Carbon Dioxide Solubility in 1-Hexyl-3-methylimidazolium Bis

Article pubs.acs.org/JPCB

Carbon Dioxide Solubility in 1‑Hexyl-3-methylimidazolium Bis(trifluormethylsulfonyl)imide in a Wide Range of Temperatures and Pressures Javid Safarov,*,†,‡ Rena Hamidova,‡ Martin Stephan,† Ismail Kul,§ Astan Shahverdiyev,‡ and Egon Hassel† †

Institute of Technical Thermodynamics, University of Rostock, Albert-Einstein-Strasse 2, D-18059 Rostock, Germany Department of Heat and Refrigeration Techniques, Azerbaijan Technical University, H. Javid Avn. 25, AZ1073 Baku, Azerbaijan § Department of Chemistry and Biochemistry, Widener University, One University Place, Chester, Pennsylvania 19013, United States ‡

ABSTRACT: Solubility measurement data of carbon dioxide (CO2) in the ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [HMIM][NTf2] at T = 273.15−413.15 K and pressures up to p = 4.5 MPa using an isochoric method in decrements of ΔT = 20 K are presented. The temperature dependency of the Henry’s law constant was calculated, and the average deviation of the Henry’s law constant is always better than ±1%. Thermodynamic properties of solution such as the free energy of solvation, the enthalpy of solvation, the entropy of solvation, and the heat capacity of solvation were calculated to evaluate the solute−solvent molecular interactions.

1. INTRODUCTION During the past several years greenhouse gases have shown an increasing concentration in the atmosphere. Some examples of such gases are water vapor, carbon dioxide, methane, nitrous oxide, and ozone. Today, one of the most active greenhouse gases is carbon dioxide (CO2). Ionic liquids (ILs) are regarded as environmentally benign solvents due to their immeasurably low vapor pressure. Recently, significant progress has been made in the application of ILs as alternative solvents for CO2 capture due to their broad ranges of liquid temperatures, excellent thermal and chemical stabilities, and other physical and chemical properties. The accuracy of gas solubility investigation in ILs is important since many of the resulting reactions are studied in ILs. If the gas solubility in the liquid is small, transfer of the gas into the liquid IL phase will be in small amounts only. This fact could affect the ability of ILs to realistically compete with conventional solvents and may require that efforts be made to increase the interfacial area or to use high pressure operations to reach the necessary concentrations of gas in the IL.1 Additionally, there is great interest in the solubility of gases in ILs from separation technology, which is the most expensive part in many industrial chemical processes. The number of research investigations in the field of gas solubility in ILs has increased during the past two decades due to the scientific and industrial interest combined with ecological issues as a result of the greenhouse effect. However, the investigations due to the accuracy of various installations and substances (IL, gas) show different qualities. Many experiments are done around room temperature and ambient pressure. But CO2 solubility in IL is more desirable at small temperatures © XXXX American Chemical Society

(T = 273.15 K or lower) because development of oil and gas production in the cold Arctic areas will also increase gas pollution to the atmosphere. As a result, future application of ILs for saving greenhouse gases in cold temperatures becomes increasingly important. On the other side high temperature− high pressure gas solubility analysis is necessary because contemporary gas emission to the atmosphere from big industrial installations also passes into the atmosphere at temperatures higher than ambient temperatures. The experimental determination of CO2 solubility in various ILs in a wide range of temperatures is examined using the high pressure−high temperature isochoric cell method.2 In this work we present the CO2 solubility in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([HMIM][NTf2]) at T = 273.15−413.15 K and pressures up to 4.5 MPa. Before the investigations, a review of available literature information with CO2 solubility in [HMIM][NTf2] was analyzed and is tabulated in the Table 1. The first literature works with the CO2 solubility in [HMIM][NTf2] were carried out in 2004. Aki et al.3 studied the solubility of carbon dioxide in [HMIM][NTf2] at T = 298.2 and 333.2 K and pressures up to 11.558 MPa. The gas solubility measurements were carried out in a stoichiometric phase equilibrium apparatus. The measurement uncertainties were ±1 K in temperature, ±0.07 bar in pressure, ±0.0002 g in mass, ±0.002 mL in liquid volume, and ±0.05 mL in gas volume. [HMIM][NTf2] was supplied from Covalent Associates. Received: February 3, 2014 Revised: May 19, 2014

A

dx.doi.org/10.1021/jp5012044 | J. Phys. Chem. B XXXX, XXX, XXX−XXX

SPE, stoichiometric phase equilibrium; LP, laboratory product (synthesis); QCM, quartz crystal microbalance; C-Tri, C-Tri (Suwon, Korea); SM, synthetic method; IUPAC, International Union of Pure and Applied Chemistry; ISM, isochoric saturation method; MB, microbalance; EMD, EMD Chemicals, Inc.; VVC, variable volume cell; IPDI, isochoric pressure drop installation; bpp, bubble point pressure; mole fr, mole fraction.

0.0229−0.1621 0.139−0.823

±0.006 (mole fr) ±0.001 (mole fr) ±0.02 MPa (bpp) ±0.001 (mole fr) ±0.4 (kH)

±1 (kH)

0.3221−0.8333 0.006−0.433

99.0 wt % was degassed and dried in a vacuum oven for several days before use. CO2 with a purity of 99.99% was used in these measurements. Solubility was measured in vapor adsorption on solids utilizing the negligible vapor pressure of ionic liquids. Kumelan et al.6 in 2006 presented the experimental results of CO2 solubility in [HMIM][NTf2] in the 293.15−413.2 K temperature interval with the maximum pressure reaching 9.086 MPa. An IUPAC task group sample of [HMIM][NTf2] was used during the measurements. The water content of the sample was less than 0.0005 mass fraction, as determined by Karl Fischer titration before and after the measurements. The Henry constants at the various temperatures were determined with an uncertainty of ±1.5%. In a 2007 publication, Anderson et al.7 presented the solubilities of various gases (CO2 also) in [HMIM][NTf2]. The solubility measurements were carried out using the gravimetric microbalance method of “Rubotherm magnetic suspension balance” measuring systems. For the high pressure measurements, a stoichiometric method based apparatus was used. The Henry constants, as well as solubility entropies and enthalpies at T = 283−333 K and p = 0.5−1.4 MPa, were determined from the obtained solubility results. Gomes et al.8 in 2007 experimentally studied the solubility of carbon dioxide, ethane, and hydrogen in [HMIM][NTf2] at T = 288.48−343.20 K and pressures p = 0.0288−0.938 48 MPa. The partial molecular solution enthalpies, entropies, and Gibbs energies were calculated from the temperature-dependent Henry constants. The total deviation of the experimental data was ±3%. The experimental method used for these measurements was based on an isochoric saturation technique. Ionic liquid samples from Prof. Brennecke’s group (University of Notre Dame, USA) with a water content of 99.6%, [H2O] = 35 mg/kg >99%, [H2O] < 100 ppm >99.6%, [H2O] = 664 ppm ±5%

0.017 20−0.040 65 0.000 070 3−0.386 0.002−0.539 0.5−1.4 0.0288−0.93848 0.000 826−1.3 0.0089−1.9764 298−333 288.48−343.20 283.16−323.17 281.9−348.5 T, T, T, T, 7 8 10 11 Anderson Gomes Muldoon Shifflet

2007 2007 2007 2007

SPE ISM MB MB

p, p, p, p,

x, H x, H x, H x

0.069−0.236 0.2459−4.6574 (m)

IL source purity of IL

0.995, [H2O] = 160 ppm n.a. >99.0 wt % [H2O] < 20 ppm 0.0002 g ±0.5 MPa (kH) 0.002 (mole fr) ±1.5% (kH) 0.0017−0.0121 mol/kg

uncertainty concn x/mole fr

0.2535−0.7586

1.315−11.558 0.1 0.164−0.859 0.601−9.086

press., p/MPa temp, T/K

298.1−333.2 298.15 298.15 293.15−413.2 x, V x, H x, H m, H T, T, T, T,

params

p, p, p, p, SPE QCM SPE SM

method

3 4 5 6

2004 2004 2005 2006

ref

Aki Baltus Kim Kumelan

year

Article

first author

Table 1. Summary of Reported Experimental Literature Works of CO2 Solubility in [HMIM][NTf2]a

LP LP C-Tri IUPAC LP

The Journal of Physical Chemistry B

B



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experiments, the sample was under vacuum for about 12 h. The measurements were carried out at pressures p = 0.5−2.5 MPa and temperatures within the range T = 313−373 K. Shimoyama and Ito23 in 2010 used a COSMO based activity coefficient model, the COSMO-SAC method, for analyzing the solubilities and selectivities for CO2, N2, and CH4 in IL. Blath et al.24 in 2011 studied the solubility of CO2 in [HMIM][NTf2] using a pressure drop setup. The setup was operated at T = 303.15−503.15 K. However, due to the discussion about the decomposition temperature of ILs, most measurements were performed at T = 333.15 K. The Henry constants were calculated from the experimental values. Yazdizadeh et al.25 in 2011 applied the literature solubility values of CO2 in [HMIM][NTf2] to the Peng−Robinson EoS, Wong−Sandler mixing rule, and van Laar model for excess Gibbs free energy. The differential evolution optimization method was applied to optimize the binary interaction parameter and activity coefficients. Good agreement was achieved in the comparison of calculated values at T = 303.15 and 313.15 K and pressures up to p = 32 MPa. The literature analysis tabulated in Table 1 shows that there are no values at T = 273.15 K and few values around room temperature. However, solubilities of gases in liquids are important for both low and elevated temperatures because at low temperatures gas solubility in liquids will increase, and at high temperatures the stabilities of ILs are directly related to the solubility measurements. The high pressure results also did not cover wide temperature intervals. This work is a continuation of our experimental investigation in the field of solubilities of gases in ILs in a wide range of temperatures and pressures. For this purpose a new fully automatic solubility apparatus using the isochoric method was set up to determine the carbon dioxide CO2 solubility measurements in 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [HMIM][NTf2] at T = 273.15−413.15 K and pressures up to p = 4.5 MPa.

liquid were examined in this work: an ultrapure sample from NIST (the IUPAC task force sample, purity ≥ 99.5%) and a commercially available sample (purity ≥ 99.0%). Andreu and Vega12 in 2008 presented a new model for imidazolium based IL with the [NTf2] anion, in the context of the soft-SAFT equation of state (EoS). The model is used to predict the solubility of several compounds in these ILs, the gas solubilities in [HMIM][NTf2] were calculated at T = 313−453 K and pressures up to p = 8 MPa, and results were compared to available experimental data. Finotello et al.13 in 2008 studied the temperature dependence of the CO2 solubility in [HMIM][NTf2] at T = 298.15− 343.15 K and close to the ambient pressure. The isochoric method was used during the experiments. The Henry’s law constants were calculated from the experimental values. Kilaru and Scovazzo14 in 2008 investigated the CO2 solubility in [HMIM][NTf2] at T = 303.15 K and ambient pressure. The traditional flow method of CO2 through [HMIM][NTf2] was used. Shin et al.15 in 2008 measured the solubility of CO2 in [HMIM][NTf2] at T = 303.85−344.55 K and pressures p = 1.4−39 MPa using a high pressure equilibrium apparatus equipped with a variable volume view cell. The exact amount of CO2 gas introduced into the cell was determined by weighing the CO2 sample cylinder before and after loading using a balance with an accuracy of ±1 mg. Yokozeki et al.16 in 2008 investigated the solubility of CO2 in 18 various ILs under isothermal conditions for T = 297.3− 297.4 K and pressures of p = 0.0091−1.9748 MPa with a gravimetric microbalance. The (p,T,x) data were analyzed using an EoS. The EMD Chemicals (Merck Group) IL sample was dried before the measurement over 5 days at T = 348 K under vacuum. The water content of IL was indicated as w < 1 × 10−3. The accuracy of measurements was x < 0.006 mole fraction. Kerlé et al.17 in 2009 theoretically calculated the solubility of CO2 in [HMIM][NTf2] at T = 300−500 K using a moleculardynamic simulation. Raeissi and Peters18 in 2009 studied the solubility of CO2 in [HMIM][NTf2] at T = 293.15−363.5 K and pressures up to 14.337 MPa. Ahn et al.19 in 2010 studied the high pressure phase equilibrium data for ternary mixtures consisting of IL, dimethyl carbonate (DMC), and carbon dioxide (CO2) using an equilibrium apparatus equipped with a variable volume view cell. CO2 solubilities in the solvent mixtures of DMC and [HMIM][NTf2] with various compositions were presented at T = 303.15−333.15 K and pressures up to p = 7 MPa. Ji and Adidharma20 in 2010 used the heterosegmented statistical associating fluid theory to represent the CO2 solubility in IL. According to the authors’ data the applied model represents the CO2 solubility in [HMIM][NTf2] within the range T = 283−415 K and at pressures up to p = 10 MPa. Ren et al.21 in 2010 presented the (vapor + liquid) equilibria of the CO2 and [HMIM][NTf2] mixture using the solubility of CO2 in IL at T = 298.15−343.15 K and pressures up to 24.708 MPa. The Peng−Robinson EoS with van der Waals two-parameter mixing rules were selected to model and correlate the phase equilibria data. Shi et al.22 in 2010 used classical molecular dynamics and Monte Carlo simulations to calculate the self-diffusivities and solubilities of pure and mixed CO2, H2, and Ar gases absorbed in [HMIM][NTf2]. For this purpose a decrease of the pressure sorption system was used. To remove all impurities before the

2. EXPERIMENTAL SECTION CO2 from Westfalen AG, Germany, with a purity of 99.9%, was used without further purification. [HMIM][NTf2] was purchased from EMD Chemicals Inc. (Merck Group), Germany (CAS No. 382150-50-7), with a purity of ≥98.0%. To reduce the water content and volatile impurities, the IL was dried by applying a low-pressure vacuum of 1−10 Pa at temperature T = 423.15 K for 48 h using magnetic stirring. The water content of dried IL was determined using Karl Fischer titration and was less than a mass fraction of 3 × 10−4. The properties of CO2 and the IL are shown in Table 2. Table 2. Provenance and Purity of the Chemicals Studied chemical formula molar mass CAS No. melting point purity

[HMIM][NTf2]

carbon dioxide

C12H19F6N3O4S2 0.447 423 0 kg·mol−1 382150-50-7 264.15 K ≥98%

CO2 0.044 009 8 kg·mol−1 124-38-9 197.15 K ≥99.9%

The experiments to determine the high pressure solubility of CO2 in [HMIM][NTf2] at various temperatures are performed in a stainless steel measuring cell in equilibrium by using the isochoric method, and the experimental apparatus is schematically presented in our previous work.2 The installation C



Article

Figure 1. Plot of CO2 solubility equilibrium pressure in [HMIM][NTf2] versus time of solubility.

Engineering Inc., Newport Electronics GmbH Germany) with an experimental uncertainty of ±0.1%. Before the beginning of the measurements, the measuring cell was washed with water and acetone. The PC was turned on, and all instruments were controlled and read by the PC using the LabVIEW program. Measurements of the temperature and pressure values of the system were recorded every 60 s. The amount of IL within the measuring cell is found by weighing the filling flask before and after filling. The solubility of CO2 in an IL is followed by a decrease in the pressure of the system. Stabilization of the experimental pressure within the system indicates the end of the solution process and gives the total solubility of CO2 in the IL for every temperature. This process takes approximately 4−5 h. The experimental pressure is measured as the equilibrium pressure of the total system (gas reservoir and measuring cell). Experiments were carried out in four different pressure steps: in the first step, the maximum possible pressure (about 5 MPa)

consists of three main parts: (a) gas reservoir; (b) stainless steel measuring (equilibrium) cell; (c) electronic tracking system box. Temperature in the gas reservoir is controlled using the heating system. It was measured using a PT100 (ITS-90) thermometer with an experimental error of ±45 mK, which connected to the electronic tracking system box. The stabilization of the temperature in the measuring cell at T = 273.15−413.15 K is controlled using the external thermostat LAUDA ECO RE 415 Gold with an error of ±(30−100) mK using the PT100 (ITS-90) thermometer, which is connected to the thermostat via a PT-100 Libus Modul. The temperature in the measuring cell is measured using another PT100 (ITS-90) thermometer implemented in it and connected to the electronic tracking system box. The pressure transducer indicates the pressure of CO2 filled to the gas reservoir and in the measuring cell, which is measured by pressure transducers PAA33X-V-100 (Omega D



Article

is created in the gas reservoir. The other steps with maximum pressure are the following: second, about 3 MPa; third, about 1.5 MPa; fourth, about 0.5 MPa. Experiments were carried out as a function of temperatures ranging from T = 413.15 K to T = 273.15 K in decrements of 20 K at selected pressures controlled by a PC with the LabVIEW program. The measurements are completed when CO2 exits to the special balloons due to opening of the valve after finishing the measurements at all temperature intervals. The total measurements of this temperature range take approximately 20−30 h depending on the respective pressure interval. The solubility dependence on time at the various temperatures of measurements is shown in Figure 1. The measured CO2 solubility values in IL are presented in Table 3 and Figure 2 as a function of pressure. In Table 4, the pressure dependency of interpolated CO2 solubility in [HMIM][NTf2] is presented in molality m/mol·kg−1 and mole fraction x of solute at selected temperatures. The interpolated CO2 solubility in mole fraction of solute x in [HMIM][NTf2] versus temperature is shown in Figure 3, and the influence of the total pressure on the ratio of CO2 fugacity f (in gaseous phase) to CO2 mole fraction x (in liquid phase) is shown in Figure 4. The figures show that the solubility of CO2 in [HMIM][NTf2] decreases exponentially as a function of temperature and increases linearly with respect to pressure as shown in Figure 4. The estimated total uncertainty of CO2 solubility in IL using this method is approximately Δm = ±0.001 mol·kg−1 or Δx = ±0.000 05 mole fraction.

Table 3. Pressure Dependence of Experimental CO2 Solubility in [HMIM][NTf2] {in Molality (m/mol·kg−1) and in Mole Fraction (x)} and of Fugacity Coefficient of Pure Carbon Dioxide ϕCO2(T,p) in the Binary [HMIM][NTf2] + CO2 Solution at Various Temperatures Ta

3. CORRELATION OF THE GAS SOLUBILITY The Henry’s law for an ideal solution with a standard-state fugacity based on infinitely dilute solution is used for the correlation of gas solubility. Henry’s law for a binary system for a nonideal gas phase can be written as26 yCO ϕCO P = xCO2kH,CO2(T ) 2

2

2

2

P/MPa

mCO2/mol·kg−1

xCO2/mole fr

ϕCO2(T,p)

413.15 393.15 373.15 353.15 333.15 313.15 293.15 413.15 393.15 373.15 353.15 333.15 313.15 293.15 273.15 413.15 393.15 373.15 353.15 333.15 313.15 293.15 273.15 413.15 393.15 373.15 353.15 333.15 313.15 293.15 273.15

4.674 4.643 4.603 4.547 4.471 4.351 4.155 3.071 3.044 3.009 2.966 2.908 2.827 2.702 2.479 1.311 1.298 1.281 1.261 1.234 1.199 1.148 1.069 0.488 0.483 0.477 0.469 0.459 0.446 0.427 0.399

1.1935 1.3029 1.4688 1.7513 2.1652 2.9203 4.2533 0.7903 0.8743 1.0048 1.1767 1.4402 1.8508 2.5665 4.0166 0.3463 0.3805 0.4358 0.5048 0.6132 0.7668 1.0186 1.4508 0.1269 0.1392 0.1561 0.1833 0.2209 0.2749 0.3641 0.5080

0.3481 0.3683 0.3966 0.4393 0.4921 0.5665 0.6555 0.2612 0.2812 0.3101 0.3449 0.3919 0.4530 0.5345 0.6425 0.1342 0.1455 0.1632 0.1843 0.2153 0.2554 0.3131 0.3936 0.0537 0.0586 0.0653 0.0758 0.0900 0.1095 0.1401 0.1852

0.927 718 0.913 765 0.896 917 0.876 512 0.851 586 0.821 538 0.786 155 0.951 857 0.942 713 0.931 752 0.918 479 0.902 432 0.883 099 0.860 549 0.837 654 0.979 142 0.975 221 0.970 543 0.964 883 0.958 087 0.949 880 0.940 261 0.929 739 0.992 182 0.990 718 0.988 960 0.986 858 0.984 317 0.981 252 0.977 669 0.973 670

a Standard uncertainties u are u(T) = ±0.015 K, u(P) = ±0.1%, u(Δm) = ±0.001 mol·kg−1, and u(Δx) = ±0.000 05 mole fraction.

(1)

Since ionic liquids have very small vapor pressures, the vapor phase of the measuring cell can be considered as pure CO2. The fugacity coefficient of pure carbon dioxide ϕCO2(T,p) at equilibrium temperature and pressure can be estimated by dividing the fugacity f CO2(T,p) of pure CO2 by the total measured pressure p of binary IL + CO2 solution: ϕCO (T , p) = fCO (T , p)/p

T/K

results of dividing the fugacity f CO2(T,p) of pure CO227 by the mole fraction of pure CO2 in the binary IL + CO2 solution: kH,CO2(T ) =

(2)

The equation of state of Span and Wagner27 for the pure CO2 were used during the calculation of fugacity f CO2(T,p) of pure CO2. The obtained values of fugacity f CO2(T,p) of pure CO2 and experimental pressure p/MPa were used for the calculation of the fugacity coefficient of pure carbon dioxide ϕCO2(T,p) at equilibrium temperature and pressure in all temperatures of measurements, including the supercritical area up to T = 413.15 K. The calculated fugacity coefficients ϕCO2(T,p) are presented in Table 3. The CO2 + IL equilibrium condition results in the extended Henry’s law for carbon dioxide.28 The Henry constant kH,CO2(T) is the linear relationship between carbon dioxide concentration and experimental pressure. It can be determined from the extrapolation procedure using experimental

⎡ f (T , p ) ⎤ ⎢ CO2 ⎥ s p → p[HMIM][NTf ] = 0⎢ ⎥⎦ x ⎣ 2 lim

(3)

In Figure 4, the calculated values for [( f CO2(T,p))/x] (for preset temperature) are plotted versus the total pressure above the CO2 + [HMIM][NTf2] solution. Extrapolations were done by linear regression, and Henry constants resulting from the extrapolations are given in Table 5 and shown in Figure 5 for the temperature T/K dependency. Thermodynamic properties of solution {CO2 + [HMIM][NTf2]} can be calculated from the correlation of the Henry constant given above by applying the well-known thermodynamic relations described in ref 28. ⎛ kH,CO (T , p) ⎞ 2 ⎟⎟ Δsol G = RT ln⎜⎜ 0 p ⎠ ⎝ E

(4)



Article

Figure 2. Plot of CO2 solubility (x, mole fraction) in [HMIM][NTf2] versus pressure p together with the some literature values: , calculated by eq 9.

Table 4. Pressure Dependence of Interpolated CO2 Solubility in [HMIM][NTf2] {in Molality (m/mol·kg−1) and in Mole Fraction (x)} at Various Temperatures Ta P/MPa T/K

0.101

0.5

1.0

1.5

2.0

2.5

mCO2/mol·kg

a

3.0

3.5

4.0

4.5

−1

413.15 393.15 373.15 353.15 333.15 313.15 293.15 273.15

0.0269 0.0283 0.0296 0.0367 0.0452 0.0613 0.0876 0.1245

0.1316 0.1469 0.1708 0.2009 0.2483 0.3137 0.4264 0.6316

0.2621 0.2938 0.3440 0.4039 0.5002 0.6346 0.8729 1.3501

0.3917 0.4387 0.5131 0.6037 0.7491 0.9607 1.3436 2.1609

0.5203 0.6480 0.5815 0.7224 0.6782 0.8391 0.8004 0.9939 0.9951 1.2381 1.2921 1.6287 1.8386 2.3580 3.0640 4.0595 xCO2/mole fraction

0.7748 0.8612 0.9959 1.1843 1.4782 1.9705 2.9017

0.9007 0.9981 1.1486 1.3715 1.7153 2.3175 3.4697

1.0257 1.1329 1.2973 1.5555 1.9495 2.6698 4.0620

1.1497 1.2657 1.4418 1.7364 2.1808 3.0272 4.6786

413.15 393.15 373.15 353.15 333.15 313.15 293.15 273.15

0.0114 0.0137 0.0151 0.0170 0.0205 0.0268 0.0371 0.0526

0.0537 0.0627 0.0702 0.0799 0.0955 0.1208 0.1594 0.2151

0.1029 0.1180 0.1318 0.1498 0.1776 0.2208 0.2847 0.3750

0.1481 0.1669 0.1856 0.2105 0.2477 0.3033 0.3834 0.4941

0.1894 0.2100 0.2326 0.2631 0.3072 0.3709 0.4600 0.5806

0.2606 0.2818 0.3093 0.3472 0.3999 0.4715 0.5665

0.2908 0.3117 0.3405 0.3807 0.4359 0.5097 0.6056

0.3175 0.3385 0.3681 0.4097 0.4669 0.5431 0.6417

0.3409 0.3628 0.3928 0.4352 0.4942 0.5742 0.6795

0.2268 0.2481 0.2736 0.3083 0.3574 0.4261 0.5195 0.6427

Standard uncertainties u are u(T) = ±0.015 K, u(P) = ±0.1%, u(Δm) = ±0.001 mol·kg−1, and u(Δx) = ±0.000 05 mole fraction.

⎛ kH,CO2(T , p) ⎜ ∂ ln p0 Δsol H = R ⎜ 1 ⎜ ∂ T ⎝

(

()

Δsol S =

Δsol H − Δsol G T

⎛ ∂Δ H ⎞ Δsol cp = ⎜ sol ⎟ ⎝ ∂T ⎠ p

) ⎞⎟⎟

⎟ ⎠p

discrete temperatures between 273.15 and 413.15 K are given in Table 5. ΔsolG and ΔsolH increase with increasing temperature, whereas Δsolcp decreases with increasing temperature. The negative enthalpies of solvation indicate an exothermal solvation process. Similarly, the entropy of solvation values are also negative, which indicates an increase in order of the solvent molecules surrounding the solute. The measured CO2 solubility values in [HMIM][NTf2] as a function of temperature and pressure were fitted to the following virial equations using the mole fraction x or molality m/mol·kg−1 dependence:

(5)

(6)

(7)

where ΔsolG, ΔsolH, ΔsolS, and Δsolcp, are the Gibbs free energy of solvation, enthalpy of solvation, entropy of solvation, and heat capacity of solvation, respectively. Their values at eight

3

x=

i=0

F

3

∑ (p/MPa)i ∑ aij(T /K) j j=0

(8)


The Journal of Physical Chemistry B 3

m=

Article

3

∑ (p/MPa)i ∑ bij(T /K) j i=0

j=0

(9)

where bij are the coefficients of eqs 8 and 9. They are presented in Tables 6 and 7.

4. LITERATURE COMPARISON 4.1. Solubility. Experimental and theoretical investigations of CO2 solubility in [HMIM][NTf2] are available in the literature (Table 1). Values from the present study of the CO2 solubility data in [HMIM][NTf2] were compared to the literature values at similar temperature and pressure conditions using different experimental techniques. Figures 6 and 7 show the differences between the various literature sources and the correlation of the present data of CO2 solubility in [HMIM][NTf2] versus pressure p at various temperatures T. With a detailed analysis of the figures, we can reach the following conclusions: 1. The 13 values from 28 experimental results studied by Aki et al.3 at T = 298.2 and 333.3 K, with pressures up to p = 4.397 MPa, were compared to our results, and good agreement with our results within Δx = ±0.031 mole fraction were obtained. The maximum deviation between two results is Δx = 0.0748 mole fraction at T = 333.3 K and p = 1.715 MPa. Our results are higher than the values obtained by Aki et al.3 2. The comparison of nine experimental results of Kim et al.4 at T = 298.15 K and pressures up to p = 0.859 MPa demonstrate very good agreement with our values with the middle deviation in mole fraction Δx = ±0.011. The maximum deviation of both results is Δx = 0.0164 mole fraction at p = 0.242 MPa. Our results are smaller than the values obtained by Kim et al.4 3. The comparison of 11 CO2 solubility results in [HMIM][NTf2] investigated by Gomes et al.8 at T = 293.06−343.20 K shows Δx = ±0.001 mole fraction, an average deviation from our values. The maximum deviation between these studies is Δx = 0.011 mole fraction at T = 343.2 K. Mostly, our results are smaller than values of Gomes et al.8 4. The 70 CO2 solubility values in [HMIM][NTf2] reported by Shiflett and Yokozeki11 were compared with our results and Δx = ±0.008 mole fraction middle deviation was obtained. These literature values are mostly smaller than our results at high temperatures. The maximum deviation of this comparison is Δx = 0.0201 mole fraction at temperature T = 281.9 K and pressure p = 0.9882 MPa. 5. The 60 CO2 solubility values in [HMIM][NTf2] reported by Muldoon et al.10 were also compared with our results, and Δx = ±0.007 mole fraction middle deviation was obtained. The maximum deviation between both compared values is Δx = 0.0171 mole fraction at T = 323.17 K and p = 1.1 MPa. Our results are generally higher than values of Muldoon et al.10 6. The comparison of 19 CO2 solubility results of Shin et al.15 in [HMIM][NTf2] from 90 with our measured values provides Δx = ±0.021 mole fraction deviation. The maximum deviation of this comparison is Δx = 0.0442 mole fraction at T = 303.85 K and p = 4.20 MPa. 7. The eight CO2 solubility results in [HMIM][NTf2] of Yokozeki et al.16 at ΔT = 297.4 K were compared to our values, and the middle deviation of these comparison is Δx = ±0.002 mole fraction. The maximum deviation of both values is Δx = 0.3943 mole fraction at p = 0.0091 MPa. 8. The comparison of six CO2 solubility values in [HMIM][NTf2] from 26 values of Ren et al.21 to our results demonstrates with the middle deviation in mole fraction

Figure 3. Plot of interpolated CO2 solubility in mole fraction x in [HMIM][NTf2] versus temperature T/K: ◆, 0.101 MPa; ■, 0.5 MPa; ▲, 1.0 MPa; ●, 1.5 MPa; ◇, 2.0 MPa; □, 2.5 MPa; △, 3.0 MPa; ○, 3.5 MPa; ∗, 4.0 MPa; ×, 4.5 MPa.

Figure 4. Influence of total pressure on the ratio of CO2 fugacity f (in gaseous phase) to CO2 mole fraction x (in liquid phase of [HMIM][NTf2] + CO2 solution): experimental results at various temperatures (○, 273.15 K; △, 293.15 K; □, 313.15 K; ◇, 333.15 K; ●, 353.15 K; ▲, 373.15 K; ■, 393.15 K; ◆, 413.15 K) and () linear fit.

Δx = ±0.051. The maximum deviation of this comparison is Δx = 0.1208 mole fraction at T = 343.15 and p = 1.793 MPa. Our values are smaller than the values of Ren et al.21 9. The last comparison of CO2 solubility in [HMIM][NTf2] using 35 selected literature values out of 48 at the same pressure interval with our measurements provided by Raeissi and Peters18 gives us Δx = ±0.015 mole fraction middle deviation. The maximum deviation of this comparison is Δx = 0.0336 mole fraction at T = 363.15 and p = 1.303 MPa. Our results are mostly higher than the values of Raeissi and Peters.18 G



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Table 5. Values of Calculated Henry Constant (kH,CO2/MPa) Resulting from the Extrapolations, Free Energy of Solvation ΔsolG, Enthalpy of Solvation ΔsolH, Entropy of Solvation ΔsolS, and Heat Capacity of Solvation Δsolcp at Various Temperatures T T/K

kH,CO2/MPa

ln(kH12/p0)

ΔsolG/J·mol−1

ΔsolH/J·mol−1

ΔsolS/J·mol−1·K−1

Δsolcp/J·mol−1·K−1

413.15 393.15 373.15 353.15 333.15 313.15 293.15 273.15

8.68 7.54 6.65 5.74 4.74 3.75 2.82 1.95

4.463 607 4.322 807 4.197 202 4.050 044 3.858 622 3.624 341 3.339 322 2.970 414

15 332.17 14 129.74 13 021.27 11 891.29 10 687.65 9 436.08 8 138.76 6 745.72

−8 073.10 −8 201.33 −8 444.34 −8 839.76 −9 438.89 −10 312.61 −11 560.41 −13 324.56

−56.65 −56.80 −57.53 −58.70 −60.41 −63.06 −67.20 −73.48

7.66 9.11 14.43 23.60 36.62 53.50 74.24 98.83

Figure 5. Henry constant of CO2 in [HMIM][NTf2] at zero pressure: (◆) extrapolated experimental results in this work; () correlation, this work.

Figure 6. Deviation of experimental CO2 solubility in mole fraction xexp in [HMIM][NTf2] from calculated xcal versus pressure P/MPa at various temperatures T/K.

Table 6. Values of the Coefficients aij in eq 8 a00 a01 a02 a03 a10 a11 a12 a13

= = = = = = = =

0.388 880 836 3 −0.317 348 907 0 × 10−2 0.859 551 643 4 × 10−5 −0.772 307 735 4 × 10−8 10.474 694 36 −0.079 076 578 04 0.203 759 439 3 × 10−3 −0.176 874 370 5 × 10−6

a20 a21 a22 a23 a30 a31 a32 a33

= = = = = = = =

−4.237 907 69 0.033 519 042 37 −0.891 101 180 2 × 10−4 0.792 865 629 1 × 10−7 0.506 311 557 1 −0.406 399 281 7 × 10−2 0.109 114 411 7 × 10−4 −0.977 885 532 2 × 10−8

1. Baltus et al.4 calculated the Henry constant kH,CO2/MPa at T = 298.15 K as kH,CO2 = 3.5 MPa. Our interpolated data at the same temperature is kH,CO2 = 3.08 MPa with the difference between both values as ΔkH,CO2 = 0.421 MPa. 2. We compared our three calculated and interpolated values of Henry constants kH,CO2/MPa with the values of Anderson et al.7 for the temperature range from T = 283 K to T = 323 K and obtained ΔkH,CO2 = 0.149 MPa middle deviation between both studies. 3. The 11 Henry constants kH,CO2/MPa of Gomes8 at T = 288.48−343.20 K have ΔkH,CO2 = 0.190 MPa middle deviation from our interpolated values. 4. The three Henry constants kH,CO2/MPa of Muldoon et al.10 at T = 283.15 and 333.15 K have ΔkH,CO2 = 0.091 MPa middle deviation from our interpolated values. 5. The four calculated Henry constants kH,CO2/MPa of Finotello et al.13 at T = 298.15−343.15 K have ΔkH,CO2 = 0.780 MPa middle deviation with our interpolated values. 6. Raeissi and Peters18 calculated the Henry constant kH,CO2/ MPa at T = 298.15 K as kH,CO2 = 3.5 MPa. Our interpolated value at this temperature is kH,CO2 = 3.08 MPa.

Table 7. Values of the Coefficients bij in eq 9 b00 b01 b02 b03 b10 b11 b12 b13

= = = = = = = =

−0.832 218 620 1 0.774 175 051 1 × 10−2 −0.236 967 712 2 × 10−4 0.238 226 631 6 × 10−7 23.140 679 2 −0.173 683 85 0.446 275 058 × 10−3 −0.387 148 923 6 × 10−6

b20 b21 b22 b23 b30 b31 b32 b33

= = = = = = = =

26.752 633 93 −0.223 472 126 0.618 620 833 8 × 10−3 −0.567 671 730 1 × 10−6 5.095 426 075 0.043 105 070 69 −0.120 739 76 × 10−3 0.112 005 637 1 × 10−6

4.2. Henry Constant. Many authors have analyzed the Henry constant, kH,CO2/MPa of CO2 solubility in [HMIM][NTf2] for several years. We have compared the literature data with respect to our interpolated data as a function of temperature and presented in Figure 8. With a detailed analysis of the figure, we can reach the following conclusions: H



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9. The calculated Henry constant kH/MPa of Blath et al.24 at T = 333.15 K as kH,CO2 = 5.8 MPa has ΔkH,CO2 = 1.080 MPa deviation from our interpolated kH,CO2 = 4.72 MPa value.

5. CONCLUSION We report in this work the gas−liquid equilibrium data of the carbon dioxide and 1-hexyl-3-methyl-imidazolium bis(trifluormethylsulfonyl)imide binary system in a wide range of temperatures and pressures. The measured values are fitted to a polynomial equation which can be used for the interpolation of measured results. This equation is also used for the analyses of deviation of literature values from our results. The partial Gibbs energy, enthalpies, and entropies of solvation are estimated from Henry constants in the standard pressure (0.1 MPa). The results obtained here are compared with values published in the literature by different research groups. The increase in solubility with increasing pressure becomes quite small at high pressures around p = 2 MPa. The literature measurements of molar volumes of the liquid phase in all of the experiments for [HMIM][NTf2] show that this IL expands with a relatively small amount when CO2 is added.

Figure 7. Plot of deviation of experimental xexp and literature xcal values of CO2 solubility in [HMIM][NTf2] versus pressure p at various temperatures T: ■, Aki et al.3 at T = 298.2 and 333.3 K; ∗, Kim et al.3 at T = 298.15 K; ◆, Gomes8 at T = 293.06−343.20 K; ●, Muldoon et al.10 at T = 283.16−323.17 K; ◇, Shiflett and Yokozeki11 at T = 282.0−348.6 K; ▲, Shin et al.15 at T = 303.85−344.55 K; △, Yokozeki et al.16 at T = 297.4 K; +, Raeissi and Peters18 at T = 293.15−363.15 K; □, Ren et al.21 at T = 298.15−343.15 K.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 381 4989415. Fax: +49 381 4989402. E-mail: javid. [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 8. Plot of deviation of interpolated Henry constant of CO2 solubility in [HMIM][NTf2] of present work with respect to literature data as a function of temperature: ▲, Baltus et al.4 at T = 298.15 K; ■, Anderson et al.7 at T = 298.15 K; ◇, Gomes8 at T = 288.48−343.20 K; □, Muldoon et al.10 at T = 283.15−333.15 K; △, Finotello et al.13 at T = 298.15−343.15 K; ●, Kilaru and Scovazzo14 at T = 303.15 K; ○, Raeissi and Peters18 at T = 298.15 K; +, Blath et al.24 at T = 333.15 K.

7. Kilaru and Scovazzo14 calculated the Henry constant kH,CO2/MPa at T = 303.15 K as kH,CO2 = 4.4583 MPa. Our interpolated value at this temperature is kH,CO2 = 3.31 MPa. 8. The three theoretical obtained Henry constants kH,CO2/ MPa of Kerlé et al.17 from five obtained at T = 300−400 K have ΔkH,CO2 = 1.255 MPa, a deviation from our interpolated value. I



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Carbon Dioxide Solubility in 1-Hexyl-3-methylimidazolium Bis

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