3040
J. Phys. Chem. B 2008, 112, 3040-3047
Solubility of Tetrafluoromethane in the Ionic Liquid [hmim][Tf2N] Jacek Kumełan,† A Ä lvaro Pe´ rez-Salado Kamps,† Dirk Tuma,† Akimichi Yokozeki,‡ § Mark B. Shiflett, and Gerd Maurer*,† Applied Thermodynamics, UniVersity of Kaiserslautern, P. O. Box 30 49, D-67653 Kaiserslautern, Germany ReceiVed: August 22, 2007; In Final Form: NoVember 5, 2007
Experimental results for the solubility of tetrafluoromethane (CF4, R14) in the ionic liquid 1-hexyl-3methylimidazolium bis(trifluoromethylsulfonyl)amide ([hmim][Tf2N]) are presented for temperatures between 293.3 and 413.3 K, at pressures (gas molalities) up to 9.6 MPa (0.22 mol kg-1). The experimental results were determined with a high-pressure view-cell technique operating on the synthetic method. The experimental data were used to determine Henry’s constant of tetrafluoromethane in [hmim][Tf2N]. The results for the Henry’s constant (at zero pressure) are correlated (on the molality scale) within the experimental uncertainty (0) /MPa) ) 7.537 - 893.8/(T/K) - 0.003977(T/K). Henry’s law was also (i.e., about 1.1%) by ln(kH,CF 4 extended to describe the gas solubility at higher pressures. Furthermore, a cubic equation of state was used to correlate the gas solubility over the entire range of experimentally investigated temperature and pressure. Both methods proved suited for a reliable correlation of the new experimental data.
Introduction Studies of solubility (or phase behavior) for various chemicals with room-temperature ionic liquids (RTILs, a new kind of solvents) are highly important in order to evaluate and realize proposals for applications of RTILs such as chemical separation and extraction, absorption cycle processes, gas storage, reaction media, battery electrolytes, and various other solvent applications.1-4 The solubility of gases have thus been a matter of interest from the very beginning, and several papers highlight the current activities by different research groups in this field.1-4 At the same time, the solubility of gases provide useful information on the fundamental knowledge for physical and/or chemical interactions between these compounds on the molecular level. At present, there are three major methods employed to investigate gas solubility in ionic liquids: the gravimetric microbalance method,5,6 which is suitable for very soluble gases; the synthetic method, which is a well-established technique over a broad range of gas solubilities and in particular also gassolvent systems which reveal a low gas solubility,7,8 and an NMR technique that allows fast screening of many gas-solvent systems.9,10 Recently, researchers at DuPont investigated solubilities of various gases (such as halocarbons, CO2, and NH3) in RTILs11-22 using a gravimetric microbalance method.14 During the course of their studies, that particular method failed to produce high-quality data for the system tetrafluoromethane (CF4) + [hmim][Tf2N]. On the other hand, at the University of Kaiserslautern, Germany, there is long-run experience with a high-pressure view-cell technique that has proven to be particularly suited to investigate the solubility of sparsely soluble gases in liquids also at high pressures with high accuracy.23-27 * Corresponding author. Tel.: +49 631 205 2410. Fax: +49 631 205 3835. E-mail:
[email protected]. † University of Kaiserslautern. ‡ DuPont Fluoroproducts Laboratory, Chestnut Run Plaza 711, Wilmington, Delaware 19880. § DuPont Central Research and Development, Experimental Station, Wilmington, Delaware 19880.
Since CF4 is an important industrial gas (e.g., for plasma etching in the chip industries), both groups joined their efforts. This paper presents the first results of that collaboration. The solubility of CF4 in [hmim][Tf2N] was measured at four temperatures (about 293, 333, 373, and 413 K) and at pressures between about 1.1 and 9.6 MPa at the University of Kaiserslautern. The gas was provided by DuPont, and commercially available high-purity [hmim][Tf2N] served as the RTIL. The experimental results were correlated following two procedures. One method is based on an equation of state approach that was established in previous work by Yokozeki and Shiflett.11-14 The other method employs an extended Henry’s law approach, that was introduced in the correlation of the solubility of CO2 in 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim] [PF6])7 and then used in all following investigations at Kaiserslautern.7,23-28 Experimental Details and Results Apparatus and Method. The apparatus and the measuring technique were described in previous publications.7,26,28 Thus, the applied method is briefly sketched only. The mass of the gas introduced into the cell was determined volumetrically, i.e., from the known volume of the cell (approximately 29.7 cm3) and the gas density (at measured temperature and pressure), which was calculated via the Bender equation of state (EoS) for CF4 developed by Platzer and Maurer29 (see also the work of Platzer et al.30). This EoS is, among others, implemented in the software package REFPROP.31 The amount of mass of the solvent (i.e., the ionic liquid [hmim][Tf2N]) filled into the cell (about 39 g) is determined from the volume displacement in a calibrated spindle press, which is used for the displacement of the solvent, and the solvent density.28 The temperature was measured using two calibrated platinum resistance thermometers with an uncertainty of less than (0.1 K. When the cell was charged with tetrafluoromethane, the pressure was recorded with three pressure transducers suitable for a maximum pressure of 0.6, 1.6, and 2.5 MPa. The corresponding solubility pressure was measured
10.1021/jp076737t CCC: $40.75 © 2008 American Chemical Society Published on Web 02/20/2008
Solubility of CF4 in [hmim][Tf2N] with two pressure transducers suitable up to 2.5 and 10 MPa. All pressure transducers were purchased from WIKA GmbH, Klingenberg, Germany, and calibrated against a high-precision pressure balance (Desgranges & Huot, Aubervilliers, France) before and after each measurement series. The maximum systematic uncertainty in the solubility pressure measurement results from the intrinsic uncertainty of the pressure transducers (i.e., 0.1% of the transducer’s full scale) and an additional contribution of about (0.01 MPa from a small temperature drift inside the isolated (high-pressure) tubes filled with the solvent, that connect the view-cell with the pressure transducers. Several test runs verified that particular drift. Materials and Sample Pretreatment. Tetrafluoromethane (mole fraction g 0.999999) was supplied by DuPont Fluoroproducts, Wilmington, Delaware. Its purity was determined using a gas chromatography mass spectrometry method (Agilent 6890N, Restek Rtx-200 column, 105 m × 0.25 mm) and found to contain no measurable impurities within detection limit (1 ppm). It was used without further purification. The ionic liquid [hmim][Tf2N] (C12H19N3F6O4S2, high purity, mass fraction g 0.99, slightly yellowish liquid, relative molar mass M ) 447.42) was synthesized by Merck KGaA, Darmstadt, Germany. The samples were degassed and dried under vacuum over a period of 2 days to remove traces of water and other volatile impurities.1H-, 13C-, and 19F-NMR spectroscopic investigations were carried out with a Bruker Avance 600 MHz spectrometer (Bruker AXS GmbH, Karlsruhe, Germany), proving that the impurities of [hmim][Tf2N] were below 0.01 mole fraction. The water content of the sample was less than 0.00016 mass fraction, as determined by Karl Fischer titration analysis after the completion of the measurement series. A glass burette served as a sample container, so that the ionic liquid could be handled and introduced into the apparatus always under vacuum. The ionic liquid was collected after each measurement and reconditioned (i.e., degassed and dried under vacuum) for further use. No degradation was observed for [hmim][Tf2N], and new NMR measurements for the processed material did not give different results. In order to see the material stability, in one experiment, we kept the sample under CF4 at 413 K for 5 days. The resulting solubility data point was in perfect agreement with data points done in the usual way. We did this, because in prior gas solubility experiments with oxygen significant degradation after longer exposure at high temperatures such as 373 K was observed.32 Experimental Results. Four isotherms of about 293, 333, 373, and 413 K were investigated at pressures up to approximately 10 MPa. The corresponding solubility results are given in Table 1. The listed pressure p is the pressure required to dissolve the given amount of CF4 in 1 kg of the ionic liquid at a fixed temperature. The solubility pressure p is plotted versus the gas molality mG {i.e., the amount of substance (the number of moles) of the gas per kilogram of [hmim][Tf2N]} at constant temperature T in Figure 1. Within the temperature and pressure regions investigated during this study, the solubility pressure monotonously increases with increasing gas molality at a given temperature. Figure 1 shows that the shape of the solubility isotherms is almost linear. The solubility isotherms manifest purely physical solubility behavior, that is in accordance with prior investigations in [hmim][Tf2N].26,28,35 The solubility of CF4 in [hmim][Tf2N] decreases with rising temperature. For example, at p ) 6 MPa and T ) 293 K (413 K), about 0.16 (0.13) mol of CF4 dissolve in 1 kg of [hmim][Tf2N]. However, in the case of the highest two temperatures (373.2 and 413.3 K), the two solubility
J. Phys. Chem. B, Vol. 112, No. 10, 2008 3041
Figure 1. Total pressure above solutions of CF4 + [hmim][Tf2N]: (2, ≈293 K; O, ≈333 K; 9, ≈373 K; 0, ≈413 K) experimental results; (s) correlation by the extended Henry’s law (i.e., method I).
TABLE 1: Experimental Results for the Solubility of Gas G ) CF4 in [hmim][Tf2N] T (K)
mG (mol kg-1)
293.3 ( 0.1 0.05216 ( 0.00024a 0.07506 ( 0.00029 0.10018 ( 0.00035 0.12130 ( 0.00040 0.14223 ( 0.00046 0.16303 ( 0.00051 0.18422 ( 0.00057 0.2182 ( 0.0010 333.2 ( 0.1 0.03852 ( 0.00020a 0.06679 ( 0.00026 0.09726 ( 0.00033 0.12902 ( 0.00041 0.15020 ( 0.00047 0.17170 ( 0.00053 373.2 ( 0.1 0.02759 ( 0.00017a 0.05197 ( 0.00021 0.07428 ( 0.00026 0.10707 ( 0.00035 0.14144 ( 0.00044 0.17609 ( 0.00065 413.3 ( 0.1 0.02818 ( 0.00016 0.03942 ( 0.00018 0.04669 ( 0.00019 0.07052 ( 0.00025 0.10533 ( 0.00034 0.13924 ( 0.00043 0.18578 ( 0.00066
p (MPa)
(fG/mG) (MPa mol-1 kg)
1.633 ( 0.027 2.346 ( 0.028 3.250 ( 0.030 4.116 ( 0.032 5.086 ( 0.033 6.123 ( 0.035 7.322 ( 0.037 9.582 ( 0.048 1.428 ( 0.019 2.508 ( 0.029 3.799 ( 0.032 5.323 ( 0.035 6.474 ( 0.037 7.695 ( 0.039 1.127 ( 0.019 2.131 ( 0.021 3.133 ( 0.030 4.668 ( 0.034 6.459 ( 0.038 8.386 ( 0.046 1.202 ( 0.019 1.693 ( 0.020 2.010 ( 0.021 3.117 ( 0.030 4.766 ( 0.034 6.451 ( 0.038 9.006 ( 0.048
29.36 ( 0.53 28.50 ( 0.39 28.56 ( 0.32 28.88 ( 0.28 29.30 ( 0.26 29.57 ( 0.25 29.91 ( 0.23 30.50 ( 0.30 35.84 ( 0.54 35.40 ( 0.46 35.76 ( 0.35 36.51 ( 0.30 37.22 ( 0.28 37.74 ( 0.26 40.21 ( 0.74 39.82 ( 0.44 40.42 ( 0.44 40.97 ( 0.35 42.01 ( 0.30 42.87 ( 0.31 42.27 ( 0.72 42.44 ( 0.54 42.43 ( 0.48 43.23 ( 0.46 43.79 ( 0.36 44.38 ( 0.31 45.81 ( 0.31
a Those experimental points were not taken into account for the extrapolation procedure to determine Henry’s constant.
isotherms are nearly overlapped; the solubility thus being almost temperature-independent. In contrast to the other gases that were investigated up to now,26,28,35 CF4 by far featured the slowest solution kinetics. Depending on the gas amount introduced, equilibration needed from a minimum of 3 up to 6 days at 293 K. Higher temperatures accelerate the gas absorption, but at 413 K, a period of 1-2 days is still required. The experimental uncertainty for the gas molality ∆mG (caused by the filling procedure) was estimated from a Gauss error propagation calculation and amounts at average to 0.00038
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mol kg-1 (0.38%). The experimental uncertainty for the solubility pressure p was calculated from ∆p ) ((∆psys + ∆pstat). The first term accounts for the systematic uncertainties {i.e., pressure transducer’s uncertainty (0.1% of the transducer’s full scale) + uncertainty resulting from the temperature drift (0.01 MPa)}. The second term is a statistical one from a Gauss error propagation calculation (by applying the vapor-liquid equilibrium (VLE) model described below (method I)). It reflects the effect of the uncertainties of temperature and gas molality on the solubility pressure p. The absolute (relative) uncertainty in the pressure ∆p (∆p/p) amounts in average to about 0.032 MPa (0.9%). The relative uncertainty decreases from at maximum 1.7% at low pressures to (at minimum) 0.5% at the highest pressure. Correlation of the Gas Solubility The correlation of the solubility of CF4 in [hmim][Tf2N] was achieved with two methods. One method (here labeled “method I”) expresses the VLE through the extended Henry’s law. It accounts for the influence of temperature and pressure on the Henry’s law constant, and it combines an expression for the Gibbs excess energy of the liquid phase (to express the activity of the gas in the ionic liquid) with an equation of state (to express the fugacity of the gas in the vapor). The other method (here labeled “method II”) expresses the VLE through the “equal fugacity” criterion and calculates fugacity coefficients from an equation of state. Both methods and the resulting correlations are discussed in the following sections. Method I. Correlation with the Extended Henry’s Law. This method was used in previous work of the group at the University of Kaiserslautern.7,23-28,32 As the vapor pressure of the particular ionic liquid is negligibly small, the VLE is solely expressed through the extended Henry’s law. Arbitrarily, this law is applied on a molality scale basis.
kH,G(T,p)aG(T,mG) ) fG(T,p)
(1)
kH,G(T,p) is Henry’s constant of the gas G (tetrafluoromethane) in [hmim][Tf2N] at temperature T and pressure p (based on the molality scale). The term aG(T,mG) is the activity of the gas in the liquid phase at temperature T and gas molality mG. Also, fG(T,p) is the fugacity of the gas in the vapor phase. The influence of pressure on Henry’s constant is expressed as
kH,G(T,p) ) k(0) H,G(T) exp k(0) H,G(T)
( ) V(∞) m,G p RT
(2)
V(∞) m,G
where and are the Henry’s constant at zero pressure and the partial molar volume of the gas at infinite dilution in the ionic liquid, respectively, and R is the universal gas constant. The activity of the gas in the ionic liquid is
aG )
mG γ m° G
(3)
where m° ) 1 mol kg-1. The activity coefficient γG is calculated employing the virial expansion for the excess Gibbs energy according to Pitzer:33,34
( )
mG 2 mG ln γG ) 2 β(0) µ G,G + 3 m° m° G,G,G
(4)
Figure 2. Influence of the total pressure on the ratio of the fugacity of CF4 (in the gaseous phase) to the molality of that gas (in the ionic liquid [hmim][Tf2N]): (2, ≈293 K; O, ≈333 K; 9, ≈373 K; 0, ≈413 K) experimental results (and estimated uncertainties); (s) linear fit.
TABLE 2: Henry’s Constant of Gas G ) CF4 in [hmim][Tf2N] (at Zero Pressure and on the Molality Scale) k(0) H,G (MPa) T (K)
experimental result
calculated from EoS
293.3 333.2 373.2 413.3
27.74 ( 0.37 34.10 ( 0.34 38.82 ( 0.37 41.67 ( 0.49
28.56 35.44 39.74 42.03
The parameters β(0) G,G and µG,G,G in eq 4 describe binary and ternary interactions, respectively, between gas molecules in the solvent. Ultimately, the fugacity of the pure gas fG(T, p) is the product of the total pressure p and the fugacity coefficient φG(T,p):
fG(T,p) ) pφG(T,p)
(5)
The fugacity coefficient was calculated using the Bender equation of state for CF4 developed by Platzer and Maurer.29 An extrapolation (at constant temperature) of the experimental results for the solubility pressure of the gas in [hmim][Tf2N] gives Henry’s constant of the gas in [hmim][Tf2N] at zero pressure:
k(0) H,G(T) ) lim pf0
[ ] fG(T,p) mG/m°
(6)
The results for fG/(mG/m°) are given together with the estimated uncertainties in Table 1. Figure 2 shows the extrapolation according to eq 6. As can be seen from this figure, the experimental results at T ) 293.3, 333.2, and 373.2 K at the lowest investigated pressure are obviously not in line with the other experimental points (outside their estimated experimental uncertainty). It is assumed that the experimental uncertainty of those solubility pressures somewhat exceeds the assigned magnitude due to the extremely slow solubility kinetics. These data points therefore were excluded from the extrapolation process. Table 2 lists the numerical values for Henry’s constant (at zero pressure and on the molality scale). The estimated relative uncertainty for these Henry’s constants amounts in average to 1.1%.
Solubility of CF4 in [hmim][Tf2N]
J. Phys. Chem. B, Vol. 112, No. 10, 2008 3043
∆solSm ) (∆solHm - ∆solGm)/T
(11)
(
(12)
∆solCp,m )
)
∂∆solHm ∂T
p
It may be worth mentioning that Henry’s constant on the molality scale k(0) H,G(T) is related to Henry’s constant on the mole fraction scale k(0),(x) H,G (T) by (0) k(0),(x) H,G (T) ) kH,G(T)/(MSolvent/1000)
Figure 3. Henry’s constant of CF4 in [hmim][Tf2N] (at zero pressure, on the molality scale) plotted against the (inverse) temperature: symbols ) extrapolated experimental results (and estimated uncertainties); solid curve ) correlation employing eq 7; dashed curve ) calculated from the RK-EoS.
The results were correlated by the following equation:
ln(k(0) H,G/MPa) ) 7.537 - 893.8/(T/K) - 0.003977(T/K) (7) The deviation between experimental and correlated values for Henry’s constant evidently remains within the experimental uncertainty that is given in Table 2. In Figure 3, both the experimental data (obtained from the extrapolation to zero pressure) and the results from the correlation function for Henry’s constant (cf. eq 7) are plotted versus the inverse absolute temperature. Parameter studies revealed that, as the solubility of CF4 in [hmim][Tf2N] is so small, it is sufficient to assume ideal mixing (i.e., setting the activity coefficient of the gas γG ) 1, corresponding to β(0) G,G ) µG,G,G ) 0). Therefore, the experimental data were only used to fit V(∞) m,G, resulting in the following: 3 -1 2 V(∞) m,G/(cm mol ) ) -261.4 + 1.61(T/K) - 0.00216(T/K) (8)
The full lines shown in Figure 1 represent the correlation results for the solubility pressure. The correlation results for the gas solubility (i.e., the gas molalities at a given temperature and solubility pressure) agree with the experimental results within an average absolute (relative) deviation of about 0.00039 mol kg-1 (0.55%) {0.00027 mol kg-1 and 0.23%, respectively, after excluding the three data points at the lowest investigated pressure mentioned before}. Properties of Solution. From Henry’s constant kH,G(T,p) {eqs 2, 7, and 8} various related (molar) solution thermodynamic properties, ∆solXm, can be deduced.7 For example, X can be replaced by G (the Gibbs energy), H (the enthalpy), S (the entropy), or Cp (the heat capacity at constant pressure). The properties are determined from the following relations:
∆solGm ) RT ln(kH,G(T,p)/p°) ∆solHm ) R
[
(9)
]
∂ ln(kH,G(T,p)/p°) ∂(1/T)
p
(10)
(13)
where MSolvent is the relative molar mass of the solvent (here, [hmim][Tf2N]; MSolvent ) 447.42). Consequently, the Gibbs energy and the entropy of solution depend on the selection of the composition scale, too. The solution properties which directly follow from kH,G(T,p) are on the molality scale. They are converted to the corresponding properties on the mole fraction (x) scale (i.e., ∆solG(x) m and ∆solSm ) through the following:
∆solG(x) m ) ∆solGm - RT ln(MSolvent/1000)
(14)
∆solS(x) m ) ∆solSm + R ln(MSolvent/1000)
(15)
Table 3 shows the resulting values at standard conditions {that is, at standard pressure (p° ) 0.1 MPa) and at standard temperature (T° ) 298.15 K)} and their estimated uncertainties on both the molality scale and the mole fraction scale {designated by superscript (x)}. The uncertainty for ∆solG °m corresponds to the uncertainty of Henry’s constant (at zero pressure). The uncertainties of the derived properties (determined by differentiation) were deduced from the uncertainty of Henry’s constant (at zero pressure) as follows: Two additional sets of parameters for the correlation equation for Henry’s constant were determined. The first set was determined assuming that Henry’s constant at 413 K (the highest investigated temperature) was the upper number given in Table 2 and that Henry’s constant at 293 K (the lowest investigated temperature) was the lower number given in Table 2. The second set of parameters was determined assuming the assumption that Henry’s constant at 413 K was the lower number given in Table 2 and that Henry’s constant at 293 K was the upper number given in Table 2. All three correlations were used to calculate the derived properties (∆solHm°, ∆solSm°, and ∆solCp,m ° ). The differences of these correlations were used to estimate the uncertainties. Method II. Correlation with an EoS. This method was used in previous work of the group at DuPont to correlate the solubility of NH3, CO2, and various hydrofluorocarbon gas mixtures in ionic liquids.11-14 It is based on the equal fugacity criterion for components in coexisting phases:
f Li ) xi p φLi ) f Vi ) yi p φVi (i ) 1, 2)
(16)
where f Li (and φLi ) and f Vi (and φVi ) are the fugacity (and fugacity coefficient) of component i in the liquid phase and in the vapor phase, respectively. Here xi and yi are the mole fractions of component i in the liquid and vapor phase. A Redlich-Kwong type of equation of state (RK-EoS) is used to calculate the fugacity coefficients. As usual, that equation corrects the ideal gas equation of state by considering attractive intermolecular forces (through parameter a) and the size of the molecules (through parameter b).
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TABLE 3: Results for the Molar Solution Properties ∆solXm° of CF4 in [hmim][Tf2N] at Standard Temperature (T° ) 298.15 K) and Standard Pressure (p° ) 0.1 MPa) from Henry’s Constant ∆solGm° (kJ ∆solHm° (kJ mol-1) ∆solSm° (J mol-1 K-1) ∆solCp,m ° (J mol-1 K-1) mol-1)
molality scale
mole fraction scale
14.02 ( 0.03 -4.5 ( 0.2 -62.1 ( 0.5 19.8 ( 0.4
16.02 ( 0.03 -4.5 ( 0.2 -68.8 ( 0.5 19.8 ( 0.4
the composition of the mixture (expressed through mole fractions xi).14 N
a)
N
∑ ∑xai aj fij(T)(1 - kij)xixj i)1 j)1
The term kij is a binary, composition-dependent parameter
kij ) TABLE 4: Parameters for the Modified RK-EoS for the Binary System of CF4 + [hmim][Tf2N] M Tc (K) pc (MPa) β0 β1 β2 β3 a
CF4
[hmim][Tf2N]
88.01 227.5 3.7724 1.00153 0.39746 -0.071655 0.021057
447.42 815.0 1.6112 3.45264a 0.813588a -0.006256a 0.0
R2Tc2 R(T) pc
b) (17)
(18)
RTc pc
ln φi ) ln
(
∑∑(bi + bj)(1 - kij)(1 - mij)xixj
(26)
2 i)1 j)1
) (
)
(
)(
)
where
k
a′i )
R(T) ) β0 + β1[exp{2(1 - Tr)} - 1]
(21)
b′i )
a′i ) 2 (22)
For CF4, the coefficients βk were determined so as to reproduce the vapor pressure of that pure compound. They are given in Table 4. For the ionic liquid [hmim][Tf2N], the Tc and pc values were taken from a previous publication,11 and βk (k ) 0, 1, 2, 3) were determined from the present data analysis discussed below. It should be mentioned that eq 21 is here implemented in order to deal with very high reduced temperatures (similar to the solubility analysis of hydrogen + ionic liquid systems12). Equations 20 and 21 are analytically continuous at Tr ) 1. For general N-component mixtures parameters a and b are modeled in terms of their respective binary interaction parameters and
∂(na) ∂ni
nj*i
( )
nj*i
(28)
∂(nb) ∂ni
(29)
The total mole number is n, and ni is the mole number of species i. The explicit forms of a′i and b′i may be useful for readers and are given as follows: N
where
( )
and
(20)
and for temperatures above Tc
Tr ) T/Tc
N
RT 1 a + b′i + Vm - b RTb(Vm + b) p(Vm - b) Vm a a′i b′i (27) - + 1 ln RTb a b Vm + b
3
∑βk(1/Tr - Tr) k)0
N
(19)
The subscript c denotes a property at the critical point of the pure compound. The temperature-dependent part of the parameter a in the EoS for pure compounds R(T) is modeled by the following empirical relations12,14 for temperatures up to the critical temperature Tc
R(T) )
1
where another binary interaction parameter is introduced: mij ) mji, mii ) 0. There is a maximum of four binary interaction parameters: lij, lji, mij, and τij for each binary pair. The fugacity coefficient φi of the ith species for that EoS model is given by
and
b ) 0.08664
(25)
with another binary parameter τij ) τji and τii ) 0. The covolume parameter of the mixture is expressed by
where Vm is the molar volume,
a(T) ) 0.427480
(24)
fij(T) ) 1 + τij/T
For a pure compound
a(T) RT Vm - b Vm(Vm + b)
lijlji(xi + xj) ljixi + lijxj
where kii ) 0 and lij is a binary parameter. The term fij(T) is introduced to describe the influence of temperature on the mixing rule for parameter a
Determined in the present EoS analysis; see text for details.
p)
(23)
N
b′i )
∑ j)1
{
xai aj fijxj ∑ j)1
1 - kij -
{
}
lijlji(lij - lji)xixj (ljixi + lijxj)2
(bi + bj) (1 - mij)xj 1 - kij -
-a
}
lijlji(lij - lji)xixj (ljixi + lijxj)2
(30) -b (31)
In a first step, parameters βk (eqs 20 and 21) for [hmim] [Tf2N] were taken from a previous publication,11 and all four binary interaction parameters (lij, lji, mij, and τij) were made to correlate the new gas solubility data. However, that procedure failed to give a satisfying correlation. This difficulty was quite surprising, since previously it was successfully applied to many binary systems containing RTILs.11-14 After various tests (by
Solubility of CF4 in [hmim][Tf2N]
J. Phys. Chem. B, Vol. 112, No. 10, 2008 3045
Figure 5. Plot of experimental data for Henry’s constants (at zero pressure, on the mole fraction scale) of CHnF4-n gases (n ) 0 to 4) {(a) CH4, (b) CHF3, (c) CH2F2, (d) CH3F, and (e) CF4} in RTILs at 298.15 K as a function of the gas critical temperature: (b) RTIL ) [bmim][PF6] {a,5 b-d17}; (O) RTIL ) [hmim][Tf2N] {a,35 e (this work)}; (2) RTIL ) [bmim][CH3SO4] {a46}; (4) RTIL ) [bmim][BF4] {a,5 d20}; (s) trend line.
Figure 4. Correlation results for Henry’s constant (at zero pressure, on the molality scale) of five different gases in [hmim][Tf2N]: (a) H2,26 (b) CF4 (this work), (c) CH4,35 (d) Xe,35 and (e) CO2.28
trial and error), it was found that this binary system is quite unusual, because the four binary interaction parameters are not needed at all when only the βk parameters (for k ) 0, 1, 2, and 3) of [hmim][Tf2N] were adjusted. When all four binary parameters are set to zero, the mixing rules reduce to the original van der Waals mixing rule without any adjustable parameter. Finally, we set β3 ) 0 and fitted the remaining three parameters β0, β1, and β2 of [hmim][Tf2N] in a nonlinear regression analysis to the new experimental data for the solubility pressure. The resulting parameters are given in Table 4. The average absolute deviation (AAD) between the experimental results and the correlation results for the solubility pressure (as well as for the solubility of the gas at constant pressure and temperature) is 0.70%. The equation of state also allows for the direct calculation of Henry’s constant on a mole fraction scale. Details are given in the appendix. The resulting Henry’s coefficients (converted to the molality scale by eq 13) are also given in Table 2 and compared with the experimental results in Figure 3. The calculated Henry’s constants are slightly higher but agree with the experimental results within an average relative deviation of 2.5% for the isotherms investigated here. In Figure 4, Henry’s constants for all gases in the RTIL [hmim][Tf2N] (at zero pressure and on the molality scale) published so far26,28,35 are plotted versus the inverse temperature. Some of these particular systems were previously investigated by several groups.11,36-43 The solid curves refer to the correlation results reported in the respective references. These solid curves converge at the -imaginary- critical temperature of the RTIL, where the slope of all curves is equal to infinity.44,45 The sequence of the curves shows that within the investigated temperature range CO2 has the largest solubility in [hmim] [Tf2N], followed by Xe, CH4, CF4, and ultimately H2. Furthermore, the slope of these curves displays a decreasing gas
solubility with rising temperatures for all gases except H2. Figure 4 also shows that the curves for CF4 and H2 might intersect at T > 453 K. Recently, two of the authors (M.B.S. and A.Y.) have found an empirical relationship between the Henry’s constants of a series of hydrofluorocarbon gases in an RTIL (at a given temperature) and the critical temperatures of those pure gases.17 A linear relationship between ln k(0),(x) H,G (T) (on the mole fraction scale) and Tc,G exists for both series CHnF4-n (n ) 1 to 3) and C2HnF6-n (n ) 1 to 5) in [bmim][PF6]; those straight lines have different slopes. The qualitative physical reason given there17 was, roughly speaking, that ln k(0),(x) H,G (T) is closely related to the intermolecular interaction potential and Tc,G is nearly proportional to the intermolecular potential well-depth () (at least for the case of noble gases). In the CHnF4-n series, the CF4 + [bmim][PF6] system was missing at that time. Although the binary system investigated in the present publication contains a different ionic liquid ([hmim][Tf2N]), ln k(0),(x) H,G (T ) 298.15 K) for CF4 + [hmim][Tf2N] falls onto the same straight line, as can be seen in Figure 5, whereas the corresponding value for CH4 + [hmim][Tf2N]35 is far off that line. Figure 5 also shows results for ln k(0),(x) H,G (T ) 298.15 K) for CH2F4 + [bmim] [BF4],20 CH4 + [bmim][BF4],5 and CH4 + [bmim][CH3SO4].46 Here, the ionic liquid has the same cation (i.e., [bmim]+), and the anions are of comparable size resulting in a not drastically different (relative) molar mass of the ionic liquid (M ) 226.0 for [bmim][BF4], M ) 250.3 for [bmim][CH3SO4], and M ) 284.2 for [bmim][PF6]). Compared to these ionic liquids, the (relative) molar mass of [hmim][Tf2N] is significantly higher. Again, those data agree with the linear relationship quite well. Conclusions We report experimental results for the solubility of tetrafluoromethane in the ionic liquid [hmim][Tf2N] from about 293 to 413 K and up to approximately 10 MPa. The data are used to determine Henry’s law constants. Furthermore, the gas solubility data were correlated with two methods. One method is based on Henry’s constant and an equation of state for describing the vapor-phase properties of pure CF4, whereas the other method uses an equation of state to calculate fugacities in both coexisting
3046 J. Phys. Chem. B, Vol. 112, No. 10, 2008
Kumełan et al.
phases. Both methods prove to provide good correlation instruments for the gas solubility of CF4 in [hmim][Tf2N].
xaGaIL fij(1 - kij) - aIL; in the present binary system, kij ) mij
Acknowledgment. J.K. and G.M. appreciate financial support by Deutsche Forschungsgemeinschaft (DFG), Bonn-Bad Godesberg, Germany. M.B.S. and A.Y. thank DuPont Central Research and Development for supporting a part of the present work. The authors thank Dr. K. Massonne, BASF AG, Ludwigshafen, Germany, for generously supplying the ionic liquid [hmim][Tf2N] for this study.
References and Notes
Appendix Henry’s Law Constant of a Gas G in a Pure RTIL from the Particular Version of the RK-EoS. The fugacity fLG of a gas G in a liquid phase (of the ionic liquid) can be expressed as /,(x) f LG ) k(x) H,G(T,p)xGγG
(A.1)
where k(x) H,G(T,p) is Henry’s constant of the gas in the ionic liquid (on a mole fraction scale basis), and xG and γ/,(x) are the G mole fraction and the activity coefficient of the gas (normalized according to Henry’s law) in the liquid phase, respectively. Applying an equation of state gives for the same property
fLG ) xGpφLG
(A.2)
where φLG is the fugacity coefficient of the gas in the liquid phase. From eqs A.1 and A.2, one easily recognizes that Henry’s law constant at zero pressure k(0),(x) H,G can be calculated as L k(0),(x) H,G ) lim (pφG)
(A.3)
xGf0
where the fugacity coefficient is given by eq 27:
ln φi ) ln
(
) (
)
RT 1 a + b′i + Vm - b RTb(Vm + b) p(Vm - b) Vm a a′i b′i - + 1 ln (A.4) RTb a b Vm + b
(
)(
)
In the limiting case described in eq A.3, Vm, b, and a in eq A.4 become the molar volume Vm,IL, the covolume parameter bIL, and the attractive parameter aIL of the ionic liquid, respectively. Furthermore, the molar volume of the ionic liquid is easily calculated from setting p ) 0 in the equation of state for the pure ionic liquid, resulting in the following:
Vm,IL)
[ ][ x
1 aIL - bIL 1 2 RT
1-
]
4aILbILRT (bILRT - aIL)2
(A.5)
Henry’s law constant at zero pressure is then expressed as
ln(k(0),(x) H,G ) ) ln b′G
(
(
)
RT + Vm,IL - bIL
)
aIL 1 + Vm,IL - bIL RTbIL(Vm,IL + bIL) Vm,IL aIL a′G b′G + 1 ln (A.6) RTbIL aIL bIL Vm,IL + bIL
(
)(
)
where b′G ) (bG + bIL)(1 - kij)(1 - mij) - bIL and a′G ) 2
) 0 and fij ) 1.
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