Vapor–liquid equilibria and excess properties for methyl tert-butyl ether (MTBE) containing binary systems

Fluid Phase Equilibria 200 (2002) 399–409

Vapor–liquid equilibria and excess properties for methyl tert-butyl ether (MTBE) containing binary systems So-Jin Park a,∗ , Kyu-Jin Han a , J. Gmehling b a

b

Department of Chemical Engineering, College of Engineering, Chungnam National University, Daejeon 305-764, South Korea Technische Chemie FB9, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany Received 18 December 2001; accepted 12 February 2002

Abstract Methyl tert-butyl ether (MTBE) is recently widely used in the chemical and petrochemical industry as a nonpolluting octane booster for gasoline and as an organic solvent. The isobaric or isothermal vapor–liquid equilibria (VLE) were determined directly for MTBE + C1 –C4 alcohols. The excess enthalpy (HE ) for butane + MTBE or isobutene + MTBE and excess volume (VE ) for MTBE + C3 –C4 alcohols were also determined. Besides, the infinite dilute activity coefficient, partial molar excess enthalpies and volumes at infinite dilution (γ ∞ , HE,∞ , VE,∞ ) were calculated from measured data. Each experimental data were correlated with various gE models or empirical polynomial. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Methyl tert-butyl ether (MTBE); Vapor–liquid equilibria; Activity coefficient; Excess molar property; Infinite dilution; Correlation

1. Introduction Accurate representation of the chemical activities is not only essential for the design of fluid phase separation equipment but also helpful information to describe the mixing rules and the extension of the database for thermodynamic models. The thermodynamic behaviors at infinite dilution have become a subject of considerable interest in the chemical, petroleum, food and pharmaceutical industries. However, accurate measurement and prediction of infinite dilute properties still have some problems because it treats the mixtures containing a very low amount of one component. Sometimes, the simple extrapolation of the measured physical properties is suggested as a rapid and convenient method, giving reasonable values of infinite dilute properties; γ ∞ , HE,∞ , VE,∞ , etc. ∗

Corresponding author. Tel.: +82-42-821-5684; fax: +82-42-823-6414. E-mail address: [email protected] (S.-J. Park). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 2 ) 0 0 0 4 7 - X

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Tertiary-alkyl ethers are low toxic and low polluting oxygenated petrochemical compounds, used as an octane booster for lead-free or low-leaded gasoline and also increasingly valued as a solvent and a chemical reactant [1,2]. They are usually being produced by the conversion of alkanol with isoalkene. Therefore, the fluid phase equilibria, thermodynamic properties and infinite dilute properties for systems containing tertiary-alkyl ether, alcohols and hydrocarbons are of interest to optimize the manufacturing process or using them as additives for gasoline. Some investigations were carried out for the methyl tert-butyl ether (MTBE) + alcohol systems previously [3], but more data are required to develop thermodynamic models and to understand solution behaviors. We have carried out a systematic study of phase equilibria and the fundamental thermophysical properties for binary and ternary mixtures for tertiary-alkyl ether compounds, MTBE, tert-amyl methyl ether (TAME) and ethyl tert-butyl ether (ETBE) [4–7]. This work is a part of the systematic study for the systems of MTBE with alcohols or with butane and isobutene, since MTBE is usually synthesized from methanol and isobutene. The vapor–liquid equilibria (VLE) and two different excess properties (HE , VE ) were experimentally determined. These experimental properties were correlated with common gE models or Redlich–Kister polynomial [8]. The activity coefficient at infinite dilution (γ ∞ ) was calculated by second order extrapolation from the calculated activity coefficient, and excess molar properties at infinite dilution (HE,∞ , VE,∞ ) were also calculated using Redlich–Kister parameters. The extrapolated activity coefficients at infinite dilution were compared with the directly measured values by using differential ebulliometry [9] or calculated values using UNIFAC equation [10].

2. Experimental 2.1. Materials Commercial grade MTBE and alcohols from Aldrich and Merck were used. They were carefully dried with Union Carbide type 3 Å molecular sieves (from Fluka) and then distilled and degassed using a ca. 20 theoretical staged fractionating column. Their purities were more than 99.9 wt.% by gas chromatographic analysis. Butane and isobutene were supplied from Messer Griesheim GmbH. Their purities were better than 99.5%. The observed densities (ρ) of liquid pure components at 298.15 K are given in Table 1, along with the published values [11–13] for comparison. 2.2. VLE measurement Recirculating still [14] is a conventional apparatus to determine isobaric VLE. A recently developed modified headspace gas chromatographic method [5] allows the rapid and precise determination methods for isothermal VLE. In this work, isobaric VLE for MTBE+methanol and MTBE+ethanol systems were measured at 101.33 kPa using a Sieg & Röck type recirculator, which is shown in Fig. 1. Isothermal VLE for systems of MTBE + 1-propanol and MTBE + 1-butanol at 313.15 K were measured with the help of Hewlett-Packard (HP) 19395A headspace sampler and the HP 5890 gas chromatograph. In the isobaric method, ca. 250 ml liquid mixture was introduced to the still and a Baratron pressure regulating system was used to regulate pressure with an accuracy of ±0.1 kPa. For the headspace analysis method, about 3 ml of the liquid sample mixture for known composition was added to the glass vial with an accuracy of 1×10−5 g by Mettler Balance. The glass vials were sealed with a teflon/rubber septum and aluminum cap,

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Table 1 Experimental densities (ρ) with literature values and Antoine constants of pure components Chemicals

Supplier

Observed values MTBE Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol

Aldrich Merck Merck Merck Aldrich Merck Merck

Antoine constantsa

Density (ρ) at 298.15 K

0.73533 0.78645 0.78503 0.79948 0.78101 0.80583 0.80256

Literature values b

0.73530 0.78640c 0.78500c 0.79957c 0.78082c 0.8060d 0.8026d

A

B

C

7.12997 8.08097 8.11220 7.74887 8.00308 7.92484 7.47429

1265.40 1582.27 1592.86 1440.74 1505.50 1617.52 1314.19

242.517 239.970 226.184 198.806 211.600 203.296 186.500

a

Data from Dortmund Data Bank (DDB, version 1998). [11]. c [12]. d [13]. b

and then kept in the thermostat, the temperature of which was regulated with an accuracy of 0.1 K. After the equilibrium was achieved, the liquid and vapor phase (in the head space analysis, vapor phase only) components were then analyzed by gas chromatography. Highly pure He gas (99.9999%) and TCD were used for analysis. Determination methods and operating procedures have been described previously [5–7]. 2.3. Excess molar enthalpy measurement The excess molar enthalpies (HE ) for butane + MTBE and isobutene + MTBE mixtures were measured directly at 363.15 K under 2 × 103 kPa using the Hart Scientific isothermal flow calorimeter. This flow calorimeter was equipped with syringe pumps capable of delivering accurately small pulse-free flows. It also has several advantages over batch calorimeters with which most currently available HE data have been measured. This flow calorimeter works by monitoring the power required by the control heater to keep the flow cell under isothermal conditions. The operating procedure is described elsewhere [6].

Fig. 1. Schematic diagram for the recirculating still (Sieg & Röck type).

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2.4. Excess molar volume measurement The vibrating tube digital densitometry (Anton Paar DMA 602) was employed to determine the densities of the pure compound and the binary mixtures. The densitometry was calibrated for each measurement using doubly distilled water and dried air at atmospheric pressure. About 3.5 ml of sample mixtures were prepared by weight with precisions of 1 × 10−5 g. To minimize the experimental error due to evaporation, 4 ml small glass vials were used as mixture vessels. The experimental systematic error was estimated to be less than 1 × 10−4 g/cm3 . All the measurements were carried out under atmospheric pressure. The temperature of the vibrating U tube was regulated by Lauda thermostat of which the temperature was calibrated against a HP resistance thermometer with an accuracy of 0.01 K. The time interval of measurements was chosen to be 15 min to attain a constant temperature and stability in oscillation. Apparatus and operating procedure are described elsewhere [6,7]. 2.5. Calculation of the thermodynamic properties at infinite dilution The γ ∞ , HE,∞ and VE,∞ are calculated from calculated or measured thermodynamic properties (γ , H , VE ). The γ ∞ value was obtained by using second order extrapolation program and HE,∞ , VE,∞ were calculated by the correlated parameters of Redlich–Kister polynomial [8]. E

3. Results and discussion For the VLE determination, the simplified VLE Eq. (1) and Antoine Eq. (2) were used. For the headspace analysis method, true liquid mole fraction must be calculated. The calculation procedure has been previously described [5]. y1 P = x1 γ1 P1s log Pis (mmHg) = A −

(1) B T (◦ C)

+C

(2)

The excess molar volume of mixing, VE , is defined as H E = Hm − x1 H1 − x2 H2 
x1 M1 x2 M2 x1 M1 + x2 M2 E − − V = ρm ρ1 ρ2

(3) (4)

The Redlich–Kister polynomial function was used to correlate the experimental excess molar properties, ME (HE , VE ). M E = x1 x2

n  Ai (x1 − x2 )i−1

(5)

i=1

Standard deviation of the fits, S.D., for excess molar properties is then defined as   E E 2 1/2 (M − M ) i calculated experimental i S.D. = N −n

(6)

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Table 2 Vapor–liquid equilibria for MTBE with methanol and ethanol mixtures at 101.33 kPa T (K)

x1

y1

T (K)

x1

y1

T (K)

x1

y1

MTBE + methanol 334.95 0.0378 333.05 0.0694 331.45 0.1077 330.25 0.1438 329.05 0.1807 328.15 0.2217 327.15 0.2772 326.65 0.3061 326.35 0.3279

0.1311 0.2153 0.2850 0.3389 0.3903 0.4213 0.4789 0.5042 0.5184

326.15 325.95 325.65 325.45 325.15 324.95 324.85 324.65 324.55

0.3543 0.3765 0.4051 0.4312 0.4637 0.4998 0.5316 0.5700 0.6098

0.5321 0.5581 0.5571 0.5714 0.5905 0.6085 0.6219 0.6368 0.6563

324.45 324.45 324.55 324.65 324.85 325.35 325.45 326.25 327.55

0.6560 0.7052 0.7659 0.7414 0.8289 0.8520 0.8967 0.9461 0.9915

0.6785 0.7038 0.7346 0.7212 0.7763 0.8002 0.8386 0.9000 0.9807

MTBE + ethanol 351.25 0.0027 348.95 0.0283 346.05 0.0685 343.35 0.1090 341.05 0.1478 339.35 0.1902 337.95 0.2213 337.65 0.2354 337.05 0.2520 336.45 0.2550

0.0130 0.0952 0.2473 0.3479 0.4114 0.4730 0.5120 0.5416 0.5628 0.5801

335.75 335.15 334.65 334.05 333.55 333.05 332.55 332.15 331.55 331.25

0.2980 0.3221 0.3394 0.3460 0.3831 0.4108 0.4434 0.4615 0.5109 0.5433

0.5892 0.6209 0.6350 0.6548 0.6651 0.6812 0.7044 0.7163 0.7361 0.7434

330.75 330.35 329.85 329.45 329.05 328.65 328.35 328.05 327.85 327.75

0.5801 0.6045 0.6505 0.6992 0.7451 0.7880 0.8261 0.8738 0.9173 0.9611

0.7610 0.7754 0.7937 0.8133 0.8326 0.8520 0.8724 0.8982 0.9263 0.9613

E E where Mcalculated is the excess molar property, which is calculated by Eq. (5) and Mexperimental is the experimental excess property. From the experimental values, the properties at infinite dilution are calculated. The partial molar excess enthalpy and volume at infinite dilution were calculated with the adjustable parameters of the Redlich–Kister polynomial. The partial molar excess properties at infinite dilution are the limit of the partial molar excess properties, as shown in Eqs. (7) and (8). In this work, we used five adjustable parameters of the Redlich–Kister polynomial.

M¯ 1E,∞ = lim M¯ 1E = A1 − A2 + A3 − A4 + A5

(7)

M¯ 2E,∞ = lim M¯ 2E = A1 + A2 + A3 + A4 + A5

(8)

x1 →0

x1 →1

The experimental isobaric or isothermal VLE compositions of MTBE + C1 –C4 alcohol systems are listed in Tables 2 and 3, respectively. The activity coefficients were correlated using common gE models (Margules, van Laar, Wilson, NRTL, UNIQUAC). The correlation results of the various model equations were almost the same. The best-fitted model parameters and the mean deviations in the vapor phase, y are given in Table 4, with the extrapolated activity coefficient at infinite dilution. Extrapolated activity coefficients at infinite dilution agreed well with directly measured values by differential ebulliometry [14] or calculated values by UNIFAC equation [10]. The mean deviation, y means |yexperimental − ycalculated |/N , and the parameters Aij for the Wilson, NRTL, and UNIQUAC equations are

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Table 3 Vapor–liquid equilibria for MTBE systems with 1-propanol and 1-butanol at 313.15 K P (kPa)

x1

y1

P (kPa)

x1

y1

P (kPa)

x1

y1

MTBE + 1-propanol 7.65 0.0078 8.58 0.0159 9.26 0.0219 10.00 0.0280 10.74 0.0351 11.24 0.0422 12.31 0.0489 13.21 0.0568 17.92 0.0972 22.89 0.1491 27.13 0.2013

0.1461 0.2443 0.3043 0.3592 0.4075 0.4276 0.4907 0.5291 0.6682 0.7527 0.8012

28.80 33.43 36.45 37.46 38.75 42.11 43.65 43.97 46.76 47.87 49.31

0.2476 0.2980 0.3506 0.3998 0.4419 0.5222 0.5699 0.5826 0.6453 0.6832 0.7365

0.8170 0.8535 0.8722 0.8782 0.8858 0.9047 0.9129 0.9146 0.9290 0.9346 0.9421

51.74 52.56 55.47 57.65 57.89 58.40 58.48 58.61 59.02 59.31 59.62

0.7994 0.8384 0.8890 0.9473 0.9559 0.9669 0.9723 0.9749 0.9858 0.9922 0.9987

0.9550 0.9597 0.9758 0.9864 0.9879 0.9911 0.9917 0.9926 0.9956 0.9977 0.9997

MTBE + 1-butanol 3.19 0.0072 4.48 0.0164 4.62 0.0205 5.59 0.0292 6.59 0.0389 6.89 0.0425 7.28 0.0482 8.15 0.0566 13.07 0.1006 17.17 0.1484 21.14 0.1947

0.2455 0.4689 0.4851 0.5784 0.6459 0.6624 0.6816 0.7182 0.8330 0.8786 0.9061

24.55 27.84 29.62 33.09 36.50 38.74 44.25 43.99 46.09 47.92 49.70

0.2473 0.2965 0.3483 0.3920 0.4615 0.5021 0.5482 0.5925 0.6478 0.6944 0.7598

0.9229 0.9354 0.9413 0.9511 0.9589 0.9636 0.9727 0.9723 0.9757 0.9785 0.9814

51.83 53.49 55.35 54.98 57.49 57.96 58.22 58.46 58.96 59.17 59.56

0.7989 0.8454 0.8935 0.9194 0.9555 0.9670 0.9705 0.9768 0.9864 0.9908 0.9979

0.9848 0.9875 0.9897 0.9904 0.9954 0.9964 0.9969 0.9974 0.9985 0.9990 0.9998

expressed as Wilson

Aij = λij − λii

NRTL

Aij = gij − gii

UNIQUAC

(cal/mol)

(9)

(cal/mol)

Aij = uij − uii

(10)

(cal/mol)

(11)

Table 4 Fitted gE model parameters and mean deviations of the vapor phase mole fraction and the extrapolated activity coefficient at infinite dilution System

gE model

A12

MTBE + methanol MTBE + ethanol MTBE + 1-propanol MTBE + 1-butanol

Wilson NRTL UNIQUAC Wilson

−375.56 492.82 769.76 −272.90

a

A21 1090.11 288.76 −283.93 958.50

Calculated values by extrapolation. Unpublished data obtained by differential ebulliometry [14]. c Calculated values by UNIFAC equation [10]. b

α

y

γ1∞

γ1∞

γ2∞

γ2∞

– 0.3 – –

0.0050 0.0068 0.0053 0.0030

3.114a 2.677a 2.315a 1.720a

3.208b 2.850b 2.304c 1.940c

3.526a 3.097a 2.751a 2.958a

3.421b 2.983b 2.912c 2.529c

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405

Fig. 2. Isobaric VLE data at 101.33 kPa and isothermal VLE data at 313.15 K for the systems of MTBE + n-alcohols(C1 –C4 ), (x: liquid phase, y: vapor phase).

All the measured VLE data were thermodynamically consistent by the Redlich–Kister integral method. Fig. 2 shows the isobaric VLE compositions for MTBE + methanol and MTBE + ethanol systems and isothermal VLE for MTBE + 1-propanol and MTBE + 1-butanol systems. Solid lines represent the data calculated with the NRTL parameters for MTBE + ethanol system and with UNIQUAC parameters for MTBE + 1-propanol system and with Wilson parameters for MTBE + methanol and MTBE + 1-butanol systems. The MTBE +methanol system has a minimum boiling azeotrope, while the other systems do not show azeotropic behavior. As shown in the figure, MTBE + 1-propanol and MTBE + 1-butanol systems show relatively large positive deviations from Raoult’s law. Table 5 gives the experimental HE data of butane+MTBE and isobutene+MTBE. They were smoothed by the least-square method to Redlich–Kister equation. Parts of these data were reported in the International Data Series [15]. Fig. 3 shows the excess molar enthalpies of these binaries. Continuous lines represent the calculated data by means of Eq. (5). The mixing enthalpies of butane +MTBE mixture show positive values and are almost symmetric while the isobutene + MTBE mixture show negative values and the minimum is slightly shifted in the MTBE rich region. Table 6 shows the fitted parameters of the

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Table 5 Excess molar enthalpies of the butane + MTBE and isobutene + MTBE systems at 363.15 K x1

HE (J/mol)

x1

HE (J/mol)

HE (J/mol)

x1

x1

HE (J/mol)

Butane + MTBE 0.0588 39.18 0.1164 73.83 0.1731 104.13 0.2287 130.42

0.3370 0.4415 0.5425 0.5425

165.63 185.66 191.61 190.31

0.6402 0.7346 0.8259 0.8705

178.05 151.47 114.50 90.06

0.9143 0.9143 0.9575 0.9894

63.27 63.09 32.82 8.19

Isobutene + MTBE 0.0157 −2.81 0.0623 −11.59 0.1230 −22.34 0.1821 −32.99

0.2398 0.3510 0.4569 0.5579

−41.13 −56.05 −68.18 −75.47

0.5579 0.6543 0.7465 0.7465

−74.65 −75.70 −69.90 −70.85

0.8346 0.8773 0.9191 0.9600

−57.09 −47.16 −34.00 −18.11

Fig. 3. Excess molar enthalpies of the butane + MTBE and isobutene + MTBE systems at 363.15 K.

Redlich–Kister equation for each binary and S.D., related to Eq. (6), with the calculated partial excess molar enthalpy at infinite dilution. The volume changes of mixing of MTBE with C3 –C4 alcohols are given in Table 7 and the values of fitted Redlich–Kister parameters Ai and S.D. are presented in Table 8 with the calculated partial excess Table 6 Fitted parameters, standard deviations (S.D.) and partial excess molar enthalpies at infinite dilution (J/mol) for the butane+MTBE and isobutene + MTBE systems at 363.15 K System

A1

A2

A3

A4

Butane + MTBE 762.0684 45.6986 −13.9318 10.5542 Isobutene + MTBE −285.9552 −142.7336 −59.4911 −12.4489

A5 18.2889 −5.4356

S.D. (J/mol) H¯ 1E,∞ 0.8188 0.4519

H¯ 2E,∞

710.1727 822.6783 −195.6994 −506.0644

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Table 7 Excess molar volumes of the MTBE systems with C3 –C4 alcohols at 298.15 K x1

VE (cm3 /mol)

MTBE + 1-propanol 0.0246 −0.0807 0.0636 −0.1782 0.0993 −0.2611 0.1493 −0.3653 0.1994 −0.4550 0.2482 −0.5324 MTBE + 2-propanol 0.0243 −0.0378 0.0597 −0.0768 0.0996 −0.1160 0.1312 −0.1408 0.1898 −0.1824 MTBE + 1-butanol 0.0208 −0.0736 0.0717 −0.2049 0.1004 −0.2785 0.1497 −0.3834 0.2005 −0.4837 0.2507 −0.5713 MTBE + 2-butanol 0.0322 −0.0530 0.0788 −0.1214 0.1507 −0.2094 0.2015 −0.2429 0.2530 −0.2844

x1

VE (cm3 /mol)

x1

VE (cm3 /mol)

x1

VE (cm3 /mol)

0.3006 0.3481 0.4067 0.4507 0.5030

−0.5902 −0.6402 −0.6856 −0.7103 −0.7050

0.5503 0.6008 0.6500 0.7009 0.7366

−0.7100 −0.7037 −0.6784 −0.6254 −0.5927

0.8001 0.8486 0.8903 0.9343 0.9747

−0.5067 −0.4090 −0.3252 −0.2200 −0.1077

0.2495 0.3004 0.3484 0.4015 0.4480

−0.2201 −0.2480 −0.2681 −0.2722 −0.2804

0.4997 0.5509 0.5991 0.6490 0.7009

−0.2929 −0.2911 −0.2727 −0.2657 −0.2522

0.7505 0.7943 0.8511 0.8968 0.9420

−0.2309 −0.1976 −0.1609 −0.1263 −0.0889

0.3002 0.3685 0.4031 0.4490 0.4962

−0.6460 −0.7153 −0.7442 −0.7551 −0.7737

0.5535 0.5977 0.6485 0.6948 0.7479

−0.7494 −0.7429 −0.7295 −0.6967 −0.6726

0.7997 0.8516 0.9004 0.9325 0.9808

−0.5840 −0.4893 −0.3715 −0.2802 −0.1043

0.3008 0.3481 0.4043 0.4489 0.4994

−0.3243 −0.3362 −0.3629 −0.3762 −0.3706

0.5500 0.5981 0.6503 0.6970 0.7499

−0.3732 −0.3700 −0.3596 −0.3379 −0.2929

0.7962 0.8542 0.9023 0.9395

−0.2670 −0.2149 −0.1547 −0.1082

molar volume at infinite dilution. Fig. 4 shows the fitted VE curves, together with the experimental points. In all the systems, measured VE appear to be negative over the entire range of MTBE concentration. The curves are approximately symmetric with a minimum at a mole fraction at about 0.5. The negative deviations from the linear volumetric behavior are assumed to be caused by strong hydrogen bonding or the different molecular sizes. Table 8 Fitted parameters, standard deviations (S.D.) and partial excess molar volumes at infinite dilution (cm3 /mol) for the MTBE systems at 298.15 K System

A1

A2

A3

A4

A5

S.D. (cm3 /mol)

V¯1E,∞

V¯2E,∞

MTBE + 1-propanol MTBE + 2-propanol MTBE + 1-butanol MTBE + 2-butanol

−2.8648 −1.1600 −3.0653 −1.5100

−0.1977 −0.0101 −0.1687 −0.0916

−0.1925 −0.0134 −0.7008 −0.1570

−0.1433 −0.0839 −0.8906 0.0165

−0.4748 −0.4340 −0.2977 −0.2490

0.0068 0.0048 0.0097 0.0054

−3.1911 −1.5134 −3.0045 −1.8409

−3.8731 −1.7014 −5.1231 −1.9911

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Fig. 4. Excess molar volumes of the MTBE systems with C3 –C4 alcohols at 298.15 K.

4. Conclusion Isobaric or isothermal VLE for systems of MTBE +C1 –C4 alcohols were measured and correlated. The non-ideality was decreased with increasing carbon number of alcohols where’s the MTBE+methanol system shows azeotropic behavior. Extrapolated infinitely dilute activity coefficients were relatively agreed well with measured or estimated values by UNIFAC equation. Mixing process of butane + MTBE system was endothermic while that of isobutene + MTBE system was exothermic. Excess molar volumes of MTBE + C3 –C4 alcohol systems show negative deviation from the ideality because of hydrogen bonding of alcohols. Partial excess molar properties at infinite dilution were also successively calculated using the correlated Redlich–Kister. List of symbols A, B, C Antoine constants Ai parameter in the smoothing equation Aij parameter used in Margules, van Laar, Wilson, NRTL, UNIQUAC equation gij interaction energy in the NRTL equation E H excess molar enthalpy (J/mol) ME excess molar property Mi molecular weight of component i n number of parameters Ai N number of experimental values P total pressure (kPa) Pis vapor pressure of pure component i (kPa) S.D. standard deviation uij interaction energy in the UNIQUAC equation

S.-J. Park et al. / Fluid Phase Equilibria 200 (2002) 399–409

VE xi yi

409

excess molar volume (cm3 /mol) liquid phase mole fraction of component i vapor phase mole fraction of component i

Greek letters α non-randomness parameter in the NRTL equation γi activity coefficient of component i λij interaction energy in the Wilson equation (cal/mol) ρi density of component i (g/cm3 ) ρm density of the binary mixture (g/cm3 ) Acknowledgements This work was supported by grant no. 2000-1-30700-011-2 from the Basic Research Program of the Korea Science & Engineering Foundation. References [1] F.A. Mato, J. Chem. Eng. Data 36 (1991) 262. [2] E. Tusel-langer, J.M. Garcia Alonso, M.A. Villamanan Olfos, R.N. Lichtenthaler, J. Sol. Chem. 20 (1991) 153. [3] J. Gmehling, K. Fischer, J. Menke, J. Rarey, J. Weinert, J. Krafczyk, Dortmund Data Bank (DDB) overview, DDB data directory, version 2001. [4] K. Fischer, S.J. Park, J. Gmehling, Int. Electron. J. Phys. Chem. Data 2 (1996) 135. [5] J.H. Oh, S.J. Park, J. Chem. Eng. Data 42 (1997) 517. [6] S.J. Park, T.J. Lee, Korean J. Chem. Eng. 12 (1995) 110. [7] J.H. Oh, S.J. Park, J. Chem. Eng. Data 43 (1998) 1009. [8] O. Redlich, A.T. Kister, Indian Eng. Chem. 40 (1948) 345. [9] D.M. Trampe, C.A. Eckert, J. Chem. Eng. Data 36 (1991) 112. [10] U. Weidlich, J. Gmehling, Indian Eng. Chem. Res. 26 (1987) 1372. [11] TRC Thermodynamic Tables-Non-Hydrocarbons; Thermodynamics Research Center, The Texas A&M University system (1973). [12] C. Pettenati, P. Alessi, M. Fermeglia, I. Kikic, Thermochim. Acta 162 (1990) 203. [13] J.A. Dean, Handbook of Organic Chemistry, Donelly & Sons Co. (1987). [14] S.J. Park, Unpublished experimental data (2000). [15] J. Gmehling, S.J. Park, K. Fisher, B. Meents, Int. Data Ser. 3 (1992) 146.