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GENERAL RESEARCH Vapor-Liquid Equilibria for the Binary System Hexane + 1,1-Dimethylpropyl Methyl Ether at 298.15, 308.15, 318.15, and 328.15 K Armando del Rı´o,† Baudilio Coto,‡ Concepcio´ n Pando,† and Juan A. R. Renuncio*,† Departamento de Quı´mica Fı´sica I, Universidad Complutense, E-28040 Madrid, Spain, and ESCET, Universidad Rey Juan Carlos, E-28933 Mo´ stoles, Madrid, Spain
Vapor-liquid equilibrium (VLE) data are reported for the binary mixtures formed by hexane and the branched ether 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME). A Gibbs-van Ness type apparatus was used to obtain total vapor pressure measurements as a function of composition at 298.15, 308.15, 318.15, and 328.15 K. The system shows positive deviations from Raoult’s law. VLE data are analyzed together with excess enthalpy (HEm) and excess volume (VEm) data previously obtained at 298.15 K for these mixtures. The UNIQUAC model, the lattice-fluid model, and the Flory theory are used to simultaneously correlate VLE and HEm data and to correlate or predict VEm data. The original UNIFAC group contribution model and the modified UNIFAC (Dortmund model) are used to predict VLE data. Introduction
Experimental Section
Branched ethers have been the subject of numerous investigations in the recent years because of their use as additives in lead-free gasoline. These ethers are synthesized by reaction between an isoolefin and an alcohol in excess. The ether purification and the estimation of the phase behavior of the so-called “oxi-gasoline” require an accurate knowledge of the phase equilibrium and other thermodynamic properties for the involved mixtures. Both 1,1-dimethylethyl methyl ether (tertbutyl methyl ether or MTBE) and 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME) are being widely used as gasoline blending agents, and a program is underway in our laboratory to measure the vapor-liquid equilibrium (VLE) data of mixtures formed by MTBE or TAME and a hydrocarbon or an alcohol. VLE data (and surface tension data in some cases) have been reported at several temperatures for binary systems formed by methanol, heptane, cyclohexane, decane, and MTBE or TAME.1-8 The purpose of this paper is to report phase equilibria in the binary system hexane + TAME, for which no data (isobaric or isothermal) have been published in the literature. VLE data taken at 298.15, 308.15, 318.15, and 328.15 K will be discussed together with excess enthalpy (HEm) and excess volume (VEm) data previously obtained at 298.15 K by Zhu et al.9 and Witek et al.10
Hexane was purchased from Sigma, with a purity higher than 99%. TAME (Fluka, 97% purity) was fractionally distilled over 0.3 nm molecular sieves for several hours. The middle distillate used in the present work (approximately 50% of the initial amount) had a purity better than 99.6%, as measured by a gas chromatographic analysis. Chemicals were handled under a dry nitrogen atmosphere and were degassed by reflux distillation for several hours following a procedure described elsewhere.11 VLE data were measured using a Gibbs-van Ness type static apparatus.12 Binary liquid solutions of known composition were prepared in a test cell by volumetric injection of degassed liquids using calibrated pistons. The accuracy of the mole fraction is estimated to be about 0.0001 in the dilute regions and about 0.0003 in the middle of the concentration range. Cell and piston injectors were immersed in a water bath in which the temperature was controlled within (0.002 K. The temperature was measured with a quartz thermometer, Testo 781, to an accuracy of 0.01 K. The total vapor pressure was measured when phase equilibrium was reached using a differential MKS Baratron pressure gauge with a resolution of 0.08% of the reading. The pressure accuracy is estimated to be 0.01 kPa. Table 1 lists values for the molar volumes, isothermal compressibilities, and vapor pressures for hexane and TAME at the temperatures studied. Pure-component vapor-pressure values obtained in this work are compared to those previously reported. The source for purecomponent properties is also given in Table 1. The vapor pressures measured in this work are in good agreement with literature values, and this is considered to be an indication of the chemicals purity.
* To whom correspondence should be addressed. Fax: 34-913944135. Phone: 34-913944120. E-mail: Renuncio@ quim.ucm.es. † Universidad Complutense. ‡ Universidad Rey Juan Carlos.
10.1021/ie0106128 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/08/2002
Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002 1365 Table 1. Properties of Pure Components Used in This Study T (K) hexane 298.15 308.15 318.15 328.15 TAME 298.15 308.15 318.15 328.15
Vm (cm3 mol-1) 131.59a 133.45a 135.42a 137.48a 133.44e 134.65e 135.86e 136.85e
κT × 109 R × 104 p (Pa-1) (K-1) (kPa) 1.67a 1.83a 2.03a 2.27a 1.26e 1.53e 1.80e 2.07e
13.9b 13.9b 13.9b 13.9b 9.71e 9.62e 9.52e 9.43e
20.15 30.60 45.03 64.45 10.01 15.82 24.02 35.41
lit. values range p (kPa) 20.13-20.19c,d 30.24-30.63c,d 45.02-45.13c,d 64.39-64.49c,d 10.01-10.10f,g,h 15.79-15.88g,h,i 23.99-24.13g,h 35.36-35.57g,h,i
a Reference 13. b Reference 14. c Reference 15. d Reference 16. Reference 17. f Reference 3. g Reference 18. h Reference 19. i Reference 2.
e
Experimental Results VLE measurements for hexane + TAME were carried out at 298.15, 308.15, 318.15, and 328.15 K. Results were analyzed using a modified Barker’s method and the maximum likelihood principle.20 The temperature, T, and the amounts of substance for components 1 and 2 were considered to be the independent variables in the data reduction. Equations of material balance were included to take into account the amounts of substance present in the vapor phase. The excess Gibbs energy, GEm, of the liquid phase was assumed to be described by an (m/n) Pade´ approximant and is given by m
GEm RT
) x1(1 - x1)
Pi(2x1 - 1) ∑ i)0
1+
n
i
(1)
Qj(2x1 - 1)j ∑ j)1
where Pi and Qj are adjustable parameters and x1 is the mole fraction of hexane. Data at the four temperatures studied are adequately described by (3/0) Pade´ approximants. This makes eq 1 equivalent to a Redlich-Kister equation. The vapor phase is described using the virial equation. Values for the second virial coefficients of the pure component and the cross virial coefficients were calculated by means of the Hayden and O’Connell method.21 Table 2 lists values for the hexane liquid composition, x1, and the total pressure, p, at the four temperatures studied, together with the calculated total pressure, pcalc, the hydrocarbon vapor composition, y1, the excess Gibbs energy, GEm, the activity coefficients, ln γ1 and ln γ2, for hexane (1) + TAME (2), the Pade´ coefficients, Pi, for GEm representation by eq 1 and their uncertainties, and the standard deviations between experimental and calculated values of x1, σx and p, σp. Figure 1 shows plots of the total pressure against liquid and vapor compositions for the hexane + TAME system at the four temperatures studied. Both experimental values and those calculated using eq 1 are shown. Deviations from Raoult’s law are positive and small. A similar behavior was reported for the heptane + TAME5 and cyclohexane + TAME mixtures.7 Plots of vapor composition against liquid composition at the four temperatures studied are almost coincident, thus indicating that within experimental error there is not a temperature effect on the vapor compositions. Figure 2 shows plots of GEm values
Figure 1. VLE data for the hexane (1) + TAME (2) system: ], 298.15 K; ∇, 308.15 K; 4, 318.15 K; O, 328.15 K; s, calculated values using eq 1.
against x1 for the four temperatures studied. Values for the excess Gibbs energy of the hexane + TAME mixtures are positive and decrease as the temperature increases for a given mole fraction. Maximum GEm values range from 133 J mol-1 at 298.15 K to 88 J mol-1 at 328.15 K. These maxima appear at approximately the same mole fraction (x1 ≈ 0.55) for all of the temperatures studied. This behavior is in agreement with the moderately endothermic HEm values reported at 298.15 K for these mixtures.9 Modeling and Discussion The UNIQUAC model 22 was used to correlate the isothermal VLE data together with excess enthalpy data previously obtained at 298.15 K. Zhu et al.9 reported endothermic HEm data for the hexane + TAME mixtures, with a maximum value of 270 J mol-1 occurring at x1 ) 0.5. The interaction parameters of this model, Aji, were considered to vary linearly with temperature according to
Aji ) Aji,1 + Aji,2(T - 298.15 K)
(2)
The resulting values for the interaction parameters are A12,1 ) 29.70 K, A12,2 ) -0.0197, A21,1 ) -15.10 K, and A21,2 ) -0.0464. Values for the standard deviation between experimental and calculated excess enthalpies, σH, and values for the standard deviations between experimental and calculated vapor pressures, σp, and the percent ratio of σp and the maximum value of the vapor pressure, σp(%), are listed in Table 3. Values for these deviations indicate that the UNIQUAC equation is able to correlate simultaneously the VLE and HEm data. Figure 4 shows plots of experimental vapor pressures and those calculated from the UNIQUAC equation.
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Table 2. VLE Data and Coefficients and Standard Deviations for a GEm Representation by Eq 1 for Hexane (1) + TAME (2) at 298.15, 308.15, 318.15, and 328.15 K x1
p (kPa)
pcalc (kPa)
y1
GEm (J mol-1)
ln γ1
ln γ2
x1
p (kPa)
pcalc (kPa)
y1
GEm (J mol-1)
ln γ1
ln γ2
16.43 16.92 17.34 17.78 18.26 18.66 19.05 19.33 19.58 19.85 20.15
16.42 16.90 17.36 17.80 18.26 18.66 19.03 19.32 19.57 19.87 20.15
0.7075 0.7447 0.7796 0.8128 0.8467 0.8769 0.9055 0.9286 0.9492 0.9748 1.0000
133 131 127 120 109 95 79 63 47 25 0
0.0524 0.0436 0.0353 0.0274 0.0197 0.0134 0.0083 0.0048 0.0025 0.0006 0.0000
0.0524 0.0436 0.0353 0.0274 0.0197 0.0134 0.0083 0.0048 0.0025 0.0006
0.1873 0.1683 0.1544 0.1402 0.1234 0.1098 0.0983 0.0859 0.0741 0.0699 0.0609
T ) 298.15 0.0000 0.5487 0.1873 0.5996 0.1683 0.6499 0.1544 0.7001 0.1402 0.7533 0.1234 0.8022 0.1098 0.8488 0.0983 0.8866 0.0859 0.9201 0.0741 0.9609 0.0699 1.0000 0.0609
0.1573 0.1381 0.1229 0.1102 0.0976 0.0867 0.0773 0.0679 0.0593
T ) 308.15 Kb 0.0000 0.5015 0.0005 0.5504 0.0021 0.6056 0.0043 0.6585 0.0070 0.7130 0.0107 0.7683 0.0149 0.8224 0.0195 0.8722 0.0252 0.9250 0.0317 1.0000
24.34 25.04 25.81 26.54 27.21 27.91 28.57 29.20 29.81 30.60
24.35 25.05 25.81 26.52 27.23 27.92 28.58 29.17 29.77 30.60
0.6608 0.6999 0.7415 0.7792 0.8163 0.8526 0.8871 0.9185 0.9518 1.0000
116 116 115 110 103 91 77 60 38 0
0.0517 0.0440 0.0357 0.0283 0.0211 0.0146 0.0090 0.0049 0.0018 0.0000
0.0387 0.0472 0.0586 0.0714 0.0871 0.1058 0.1273 0.1502 0.1780
0.1185 0.1161 0.1107 0.1016 0.0913 0.0808 0.0692 0.0599 0.0501
T ) 318.15 Kc 0.0000 0.4904 0.0000 0.5393 0.0002 0.5886 0.0009 0.6427 0.0027 0.6926 0.0056 0.7410 0.0094 0.7907 0.0149 0.8420 0.0203 0.8963 0.0274 1.0000
35.67 36.66 37.63 38.74 39.65 40.60 41.47 42.39 43.27 45.03
35.68 36.67 37.65 38.71 39.66 40.56 41.47 42.38 43.32 45.03
0.6420 0.6825 0.7213 0.7621 0.7981 0.8317 0.8652 0.8987 0.9335 1.0000
101 101 100 95 90 82 72 60 43 0
0.0427 0.0355 0.0292 0.0231 0.0182 0.0139 0.0100 0.0063 0.0031 0.0000
0.0339 0.0415 0.0497 0.0595 0.0694 0.0802 0.0931 0.1094 0.1310
0.0933 0.0901 0.0866 0.0823 0.0762 0.0705 0.0640 0.0577 0.0482 0.0466
T ) 328.15 Kd 0.0000 0.4920 0.0001 0.5464 0.0003 0.6042 0.0007 0.6524 0.0014 0.6985 0.0029 0.7534 0.0048 0.8054 0.0075 0.8521 0.0107 0.9052 0.0169 0.9508 0.0182 1.0000
51.33 52.89 54.47 55.80 57.00 58.43 59.70 60.80 62.19 63.25 64.45
51.37 52.90 54.49 55.78 56.99 58.39 59.70 60.86 62.16 63.27 64.45
0.6372 0.6826 0.7281 0.7643 0.7977 0.8363 0.8719 0.9033 0.9384 0.9682 1.0000
87 88 86 83 78 69 59 47 32 18 0
0.0393 0.0318 0.0244 0.0188 0.0141 0.0092 0.0056 0.0031 0.0012 0.0003 0.0000
0.0246 0.0326 0.0426 0.0521 0.0620 0.0749 0.0877 0.0997 0.1134 0.1250
Ka
0.0000 0.0520 0.0928 0.1270 0.1663 0.2196 0.2694 0.3167 0.3733 0.4315 0.4533 0.5017
10.01 10.76 11.31 11.75 12.25 12.89 13.48 14.01 14.62 15.22 15.48 15.98
10.01 10.76 11.31 11.75 12.25 12.89 13.47 14.01 14.63 15.24 15.47 15.96
0.0000 0.1166 0.1943 0.2523 0.3128 0.3860 0.4473 0.5001 0.5578 0.6118 0.6308 0.6709
0 26 44 57 71 87 100 110 120 127 129 132
0.0000 0.0491 0.1030 0.1528 0.2002 0.2534 0.3043 0.3530 0.4044 0.4546
15.82 16.81 17.84 18.73 19.55 20.48 21.32 22.10 22.90 23.65
15.82 16.81 17.83 18.74 19.57 20.47 21.31 22.09 22.89 23.65
0.0000 0.1036 0.2010 0.2798 0.3467 0.4145 0.4733 0.5250 0.5754 0.6209
0 21 41 57 71 84 94 102 109 113
0.0000 0.0473 0.0961 0.1403 0.1927 0.2431 0.2916 0.3462 0.3924 0.4460
24.02 25.29 26.53 27.73 29.02 30.24 31.38 32.65 33.64 34.75
24.02 25.27 26.56 27.71 29.02 30.25 31.39 32.62 33.63 34.76
0.0000 0.0937 0.1809 0.2519 0.3275 0.3928 0.4497 0.5081 0.5538 0.6033
0 15 30 43 58 70 80 89 95 99
0.0000 0.0430 0.0844 0.1248 0.1679 0.2217 0.2676 0.3168 0.3620 0.4288 0.4404
35.41 36.93 38.35 39.78 41.20 42.97 44.54 46.10 47.53 49.52 49.87
35.41 36.92 38.36 39.75 41.22 43.01 44.52 46.09 47.50 49.52 49.86
0.0000 0.0810 0.1528 0.2175 0.2813 0.3541 0.4110 0.4673 0.5153 0.5806 0.5913
0 11 21 31 41 52 61 69 76 83 84
P0 ) 0.213 ( 0.001; P1 ) 0.032 ( 0.003; P2 ) 0.030 ( 0.004; P3 ) -0.005 ( 0.009; σx ) 0.000 06; σp ) 13 Pa. P0 ) 0.1808 ( 0.0009; P1 ) 0.027 ( 0.003; P2 ) 0.020 ( 0.004; P3 ) -0.003 ( 0.008; σx ) 0.000 01; σp ) 16 Pa. c P ) 0.153 ( 0.001; P ) 0.012 ( 0.003; P ) 0.000 ( 0.004; P ) 0.027 ( 0.009; σ ) 0.000 02; σ ) 23 Pa. 0 1 2 3 x p d P ) 0.1276 ( 0.0007; P ) 0.025 ( 0.002; P ) -0.011 ( 0.003; P ) -0.005 ( 0.006; σ ) 0.000 01; σ ) 25 Pa. 0 1 2 3 x p a b
Table 3. Correlation and Prediction of VLE, HEm, and VEm Data for Hexane (1) + TAME (2) Using the UNIQUAC, Flory, LF, UNIFAC, and Modified UNIFAC (Dortmund) Modelsa 298.15 K σp (kPa)
σp (%)
UNIQUAC Flory LF
0.08 0.07 0.07
0.38 0.36 0.37
UNIFAC mod UNIFAC (Dortmund)
0.42 0.03
2.1 0.17
σH (J
308.15 K
mol-1)
σV
(cm3 mol-1)
σp (kPa)
VLE, HEm, and VEm Correlation 1.6 0.06 2.0 0.24 0.09 2.7 0.006 0.05
318.15 K
328.15 K
σp (%)
σp (kPa)
σp (%)
σp (kPa)
σp (%)
0.20 0.30 0.16
0.08 0.16 0.12
0.17 0.36 0.28
0.23 0.33 0.33
0.35 0.51 0.52
2.4 0.14
1.3 0.19
2.8 0.42
1.9 0.40
2.9 0.62
VLE Prediction 0.74 0.04
a Standard deviations between experimental and calculated vapor pressures, σ , and percent ratio of σ and the maximum value of the p p vapor pressure, σp(%), standard deviations between experimental and calculated excess enthalpies, σH, and standard deviations between experimental and calculated excess volumes, σV.
Peng et al.23 have recently shown that the free-volume theory of Flory24 may be used to predict excess enthalpy
data for mixtures involving a hydrocarbon and a branched ether. In this work, the theory of Flory is used
Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002 1367
Figure 2. GEm against x1 values for the hexane (1) + TAME (2) system: ], 298.15 K; ∇, 308.15 K; 4, 318.15 K; O, 328.15 K.
Figure 3. HEm (0) and VEm (O) data for the hexane (1) + TAME (2) system at 298.15 K: symbol, experimental data taken from Zhu et al.9 and Witek et al.;10 s, correlated using the LF model; - - -, calculated using Flory’s theory.
to simultaneously correlate VLE and HEm data available for the hexane + TAME system. Each fluid is characterized by three characteristic magnitudes, p*, v*, and T*, which are evaluated from volumetric properties (molar volumes, cubic expansion coefficients, and isothermal compressibilities). The mixing rules introduce
Figure 4. VLE data for hexane (1) + TAME (2): ], 298.15 K; ∇, 308.15 K; 4, 318.15 K; O, 328.15 K; s, correlated using the UNIQUAC model; - - -, predicted using the modified UNIFAC (Dortmund) model.
a binary parameter for the energy interaction, XAB. An entropic correction parameter, QAB, is introduced in the expression for the chemical potential. A value of 10.83 J cm-3 was obtained for the energy interaction parameter, XAB, from the HEm data. The value for the QAB parameter obtained from VLE data was 0.017 J cm-3. Table 3 summarizes the results for the correlation of HEm and VLE data by means of the Flory theory. Vaporpressure values calculated using Flory’s theory are very accurate; the values of σp and σp(%) are similar to those also reported in Table 3 for the other correlation procedures. Although the theory of Flory does not include any volumetric parameter, in principle this model can be used to predict VEm data. Table 3 gives the value for the standard deviation between experimental and calculated excess volumes, σV, and Figure 3 shows plots of HEm and VEm data calculated by means of Flory’s theory for the hexane + TAME system at 298.15 K. As indicated by the arrows, HEm data are represented on the left axis and VEm data on the right axis. HEm data are correctly described by the model, and a value of 2.0 J mol-1 was obtained for σH. However, calculated excess volumes are only a poor estimation of the experimental VEm values. VLE, HEm, and VEm data for the hexane + TAME system were also correlated using the physical interaction model proposed by Sanchez and Lacombe: the lattice-fluid (LF) theory.25,26 In the LF model, each fluid is characterized by the number of segments of the molecule, r, and two scaling constants: the closedpacked volume, v*, and the characteristic temperature, T*. Values for the hexane and TAME parameters were taken from Lacombe and Sanchez25 and Coto et al.,4 respectively. The mixing rules include two binary parameters, the energy interaction parameter, ζAB, and
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the volume interaction parameter, ξAB. These two parameters adopt values close to unity and should be calculated from excess enthalpy data and volumetric properties, respectively. A dimensionless entropic correction parameter, qAB, is introduced in the expression for the chemical potential. All of these binary parameters are assumed to be temperature-independent. The resulting values for these parameters are ζAB ) 0.9871, ξAB ) 0.9987, and qAB ) 0.0158. Table 3 summarizes the results for the correlation of HEm, VEm, and VLE data by means of this model, and Figure 3 shows plots of the experimental and calculated HEm and VEm data. The LF model is shown to successfully correlate the experimental data available for the hexane + TAME mixtures. Predictions of VLE data from pure-component data and the model parameters available in the literature are of great industrial interest and were carried out using the original UNIFAC27,28 and the modified UNIFAC (Dortmund)29,30 models. Values for σp and σp(%) are listed in Table 3. Vapor pressures are accurately predicted using the modified UNIFAC (Dortmund) model: σp(%) values range from 0.14% to 0.62%. The original UNIFAC model leads to higher deviations than those obtained when the modified UNIFAC (Dortmund) model is used. Figure 4 shows a comparison of UNIQUAC and modified UNIFAC (Dortmund) calculations of VLE data. The predicted vapor pressures are almost coincident with the experimental data. Conclusions VLE data have been reported for hexane + TAME at four different temperatures. Deviations from Raoult’s law are positive and small, and there is nearly no temperature effect on the vapor compositions in the temperature range 298.15-328.15 K. Experimental VLE data reported here and HEm and E Vm data at 298.15 K previously available for the hexane + TAME mixtures9,10 are analyzed in terms of the UNIQUAC, Flory, and LF models, the original version of the UNIFAC group contribution model, and the modified UNIFAC (Dortmund) model. The UNIQUAC model and Flory’s theory provide a simultaneous and accurate correlation of VLE and HEm data. Both properties can be described by a unique set of four parameters (UNIQUAC model) or two parameters (Flory’s theory). The LF model is able to correlate simultaneously the VLE, HEm, and VEm data using a set of three temperature-independent parameters. Like VLE predictions, the modified UNIFAC (Dortmund) model is shown to lead to accurate predictions at the four temperatures studied. Acknowledgment This work was funded by the Spanish Ministry of Education (DGICYT PB97-0315). A.d.R. acknowledges the Comunidad Autonoma de Madrid for its support through a predoctoral grant. Nomenclature Latin Letters Aij ) UNIQUAC model interaction parameters G ) Gibbs energy H ) enthalpy J ) Joule
K ) Kelvin kPa ) 103 Pa Pi ) Pade´ approximant parameter p ) vapor pressure Qj ) Pade´ approximant parameter QAB ) entropic correction parameter, Flory’s theory qAB ) entropic correction parameter, lattice-fluid theory R ) gas constant T ) temperature V ) volume XAB ) energy interaction parameter, Flory’s theory x ) mole fraction in the liquid phase y ) mole fraction in the vapor phase Greek Symbols R ) thermal expansion coefficient γ ) activity coefficient ζAB ) energy interaction parameter, lattice-fluid theory κ ) isothermal compressibility ξAB ) volume interaction parameter, lattice-fluid theory σ ) standard deviation σ(%) ) percent ratio of the standard deviation and the maximum value of a magnitude Superscripts * ) characteristic magnitude for a fluid E ) excess property Subscripts calc ) calculated i, j ) components of binary systems H ) excess enthalpy m ) molar property p ) vapor pressure V ) excess volume x ) liquid composition of component 1 Abbreviations LF ) lattice fluid MTBE ) 1,1-dimethylethyl methyl ether (tert-butyl methyl ether) TAME ) 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether) VLE ) vapor-liquid equilibrium
Literature Cited (1) Coto, B.; Wiesenberg, R.; Pando, C.; Rubio, R. G.; Renuncio, J. A. R. Vapor-liquid equilibrium for methanol-tert-butyl methyl ether (MTBE) system. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 482-489. (2) Mo¨ssner, F.; Coto, B.; Pando, C.; Rubio, R. G.; Renuncio, J. A. R. Vapor-liquid equilibrium for methanol + 1,1-dimethylpropyl methyl ether at (288.15, 308.15, and 328.15) K. J. Chem. Eng. Data 1996, 41, 537-542. (3) Coto, B.; Mo¨ssner, F.; Pando, C.; Rubio, R. G.; Renuncio, J. A. R. Bulk and surface properties for the methanol-1,4-dimethylpropyl methyl ether and methanol-1,1-dimethylethyl methyl ether systems. J. Chem. Soc., Faraday Trans. 1996, 92, 44354440. (4) Coto, B.; Mo¨ssner, F.; Pando, C.; Rubio, R. G.; Renuncio, J. A. R. Vapor-liquid equilibrium of methanol-[1,1-dimethylethyl methyl ether (MTBE) or 1,1-dimethylpropyl methyl ether (TAME)] systems. Fluid Phase Equilib. 1997, 133, 89-103. (5) Mo¨ssner, F.; Coto, B.; Pando, C.; Renuncio, J. A. R. Vaporliquid equilibria of binary systems of n-heptane with 1,1-dimethylpropyl methyl ether and 1,1-dimethylethyl methyl ether. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1146-1153. (6) del Rı´o, A.; Coto, B.; Pando, C.; Renuncio, J. A. R. Vaporliquid equilibria for the binary system cyclohexane-1,1-dimethylethyl methyl ether (MTBE) at 298.15, 308.15, and 318.15 K. Phys. Chem. Chem. Phys. 1999, 1, 4495-4998. (7) del Rı´o, A.; Coto, B.; Pando, C.; Renuncio, J. A. R. VaporLiquid Equilibria and Excess Properties of Cyclohexane-1,1-
Ind. Eng. Chem. Res., Vol. 41, No. 5, 2002 1369 Dimethylpropyl Methyl Ether (TAME) Mixtures. Ind. Eng. Chem. Res. 2001, 40, 689-695. (8) del Rı´o, A.; Coto, B.; Pando, C.; Renuncio, J. A. R. Vaporliquid equilibria for the binary systems decane + 1,1-dimethylethyl methyl ether (MTBE) and decane + 1,1-dimethylpropyl methyl ether (TAME) at 308.15, 318.15 and 328.15 K. Fluid Phase Equilib. 2001, 187-188, 299-310. (9) Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. Excess enthalpies of methyl 1,1-dimethylpropyl ether + a C6 hydrocarbon at 298.15 K. J. Chem. Eng. Data 1994, 39, 302-303. (10) Witek, M.; Goldon, A.; Hofman, T.; Domanska, U. Densities and excess volumes of ethyl 1,1-dimethylpropyl ether + benzene, or cyclohexane, or an alkane (C6-C16) at 298.15 K. J. Chem. Eng. Data 1997, 42, 60-63. (11) Coto, B.; Pando, C.; Rubio, R. G.; Renuncio, J. A. R. Vaporliquid equilibrium of the ethanol-propanal system. J. Chem. Soc., Faraday Trans. 1995, 91, 273-278. (12) Gibbs, R. E.; van Ness, H. C. Vapor-liquid equilibria from total pressure measurements. A new apparatus. Ind. Eng. Chem. Fundam. 1972, 11, 410-413. (13) Dı´az Pen˜a, M.; Tardajos, G. Isothermal compressibilities of liquids. J. Chem. Thermodyn. 1978, 10, 19-24. (14) Funke, H.; Wetzel, M.; Heintz, A. New applications of the ERAS model. Thermodynamics of amine + alkane and alcohol + amine mixtures. Pure Appl. Chem. 1989, 61, 1429-1439. (15) Gmehling, J.; Onken, U.; Arlt, W. Vapor-liquid equilibrium data collection; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt Main, Germany, 1980; Vol. I, Part 6b. (16) TRC Thermodynamic Tables; Thermodynamic Research Center, Texas A&M University System: College Station, TX 1994. (17) Govender, U. P.; Letcher, T. M. Effect of Temperature and Pressure on the Volumetric Properties of Branched and Cyclic Ethers. J. Chem. Eng. Data 1996, 41, 147-150. (18) Cervenkova, I.; Boublik, T. Vapor Pressures, Refractive Indexes, and Densities at 20.0 °C, and Vapor-liquid equilibrium at 101.325 kPa, in the tert-amyl methyl ether-methanol system. J. Chem. Eng. Data 1984, 29, 425-427. (19) Pallczewska-Tulinska, M.; Wyrzykowska-Stankiewicz, D.; Cholinski, J.; Zieborak, K. Isobaric vapor-liquid equilibrium in two binary systems involving tert-amyl methyl ether. Fluid Phase Equilib. 1990, 54, 57-68.
(20) Rubio, R. G.; Renuncio, J. A. R.; Diaz Pen˜a, M. Regression of vapor-liquid equilibrium data based on application of the maximum likelihood principle. Fluid Phase Equilib. 1983, 12, 217-234. (21) Hayden, J. G.; O’Connell, J. P. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209-216. (22) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures. A new expression for the excess Gibbs energy of partly and completely miscible systems. AIChE J. 1975, 21, 116-128. (23) Peng, D.-Y.; Benson, G. C.; Lu, B. C.-Y. Predicting excess enthalpies of ether and/or hydrocarbon binary mixtures. J. Solution Chem. 1999, 28, 505-519. (24) Flory, P. J. Statistical theory of liquid mixtures. J. Am. Chem. Soc. 1965, 87, 1833-1838. (25) Lacombe, R. H.; Sanchez, I. C. Statistical thermodynamics of fluid mixtures. J. Phys. Chem. 1976, 80, 2568-2580. (26) Sanchez, I. C.; Lacombe, R. H. An elementary molecular theory of classical fluids. Pure fluids. J. Phys. Chem. 1976, 80, 2352-2362. (27) Fredeslund, A.; Gmehling, J.; Rasmussen, P. Vapor-liquid equilibria using UNIFAC; Elsevier: Amsterdam, The Netherlands, 1977. (28) Hansen, H. K.; Rasmussen, P.; Fredeslund, A.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30, 2352-2355. (29) Weidlich, U.; Gmehling, J. A Modified UNIFAC Model. 1. Prediction of VLE, hE, and γ∞. Ind. Eng. Chem. Res. 1987, 26, 1372-1381. (30) Gmehling, J.; Jiding, L.; Schiller, M. A Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178193.
Received for review July 12, 2001 Revised manuscript received November 6, 2001 Accepted November 9, 2001 IE0106128
