Extension of the Simple Equations for Prediction of the Properties of

Feb 28, 2011 - Extension of the Simple Equations for Prediction of the Properties of Mixed Electrolyte Solutions to the Mixed Ionic Liquid Solutions. ...
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Extension of the Simple Equations for Prediction of the Properties of Mixed Electrolyte Solutions to the Mixed Ionic Liquid Solutions Yu-Feng Hu,* Hong-Da Chu, Ji-Guang Li, Zhi-Chang Liu, Xiao-Ming Peng, Shan Ling, and Jin-Zhu Zhang State Key Laboratory of Heavy Oil Processing and High Pressure Fluid Phase Behavior & Property Research Laboratory, China University of Petroleum, Beijing 102249, China

bS Supporting Information ABSTRACT: The simple equations for predictions of the density, viscosity, and conductivity of mixed electrolyte solutions were extended to the related properties of mixed ionic liquid solutions. The densities, viscosities, and conductivities were measured for the ternary solutions [C4mim]Cl (1-butyl-3-methylimidazolium chloride) þ [C4mim]Br (1- butyl-3-methylimidazolium bromide) þ H2O and [C6mim]Cl (1-hexyl-3-methylimidazolium chloride) þ [C6mim]Br (1-hexyl-3-methylimidazolium bromide) þ H2O and their binary subsystems [C4mim]Cl þ H2O, [C4mim]Br þ H2O, [C6mim]Cl þ H2O, and [C6mim]Br þ H2O at (293.15, 298.15, and 308.15) K, respectively. The results were used to test the predictability of the extended equations. The comparison results show that these simple equations can be used to predict the density, viscosity, and conductivity of the mixed ionic liquid solutions from the properties of their binary subsystems of equal ionic strength.

1. INTRODUCTION The thermodynamic and transport properties of mixed electrolyte solutions play an important role in a variety of fields such as chemical engineering, separation processes, wastewater treatment, pollution control, and oil recovery. A number of groups have reported the physical properties of binary electrolyte solutions.1-5 For example, Ruby and Kawai1 reported densities, equivalent conductivities, and relative viscosities of the binary solutions HCl þ H2O, KCl þ H2O, and NaCl þ H2O at 298.15 K. Isono2 reported the densities, electrolytic conductivities, and viscosities of binary aqueous solutions of alkaline-earth chlorides, LaCl3, Na2SO4, NaNO3, NaBr, KNO3, KBr, and Cd(NO3)2 at several temperatures. Zhang and Han3 reported the densities and viscosities of the binary solutions NaCl þ H2O and KCl þ H2O at 298.15 K. Zhang et al.4 reported the densities and viscosities of the binary solution CaCl2 þ H2O at 298.15 K. K€onigsberger et al.5 reported the densities, viscosities, and heat capacities of the binary solution MgCl2 þ H2O in the 298.15-363.15 K temperature range. However, relatively few measurements have been made for the mixed electrolyte solutions. At the same time, one of the objectives of the theory of electrolyte solutions is to calculate various properties of mixed electrolyte solutions in terms of the properties of binary solutions, and much effort has indeed been made in the literature to develop simple equations that can make full use of the available information on binary electrolyte solutions and provide sufficient accuracy to predict the properties of mixed solutions.6,7 Such simple equations have been established for thermodynamic properties. For example, there are several simple approaches for the prediction of density of mixed electrolyte solutions, including the rule of Patwardhan and Kumar,8,9 the rule of Young and Smith,10 and the semi-ideal solution theory.11,12 The rule of Young and Smith10 and the semi-ideal solution theory11,12 have been extended to the conductivity of mixed electrolyte solutions.13 The equations of Patwardhan and Kumar8,9 and the semi-ideal solution theory11,12 r 2011 American Chemical Society

have been used together with Eyring’s absolute rate theory to establish the simple equations for the viscosity of mixed electrolyte solutions.6 These approaches can be used to predict the thermodynamic and transport properties of mixed solutions in terms of the properties of their binary subsystems. Recently, excellent tests of these equations have been performed by systematic comparison with the experimental data of mixed nonelectrolyte solutions, mixed electrolyte solutions, and mixed solutions of electrolytes and nonelectrolytes.14 However, the tests were limited to relatively lower ionic strength because the solubilities of the examined electrolytes in water are relatively low. Ionic liquids (ILs) are comprised entirely of ions.15 The ILs have unique properties such as very low vapor pressure, high ionic conductivity, outstanding catalytic properties, and high thermal stability. Consequently, ILs have attracted a great deal of attention for their potential use in various fields.15 Generally, to design an industrial process involving ILs, it is necessary to know a range of their physical properties including density, viscosity, and conductivity. A key strategy in the application of ILs is the use of binary and ternary mixtures of ILs to generate the targeted property set.16-18 Therefore, recently, the mixtures of ILs have received growing attention.16-18 Up to now, the studies on IL mixtures have focused on their volumetric behavior,19 their effects on gas solubility properties18,20 and on the local environment of solvatochromic probes,21,22 and their use as stationary phases in gas chromatography23 and as electrolytes in solar cells.24 A molecular level understanding of the structure and dynamics of IL mixtures has also been achieved. For example, Xiao et al.25 have studied the intermolecular dynamics of binary Received: November 7, 2010 Accepted: February 8, 2011 Revised: January 24, 2011 Published: February 28, 2011 4161

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Industrial & Engineering Chemistry Research IL mixtures through the use of optical heterodyne-detected Raman-induced Kerreffect spectroscopy (OHD-RIKES). On the other hand, the presence of water in ILs can dramatically affect their physicochemical properties.26,27 In addition, with the development of ILs for the colloid and surfactant fields, it has become even more important to study the properties of aqueous solutions of ILs.28,29 Therefore, a number of groups have studied the physical properties of aqueous solutions of ILs.30-37 The properties of aqueous solutions of IL mixtures are important not only for technical and industrial applications of ILs, but also for tests of electrolyte theories, especially of their applicability at very high ionic strength. Therefore, in this study, the above-mentioned predictive equations developed for the properties of mixed electrolyte solutions were extended to the thermodynamic and transport properties of mixed IL solutions. At the same time, the densities, viscosities, and conductivities were measured for the ternary solutions [C4mim]Cl þ [C4mim]Br þ H2O and [C6mim]Cl þ [C6mim]Br þ H2O and their binary subsystems [C4mim]Cl þ H2O, [C4mim]Br þ H2O, [C6mim]Cl þ H2O, and [C6mim]Br þ H2O at different temperatures and up to Imax e 20.5 mol 3 kg-1 (I is ionic strength). The results were used to study the predictability of the well-known approaches.

2. EXPERIMENTAL SECTION Deionized water was distilled in a quartz still, and its conductivity was 0.8-1.2  10-6 S 3 cm-1. All chemicals used in this study were of reagent grade with the claimed purity >99%. Nmethylimidazole, n-C4H9Cl, n-C4H9Br, n-C6H13Cl, and n-C6H13Br were supplied by Shanghai Jiachen Chemical Co., Ltd. Nmethylimidazole was stored over 4 Å molecular sieves before use.38,40 n-C4H9Cl, n-C4H9Br, n-C6H13Cl, and n-C6H13Br were distilled before use.38,40 These chemicals were then used for the synthesis of the [C4mim]Cl, [C4mim]Br, [C6mim]Cl, and [C6mim]Br ILs. These four ILs were prepared by well established procedures described in our previous studies.39,40 The obtained [C4mim]Cl and [C4mim]Br are white crystals at room temperature, and [C6mim]Cl and [C6mim]Br are liquid at room temperature. After purification, the ILs were dried under vacuum conditions over CaCl2 for several days at 353 K and were then further dried with 3 Å molecular sieves for several days immediately before use. The water content after drying, measured by Karl Fisher titration, was within 0.012 wt %. Samples were prepared by syringing weighed amounts of the pure liquids into stoppered bottles in a glovebox. The experimental procedures are similar to those used in our previous studies41 and are described briefly as follows. The binary aqueous solutions were prepared by mass from double-distilled deionized water and the IL using a Sartorius CT225D balance with a precision of (5  10-5 g. The molalities of IL stock solutions were also analyzed using AgNO3 titration.13 The ternary solutions were prepared by mixing the binary solutions. The uncertainty was (5  10-5 mol 3 kg-1. The solutions were placed into stoppered bottles and stirred for 2 h. All solutions were prepared in glass flasks, and measurements were carried out one week after preparation to ensure complete dissolution and aggregation. The conductivity measurements were carried out with a METLER TOLEDO SevenEasyTM conductivity meter calibrated with standard aqueous potassium chloride solutions.13 The temperature of the cell was kept constant to within (0.005 K by circulating thermostatted liquid, and the temperature was

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measured with a calibrated calorimeter thermometer ((0.006 K).13 Densities of solutions were measured using a KEM oscillatingtube digital densimeter (DA-505) thermostatted to better than (0.01 K.40,41 The temperature in the measuring cell was monitored with a digital thermometer. The densimeter was calibrated with double-distilled water and dry air.41,42 The densities of water at different temperatures were obtained from the literature.43,44 The densities of dry air at different temperatures were taken from ref 45. The uncertainty in density measurements was (5  10-5g 3 cm-3. Viscosities were measured using a modified Cannon-Ubbelohde suspended level capillary viscometer.40 A thoroughly cleaned and perfectly dried viscometer filled with liquid was placed vertically in a glass sided water thermostat (controlled to (0.01 K). After thermal equilibrium was attained, the efflux times of flow of the liquids were recorded with a digital stop watch with a precision of (0.01 s. Triplicate measurements were performed at each composition. The capillary viscometers are calibrated and credited by the company,32,40 and all of the deviations were within 0.2%.40 In our preliminary measurements, the capillary viscometers were also calibrated with materials of known viscosity such as water (0.8903 mPa 3 s at 298.15 K),43 ethylene glycol (9.408 mPa 3 s at 298.15 K), and diethylene glycol (26.812 mPa 3 s at 298.15 K).46 The measured viscosities for the system [C6mim]Br þ H2O at 293.15 K and for the systems [C4mim]Cl þ H2O and [C6mim]Cl þ H2O at 298.15 K are compared with the values reported in the literature.32,40 The agreements are good.

3. PREDICTIVE EQUATIONS FOR DENSITY, VISCOSITY, AND CONDUCTIVITY OF AQUEOUS SOLUTIONS OF IONIC LIQUIDS In the following section, the variables with the superscript (o,I) together with the subscript MiXi were used to denote the quantities of component MiXi in the binary solution MiXi þ H2O(i = 1, 2, ..., n) having the same ionic strength as that of a mixed solution, and those without the superscript (o,I) denote the corresponding quantities in the mixed solution. The equation of Patwardhan and Kumar8 can be expressed as .

n

F¼

n

∑ YM X i∑¼ 1ðYM X =FoM, IX Þ i¼1 i i

i i

i i

ð1Þ

with YMiXi = yMiXi þ mMiXiMMiXi, where y, m, F, and M denote ionic strength fraction, molality, density, and molar mass, respectively. Hu’s equation for the viscosity of a mixed IL solution can be expressed as6 n

ln η ¼

xM X ∑ o, I i¼1

i i

x Mi X i

o, I ln ηMi Xi

ð2Þ

where x is mole fraction. Young’s rule47,48 for the conductivity of a mixed IL solution M1X1 þ M2X2þ ... þMnXn þ H2O in terms of the conductivities of its binary solutions MiXi þ H2O (i = 1, 2, ..., n) of equal ionic strength can be expressed as n

σ ¼ 4162

∑ yM X σMo, IX i¼1 i i

i i

ð3Þ

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with yMiXi = IMiXi/∑ni=1IMiXi, where I and y are ionic strength and the ionic strength fraction, respectively.

4. COMPARISONS WITH THE EXPERIMENTAL DATA The measured densities, viscosities, and conductivities were used to test eqs 1-3, and the test procedure is briefly summarized as follows: (1) Represent the measured densities, viscosities, and conductivities of the binary solutions by the following polynomial equations: FoMi Xi ðcalcÞ ¼

ηoMi Xi ðcalcÞ ¼ σ oMi Xi ðcalcÞ ¼

∑ Al ðmoM X Þl=2

ð4Þ

∑ Bl ðmoM X Þl

ð5Þ

∑ Cl ðmoM X Þl=2

ð6Þ

l¼0

l¼0

l¼0

i i

i

i i

i

where FMiXio(calc), ηMiXio(calc), σMiXio(calc), and mMiXio denote the density, viscosity, conductivity, and molality of the binary solution MiXi þ H2O (i = 1, 2, ..., n). The optimum fit was obtained by variation of l until the o o values of ΔF,MiXio = ∑N j=1(|FMiXi (calc) - FMiXi (expt)|/FMiXi o o N o o (expt) )/N, Δη,MiXi = ∑j=1(|ηMiXi (calc) - ηMiXi (expt)|/ o o N o ηMiXi (expt))/N, and Δσ,MiXi = ∑j=1(|σMiXi (calc) - σMiXi o o -4 (expt) |/σMiXi (expt))/N are less than a few parts in 10 . The values of Al, Bl, Cl, δF,MiXio, δη,MiXio, and δσ,MiXio obtained for the examined binary solutions are shown in Table 1 of the Supporting Information. (2) Determine the compositions (mMiXio,I) of the binary solutions having the same ionic strength as that of the mixed solution of given molalities mMiXi (i = 1, 2, ..., n). (3) Insert the values of FMiXio,I, ηMiXio,I, and σMiXio,I calculated from eqs 4-6 into eqs 1-3 to yield the predictions for the mixed solutions of given mMiXi (i = 1, 2, ..., n), which are then compared with the corresponding experimental data. In this article, the average relative differences between predicted and measured densities (δF), viscosities (δη), and conductivities (δη) over the entire experimental composition range of the mixed solution are defined by41 N

δF ¼

∑ jδF, i j=N i¼1

δη ¼

∑ jδη, i j=N i¼1

δσ ¼

∑ jδσ, i j=N i¼1

ð7Þ

N

ð8Þ

N

ð9Þ

with δF,i = (Fi,(calc) - Fi,(expt))/Fi,(expt), δη,i = (ηi,(calc) - ηi,(expt))/ ηi,(expt), and δσ,i = (σi,(calc) - σi,(expt))/σi,(expt), where N is the number of experimental data.

5. RESULTS AND DISCUSSION Tables 2-5 are listed in the Supporting Information and show the measured densities, viscosities, and conductivities of the binary solutions [C4mim]Cl þ H2O, [C4mim]Br þ H2O,

[C6mim]Cl þ H2O, and [C6mim]Br þ H2O at different temperatures. The results were compared with the values reported in the literature.32,40,49,50 The agreements are good. Table 6 is listed in the Supporting Information and compares measured and predicted densities for the ternary solutions [C4mim]Cl þ [C4mim]Br þ H2O and [C6mim]Cl þ [C6mim]Br þ H2O at different temperatures. The third to fifth columns show that the agreements are good; the Δeq1 F values for the ternary solution [C4mim]Cl þ [C4mim]Br þ H2O at 293.15, 298.15, and 308.15 K are 3.1  10-4, 3.8  10-4, and 3.3  10-4, respectively. The Δeq1 F values for the ternary solution [C6mim]Cl þ [C6mim]Br þ H2O at 293.15, 298.15, and 308.15 K are 3.2  10-4, 3.5  10-4, and 2.9  10-4, respectively. Table 7 is listed in the Supporting Information and compares measured and predicted viscosities for the ternary solutions [C4mim]Cl þ [C4mim]Br þ H2O and [C6mim]Cl þ [C6mim]Br þ H2O at different temperatures. The third to fifth columns show that the agreements are also good; the Δeq2 η values for the ternary solution [C4mim]Cl þ [C4mim]Br þ H2O at 293.15, 298.15, and 308.15 K are 2.4  10-3, 2.5  10-3, and 3.7  10-3, respectively. The Δeq2 η values for the ternary solution [C6mim][Cl] þ [C6mim]Br þ H2O at 293.15, 298.15, and 308.15 K are 3.3  10-3, 3.5  10-3, and 3.4  10-3, respectively. Table 8 is listed in the Supporting Information and compares measured and predicted conductivities for the ternary solutions [C4mim]Cl þ [C4mim]Br þ H2O and [C6mim]Cl þ [C6mim]Br þ H2O at different temperatures. The third to fifth columns show that the agreements are good; the Δeq3 σ values for the ternary solution [C4mim]Cl þ [C4mim]Br þ H2O at 293.15, 298.15, and 308.15 K are 2.4  10-3, 2.2  10-3, and 2.4  10-3, respectively. The Δeq3 σ values for the ternary solution [C6mim]Cl þ [C6mim]Br þ H2O at 293.15, 298.15, and 308.15 K are 4.8  10-3, 3.7  10-3, and 3.3  10-3, respectively.

6. CONCLUSIONS The simple equations for prediction of the density, viscosity, and conductivity of mixed electrolyte solutions were extended to the corresponding properties of mixed IL solutions. Their predictabilities have been tested by comparisons with the measured densities, viscosities, and conductivities of the ternary solutions [C4mim]Cl þ [C4mim]Br þ H2O and [C6mim]Cl þ [C6mim]Br þ H2O at different temperatures and up to Imax e 20.5 mol 3 kg-1. The comparison results show that eqs 1-3 can provide good predictions for the densities, viscosities, and conductivities of the ternary IL solutions from the data of their binary subsystems of equal ionic strength, which indicates that these simple equations can make full use of the information on the binary IL solutions, avoiding much complexity in the calculation of multicomponent thermodynamic and transport properties, and provide good predictions for the multicomponent IL solutions. ’ ASSOCIATED CONTENT

bS

Supporting Information. The parameters for the binary systems [C4mim]Cl (B) þ H2O (A), [C4mim]Br (B) þ H2O (A), [C6mim]Cl (B) þ H2O (A), and [C6mim]Br (B) þ H2O (A) at different temperatures (Table 1); the densities, viscosities, and conductivities of the binary system [C4mim]Cl (B) þ H2O (A) at different temperatures (Table 2); the densities, viscosities,

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and conductivities of the binary system [C4mim]Br (B) þ H2O (A) at different temperatures (Table 3); the densities, viscosities, and conductivities of the binary system [C6mim]Cl (B) þ H2O (A) at different temperatures (Table 4); the densities, viscosities, and conductivities of the binary system [C6mim]Br (B) þ H2O (A) at different temperatures (Table 5); comparisons of measured and predicted densities of the ternary systems [C4mim]Cl (B) þ [C4mim]Br (C) þ H2O (A) and [C6mim]Cl (B) þ [C6mim]Br (C) þ H2O (A) at different temperatures (Table 6); comparisons of measured and predicted viscosities of the ternary systems [C4mim]Cl (B) þ [C4mim]Br (C) þ H2O (A) and [C6mim]Cl (B) þ [C6mim]Br (C) þ H2O (A) at different temperatures (Table 7); comparisons of measured and predicted conductivities of the ternary systems [C4mim]Cl (B) þ [C4mim]Br (C) þ H2O (A) and [C6mim]Cl (B) þ [C6mim]Br (C) þ H2O (A) at different temperatures (Table 8). This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: 86-10-89733846. [email protected].

Fax:

86-10-89733846.

E-mail:

’ ACKNOWLEDGMENT The authors thank the National Natural Science Foundation of China (20976189, 21076224, 21036008, B060902, and 20925623) and the Program for New Century Excellent Talents in University of Ministry of Education of China (NCET-060088) for financial support. ’ REFERENCES (1) Ruby, C. E.; Kawai, J. The Densities, Equivalent Conductances and Relative Viscosities at 25°C, of Solutions of Hydrochloric Acid, Potassium Chloride and Sodium Chloride, and of Their Binary and Ternary Mixtures of Constant Chloride-ion-constituent Content. J. Am. Chem. Soc. 1926, 48, 1119–1128. (2) Isono, T. Density, Viscosity, and Electrolytic Conductivity of Concentrated Aqueous Electrolyte Solutions at Several Temperatures. Alkaline-earth Chlorides, LaCl3, Na2SO4, NaNO3, NaBr, KNO3, KBr, and Cd(NO3)2. J. Chem. Eng. Data 1984, 29, 45–52. (3) Zhang, H. L.; Han, S. J. Viscosity and Density of Water þ Sodium Chloride þ Potassium Chloride solutions at 298.15 K. J. Chem. Eng. Data 1996, 41, 516–520. (4) Zhang, H. L.; Chen, G. H.; Han, S. J. Viscosity and Density of NaCl-CaCl2-H2O and KCl-CaCl2-H2O at 298.15 K. J. Chem. Eng. Data 1997, 42, 526–530. (5) K€onigsberger, E.; K€onigsberger, L.-C.; May, P.; Harris, B. Properties of Electrolyte Solutions Relevant to High Concentration Chloride leaching. II. Density, Viscosity and Heat Capacity of Mixed Aqueous Solutions of Magnesium Chloride and Nickel Chloride Measured to 90 °C. Hydrometallurgy 2008, 90, 168–176. (6) Hu, Y. F. Prediction of Viscosity of Mixed Electrolyte Solutions Based on the Eyring’s Absolute Rate Theory and the Equations of Patwardhan and Kumar. Chem. Eng. Sci. 2004, 59, 2457-2464. (7) Hu, Y. F. Reply to “Comments on ‘Prediction of Viscosity of Mixed Electrolyte Solutions Based on the Eyring’s Absolute Rate Theory and the Equations of Patwardhan and Kumar’”. Chem. Eng. Sci. 2005, 60, 3121–3122. (8) Patwardhan, V. S.; Kumar, A. A United Approach for Prediction of Thermodynamic Properties of Aqueous Mixed-electrolyte Solutions.

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