J. CHEM. SOC. FARADAY TRANS., 1995, 91(14), 2071-2079 207 1

Experimental and Predicted Excess Enthalpies of the 2,2,2-Trifluoroethanol-Water-Tetraethylene glycol dimethyl ether Ternary System using Binary Mixing Data

Enriqueta R. Lopez, Josefa Garcia, Jose L. Legido,? Albert0 Coronas$ and Josefa Fernandez" Departamento de Fisica Aplicada , Campus Universitario , Universidad de Santiago, E-15706 Santiago de Compostela, Spain

Excess enthalpies of the ternary mixture 2,2,2-trifluoroethanol-water-tetraethylene glycol dimethyl ether and the corresponding binary mixtures at 298.15 K have been measured using a standard Calvet microcalorimeter. Wilson, NRTL, UNIQUAC and Wang et a/ . models have been used to correlate the binary excess enthalpies and, using the parameters obtained, to predict ternary excess molar enthalpies, HE. Several empirical equations predicting ternary-mixture properties from the binary-mixing data have been also examined.

Most marketable absorption heat pumps are operated with ammonia-water as the working mixture. However this working pair has some important disadvantages, such as the need for high pressures and the necessity of a rectification column in the generator. In the last few years, different organic fluids for Rankine engines and absorption refriger- ation processes have been suggested.'

Stephan and Seher2 have proposed a mixture of 2,2,2-tri- fluoroethanol (TFE) and tetraethylene glycol dimethyl ether (TEGDME) as a working pair in absorption heat pumps and heat transformers. Subsequently, in order to improve the general characteristic of the cycle, Stephan and Hengerer3 have proposed adding water, using a mixture of TFE and water as refrigerant and TEGDME as absorbant. Tetra- ethylene glycol dimethyl ether is also named 2,5,8,11,14-pen- taoxapentadecane, tetraglyme and E 18 1, depending on the field of chemistry and chemical engineering in which this compound is studied.

Thermodynamic properties of the ternary mixture TFE-H20-TEGDME and of the corresponding binary mix- tures are needed in order to study the performance of the cycle. Among the thermodynamic properties necessary to know the performances of the working mixtures are the den- sities, the viscosities and the enthalpies of mixing. We have ~ t a r t e d ~ - ~ an investigation of these properties of this ternary system and the corresponding binaries in order to complete the literature data on thermodynamic magnitudes.

Experimental densities and kinematic viscosities at 303.15 K for TFE-H,O, TFE-TEGDME, TEGDME-H,O and TFE-H,O-TEGDME were reported by Olive et Esteve et aL6 and Olive et aL7 have extended this study over the temperature range 283.15-333.15 K presenting experimental values for densities and viscosities for the binary systems and predicted data for the ternary system using several empirical methods.

Several authors8-I0 have analysed the applications and limitations of the empirical expressions for predicting multi- component thermodynamic properties from measured binary data. Recently Pando et al." studied the relation between the performance of these methods and the characteristics of the components in the mixture. However, experimental measure- ments of HE for ternary aqueous mixtures are very scarce,

t Current address : Departamento de Fisica Aplicada, Facultad de

1 Current address : Departamento de Quimica, Universitat Rovira Ciencias, Universidad de Vigo, Vigo, 36200, Spain.

i Virgili, Plaza Imperial Tarraco 1,43005 Tarragona, Spain.

and as a consequence it is difficult to know which are the best predictive methods.

In the case of excess enthalpies other different approaches based on the concept of local composition, such as Wilson," NRTL" and UNIQUAC13 equations, can be applied. Recently Wang et developed a new model for predicting the excess enthalpy of a ternary mixture from correlations of the enthalpies of its constituent binaries. This model is based on an approximation of the radial distribution function and the quasi-lattice two-liquid theory. They have found for non- aqueous ternary systems that their model provides a better prediction of the ternary excess enthalpies than the NRTL and UNIQUAC equations.

In this paper we report experimental excess molar enth- alpies, at 298.15 K and atmospheric pressure, of the ternary mixture TFE-H,O-TEGDME and the corresponding binary mixtures. The excess molar enthalpies obtained were used to test the empirical methods of many other worker^.'^-^^ Fur- thermore, the binary HE values were fitted with the Wilson, NRTL, UNIQUAC and Wang et all4 theories using the parameters obtained to predict ternary HE data.

Experimental Material

TFE (Aldrich, mole fraction > 0.99), TEGDME (Aldrich, mole fraction 0.99) were subjected to no further purification other than drying with Union Carbide 0.4 nm molecular sieves. H,O was partially degassed, doubly distilled and deionized. Sample densities were measured with an Anton- Paar 60/602H densimeter and agreed well with the literature values. 26-2

Apparatus

Excess molar enthalpies were determined using a standard Calvet microcalorimeter (precision 1 pW) linked to a Philips voltmeter PM2525. The calorimeter was equipped with a batch mixing cell with small ( ~ 2 % ) vapour space. The experimental technique of Paz Andrade et aL2' was used to determine the enthalpy of mixing over the entire mole- fraction (x) range. The mole fractions of the binary and ternary mixtures were determined by weight using a Salter- And balance ER- 182A. The apparatus was calibrated electri- cally using a stabilized current source (EJP-30, Setaram). The calibration was checked by determining the excess molar enthalpy of the standard system n-hexane-cyclohexane at

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2072 J. CHEM. SOC. FARADAY TRANS., 1995, VOL. 91

298.15 K; our results differ by < 1% from those of McGla- shan and St~eckli.~'

It was found that the corrections in H E and x1 due to the vapour phase were <0.1 J mol-' and 0.0002, respectively. The calorimeter was thermostatted at 298.150 K f 0.005; the accuracy of H E was better than 1%.

Experimental Results Excess molar enthalpies of the binary mixtures are listed in Table 1. Excess properties presenting asymmetrical composi- tion dependence are dificult to fit. Different smoothing equa- tions have been proposed for H E of aqueous mixtures. For TFE-H,O and TEGDME-H,O the following modified Redlich-Kister function presented the best correlation :

H E = (x(1 - x)/[1 + k(2x - l)]} c AA2x - 1)' (1) I

The parameters, k and A', calculated by unweighted least- squares using a Marquardt algorithm,' are shown in Table 2 together with the standard deviations s. In the case of the binary mixture TFE-TEGDME the best correlation was found with k = 0. Fig. 1-3 show the measured values of HE plotted us. x, together with the curves fitted to the data.

The experimental ternary enthalpies were determined using the equation:

H5k = HZ + (xi + xj)H5

where HF is the excess enthalpy measured for the pseudo- binary mixtures and HE is the enthalpy of the binary i-j, xi and xi are the mole fractions of the components i and j for the ternary mixture. Table 3 shows H:23 and H ; for the seven pseudo-binary mixtures studied.

The excess enthalpies for the ternary mixtures were corre-

l 0 O 0 4

I -254 0.5 1

X

Fig. 1 Experimental excess molar enthalpies at 298.15 K for the system xTFE + (1 - x)H,O. Experimental points: (0) this work, (0) Krumbeck and S C ~ U ~ Z , ~ ~ (A) Denda et ~ l . , ~ ' (0) Cooney and M ~ r c o m . ~ ~

lated following the Morris et aL3, equation:

H?23 = HEin + (3) where HEin, known as the binary contribution to the excess ternary enthalpies, is simply a sum of the binary enthalpies of mixing :

HEin = H?2(x1, x2) + H;3(x1 , x3) + x3) (4)

and HE, is the ternary contribution given by :

HEr = xlx2 x3(A0 + Alxl + A , x2 + A , X: + A, x i

+ A5x1x2) ( 5 )

Table 1 Excess molar enthalpies, HE, for binary mixtures at 298.15 K and atmospheric pressure

X HE/J mol-' X H ~ / J mol-' X HE/J mol - X H ~ / J mol-'

0.0074 0.0 104 0.02 19 0.0386 0.0727 0.0920 0.1 139 0.1650

0.0363 0.0862 0.1536 0.1783 0.1841 0.2088 0.2337 0.2754 0.2950 0.3644 0.3858 0.4106

0.0867 0.1811 0.1989 0.2249 0.2952 0.3870 0.4098

- 42 - 57 - 106 - 143 - 103 - 54 -1 142

38 60 46 20 22 2

-40 - 54 - 90 - 230 - 252 -321

- 703 - 1472 - 1635 - 1789 - 2292 - 2905 - 2988

0.1954 0.2046 0.2397 0.2773 0.3241 0.343 1 0.3594 0.4427

0.4825 0.4958 0.5301 0.5987 0.6428 0.6579 0.6682 0.7084 0.7097 0.7291 0.7385 0.7426

0.4568 0.5204 0.5590 0.62 15 0.6766 0.7542

xTFE + (1 - x)H,O

212 0.4732 227 0.4792 312 0.4972 395 0.5470 486 0.6261 5 14 0.6314 548 0.6686 677

x H ~ O + (1 - x)TEGDME

- 524 - 557 -717 - 984 - 1208 - 1243 - 1289 - 1517 - 1481 - 1573 - 1610 - 1633

0.7955 0.8343 0.8813 0.8853 0.9008 0.9 156 0.9448 0.9653 0.9675 0.97 12 0.9727 0.9761

xTFE + (1 - x)TEGDME

- 3294 0.7569 - 3574 0.7745 - 3759 0.8264 - 391 1 0.8374 - 3929 0.8657 - 3826 0.8756

706 702 720 760 76 1 758 730

- 1847 - 2015 - 2046 -2000 - 1982 - 1841 - 1522 -1151 - 1103 - 1005 - 1004 - 865

- 3820 - 3702 - 3329 - 3290 - 2925 -2818

0.7084 0.7087 0.7409 0.7735 0.8384 0.8823 0.9533

0.9794 0.9806 0.9824 0.9837 0.9860 0.9886 0.9898 0.9923 0.9975 0.9990 0.9999

0.8835 0.8945 0.9 157 0.9295 0.9490 0.9682

709 695 644 606 462 358 156

- 777 - 720 -671 - 655 - 574 - 476 -431 - 334 -110 - 45 - 16

-2718 -2551 - 2205 - 1984 - 1539 - 1047

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Table 2 Parameters, Ai , of eqn. (l), (2) and (5 ) and standard deviations, s

1634.29 0.00 6 HzO-TEGDME - 0.59 - 2350.70 - 5676.03 - 3078.15 -341.00 -2419.43 -4570.17 0.00 17

TFE-H,@TEGDME -59851.1 166394.8 143 379.4 -231 337.4 - 162 119.9 -406965.3 36

TFE-HZO 0.78 2910.73 3942.31 245.86 - 1587.61 - 855.40

TFE-TEGDME 0.00 - 13960.85 -9437.73 -6833.18 0.00 4530.35 -5140.09 -7016.82 23

The parameters Ai were determined by a least-squares method including a Marquardt algorithm. Table 2 presents these parameters together with the standard deviations. In Fig. 4 the experimental points and the fitted curves of Hg and HYz3 for some of the measured pseudo-binaries are plotted. Fig. 5 and 6 show the ternary diagrams for overall ternary enthalpies, H723 and for the ternary contributions HEr, respectively.

Prediction Methods Empirical Equations

Several empirical methods have been proposed to estimate ternary excess properties from experimental results on con- stituent binaries. These methods are asymmetric when the

5001

-1500

I -2504 0.5 1

X

Fig. 2 Experimental excess molar enthalpies at 298.15 K for the system xH,O + (1 - x)TEGDME. Experimental points: (0) this work, (0) Krumbeck and S c h ~ l z . ~ ~

I 1 -450% 0.5 1

X

Fig. 3 Experimental excess molar enthalpies at 298.15 K for the system xTFE + (1 - x)TEGDME. Experimental points: (0) this work, (0) Krumbeck and S ~ h u l z . ~ ~

1000 (a)

1 I -5004 0.5 1

X

1000 I 1 I -look*--=--=. . .&---

-2000 <\* 1 u -3000t "'k t -4000

I I -500% 0.5 1

X

Fig. 4 Experimental values of excess molar enthalpies at 298.15 K for the pseudo-binary mixtures: (a) H$ (0) run 1, (0) run 2; (b) Hf.,, (0) run 5, (0) run 6, (m) run 7; -, fittindeqn. (4).

1 0.5 Xl

0

Fig. 5 Curves of constant HYz3 (J mol-') at the 298.15 K for (x,TFE + x,H,O + x,TEGDME) calculated from eqn. (4)

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Table 3 Excess molar enthalpies, HF23, of the ternary mixtures at 298.15 K and excess molar enthalpies, H: , of the pseudo-binary systems and ternary contribu- tion, HEr

run 1, x(0.1298TFE + 0.8702H20) + (1 - x)TEGDME, HF2 = 40

0.1283 0.1266 0.1241 0.1138 0.1059 0.1009 0.08 17 0.0605 0.0548 0.0228 0.009 1

0.8604 0.8484 0.8318 0.7627 0.7098 0.6763 0.5476 0.4059 0.3673 0.1532 0.0608

- 356 -713 - 1129 -2102 - 2206 -2128 - 1684 - 1066 - 896 - 198 - 63

-317 - 674 - 1091 - 2067 -2173 - 2097 - 1658 - 1047 - 879 - 191 - 60

- 105 -218 - 354 - 688 - 767 - 766 - 599 - 382 - 335 -114 - 26

run 2, x(0.6929TFE + 0.3071H20) + (1 - x)TEGDME, HF2 = 715

0.6656 0.6409 0.6303 0.5981 0.5239 0.4193 0.3298 0.2834 0.2329 0.1473 0.1045 0.095 1 0.0578 0.0562 0.0290 0.0092

0.2950 0.2841 0.2794 0.2651 0.2322 0.1859 0.1462 0.1256 0.1032 0.0653 0.0463 0.042 1 0.0256 0.0249 0.0 128 0.0041

- 1558 - 2537 - 2862 -3581 - 4259 - 3900 - 3255 -2810 - 2332 - 1472 - 1014 -951 - 530 - 493 - 277 - 54

- 871 - 1876 -2212 - 2965 - 3719 - 3467 -2915 -2518 - 2092 - 1320 - 906 - 852 - 470 - 436 - 274 - 45

- 799 - 1293 - 1449 - 1757 - 1814 - 1275 -815 - 638 - 484 - 270 - 167 - 145 - 65 - 62 - 19 -2

run 3, x(0.2499TFE + 0.7501TEGDME) + (1 - x)H 20, HY2 = - 2023

0.1944 0.1683 0.1254 0.07 19 0.0463 0.0323 0.0228 0.0147 0.0056 0.0020 0.0018

0.2220 0.3265 0.4983 0.7124 0.8146 0.8708 0.9088 0.94 1 2 0.9778 0.9921 0.9930

- 371 - 566 - 905 - 1454 - 1680 - 1642 - 1533 - 1272 -631 - 264 - 239

- 1919 - 1906 - 1904 - 2026 - 2049 - 1900 - 1714 - 1389 - 675 - 280 - 253

- 755 - 867 - 867 - 553 - 308 - 175 - 97 -44 -7 -1 -1

run 4, x(0.8018TFE + 0.1982TEGDME) + (1 - x)H ,O, Hy2 = - 3620

0.7307 0.0785 - 306 - 3571 -819 0.6637 0.1723 -402 - 3335 - 1462 0.6309 0.2131 -416 - 3204 - 1646 0.5901 0.2641 - 432 - 3040 - 1797 0.3371 0.5795 - 269 - 1759 - 1318 0.2772 0.6543 - 246 - 1470 - 1005 0.2597 0.6762 -251 - 1398 -910

run 5, x(0.2603H20 + 0.7397TEGDME) + (1 - x)TFE, HY2 = - 49

0.1307 0.2223 0.3731 0.4824 0.5893 0.7120 0.8069 0.8969 0.9252 0.9553 0.9743

0.2263 0.2024 0.1632 0.1347 0.1069 0.0750 0.0503 0.0268 0.01 95 0.01 16 0.0067

- 1326 -2110 -3127 - 3680 - 3942 - 3723 - 3089 -2116 - 1585 - 1040 - 703

- 1366 - 2146 -3157 - 3704 - 3962 - 3737 - 3098 -2120 - 1588 - 1042 - 704

- 570 - 782 - 1007 - 1082 - 1039 - 802 - 498 - 189 - 108 - 42 - 15

run 6, x(0.7381H20 + 0.2619TEGDME) + (1 - x)TFE, H f 2 = - 1660

0.0736 0.6838 - 530 -2031 - 575 0.1364 0.6375 - 896 - 2295 - 1009 0.2906 0.5236 - 1605 - 2755 - 1762 0.3739 0.4621 - 1856 - 2870 - 1945

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Table >continued

run 6, x(0.7381H20 + 0.2619TEGDME) + (1 - x)TFE, H y 2 = - 1660 0.48 18 0.3825 - 1919 - 2759 - 1932 0.4945 0.373 1 - 1958 - 2777 - 1213 0.5957 0.2984 - 1830 - 2486 - 1634 0.6925 0.2269 - 1523 - 2022 - 1207 0.7632 0.1748 - 1213 - 1597 - 842 0.8558 0.1064 - 762 - 996 - 380 0.9099 0.0664 - 559 - 705 - 166

run 7, x(0.9814H20 + 0.0186TEGDME) + (1 - x)TFE, HF2 = -734

0.0235 0.0747 0.0965 0.2267 0.3201 0.4229 0.6183 0.7519 0.7863 0.798 1 0.8026 0.8792 0.9501 0.9775

0.9584 0.908 1 0.8867 0.7589 0.6673 0.5664 0.3746 0.2435 0.2097 0.1981 0.1937 0.1185 0.0490 0.022 1

24 87

113 370 526 658 739 618 562 544 544 369 165 72

- 671 - 572 - 530 - 181

42 247 468 441 410 400 403 283 130 56

-31 - 93

-117 - 220 - 252 - 254 - 179 - 97 - 77 - 70 - 67 - 29 -5 -1

numerical predictions depend on the arbitrary designation of component numbering and symmetric otherwise. We shall represent the mole fractions of the ternary mixtures by xi ( i = 1, 2, 3).

The simplest method assumes that there are no ternary effects; i.e. that H:23 is determined by eqn. (4), where HE&, xi) are the excess enthalpies calculated from correlated data of the binary properties using the ternary mole fractions xi, x j . Here we shall refer to this method as ‘ideal’. The Jacob-Fitzner’ and MugginauI6 equations give the same predictions as the ideal method when eqn. (1) is used in the correlation of the binary data.

According to the KohlerI7 expression, the excess molar enthalpy for a ternary mixture of composition xl, x2 and x3 is given by :

~ F 2 3 = (XI + x2)’HE(x;, x;) + (xi + x3)HE(x;, xi)

+ (x2 + x3)WE(x;, xj) (6)

in which HE(xf, xi) is the measured binary enthalpy at binary compositions (xi, xi) such that xi = 1 - xi = xi/(xi + xi).

1 0.5 0 X .

Lakhanpal et a/.’* expressed the ternary enthalpy in terms of the volume fractions as:

H:23 = (xl + x 2 H 4 1 + 42)HE(X;, + (xl + x3x41 + 43)HE(x;, $3)

+ (x2 + x 3 x 4 2 + 43)HE(X; 9 (7)

The binary enthalpies in this model are evaluated at the same compositions as in the Kohler method.

suggested an equation to predict excess molar properties where six different binary compositions appear :

Colinet

H?23 = (1/2){[x2(1 - x1)1H?2(x1, - xl)

+ [x3/(1 - Xi)IH?3(Xi , 1 - xi)

Cxi/(l - X3)IH?3(1 - x3, x3)

[x3/(1 - xz)lH%x2 7 1 - x2)

i- [x2/(1 - x3)lH53(1 - x3 9 X3)> (8) Eqn. (4) and (6)-(8) are symmetric in the sense that all

three binary mixtures are treated identically. Their numerical predictions do not depend on the arbitrary designation of component numbering. Contrarily, Tsao and Smith2’ pro- posed an asymmetric equation :

H723 = [x2/(1 - x1)IHE(x;, x;) + [x3/(1 - xl)lHE(x;, xi)

+ (1 - x,)HE(x;, xj) (9)

in which HE(xi, xi) refers to the excess enthalpies of the binary mixtures at compositions (xi, xi) where x; = x1 for the 1 ,2 and 1, 3 binary systems and x i = xZ/(x2 + x3) for the 2 , 3 binary system.

Toop21 developed an asymmetric equation which is very similar to that of Tsao and Smith,20 taking the mathematical form of:

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with H E ( x i , xi) calculated using the same method as Tsao and Smith.20

Scatchard et ~ 1 . ~ ~ modified eqn. (4) for the mixtures of a polar substance with two non-polar liquids, obtaining another asymmetric equation whose first two terms are equal to those of eqn. (9) and (10) and whose third term coincides with the last term of eqn. (4):

H?23 = Cx2/(l - xl)lHE(X;, x;) + Lx3/(l - X1)lHE(X;, + H?3(x2, x3) (11)

Hillert23 also exchanged the third term of the above equa- tions for the last two terms of the Colinet equation:

H?23 = Cx2N1 - xl)lHE(x;, x;) + Cx3/(l - xl)lHE(x;, x;)

+ cx3/(1 - x2)1H% 9 1 - x2)

Cx2/(1 - Xi)IH;3(1 - x3 7 x3) (12)

Mathieson and T ~ n n e ~ ~ proposed an equation in which the third term is the same as in eqn. (4) and the two first terms are changed in the following form

x; x;

+ H53(x2, x3) (13) verifying that x; - x; = x1 - x2 - x3/2 and x; - x i = x1

Finally, Knobeloch and S c h w a r t ~ ~ ~ have proposed another equation based on the Tsao-Smith expression. The ternary heat of mixing is given by

- x3 - x2/2.

H?23 = (A1H?23 + A2 H?23 + A3 H?23)/3 (14) where AiH?23, A2 Hy23 and A3 HT23 are determined in a way similar to that of Tsao-Smith:

The Knobeloch and Schwartz’ expression is symmetric because all three components are treated equally.

Solution Theories

The fundamental expressions of the Wilson, NRTL, UNIQUAC and Wang et a l l4 models, whose parameters for the binary systems are listed in Table 4, are:

Wilson’

with

where gij is proportional to the interaction energy between molecules i and j and VT is the molar volume of the pure liquid.

N R T L ’ ~

(Cz - 273.15C;) aij zj i xi

x i + xjGji - x i + xjGji HE = 7 7 [ X i X j G i j

+ a: RT2xi xi

where

(19) Cij

G, = exp( --aijqj) , zi j = - RT

For the parameters Cij and aij the following linear depen- dence on the temperature is considered:

Cij = Cc. + CT.(T - 273.15); aij = a;+ a${T - 273.15) (20)

UNZQUACi3

Table 4 Parameters and standard deviations, s, for binary systems using Wilson, NRTL, UNIQUAC and Wang et al. equations

model TFE-H,O parameters S H,O-TEGDME parameters S TFE-TEGDME parameters S

Wilson g12 - g l l = 2262.189

g12 - g2, = 1616.374 104

NRTL CC,, = 342.802 c;, = -5.374 93 CC,, = -428.504 Czl = 9.828 ai2 = 1.036 a:, = -1.137

UNIQUAC at2 = -445.769 a:, = 18.852 10 a;, = 1575.251 a;, = 10.998

Wang et al. A&,, = - 638.839 A&,, = 1717.504 89

a, = 1.855

g12 - g l l = 4599.260

gZ1 - gZ2 = -8166.093

Cf, = 447.236 c:, = -3.355 CC,, = -123.165 C z , = 3.268 a;, = 11.474 a;, = -0.854

a; , = - 10479.086

a;, = 8184.521 a;, = 21.692

U:, = -37.716

A&,, = -434.156 = 151.297

~ 1 , = 11.233

g12 - g l l = -910.057 519 105

gzl - gzz = -7104.200

Cf, = 443.092 CTZ = -2.571 C;, = -1309.310

66 21

Czl = 37.313 at2 = 14.276

a;, = -1711.824 17 a:, = -8.865 29

aC,, = -2365.753 a:, = -4.984

= -0.743

A E ~ ~ = -2219.855 295 = 1036.662 26

a, = 0.624

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the zii being Fig. 4 shows the excess molar enthalpies for several pseudo-binary mixtures together with the fitted equation. The pseudo-binary curves H : 2 3 ( ~ ) are all asymmetrical, as are the binary H$x) curves. This is due to the strong interactions between the three components: water, polyether and tri- fluoroethanol. The Hf23 values are negative in most of the ternary diagram (Fig. 5), which means that in general the exo- thermic energy due to the formation of the hydrogen bonds is greater than the endothermic energy due to the breaking of the hydrogen bonds of the pure compounds.

In Fig. 6 we can see that as the water mole fraction decreases, Hf23 also decreases reaching a minimum at ca. 4000 J mol- ’ in the ternary diagram. Endothermic enthalpies of mixing can be found when the TEGDME mole fractions approach zero.

The ternary contribution HEr is, in general, important as can be seen in the ternary diagram (Fig. 6). In some cases, as in the pseudo-binary of Fig. 7(a), the ternary contributions to I f f 2 3 are ca. 60% of the overall excess enthalpies. This means that this contribution cannot be neglected.

The results of the ten empirical equations can be seen in Table 5 and Fig. 7. In general the predictions are poor. The symmetrical Knobeloch equation presented lower deviations. This equation is not commonly used, perhaps because it is one of the most complicated of these empirical methods. The best predictions with the empirical expressions were found with the asymmetrical equations of Hillert, Scatchard and Toop when TEGDME is taken as component 1 [for which the ratio S ( H ~ Z ~ ) / H Y ~ ~ , , , ~ ~ is ca. lo%], but the goodness of the predictions depends on the pseudo-binary mixture.

In this case the aij linear dependence on T is:

Wang et a1.14

HE = 1 x i ~ j i A ~ j j (24) 2 i j

where the local mole fraction xi j is given by:

and the binary adjustable parameters are ai , The ratio of the collision diameters aji/oii was determined

assuming that aicc ri and a;iccrji where rji is the pure- component volume parameter from the UNIQUAC model and rji = (r j + rJ2. Values of ri for this model and of qi for the UNIQUAC model were taken from Gmehling et ~ 1 . ~ ~

For the four models the energetic parameters were fitted to the experimental HE values of the binary mixtures by a least- squares method and a Marquardt algorithm. The HE for the ternary system was estimated using the above equations and the parameter vaIues obtained from the correlations of the three cons ti tuen t binaries.

and Aqj.

Discussion Fig. 1-3 show that our experimental HE results are in accept- able agreement with the literature values27.34*35 for the three binaries. The experimental data of Krumbeck and Schu1z3’ were measured at 298.15 K and 0.4 MPa. Using the equation (aHE/dp), = uE - T(duE/aT), (and the experimental values of vE from Esteve et aL6) we have calculated that the differences between the excess enthalpies at atmospheric pressure and at 0.4 MPa are lower than the experimental uncertainties for all the systems.

Excess molar enthalpies can be explained in terms of nega- tive contributions due to the formation of interactions between unlike molecules and of positive contributions due to the breaking of interactions between like molecules.

The excess enthalpies of TFE-H,O show a change in sign (x = 0.1 l), becoming negative in the water rich region, but are much more positive than the corresponding measure- ments for ethanol-H,O and for TEGDME-H,O. This is because the fluorine group reduces the ability of the oxygen atom to act as potential acceptor for hydrogen bonding with water, giving rise to a decrease of the negative contributions.

H,O-TEGDME also presents an S-shaped behaviour of HE, being large and negative in the water-rich region. This, together which the large negative excess volumes and the large but positive viscosities,4 indicates very strong inter- actions between ether and water. This is because of the capa- bility of the oxygens of the polyether to hydrogen bond with water molecules.

The TFE-TEGDME mixture presents a large exothermic excess enthalpy, which indicates formation of a complex between the fluoroalkanol and the polyether. This interpreta- tion is confirmed by the asymmetrical and negative excess volumes and the positive excess visco~ities.~ However, for this system the last properties are much smaller in magnitude than for TEGDME-H,O, whereas the opposite occurs with the excess molar enthalpies.

1000 . 1

1 O o o y o 1 -300% 0.5 1

X

.- I - 0 E

- (b)

-500 -

1 -2500 0.5 1

X

Fig. 7 Experimental and predicted HYz3 values at 298.15 K for the pseudo-binary mixtures: (a) 0, run 6; 0, run 7; (b) 0, run 3. (-) ideal method; (- -) Knobeloch equation; (---) Hillert equation.

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Table 5 Model mean deviation, s, for the mixtures studied

equation s/J mol -

Jacob-Fi tzner Kholer Lakhanpal Colinet Kn o be1 och Tsao-Smith Toop Scat chard Hillert Mathieson-Tynne Wilson NRTL UNIQUAC Wang et al.

843 694 984 710 475 757" 884" 952" 864" 906" 313 397 415 569

493b 889' 961' 921' 912'

437' 376' 377' 37v 661'

For the asymmetrical equations the values depend on the component ordering: " TFE-H,O-TEGDME. ' H,O-TFE-TEGDME. ' TEGDME-H,O-TFE.

The asymmetrical equations give more weight to the binary contributions 1-2 and 1-3, and therefore component 1 plays the more important role. The rule for selecting the numbering of the components in these equations has been given by Pando et al." and consists in designating as com- ponent 1 the common component of the two mixtures which exhibit the largest absolute values of HE in their maxima or minima. For TFE-H,O-TEGDME, the two largest absolute values of HE, correspond to the minima of TEGDME-H,O and TEGDME-TFE. This means that following this rule TEGDME must be component 1, which coincides with our results for all the asymmetrical equations.

In an earlier paper we have found for the vE at 303.15 K of the same ternary system, that the best predictions were found taking water as component 1 for all the analysed asym- metrical equations. In this case all the vE values for the binary systems were negative and the most negative ones were those corresponding to the mixtures with water. This fact is also in agreement with the rule of Pando et al." In the case of excess viscosities of the same ternary system, OlivC et a1.' have found a case in which the above rule presents problems: two binaries have maxima of similar magnitude and the third binary has a higher maximum. Thus, the magnitudes at the maximum for the excess viscosities of TFE-TEGDME and TFE-H,O are similar and lower than those of TEGDME-H,O. In this case, the results of Olive et al.' show that for some asymmetrical equations the best predictions are

1000 I I 1

X

Fig. 8 Experimental excess molar enthalpies at 298.15 K for the binary mixtures: (0) TFE + H,O; (0) H,O + TEGDME; (A) TFE + TEGDME. (-) fitting UNIQUAC equation, (---) fitting Wilson equation.

obtained taking TEGDME as component 1 and for others H,O. Otherwise, the symmetrical Colinet equation gives rise to lower deviations. This analysis confirms that for the designation of component 1 it is much better to follow the Pando et al. rule than to choose the most dissimilar com- pound.

As it can be seen in Table 4, the lower deviations in the correlation of the binary systems with local composition models correspond to the UNIQUAC model with four adjustable parameters and the larger deviations correspond to the Wilson model with two fitted parameters. In Fig. 8 the

-40001 -5000 0.5 1

X

Fig. 9 Experimental and predicted values at 298.15 K for the pseudo-binary mixtures: (a) 0, run 1 ; 0, run 2; (b) A, run 5; 0, run 7. (----) Wilson equation; (---) Wang et al. equation.

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H E values associated with both models are plotted together with the experimental results. H,O-TEGDME is the system which has presented the most difficulties to correlate. This fact may be due to the S-shape and strong asymmetry of the HE(x) curve, which presents a strong minimum at the mole fraction of water, x = 0.86. The limitations of these types of models to correlate excess enthalpies of systems with larger enthalpies of mixing were pointed out by Christensen et

Surprisingly the Wilson model presents the best predic- tions for the ternary systems (see Table 5 and Fig. 9). We have not found an explanation for the lower mean deviations obtained with this model. The UNIQUAC and NRTL methods have been used more frequently than the Wilson model to predict excess enthalpies of multicomponent systems, because the Wilson model does not fit well the excess enthalpies of binary mixtures. No improvement in the correlations and the prediction was found using the modified UNIQUAC3’ instead of UNIQUAC. Contrary to what happens with non-aqueous mixture^,'^ for the aqueous mix- tures studied here, the Wang et al. theory did not give better results than the UNIQUAC and NRTL models.

The authors gratefully acknowledge the financial support of Xunta de Galicia-Spain (XUGA20602A92 and XUGA20605B93) and of DGICYT-Spain (PB90-0456).

A i

a i j

S i j

G j i H E HE H?

HE(x: , xi)

4i ri

V E

S

iq

x i (i = 1, 2, 3) XJ

X

Xi j

Greek letters

“i

“ i j beij 6 i

4 i

o j i

‘ji

A i j

Symbols parameters of eqn. (l), (2) or (5 ) energetic parameter of UNIQUAC model parameter of Wilson model parameter of NRTL model excess molar enthalpy excess enthalpies for the ternary mixture measured excess enthalpy for the pseudo- binary mixtures enthalpy of the i-j binary mixture binary contribution to the excess ternary enthalpies ternary contribution to the excess ternary enthalpies binary enthalpy at binary compositions (xi ,

UNIQUAC surface area parameters UNIQUAC volume parameters mean deviation excess molar volume molar volume of the pure liquid. mole fraction of binary mixtures mole fractions of ternary mixtures binary compositions in the ternary enthalpy local composition fraction

xi)

Wang et d. model adjustable energy correc- tion factor parameter of NRTL model, (orij = uji) energy parameter of Wang et al. model surface fraction of component i in the mixture hard-core volume fraction of component i in the mixture Wang et al. model collision parameters NRTL and UNIQUAC binary parameters Wilson binary parameters.

Superscripts

C E T

temperature-independent parameter excess property temperature-dependent parameter

Subscripts

1,2,3, i,j, k component indices bin binary contribution ter ternary contribution

References 1 2 3 4

5

6

7

8 9

10

11 12 13 14

15 16

17 18

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20

21 22

23 24 25

26

27

28

29

30

31 32

33

34

35 36

37

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PaDer 4/07178F: Received 24th November. 1994

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