J. Chem. Thermodynamics 36 (2004) 87–93

www.elsevier.com/locate/jct

(Vapour + liquid) equilibrium of binary mixtures (1,3-dioxolaneor 1,4-dioxane+ 2-methyl-1-propanol or 2-methyl-2-propanol)

at isobaric conditions

Antonio Reyes a, Carlos Lafuente a, Jos�e Mi~nones Jr. b, Udo Kragl c, F�elix M. Royo a,*

a Departamento de Qu�ımica Org�anica-Qu�ımica F�ısica, Facultad de Ciencias, Universidad de Zaragoza, Ciudad Universitaria, 50009 Zaragoza, Spainb Departamento de Qu�ımica F�ısica, Facultad de Farmacia, Campus Universitario Sur, Santiago de Compostela 15706, Spain

c Technische Chemie, Universit€at Rostock, 18055 Rostock, Germany

Received 14 July 2003; accepted 11 September 2003

Abstract

Isobaric (vapour+ liquid) equilibrium of (1,3-dioxolane or 1,4-dioxane+ 2-methyl-1-propanol or 2-methyl-2-propanol) at 40.0

kPa and 101.3 kPa has been studied with a dynamic recirculating still. The experimental VLE data are thermodynamically con-

sistent. From these data, activity coefficients were calculated and correlated with the Margules, van Laar, Wilson, NRTL and

UNIQUAC equations. The VLE results have been compared with the predictions by the UNIFAC and ASOG methods.

� 2003 Elsevier Ltd. All rights reserved.

Keywords: (Vapour+ liquid) equilibrium; Cyclic ethers; Butanols; ASOG; UNIFAC

1. Introduction

We present here the study of the (vapour + liquid)

equilibrium at isobaric conditions for the mixtures

1,3-dioxolane (C3H6O2) or 1,4-dioxane (C4H8O2), with

2-methyl-1-propanol {CH3CH(CH3)CH2OH} or 2-meth-yl-2-propanol {CH3C(CH3)(OH)CH3}. This work fol-

lows our investigations about thermodynamic properties

of liquid mixtures containing oxygenated compounds

[1–4].

For each binary mixture, the experimental data have

been checked for thermodynamic consistency and the

calculated activity coefficients have been correlated with

several equations [5–9]. Predictions with some groupcontribution methods [10,11] have been performed and

compared with the experimental data.

A survey of the literature shows that there are one

study of the (vapour + liquid) equilibrium for (1,4-di-

oxane + 2-methyl-1-propanol) at isothermal conditions

[12] and other one for (1,4-dioxane+ 2-methyl-2-pro-

panol) at isobaric conditions [13].

* Corresponding author. Tel.: +349-76-761298; fax: +34-976761202.

E-mail address: femer@posta.unizar.es (F.M. Royo).

0021-9614/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jct.2003.09.001

2. Experimental

The liquids used were: C4H8O2 (mole fraction purity

>0.999), CH3CH(CH3)CH2OH and CH3C(CH3)(OH)

CH3 (mole fraction purity >0.995) and C3H6O2 (mole

fraction purity >0.99) supplied by Aldrich. The purityof the materials was checked by a chromatographic

method, confirming the absence of other significant or-

ganic components. All liquids were used without further

purification, and the isomeric butanols were stored over

activated molecular sieve type 0.3 nm from Merck. The

comparison of measured densities and normal boiling

points of the chemicals with literature values [14–16] is

shown in table 1.The still used to study the (vapour+ liquid) equilib-

rium was an all-glass dynamic recirculating one, equip-

ped with a Cottrell pump. It was a commercial unit

(Labodest model) built in Germany by Fischer. The

equilibrium temperatures were measured to an accuracy

of �0.01 K by means of a thermometer (model F25)

from Automatic Systems Laboratories, and the pressure

in the still was measured with a pressure transducerDruck PDCR 110/W (pressure indicator DPI201) with

an accuracy of �0.1 kPa. Compositions of both phases

TABLE 1

Densities at T ¼ 298:15 K and normal boiling points of the pure compounds and comparison with literature data

Compound q/(kg �m�3) Tb/K

Expt. Lit. Expt. Lit.

C3H6O2 1058.62 1058.66a 348.55 348.8b

C4H8O2 1027.88 1027.97b 374.56 374.47b

CH3CH(CH3)CH2OH 797.98 797.8c 380.72 380.81c

CH3C(CH3)(OH)CH3 781.00 781.2c 355.50 355.57c

aReference [14].bReference [15].cReference [16].

88 A. Reyes et al. / J. Chem. Thermodynamics 36 (2004) 87–93

vapour and liquid were determined by a densimetric

analysis. The estimated error in the determination of

both liquid and vapour phase mole fractions is �0.0001.

The correct running of the different devices was pe-

riodically checked and rearranged if necessary.

3. Results

The (vapour + liquid) equilibrium data, T, x1 and y1,along with activity coefficients, ci, are gathered in table 2.

The corresponding (T ; x1; y1) diagrams are shown in fig-

ures 1 to 4. Some of the systems show minimum tem-

perature azeotropes, information about the composition

and boiling temperature of the azeotropes is summarisedin table 3.

The activity coefficients of the components in the li-

quid phase were calculated from the following equations:

ci ¼yiPxip�i

expBii � V �

i

� �P � p�i� �

þ ð1� yiÞ2PdijRT

" #; ð1Þ

where

dij ¼ 2Bij � Bii � Bjj; ð2Þ

where xi and yi are the liquid and vapour phase

compositions, P is the total pressure, p�i are the va-pour-pressures of the pure compounds calculated by

using the Antoine�s equation, where the constants

[15,17,18] are given in table 4, Bii are the second virial

coefficients: the second virial coefficients of the cyclic

ethers were estimated by the Redlich–Kwong equation

[19], while for the butanols, the equations of the TRC

tables were used, Bij is the cross second virial coeffi-

cient calculated using a suitable mixing rule [20], andV �i are the molar volumes of the saturated liquids,

these molar volumes were calculated using the Yen

and Woods method [21].

The thermodynamic consistency of the experimental

results was checked using the Van Ness method [22],

described by Fredenslund et al. [23] using a third order

Legendre polynomial for the excess Gibbs energies.

According to this test, experimental data are consideredconsistent if the average deviation in y ðDyÞ is smaller

than 0.01. All the experimental data are consistent, as

one can see in table 5.

The activity coefficients were correlated with the

Margules, Van Laar, Wilson, NRTL and UNIQUAC

equations. Estimation of the parameters for all the

equations was based on minimisation of an objective

function in terms of experimental and calculated civalues [24]. These adjustable parameters, A12 and A21

(see definitions in reference [18]) along with the average

deviation in T ðDT Þ, the average deviation in y ðDyÞ andthe activity coefficients at infinite dilution, c1i , are listed

in table 6. All the equations correlated the activity co-

efficients quite well.

As the results show, the interactions between the

unmixed compounds, that is dispersion forces and di-pole–dipole interactions in cyclic ethers and hydrogen-

bonding in butanols, are stronger than interac-

tions in the mixture. This fact leads to slightly positive

deviations from ideality of the systems studied at both

pressures. Nevertheless, the dipole moment for pure

C4H8O2 is appreciably lower than for the C3H6O2 one

[15], so the weakening of dipole–dipole interactions have

minor influence over the observed behaviour and thedeviations from ideality are less marked for the systems

containing C4H8O2.

The same effect was described in a previous work

[2] with systems of both cyclic ethers with 1-butanol

and 2-butanol. Combining the results of reference [2]

with those here obtained it can be pointed out that

given a cyclic ether, the biggest deviations from ide-

ality correspond to the mixtures with the primary al-cohols (1-butanol and 2-methyl-1-propanol), being

very similar those with the secondary and the tertiary

butanols.

4. (Vapour + liquid) equilibrium predictions

The UNIFAC and ASOG methods were used to

predict the (vapour + liquid) equilibrium of the systems

studied. The temperature and vapour-phase composition

obtained experimentally were compared with the theo-

retical predictions using UNIFAC and ASOG methodsand in table 7, the average deviations in temperature and

TABLE 2

Experimental VLE data and activity coefficients for the binary

mixtures at indicated pressure

T/K x y ci cj

xC3H6O2 + (1� x)CH3CH(CH3)CH2OH

P ¼ 40:0 kPa

352.63 0.0436 0.2180 1.756 1.044

348.56 0.0840 0.3822 1.820 1.035

343.95 0.1447 0.5296 1.706 1.047

339.36 0.2259 0.6629 1.601 1.037

335.55 0.3263 0.7443 1.424 1.095

331.90 0.4615 0.8044 1.243 1.268

330.74 0.5138 0.8333 1.207 1.273

328.80 0.6263 0.8694 1.111 1.440

327.71 0.6889 0.8919 1.080 1.520

326.22 0.7898 0.9245 1.034 1.706

325.40 0.8442 0.9427 1.018 1.829

324.43 0.9163 0.9659 0.998 2.140

323.41 0.9854 0.9943 0.994 2.174

P ¼ 101:3 kPa

377.31 0.0425 0.1465 1.481 1.040

374.38 0.0810 0.2691 1.543 1.033

369.88 0.1627 0.4332 1.399 1.042

366.53 0.2211 0.5383 1.406 1.040

361.79 0.3517 0.6635 1.251 1.102

359.13 0.4446 0.7302 1.179 1.152

356.68 0.5237 0.7844 1.158 1.190

354.83 0.6237 0.8317 1.092 1.274

353.26 0.7019 0.8673 1.063 1.358

351.67 0.7862 0.9054 1.041 1.448

350.70 0.8525 0.9334 1.021 1.543

349.85 0.9089 0.9563 1.009 1.704

348.74 0.9867 0.9934 1.001 1.854

xC3H6O2 + (1� x)CH3C(CH3)(OH)CH3

P ¼ 40:0 kPa

333.27 0.0154 0.0439 1.940 1.000

331.10 0.0819 0.1869 1.681 1.008

328.67 0.1808 0.3343 1.491 1.038

327.43 0.2436 0.4144 1.437 1.050

326.14 0.3372 0.5048 1.328 1.080

324.39 0.5159 0.6338 1.166 1.193

324.16 0.5631 0.6607 1.124 1.239

323.78 0.6018 0.6862 1.108 1.281

323.32 0.7114 0.7548 1.050 1.415

323.18 0.7534 0.7846 1.036 1.465

322.94 0.8450 0.8787 1.044 1.330

322.95 0.8881 0.8858 1.001 1.734

323.04 0.9547 0.9486 0.994 1.920

P ¼ 101:3 kPa

354.19 0.0206 0.0603 2.455 1.008

352.15 0.1210 0.2052 1.516 1.027

351.89 0.1725 0.2643 1.380 1.020

351.02 0.2437 0.3397 1.290 1.036

349.80 0.3630 0.4428 1.173 1.090

348.63 0.5056 0.5627 1.111 1.155

348.38 0.5672 0.6148 1.091 1.174

348.26 0.6011 0.6319 1.062 1.223

347.91 0.7104 0.7243 1.042 1.281

347.88 0.7535 0.7589 1.030 1.318

347.90 0.8452 0.8363 1.011 1.425

TABLE 2 (continued)

T/K x y ci cj

348.05 0.8870 0.8749 1.003 1.483

348.28 0.9548 0.9457 0.999 1.596

xC4H8O2 + (1� x)CH3CH(CH3)CH2OH

P ¼ 40:0 kPa

356.97 0.0432 0.0846 1.368 1.011

355.95 0.0874 0.1597 1.321 1.017

354.65 0.1556 0.2647 1.285 1.017

353.39 0.2323 0.3585 1.217 1.032

351.93 0.3335 0.4734 1.177 1.041

350.76 0.4334 0.5573 1.111 1.085

350.08 0.4869 0.5997 1.089 1.118

349.08 0.5952 0.6826 1.051 1.176

348.56 0.6720 0.7378 1.024 1.228

347.96 0.7498 0.7949 1.010 1.295

347.59 0.8075 0.8379 1.002 1.353

347.02 0.8810 0.9241 1.034 1.053

346.80 0.9563 0.9583 0.996 1.592

P ¼ 101:3 kPa

380.75 0.0428 0.0618 1.202 1.011

380.20 0.0854 0.1206 1.194 1.011

379.24 0.1560 0.2094 1.167 1.020

378.40 0.2387 0.3067 1.144 1.022

377.40 0.3322 0.4010 1.107 1.043

376.36 0.4364 0.4962 1.075 1.080

375.99 0.4866 0.5430 1.066 1.090

375.37 0.5966 0.6416 1.046 1.114

375.05 0.6756 0.7081 1.030 1.142

374.79 0.7446 0.7676 1.020 1.166

374.59 0.8106 0.8220 1.010 1.214

374.52 0.8848 0.8778 0.990 1.374

374.49 0.9538 0.9536 0.998 1.303

xC4H8O2 + (1� x)CH3C(CH3)(OH)CH3

P ¼ 40:0 kPa

334.21 0.1296 0.0972 1.198 1.023

334.90 0.2298 0.1765 1.194 1.022

335.07 0.3135 0.2524 1.242 1.033

335.74 0.4051 0.3228 1.198 1.048

337.05 0.5515 0.4464 1.156 1.072

337.83 0.5929 0.4694 1.097 1.093

338.55 0.6530 0.5177 1.069 1.130

339.63 0.7406 0.6013 1.051 1.192

340.61 0.7926 0.6493 1.022 1.257

341.41 0.8344 0.6988 1.014 1.307

341.99 0.8872 0.7747 1.034 1.400

343.98 0.9312 0.8461 1.000 1.442

P ¼ 101:3 kPa

356.28 0.1256 0.0890 1.267 1.012

357.13 0.2289 0.1556 1.180 1.031

358.01 0.3127 0.2168 1.169 1.038

359.38 0.4154 0.2906 1.126 1.052

360.82 0.5524 0.3956 1.099 1.112

361.78 0.5949 0.4354 1.088 1.109

362.57 0.6530 0.4800 1.065 1.159

363.71 0.7296 0.5613 1.075 1.206

365.03 0.7898 0.6194 1.050 1.285

365.83 0.8227 0.6645 1.054 1.307

368.12 0.8824 0.7444 1.024 1.388

370.84 0.9413 0.8318 0.986 1.671

A. Reyes et al. / J. Chem. Thermodynamics 36 (2004) 87–93 89

FIGURE 1. Temperature plotted against mole fraction in the (T ; x1; y1)diagram for (xC3H6O2 + (1� x)CH3CH(CH3)CH2OH): (�, j) ex-

perimental data at 40.0 kPa; (s, d) at 101.3 kPa; (——) Wilson

equation.

FIGURE 4. Temperature plotted against mole fraction in the (T ; x1; y1)diagram for (xC4H8O2 + (1� x)CH3C(CH3)(OH)CH3): (�, j) exper-

imental data at 40.0 kPa; (s, d) at 101.3 kPa; (——) Wilson equation.

FIGURE 3. Temperature plotted against mole fraction in the (T ; x1; y1)diagram for (xC4H8O2 + (1� x)CH3CH(CH3)CH2OH): (�, j) ex-

perimental data at 40.0 kPa; (s, d) at 101.3 kPa; (——) Wilson

equation.

FIGURE 2. Temperature plotted against mole fraction in the (T ; x1; y1)diagram for (xC3H6O2 + (1� x)CH3C(CH3)(OH)CH3): (�, j) exper-

imental data at 40.0 kPa; (s, d) at 101.3 kPa; (——) Wilson equation.

90 A. Reyes et al. / J. Chem. Thermodynamics 36 (2004) 87–93

TABLE 3

Composition and boiling temperature of the azeotropic mixtures

System P/kPa x T/K

xC3H6O2 + (1� x)CH3C(CH3)(OH)CH3 40.0 0.922 323.0

101.3 0.725 348.0

xC4H8O2 + (1� x)CH3CH(CH3)CH2OH 40.0 0.929 374.4

TABLE 6

Correlation parameters, average deviations DT and Dy, and activity coefficients at infinite dilution, c1i and c1j

Equation Aij Aji DT /K Dy c1i c1j

xC3H6O2 + (1� x)CH3CH(CH3)CH2OH

P ¼ 40:0 kPa

Margulesa 0.6988 0.8566 0.17 0.0079 2.01 2.35

Van Laara 0.7108 0.8535 0.14 0.0081 2.04 2.35

Wilsonb 1693.8499 748.3938 0.14 0.0070 2.01 2.35

NRTLb 1653.7526 682.3528 0.14 0.0070 2.01 2.34

UNIQUACb 1012.4786 )265.2962 0.13 0.0072 2.03 2.33

P ¼ 101:3 kPa

Margules 0.4736 0.6440 0.23 0.0065 1.61 1.90

Van Laar 0.4857 0.6482 0.22 0.0063 1.63 1.91

Wilson 1119.3325 770.4345 0.24 0.0054 1.61 1.91

NRTL 1998.7074 )130.7100 0.24 0.0055 1.62 1.90

UNIQUAC )108.3582 856.9975 0.24 0.0054 1.61 1.91

xC3H6O2+(1� x)CH3C(CH3)(OH)CH3

P ¼ 40:0 kPa

Margules 0.6450 0.6204 0.08 0.0051 1.91 1.86

Van Laar 0.6463 0.6193 0.08 0.0051 1.91 1.86

Wilson 1979.5679 )94.2541 0.08 0.0049 1.91 1.86

NRTL 576.6816 1242.1782 0.08 0.0049 1.90 1.85

UNIQUAC 350.3636 143.2298 0.08 0.0049 1.90 1.85

TABLE 5

Results of the thermodynamic consistency test with average deviations DP and Dy

System P/kPa DP /kPa Dy

xC3H6O2 + (1� x)CH3CH(CH3)CH2OH 40.0 0.4 0.0083

101.3 0.9 0.0070

xC3H6O2 + (1� x)CH3C(CH3)(OH)CH3 40.0 0.2 0.0069

101.3 0.5 0.0043

xC4H8O2 + (1� x)CH3CH(CH3)CH2OH 40.0 0.3 0.0084

101.3 0.4 0.0066

xC4H8O2 + (1� x)CH3C(CH3)(OH)CH3 40.0 0.5 0.0029

101.3 0.7 0.0053

TABLE 4

Coefficients of Antoine�s equation of the pure compounds with temperature in �C and pressure in kPa

Compound A B C

C3H6O2a 6.23182 1236.700 217.235

C4H8O2b 6.55635 1554.679 240.337

CH3CH(CH3)CH2OHc 6.50091 1275.197 175.187

CH3C(CH3)(OH)CH3c 6.35648 1107.060 172.102

aReference [17].bReference [18].cReference [15].

A. Reyes et al. / J. Chem. Thermodynamics 36 (2004) 87–93 91

TABLE 6 (continued)

Equation Aij Aji DT /K Dy c1i c1j

P ¼ 101:3 kPa

Margules 0.7593 0.3909 0.23 0.0085 2.14 1.48

Van Laar 0.9266 0.3917 0.21 0.0073 2.52 1.48

Wilson 4816.1157 )1883.8431 0.21 0.0071 2.53 1.49

NRTL )1715.2275 4553.9250 0.23 0.0081 2.34 1.48

UNIQUAC )1662.1779 3428.6457 0.23 0.0081 2.35 1.47

xC4H8O2 + (1� x)CH3CH(CH3)CH2OH

P ¼ 40:0 kPa

Margules 0.3664 0.3169 0.18 0.0068 1.44 1.37

Van Laar 0.3669 0.3191 0.18 0.0068 1.44 1.37

Wilson 1281.5962 )191.3961 0.18 0.0066 1.44 1.38

NRTL )263.5340 1359.1255 0.18 0.0066 1.44 1.37

UNIQUAC )622.0819 1077.3735 0.18 0.0067 1.44 1.38

P ¼ 101:3 kPa

Margules 0.2140 0.3200 0.13 0.0063 1.24 1.38

Van Laar 0.2233 0.3251 0.13 0.0066 1.25 1.38

Wilson )307.3643 1369.7047 0.13 0.0064 1.25 1.38

NRTL 2238.2639 )1108.9839 0.13 0.0065 1.25 1.38

UNIQUAC 851.6626 )505.3807 0.13 0.0064 1.25 1.38

xC4H8O2 + (1� x)CH3C(CH3)(OH)CH3

P ¼ 40:0 kPa

Margules 0.1854 0.4899 0.29 0.0031 1.20 1.63

Van Laar 0.2521 0.5255 0.25 0.0043 1.29 1.69

Wilson )790.4949 2528.5893 0.25 0.0042 1.28 1.69

NRTL 3688.0975 )1837.4161 0.27 0.0037 1.26 1.66

UNIQUAC 1753.1719 )1089.2204 0.25 0.0043 1.29 1.69

P ¼ 101:3 kPa

Margules 0.2237 0.5202 0.24 0.0079 1.25 1.68

Van Laar 0.2609 0.6171 0.25 0.0069 1.30 1.85

Wilson )984.8872 3193.8309 0.25 0.0071 1.30 1.84

NRTL 4241.0434 )2041.0800 0.24 0.0075 1.27 1.76

UNIQUAC 2179.5085 )1311.4076 0.25 0.0069 1.29 1.84

aDimensionless.b J �mol�1.

TABLE 7

VLE predictions with the contribution group methods ASOG and UNIFAC, average deviations DT and Dy

System P /kPa ASOG UNIFAC

DT /K Dy DT /K Dy

xC3H6O2 + (1� x)CH3CH(CH3)CH2OH 40.0 4.92 0.0652 0.98 0.0154

101.3 3.87 0.0453 0.65 0.0092

xC3H6O2 + (1� x)CH3C(CH3)(OH)CH3 40.0 3.40 0.0563 1.25 0.0227

101.3 3.28 0.0467 1.64 0.0324

xC4H8O2 + (1� x)CH3CH(CH3)CH2OH 40.0 1.38 0.0218 1.04 0.0159

101.3 1.12 0.0132 0.75 0.0099

xC4H8O2 + (1� x)CH3C(CH3)(OH)CH3 40.0 1.34 0.0166 1.56 0.0260

101.3 1.50 0.0168 1.31 0.0191

92 A. Reyes et al. / J. Chem. Thermodynamics 36 (2004) 87–93

vapour-phase composition are given. This table shows

that the two methods give satisfactory predictions for the

systems containing C4H8O2, while UNIFAC predictions

for the mixtures containing C3H6O2 are better than the

predictions using the ASOG.

Acknowledgements

This work was financially supported by IBERCAJA

(IBE2002-CIEN-02), for which the authors are very

grateful.

A. Reyes et al. / J. Chem. Thermodynamics 36 (2004) 87–93 93

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JCT 03/099