Liquid densities and excess molar volumes for (ionic liquids + methanol + water) ternary system at atmospheric pressure and at various temperatures

J. Chem. Thermodynamics 39 (2007) 1318–1324 www.elsevier.com/locate/jct

Liquid densities and excess molar volumes for (ionic liquids + methanol + water) ternary system at atmospheric pressure and at various temperatures Nirmala Deenadayalu *, Satish Kumar, Pravena Bhujrajh Department of Chemistry, Durban University of Technology, Steve Biko Campus, P.O. Box 1334, Durban, KwaZulu-Natal 4001, South Africa Received 8 November 2006; received in revised form 16 January 2007; accepted 16 January 2007 Available online 30 January 2007

Abstract Excess molar volumes, V Em have been evaluated from density measurements over the entire composition range for ternary liquid system of ionic liquid (1-ethyl-3-methyl-imidazolium diethylenglycol monomethylether sulphate {[EMIM][CH3(OCH2CH2)2OSO3]) (1) + methanol (2) + water (3)} at T = (298.15, 303.15, and 313.15) K. A vibrating tube densimeter was used for these measurements at atmospheric pressure. The V Em values were found to be negative at T = (298.15 and 303.15) K. For {[EMIM][CH3(OCH2CH2)2OSO3] (1) + methanol (2) + water (3)} at T = 313.15 K the V Em values become positive at higher mole fraction of ionic liquid and at a corresponding decrease in mole fraction of water. All the experimental data were fitted with the Redlich–Kister equation. The results have also been analysed in term of graph theoretical approach.  2007 Elsevier Ltd. All rights reserved. Keywords: Densities; Excess molar volumes; Ternary systems; Ionic liquids

1. Introduction An ionic liquid is defined as a material containing only ionic species. Most of the organic ionic liquids are the combinations of a 1-butyl-3-methylimidazolium, 1-ethyl3-methylimidazolium or n-butylpyridinium cation and a charge diffuse inorganic anion [1] so they are also called as ‘‘designer solvents’’ [2,3]. Ionic liquids have been found to be viable reaction media for numerous types of reactions [4]. Ionic liquids have also received attention from both the industrial and academia in research as diverse as electrochemistry, catalysis, synthesis, biotechnology, and material separations [5–9]. Ionic liquids are also used as catalyst for the most important carbon–carbon bond forming reaction called Diels–Alder reaction *

Corresponding author. Tel.: +27 (0) 31 2042781; fax: +27 (0) 31 2022671. E-mail address: [email protected] (N. Deenadayalu). 0021-9614/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2007.01.012

[10]. These are also used as solvents for green chemistry [11,12]. This is all due to their unique physical and chemical properties such as thermal stability, high solubility for polar and non-polar organic and inorganic substances. Moreover, there exist very few reliable data of liquid densities and excess molar volumes of multi component systems on ionic liquids in literature. Moreover, these thermophysical data of multicomponent systems are used for the design of several type of relevant industrial equipments and many industrial applications like design calculation, heat transfer, and fluid flow. Moreover, these properties can provide an important tool to extract information about the state of aggregation of components in pure as well as in mixed state and also about the nature and extent of interactions operating between the constituents of systems. We have analysed the densities and molar excess volumes of {[EMIM][CH3(OCH2CH2)2OSO3] + water + methanol} ternary system. This work is a

N. Deenadayalu et al. / J. Chem. Thermodynamics 39 (2007) 1318–1324

continuation of our previous study [13]. In our earlier work, we have reported the densities and molar excess volumes of binary systems containing ionic liquid and water or methanol. 2. Experimental The 1-ethyl-3-methyl-imidazoliumdiethylenglycolmonomethylethersulphate was used without further purification. Methanol was dried by refluxing with Grignard reagent (Mg + I2) for 6 h and then distilled over freshly activated 4 nm molecular sieves. Doubly distilled water was used. Ternary system was prepared by mass using a Mettler mass balance (Switzerland, model AE-200) with an accuracy of ±0.0001 g. The more volatile component was filled directly into the air-tight Stoppard 5 cm3 glass vial, and then weighed. The second and third components were then injected into the vial through the stopper by means of a syringe. This method prohibited significant evaporation and contamination, which would have resulted in composition errors. The possible error in mole fraction using this procedure is estimated to be lower than 0.001. Densities of pure components and ternary system were measured using an Anton Paar digital vibrating glass tube densimeter (model DMA 38) at T = (298.15, 303.15, and 313.15) K with a precision of ±0.0001 g Æ cm3. The densities of the pure components together with their literature values are given in table 1. Excess molar volumes were determined for binary system {benzene (x1) + toluene (x2)} [14]. This was done to validate the technique used for the determination of the excess molar volumes of mixing. The V Em results from our measurements and that of the literature values were better than 0.0004 cm3 Æ mol1.

Molar excess volumes, V Em for ternary system was calculated from experimental densities using the following equation:

TABLE 1 Pure component specifications: supplier, purity, experimental and literature densities at different temperatures Purity/%

Water

Methanol

>99

[EMIM][CH3(OCH2 CH2)2OSO3]

P98

a b

x1 M 1 þ x2 M 2 þ x3 M 3 x1 M 1 x1 M 2 x3 M 3    ; d d1 d2 d3

ð1Þ

where x1, x2, and x3 are mole fractions, M1, M2, and M3 denote molar masses, q1, q2, and q3 are the densities of the pure components 1, 2, and 3, respectively, and q the density of the ternary system. Experimental densities and the calculated excess molar volumes are given in tables 2 to 4. Excess molar volumes were then fitted to the Redlich– Kister equation (2). " V

E 123

¼ x1 x2

2 X

# ðnÞ n A12 ðx1  x2 Þ

n¼0

x1 x3

" 2 X

þ x2j x3

" 2 X

þ

n¼0

#

ðnÞ n A13 ðx1  x3 Þ

# ðnÞ n A23 ðx2  x3 Þ

þ x1 x2 x3

n¼0

" 2 X

# V

ðnÞ n n 123 ðx2  x3 Þ x1

ð2Þ

n¼0

TABLE 2 Densities and excess molar volumes for {ionic liquid (x1) + water (x2) + methanol (x3)} at T = 298.15 (x1)

(x3)

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ Experimental

Graph

[EMIM][CH3(OCH2CH2)2OSO3] (x1) + methanol (x2) + water (x3) 0.0019 0.7078 0.9334 0.871 1.131 0.0027 0.6147 0.9152 0.961 1.506 0.0033 0.5048 0.8933 0.998 0.998 0.0040 0.4016 0.8739 0.977 1.816 0.0050 0.3102 0.8583 0.869 1.649 0.0053 0.2273 0.8434 0.738 1.253 0.0064 0.1101 0.8250 0.247 0.247 0.0871 0.6008 1.0753 0.909 0.890 0.1928 0.5887 1.1523 0.719 0.436 0.3087 0.4066 1.1722 0.660 0.660 0.3403 0.5555 1.1948 0.423 0.450 0.4820 0.4648 1.2156 0.194 0.078 0.5212 0.2834 1.2058 0.320 0.320 v12 ¼ 546:784; v23 ¼ 4:355; v13 ¼ 0:751; v ¼ 0:141; (3ni)=0.0014; (3nj) = 1.03; (3nk) = 1.01.

3. Results

Component

V E123 ¼

1319

Literature source [11]. Literature source [12].

T/K

q/(g Æ cm3) Experimental

Literature

298.15 303.15 313.15 298.15 303.15 313.15 298.15

0.9970 0.9956 0.9922 0.7867 0.7820 0.7727 1.2365

0.99704a 0.99564a 0.99221a 0.78664b 0.78196b

303.15 313.15

1.2326 1.2256

TABLE 3 Densities and excess molar volumes for {ionic liquid (x1) + water (x2) + methanol (x3)} at T = 303.15 (x1)

(x3)

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ Experimental

Graph

[EMIM][CH3(OCH2CH2)2OSO3 ] (x1) + methanol (x2) + water (x3) 0.0019 0.7078 0.9300 0.748 0.405 0.0027 0.6147 0.9115 0.854 0.649 0.0033 0.5048 0.8894 0.888 0.888 0.0040 0.4016 0.8698 0.828 0.978 0.0050 0.3102 0.8541 0.702 0.917 0.0053 0.2273 0.8390 0.552 0.746 0.0064 0.1101 0.8205 0.247 0.247 0.0871 0.6008 1.0713 0.742 0.240 0.1928 0.5887 1.1484 0.490 0.023 0.3087 0.4066 1.1683 0.255 0.255 0.3403 0.5555 1.1947 0.119 0.315 0.4820 0.4648 1.2119 0.207 0.341 0.5212 0.2834 1.2021 0.121 0.121 v12 ¼ 546:784;v23 ¼ 4:355;v13 ¼ 0:751;v ¼ 0:141; (3ni) = 0.0014; (3nj) = 1.03; (3nk) = 1.01.

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TABLE 4 Densities and excess molar volumes for {ionic liquid (x1) + water (x2) + methanol (x3)} at T = 313.15 (x1)

V Em =ðcm3  mol1 Þ

q/(g Æ cm3)

(x3)

Experimental

Graph

[EMIM][CH3(OCH2CH2)2OSO3 ] (x1) + methanol (x2) + water (x3) 0.0019 0.7078 0.9234 0.364 4.443 0.0027 0.6147 0.9042 0.531 2.579 0.0033 0.5048 0.8816 0.181 0.181 0.0040 0.4016 0.8617 0.630 1.306 0.0050 0.3102 0.8457 0.174 1.795 0.0053 0.2273 0.8305 0.640 1.203 0.0064 0.1101 0.8118 0.574 0.574 0.0871 0.6008 1.0638 0.427 5.638 0.1928 0.5887 1.1411 0.059 6.863 0.3087 0.4066 1.1611 0.340 0.340 0.3403 0.5555 1.1876 0.476 7.699 0.4820 0.4648 1.2049 0.965 7.078 0.5212 0.2834 1.1951 0.972 0.972 v12 ¼ 10536:0; v23 ¼ 18:172; v13 ¼ 14:859; v ¼ 20:318; (3nj) = 1.03; (3nk) = 1.01.

(3ni)=0.0014;

TABLE 5 ðnÞ Redlich–Kister parameters, A123 and standard deviations, rV Em obtained from equations (3) and (4), respectively, for {ionic liquid (x1) + methanol (x2) + water (x3)} at T = (298.15, 303.15, and 313.15) K T /K

ð0Þ

A123 = ðcm3  mol1 Þ

ð1Þ

A123 = ðcm3  mol1 Þ

ð2Þ

A123 = ðcm3  mol1 Þ

rV Em = ðcm3  mol1 Þ

[EMIM][CH3(OCH2CH2)2OSO3] (x1) + methanol (x2) + water (x3) 298.15 2.3580 15.5325 13.4550 0.006 303.15 15.802 26.666 1992. 383 0.005 313.15 6.3960 2.6981 5100.369 0.006

and have been taken from the literature [13,15,16]. The ðnÞ V 123 ðn ¼ 0 to 2Þ are parameters characteristic of (1 + 2 + 3) ternary systems and were fitted to equation ðnÞ (3) to get A123 ðn ¼ 0; . . . ; 2Þ adjustable parameters of the ternary system: 222  2  333 P ðnÞ ðnÞ n V 12 ðx1  x2j Þ 777 666 V 123  x1 x2 666 777 n¼0 666  2  777 666 777 P ðnÞ n 666 x2 x3 777½ x1 x2 x3 1 ¼ V 23 ðx2  x3 Þ 666 777 n¼0 666 777  2  777 666 444 555 P ðnÞ n V 13 ðx3  x1 Þ x1 x3 n¼0 2 X

ðnÞ

n

A123 ðx2  x3 Þ xni :

ð3Þ

n¼0

The parameters of equation (3) are given in table 5. These parameters were then utilised to calculate the molar excess volumes over the entire composition range and are given in tables 6 to 8. The resultant graphs are plotted in figures 1 to 3. Standard deviations for the ternary systems were determined by the following equation: hX i0:5 rV Em ¼ ðV Em exp V Em calcÞ2 =ðm  N Þ ; ð4Þ where m is the number of data points and N is the number of adjustable parameters of equation (3) and are given in table 5. 4. Discussion

where x1, x2, and x3 are the mole fractions of components ðnÞ (1), (2) and (3) of (1 + 2 + 3). A12 ðn ¼ 0 to 2Þ etc. are the parameters of (1 + 2), (2 + 3) and (1 + 3) binary systems

There are no literature values of V E123 for the studied ternary systems to compare our results. The densities of the pure ionic liquid as well as of their system decreased with

TABLE 6 ðnÞ Molar excess volumes values obtained from, A123 parameters of equation (3) for {ionic liquid (x1) + methanol (x2) + water (x3)} at T = 298.15 K xj

xi 0.101

0.201

0.301

0.401

0.501

0.601

0.701

0.801

0.101 0.201 0.301 0.401 0.501 0.601 0.701 0.801

0.475 0.648 0.842 0.938 0.959 0.893 0.727 0.445

0.551 0.737 0.868 0.928 0.899 0.759 0.485

0.620 0.791 0.897 0.912 0.806 0.543

0.721 0.870 0.931 0.863 0.618

0.851 0.952 0.925 0.704

0.970 0.976 0.782

0.999 0.831

0.817

xi

xk 0.101

0.201

0.301

0.401

0.501

0.601

0.701

0.801

0.455 0.496 0.554 0.629 0.714 0.792 0.841 0.826

0.734 0.765 0.811 0.868 0.928 0.978 1.001

0.897 0.901 0.914 0.931 0.951 0.968

0.960 0.928 0.895 0.867 0.846

0.936 0.865 0.787 0.715

0.839 0.732 0.615

0.679 0.546

0.468

0.101 0.201 0.301 0.401 0.501 0.601 0.701 0.801

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TABLE 7 ðnÞ Molar excess volumes values obtained from A123 parameters of equation (3) for {ionic liquid (x1) + methanol (x2) + water (x3)} at T = 303.15 K xj

xi 0.101

0.201

0.301

0.401

0.501

0.601

0.701

0.801

0.101 0.201 0.301 0.401 0.501 0.601 0.701 0.801

0.421 0.702 0.992 1.215 1.316 1.358 1.026 0.623

0.220 0.350 0.950 1.417 1.541 1.271 0.708

0.556 0.112 1.114 1.643 1.413 0.660

0.769 0.823 1.462 1.536 0.661

0.471 0.884 1.566 0.809

0.198 1.319 1.029

0.826 1.116

0.921

xi

xk 0.101

0.201

0.301

0.401

0.501

0.601

0.701

0.801

0.638 0.728 0.685 0.691 0.843 1.059 1.130 0.920

1.036 1.284 1.430 1.551 1.569 1.300 0.800

1.262 1.544 1.638 1.441 0.843 0.165

1.315 1.407 1.088 0.280 0.159

1.209 0.932 0.782 0.715

0.984 0.334 0.559

0.693 0.023

0.410

0.101 0.201 0.301 0.401 0.501 0.601 0.701 0.801

TABLE 8 ðnÞ Molar excess volumes values obtained from, A123 parameters of equation (3) for {ionic liquid (x1) + methanol (x2) + water (x3)} at T = 313.15 K xj

xi 0.101

0.201

0.301

0.401

0.501

0.601

0.701

0.801

0.101 0.201 0.301 0.401 0.501 0.601 0.701 0.801

0.306 0.600 0.890 1.067 1.072 0.900 0.601 0.276

0.403 0.114 0.822 1.114 0.801 0.068 0.048

0.598 0.220 -0.969 0.930 0.326 0.455

0.691 0.088 1.146 0.967 0.937

0.207 0.810 0.668 0.557

0.122 1.125 0.520

0.812 0.503

0.866

xi

xk 0.101

0.201

0.301

0.401

0.501

0.601

0.701

0.801

0.284 0.476 0.545 0.701 0.504 0.455 0.553 0.877

0.612 0.540 0.680 0.605 0.718 1.130 0.779

0.908 0.818 0.952 1.147 0.766 0.177

1.074 1.118 0.947 0.030 0.846

1.064 0.805 0.264 1.715

0.883 0.092 1.315

0.590 0.406

0.298

0.101 0.201 0.301 0.401 0.501 0.601 0.701 0.801

an increase in temperature. In interpreting V E123 in terms of molecular interactions, positive values can be explained by the breaking of intermolecular interactions in the pure components during the mixing process. Negative V Em is due to a more efficient packing and/or an attractive intermolecular interaction in the systems than in the pure liquids. The negative V Em values mean that there is a contraction in volume which can be attributed to electron-donor–acceptor type interactions between the ionic liquid and methanol as well as water (methanol acts as a proton acceptor). There are negative V Em values for the {[EMIM][CH 3(OCH 2CH2) 2OSO 3] + water + methanol}

ternary system at T = (298.15 and 303.15) K over the whole composition range. The V Em values for the {[EMIM][CH3(OCH2CH2)2OSO3] + water + methanol} ternary system becomes positive at T = 313.15 K at the higher mole fraction of ionic liquid and at a corresponding decrease in mole fraction of water. 4.1. Conceptual aspects of graph theoretical approach and results According to mathematical discipline of graph theory, if atoms in the structural formula of a molecule are repre-

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FIGURE 1. Plot of excess molar volume V E123 against mole fraction for {1-ethyl-3-methyl monomethylethersulphate (1) + methanol (2) + water (3)} at T = 298.15 K. — from calculated V E123 ; - - - - from interpolated V E123 .

FIGURE 3. Plot of excess molar volume V E123 against mole fractions for {1-ethyI-3-methyl monomethylethersulphate (1) + methanol (2) + water (3)} at T = 313.15 K — from calculated V E123 ; - - - - from interpolated V E123 .

the first, second and third degree of the molecule are defined [20] by X v v 0:5 1 n¼ ðdm dn Þ ð5Þ m
n¼

X

ðdvm dvn dvo Þ

0:5

ð6Þ

m
n¼

X

ðdvm dvn dvo dvp Þ

0:5

ð7Þ

m
FIGURE 2. Plot of excess molar volume V E123 against mole fraction for {1-ethyI-3-methyl monomethylethersulphate (1) + methanol (2) + water (3)} at T = 303.15 K — from calculated V E123 ; - - - - from interpolated V E123 .

sented by letters and the bonds joining them by lines, the resulting graph then provides the total information contained in that molecule [17–19]. Consequently, if dvm , dvn , dvo , etc. represent the degree of m and n, etc. vertices of the graph of a molecule, then connectivity parameter of

where dvm , etc. values explicitly reflect the valency of the atoms forming the bonds and is expressed as [20] dvm ¼ Z m  h; where Zm is the maximum valence of the atom and h is the number of hydrogen atoms attached to it . Consequently, for carbon in benzene, dvðCÞ ¼ 4  1 ¼ 3 and for carbon in 1,3-dioxolane, dvðCÞ ¼ 4  2 ¼ 2. The connectivity parameter of first degree of a molecule is assumed to be a measure of oscillation of bond length (as it depends on the degree of its closest vertices taken two at a time) and as bond length remains constant with concentration and temperature, 1n would be independent of temperature and concentration. The connectivity parameter, of 2n second-order appears first to encode some information about the effect of branching on the structural formulation of a molecule; but Kier [19,20] has suggested that information regarding effect of branching in molecules can be obtained by evaluation of 3n of molecule. Since the addition of i to j in mixtures leads to change in topology of i or j in the (i + j) mixture and as VE is a packing effect, VE data of these mixtures would reflect change in topology of 1 or 2.

N. Deenadayalu et al. / J. Chem. Thermodynamics 39 (2007) 1318–1324

1323

Thermodynamic studies of {water (1) + methanol (2)} binary mixture have revealed [15,16] that water and methanol exist as associated molecular entities and mixtures formation involves processes (I) the establishment of unlike contacts between (1) and (2); (II) unlike contact formation between 1n and 2n then causes de-polymerisation of 1n or 2n to yield their respective monomers; and (III) the monomers (1) and (2) then undergo interaction to form 1:2 molecular entity. If v12, v11, v22, and v are molar excess volume interactions parameter for 1–2 contact, 1–1 and 2–2 contact formation and specific interactions between the monomers of (1) and (2), then change in molar excess volume due to processes (I to III) is given by [21–23] h .X i DX 1 ðX ¼ V Em Þ ¼ x1 x2 v12 v2 x 1 v1 ; ð8Þ .X x 1 v1 ; ð9Þ DX 2 ðX ¼ V Em Þ ¼ x21 x2 vj v11 .X x 1 v1 ; ð10Þ DX 3 ðX ¼ V Em Þ ¼ x21 x2 v2 v22 .X x 1 v1 ; ð11Þ DX 4 ðX ¼ V Em Þ ¼ x1 x22 v2 v

have evaluated these parameters by employing V Em data of binary mixtures at two compositions (x1 = 0.4 and 0.5). If a third component water (3) is added to the {ionic liquid (1) + methanol (2)} binary mixtures, then ternary (1 + 2 + 3) mixture formation would involve the processes (I) the establishment of (a) 1–2n, (b) 2n–3n, and (c) 1n–3n unlike contacts between 1, 2, and 3 component of (1 + 2 + 3) mixtures; (II) unlike contact formation between 1, 2, and 3 would lead to de-polymerisation of (a) 2n and (b) 3n to yield respective monomers and (III) the monomers of 1, 2, and 3 undergo specific interaction to form (a) 1:2 (b) 2:3, and 1:3 molecular entities. If v012 ; v023 ; v013 are the excess molar volume interaction parameters of unlike contacts between i, j, and k monomers, then molar excess volume of mixing, V Em due to processes 1(a) to (c) can be expressed [21–23] by the following equation: h .X i h .X i DX 1 ðX ¼ V Þ ¼ x1 x2 v2 x1 v1 v012 þ x2 x3 v3 x2 v2 v023 þ h .X i x3 v3 v013 : ð17Þ x 1 x 3 v1

where vi is the molar of component (1). The overall molar excess volume of mixing, V Em for (1 + 2) mixture formation would then be expressed by 4 h i .X i X x1 v1 ½v12 þ x1 v11 þ x1 v22 þ x2 v : V Em ¼ DX 1 ¼ x1 x2 v2

Further, if v22 ; v33 ; and; v12 ; v012 ; v012 are the molar excess volume interaction parameters for 2–2, 3–3 contacts and specific interactions between 1, 2, and 3 component of (1 + 2 + 3) mixtures, then change in molar excess volume, due to processes II(a) to (b) and III(a) to III(b) [21–23] is given by .X .X DX 2 ðX ¼ V Þ ¼ x21 x2 v2 v022 x1 v1 þ x23 x1 v2 v033 x 3 v3 ;

i¼1

ð12Þ 3

3

Since v2/v1 = n1/ n2 [24] consequently equation (12) reduces to the following equation: V Em ¼ ½x1 x2 ð3 n1 =3 n2 Þ=x1 þ x2 ð3 n1 =3 n2 Þ ½v12 þ x1 v11 þ x1 v22 þ x2 v:

ð13Þ

For the mixtures studied, if it is assumed that v12 ffi v ¼ v012 and v11 @ v22 = v* then equation (13) would be expressed by V Em ¼ ½x1 x2 ð3 n1 =3 n2 Þ=x1 þ x2 ð3 n1 =3 n2 Þ½ð1 þ x2 Þv012 þ 2x1 v : ð14Þ Further thermodynamic analysis of (ionic liquid + water) suggests [13] that ionic liquid exists as a monomer and water exists as an associated molecule and entity. Thus, v11 = 0 and consequently equation (14) for these binary mixtures would be reduced to the following equation:

.X

x1 v1 þ x2 x23 v3 v012 DX 3 ðX ¼ V Þ ¼ x1 x22 v2 v12 .X x3 v3 : x21 x3 v012 v1

.X

ð18Þ x 2 v2 þ ð19Þ

The overall change in molar excess volume due to processes I(a)–(b), II(a)–(b) and III(a)–(c) can then be expressed by the following equation: 3 h .X i X  x1 v1 v022 þ x1 v011 þ x2 v12 þ DX i ¼ x1 x2 v2 V E123 ¼ h

i¼1

i  x2 v2 v023 þ x3 v12 þ h .X i  x1 x3 v1 x3 v3 v013 þ x3 v033 þ x1 v012 ; x2 x3 v3

.X

ð20Þ

since v2/v1 = (3n1/3n2) [24] so equation (20) reduces to

V Em ¼ ½x1 x2 ð3 n1 =3 n2 Þ=x1 þ x2 ð3 n1 =3 n2 Þ½v12 þ x1 v22 þ x2 v ð15Þ if it is assumed that v12 ffi v22 ¼ v012 so equation (15) reduces to the following equation: V Em ¼ ½x1 x2 ð3 n1 =3 n2 Þ=x1 þ x2 ð3 n1 =3 n2 Þ½ð1 þ x1 Þv012 þ x2 v: ð16Þ Equations (14) and (16) contain two unknown parameters (v0ij ; v, etc.). For the present analysis of binary mixtures, we

   V E123 ¼ x1 x2 ð3 n1 =3 n2 Þ=x1 þ x2 ð3 n1 =3 n2 Þ v012 þ x1 v022 þ x2 v12 þ    x2 x3 ð3 n1 =3 n3 Þ=x2 þ x3 ð3 n2 =3 n3 Þ v023 þ x3 v12 þ    x1 x3 ð3 n3 =3 n1 Þ=x3 þ x1 ð3 n3 =3 n1 Þ v013 þ x3 v033 þ x1 v012 : ð21Þ Further, if it is assumed that v012 ffi v12 ¼ v12 ; v0jk ffi v012 ¼ v23 ; v013 ffi v012 ¼ v13 and v011 ¼ v033 ¼ v then equation (21) reduces to

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N. Deenadayalu et al. / J. Chem. Thermodynamics 39 (2007) 1318–1324

h i  3 V E123 ¼ x1 x2 ð3 n1 =3 n2 Þ=x1 þ x2 ð3 n1 = n2 Þ ð1 þ x2 Þv12 þ x1 v þ h i  3 x2 x3 ð3 n2 =3 n3 Þ=x2 þ x3 ð3 n2 = n3 Þ ð1 þ x3 Þv23 þ    x1 x3 ð3 n3 =3 n1 Þ=x3 þ x1 ð3 n3 =3 n1 Þ ð1 þ x1 Þv13 þ x3 v : ð22Þ Equation (22) contains four unknown parameters (v13 , v23 ; v12 ; and v Þ and these were calculated by employing experimental V E123 data of the (1 + 2 + 3) ternary mixtures at four arbitrary compositions. These parameters were subsequently utilized to predict V E123 values as functions of x1 and x2. The V E123 values calculated from the parameters for the studied ternary mixtures are recorded in tables 6 to 8. Examination of data in tables 2 to 4 reveals that V E123 predicted by graphical approach compares well with their corresponding experimental V E123 values. Even in those cases where agreement between experimental and calculated values is not good, the predicted values are of same sign and right order of magnitude. The failure to predict correctly the magnitude of V E123 values may be due to formation of ternary contacts, which have not been presently considered. Acknowledgement The authors thank the National Research Foundation (South Africa) for financial support. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jct.2007.01. 012.

References [1] M. Freementale, Chem. Eng. News 76 (13) (1998) 32. [2] C.T. Wu, Kenneth N. Marsh, Alexander V. Deev, John A. Boxall, J. Chem. Eng. Data. 48 (2003) 486–491. [3] A.J. Carmichael, K.R. Seddon, J. Phys. Org. Chem. 13 (2000) 591– 598. [4] R. Hagiwara, Y. Ito, J. Flourine Chem. 105 (2000) 222–227. [5] D.S.H. Wong, J.P. Chen, J.M. Chanh, C.H. Chou, Fluid Phase Equilib. (2002) 194–197. [6] P. Wasserscheid, C.M. Gordon, C. Hilgers, M.J. Muldoon, I.R. Dunkin, Chem. Commun. (2001) 1186–1187. [7] C.E. Song, W.H. Shim, E.J. Roh, S.G. Lee, L.H. Choi, Chem. Commun. (2001) 1122–1123. [8] V. Najdanovic-Visak, J.M.S. Esperanca, L.P.N. Rebelo, Phys. Chem. Chem. Phys. 4 (2002) 1701–1703. [9] P. Vasserscheid, W. Keim, Angew. Chem., Int. Ed. 39 (2000) 3772– 3789. [10] T. Fischer, A. Sethi, T. Welton, J. Woolf, Tetrahedron Lett. 40 (1999) 793–796. [11] Y. Chauvin, H. Olivier-Bourbigou, CHEMTECH 25 (1995) 26. [12] Y. Chauvin, S. Einloft, H. Olivier, Ind. Eng. Chem. Res. 34 (1995) 2698. [13] N. Deenadayalu, P. Bhujrajh, J. Solution Liquids (in press). [14] A. Petek, V. dolecek, Acta Chim. Solv. 45 (1998) 153–160. [15] S.Z. Mikhal, W.R. Kimel, J. Chem. Eng. Data 6 (4) (1961) 533–537. [16] A.J. Easteal, L.A. Woolf, J. Chem. Thermodyn. 17 (1985) 69–82. [17] D.H. Rouvary, RIC Rev. 4 (1971) 173–175. [18] A.T. Balaban, Chemical Applications of Graph theory, Academic Press, London, 1976. [19] C.A. Coulson, Proc. Camb. Phil. Soc. 46 (1950) 202–208. [20] L.B. Kier, S.H. Yalkowasky, A.A. Sinkula, S.C. Valvani, Physio Chemical Properties of drugs, Marcel Dekker, New York, 1980, p. 297. [21] M.L. Huggins, J. Phys. Chem. 34 (1970) 371–378. [22] M.L. Huggins, Polymer 12 (1971) 389–399. [23] P.P. Singh, M. Bhatia, J. Chem. Soc. Faraday Trans. 1 85 (1989) 3807–3812. [24] P.P. Singh, R.K. Nigam, K.C. Singh, V.K. Sharma, Thermochim. Acta 46 (1981) 175–190.

JCT 06-297