J. Phys. Chem. B 2009, 113, 3461–3468
3461
Advantages of Ion-based Mole Fractions for Describing Phase Equilibria in Ionic Liquids: Application to Gas Solubility Marı´a Paula Longinotti,†,‡ Jorge L. Alvarez,†,§ and M. Laura Japas*,†,| Gerencia de Quı´mica, Comisio´n Nacional de Energı´a Ato´mica, AV. del Libertador 8250, 1429-Buenos Aires, Argentina, Departamento de Quı´mica Inorga´nica, Analı´tica y Quı´mica Fı´sica, Facultad de Ciencias Exactas y Naturales, UniVersidad de Buenos Aires, Ciudad UniVersitaria, 1428-Buenos Aires, Argentina, UniVersidad Tecnolo´gica Nacional, Facultad Regional Buenos Aires, Medrano 951, 1179-Buenos Aires, Argentina, and ECyT, UNSAM, Martı´n de Irigoyen N° 3100(1650), San Martı´n, ProV. Buenos Aires, Argentina ReceiVed: October 31, 2008; ReVised Manuscript ReceiVed: January 9, 2009
Despite the obvious ionic character of ionic liquids (ILs), previous studies of phase equilibria in these media were formulated implicitly assuming a “molecular” behavior of the ionic solvent. In this work, a more appropriate thermodynamic treatment is applied to describe the solubility of gases in ILs. According to our results, if the concentration is expressed on an ionic basis, solutions of simple gases in ILs display rather small deviations from ideal behavior in wide composition ranges, whereas deviations are larger when the solvent is considered as an anion-cation pair. The present thermodynamic formulation also accounts for the observed solid-liquid phase equilibria of molecular and IL binary mixtures. Introduction Ionic Liquids (ILs) are a group of compounds formed by bulky organic cations and comparatively small anions that melt at relatively low temperatures, close to ambient.1,2 During the past decade, ILs have been the subject of intense studies, spurred by an increasing demand for replacing toxic, flammable, volatile liquids in industrial processes by more benign solvents. ILs are considered alternative reaction media to organic solvents mainly due to their very low volatility and versatile solvent power, tunable in some degree by the selection of anion and cation, rendering liquids with different hydrophobicity, basicity, hydrogenbond capabilities, etc. (task-specific ILs).3,4 Also, these liquids have attracted the attention of the scientific community since they provide an excellent opportunity to broaden our knowledge of the liquid state. For both purposes, the properties of solutions in ILs are of paramount importance. First, because in most potential industrial applications ssuch as catalytic reactions, gas or liquid separations, removal of metal ions, matrices for mass spectroscopy, cleaning operations, and fuel cells5–10s ILs are the media where the process takes place, that is, the solvent, and properties of the dissolved substances, such as reactivity or selectivity, are strongly affected by the medium. In addition, the properties of solutions, especially those containing simple solutes, can help understanding structural aspects and interaction characteristics of the solvent. As a matter of fact, dissolution properties of simple gases in molecular solvents have played a significant role in the development of the present ideas about the microscopic structure of solutions, that is, about solvation.11 In this work, we present a thermodynamic analysis of gas solubility in ILs. We focus specially on CO2-ILs systems, mainly because there is abundant information of phase equilibria * To whom correspondence should be addressed. E-mail: mljapas@ cnea.gov.ar. † Comisio´n Nacional de Energı´a Ato´mica. ‡ Universidad de Buenos Aires. § Universidad Tecnolo´gica Nacional. | ECyT, UNSAM.
in these systems and also owing to the interest for the surprisingly high solubility of CO2 in most ILs. In addition, the solubility of few other representative gases in ILs are analyzed to illustrate the coupling between pressure and concentration in the thermodynamic description, but without the intention of exhaustively covering the available experimental information. Actually, the main goal of this paper is to draw the attention to an aspect that has been surprisingly overlooked in previous thermodynamic analysis: the fact that ILs are composed by ions, thus requiring a consistent thermodynamic treatment. Neglecting this fact may lead to wrong conclusions. Thermodynamic Analysis The solubility of gases in liquids is frequently described in terms of the Henry’s constant kH, defined as the limiting (x f 0) value of the ratio between the solute’s fugacity f2 and its concentration in the liquid phase x. Solution thermodynamics provides an expression for kH in terms of the variables T, p, and x,12
kH(T) ) lim xf0
(
f2 f2 exp ) H x xγ2 (T, x)
∫pp * 1
)
V2(T, p, x) dp (1) RT
where, in the liquid phase, the effects of concentration and pressure values different from those corresponding to x f 0 (and p f p*1, with p*1 the vapor pressure of the solvent) are taken into account through the activity coefficient γ2H and the exponential (Poynting) term, with V2 denoting the partial molar volume of the solute in solution. The composition x in eq 1 arises from the entropic (ideal mixing) term and represents the fraction of the solute’s particles among all independent particles. Due to the ionic character of the solvent, for singly charged ILs, an appropriate expression for the solute’s concentration is
10.1021/jp809651e CCC: $40.75 2009 American Chemical Society Published on Web 02/23/2009
3462 J. Phys. Chem. B, Vol. 113, No. 11, 2009
x)
Longinotti et al.
n2 2n1 + n2
(2)
where n2 indicates the amount (in moles) of the solute, and n1 is that of the fused salt. Surprisingly, most thermodynamic treatments published previously used, instead, a formula-based definition of the concentration variable, implicitly assigning a molecular character to the solvent:
X)
n2 n1 + n2
(3)
This alternative definition of the composition, related with the ion-based concentration x through X ) 2x/(1 + x), implies the definition of an alternative Henry’s constant KH, as given in most studies
KH(T) ) lim
Xf0
(
f2 f2 exp ) X XΓH2 (T, X)
∫pp * 1
)
V2(T, p, X) dp RT
(4) where Γ2H represents the activity coefficient within this formalism. Cleary, this representation renders values of Henry’s constant KH that are half-those of the ion-based kH
kH(T) KH(T) ) 2
ΓH2 ) γH2 (x + 1)
(6)
differ in their concentration dependence: both activity coefficients are equal to 1 in the limit x f 0 by definition, but as the concentration of solute increases, the activity coefficient in the formula-based representation Γ2H becomes larger than that of the ion-based representation. Therefore, the two formulations will have a different range of validity of the infinite-dilution assumption. The last observation has an important consequence in the way isothermal values of f2/x (or f2/X) change with pressure along phase equilibria. This pressure dependence, denoted here as ω and Ω, can be obtained from eqs 1 and 4:
[
d ln(f2 /x) dp
]
d ln(f2 /X) Ω) dp
]
[
) T,σ
T,σ
Ω)ω+
V2 d ln γH2 + RT dx
(
)(
(
)(
V2 d ln ΓH2 ) + RT dX
T
T
dx dp
)
dX dp
T,σ
)
T,σ
(7)
(8)
where subscript σ indicates phase equilibrium conditions. According to eqs 7 and 8, for slightly soluble gases, that is systems with small values of (dx/dp)T,σ or (dX/dp)T,σ, both ω and Ω equal V2/RT; however, for very soluble gases, V2 can not be computed from phase equilibria data without information of the activity coefficients.
1 dX 2 - X dp
( )
T,σ
)ω+
1 dx 1 + x dp
( )
(9)
T,σ
showing that ω and Ω adopt similar values only for slightly soluble gases, whereas for very soluble gases Ω takes values that are larger than those of the ion-based representation ω. Another alternative scale to express the solute’s concentration in ILs has been used by Maurer and collaborators (ref 13 and references therein). In their works, they analyzed the solubility of gases in ILs using the molality m as concentration variable, related to x through
m)
2000 x Mr,IL 1 - x
(10)
where Mr,IL represents the formula weight of the IL in g/mol. For highly soluble solutes this choice is clearly inadequate, as m represents the ideal entropic contribution of mixing only for dilute solutions. The associated Henry’s constant KH,m, activity coefficient ΓH2 ,m and slope Ωm are related with the corresponding ion-based quantities through eqs 11, 12, and 14:
Mr,IL 2000
(11)
ΓH,m ) γH2 (1 - x) 2
(12)
KH,m(T) ) kH
(5)
More important, activity coefficients Γ2H and γ2H, related through eq 6,
ω)
Taking into account that partial molar volumes do not depend on the speciation of the solvent, the slopes ω and Ω are related to each other through eq 9,
[
d ln(f2 /m) Ωm ) dp Ωm ) ω -
]
(
V2 ∂ ln ΓH,m 2 ) + RT ∂m
T,σ
1 dx 1 - x dp
( )
T,σ
)ω-
)( T
dm dp
)
T,σ
Mr,IL dm (1 - x) 2000 dp
(13)
( )
T,σ
(14) According to eq 12, activity coefficients in the molality scale H are smaller than γ2H; moreover, they go to zero as x f 1 Γ2,m due to the unbounded nature of the molality scale. Equation 14 shows that the slope Ωm in the molality scale differs from ω by a term that is proportional to (dx/dp)T,σ, as does Ω, but with an opposite sign. For each formulation, the enthalpy and entropy of dissolution (∆disH2∞ and ∆disS2∞) can be computed from the temperature derivative of the Henry’s constant. For the ion-based representation, the well-known expressions are:
(
∆disH2∞ ) H2∞ - H†2 ) R
∆disS∞2 ) S∞2 - S†2 )
d ln kH d(1/T)
)
∆disH∞2 - R ln kH T
(15)
(16)
where H2∞ and S2∞ are the solute’s partial molar enthalpy and entropy (Henrian limit) in the liquid phase at standard conditions (T, p ) p1*, x ) 1) whereas H2† and S2† are the enthalpy and
Phase Equilibria of Molecular and IL Binary Mixtures entropy of the ideal gas at T and p2 ) 1 MPa. Similar equations hold for the other two formulations. Since the various Henry’s constants differ just in a numerical factor, independent of temperature, values of the enthalpy of dissolution should be independent of the concentration scale. However, the entropies of dissolution in the ion-based representation will be lower than those of the formula-based description by -R ln 2. In summary, each of these alternative definitions of the concentration variable, generally referred to as c, has associated not only its own values of Henry’s constant and entropy of dissolution but also a range of validity of the infinite-dilution limit and a pressure dependence of f2/c. Although Henry’s constants and entropies of dissolution differ only in a scale factor, for highly soluble solutes the different concentration dependence of the activity coefficients has a more profound effect on data analysis and on the possibility of interpreting experimental data in terms of thermodynamic properties in a simple way. Data Selection and Analysis There are many studies of gas solubility in ILs. To illustrate the difference between concentration variables and to compare their corresponding thermodynamic properties we have selected few binary systems, without performing neither an exhaustive literature search nor a deep comparison between data sets. The ILs analyzed are all imidazolium-based, combined with fluorinated (PF6-, BF4-, or bis[(trifluoromethyl) sulfonyl]imide NTf2-) and nonfluorinated (CH3SO4-) anions. We analyze here the solubilities of CO2, Xe, CH4, and H2 in some of these ILs: CO2 since there is abundant information and because its high solubility represents a stringent test to our analysis; Xe, another gas that displays high solubilities in ILs, was included to compare its properties with those of CO2. To evaluate the influence of the (dc/dp)T,σ term in eqs 7, 8, and 13, we have also analyzed systems composed by gases with low (H2) and intermediate (CH4) solubilities. For the CO2-ILs systems, the data of Peters and collaborators were selected since they cover the widest range of pressures, that is, of concentrations. These systems are 1-ethyl-3-methylimidazolium hexafluorophosphate (emimPF6),14 1-butyl-3-methylimidazolium hexafluorophosphate (bmimPF6),15 1-hexyl-3methylimidazolium hexafluorophosphate (hmimPF6),16 1-butyl3-methylimidazolium tetrafluoroborate (bmimBF4),17 1-hexyl3-methylimidazolium tetrafluoroborate (hmimBF4),18 1-octyl-3methylimidazolium tetrafluoroborate (omimBF4),19 and 1-ethyl3-methylimidazolium bis[(trifluoromethyl) sulfonyl]imide (emimNTf2).20 For one of these systems (CO2 + bmimPF6) we have also included the data reported by Maurer and collaborators21,22 for comparison and to test the procedure applied by us to Peters data to obtain isothermal solubility values from experimental data. To have a better picture of the influence of the anion in the gas solubility, the systems 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl] imide (hmimNTf2)23 and 1-butyl3-methylimidazolium methylsulfate (bmimCH3SO4),22 as studied by Maurer and colleagues, were also analyzed. For the other gases, the data of Maurer and collaborators were chosen since they cover a considerable pressure range (up to 12 MPa) and show low scattering. From this source, we analyzed the following systems: Xe in hmimNTf224 and in bmimCH3SO4;25 CH4 in hmimNTf224 and in bmimCH3SO4;25 and H2 in bmimPF6,26 in hmimNTf2,27 and in bmimCH3SO4.28 In all these cases, due to the negligible vapor pressure of the ILs, the gas phase was assumed to be a pure gas. This assumption appears to be valid for these nonpolar gases. Systems
J. Phys. Chem. B, Vol. 113, No. 11, 2009 3463 containing CHF3 were excluded from the analysis because at moderate and high pressures the concentration of the IL in the gaseous phase is known to be significant, concomitantly requiring information of cross interactions in that phase. Measurements by Peters and colleagues were performed along isopleths (lines of constant composition) by determining the bubble pressure as a function of the temperature. To obtain values of Henry’s constant from these data sets, the following procedure was applied: (1) The solute’s fugacity, f2, of the pure gas was calculated for each data point using the REFPROP program.29 (2) Along isopleths, a polynomial representation of degree 2 in T was fitted to the fugacity f2 data within the experimental uncertainty. (3) For each isopleth, f2 was calculated, by interpolation, at predefined temperatures using the polynomial representation obtained in step 2. (4) Values of f2/x, f2/X, and f2/m were calculated along isotherms as a function of the pressure. Instead, Maurer and colleagues determined the solubility of gases as a function of the pressure along isotherms. For these data, only steps 1 and 4 needed to be applied. For the calculation of kH, KH, and KH,m, isothermal values of ln(f2/c) were fitted to a linear function of the pressure; the fitting set was restrained to x e 0.3 (dilute region). The intercepts represent the logarithm of Henry’s constants and the slopes provide the values of ω∞, Ω∞, and Ωm∞. Enthalpies of dissolution ∆disH2∞ were obtained, according to eq 15, by fitting the logarithm of Henry’s constants to a linear dependence in T-1. Entropies of dissolution ∆disS2∞, were then calculated from Henry’s constants and ∆disH2∞ according to eq 16. Results and Discussion Figure 1 depicts the values of ln(f2/c), with c either x (panel A), X (panel B), or m (panel C), as a function of the pressure along three isotherms for the system bmimPF6 + CO2. Also represented in Figure 1 are the values of (∆c/∆p)T,σ for one of the isotherms. This ratio (∆c/∆p)T,σ should be considered as an approximation to the derivative (dc/dp)T,σ. Panel A shows that ln(f2/x) changes smoothly with pressure, apparently uncoupled from the changes in (∆x/∆p)T,σ. On the other hand, ln(f2/X) in panel B exhibits an initial pressure dependence that is rather curved and a strong reduction in slope at pressures around 10 MPa, which is the range where (∆X/ ∆p)T,σ reaches a small and almost constant value. For pressures larger that 10 MPa, the data seem to be linear in p, with slopes similar to those obtained for ln(f2/x). Moreover, the data in panel B also show that the higher the temperature, the smaller the values of the initial slope, whereas in the high-pressure range all slopes are rather alike. These observations suggest that in the low pressure region, where (∆X/∆p)T,σ is large, the contribution of the activity term (second term in the right-hand side of eq 8) is significant and that it becomes less important at higher temperatures where the values of (∆X/∆p)T,σ are smaller. Finally, panel C shows a strong, negative variation of ln(f2/m) with pressure, for p e 12 MPa approximately, whereas for higher pressures the sign of the slope is inverted. Again, the change in behavior occurs in a pressure range similar to the one observed for the change in (∆m/∆p)T,σ, suggesting that the behavior of ln(f2/m) in the low concentration limit is actually determined by the activity term (second term in the right-hand side of eq 13).
3464 J. Phys. Chem. B, Vol. 113, No. 11, 2009
Longinotti et al. in Figure 2, RTΩ ) RT(d ln(f2/X)/dp)T,σ and RTΩm ) RT(d ln(f2/ m)/dp)T,σ change strongly and quite linearly with dX/dp and dm/ dp respectively, and both extrapolate to similar values (V2∞ between 30 and 50 cm3/mol) as dc/dp goes to zero, while RTω does not show a definite trend, just experimental noise probably amplified by our crude data treatment. Slopes in Figure 2 are (d ln Γ2Η/dX)T ) 0.50 ( 0.10 and (d ln Γ2H,m/dm)T ) -0.14 ( 0.02. Using eqs 6 and 12, these slopes can be related to (d ln γ2H/dx)T by
(
Figure 1. Dependence of the solubility on pressure for the system bmimPF6 + CO2. The circles denote data from ref 15 along three selected isotherms. Triangles indicate data from references 21 and 22. Panel A shows data of ln(f2/x), panel B is ln(f2/X), and panel C is ln(f2/ m). Pressure units are MPa. For all panels, stars indicate (∆c/∆p)T,σ (right scale of each panel). Lines are a guide to the eye.
Figure 2. Ratio between ∆ln(f2/c) and ∆p as a function of ∆c/∆p along the 313.75 K isotherm for the system bmimPF6 + CO2,.15 The ordinates are crude approximations of RTω∞, RT Ω∞, and RT Ωm∞. For the X and m representations, linear regressions to the data are shown as solid and dashed lines respectively. Note that, for each representation, the dilute region is actually that with the largest values of ∆c/∆p.
The dependence of ln(f2/c) on p and c is further explored in Figure 2, where the values of RT(d ln(f2/c)/dp)T,σ and (dc/dp)T,σ (actually, the incremental ratios) are plotted for bmimPF6 + CO2 at 313.75 K for the three concentration variables. According to eq 7, if the concentration range is not too large, the representation of RT(d ln(f2/x)/dp)T,σ ) RTω as a function of (dx/dp)T,σ should give a straight line with intercept V2∞ and slope RT(d ln γ2Η/dx)T (similar expressions hold for the other concentration variables as given by eqs 8 and 13). As depicted
d ln ΓH2 dX
) [( T
≈
) ] ( ) [(
d ln γH2 dx
T
+1
1 2
d ln ΓH,m 2 dm
T
≈
d ln γH2 dx
) ] T
-1
Mr,IL 2000
with Mr,IL/2000 ) 284.18/2000 ) 0.1421. These values are consistent with |(d ln γ2Η/dx)T| , 1 and with the assumption of a linear relation between variables in Figure 2. Note that, in Figure 2, the dilute regime (c f 0) is characterized by the largest (dc/dp)T,σ values; in that region Ω and Ωm adopt respectively very large positive or negative values, meaning that they are strongly affected by the activity coefficient term. In contrast, the fact that the values of RTω are all around the limiting value of 26 cm3/mol for 313.75 K, with little influence of (dx/dp)T,σ, indicates a small contribution of (d ln γ2Η/dx)T, as previously mentioned. Table 1 gives the values of ln kH and ln KH and the initial slopes RTω∞ and RTΩ∞ for all studied systems at a common temperature (333 K). Due to the very large effect of the term containing (∂ ln Γ2H,m/∂m)T in eq 13, which prevails over the V2∞/RT term, the values corresponding to the molality scale RTΩm∞ and KH,m were not included. Results in Table 1 show some general trends. First, for systems with high solubility (all systems with CO2 and Xe) the values of kH and KH do not exactly differ by a factor of 2 (see eq 5): values of ln KH are slightly but systematically larger than ln(kH /2) due to the curvature of ln(f2/X) as a function of p and the relatively large values of concentration of the dilute solutions. On the contrary, the molality representation (not shown) gives values of KH,m that, converted to kH using eq 11, show good agreement with those obtained from the extrapolation of (f2/x) to p f p1*. This observation is consistent with the linearity observed for ln(f2/m) in terms of p for dilute solutions, in contrast to what is observed for the formula-based representation. More important, for the CO2 systems, RTΩ∞ adopts large values, whereas those of RTω∞ are closer to what is expected for the partial molar volume of CO2 in these solvents.30–32 Figure 3 depicts the values of RTΩ∞ (panel A) and of RTω∞ (panel B) for some selected systems as a function of the temperature. Only some representative systems were chosen in order to illustrate the differences between the two formalisms. Although the uncertainties in these quantities are rather large (ca. 10%), the general trend is the same for all systems: RTΩ∞ decreases strongly with temperature, due to the large influence of the righthand side of eq 8, whereas RTω∞ exhibits modest temperature dependence. Results for H2 reported in Table 1 show that all these differences, that is, those between ln KH and ln(kH/2), between RTΩ∞ and RTω∞, and between their different temperature dependence, strongly diminish for gases with low solubility. Table 2 lists the values of ∆disH2∞ and ∆disS2∞, for the analyzed systems. Enthalpies of dissolution for the formula- and ionbased representations do not differ substantially; the major difference between both formulations are the values of ∆disS2∞,
Phase Equilibria of Molecular and IL Binary Mixtures
J. Phys. Chem. B, Vol. 113, No. 11, 2009 3465
TABLE 1: Values of the Initial Slopes (Multiplied by RT) and Intercepts of the Linear Fits of ln(f2/c) vs p, for Different Choices of the Concentration ca c ≡ X (molecular)
a
c ≡ x (ionic)
ionic liquid
gas
RT Ω∞ (cm3/mol)
ln (KH/MPa)
RT ω∞ (cm3/mol)
ln (kH/MPa)
ref
emimPF6 bmimPF6 hmimPF6 bmimBF4 hmimBF4 omimBF4 emimNTf2 hmimNTf2 bmimCH3SO4 hmimNTf2 bmimCH3SO4 hmimNTf2 bmimCH3SO4 bmimPF6 hmimNTf2 bmimCH3SO4
CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 Xe Xe CH4 CH4 H2 H2 H2
61 ( 3 109 ( 5 120 ( 6 84 ( 8 115 ( 8 147 ( 10 203 ( 21 233 ( 22 52 ( 2 68 ( 4 21 ( 2 59 ( 3 45 ( 4 26 ( 1 34 ( 2 35 ( 2
2.535 ( 0.008 2.303 ( 0.008 2.190 ( 0.008 2.42 ( 0.01 2.24 ( 0.01 2.08 ( 0.01 1.89 ( 0.02 1.73 ( 0.02 2.674 ( 0.005 2.418 ( 0.008 3.739 ( 0.004 3.705 ( 0.006 5.048 ( 0.008 5.908 ( 0.002 5.120 ( 0.003 6.267 ( 0.003
19 ( 5 24 ( 4 18 ( 2 7(5 20 ( 3 35 ( 2 64 ( 15 62 ( 16 -5 ( 3 2(1 1(3 34 ( 2 38 ( 4 22 ( 1 26.40 ( 0.03 32 ( 2
3.15 ( 0.02 2.969 ( 0.006 2.860 ( 0.003 3.088 ( 0.008 2.909 ( 0.005 2.745 ( 0.002 2.56 ( 0.02 2.40 ( 0.01 3.346 ( 0.006 3.066 ( 0.002 4.423 ( 0.006 4.393 ( 0.004 5.740 ( 0.008 6.601 ( 0.002 5.813 ( 0.004 6.960 ( 0.003
14 15 16 17 18 19 20 23 22 24 25 24 25 26 27 28
All data are reported at 333 K.
Brennecke et al. can take positive or negative values (the same sign as the enthalpic term), although there is an evident reduction in the entropy of the standard state when passing from the ideal gas to the liquid solution. Further Evidences The differences between the ionic and the molecular representations of the IL are more appreciable close to the limit x1 ) (1 - x) ) 1, where x is only half the value of X. A strong test to our thermodynamic treatment will be then given by the analysis of the behavior of the solvent’s chemical potential around that concentration region. Since ILs have negligible vapor pressure, this opportunity has to be provided by studying the solid-liquid phase equilibria of the IL in the presence of a dissolved species. Solid-liquid equilibria (SLE) of emimPF6 in binary mixtures with alcohols have been studied by Doman´ska and Marciniak.34,35 From these SLE data, the solvent’s activity coefficients can be easily obtained by equaling the chemical potentials of the solvent in the solid and liquid phases. The well-known result is, for the ion-based representation,12 eq 17,
ln γR1 ) -ln x1 Figure 3. Initial slopes (x e 0.3) of the RT ln(f2/c) vs p representation as a function of temperature for CO2 + IL systems. Panel A: c ≡ X; panel B: c ≡ x. Data for (0) emimPF6, (1) bmimPF6, (9) bmimBF4, (O) omimBF4, and (2) emimNTf2. References are given in Table 1.
as expected. However, the values of ∆disS2∞, obtained for the more soluble gases (CO2 and Xe) using the two formalisms, do not exactly differ in the factor -R ln 2, due to the overestimation in the extrapolation of ln KH, as already mentioned. Note that our definition of entropy of dissolution ∆disS2∞, differs from the ∆s employed by Brennecke and colleagues;31–33 they evaluate the liquid phase entropy at T, p ) p1*, and at the equilibrium concentration, whereas here S2∞ refers to standard conditions (T, p ) p1*, x ) 1). Their enthalpy and entropy of dissolution are related through ∆h - T∆s ) 0, whereas here ∆disH2∞ - T∆disS2∞ ) RT ln kH. The reason for preferring ∆disS2∞ is that ∆s ) ∆h/T blends structural and concentration effects in one function, making it more difficult to be interpreted in microscopic terms. As a matter of fact, ∆s as defined by
(
)
∆fusH 1 1 + R T To To ∆fuscp T ln + - 1 (17) R To T
[( )
]
where γ1R represents the activity coefficient of the IL in the Raoult reference state; x1 is its concentration; To and T the melting temperatures of the IL, pure and in solution, respectively; and ∆fusH and ∆fuscp are the enthalpy and heat capacity of fusion (note that a similar equation applies for the formulabased representation replacing x1 by X1 and γ1R by Γ1R). Activity coefficients of the IL have been calculated from the experimental melting temperatures using the formula-based and the ion-based approaches. Figure 4 shows the results for the system emimPF6 + methanol.34 Since only the heat capacity of the liquid phase is known (289 J mol-1 K-1 at 353.3 K),36 the calculations were done for two scenarios: ∆fuscp ) 0 and ∆fuscp ) 200 J mol-1 K-1. As shown in Figure 4, the results are qualitatively independent of the value of ∆fuscp. The more relevant difference
3466 J. Phys. Chem. B, Vol. 113, No. 11, 2009
Longinotti et al.
TABLE 2: Thermodynamic Properties of Dissolution of Several Gases in ILs as Obtained from Solubility Data for x e 0.30 c ≡ X (molecular) ionic liquid
gas
∆disH2∞
emimPF6 bmimPF6 hmimPF6 bmimBF4 hmimBF4 omimBF4 emimNTf2 hmimNTf2 bmimCH3SO4 hmimNTf2 bmimCH3SO4 hmimNTf2 bmimCH3SO4 bmimPF6 hmimNTf2 bmimCH3SO4
CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 Xe Xe CH4 CH4 H2 H2 H2
-13.4 ( 0.4 -14.4 ( 0.1 -13.6 ( 0.2 -14.1 ( 0.3 -13.05 ( 0.04 -13.3 ( 0.3 -13.5 ( 0.5 -11.1 ( 0.1 -12.4 ( 0.1 -7.6 ( 0.2 -6.0 ( 0.1 -3.6 ( 0.3 -1.8 ( 0.3 4.92 ( 0.08 4.08 ( 0.04 5.01 ( 0.05
c ≡ x (ionic)
∆disS2∞
(kJ/mol)
(J/mol K)
-61 ( 1 -62.4 ( 0.4 -59.0 ( 0.7 -63 ( 1 -57.8 ( 0.2 -57.2 ( 0.9 -56 ( 2 -47.7 ( 0.4 -59.5 ( 0.6 -42.9 ( 0.6 -49.2 ( 0.4 -41.4 ( 0.9 -47.5 ( 0.7 -34.4 ( 0.2 -30.4 ( 0.1 -37.1 ( 0.1
∆disH2∞
(kJ/mol)
-12.6 ( 0.6 -14.0 ( 0.1 -13.2 ( 0.2 -13.8 ( 0.2 -13.35 ( 0.09 -13.28 ( 0.06 -13.2 ( 0.4 -11.50 ( 0.03 -12.57 ( 0.02 -8.2 ( 0.2 -6.15 ( 0.08 -3.6 ( 0.3 -1.8 ( 0.3 4.92 ( 0.08 4.08 ( 0.04 5.01 ( 0.05
∆disS2∞ (J/mol K) -64 ( 2 -66.8 ( 0.3 -63.3 ( 0.5 -67.1 ( 0.7 -64.3 ( 0.3 -62.7 ( 0.2 -61 ( 1 -54.4 ( 0.2 -65.6 ( 0.3 -50.0 ( 0.5 -55.2 ( 0.2 -47.3 ( 0.7 -53.1 ( 0.6 -40.2 ( 0.2 -36.1 ( 0.1 -42.8 ( 0.1
contributes to loosen the repulsions between ions bearing the same charge, therefore lowering the energy. Analysis of the Dissolution Process of Gases in Ionic Liquids
Figure 4. Activity coefficient of emimPF6 along the melting line as a function of its composition in the liquid mixtures with methanol.34 The squares denote activity coefficients calculated with ∆fuscp ) 0, and circles denote ∆fuscp ) 200 J · mol-1 · K-1. The cp of this IL in the liquid state is 289 J · mol-1 · K-1 at 353 K (ref 36) but unknown for the solid phase. Lines are only a guide to the eye.
between the two formalisms (formula- or ion-based) is the way the solvent’s activity coefficients approach the pure-solvent’s limit: in the first case, the slope (d ln Γ1R/dX1)p,SLE at X ) 0 is nonzero, whereas in the second it vanishes. Taking into account the Gibbs-Duhem relation (eq 18),12
( )
x1
d ln γR1 dx1
( )
+ (1 - x1) p,SLE
d ln γR2 dx1
) p,SLE
-
hE dT RT2 dx
( )
p,SLE
(18)
and considering that hE vanishes as x1 f 1, asymptotically close to the pure-solvent limit, the dependence of the solvent’s activity coefficient with composition must vanish. In other words, SLE confirms that x is the proper concentration variable to describe the thermodynamic behavior of dilute molecular solutes in ILs. Incidentally, Figure 4 shows that, for small additions of a polar compound such as methanol, the chemical potential of the IL becomes slightly smaller than the one expected from ideal behavior; however, as the concentration of the molecular species further increases, the tendency reverts. A conceivable microscopic interpretation is that, as long as the amount of the molecular species remains small enough so as not to interfere with the attractive cation-anion interactions, its presence
From the analysis performed in the previous section it can be concluded that the ion-based mole fraction is the more appropriate concentration variable to describe phase equilibria in ionic liquids. In this section, we will analyze the thermodynamic functions of dissolution of gases as obtained within this formulation. In absence of experimental volumetric data, RTω∞ can be taken as an estimate of the solute’s partial molar volumes, that ∞ . According to the values given in Table 1 for is, RTω∞ ≡ V2,est ∞ 333 K, V2,est takes values around 20 cm3/mol for CO2 in several ILs, with the exception of emimNTf2 and hmimNTf2 that are larger and of bmimBF4 and bmimCH3SO4 with smaller values (see Table 1). For Xe, V∞2,est adopts values close to zero, whereas for CH4 and H2 the values are around 36 and 26 cm3/mol, respectively. For comparison, partial molar volumes of these gases in aqueous solutions V2∞ are 33.8 (CO2 at 323.15 K),37 42.5 (Xe at 299 K),38 37.5 (CH4 at 323.15 K),37 and 26 cm3/mol (H2 at 298 K),39 and partial molar volumes of gases in nonaqueous systems are typically larger (for CH4 at 298 K, V2∞ values are 69.3 in n-hexane, 66 in Cl4C, and 37.3 cm3/mol in H2O).40 ∞ These values show that V2,est in ILs for CH4 and for H2 (the less soluble gases) are similar to the corresponding V2∞ values in aqueous solution; for CO2, they are smaller in most ILs but are twice as large in those ILs containing the NTf2- anion. The most unexpected values are those of Xe: although its V2∞ in aqueous solutions is the largest among these gases, the values ∞ of V2,est obtained here are the smallest. Whether this apparent anomaly is due to remaining activity-coefficients effects is yet uncertain. To answer this question, direct volumetric measurements of partial molar volumes should be carried out. A comparison between the values of ∆disH2∞ in Table 2 for the different gases shows trends compatible with our a priori expectations: as attractive interactions become more significant (following the order H2 < CH4 < Xe < CO2), ∆disH2∞ adopts more negative values. For CO2, the values of ∆disH2∞ in the different ILs do not change radically; they all lie between -11.5 (in hmimNTf2) and -14 kJ/mol (in bmimPF6). Similar results were obtained by Brennecke et al.41,42 for CO2 dissolved in various imidazolium, pyrrolidinium, tetraalkyl ammonium, and
Phase Equilibria of Molecular and IL Binary Mixtures tetraalkyl phosphonium ILs. Despite having the least-exothermic ∆disH2∞, hmimNTf2 is the IL with the highest CO2 solubility among those analyzed here, as it also has the least-negative ∆disS2∞, -54.4 J mol-1 K-1. The trend of ∆disS2∞ among the different gases is similar to that of ∆disH2∞ (i.e., decreasing values of ∆disS2∞, as going from H2 to CO2), although less pronounced. As a result, the trend in solubilities of these gases (H2 < CH4 < Xe < CO2) appears to be controlled mainly by the enthalpic term. On the other hand, for CO2, for which there is information in many ILs, the comparison of the results in Tables 1 and 2 suggests a stronger correlation of ln kH with ∆disS2∞, than with ∆disH∞2 , implying that the higher solubilities observed for CO2 in some ILs (i.e., in hmimNTf2 versus in bmimCH3SO4) might not be driven by enthalpic (i.e., stronger interactions) but by entropic reasons. From the comparison of ln kH in the two ILs (hmimNTf2 and bmimCH3SO4) where we have information for all gases, it can be concluded that the solubilities of all gases are larger in hmimNTf2, see Table 1. Moreover, for CO2 the difference in solubility between the two solvents is smaller than that of the other gases. Consequently, we find little support to the generalized idea that fluorinated moieties have specific interactions exclusively with CO2. Conclusions In this work we compare the descriptions of dilute solutions in ILs, mainly of gaseous solutes, as given by different concentration variables: mole fraction x (considering the solvent as an ionic species), mole fraction X (considering the solvent as composed by cation-anion pairs) and molality. Our analysis proves that, when the concentration is expressed on an ionic basis, solutions of simple gases in ILs display small deviations from ideal behavior in wide composition ranges. By formulating the description in terms of x, extrapolations to the infinite dilution limit, as required to get Henry’s constants, are performed in a more appropriate way. Perhaps the more interesting result is that, even for highly soluble gases, this formulation gives reasonable estimations of V2∞, the solute’s partial molar volumes at infinite dilution, employing only phase equilibria data. In addition, we prove here that only the ion-based formulation represents adequately the solid-liquid equilibrium, as the formula-based treatment fails in complying with the Gibbs-Duhem equation. Obviously, the concentration x should also be preferred to describe liquid-vapor equilibria: although thermodynamic consistency can not be checked due to the insignificant vapor pressure of the solvent, the arguments discussed here are clearly applicable to all phase equilibria. As an illustration, in acetone + emimNTf243 and in acetonitrile + emimNTf2,44 both molecular liquids were reported to have large negative deviations from ideality (Γ2R < 1, for the formula-based activity coefficient), but they display small deviations when analyzed in terms of x. In other words, the apparent strong interactions between these polar liquids and emimNTf2 disappear when the speciation of the IL is taken into account. Furthermore, in 2-propanol + emimNTf2,43 Γ2R of the alcohol shows relatively small deviations, whereas large values of γ2R are obtained when using the ion-based formulation. These large values of γ2R are actually not unexpected: despite being completely soluble in emimNTf2, 2-propanol shows liquid-liquid phase separation with other ILs, such as emimPF6.34 It should be borne in mind that in mixtures near a phase separation, activity coefficients always adopt large values. In summary, interpreting thermodynamic properties obtained using inadequate formalisms can lead to wrong conclusions.
J. Phys. Chem. B, Vol. 113, No. 11, 2009 3467 The importance of a proper representation is further illustrated by another example. Activity coefficients at infinite dilution (Raoultian reference state) of solutes dissolved in ILs have been measured and modeled by several authors (ref 45 and references therein). In all cases, the ionic nature of the solvent was ignored, that is, the reported activity coefficients, Γ2R,∞ in our notation, are actually one-half of their values in the ion-based representa) 2 · ΓR,∞ tion (γR,∞ 2 2 ). Again, interaction parameters obtained by will then have dubious physical meaning. fitting models to ΓR,∞ 2 Moreover, these parameters will poorly predict the values of Γ2R for nonzero solute concentrations, which will in general display a pronounced concentration effect to account for the inadequate speciation of the reference state. The extension of the present approach to ILs with stoichiometries other than 1:1 (general formula MRYβ) is straightforward: generalizing eq 2, the concentration x is defined as x ) n2/(υn1 + n2), and the properties at infinite dilution in the ionbased and formula-based representations are related through kH ) υKH, or γ2R,∞ ) υΓ2R,∞, where υ ) (R + β). In mixed solvents of molecular and ionic liquids, the solubility of gases will be better represented by kH ) KH(υ - X3) where X3 ) n3/(n1 + n3) refers to the concentration of the molecular liquid in the formula-based representation. As an example, the data of Hong et al.44 for CO2 dissolved in mixtures of acetonitrile (component 3) and emimNTf2 show that the values of kH are a smoother function of the acetonitrile composition than the reported KH. The values of the thermodynamic functions of dissolution of the analyzed gases in ILs obtained here using the ion-based formalism suggest that partial molar volumes in IL are probably similar to those in aqueous solution and reinforce the need of direct experimental information. The values of the other thermodynamic functions induce us to believe that the entropy of dissolution plays a more important role in determining the solubility of CO2 in different ILs than presently considered. The final consideration is to give credit to whom made outstanding contributions to the field of ionic systems. In 1980, that is long before the spectacular burst of interest in ILs, Pitzer,46 revisiting an older work of Kraus,47 described the behavior of solutions composed by electrolytes and molecular liquids, from dilute solutions to fused salts. The concentration variable chosen to represent the thermodynamic behavior was the one called here x (ion-based), with the argument that the ionic compound should be considered completely dissociated in both concentration limits: at infinite dilution and in the pure ionic liquid. Probably due to the fact that ionic species traditionally play the role of solutes, Kraus-Pitzer’s fundamental contribution was overlooked. By ignoring it, the thermodynamic formulation of solutions in ionic solvents definitively loses an essential aspect of its nature. Acknowledgment. We thank Professors R. Ferna´ndez-Prini and H. Bianchi for carefully reading the manuscript. This research was supported by ANPCyT, Argentina (PICT 0614332). M.P.L. acknowledges CONICET for a postdoctoral fellowship. References and Notes (1) Wilkes, J. S.; Levisky, J. A.; Wilson, R. A.; Hussey, C. L. Inorg. Chem. 1982, 21, 1263–1264. (a) Wilkes, J. S.; Zaworotko, M. J. J. Chem. Soc., Chem. Commun. 1992, 13, 965–967. (2) Bonhoˆte, P.; Dias, A.-P.; Papageorgiou, N.; Kalyanasundaram, K.; Gra¨tzel, M. Inorg. Chem. 1996, 35, 1168–1178. (3) Dzyuba, S. V.; Bartsch, R. A. Chem. Phys. Chem. 2002, 3, 161– 166. (4) Brennecke, J. F.; Maginn, E. J. AIChE J. 2001, 47, 2384–2389.
3468 J. Phys. Chem. B, Vol. 113, No. 11, 2009 (5) Welton, T. Chem. ReV. 1999, 99, 2071–2083. (6) Sheldon, R. Chem. Commun. 2001, 23, 2399–2407. (7) Blanchard, L. A.; Hancu, D.; Beckman, E. J.; Brennecke, J. F. Nature 1999, 399, 28–29. (8) Scurto, A. M.; Aki, S. N. V. K.; Brennecke, J. F. J. Am. Chem. Soc. 2002, 124, 10276–10277. (9) Quinn, B. M.; Ding, Z.; Moulton, R.; Bard, A. J. Langmuir 2002, 18, 1734–1742. (10) Xu, W.; Angell, C. A. Science 2003, 302, 422–425. (11) Ferna´ndez-Prini, R.; Crovetto, R.; Japas, M. L.; Laria, D. Acc. Chem. Res. 1985, 18, 207–212. (12) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1999. (13) Kumean, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Yokozeki, A.; Shiflett, M. B.; Maurer, G. J. Phys. Chem. B 2008, 112, 3040–3047. (14) Shariati, A.; Peters, C. J. J. Supercrit. Fluids 2004, 29, 43–48. (15) Shariati, A.; Gutkowski, K.; Peters, C. J. AIChE J. 2005, 51, 1532– 1540. (16) Shariati, A.; Peters, C. J. J. Supercrit. Fluids 2004, 30, 139–144. (17) Kroon, M. C.; Shariati, A.; Costantini, M.; van Spronsen, J.; Witkamp, G.-J.; Sheldon, R. A.; Peters, C. J. J. Chem. Eng. Data 2005, 50, 173–176. (18) Costantini, M.; Toussaint, V. A.; Shariati, A.; Peters, C. J.; Kikic, I. J. Chem. Eng. Data 2005, 50, 52–55. (19) Gutkowski, K. I.; Shariati, A.; Peters, C. J. J. Supercrit. Fluids 2006, 39, 187–191. (20) Schilderman, A. M.; Raeissi, S.; Peters, C. J. Fluid Phase Equilib. 2007, 260, 19–22. (21) Pe´rez-Salado Kamps, A.; Tuma, D.; Xia, J.; Maurer, G. J. Chem. Eng. Data 2003, 48, 746–749. (22) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. J. Chem. Eng. Data 2006, 51, 1802–1807. (23) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. J. Chem. Thermodynamics 2006, 38, 1396–1401. (24) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. Ind. Eng. Chem. Res. 2007, 46, 8236–8240. (25) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. J. Chem. Eng. Data 2007, 52, 2319–2324. (26) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. J. Chem. Eng. Data 2006, 51, 11–14.
Longinotti et al. (27) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. J. Chem. Eng. Data 2006, 51, 1364–1367. (28) Kumelan, J.; Pe´rez-Salado Kamps, A.; Tuma, D.; Maurer, G. Fluid Phase Equilib. 2007, 260, 3–8. (29) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23; Version 8.0, 2007. (30) Huang, X.; Margulis, C. J.; Li, Y.; Berne, B. J. J. Am. Chem. Soc. 2005, 127, 17842–17851. (31) Aki, S. N. V. K.; Mellein, B. R.; Saurer, E. M.; Brennecke, J. F. J. Phys. Chem. B 2004, 108, 20355–20365. (32) Cadena, C.; Anthony, J. L.; Shah, J. K.; Morrow, T. I.; Brennecke, J. F.; Maginn, E. J. J. Am. Chem. Soc. 2004, 126, 5300–5308. (33) Anthony, J. L.; Maginn, E. J.; Brennecke, J. F. J. Phys. Chem. B 2002, 106, 7315–7320. (34) Doman´ska, U.; Marciniak, A. J. Phys. Chem. B 2004, 108, 2376– 2382. (35) Doman´ska, U.; Bogel-Lukasik, E.; Bogel-Lukasik, R. J. Phys. Chem. B 2003, 107, 1858–1863. (36) Ionic Liquids Database- (ILThermo). NIST Standard Reference Database 147; 2008. (37) Hneˇdkovsky´, L.; Wood, R. H.; Majer, V. J. Chem. Thermodyn. 1996, 28, 125–142. (38) Biggerstaff, D. R.; Wood, R. H. J. Phys. Chem. 1988, 92, 1988– 1994. (39) Moore, J. C.; Battino, R.; Rettich, T. R.; Handa, Y. P.; Wilhelm, E. J. Chem. Eng. Data 1982, 27, 22–24. (40) Masterton, W. L. J. Chem. Phys. 1954, 22, 1830–1833. (41) Muldoon, M. J.; Aki, S. N. V. K.; Anderson, J. L.; Dixon, J. K.; Brennecke, J. F. J. Phys. Chem. B 2007, 111, 9001–9009. (42) Anthony, J. L.; Anderson, J. L.; Maginn, E. J.; Brennecke, J. F. J. Phys. Chem. B 2005, 109, 6366–6374. (43) Kato, R.; Gmehling, J. Fluid Phase Equilib. 2005, 231, 38–43. (44) Hong, G.; Jacquemin, J.; Husson, P.; Costa Gomes, M. F.; Deetlefs, M.; Nieuwenhuyzen, M.; Sheppard, O.; Hardacre, C. Ind. Eng. Chem. Res. 2006, 45, 8180–8188. (45) Heintz, A. J. Chem. Thermodynamics 2005, 37, 525–535. (46) Pitzer, K. S. J. Am. Chem. Soc. 1980, 102, 2902–2906. (47) Kraus, C. A. J. Phys. Chem. 1954, 58, 673–683.
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