Critical Properties and Normal Boiling Temperature of Ionic Liquids

May 9, 2012 - Valderrama and Zarricueta(8) proposed a general model to estimate the density of ionic liquids in which the estimated critical propertie...
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Critical Properties and Normal Boiling Temperature of Ionic Liquids. Update and a New Consistency Test José O. Valderrama,†,‡,* Luis A. Forero,‡,§ and Roberto E. Rojas4 †

Faculty of Engineering, Department of Mechanical Engineering, and 4Faculty of Sciences, Department of Chemistry, University of La Serena, Casilla 554, La Serena, Chile ‡ Center for Technological Information (CIT), Mons. Subercaseaux 667, La Serena, Chile § Faculty of Chemical Engineering, University Pontificia Bolivariana, A.A. 56006, Medellín, Colombia S Supporting Information *

ABSTRACT: The group contribution method proposed by Valderrama and Robles in 2007 and extended by Valderrama and Rojas in 2009 to estimate the critical properties of ionic liquids is revised and an additional test for determining the consistency of the estimated properties is proposed. The new testing method includes the calculation of the saturation pressure at the normal boiling temperature using an equation of state and an accurate model to represent the temperature function of the attractive term in the equation of state. In determining the vapor pressure, the critical temperature, the critical pressure, the critical volume, and the acentric factor determined by group contribution are included. The proposed method complements the previous density test of the authors that tested the critical temperature, the critical volume, and the normal boiling temperature only. A total of 1130 ionic liquids are considered in this work, and double checking, using the density and the normal vapor pressure, is applied. Also, a spreadsheet file that allows any reader to calculate and check the critical properties of other ionic liquids containing any of the 44 groups defined by the method is provided.

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INTRODUCTION In a series of previous papers the authors proposed and applied a group contribution method to determine several basic properties of ionic liquids.1−3 The critical properties (Tc, Pc, Vc), the normal boiling temperature (Tb), and the acentric factor (ω) of ionic liquids were calculated and checked for accuracy and consistency. The proposed group contribution method has been used by several researchers for correlating and estimating several properties of ionic liquids and even determining gas−liquid equilibrium in mixtures.4−14 These studies have demonstrated the importance of estimation methods from a point of view of fundamental thermodynamics, but this type of information is also useful in chemical engineering applications. One of the main reasons is that due to the very large number of possible ionic liquids that can be synthesized, all desired properties cannot be measured because of time and cost limitations, but properties are needed now and with reasonable accuracy. The critical properties are of the type of basic properties needed to estimate some physical, thermodynamic, and transport properties of ionic liquids. They are also needed in phase equilibrium calculations using equations of state and in generalized correlations for estimating density, heat capacity, heat of vaporization, vapor pressure, viscosity, and thermal conductivity, among others.15 And although it is true that an estimated value cannot replace a good experimental datum, sometimes the experimental datum is not available or cannot be measured, so good estimation methods can be the solution.16 Gardas et al.4 calculated the critical properties and use them for estimating the density of five ionic liquids, and according to the authors, the estimated values are in good agreement with their experimental results. Carvalho et al.5 and Alvarez et al.6 © 2012 American Chemical Society

used the calculated critical properties to correlate high pressure phase behavior of carbon dioxide (CO2) + ionic liquid (IL) mixtures. Ge et al.7 used the method to estimate the critical temperature, the normal boiling temperature, and the acentric factor to then determine the heat capacity of several ionic liquids, using a generalized correlation. Valderrama and Zarricueta8 proposed a general model to estimate the density of ionic liquids in which the estimated critical properties are included. Estimated critical properties and equations of state have been used to correlate vapor + liquid equilibrium and liquid + liquid equilibrium in ionic liquids + CO2 mixtures.9−11 Valderrama et al.12 presented a study on thermodynamic consistency of high pressure mixtures containing ionic liquids using an equation of state model that requires the critical properties. More recently, Shen et al.13 extended the group contribution model to the prediction of densities of ionic liquids using the Patel−Teja equation of state. Also, Hiraga et al.14 used the estimated critical properties in an application of the Sanchez−Lacombe equation of state for estimating infinite dilution partition coefficients of mixtures containing benzene derivative compounds in supercritical CO2 + IL. In their paper of 2007, Valderrama and Robles1 estimated the critical properties of fifty ionic liquids using a modified Lydersen−Joback−Reid method and proposed three new groups and their values for the contributions for Tc, Pc, Vc, and Tb. Soon after being published, the method of Valderrama and Robles and their values of the critical properties were Received: Revised: Accepted: Published: 7838

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questioned in the literature,17 but the authors18 demonstrated that the claims were not conceptually solid and contained several basic mistakes. Later, the authors revised the information and provided critical properties for about 300 ionic liquids.3 That information is updated in this paper and properties for 1130 ionic liquids are provided. Also, a new consistency method based on vapor pressure calculations, to check the appropriateness of the estimated data is presented. This is a novel test in which an independent method that uses an equation of state to check the accuracy of the properties estimated by the group contribution method. The work also adds in the sense that since experimental density values present some discrepancies in the literature, as discussed later in this paper, the use of an additional property for testing was necessary.

densities were within experimental errors as shown by the authors. The authors did not mentioned, however, that if an experimental density value is not available, computational methods such as COSMO,19,20 that can accurately predict the density, could be used instead of the experimental density. The density equation used by the authors was previously used in calculating the density of several organic compounds and, in principle, could be used for any substance for which the critical temperature, the critical volume and the normal boiling temperature were available, and within the restrictions of that model. For instance, the density equation can be applied between 0.5 to approximately 1.6 (g/cm3), the range in which the constants of the model were determined:21

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ρL = (0.01256 + 0.9533M /Vc) [(0.0039/M + 0.2987/Vc)Vc1.033]Ψ

THE GROUP CONTRIBUTION METHOD Details of the group contribution method has been previously provided by Valderrama and Robles1 and later extended by the authors.3 The equations that defined the method for the critical temperature, the critical pressure, the critical volume, the normal boiling temperature and the acentric factor can be found elsewhere but are included in Table 1 for better clarity.

Ψ = − [(1 − T /Tc)/(1 − Tb/Tc)]2/7

In these equations, ρL is the liquid density in grams per cubic centimeter, T is the temperature, R is the ideal gas constant, M is the molecular mass, Vc is the critical volume, Tc is the critical temperature, and Tb is the normal boiling temperature (at Pb = 1.01325 bar). The authors also calculated the acentric factor of the ionic liquids using the estimated critical pressure and temperature and the calculated normal boiling temperature using Rudkin's equation:22

Table 1. Groups Considered in the Modified Lydersen− Joback−Reid Method for Ionic Liquids3 without rings CH3 O [O]− CH2 >CO >CH CHO >C< [>C]− COOH CH2 COO CH HCOO C< O (any other) C NH2 CH NH3 C COO NH OH >N model equations

Tb(K) = 198.2 + Tc(K) =

with rings N CN NO2 F Cl Br I P B S OSO

∑ nΔTb

Tb [A + B ∑ nΔTc − (∑ nΔTc)2 ]

Pc(bar) =

M [C + ∑ nΔPc]2

Vc(cm 3/mol) = D +

∑ nΔVc

(1)

CH2 >CH CH >C< C< O −OH (phenols) >CO NH >N [>N< ]+ N [>N]+ constants

ω=

⎡P ⎤ (Tb − 43)(Tc − 43) Log⎢ c ⎥ (Tc − Tb)(0.7Tc − 43) ⎣ Pb ⎦ −

⎡P ⎤ ⎡P ⎤ (Tc − 43) Log⎢ c ⎥ + Log⎢ c ⎥ − 1 (Tc − Tb) ⎣ Pb ⎦ ⎣ Pb ⎦

(2)

As seen in the density eq 1 only Tb, Tc, and Vc are tested for consistency. The critical pressure and therefore the acentric factor (which includes the critical pressure) were not tested in all previous works. In this paper a test for these estimated properties is proposed. The method consists of calculating the saturation pressure at Tb (which should be 1.01325 bar) and comparing the predicted pressure with 1.01325 bar, as explained in the following section. Once the critical pressure is tested, the acentric factor defined by eq 2 is determined using properties already tested (Tb, Tc, and Pc). In summary, the density test previously proposed checks Tb, Tc, and Vc while the vapor pressure test checks Tb, Tc, and Pc. By extension, the acentric factor can be considered consistent if the properties involved in its calculation are consistent. Additionally, it should be mentioned that most group contribution methods for the critical properties over predict the values of Tc and Tb for high molecular weight compounds, as discussed in the literature.15,23 Therefore, the group contribution method has been applied for ionic liquids with molecular mass below 500. As stated by Gao et al.,23 different group contribution methods predict similar values for the critical properties up to approximately this limit, but extrapolations cannot be done. Since the method analyzed and extended in this paper is derived from the methods of Lydersen et al. and of Joback and Reid,1 it has the same limitations.

A = 0.5703 B = 1.0121 C = 0.2573 D = 6.75

The groups considered are also the same as in previous papers and are listed in Table 1 so users can easily see if the method is applicable for a new ionic liquid of interest. As established, in any group contribution scheme the method is applicable as long as the molecule contains the groups previously defined by the method. In the case analyzed in this paper, the 44 groups are shown in Table 1. Since there are not experimental critical properties to evaluate the accuracy of the estimates, the authors1−3 tested the accuracy and consistency of their values by determining the density of the ionic liquids, for which experimental data were available.1−3 To do the checking, an independent equation not employed in determining the critical properties was applied. The deviations found between experimental and calculated 7839

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Table 2. Equations to Test the Consistency of the Calculated Critical Properties and Normal Boiling Temperaturea Saturation Pressure Test for Tc, Pc, ω, and Tb (this paper) Psat is determined from the equality of fugacities (or fugacity coefficients) given the value of Tb The fugacity coefficients are determined from the PR equation.

φ V (Tb , P sat) = φL(Tb , P sat)

(T1)

Tb is the normal boiling temperature.

ln φ V = (Z V − 1) − ln(Z V − B) −

2 )B ⎤ ⎥ 2 )B ⎦

⎡ Z + (1 + A ln⎢ V 2 2 B ⎣ Z V + (1 −

2 )B ⎤ ⎥ 2 )B ⎦

⎡ Z + (1 + A ln φL = (Z L − 1) − ln(Z L − B) − ln⎢ L 2 2 B ⎣ Z L + (1 − The compressibility factor of the PR equation for the vapor (ZV) and liquid phases (ZL) are

3

2

2

3

2

2

2

3

Z V − (1 − B)Z V + (A − 2B − 3B )Z V − (AB − B − B ) = 0 2

3

Z L − (1 − B)Z L + (A − 2B − 3B )Z L − (AB − B − B ) = 0 sat

The parameters of the equations for ZV and ZL are

A=

aP ; RTb2

(T2) (T3) (T4) (T5)

sat

B=

bP ; RTb

a = acα(Tb)

(T6)

R2Tc 2 ac = 0.457235 b = 0.077796RTc/Pc Pc The α function of Joshipura et al.32 is

α = exp[m2(1 − Tb/Tc)]

(T7)

m2 = 1.252ω + 0.4754 Density Test for Tc, Vc, and Tb (Valderrama and Rojas 2009) density model for testing

ρ = (A /B) + (2/7){(A ln B)/B}

(T − Tb) (Tc − Tb)

(T8)

A = a + bM /Vc B = (c /Vc + d /M )Vc δ a = 0.3411, b = 2.0443, c = 0.5386 d = 0.0393, δ = 1.0476 a

In the equations, M is in grams per mole, Tb and Tc are in kelvin, Pc is in bar, and Vc is in cubic centimeters per mole.

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Gasem et al.31 modified Heyen's model and applied it to correlate and predict the saturation pressure of heavy hydrocarbons. For m1 and m2, Gasem et al. proposed

SATURATION PRESSURE CALCULATION The generalized equation of state proposed by Peng and Robinson24 was used to estimate the saturation pressure at Tb. P=

acα(T ) RT − V−b V (V + b) + b(V − b)

m1 = 2 + 0.836T /Tc

and

(3)

In this equation, Peng and Robinson used the α(T) expression proposed by Soave25 for the temperature function, as follows: α(T ) = [1 − k(1 −

m2 = 0.134 + 0.508ω − 0.0467ω 2

More recently, Joshipura et al. also used a simplified version of the original expression of Heyen (they did m2 = 1 in eq 5). The authors used vapor pressure data from 32 pure substances including 27 hydrocarbons and 5 polar substances. They employed the Peng−Robinson equation of state with their proposed α function. The simplified Heyen model used by Joshipura et al.32 is

(4)

Despite its wide use in several applications, this function has been extensively analyzed, its deficiencies have been pointed out, and several authors have proposed alternative expressions for this temperature function.26 Modifications of α(T) have been done with several purposes, although improving vapor pressure correlation of pure substances has been the main target of most proposals. Exponential type functions have received some attention considering that this type of expressions fulfill certain physical requirements for this function.26 Heyen27 was the first who suggested an exponential type function for α(T), although he did not use it for the Peng− Robinson equation of state. The model proposed by Heyen is α(T ) = exp[m1{1 − (T /Tc)m2 ]

(7)

32

T /Tc )]2

k = 0.37464 + 1.54226ω − 0.26992ω 2

(6)

m1 = 1.252ω + 0.4754 m2 = 1

(8)

The α(T) expressions of Soave (S) and Heyen's versions of Gasem et al.31 (HG) and of Joshipura et al.32 (HJ) were evaluated in this paper to determine the saturation pressure at the normal boiling temperature. First, data for different substances including heavy hydrocarbons were used for evaluating these α functions and to select the best one for its extension to ionic liquids. For calculating the saturation pressure, the fundamental equation of phase equilibrium is applied and the fugacity of the substance in the vapor phase equals the fugacity of the substance in the liquid phase, The equality is also valid for the fugacity coefficient (φ = f/P, eq T1 in Table 2) since the 25

(5)

Modifications to this exponential model have been done by several authors with the use of the Peng−Robinson equation of state.28−32 7840

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pressure is the same in both phases. Table 2 shows the working equations for the vapor pressure test. The fugacity coefficient of the substance in the vapor and liquid phases are estimated with eqs T2 and T3 of Table 2, with Psat as the unknown variable. The compressibility factors ZL and ΖV needed for calculating the fugacity coefficients are determined from the Peng− Robinson model expressed by eqs T4 and T5 in Table 2. In determining ZL and ZV, the parameters defined by eqs T6 and T7 are used, including the estimated values of Tc, Pc and Tb. It is expected that the value of Psat at Tb be equal to 1.01325 bar. The accuracy of the prediction is determined by the relative percent deviation and the absolute percent deviation between calculated values and 1.01325 bar. As mentioned above, this procedure was applied in two parts: (i) forty organic compounds were considered for showing the appropriateness of the saturation pressure test and (ii) the estimated values of the critical properties of 1130 ionic liquids were tested using this saturation pressure calculation.

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EXPERIMENTAL DENSITY DATA FOR IONIC LIQUIDS As explained above, the density test for checking the consistency of the estimated critical properties makes use of experimental density data. The density of ionic liquids presented in the literature, however, show clear inconsistencies and in some cases important dispersion is observed. Therefore, experimental data of density cannot be used without appropriate analysis. For instance values of liquid density reported at temperatures below of a reported experimental melting temperature or values that in a family of ionic liquids do not follow a certain smooth and continuous pattern are not considered as true experimental values, and the density testing method is not done. The following examples clarify these arguments. For instance, for methylimidazolium hexafluorofosfate [C1im][PF6], Gu and Brennecke33 reported a value of liquid density of 1.478 g/cm3 at 298.15 K while Ohno and Yoshizawa34 reported a value of 389.15 K for the melting temperature, indicating that at 298.15 K the ionic liquid is solid. For glycinium hexafluorofosfate [Gly][PF6], Tao et al.35 reported a density of 1.37 g/cm3 at 20 °C while a plot of density of [X][PF6] compounds-versus-density of [X][BF4] compounds indicate that the density of [Gly][PF6] or [Gly][BF4] do not follow the expected pattern as suggested by the homologous compounds concept described in the literature.36,37 Figure 1 clarifies this point and the concept of homologous compounds. What is interesting to note is the clear pattern of the experimental values when the density of [X][Cl] compounds are plotted against the density of [X][BF4] compounds. When the density of [X][PF6] is plotted against the density of [X][BF4] the same pattern is observed, except for the pair [Gly][PF6] and [Gly] [BF4] (the outlier point in Figure 1b). Thus, one of the densities is considered to be wrong; and since clearly the densities of [X][PF6] compounds are greater than those of [X][BF4] compounds, it is considered that the datum for the density of [Gly][PF6] is wrong. In Figure 1a for the same type of compounds, [Gly][Cl] and [Gly][BF4] the values follow the expected behavior. In addition to that, of the available experimental data, 32 values of density are higher than 1.6 g/cm3 values for which the density model does not apply as explained above.21 Finally, the critical properties, the normal boiling temperature and the acentric factor was determined for all 1130 ionic liquids and the

Figure 1. Homologous compound concept applied to the density of [X][PF6]-vs-[X][BF4] and [X][Cl]-vs-[X][BF4].

vapor pressure test was applied to all of them. The density test however was applied to 526 ionic liquids only, with molecular mass below 500.

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RESULTS As indicated above the saturation pressure test was first applied to forty organic compounds for which the critical properties are known. Therefore the set of critical properties correspond to true known values and the vapor pressure test has a clear meaning. Then the test is applied to ionic liquids for which the critical properties are estimated using a group contribution method and experimental critical properties are not available. The density test was directly applied to ionic liquids since its applicability has been already demonstrated, if accurate experimental density data are available.3 As mentioned earlier, however, if a computational method such as COSMO is available and the density can be accurately predicted, one could use this estimation as a pseudoexperimental value for those cases in which an experimental density datum is not found. Organic Compounds. The 40 organic compounds used for testing the method, before extending it to ionic liquids, included alkanols, amines, carboxylic acids, aldehydes, ethers, esters, and high molecular weight alkanes, among others. The basic properties needed for the calculations of the vapor pressure were taken from the DIPPR database.38 The absolute average deviations are 12.8% for Soave, 6.15% for Gasem, and 4.4% for Heyen-1. The maximum deviations are 69.8%, 33.14%, and 18.6%, respectively. The model of Heyen-1 is the only one with individual deviations below 20% and with only 4 compounds showing deviations higher than 10%. Therefore this is the model to be used in testing the consistency of the calculated properties of the 1130 ionic liquids, as explained in what follows. Details about these results for organic compounds 7841

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As previously explained by the authors,1,3 the calculation of the density showed to be a good global test of the consistency of three estimated properties (Tc, Vc, and Tb). The new test presented in this paper also uses Tc and Tb, but the critical pressure Pc is added in the testing method. Since now Tc, Pc, and Tb are tested, the acentric factor that includes these properties is considered to be implicitly checked (see eq 2). The deviations in the density and in the normal vapor pressure are within deviations found between experimental data reported by different authors for some ionic liquids, as shown in Table 3.

are presented in Table S1 reported as the Supporting Information. To ensure that the proposed method is a test for checking the consistency of the critical properties and of the normal boiling point being input into the equation of state and not of the alpha-function, additional calculations were performed. Random negative and positive variations up to 50% in Pc were introduced, and the test was applied again. As expected the test gave deviations in the normal vapor pressure (Psat = 1.0325 at Tb) usually higher that the variation introduce in Pc. This is shown in Figure 2 in which the effect of variations of the critical pressure on the calculated Psat is clearly seen.

Table 3. Deviations in Correlating the Density at Room Temperature and the Normal Vapor Pressure (P = 1.0325 at Tb) for 1130 Ionic Liquids Using the Estimated Critical Properties and Normal Boiling Temperature number of ILs

%ΔY

| %ΔY|

| %ΔY|max

fluids with | %Δ| < 10%

fluids with | %Δ| < 20%

526

5

15

19

455

526

1130

2

7

11

1111

1130

density test pressure test

In this table, the deviations %ΔY, |%ΔY|, and max|%ΔY| are defined as follows: %ΔY =

Y ical − Y iexp Y iexp

|Y cal − Y exp| Y exp ⎡ |Y cal − Y exp| ⎤ ⎥ max|%ΔY | = max⎢ Y exp ⎣ ⎦

Figure 2. Effect of variations in the critical pressure on the deviation in determining the normal saturation pressure (Psat = 1.0325 at Tb). In the figure, the symbol “○” represents positive random deviations (from 0 to 50%), and the “∗” symbol represents negative random deviations (from 0 to −50%).

|%ΔY | =

(9)

In these equations, Y represents the density for the density test and the vapor pressure for the vapor pressure test. As observed in Table 3, for the ionic liquids considered in this study the deviations in estimating the density and the saturation pressure at Tb using the estimated properties are below 19% for the density and 11% for the saturation pressure. Also, average deviations are 5% for density and 2% for vapor pressure indicating that negative and positives deviations are well distributed. The meaning of these relatively low deviations is that the set of estimated properties (Tc, Pc, Vc, Tb, and ω) are acceptable enough for thermodynamic and engineering calculations.

Ionic Liquids. This work includes the values of critical properties for all ionic liquids presented earlier by the authors1,3 and new values for many other ionic liquids are provided, with a total of 1130 substances. For all ionic liquids both tests, density, and vapor pressure calculations are included. Repeated substances were eliminated, global formulas were revised, molecular masses were recalculated, and the IUPAC names were included for complete names and short names. In addition to that, values of the properties Tc, Pc, Vc, Tb, and ω were determined for hundreds of new ionic liquids. Other ionic liquids can be easily included for any further study. The only restrictions are that the ionic liquid can be represented by the same 44 groups defined by the group contribution method and its molecular weight is lower than 500 as explained above. The methods for estimating the critical properties, the acentric factor, and for applying both tests (density and saturation pressure) are reported as Supporting Information. The Supporting Information includes an easy to use spreadsheet in which users only need to define the groups of the ionic liquid of interest and a value of density for the checking process (optional). If this value is not available, the method can still be used but consistency is checked only with the saturation pressure test defined in this paper. The spreadsheet is similar to that previously published by the authors3 in which four new columns, for applying the vapor pressure test, were added. Behind the calculation of the saturation pressure at Tb is the code that uses the Peng−Robinson equation, the α(T) function Heyen-1 and the equation for the equality of fugacities.

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CONCLUSIONS The group contribution method proposed by the authors in previous communications has been revised and a new test to check the estimated properties, which uses the calculated saturation pressure at the normal boiling temperature, is proposed. The method, as described in this paper could be used for any reasonable estimation of critical properties of ionic liquids. The values provided represent the most complete database on estimated critical properties, normal boiling temperature and acentric factor of ionic liquids available in the open literature.

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ASSOCIATED CONTENT

S Supporting Information *

Complete table of estimated critical properties, an easy-to-use spreadsheet and detailed results for organic compounds. This 7842

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(3) Valderrama, J. O.; Rojas, R. E. Critical Properties of Ionic Liquids. Revisited. Ind. Eng. Chem. Res. 2009, 48, 6890. (4) Gardas, R. L.; Freire, M. G.; Carvalho, P. J.; Marrucho, I. M.; Fonseca, I. M. A.; Ferreira, A. G. M.; Coutinho, J. A. P. PρT Measurements of Imidazolium-Based Ionic Liquids. J. Chem. Eng. Data 2007, 52, 1881. (5) Carvalho, P. J.; Alvarez, V. H.; Marrucho, I. M.; Aznar, M.; Coutinho, J. A. P. High pressure phase behavior of carbon dioxide in 1alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids. J. Supercrit. Fluids 2009, 50, 105. (6) Alvarez, V. H.; Larico, R.; Lanos, Y.; Aznar, M. Parameter Estimation for VLE Calculation by Global Minimization: The Genetic Algorithm. Braz. J. Chem. Eng. 2008, 25, 409. (7) Ge, R.; Hardacre, C.; Jacquemin, J.; Nancarrow, P.; Rooney, D. W. Heat Capacities of Ionic Liquids as a Function of Temperature at 0.1 MPa. Measurement and Prediction. J. Chem. Eng. Data 2008, 53, 2148. (8) Valderrama, J. O.; Zarricueta, K. A. A Simple and Generalized Model for Predicting the Density of Ionic Liquids. Fluid Phase Equilib. 2009, 275, 145. (9) Ren, W.; Sensenich, B.; Scurto, A. M. High-pressure phase equilibria of {carbon dioxide (CO2) + n-alkyl-imidazolium bis(trifluoromethylsulfonyl)amide} ionic liquids. J. Chem. Thermodynamics 2010, 42, 305. (10) Yim, J.; Song, H. N.; Lee, B.; Lim, J. S. High-pressure phase behavior of binary mixtures containing ionic liquid [HMP][Tf2N], [OMP][Tf2N] and carbon dioxide. Fluid Phase Equilib. 2011, 308, 147. (11) Bermejo, M. D.; Mendez, D.; Marín, A. Application of a Group Contribution Equation of State for the Thermodynamic Modelling of Gas + Ionic Liquid Mixtures. Ind. Eng. Chem. Res. 2010, 49, 4966. (12) Valderrama, J. O.; Reategui, A.; Sanga, W. W. Thermodynamic Consistency Test of Vapor-Liquid Equilibrium Data for Mixtures Containing Ionic Liquids. Ind. Eng. Chem. Res. 2008, 47, 8416. (13) Shen, C.; Li, C.; Li, X.; Lu, Y.; Yaseen, M. Estimation of densities of ionic liquids using Patel-Teja equation of state and critical properties determined from group contribution method. Chem. Eng. Sci. 2011, 66, 2690. (14) Hiraga, Y.; Endo, W.; Machida, H.; Sato, Y.; Aida, T. M.; Watanabe, M.; Smith, R. L., Jr. Infinite dilution partition coefficients of benzene derivative compounds in supercritical carbon dioxide + ionic liquid systems: 1- butyl-3-methylimidazolium chloride [bmim][Cl], 1butyl-3-methylimidazolium acetate [bmim][Ac] and 1-butyl-3-methylimidazolium octylsulfate [bmim][OcSO4]. J. Supercrit. Fluids 2011, 66, 49−58. (15) Reid, R. J.; Prausnitz, M.; Sherwood, T. K. The Properties of Gases and Liquids. Mc Graw-Hill: New York, 1977. (16) Harg, M. Shortcomings in physical property correlations-an industrial view. Fluid Phase Equilib. 1983, 14, 303. (17) Jones, R. G.; Licence, P.; Lovelock, K. R. J.; Villar-Garcia, I. J. Comment on Critical Properties, Normal Boiling Temperatures, and Acentric Factors of Fifty Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 6061. (18) Valderrama, J. O.; Robles, P. A. Reply to Comment on Critical Properties, Normal Boiling Temperature, and Acentric Factor of Fifty Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 6063. (19) COSMOtherm, version C2.1, release 01.06; GmbH&CoKG: Leverkusen, Germany, 2003; http://www.cosmologic.de. (20) Klamt, A. COSMO-RS: From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, 1st ed.; Elsevier: Amsterdam, 2005. (21) Valderrama, J. O.; Abu-Shark, B. Generalized Correlations for the Calculation of Density of Saturated Liquids and Petroleum Fractions. Fluid Phase Equilib. 1989, 51, 87. (22) Rudkin, J. Equation predicts vapor pressures. Chem. Eng. 1961, April 17, 202. (23) Gao, W.; Robinson, R. L., Jr; Gasem, K. A. M. Improved correlations for heavy n-paraffin physical properties. Fluid Phase Equilib. 2001, 179, 207.

material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 56-51-204260. Fax: 56-51-551158. E-mail: jvalderr@ userena.cl. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the support of the Direction of Research of the University of La Serena, of the Center for Technological Information of La Serena−Chile, and of the National Council for Scientific and Technological Research (CONICYT), through the research grants FONDECYT 1070025 and 1120162. L.A.F. thanks the Administrative Department of Science Technology and Innovation (Colciencias-Colombia), for the financial support through the program National Doctorates-Bicentennial Generation 2009.

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NOTATION

Symbols

ac = force constant at critical point in the PR equation of state (eq 3) b = volume constant in the PR equation of state (eq 3) k = parameter in the α function of Soave (eq 4) M = molecular mass m1, m2 = parameters of the α function of Heyen (eq 5) Pb = normal boiling pressure (1.01325 bar) Pc = critical pressure R = ideal gas constant (83.144 bar cm3/mol K) T = temperature Tb = normal boiling temperature Tc = critical temperature Vc = critical volume Y = auxiliary variable in eq 9 Y = density or Psat Z = compressibility factor Abbreviations

IL = ionic liquid max = maximum Log = base 10 logarithm Sub- and Superscripts

cal = calculated value exp = experimental value sat = saturation L = liquid phase V = vapor phase Greek Letters

ρ = density φ = fugacity coefficient ψ = temperature function in eq 1 ω = acentric factor

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REFERENCES

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