Vapour-liquid equilibria. X. The ternary system cyclohexane-methanol-acetone at 293.15 and 303.15 K

mE

EIllllll

ELSEVIER

Fluid Phase Equilibria 126 (1996) 71-92

Vapour-liquid equilibria. X. The ternary system cyclohexane-methanol-acetone at 293.15 and 303.15 K P. Oracz, M. G6ral, G. Wilczek-Vera 1, S. Warycha Warsaw University, Department of Chemistry, Pasteura 1, 02-093 Warsaw, Poland Received 16 March 1996; accepted 14 May 1996

Abstract Total vapour pressure measurements made by the modified static method for the ternary system cyclohexane-methanol-acetone and all the constituent binary systems at 293.15 and 303.15 K are presented. The alcohol high-dilution region of the cyclohexane-methanol system has been thoroughly studied. Different expressions for G E suitable for correlation of these data are tested. The prediction of ternary VLE from the constituent binaries is studied. The accuracy of the prediction of H E from two (P,x) isotherms is studied for the binary systems. The possibility of predicting the ternary H E from VLE isotherms is also studied. Our results are compared with literature data. Keywords: Experiments; Data VLE; Binary system; Ternary system; Correlation; Cyclohexane; Methanol; Acetone

1. Introduction The cyclohexane-methanol-acetone system at 313.15 K was investigated in our laboratory (Oracz et al., 1995) as part of our project on measurements, correlation and prediction of the ternary VLE systems of non-electrolytes. In this paper we report the results of total vapour pressure measurements at 293.15 and 303.15 K for the ternary system and the constituent binary systems.

2. Materials The chemicals used were of the highest purity available from the suppliers. Acetone (analytical reagent grade, POCh) was purified as a sodium iodide addition compound, in accordance with the

Present address: Otto Maass Chemistry Bldg., R.300, Department of Chemistry, McGill University, 801 Sherbrooke St. W., Montreal, P.Q., H3A 2K6, Canada. 0378-3812/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0378-381 2(96)03126-3

72

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

Table 1 Vapour pressures P and second virial coefficients /3a~ of the pure substances used Compound

P(293.15 K)/kPa

-/3aa(293.15 K ) /

P(303.15 K)/kPa

-/3~(303.15 K ) /

This work

Literature

(dm 3 mol- l)

This work

Literature

(dm 3 mol- l)

Acetone

24.647

24.729 + 0.023 a 24.720 b

2.323 c

37.977

1.906 c

Methanol

13.004

2.339 d

21.913

Cyclohexane

10.336

12.995+0.012 a 13.021 b 10.336__+0.005a 10.338 b

1.905 c

16.229

38.008__+0.012a 38.009 + 0.023 a 38.000 b 21.860+0.012 a 21.887 b 16.229+0.005 a 16.234 b

1.833 d 1.712 c

Calculated according to Boublik et al. (1973). b Calculated according to Dykyj and Repa~ (1979) and Dykyj et al. (1984). c Calculated according to Dymond et al. (1992) with parameters fitted to the recommended data of Dymond and Smith (1980). d Calculated with the Tsonopoulos parameters fitted to the recommended data of Dymond (1985). (Note: molar liquid volumes were calculated according to Yen and Woods (1966).) a

recommendations o f Vogel (1961). The product obtained was then rectified on an efficient column and dried by 3 A molecular sieves. It is very important to use neither basic nor acidic dehydrated reagents due to formation o f the enol f o r m of acetone. Methanol (analytical reagent grade, POCh) was fractionated on an efficient column having 80 theoretical plates and stored o v e r 3 A sieves. Cyclohexane (analytical reagent grade, POCh) was crystallized three times, fractionated on an 80 TP column and stored over 4 A sieves. Impurities were determined chromatographically. W a t e r content was checked using Fischer's reagent and was on the limit of detectability. All the substances had a purity of not less than 99.95 mol%. Table 1 gives the v a p o u r pressures of the pure substances, measured both in our laboratory and reported in the literature, along with the second virial coefficients.

3. Method The vapour pressures o f the mixtures were determined by a modified static method. T h e apparatus and experimental procedure have been described previously (Janaszewski et al., 1982). During our measurements, the temperature was constant to within 0.004 K and was controlled up to 0.001 K; the absolute deviation is estimated to be equal to + 0 . 0 2 K (ITS-90). The cathetometer readings contribute less than 0.004 kPa to the error o f a single pressure measurement. This is a m a j o r part o f the error in pressure if both errors in temperature and pressure are treated separately. For the ternary system, the errors in the mole fractions were not higher than 0.0005. For the binary system c y c l o h e x a n e - m e t h a n o l , the errors in the m o l e fractions in the concentration range 0 . 1 - 0 . 9 were < 0.0005. In the high dilution regions, the errors were as follows: for the mole fractions < 0.1, the errors were not > 0.0002; for the m o l e fractions < 0.05, the errors were not > 0.0001; and for the mole fractions < 0.001; the errors were not > 0.00005. The t e m a r y samples were prepared from mixtures o f acetone with methanol, to which cyclohexane was added.

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

73

4. Results and discussion

The results of total vapour pressure measurements are given in Table 2 for binary mixtures and in Table 3a and b for ternary mixtures. The methanol high-dilution region of the system cyclohexanemethanol was studied thoroughly. We performed two independent series of measurements in the methanol concentration range 0-0.02 at 293.15 K and three independent series at 303.15 K. The results of the vapour pressure measurements presented in Fig. 1 (293.15 K) and Fig. 2 (303.15 K) show excellent internal agreement. The binary systems were correlated by various equations such as: Redlich and Kister (1948), Van Laar extended by Van Ness (1964), Myers and Scott (1963), Marsh (1977), SSF (Rogalski and Malanowski, 1977), Wilson (1964), the 3-parameter Wilson (Novak et al., 1974), Wilson as modified by Tsuboka and Katayama (1975), NRTL (Renon and Prausnitz, 1968), and UNIQUAC (Anderson and Prausnitz, 1978), Abbott and Van Ness (1975), Ortega et al. (1986). For the cyclohexane-methanol system, the Wilson and NRTL equations were also used with an additional term accounting for the association of methanol; the Kretschmer-Wiebe model was used (Kehiaian and Treszczanowicz, 1970). The coefficients of these equations were obtained by a modified Barker method (G6ral, 1977; G6ral and Janaszewski, 1977; Kolasifiska and Oracz, 1979). The values of the second virial coefficients for the pure substances were calculated using literature data (see Table 1) and for the mixtures they were calculated according to Tsonopoulos (1974). Table 4 shows the efficiency of these equations applied to our data. We assumed that the maximum number of the coefficients used should not exceed six. For the methanol-cyclohexane system, a phase split occurs. The recommended values of the solubility of methanol in both phases (according to Shaw et al., 1994) are 0.118 ___0.008 and 0.831 + 0.008 (at 293.15 K) and 0.167 + 0.008 and 0.795 ___0.008 (at 303.15 K). These values are not used as constraints in our calculations, but for comparison, the results of predictions with parameters fitted to LLE data are also included. The presented results demonstrate that the expressions for G E based both on the local composition concept and on polynomials do not provide a sufficiently accurate description of highly non-ideal vapour-liquid equilibrium and liquid-liquid equilibrium data for the system cyclohexane-methanol. This conclusion agrees with the literature (see, for example,Novak et al., 1987). Expressions for G E based on the local composition concept also give poor results for the cyclohexane-acetone system. This conclusion is particularly valid because process simulators usually rely on these equations. The moderately non-ideal system methanol-acetone can be described by any equation with approximately the same accuracy. For correlation of our binary measurements, we chose the rational equation (Marsh, 1977)

GE/RT=x.(1-x.)

Y'. Ki(2x a - 1)i/ 1 + i=0

Ki(2x a - 1) i-""+'

(1)

i=nn

where n < 6. Values of the K i coefficients in Eq. (1) together with their standard errors o-(Ki) and the correlation coefficients q~t for pairs (Kr,K t) are given in Table 5 for all the binary systems. The qrt values together with the standard errors o-(K i) allow, if necessary, the estimation of standard errors of all values which depend on K. The acetone-methanol system was measured at 293.15 K by Morton (1929) and Bekarek (1968) and at 303.15 K by Bekarek (1968). None of these data sets can be used as a reference. The data of

P. Oracz et al. / Fluid Phase Equilibria 126 (1996) 71-92

74

Table 2 Liquid mole fraction Xa, calculated vapour mole fractions Ya, total vapour pressures P and deviations d P for the binary systems at 293.15 and 303.15 K; ( d P = P - Pcalc and Ya calculated with Eq. (1)) Xa

Ya

P/kPa

dP /kPa

xa

Ya

P /kPa

dP /kPa

0.1404 0.5098 0.8257 0.8286 0.8506 0.8660 0.9002 0.9135 0.9390 0.9609 0.9811 1

0.5471 0.5436 0.5443 0.5446 0.5486 0.5529 0.5702 0.5817 0.6177 0.6760 0.7809 1

22.315 22.311 22.297 22.313 22.244 22.184 21.578 21.345 20.194 18.793 16.345 13.004

-

0.042 0.046 0.057 0.032 0.003 0.062 - 0.037 0.067 - 0.051 0.075 - 0.072

0.19870 0.19950 0.35270 0.79000 0.81960 0.84920 0.87190 0.92080 0.97348 0.97475 0.97642 0.97797 0.97917 0.98210 0.98413 0.98648 0.98839 0.99172 0.99440 0.99627 0.99751 0.96364 0.96479 0.96627 0.96759 0.96903 0.97028 0.97170 0.97283 0.97421 0.97544

0.56186 0.56189 0.56356 0.55911 0.56197 0.56789 0.57592 0.61 463 0.75825 0.76513 0.77464 0.78396 0.79153 0.81143 0.82653 0.84551 0.86229 0.89485 0.92463 0.94762 0.96400 0.71346 0.71801 0.72412 0.72980 0.73628 0.74213 0.74908 0.75484 0.76217 0.76899

36.154 36.200 36.177 36.160 36.145 36.020 35.605 33.924 28.356 28.103 27.782 27.467 27.216 26.630 26.179 25.494 25.153 24.290 23.541 22.998 22.629 30.084 29.834 29.608 29.371 29.236 28.912 28.684 28.474 28.211 27.980

-0.189 - 0.146 -0.250 - 0.245 -0.156 -0.044 - 0.112 - 0.061 0.012 -0.010 - 0.018 - 0.032 -0.042 - 0.016 -0.019 - 0.157 -0.036 - 0.043 - 0.056 -0.059 - 0.058 0.150 0.070 0.067 0.036 0.130 0.014 0.027 0.014 - 0.001 - 0.005

Methanol (a)+ cyclohexane (b) at 293.15 K 0 0.00007 0.00058 0.00152 0.00277 0.00402 0.00730 0.01225 0.02257 0.04035 0.05726 0.0870 0.0901

0 0.01175 0.08554 0.18283 0.26676 0.32198 0.40273 0.45551 0.49455 0.51696 0.52785 0.5391 0.5399

10.336 10.430 11.016 12.368 14.063 15.409 17.465 18.886 20.238 21.242 21.729 22.158 22.198

-

0.029 0.286 0.280 0.033 0.168 0.181 - 0.044 - 0.111 - 0.001 0.038 0.005 0.012

Methanol (a) + cyclohexane (b) at 303.15 K 0 0.00040 0.00110 0.00280 0.00500 0.01060 0.00005 0.00025 0.00072 0.00154 0.00261 0.00361 0.00519 0.00693 0.00964 0.01347 0.02178 0.03838 0.05749 0.07399 0.00570 0.00802 0.01059 0.01287 0.01595 0.01919 0.02154 0.02879 0.03551 0.04239 0.04916

0 0.04804 0.11686 0.23167 0.32040 0.42718 0.00642 0.03089 0.08161 0.15245 0.22143 0.26988 0.32613 0.36974 0.41527 0.45436 0.49578 0.52496 0.53786 0.54437 0.34051 0.39060 0.42705 0.44952 0.47093 0.48655 0.49502 0.51234 0.52191 0.52854 0.53333

16.229 16.623 17.675 20.281 23.285 27.928 16.309 16.559 17.283 18.724 20.592 22.194 24.433 26.250 28.163 29.886 31.921 33.792 34.814 35.330 24.946 27.070 28.602 29.591 30.575 31.351 31.801 32.867 33.551 34.043 34.444

- 0.423 -0.699 - 0.837 -0.585 -0.351 - 0.025 - 0.187 - 0.388 -0.426 - 0.257 - 0.040 0.346 0.506 0.438 0.212 -0.119 - 0.123 0.025 0.097 0.337 0.453 0.317 0.174 - 0.004 -0.131 -0.191 - 0.215 -0.160 -0.113 - 0.037

P. Oracz et al./ Fluid Phase Equilibria 126 (1996) 71-92

75

Table 2 (continued)

Xa

Ya

P/kPa

dP/kPa

Xa

Ya

P/kPa

dP/kPa

0.05677 0.06359 0.06916 0.07616 0.14160

0.53751 0.54056 0.54270 0.54507 0.55774

34.778 35.028 35.196 35.454 36.117

0.012 0.055 0.076 0.172 0.011

0.97662 0.97803 0.97901 1

0.77581 0.78433 0.79050 1

27.755 27.459 27.248 21.913

-0.007 -0.028 -0.043

0.000 0.023 0.037 0.023 0.033 0.016 0.038 0.099 0.138 0.090 0.180 0.342 a 0.068 0.035

0.2417 0.3051 0.4251 0.5055 0.5104 0.5848 0.6367 0.7010 0.7577 0.8045 0.8851 0.9419 1.0000

0.6462 0.6623 0.6854 0.6965 0.6971 0.7064 0.7139 0.7264 0.7428 0.7624 0.8175 0.8845 1.0000

25.745 26.464 27.256 27.600 27.603 27.832 27.946 28.059 28.072 28.014 27.499 26.045 24.647

0.036 0.041 0.058 0.043 0.055 0.018 0.006 0.020 0.025 0.056 0.098 0.395 0.000

0.0506 0.0578 0.0683 0.0778 0.0912 0.1030 0.1123 0.1761 0.2440 0.2998 0.4206 0.5104 0.5469 0.5744 0.6478 0.6999 0.7557 0.8184 0.8783 0.9410 1

0.4144 0.4387 0.4684 0.4905 0.5162 0.5347 0.5471 0.6028 0.6340 0.6508 0.6761 0.6919 0.6984 0.7035 0.7189 0.7323 0.7504 0.7786 0.8186 0.8864 1

26.587 27.744 29.059 30.120 31.407 32.439 33.184 36.638 38.691 39.837 41.269 41.930 42.155 42.294 42.618 42.755 42.800 42.640 42.065 40.669 37.977

- 0.064 0.072 0.050 0.033 - 0.016 - 0.009 0.014 - 0.024 - 0.048 0.018 0.017 0.006 0.012 0.004 0.009 - 0.002 - 0.007 0.002 - 0.009 - 0.019

0.5143 0.5689 0.6452

0.6614 0.6923 0.7351

22.818 23.259 23.793

0.004 - 0.002 - 0.000

Acetone (a) + cyclohexane (b) at 293.15 K 0.0000 0.0025 0.0051 0.0090 0.0141 0.0239 0.0302 0.0396 0.0470 0.05 44 0.0613 0.0644 0.1228 0.1855

0.0000 0.0444 0.0859 0.1406 0.2011 0.2917 0.3370 0.3915 0.4260 0.4549 0.4778 0.4870 0.5873 0.6273

10.336 10.816 11.295 11.958 12.816 14.315 15.159 16.332 17.179 18.044 18.652 19.477 22.903 24.785

-

-

-

Acetone (a) + cyclohexane (b) at 303.15 K 0 0.0007 0.0014 0.0019 0.0025 0.0030 0.0044 0.0049 0.0061 0.0079 0.0087 0.0121 0.0129 0.0159 0.0200 0.0203 0.0256 0.0309 0.0347 0.0371 0.0438 0.0462

0 0.0125 0.0246 0.0329 0.0428 0.0507 0.0722 0.0795 0.0965 0.1205 0.1306 0.1703 0.1789 0.2090 0.2455 0.2480 0.2880 0.3222 0.3438 0.3563 0.3875 0.3974

16.229 16.420 16.607 16.783 16.929 17.055 17.425 17.564 17.873 18.332 18.521 19.345 19.569 20.233 21.208 21.209 22.282 23.341 24.125 24.422 25.547 26.062

- 0.005 - 0.012 0.026 0.009 - 0.001 - 0.005 0.002 - 0.003 - 0.005 - 0.017 - 0.025 0.008 - 0.024 0.040 - 0.023 - 0.052 - 0.024 0.061 - 0.064 - 0.059 0.075

Acetone ( a ) + methanol (b) at 293.15 K 0 0.0306 0.0939

0 0.1075 0.2630

13.004 14.150 16.136

0.000 - 0.008

P. Oracz et al./ FluidPhase Equilibria 126 (1996) 71-92

76 Table 2 (continued) Xa

Ya

P/kPa

d P/kPa

xa

Ya

P/kPa

d P/kPa

0.1452 0.1954 0.2531 0.3203 0.4118 0.4563

0.3505 0.4167 0.4775 0.5350 0.5995 0.6272

17.472 18.561 19.624 20.653 21.809 22.266

0.007 0.002 0.001 - 0.006 0.005 - 0.007

0.7348 0.7793 0.8371 0.8792 0.9320 1

0.7874 0.8152 0.8545 0.8862 0.9309 1

24.289 24.481 24.667 24.745 24.771 24.647

0.001 0.002 0.003 - 0.002 - 0.004

0.5808 0.6322 0.7234 0.7805 0.8412 0.8795 0.9404 1

0.6806 0.7113 0.7676 0.8056 0.8497 0.8805 0.9356 1

36.673 37.157 37.824 38.121 38.320 38.361 38.276 37.977

0.015 0.012 0.002 0.004 0.000 0.004 0.009

Acetone (a)+ methanol (b) at 303.15 K 0 0.0339 0.0907 0.1561 0.1927 0.2471 0.3257 0.3974 0.4514

0 0.1051 0.2342 0.3396 0.3861 0.4443 0.5130 0.5657 0.6015

21.913 23.709 26.269 28.623 29.768 31.227 32.961 34.251 35.065

0.001 0.010 - 0.015 0.003 0.005 0.001 - 0.003 - 0.016

-

a Point not taken for parameters fitting.

Morton are thermodynamically inconsistent. The data o f Bekarek are also o f low quality (strict t h e r m o d y n a m i c consistency test cannot be performed), but nevertheless agree with our data within the quite reasonable error of 0.2 kPa (about 1% in pressure). The binary systems under consideration have been investigated by other authors, w h o have measured the V L E under isobaric or isothermal conditions as well as the m o l a r enthalpy o f mixing ( H E ) . Therefore it is possible to compare, simultaneously, various V L E and H E sets o f data. In the previous p a p e r (Oracz et al., 1995), we have presented different tests comparing our data for the m e t h a n o l - c y c l o h e x a n e system with literature data, including the G E / R T vs. 1 / T test, and comparison o f the limiting activity coefficients and the test o f the azeotropic points. For these tests, the above data at 293.15 and 313.15 K were also used. For the a c e t o n e - c y c l o h e x a n e and m e t h a n o l - a c e t o n e systems, comparison o f our data at 313.15 K with literature data has been presented previously using the G E / R T vs. 1 / T test (G6ral et al., 1992; G6ral et al., 1985). To c o m p a r e our data at 293.15 and 303.15 K with the literature, we use the a b o v e test. For this purpose, each V L E data set under comparison m a y be represented by the value o f G E / R T at, for example, a methanol mole fraction equal to 0.5, henceforth denoted Q0.5. The Q0.5 values calculated from various data sets were plotted against 1 / T . From the G i b b s - H e l m h o l t z equation, the slope o f the resulting line should be equal to HoEs/R. Resulting plots for the a c e t o n e - c y c l o h e x a n e and a c e t o n e - m e t h a n o l systems, not presented here, show an excellent consistency between our data at the three temperatures and published data, as well as their consistency with the chosen values o f H E. It is also possible to c o m p a r e our values for the azeotropic point with the literature V L E data. For the c y c l o h e x a n e - m e t h a n o l system, such a comparison, with included current data at 293.15 and 303.15 K, is presented in the p a p e r o f Oracz et al. (1995). For the m e t h a n o l - a c e t o n e system, the mole fraction o f methanol can be expressed as a function o f temperature using the p o l y n o m i a l Xaz = 0.75343 - 7.921 • 10 -3 • T + 1.9135 • 10 -5 • T 2, with standard e r r o r o r ( X a z ) = 0.006, in the tempera-

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

77

Table 3 a. Ternary system cyclohexane (a)-methanol(b)-acetone(c) at 293.15 K: experimental liquid mole fractions x a, x b and total pressure P; vapour mole fractions ya, Yb and deviations d P ( d P = P - Pc~lc) calculated with Eqs. (3) and (4) having five ternary parameters fitted to the data Xa

Xb

Ya

Yb

P/kPa

d P/kPa

0.8034 0.7457 0.7041 0.6454 0.5842 0.4615 0.3347 0.2500 0.2077 0.1880 0.1211 0.6275 0.5507 0.5126 0.4634 0.4182 0.3716 0.3150 0.2618 0.2196 0.1662 0.1205 0.0650 0.0314 0.4695 0.4355 0.3935 0.3568 0.3123 0.2774 0.2750 0.2470 0.2067 0.1716 0.1330 0.0927 0.0538 0.0250 0.3115 0.2814 0.2601 0.2279 0.2048 0.1668 0.1536 0.1254

0.0444 0.1131 0.1625 0.2324 0.3051 0.4511 0.6019 0.7026 0.7530 0.7764 0.8560 0.0621 0.1768 0.2338 0.3074 0.3749 0.'!,446 0.5292 0.6086 0.6717 0.7515 0.8199 0.9028 0.9531 0.0657 0.1334 0.2169 0.2900 0.3786 0.4480 0.4527 0.5085 0.5887 0.6585 0.7352 0.8154 0.8929 0.9502 0.0594 0.1505 0.2148 0.3119 0.3817 0.4963 0.5361 0.6214

0.3513 0.3553 0.3580 0.3631 0.3702 0.3896 0.4125 0.4255 0.4298 0.4308 0.4232 0.3231 0.3266 0.3303 0.3375 0.3464 0.3571 0.3711 0.3838 0.3924 0.3993 0.3969 0.3615 0.2792 0.3044 0.3059 0.3088 0.3136 0.3223 0.3306 0.3312 0.3384 0.3485 0.3558 0.3601 0.3546 0.3218 0.2394 0.2823 0.2829 0.2829 0.2852 0.2889 0.2969 0.2997 0.3047

0.1942 0.2830 0.3255 0.3674 0.3963 0.4328 0.4614 0.48 14 0.4931 0.4992 0.5300 0.1356 0.2452 0.2820 0.3178 0.3426 0.3636 0.3866 0.4088 0.4285 0.4584 0.4929 0.5689 0.6797 0.1017 0.1641 0.2230 0.2620 0.2982 0.3216 0.3231 0.3409 0.3676 0.3941 0.4298 0.4811 0.5645 0.6937 0.0721 0.1475 0.1902 0.2408 0.2697 0.3115 0.3261 0.3607

26.712 27.038 26.800 26.387 25.915 25.050 24.225 23.705 23.439 23.329 22.607 28.015 28.055 27.803 27.416 27.011 26.594 26.038 25.509 25.029 24.335 23.453 21.342 18.416 28.368 28.602 28.475 28.234 27.804 27.399 27.363 27.019 26.454 25.842 24.970 23.569 21.222 17.971 28.522 28.787 28.742 28.456 28.152 27.462 27.164 26.358

- 0.212 0.191 0.122 0.047 - 0.017 - 0.048 -0.102 - 0.128 - 0.115 - 0.076 0.015 - 0.074 0.028 0.010 0.019 0.014 0.013 - 0.036 - 0.057 - 0.072 - 0.024 0.023 0.073 - 0.006 - 0.172 - 0.033 - 0.003 0.034 0.029 - 0.005 - 0.014 - 0.027 - 0.029 - 0.012 0.048 0.087 0.093 0.003 - 0.157 - 0.027 0.021 0.049 0.055 0.018 0.010 0.002

P. Oracz et al./ Fluid Phase Equilibria 126 (1996) 71-92

78 Table 3 (continued)

Xa

Xb

Ya

Yb

P /kPa

d P /kPa

0.1050 0.0780 0.0571 0.0312 0.0167 0.1510 0.1389 0.1266 0.1146 0.1043 0.0897 0.0729 0.0650 0.0531 0.0410 0.0302 0.0169 0.0086

0.6831 0.7645 0.8274 0.9059 0.9495 0.0670 0.1424 0.2182 0.2923 0.3557 0.4458 0.5500 0.5985 0.6723 0.7467 0.8136 0.8951 0.9471

0.3061 0.3019 0.2889 0.2431 0.1799 0.2209 0.2169 0.2144 0.2148 0.2165 0.2198 0.2223 0.2218 0.2183 0.2092 0.1937 0.1545 0.1053

0.3909 0.4423 0.4979 0.6108 0.7249 0.0663 0.1267 0.1768 0.2167 0.2459 0.2833 0.3276 0.3509 0.3925 0.4464 0.5120 0.6344 0.7634

25.598 24.198 22.661 19.674 17.129 28.131 28.306 28.220 27.964 27.644 27.062 26.134 25.567 24.513 23.094 21.408 18.606 16.199

0.031 0.073 0.115 0.067 0.021 0.140 0.030 0.103 0.102 0.062 0.005 0.074 0.094 0.081 0.052 0.030 0.012 0.021

-

-

b. Ternary system cyclohexane(a)-methanol(b)-acetone(c) at 303.15 K: experimental liquid mole fractions x a, x b and total pressure P; vapour mole fractions Ya, Yb and deviations d P ( d P = P - Pc~c) calculated with Eqs. (3) and (4) having five ternary parameters fitted to the data 0.7528 0.6732 0.6416 0.5719 0.5158 0.4499 0.3880 0.3219 0.2603 0.2105 0.1316 0.0830 0.0383 0.6318 0.5805 0.5206 0.4680 0.4162 0.3699 0.3170 0.2607 0.2205 0.1677 0.1195 0.0679 0.0312 0.4714 0.4087

0.1047 0.1993 0.2369 0.3198 0.3865 0.4649 0.5385 0.6171 0.6904 0.7496 0.8435 0.9013 0.9544 0.0567 0.1332 0.2227 0.3013 0.3786 0.4477 0.5267 0.6107 0.6708 0.7496 0.8216 0.8987 0.9534 0.0539 0.1796

0.3602 0.3637 0.3658 0.3721 0.3787 0.3875 0.3963 0.4054 0.4125 0.4157 0.4076 0.3777 0.2884 0.3294 0.3313 0.3340 0.3390 0.3464 0.3544 0.3645 0.3748 0.3809 0.3849 0.3790 0.3428 0.2538 0.3083 0.3089

0.2939 0.3679 0.3880 0.4210 0.4402 0.4583 0.4729 0.4876 0.5017 0.5147 0.5470 0.5911 0.6942 0.1414 0.2243 0.2920 0.3339 0.3648 0.3874 0.4107 0.4354 0.4545 0.4839 0.5207 0.5916 0.7089 0.0946 0.2103

41.850 41.587 41.325 40.703 40.179 39.634 39.139 38.627 38.124 37.697 36.530 34.717 30.504 42.716 43.459 43.315 42.851 42.313 41.763 41.115 40.343 39.742 38.767 37.372 34.420 29.823 43.295 44.151

0.120 0.081 0.014 - 0.071 - 0.119 - 0.113 - 0.121 - 0.143 - 0.188 - 0.188 - 0.136 - 0.043 - 0.009 - 0.296 0.106 0.105 0.053 0.046 0.014 -0.016 - 0.071 - 0.075 - 0.045 - 0.013 0.037 0.038 - 0.242 0.050

P. Oracz et al./ Fluid Phase Equilibria 126 (1996) 71-92

79

Table 3 (continued) Xa

Xb

Ya

Yb

P/kPa

d P/kPa

0.3904 0.3502 0.3080 0.2535 0.2358 0.1913 0.1497 0.1139 0.0824 0.0469 0.0222 0.3098 0.2806 0.2613 0.2360 0.2077 0.1753 0.1662 0.1323 0.1053 0.0794 0.0577 0.0339 0.0143 0.1497 0.1 40 1 0.1269 0.1173 0.1049 0.0874 0.0815 0.0666 0.0533 0.0407 0.0296 0.0174 0.0074

0.2164 0.2971 0.3818 0.4911 0.5267 0.6160 0.6996 0.7713 0.8346 0.9059 0.9555 0.0674 0.1552 0.2134 0.2897 0.3747 0.4723 0.4998 0.6018 0.6830 0.7610 0.8262 0.8978 0.9569 0.0646 0.1249 0.2077 0.2668 0.3447 0.4542 0.4904 0.5840 0.6672 0.7458 0.8151 0.8913 0.9537

0.3094 0.3121 0.3176 0.3276 0.3312 0.3395 0.3443 0.3425 0.3305 0.2867 0.2030 0.2796 0.2774 0.2760 0.2759 0.2784 0.2837 0.2854 0.2907 0.2918 0.2865 0.2718 0.2309 0.1465 0.2102 0.2063 0.2027 0.2020 0.2035 0.2068 0.2075 0.2077 0.2036 0.1937 0.1769 0.1417 0.0837

0.2358 0.2815 0.3187 0.3584 0.3708 0.4034 0.4394 0.4786 0.5265 0.6163 0.7405 0.0848 0.1614 0.2026 0.2470 0.2866 0.3257 0.3365 0.3786 0.4191 0.4695 0.5276 0.6264 0.7768 0.0688 0.1217 0.1822 0.2178 0.2578 0.3074 0.3236 0.3688 0.4173 0.4761 0.5457 0.6579 0.8085

44.116 43.848 43.368 42.543 42.234 41.241 40.122 38.662 36.752 33.051 28.539 43.755 44.340 44.416 44.215 43.791 43.071 42.799 41.583 40.157 38.330 35.968 32.124 27.1 48 43.135 43.416 43.450 43.302 42.895 41.945 41.529 40.150 38.522 36.418 33.900 30.147 25.958

0.051 0.058 0.055 0.024 0.022 - 0.040 0.048 0.083 0.136 0.115 0.040 - 0.194 -0.011 0.063 0.078 0.094 0.086 0.063 0.040 0.024 0.156 0.142 0.111 - 0.005 - 0.142 - 0.051 0.027 0.063 0.042 - 0.068 - 0.105 - 0.191 - 0.150 - 0.069 - 0.023 - 0.006 - 0.011

ture r a n g e 2 8 3 - 4 3 3 K. F o r the c y c l o h e x a n e - a c e t o n e s y s t e m , e x p e r i m e n t a l V L E d a t a c o v e r the r a n g e 2 7 3 - 3 2 7 K. T h e c a l c u l a t e d m o l e f r a c t i o n s at the a z e o t r o p i c p o i n t e x h i b i t g r e a t scatter; the c o r r e s p o n d i n g e q u a t i o n e x p r e s s i n g the m o l e f r a c t i o n o f a c e t o n e at the a z e o t r o p i c p o i n t v e r s u s t e m p e r a t u r e is g i v e n b y Xaz = 0 . 6 3 2 0 + 3 . 6 9 8 8 - l 0 - 4 . T w i t h s t a n d a r d e r r o r Or(Xaz) = 0.002. F o r this e q u a t i o n o n l y s e l e c t e d d a t a w e r e u s e d ; f o r o t h e r d a t a , r e s i d u a l s a r e u p to 0.015. A c c o r d i n g to t h e s u g g e s t i o n s o f M a l e s i n s k i ( 1 9 6 5 ) , w e h a v e u s e d the C l a p e y r o n e q u a t i o n l n ( P a z / k P a ) = A + B / T ~ z for fitting e x p e r i m e n t a l a z e o t r o p i c p r e s s u r e d a t a f o r t h e c y c l o h e x a n e - a c e t o n e s y s t e m ; the r e s u l t i n g e q u a t i o n ln(P~/kPa) = 15.9279- 3692.12/T~z represents data with standard deviation o-(P/kPa)=0.56.

80

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

2O

-~

15

i

10

I

I

×m

Fig. 1. Methanol-cyclohexane. Total vapour pressure versus mole fraction of methanol in the concentration range 0-0.02. Results of two independent series of measurements at 293.15 K.

For the m e t h a n o l - a c e t o n e system, we have used the Antoine equation. Parameter fitting for data in the whole temperature range ( 2 8 8 - 4 2 3 K) gives the equation l n ( P a z / k P a ) = 17.6443 - 4838.18/(T~z + 42.73) and standard deviation t y ( P / k P a ) = 2.0 kPa. Data for the range 2 8 8 - 3 2 5 K, can be represented by l n ( P ~ z / k P a ) = 1 6 . 2 7 5 4 - 3 8 2 8 . 9 8 / T a z with standard deviation t r ( P / k P a ) = 0.57. Results for the c y c l o h e x a n e - m e t h a n o l system, together with the plot o f ln(Paz) vs. Xaz, have been presented previously (Oracz et al., 1995). All the above results indicate excellent internal consistency of our data.

30

a.

20

i

i

001

i

002

Xm

Fig. 2. Methanol-cyclohexane. Total vapour pressure versus mole fraction of methanol in the concentration range 0-0.02. Results of three independent series of measurements at 303.15 K.

P. Oracz et al. / Fluid Phase Equilibria 126 (1996) 71-92

81

Table 4 Comparison of the efficiency of different equations for the binary systems at 293.15 and 303.15 K (number of parameters n, number of experimental points (including those for pure components) m, average standard error of the total vapour pressure

¢(p)) Equation

n

~r( P ) / k P a

Number of sign changes b

Calculated azeotropic point Predicted phase split Xa

P/kPa

x'a

x:

0.831

28.19 24.01 22.24 22.41 22.57 21.48 22.35 22.24 22.29 22.59 22.21 21.53 21.26 22.67 22.19 22.50 22.25

0.118 ( + 0.008) c 0.089 0.090 (2 regions) 0.112 0.098 (2 regions) 0.113 0.163 0.036 0.055 (unstable) (2 regions) 0.054 0.107 0.103 0.127

Methanol (a)+cyclohexane (b) at 293.15 K, m ~ 26

Redlich-Kister Van Laar-Van Ness Myers-Scott Marsh, Eq. (1) Abbott-Van Ness Ortega (k = 0.3) SSF Wilson (Tsuboka-Katayama) + Kretschmer-Wiebe NRTL ( a ~ 0.45) + Kretschmer-Wiebe (LLE) d UNIQUAC (3 isotherms)

6 6 5 2+3 5 6 6 2 3 2 2 2 3 2 (6) 2 4

0.363 0.212 0.128 0.129 0.132 0.149 0.128 0.309 0.307 0.475 0.46 1 1.041 1.039 0.558 3.275 0.194 0.395

9 7 4 6 5 9 5 7 8 4 3 6 6 6 0 6 3

0.458 0.484 0.544 0.543 0.536 0.602 0.545 0.543 0.543 0.536 0.540 0.555 0.561 0.534 0.535 0.542 0.543

0.834 0.830 0.825 0.830 0.794 0.511 0.832 0.828

0.854 0.850 0.843 0.826

Methanol (a)+ cyclohexane (b) at 303.15 K, m = 71

Redlich-Kister Van Laar-Van Ness Myers-Scott Marsh, Eq. (1) Abbott-Van Ness Ortega (k = 0.3) SSF Wilson (Tsuboka-Katayama) + Kretschmer-Wiebe NRTL ( a = 0.45) + Kretschmer-Wiebe (LLE) d UNIQUAC (3 isotherms)

6 6 6 2+3 5 5 6 2 3 2 2 2 '3 2 (6) 2 2

0.278 0.239 0.248 0.249 0.247 0.236 0.245 0.355 0.357 1.027 0.626 1.326 0.948 0.767 5.972 0.314 0.355

18 20 10 12 10 14 10 10 10 9 9 10 10 9 0 11 11

0.464 0.502 0.559 0.561 0.557 0.580 0.561 0.558 0.557 0.556 0.557

46.72 38.64 36.33 36.41 36.50 35.55 36.31 35.84 35.97 36.12 36.16

0.550 0.560 0.559 0.559

36.82 34.75 36.50 36.50

0.167 0.795 ( + 0.008) c 0.081 0.843 0.090 0.826 0. t 48 0.749 0.189 0.815 0.141 0.811 (2 regions) 0.153 0.762 (not predicted) 0.047 0.832 0.075 0.813 (unstable) (unstable) 0.064 0.844 0.168 0.810 0.136 0.821 0.137 0.823

82

P. Oracz et a l . / F l u i d Phase Equilibria 126 (1996) 7 1 - 9 2

Table 4 (continued) Equation

n

o'(P)/kPa

Number of sign changes b

Calculated azeotropic point Predicted phase split Xa

P/kPa

0.744 0.740 0.745 0.740 0.740 0.745 0.747 0.745 0.730 0.742 0.728

28.09 28.09 28.09 28.08 28.09 28.09 28.16 28.20 27.89 28.08 27.85

0.746 0.750 0.747 0.747 0.746 0.747 0.750 0.750 0.734 0.750 0.733

42.81 42.82 42.81 42.81 42.81 42.81 42.83 42.94 42.48 42.82 42.43

r

xa

et

xa

Acetone (a)+ cyclohexane (b) at 293.15 K, m = 27 Homogeneous Redlich-Kister Van Laar-Van Ness Myers-Scott Marsh, Eq. (1) Abbott-Van Ness SSF Wilson (3 isotherms) NRTL ( a ~ 0.3)

3 5 4 3+2 5 4 2 4 2 3 UNIQUAC 2 Acetone (a)+cyclohexane (b) at 303.15

0.049 0.037 0.050 0.035 0.038 0.053 0.125 0.151 0.196 0.059 0.223 K, m = 43

Redlich-Kister Van Laar-Van Ness Myers-Scott Marsh, Eq. (1) Abbott-Van Ness SSF Wilson (3 isotherms) NRTL ( a = 0.3)

4 3 4 2+2 4 4 2 4 2 3 UNIQUAC 2 Acetone (a) +methanol (b) at 293.15 K,

0.034 0.042 0.033 0.034 0.034 0.033 0.046 0.058 0.286 0.040 0.310 m = 18

Redlich-Kister Van Laar-Van Ness Myers-Scott Marsh, Eq. (1) Abbott-Van Ness SSF Wilson (4 isotherms) NRTL ( tr = 0.3)

3 3 3 2+2 4 4 2 4 2 3 UNIQUAC 2 Acetone (a) + methanol (b) at 303.15 K,

0.005 0.005 0.017 0.005 0.005 0.005 0.012 0.014 0.019 0.005 0.014 m = 17

0.921 0.921 0.927 0.921 0.921 0.921 0.923 0.923 0.924 0.921 0.923

24.78 24.78 24.78 24.78 24.78 24.78 24.77 24.77 24.76 24.78 24.76

Redlich-Kister Van Laar-Van Ness Myers-Scott Marsh, Eq. (1) Abbott-Van Ness SSF

0.010 0.010 0.029 0.010 0.010 0.010

0.886 0.886 0.886 0.885 0.885 0.885

38.37 38.37 38.33 38.36 38.36 38.36

Homogeneous 15 14 23 20 15 24 12 14 2 14 2

Homogeneous

Homogeneous 3 3 3 2+2 4 4

83

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 7 1 - 9 2

Table 4 (continued) Equation

Wilson (4 isotherms) NRTL ( o~ = 0.3) UNIQUAC

n

2 4 2 3 2

tr(P)/kPa

0.019 0.024 0.028 0.010 0.023

Number of sign b changes

Calculated azeotropic point

Predicted phase split

Xa

P/kPa

xa

4 2 2 7 4

0.886 0.887 0.886 0.886 0.886

38.35 38.34 38.34 38.37 38.34

p

rt

xa

a o ' ( P ) = [Y"(Pexp.- P c a l c . ) 2 / ( m - n)]l/2, where m = number of points. b If two neighbouring points lie on opposite sides of an approximation curve then one speaks of a sign change of their deviations. The points should be scattered randomly with respect to the correlating curve. An easy measure of the randomness is the number of sign changes, which should be roughly equal to m / 2 +_+(_m / 2 ) z/2. c Solubilities of methanol in (a)-rich and (b)-rich phases according to the recommended data of Shaw et al. (1994). d Parameters (fitted to experimental LLE data) according to Novak et al. (1987).

Recently Dohnal and Horakova (1991) have measured, using the Rayleigh distillation method, the limiting activity coefficient of cyclohexane in acetone at 308.15 K as 5.77 _ 0.06. The corresponding value estimated from our data is equal to 5.81 + 0.04 and agrees excellently with the experimental value. The calculated limiting activity coefficients at 293.15,303.15 and 313.15 K may be used to test the E e. agreement with the corresponding limiting partial molar enthalpy of acetone in cyclohexane, Haceton To this end, the relation [8ln'yi/O(1/T)]e. x = H i E / R is used, where HiE is the partial molar enthalpy E of mixing of component i. The calculated value of /-/acetone at infinite dilution is equal to 5.3 kJ mol-2, with confidence range ( + 2 , - 1) kJ mol-2. Calculated from experimental H E data at 298.15 K, the value is 8.5 _ 1 kJ mol-2. Taking into account that each difference in ln'Yi is reflected in the calculated Haceton E e about 38000 times, the agreement is, at least, satisfactory. Use of the local composition model with temperature dependent parameters for several isotherms a n d / o r isobars results in "general" parameters. Such parameters are built-in in process simulator data-bases. We have performed such calculations using the Wilson (UNIQUAC) equation. For the acetone-methanol system, we have used four isotherms, at 293.15,303.15, 313.15 and 323.15 K, (the last two taken from G6ral et al., 1985). The standard error for the Wilson equation is 0.022 kPa (the relative standard error being 0.07%). For acetone-cyclohexane, we have used three isotherms (that at 313.15 K taken from G6ral et al., 1992) with the resulting standard error for the Wilson equation being 0.098 kPa (0.43%). The above calculations confirm the high quality and internal consistency of our data, as well as the applicability of the Wilson equation for such calculations. For the methanol-cyclohexane system, unfortunately, none of the local composition equations is flexible enough (see Table 4). A similar test performed using UNIQUAC for 3 isotherms gives a standard error of 0.52 kPa (2.06%). The "general" parameters may be used for both inter- and extrapolation, and prediction of the enthalpy of mixing. For example, the "general" parameters for the methanolacetone system used for the isobaric data (101.325 kPa) of Tochigi et al. (1984) predict boiling temperatures with a standard error 0.08 K and vapour-phase mole fractions within 0.004; the experimental values are 0.03 and 0.0032, correspondingly.

84

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

Table 5 Parameters K; of Eq. (1) with their standard errors or(K;), correlation coefficients qij, number of adjustable parameters in the numerator of Eq. (1) ( n n ) and cross second virial coefficients ~ a b at 293.15 and 303.15 K Methanol (a)+ cyclohexane (b) at 293.15 K [~ab ~

--

1.297 dm 3 m o l - z, ( n n ) ~ 2

i

0

1

2.59784 2.28117 0.01011 0.02021 qli -0.2407 q2i -0.5693 0.9128 q3i 0.8396 -0.2487 q4i 0.8624 --0.6304 Methanol (a) + cyclohexane (b) at 303.15 K [~ab = -- 1.089 dm 3 m o l - 1, ( n n ) = 2

2

Ki

0.92049 0.01097

OrK i

i

0

-0.18832 0.00780

--0.4326 --0.8177

1

2.56976 2.12476 0.01246 0.03413 qli -0.4011 q2i -0.6509 0.9524 q3i 0.8348 -0.1731 qai 0.8516 -0.8012 Acetone (a)+ cyclohexane (b) at 293.15 K ~ a b ~ - - 1.330 dm 3 m o l - 1, ( n n ) = 3

3

0.86417 0.01944

OrK i

-0.17316 0.01123

0.8681

2

Ki

4

3 -0.17927 0.00523

-0.3785 -0.9310

4 -0.14063 0.01313

0.6842

i

0

1

2

3

4

Ki OrK i qli q2i q3i

1.84150 0.00162

1.28596 0.29058

1.19309 0.20585

0.73930 0.15608

0.57431 0.11617

0.8759 0.9999

0.8761

0.3182

0.0374 0.3159

q4i

Acetone(a)+cyclohexane(b)at303.15 K ~ a b ~ - - l . 1 4 2 dm 3 m o l - I , ( n n ) = 2 i 0 K;

1.75950 0.00099 0.5823 0.5795 0.6600 Acetone(a)+methanol(b) at293.15 K

~g i qli q2i q3i

1

2

0.21395 0.04787

0.17009 0.02683

0.9994 0.9254

0.9350

flab = -- 1.648 dm 3 m o l - l, ( n n ) = 1

i

0

Ki Org i qli q2i

0.74799 0.00028 0.1653 0.4056

l - 0.00277 0.00085 -0.1973

- 0.02832 0.00165

3 -0.08412 0.00360

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

85

Table 5 (continued) Acetone (a) + methanol (b) at 303.15 K /3~b = -- 1.357 dm 3 m o l - 1, ( n n ) = 1 i

0

1

Ki

0.71072 0.00041 0.0571 0.4775

0.00355 0.00125

o'K; qli q2i

2 - 0.02801 0.00251

- 0.2072

Having two sets of VLE data at 293.15 and 303.15 K, we can calculate, using the Gibbs-Helmholtz equation, the molar enthalpy of mixing, H E. Such calculations could be treated as a consistency test of our data and a test of the practical possibility of predicting H E from narrow temperature range VLE data. To this end, we have rewritten the Gibbs-Helmholtz equation in the form

He(298.15K)=R

Q(303.15 K) - Q(293.15

K) (2)

1/303.15 - 1/293.15

Figs. 3, 4 and 5 show the comparison of the H E values calculated with Eq. (2) with the corresponding experimental data, at 298.15 K, for all the binary systems. The experimental H E data at 298.15 K were taken from Marsh and Maczyfiski (1993). For the system cyclohexane-methanol, there are 3 data sets; for the cyclohexane-acetone system, there is one data set; and for the methanol-acetone system, there are seven data sets. It should be noted that for the methanol-acetone system, the scatter of the experimental data points of different authors is up to 290 J m o l - l , and for 600

o

o.5

I

Xn%

Fig. 3. Methanol-cyclohexane. Comparison of calculated enthalpy of mixing with experimental data: O , Touhara et al. (1975); O, Kurtynina et al. (1968); (D, Dai and Chao (1985).( ) represents the H E curve calculated using Eq. (2) with our VLE data. ( - - - - - - ) marks the range calculated with the assumption that the relative standard error of a single pressure measurement is equal to 0.001. ( - . - ) represents the H E curve calculated using UNIQUAC with "general" parameters. All the literature H E data were taken from Maczyfiski (1993).

86

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

/O~Q

1500

E

\

/ /

1000

500

"

i

I

I

I

l

n

I

I

I

05

×CI

Fig. 4. Acetone-cyclohexane. Comparison of calculated enthalpy of mixing with experimental data: O, Handa and Fenby (1975). ( ) represents the H E curve calculated using Eq. (2) with our VLE data. ( - - - - - - ) marks the range calculated with the assumption that the relative standard error of a single pressure measurement is equal to 0.001. ( - • - ) represents the H E curve calculated using the Wilson equation with "general" parameters. The literature H E data were taken from Marsh and Maczyfiski (1993).

the cyclohexane-methanol system, it is up to 80 J m o l - ~. For a proper understanding of Figs. 3 - 5 , one should realize that each inaccuracy in the difference Q(303.15 K ) - Q(293.15 K) is reflected more than 70000 times in the H E value. To account for random errors in the total vapour pressure, 1000

E

~

1

1

1

1

1

,

1

500

0

i

0

i

i

i

i

i

i

i

I

0.5

xm

Fig. 5. Methanol-acetone. Comparison of calculated enthalpy of mixing with experimental data: H, Coomber and Wormald (1976); v , Campbell and Kartzmark (1973); zx, Belousov et al. (1970); ~ , Drinkard and Kivelson (1958); e , Kister and Waidman (1958); I-1, Hirobe (1926); O, Nagata and Tamura (1983). ( ~ ) represents the H E curve calculated using Eq. (2) with our VLE data. ( - • - ) marks the range calculated with the assumption that the relative standard error of a single pressure measurement is equal to 0.0002. (-.-.-) represents the H E curve calculated using the Wilson equation with "general" parameters. All the literature H E data were taken from Marsh and Maczyfiski (1993).

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

87

we plot on Figs. 3-5 the boundaries (dashed lines) estimated for the relative standard error in pressure equal to 0.001 for the cyclohexane-methanol and cyclohexane-acetone systems, and 0.0002 for the methanol-acetone system. The boundaries were calculated at a confidence level equal to 0.95. The dash-dotted lines in Figs. 3-5 represent the H E values calculated from the Wilson (UNIQUAC) equation with the "general", temperature-dependent parameters. The root mean square deviations, defined as [ HiEcalc)2/m] 0"5, are 47.8 J m o l - l for the cyclohexane-methanol system, 120 J mol-~ for cyclohexane-acetone, and 10.8 J mol-~ for methanol-acetone. The corresponding values obtained using "general" parameters are 205 J mol-~ (UNIQUAC), 51 J mol-1 (Wilson) and 7.5 J mol-~ (Wilson). According to the criteria discussed by Olson (1983), the results shown in Figs. 3-5 can be regarded as thermodynamically consistent. For the cyclohexane-methanol system, the "general" -parameter UNIQUAC is not applicable to the correct description of the temperature dependence of the excess Gibbs energy, G E, and therefore to the prediction of the enthalpy of mixing. The ternary system was correlated by Eq. (3) and Eq. (4) using rational equations as well as Wilson, NRTL and UNIQUAC. Eq. (3) has been discussed previously by Oracz (1987), to which ternary terms were added. The equation has the form

~(HiEexptl-

2

3

G E / R T = y"

y"

,~E, X i* ) / R T + G E ( t e r ) / R T ( xi "[-~jJ~2+ t~IJij~,

(3)

i=1 j=i+l

where xi* = x i / ( x i + x j). G E is any equation suitable for the correlation of a binary mixture (i + j). For this reason, Eq. (3) is much more general than any other proposed in the literature. Parameter fl is adjustable. In this work we used /3 = - 0 . 1 5 taken from our previous publication (Oracz et al., 1995). This value is suitable for systems with high positive deviations from Raoult's law. If/3 = 0 then Eq. (3) is equivalent to Kohler's equation. For the ternary contribution, GE(ter), the following equation was used G E ( t e r ) / R T = XaXoXc(Ct + C 2 f 1 + C 3 f 2 + C 4 f ? "[- C5f 2)

(4)

where fl = 3x~ - 1 and f2 - 3Xb -- 1. Table 6 shows the efficiency of various equations applied to the ternary data. According to these results, the Wilson equation, not predicting the liquid-phase split, is superior to Kohler's equation but worse than Eq. (3) with rational binary contributions. Use of the ternary terms, in all cases, yields better results. Therefore we have decided to use the rational equation with the ternary term with 3 or 5 adjustable parameters, given by Eq. (4). Rational equations used together with a ternary term having three adjustable parameters reproduce the ternary liquid-liquid data best; the use of 5 parameters gives the best description of ternary VLE data but overestimates the liquid-liquid range. Table 7a and b report values of the parameters in Eq. (4) with their standard errors and correlation parameters, as well as the calculated parameters of the ternary azeotropic point and the composition of the plait point. The ternary system was measured by Marinichev and Susarev (1965) at 308.15, 318.15 and 328.15 K and at 101.325 kPa, but these data cannot be compared directly with ours. Nor have we found ternary enthalpy of mixing data for our system; the recently published data for the system hexane-acetone-methanol at 298.15 K (Nagata, 1994) can be used for semi-quantitative purposes. Having VLE data at two temperatures (293.15 and 303.15 K) we can predict values of the enthalpy of mixing at 298.15 K. The calculated values can be tested for trends similar to those in the

88

P. Oracz et a l . / Fluid Phase Equilibria 126 (1996) 71-92

Table 6 Comparison of different equations for the ternary system cyclohexane (a)-methanol (b)-acetone (c) at 293.15 and 303.15 K (average standard error of the total vapour pressure, o-(P), relative standard error of the total vapour pressure, t r ( d P / P ) a, mole fraction of acetone at the plait point, x c) Equation

Number of parameters Binary b

Ternary

o- ( P ) /

o"(d P / P ) /

kPa

%

xc

System at 293.15 K 0.14 c Eqs. (3) and (4) with/3 = 0 (Kohler) using Rational eqs. 2 + 4/2 + 4/2 + 1

Eqs. (3) and (4) with/3 = - 0.15 using Rational eqs. 2 + 4/2 + 2/2 + 1

NRTL Wilson UNIQUAC System at 303.15 K

3/3/3 3/2/2 2/2/2

Eqs. (3) and (4) with/3 = 0 (Kohler) using Rational eqns. 2 + 4/2 + 4/2 + 1 Eqs. (3) and (4) with/3 = - 0 . 1 5 using Rational eqns. 2 + 4/2 + 2/2 + 1

NRTL Wilson UNIQUAC

3/3/3 3/2/2 2/2/2

a t r ( P ) = [E(Pexp - ecalc)2/( m

Pcalc/Pexp)2/(m'- n)]l/2"

-

n)]l/2

(+0.02) 0 3 5

0.822 0.143 0.071

3.095 0.556 0.277

0.04 0.09 0.22

0 2 5 0 0 0

0.281 0.134 0.077 0.590 0.286 0.352

1.073 0.511 0.299 2.474 1.226 1.417

0.08 0.18 0.21 -

d

0.27

0 5

1.034 0.095

2.483 0.239

0.07 c (+O.O1) 0.04 0.13

0 3 5 0 0 0

0.326 0.157 0.104 1.215 0.524 0.481

0.814 0.383 0.263 3.093 1.330 1.212

0.08 0.08 0.14 - d 0.22

(n = number of parameters,

m = number of points);

b ;Finis column should be read: number of adjustable parameters for the mixture a + b / f o r b + c. The parameters are those fitted to the binary data (see Table 4). c Estimated from data of Marinichev and Susarev (1965). o Unstable solution for liquid-liquid phase split prediction.

t r ( d P / P ) = [•(1 -

the mixture a + c / f o r

the mixture

above-mentioned data of Nagata. To this end we have used Eq. (2) with Q(T) calculated for ternary mixtures. The calculated values follow the values and shape of the hexane-methanol-acetone system of Nagata. The root mean square deviation, rmsd, is equal to 188 J mol-~; the relative rmsd is equal to 13.9%. Taking into account the difference between the cyclohexane-methanol-acetone and hexane-methanol-acetone systems, the agreement is surprisingly good. The background for comparison of the H E values predicted from our VLE data with H E measured for the hexane-acetonemethanol system has been tested by comparison of experimental H E data for the corresponding binary systems containing cyclohexane or hexane; the differences were within experimental error. We have also recalculated the cyclohexane-methanol and cyclohexane-acetone systems at 313.15 K

P. Oracz et al./ Fluid Phase Equilibria 126 (1996) 71-92

89

(Oracz et al., 1995) using the correlation equation, Eq. (3), with parameters fitted to the corresponding systems containing hexane (Oracz and Warycha, 1995). The calculated rmsd(P/kPa) are 1.64 and 1.07, respectively. In this recalculation of the cyclohexane-methanol system, we have excluded points with

Xmethanol < 0 . 0 2 .

Susarev and Marinichev (1965) reported ternary azeotropic points measured (by the distillation method) at 307.9, 318.4, 324.4 and 328.8 K. Extrapolation from these data to 293.15 K gave: Xcyclohexane = 0 . 2 8 5 , Xmethanol ~-- 0 . 0 5 2 ( P a z / / k P a = 2 8 . 1 4 + 0.3). The corresponding v a l u e s c a l c u l a t e d from our data are: Xcydohexane= 0.282 and Xmethanol= 0.136, (Paz/kPa = 28.816). Extrapolation to 303.15 K gives: X c y c l o h e x a n e = 0.284, Xmethanol= 0.126 (Paz/kPa= 38.12 ___0.3); the corresponding values calculated from our data are: X~ydoh~x~n~= 0.279 and Xmethanol= 0.184 (P~z/kPa = 44.369). The literature azeotropic pressures are calculated from the equation, l n ( P a z / k P a ) = 16.6578-

Table 7 a. C o e f f i c i e n t s C i o f E q . (4) f o r the t e r n a r y p a r t o f the e x c e s s G i b b s e n e r g y , t h e i r s t a n d a r d e r r o r s

tr(Ci), correlation

coefficients qij, c a l c u l a t e d p a r a m e t e r s o f the a z e o t r o p i c p o i n t a n d the p l a i t p o i n t f o r the t e r n a r y s y s t e m c y c l o h e x a n e (a)-methanol

( b ) - a c e t o n e (c) at 2 9 3 . 1 5 K

i=

1

Ci =

0.0539 0.0131

t r ( C i) =

q2i =

2

0.1186 0.0236

q3i ~ q4i = -- 0.2723 q5i = -- 0 . 1 8 2 4 Azeotropic point: x a = 0.282; x b

Ci = tr( C i) = qzi =

=

3

4

5

- 0.2576

0.2595

- 0.6063

- 0.4048

0.0353

0.0335

0.0517

0.0378

0.5486 - 0.2053

0.0942

0.0456

- 0.4945

- 0.5095 0.136; P / k P a = 28.816. Plait point: xa = 0.397; x b = 0.378 - 0.3192 0.0451

-0.8154 0.0674

0.0164 Azeotropic point: x a = 0.285; x b = 0.128; P / k P a = 28.981. Plait point: x a = 0.393; x b ~ 0.427

b. C o e f f i c i e n t s C i o f E q . (4) for the t e r n a r y p a r t o f the e x c e s s G i b b s e n e r g y , t h e i r s t a n d a r d e r r o r s o-(Ci), c o r r e l a t i o n c o e f f i c i e n t s qij, c a l c u l a t e d p a r a m e t e r s o f the a z e o t r o p i c p o i n t a n d the p l a i t p o i n t for the t e r n a r y s y s t e m c y c l o h e x a n e ( a ) - m e t h a n o l ( b ) - a c e t o n e (c) at 3 0 3 . 1 5 K i=

Ci = tr(C i) = q2i = q3i = qai = q5i =

1 - 0.0808 0.0121

2 - 0.2190 0.0317

3 0.1794 0.0302

4

5

- 0.3393 0.0561

0.0399 -0.0124 -- 0 . 2 7 5 7

0.4616

0.0888 -0.5219 - 0.a.A,n.A --0.1861 A z e o t r o p i c p o i n t : x a = 0 . 2 7 9 ; Xb = 0 . 1 8 4 ; P / k P a = 4 4 . 3 6 9 . P l a i t p o i n t : x a = 0 . 4 1 6 ; x b = 0 . 4 5 4 Ci = -0.1042 - 0.3178 - 0.3627

~ ( C i) =

0.0174

q2i ~

0.0374

-

0.0032 0.0469

0.0414

0.0391

qsi =

0.3968 - 0.4221 Azeotropic point: x a = 0.276; x b = 0.180; P / k P a = 44.478. Plait point: x a = 0.509; x b

0.411

- 0.3785 0.0348

90

P. Oracz et al. / Fluid Phase Equilibria 126 (1996) 71-92

3905.31/Taz, fitted to the data of Susarev and Marinichev with the standard deviation tr(P/kPa) = 0.32. The ternary system contains a two-liquid-phase region of type 1 (see, for example, Sorensen and Arlt, 1980 or Novak et al., 1987). Marinichev and Susarev (1965) have measured mutual solubility in ternary mixtures at 293.15 and 303.15 K. Estimated from these data, the mole fraction of acetone at the plait point at 293.15 K is equal to 0.14+ 0.02, and at 303.15 K is equal to 0.07 + 0.01. These values agree very well with those predicted using Eq. (4) With 3 ternary parameters (see Table 6). The use of 5 adjustable ternary parameters, which is the best from the point of view of the ternary VLE data, results in worse, but still acceptable, agreement of the plait point.

5. List of symbols Ci GE H E gi

m n (nn) P Q 0.5

qij

R T x x* x r, x"

Y

coefficients in Eq. (4) excess Gibbs energy molar enthalpy of mixing parameters in Eq. (1) number of experimental points number of adjustable parameters number of adjustable parameters in numerator of Eq. (1) vapour pressure/kPa value of GE/RT value of GE/RT at mole fraction 0.5 correlation coefficients between parameter pairs (Ki,K J) or (Ci,C) gas constant temperature/K mole fraction in liquid mole fraction in Eq. (3) mole fractions in coexisting liquid phases mole fraction in vapour

5.1. Greek letters c~ /3 /3aa'/3bb'/3ab

tr

NRTL parameter exponent in Eq. (3) second virial coefficients standard error

Acknowledgements This work was partially supported by KBN funds through the Department of Chemistry, University of Warsaw within the project BST-502/16/95.

P. Orucz et al. / Fluid Phase Equilibria 126 (1996) 71-92

91

References M.M. Abbott and H.C. Van Ness, Vapor-liquid equilibrium: Part III, Data reduction with precise expressions for G E, AIChE J., 21 (1975) 62-71. T.F. Anderson and J.M. Prausnitz, Application of the UNIQUAC equation to calculation of multicomponent phase equilibria, lm Vapor-liquid equilibria, Ind. Eng. Chem. Process Des. Dev., 17 (1978) 552-561. V. Bekarek, Liquid-vapour equilibrium. XL. Liquid-vapour equilibrium in the systems SO2-CH3COOCH3-CH3OH and SO2-CH 3 COCH3-CH3OH, Coll. Czech. Chem. Commun., 33(8) (1968) 2608- 2619. V.P. Belousov, L.M. Kurtynina and A.A. Kozulayev, Vestn. Leningr. Univ., Fiz., Khim., 10 (1970) 163. T. Boublik, V. Fried and E. Hala, The Vapour Pressures of Pure Liquids, Elsevier, Amsterdam, 1973. R.H. Campbell and E.M. Kartzmark, J. Chem. Thermodyn., 5 (1973) 163. R.A. Coomber and C.J. Wormald, J. Chem. Thermodyn., 8 (1976) 793. M. Dai and J.P. Chao, Fluid Phase Equilibria, 23 (1985) 315. V. Dohnal and I. Horakova, A new variant of the Rayleigh distillation method for the determination of limiting activity coefficients. Fluid Phase Equilbria, 68 (1991) 173-185. W. Drinkard and D. Kivelson, J. Phys. Chem., 62 (1958) 1494. J. Dykyj and M. RepaL Tlak Nasytenej Pary Organickych Zlu~enin. Veda, Bratislava, 1979. J. Dykyj, M. Repa~ and J. Svoboda, Tlak Nasytenej Pary Organickych Zlu~enin. Veda, Bratislava, 1984. J.H. Dymond and E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Clarendon Press, Oxford, 1980. J.H. Dymond, Virial coefficients for l-alkanol+ n-alkane mixtures. The Second International IUPAC Workshop on Vapor-Liquid Equilibria in 1-Alkanol + n-Alkane Mixtures, Paris, 5-7 September, 1985. J.H. Dymond, J.N. Marsh and A. Maczyfiski, A., 1992. Floppy Book on Virial Coefficients of Pure Gases and Mixtures, Thermodynamic Research Center, The Texas Engineering Experimental Station, The Institute of Coal Chemistry of the Polish Academy of Sciences, 1992. M. G6ral, Error analysis in Barker's method of vapour pressure isotherm data processing, Z. Phys. Chem. (Leipzig), 258 (1977) 1040-1044. M. G6ral and B. Janaszewski, The problem of vapour non-ideality in Barker's method of vapour pressure isotherm data processing, Z. Phys. Chem. (Leipzig), 258 (1977) 417-425. M. G6ral, G. Kolasifiska, P. Oracz and S. Warycha, Vapour-liquid equilibria. II. The ternary system methanolchloroform-acetone at 313.15 and 323.15 K, Fluid Phase Equilibria, 23 (1985) 89-116. M. G6ral, P. Oracz and S. Warycha, Vapour-liquid equilibria. VI. The ternary system acetone-hexane-cyclohexane at 313.15 K, Fluid Phase Equilibria, 81 (1992) 261-272. Y.P. Handa and D.V. Fenby, J. Chim. Phys. Phys.-Chim. Biol., 72 (1975) 1235. H. Hirobe, J. Fac. Sci., Imp. Univ. Tokyo, 1 (1926) 155. B. Janaszewski, P. Oracz, M. G6ral and S. Warycha, Vapour liquid equilibria. I. An apparatus for isothermal total vapour pressure measurements: binary mixtures of ethanol and t-butanol with n-hexane, n-heptane and n-octane at 313.15 K, Fluid Phase Equilibria, 9 (1982) 295-310. H. Kehiaian and A. Treszczanowicz, Excess free enthalpy of athermal associated mixtures of the Kretschmer-Wiebe type, Bull. Acad. Polon. Sci., Ser. Sci. Chim., 18 (1970) 693. A.T. Kister and D.C. Waldman, J. Phys. Chem., 62 (1958) 245. G. Kolasifiska and P. Oracz, Generalization of error analysis and problem of vapour non-ideality in Barker's method of vapour pressure isotherm data processing, Z. Phys. Chem. (Leipzig), 260 (1979) 169-173. L.M. Kurtynina, N.A. Smirnova and P.F. Andrukovich, Khim. Termodin. Rastvorov (Leningrad), 2 (1968) 43. Malesinski, W., 1965. Azeotropy and Other Problems of Vapor-liquid Equilibrium, PWN, Polish Scientific Publishers, Warzawa,. A.N. Marinichev and M.P. Susarev, Investigation of phase equilibria in system acetone-methanol-cyclohexane, Zh. Prikl. Khim., 38 (1965) 1054-1057 (in Russian). K.N. Marsh, K.N., A general method for calculating the excess Gibbs free energy from isothermal vapour-liquid equilibria, J. Chem. Thermodyn., 9 (1977) 719-724. K.N. Marsh and A. Maczyfiski, Floppy Book on Heat of Mixing, Version 1993-1.1, Thermodynamic Research Center, The Texas Engineering Experimental Station, The Institute of Coal Chemistry of the Polish Academy of Sciences, 1993.

92

P. Oracz et al./Fluid Phase Equilibria 126 (1996) 71-92

A. Maczyfiski, Floppy Book on Vapor-Liquid Equilibrium Data of Organic Compounds and Water, Version 1993-1.3, Institute of Physical Chemistry and Institute of Coal Chemistry of the Polish Academy of Sciences, Thermodynamic Research Center, The Texas Engineering Experimental Station, 1993. D.S. Morton, J. Phys. Chem., 33 (1929) 384. D.B. Myers and R.L. Scott, Computer methods for the systematic processing of data on binary mixtures, Ind. Eng. Chem., 55(7) (1963) 43-46. I. Nagata, (Liquid-liquid) equilibria and excess enthalpies for (methanol + benzene or propanone + hexane) at the temperature 298.15 K, J. Chem. Thermodyn., 26 (1994) 545-551. I. Nagata and K. Tamura, Fluid Phase Equilibria, 15 (1983) 67. J.P. Novak, J. Matou~ and J. Pick., Liquid-Liquid Equilibria, Academia, Prague, 1987. J.P. Novak, P. Vodka, J. Sulka and J. Pick, Applicability of the three-constant Wilson equation for correlations of strongly nonideal systems. II, Coll. Czech. Chem. Commun., 39 (1974) 3593-3598. Olson, J., 1983. Thermodynamic consistency testing of Ptx data via the Gibbs-Helmholtz equation. Fluid Phase Equilibria, 14: 383-392. P. Oracz, Vapour-liquid equilibria in complex ternary systems from binary contributions, 3rd CODATA Symposium on Critical Evaluation and Prediction of Phase Equilibria in Multicomponent Systems, Budapest, 6-8 Sept., 1987 P. Oracz, M. G6ral, G. Wilczek-Vera and S. Warycha, Vapour-liquid equilibria. VIII. The ternary system cyclohexanemethanol-acetone at 313.15 K, Fluid Phase Equilibria, 112 :(1995) 291-306. P. Oracz and S. Warycha, Vapour-liquid equilibria. VII. The ternary system hexane-methanol-acetone at 313.15 K, Fluid Phase Equilibria, 108 (1995) 199-211. J. Ortega, J.A. Pefia and C. de Alfonso, Isobaric vapor-liquid equilibria of ethyl acetate + ethanol mixtures at 760 + 0.5 mmHg, J. Chem. Eng. Data, 31 (1986) 339-342. O. Redlich and A.T. Kister, Algebraic representation of thermodynamic properties and the classification of solutions, Ind. Eng. Chem., 40 (1948) 345-348. H. Renon and J.M. Prausnitz, Local compositions in thermodynamic excess functions for liquid mixtures, AIChE J., 14 (1968) 135-144. M. Rogalski and S. Malanowski, A new equation for correlation of vapour-liquid equilibrium data of strongly non-ideal mixtures, Fluid Phase Equilibria, 1 (1977) 137-152. D. Shaw, A. Skrzecz, J.W. Lorimer and A. Maczynski, Alcohols with Hydrocarbons. Solubility Data Series, Vol. 56, Oxford University Press, Oxford, 1994. J.M. Sorensen and W. Arlt, Liquid-Liquid Equilibrium Data Collection. Ternary Systems. Chemistry Data Series, Vol. V. Part 2, Dechema, 1980. M.P. Susarev and A.N. Marinichev, Differential equation for curves of constant distribution ( x ~ 2 ) / x m ) = const) of the component of ternary system between coexisting solution and ideal vapour. II. Curves shift with temperature changing, Zh. Fiz. Khim., 39 (1965) 2219-2225. (in Russian). K. Tochigi, K. Hiaki and K. Kojima, The First CODATA Symposium on Critical Evaluation and Prediction of Phase Equilibria in Multicomponent Systems, Zaborrw near Warsaw, Poland, 1984. H. Touhara, M. Ikeda, K. Nakanishi and N. Watanabe, J. Chem. Thermodyn., 7 (1975) 887. C. Tsonopoulos, An empirical correlation of second virial coefficients, AIChE J., 20 (1974) 263-272. T. Tsuboka and T. Katayama, Modified Wilson equation for vapor-liquid and liquid-liquid equilibria, J. Chem. Eng. Jpn., 8 (1975) 181-187. H.C. Van Ness, Classical Thermodynamics of Non-Electrolyte Solutions. Pergamon Press, London, 1964. A.J. Vogel, A Text-Book of Practical Organic Chemistry Including Qualitative Organic Analysis, Longmans, London, 1961. G.M. Wilson, Vapour-liquid equilibrium. XI. A new expression for the excess free energy of mixing, J. Am. Chem. Soc., 86 (1964) 127-130. L.C. Yen and S.S. Woods, A generalized equation for computer calculations of liquid densities, AIChE J., 12 (1966) 95-99.