J. Chem. Thermodynamics 40 (2008) 1208–1216

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J. Chem. Thermodynamics

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Excess molar properties of ternary system(ethanol + water + 1,3-dimethylimidazolium methylsulphate)and its binary mixtures at several temperatures

Elena Gómez, Begoña González, Noelia Calvar, Ángeles Domínguez *

Chemical Engineering Department, University of Vigo, 36310 Vigo, Pontevedra, Spain

a r t i c l e i n f o

Article history:Received 25 January 2008Received in revised form 3 April 2008Accepted 12 April 2008Available online 18 April 2008

Keywords:ViscosityDensity1,3-Dimethylimidazolium methylsulphateTernary systemsBinary systems

0021-9614/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.jct.2008.04.006

* Corresponding author. Tel.: +34 986812422; fax:E-mail address: admguez@uvigo.es (Á. Domínguez

a b s t r a c t

The density, dynamic viscosity, and refractive index of the ternary system (ethanol + water + 1,3-dime-thylimidazolium methylsulphate) at T = 298.15 K and of its binary systems 1,3-dimethylimidazoliummethylsulphate with ethanol and with water at several temperatures T = (298.15, 313.15, and328.15) K and at 0.1 MPa have been measured over the whole composition range. From these physicalproperties, excess molar volumes, viscosity deviations, refractive index deviations, and excess free energyof activation for the binary systems at the above mentioned temperatures, were calculated and fitted tothe Redlich–Kister equation to determine the fitting parameters and the root-mean-square deviations.For the ternary system, the excess properties were calculated and fitted to Cibulka, Singh et al., and Nag-ata and Sakura equations. The ternary excess properties were predicted from binary contributions usinggeometrical solution models.

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1. Introduction

Room temperature ionic liquids or ionic liquids (RTILs or ILs) area class of organic salts that are comprised entirely of ions and areliquids at conditions around room temperature in their pure state.

In recent years, the properties of ILs have attracted considerableattention [1–11]. In addition, their perceived status as ‘‘designer”,alternative ‘‘green” solvents has contributed to this interest. De-spite their interest and importance, the physicochemical proper-ties of ILs and the detailed knowledge of the thermodynamicbehaviour of the mixtures of ILs with molecular solvents havenot been studied systematically. In this context, a systematicinvestigation of the thermodynamic and thermophysical proper-ties of ILs and their mixtures is an important issue.

This work is a continuation of our research group’s investigationof the thermodynamic properties of ionic liquids [12–16]. In thispaper, we show at atmospheric pressure experimental densityand dynamic viscosity data over the whole composition range for{x1 ethanol + x2 water + (1 � x1 � x2) [MMIM][MeSO4]} at T =298.15 K and its binary systems {x1 ethanol + 1 � x1 [MMIM][Me-SO4]} and {x1 water + (1 � x1) [MMIM][MeSO4]}. These propertieswere measured at T = (298.15, 313.15, and 328.15) K in order to ob-serve the evolution of the studied properties with the increase of

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the temperature. The results were used to calculate excess molarvolumes, viscosity deviations and excess free energies of activationof viscous flow. Refractive indices were measured fromT = 298.15 K over the whole composition range for {x1 ethanol + x2

water + (1 � x1 � x2) [MMIM][MeSO4]}, {x1 ethanol + (1 � x1)[MMIM][MeSO4]} and {x1 water + (1 � x1) [MMIM][MeSO4]}. Theresults were used to calculate refractive index deviations.

The treatment of experimental ternary data was carried out intwo ways: (i) correlation using empirical equations [17–19], and(ii) prediction using geometrical models that assume that interac-tions in a ternary mixture depend on the interactions in binary sys-tems [20–26].

2. Experimental

2.1. Chemicals

Ethanol was supplied by Merck. The component was degassedultrasonically, and dried over molecular sieves 4 � 10�8 (Type 4Å),that were supplied by Aldrich, and kept in inert argon with a maxi-mum content in water of 2 � 10�6 by mass fraction. The mass fractionpurity was >0.998 for ethanol. Water was doubly distilled and deion-ised. The ionic liquid used in this work was synthesised in our labo-ratory, following the published procedure [27]. To assure its purity, aNMR was made and compared with Pereiro et al. [27]; no differenceswere found. To reduce the water content to negligible values (lower

TABLE 1Comparison of experimental density, q, and viscosity, g, with literature data for purecomponents at T = 298.15 K

Component T/K q/(g � cm�3) g/(mPa � s)

Experimental Literature Experimental Literature

[MMIM][MeSO4]

298.15 1.32912 1.32725a

1.3290b 77.7 72.91a

1.328c

1.33059d

313.15 1.31856 1.31657a 41.68 39.21a

1.32009d

328.15 1.30813 1.30606a 25.21 20.37a

1.31121d

Ethanol 298.15 0.78546 0.7854e 1.082 1.082e

313.15 0.77200 0.77207f 0.827 0.826f

328.15 0.75855 0.75861f 0.641 0.641f

Water 298.15 0.99720 0.9971g 0.890 0.890g

313.15 0.99221 0.99222h 0.653 0.6530h

328.15 0.98569 0.98570i 0.504 0.5042i

a Pereiro et al. [27].b Domanska et al. [28].c Kato et al. [29].d Golden et al. [30].e Nikam et al. [31].f González et al. [32].g Kapadi et al. [33].h Grande et al. [34].i Krishnaiah et al. [35].

TABLE 2Density, q, refractive index, nD, dynamic viscosity, g, excess molar volumes, VE,deviations in the refractive index, DnD, viscosity deviations, D g and excess free energyof activation, DG*E, for {x1 water + (1 � x1) [MMIM][MeSO4]}

x1 q/(g � cm�3)

nD g/(mPa � s)

VE/(cm3�mol�1)

DnD Dg/(mPa � s)

DG*E/(J �mol�1)

T = 298.15 K0.0000 1.32912 1.48296 77.7 0.000 0.0000 0.000 0.00.0497 1.32699 1.48187 68.1 0.016 0.0064 �5.788 378.80.1475 1.32281 1.47986 53.6 �0.019 0.0191 �12.858 1152.60.2128 1.31954 1.47824 44.93 �0.044 0.0273 �16.467 1618.90.3086 1.31375 1.47536 35.23 �0.076 0.0388 �18.800 2316.70.3869 1.30771 1.47252 27.57 �0.087 0.0478 �20.439 2747.10.4947 1.29697 1.46739 19.55 �0.103 0.0589 �20.177 3276.80.5959 1.28277 1.46071 13.88 �0.109 0.0674 �18.065 3660.90.6947 1.26217 1.45105 9.599 �0.098 0.0726 �14.753 3863.30.7966 1.22682 1.43485 5.928 �0.035 0.0717 �10.599 3684.00.8962 1.16206 1.40572 2.925 0.042 0.0576 �5.945 2697.00.9485 1.10041 1.37848 1.745 0.070 0.0382 �3.104 1653.81.0000 0.99720 1.33251 0.890 0.000 0.0000 0.000 0.0

T = 313.15 K0.0000 1.31856 41.68 0.000 0.000 0.00.0497 1.31644 37.51 0.019 �2.128 426.70.1475 1.31231 30.44 �0.012 �5.188 1243.40.2128 1.30903 25.86 �0.030 �7.088 1713.40.3086 1.30327 20.76 �0.056 �8.257 2429.90.3869 1.29725 16.93 �0.062 �8.871 2926.20.4947 1.28656 12.41 �0.070 �8.970 3481.90.5959 1.27239 9.041 �0.067 �8.188 3870.10.6947 1.25191 6.368 �0.050 �6.807 4050.70.7966 1.21682 4.027 0.017 �4.972 3841.60.8962 1.15298 2.069 0.086 �2.843 2828.80.9485 1.09264 1.261 0.099 �1.504 1745.81.0000 0.99221 0.653 0.000 0.000 0.0

T = 328.15 K0.0000 1.30813 25.21 0.000 0.000 0.00.0497 1.30609 23.95 0.013 �0.031 561.80.1475 1.30196 19.85 �0.011 �1.718 1410.40.2128 1.29864 17.11 �0.021 �2.839 1900.20.3086 1.29281 13.79 �0.036 �3.792 2598.90.3869 1.28689 10.50 �0.044 �5.154 2877.90.4947 1.27622 8.521 �0.047 �4.468 3667.10.5959 1.26204 6.336 �0.036 �4.152 4063.60.6947 1.24095 4.518 0.019 �3.528 4222.90.7966 1.20664 2.917 0.058 �2.614 3991.90.8962 1.14343 1.548 0.121 �1.521 2953.30.9485 1.08403 0.990 0.122 �0.786 1913.41.0000 0.98569 0.504 0.000 0.000 0.0

E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216 1209

than 0.03% determined using a 756 Karl Fisher coulometer) vacuum(2 � 10�1Pa) and moderate temperature (343.15 K) were applied tothe IL for several days, always immediately prior to their use. TheIL was kept in bottles with inert gas.

Table 1 shows a comparison between experimental and litera-ture data of pure components at T = (298.15, 313.15, and328.15) K. Compared to literature, the density value for pure[MMIM][MeSO4] is higher than those reported by Pereiro et al.[27], Domanska et al. [28] and Kato et al. [29] and lower than theone reported by Goldon et al. [30]. These discrepancies can bedue to the effect of temperature or to the presence of some tracesof water or impurities in our mixtures or in their mixtures.These impurities can have dramatic effects on the density andviscosity values as was established from the studies of Seddonand co-workers [11].

2.2. Apparatus and procedure

Samples were prepared by syringing known amounts of thepure liquids into stoppered bottles, in an inert-atmosphere glovebox, using a Mettler AX-205 Delta Range balance with a precisionof ±10�5 g, covering the whole composition range of the mixture. Aglove box was used because the ionic liquid is sensitive to mois-ture. Good mixing was ensured by magnetic stirring. All sampleswere prepared immediately prior to performing density, refractiveindex or viscosity measurements to avoid variations in composi-tion due to evaporation of solvent or pickup of water by the hygro-scopic IL.

Kinematic viscosities were determined using an automatic vis-cosimeter Lauda PVS1 with four Ubbelhode capillary microviscos-imeters of 0.4 � 10�3 m, 0.53 � 10�3 m, 0.70 � 10�3 m, and 1.26 �10�3 m diameter (the uncertainty in experimental measurementis ±0.0001, ±0.003, ±0.03, and ±0.2 mPa � s respectively). Gravity fallis the principle of measurement on which this viscosimeter isbased. The capillary is maintained in a D20KP LAUDA thermostatwith a resolution of 0.01 K. The capillaries are calibrated and cred-ited by the company. The equipment has a control unit PVS1 (Pro-

cessor Viscosity System) that is a PC-controlled instrument for theprecise measurement of fall time, using standardized glass capil-laries, with an uncertainty of 0.01 s. In order to verify the calibra-tion, the viscosity of the pure liquids was compared withliterature data (table 1).

The density of the pure liquids and mixtures were measuredusing an Anton Paar DSA-5000 digital vibrating tube densimeter.The repeatability and the uncertainty in experimental measure-ment have been found to be lower than (±2 � 10�6 and±2.6 � 10�5) g � cm�3. The DSA 5000 automatically corrects theinfluence of viscosity on the measured density.

To measure refractive indices, an automatic refractometer Abb-emat-HP Dr. Kernchen with a resolution of ±10�6 and an uncer-tainty in the experimental measurements of ±4 � 10�5 was used.

3. Results and discussion

Dynamic viscosity, density, excess molar volume, viscosity devi-ation, and excess free energy of activation for the ternary system

1210 E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216

{x1 ethanol + x2 water + (1 � x1 � x2) [MMIM][MeSO4]} at T =298.15 K and its binary systems {x1 ethanol + (1 � x1) [MMIM][Me-SO4]} and {x1 water + (1 � x1) [MMIM][MeSO4]} at T = (298.15,313.15, and 328.15) K, and refractive indices at T = 298.15 K forall studied system are reported in tables 2–4.

The excess molar volumes, viscosity deviations, and refractiveindex deviations were calculated from experimental values asfollows:

VE ¼XN

i¼1

xiMiðq�1 � q�1i Þ; ð1Þ

Dg ¼ g�XN

i

xigi; ð2Þ

DnD ¼ nD �XN

i

xinD;i; ð3Þ

where q and qi are the density of the mixture and the density of thepure components, respectively; xi represents the mole fraction ofthe i component; g and gi are the dynamic viscosity of the mixture

TABLE 3Density, q, refractive index, nD, dynamic viscosity, g, excess molar volumes, VE,deviations in the refractive index, DnD, viscosity deviations, Dg, and excess free energyof activation, DG*E, for {x1 ethanol + (1 � x1) [MMIM][MeSO4]}

x1 q/(g � cm�3)

nD g/(mPa � s)

VE/(cm3�mol�1)

DnD Dg/(mPa � s)

DG*E/(J �mol�1)

T = 298.15 K0.0000 1.32912 1.48296 77.7 0.000 0.0000 0.000 0.00.0669 1.31647 1.48028 62.1 �0.179 0.0055 �10.548 204.90.1228 1.30519 1.47773 51.6 �0.348 0.0098 �16.726 380.20.2212 1.28246 1.47336 36.97 �0.589 0.0176 �23.816 659.90.2944 1.26318 1.46936 29.56 �0.760 0.0225 �25.617 919.70.3984 1.23122 1.46252 20.26 �0.966 0.0285 �26.946 1126.50.5000 1.19280 1.45421 12.83 �1.062 0.0326 �26.580 1095.70.5926 1.15085 1.44554 8.784 �1.148 0.0353 �23.532 1139.60.6921 1.09430 1.43248 5.706 �1.104 0.0345 �18.984 1106.10.7970 1.01810 1.41494 3.513 �0.965 0.0298 �13.132 967.00.8957 0.92316 1.39329 2.096 �0.652 0.0203 �6.980 654.20.9450 0.86426 1.37874 1.602 �0.420 0.0118 �3.696 457.31.0000 0.78546 1.36023 1.082 0.000 0.0000 0.000 0.0

T = 313.15 K0.0000 1.31856 41.68 0.000 0.000 0.00.0669 1.30589 34.42 �0.204 �4.522 240.40.1228 1.29459 29.38 �0.393 �7.278 440.20.2212 1.27177 22.80 �0.663 �9.841 849.00.2944 1.25246 17.97 �0.860 �11.675 1016.50.3984 1.22040 12.87 �1.093 �12.532 1249.80.5000 1.18188 8.823 �1.216 �12.427 1327.70.5926 1.13974 6.258 �1.316 �11.210 1380.40.6921 1.08298 4.309 �1.280 �9.096 1404.30.7970 1.00641 2.649 �1.133 �6.470 1157.40.8957 0.91098 1.603 �0.787 �3.482 778.20.9450 0.85176 1.225 �0.521 �1.848 526.91.0000 0.77200 0.827 0.000 0.000 0.0

T = 328.15 K0.0000 1.30813 25.21 0.000 0.000 0.00.0669 1.29553 21.43 �0.240 �2.139 283.10.1228 1.28420 18.72 �0.451 �3.476 516.50.2212 1.26138 15.07 �0.762 �4.705 977.00.2944 1.24197 12.28 �0.977 �5.700 1191.10.3984 1.20957 9.141 �1.220 �6.281 1470.60.5000 1.17112 6.461 �1.387 �6.465 1564.50.5926 1.12874 4.727 �1.496 �5.923 1640.90.6921 1.07175 3.246 �1.472 �4.961 1590.70.7970 0.99472 2.077 �1.310 �3.552 1370.90.8957 0.89870 1.265 �0.921 �1.938 926.30.9450 0.83906 0.961 �0.613 �1.030 618.11.0000 0.75855 0.641 0.000 0.000 0.0

and the pure components, respectively, and nD and nD,i are therefractive index of the mixture and the refractive index of the purecomponents, respectively.

The excess Gibbs free energies of activation of viscous flow wereobtained from the following equation:

DG�E ¼ RT lnðgVÞ �XN

i¼1

xi lnðgiV iÞ" #

; ð4Þ

where R is the universal constant of gases, T is the absolute temper-ature, Vi is the molar volume of component i, V is the molar volumeof the mixture, xi represents the mole fraction of the component iand g, gi are the dynamic viscosity of the mixture and the pure com-ponent, respectively.

The binary deviations at several temperatures were fitted to aRedlich–Kister [36] type equation:

DQ12 ¼ x1x2

XM

p¼0

Bpðx1 � x2Þp; ð5Þ

where DQ12 is the excess property, x1 and x2 are the mole fraction ofcomponent 1 and 2, respectively, Bp is the fitting parameter and M isthe degree of the polynomic expansion. The fitting parameters aregiven in table 5 together with the root-mean-square deviations, r

r ¼Xndat

i

ðzexp � zcalcÞ2( ,

ndat

)1=2

; ð6Þ

where zexp, zcalc, and ndat, are the values of the experimental and cal-culated property and the number of experimental data,respectively.

Figure 1 shows the fitted curve of excess molar volume values ofsystems {x1 water + (1 � x1) [MMIM][MeSO4]} and {x1 etha-nol + (1 � x1) [MMIM][MeSO4]}. The excess molar volumes arenegative over the entire composition range for x1 ethanol with(1 � x1) [MMIM][MeSO4] mixture presenting a minimum in a molecomposition of 0.6 for the three studied temperatures. It is remark-able that in the work of Goldon et al. [30] the excess molar volumespresented for the binary system {x1 methanol + (1 � x1) [MMIM][-MeSO4]} are also negative over the whole composition range, pre-senting a minimum at x1 � 0.65. Comparing the two systems (withethanol and with methanol), we can observe that when the chainof carbon increases the minimum of VE is less negative. For thewater, a sinusoidal curve was observed with the VE (minimum)��0.109, �0.067 and �0.04 cm3 �mol�1 at x1 � 0.6 for T =(298.15, 313.15, and 328.15) K, respectively and a maximum atx1 � 0.95 with a value of 0.07, 0.099, and 0.122 for T = (298.15,313.15, and 328.15) K, respectively and at low mole fraction ofwater the VE show positive values for the three studied tempera-tures. This behaviour can be explained because hydrogen bondingis certainly more T-dependent (becoming negligible at high tem-peratures) than Coulombic interactions. This result agrees withthe work of Rebelo et al. [37]. We can observe that when we in-crease the temperature the deviations of the excess molar volumeare more negative for the case of the binary system containing eth-anol and less negative for the other binary system. In figure 1, theexperimental data of Pereiro et al. [38] and Domanska et al. [28] arealso shown too and it is seen that good agreement exists betweenour data and those published.

In figure 2, we can observe the variation of viscosity deviationswith the composition and with the temperature. The sign is nega-tive over the whole composition range and approach to minimumat 0.4 mole fraction for both systems. The viscosity deviations de-crease as the temperature increases and this behaviour is similarfor both systems.

TABLE 4Density, q, refractive index, nD, dynamic viscosity, g, excess molar volumes, VE, deviations of refractive index, DnD, viscosity deviations, Dg and excess free energies of activation ofviscous flow, DG*E, for the ternary system {x1 ethanol + x2 water + (1 � x1 � x2) [MMIM][MeSO4]} at T = 298.15 K

x1 x2 q/(g � cm�3) nD g/(mPa � s) VE/(cm3 �mol�1) DnD Dg mPa � s DG*E/(J �mol�1)

0.0567 0.9117 1.04795 1.36927 1.857 �0.304 0.030 �1.470 1859.70.1168 0.8536 1.02304 1.37265 2.306 �0.595 0.032 �0.878 2407.10.1877 0.7851 0.99517 1.37432 2.547 �0.862 0.033 �0.468 2657.90.0674 0.8724 1.08892 1.38837 2.493 �0.347 0.045 �3.039 2489.40.1409 0.8036 1.05623 1.38872 2.793 �0.684 0.044 �2.389 2763.90.2203 0.7294 1.02107 1.38736 2.903 �0.908 0.041 �1.900 2851.20.3053 0.6498 0.98536 1.38487 2.790 �1.039 0.037 �1.608 2738.10.3959 0.5651 0.95067 1.38179 2.620 �1.101 0.032 �1.345 2558.60.6047 0.3697 0.88294 1.37434 2.050 �1.030 0.021 �0.918 1858.90.0395 0.9469 1.01567 1.35275 1.476 �0.180 0.017 �0.465 1312.90.1015 0.8858 0.99373 1.35907 2.008 �0.520 0.022 0.122 2105.40.1629 0.8252 0.97221 1.36307 2.345 �0.772 0.024 0.514 2510.60.2319 0.7572 0.94804 1.36540 2.430 �0.939 0.025 0.661 2610.60.3106 0.6797 0.92259 1.36652 2.401 �1.041 0.024 0.702 2578.50.5094 0.4837 0.87025 1.36644 2.023 �1.064 0.019 0.502 2070.70.0859 0.8132 1.12902 1.40706 3.449 �0.445 0.057 �5.215 3051.70.1736 0.7351 1.08808 1.40412 3.548 �0.774 0.053 �4.388 3112.30.2646 0.6542 1.04602 1.39976 3.378 �0.973 0.048 �3.804 2983.20.3603 0.5691 1.00379 1.39462 3.080 �1.076 0.041 �3.308 2745.20.4561 0.4839 0.96451 1.38933 2.789 �1.113 0.035 �2.805 2485.40.5579 0.3933 0.92582 1.38377 2.433 �1.080 0.028 �2.316 2129.10.1180 0.7046 1.17378 1.42814 4.992 �0.527 0.066 �9.553 3321.70.2333 0.6125 1.12169 1.42101 5.161 �0.862 0.059 �7.626 3451.50.3421 0.5256 1.07136 1.41318 4.150 �1.024 0.051 �6.976 2962.80.4400 0.4474 1.02633 1.40571 3.565 �1.080 0.044 �6.065 2636.30.5500 0.3595 0.97677 1.39703 2.981 �1.067 0.036 �4.970 2250.70.7386 0.2088 0.89473 1.38184 2.056 �0.860 0.021 �3.016 1432.70.8266 0.1385 0.85786 1.37463 1.706 �0.684 0.014 �2.023 1020.40.0987 0.5532 1.24598 1.45376 10.82 �0.494 0.066 �16.846 3484.70.1993 0.4914 1.20769 1.44719 8.770 �0.761 0.063 �15.931 3203.40.2974 0.4312 1.16748 1.43994 7.164 �0.956 0.058 �14.643 2937.20.3982 0.3694 1.12289 1.43140 5.798 �1.075 0.053 �13.037 2656.40.4936 0.3108 1.07751 1.42247 4.661 �1.107 0.047 �11.360 2347.60.5968 0.2475 1.02579 1.41190 3.677 �1.108 0.039 �9.299 2012.10.6995 0.1844 0.97002 1.40033 2.827 �0.980 0.031 �7.120 1614.60.0984 0.3754 1.27805 1.46636 19.42 �0.422 0.052 �21.927 2761.50.1977 0.3341 1.24733 1.46062 14.81 �0.695 0.052 �22.098 2590.40.2977 0.2925 1.21246 1.45368 11.29 �0.908 0.051 �21.157 2416.70.4003 0.2497 1.17178 1.44555 8.498 �1.048 0.049 �19.370 2220.50.4999 0.2083 1.12715 1.43624 6.438 �1.128 0.046 �16.980 2021.60.6032 0.1652 1.07411 1.42503 4.767 �1.108 0.041 �14.036 1780.10.7142 0.1190 1.00889 1.41078 3.381 �1.008 0.033 �10.464 1463.90.1018 0.1512 1.29771 1.47397 33.76 �0.157 0.026 �24.559 1194.90.2074 0.1334 1.27113 1.46879 24.62 �0.454 0.031 �26.975 1328.60.3097 0.1162 1.24115 1.46277 17.87 �0.707 0.035 �27.199 1412.80.4116 0.0990 1.20604 1.45547 12.80 �0.9057 0.038 �25.774 1448.7

E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216 1211

3.1. Correlation of physical properties

The VE, DnD, Dg, and DG*E values calculated from equations (1) to(4) for the ternary system were correlated using the equations pro-posed by Cibulka [17], Singh et al. [18], and Nagata and Sakura [19].The following expressions were used: Cibulka equation:

Q E123 ¼ Q E

12 þ Q E13 þ QE

23 þ x1x2x3ðAþ Bx1 þ Cx2Þ; ð7Þ

Singh et al. equation:

Q E123 ¼ Q E

12 þ Q E13 þ QE

23 þ Ax1x2x3 þ Bx1ðx2 � x3Þ þ Cx21ðx2 � x3Þ2;

ð8Þ

where A, B and C are fitting parameters. Nagata and Sakuraequation:

Q E123 ¼ Q E

12 þ Q E13 þ QE

23 þ x1x2x3A; ð9Þ

where A is the fitting parameter.

The QEij is the contribution to the excess property of the constit-

uent binary mixtures evaluated by the Redlich–Kister equation[36]:

QEij ¼ xixj

XM

p¼0

Bpðxi � xjÞp; ð10Þ

where xi is the mole fraction of component i and Bp are adjustableparameters. The parameters Bp and the root-mean-square devia-tions for the excess properties of the two binary mixtures contain-ing ionic liquid involved in the ternary system are presented in thispaper and are listed in table 5 as indicated previously. The proper-ties of the binary mixture (ethanol + water) were determined in ourlaboratory, and its fitting Redlich–Kister parameters were publishedin a previous work [14].

The fitting parameters of the correlation equations androot-mean-square deviations are given in table 6. As can beobserved in this table, for all the studied properties the betterfitting is given by Cibulka, where the correlated values are in goodagreement with the experimental data. In figures 3 to 5, the

TABLE 5Fitting parameters and root-mean-square deviation, r, for binary mixtures {x1 ethanol + (1 � x1) [MMIM][MEtSO4]} and {x1 water + (1 � x1) [MMIM][MEtSO4]} at T = (298.15,313.15, 328.15) K

Water (1) + [MMIM][MESO4] (2)T = 298.15 K

VE/(cm3 �mol�1) B0 = �0.406 B1 = �0.297 B2 = �0.353 B3 = 0.970 B4 = 2.316 r = 0.004DnD B0 = 0.2384 B1 = 0.1722 B2 = 0.1185 B3 = 0.2053 B4 = 0.1853 r = 0.006Dg/(mPa � s) B0 = �80.229 B1 = 24.357 B2 = 7.456 B3 = 8.293 B4 = �28.96 r = 0.144DG*E/(J �mol�1) B0 = 13222.8 B1 = 8521.7 B2 = 7806.8 B3 = 7047.9 B4 = 1946.1 r = 11.19

T = 313.15 KVE/(cm3 �mol�1) B0 = �0.271 B1 = �0.151 B2 = �0.210 B3 = 1.166 B4 = 2.412 r = 0.004Dg/(mPa � s) B0 = �35.594 B1 = 9.209 B2 = �0.155 B3 = �1.544 B4 = �3.009 r = 0.082DG*E/(J �mol�1) B0 = 14055.7 B1 = 8879.8 B2 = 6829.8 B3 = 7070.7 B4 = 4224.6 r = 10.34

T = 328.15 KVE/(cm3 �mol�1) B0 = �0.168 B1 = 0.052 B2 = 0.261 B3 = 1.253 B4 = 1.835 r = 0.008Dg/(mPa � s) B0 = �18.610 B1 = 6.728 B2 = 2.804 B3 = �18.351 B4 = 10.887 r = 0.179DG*E/(J �mol�1) B0 = 14590.3 B1 = 9605.3 B2 = 7105.6 B3 = 5372.8 B4 = 7273.7 r = 56.08

Ethanol (1) + [MMIM][MESO4] (2)T = 298.15 K

VE/(cm3 �mol�1) B0 = �4.319 B1 = �1.813 B2 = �0.907 B3 = �0.967 B4 = �0.296 r = 0.008DnD B0 = 0.1313 B1 = 0.0679 B2 = 0.0341 B3 = 0.0075 B4 = �0.0107 r = 0.0001Dg/(mPa � s) B0 = �104.79 B1 = 39.362 B2 = �9.703 B3 = 27.215 B4 = �12.494 r = 0.207DG*E/(J �mol�1) B0 = 4588.7 B1 = 358.6 B2 = 730.1 B3 = 3895.3 B4 = 1332.2 r = 24.11

T = 313.15 KVE/(cm3 �mol�1) B0 = �4.945 B1 = �2.106 B2 = �0.790 B3 = �1.742 B4 = �1.53 r = 0.011Dg/(mPa � s) B0 = �49.556 B1 = 14.219 B2 = 6.755 B3 = 8.539 B4 = �18.751 r = 0.109DG*E/(J �mol�1) B0 = 5349.1 B1 = 1838.7 B2 = 3276.8 B3 = 546.6 B4 = �4089.3 r = 15.59

T = 328.15 KVE/(cm3� mol�1) B0 = �5.598 B1 = �2.514 B2 = �1.201 B3 = �1.976 B4 = �1.796 r = 0.012Dg/(mPa � s) B0 = �25.666 B1 = 3.712 B2 = 5.363 B3 = 5.903 B4 = �10.733 r = 0.060DG*E/(J �mol�1) B0 = 6334.5 B1 = 1795.8 B2 = 2447.8 B3 = 2031.5 B4 = �1700.9 r = 11.95

x1

0.0 0.5 1.00.0 0.5 1.0

VE /

(cm

-3 .m

ol-1)

-1.8

-1.5

-1.2

-0.9

-0.6

-0.3

0.0

x1

VE /

(cm

-3 .m

ol-1)

-0.2

-0.1

0.0

0.1

a b

FIGURE 1. Experimental excess molar volume, VE, and calculated values from the Redlich–Kister equation (—) plotted against mole fraction at T = 298.15 K (d), T = 313.15 K(j) and T = 328.15 K (N), for the binary mixtures: (a) {x1 water +(1 � x1) [MMIM][MeSO4]}, Domanska et al. data (M) and (b) {x1 ethanol + (1 � x1) [MMIM][MeSO4]}, Pereiroet al. data (�).

1212 E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216

isolines of the excess properties VE, DnD, and Dg calculated from Ci-bulka, are shown.

3.2. Prediction of physical properties

Several empirical methods have been proposed to estimate ter-nary excess properties from experimental results of the constituentbinary systems. These methods are of great interest, since as the

number of components in the mixture increases, the determinationof its properties becomes more laborious.

The predictive methods can be divided into symmetric andasymmetric, depending on whether the assumption of the threebinary mixtures contributing equally to the ternary mixture mag-nitude is accepted or not. Asymmetry is usually understood to becaused by the strongly polar or associative behaviour of any ofthe compounds in the mixture. In these cases, different geometric

x1

0.0 0.2 0.4 0.6 0.8 1.0

Δη /

(mPa

·s)

-30

-25

-20

-15

-10

-5

0

x1

0.0 0.2 0.4 0.6 0.8 1.0

Δη/ (

mPa

·s)

-25

-20

-15

-10

-5

0a b

FIGURE 2. Experimental dynamic viscosity deviations, Dg, and calculated values from the Redlich–Kister equation (—) plotted against mole fraction at T = 298.15 K (�),T = 313.15 K (j) and T = 328.15 K (N), for the binary mixtures: (a) {x1 water + (1 � x1) [MMIM][MeSO4]} and (b) {x1 ethanol + (1 � x1) [MMIM][MeSO4]}.

TABLE 6Fitting parameters and root-mean-square deviations for empirical equations

VE/(cm3 �mol�1) DnD Dg/(mPa � s) DG*E/(J �mol�1)

{x1 ethanol + x2 water + (1 � x1 � x2) [MMIM][MeSO4]}Cibulka equation (7)

A 8.185 �6.2471 �55.242 �20,302B �7.845 0.3722 148.355 47,357C �11.690 0.7189 142.535 �13,386r 0.031 0.0013 0.410 113

Singh et al. equation (8)A 1.376 0.1299 47.958 �7992B 0.106 �0.0114 �0.982 �32C 0.067 �0.0189 �2.424 �73r 0.036 0.0013 0.496 162

Nagata and Sakura equation (9)A 1.220 0.1415 48.589 �8082r 0.038 0.0018 0.511 162

E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216 1213

criteria are applied to match each point of ternary compositionwith the contributing binary compositions.

To predict the excess properties (VE, DnD, Dg, and DG*E), we haveused symmetric [20–23] and asymmetric [24–26] geometricalsolution models.

In this work, we applied the symmetric equations of Radojkovicet al. [20]:

Q E123 ¼ Q E

12ðx1; x2Þ þ Q E13ðx1; x3Þ þ QE

23ðx2; x3Þ ð11Þ

in which QEij or QE

ijk is the excess property, the equation of Rastogi etal. [21]:

Q E123 ¼ 0:5½ðx1 þ x2ÞQ E�

12ðx�1; x�2Þ þ ðx1 þ x3ÞQE�13ðx�1; x�3Þþ

ðx2 þ x3ÞQE�23ðx�2; x�3Þ�; ð12Þ

Jacob and Fitzer [22]:

Q E123 ¼ 4 x1x2

ð2x1þx3Þð2x2þx3ÞQ E�

12ðx�1; x�2Þ þx1x3

ð2x1þx2Þð2x3þx2ÞQ E�

13ðx�1; x�3Þh ih i

þ

4 x2x3ð2x2þx1Þð2x3þx1Þ

Q E�23ðx�2; x�3Þ

h ih i ;

ð13Þ

Kohler [23]:

QE123 ¼ ½ðx1 þ x2Þ2QE�

12ðx�1; x�2Þ þ ðx1 þ x3Þ2QE�13ðx�1; x�3Þþ

ðx2 þ x3Þ2QE�23ðx�2; x�3Þ�: ð14Þ

The following models are asymmetrical, so we alternativelyconsider each component of the ternary mixture as the asymmetriccomponent, Toop [24]:

QE123 ¼

x2

1� x1

� �Q E�

12ðx�1; x�2Þ þx3

1� x1

� �Q E�

13ðx�1; x�3Þþ�

1� x1Þ2QE�23ðx�2; x�3Þ

� ið15Þ

Tsao and Smith [25]:

QE123 ¼

x2

1� x1

� �Q E�

12ðx�1; x�2Þ þx3

1� x1

� �Q E�

13ðx�1; x�3Þþ�

1� x1ÞQ E�23ðx�2; x�3Þ

� ið16Þ

Scarchard et al. [26]:

QE123 ¼

x2

1� x1

� �Q E�

12ðx�1; x�2Þ þx3

1� x1

� �Q E�

13ðx�1; x�3Þ þ Q E�23ðx�2; x�3Þ

� �ð17Þ

where the arguments of QE�ðx�i ; x�j Þ are x�i ¼ xi=ðxi þ xjÞ andx�j ¼ xj=ðxi þ xjÞ.

Table 7 lists the root-mean-square deviations of fitting for eachdependent variable and equation.

4. Conclusions

In this work, the dynamic viscosity and density data over thewhole composition range for {x1 ethanol + x2 water + (1 � x1 � x2)[MMIM][MeSO4]} at T = 298.15 K and its binary systems {x1 etha-nol + (1 � x1) [MMIM][MeSO4]} and {x1 water + (1 � x1) [BMIM][-MeSO4]} at temperatures of (298.15, 313.15, and 328.15) K havebeen determined. The refractive indices at T = 298.15 K for all sys-tems have been obtained as well.

Excess molar volumes, viscosity deviations, and excess Gibbsfree energies of activation were calculated and fitted to the Red-lich–Kister equation to test the quality of the experimental values.

EtOH0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

MMIMMeSO4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

H2O

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-0.2

-0.4

-0.6

-0.8

-1.0

-1.1

-1.0

-0.8-0.6

-0.4

FIGURE 3. Isolines for excess molar volumes, VE123, from the Cibulka equation (7) for the ternary system {x1 ethanol + x2 water + 1(1 � x1 � x2) [MMIM][MeSO4]}.

EtOH0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

MMIMMeSO4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

H2O

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.03

0.020.01

FIGURE 4. Isolines for the changes of refractive index, DnD123, from the Cibulka equation (7) for the ternary system {x1 ethanol + x2 water + 1(1 � x1 � x2) [MMIM][MeSO4]}.

1214 E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216

The ternary system has been correlated used Cibulka, Singh etal., and Nagata and Sakura equations. All the correlative modelsare capable of representing the behaviour of the ternary mixturewith a higher or lesser degree of accuracy. In the correlation, theCibulka equation gives the smaller deviations for all the studied ex-cess properties.

The prediction of the ternary system has been done using sym-metric and asymmetric geometrical solution models. Deviationsobtained with the empirical equations to predict the excess prop-

erties are rather high. This fact can be due to the importance of theternary contribution term to the quantity studied. Of the geomet-rical solution models used to predict the excess properties, the bestfor prediction of the VE was the that by Radojkovic et al.; for theDnD and Dg the best was by Kohler and for DG*E was that of Jacoband Fitzner. In general, the symmetric equations give better predic-tive results, specially those of Radojkovic, Jacob and Fitzner, andKohler. The predictions of the asymmetric equations of Tsao andSmith and Scatchard erred significantly.

EtOH0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

MMIMMeSO4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

H2O

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-4

-8

-12

-16

-20

-24

FIGURE 5. Isolines for the deviation of dynamic viscosity, Dg123, from the Cibulka equation (7) for the ternary system {x1 ethanol + x2 water + 1(1 � x1 � x2) [MMIM][MeSO4]}.

TABLE 7Root-mean-square deviations of predictions of excess molar volumes, refractive index deviations, viscosity deviations and excess free energies of activation of viscous flow for {x1

ethanol + x2 water + (1 � x1-x2) [MMIM][MeSO4]} at T = 298.15 K

VE123/(cm3 �mol�1) DnD Dg/(mPa � s�1) DG�E123/(J �mol�1)

Radojkovic 0.054 0.004 1.110 980Rastogi 0.313 0.013 3.696 1519Jacob and Fitzner 0.076 0.008 1.562 943Kohler 0.060 0.003 0.940 1138Toopa 0.151 0.005 2.169 1276Toopb 0.122 0.009 1.819 796Toopc 0.123 0.0012 3.588 1337Tsao and Smitha 0.153 0.010 3.822 1410Tsao and Smithb 0.210 0.007 4.355 799Tsao and Smithc 0.224 0.014 3.544 1473Scatcharda 0.154 0.031 8.415 2089Scatchardb 0.621 0.012 12.656 976Scatchardc 0.440 0.014 3.554 1739

a Ethanol is the asymmetric component.b Water is the asymmetric component.c [MMIM][MeSO4] is the asymmetric component.

E. Gómez et al. / J. Chem. Thermodynamics 40 (2008) 1208–1216 1215

Acknowledgements

The authors are grateful to the Ministerio de Ciencia y Tec-nología of Spain (Project CTQ2004-00454) and Xunta de Galicia(Project PGIDIT05PXIC38303PN) for financial support.

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JCT 08-43