J. Chem. Thermodynamics 38 (2006) 547–553 www.elsevier.com/locate/jct

Phase equilibrium properties of binary and ternary systems containing di-isopropyl ether + 1-butanol + benzene at 313.15 K Rosa M. Villaman˜a´n, M. Carmen Martı´n, Ce´sar R. Chamorro, Miguel A. Villaman˜a´n, Jose´ J. Segovia * Grupo de Termodina´mica y Calibracio´n TERMOCAL, Dpto. Ingenierı´a Energe´tica y Fluidomeca´nica, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, Paseo del Cauce s/n, E-47071 Valladolid, Spain Received 7 June 2005; received in revised form 11 July 2005; accepted 12 July 2005 Available online 19 September 2005

Abstract (Vapour + liquid) equilibria data of (di-isopropyl ether + 1-butanol + benzene), (di-isopropyl ether + 1-butanol) and (1-butanol + benzene) have been measured at T = 313.15 K using an isothermal total pressure cell. Data reduction by Barkers method provides correlations for the excess molar Gibbs energy using the Margules equation for the binary systems and the Wohl expansion for the ternary. The Wilson, NRTL and UNIQUAC models have been applied successfully to both the binary and the ternary systems reported here.  2005 Elsevier Ltd. All rights reserved. Keywords: VLE; Excess Gibbs energy; Ternary mixture; DIPE, 1-Butanol; Benzene

1. Introduction This work is part of a research program on the thermodynamic characterization of ternary mixtures, as the simplest multicomponent system, containing oxygenated additives (ethers and alcohols) and different type of hydrocarbons. Ethers and alcohols have been traditionally used as blending agents in the formulation of unleaded gasolines for enhancing the octane number. In previous studies VLE data of ethers as methyl tert-butyl ether (MTBE) [1–4], tert-amylmethyl ether (TAME) [5] or di-isopropyl ether (DIPE) [6–11] and two hydrocarbons have been measured as

*

Corresponding author. Tel.: +34 983 423420; fax: +34 983 423420. E-mail addresses: [email protected] (R.M. Villaman˜a´n), [email protected] (M.C. Martı´n), [email protected] (C.R. Chamorro), [email protected] (M.A. Villaman˜a´n), [email protected] (J.J. Segovia). 0021-9614/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2005.07.004

well as some mixtures containing ether + alcohol + hydrocarbon [12–17]. Now we want to focus on ternary systems containing di-isopropyl ether + benzene + different alcohols. These data not only contribute to a direct knowledge on (vapour + liquid) equilibria, they are useful to recalculate the parameters of the predictive models in order to improve them. But it is required experimental data of the highest quality available. The technique used in this work is one of the best because of its high accuracy, even some data measured previously have been selected for different data base banks. In this paper we report the (vapour + liquid) equilibria data of the ternary system (di-isopropyl ether + 1-butanol + benzene) and two of the corresponding binaries (di-isopropyl ether + 1-butanol) and (1-butanol + benzene), which have been measured at 313.15 K. The third binary system involved (di-isopropyl ether + benzene) has been measured previously by our group [6].

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R.M. Villaman˜a´n et al. / J. Chem. Thermodynamics 38 (2006) 547–553

2. Experimental Di-isopropyl ether and benzene used were purchased from Fluka Chemie AG and were of the highest purity available, chromatography quality reagents (of the series puriss. p.a.) with a purity >0.99 and >0.995 (GC), respectively. 1-Butanol used was anhydrous Aldrich product with a purity >0.999. All liquids degassed prior to measurements using a modified distillation method based on the technique of Van Ness and Abbott [18], under a vacuum. The purities of the chemicals were checked by gas chromatography and were found to be >0.995 for all the compounds. A static (vapour + liquid) equilibrium (VLE) apparatus consisting of an isothermal total pressure cell has been employed for measuring the binary and ternary mixtures. The technique was developed by Van Ness and co-workers [19,20]. Three positive displacement pumps of 100 ml capacity (Ruska, mod. 2200-801) equipped with piston injectors were used to inject known volumes of degassed components into a cell. The pump resolution is 0.01 ml and the resulting uncertainty in the volume injected is ±0.03 ml. The cell is a cylindrical stainless steel vessel with a capacity of about 180 ml and is provided with an externally-operated magnetic stirrer. Initially about 50 ml of one component are injected into the evacuated cell and the vapour pressure is recorded. The second and third components are then injected in appropriate proportions so as to achieve a desired composition. The total mass injected is determined from the volume differences corresponding to the initial and final positions of the pistons, the temperature of the injectors and the densities of the injected component, allowing us assuring an uncertainty in the mole fraction less than ±5 · 104, without sampling the phases. The cell is immersed in a high precision water bath (Hart Scientific model 6020) assuring a temperature stability of ±0.5 mK and thermostated at T = 313.15 K. The temperature is measured by a calibrated standard PRT-100 (SDL model 5385/100) connected to an a/c resistance bridge (ASL model F250) with a temperature resolution of 1 mK. The estimated uncertainty of the temperature measurement is ±10 mK. The pressure is measured using a differential pressure cell provided with a null indicator (Ruska models 2413705 and 2416-711, respectively). Atmospheric air balances the vapour pressure of the cell, a Bourdon fused quartz precision pressure gauge (Texas Instruments model 801) indicates the pressure with an estimated uncertainty of ±5 Pa for the 125 kPa range. Both temperature and pressure devices have been calibrated with own standards traceable to National Standards. Experimental values of total vapour pressure for the binary mixtures are obtained in two overlapping runs

starting from opposite ends of the composition range; for the ternary mixture they are obtained by adding a third component up to a mole fraction of x = 0.5, to a binary mixture with a mole fraction of one component close to x = (0.3, or 0.7), six dilution lines were carried out.

3. Results and correlations The use of this static technique gives us a set of equilibrium x, p data at constant T, so that Thermodynamics allows the calculation of the y values. Data reduction of the binary and ternary mixtures has been performed using Barkers method [21] according to well established procedures [22,23]. The non-ideality of the vapour phase is taken into account by the virial equation of state, truncated at the second term. The second virial coefficients are calculated by the Hayden OConnell method [24] using the coefficients given by Dymond et al. [25]. In table 1, the pure-component and interaction second virial coefficients (Bij) are given; it also contains the average vapour pressures of the pure constituents measured in this work and they are compared with those reported in the literature as a check for complete degassing. Correlations for both measured binary systems are given by five-parameter Margules [26] equation:

TABLE 1 Average values used for the reduction of the data for experimental vapour pressures psi compared with those obtained from the literature psi (lit.), molar volumes V Li and second virial coefficients Bii and Bij for the compounds investigated in this work at T = 313.15 K DIPE (i = 1) psi =ðkPaÞ

37.108 a

psi ðlit.Þ=ðkPaÞ

37.081 37.090b 37.128c

V Li =ðcm3  mol1 Þi

145

1-Butanol (i = 2)

Benzene (i = 3)

2.499

24.386

d

2.477 2.518e 2.516f 93

24.367f 24.398c,g 24.320h 91

1 j

Bi1/(cm Æ mol )

1687.8

1625.9

1701.0

Bi2/(cm3 Æ mol1)j

1625.9

5179.5

1071.8

1 j

1701.0

1071.8

1310.5

3

3

Bi3/(cm Æ mol ) a

Calculated from the Antoine equation using constants reported by Riddick et al. [32]. b Reported by Ambrose et al. [33]. c Reported by Chamorro et al. [6]. d Reported by Ambrose et al. [34]. e Reported by Garriga et al. [35]. f Reported by Oracz [31]. g Reported by Garriga et al. [36]. h Calculated from the Antoine equation using constants reported by Reid et al. [37]. i Reported in TRC.[38]. j Calculated by Hayden et al. [24] from Dymond et al. [25].

R.M. Villaman˜a´n et al. / J. Chem. Thermodynamics 38 (2006) 547–553 TABLE 2 Total pressure p for the binary systems at T = 313.15 K, and at various compositions of the liquid phase x1 and the calculated composition of the vapour phase y1 using Margules equation x1

y1

p/(kPa)

0.0000 0.0591 0.1010 0.1480 0.2012 0.2491 0.3005 0.3503 0.3993 0.4003 0.4482 0.4487 0.4980 0.4983 0.5486 0.5490 0.5991 0.5993 0.6491 0.6996 0.7494 0.7998 0.8504 0.9016 0.9520 1.0000

Di-isopropyl ether (1) + 1-butanol (2) 0.0000 0.6607 0.7688 0.8290 0.8672 0.8890 0.9053 0.9171 0.9262 0.9264 0.9336 0.9337 0.9401 0.9401 0.9458 0.9458 0.9509 0.9509 0.9557 0.9604 0.9650 0.9700 0.9756 0.9823 0.9903 1.0000

0.0000 0.0590 0.1080 0.1510 0.1980 0.2559 0.3023 0.3533 0.4027 0.4028 0.4501 0.4519 0.4997 0.5019 0.5497 0.5506 0.5999 0.6001 0.6497 0.7001 0.7502 0.8010 0.8591 0.9108 0.9547 1.0000

Benzene (1) + 1-butanol (2) 0.0000 0.6320 0.7533 0.8067 0.8423 0.8699 0.8850 0.8973 0.9064 0.9064 0.9135 0.9137 0.9197 0.9200 0.9252 0.9253 0.9301 0.9301 0.9346 0.9389 0.9431 0.9474 0.9533 0.9613 0.9735 1.0000

2.490 6.973 9.837 12.729 15.573 17.828 19.943 21.756 23.301 23.361 24.743 24.740 26.029 26.052 27.238 27.257 28.357 28.343 29.381 30.391 31.369 32.362 33.396 34.525 35.772 37.091

TABLE 2 (continued) x1

y1

p/(kPa)

0.1994 0.2497 0.2998 0.3500 0.3992 0.3992 0.4489 0.4501 0.4991 0.5003 0.5490 0.5499 0.5986 0.6005 0.6485 0.6991 0.7493 0.7978 0.8508 0.9078 0.9640 1.0000

0.2936 0.3515 0.4054 0.4563 0.5039 0.5040 0.5503 0.5514 0.5954 0.5965 0.6391 0.6399 0.6814 0.6830 0.7231 0.7646 0.8052 0.8438 0.8854 0.9296 0.9727 1.0000

28.019 28.770 29.481 30.155 30.785 30.794 31.400 31.405 31.988 31.995 32.563 32.565 33.113 33.127 33.642 34.184 34.698 35.174 35.707 36.253 36.790 37.126

a

Data published in [6].

gij ¼ GEm =RT ¼ fAji xi þ Aij xj  ðkji xi þ kij xj Þxi xj þ gx2i x2j gxi xj .

ð1Þ The data of the ternary mixture are adequately correlated by the three-parameter Wohl [27] expansion,

2.492 6.418 9.176 11.265 13.232 15.244 16.580 17.825 18.835 18.833 19.658 19.673 20.383 20.402 21.004 21.005 21.548 21.541 22.034 22.452 22.831 23.176 23.516 23.834 24.138 24.372 a

0.0000 0.0504 0.1011 0.1498

549

Di-isopropyl ether (1) + benzene (2) 0.0000 0.0878 0.1652 0.2318

24.398 25.442 26.387 27.221

g123 ¼ GEm =RT ¼ g12 þ g13 þ g23 þ ðC 0 þ C 1 x1 þ C 2 x2 Þx1 þ x2 þ x3 ;

ð2Þ

which includes the parameters of the corresponding binary systems. The adjustable parameters C0, C1 and C2 are found by regression of the ternary data. The binary and ternary systems have also been correlated using Wilson [28], NRTL [29] and UNIQUAC [30] models, whose respective excess Gibbs energy expressions are given by the following equations ! X X GEm =RT ¼  xi ln xj Aij ; ð3Þ i

GEm =RT

¼

X i

GEm =RT ¼

X

xi

j

X

Aji Gji xj =

j

i

xi lnðui =xi Þ þ z=2 qi xi ln

! Gki xk ;

ð4Þ

k

i

X

X

X

X

!

qi xi lnð#i =qi Þ

i

#j Aji ;

ð5Þ

j

P where Gji = exp(ajiAji), #i ¼ qj xi = j qj xj , ui ¼ ri xi = P j rj xj , and z = 10. Tables 2 and 3 give experimental values of total pressure and the corresponding compositions of the liquid and vapour phases for the binary systems and the

R.M. Villaman˜a´n et al. / J. Chem. Thermodynamics 38 (2006) 547–553

550

TABLE 3 Total pressure p for the ternary system di-isopropyl ether (1) + 1butanol(2) + benzene(3) at T = 313.15 K, and at various compositions of the liquid x1, x2 and the vapour phases y1, y2 calculated using Wohl expansion x1

x2

y1

y2

p/kPa

1.0000 0.6992 0.6818 0.6643 0.6310 0.5951 0.5594 0.5247 0.4893 0.4547 0.4198 0.3846 0.3500 0.0000 0.3006 0.2904 0.2855 0.2707 0.2557 0.2406 0.2240 0.2106 0.1945 0.1806 0.1648 0.0000 0.3032 0.2953 0.2881 0.2729 0.2578 0.2425 0.2274 0.2123 0.1972 0.1820 0.1666 0.1516 0.9999 0.7000 0.6832 0.6653 0.6308 0.5954 0.5598 0.5237 0.4897 0.4545 0.4198 0.3847 0.3497 0.0000 0.0000 0.0328 0.0569 0.1044 0.1548 0.1988 0.2485 0.2980

0.0000 0.3008 0.2934 0.2859 0.2715 0.2560 0.2407 0.2257 0.2105 0.1956 0.1805 0.1654 0.1505 1.0000 0.6994 0.6754 0.6643 0.6296 0.5945 0.5594 0.5206 0.4895 0.4518 0.4195 0.3829 0.0000 0.0000 0.0259 0.0497 0.0999 0.1497 0.2003 0.2502 0.3000 0.3498 0.4000 0.4505 0.5003 0.0000 0.0000 0.0240 0.0496 0.0989 0.1494 0.2003 0.2518 0.3004 0.3507 0.4003 0.4505 0.5004 1.0000 0.6922 0.6695 0.6528 0.6199 0.5849 0.5544 0.5200 0.4857

1.0000 0.9603 0.9343 0.9081 0.8590 0.8066 0.7557 0.7071 0.6584 0.6117 0.5654 0.5195 0.4750 0.0000 0.9054 0.8331 0.8009 0.7084 0.6253 0.5521 0.4814 0.4317 0.3783 0.3374 0.2957 0.0000 0.4089 0.3979 0.3895 0.3756 0.3653 0.3569 0.3498 0.3435 0.3375 0.3316 0.3256 0.3197 0.9999 0.7654 0.7589 0.7529 0.7433 0.7355 0.7291 0.7234 0.7186 0.7139 0.7093 0.7045 0.6992 0.0000 0.0000 0.0955 0.1606 0.2759 0.3796 0.4565 0.5302 0.5924

0.0000 0.0397 0.0393 0.0388 0.0381 0.0373 0.0366 0.0359 0.0352 0.0345 0.0338 0.0330 0.0322 1.0000 0.0946 0.0908 0.0890 0.0838 0.0790 0.0747 0.0705 0.0676 0.0644 0.0619 0.0593 0.0000 0.0000 0.0097 0.0167 0.0274 0.0348 0.0407 0.0457 0.0504 0.0551 0.0600 0.0655 0.0715 0.0000 0.0000 0.0061 0.0116 0.0203 0.0272 0.0330 0.0382 0.0427 0.0474 0.0523 0.0576 0.0636 1.0000 0.1135 0.1061 0.1009 0.0915 0.0827 0.0760 0.0694 0.0637

37.116 30.395 30.290 30.205 30.022 29.817 29.606 29.394 29.178 28.949 28.710 28.464 28.211 2.510 19.931 20.358 20.551 21.128 21.660 22.130 22.588 22.908 23.239 23.483 23.720 24.385 29.508 29.023 28.576 27.786 27.096 26.440 25.802 25.150 24.469 23.733 22.933 22.057 37.131 34.197 33.577 32.963 31.907 30.939 30.032 29.148 28.305 27.404 26.474 25.462 24.369 2.505 16.790 17.568 18.184 19.391 20.676 21.774 22.932 24.025

TABLE 3 (continued) x1

x2

y1

y2

p/kPa

0.3480 0.3987 0.4503 0.4985 0.0000 0.0000 0.0336 0.0516 0.1139 0.1489 0.1999 0.2517 0.2991 0.3491 0.3962 0.4497 0.4999

0.4511 0.4160 0.3803 0.3469 0.0000 0.3006 0.2905 0.2851 0.2663 0.2558 0.2404 0.2249 0.2106 0.1955 0.1814 0.1653 0.1502

0.6460 0.6927 0.7341 0.7681 0.0000 0.0000 0.0579 0.0879 0.1862 0.2378 0.3087 0.3755 0.4327 0.4891 0.5389 0.5919 0.6388

0.0587 0.0541 0.0499 0.0462 0.0000 0.0611 0.0582 0.0567 0.0518 0.0493 0.0459 0.0427 0.0398 0.0370 0.0344 0.0315 0.0289

25.073 26.083 27.063 27.941 24.393 22.455 22.978 23.261 24.236 24.780 25.565 26.352 27.045 27.775 28.452 29.215 29.925

ternary system where the vapour compositions have been calculated by Margules equation and Wohl expansion, respectively. The data correlation results for the binary systems are summarized on table 4. It contains the values of the adjustable parameters of the models which lead to the best results using Barkers method, the root mean square deviation (r.m.s.d.) of the difference between the experimental and the calculated pressure and the maximum value of this difference (max Dp). For the ternary system, the results of the correlation are given on table 5. The results are shown graphically on figures 1 and 2 where p–x–y diagrams and GEm –x curves are plotted for the binary systems. A three dimensional oblique view for pressure and excess Gibbs energy as a function of the ternary liquid composition are shown on figures 3 and 4.

4. Discussion The two binary systems containing 1-butanol exhibit a large deviation from the ideality. Five-parameter Margules equation fits better than the other models the experimental data. The values of the difference between experimental and calculated pressure for the binary systems are represented in figure 5 where it is shown how the model fits the data and a good agreement of experimental pressure measured twice for compositions 0.4 6 x1 6 0.6. The root mean square deviations in pressure are 10 Pa for the system with DIPE and 11 Pa for the system with benzene, the maximum deviations are 21 Pa and 18 Pa, respectively. In both binary system, the values of the excess Gibbs energy are positive in

R.M. Villaman˜a´n et al. / J. Chem. Thermodynamics 38 (2006) 547–553

551

TABLE 4 Determined parameters of the models used for the binary subsystems of ternary system di-isopropyl ether (1) + 1-butanol (2) + benzene (3) at T = 313.15 K, together with the root mean square deviation of pressure (r.m.s.d. Dp) and the maximum value of the deviation (max|Dp|) Margules A12 A21 k12

0.8169 1.2049 0.0582 0.1702 0.2329

21

g a12 r.m.s.d. Dp/kPa max |Dp|/kPa

Wilson

0.010 0.021

A12 A21 k12 k21 g a12 r.m.s.d. Dp/kPa max |Dp|/kPa

1.1521 2.1355 0.7754 1.9784 1.3924

0.036 0.103 Benzene (1) + 1-butanol (2) 0.7373 0.1508

0.011 0.018

A12 A21 k12 = k21 a12 r.m.s.d. Dp/kPa max |Dp|/kPa

0.2134 0.1277 0.0282

NRTL

Di-isopropyl ether (1) + 1-butanol (2) 0.7994 0.3574

0.029 0.062 Di-isopropyl ether (1) + benzene (2)a 0.5515 1.3762 0.3 0.006 0.013

0.005 0.009

UNIQUAC

0.6238 0.8953

0.4509 1.3949

0.4741 0.023 0.065

0.041 0.079

0.3838 0.7404

0.4969 1.1229

0.5668 0.052 0.096

0.145 0.291

0.4967 0.7905

0.9014 1.0698

0.005 0.008

0.006 0.013

The Dp term is defined as the difference between the experimental and calculated pressure. a Data published in [6].

TABLE 5 Determined parameters of the models used for ternary system diisopropyl ether (1) + 1-butanol (2) + benzene(3) at T = 313.15 K, together with the root mean square deviation of pressure (r.m.s.d. Dp) and the maximum value of the deviation (max |Dp|)

C0 C1 C2 A12 A21 A13 A31 A23 A32 a12 a13 a23 r.m.s.d. Dp/kPa max |Dp|/kPa

Wilson

NRTL

30

UNIQUAC

2.3726 0.5804 0.7023 0.8375 0.3380 0.3530 1.7319 0.1759 0.6960

0.033 0.058

35

25 p/kPa

Wohl

40

0.060 0.226

1.0496 0.1925 0.6603 1.0585 0.5703 1.6122 0.4741 0.3000 0.5668 0.043 0.142

0.4246 1.4449 1.3438 0.6718 1.2033 0.4427

20 15 10 5 0

0

0.2

0.4

0.6

0.8

1

x1, y1 0.048 0.181

The Dp is defined as the difference between the experimental and calculated pressure.

FIGURE 1. Total vapour pressure at 313.15 K of the three binary systems as a function of the liquid, x1, and vapour composition, y1: (e) di-isopropyl ether(1) + 1-butanol(2); (n) benzene(1) + 1-butanol (2); and (h) di-isopropyl ether(1) + benzene(2).

the whole range of compositions, the highest values are obtained for an alcohol mole fraction in the liquid phase of 0.45, they are 644 J Æ mol1 and 917 J Æ mol1, respectively.

We have found in the literature data for the system 1butanol + benzene at the same temperature [31] we have correlated their data using five-parameter Margules equation and the value of the root mean square deviation is 38 Pa with a maximum deviation of 70 Pa. Both

R.M. Villaman˜a´n et al. / J. Chem. Thermodynamics 38 (2006) 547–553

552

1000 900 800

600 500

E

-1

G /(J·mol )

700

400 300 200 100 0 0

0.2

0.4

0.6

0.8

1

x1 FIGURE 2. Excess Gibbs energy of the three binary systems as a function of the liquid composition, x1: (—) di-isopropyl ether (1) + 1-butanol (2); (3) benzene (1) + 1-butanol (2); and (  ) di-isopropyl ether (1) + benzene (2).

FIGURE 4. Oblique view of the excess Gibbs energy surface reduced by the Wilson equation for the ternary system di-isopropyl ether (1) + 1-butanol (2) + benzene (3) at 313.15 K.

(pcalc-pexp)/kPa

0.03

0

-0.03

0

0.2

0.4

x1

0.6

0.8

1

FIGURE 5. Pressure residuals, pcalc  pexp, defined as differences between calculated pressures and experimental pressures as a function of the liquid composition, x1: (e) di-isopropyl ether(1) + 1-butanol(2); (n) benzene(1) + 1-butanol(2). FIGURE 3. Oblique view of the pressure surface reduced by the Wohl equation for the ternary system di-isopropyl ether (1) + 1-butanol (2) + benzene (3) at 313.15 K.

(pcalc-pexp)/kPa

set of data have been compared through the calculation of the difference between the pressure calculated using our correlation of five-parameter Margules equation and their experimental pressures. This comparison is shown on figure 6 and it can be observed that the experimental pressure measured by Oracz is slight higher than our values in alcohol rich region. Data for the ternary system have also been well-correlated by all the models however Wohl expansion gives the best fit. The root mean square deviation in pressure is 33 Pa with a maximum deviation of 58 Pa. The figures plot for the ternary system show how pressure and ex-

0.2

0

-0.2

0

0.2

0.4

x1

0.6

0.8

1

FIGURE 6. Pressure residuals, pcalc  pexp, for the binary system benzene (1) + 1-butanol (2), defined as differences between calculated pressures with Margules equation fitted with data from this work and experimental pressures, as a function of the liquid composition, x1: (n) this work; (s) Oracz.

R.M. Villaman˜a´n et al. / J. Chem. Thermodynamics 38 (2006) 547–553

cess Gibbs energy change with composition. The ternary system present a positive deviation from ideality and the highest value of GEm corresponds to the maximum of the least ideal binary system that is 917 J Æ mol1 for the mixture (0.55 benzene + 0.45 1-butanol). Acknowledgement Support for this work came from the Spanish Ministry of Science and Technology, project PPQ2002-04414C02-02.

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JCT 05-144

Phase equilibrium properties of binary and ternary ...

Data reduction by BarkerÕs method pro- vides correlations for the excess molar Gibbs energy using the Margules equation for the binary systems and the Wohl ...

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