTILEa

vis

(kJ/mol) 10 °C 25 °C 40 °C ref

Bmpy BF4 42 189.0 190.7 192.4viscosity: 51density: 52

Omim BF4 40 253.1 254.7 258.1 viscosity and density: 53Hmim BF4 39 219.8 221.9 224.1 viscosity and density: 53

Hmim Tf2N 31 323.0 324.7 329.5viscosity: 51density: 54

Emim Tf2N 24 255.2 257.8 260.4 viscosity and density: 55Emim BETI 36 305.7 308.8 312.2 viscosity and density: 55Emim TfA 23 185.1 186.7 188.3 viscosity and density: 56Emim TfO 23 171.8 173.5 175.1 viscosity and density: 56

Bmim Tf2N 32 289.0 291.8 294.7viscosity: 15density: 47

Pmmim Tf2N 35 285.3 287.7 290.2viscosity: 15density: 57

Bmpy Tf2N 34 301.3viscosity: 51density: 15

Bmim BF4 35 186.6 188.3 190.1 viscosity and density: 58

a The activation energy of viscosity values were calculated fromviscosity at different temperatures.

Table 5. Hildebrand Solubility Parameters Determined Using Eq 8

δIL (J/cm3)1/2

RTIL 10 °C 25 °C 40 °C

Bmpy BF4 29.8 29.7 29.6Omim BF4 25.2 26.6 26.5Hmim BF4 26.7 27.5 27.4Hmim Tf2N 19.6 19.5 19.4Emim Tf2N 19.4 19.3 19.2Emim BETI 21.7 21.6 21.5Emim TfA 22.1 22.2 22.3Emim TfO 23.1 23.0 22.9Bmim Tf2N 21.0 20.9 20.8Pmmim Tf2N 22.2 22.1 22.0Bmpy Tf2N 21.2Bmim BF4 24.9 24.8 24.7

Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 5849

with slope and intercept values (A and B) listed in Table 7.Observed deviations from linearity may result from complexinteractions between the CO2 and the RTIL that are not capturedby the RST approach. Using eq 8 to estimate δIL from Ea

vis

may also lead to deviations from RST predictions.The fitted values for A and B can be used to estimate values

for the standard state fugacity of CO2 as well as the molar

volume of CO2 as a hypothetical liquid. The standard statefugacity was calculated directly from the fitted values for A (eq6), and these values are included in Table 7, with values rangingfrom 22 bar at 10 °C to 41 bar at 40 °C. Prausnitz and Shaircorrelated low pressure solubility data for a collection of gasesin nine different organic solvents (not ionic liquids) anddeveloped a corresponding states relationship between thereduced fugacity (standard state fugacity relative to the criticalpressure) and the reduced temperature.45 Using this relationship,the standard state fugacity for CO2 was estimated to be 32 barat 10 °C, 48 bar at 25 °C, and 59 bar at 40 °C. The agreementbetween these estimates and the fugacity values determined froma fit of the experimentally determined solubility values isreasonably good and provides further evidence of the validityof the approach used to estimate the ionic liquid solubilityparameters.

The parameter B is proportional to both the molar volume ofCO2 as a hypothetical liquid, VCO2, and �IL

2. With CO2 molefractions in these ionic liquids less than 0.05 (Table 3), it isreasonable to assume �IL ) 1. With this assumption, the molarvolume of the hypothetical liquid was calculated for CO2 ateach temperature, and these values are included in Table 7.Prausnitz and Shair45 report a value of 55 cm3/mol for the liquidmolar volume of CO2. Hildebrand and Scott46 report a value of40 cm3/mol. These values are 5-10 times larger than the valuesdetermined from the fit of the solubility data reported here. Thisagreement is reasonable, given the uncertainty arising from thelinear fit and the assumptions made in deriving the regularsolution model and the approximations involved in estimatingthe solubility parameters for each ionic liquid.

A comparison of experimental and predicted Henry’s lawconstant values is shown in Figure 4, where predicted valueswere determined using A and B values determined at eachtemperature. Excellent agreement is observed between thepredicted and the experimental values. Most of the predictionsfall within 10% of measured values, with all predictions within27% of experimental values. The largest deviation betweenprediction and experiment is found for Emim TfO, withdeviations of 23-27%. It is not clear why this particular ionicliquid might behave differently than the others with respect tointermolecular interactions governing viscosity and CO2 solubility.

The agreement between RST prediction and experimentalobservation in this study (Figure 4) is generally comparable to

Table 6. Hildebrand Solubility Parameters for RTILs Estimated Using Different Approachesa

δIL (J/cm3)1/2

from measured ∆Uvap (eq 7)

RTIL this work ref 38 ref 37 ref 39from surface tensionmeasurements, ref 34

Hansen solubility parameter fromsurface tension measurements, ref 26

from free energy ofactivation of viscosity, 27

Emim Tf2N 19.3 22.8 22.7 21.3 22.7 27.5Bmim Tf2N 20.9 22.9 21.4 19.8 21.3 26.5Hmim Tf2N 19.5 22.9 20.6 19.0 20.6 25.2Bmim BF4 24.8 24.8 26.5Omim BF4 26.6 25.2 26.6 26.6Bmim PF6 22.7 25.1 25.3 29.5Emim BETI 21.6 18.7

a Values are at 25 °C, except those estimated by Kilaru et al.26 and Kilaru and Scovazzo,27 which are at 30 °C.

Figure 2. Solubility parameter vs measured CO2 solubility in various RTILsat 25 °C.

Figure 3. Logarithm of the Henry’s law constant vs the square of the differencein solubility parameters between RTIL and CO2 at 10, 25, and 40 °C.

Table 7. Fitted Parameters in the Regular Solution Model (Eq 6)a

RST parameter 10 °C 25 °C 40 °C

A 3.1 ( 0.2 3.3 ( 0.2 3.7 ( 0.2B × 103 3.4 ( 1.5 3.0 ( 1.3 2.4 ( 1.3fCO2

0(bar) 22 ( 1 27 ( 1 41 ( 1VCO2 (cm3/mol) 8.0 ( 3.5 7.4 ( 3.2 6.2 ( 3.4

a The molar volume of CO2 as a hypothetical liquid was calculatedfrom the fitted values for B, assuming �CO2 ) 1. Uncertainty valuesrepresent 95% confidence intervals.

5850 Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010

agreement reported by others who have used other approachesfor determining solubility parameters for RTILs from differentmeasured properties.26,27,34,37-39 Measuring the activation en-ergy of viscosity involves a relatively simple and inexpensiveapproach for estimating δIL when compared to measuring surfacetension or energy of vaporization. Therefore, the approachpresented here provides a simple yet reasonably accurate meansto predict low pressure solubility of CO2 in RTILs.

Effect of Temperature on Solubility. In all of the testedRTILs, CO2 solubility was found to decrease with increasingtemperature, in agreement with other reports in the literaturefor CO2 solubility in different RTILs. The sensitivity of H totemperature can be related to the partial molar enthalpy andpartial molar entropy due to CO2 absorption:

Values for ∆hjCO2 reflect energetic interactions between CO2 andthe RTIL, while ∆sjCO2 values provide an indication of orderingresulting from absorption of CO2 into the RTIL. Values for∆hjCO2 and ∆sjCO2 were determined from appropriate plots of Hversus T and are listed in Table 8. These values are in generalagreement with values reported by others for the same ionic

liquids.6,10,47-49 A table showing a comparison of values is inthe Supporting Information. As discussed by Finotello et al,49

the negative values for both ∆hjCO2 and ∆sjCO2 are consistentwith expectations developed from thermodynamic argumentsfor relatively high solubility gases.

With data collected at only three temperatures, the uncertaintyin ∆hjCO2 and ∆sjCO2 values is relatively large, making it difficultto draw conclusions about any effect of RTIL structure on theseparameters. However, it does appear that both ∆hjCO2 and ∆sjCO2

are smaller for the two pyridinium-based RTILs (Bmpy BF4

and Bmpy Tf2N) when compared to the other imidazolium-basedRTILs. With the larger ring in the pyridinium cation comparedto imidazolium, the positive cation charge can be moredelocalized, reducing the strength of the interaction betweenthe CO2 and the RTIL, consistent with the smaller values for∆hjCO2. Similarly, the more delocalized charge is also expectedto impact the ordering or structure resulting from introductionof CO2 into the RTIL, yielding smaller values for ∆sjCO2 for thepyridinium-based ionic liquids.

Conclusions

The solubility of carbon dioxide in eight different com-mercially available RTILs was measured at three differenttemperatures using a transient liquid thin film method. Measure-ments were performed at low CO2 pressures, with solubilityreported as the Henry’s law constant for each system. Of thetested ionic liquids, CO2 solubility on a mole fraction basis wasfound to be highest in Hmim Tf2N and lowest in Bmpy BF4.Experiments were performed with four different ionic liquidswith Emim cation. Carbon dioxide solubility was comparablein Emim Tf2N and Emim BETI and lowest in Emim TfO.Consistent with previous reports, the solubility was found toincrease as the length of the alkyl chain on the cation increased.This can be attributed to the increasing free volume and thereduction in cation-anion columbic forces that result with alonger alkyl chain length.

RST was applied to interpret CO2 solubility with RTILsolubility parameters estimated using Eyring’s reaction ratetheory to relate the RTIL solubility parameter to the activationenergy of viscosity. Solubility parameters estimated using thisapproach were found to be in very good agreement with valuesdetermined from literature values for the energy of vaporization.Carbon dioxide solubility was found to be inversely proportionalto the ionic liquid solubility parameter and correlated well withthe square of the difference in solubility parameter between ionicliquid and carbon dioxide.

The temperature sensitivity of the Henry’s law constant wasused to determine the partial molar enthalpy and partial molarentropy of CO2 absorption. Values for ∆hjCO2 and ∆sjCO2 werenot strongly dependent on ionic liquid structure for the ionicliquids with imidazolium cation. A comparison of ∆hjCO2 and∆sjCO2 in pyridinium-based ionic liquids to values in imidazo-lium-based ionic liquids shows smaller values for the ionicliquids with pyridinium cation, indicating weaker RTIL-CO2

interactions for the pyridinium-based ionic liquids.The transient thin liquid film technique used to determine

gas solubility also yields the infinite dilution diffusion coefficientfor carbon dioxide in the tested ionic liquids. Diffusioncoefficient values will be reported and discussed in a subsequentpublication.41

Acknowledgment

We acknowledge the financial support from the NationalScience Foundation through Grant No. CTS-0522589.

Figure 4. Comparison between the predicted Henry’s law constant and themeasured Henry’s law constant for CO2 in a variety of ionic liquids. Valueswere predicted using RST with the RTIL solubility parameter estimatedfrom the activation energy of viscosity (eq 8) and A and B values fromTable 7 for each temperature (eq 6).

Table 8. Partial Molar Enthalpy and Partial Molar Entropy ofAbsorption for CO2 in RTILsa

RTIL ∆hjCO2 (kJ/mol) ∆sjCO2 (J/mol K)

Bmpy BF4 -8 ( 3 -27 ( 10Omim BF4 -13 ( 3 -42 ( 12Hmim BF4 -14.6 ( 0.6 -50 ( 2Hmim Tf2N -14.7 ( 0.7 -50 ( 2Emim Tf2N -18 ( 3 -59 ( 10Emim BETI -15 ( 4 -50 ( 13Emim TfA -12 ( 4 -41 ( 15Emim TfO -13 ( 5 -42.6 ( 0.2Bmim Tf2N -12 ( 4 -40 ( 13Pmmim Tf2N -11 ( 1 -36 ( 5Bmpy Tf2N -10.4 ( 0.9 -34 ( 3Bmim BF4 -14 ( 1 -44 ( 5

a Values for Bmim Tf2N, Pmmim Tf2N, Bmpy Tf2N, and Bmim BF4

were reported by Hou and Baltus.14 Uncertainty values represent 95%confidence intervals.

∆hjCO2) R( ∂ln H

∂(1/T)) (11)

∆sjCO2) -R(∂ln H

∂ln T )P(12)

Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 5851

Supporting Information Available: Tables of partial molarenthalpy and partial molar entropy of absorption for CO2 inRTILs. This material is available free of charge via the Internetat http://pubs.acs.org.

Nomenclature

A ) regular solution theory constant in eq 6B ) regular solution theory constant in eq 6D ) diffusion coefficient of target gas in RTIL (m2/s)Ea

vis ) activation energy for viscosity (kJ/mol)fCO2

0 ) fugacity of pure CO2 at standard state conditions (bar)fCO2

G ) fugacity of pure CO2 in the gas phase at system temperatureand pressure (bar)

fCO2G ) fugacity of CO2 in RTIL at system temperature and pressure

(bar)H ) Henry’s law constant (bar)∆hjCO2 ) partial molar enthalpy of absorption for CO2 in RTIL

(kJ/mol)L ) thickness of RTIL film (m)MWIL ) molecular weight of RTIL (g/mol)P ) gas pressure (bar)P0 ) gas pressure at t ) 0 (bar)R ) universal gas constant (8.314 Pa m3 mol-1 K-1)∆sjCO2 ) partial molar entropy of absorption for CO2 in RTIL

(kJ/mol K)t ) time (s)T ) temperature (°C or K)∆Uvap ) internal energy change of vaporization (kJ/mol)V ) molar volume (m3/mol)V ) volume of gas (m3)VCO2 ) molar volume of hypothetical liquid CO2 (cm3/mol)VIL ) molar volume of RTIL (m3/mol)VIL ) volume of RTIL sample (m3)xCO2 ) mole fraction of CO2 in RTILγCO2 ) activity coefficient of CO2 in RTILδ ) solubility parameter [(J/cm3)1/2]δCO2 ) solubility parameter of CO2 [(J/cm3)1/2]δIL ) solubility parameter of RTIL [(J/cm3)1/2]FIL ) density of RTIL (g/cm3)�IL ) volume fraction of RTIL

Literature Cited

(1) Bara, J. E.; Carlisle, T. K.; Gabriel, C. J.; Camper, D.; Finotello,A.; Gin, D. L.; Noble, R. D. Guide to CO2 separations in imidazolium-based room-temperature ionic liquids. Ind. Eng. Chem. Res. 2009, 48, 2739.

(2) Huang, J. H.; Ruther, T. Why are ionic liquids attractive for CO2

absorption? An overview. Aust. J. Chem. 2009, 62, 298.(3) Maiti, A. Theoretical screening of ionic liquid solvents for carbon

capture. ChemSusChem 2009, 2, 628.(4) Raeissi, S.; Peters, C. J. A potential ionic liquid for CO2-separating

gas membranes: Selection and gas solubility studies. Green Chem. 2009,11, 185.

(5) Ciferno, J. P.; Fout, T. E.; Jones, A. P.; Murphy, J. T. Capturingcarbon from existing coal-fired power plants. Chem. Eng. Prog. 2009, 105,33.

(6) 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.

(7) Shiflett, M. B.; Yokozeki, A. Solubilities and diffusivities of carbondioxide in ionic liquids: [bmim][PF6] and [bmim][BF4]. Ind. Eng. Chem.Res. 2005, 44, 4453.

(8) Shiflett, M. B.; Harmer, M. A.; Junk, C. R.; Yokozeki, A. Solubilityand diffusivity of 1,1,1,2-tetrafluoroethane in room-temperature ionic liquids.Fluid Phase Equilib. 2006, 242, 220.

(9) Shiflett, M. B.; Yokozeki, A. Solubility of CO2 in room temperatureionic liquid [hmim][Tf2N]. J. Phys. Chem. B 2007, 111, 2070.

(10) Anthony, J. L.; Maginn, E. J.; Brennecke, J. F. Solubilities andthermodynamic properties of gases in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate. J. Phys. Chem. B 2002, 106, 7315.

(11) Baltus, R. E.; Culbertson, B. H.; Dai, S.; Luo, H. M.; DePaoli,D. W. Low-pressure solubility of carbon dioxide in room-temperature ionicliquids measured with a quartz crystal microbalance. J. Phys. Chem. B 2004,108, 721.

(12) Blanchard, L. A.; Gu, Z. Y.; Brennecke, J. F. High-pressure phasebehavior of ionic liquid/CO2 systems. J. Phys. Chem. B 2001, 105, 2437.

(13) Kamps, A. P. S.; Tuma, D.; Xia, J. Z.; Maurer, G. Solubility ofCO2 in the ionic liquid [bmim][PF6]. J. Chem. Eng. Data 2003, 48, 746.

(14) Hou, Y.; Baltus, R. E. Experimental measurement of the solubilityand diffusivity of CO2 in room-temperature ionic liquids using a transientthin-liquid-film method. Ind. Eng. Chem. Res. 2007, 46, 8166.

(15) Hou, Y. Experimental Measurement of Solubility and DiffusiVityof CO2 in Room Temperature Ionic Liquids; M.S. Thesis; ClarksonUniversity: Potsdam, NY, 2006.

(16) Moganty, S. S. Thermodynamic, Transport and ElectrochemicalProperties of Room Temperature Ionic Liquids; Ph.D. Thesis; ClarksonUniversity: Potsdam, NY, 2009.

(17) Shiflett, M. B.; Yokozeki, A. Solubility and diffusivity of hydrof-luorocarbons in room-temperature ionic liquids. AIChE J. 2006, 52, 1205.

(18) Yokozeki, A.; Shiflett, M. B. Ammonia solubilities in room-temperature ionic liquids. Ind. Eng. Chem. Res. 2007, 46, 1605.

(19) Eike, D. M.; Brennecke, J. F.; Maginn, E. J. Predicting infinite-dilution activity coefficients of organic solutes in ionic liquids. Ind. Eng.Chem. Res. 2004, 43, 1039.

(20) Shi, W.; Maginn, E. J. Molecular simulation and regular solutiontheory modeling of pure and mixed gas absorption in the ionic liquid 1-n-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([hmim][Tf2N]).J. Phys. Chem. B 2008, 112, 16710.

(21) Camper, D.; Scovazzo, P.; Koval, C.; Noble, R. Gas solubilities inroom-temperature ionic liquids. Ind. Eng. Chem. Res. 2004, 43, 3049.

(22) Camper, D.; Becker, C.; Koval, C.; Noble, R. Low pressurehydrocarbon solubility in room temperature ionic liquids containingimidazolium rings interpreted using regular solution theory. Ind. Eng. Chem.Res. 2005, 44, 1928.

(23) Camper, D.; Becker, C.; Koval, C.; Noble, R. Diffusion andsolubility measurements in room temperature ionic liquids. Ind. Eng. Chem.Res. 2006, 45, 445.

(24) Carlisle, T. K.; Bara, J. E.; Gabriel, C. J.; Noble, R. D.; Gin, D. L.Interpretation of CO2 solubility and selectivity in nitrile-functionalized room-temperature ionic liquids using a group contribution approach. Ind. Eng.Chem. Res. 2008, 47, 7005.

(25) Scovazzo, P.; Camper, D.; Kieft, J.; Poshusta, J.; Koval, C.; Noble,R. Regular solution theory and CO2 gas solubility in room-temperature ionicliquids. Ind. Eng. Chem. Res. 2004, 43, 6855.

(26) Kilaru, P. K.; Condemarin, P. A.; Scovazzo, P. Correlations of low-pressure carbon dioxide and hydrocarbon solubilities in imidazolium-,phosphonium-, and ammonium-based room-temperature ionic liquids. Part1. Using surface tension. Ind. Eng. Chem. Res. 2008, 47, 900.

(27) Kilaru, P. K.; Scovazzo, P. Correlations of low-pressure carbondioxide and hydrocarbon solubilities in imidazolium-, phosphonium-, andammonium-based room-temperatuire ionic liquids. Part 2. Using activationenergy of viscosity. Ind. Eng. Chem. Res. 2008, 47, 910.

(28) Glasstone, S.; Laidler, K.; Eyring, H. The Theory of Rate Processes;McGraw Hill: New York, NY, 1941.

(29) Hildebrand, J. H.; Scott, R. L. The Solubility of Electrolytes; DoverPublications: New York, NY, 1964.

(30) Hildebrand, J. H.; Scott, R. L. Regular and Related Solutions; vanNostrand Reinhold: New York, NY, 1970.

(31) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. d. MolecularThermodynamics of Fluid Phase Equilibria, 3rd ed.; Prentice Hall: UpperSaddle River, NJ, 1999.

(32) Takamatsu, T. The application of regular solution theory to theion pair systems. Bull. Chem. Soc. Jpn. 1974, 47, 1287.

(33) Lee, S. H.; Lee, S. B. The Hildebrand solubility parameters,cohesive energy densities and internal energies of 1-alkyl-3-methylimida-zolium-based room temperature ionic liquids. Chem. Commun. 2005, 3469.

(34) Jin, H.; O’Hare, B.; Dong, J.; Arzhantsev, S.; Baker, G. A.; Wishart,J. F.; Benesi, A. J.; Maroncelli, M. Physical properties of ionic liquidsconsisting of the 1-butyl-3-methylimidazolium cation with various anionsand the bis(trifluoromethylsulfonyl)imide anion with various cations. J. Phys.Chem. B 2008, 112, 81.

(35) Kincaid, J.; Eyring, H.; Stern, A. Theory of absolute reaction ratesand its application to viscosity and diffusion in liquid state. Chem. ReV.1941, 28, 310.

(36) Ewell, R.; Eyring, H. Theory of the viscosity of liquids as a functionof temperature and pressure. J. Chem. Phys. 1937, 5, 726.

5852 Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010

(37) Armstrong, J. P.; Hurst, C.; Jones, R. G.; Licence, P.; Lovelock,K. R. J.; Satterley, C. J.; Villar-Garcia, I. J. Vapourisation of ionic liquids.Phys. Chem. Chem. Phys. 2007, 9, 982.

(38) Santos, L. M. N. B. F.; Lopes, J. N. C.; Coutinho, J. A. P.;Esperanca, J. M. S. S.; Gomes, L. R.; Marrucho, I. M.; Rebelo, L. P. N.Ionic liquids: First direct determination of their cohesive energy. J. Am.Chem. Soc. 2007, 129, 284.

(39) Luo, H. M.; Baker, G. A.; Dai, S. Isothermogravimetric determi-nation of the enthalpies of vaporization of 1-alkyl-3-methylimidazoliumionic liquids. J. Phys. Chem. B 2008, 112, 10077.

(40) Barton, A. CRC Handbook of Solubility Parameters and OtherCohesion Parameters; CRC Press: Boca Raton, FL, 1983.

(41) Moganty, S. S.; Baltus, R. E. Diffusion of carbon dioxide in roomtemperature ionic liquids. Ind. Eng. Chem. Res. 2009, to be submitted.

(42) Aki, S. N. V. K.; Mellein, B. R.; Saurer, E. M.; Brennecke, J. F.High-pressure phase behavior of carbon dioxide with imidazolium-basedionic liquids. J. Phys. Chem. B 2004, 108, 20355.

(43) Raeissi, S.; Peters, C. J. Carbon dioxide solubility in the homologous1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide family.J. Chem. Eng. Data 2009, 54, 382.

(44) Morrow, T. I.; Maginn, E. J. Molecular dynamics study of the ionicliquid 1-n-butyl-3-methylimidazolium hexafluorophosphate. J. Phys. Chem.B 2002, 106, 12807.

(45) Prausnitz, J. M.; Shair, F. H. A thermodynamic correlation of gassolubilities. AIChE J. 1961, 7, 682.

(46) Hildebrand, J. H.; Scott, R. L. Solubility of Non-Electrolytes, 3rded.; Reinhold Publishing Corp.: New York, NY, 1950.

(47) 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.

(48) 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 ionicliquids. J. Am. Chem. Soc. 2004, 126, 5300.

(49) Finotello, A.; Bara, J. E.; Camper, D.; Noble, R. D. Room-temperature ionic liquids: Temperature dependence of gas solubilityselectivity. Ind. Eng. Chem. Res. 2008, 47, 3453.

(50) Shiflett, M. B.; Yokozeki, A. Phase behavior of carbon dioxide inionic liquids: [emim][acetate], [emim][trifluoroacetate], and [emim][acetate]plus [emim][trifluoroacetate] mixtures. J. Chem. Eng. Data 2009, 54, 108.

(51) Crosthwaite, J. M.; Muldoon, M. J.; Dixon, J. K.; Anderson, J. L.;Brennecke, J. F. Phase transition and decomposition temperatures, heatcapacities and viscosities of pyridinium ionic liquids. J. Chem. Thermodyn.2005, 37, 559.

(52) Garcia-Miaja, G.; Troncoso, J.; Romani, L. Density and heatcapacity as a function of temperature for binary mixtures of 1-butyl-3-methylpyridinium tetrafluoroborate plus water, plus ethanol, and plusnitromethane. J. Chem. Eng. Data 2007, 52, 2261.

(53) Sanmamed, Y. A.; Gonzalez-Salgado, D.; Troncoso, J.; Cerdeirina,C. A.; Romani, L. Viscosity-induced errors in the density determination ofroom temperature ionic liquids using vibrating tube densitometry. FluidPhase Equilib. 2007, 252, 96.

(54) Kumelan, J.; Kamps, I. P. S.; Tuma, D.; Maurer, G. Solubility ofCO2 in the ionic liquid [hmim][Tf2N]. J. Chem. Thermodyn. 2006, 38, 1396.

(55) Shiflett, M. B.; Harmer, M. A.; Junk, C. P.; Yokozeki, A. Solubilityand diffusivity of difluoromethane in room-temperature ionic liquids.J. Chem. Eng. Data 2006, 51, 483.

(56) Rodriguez, H.; Brennecke, J. F. Temperature and compositiondependence of the density and viscosity of binary mixtures of water plusionic liquid. J. Chem. Eng. Data 2006, 51, 2145.

(57) Fredlake, C. P.; Crosthwaite, J. M.; Hert, D. G.; Aki, S. N. V. K.;Brennecke, J. F. Thermophysical properties of imidazolium-based ionicliquids. J. Chem. Eng. Data 2004, 49, 954.

(58) Jacquemin, J.; Husson, P.; Padua, A. A. H.; Majer, V. Density andviscosity of several pure and water-saturated ionic liquids. Green Chem.2006, 8, 172.

ReceiVed for reView November 19, 2009ReVised manuscript receiVed April 12, 2010

Accepted April 28, 2010

IE901837K

Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 5853