Ž .Fluid Phase Equilibria 168 2000 267–279www.elsevier.nlrlocaterfluid

Densities and viscosities of binary mixtures of butanone with butanolisomers at several temperatures

Santiago Martınez, Rosa Garriga, Pascual Perez, Mariano Gracia )´ ´´( )Departamento de Quımica Organica y Quımica Fısica Area de Quımica Fısica , Facultad de Ciencias, UniÕersidad de´ ´ ´ ´ ´ ´

Zaragoza, Ciudad UniÕersitaria srn Saragossa 50009, Spain

Received 9 September 1999; accepted 23 December 1999

Abstract

Densities and viscosities of butanoneq1-butanol, q2-methyl-1-propanol, q2-butanol, or q2-methyl-2-pro-panol were measured at several temperatures between 288.15 and 318.15 K. At each temperature, theexperimental viscosity data were correlated by means of the McAllister bi-parametric equation and according to

Ž U U .the model, the four pairs of activation parameters D H , DS have been calculated. By using our previousj jŽ E .thermodynamic measurements VLE, H , we have tested the Wei and Rowley non-parametric model, at

Ts298.15 K, obtaining average absolute deviations which are comparable to those calculated for thebi-parametric model. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Experiments; Data; Excess volume; Viscosity; Alcohol; Ketone

1. Introduction

w xIn recent publications 1–4 , we presented equilibrium properties for mixtures of butanol isomersand butanone. In this paper, we report viscosity data for these systems at four temperatures between288.15 and 318.15 K as well as density data at three temperatures. Excess volumes at 298.15 K for

w xthe same mixtures have been published previously 1–4 .

2. Experimental

Ž . Ž . ŽButanone purity 99.5 mol% , 1-butanol purity 99.8 mol% , 2-methyil-1-propanol purity 99.5. Ž .mol% , and 2-methyl-2-propanol purity 99.5 mol% were Aldrich products. All the chemicals were

) Corresponding author. Tel.: q34-976-761-195; fax: q34-976-761-202.Ž .E-mail address: perez.gracia@posta.unizar.es M. Gracia .

0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0378-3812 00 00300-9

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´268

Ž .of low water content, were stored over activated molecular sieve 3 A , and were used without furtherŽ . Ž .purification. Ubbelohde viscosimeters Schott of relatively long flow times 60–600 s were used to

minimize the kinetic energy corrections. At least three readings of the flow time with variations notexceeding "0.1 s were taken for each solution. The viscosities were calculated from the average flowtime, t, by means of the equation:

nsAty Brt , 1Ž . Ž .where n is the kinematic viscosity. A and B are viscosimeter constants which were determined by

w xusing values 5 for the water viscosity together with the corresponding flow times measured in thisstudy. The viscosimeter was held in a water bath whose temperature was controlled to within "10mK. Three different viscosimeters were used during the course of this investigation. The masses ofboth components were determined by weighing, and the uncertainties in the mole fractions wereestimated to be less than 0.0003. Flow time measurements were performed to "0.01 s with anelectrical stop watch . The uncertainty in the viscosity measurements is estimated to be "2=10y9

m2 sy1.ŽExcess volumes were calculated from density measurements made with a densimeter Anton Paar

. E 3 y1DMA 60rDMA 602 . The accuracy for V is 0.002 cm mol .

3. Results

Table 1 presents density and dynamic viscosity data of the pure compounds which are comparedwith values found in the literature. Excess volumes, dynamic viscosity and viscosity deviations werecalculated according to the following equations:

V E sx M 1rry1rr qx M 1rry1rr , 2Ž . Ž . Ž .1 1 1 2 2 2

hsnr , 3Ž .Dhshy x h qx h , 4Ž . Ž .1 1 2 2

where r and h are the density and the viscosity of the mixture, x the mole fraction, M the molarmass, and subscripts 1 and 2 indicate butanone and alcohol, respectively.

Tables 2 and 3 show the density and viscosity measurements at several temperatures together withexcess volumes and viscosity deviations which were fitted to a polynomial:

mi

Qsx x A x yx , 5Ž . Ž .Ý1 2 i 1 2is0

where Q denotes V E or Dh. Table 4 lists the A coefficients together with the standard deviationi

which is defined by:

2Ý Q yQŽ .exp cals Q s , 6Ž . Ž .

Nym

where N is the number of experimental points, and m is the number of parameters in the

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´ 269

Table 1Ž . Ž .Density r and dynamic viscosity h of the pure compounds

3 y1Ž . Ž . Ž .Compound T K r cm mol h mPa s

Experimental Literature Experimental Literaturea b2-Butanone 288.15 0.81001 0.8104 0.436 0.4477

c b298.15 0.79961 0.80002 0.392 0.4000c b303.15 0.79438 0.79483 0.372 0.3791

a b308.15 0.78918 0.7896 0.354 0.3600c b313.15 0.78375 0.7844 0.338 0.3424a b318.15 0.77837 0.7791 0.322 0.3261d e1-Butanol 288.15 0.81324 0.8134 3.354 3.3790f g298.15 0.80548 0.8060 2.560 2.5710d g308.15 0.79811 0.7983 1.991 2.000d g318.15 0.79020 0.7907 1.574 1.5786d g2-Methyl-1-propanol 288.15 0.80568 0.8055 4.792 4.6556f g298.15 0.79742 0.7978 3.410 3.3330d g308.15 0.79029 0.7897 2.489 2.445d g318.15 0.78220 0.7818 1.861 1.834d g2-Butanol 288.15 0.81044 0.8111 4.564 4.444f g298.15 0.80206 0.8026 3.068 2.998d g308.15 0.79398 0.7939 2.128 2.1019d g318.15 0.78500 0.7854 1.533 1.525f g2-Methyl-2-propanol 298.15 0.78049 0.7812 4.444 4.438f g303.15 0.77573 0.7757 3.361 3.390d g308.15 0.77020 0.7703 2.609 2.644f g313.15 0.76484 0.7649 2.077 2.1037d g318.15 0.75941 0.7594 1.690 1.705

a w xInterpolated from Ref. 6 .b w xInterpolated from Ref. 7 .c w xRef. 6 .d w xInterpolated from Ref. 8 .e w xRef. 9 .f w xRef. 8 .g w xRef. 10 .

corresponding analytical equation. In Fig. 1, the experimental results and the results of the fit areplotted at 318.15 K.

4. Discussion

For all systems, both V E and Dh increase with increasing temperature except for mixturescontaining tert-butanol where a minor and opposing variation is observed. At Ts318.15 K, Fig. 1

Ž .shows the experimental behaviour for the four mixtures butanoneqbutanol isomers . The excessvolume increases with the shielding around the OH group; however, for the viscosity, the branchingseems to be the most important effect.

Many semi-theoretical and empirical equations have been used to fit isothermal viscosity data ofmixtures. These equations can be distinguished as predictive or correlative and have been reviewed

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´270

Table 2Ž y3. E Ž 3 y1. � Ž . Ž .4Experimental densities r g cm and excess volumes V cm mol for butanone 1 qbutanol isomers 2 at several

temperaturesE E Ex r V x r V x r V2 2 2

( ) ( )Butanone 1 q1-butanol 2T s288.15 K0.0638 0.81023 y0.001 0.4038 0.81141 y0.009 0.7998 0.81269 y0.0090.1272 0.81046 y0.003 0.4968 0.81172 y0.010 0.8704 0.81290 y0.0080.2131 0.81076 y0.005 0.5990 0.81205 y0.010 0.9475 0.81312 y0.0050.3035 0.81107 y0.007 0.6980 0.81237 y0.010

T s308.15 K0.0638 0.78968 0.009 0.4987 0.79346 0.024 0.8442 0.79667 0.0080.1350 0.79028 0.014 0.5931 0.79431 0.023 0.8961 0.79716 0.0040.2037 0.79087 0.018 0.6787 0.79511 0.019 0.9184 0.79737 0.0030.3146 0.79183 0.022 0.6952 0.79526 0.018 0.9441 0.79760 0.0020.4003 0.79259 0.023 0.7846 0.79610 0.013

T s318.15 K0.0618 0.77903 0.009 0.4027 0.78282 0.042 0.7995 0.78767 0.0220.1376 0.77985 0.020 0.5016 0.78398 0.043 0.8898 0.78884 0.0080.2041 0.78058 0.027 0.5957 0.78512 0.040 0.9429 0.78951 0.0030.3050 0.78170 0.037 0.6984 0.78639 0.032

( ) ( )Butanone 1 q iso-butanol 2T s288.15 K0.0645 0.80956 0.018 0.4025 0.80771 0.058 0.7825 0.80624 0.0410.1372 0.80910 0.033 0.4903 0.80734 0.057 0.8654 0.80604 0.0230.2146 0.80866 0.044 0.5936 0.80693 0.053 0.9416 0.80580 0.0140.2974 0.80822 0.053 0.6921 0.80657 0.047

T s308.15 K0.0657 0.78900 0.030 0.4009 0.78873 0.106 0.7998 0.78948 0.0700.1241 0.78884 0.056 0.4987 0.78882 0.108 0.8839 0.78979 0.0440.2057 0.78875 0.077 0.5940 0.78895 0.105 0.9419 0.79004 0.0220.3175 0.78870 0.098 0.6950 0.78918 0.092

T s318.15 K0.0640 0.77832 0.036 0.4035 0.77885 0.130 0.7710 0.78051 0.1000.1462 0.77834 0.072 0.5002 0.77915 0.139 0.8840 0.78127 0.0600.2029 0.77839 0.092 0.5973 0.77957 0.134 0.9441 0.78175 0.0290.3039 0.77857 0.118 0.6976 0.78009 0.117

( ) ( )Butanone 1 q 2-butanol 2T s288.15 K0.0667 0.80930 0.081 0.4028 0.80746 0.304 0.7868 0.80825 0.2360.1518 0.80851 0.173 0.4982 0.80739 0.317 0.8701 0.80890 0.1670.2200 0.80813 0.219 0.5956 0.80749 0.311 0.9418 0.80965 0.0860.3032 0.80771 0.270 0.6930 0.80778 0.284

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´ 271

Ž .Table 2 continuedE E Ex r V x r V x r V2 2 2

( ) ( )Butanone 1 q 2-butanol 2T s308.15 K0.0645 0.78872 0.090 0.3966 0.78804 0.359 0.7958 0.79077 0.2640.1443 0.78826 0.189 0.4979 0.78837 0.378 0.8860 0.79198 0.1720.2072 0.78804 0.251 0.5973 0.78893 0.369 0.9446 0.79295 0.0900.2729 0.78793 0.301 0.6911 0.78967 0.335

T s318.15 K0.0620 0.77799 0.095 0.4012 0.77786 0.384 0.7995 0.78142 0.2730.1398 0.77768 0.195 0.4975 0.77839 0.398 0.8793 0.78269 0.1830.2032 0.77756 0.260 0.5947 0.77910 0.390 0.9419 0.78382 0.0960.2996 0.77762 0.331 0.6981 0.78014 0.347

( ) ( )Butanone 1 q tert-butanol 2T s303.15 K0.0787 0.79154 0.150 0.3748 0.78342 0.442 0.7861 0.77719 0.2880.1367 0.78965 0.239 0.4890 0.78110 0.467 0.8830 0.77646 0.1660.2143 0.78730 0.340 0.5839 0.77954 0.446 0.9430 0.77607 0.0830.2944 0.78529 0.399 0.6870 0.77821 0.381

T s308.15 K0.0651 0.78663 0.146 0.3985 0.77759 0.455 0.7868 0.77184 0.2770.1337 0.78443 0.246 0.4829 0.77592 0.465 0.8892 0.77103 0.1460.2041 0.78230 0.336 0.5907 0.77418 0.432 0.9385 0.77072 0.0740.3000 0.77980 0.414 0.6957 0.77284 0.359

T s313.15 K0.0690 0.78113 0.148 0.3901 0.77246 0.447 0.7871 0.76661 0.2620.1376 0.77894 0.249 0.4830 0.77065 0.456 0.8849 0.76581 0.1390.2020 0.77704 0.327 0.5904 0.76890 0.426 0.9394 0.76540 0.0670.2910 0.77467 0.407 0.6865 0.76766 0.360

T s318.15 K0.0712 0.77570 0.150 0.3995 0.76696 0.444 0.7903 0.76133 0.2400.1391 0.77357 0.246 0.4884 0.76528 0.445 0.8841 0.76051 0.1270.2046 0.77162 0.329 0.5966 0.76358 0.406 0.93696 0.76009 0.0590.2955 0.76926 0.404 0.6928 0.76234 0.339

w x w xand discussed extensively by Mehrotra et al. 11 . We have selected the McAllister 12 two-parameterequation based on Eyring’s equation, which takes into account interactions both like and unlikemolecules by a two-dimensional three-body model. The McAllister equation is given by:

M23 2 2 3lnnsx lnn q2 x x lnn q2 x x lnn qx lnn y ln x qx1 1 1 2 12 1 2 21 2 2 1 2ž /M1

2qM rM 1q2 M rM M2 1 2 1 22 2 3q3 x x ln q3 x x ln qx ln , 7Ž .1 2 1 2 2ž / ž / ž /3 3 M1

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´272

Table 3Ž . Ž . � Ž . Ž .4Absolute viscosities h mPa s and viscosity deviations Dh mPa s for butanone 1 qbutanol isomers 2 at different

temperatures

x T s288.15 K T s298.15 K T s308.15 K T s318.15 K2

h Dh h Dh h Dh h Dh

( ) ( )Butanone 1 q1-butanol 20.0987 0.480 y0.244 0.428 y0.178 0.385 y0.130 0.349 y0.0970.1988 0.537 y0.479 0.476 y0.347 0.425 y0.254 0.382 y0.1890.3004 0.613 y0.700 0.538 y0.506 0.476 y0.370 0.425 y0.2730.3991 0.710 y0.891 0.616 y0.641 0.540 y0.467 0.478 y0.3440.4973 0.842 y1.045 0.722 y0.749 0.626 y0.542 0.547 y0.3980.5972 1.021 y1.158 0.861 y0.825 0.737 y0.595 0.636 y0.4340.6979 1.279 y1.194 1.060 y0.845 0.891 y0.605 0.758 y0.4380.7995 1.677 y1.092 1.361 y0.765 1.121 y0.542 0.931 y0.3920.9028 2.293 y0.777 1.815 y0.535 1.458 y0.374 1.188 y0.265

( ) ( )Butanone 1 q iso-butanol 20.0854 0.473 y0.335 0.423 y0.227 0.380 y0.156 0.344 y0.1090.1986 0.539 y0.762 0.477 y0.514 0.426 y0.352 0.382 y0.2450.3001 0.613 y1.130 0.538 y0.759 0.476 y0.519 0.424 y0.3600.3904 0.708 y1.428 0.613 y0.957 0.535 y0.652 0.473 y0.4500.4974 0.861 y1.742 0.734 y1.159 0.630 y0.786 0.548 y0.5400.5941 1.061 y1.963 0.885 y1.300 0.748 y0.874 0.640 y0.5960.6983 1.389 y2.088 1.130 y1.370 0.933 y0.911 0.781 y0.6150.7991 1.903 y2.014 1.500 y1.303 1.206 y0.855 0.983 y0.5680.8965 2.790 y1.551 2.115 y0.982 1.637 y0.631 1.289 y0.412

( ) ( )Butanone 1 q 2-butanol 20.1018 0.474 y0.383 0.423 y0.241 0.380 y0.155 0.344 y0.1020.1991 0.520 y0.738 0.461 y0.464 0.415 y0.293 0.369 y0.1940.2984 0.584 y1.084 0.511 y0.679 0.452 y0.432 0.402 y0.2820.3970 0.670 y1.405 0.578 y0.876 0.505 y0.554 0.445 y0.3580.4966 0.790 y1.696 0.671 y1.050 0.576 y0.659 0.501 y0.4230.5968 0.968 y1.931 0.804 y1.185 0.677 y0.736 0.578 y0.4670.6985 1.247 y2.072 1.005 y1.256 0.824 y0.769 0.686 y0.4820.8007 1.718 y2.024 1.332 y1.203 1.053 y0.722 0.849 y0.4430.9003 2.585 y1.568 1.896 y0.905 1.426 y0.526 1.099 y0.313

T s298.15 K T s303.15 K T s308.15 K T s313.15 K T s318.15 K

( ) ( )Butanone 1 q tert-butanol 20.0985 0.423 y0.368 0.401 y0.266 0.380 y0.196 0.361 y0.148 0.343 y0.1130.1968 0.464 y0.725 0.438 y0.523 0.413 y0.385 0.391 y0.289 0.370 y0.2210.2962 0.520 y1.072 0.487 y0.770 0.457 y0.565 0.429 y0.423 0.405 y0.3230.3941 0.595 y1.393 0.553 y0.997 0.514 y0.728 0.480 y0.543 0.449 y0.4120.4949 0.705 y1.693 0.647 y1.204 0.596 y0.874 0.551 y0.647 0.511 y0.4880.5928 0.859 y1.935 0.779 y1.365 0.708 y0.983 0.647 y0.722 0.593 y0.5400.6950 1.116 y2.093 0.990 y1.459 0.884 y1.037 0.793 y0.753 0.716 y0.5570.8003 1.577 y2.058 1.357 y1.407 1.178 y0.981 1.031 y0.699 0.909 y0.5080.9037 2.474 y1.581 2.029 y1.044 1.687 y0.705 1.421 y0.488 0.212 y0.346

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´ 273

Table 4Ž E. Ž 3 y1. Ž . Ž .Coefficients, A , and standard deviations, s V cm mol and s Dh mPa s for Eq. 5i

EŽ .T K V Dh

EŽ . Ž .A A A A s V A A A A s Dh0 1 2 3 0 1 2 3

( ) ( )Butanone 1 q1-butanol 2288.15 y0.039 0.024 y0.016 – 0.001 y4.169 2.647 y2.271 1.673 0.014298.15 – – – – – y2.991 1.840 y1.473 1.024 0.008308.15 0.096 0.007 y0.011 0.073 0.0004 y2.170 1.281 y0.971 0.658 0.005318.15 0.174 0.015 y0.074 0.053 0.001 y1.593 0.906 y0.664 0.434 0.003

( ) ( )Butanone 1 q iso-butanol 2288.15 0.299 0.037 0.044 – 0.002 y6.906 5.065 y5.288 4.161 0.029298.15 – – – – – y4.610 3.270 y3.172 2.368 0.016308.15 0.436 0.036 0.050 – 0.002 y3.129 2.129 y1.902 1.356 0.009318.15 0.550 y0.001 0.049 – 0.002 y2.151 1.397 y1.158 0.786 0.005

( ) ( )Butanone 1 q 2-butanol 2288.15 1.269 y0.095 0.243 – 0.002 y6.715 5.060 y5.778 4.880 0.035298.15 – – – – – y4.170 3.013 y3.111 2.473 0.017308.15 1.513 y0.090 0.169 – 0.002 y2.624 1.804 y1.643 1.224 0.008318.15 1.598 y0.075 0.138 – 0.002 y1.687 1.083 y0.897 0.616 0.003

( ) ( )Butanone 1 q tert-butanol 2298.15 – – – – – y6.718 5.176 y6.082 5.178 0.039303.15 1.858 0.165 y0.040 0.215 0.003 y4.795 3.569 y3.757 2.978 0.021308.15 1.843 0.260 y0.011 0.363 0.005 y3.490 2.495 y2.349 1.719 0.011313.15 1.820 0.286 y0.097 0.398 0.003 y2.592 1.770 y1.497 1.008 0.006

Ž .where n is de kinematic viscosity of the pure compounds is1 for butanone, and 2 for alcohol , xi i

is the mole fraction, M the molar mass, n and n are fit parameters which denote viscosityi 12 21

contributions for 112 and 221 interactions, respectively, and which have been calculated for eachtemperature by a least squares method. For each system at several temperatures, the mixed viscosity

Ž .parameters are collected in Table 5 together with the average absolute deviations AAD .According to the Eyring’s equation, each contribution n to the total kinematic viscosity is relatedj

Ž U U.to the corresponding activation parameters D H , DS by the equation:j j

hN U UA yD S r R D H r RTj jn s e e , 8Ž .j Mj

where h is the Plank constant, N the Avogadro’s number, and js1, 2, 12, 21; for js12, 21 the MA j

are given by:

M s 2 M qM r3 and M s M q2 M r3. 9Ž . Ž . Ž .12 1 2 21 1 2

By assuming that the activation parameters are independent of temperature, we calculated the fourpairs of parameters corresponding to the four contributions to the kinematic viscosity which arecollected in Table 6.

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´274

Ž . Ž . Ž . � Ž . Ž .4 Ž . �Fig. 1. Excess volume a and viscosity deviation b at T s318 K for ` butanone 1 q1-butanol 2 , ^ butanoneŽ . Ž .4 Ž . � Ž . 4 Ž . � Ž . Ž .4 Ž .1 q iso-butanol 2 , I butanone 1 q2-butanol , e butanone 1 q tert-butanol 2 . — From analytical equations.

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´ 275

Table 5Ž .The mixed kinematic viscosity parameters and average absolute deviations AAD of experimental and calculated kinematic

viscosities for each system at several temperatures

Ž . Ž . Ž . Ž . Ž .T K Butanone 1 q Butanone 1 q Butanone 1 q Butanone 1 qŽ . Ž . Ž . Ž .1-butanol 2 iso-butanol 2 2-butanol 2 tert-butanol 2

n n n n n n n n21 12 21 12 21 12 21 12

288.15 1.098 0.759 0.980 0.799 0.809 0.780 – –298.15 0.955 0.673 0.865 0.704 0.732 0.679 0.712 0.720303.15 – – – – – – 0.710 0.660308.15 0.840 0.602 0.772 0.624 0.669 0.601 0.699 0.610313.15 – – – – – – 0.682 0.568318.15 0.743 0.547 0.695 0.559 0.618 0.530 0.659 0.533

Ž .AAD % 4.5 4.5 5.8 5.8 7.4 7.4 8.0 8.0

For alkanols, D H U and DSU increase from 1-butanol to tert-butanol. Positive values of DSU

2 2

suggest that order is destroyed on the activation process as bonds are broken between the associatedmolecules to make small units which can flow easier. According to the McAllister model, subscripts

Ž21 and 12 stand for interactions of three molecules: 221 two alkanol molecules and one butanone. Ž . U Umolecule and 112 two butanone molecules and one alkanol molecule , respectively. D H and DS21 21

decrease on going from 1-butanol to tert-butanol, whereas an opposing variation is observed for D H U

12

and DSU .12

A non-speculative interpretation of these results is a complicated problem as in these mixtures,strong solvent–solvent and hydroxy-group–solvent interactions come into play. On the other hand,

Table 6� 4Flow activation parameters for mixtures of butanoneqbutanol isomers according to the McAllister model

U U U U U U U UD H D H D H D H DS DS DS DS1 21 12 2 1 21 12 2

y1 y1 y1kJ mol J mol K

Ž . Ž .Butanone 1 q1-butanol 2 6. 7 9.9 8.4 18.5 y15 y10 y12 9Ž . Ž .Butanone 1 q iso-butanol 2 – 8.7 9.1 23.3 – y13 y10 23Ž . Ž .Butanone 1 q2-butanol 2 – 6.7 9.8 26.9 – y18 y7 36Ž . Ž .Butanone 1 q tert-butanol 2 – 3.1 11.9 37.1 – y30 y1 67

Table 7Ž .Average absolute deviations AAD for experimental and calculated dynamic viscosity according to the Wei and Rowley

Ž .model, at T s298.15 K, for s s0.00, s s0.25, and s fitted

Ž .System AAD %

s h s h s h

Ž . Ž .Butanone 1 q1-butanol 2 0.00 2.7 0.25 5.5 0.05 2.2Ž . Ž .Butanone 1 q iso-butanol 2 0.00 7.4 0.25 5.8 0.14 5.2Ž . Ž .Butanone 1 q2-butanol 2 0.00 11.4 0.25 5.2 0.25 5.2Ž . Ž .Butanone 1 q tert-butanol 2 0.00 21.0 0.25 10.7 0.45 8.0

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´276

Ž . � Ž . Ž .4 Ž . � Ž . Ž .4 Ž .Fig. 2. Dynamic viscosity at T s298.15K of a butanone 1 q1-butanol 2 , b butanone 1 q iso-butanol 2 , c� Ž . 4 Ž . � Ž . Ž .4 Ž . Ž .butanone 1 q2-butanol , d butanone 1 q tert-butanol 2 . ` Experimental, from the NRTL model: PPP with

Ž . Ž . Ž . Ž .s s0.00, — with s s0.25 predictive , –P– with s fitted .

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´ 277

Ž .Fig. 2 continued .

physical and thermodynamics properties reveal that the effect of the hydrogen bonding in butanolisomers depends on the shielding around the hydroxyl group. This effect is evident for V E as can be

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´278

seen in Fig. 1. For mixtures containing tert-butanol, it is remarkable that the D H U and DSU values21 21

are of the same order or even lower than those observed for non-associated systems.w xWei and Rowley 13,14 proposed a local composition model for multicomponent non-electrolyte

Ž Eliquid mixture viscosity, which requires only binary equilibrium thermodynamic information H ,E.G in addition to pure component data. No mixture viscosities and no adjustable parameters are

required. The basic equations of the model are given by:

hsexp j rV , 10Ž . Ž .

0 0 Ejs f j q f f G j yj f G ys H rRT , 11Ž .Ý Ý Ý Ýž /i i i j ji ji j l liž /i i i l

j sj s fUf

Uj 0 f

Uf

U , 12Ž .Ž .Ž .Ý Ýji i j i ii i j j ji j

Ž .where for i, j i/ j pair of interactions:

G sexp ya A rRT , 13Ž .Ž .ji ji

y1 y1U U U Uf s 1qG f s 1qf G rf , 14Ž .Ž . Ž .j ji ii j ji i

1r2 0 0G s V rV G rG exp j yj r2 , 15Ž .Ž . Ž . ž /ji i j i j ji i j

and j 0 denotes the pure component i value:i

j 0 s ln h V . 16Ž . Ž .i i i

The same notation as in the original paper is used. a , A , and A stand for the binary NRTLi j ji

parameters. In this work, these parameters have been calculated from our vapor pressure data, and H E

w xvalues have been taken from our experimental results 1–4 . f represents volume fraction, V molarvolume, and ss0.25, the same value as in the original paper to test the validity of the model as anon-parametric predictive method. In Table 7, average absolute deviations at 298.15 K for three

Ž E . Ž . Ž .s-values — ss0.00 no H contribution , ss0.25 predictive , and s fitted — are collectedand the corresponding dynamic viscosity is plotted in Fig. 2. For these systems, h is well-described

Ž .by the predictive model ss0.25 . The agreement with the experimental results is comparable to thatŽ .obtained with s fitted mono-parametric or with McAllister bi-parametric equation. In all cases, for

mixtures containing tert-butanol, the AAD is somewhat worse. By taking into account the strongŽ .interactions in these mixtures, we can conclude that the NRTL model predictive gives an adequate

representation of these systems.

List of symbolsA capillary viscosimeter constantA coefficients of analytical equationi

A NRTL parametersi j

AAD average absolute deviationB Hagenbach–Couette error correction factorG NRTL nonrandomness factori j

h Plank constant

( )S. Martınez et al.rFluid Phase Equilibria 168 2000 267–279´ 279

H E excess enthalpyD H U activation enthalpyj

M molar massi

N Avogadro’s numberA

R gas constantDSU activation entropyj

t timeT absolute temperatureV molar volumeV E excess volumex mole fraction of the i componenti

Greeka nonrandomness parameterG ratio defined by Eq. 15i j

h dynamic viscosityn kinematic viscosityn viscosity contributions in the McAllister modeli j

r density of the mixtureŽ .j ln hV

s free energy mixing parameterf local volume fraction of j around component iji

References

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