Phase Equilibrium of Binary Mixtures of n-Hexane + Branched

Article pubs.acs.org/jced

Phase Equilibrium of Binary Mixtures of n‑Hexane + Branched Chlorobutanes: Experimental Results and Group Contribution Predictions Victor Antón,† Ma Carmen Lopez,† Beatriz Giner,‡ and Carlos Lafuente*,† †

Departamento de Química Física, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain Facultad de Ciencias de la Salud, Universidad San Jorge, Villanueva de Gállego, 50830, Zaragoza, Spain

‡

S Supporting Information *

ABSTRACT: In this work the study of the phase equilibrium (experimental and modeled) of three binary mixtures formed by n-hexane and a branched chlorobutane (2-chlorobutane, 1-chloro-2-methylpropane, or 2-chloro-2-methylpropane) is presented. New and consistent experimental vapor−liquid equilibrium data at isothermal conditions T = (288.15, 298.15, and 308.15) K have been obtained and correlated using the Wilson equation. In addition, two group contribution models, modified-UNIFAC (universal functional activity coefficient) and VTPR (volume-translated Peng−Robinson), have been used to predict the vapor−liquid equilibrium of the mixtures. The agreement between experimental results and predicted ones is not satisfactory.

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models.11,12 However, when experimental data are missing another type of tools, namely, group contribution methods, such as ASOG13 or UNIFAC,14 can be employed for the prediction of VLE. Moreover, the combination, through adequate mixing rules, of equations of state with excess Gibbs energy models and group contribution methods has improved some results regarding the predictions of phase equilibrium for polar and nonpolar mixtures as well as asymmetric systems over a wide pressure and temperature ranges and the description of density of liquid phases; on the other hand these methods can be easily extended to mixtures containing supercritical compounds.15−20 One of these methods is the volume-translated Peng−Robinson group contribution equation of state (VTPR) model,15−17 a combination of the Peng−Robinson equation of state,8 the concept of volume translation,21 and the group contribution method UNIFAC.14,22 Here we study the isothermal VLE of mixtures formed by n-hexane and 2-chlorobutane, 1-chloro-2-methylpropane, or 2-chloro-2-methylpropane has been measured at T = (288.15, 298.15, and 308.15) K. The data have been checked for thermodynamic consistency and correlated using the Wilson equation. Furthermore, using this experimental information we have tested the accuracy of the VLE predictions of two group contribution methods: modified-UNIFAC22 and VTPR15−17 (volumetranslated Peng−Robinson group contribution equation of state).

INTRODUCTION There is no doubt about the importance of n-hexane as an organic solvent. However, to modulate its properties, mixtures are required in the vast majority of applications. That is why, n-hexane and its mixtures have been studied for a long time; information regarding numerous physicochemical, transport, or molecular properties is available in literature for a large number of mixtures containing n-hexane. On the other hand, the design of chemical engineering processes needs the information provided by physicochemical properties of key chemicals and mixtures. Among these properties, phase equilibrium is crucial for separation processes, especially in case of azeotropic mixtures, in which achieving efficient, lower economic cost methods are needed. In this work, we have investigated the vapor−liquid equilibrium (VLE) of mixtures containing n-hexane and a branched chlorobutane. A great effort has been spent in the measurement, correlation, and prediction of VLE of binary, tertiary, and even quaternary mixtures.1,2 In general, experimental data are more trustworthy but are also more expensive and are not always available. Correlation and prediction methods are then the choice. Correlation methods, such as Wilson, nonrandom two-liquid (NRTL), or universal quasichemical activity coefficient (UNIQUAC) equations,3−5 can be very accurate but are limited to conditions in which experimental data are available. It is also possible to use equations of state to represent thermodynamic properties of fluid compounds and their mixtures. Most conventional equations of state are variations on the van der Waals equation. These are, for example, the analytic equations of state such as Soave−Redlich− Kwong6,7 or Peng−Robinson−Stryjek−Vera8,9 or nonanalytic equations of state such as Benedict−Webb−Rubin10 and Wagner © XXXX American Chemical Society

Special Issue: Modeling and Simulation of Real Systems Received: January 31, 2014 Accepted: May 21, 2014

A

dx.doi.org/10.1021/je500116z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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A survey of the literature shows one reference reporting information about the azeotrope at atmospheric pressure for the system n-hexane + 2-chlorobutane (Taz = 339.00 K, x1,az = 0.4476).23

Table 2. Properties of the Pure Compounds and Comparison of Vapor Pressures with Literature Data at T = 298.15 Ka

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EXPERIMENTAL SECTION In Table 1 the information about the liquids used in this work is summarized. No additional purification was carried out because

compound n-hexane

Table 1. Provenance and Purity of the Compounds chemical name

source

purity (mass fraction)

n-hexane 2-chlorobutane 1-chloro-2-methylpropane 2-chloro-2-methylpropane

Sigma-Aldrich Aldrich Fluka Aldrich

0.99 0.99 0.99 0.99

2-chlorobutane analysis method GC GC GC GC

1-chloro-2methylpropane

2-chloro-2methylpropane

the impurities are in such a low concentration that the physical properties of the compound are almost unaffected within the quoted uncertainty limits.24 The VLE was determined using an all-glass dynamic recirculating type still that was equipped with a Cotrell pump. It is a commercial unit (Labodest model) from Fischer. The equilibrium temperature was measured by means of a thermometer (model F25 with a PT100 probe) from Automatic Systems Laboratories, and the pressure in the still was measured with a Digiquartz 735-215A-102 pressure transducer from Paroscientific equipped with a Digiquartz 735 display unit. The uncertainty in the temperature and pressure equilibrium measurement in the still is ± 0.02 K and ± 0.01 kPa, respectively. After constant temperature and pressure were attained, the system was left to recirculate for about 45 min; after this time it was considered to have reached equilibrium. After measurement of the temperature and pressure samples of the liquid and vapor phases were withdrawn by a drop valve mechanism.25 Compositions of both phases vapor and liquid were determined by a densimetric analysis; the error in the determination of liquid and vapor mole fractions was estimated to be ± 0.002. The densimeter used to analyze the samples was an Anton Paar DMA 5000 vibrating tube densimeter thermostated within ± 0.005 K. The calibration was determined with ultrapure water supplied by SH calibration service GmbH and dry air. The uncertainty of density can be estimated in ± 5·10−2 kg·m−3. The density−composition curves can be found in a previous paper.26 Both the apparatus and procedure were periodically checked and rearranged if necessary. The vapor pressures of the pure compounds at working temperatures together with literature data at T = 298.15 K27−30 are collected in Table 2.

j

k

xk Λki ∑j xj Λkj

exptl

288.15 298.15 308.15 288.15 298.15 308.15 288.15 298.15

12.895 20.220 30.705 13.360 20.905 31.550 13.000 20.350

308.15 288.15 298.15

30.450 26.420 40.130

308.15

59.520

lit.

−1

m ·mol

B·106 m3·mol−1

19.85d

129.755 131.584 133.407 105.340 106.710 108.135 104.808 106.176

−2137 −1919 −1734 −1815 −1641 −1492 −1896 −1691

40.054e

107.597 109.000 110.582

−1522 −1209 −1140

112.234

−1076

20.237b

20.969c

Standard uncertainties u are u(T) = 0.02 K and u(p) = 0.01 kPa. b Reference 27. cReference 28. dReference 29. eReference 30.

V jo

⎛ λij − λii ⎞ ⎟ RT ⎠

exp⎜ − V io ⎝

Λij =

(2)

where (λij − λij) are the Wilson parameters, is the molar volume at T = 298.15 K of component i in the liquid phase, R is the general gas constant, and T is the absolute temperature. These parameters have been estimated by minimizing the following objective function in terms of experimental and calculated pressures:31 Voi

⎛ pexp − pcal ⎞2 ∑ ⎜⎜ exp ⎟⎟ p ⎠i i=1 ⎝ n

F=

(3)

The calculated pressure is obtained taking into account both the nonideality of the vapor phase, through second virial coefficients, and the variation of the Gibbs energies of the pure compounds with pressure, by using the Poynting factor, as follows:32,33 2

pcal =

⎡ (V o − B )(p − po ) − (1 − y )2 pδ ⎤ i ii ij i i ⎥ ⎢⎣ ⎥⎦ RT

∑ xiγipio exp⎢ i=1

(4)

δij = 2Bij − Bii − Bjj

(5)

where yi is the vapor phase mole fraction, p is the total pressure, poi is the vapor pressure of the pure compound i, Bii is the second virial coefficient of component i that, for n-hexane, 2-chlorobutane, and 2-chloro-2-methylpropane, were taken from TRC tables,34 and for 1-chloro-2-methylpropane was estimated using the Tsonopoulos method.35,36 Bij is the cross second virial coefficient; for these kind of mixtures this coefficient can be calculated as the average of the second virial coefficients of the pure compounds,37 and the rest of the symbols have been previously defined. Parameters of the Wilson equation together with average deviations in pressure, Δp, and vapor-phase composition, Δy, for each binary system are gathered in Table 4. The thermodynamic consistency of the experimental results was checked by means of the van Ness method, described by

RESULTS AND DISCUSSION Experimental VLE data are collected in Table 3; the correlated activity coefficients and excess Gibbs energies can be found in the Supporting Information. The pressure−composition diagrams, p−x1−y1, are shown in Figures 1 to 3, and the excess Gibbs energies at T = 298.15 K have been plotted in Figure 4. The Wilson equation3 has been used to correlate the activity coefficients, γi, of the components in the liquid phase:

∑

T/K

3

a

■

ln γi = −ln(∑ xj Λij) + 1 −

V°·106

p/kPa

(1) B



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Table 3. Isothermal VLE Data of the Binary Mixtures: Experimental Pressure, p, and Liquid-Phase, x1, and Vapor-Phase, y1, Mole Fractionsa p/kPa

x1

y1

p/kPa

x1

p/kPa

y1

n-Hexane (1) + 2-Chlorobutane (2) at T = 288.15 K 0.0000 0.0000 14.585 0.5277 0.5162 0.0574 0.0747 14.540 0.5583 0.5413 0.1476 0.1868 14.440 0.6269 0.5953 0.2386 0.2737 14.285 0.7126 0.6642 0.3098 0.3353 13.970 0.8235 0.7547 0.3804 0.4007 13.295 0.9377 0.9115 0.4244 0.4345 12.895 1.0000 1.0000 0.4853 0.4843 n-Hexane (1) + 2-Chlorobutane (2) at T = 298.15 K 20.905 0.0000 0.0000 22.715 0.5253 0.5162 21.215 0.0566 0.0770 22.675 0.5559 0.5408 21.880 0.1532 0.1901 22.570 0.6219 0.5948 22.290 0.2390 0.2771 22.345 0.7042 0.6636 22.525 0.3101 0.3357 21.865 0.8064 0.7504 22.670 0.3912 0.4057 20.875 0.9377 0.9109 22.685 0.4253 0.4363 20.220 1.0000 1.0000 22.755 0.4853 0.4843 n-Hexane (1) + 2-Chlorobutane (2) at T = 308.15 K 31.550 0.0000 0.0000 34.310 0.5258 0.5148 32.145 0.0555 0.0747 34.230 0.5544 0.5403 33.100 0.1431 0.1885 34.065 0.6163 0.5943 33.685 0.2377 0.2719 33.755 0.7121 0.6662 34.000 0.3105 0.3351 33.110 0.8080 0.7676 34.250 0.3813 0.3989 31.715 0.9383 0.9121 34.325 0.4253 0.4349 30.705 1.0000 1.0000 34.325 0.4853 0.4843 n-Hexane (1) + 1-Chloro-2-methylpropane (2) at T = 288.15 K 13.000 0.0000 0.0000 14.195 0.6251 0.6049 13.105 0.0426 0.0653 14.110 0.6530 0.6301 13.575 0.1396 0.1700 14.065 0.6942 0.6656 13.900 0.2547 0.3010 13.845 0.7487 0.7091 13.955 0.3035 0.3470 13.825 0.8002 0.7600 14.125 0.3893 0.4200 13.440 0.9011 0.8680 14.155 0.4361 0.4570 13.340 0.9228 0.8944 14.170 0.5223 0.5256 12.895 1.0000 1.0000 14.160 0.5956 0.5839 n-Hexane (1) + 1-Chloro-2-methylpropane (2) at T = 298.15 K 20.350 0.0000 0.0000 22.165 0.6226 0.6049 20.545 0.0448 0.0664 22.080 0.6505 0.6291 21.250 0.1401 0.1715 21.990 0.6921 0.6656

n-Hexane (1) + 21.765 0.2489 21.940 0.3081 22.125 0.3937 22.155 0.4411 22.205 0.5227 22.160 0.5941 n-Hexane (1) + 30.450 0.0000 31.100 0.0485 31.870 0.1403 32.735 0.2559 33.025 0.3064 33.350 0.3929 33.475 0.4415 33.550 0.5227 33.500 0.5927 n-Hexane (1) + 26.420 0.0000 25.855 0.0697 25.150 0.1663 24.425 0.2225 23.700 0.3376 22.485 0.4470 21.225 0.5429 n-Hexane (1) + 40.130 0.0000 39.325 0.0700 38.320 0.1578 37.455 0.2210 36.055 0.3330 34.760 0.4105 32.505 0.5401 n-Hexane (1) + 59.520 0.0000 58.405 0.0702 56.575 0.1545 55.645 0.2215 53.185 0.3304 51.650 0.4030 48.510 0.5294

13.360 13.565 13.970 14.270 14.410 14.525 14.565 14.565

a

x1

y1

p/kPa

1-Chloro-2-methylpropane 0.3001 21.845 0.3457 21.640 0.4191 21.065 0.4597 20.875 0.5251 20.220 0.5829 1-Chloro-2-methylpropane 0.0000 33.445 0.0656 33.405 0.1725 33.230 0.2972 33.030 0.3414 32.755 0.4177 31.955 0.4579 31.650 0.5246 30.705 0.5844 2-Chloro-2-methylpropane 0.0000 19.995 0.0480 18.790 0.1136 17.690 0.1663 16.295 0.2259 13.600 0.3004 12.895 0.3635 2-Chloro-2-methylpropane 0.0000 30.995 0.0520 29.540 0.1122 28.190 0.1540 25.660 0.2259 22.000 0.2898 20.220 0.3672 2-Chloro-2-methylpropane 0.0000 46.510 0.0531 44.240 0.1126 42.270 0.1545 38.880 0.2303 33.555 0.2823 30.705 0.3803

x1

y1

(2) at T = 298.15 K 0.7451 0.7091 0.8006 0.7620 0.8989 0.8674 0.9222 0.8966 1.0000 1.0000 (2) at T = 308.15 K 0.6231 0.6069 0.6485 0.6311 0.6936 0.6687 0.7503 0.7189 0.7645 0.7345 0.8887 0.8658 0.9251 0.8989 1.0000 1.0000 (2) at T = 288.15 K 0.6239 0.4626 0.7201 0.5172 0.7856 0.5692 0.8667 0.7037 0.9704 0.9412 1.0000 1.0000 (2) at T = 298.15 K 0.6210 0.4555 0.6941 0.5114 0.7509 0.5681 0.8443 0.6801 0.9563 0.8853 1.0000 1.0000 (2) at T = 308.15 K 0.6046 0.4335 0.6843 0.5097 0.7459 0.5681 0.8372 0.6807 0.9494 0.8773 1.0000 1.0000

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.01 kPa, u(x1) = 0.002, and u(y1) = 0.002.

excess Gibbs energies follow the sequence: 2-chlorobutane ≈ 2-chloro-2-methylpropane > 1-chloro-2-methylpropane. On the other hand, it can be highlighted that these GE values are lower than those for the mixture n-hexane + 1-chlorobutane.40

Fredenslund et al.38,39 using the Wilson equation for fitting the excess Gibbs energies. According to this test, experimental data are considered consistent if the average deviation in vapor composition, Δy, is less than 0.01, our systems satisfactorily fulfill this condition as can be seen in Table 4. The mixtures containing 2-chlorobutane and 1-chloro-2methylpropane show maximum vapor pressure azeotropes. The location of the azeotropic points were made by using y1−x1 versus x1 diagrams in order to determine x1,az at y1−x1 = 0 together with p versus x1 diagrams where paz should be minimum at x1,az. The composition and vapor pressure of the azeotropes is summarized in Table 5. Excess Gibbs energies are positive for all the mixtures at the three temperatures, the curves GE vs x1 being symmetrical. The temperature dependence of the excess Gibbs energies is small; GE slightly increases with temperature. At T = 298.15 K the

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GROUP CONTRIBUTION PREDICTIONS The most successful of the group contribution methods used to predict phase equilibria is the modified UNIFAC model. Here we have tested the accuracy of the VLE predictions of the modified UNIFAC method by comparing the VLE experimental data with the predicted ones. The UNIFAC group parameters and group interaction parameters needed for the calculations are given in Table 6. The results of the predictions are shown in Tables 5 and 7 and in Figures 5 to 7. The modified UNIFAC method predicts the existence of maximum vapor pressure azeotropes for the mixtures containing 2-chlorobutane or C



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Figure 1. p−x1−y1 diagrams for the binary mixture n-hexane (1) + 2-chlorobutane (2): □, ■, experimental data at T = 288.15 K; ○, ●, data at T = 298.15 K; △, ▲, data at T = 308.15 K; , Wilson correlation.

Figure 3. p−x1−y1 diagrams for the binary mixture n-hexane (1) + 2-chloro-2-methylpropane (2): □, ■, experimental data at T = 288.15 K; ○, ●, data at T = 298.15 K; △, ▲, data at T = 308.15 K; , Wilson correlation.

Figure 4. Excess Gibbs functions, GE, at T = 298.15 K for n-hexane (1) + branched chlorobutane (2): black dashed line, 2-chlorobutane; blue dashed line, 1-chloro-2-methylpropane; red solid line, 2-chloro-2methylpropane.

Figure 2. p−x1−y1 diagrams for the binary mixture n-hexane (1) + 1-chloro-2-methylpropane (2): □, ■, experimental data at T = 288.15 K; ○, ●, data at T = 298.15 K; △, ▲, data at T = 308.15 K; , Wilson correlation.

predicted values are presented by the mixture containing 2-chloro2-methylpropane with Δp = 1.906 kPa and Δy = 0.0222. It can be also outlined that for the three systems the predictions are better at low temperatures. Furthermore, we have also tested the predictions of the volume translated Peng−Robinson group contribution equation of state (VTPR model). As we have mentioned, this model combines both the VTPR-EoS with the UNIFAC group contribution method.

1-chloro-2-methylpropane, although the predicted composition of the azeotropes are somewhat lower than the compositions calculated from experimental data. The overall Δp average is 1.076 kPa, and the corresponding overall average for Δy is 0.0150; the best predictions are obtained for the mixture n-hexane + 1-chloro-2-methylpropane with average pressure and vapor-phase composition deviations are 0.344 kPa and 0.0063, respectively. The highest deviations between experimental and D



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Table 4. Correlation Parameters of the Wilson Equation, Average Deviation in Pressure, Δp, and Average Deviation in Vapor-Phase Composition, Δy λ12 − λ11 −1

system n-hexane + 2-chlorobutane n-hexane + 1-chloro-2methylpropane n-hexane + 2-chloro-2methylpropane

Table 7. UNIFAC and VTPR Model Predictions: Average Deviation in Vapor Pressure, Δp, and in Vapor-Phase Composition, Δy

λ21 − λ22

UNIFAC

−1

VTPR

J·mol

J·mol

Δp/kPa

Δy

system

Δp/kPa

Δy

Δp/kPa

Δy

−659.26 −578.90

1797.87 1572.81

0.044 0.045

0.0044 0.0033

0.979 0.344

0.0165 0.0063

0.938 0.269

0.0155 0.0083

−402.42

1489.55

0.108

0.0067

n-hexane + 2-chlorobutane n-hexane + 1-chloro-2methylpropane n-hexane + 2-chloro-2methylpropane overall average

1.906

0.0222

1.761

0.0203

1.076

0.0150

0.989

0.0147

Table 5. Experimental and Predicted Compositions, x1,az, and Vapor Pressure of the Azeotropic Mixtures, paz exptl T/K

x1,az

UNIFAC

paz/kPa

x1,az

VTPR

paz/kPa

n-Hexane (1) + 2-Chlorobutane (2) 0.491 14.54 0.384 13.74 0.491 22.73 0.380 21.43 0.497 34.34 0.389 32.31 n-Hexane (1) + 1-Chloro-2-methylpropane 0.519 14.20 0.478 13.99 0.519 22.20 0.478 21.77 0.535 33.45 0.504 32.61

288.15 298.15 308.15 288.15 298.15 308.15

x1,az

paz/kPa

0.371 0.383 0.392 (2) 0.421 0.431 0.440

13.84 21.50 32.37 14.42 22.32 33.45

The VTPR equation of state is p=

a (T ) RT − (V + c − b ) (V + c)(V + c + b) + b(V + c − b) (6)

where the translation parameter, c, is defined as the difference between the volume calculated with the Peng−Robinson-EoS and the experimental volume at a reduced temperature, Tr = 0.7.41 It can be outlined that this translation parameter improves the results for the description of liquid densities, but it has no influence on the VLE calculations. For pure component i, the temperature-dependent parameters a and b are given by the following equations: a ii(T ) = 0.45724

R2TC,2 i pC, i

Figure 5. p−x1−y1 diagrams for the binary mixture n-hexane (1) + 2-chlorobutane (2): □, ■, experimental data at T = 288.15 K; ○, ●, data at T = 298.15 K; △, ▲, data at T = 308.15 K; red solid line, UNIFAC prediction; blue dashed line, VTPR prediction. (NiMi)

αi(T ) = Tr,Nii(Mi − 1)e Li[1 − Tr, i

·αi(T )

bii = 0.0778

(7)

]

(8)

RTC, i pC, i

(9)

Table 6. UNIFAC and VTPR Group Parameters and Group Interaction Parameters UNIFAC main group

subgroup

R

CH2

CH3 CH2 CH CH2Cl CHCl CCl

0.6325 0.6325 0.6325 0.9919 0.9919 0.9919

CCl

Q

aCH2CCl/K

1.0608 0.7081 0.3554 1.3654 1.0127 0.6600 VTPR

401.00

aCClCH2/K −65.685

bCH2CCl

cCH2CCl/K−1

−0.7277

0

bCClCH2 0.07409

cCClCH2/K−1 0

main group

subgroup

Q

aCH2CCl/K

bCH2CCl

cCH2CCl/K−1

CH2

CH3 CH2 CH CH2Cl CHCl CCl

1.2958 0.9471 0.2629 1.264 0.952 0.724

439.8547

−0.46183

0

aCClCH2/K −87.8717

bCClCH2 −0.10659

cCClCH2/K−1 0

CCl

E



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subscripts C and r denote critical and reduce values, respectively. αi(T) is the Twu function42 that provides the dependence of aii parameter with temperature. These pure compound properties taken directly from the Dortmund Data Bank43 are collected in Table 8. In the VTPR model, the following mixing rules for the parameters a and b, suggested by Chen et al.,44 are used: a = b

∑ xi

aii GE + res bii A

(10)

where A = −0.53087. b=

∑ ∑ xixjbij i

bij3/4 =

(11)

j

(bii3/4 + bjj3/4) (12)

2

To obtain the translation parameter of the mixture, c, a linear mixing rule is employed: The GE mixing rule used in this model only contains the residual part of the UNIFAC method, GEres. In the VTPR model, as in modified UNIFAC, temperature-dependent group interactions parameters are used. Group surface areas and VTPR group E interaction parameters45 used in the Gres calculations are collected in Table 6. In Table 5 are shown the VTPR azeotrope predictions for the mixtures involving 2-chlorobutane, or 1-chloro-2-methylpropane, as it can be seen the VTPR composition of the azeotropes are lower than the compositions calculated from experimental data. The predicted vapor pressures of the azeotropes containing 2-chlorobutane are also lower than the experimental ones. On the other hand, for the mixture n-hexane + 1-chloro-2-methylpropane the agreement between predicted and experimental azeotropic pressures is good. In Figures 5 to 7 the VTPR predicted pressure− composition diagrams are graphically shown. In Table 8 the average deviations in vapor pressure and vapor phase composition are reported. For this method the overall Δp average is 0.989 kPa, and the overall average for Δy is 0.0147; the best and worst predictions are obtained again for the mixtures n-hexane + 1-chloro-2methylpropane and n-hexane + 2-chloro-2-methylpropane. It can be outlined that the results obtained with both methods: UNIFAC and VTPR are quite similar, and these results are not satisfactory.

Figure 6. p−x1−y1 diagrams for the binary mixture n-hexane (1) + 1-chloro-2-methylpropane (2): □, ■, experimental data at T = 288.15 K; ○, ●, data at T = 298.15 K; △, ▲, data at T = 308.15 K; red solid line, UNIFAC prediction; blue dashed line, VTPR prediction.

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CONCLUSIONS VLE at three temperatures T = (288.15, 298.15, and 308.15) K have been reported for the binary mixtures containing n-hexane and a branched chlorobutane (2-chlorobutane, 1-chloro-2-methylpropane, or 2-chloro-2-methylpropane). From the reduction of VLE data, the excess Gibbs energies have been obtained. The GE values decreases following the sequence: 2-chlorobutane ≈ 2-chloro-2-methylpropane > 1-chloro-2-methylpropane. Apart from this experimental work,

Figure 7. p−x1−y1 diagrams for the binary mixture n-hexane (1) + 2-chloro-2-methylpropane (2): □, ■, experimental data at T = 288.15 K; ○, ●, data at T = 298.15 K; △, ▲, data at T = 308.15 K; red solid line, UNIFAC prediction; blue dashed line, VTPR prediction.

Table 8. Properties of the Pure Compounds: Critical Data and PR-Twu α-Function Parameters compound

pc/kPa

Tc/K

L

M

N

n-hexane 2-chlorobutane 1-chloro-2-methylpropane 2-chloro-2-methylpropane

3025 3951.67 3989 3951.68

507.6 520.6 527.05 507

0.965 06 0.947 079 0.859 223 0.109 132

0.942 50 1.067 18 1.002 72 0.890 767

0.816 37 0.870 236 0.878 194 3.525 74

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Pure Compounds with a Volume Translated Peng-Robinson Equation of State. Fluid Phase Equilib. 2001, 191, 177−188. (16) Ahlers, J.; Gmehling, J. Development of a Universal Group Contribution Equation of State. 2. Prediction of Vapor-Liquid Equilibria for Asymmetric Systems. Ind. Eng. Chem. Res. 2002, 41, 3489−3498. (17) Ahlers, J.; Gmehling, J. Development of a Universal Group Contribution Equation of State. III. Prediction of Vapor-Liquid Equilibria, Excess Enthalpies, and Activity Coefficients at Infinite Dilution with the VTPR Model. Ind. Eng. Chem. Res. 2002, 41, 5890− 5899. (18) Voutsas, E.; Magoulas, K.; Tassios, D. Universal Mixing Rule for Cubic Equations of State Applicable to Symmetric and Asymmetric Systems: Results with the Peng-Robinson Equation of State. Ind. Eng. Chem. Res. 2004, 43, 6238−6246. (19) Jaubert, J.-N.; Privat, R. Relationship between the Binary Interaction Parameters (k(ij)) of the Peng-Robinson and those of the Soave-Redlich-Kwong Equations of State: Application to the Definition of the PR2SRK model. Fluid Phase Equilib. 2010, 295, 26−37. (20) Jaubert, J.-N.; Privat, R.; Mutelet, F. Predicting the Phase Equilibria of Synthetic Petroleum Fluids with the PPR78 Approach. AIChE J. 2010, 56, 3225−3235. (21) Peneloux, A.; Rauzy, E.; Freze, R. A Consistent Correction for Redlich-Kwong-Soave Volumes. Fluid Phase Equilib. 1982, 1, 7−23. (22) Gmehling, J.; Li, J.; Schiller, M. A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178−193. (23) Lecat, M. Table Azeotropiques. Tome Premier: Azeotropes binaires orthobares, 2nd ed.; L’Auteur: Bruxelles, 1949. (24) Dávila, M. J.; Aparicio, S.; Alcalde, R.; García, B.; Leal, J. M. On the Properties of 1-Butyl-3-methylimidazolium octylsulfate Ionic Liquid. Green Chem. 2007, 9, 221−232. (25) Sayar, A. A. On the Isobaric Vapor-Liquid-Equilibrium of the Ciclohexanol-Phenylmethanol Binary at 101.325 ± 0.067 KPa. Fluid Phase Equilib. 1991, 63, 341−354. (26) Guerrero, H.; Pera, G.; Giner, I.; Bandrés, I.; Lafuente, C. Volumetric and Acoustic Behaviour of Systems Containing n-Hexane, or n-Heptane and Isomeric Chlorobutanes. J. Chem. Thermodyn. 2010, 42, 1406−1412. (27) Hwang, S. C.; Robinson, R. L. Vapor-Liquid Equilibria at 25 °C for Nine Alcohol-Hydrocarbon Binary Mixtures. J. Chem. Eng. Data 1977, 22, 319−325. (28) Roland, M. Concentrated Solutions. V. Experimental Determination of the Thermodynamic Activity of the Components of Binary Mixtures of Organic Compounds. Bull. Soc. Chim. Belg. 1928, 37, 117− 140. (29) Hirshberg, J. Theory of Concentrated Solutions. VIII. The Activity Coefficient in its Relations with the Freezing Curve. Bull. Soc. Chim. Belg. 1932, 41, 163−195. (30) Chóliz Calero, G.; Mínguez Valle, M.; Gutiérrez Losa, C. Estudio Termodinámico del Sistema 2-Cloro-2-metilpropano + 2́ Quim. ́ Nat. Bromo-2-metilpropano. Rev. Acad. Cienc. Exactas, Fis., Zaragoza 1969, 24, 137−158. (31) Silverman, N.; Tassios, D. P. Prediction of Multicomponent VLE with the Wilson Equation. Effect of the Minimization Function and of the Quality of Binary Data. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 586−589. (32) Smith, J. M.; van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics, 5th ed.; McGraw-Hill: New York, 1996. (33) Villa, S.; Garriga, R.; Pérez, P.; Gracia, M.; González, J. A. Thermodynamics of Mixtures with Strongly Negative Deviations from Raoult’s Law: Part 9. Vapor-Liquid Equilibria for the System 1Propanol + di-n-Propylamine at Six Temperatures between 293.15 and 318.15 K. Fluid Phase Equilib. 2005, 231, 211−220. (34) TRC Thermodynamic Tables-Non-hydrocarbons, Selected Values of Properties of Chemical Compounds; Thermodynamics Research Center, Texas A&M University: College Station, TX, 1970.

the experimental data have been used to check the accuracy of the predictions of VLE of the modified UNIFAC and VTPR models. The results obtained indicate that both models do not provide satisfactory predictions.

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ASSOCIATED CONTENT

* Supporting Information S

Additional table as described in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +34976762295. Fax: +34976761202. E-mail: [email protected]. Funding

The authors (Platón and GIMACES research groups) are grateful for financial assistance from Gobierno de Aragón and Fondo Social Europeo “Construyendo Europa desde Aragón”. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Lai, H.-S.; Lin, Y.-F.; Tu, C.-H. Isobaric (Vapor plus Liquid) Equilibria for the Ternary System of (Ethanol + Water + 1,3Propanediol) and Three Constituent Binary Systems at p =101.3 kPa. J. Chem. Thermodyn. 2014, 68, 13−19. (2) Garcia-Flores, B. E.; Aguila-Hernandez, J.; Garcia-Sanchez, F.; Aquino-Olivos, M. A. (Liquid-Liquid) Equilibria for Ternary and Quaternary Systems of Representative Compounds of Gasoline plus Methanol at 293.15 K: Experimental Data and Correlation. Fluid Phase Equilib. 2013, 348, 60−69. (3) Wilson, G. Vapor-Liquid Equilibrium. 11. New Expression for Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127−130. (4) Renon, H.; Prausnitz, J. M. Local Composition in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135− 144. (5) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures. New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116−128. (6) Redlich, O.; Kwong, J. N. S. On the Thermodynamic of Solutions. 5. An Equation of State - Fugacities of Gaseous Solutions. Chem. Rev. 1949, 44, 233−244. (7) Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972, 27, 1197−1203. (8) Peng, D.; Robinson, D. B. New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (9) Stryjek, R.; Vera, J. H. PRSVAn Improved Peng-Robinson Equation of State for Pure Compounds and Mixtures. Can. J. Chem. Eng. 1986, 64, 323−333. (10) Benedict, M.; Webb, G. B.; Rubin, L. C. An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures II. Mixtures of Methane, Ethane, Propane, and n-Butane. J. Chem. Phys. 1942, 10, 747−758. (11) Setzmann, U.; Wagner, W. A New Method for Optimizing the Structure of Thermodynamic Correlation Equations. Int. J. Thermophys. 1989, 10, 1103−1126. (12) Setzmann, U.; Wagner, W. A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures Up to 1000 MPa. J. Phys. Chem. Ref. Data 1991, 20, 1061−1155. (13) Tochigi, K.; Tiegs, D.; Gmehling, J.; Kojima, K. Determination of New ASOG Parameters. J. Chem. Eng. Jpn. 1990, 23, 453−463. (14) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 1086−1099. (15) Ahlers, J.; Gmehling, J. Development of an Universal Group Contribution Equation of State I. Prediction of Liquid Densities for G



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(35) Tsonopoulos, C. Empirical Correlation of Second VirialCoefficients. AIChE J. 1974, 20, 263−272. (36) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; Mc Graw-Hill: New York, 2001. (37) Fox, J. H. P.; Lambert, J. D. The 2nd Virial Coefficients of Mixed Organic Vapours. Proc. Royal Soc. London Ser. A 1952, 210, 557−564. (38) van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-Liquid Equilibria. I. Appraisal of Data Reduction Methods. AIChE J. 1973, 19, 238−244. (39) Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. (40) Pérez-Gregorio, V.; Montaño, D.; Giner, B.; Lafuente, C.; Royo, F. M. Surface and Bulk Behaviour of Some n-Hexane and Chloroalkane Mixtures. J. Chem. Thermodyn. 2009, 41, 553−559. (41) Ahlers, J.; Yamaguchi, T.; Gmehling, J. Development of a Universal Group Contribution Equation of State. 5. Prediction of the Solubility of High-Boiling Compounds in Supercritical gases with the Group Contribution Equation of State Volume-Translated PengRobinson. Ind. Eng. Chem. Res. 2004, 43, 6569−6576. (42) Twu, C. H.; Coon, J. E.; Cunningham, J. R.; Gmehling, J. A New Generalized Alpha Function for a Cubic Equation of State. 1. PengRobinson Equation. Fluid Phase Equilib. 1995, 105, 49−59. (43) http://www.ddbst.de. (44) Chen, J.; Fischer, K.; Gmehling, J. Modification of PSRK Mixing Rules and Results for Vapour-Liquid Equilibria, Enthalpy of Mixing and Activity Coefficients at Infinite Dilution. Fluid Phase Equilib. 2002, 200, 411−429. (45) Schmid, B.; Gmehling, J. Revised Parameters and Typical Results of the VTPR Group Contribution Equation of State. Fluid Phase Equilib. 2012, 317, 110−126.

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Phase Equilibrium of Binary Mixtures of n-Hexane + Branched

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