Estimation of the Densities of Ionic Liquids Using a Group Contribution

Article pubs.acs.org/jced

Estimation of the Densities of Ionic Liquids Using a Group Contribution Method Hamid Taherifard and Sona Raeissi* School of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Avenue, Shiraz 71345, Iran S Supporting Information *

ABSTRACT: A simple and general atomic group contribution method is developed for the prediction of liquid densities of ionic liquids as a function of temperature and pressure. Available literature data are used as a comprehensive database, consisting of 25 850 data points for a vast variety of ionic liquid families, and within wide ranges of pressures (0.10−300 MPa) and temperatures (217.58− 473.15 K). In developing the group contribution model, the idea was to propose a simple equational form, with straightforward groups which will be easy to use, yet be general and predictive for a vast range of ionic liquids at the same time. To do this, as functional groups, we have chosen atoms and a few small and simple groups. This feature makes the model rather capable and global for a wide range of ionic liquids. Despite the generality and simplicity of the model, and by considering that the only necessary information required to use this method is the chemical structure of the ionic liquid, a good accuracy (AARD% of 0.95%) was achieved. This makes the proposed model a reliable method for prediction of the densities of ionic liquids whenever experimental data are not available.

1. INTRODUCTION Ionic liquids (ILs) are molten salts composed only of cations (usually asymmetric and bulky) and anions (could be organic or inorganic), with melting points below 100 °C. Because of their unique properties, such as low vapor pressure, nonflammability, high thermal stability, and ability of dissolving a wide range of substances including organic and inorganic compounds, ionic liquids are considered as potential replacements for conventional organic solvents.1,2 By combination of different cations and anions, about 1018 different ionic liquids, with different characteristics and properties, can be created, and as a result, ionic liquids are considered as designer solvents with tunable properties which make them interesting for industrial applications.3,4 Liquid density is one of the important properties of substances in design and operation. Experimental data for this property are generally abundant in literature, but in cases that experimental data are not available or where repetitive calculations are required in process simulations, estimation methods that can accurately predict density can be quite useful.5 There are a number of methods that have been developed for the prediction of ionic liquid densities.1,6−23 These include the quantitative structure property relationship (QSPR), equations of states, correlations, group contribution models, and neural networks.1 However, most of these methods require additional information or are developed for a small variety of ionic liquids or small ranges of pressures and temperatures. For example, equations of states can be used for the prediction of ionic liquid densities; however, they require knowledge of the critical properties and acentric factors. By considering that there are no experimental data available for the © XXXX American Chemical Society

critical properties of ionic liquids, it is necessary to rely on methods that can predict these properties. However, owing to the absence of experimental data, the accuracy of these methods cannot be guaranteed. Because of this, group contribution methods for liquid density are attractive alternatives as they do not require knowledge of any experimental physical property data of the ionic liquid under consideration. Ye and Shreeve8 initially proposed one such group contribution method to predict the densities of ionic liquids at only room temperature and atmospheric pressure, which was later extended by Gardas and Coutinho9 to cover a range of pressures (0.10−100 MPa) and temperatures (273.15−393.15 K). For this purpose, Gardas and Coutinho9 used different imidazolium-, phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids to develop their method. They reported a mean percent deviation (MPD) of 0.45%, 1.49%, 0.41%, and 1.57% for each of these families, respectively. To predict the densities of ionic liquids, Lazzus10 used a group contribution method, including the whole core of the cation as a functional group together with smaller groups as additives for the cations, and small groups for the anion. A total of 210 different ionic liquids were used to obtain the contributions of the functional groups at a temperature of 298.15 K and a pressure of 0.101 MPa. A set of 100 ionic liquids, not used in a previous step, were used to evaluate the model. Then, 3530 data points from 76 ionic liquids within a temperature range of Special Issue: Proceedings of PPEPPD 2016 Received: June 28, 2016 Accepted: September 21, 2016

A

DOI: 10.1021/acs.jced.6b00535 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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only atoms and a limited number of small functional groups as the characterizing groups of the model.

258 to 393 K and pressure range of 0.09 to 207 MPa were used to obtain the temperature and pressure dependencies of ionic liquid densities. For this purpose, a linear dependency of density for both temperature and pressure was assumed. The results showed an AARD of 1.93% for the group contribution method for calculation of density only at 298.15 K and a pressure of 0.101 MPa, and 0.73% for the linear model of temperature and pressure dependency. Qiao et al.11 also used a linear group contribution method for the estimation of ionic liquid densities. They used 51 different groups, including six cation centers, substituted groups, and various groups for anions, making up a total of 7381 data points for 123 different pure ionic liquids and 13 different binary mixtures of ionic liquids. They reported average relative errors of 0.88% and 0.27% for their correlation and validation data sets, respectively. They also used their model to estimate the densities of 13 different binary mixtures of ionic liquids and reported a relative error of 1.22%, but using only three ionic liquids and 188 data points among the available 6570 data points and 123 ionic liquids for validation of the model, which seems to be an inadequate number. Paduszynski and Domanska1 used 18 500 data points from 1028 ILs in a wide range of pressures (0.1− 300 MPa) and temperatures (253−473 K) to develop a group contribution model for the prediction of liquid densities of ionic liquids. They used 177 functional groups, assigned to the cation core, the anion core, and the substituted functional groups. They reported an AARD of 0.53% for their correlation set and 0.45% for their prediction set. Evangelista et al.6 used a group contribution method, based on CVOL as proposed by Elbro et al.,12 for the prediction of ionic liquid densities. They used 21 845 data points from 864 different ionic liquids within a temperature range of 251.62−473.15 K and pressure range of 0.1−300.0 MPa. They added 102 groups to the already-existing 60 functional groups proposed by Ihmels and Gmehling,13 including 97 charged and 5 neutral functional groups, and reported an AARD of 0.83%. Jacquemin et al.14,15 used a group contribution method for over 5080 data points to predict the densities of ionic liquids up to a maximum temperature of 473 K, within a pressure range from 0.1 to 207 MPa. The temperature dependency of each functional group was obtained separately in a quadratic form, while the pressure dependency of ionic liquid densities was designated a Tait-type equation. Keshavarz et al.16 used a number of atoms to predict densities of 484 different ionic liquids at the temperature of 298.15 K and the pressure of 0.1 MPa only. They assumed that the contributions of other atoms are negligible. They initially reported an AARD of 4.3%, but incorporated two corrections for improvements which reduced their average error to 2.2%. As mentioned, most of the recent group contribution methods for the prediction of ionic liquid densities take large functional groups as the cores for the cation or anion, or both, and further use smaller functional groups for the substitutes.1,6,10,11 This approach increases the accuracy, but limits the applicability of the model to only those specific ionic liquids whose cation and anion cores are among the large functional groups. Specially, by taking into account that ionic liquids are considered to be designer solvents, with possible variations of about 1018 ionic liquids,3,4 using the anion and cation cores as direct functional groups in such methods is a severely limiting disadvantage. To overcome this problem, in this work we attempted to develop a simple group contribution method for prediction of the liquid densities of ionic liquids which utilizes

2. METHOD 2.1. Data Preparation. To prepare a comprehensive database, various data sets available in literature were collected, including the database of NIST.24,25 The result was a set consisting of 25 850 different data points from various families of ionic liquids, within a wide range of pressures (0.1 to 300 MPa) and temperatures (217.58 to 473.15 K). From the 25 850 collected data, 12 516 points were used as a correlation set to obtain the values of the constants of the group contribution equations and the weights of the functional groups and the remaining 13 334 data, from ionic liquids that were not included in the development of the model, were used to test the model. 2.2. Development of the Model. Wilson and Jasperson26 proposed three methods for the estimation of critical pressures and temperatures of organic and inorganic substances. At the zero’th order of the method, the boiling point, liquid density, and molecular weight are used as the descriptors. The atomic contributions, along with boiling point and number of rings are used in the first order calculations, while in the second order, group contributions are also incorporated. In this work in an attempt to develop a very simple group contribution method for ionic liquid density predictions, and taking inspiration from the work done by Wilson and Jasperson, we have chosen atoms as the main functional groups and further enhanced the method by incorporating a limited number of small functional groups to take into account the complexity of the structures of ionic liquids. However, unlike the method developed by Wilson and Jasperson, in this work, group contributions are not second order to atoms and both atom and group contributions are used simultaneously. Also, different contributions are assigned for the same atom or group, depending on whether they appear in the cation or the anion. A further difference is that in the method developed in this work, ionic liquids densities are not descriptors, rather, they are predicted. A simple form of a density equation, as inspired by the works of Ye and Shreeve8 and Gardas and Coutinho,9 has been chosen and incorporated with the selected functional groups, in order to develop a simple and general method. The resulting correlation for prediction of the liquid densities of ionic liquids has the functional form given by eq 1 M ρ= Vm (1) In this equation, ρ is density in g/cm3, M is molecular weight in g/mol, and Vm is molar volume in cm3/mol. The term Vm is obtained by group contribution through eq 2: Vm = dm +

Nat (c + aT + bP) 100

(2)

dm can be obtained through eq 3: dm = V0 + nrVr +

∑ niVc

i

+

∑ mjVa

j

(3)

In eq 3, V0 and Vr are constants, nr is the total number of rings existing in the ionic liquid structure in both the cation and the anion, Vc and Va are the contributions (or weights) of the functional groups for the cation and anion, respectively, ni and mj, respectively, indicate the number of times of occurrence of the ith and jth functional groups in the structure of the ionic B



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liquid, Nat is the number of atoms in the structure of the ionic liquid, T is temperature in degrees Kelvin, and P is pressure in MPa. 2.3. Optimization. To optimize the constants and the weights of the functional groups in eqs 2 and 3, genetic algorithm (GA) was used as the optimization method. Genetic algorithm is a general numerical optimization method that is based on both natural selection and natural genetics which can be used in various types of problems. A typical genetic algorithm includes a “population” of guesses as the solution of the problem. Each individual population is checked against the desired criteria for evaluating how good or bad the match of the solution is. The next step involves a method to mix fragments of the better solutions to partially improve the solutions in a stepwise manner until the desired solution is reached.27 The objective function (OF) for minimization is given in eq 4: clc

OF =

Table 2. Functional Groups for the Cation and Their Optimized Weights groups

Atom Contributions N C H O F Si P S Br Fe Cl I C< (ring) NH(ring) >CH−d CO COO OH CN COOH Rne

(4)

In eq 4, ρclc and ρexp are the calculated and experimental values of density, in g/cm3, respectively, and N is the total number of data points used in the optimization process.

3. RESULTS AND DISCUSSIONS Following the procedures mentioned above, the optimized values of the constants of eq 2 and 3 are given in Table 1. The

values

V0 a b c Vr

−4.0059 0.3749 −0.2489 −20.8279 −17.3357

|ρclc − ρexp | 100 ∑ ρexp N

and average absolute deviation (AAD), define as 1 AAD = ∑ |ρclc − ρexp | N

c

n>2

−3.4898 9.3246 2.7969 14.3775 5.4468 2.0058 −11.8741 11.9135 0.0851

m shows the number of times of occurrence of that atom in the structure of the cation. bThose groups that are not indicated by the signs > or − , (such as NH(ring) CO, COO, etc.) can be connected to any number of atoms (including H) or any number of groups with any type of bond (single, double). c(ring); meaning that the group is within a ring. dThe signs > or − indicate a group connected to other groups or atoms other than H. eNormal alkyl chain with n carbon atoms such as butyl or pentyl.

In eqs 5 and 6, ρclc and ρexp are the calculated and experimental density values, and N is the total number of data points that were considered in the calculation. It should be noted that the values of Va and Vc in Tables 2 and 3 are only contributions for the atoms and groups in the molar volume. They are not representative of the actual molar volumes of the atoms or groups. The statistical results for the model are given in Table 4. An AARD% of 0.95% and an AAD of 0.012 (g/cm3) was obtained for the complete data set. Such error values are commonly considered to be accurate enough for many engineering and scientific applications. Therefore, high accuracy, along with simplicity and generality, make the model a very good candidate for estimation of density whenever experimental values are not available. The predicted values of densities for the test (prediction) set versus the corresponding experimental values are shown in Figure 1. It can be seen from the figure that most of the points are near the diagonal line, which indicates that the predicted values are very close to the experimental values and the predictability of the model is quite accurate. The relative deviation of the predicted densities versus experimental densities for the test (prediction) set can be seen in Figure2. The high density of points around the line of 0% deviation emphasizes our earlier statement about the high accuracy of the model.

functional groups for the cation and anion and their weights are presented, respectively, in Tables 2 and 3. When using this model, one should note the following: (a) Groups do not replace the atoms. Group and atom contributions should both be used simultaneously. For example, for a hydroxyl group in the structure of an ionic liquid, both the OH groups and the atoms of H and O should be considered. (b) Those groups which are not particularly specified to belong to a ring can be applied for both ring and nonring groups. To better understand the use of the method for different ionic liquids, some examples are provided in the Supporting Information section. Using the proposed method, values of densities were estimated for the correlation set, the test set, and the overall data set and compared to the corresponding experimental data. The errors are presented as average absolute relative deviation percent (%AARD), define as %AARD =

m = 1a m=1

a

Table 1. Values of the constants in eqs 1 and 2 constants

12.0965 12.2105 0.9746 0.6759 0.7919 27.2494 14.5812 17.5598 5.9869 −81.9660 82.7637 20.4978

Group Contributionsb

exp

|ρ − ρ | 1 ∑ N ρexp

Vc (cm3/mol)

condition

(5)

(6) C



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Table 3. Functional Groups for the Anion and Their Optimized Weights Va (cm3/mol)

groups Atom Contributions Cl Br I O B F N S C P H Al Nb Ta W Ga Fe In

21.6536 29.6404 46.3084 6.2398 20.3946 6.2740 8.4436 23.3129 11.1926 25.6053 1.2163 18.7904 42.3397 39.0276 32.3795 19.3993 18.6362 26.2812

Figure 2. Relative deviation versus experimental densities for the test (prediction) data set.

Group Contributions CN C< (ring)a CO COO COOH OH a

1.7655 −1.1086 −12.6131 8.0128 −22.7409 −6.6065

Figure 3. Calculated density versus experimental values for the correlation data set.

(ring) meaning that the group is within a ring.

Table 4. Statistical Results for the Proposed Model constants

correlation set

prediction set

total set

data points %AARD AAD (g/cm3)

12 516 1.02 0.013

13 334 0.89 0.011

25 850 0.95 0.012

Figure 4. Relative deviation versus experimental densities for the correlation data set.

pressure-dependency of density for different ionic liquids within a wide range of temperatures and pressures. Similarly, to investigate the accuracy of the proposed model in predicting the temperature-dependency of ionic liquid densities, experimental and predicted densities are compared at atmospheric pressure for four different ionic liquids, chosen from the test set. The results of this comparison are shown in Figure 6. Although a wide range of temperatures were considered, the model successfully predicted the temperaturedependency of the ionic liquids. 3.1. Binary Mixtures. For estimation of density of binary mixtures of ionic liquids dm, M, Nat, and Vm in eq 2 and 3 are defined for mixtures by eqs 7 to 10:

Figure 1. Calculated density versus experimental values for the test (prediction) set.

In Figures 3 and 4, the calculated densities and the relative deviations are presented for the correlation data set. These figures also confirm the high accuracy of the model. To examine the capability of the model for prediction of the pressure-dependency of ionic liquid densities, experimental data for five different ionic liquids for the test set at constant temperature and different pressures are compared in Figure 5. As can be seen in this figure, the model succeeds to predict the

dmmix = x1dm1 + x 2dm2 D

(7) DOI: 10.1021/acs.jced.6b00535 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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It is seen from Table 5 that the proposed method can successfully estimate the densities of binary mixtures of ionic liquids, giving an AARD% of 0.45%, which is accurate enough for many engineering and scientific applications. 3.2. Comparison with Literature Models. The group contribution model of this study was also compared to that proposed by Gardas and Coutinho,9 as well as the method developed by Paduszynski and Domanska.1 To make a fair and reliable comparison between the models, two different comparisons were carried out: In comparison (A), only those ionic liquids from the NIST data in the test set whose densities could be predicted by the method of Paduszynski and Domanska1 were considered. In comparison (B), only those ionic liquids from the NIST database for which the molecular volume of both the cation and anion could be obtained directly from the studies of Gardas and Coutinho9,55,56 were used for comparison. The final results for these comparisons are shown in Table 6. A similar comparison is also made for the model presented in this study for binary mixtures of ionic liquids to the literature methods proposed by Gardas and Coutinho9 and Paduszynski and Domanska.1 The results of the comparisons are presented in Table 7. The most accurate method among the three models investigated in Table 6 is the method proposed by Paduszynski and Domanska.1 Such a result was to be expected since their method uses 177 functional groups, most being quite large groups. In addition, the equation proposed by Paduszynski and Domanska1 is more complicated than that of this work and Gardas and Coutinho’s method.9 However, despite the much greater simplicity of both the equation and the functional groups of this work, the difference between the %AARD of Paduszynski and Domanska’s model and this work is only 0.19%. Gardas and Coutinho incorporated a simple equation; however, their method requires values of molecular volumes of the cation and anion. The %AARD of their model is also higher than the model proposed in this work. Regarding mixtures, it can be seen from Table 7 that the results for binary mixtures for this work and Paduszynski and Domanska methods 1 do not differ greatly (0.05% in comparison (A) and 0.09% in comparison (B)). The % AARD for Gardas and Coutinho’s9 method is higher than the others, but still has good accuracy.

Figure 5. Pressure-dependency of density for five different ionic liquids. Red lines represent predicted values of densities by the model: (A) 1-(2-methoxyethyl)-1-methylpyrrolidinium bis ((trifluoromethyl)sulfonyl) amide28 at 278.15 K and 0.1 to 120 MPa; (B) 1-ethyl-3methylimidazolium tetrafluoroborate29 at 298.15 K and 0.1 to 60 MPa; (C) 1-butyl-4-methylpyridinium tetrafluoroborate30 at 283.15 K and 0.1 to 65 MPa; (D) 1-butyl-3-methylimidazolium acetate31 at 331.1 K and 0.1 to 200 MPa; (E) tetradecyl(trihexyl)phosphonium dicyanamide32 at 313.15 K and 0.1 to 45 MPa.

Figure 6. Temperature-dependency of density for four different ionic liquids: (A) 1,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide; temperature,33,34 293.15 to 353.15 K; (B) butyltrimethylammonium bis (trifluoromethylsulfonyl) imide;35,36 temperature, 282 to 353.15 K; (C) 1-methyl-3-octylimidazolium tricyanomethanide;37 temperature, 283.15 to 363.15 K; (D) tetradecyl(trihexyl)phosphonium chloride;38,39 temperature, 278.15 to 363.15 K.

M mix = x1M1 + x 2M 2

(8)

Natmix

(9)

= x1Nat1 + x 2Nat2

Vmmix = dmmix +

Natmix (c + aT + bP) 100

4. CONCLUSIONS A very simple and general group contribution method is developed for the prediction of liquid densities of ionic liquids over a wide range of temperatures and pressures. Instead of defining large functional groups of the cations and anions, as is commonly done in group contribution methods developed for ionic liquids, atoms are considered in this work, as well as a few simple and small functional groups assigned within the cation and anion in order to account for the complexity of the structures of ionic liquids. Using such simple and small functional groups remarkably increases the generality and applicability of the model with respect to group contribution methods that define large functional groups. As long as the ionic liquids in question consist of only the atoms considered in the proposed model, their density can be predicted by this method. Despite the simplicity and generality, the model is quite accurate, showing a total %AARD of 0.95% and a total AAD of 0.012 (g/cm3). The method can also be used for estimation of densities of binary mixtures of ionic liquids. A %

(10)

In the equations above, the superscript mix refers to mixture, the subscripts 1 and 2 refer to components 1 and 2, respectively, and xi is mole fraction of component i in the mixture. The density of a mixture can then be estimated as follows:

ρ mix =

M mix Vmmix

(11)

Equation 11 was used for estimation of the densities of 29 different binary mixtures of ionic liquids from the NIST database.24 The results of these estimations are given in Table 5. E



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Table 5. Estimation Errors of Binary Ionic Liquid Mixture Densities by the Proposed Model mixtures

data points

temperature range

%AARD

ref

[C4mmim][N3] + [C4mmim][BF4] [C2mim][EtSO4] + [C2mim] [SCN] [C2mim][dca] + [C2mim][SCN] [C4py][BF4]+[C4py][Tf2N] [C4py][BF4]+[C4m’py][Tf2N] [C2mim][C(CN)3]+[C2mim][dca] [C4m’py][Tf2N]+[C2mim][TFES] [C4m’py][Tf2N]+[C2mim] [EtSO4] [C4mim][BF4]+[C4mmim][MeSO4] [C6mim][BF4]+[C2mim][BF4] [C4mim][PF6]+[C4mim][BF4] [C6mim][BF4]+[C4mim][BF4] [C6mim][Cl]+[C6mim][BF4] [C8mim][Cl]+[C8mim][BF4] [C6mim][Cl]+[C6mim][PF6] [C3mpy][Tf2N]+[C4mim][Tf2N] [C3mpip][Tf2N]+[C4mim][Tf2N] [C3mpyr][Tf2N]+[C4mim][Tf2N] [C4mmim][Tf2N]+[C4mim][Tf2N] [C2mim][CH3CO2]+[C2mim][EtSO4] [C2mim][CF3CO2]+[C2mim][CH3CO2] [C2mim][BF4]+[C3mim][BF4] [C3mim][BF4]+[C6mim][BF4] [C2mim][BF4]+[C6mim][BF4] [EtOHmim][BF4]+[C4mim][BF4] [EtOHmim][BF4]+[C4py][BF4] [C4mim][BF4]+[C4py][BF4] [C2mim][dca]+[C2mim][BF4] [C2mim][Cl]+[C2mim][GaCl4] overall

35 96 60 72 84 42 70 70 144 135 126 108 42 42 35 7 7 7 7 77 20 121 121 121 121 121 121 9 30 2051

313.15−373.15 298.15−353.15 298.15−353.15 303.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 293.15−353.15 298.15−308.15 298.15−308.15 298.15−308.15 298.15−308.15 303.15−333.15 303.15−333.15 303.15−333.15 298.2−298.2 298.2−298.2 298.2−298.2 298.2−298.2 298.15−358.15 298.1−373.1 293.15−343.15 293.15−343.15 293.15−343.15 293.15−343.15 293.15−343.15 293.15−343.15 298.15−298.15 308.15−343.15 293.15−373.15

0.26 0.67 0.43 0.72 0.64 0.59 0.48 0.47 0.45 0.13 0.09 0.03 0.14 0.06 0.17 0.13 0.41 0.12 0.04 1.05 0.79 0.31 0.18 0.19 0.14 0.81 0.62 0.5 4.2 0.45

40 41 41 42 43 44 45 45 46 46 46 46 47 47 47 48 48 48 48 49 50 51 51 51 52 52 52 53 54

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Table 6. Comparison of Models for Estimation of Density of Pure Ionic Liquids method this work Paduszynski and Domanska1 this work Gardas and Coutinho9

data points

temperature range

12506 12506

Comparison A 217.577−473.15 217.577−473.15

7667 7667

Comparison B 220.78−473.15 220.78−473.15

pressure range

% AARD

0.096−300 0.096−300

0.76 0.57

0.096−300 0.096−300

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00535. Abbreviation list of the ILs mentioned in this study; solved examples on the proposed method (PDF)

■

this work Paduszynski and Domanska1 this work Gardas and Coutinho9 Paduszynski and Domanska1

data points Comparison A 2016 2016 Comparison B 1239 1239 1239

0.58 1.3

temperature range

%AARD

293.15−353.15 293.15−353.15

0.45 0.40

293.15−353.15 293.15−353.15 293.15−353.15

AUTHOR INFORMATION

Corresponding Author

*Tel.: +98 71 36133707. Fax: +98 71 36474619. E-mail: [email protected]. Funding

Table 7. Comparison of Models for Estimation of Density of Binary Mixtures of Ionic Liquids method

ASSOCIATED CONTENT

S Supporting Information *

The authors are grateful to Shiraz University for financial support. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Paduszynski, K.; Domanska, U. A New Group Contribution Method For Prediction of Density of Pure Ionic Liquids over a Wide Range of Temperature and Pressure. Ind. Eng. Chem. Res. 2012, 51, 591−604. (2) Ji, X.; Held, C. Modeling the density of ionic liquids with ePCSAFT. Fluid Phase Equilib. 2016, 410, 9−22. (3) Gardas, R. L.; Ge, R.; Goodrich, P.; Hardacre, C.; Hussain, A.; Rooney, D. W. Thermophysical Properties of Amino Acid-Based Ionic Liquids. J. Chem. Eng. Data 2010, 55, 1505−1515. (4) Trohalaki, S.; Pachter, R. Prediction of Melting Points for Ionic Liquids. QSAR Comb. Sci. 2005, 24, 485−490.

0.36 0.89 0.27

AARD of 0.45% confirms that the model is quite capable to estimate densities of binary mixtures. In conclusion, the model is a suitable tool for prediction of densities of ionic liquids whenever experimental data are not available or hard to measure. F



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Estimation of the Densities of Ionic Liquids Using a Group Contribution

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