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Phase equilibria in the systems 3-methylpentane + methylcyclohexane, diisopropyl ether + methylcyclohexane and 3-methylpentane + diisopropyl ether + methylcyclohexane at 101.3 kPa
Fluid Phase Equilibria 194–197 (2002) 957–968
Phase equilibria in the systems 3-methylpentane + methylcyclohexane, diisopropyl ether + methylcyclohexane and 3-methylpentane + diisopropyl ether + methylcyclohexane at 101.3 kPa Sonia Loras, Antonio Aucejo∗ , Rosa Muñoz Falcultad de Qu´ımica, Departamento de Ingenier´ıa Qu´ımica, Universitat de València, Burjassot, 46100 Valencia, Spain Received 6 February 2001; accepted 17 September 2001
Abstract Consistent vapor–liquid equilibria (VLE) at 101.3 kPa has been determined for the ternary system 3methylpentane + diisopropyl ether (DIPE) + methylcyclohexane and the binary subsystems 3-methylpentane + methylcyclohexane and DIPE + methylcyclohexane in the temperature range from 336 to 374 K. According to the experimental results, the systems exhibit slight positive deviation from ideal behavior and no azeotrope is present. The VLE data have been correlated with the composition using the Wilson, UNIQUAC and NRTL relations. These models allow good prediction of the VLE properties of the ternary system from those of the pertinent binary subsystems. © 2002 Elsevier Science B.V. All rights reserved. Keywords: VLE data; Activity coefficients; Experimental
1. Introduction This work presents a continuation of the thermodynamic research on vapor–liquid equilibrium (VLE) of mixtures formed by oxygenated additives (ethers and alkanols) to unleaded gasoline and hydrocarbons [1]. Methyl 1,1-dimethylethyl ether (MTBE) is used mostly because of its low Reid vapor pressure (RVP) and the availability of the feedstock ethanol from renewable resources. However, MTBE has the drawbacks of easily dissolving in water and of difficult removal from water. In addition, it is resistant to microbial decomposition. These facts have promoted research on the possible use of ethers of higher molecular weights, harmless for the environment. Diisopropyl ether (DIPE) is effective in reducing automotive CO emissions and has been considered a good alternative to MTBE as an oxygenated additive. ∗
Corresponding author. Tel.: +34-96-386-9318; fax: +34-96-386-4898. E-mail address: [email protected] (A. Aucejo). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 6 5 3 - 7
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Phase equilibrium data on oxygenated mixtures are important for predicting the vapor-phase composition that would be in equilibrium with hydrocarbon mixtures, and the systems reported here constitute examples of such mixtures. The present work was undertaken to measure VLE data of the ternary system 3-methylpentane (1)+DIPE (2)+methylcyclohexane (3) and the binary subsystems and 3-methylpentane (1) + methylcyclohexane (3) and DIPE (2) + methylcyclohexane (3) at 101.3 kPa. For these systems, no VLE data have been previously published. VLE data at 101.3 kPa for the other binary subsystem, 3-methylpentane (1) + DIPE (2), have already been reported in a previous work [2]. According to this source, this binary system shows a small positive deviation from ideality and presents no azeotrope.
2. Experimental 2.1. Chemicals 3-Methylpentane (≥99 mass%), DIPE (≥99.8 mass%, HPLC grade) and methylcyclohexane (≥99 mass%, anhydrous) were supplied by Aldrich. The reagents were used without further purification after chromatography failed to show any significant impurities. The densities of the pure liquids were measured at 298.15 K using an Anton Paar DMA 55 densimeter. The refractive indexes of the pure liquids were measured at 298.15 K in an Abbe refractometer, Atago 3T. Temperature was controlled to ±0.01 K with a thermostated bath. The accuracies in density and refractive index measurements are ±0.01 kg m−3 and ±0.0002, respectively. The experimental values of these properties and the boiling points are given in Table 1 together with those given in [3–9]. 2.2. Apparatus and procedure An all glass Fischer LABODEST VLE apparatus model 602/D, manufactured by Fischer Labor und Verfahrenstechnik (Germany), was used in the equilibrium determinations. The equilibrium vessel was a dynamic-recirculating still described by Walas [10], equipped with a Cottrell circulation pump. The still is capable of handling pressures from 0.25 to 400 kPa, and temperature up to 523 K. The Cottrell pump ensures that both liquid and vapor phases are in intimate contact during boiling and also in contact with the temperature sensing element. The equilibrium temperature was measured with a digital Fischer thermometer with an accuracy of ±0.1 K. The apparatus is equipped with two digital pressure sensors: one for the low pressure region with an accuracy of ±0.01 kPa, and another for the high pressure region with an accuracy of ±0.1 kPa. The temperature probe was calibrated against the ice and steam points of distilled water. The manometers were calibrated using the vapor pressure of ultrapure water. The still was Table 1 Density, d, refractive index, nD , and normal boiling point, Tb , of the chemicals Compound
3-Methylpentane DIPE Methylcyclohexane
d (298.15 K) (kg m−3 )
nD (298.15 K)
Experimental
Literature
Experimental
Literature
Experimental
Literature
659.91 718.14 764.87
660.04 [3] 718.36 [6] 764.59 [9]
1.3738 1.3656 1.4204
1.3739 [4] 1.3655 [7] 1.4206 [9]
336.3 341.4 374.0
336.43 [5] 341.42 [8] 374.09 [9]
Tb (101.3 kPa) (K)
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operated under constant pressure until equilibrium was reached. Equilibrium conditions were assumed when constant temperature and pressure were obtained for 30 min or longer. Then, samples of liquid and condensate were taken for analysis. The sample extractions were carried out with special syringes that allowed one to withdraw small volume samples (1.0 l) in a system under partial vacuum or under overpressure conditions. 2.3. Analysis Compositions of the liquid and condensed vapor phase samples were determined using a HewlettPackard 5890 S-II gas chromatograph (GC), after calibration with gravimetrically prepared standard solutions. A flame ionization detector was used together with a 60 m, 0.2 mm i.d. fused silica capillary column, SUPELCOWAX 10. The GC response peaks were treated with a Hewlett-Packard 3396 integrator. Column, injector and detector temperatures were 343, 498, 523 K for all the systems. Very good separation was achieved under these conditions. At least two analyses were made of each composition; the standard deviation in the mole fraction was usually <0.001. 3. Results and discussion The temperature T, and the liquid-phase and vapor-phase mole fractions, xi and yi , at 101.3 kPa are reported in Tables 2–4 and are plotted in Figs. 1–3. The activity coefficients i were calculated from the following equation [11]: γi =
yi P xi Pi0
(1)
where P is the total pressure and Pi0 is the vapor pressure. In Eq. (1), also known as modified Raoult’s law, the vapor phase is assumed to be an ideal gas and the pressure dependence of the liquid phase fugacity is neglected. Eq. (1) was selected to calculate activity coefficients because the low pressures observed in the present VLE data makes these simplifications reasonable. In addition, in such almost ideal mixtures the activity coefficients become very sensitive to the vapor phase corrections and the estimation methods of vapor phase corrections can introduce uncertainties in the calculated activity coefficients [12]. Vapor pressures Pi0 were calculated with the Antoine equation whose parameters Ai , Bi , and Ci are reported in Table 5. ln Pi0 = Ai −
Bi T − Ci
(2)
The Antoine constants were taken from [13] for 3-methylpentane, from [8] for DIPE and from [14] for methylcyclohexane. The calculated activity coefficients reported in Tables 2–4 are estimated to be accurate to within ±3%. The results reported in those tables indicate that the systems exhibit small positive deviations from ideal behavior and that no azeotrope is present. The VLE data reported in Tables 2 and 3 for the binary subsystems 3-methylpentane (1)+methylcyclohexane (3) and DIPE (2) + methylcyclohexane (3) were found to be thermodynamically consistent
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Table 2 Experimental vapor–liquid equilibrium data and activity coefficients for 3-methylpentane (1) + methylcyclohexane (3) at 101.3 kPa T (K)
x1
y1
γ1
336.30 336.75 337.55 338.85 340.05 341.25 342.65 343.95 345.55 346.95 348.65 350.25 351.75 353.55 356.15 358.15 359.95 361.95 364.85 367.75 370.35 372.35 374.00
1.000 0.978 0.945 0.890 0.838 0.789 0.738 0.694 0.640 0.593 0.543 0.494 0.448 0.400 0.337 0.293 0.251 0.208 0.151 0.099 0.056 0.025 0.000
1.000 0.993 0.982 0.963 0.944 0.924 0.901 0.880 0.853 0.826 0.795 0.762 0.727 0.687 0.624 0.570 0.511 0.448 0.357 0.254 0.154 0.071 0.000
1.000 1.000 0.998 0.998 1.001 1.002 1.002 1.000 1.003 1.005 1.004 1.010 1.017 1.023 1.026 1.016 1.015 1.017 1.030 1.034 1.039 1.041
γ3 1.029 1.040 1.023 1.015 1.019 1.010 1.002 0.987 0.986 0.978 0.975 0.974 0.970 0.969 0.978 0.992 0.996 0.992 0.995 0.999 1.002 1.000
by the point-to-point method of Van Ness and Abbott [15], as modified by Fredenslund et al. [16]. The consistency criterium (y(MAD) ≤ 10−2 ) was met using a one parameter Legendre polynomial, which reduces the functionality of the excess Gibbs energy GE to the following symmetric relation: GE = Ax1 x2 RT
(3)
Table 6 presents the value of parameter A and the pertinent consistency statistics. The statistics show that Eq. (3) gives a good-fit of the data. The VLE data reported in Table 4 for the ternary system 3-methylpentane (1)+DIPE (2)+methylcyclohexane (3) were found to be thermodynamically consistent by the McDermott–Ellis method [17] modified by Wisniak and Tamir [18]. The test requires that D < D max for every experimental point, where the local deviation D is given by D=
N (xia + xib )(ln γia − ln γib ) i=1
(4)
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Table 3 Experimental vapor–liquid equilibrium data and activity coefficients DIPE (2) + methylcyclohexane (3) at 101.3 kPa T (K)
x2
y2
γ2
341.40 341.45 342.05 343.15 344.25 345.25 346.45 347.45 348.65 349.95 351.35 352.75 353.95 355.75 357.45 359.25 361.05 362.75 366.15 368.55 371.15 372.75 374.00
1.000 0.982 0.952 0.901 0.852 0.800 0.749 0.698 0.653 0.602 0.551 0.506 0.458 0.398 0.347 0.300 0.252 0.214 0.137 0.091 0.045 0.019 0.000
1.000 0.993 0.980 0.958 0.937 0.913 0.887 0.861 0.834 0.805 0.771 0.737 0.703 0.653 0.604 0.552 0.495 0.443 0.319 0.226 0.122 0.054 0.000
1.000 1.016 1.016 1.014 1.012 1.018 1.018 1.028 1.027 1.033 1.037 1.036 1.054 1.068 1.079 1.083 1.099 1.107 1.130 1.139 1.141 1.174
γ3 1.114 1.119 1.103 1.081 1.068 1.056 1.049 1.043 1.026 1.020 1.016 1.005 0.999 0.996 0.994 0.992 0.989 0.995 0.999 1.002 1.003 1.000
where N is the number of components. The maximum deviation Dmax is given by Dmax
N 1 1 1 1 P = (xia + xib ) + (xia + xib ) x + + + xia yia xib yib P i=1 i=1 N
N N +2 |ln γib − ln γia |x + (xia + xib )Bj [(Ta + Cj )−2 + (Tb + Cj )−2 ] T i=1
(5)
i=1
The error in the measurements x, P and T were as previously indicated. The first and fourth terms in Eq. (5) are the dominant. For each experimental point reported here, the value of D was always smaller than the value of Dmax . The activity coefficients of the binary systems were correlated with Wilson, NRTL and UNIQUAC equations. The parameters of these models were obtained by minimizing the following objective function (OF) exp N Pi − Picalc exp calc + |y − y | OF = 100 × (6) exp i i P i i=1 and are reported in Table 7, together with the pertinent statistics of VLE interpolation. The parameters of the system 3-methylpentane (1) + DIPE (2) have been recalculated from the data reported in
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Table 4 Experimental vapor–liquid equilibrium data and activity coefficients for 3-methylpentane (1) + DIPE (2) + methylcyclohexane (3) at 101.3 kPa T (K)
x1
x2
y1
y2
γ1
336.30 341.40 374.00 337.65 338.75 339.15 339.65 340.45 340.45 340.65 340.75 341.25 341.65 342.15 342.35 342.45 342.55 342.65 342.75 344.25 344.35 344.65 344.75 344.75 345.35 346.55 347.25 347.65 347.65 347.95 348.55 348.55 350.55 350.65 350.85 351.55 353.45 354.25 355.45 355.95 356.85 358.25 362.15 362.85 367.55
1.000 0.000 0.000 0.904 0.796 0.694 0.355 0.399 0.243 0.526 0.448 0.699 0.054 0.586 0.102 0.704 0.502 0.401 0.246 0.592 0.097 0.246 0.498 0.401 0.304 0.099 0.492 0.400 0.149 0.299 0.500 0.204 0.393 0.305 0.057 0.190 0.067 0.291 0.307 0.097 0.151 0.197 0.048 0.104 0.058
0.000 1.000 0.000 0.045 0.105 0.204 0.599 0.502 0.704 0.336 0.432 0.105 0.899 0.203 0.804 0.047 0.278 0.400 0.591 0.106 0.706 0.500 0.192 0.306 0.399 0.610 0.105 0.194 0.498 0.306 0.047 0.394 0.101 0.197 0.494 0.305 0.389 0.102 0.050 0.278 0.192 0.100 0.174 0.097 0.048
1.000 0.000 0.000 0.940 0.862 0.764 0.410 0.467 0.292 0.610 0.523 0.818 0.069 0.704 0.131 0.856 0.615 0.496 0.311 0.758 0.132 0.328 0.651 0.527 0.409 0.141 0.692 0.573 0.217 0.432 0.735 0.304 0.613 0.480 0.092 0.307 0.117 0.509 0.557 0.179 0.284 0.388 0.106 0.232 0.148
0.000 1.000 0.000 0.044 0.105 0.202 0.574 0.498 0.689 0.341 0.434 0.113 0.912 0.219 0.832 0.053 0.303 0.429 0.626 0.125 0.787 0.569 0.227 0.356 0.468 0.731 0.137 0.252 0.625 0.393 0.065 0.513 0.147 0.282 0.685 0.441 0.595 0.166 0.085 0.462 0.333 0.184 0.357 0.205 0.117
1.000
γ2
γ3
1.000 0.996 1.003 1.006 1.039 1.027 1.056 1.012 1.014 1.002 1.086 1.001 1.065 1.003 1.008 1.014 1.033 1.000 1.059 1.026 1.007 1.011 1.018 1.039 1.006 1.011 1.031 1.012 1.010 1.023 1.013 1.018 1.036 1.018 1.037 1.020 1.025 1.022 1.023 1.029 1.040 1.029 1.040
1.092 1.082 1.062 1.017 1.024 1.010 1.040 1.026 1.077 1.007 1.053 1.004 1.100 1.047 1.029 1.014 1.075 1.013 1.024 1.060 1.043 1.033 1.017 1.080 1.065 1.029 1.043 1.107 1.039 1.089 1.071 1.028 1.052 1.050 1.093 1.113 1.057 1.075 1.100 1.092 1.098 1.112
1.000 1.016 1.027 1.015 1.005 1.019 1.018 1.021 1.028 0.989 1.101 0.991 1.068 0.981 1.007 1.011 1.037 0.983 1.042 1.021 0.979 0.997 1.008 1.030 0.970 0.976 1.008 0.987 0.967 0.996 0.970 0.973 1.011 0.991 0.988 0.973 0.970 0.990 0.975 0.973 0.979 0.980 0.993
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Fig. 1. Boiling temperature diagram for the system 3-methylpentane (1) + methylcyclohexane (3) at 101.3 kPa. Experimental data (䊉). Smoothed using Wilson model (—).
Table 5 Antoine coefficients, Eq. (2) Compound
Ai
Bi
Ci
3-Methylpentane [13] DIPE [8] Methylcyclohexane [14]
14.3708 14.3267 13.6438
2999.76 2895.75 2891.01
28.69 43.15 53.81
Table 6 Consistency test for the binary subsystems 3-methylpentane (1) + methylcyclohexane (3) and DIPE (2) + methylcyclohexane (3) System
100 × y(MAD) a
PMAD b (kPa)
Ac
(1) + (3) (2) + (3)
0.42 0.33
0.18 0.31
0.009 0.103
a
Mean absolute deviation in vapor phase composition. Mean absolute deviation in pressure. c Parameter in Eq. (3). b
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Fig. 2. Boiling temperature diagram for the system DIPE (2) + methylcyclohexane (3) at 101.3 kPa. Experimental data (䊉). Smoothed using Wilson model (—).
Fig. 3. Diagram of VLE for the ternary system 3-methylpentane (1) + DIPE (2) + methylcyclohexane (3) at 101.3 kPa: (䊏) liquid phase mole fractions; (䉱) vapor phase mole fractions.
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Fig. 4. Isothermals (K) for the ternary system 3-methylpentane (1) + DIPE (2) + methylcyclohexane (3) at 101.3 kPa, calculated with Wilson model with the binary interaction parameters shown in Table 7.
[2]. Inspection of the results given in Table 7 shows that all models are adequate to predict the binary data. Likewise, the VLE data of the ternary system were predicted using the binary model parameters of the Table 7. The result of the pertinent statistics for the prediction of the ternary data appears in this table. From these results, it can be concluded again that the binary data allow a good prediction of the ternary system. The three models yield similar deviations, but the best fit is obtained with the Wilson model. Fig. 4 show the boiling isotherms for the ternary system calculated by this model.
4. Conclusions VLE data are reported for ternary system and two binary subsystems containing 3-methylpentane, DIPE and methylcyclohexane. From the results, we see that DIPE forms only slightly nonideal mixture with methylcyclohexane and can be successfully described using the Wilson, the NRTL, and the UNIQUAC model. This fact is in agreement with the previous results obtained for the mixtures formed from branched ethers and hydrocarbons [1]. The ternary system does not present azeotrope and can be predicted from binary data with Wilson, NRTL and UNIQUAC equations. List of symbols A parameter in Eq. (3) Ai Antoine’s equation parameter, Eq. (2) Bi Antoine’s equation parameter, Eq. (2)
S. Loras et al. / Fluid Phase Equilibria 194–197 (2002) 957–968
Ci D Dmax GE P P0 R T x, y
967
Antoine’s equation parameter, Eq. (2) parameter in Eq. (4) parameter in Eq. (5) excess Gibbs energy (J mol−1 ) total vapor pressure of mixture (kPa) pure component vapor pressure (kPa) universal gas constant (J mol−1 K−1 ) absolute temperature (K) compositions of the liquid and vapor phases
Greek letter γ activity coefficient Superscripts E excess property L pertaining to the liquid phase Subscripts i component i j component j Acknowledgements This work was financed by MEC, Spain (Project no. PB96-07 88). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
S. Loras, Ph.D. Thesis, University of Valencia, Spain, 1999. S. Loras, A. Aucejo, R. Muñoz, J. Wisniak, J. Chem. Eng. Data 44 (1999) 583–587. M. Awwad, R.A. Pethrick, J. Mol. Liq. 25 (1983) 115–127. T.E. Daubert, R.P. Danner (Eds.), Physical and Thermodynamic Properties of Pure Chemicals. Data Compilation, Taylor and Francis, Washington, DC, 1995. C.B. Willingham, W.J. Taylor, J.M. Pignocco, F.D. Rossini, J. Res. Natl. Bur. Stand. (U.S.) 35 (1945) 219–244. K. Nakanishi, H. Shirai, Bull. Chem. Soc. Jpn. 43 (1970) 1634–1642. K.A. Kobe, A.E. Ravica, S.P. Vohra, J. Chem. Eng. Data 1 (1956) 50–56. R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The Properties of Gases and Liquids, 3rd Edition, McGraw-Hill, New York, 1977. TRC Thermodynamic Tables Hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996a. S.M. Walas, Phase Equilibria in Chemical Engineering, Butterworth, London, 1985. H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions, McGraw-Hill, New York, 1982. R. Reich, M. Cartes, H. Segura, J. Wisniak, Phys. Chem. Liq. 38 (2000) 218–232. A. Aucejo, S. Loras, R. Muñoz, Fluid Phase Equilib. 156 (1999) 185–195. V. Mart´ınez-Soria, M.P. Peña, J.B. Montón, J. Chem. Eng. Data 44 (1999) 148–151. H.C. Van Ness, S.M. Byer, R.E. Gibbs, AIChE J. 19 (1973) 238–244.
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[16] A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC. A Group Contribution Method, Elsevier, Amsterdam, 1977, pp. 68–74. [17] C. McDermott, S.R.M. Ellis, Chem. Eng. Sci. 20 (1965) 293–296. [18] J. Wisniak, A. Tamir, J. Chem. Eng. Data 22 (1977) 253–260. [19] H.G. Rackett, J. Chem. Eng. Data 15 (1970) 514–517. [20] J. Gmehling, U. Onken (Eds.), Vapor–Liquid Equilibrium Data Collection, Chemistry Data Series, DECHEMA, Frankfurt, Main, 1990.
Phase equilibria in the systems 3-methylpentane + methylcyclohexane, diisopropyl ether + methylcyclohexane and 3-methylpentane + diisopropyl ether + methylcyclohexane at 101.3 kPa Sonia Loras, Antonio Aucejo∗ , Rosa Muñoz Falcultad de Qu´ımica, Departamento de Ingenier´ıa Qu´ımica, Universitat de València, Burjassot, 46100 Valencia, Spain Received 6 February 2001; accepted 17 September 2001
Abstract Consistent vapor–liquid equilibria (VLE) at 101.3 kPa has been determined for the ternary system 3methylpentane + diisopropyl ether (DIPE) + methylcyclohexane and the binary subsystems 3-methylpentane + methylcyclohexane and DIPE + methylcyclohexane in the temperature range from 336 to 374 K. According to the experimental results, the systems exhibit slight positive deviation from ideal behavior and no azeotrope is present. The VLE data have been correlated with the composition using the Wilson, UNIQUAC and NRTL relations. These models allow good prediction of the VLE properties of the ternary system from those of the pertinent binary subsystems. © 2002 Elsevier Science B.V. All rights reserved. Keywords: VLE data; Activity coefficients; Experimental
1. Introduction This work presents a continuation of the thermodynamic research on vapor–liquid equilibrium (VLE) of mixtures formed by oxygenated additives (ethers and alkanols) to unleaded gasoline and hydrocarbons [1]. Methyl 1,1-dimethylethyl ether (MTBE) is used mostly because of its low Reid vapor pressure (RVP) and the availability of the feedstock ethanol from renewable resources. However, MTBE has the drawbacks of easily dissolving in water and of difficult removal from water. In addition, it is resistant to microbial decomposition. These facts have promoted research on the possible use of ethers of higher molecular weights, harmless for the environment. Diisopropyl ether (DIPE) is effective in reducing automotive CO emissions and has been considered a good alternative to MTBE as an oxygenated additive. ∗
Corresponding author. Tel.: +34-96-386-9318; fax: +34-96-386-4898. E-mail address: [email protected] (A. Aucejo). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 6 5 3 - 7
958
S. Loras et al. / Fluid Phase Equilibria 194–197 (2002) 957–968
Phase equilibrium data on oxygenated mixtures are important for predicting the vapor-phase composition that would be in equilibrium with hydrocarbon mixtures, and the systems reported here constitute examples of such mixtures. The present work was undertaken to measure VLE data of the ternary system 3-methylpentane (1)+DIPE (2)+methylcyclohexane (3) and the binary subsystems and 3-methylpentane (1) + methylcyclohexane (3) and DIPE (2) + methylcyclohexane (3) at 101.3 kPa. For these systems, no VLE data have been previously published. VLE data at 101.3 kPa for the other binary subsystem, 3-methylpentane (1) + DIPE (2), have already been reported in a previous work [2]. According to this source, this binary system shows a small positive deviation from ideality and presents no azeotrope.
2. Experimental 2.1. Chemicals 3-Methylpentane (≥99 mass%), DIPE (≥99.8 mass%, HPLC grade) and methylcyclohexane (≥99 mass%, anhydrous) were supplied by Aldrich. The reagents were used without further purification after chromatography failed to show any significant impurities. The densities of the pure liquids were measured at 298.15 K using an Anton Paar DMA 55 densimeter. The refractive indexes of the pure liquids were measured at 298.15 K in an Abbe refractometer, Atago 3T. Temperature was controlled to ±0.01 K with a thermostated bath. The accuracies in density and refractive index measurements are ±0.01 kg m−3 and ±0.0002, respectively. The experimental values of these properties and the boiling points are given in Table 1 together with those given in [3–9]. 2.2. Apparatus and procedure An all glass Fischer LABODEST VLE apparatus model 602/D, manufactured by Fischer Labor und Verfahrenstechnik (Germany), was used in the equilibrium determinations. The equilibrium vessel was a dynamic-recirculating still described by Walas [10], equipped with a Cottrell circulation pump. The still is capable of handling pressures from 0.25 to 400 kPa, and temperature up to 523 K. The Cottrell pump ensures that both liquid and vapor phases are in intimate contact during boiling and also in contact with the temperature sensing element. The equilibrium temperature was measured with a digital Fischer thermometer with an accuracy of ±0.1 K. The apparatus is equipped with two digital pressure sensors: one for the low pressure region with an accuracy of ±0.01 kPa, and another for the high pressure region with an accuracy of ±0.1 kPa. The temperature probe was calibrated against the ice and steam points of distilled water. The manometers were calibrated using the vapor pressure of ultrapure water. The still was Table 1 Density, d, refractive index, nD , and normal boiling point, Tb , of the chemicals Compound
3-Methylpentane DIPE Methylcyclohexane
d (298.15 K) (kg m−3 )
nD (298.15 K)
Experimental
Literature
Experimental
Literature
Experimental
Literature
659.91 718.14 764.87
660.04 [3] 718.36 [6] 764.59 [9]
1.3738 1.3656 1.4204
1.3739 [4] 1.3655 [7] 1.4206 [9]
336.3 341.4 374.0
336.43 [5] 341.42 [8] 374.09 [9]
Tb (101.3 kPa) (K)
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operated under constant pressure until equilibrium was reached. Equilibrium conditions were assumed when constant temperature and pressure were obtained for 30 min or longer. Then, samples of liquid and condensate were taken for analysis. The sample extractions were carried out with special syringes that allowed one to withdraw small volume samples (1.0 l) in a system under partial vacuum or under overpressure conditions. 2.3. Analysis Compositions of the liquid and condensed vapor phase samples were determined using a HewlettPackard 5890 S-II gas chromatograph (GC), after calibration with gravimetrically prepared standard solutions. A flame ionization detector was used together with a 60 m, 0.2 mm i.d. fused silica capillary column, SUPELCOWAX 10. The GC response peaks were treated with a Hewlett-Packard 3396 integrator. Column, injector and detector temperatures were 343, 498, 523 K for all the systems. Very good separation was achieved under these conditions. At least two analyses were made of each composition; the standard deviation in the mole fraction was usually <0.001. 3. Results and discussion The temperature T, and the liquid-phase and vapor-phase mole fractions, xi and yi , at 101.3 kPa are reported in Tables 2–4 and are plotted in Figs. 1–3. The activity coefficients i were calculated from the following equation [11]: γi =
yi P xi Pi0
(1)
where P is the total pressure and Pi0 is the vapor pressure. In Eq. (1), also known as modified Raoult’s law, the vapor phase is assumed to be an ideal gas and the pressure dependence of the liquid phase fugacity is neglected. Eq. (1) was selected to calculate activity coefficients because the low pressures observed in the present VLE data makes these simplifications reasonable. In addition, in such almost ideal mixtures the activity coefficients become very sensitive to the vapor phase corrections and the estimation methods of vapor phase corrections can introduce uncertainties in the calculated activity coefficients [12]. Vapor pressures Pi0 were calculated with the Antoine equation whose parameters Ai , Bi , and Ci are reported in Table 5. ln Pi0 = Ai −
Bi T − Ci
(2)
The Antoine constants were taken from [13] for 3-methylpentane, from [8] for DIPE and from [14] for methylcyclohexane. The calculated activity coefficients reported in Tables 2–4 are estimated to be accurate to within ±3%. The results reported in those tables indicate that the systems exhibit small positive deviations from ideal behavior and that no azeotrope is present. The VLE data reported in Tables 2 and 3 for the binary subsystems 3-methylpentane (1)+methylcyclohexane (3) and DIPE (2) + methylcyclohexane (3) were found to be thermodynamically consistent
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Table 2 Experimental vapor–liquid equilibrium data and activity coefficients for 3-methylpentane (1) + methylcyclohexane (3) at 101.3 kPa T (K)
x1
y1
γ1
336.30 336.75 337.55 338.85 340.05 341.25 342.65 343.95 345.55 346.95 348.65 350.25 351.75 353.55 356.15 358.15 359.95 361.95 364.85 367.75 370.35 372.35 374.00
1.000 0.978 0.945 0.890 0.838 0.789 0.738 0.694 0.640 0.593 0.543 0.494 0.448 0.400 0.337 0.293 0.251 0.208 0.151 0.099 0.056 0.025 0.000
1.000 0.993 0.982 0.963 0.944 0.924 0.901 0.880 0.853 0.826 0.795 0.762 0.727 0.687 0.624 0.570 0.511 0.448 0.357 0.254 0.154 0.071 0.000
1.000 1.000 0.998 0.998 1.001 1.002 1.002 1.000 1.003 1.005 1.004 1.010 1.017 1.023 1.026 1.016 1.015 1.017 1.030 1.034 1.039 1.041
γ3 1.029 1.040 1.023 1.015 1.019 1.010 1.002 0.987 0.986 0.978 0.975 0.974 0.970 0.969 0.978 0.992 0.996 0.992 0.995 0.999 1.002 1.000
by the point-to-point method of Van Ness and Abbott [15], as modified by Fredenslund et al. [16]. The consistency criterium (y(MAD) ≤ 10−2 ) was met using a one parameter Legendre polynomial, which reduces the functionality of the excess Gibbs energy GE to the following symmetric relation: GE = Ax1 x2 RT
(3)
Table 6 presents the value of parameter A and the pertinent consistency statistics. The statistics show that Eq. (3) gives a good-fit of the data. The VLE data reported in Table 4 for the ternary system 3-methylpentane (1)+DIPE (2)+methylcyclohexane (3) were found to be thermodynamically consistent by the McDermott–Ellis method [17] modified by Wisniak and Tamir [18]. The test requires that D < D max for every experimental point, where the local deviation D is given by D=
N (xia + xib )(ln γia − ln γib ) i=1
(4)
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Table 3 Experimental vapor–liquid equilibrium data and activity coefficients DIPE (2) + methylcyclohexane (3) at 101.3 kPa T (K)
x2
y2
γ2
341.40 341.45 342.05 343.15 344.25 345.25 346.45 347.45 348.65 349.95 351.35 352.75 353.95 355.75 357.45 359.25 361.05 362.75 366.15 368.55 371.15 372.75 374.00
1.000 0.982 0.952 0.901 0.852 0.800 0.749 0.698 0.653 0.602 0.551 0.506 0.458 0.398 0.347 0.300 0.252 0.214 0.137 0.091 0.045 0.019 0.000
1.000 0.993 0.980 0.958 0.937 0.913 0.887 0.861 0.834 0.805 0.771 0.737 0.703 0.653 0.604 0.552 0.495 0.443 0.319 0.226 0.122 0.054 0.000
1.000 1.016 1.016 1.014 1.012 1.018 1.018 1.028 1.027 1.033 1.037 1.036 1.054 1.068 1.079 1.083 1.099 1.107 1.130 1.139 1.141 1.174
γ3 1.114 1.119 1.103 1.081 1.068 1.056 1.049 1.043 1.026 1.020 1.016 1.005 0.999 0.996 0.994 0.992 0.989 0.995 0.999 1.002 1.003 1.000
where N is the number of components. The maximum deviation Dmax is given by Dmax
N 1 1 1 1 P = (xia + xib ) + (xia + xib ) x + + + xia yia xib yib P i=1 i=1 N
N N +2 |ln γib − ln γia |x + (xia + xib )Bj [(Ta + Cj )−2 + (Tb + Cj )−2 ] T i=1
(5)
i=1
The error in the measurements x, P and T were as previously indicated. The first and fourth terms in Eq. (5) are the dominant. For each experimental point reported here, the value of D was always smaller than the value of Dmax . The activity coefficients of the binary systems were correlated with Wilson, NRTL and UNIQUAC equations. The parameters of these models were obtained by minimizing the following objective function (OF) exp N Pi − Picalc exp calc + |y − y | OF = 100 × (6) exp i i P i i=1 and are reported in Table 7, together with the pertinent statistics of VLE interpolation. The parameters of the system 3-methylpentane (1) + DIPE (2) have been recalculated from the data reported in
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Table 4 Experimental vapor–liquid equilibrium data and activity coefficients for 3-methylpentane (1) + DIPE (2) + methylcyclohexane (3) at 101.3 kPa T (K)
x1
x2
y1
y2
γ1
336.30 341.40 374.00 337.65 338.75 339.15 339.65 340.45 340.45 340.65 340.75 341.25 341.65 342.15 342.35 342.45 342.55 342.65 342.75 344.25 344.35 344.65 344.75 344.75 345.35 346.55 347.25 347.65 347.65 347.95 348.55 348.55 350.55 350.65 350.85 351.55 353.45 354.25 355.45 355.95 356.85 358.25 362.15 362.85 367.55
1.000 0.000 0.000 0.904 0.796 0.694 0.355 0.399 0.243 0.526 0.448 0.699 0.054 0.586 0.102 0.704 0.502 0.401 0.246 0.592 0.097 0.246 0.498 0.401 0.304 0.099 0.492 0.400 0.149 0.299 0.500 0.204 0.393 0.305 0.057 0.190 0.067 0.291 0.307 0.097 0.151 0.197 0.048 0.104 0.058
0.000 1.000 0.000 0.045 0.105 0.204 0.599 0.502 0.704 0.336 0.432 0.105 0.899 0.203 0.804 0.047 0.278 0.400 0.591 0.106 0.706 0.500 0.192 0.306 0.399 0.610 0.105 0.194 0.498 0.306 0.047 0.394 0.101 0.197 0.494 0.305 0.389 0.102 0.050 0.278 0.192 0.100 0.174 0.097 0.048
1.000 0.000 0.000 0.940 0.862 0.764 0.410 0.467 0.292 0.610 0.523 0.818 0.069 0.704 0.131 0.856 0.615 0.496 0.311 0.758 0.132 0.328 0.651 0.527 0.409 0.141 0.692 0.573 0.217 0.432 0.735 0.304 0.613 0.480 0.092 0.307 0.117 0.509 0.557 0.179 0.284 0.388 0.106 0.232 0.148
0.000 1.000 0.000 0.044 0.105 0.202 0.574 0.498 0.689 0.341 0.434 0.113 0.912 0.219 0.832 0.053 0.303 0.429 0.626 0.125 0.787 0.569 0.227 0.356 0.468 0.731 0.137 0.252 0.625 0.393 0.065 0.513 0.147 0.282 0.685 0.441 0.595 0.166 0.085 0.462 0.333 0.184 0.357 0.205 0.117
1.000
γ2
γ3
1.000 0.996 1.003 1.006 1.039 1.027 1.056 1.012 1.014 1.002 1.086 1.001 1.065 1.003 1.008 1.014 1.033 1.000 1.059 1.026 1.007 1.011 1.018 1.039 1.006 1.011 1.031 1.012 1.010 1.023 1.013 1.018 1.036 1.018 1.037 1.020 1.025 1.022 1.023 1.029 1.040 1.029 1.040
1.092 1.082 1.062 1.017 1.024 1.010 1.040 1.026 1.077 1.007 1.053 1.004 1.100 1.047 1.029 1.014 1.075 1.013 1.024 1.060 1.043 1.033 1.017 1.080 1.065 1.029 1.043 1.107 1.039 1.089 1.071 1.028 1.052 1.050 1.093 1.113 1.057 1.075 1.100 1.092 1.098 1.112
1.000 1.016 1.027 1.015 1.005 1.019 1.018 1.021 1.028 0.989 1.101 0.991 1.068 0.981 1.007 1.011 1.037 0.983 1.042 1.021 0.979 0.997 1.008 1.030 0.970 0.976 1.008 0.987 0.967 0.996 0.970 0.973 1.011 0.991 0.988 0.973 0.970 0.990 0.975 0.973 0.979 0.980 0.993
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Fig. 1. Boiling temperature diagram for the system 3-methylpentane (1) + methylcyclohexane (3) at 101.3 kPa. Experimental data (䊉). Smoothed using Wilson model (—).
Table 5 Antoine coefficients, Eq. (2) Compound
Ai
Bi
Ci
3-Methylpentane [13] DIPE [8] Methylcyclohexane [14]
14.3708 14.3267 13.6438
2999.76 2895.75 2891.01
28.69 43.15 53.81
Table 6 Consistency test for the binary subsystems 3-methylpentane (1) + methylcyclohexane (3) and DIPE (2) + methylcyclohexane (3) System
100 × y(MAD) a
PMAD b (kPa)
Ac
(1) + (3) (2) + (3)
0.42 0.33
0.18 0.31
0.009 0.103
a
Mean absolute deviation in vapor phase composition. Mean absolute deviation in pressure. c Parameter in Eq. (3). b
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Fig. 2. Boiling temperature diagram for the system DIPE (2) + methylcyclohexane (3) at 101.3 kPa. Experimental data (䊉). Smoothed using Wilson model (—).
Fig. 3. Diagram of VLE for the ternary system 3-methylpentane (1) + DIPE (2) + methylcyclohexane (3) at 101.3 kPa: (䊏) liquid phase mole fractions; (䉱) vapor phase mole fractions.
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Fig. 4. Isothermals (K) for the ternary system 3-methylpentane (1) + DIPE (2) + methylcyclohexane (3) at 101.3 kPa, calculated with Wilson model with the binary interaction parameters shown in Table 7.
[2]. Inspection of the results given in Table 7 shows that all models are adequate to predict the binary data. Likewise, the VLE data of the ternary system were predicted using the binary model parameters of the Table 7. The result of the pertinent statistics for the prediction of the ternary data appears in this table. From these results, it can be concluded again that the binary data allow a good prediction of the ternary system. The three models yield similar deviations, but the best fit is obtained with the Wilson model. Fig. 4 show the boiling isotherms for the ternary system calculated by this model.
4. Conclusions VLE data are reported for ternary system and two binary subsystems containing 3-methylpentane, DIPE and methylcyclohexane. From the results, we see that DIPE forms only slightly nonideal mixture with methylcyclohexane and can be successfully described using the Wilson, the NRTL, and the UNIQUAC model. This fact is in agreement with the previous results obtained for the mixtures formed from branched ethers and hydrocarbons [1]. The ternary system does not present azeotrope and can be predicted from binary data with Wilson, NRTL and UNIQUAC equations. List of symbols A parameter in Eq. (3) Ai Antoine’s equation parameter, Eq. (2) Bi Antoine’s equation parameter, Eq. (2)
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Ci D Dmax GE P P0 R T x, y
967
Antoine’s equation parameter, Eq. (2) parameter in Eq. (4) parameter in Eq. (5) excess Gibbs energy (J mol−1 ) total vapor pressure of mixture (kPa) pure component vapor pressure (kPa) universal gas constant (J mol−1 K−1 ) absolute temperature (K) compositions of the liquid and vapor phases
Greek letter γ activity coefficient Superscripts E excess property L pertaining to the liquid phase Subscripts i component i j component j Acknowledgements This work was financed by MEC, Spain (Project no. PB96-07 88). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
S. Loras, Ph.D. Thesis, University of Valencia, Spain, 1999. S. Loras, A. Aucejo, R. Muñoz, J. Wisniak, J. Chem. Eng. Data 44 (1999) 583–587. M. Awwad, R.A. Pethrick, J. Mol. Liq. 25 (1983) 115–127. T.E. Daubert, R.P. Danner (Eds.), Physical and Thermodynamic Properties of Pure Chemicals. Data Compilation, Taylor and Francis, Washington, DC, 1995. C.B. Willingham, W.J. Taylor, J.M. Pignocco, F.D. Rossini, J. Res. Natl. Bur. Stand. (U.S.) 35 (1945) 219–244. K. Nakanishi, H. Shirai, Bull. Chem. Soc. Jpn. 43 (1970) 1634–1642. K.A. Kobe, A.E. Ravica, S.P. Vohra, J. Chem. Eng. Data 1 (1956) 50–56. R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The Properties of Gases and Liquids, 3rd Edition, McGraw-Hill, New York, 1977. TRC Thermodynamic Tables Hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996a. S.M. Walas, Phase Equilibria in Chemical Engineering, Butterworth, London, 1985. H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions, McGraw-Hill, New York, 1982. R. Reich, M. Cartes, H. Segura, J. Wisniak, Phys. Chem. Liq. 38 (2000) 218–232. A. Aucejo, S. Loras, R. Muñoz, Fluid Phase Equilib. 156 (1999) 185–195. V. Mart´ınez-Soria, M.P. Peña, J.B. Montón, J. Chem. Eng. Data 44 (1999) 148–151. H.C. Van Ness, S.M. Byer, R.E. Gibbs, AIChE J. 19 (1973) 238–244.
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[16] A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC. A Group Contribution Method, Elsevier, Amsterdam, 1977, pp. 68–74. [17] C. McDermott, S.R.M. Ellis, Chem. Eng. Sci. 20 (1965) 293–296. [18] J. Wisniak, A. Tamir, J. Chem. Eng. Data 22 (1977) 253–260. [19] H.G. Rackett, J. Chem. Eng. Data 15 (1970) 514–517. [20] J. Gmehling, U. Onken (Eds.), Vapor–Liquid Equilibrium Data Collection, Chemistry Data Series, DECHEMA, Frankfurt, Main, 1990.