Excess molar volume and viscosity study for the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15, 298.15 and 313.15 K

Fluid Phase Equilibria 207 (2003) 193–207

Excess molar volume and viscosity study for the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15, 298.15 and 313.15 K Miguel Postigo a,∗ , Alejandra Mariano a , Lelia Mussari a , Alberto Camacho a , José Urieta b a

b

Departamento de Qu´ımica, Facultad de Ingenier´ıa, Cátedra de Fisicoqu´ımica, Universidad Nacional del Comahue, Buenos Aires, 1400-8300 Neuquén, Argentina Departamento de Qu´ımica Orgánica y Qu´ımica F´ısica, Facultad de Ciencias, Universidad de Zaragoza, Ciudad Universitaria, Zaragoza 50009, Spain Received 18 October 2002; accepted 14 January 2003

Abstract Densities, ρ, and viscosities, η, for ternary liquid mixtures of tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) have been measured as a function of composition at temperatures of 283.15, 298.15 and 313.15 K and atmospheric pressure over the full range of composition. From theses results excess molar volume, V E , viscosity deviations, η, from mole fraction average, and excess free energies of activation of viscous flow, G∗E , have been calculated. Excess molar volume, viscosity deviations and excess free energies of activation of viscous flow were fitted to Cibulka, Singh and Nagata equations. The results are discussed in terms of the molecular interaction between the components of the mixtures. Excess molar volumes and deviations of the viscosities for this ternary system were predicted from binary contributions using geometrical solution models, Tsao–Smith, Jacob–Fitzner, Kholer, Rastogi and Radojkovic. Additionally, experimental results are compared with those obtained by applying group-contribution method proposed by Wu. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Excess volume; Viscosity; Ternary mixtures; Group-contribution method

1. Introduction The thermodynamics of ternary mixtures of non-electrolytes has not received as much attention as the thermodynamics of binary mixtures. It is therefore interesting to estimate excess molar volumes and viscosity deviations for systems with more than two components. A search in the literature of ternary ∗

Corresponding author. Fax: +54-299-4488306. E-mail address: [email protected] (M. Postigo). 0378-3812/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0378-3812(03)00021-9

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systems suggests the availability of some empirical correlation used to calculate the excess molar volumes, and transport properties of liquid mixtures. Continuing our work on volumetric and transport properties of binary and ternary mixtures [1–7], we present here experimental density and viscosity measurements of the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at atmospheric pressure at 283.15, 298.15 and 313.15 K over the full range of composition. Excess molar volumes, viscosity deviations and excess free energies of activation of viscous flow are calculated from these experimental data and fitted to empirical equations [8–10]. Assuming that interactions in a ternary mixture are closely dependent on the interactions in binary systems, we consider the application of geometrical solution models [11–15] to predict excess molar volumes and deviations of the viscosities for this ternary system from binary contributions. Of particular importance, however, are the predictive methods based on the concept of functional group, which allow the determination of viscosities for systems that have not been investigated. Wu [16] proposed the group-contribution method UNIVAC to predict mixture viscosities, but the viscosities of the pure components are required. We have used UNIVAC to predict mixture viscosities and to compare with experimental results.

2. Experimental 2.1. Materials The liquids used were tetrahydrofuran (>99.8%), and 1-chlorobutane (>99.5%) obtained from Aldrich, and 1-butanol (>99.5%) provided by Fluka. Their purities were checked by comparing the measured densities and viscosities with those reported in the literature. All liquids were partially degassed by ultrasound and were stored over activated molecular sieve type 0.4 nm from Fluka. The pure components properties at 283.15, 298.15 and 313.15 K, along with literature values are given in Table 1. 2.2. Apparatus and procedure Mixtures were prepared by weighing an appropriate volume of each solvent (Sartorious analytical balance, precision of 10−7 kg). Each mixture was prepared in an airtight bottle to avoid preferential evaporation and, its density and viscosity were measured immediately. The estimated error in mole fractions is ±2 × 10−4 . Densities of the purified chemicals and their ternary mixture were measured with a precision of 10−2 kg m−3 using a vibrating tube density meter (Mettler DA 310), which measures oscillating periods, calculates densities and controls temperature with a precision of ±0.01 K. The density meter was calibrated with dry air and with double distilled and degassed water. Viscosities were measured with a Cannon–Fenske type viscometer, placed in a water bath thermostated with a HAAKE D8. Temperature was determined with a calibrated platinum resistance (Pt-100) using a digital multimeter (HP, 34401 A). The accuracy of the temperature readings is estimated in ±0.01 K. Efflux time was determined using a digital chronometer to within ±0.01 s. Detection of the meniscus was visual and for each sample, the determinations were repeated until at least three successive values reproduced.

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Table 1 Properties of the pure components Component

Temperature (K) 283.15

298.15

313.15

ρ (kg m−3 )

η (mPa s)

ρ (kg m−3 )

η (mPa s)

ρ (kg m−3 )

η (mPa s)

Tetrahydrofuran Experimental Literature

898.65 –

0.531 –

882.50 882.3a

0.459 0.460b

865.93 866.2a

0.401 –

1-Chlorobutane Experimental Literature

897.44 –

0.492 –

881.19 880.95b

0.425 0.4260b

864.04 863.88c

0.366 0.3645c

1-Butanol Experimental Literature

817.12 –

3.942 –

805.74 805.75b

2.564 2.5710d

794.36 793.96c

1.766 1.7734d

a

Garc´ıa and Postigo [20]. Riddick et al. [18]. c Dom´ınguez et al. [19]. d TRC [17]. b

Calibration of the viscometer was made using double distilled and degassed water and benzene (Merck, p.a.), purified by recrystallization. The dynamic viscosity was indirectly determined by the Poiseuille equation, including the correcting term for the kinetic energy. Viscosity values are accurate within the range ±3 × 10−3 mPa s. 3. Results and discussion Densities, ρ, viscosities, η, excess molar volumes, V E , viscosity deviations, η, and excess free energies of activation of viscous flow, G∗E , for the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15, 298.15 and 313.15 K are given in Table 2. Molar volumes of the ternary mixtures, V, were calculated from the equation: 1
xi Mi ρ i=1 3

V =

(1)

where xi and Mi are the molar fraction and molar mass of component i and ρ is the measured density of the solution. The excess molar volumes, V E , for the ternary system were evaluated with the equation: VE = V −

3
xi Mi i=1

ρ

The estimated error in V E is ±2 × 10−9 m3 mol−1 .

(2)

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Table 2 Densities, viscosities, excess molar volume, deviations of the viscosity and excess free energies of activation of viscous flow for the ternary system at indicated temperatures x1

x2

ρ (kg m−3 )

η (mPa s)

V E (×106 ) (m3 mol−1 )

Tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15 K 0.0525 0.0445 825.24 2.879 −0.030 0.0461 0.8447 889.23 0.544 0.040 0.0578 0.8875 893.36 0.509 0.022 0.1017 0.0456 829.02 2.365 −0.037 0.1072 0.1015 834.60 2.068 −0.055 0.0990 0.2226 844.65 1.592 −0.063 0.0995 0.3058 851.73 1.309 −0.059 0.1012 0.4091 860.20 1.045 −0.035 0.0963 0.5024 867.20 0.863 −0.015 0.1009 0.5925 874.38 0.709 0.015 0.1038 0.6730 880.66 0.617 0.032 0.0986 0.7984 889.81 0.513 0.022 0.1015 0.8350 892.80 0.491 0.013 0.1957 0.1058 841.62 1.616 −0.057 0.2007 0.2071 850.82 1.276 −0.052 0.2007 0.3073 859.30 1.057 −0.046 0.2099 0.3982 867.45 0.856 −0.037 0.2050 0.5051 875.63 0.707 −0.027 0.1916 0.6044 882.34 0.613 −0.017 0.2046 0.6987 890.57 0.519 −0.018 0.3126 0.0976 849.93 1.291 −0.065 0.3135 0.1992 858.97 1.041 −0.071 0.2989 0.3005 866.44 0.870 −0.068 0.3001 0.4069 875.24 0.717 −0.056 0.2967 0.5051 882.81 0.611 −0.047 0.3207 0.5721 889.84 0.537 −0.036 0.4026 0.1023 857.36 1.015 −0.059 0.4030 0.2021 866.21 0.875 −0.067 0.4058 0.3006 874.74 0.728 −0.060 0.3952 0.4046 882.47 0.624 −0.055 0.4037 0.4977 890.63 0.534 −0.054 0.4956 0.1276 867.13 0.847 −0.066 0.4991 0.2021 873.99 0.746 −0.074 0.4978 0.3021 882.51 0.627 −0.087 0.5010 0.4035 891.24 0.526 −0.097 0.6073 0.1000 873.73 0.748 −0.050 0.5899 0.2064 881.64 0.637 −0.057 0.6028 0.3023 890.79 0.541 −0.052 0.6858 0.0995 880.46 0.664 −0.066 0.6985 0.2066 891.00 0.559 −0.079 0.8009 0.0983 890.25 0.566 −0.063 0.8553 0.0483 890.55 0.575 −0.058 0.8720 0.1059 897.26 0.504 −0.068 0.9024 0.0413 894.19 0.547 −0.064

η (mPa s)

G∗E (J mol−1 )

−0.730 −0.327 −0.174 −1.073 −1.158 −1.244 −1.239 −1.140 −1.017 −0.845 −0.649 −0.338 −0.224 −1.293 −1.267 −1.140 −0.996 −0.793 −0.590 −0.315 −1.248 −1.144 −1.016 −0.798 −0.576 −0.337 −1.201 −0.995 −0.793 −0.574 −0.314 −0.964 −0.796 −0.575 −0.315 −0.777 −0.581 −0.302 −0.595 −0.288 −0.305 −0.283 −0.098 −0.174

−273 −301 −193 −498 −513 −573 −622 −637 −653 −651 −570 −416 −327 −653 −687 −638 −644 −593 −505 −373 −669 −672 −665 −591 −502 −362 −787 −643 −577 −479 −348 −649 −564 −487 −386 −550 −485 −336 −463 −279 −302 −256 −202 −186

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Table 2 (Continued ) x1

x2

ρ (kg m−3 )

η (mPa s)

V E (×106 ) (m3 mol−1 )

Tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 298.15 K 0.0488 0.0486 813.42 1.988 −0.020 0.0490 0.1041 818.17 1.739 −0.026 0.0492 0.8524 873.76 0.429 0.097 0.0451 0.9096 877.55 0.408 0.076 0.0987 0.0532 817.30 1.677 −0.023 0.0993 0.1012 821.45 1.479 −0.030 0.1070 0.2031 830.36 1.179 −0.027 0.0998 0.3015 837.58 0.971 −0.007 0.0991 0.4027 845.22 0.797 0.017 0.0977 0.5017 852.44 0.663 0.040 0.0960 0.6146 860.47 0.552 0.062 0.0974 0.7056 867.00 0.485 0.075 0.0972 0.8057 874.04 0.430 0.071 0.0980 0.8493 877.22 0.414 0.057 0.1989 0.1021 828.54 1.196 −0.029 0.2017 0.2046 837.14 0.968 −0.024 0.2007 0.3011 844.72 0.800 −0.016 0.1979 0.4065 852.58 0.666 0.001 0.1934 0.5088 859.87 0.572 0.017 0.1995 0.6013 867.04 0.496 0.026 0.1954 0.7079 874.39 0.438 0.028 0.2971 0.1003 835.49 0.978 −0.032 0.3029 0.2003 844.18 0.800 −0.035 0.2940 0.3013 851.57 0.678 −0.030 0.3072 0.3990 860.03 0.575 −0.019 0.3018 0.4986 867.11 0.505 −0.011 0.3089 0.5913 874.31 0.447 0.005 0.4232 0.1112 845.76 0.756 −0.035 0.4063 0.2009 851.86 0.681 −0.035 0.4037 0.2998 859.45 0.585 −0.023 0.4055 0.4006 867.37 0.506 −0.019 0.3926 0.5093 874.58 0.451 −0.015 0.5173 0.0789 849.97 0.697 −0.011 0.5048 0.1992 859.03 0.593 −0.022 0.4993 0.2986 866.55 0.519 −0.024 0.5026 0.3965 874.41 0.459 −0.026 0.6110 0.0983 858.88 0.595 −0.013 0.6051 0.1992 866.76 0.518 −0.021 0.6037 0.2998 874.57 0.462 −0.013 0.7050 0.0994 866.39 0.535 −0.010 0.6980 0.1992 874.11 0.471 −0.023 0.7948 0.0987 873.54 0.478 −0.003 0.8522 0.0507 874.29 0.477 −0.004 0.8715 0.0780 878.26 0.451 −0.012 0.9062 0.0423 878.15 0.453 −0.008

η (mPa s)

G∗E (J mol−1 )

−0.369 −0.499 −0.208 −0.115 −0.565 −0.660 −0.725 −0.738 −0.697 −0.622 −0.495 −0.365 −0.206 −0.127 −0.731 −0.734 −0.697 −0.612 −0.497 −0.362 −0.200 −0.746 −0.698 −0.623 −0.489 −0.357 −0.202 −0.679 −0.598 −0.488 −0.348 −0.197 −0.609 −0.482 −0.355 −0.199 −0.473 −0.346 −0.190 −0.332 −0.198 −0.202 −0.185 −0.112 −0.113

−205 −287 −420 −306 −393 −487 −559 −631 −672 −691 −648 −557 −412 −312 −582 −637 −681 −675 −614 −530 −379 −669 −695 −689 −604 −507 −365 −721 −649 −592 −495 −349 −665 −580 −485 −338 −571 −484 −320 −426 −326 −326 −307 −239 −239

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Table 2 (Continued ) x1

x2

ρ (kg m−3 )

η (mPa s)

V E (×106 ) (m3 mol−1 )

Tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 313.15 K 0.0516 0.0425 800.84 1.400 0.025 0.0512 0.1145 806.44 1.228 0.025 0.0443 0.8637 857.57 0.385 0.101 0.0584 0.8960 860.87 0.371 0.053 0.1010 0.0503 804.73 1.268 0.016 0.1039 0.1045 809.21 1.105 0.010 0.1110 0.2013 816.99 0.912 0.018 0.1054 0.3103 824.60 0.750 0.031 0.1066 0.4035 831.23 0.633 0.049 0.1050 0.4991 837.65 0.544 0.071 0.0957 0.6061 844.24 0.474 0.084 0.0975 0.7092 851.13 0.423 0.091 0.0977 0.8052 857.42 0.386 0.081 0.1005 0.8495 860.55 0.375 0.063 0.2114 0.1019 816.22 0.911 −0.004 0.2033 0.2034 823.43 0.769 −0.006 0.1968 0.3055 830.51 0.647 −0.001 0.2025 0.4035 837.83 0.552 0.011 0.2231 0.4940 845.42 0.485 0.022 0.2000 0.6020 851.23 0.434 0.024 0.1975 0.6849 856.59 0.392 0.020 0.3223 0.1144 824.86 0.771 −0.025 0.3141 0.2030 831.07 0.652 −0.030 0.2612 0.3144 835.69 0.593 −0.029 0.3420 0.3850 846.19 0.490 −0.026 0.3105 0.4983 851.90 0.439 −0.018 0.3082 0.5954 858.21 0.399 −0.005 0.4196 0.0918 829.89 0.652 −0.030 0.4132 0.2000 837.73 0.565 −0.037 0.4007 0.2948 843.82 0.497 −0.034 0.4064 0.4012 851.84 0.441 −0.036 0.3935 0.5106 858.57 0.404 −0.040 0.5127 0.1017 836.83 0.578 0.013 0.5078 0.1996 844.01 0.505 0.000 0.5122 0.3008 851.93 0.454 −0.020 0.5058 0.3988 858.58 0.409 −0.034 0.6096 0.1017 844.18 0.508 −0.026 0.6093 0.1953 851.33 0.453 −0.038 0.5993 0.3032 858.48 0.413 −0.036 0.7195 0.0987 851.95 0.461 −0.013 0.7083 0.2019 859.00 0.420 −0.028 0.8090 0.0994 858.81 0.426 −0.018 0.8561 0.0461 858.38 0.425 −0.021 0.8439 0.1017 861.78 0.405 −0.030 0.9090 0.0464 862.59 0.409 −0.028

η (mPa s)

G∗E (J mol−1 )

−0.236 −0.308 −0.111 −0.061 −0.290 −0.373 −0.421 −0.438 −0.423 −0.380 −0.313 −0.217 −0.120 −0.064 −0.424 −0.435 −0.423 −0.372 −0.284 −0.217 −0.146 −0.395 −0.401 −0.376 −0.270 −0.206 −0.113 −0.413 −0.357 −0.309 −0.208 −0.110 −0.346 −0.289 −0.192 −0.108 −0.284 −0.208 −0.111 −0.185 −0.097 −0.096 −0.107 −0.067 −0.051

−229 −275 −246 −162 −263 −387 −460 −544 −596 −603 −562 −425 −276 −153 −483 −538 −594 −580 −463 −404 −340 −438 −541 −533 −426 −368 −229 −593 −543 −533 −382 −213 −503 −472 −313 −204 −466 −379 −214 −307 −167 −163 −208 −153 −105

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199

The viscosity deviation, η, from linear dependence on mole fraction has been calculated from the following relation: η = η −

3


xi ηi

(3)

i=1

where η (mPa s) is the mixture dynamic viscosity, and ηi is the pure component viscosity. The estimated error in η is ±10−2 mPa s. On the basis of the theory of reaction rate [21], the excess free energies of activation of viscous flow, G∗E , were obtained from the expression:   3
xi ln(ηi Vi ) (4) G∗E = RT ln(ηV ) − i=1

where Vi is the molar volume of component i. The excess molar volume, the viscosity deviations and the excess free energies of activation of viscous flow have been fitted to the Cibulka [8], Singh et al. [9] and Nagata and Sakura [10] equations. These expressions include three terms corresponding to binary contributions evaluated by Redlich–Kister [22] equations adjusted to the binaries data, but calculated by the authors, at the molar fractions of the ternary system. For that reason we define these contributions as QEij∗ to distinguish the fact that the sum xi + xj does not equals one, where QE stands for V E , η or G∗E . The followings expressions were used. Cibulka equation [8]: QE123 = QE12∗ + QE13∗ + QE23∗ + x1 x2 x3 (A + Bx1 + Cx2 )

(5)

where A, B and C are fit parameters. Singh equation [9]: QE123 = QE12∗ + QE13∗ + QE23∗ + Ax1 x2 x3 + Bx1 (x2 − x3 ) + Cx21 (x2 − x3 )2

(6)

where A, B and C are fit parameters. Nagata equation [10]: QE123 = QE12∗ + QE13∗ + QE23∗ + x1 x2 x3 ∆

(7)

where ∆ is a fit parameter. Fit parameters, and standard deviations are presented in Table 3. Redlich–Kister [22] parameters for the binary systems, reported in previous works [7,23], are giving in Table 4. The three-dimensional surface of V E , η and G∗E calculated from the Cibulka’s equation (Eq. (5)) and experimental data for the ternary system at 283.15 K are plotted in Figs. 1a, 2a and 3a, respectively. The isolines at constant values of V E , η and G∗E are in Figs. 1b, 2b and 3b, respectively. The ternary excess molar volume shows small values, negative and positive, and it changes hardly when varying the temperature. The ternary viscosity deviations and excess Gibbs energies of activation of viscous flow are negative over the whole composition range at the three investigated temperatures. An increase of temperature considerably modifies the η of the ternary mixtures, however, the G∗E hardly modifies. According to Kaufman and Eyring [24], the viscosity of a mixture strongly depends on the entropy

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Table 3 Fit parameters, and standard deviations Temperature (K) 283.15

298.15 ∗E

313.15 ∗E

η (mPa s)

G (J mol−1 )

V (×10 ) (m3 mol−1 )

η (mPa s)

G (J mol−1 )

V E (×106 ) (m3 mol−1 )

η (mPa s)

G∗E (J mol−1 )

Cibulka model A −0.149 B −2.195 C −0.757 σ 0.011

11.7 −11.2 −11.5 0.013

6041 −12828 −14112 46

−0.976 1.183 0.805 0.009

9.1 −10.7 −9.9 0.018

11459 −21277 −19816 45

−1.022 0.373 −1.618 0.011

5.5 −5.8 −5.7 0.007

9295 −12488 −14013 24

Singh model A −0.939 B −0.564 C −16.368 σ 0.009

4.3 −15.8 −13.2 0.021

−2505 −20433 −38300 44

−0.372 1.261 4.488 0.009

2.4 −11.3 −13.8 0.026

−1584 −23434 −50834 51

−1.453 −1.015 1.312 0.012

1.7 −7.8 −4.6 0.011

662 −20245 −14994 29

Nagata model ∆ −0.939 σ 0.013

4.3 0.030

−2505 56

−0.372 0.009

2.4 0.031

−1584 67

−1.453 0.012

1.7 0.015

662 40

E

6

V (×10 ) (M3 mol−1 )

E

6

of mixture, which is related with the structure of the liquid and the enthalpy (and consequently with molecular interactions between the components of the mixture). So, the viscosity deviations are functions of molecular interactions as well as of size and shape of molecules. Vogel and Weiss [25] affirm that mixtures with strong interactions between different molecules (HE < 0 and negative deviations from Raoult’s law) present positive viscosity deviations; whereas, for mixtures with positive deviations of Raoult’s law and without specific interactions the viscosity deviations are negative. In this way, Meyer et al. [26] state that excess Gibbs energy of activation of viscous flow, like viscosity deviations, can be used to detect molecular interactions. The breaking of hydrogen bonding of alcohol, and dipole–dipole specific interactions of the halogenated compound make the mixture to flow more easily. Whereas, the OH–Cl interactions increase the viscosity, but the effect is not as important as the breaking of associations. The negative values observed for η and G∗E of the ternary system under study point out the easier flow of mixture compared with the behavior of pure liquids, and according to Fort and Moore [27] this behavior correspond to systems containing an associated component. Excess molar volumes and viscosity deviations for this ternary system were predicted using five geometrical solution models presented in references [11–15], the standard deviations are presented in Table 5. These models use binary contributions evaluated by Redlich–Kister [22] equations at molar fractions calculated by arbitrary chosen combination ternary molar fractions. The expressions for the geometrical solution models used are: Tsao–Smith [11] model: QE123 =

x3 QE13 x2 QE12 + + (1 − x1 )QE23 1 − x1 1 − x1

(8)

Binary contributions were evaluated at xi0 = x1 and xj 0 = 1 − xi0 for 1–2 and 1–3 binaries, and x20 = x2 /(x2 + x3 ) and x30 = x3 /(x2 + x3 ), for 2–3 binary, option (a) in Table 5. As this model is an

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201

Table 4 Redlich–Kister [22] parameters for the binary systems and standard deviations, reported in previous works [7,23] a0

a1

a2

σ

a3

Tetrahydrofuran + 1-chlorobutane at 283.15 K V E (×106 ) (m3 mol−1 ) −0.2394 η (mPa s) 0.0647 G∗E (J mol−1 ) 345

−0.0695 −0.0198 −99

−0.0383 – 161

– – –

0.0012 0.0010 2

Tetrahydrofuran + 1-chlorobutane at 298.15 K V E (×106 ) (m3 mol−1 ) −0.2628 η (mPa s) 0.0520 G∗E (J mol−1 ) 342

−0.0559 −0.0216 −126

−0.0218 – 161

– – –

0.0001 0.0010 2

Tetrahydrofuran + 1-chlorobutane at 313.15 K V E (×106 ) (m3 mol−1 ) −0.2823 η (mPa s) 0.0440 G∗E (J mol−1 ) 362

−0.0443 −0.0216 −154

– – 134

– – –

0.0003 0.0010 2

Tetrahydrofuran + 1-butanol at 283.15 K V E (×106 ) (m3 mol−1 ) −0.1020 η (mPa s) −4.6938 G∗E (J mol−1 ) −2753

0.1370 2.7876 622

0.0195 −2.7969 −1131

0.0917 2.2336 853

0.0018 0.0130 9

Tetrahydrofuran + 1-butanol at 298.15 K V E (×106 ) (m3 mol−1 ) −0.0293 η (mPa s) −2.7099 G∗E (J mol−1 ) −2652

0.1928 1.5044 588

0.0280 −1.4862 −958

1.2635 890

0.0016 0.0090 8

Tetrahydrofuran + 1-butanol at 313.15 K V E (×106 ) (m3 mol−1 ) 0.0402 η (mPa s) −1.6730 G∗E (J mol−1 ) −2432

0.1700 0.9726 503

−0.4928 −194

1-Chlorobutane + 1-butanol at 283.15 K V E (×106 ) (m3 mol−1 ) 0.0902 η (mPa s) −4.6508 G∗E (J mol−1 ) −2600

0.6075 2.0603 −862

0.1809 −0.5249 442

0.1038

0.0001 0.0054 8

1-Chlorobutane + 1-butanol at 298.15 K V E (×106 ) (m3 mol−1 ) 0.2487 η (mPa s) −2.8622 G∗E (J mol−1 ) −2897

0.7473 1.2914 −545

0.3048 −0.8022 −546

0.3938

0.0066 0.0067 18

1-Chlorobutane + 1-butanol at 313.15 K V E (×106 ) (m3 mol−1 ) 0.5295 η (mPa s) −1.7978 G∗E (J mol−1 ) −2708

0.6769 0.7168 −359

0.4749 −0.1717 241

0.0016 0.0040 9

0.4606 −658

0.0001 0.0028 8

asymmetrical one, we alternatively evaluated binary contributions with xi0 = x2 and xj 0 = 1 − xi0 for 2–1 and 2–3 binaries and, x30 = x3 /(x1 + x3 ) and x10 = x1 /(x1 + x3 ), for 3–1 binary, option (b) in Table 5. The third alternative, option (c) in Table 5, was using xi0 = x3 and xj 0 = 1 − xi0 for 3–1 and 3–2 binaries, and x20 = x2 /(x2 + x1 ) and x10 = x1 /(x2 + x1 ), for 1–3 binary.

202

M. Postigo et al. / Fluid Phase Equilibria 207 (2003) 193–207

Fig. 1. Experimental excess molar volumes (V E ) for the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15 K. (a) Three-dimensional surface calculated from Cibulka’s equation (Eq. (5)) and (b) isolines at constant values.

Jacob–Fitzner [12] model: QE123 =

x1 x3 QE13 x1 x3 QE23 x1 x2 QE12 + + [(x1 + x3 /2)(x2 + x3 )/2] [(x1 + x2 /2)(x3 + x2 )/2] [(x2 + x1 /2)(x3 + x1 )/2]

Binary contributions were evaluated with molar fractions calculated by xi0 = (1 + xi − xj ).

(9)

M. Postigo et al. / Fluid Phase Equilibria 207 (2003) 193–207

203

Fig. 2. Experimental viscosity deviations (η) for the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15 K. (a) Three-dimensional surface calculated from Cibulka’s equation (Eq. (5)) and (b) isolines at constant values.

Kohler [13] model: QE123 = (x1 + x2 )2 QE12 + (x1 + x3 )2 QE13 + (x2 + x3 )2 QE23 Molar fractions in binary contributions were evaluated with xi0 = (1 − xj 0 ) = xi /(xi + xj ).

(10)

204

M. Postigo et al. / Fluid Phase Equilibria 207 (2003) 193–207

Fig. 3. Excess Gibbs energies of activation of viscous flow (G∗E ) for the ternary system tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) at 283.15 K. (a) Three-dimensional surface calculated from Cibulka’s equation (Eq. (5)) and (b) isolines at constant values.

Rastogi [14] model: QE123 =

(x1 + x2 )QE12 + (x1 + x3 )QE13 + (x2 + x3 )QE23 2

(11)

M. Postigo et al. / Fluid Phase Equilibria 207 (2003) 193–207

205

Table 5 Standard deviations for geometrical solutions models Temperature (K) 283.15

298.15

313.15

G∗E (J mol−1 )

V E (×106 ) (m3 mol−1 )

η (mPa s)

G∗E (J mol−1 )

V E (×106 ) (m3 mol−1 )

η (mPa s)

G∗E (J mol−1 )

Tsao–Smith, Eq. (8) (a) 0.026 0.261 (b) 0.023 0.318 (c) 0.022 0.323

58 128 116

0.016 0.025 0.037

0.155 0.197 0.200

78 151 137

0.042 0.048 0.046

0.092 0.120 0.121

84 143 134

Jacob-Fitzner, Eq. (9) 0.021 0.070

71

0.010

0.045

73

0.025

0.030

39

Kohler, Eq. (10) 0.023 0.098

71

0.011

0.065

74

0.028

0.037

38

Rastogi, Eq. (11) 0.023 0.329

93

0.016

0.194

113

0.040

0.118

126

Radojkovic, Eq. (12) 0.014 0.177

72

0.012

0.107

76

0.015

0.058

37

V E (×106 ) (m3 mol−1 )

η (mPa s)

Binary contributions were evaluated with molar fractions calculated by xi0 = (1 − xj 0 ) = xi /(xi + xj ). Radojkovic [15] model: QE123 = QE12∗ + QE13∗ + QE23∗ Binary contributions were evaluated using directly the ternary molar fractions. Standard deviations, σ , presented in Tables 3 and 5, were determined for all models as:   n 
(QE123 (exp)i − QE123 (calc)i )2 σ = n−p i=1

(12)

(13)

where p is the number of parameters and n is the number of experimental data. Wu used the following modified Eyring viscosity equation [28] to predict the viscosity of liquid mixtures, ηm :    ∗ E hN i xi Gi − (G /A) exp (14) ηm = Vm RT where h is the Planck’s constant, N the Avogadro’s number, Vm the molar volume of the liquid mixture, G∗i the Gibbs energy of activation of viscous flow of pure liquid i, GE the Gibbs excess energy, A an empirical factor, and R is the gas constant. According to the original Wu model two values (1.0 and 2.45) have been used for the empirical factor. GE is obtained using the UNIFAC parameters proposed by Gmehling et al [29]. Table 6 shows the percent relative error for viscosity of the group-contribution model, UNIVAC.

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Table 6 Percent relative error for viscosity of the group-contribution model, UNIVAC Temperature (K)

Percent relative error

283.15 298.15 313.15

Empirical factor A = 1

Empirical factor A = 2.45

5.30 4.56 7.12

11.48 10.99 5.72

4. Conclusions Densities and viscosities for the ternary liquid mixtures of tetrahydrofuran (1) + 1-chlorobutane (2) + 1-butanol (3) were measured at the temperatures of 283.15, 298.15, and 313.15 K and atmospheric pressure over the whole range of compositions. The ternary viscosity deviations and excess Gibbs energies of activation of viscous flow are significant and negative over the whole composition range at the three investigated temperatures. This behavior is characteristic for systems containing an associated component. All of the selected correlative models are capable of representing with a higher or lesser degree of accuracy the volumetric and the viscometric behavior of the studied mixture. The geometrical models used to predict ternary excess molar volume and viscosity deviations from binary contributions produce standard deviation lower than 4.8 × 10−8 m3 mol−1 and 3.3 × 10−1 mPa s, respectively. The tested group-contribution model, UNIVAC, forecast viscosities which are in satisfactory agreement with our experimental results, the percent relative error is lower than 12%. List of symbols A, B and C GE G∗E Mi QE V VE xi

fit parameters Gibbs excess energy free energies of activation of viscous flow molar mass of component i (=1–3) represent V E , or η or G∗E molar volume excess molar volume molar fraction of component i (=1–3)

Greek letters ∆ η η ρ

fit parameter dynamic viscosity dynamic viscosity deviation density

Subscripts calc exp

calculated value experimental value

M. Postigo et al. / Fluid Phase Equilibria 207 (2003) 193–207

i j

207

component i component j

Acknowledgements The authors are grateful for financial assistance from CONICET and Universidad Nacional del Comahue. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

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