4

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Phase equilibrium properties of binary and ternary systems

containing di-isopropyl ether + 1-butanol + benzene at 313.15 K

Rosa M. Villamanãń, M. Carmen Martıń, Ce´sar R. Chamorro,

Miguel A. Villaman˜a´n, Jose´ J. Segovia

*

Grupo de Termodina´mica y Calibracioń TERMOCAL, Dpto. Ingenierıá Energe´tica y Fluidomecańica, 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-buta-nol + benzene) have been measured at T = 313.15 K using an isothermal total pressure cell. Data reduction by Barkers method

pro-vides 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

diﬀer-ent type of hydrocarbons. Ethers and alcohols have

been traditionally used as blending agents in the

for-mulation of unleaded gasolines for enhancing the

oc-tane number. In previous studies VLE data of ethers

as methyl tert-butyl ether (MTBE)

[1–4]

,

tert-amylm-ethyl ether (TAME)

[5]

or di-isopropyl ether (DIPE)

[6–11]

and two hydrocarbons have been measured as

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

(va-pour + liquid) equilibria, they are useful to recalculate

the parameters of the predictive models in order to

im-prove them. But it is required experimental data of the

highest quality available.

The technique used in this work is one of the best

be-cause 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

corre-sponding binaries (di-isopropyl ether + 1-butanol) and

(1-butanol + benzene), which have been measured at

313.15 K. The third binary system involved

(di-isopro-pyl ether + benzene) has been measured previously by

our group

[6]

.

*

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).

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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]

,

un-der 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)

appara-tus 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

capac-ity (Ruska, mod. 2200-801) equipped with piston

injec-tors 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

exter-nally-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

propor-tions 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

densi-ties of the injected component, allowing us assuring an

uncertainty in the mole fraction less than ±5

· 10

4

,

without sampling the phases.

The cell is immersed in a high precision water bath

(Hart Scientiﬁc model 6020) assuring a temperature

sta-bility 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

2413-705 and 2416-711, respectively). Atmospheric air

bal-ances 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

tem-perature 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

equi-librium 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

ac-count 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

coeﬃ-cients given by Dymond et al.

[25]

. In

table 1

, the

pure-component and interaction second virial

coeﬃ-cients (B

ij

) 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

liter-ature as a check for complete degassing.

Correlations for both measured binary systems are

gi-ven by ﬁve-parameter Margules

[26]

equation:

TABLE 1

Average values used for the reduction of the data for experimental vapour pressures ps

icompared with those obtained from the literature

ps

i (lit.), molar volumes V L

i and second virial coeﬃcients Biiand Bijfor

the compounds investigated in this work at T = 313.15 K

DIPE (i = 1) 1-Butanol (i = 2) Benzene (i = 3) ps i=ðkPaÞ 37.108 2.499 24.386 ps iðlit.Þ=ðkPaÞ 37.081 a 2.477d 24.367f 37.090b 2.518e 24.398c,g 37.128c 2.516f 24.320h VL_i=ðcm3_mol1 Þi ₁₄₅ ₉₃ ₉₁ Bi1/(cm3Æmol1)j 1687.8 1625.9 1701.0 Bi2/(cm 3 Æmol1)j 1625.9 5179.5 1071.8 Bi3/(cm3Æmol1)j 1701.0 1071.8 1310.5

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]_.

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g

_ij

¼ G

E

m

=RT

.

ð1Þ

The data of the ternary mixture are adequately

corre-lated by the three-parameter Wohl

[27]

expansion,

g

₁₂₃

¼ G

E m

=RT

¼

g

₁₂

þ g

13

þ g

23

þ ðC

0

þ C

1

x

1

þ C

2

x

2

Þx

1

þ x

2

þ x

3

;

ð2Þ

which includes the parameters of the corresponding

bin-ary systems. The adjustable parameters C

0

, C

1

and C

2

are found by regression of the ternary data.

The binary and ternary systems have also been

corre-lated using Wilson

[28]

, NRTL

[29]

and UNIQUAC

[30]

models, whose respective excess Gibbs energy

expres-sions are given by the following equations

G

E_m

i

x

i

x

i

=

=

Total pressure p for the binary systems at T = 313.15 K, and at various compositions of the liquid phase x1and the calculated composition of

the vapour phase y1using Margules equation

x1 y1 p/(kPa)

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

0.0000 0.0000 2.490 0.0591 0.6607 6.973 0.1010 0.7688 9.837 0.1480 0.8290 12.729 0.2012 0.8672 15.573 0.2491 0.8890 17.828 0.3005 0.9053 19.943 0.3503 0.9171 21.756 0.3993 0.9262 23.301 0.4003 0.9264 23.361 0.4482 0.9336 24.743 0.4487 0.9337 24.740 0.4980 0.9401 26.029 0.4983 0.9401 26.052 0.5486 0.9458 27.238 0.5490 0.9458 27.257 0.5991 0.9509 28.357 0.5993 0.9509 28.343 0.6491 0.9557 29.381 0.6996 0.9604 30.391 0.7494 0.9650 31.369 0.7998 0.9700 32.362 0.8504 0.9756 33.396 0.9016 0.9823 34.525 0.9520 0.9903 35.772 1.0000 1.0000 37.091 Benzene (1) + 1-butanol (2) 0.0000 0.0000 2.492 0.0590 0.6320 6.418 0.1080 0.7533 9.176 0.1510 0.8067 11.265 0.1980 0.8423 13.232 0.2559 0.8699 15.244 0.3023 0.8850 16.580 0.3533 0.8973 17.825 0.4027 0.9064 18.835 0.4028 0.9064 18.833 0.4501 0.9135 19.658 0.4519 0.9137 19.673 0.4997 0.9197 20.383 0.5019 0.9200 20.402 0.5497 0.9252 21.004 0.5506 0.9253 21.005 0.5999 0.9301 21.548 0.6001 0.9301 21.541 0.6497 0.9346 22.034 0.7001 0.9389 22.452 0.7502 0.9431 22.831 0.8010 0.9474 23.176 0.8591 0.9533 23.516 0.9108 0.9613 23.834 0.9547 0.9735 24.138 1.0000 1.0000 24.372

Di-isopropyl ether (1) + benzene (2)a

0.0000 0.0000 24.398 0.0504 0.0878 25.442 0.1011 0.1652 26.387 0.1498 0.2318 27.221 TABLE 2 (continued) x1 y1 p/(kPa) 0.1994 0.2936 28.019 0.2497 0.3515 28.770 0.2998 0.4054 29.481 0.3500 0.4563 30.155 0.3992 0.5039 30.785 0.3992 0.5040 30.794 0.4489 0.5503 31.400 0.4501 0.5514 31.405 0.4991 0.5954 31.988 0.5003 0.5965 31.995 0.5490 0.6391 32.563 0.5499 0.6399 32.565 0.5986 0.6814 33.113 0.6005 0.6830 33.127 0.6485 0.7231 33.642 0.6991 0.7646 34.184 0.7493 0.8052 34.698 0.7978 0.8438 35.174 0.8508 0.8854 35.707 0.9078 0.9296 36.253 0.9640 0.9727 36.790 1.0000 1.0000 37.126 a _{Data published in}_[6]_.

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ternary system where the vapour compositions have

been calculated by Margules equation and Wohl

expan-sion, 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

ter-nary 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 G

E_m

–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

Mar-gules equation ﬁts better than the other models the

experimental data. The values of the diﬀerence between

experimental and calculated pressure for the binary

sys-tems are represented in

ﬁgure 5

where it is shown how

the model ﬁts the data and a good agreement of

exper-imental pressure measured twice for compositions

0.4 6 x

1

6 0.6. The root mean square deviations in

pres-sure 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

TABLE 3

Total pressure p for the ternary system di-isopropyl ether (1) + 1-butanol(2) + benzene(3) at T = 313.15 K, and at various compositions of the liquid x1, x2and the vapour phases y1, y2calculated using Wohl

expansion x1 x2 y1 y2 p/kPa 1.0000 0.0000 1.0000 0.0000 37.116 0.6992 0.3008 0.9603 0.0397 30.395 0.6818 0.2934 0.9343 0.0393 30.290 0.6643 0.2859 0.9081 0.0388 30.205 0.6310 0.2715 0.8590 0.0381 30.022 0.5951 0.2560 0.8066 0.0373 29.817 0.5594 0.2407 0.7557 0.0366 29.606 0.5247 0.2257 0.7071 0.0359 29.394 0.4893 0.2105 0.6584 0.0352 29.178 0.4547 0.1956 0.6117 0.0345 28.949 0.4198 0.1805 0.5654 0.0338 28.710 0.3846 0.1654 0.5195 0.0330 28.464 0.3500 0.1505 0.4750 0.0322 28.211 0.0000 1.0000 0.0000 1.0000 2.510 0.3006 0.6994 0.9054 0.0946 19.931 0.2904 0.6754 0.8331 0.0908 20.358 0.2855 0.6643 0.8009 0.0890 20.551 0.2707 0.6296 0.7084 0.0838 21.128 0.2557 0.5945 0.6253 0.0790 21.660 0.2406 0.5594 0.5521 0.0747 22.130 0.2240 0.5206 0.4814 0.0705 22.588 0.2106 0.4895 0.4317 0.0676 22.908 0.1945 0.4518 0.3783 0.0644 23.239 0.1806 0.4195 0.3374 0.0619 23.483 0.1648 0.3829 0.2957 0.0593 23.720 0.0000 0.0000 0.0000 0.0000 24.385 0.3032 0.0000 0.4089 0.0000 29.508 0.2953 0.0259 0.3979 0.0097 29.023 0.2881 0.0497 0.3895 0.0167 28.576 0.2729 0.0999 0.3756 0.0274 27.786 0.2578 0.1497 0.3653 0.0348 27.096 0.2425 0.2003 0.3569 0.0407 26.440 0.2274 0.2502 0.3498 0.0457 25.802 0.2123 0.3000 0.3435 0.0504 25.150 0.1972 0.3498 0.3375 0.0551 24.469 0.1820 0.4000 0.3316 0.0600 23.733 0.1666 0.4505 0.3256 0.0655 22.933 0.1516 0.5003 0.3197 0.0715 22.057 0.9999 0.0000 0.9999 0.0000 37.131 0.7000 0.0000 0.7654 0.0000 34.197 0.6832 0.0240 0.7589 0.0061 33.577 0.6653 0.0496 0.7529 0.0116 32.963 0.6308 0.0989 0.7433 0.0203 31.907 0.5954 0.1494 0.7355 0.0272 30.939 0.5598 0.2003 0.7291 0.0330 30.032 0.5237 0.2518 0.7234 0.0382 29.148 0.4897 0.3004 0.7186 0.0427 28.305 0.4545 0.3507 0.7139 0.0474 27.404 0.4198 0.4003 0.7093 0.0523 26.474 0.3847 0.4505 0.7045 0.0576 25.462 0.3497 0.5004 0.6992 0.0636 24.369 0.0000 1.0000 0.0000 1.0000 2.505 0.0000 0.6922 0.0000 0.1135 16.790 0.0328 0.6695 0.0955 0.1061 17.568 0.0569 0.6528 0.1606 0.1009 18.184 0.1044 0.6199 0.2759 0.0915 19.391 0.1548 0.5849 0.3796 0.0827 20.676 0.1988 0.5544 0.4565 0.0760 21.774 0.2485 0.5200 0.5302 0.0694 22.932 0.2980 0.4857 0.5924 0.0637 24.025 TABLE 3 (continued) x1 x2 y1 y2 p/kPa 0.3480 0.4511 0.6460 0.0587 25.073 0.3987 0.4160 0.6927 0.0541 26.083 0.4503 0.3803 0.7341 0.0499 27.063 0.4985 0.3469 0.7681 0.0462 27.941 0.0000 0.0000 0.0000 0.0000 24.393 0.0000 0.3006 0.0000 0.0611 22.455 0.0336 0.2905 0.0579 0.0582 22.978 0.0516 0.2851 0.0879 0.0567 23.261 0.1139 0.2663 0.1862 0.0518 24.236 0.1489 0.2558 0.2378 0.0493 24.780 0.1999 0.2404 0.3087 0.0459 25.565 0.2517 0.2249 0.3755 0.0427 26.352 0.2991 0.2106 0.4327 0.0398 27.045 0.3491 0.1955 0.4891 0.0370 27.775 0.3962 0.1814 0.5389 0.0344 28.452 0.4497 0.1653 0.5919 0.0315 29.215 0.4999 0.1502 0.6388 0.0289 29.925

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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 mol

1

and 917 J Æ mol

1

,

respectively.

We have found in the literature data for the system

1-butanol + benzene at the same temperature

[31]

we have

correlated their data using ﬁve-parameter Margules

equation and the value of the root mean square

devia-tion is 38 Pa with a maximum deviadevia-tion of 70 Pa. Both

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 Wilson NRTL UNIQUAC

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

A12 0.8169 0.7994 0.6238 0.4509 A21 1.2049 0.3574 0.8953 1.3949 k12 0.0582 21 0.1702 g 0.2329 a12 0.4741 r.m.s.d. Dp/kPa 0.010 0.036 0.023 0.041 max |Dp|/kPa 0.021 0.103 0.065 0.079 Benzene (1) + 1-butanol (2) A12 1.1521 0.7373 0.3838 0.4969 A21 2.1355 0.1508 0.7404 1.1229 k12 0.7754 k21 1.9784 g 1.3924 a12 0.5668 r.m.s.d. Dp/kPa 0.011 0.029 0.052 0.145 max |Dp|/kPa 0.018 0.062 0.096 0.291

Di-isopropyl ether (1) + benzene (2)a

A12 0.2134 0.5515 0.4967 0.9014 A21 0.1277 1.3762 0.7905 1.0698 k12= k21 0.0282 a12 0.3 r.m.s.d. Dp/kPa 0.005 0.006 0.005 0.006 max |Dp|/kPa 0.009 0.013 0.008 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 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|)

Wohl Wilson NRTL UNIQUAC

C0 2.3726 C1 0.5804 C2 0.7023 A12 0.8375 1.0496 0.4246 A21 0.3380 0.1925 1.4449 A13 0.3530 0.6603 1.3438 A31 1.7319 1.0585 0.6718 A23 0.1759 0.5703 1.2033 A32 0.6960 1.6122 0.4427 a12 0.4741 a13 0.3000 a23 0.5668 r.m.s.d. Dp/kPa 0.033 0.060 0.043 0.048 max |Dp|/kPa 0.058 0.226 0.142 0.181 The Dp is deﬁned as the diﬀerence between the experimental and cal-culated pressure. 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x₁, y₁ p/kPa

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).

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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

exper-imental pressure measured by Oracz is slight higher than

our values in alcohol rich region.

Data for the ternary system have also been

well-cor-related 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-0 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 x1 G E /(J·mol -1 )

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 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.

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. -0.03 0 0.03 0 0.2 0.4 0.6 0.8 1 x1 (pcalc -pexp )/kPa

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). -0.2 0 0.2 x1 (pcalc -pexp )/kPa 0 0.2 0.4 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)

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cess Gibbs energy change with composition. The ternary

system present a positive deviation from ideality and the

highest value of G

E

m

corresponds to the maximum of

the least ideal binary system that is 917 J Æ mol

1

for

the mixture (0.55 benzene + 0.45 1-butanol).

Acknowledgement

Support for this work came from the Spanish

Minis-try of Science and Technology, project

PPQ2002-04414-C02-02.

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