Measurement and Prediction of Vapor−Liquid Equilibrium of Aqueous

Ind. Eng. Chem. Res. 2010, 49, 3893–3901

3893

Measurement and Prediction of Vapor-Liquid Equilibrium of Aqueous 1-Ethyl-3-methylimidazolium-Based Ionic Liquid Systems Luke D. Simoni, Lindsay E. Ficke, Caitlin A. Lambert, Mark A. Stadtherr, and Joan F. Brennecke* Department of Chemical and Biomolecular Engineering, UniVersity of Notre Dame, Notre Dame, Indiana 46556

Isothermal vapor-liquid equilibria were determined for two binary ionic liquid + water systems, from 323.3 to 368.2 K, and water mole fractions greater than 0.5. The ionic liquids used were 1-ethyl-3-methylimidazolium trifluoromethanesulfonate and 1-ethyl-3-methylimidazolium trifluoroacetate. In addition, predictive thermodynamic modeling of the vapor-liquid equilibrium was performed by correlating the nonrandom two-liquid,39 universal quasi-chemical,40 and electrolyte-NRTL41 models to previously measured excess enthalpy and infinite dilution activity coefficient data from the literature. For each of the systems studied at least two of the models provided adequate predictions of vapor pressure and water activity coefficients. The good predictions of vapor-liquid equilibria by these common activity coefficient models lead us to favor excess enthalpy and infinite dilution activity coefficient data over vapor-liquid equilibria data, since predictions of excess enthalpies from vapor-liquid equilibria are not satisfactory. Introduction Ionic liquids (ILs) as absorbents in absorption refrigeration systems present the possibility of overcoming some of the safety and environmental concerns of current systems. In general, absorption refrigeration is attractive since electrical energy is replaced with low value heat energy. Conventional absorption refrigeration systems use LiBr + water (which is corrosive and presents solidification problems) or water + ammonia (which is toxic and an odor nuisance). The problems associated with the current systems could potentially be avoided if they were replaced with IL + water, IL + CO2, or IL + HFC systems. ILs have many favorable characteristics including low vapor pressure, good thermal stability as liquids over a large temperature range, and the ability to be designed to dissolve compounds of interest. Many ILs are completely miscible with water, which leads our focus to investigating ILs + water for absorption refrigeration applications. The coefficient of performance (COP) is the cooling capacity divided by the energy input to the absorption refrigeration cycle, and it can be used to gauge the potential success of IL+ water systems. COPs are much lower for absorption refrigeration systems than vapor compression systems, but use low grade heat instead of electricity. Thermodynamic measurements and/ or predictive modeling of vapor-liquid equilibria and heats of mixing are needed to evaluate the IL + water systems. We have extensively studied three IL + water systems for absorption refrigeration applications: 1-ethyl-3-methylimidazolium ethylsulfate, [emim][EtSO4]; 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (or triflate), [emim][OTf]; and 1-ethyl3-methylimidazolium trifluoroacetate, [emim][TFA]. The structures and abbreviations of the ILs are shown in Table 1. Our group has reported both pure and mixture densities, viscosities, heat capacities, and excess enthalpies for all three systems.1,2 Many other groups have also reported densities, viscosities, surface tensions, heat capacities, vapor-liquid equilibria (binary and ternary), infinite dilution activity coefficients, glass transition temperatures, melting temperatures, conductivities, and other derived thermodynamic properties of these ILs with various

solvents.3-23 Three groups have reported vapor-liquid equilibria (VLE) for the [emim][EtSO4] + water system;3-5 therefore, the data collected by our group for that system, which is in agreement with the literature, is not presented here. Orchille´s et al. has presented isobaric binary VLE data for [emim][OTf] + water at 100 kPa,24 which is a good complement to the isothermal data presented here. Domanska et al. reports the infinite dilution activity coefficients for [emim][TFA] + water,9 and that data is of particular interest to this work. No groups that we are aware of have reported VLE at the system conditions used for the two IL + water systems presented here. Although there are no publications that we are aware of that use excess enthalpy (HE) data to predict VLE of IL + solvent systems, there have been activity coefficient models adjusted to fit HE data at infinite dilution.25 More relevant to the HE correlations in this work, activity coefficient models have been fit to HE data for conventional systems in the literature.26 There have been a number of publications that correlate and predict VLE and HE of IL + (mixed) solvent (binary and multicomponent) systems, primarily using group contribution models (e.g., versions of UNIFAC).27-32 However, they do not cover the systems addressed here. To evaluate ILs for various applications, VLE is used to determine activity coefficients, which account for the deviations of the mixtures from ideal behavior. In this work, new VLE was obtained for two IL + water binary mixtures ([emim][OTf] + water and [emim][TFA] + water) and predictive modeling was performed with three well-studied activity coefficient Table 1. IL Structures and Abbreviations

* To whom correspondence should be addressed. Tel.: (574) 6315847. Fax: (574) 631-8366. E-mail: [email protected]. 10.1021/ie9017868  2010 American Chemical Society Published on Web 03/22/2010

3894

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

models. Specifically, HE and infinite dilution activity coefficient data from the literature have been correlated with the NRTL, UNIQUAC, and electrolyte-NRTL models and used to predict vapor pressures and activity coefficients of the three aforementioned systems for comparison with experimental VLE data. Experimental Section Chemicals. The ILs used for the VLE measurements were purchased from Solvent Innovations ([emim][OTf]) and Merck KGaA ([emim][TFA]), both of which had a purity of >99%, and the samples were used as received except for drying. Highpurity water, deionized through a Milli-Q water system, was used for all the experiments. Vapor-Liquid Equilibria Measurements. The VLE measurements were performed using a Fischer Labodest apparatus (model 602/D), which is an all-glass dynamic recirculating still equipped with a Cottrell pump. The operating pressures and temperatures are 0.25-400 kPa and up to 523.2 K, respectively. The apparatus has been described in detail in the literature.33,34 The equilibrium temperature was measured with a Temperaturmesstechnik Geraberg GmbH resistance thermometer (type WK 93). Although the uncertainty of the resistance thermometer is (0.01 °C, we believe that the overall uncertainty in the temperature measurement is (0.5 °C, due to slight variation in impurities in different ionic liquids and fluctuation owing to boiling and recirculation in the still. The temperature accuracy was verified with boiling water and the method was verified by reproducing organic binary systems (i.e., 2-propanol + water and 1,3-propanediol + water) over the full range of pressures.35-38 The pressure of the system was measured with a WIKA pressure transmitter (model P-10) with an accuracy of (2.3 mbar. Isothermal VLE data was determined by setting the temperature indirectly by adjusting vacuum and pressure line throttle valves until the system equilibrated to the desired temperature within experimental uncertainty. Equilibrium was assumed when the liquid and vapor temperatures were constant for 30 min or longer. We were only able to acquire VLE data for mole fractions of water from approximately 0.5 to 1 because of temperature instability at lower water mole fractions, likely due to the higher viscosity of the more concentrated IL + water mixtures. The liquid phase was sampled to determine the binary mixture composition by density, measured with an Anton Parr DMA4500 density meter with an accuracy of (5× 10-5 g · cm-3. Densities of the binary mixtures used in this study were determined previously.2 The maximum uncertainty of the composition correlation (in terms of mole fraction) in the composition range of interest for [emim][OTf] + water was (0.014 and for [emim][TFA] + water was (0.023. It is important to note that the uncertainty in the composition decreases dramatically with increasing water mole fraction. Modeling. In this work, we fit the parameters in simple activity coefficient models to HE and the best available infinite dilution activity coefficient (γ∞) data. For each model, we fit only two binary interaction parameters for each binary IL (1) + water (2) system. Obviously, a better fit could be achieved using a model with more adjustable parameters. However, we wish to use as simple a model as possible to predict the IL + water VLE. Below we demonstrate that fitting the models’ parameters to excess enthalpy and infinite dilution activity coefficient data provides adequate VLE predictions. Conversely, predicting the excess enthalpy (HE), which is a temperature derivative of the excess Gibbs energy, from correlation of VLE (activity coefficient) data is not satisfactory, as shown in the

Modeling Results section. If experimental infinite dilution activity coefficient data are not available for a particular system, we choose published experimental infinite dilution activity coefficients of water in a chemically similar IL (e.g., an IL with a slightly longer alkyl chain on the imidazolium-based cation) or published predicted values (e.g., activity coefficients of the system extrapolated to infinite dilution). In this work, we use well studied conventional and electrolyte activity coefficient models, namely the nonrandom two-liquid (NRTL),39 universal quasi-chemical (UNIQUAC),40 and electrolyte-NRTL (eNRTL) models.41 Details and relevant expressions for these models are given in the Supporting Information. For the binary systems in question, the binary interaction parameters of these local composition models are the adjustable parameters, ∆θ12 and ∆θ21. The following is the objective function used for model parameter estimation: 1 min obj ) ∆θ12,∆θ21 nHE

∑g

(

E HE* i - Hi

HE

i

HE* i 1 nγ2∞

)

2

+

∑ i

(

gγ2∞

∞ γ∞* 2,i - γ2,i

γ∞* 2,i

)

2

(1)

In eq 1, quantities marked by an asterisk denote an experimental property, nk denotes the number of experimental data points of property k, and gk denotes the weighting coefficient given to the terms corresponding to property k. In this work, we give equal weighting to the excess enthalpy and infinite dilution activity coefficient data; that is, gHE ) gγ2∞ ) 1. In subsequent work, these weighting coefficients may be optimized for more accurate VLE prediction. The NRTL, UNIQUAC, and eNRTL expressions for HE and activity coefficient (γ) are given in the Supporting Information. HE and γ are related to excess Gibbs energy (GE) as follows:

(

HE ) -RT2

∂(GE /RT) ∂T

)

P,x_

(2)

and ln γ∞2 )

(

∂(nTGE /RT) ∂n2

) |

(3)

T,P,n1 x2f0

where nT is the total number of moles present in solution, ni is the number of moles of species i, R is the gas constant, and T is the absolute temperature. Once the binary interaction parameters have been fit using the above expressions (eqs 1 through 3), the models are used to calculate activity coefficients, ln γ2 )

(

∂(nTGE /RT) ∂n2

)

(4)

T,P,n1

in order to predict the VLE of the system. Although water is a very nonideal component, we assume that the water vapor is an ideal gas because the total pressures are so small ( [BF4]- > [EtSO4]- > [lactate]- > [CH3SO4]- > [glycolate]- > [(CH3)2PO4]-.4,28,30,32,43,44 The activity coefficients for [emim][OTf] + water and [emim][TFA] + water show similar behavior to [emim][BF4] and [emim][EtSO4], respectively. Modeling Results. As described above, the thermodynamic modeling of the IL (1) + water (2) systems involves both (a) correlation of the data by fitting the parameters in the models and (b) prediction of the VLE using the models. The fitting of the parameters in the models is done with literature excess enthalpy data1 and infinite dilution activity coefficients.4,9,45 By minimizing the objective function (eq 1) with a rigorous global minimization routine, based on an interval-Newton approach, we can find the global minimum with complete certainty.46 The model predictions simply use the parameters fit to the data to calculate the activity coefficients and pressures according to eq 5. The results are shown in the sections below. As noted above, the alternate approach of correlating VLE data and using the models to predict HE does not provide satisfactory results. The predictions often lack even qualitative agreement with the experimental data. As an example, Figure 5 is a plot of HE predictions using the NRTL, UNIQUAC, and eNRTL models for the [emim][TFA] + water system. The two adjustable binary interaction parameters, ∆θ12 and ∆θ21, in each model were simultaneously fit to the VLE data presented above and water infinite dilution activity coefficients from the literature.9 Fortuitously, the NRTL predictions are fairly good, but

3896

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

Table 2. Isothermal Experimental Vapor-Liquid Equilibria for the Binary [emim][OTf] (1) + Water (2) System, at Selected Temperatures and Different Mole Fractions of Water (x2) Including the Uncertainties of the Activity Coefficients ((δγ2) x2

P (mbar)

0.978 0.946 0.922 0.846 0.520

121 118 116 108 59

0.979 0.956 0.923 0.835 0.749 0.519

195 192 188 174 156 97

0.979 0.959 0.924 0.835 0.750 0.495

305 301 294 271 245 138

Table 3. Isothermal Experimental Vapor-Liquid Equilibria for the Binary [emim][TFA] (1) + Water (2) System, at Selected Temperatures and Different Mole Fractions of Water (x2) Including the Uncertainties of the Activity Coefficients ((δγ2)

γ2

(δγ2

x2

P (mbar)

0.997 1.011 1.021 1.032 0.923

0.02 0.02 0.02 0.03 0.06

1.000 0.988 0.953 0.857 0.808 0.737 0.651

161 154 146 124 111 86 63

0.999 1.001 1.020 1.045 1.044 0.931

0.02 0.02 0.02 0.02 0.02 0.05

0.998 1.006 1.018 1.040 1.046 0.895

0.01 0.01 0.01 0.01 0.02 0.05

1.000 0.943 0.928 0.866 0.817 0.829 0.809 0.726 0.639 0.497

385 356 349 308 278 286 269 212 156 72

0.999 0.989 0.944 0.914 0.822 0.796 0.744 0.663 0.523

576 566 534 512 431 394 334 255 132

1.000 0.984 0.942 0.909 0.828 0.815 0.735 0.684 0.647 0.598 0.544

844 841 782 755 621 584 485 414 357 288 212

323.3 K

343.3 K

353.3 K 465 457 448 429 285

0.997 1.004 1.013 1.026 0.994

0.01 0.01 0.01 0.01 0.03

0.997 0.999 1.012 1.027 0.968

0.01 0.01 0.01 0.01 0.02

363.3 K 0.988 0.968 0.930 0.877 0.615

693 680 661 634 419

(δγ2

1.022 0.992 0.979 0.919 0.872 0.746 0.616

0.02 0.02 0.02 0.04 0.05 0.05 0.04

0.999 0.983 0.976 0.924 0.886 0.898 0.864 0.758 0.634 0.375

0.01 0.01 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03

1.000 0.991 0.980 0.970 0.908 0.857 0.778 0.667 0.438

0.01 0.01 0.01 0.01 0.03 0.03 0.03 0.02 0.02

0.999 1.012 0.983 0.984 0.887 0.849 0.782 0.717 0.653 0.569 0.460

0.01 0.01 0.01 0.01 0.03 0.03 0.03 0.02 0.02 0.02 0.02

328.3 K

333.3 K

0.982 0.959 0.931 0.881 0.604

γ2

the UNIQUAC and eNRTL predictions lack even qualitative agreement with the experimental data. Similar results are shown for HE predictions for the [emim][OTf] + water system in Figure 6, where NRTL and eNRTL are inaccurate and the UNIQUAC predictions again lack even qualitative agreement with experimental data. However, please note that [emim][OTf] + water is an endothermic system, which is difficult to model under any circumstances. Correlations of Excess Enthalpy and Infinite Dilution Activity Coefficient Data. The parameters in the NRTL, UNIQUAC, and eNRTL models were obtained by fitting two binary interaction parameters to HE and γ2∞ data. Previously, our group measured HE data at 313.15, 323.15, 333.15, and 348.15 K for IL (1) + water (2) systems with [emim][EtSO4], [emim][OTf] and [emim][TFA].1 The only experimental (measured by gas chromotography) γ∞2 data available in the literature for water in these ILs are for [emim][TFA].9 We used predicted γ∞2 values for water in [emim][EtSO4] from the literature, where VLE data were extrapolated to infinite dilution.5 Since there are no γ2∞ values or VLE data in the literature for water in [emim][OTf], we used published γ2∞ experimental values for a chemically similar IL, 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([bmim][OTf]).45 In fact, the difference between γ2∞ values for ethanol and methanol in both [bmim][OTf]45 and [emim][OTf]23 decreases with decreasing alcohol alkyl chain length, where for methanol, γ2∞ ) 0.70 in [emim][OTf] at 323.15 K and γ2∞ ) 0.669 in [bmim][OTf] at 318.15 K. Thus, it can be inferred that the γ2∞ values of water in [emim][OTf] and [bmim][OTf] are likely very similar. Further

348.2 K

358.2 K

368.2 K

comparison with γ∞2 values of water in [hmim][OTf] strengthens the basis of our decision.47 Table 4 contains the γ∞2 values from literature sources used in this work. Since the values listed in Table 4 are not necessarily at the same temperatures as the HE

Figure 5. Experimental and predicted HE for [emim][TFA] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 313.15; 9, 323.15; 2, 333.15; [, 348.15 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrow corresponds to increasing temperature. Note that the eNRTL model predicts virtually no temperature dependence.

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

Figure 6. Experimental and predicted HE for [emim][OTf] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 313.15; 9, 323.15; 2, 333.15; [, 348.15 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrow corresponds to increasing temperature.

3897

Figure 8. UNIQUAC parameters for IL (1) + water (2) systems: b, [emim][EtSO4]; 9, [emim][OTf]; 2, [emim][TFA]. The solid lines represent the linear regressions, and the black and open symbols represent ∆u12 and ∆u21, respectively.

Table 4. Activity Coefficients of Water at Infinite Dilution Obtained from Literature Data system (IL/water) a

temp (K)

[emim][EtSO4]

310 320 330 340 350 360 328.15 338.15 348.15 358.15 368.15

0.2262 0.237 0.2476 0.2579 0.2681 0.3079

[emim][OTf]b

[emim][TFA]c

0.809 0.776 0.747 0.721 0.696

0.143 0.152 0.159

Figure 9. eNRTL parameters for IL (1) + water (2) systems: b, [emim][EtSO4]; 9, [emim][OTf]; 2, [emim][TFA]. The solid lines represent the linear regressions, and the black and open symbols represent ∆g12 and ∆g21, respectively.

a Extrapolated values by Wang et al. (2007) VLE data.5 b Doman´ska and Marciniak (2008) experimental values for water in [bmim][TfO].45 c Doman´ska and Marciniak (2007).9

Figure 7. NRTL parameters for IL (1) + water (2) systems: b, [emim][EtSO4]; 9, [emim][OTf]; 2, [emim][TFA]. The solid lines represent the linear regressions, and the black and open symbols represent ∆g12 and ∆g21, respectively.

γ2∞

data, we linearly regressed ln with respect to 1/T in order to interpolate and extrapolate the values. Parameter estimation was performed at each temperature at which HE data were available. For all three models, the binary interaction parameters, fit using eq 1, are linearly dependent on temperature. This is shown in Figures 7, 8, and 9, which contain the NRTL, UNIQUAC, and eNRTL parameters for all systems studied. The parameters shown represent solution families corresponding to global minima of eq 1. It should be noted that the parameters did not show a clear dependence on temperature for the approach where the VLE and γ2∞ data were fit and used to predict excess enthalpies. Figures 10, 11, and 12 compare the experimental HE data with the model correlations for the three IL (1) + water (2)

Figure 10. Experimental data and model results for HE of [emim][EtSO4] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 313.15; 9, 323.15; 2, 333.15; [, 348.15 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model results, respectively. The arrows correspond to increasing temperature.

systems ([emim][EtSO4], [emim][OTf] and [emim][TFA]). For the figures both HE and γ2∞ data were used to determine the parameters in the models. Obviously, better representation of the HE data can be obtained if only the HE data is used to fit the parameters. This is demonstrated in Table 5, where we compare the absolute average relative deviations (AARD%) of the excess enthalpies with and without γ2∞ values used in the parameter estimation for all the models and systems studied, according to the following equation: 100 AARD% ) nHE

∑ |H nHE

i)0

- HE HE*

E*

|

(6)

Here an asterisk denotes an experimental quantity and nHE is the number of experimental HE data points. Clearly, we see that

3898

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

Figure 11. Experimental data and model results for HE of [emim][OTf] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 313.15 K; 9, 323.15 K; 2, 333.15 K; [, 348.15 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model results, respectively. The arrows correspond to increasing temperature.

Figure 13. Experimental4 and predicted vapor pressures for [emim][EtSO4] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 302.9; 9, 312.9; 2, 322.9 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrow corresponds to increasing temperature.

Figure 12. Experimental data and model results for HE of [emim][TFA] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 313.15 K; 9, 323.15 K; 2, 333.15 K; [, 348.15 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model results, respectively. The arrow corresponds to increasing temperature.

Figure 14. Experimental4 and predicted γ2 of water for [emim][EtSO4] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 302.9; 9, 312.9; 2, 322.9 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrows correspond to increasing temperature.

Table 5. Absolute Average Relative Deviationsa for Excess Enthalpy Correlations AARD% with HE and γ∞2 system

NRTL UNIQUAC eNRTL NRTL UNIQUAC eNRTL

[emim][EtSO4]/ 26.7 water [emim][OTf]/ 93.2 water [emim][TFA]/ 2.68 water a

AARD% HE only

44.0 146 2.91

7.72 107 22.9

8.55

3.06

2.96

7.89

1.19

0.36

0.36

0.35

1.87

nHE | E* AARD% ) 100 / nHE ∑ i)0 H - HE / HE* |.

the HE correlations provide excellent fits to experimental HE data when γ2∞ values are absent from model correlations for all systems. When γ2∞ data are included in the parameter estimation, the model HE correlations are the most inaccurate for the [emim][OTf] + water system (Figure 11). This is because the system is completely miscible, yet has a positive heat of mixing (i.e., it is endothermic) over the entire composition range. Although not necessary (since GE ) HE - TSE and SE is always positive), most miscible systems are exothermic. Endothermic miscible systems present a particularly difficult challenge for relatively simple GE models like the ones considered here. Including γ2∞ in the parameter estimation results in calculated HE values that are smaller in magnitude, and even exothermic for the UNIQUAC and eNRTL models. If we fit the model parameters with just HE data, the fit of the HE data is improved dramatically compared to when we include the γ2∞ value (see

Table 5). However, if we fit the model parameters with just HE data, the predicted activity coefficients are very poor. In fact, without γ2∞ in the parameter estimation, predicted γ2∞ values are 1-2 orders of magnitude too large: >10 for NRTL; >1.5 for UNIQUAC; and >21 for eNRTL for all temperatures considered. Thus, we conclude that including the γ∞2 values in the parameter estimation is important for obtaining satisfactory VLE predictions, as shown in the next section. Activity Coefficient Estimation and Pressure Predictions. VLE can be predicted from the NRTL, UNIQUAC, and eNRTL models using the temperature dependent model parameters determined above. One can simply calculate the activity coefficients of water and total pressures at the desired temperatures using eq 5 and the equations in the Supporting Information. The water vapor pressure is calculated via the Antoine equation for the systems [emim][OTf] + water and [emim][TFA] + water48 and taken directly from the experimental VLE data source for the system [emim][EtSO4] + water as they measured pure water,4 all at the temperatures of the experimental VLE. In this section, we compare the pressure and activity coefficient predictions with the experimental values. Note that we assume the vapor is an ideal gas free of IL, so that eq 5 is sufficient to describe the relationship between pressure and activity coefficient. Figures 13 and 14 show the experimental and predicted pressures and activity coefficients of water for the [emim][EtSO4] (1) + water (2) system. The experimental VLE for the [emim][EtSO4] + water system is taken from the literature.3-5

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

3899

Figure 15. Experimental and predicted vapor pressures for [emim][OTf] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 323.3; 9, 333.3; 2, 343.3; [, 353.3; b, 363.3 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrow corresponds to increasing temperature.

Figure 17. Experimental and predicted vapor pressures for [emim][TFA] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 328.2; 9, 348.2; 2, 358.2; [, 368.2 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrow corresponds to increasing temperature.

Figure 16. Experimental and predicted γ2 values for [emim][OTf] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 323.3; 9, 333.3; 2, 343.3; [, 353.3; b, 363.3 K. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrows correspond to increasing temperature.

Figure 18. Experimental and predicted γ2 values for [emim][TFA] (1) + water (2). The symbols represent the experimental data at different temperatures: b, 328.2; 9, 348.2; 2, 358.2; [, 368.2. The solid (___), dashed (---), and dotted ( · · · ) curves represent NRTL, UNIQUAC, and eNRTL model predictions, respectively. The arrow corresponds to increasing temperature.

All three models provide good predictions of the VLE, with UNIQUAC being the most accurate. The NRTL and eNRTL pressure predictions are almost indistinguishable in Figure 13. Figures 15 and 16 show the experimental and predicted pressures and activity coefficients of water for the [emim][OTf] (1) + water (2) system. This is the endothermic system, and it is clear that the VLE predictions are less accurate. In particular, the UNIQUAC model gives qualitatively incorrect activity coefficient and total pressure predictions. In fact, UNIQUAC erroneously predicts large positive deviations from Raoult’s Law that lead to spurious liquid phase splitting (Figure 15). NRTL and eNRTL both give reasonable activity coefficients at high water compositions, but the eNRTL model is unable to predict reasonable values in the IL-rich domain. Nevertheless, COP calculations, to be presented in a subsequent study, using the experimental and these NRTL predicted activity coefficients are quite agreeable. Figures 17 and 18 show the experimental and predicted pressures and activity coefficients of water for the [emim][TFA] (1) + water (2) system. All three models give very good predictions of the activity coefficients and the total pressure. It is not clear which model performs the best overall. UNIQUAC is superior for [emim][EtSO4] + water (Figure 13), and NRTL is clearly the most accurate for [emim][OTf] + water (Figure 15). All three models performs well for [emim][TFA] + water (Figure 17). In addition, all three models provide reasonable pressure predictions except for UNIQUAC for the endothermic ([emim][OTf] + water) system, which incorrectly

Table 6. Absolute Average Relative Deviationsa for Pressure Predictions AARD% with HE and γ∞2 system

NRTL UNIQUAC eNRTL NRTL UNIQUAC eNRTL

[emim][EtSO4]/ 39.3 water [emim][OTf]/ 2.71 water [emim][TFA]/ 4.70 water a

AARD% HE only

21.6

34.2

36.6

5.98

6.33

5.87

45.9 22.1 5.20

38.3 117 4.65

113 39.8 7.09

nP | AARD% ) 100 / nP ∑ i)0 P* - P / P* |.

predicts a liquid-liquid phase split (Figure 15). Table 6 provides AARD% values for the difference between the experimental and predicted pressures for all the models: AARD% )

100 nP

∑ | P*P*- P | nP

(7)

i)0

where an asterisk denotes an experimental quantity and nP is the number of experimental VLE data points. Overall, it appears that the NRTL, UNIQUAC, and eNRTL models are adequate to describe IL + water systems, except when the excess enthalpies are positive. Predicting VLE using model parameters fit to HE and γ∞2 data is much better than fitting the model parameters to VLE data and attempting to predict excess enthalpies. Including γ∞2 data in the parameter estimation is vital. Indeed, it is recommended this procedure be used for

3900

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010

VLE predictions using more sophisticated models, which may provide more accurate results. Conclusions We have presented new vapor-liquid equilibrium (VLE) data for 1-ethyl-3-methylimidazolium trifluoromethanesulfonate + water and 1-ethyl-3-methylimidaolium trifluoroacetate + water. In addition, we have correlated VLE, HE, and γ2∞ data for these two systems, as well as for 1-ethyl-3-methylimidazolium ethylsulfate + water, using the NRTL, UNIQUAC, and electrolyte NRTL models. Not unexpectedly, predictions of excess enthalpies from models with parameters fit to VLE data were not successful. However, determination of the parameters from HE and γ2∞ data provided good predictions of VLE. The most difficult system to model was [emim][OTf] + water, because it has endothermic excess enthalpies, even though the binary is completely miscible at the temperatures studied. Acknowledgment We acknowledge the Department of Energy (Grant DOE FG02-05CH11294) for funding. Supporting Information Available: Detailed expressions for the models used can be found in Supporting Information. This material is available free of charge via the Internet at http:// pubs.acs.org. Literature Cited (1) Ficke, L. E.; Rodrı´guez, H.; Brennecke, J. F. Heat capacities and excess enthalpies of 1-ethyl-3-methylimidazolium-based ionic liquids and water. J. Chem. Eng. Data 2008, 53, 2112–2119. (2) Rodrı´guez, H.; Brennecke, J. F. Temperature and composition dependence of the density and viscosity of binary mixtures of water + ionic liquid. J. Chem. Eng. Data 2006, 51, 2145–2155. ´ . Vapor-liquid (3) Calvar, N.; Gonza´lez, B.; Go´mez, E.; Domı´nguez, A equilibria for the ternary system ethanol + water + 1-ethyl-3-methylimidazolium ethylsulfate and the corresponding binary systems containing the ionic liquid at 101.3 kPa. J. Chem. Eng. Data 2008, 53, 820–825. (4) Sumartschenkowa, I. A.; Verevkin, S. P.; Vasiltsova, T. V.; Bich, E.; Heintz, A.; Shevelyova, M. P.; Kabo, G. J. Experimental study of thermodynamic properties of mixtures of containing ionic liquid 1-ethyl3-methylimidazolium ethyl sulfate using gas-liquid chromatography and transpiration method. J. Chem. Eng. Data 2006, 51, 2138–2144. (5) Wang, J. F.; Li, C. X.; Wang, Z. H. Measurement and prediction of vapor pressure of binary and ternary systems containing 1-ethyl-3methylimidazolium ethyl sulfate. J. Chem. Eng. Data 2007, 52, 1307–1312. (6) Orchille´s, A. V.; Miguel, P. J.; Vercher, E.; Martı´nez-Andreu, A. Isobaric vapor-liquid equilibria for ethyl acetate + ethanol + 1-ethyl-3methylimidazolium trifluoromethanesulfonate at 100 kPa. J. Chem. Eng. Data 2007, 52, 2325–2330. (7) Orchille´s, A. V.; Miguel, P. J.; Vercher, E.; Martı´nez-Andreu, A. Isobaric vapor-liquid equilibria for methyl acetate + methanol + 1-ethyl3-methylimidazolium trifluoromethanesulfonate at 100 kPa. J. Chem. Eng. Data 2007, 52, 915–920. (8) Orchille´s, A. V.; Miguel, P. J.; Vercher, E.; Martı´nez-Andreu, A. Ionic liquids as entrainers in extractive distillation: Isobaric vapor-liquid equilibria for acetone + methanol + 1-ethyl-3-methylimidazolium trifluoromethanesulfonate. J. Chem. Eng. Data 2007, 52, 141–147. (9) Doman´ska, U.; Marciniak, A. Activity coefficients at infinite dilution measurements for organic solutes and water in the ionic liquid 1-ethyl-3methylimidazolium trifluoroacetate. J. Phys. Chem. B 2007, 111, 11984– 11988. ´ . Experimental (10) Calvar, N.; Go´mez, E.; Gonza´lez, B.; Domı´nguez, A determination, correlation, and prediction of physical properties of the ternary mixtures ethanol + water with 1-octyl-3-methylimidazolium chloride and 1-ethyl-3-methylimidazolium ethylsulfate. J. Chem. Eng. Data 2007, 52, 2529–2535. (11) Ferna´ndez, A.; Torrecilla, J. S.; Garcı´a, J.; Rodrı´guez, F. Thermophysical properties of 1-ethyl-3-methylimidazolium ethylsulfate and 1-butyl-

3-methylimidazolium methylsulfate ionic liquids. J. Chem. Eng. Data 2007, 52, 1979–1983. ´. (12) Go´mez, E.; Gonza´lez, B.; Calvar, N.; Tojo, E.; Domı´nguez, A Physical properties of pure 1-ethyl-3-methylimidazolium ethylsulfate and its binary mixtures with ethanol and water at several temperatures. J. Chem. Eng. Data 2006, 51, 2096–2102. ´ . Density (13) Gonza´lez, B.; Calvar, N.; Gonza´lez, E.; Domı´nguez, A and viscosity experimental data of the ternary mixtures 1-propanol or 2-propanol + water + 1-ethyl-3-methylimidazolium ethylsulfate. Correlation and prediction of physical properties of the ternary systems. J. Chem. Eng. Data 2008, 53, 881–887. (14) Hofman, T.; Goldon, A.; Nevines, A.; Letcher, T. M. Densities, excess volumes, isobaric expansivity, and isothermal compressibility of the (1-ethyl-3-methylimidazolium ethylsulfate + methanol) system at temperatures 283.15 to 333.15 K and pressures from 0.1 to 35 MPa. J. Chem. Thermodyn. 2008, 40, 580–591. (15) Jacquemin, J.; Husson, P.; Mayer, V.; Cibulka, I. High-pressure volumetric properties of imidazolium-based ionic liquids: Effect of the anion. J. Chem. Eng. Data 2007, 52, 2204–2211. (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, 1411–1417. (17) Torrecilla, J. S.; Rafione, T.; Garcı´a, J.; Rodrı´guez, F. Effect of relative humidity of air on density, apparent molar volume, viscosity, surface tension, and water content of 1-ethyl-3-methylimidazolium ethylsulfate ionic liquid. J. Chem. Eng. Data 2008, 53, 923–928. (18) Wandschneider, A.; Lehmann, J. K.; Heintz, A. Surface tension and density of pure ionic liquids and some binary mixtures with 1-propanol and 1-butanol. J. Chem. Eng. Data 2008, 53, 596–599. (19) Gardas, R. L.; Costa, H. F.; Freire, M. G.; Carvalho, P. J.; Marrucho, I. M.; Fonseca, I. M. A.; Ferreira, A. G. M.; Coutinho, J. A. P. Densities and derived thermodynamic properties of imidazolium-, pyridinium-, pyrrolidinium-, and piperidinium-based ionic liquids. J. Chem. Eng. Data 2008, 53, 805–811. (20) Vercher, E.; Orchille´s, A. V.; Miguel, P. J.; Martı´nez-Andreu, A. Volumetric and ultrasonic studies of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid with methanol, ethanol, 1-propanol, and water at several temperatures. J. Chem. Eng. Data 2007, 52, 1468–1482. (21) Jacquemin, J.; Husson, P.; Padua, A. A. H.; Majer, V. Density and viscosity of several pure and water-saturated ionic liquids. Green Chem. 2006, 8, 172–180. (22) Garcı´a-Miaja, G.; Troncoso, J.; Romanı´, L. Excess enthalpy, density, and heat capacity for binary systems of alkylimidazolium-based ionic liquids + water. J. Chem. Thermodyn. 2009, 41, 161–166. (23) Olivier, E.; Letcher, T. M.; Naidoo, P.; Ramjugernath, D. Activity coefficients at infinite dilution of organic solutes in the ionic liquid 1-ethyl3-methylimidazolium trifluoromethanesulfonate using gas-liquid chromatography at T ) 313.15, 323.15, and 333.15 K. J. Chem. Thermodyn. 2010, 42, 78–83. (24) Orchille´s, A. V.; Miguel, P. J.; Vercher, E.; Martı´nez-Andreu, A. Isobaric vapor-liquid equilibria for 1-propanol + water + 1-ethyl-3methylimidazolium trifluoromethanesulfonate at 100 kPa. J. Chem. Eng. Data 2008, 53, 2426–2431. (25) Yang, J. Z.; Zhang, Z. H.; Fang, D. W.; Li, J. G.; Guan, W.; Tong, J. Studies on enthalpy of solution for ionic liquid: The system of 1-methyl3-ethylimidazolium tetrafluoroborate (EMIBF4). Fluid Phase Equilib. 2006, 247, 80–83. (26) Sen, D.; Kim, M. G. Excess molar volumes and excess molar enthalpies of binary mixtures for 1,2-dichloropropane + 2-alkoxyethanol acetates at 298.15 K. Thermochim. Acta 2008, 471, 20–25. (27) Chen, C. C.; Simoni, L. D.; Brennecke, J. F.; Stadtherr, M. A. Correlation and prediction of phase behavior of organic compounds in ionic liquids using the nonrandom two-liquid segment activity coefficient model. Ind. Eng. Chem. Res. 2008, 47, 7081–7093. (28) Do¨ker, M.; Gmehling, J. Measurement and prediction of vaporliquid equilibria of ternary systems containing ionic liquids. Fluid Phase Equilib. 2005, 227, 255–266. (29) Kato, R.; Gmehling, J. Systems with ionic liquids: Measurement of VLE and γ∞. data and prediction of their thermodynamic behavior using original UNIFAC, mod. UNIFAC(Do), and COSMO-RS(O1). J. Chem. Thermodyn. 2005, 37, 603–619. (30) Nebig, S.; Bo¨lts, R.; Gmehling, J. Measurement of vapor-liquid equilibria (VLE) and excess enthalpies (HE) of binary systems with 1-alkyl3-methylimidazolium bis(trifluoromethylsulfonyl)imide and prediction of these properties and γ∞ using modified UNIFAC (Dortmund). Fluid Phase Equilib. 2007, 258, 168–178. (31) Nebig, S.; Liebert, V.; Gmehling, J. Measurement and prediction of activity coefficients at infinite dilution (γ∞), vapor-liquid equilibria (VLE), and excess enthalpies (HE) of binary systems with 1,1-dialkyl-pyrrolidinium

Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 bis(trifluoromethylsulfonyl)imide using mod. UNIFAC (Dortmund). Fluid Phase Equilib. 2009, 277, 61–67. (32) Kato, R.; Gmehling, J. Measurement and correlation of vaporliquid equilibria of binary systems containing the ionic liquids [EMIM] [(CF3SO2)2N], [BMIM] [(CF3SO2)2N], [MMIM] [(CH3)2PO4] and oxygenated organic compounds respectively water. Fluid Phase Equilib. 2005, 231, 38–43. (33) Stage, H.; Fischer, W. G. Experimental experiences with an improved LABODEST-recirculating gadget. Verfahrentechnik 1973, 7, 202–204. (34) Walas, S. M. Phase Equilibria in Chemical Engineering; Butterworth Publishers: Stoneham, MA, 1985. (35) Li, Q.; Xing, F.; Lei, Z.; Wang, B.; Chang, Q. Isobaric vaporliquid equilibrium for isopropanol + water + 1-ethyl-3-methylimidazolium tetrafluoroborate. J. Chem. Eng. Data 2008, 53, 275–279. (36) Mun, S. Y.; Lee, H. Vapor-liquid equilibria of the water + 1,3propandiol and water + 1,3-propanediol + lithium bromide systems. J. Chem. Eng. Data 1999, 44, 1231–1234. (37) Sada, E.; Morisue, T. Isothermal vapor-liquid equilibrium data of isopropanol-water system. J. Chem. Eng. Jpn. 1975, 8, 191–195. (38) Wilson, A.; Simons, E. L. Vapor-liquid equilibria, 2-propanolwater system. Ind. Eng. Chem. 1952, 44, 2214–2219. (39) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135–144. (40) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21, 116–128. (41) Chen, C. C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Local composition model for excess Gibbs energy of electrolyte solutions, part I:

3901

Single solvent, single completely dissociated electrolyte systems. AIChE J. 1982, 28, 588–596. (42) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice Hall: UpperSaddle River, NJ, 1999. (43) Constantinescu, D.; Schaber, K.; Agel, F.; Klingele, M. H.; Schubert, T. J. S. Viscosities, vapor pressures, and excess enthalpies of choline lactate + water, choline glycolate + water, and choline methanesulfonate + water systems. J. Chem. Eng. Data 2007, 52, 1280–1285. (44) Jork, C.; Seiler, M.; Beste, Y. A.; Arlt, W. Influence of ionic liquids on the phase behavior of aqueous azeotropic systems. J. Chem. Eng. Data 2004, 49, 852–857. (45) Doman´ska, U.; Marciniak, A. Activity coefficient at infinite dilution measurements for organic solutes and water in the ionic liquid 1-butyl-3methylimidazolium trifluoromethanesulfonate. J. Phys. Chem. B 2008, 112, 11100–11105. (46) Gau, C.-Y.; Brennecke, J. F.; Stadtherr, M. A. Reliable nonlinear parameter estimation in VLE modeling. Fluid Phase Equilib. 2000, 168, 1–18. (47) Liebert, V.; Nebig, S.; Gmehling, J. Experimental and predicted phase equilibria and excess properties for systems with ionic liquids. Fluid Phase Equilib. 2008, 268, 14–20. (48) Elliot, J. R.; Lira, C. T. Introductory Chemical Engineering Thermodynamics; Prentice Hall PTR: New York, 1999.

ReceiVed for reView November 11, 2009 ReVised manuscript receiVed February 27, 2010 Accepted March 2, 2010 IE9017868