ELSEVIER Fluid Phase Equilibria 141 (1997)207-22(/

Water + ethanol + 2-methoxy-2-methylbutane: Properties of mixing at 298.15 K and isobaric vapour-liquid equilibria at 101.32 kPa

Alberto Arce *, Jos6 Martfnez-Ageitos, Josd Mendoza, Ana Soto

Chemical Engineering Department, Unicersitv of Santiago de Compostela. E-15706 Santia~,,o Spain

Received 20 March 1997; accepted 20 May 1997

Abstract

Excess molar volumes (V E) and deviations in molar refraction (A R) and isentropic compressibility (A K~) upon mixing were determined for homogeneous mixtures of water + ethanol + 2-methoxy-2-methylbutane at 298.15 K and atmospheric pressure. These data were satisfactorily correlated by the Redlich-Kister polynomial. For the same mixtures, vapour-liquid equilibrium (VLE) data at 101.32 kPa were determined using a distillation apparatus recycling both liquid and vapour phases. The Wisniak-L-W and McDermott-Ellis tests confirmed these VLE data to be thermodynamically consistent, and they were satisfactorily correlated using the NRTL equation (with c~ = 0.3), and satisfactorily predicted using the UNIFAC-Lyngby model to estimate the liquid-phase activity coefficients. Published by Elsevier Science B.V.

Kevwords: Mixing properties: Vapour-liquid equilibria: Water; Ethanol: 2-methoxy-2-methylbutane

1. Introduction

The growing importance of oxygenated compounds as components of lead-free gasoline has spurred research into the physical properties and vapour-liquid equilibria of mixtures containing organics such as ethers and alcohols. Nonetheless, because of the large experimental effort involved in determining these data for ternary mixtures and above, there is still a paucity of data for snch systems. Here, for homogeneous mixtures of water + ethanol + 2-methoxy-2-methylbutane (TAME), we report vapour-liquid equilibrium (VLE) data at 101.32 kPa and excess molar w)lumes (V K) and deviations in molar refraction (AR) and isentropic compressibility (A K~) upon mixing at 298.15 K. As far as we are aware, these data are not available in the literature, though liquid-liquid equilibrium data for this system have been published [1].

Corresponding author. E-mail: eqaaarce@uscmail.usc.es.

0378-3812/97/$17.00 Published by Elsevier Science B.V. Pll S07,78-3812(97)00161-1

208 A. A rce et al. / Fluid Phase Equilibria 141 (1997) 207-220

The properties of mixing (V, R and t%) were calculated from the speeds of sound through the mixtures (u) and their densities ( p ) and refractive indices (nD). The VLE data were determined using a distillation apparatus recycling both liquid and vapour phases, calculating the composition of the liquid phase of the ternary mixtures from its density and refractive index. The thermodynamic consistency of the VLE data was established using the L-W test of Wisniak [2] and the McDermott- Ellis test [3,4]. The experimental VLE data were correlated using the Wilson [5], NRTL [6] and UNIQUAC equations [7], and were compared with the predictions of the ASOG-KT [8,9], UNIFAC [ 10] UNIFAC-Dortmund [ 11,12] and UNIFAC-Lyngby [ 13] group contribution methods.

2. Experimental section

2.1. Materials

Water was purified using a Milli-Q Plus system. Ethanol was supplied by Merck with nominal purity > 99.5 mass%, and 2-methoxy-2-methylbutane (TAME) by Fluka Chemika with nominal purity > 98.9 mass%. The water contents of the ethanol and TAME were 0.08 and 0.02 mass%, respectively, as determined in a Metrohm 737 KF Coulometer. The purities of all chemicals were confirmed by chromatography; none was subjected to further purification. For all the chemicals used, Table 1 lists the measured densities and refractive indices at 298.15 K, and the boiling points at 101.32 kPa, together with published values for these parameters.

2.2. Apparatus and procedure

The physical properties were determined for mixtures prepared by weight using a Mettler AE 240 balance that measured to within + 0.00001 g. Densities and speeds of sound were measured to within +0.00001 g cm -3 and + 1 m s -2, respectively, in an Anton Paar DSA-48 densimeter and sound analyzer calibrated with air and water, and refractive indices were measured to within _+ 0.0001 with an ATAGO RX-1000 refractometer. A Hetotherm ultrathermostat was used to maintain the tempera- ture at 298.15 +_ 0.02 K.

For determination of the VLE data, distillation was performed in a Labodest apparatus recycling both liquid and vapour phases (Fischer Labor und Verfahrenstechnik, Germany), which was equipped with a Fischer digital manometer and a Heraeus QuaT100 quartz thermometer that measured to within +0.01 kPa and +0.02 K respectively. Distillation was carried out under an inert atmosphere of

Table 1 Densit ies ( p ) , refractive indices (nD), and boi l ing points (Tb) of the pure componen ts

Componen t p (g cm - 3 ) (298.15 K) n D (298.15 K) T b (K) (101.325 kPa)

Exper imenta l Literature Exper imenta l Literature Exper imenta l Literature

Water - 0.99705 ~' 1.3324 1.33250 ~ 373.16 373.15 ~ Ethanol 0.7852 0.78493 a 1.3592 1.35941 ~ 351.44 351.443 a T A M E 0.7657 0.76577 h 1,3858 1.3858 b 359.33 359.39 c

~[14]; b[15]; c[16].

A. A rce et a l . / Fluid Phase Equilibria 141 (19971 207-220 209

argon, which was fed into the still at a constant pressure of 101.325 kPa. Liquid-phase and vapour-phase compositions were determined by densimetry and refractometry, making reference to the experimental data for the composition dependence of the densities and refractive indices of the system. For test samples prepared by weighing, the mol fraction compositions derived from these measurements differed from the actual composition by < 0.002 mol traction.

3. Experimental results and data treatment

3.1. Properties of mixing

For the range of homogeneous mixtures of water + ethanol + TAME, Table 2 lists the measured densities, refractive indices and speeds of sound at 298.15 K, together with the excess molar volumes and the deviations in molar refraction and in isentropic compressibility derived from them. The excess molar volumes were calculated using the expression,

vE= v - x,V, I"

where V E is the molar volume of the mixture, and V i and x~ are the molar volume and tool traction, respectively, of component i. The molar refraction, R, was calculated from the molar volume and the refractive index data using the Lorentz-Lorenz equation,

, )

n b - 1 - _ ; _ - - _ _ _

R = nb + 2 V (2)

where n D is the refractive index of the mixture. The deviation between the molar refraction of the mixture and the tool fraction average of the values for the pure components (AR) was calculated as,

= R - x,R, (3) i

where R i is the molar refraction of component i. The isentropic compressibility of each mixture, K s, was calculated as

K~=u "p 1 (4)

and the deviation between the isentropic compressibility of the mixture and the volume fraction average of the values for the pure components (A K~) was obtained using the expression

aK = E05, , (5) i

where K~ is the isentropic compressibility of component i, and 05 is the volume fraction of component i in the mixture as given by,

xiVi ¢, y , xjVi (6)

J

where the subscript j refers to all the components in the mixture.

210 A. A rce et al. / Fluid Phase Equilibria 141 (1997) 207-220

Table 2 Densities (p ) , speeds of sound (u), isentropic compressibilities (Ks), refractive indices (riD), excess molar volumes (vE),

and deviations (A K~ and A R) for mixtures of water(l) + ethanol(2) + TAME(3) at 298.15 K

x I x 2 p ( g c m 3) u ( m s - i ) K~(TPa-] ) nD V E ( c m 3 m o l - i ) AK~(TPa- ] ) A R ( c m 3 m o l - i )

0.1041 0.8959 0.7981 0.0914 0.1220 0.7919 0.0831 0.7155 0.7883 0.0738 0.6353 0.7848 0.0602 0.5180 0.7804 0.0555 0.4777 0.7790 0.0362 0.3117 0.7739 0.0325 0.2795 0.7730

0.0170 0.1464 0.7696 0.0149 0.1283 0.7691

0.0115 0.0987 0.7683 0.2096 0.7904 0.8120 0.1894 0.7141 0.8035 0.1666 0.6283 0.7956

0.1501 0.5661 0.7909 0.1319 0.4972 0.7864 0.1053 0.3971 0.7809 0.0863 0.3256 0.7777 0.0668 0.2520 0.7748 0.0449 0.1692 0.7718 0.0240 0.0903 0.7690 0.3055 0.6945 0.8259

0.2763 0.6281 0.8140 0.2273 0.5167 0.7994

0.2147 0.4881 0.7964 0.1811 0.4116 0.7894 0.1631 0.3708 0.7862 0.1267 0.2880 0.7804 0.1112 0.2527 0.7782 0.3985 0.6015 0.8408

0.3575 0.5396 0.8232 0.3182 0.4803 0.8109 0.2781 0.4198 0.8011 0.2421 0.3655 0.7940 0.2064 0.3116 0.7880 0.4939 0.5061 0.8585 0.4663 0.4778 0.8445

0.4410 0.4519 0.8341 0.4083 0.4184 0.8231 0.3762 0.3855 0.8142 0.3381 0.3464 0.8054 0.6018 0.3982 0.8802 0.5670 0.3752 0.8597 0.5538 0.3664 0.8537 0.5197 0.3438 0.8401 0.4967 0.3286 0.8318

1181 898 1.3609 - 0.387 - 5 9 -0 .0 0 6 1170 923 1.3681 -0 .5 0 2 - 58 - 0.010 1162 939 1.3716 -0 .5 4 4 - 5 3 -0 .0 1 2

1154 956 1.3747 -0 .5 6 7 - 4 8 -0 .0 1 4 1145 977 1.3783 -0 .5 6 2 - 4 0 -0 .015 1143 983 1.3793 -0 .5 5 2 - 3 7 -0 .015

1133 1007 1.3825 -0 .4 6 2 - 2 7 -0 .012 1131 1011 1.3830 -0 .435 - 2 5 -0 .0 1 2 1124 1029 1.3846 - 0 . 2 8 0 - 14 -0 .007

1123 1032 1.3848 -0 .252 - 1 3 -0 .0 0 6 1121 1036 1.3851 - 0.203 - 10 - 0.005 1219 829 1.3621 - 0 . 6 7 4 - 108 -0 .0 1 2

1199 866 1.3682 -0 .741 - 9 6 -0 .0 1 4 1180 903 1.3730 - 0 . 7 5 4 - 8 0 -0 .015 1169 926 1.3756 - 0 . 7 3 6 - 6 9 -0 .0 1 6 1159 947 1.3779 -0 .7 0 2 - 5 9 -0 .015 1147 973 1.3805 - 0.637 - 4 6 -0 .0 1 4 1141 988 1.3820 -0 .581 - 3 8 -0 .013 1135 1003 1.3833 -0 .5 1 2 - 3 1 -0.011 1128 1018 1.3845 -0 .4 0 6 - 2 2 -0 .008 1122 1033 1.3853 -0 .2 5 9 - 1 2 -0 .005

1255 769 1.3627 -0 .8 6 8 - 1 4 5 -0 .017 1224 820 1.3691 -0 .9 3 8 - 126 -0 .021

188 886 1.3759 -0 .9 6 4 - 95 -0 .025

181 900 1.3771 - 0.954 - 89 -0 .025 165 933 1.3798 -0 .8 9 7 - 7 1 -0 .0 2 6 158 948 1.3808 -0 .8 4 9 - 6 3 -0 .025 146 976 1.3826 -0 .7 1 9 - 4 7 -0 .023 141 987 1.3832 -0 .6 5 2 - 4 1 -0.021

1292 713 1.3631 - 0.990 - 174 -0.021 1244 785 1.3701 -1 .053 - 145 - 0.030 1212 839 1.3746 - 1 . 0 6 6 - 1 2 0 -0 .033 1189 883 1.3779 -1 .037 - 9 8 -0 .031 1172 916 1.3801 - 0.977 - 80 -0 .0 2 6 1159 944 1.3818 - 0 . 8 9 0 - 6 5 - 0 . 0 2 0 1337 651 1.3629 - 1.058 - 2 0 0 -0 .023 1295 707 1.3677 - 1.107 - 178 -0 .0 2 6

1264 750 1.3710 -1 .1 3 5 - 1 5 9 -0 .0 2 9 1234 798 1.3743 - 1.147 - 137 -0 .032 1212 837 1.3767 -1 .137 - 1 1 8 -0 .0 3 4 1191 876 1.3789 -1 .097 - 9 8 -0 .035 1395 584 1.3621 - 1.085 - 2 2 4 -0 .0 2 4 1325 662 1.3675 -1 .1 2 2 - 1 9 2 - 0 . 0 3 0 1304 689 1.3692 -1 .1 4 7 -181 -0 .032 1261 748 1.3728 -1 .1 8 2 - 1 5 2 -0 .0 3 7 1240 782 1.3743 - 1.152 - 135 -0 .0 4 0

A. Arce et al. / Fluid Phase Equilibria 141 (19971 207-220 211

Table 2 (continued)

x I x 2 p ( g c m 3) u ( m s - J ) K~(TPa-i) rt D VE(cm3mol i) AK~(TPa-I) AR(cm3mol l)

0.7320 0.2680 0.9139 1493 491 1.3592 -1.016 -243 -0.021 0.7037 0.2576 0.8927 1405 567 1.3639 - 1.074 -216 --0,035 0.6809 0.2493 0.8791 1350 624 1.3668 - I . 116 -191 -0.045 0.7982 0.2018 0.9331 1554 444 1.3564 -0.890 -241 0.018 0.7732 0,1955 0.9166 1459 513 1.3598 -1,107 -224 -0.084

Fig. 1 shows the excess m o l a r - v o l u m e isolines ( sys tem compos i t ions in mol fractions, xi), and Fig.

2 the isolines for the devia t ion in isentropic compress ib i l i ty ( sys tem compos i t ions in vo lume fractions,

4~i). The binodal curve (dot ted line) marks the miscibi l i ty l imit for the three c o m p o n e n t s in the liquid

phase at 298.15 K [1].

Ethanol 0 l

...........

0 0.2 0.4 0,6 0.8 1 TAME Water

Fig. 1. Excess molar-volume isolines for the system water + ethanol + TAME at 298.15 K and atmospheric pressure (V ~ in cm 3 tool- ~; system compositions in mole fraction).

Ethanol

I 0.~/i/ . . / , * , , , t , t ,~0.2t~O 0 0.2 0.4 0.6 0.8 1

TAME Water

Fig. 2. Isolines for the deviation in isentropic compressibility for the system water+ethanol+TAME at 298.15 K and atmospheric pressure (A K~ in TPa- ' ; system compositions in volume fractionl.

212 A. Arce et al. / Fluid Phase Equilibria 141 (1997) 207-220

Table 3

Polynomial coefficients ( A , , ) for the V E_, A R - a n d 2~ K~-composition curves fitted to the data for the binary systems ~

Property A o A ] A ~ A 3

Water + ethanol V E ( c m 3 t o o l - i ) - 4 . 2 9 6 - 1 . 1 1 6 - 1 .235 -

A R ( c m 3 m o l - i ) - 0 . 0 9 2 - - -

2~ K~ ( T P a - i ) - 9 7 4 . 5 - 2 8 . 0 - 2 5 9 . 1 5 8 4 . 5

Ethanol + T A M E

V E ( c m 3 m o l - ]) - - 1 . 4 5 9 3 - 0 . 0 4 7 1 - - 0 . 2 8 2 1 - - 0 . 1 4 6 7

A R ( c m 3 m o l - i ) - 0 . 0 8 1 6 - - -

2~K~ ( T P a - l ) - 7 9 . 7 2 - 3 3 . 8 4 - 4 2 . 5 1 -

~ F o r A K ~ , system compositions were in volume fractions, q5 i.

3.1.1. Correlation The V E, A R and AK~ data were correlated with the composition data by means of the

Redlich-Kister polynomial [17], which for ternary mixtures has the form,

Q123 = 012 + 032 + Q3, + x~x2x3(A + B(x t - x 2 ) + C(x 3 - x 2 ) + D ( x ~ - xl) )2 + E(x , - x 2 + F ( x 3 - xz) 2 + G(x 3 -- XI) 2) (7)

where Q is V E or AR and x i is the tool fraction of component i, or Q is 2~K, and xi is the volume fraction of component i, and the terms Qij are calculated using the Redlich-Kister equation for binary systems

Qij = x ix jEA, , ( x i - xj)" (8) I1

The term Q31, corresponding to the immiscible binary mixture water + TAME, is taken as zero. The coefficients, A,,, for water + ethanol and ethanol + TAME [18] are listed in Table 3.

Eq. (7) was fitted to the V z_, A R- and A K~- composition data by least-squares regression, applying Fisher's F-test to establish the number of coefficients. For each property of the ternary system, these coefficients and their mean standard deviations are listed in Table 4.

3.2. Vapour-liquid equilibria

3.2.1. Results Isobaric VLE data were determined only for the homogeneous mixtures for which the properties of

mixing were measured. Table 5 lists the experimentally determined compositions of the liquid and

Table 4

Polynomial coefficients and standard deviations ( o - ) for the V z_, A R-and A Ks_composition surfaces fitted to the data for the ternary system water ( 1 ) + ethanol ( 2 ) + T A M E (3 ) ( f o r A Ks, system compositions were in volume fractions, ~b i)

Property A B C D E F G o-

V E ( c m 3 m o l - J ) - 1 2 . 6 0 0 - 1 2 . 1 4 9 - 1 1 . 1 7 7 0 . 9 7 2 - 1 3 . 4 8 3 - 1 2 . 1 6 0 - 1 . 5 0 0 0 . 0 2

A R ( c m 3 t o o l - i) - 0 . 4 5 0 - 1 . 0 7 4 - - 0 . 3 1 0 0 . 7 6 5 - - - 0 . 0 0 6

AK~ ( T P a - I ) - 1 1 1 4 . 7 4 0 5 . 9 - 1 2 8 . 4 - 5 3 4 . 3 - 3 9 8 3 . 2 - 2 3 1 . 4 - 7 6 5 4 . 0 2

A. Arce et al. / Fluid Phase Equilibria 141 (19971 207-220 213

Table 5 Isobaric vapour-l iquid equilibrium data for the system water ( 1 )+ ethanol component i in the liquid and vapour phases, respectively, at temperature

( 2 ) + TAME (3): mol fractions x~ and y~ of each T b and pressure 101.32 kPa

T b (K) x t x2 Yl 3'2

344.27 0.2697 0.3665 0.2571 0.3174 344.29 0.2045 0.3508 0.2473 0.3055 344.31 0.2155 0.3589 0.2471 0.3111 344.41 0.1482 0.2832 0.2344 0.2975 344.45 0.1973 0.3802 0.2291 0.3396 344.52 0.3268 0.3900 0.2667 0.3171 344.64 0.1344 0.3087 0.2139 0.3209 344.68 0.1340 0.3198 0.2067 0.3367 344.78 0.2490 0.4466 0.2318 0.3714 344.80 0.1767 0.4301 0.2056 0.3761 344.81 0.3680 0.4102 0.2681 0.3349 344.82 0.4428 0.3651 0.2785 0.3181 344.89 0.1432 0.4116 0.1822 0.3830 344.92 0.1236 0.3574 0.1853 0.3589 345.05 0.3216 0.4521 0.2484 0.3779 345.06 0.0982 0.2162 0.2108 0.2863 345.07 0.1175 0.3777 0.1680 0.3804 345.10 0.1868 0.4982 0.1935 0.4156 345.12 0.1433 0.4630 0.1695 0.4208 345.28 0.2702 0.4985 0.2286 0.4075 345.31 0.5325 0.3576 0.2828 0.3333 345.33 0.0896 0.1939 0.2058 0.2784 345.39 0.1138 0.4703 0.1467 0.4350 345.41 0.0969 0.4257 0.1413 0.4203 345.53 0.1439 0.5532 0.1558 0.4735 345.53 0.2134 0.5506 0.1948 0.4562 345.57 0.4923 0.3866 0.2795 0.3566 345.59 0.0849 0,4492 0.1267 0.4407 345.65 0.0754 0,4624 0.1167 0.4480 345.65 0.0748 0,4257 0.1233 0.4293 345.65 0.0760 0.2454 0.1661 0.3220 345.67 0.0716 0.3494 0.1355 0.3831 345.80 0.0650 0.3894 0.1187 0.4177 345.83 0.0690 0.5041 0.1039 0.4791 345.84 0.4386 0.4332 0.2717 0.3848 345.88 0.0878 0.5805 0.1132 0.5062 345.92 0.0578 0.4128 0.1053 0.4357 345.94 0.1457 0.6063 0.1506 0.51 (14 346.02 0.0582 0.2877 0.1298 0.3658 346.05 0.0489 0.4587 0.0883 0.4653 346.07 0.3832 0.4800 0.2598 (1.4134 346.14 0.0470 0.4765 0.0742 0.489 I 346.24 0.0417 0,5191 0.0595 0.5208 346.26 0.0433 0.5835 0.0559 0.5518 346.26 0.0482 0.3148 0.1093 0.384(1 346.30 0.0396 0.5315 0.0542 0.5332 346.34 0.3304 0.5297 0.2389 0.4599

214

Table 5 ( con t inued)

A. Arce et al. / Fluid Phase Equilibria 141 (1997) 207-220

T b (K) xj x 2 3'1 3'2

346.40 0.0367 0,3634 0.0834 0.4220 346.44 0.0256 0.4999 0.0387 0.5195 346.50 0.0230 0.5695 0.0311 0.5603 346.52 0.0226 0.5734 0.0301 0,5643 346.53 0.0637 0.6747 0.0703 0.5969 346,53 0,2200 0.6195 0.1901 0.5212 346.63 0.2669 0.5976 0.2131 0.5045 346.69 0,0443 0.2065 0.1320 0.3147 346.85 0.1567 0.6791 0.1501 0.5746 347.00 0.0161 0.7136 0.0170 0,6490 347.02 0.0837 0.7272 0.0898 0.6273 347.13 0,0505 0.7407 0.0531 0.6526 347.22 0.5361 0.4019 0.2854 0.4222 347,30 0.0532 0,1057 0.1708 0.2385 347.37 0.3616 0.5463 0.2487 0.4982 347,44 0.5891 0.3577 0.2910 0,4182 347.60 0,6388 0.3154 0.2966 0.4080 347,60 0.4186 0.5062 0,2680 0.4784 347.61 0.3090 0.5978 0.2283 0.5397 347.70 0.2019 0,6970 0.1779 0.6030 347,80 0.6769 0.2890 0.3028 0.4006 347,80 0.4852 0,4551 0.2842 0.4582 347.85 0.2566 0.6527 0.2077 0,5769 348.04 0.1425 0.7595 0,1345 0.6679 348.12 0.0672 0.8150 0.0687 0.7223 348,13 0.2074 0,7068 0,1804 0.6263 348.22 0.0228 0.8456 0.0230 0.7564 349.25 0.0674 0.8691 0,0684 0.8024 349,29 0.1097 0.8361 0.1058 0.7747 349.44 0.1033 0.8460 0.1013 0.7858 349.52 0.1626 0.7941 0.1507 0.7424 349.55 0.3306 0.6321 0.2446 0.6279 349.67 0.2160 0,7475 0.1851 0.7158 349,79 0,3973 0,5712 0.2725 0.5987 349,79 0.0342 0.9170 0.0378 0.8599 349.82 0.3642 0.6023 0.2605 0.6197 349.86 0.2648 0.7028 0.2166 0.6851 350.10 0.3016 0.6713 0.2364 0.6726 350.12 0.4372 0.5348 0.2907 0.5830 350.35 0.0150 0.9519 0.0179 0.9114 350.45 0.4707 0.5078 0.3037 0,5774 350.78 0.6472 0.3350 0.3377 0.5055 350.84 0.6072 0.3771 0.3380 0.5214 350,88 0.5091 0.4721 0,3173 0.5765 351.16 0.7230 0.2702 0.3562 0.4719 351.17 0.5750 0,4088 0.3352 0.5520 351.22 0.5450 0.4391 0,3319 0.5655 351.31 0,6812 0.3095 0.3529 0.4992

A. Arce et a l . / Fluid Phase Equilibria 141 (1997) 207-220 215

Ethanol

0 1

0 0.2 0.4 0.6 0.8 1

TAME Water

Fig. 3. Isotherms (K) for the VLE data of the system water + ethanol + TAME at 101.32 kPa.

v a p o u r phases , and the c o r r e s p o n d i n g e q u i l i b r i u m t e mpe ra tu r e s , and Fig. 3 s h o w s the i so the rms . The

t h e r m o d y n a m i c c o n s i s t e n c y o f the V L E da t a was d e m o n s t r a t e d us ing the L-W test o f [2], for w h i c h

the d e v i a t i o n ( D ) was 0 .57 (a va lue o f D < 3 c o n f i r m s ove ra l l cons i s t ency ) , and a lso the m o d i f i c a t i o n

o f the M c D e r m o t t - E l l i s [3] tes t b y W i s n i a k and T a m i r [4], for w h i c h D < Dm~ × for all the

e x p e r i m e n t a l po in ts , aga in c o n f i r m i n g cons i s t enc y .

Table 6 Antoine coefficients A, B, and C for Eq. (10)

Component A B C Ref.

Water 7.07262 - 1657.160 - 46.13 [ 19] Ethanol 7.16879 - 1552.601 - 50.731 [ 14] TAME 6.06782 - 1256.258 - 50.100 [ 16]

Table 7 Correlation of the VLE data for the system water ( l)+ethanol (2)+TAME (3): activity model parameters and mean deviations (m.d,) in equilibrium temperature and vapour-phase composition

Model Parameters (J mol - I ) m.d. T (K) m.d. Yl (m.f.) m.d. Y2 (m.f.)

UNIQUAC Aul2 = -909.27 Au21 = 2489.69 0.27 0.0072 0.0087 ,-~ul3 = 909.39 Au31 = 4389.85

~u23 = --901.23 Au32 = 3114.86 WILSON AA~2 = 4002.70 AA21 = 1493.69 0.64 0.0200 0.0223

AAI3 = 10455.39 A,~.31 = 10370.03 AA23 =4991.51 A / t t 3 2 = -810.40

NRTL (~ = 0.3) Agl2 = 4355.22 Ag21 = 26.38 0.14 0.0053 0.0070 A g l 3 = 14082.25 Ag31 = 5103.72

Ag23 = 1678.68 Ag32 = 1781.27

216 A. Arce et al. / Fluid Phase Equilibria 141 (1997) 207-220

Ethanol

0 1

0 0.2 0.4 0.6 0.8 1

TAME Water

Fig. 4. Experimental VLE data ( ~ ) and the corresponding NRTL correlation ( - - []) for the ternary system water + ethanol + T A M E at 101.32 kPa.

3.2.2. Data treatment For vapour and liquid phases in equilibrium at pressure P and temperature T,

yidPiP = xiyiPSdpS exp[ ViL( P - Pis) ] ~ - (9)

where xi and y; are the mol fractions of component i in the liquid and vapour phases respectively, "y~ is its activity coefficient, and p S is its saturated vapour pressure (in kPa) as calculated from Antoine's equation

B log Pi s (kPa) = A + (10)

T(K) + C

using the coefficients A, B and C shown in Table 6. The molar volume of component i in the liquid phase, V,. L, was calculated using the equation of Yen and Woods [20], and its coefficients of fugacity and fugacity at saturation, ~b~ and ~b/s respectively, were calculated from the second virial coefficient by the method of Hayden and O'Connell [21].

3.2.3. Correlation For correlation of the VLE data, the activity coefficients, y~, were calculated using the Wilson

equation, the NRTL equation (varying the non-randomness parameter, a , and selecting the value

Table 8 Prediction of the VLE data for the system water ( l )+e thanoi ( 2 ) + T A M E (3): root mean square (rms) deviations in equilibrium temperature and vapour-phase composition

Method rms Yl (m.fl) rms Y2 (m.f.) rms Y3 ( m . f . ) r m s T (K)

ASOG-KT 0.0525 0.0527 0.0251 2.88 UNIFAC 0.0567 0.0606 0.0676 3.14 UNIFAC-Dortmund 0.0201 0.0238 0.0249 1.10 UNIFAC-Lyngby 0.0073 0.0152 0.0140 0.62

A. A rce et al. / Fluid Phase Equilibria 141 (1997) 207-220 217

Ethanol

0 I

0 0.2 0.4 0.6 0.8 q

T A M E Water

Fig. 5. Comparison of the experimental ( ~ ) and UNIFAC-Lyngby predicted (--[]) VLE data for the ternary system water + ethanol + TAME at 101.32 kPa.

affording the best correlation), and the UNIQUAC equation (calculating the structural parameters, r and q, by group contribution methods). The program used in the correlation employs least-squares regression (Simplex method) and minimizes the objective function

F= E z, f (ll) i

For each activity coefficient model, Table 7 lists the binary interaction parameters obtained, and the mean deviations (m.d.) in temperature and vapour phase composition; and Fig. 4 compares the NRTL correlation ( a = 0.3) with the experimental temperature-composition data (for clarity's sake, a reduced number of data points are shown).

3.2.4. Prediction The VLE data were predicted using the ASOG-KT, UNIFAC (employing the structural and

group-interaction parameters recommended by Gmehling et al. [22]), UNIFAC-Dortmund and UNIFAC-Lyngby group contribution methods to calculate the liquid phase activity coefficients. The root mean squared (rms) deviations between the experimental VLE data and those predicted by each model are listed in Table 8. Fig. 5 compares the prediction of the UNIFAC-Lyngby model with the experimental VLE data (for clarity's sake, a reduced number of data points are shown).

4. Conclusions

Molar volumes, molar refractions and isentropic compressibilities were evaluated for homogeneous mixtures of water + ethanol + TAME from measurements of their density and refractive index and the speed of sound through them. The effects of mixing on these properties were determined. Excess volumes were negative and relatively large (minimum, - 1.2 cm 3 tool- 1), and should be considered in the design and operation of processes using this ternary system. Deviations in molar refraction were negative but relatively small, with absolute values < 0.1 cm 3 mol- ~, whereas deviations in isentropic

218 A. Arce et al. / Fluid Phase Equilibria 141 (1997) 207-220

compressibility were negative and large, reaching - 2 4 3 TPa-J for mixtures containing little TAME. In all cases, these data were satisfactorily correlated with the composition data by the Redlich-Kister polynomial.

Vapour-liquid equilibrium (VLE) data for the range of homogeneous mixtures of this ternary system were determined, making reference to the density and refractive index data obtained above in order to estimate the phase compositions. The Wisniak-L-W and McDermott-Ellis tests both confirmed these VLE data to be thermodynamically consistent. Figs. 3-5 suggest that the system forms a ternary azeotrope in the immiscibility region.

The VLE data were satisfactorily correlated using the NRTL activity model with the non-random- ness parameter, ce, set to 0.3, and to a lesser extent using the UNIQUAC activity model. By contrast, large deviations in temperature and composition were obtained for correlation using the Wilson equation.

The best predictions of the experimental data were afforded using the UNIFAC-Lyngby method to estimate the liquid-phase activity coefficients.

5. List of symbols

A A , B , C A , B , C , D , E m.d. m.f. F/D

P q r

rms R T b/

V x

Y

Greek letters

o[

Y Ag Au AA K

P o"

Coefficient in Redlich-Kister (Eq. (8)) for binary systems Antoine Coefficients (Eq. (10)) Coefficients in Redlich-Kister (Eq. (7)) for ternary systems mean deviation E~= l]calc. - exp.I/N, where N = number of data mol fraction refractive index pressure UNIQUAC area parameter UNIQUAC volume parameter root mean squared deviation molar refraction or gas constant temperature speed of sound molar volume mol fraction in the liquid phase mol fraction in the vapour phase

NRTL non-randomness parameter fugacity coefficient activity coefficient NRTL binary interaction parameter UNIQUAC binary interaction parameter Wilson binary interaction parameter compressibility density standard deviation

A. Arce et al. / Fluid Phase Equilibria 141 (1997) 207-220 219

S u p e r s c r i p t s

E excess n coef f ic ien t n u m b e r

S saturat ion

S u b s c r i p t s

b boi l ing

calc. ca lcula ted value

exp. exper imenta l va lue

i, j c o m p o n e n t

n coeff ic ient n u m b e r

s isentropic

Acknowledgements

This w o r k was part ly f inanced by the D G I C Y T (Spain) under Project PB94-0658 , and the Xun ta de

Gal ic ia (Spain) under Project X U G A 20902B94 .

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