Vapor liquid equilibria for the binary system 2,2 dimethylbutane + 1,1 dimethylpropyl methyl ether (TAME) at , , and 338.

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1 Fluid Phase Equilibria 221 (2004) 1 6 Vapor liquid equilibria for the binary system 2,2 dimethylbutane + 1,1 dimethylpropyl methyl ether (TAME) at , , and K Armando del Río a, Baudilio Coto b, Juan A.R. Renuncio a, Concepción Pando a, a Departamento de Química Física I, Universidad Complutense, E Madrid, Spain b ESCET, Universidad Rey Juan Carlos, E Móstoles, Madrid, Spain Received 16 January 2004; accepted 2 April 2004 Available online 7 June 2004 Abstract Vapor liquid equilibrium (VLE) data are reported for the binary mixtures formed by 2,2-dimethylbutane 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 , , and K. Deviations from Raoult s law are positive and very small. These VLE data are analyzed together with excess enthalpy (Hm E ) data previously reported at K using the UNIQUAC model. The modified UNIFAC (Dortmund) model is used to predict VLE data Elsevier B.V. All rights reserved. Keywords: Binary liquid mixtures; Vapor liquid equilibria; Gibbs energy; Branched ether 1. Introduction In recent years, the interest in oxygenated gasoline has resulted in a large number of studies on the thermophysical properties of branched ethers and their binary and ternary mixtures. The purpose of this paper is to report phase equilibria for the binary system formed by 2,2-dimethylbutane and 1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME). 2. Experimental section 2,2-Dimethylbutane was purchased from Sigma, with a purity >99 mol%. TAME (Fluka 97 mol% purity) was refluxed over 0.3 nm molecular sieves for several hours and then fractionated. The middle distillate used in the present work (approximately 50% of the initial amount) had a purity Abbreviations: TAME, 1,1-dimethyl-propyl methyl ether (tert-amyl methyl ether); VLE, vapor liquid equilibrium Corresponding author. Fax: address: pando@quim.ucm.es (C. Pando). 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 [1]. VLE data were measured using a Gibbs-van Ness type static apparatus [2] which was described previously by Coto et al. [1]. Binary liquid solutions of known composition were prepared in a test cell by volumetric injection of degassed liquids using calibrated pistons. The equilibrium cell volume is ca. 100 ml. Values for the radii of the left and right pistons are ± and ± mm, respectively. The liquid inside the piston-injector is kept at a pressure higher than the cell pressure to avoid a vapor phase. The volume injected of each component can be determined from the position of the piston which is registered by a length gauge (ACU-RITE A R/1, 2 m accuracy). Therefore, the accuracy of the injected volume is ± ml. The amount injected (in mol) is calculated using the compressibility of the liquid and its density at atmospheric pressure. The accuracy of the mole fraction is estimated to be ca in the dilute regions and ca in the middle of the concentration range. Cell and piston-injectors were immersed in a water bath in which temperature was controlled within ±0.002 K /$ see front matter 2004 Elsevier B.V. All rights reserved. doi: /j.fluid

2 2 A. del Río et al. / Fluid Phase Equilibria 221 (2004) 1 6 Table 1 Properties of pure components used in this study T(K) V m (cm 3 mol 1 ) κ T 10 9 (Pa 1 ) B (cm 3 mol 1 ) p (kpa) p (kpa) (literature values range) 2,2-Dimethylbutane [3] 2.01 [4] [5,6] [3] 2.01 [4] [5,6] [3] 2.01 [4] [5,6] TAME [7] 1.26 [7] [8 10] [7] 1.80 [7] [9,10] [7] 2.34 [7] [11,12] The temperature was measured with a quartz thermometer, Testo 781, with an accuracy of 0.01 K. The total vapor pressure was measured when phase equilibrium was reached and maintained for at least 15 min using a differential MKS Baratron pressure gauge with a resolution of 0.08% of the reading. Pressure accuracy is estimated to be 0.01 kpa. Table 1 lists values for the molar volumes, isothermal compressibilities and second virial coefficients of pure components used in the data reduction and values for the vapor pressures of 2,2-dimethylbutane and TAME obtained in this study and those found in the literature at the three temperatures studied. The source of molar volumes and isothermal compressibilities is given in Table 1. Second virial coefficients were calculated by means of the Hayden and O Connell method [13]. The vapor pressures measured in this work are in good agreement with literature values and this is considered an indication of the chemicals purity. azeotrope), and the slopes of the pressure versus x 1 diagram are extremely high in the dilute regions. VLE data obtained were shown to be consistent with previous literature data. More details about this comparison ant the data-reduction procedure are found in Ref. [1]. Table 2 lists values for the 2,2-dimethylbutane liquid composition, x 1, and the total pressure, p, at the three temperatures studied, together with the calculated total pressure, p calc, the hydrocarbon vapor composition, y 1,calc, the molar excess Gibbs energy, G E m, for 2,2-dimethylbutane(1) + TAME(2), the logarithm of the activity coefficients γ 1 and γ 2, the coefficients P i for the G E m representation by Eq. (1), and their uncertainties, and the standard deviations between experimental and calculated values of x 1, σ x, and p, σ p. Fig. 1 shows plots of the total pressure against liquid and vapor compositions for the 2,2-dimethylbutane + TAME system at the three temperatures studied. Both 3. Results and discussion VLE measurements for 2,2-dimethylbutane + TAME were carried out at , , and K. Results were analyzed using a modified Barker method and the maximum likelihood principle [14]. The temperature, T, and the amount of substance for components 1 and 2 were considered to be the independent variables in the data reduction. The material balance was included to take into account the amounts of substance present in the vapor phase. The molar excess Gibbs energy, G E m, of the liquid phase was described by the Redlich Kister equation 3 G E m = RTx 1(1 x 1 ) P i (2x 1 1) i (1) i=0 where P i are adjustable parameters, and x 1 is the mole fraction of 2,2-dimethylbutane. The vapor phase is described using the virial equation. In order to test the quality of the experimental data obtained using the experimental technique and the data-reduction procedure described above, VLE data for the ethanol + cyclohexane system were previously measured at K by Coto et al. [1]. This system shows very high positive deviations from ideality (including an Fig. 1. VLE data for the 2,2-dimethylbutane(1) + TAME(2) system: ( ) K; ( ) K; ( ) K; ( ) calculated values using Eq. (1).

3 A. del Río et al. / Fluid Phase Equilibria 221 (2004) Table 2 Vapor liquid equilibrium data and coefficients and standard deviations for G E m representation by Eq. (1) for 2,2-dimethylbutane(1) + TAME(2) at , , and K x 1 p (kpa) p calc (kpa) y 1,calc G E m (J mol 1 ) ln γ 1 ln γ 2 T = K a T = K b T = K c

4 4 A. del Río et al. / Fluid Phase Equilibria 221 (2004) 1 6 Table 2 (Continued ) x 1 p (kpa) p calc (kpa) y 1,calc G E m (J mol 1 ) ln γ 1 ln γ a P 0 = ± 0.002; P 1 = ± 0.005; P 2 = ± 0.007; P 3 = 0.04 ± 0.01; σ x = ; σ p = 56 Pa. b P 0 = ± 0.002; P 1 = ± 0.004; P 2 = ± 0.006; P 3 = 0.01 ± 0.01; σ x = ; σ p = 71 Pa. c P 0 = ± 0.004; P 1 = ± 0.009; P 2 = ± 0.001; P 3 = 0.01 ± 0.03; σ x = ; σ p = 33 Pa. experimental values and those calculated using Eq. (1) are shown. Deviations from Raoult s law are positive and small. Since the mixtures behave almost ideally, the correction for real behavior of the vapor phase is not necessary. Fig. 2 shows plots of G E m values against x 1 for the three temperatures studied. Values for the excess Gibbs energy of the 2,2-dimethylbutane + TAME mixtures are positive and decrease as temperature increases for a given mole fraction. Maximum G E m values range from 142 J mol 1 at K to 97 J mol 1 at K. These maxima appear at approximately the same mole fraction (x 1 0.6) for the three temperatures studied. A similar behavior was reported for hexane + TAME mixtures [15]. Figs. 3 5 show plots of ln γ 1 and ln γ 2 against x 1 at , , and K, respectively. As could be expected for an almost ideal system, values for the activity coefficients are close to one and show a smooth variation with composition. The temperature effect on the activity coefficients is small. The limiting activity coefficients were calculated using the method of Maher and Smith [16]. Values of 1.17, 1.16 and 1.15 were obtained for γ 1 at , , and K, respectively. Values of 1.91, 1.89 and 1.87 were obtained for γ 2 at , , and K, respectively. Fig. 6 shows plots of G E m /RT against temperature in the K range for x 1 = 0.25, 0.50 and 0.75, respectively. G E m /RT decreases linearly with temperature; the temperature effect on G E m is in agreement with the moderately endothermic values of the molar excess enthalpy (Hm E) reported at K for these mixtures: Knezevic-Stevanovic et al. [17] reported a maximum value of J mol 1 occurring at x 1 = Values for Hm E calculated from the slopes of the G E m /RT against T plots at K are more endothermic than the experimental excess enthalpies: a value of 411 J mol 1 is obtained for x 1 = More accurate values for Hm E at this temperature could be obtained if similar plots could be drawn for a temperature range beginning at a temperature lower than K. The UNIQUAC model [18] was used to correlate the VLE data reported in this paper at , , and K and the Hm E data previously obtained at K. Uncertainties in temperature, pressure and composition were considered to be smaller than those of vapor pressures and excess enthalpies. The interaction parameters of the UNIQUAC model, A ji, were considered to vary linearly with temperature according to A ji = A ji,1 + A ji,2 (T ) (2) A least-square procedure was used to minimize deviations between experimental and calculated vapor pressure and enthalpies. The resulting values for the interaction parameters Fig. 2. G E m against x 1 values for the 2,2-dimethylbutane(1) + TAME(2) system: ( ) K; ( ) K; ( ) K; ( ) calculated values using Eq. (1). Fig. 3. Activity coefficients against x 1 values for the 2,2-dimethylbutane(1) + TAME(2) system at K: ( ) lnγ 1 ;( ) lnγ 2.

5 A. del Río et al. / Fluid Phase Equilibria 221 (2004) Table 3 Vapor liquid equilibrium for 2,2-dimethylbutane(1) + TAME(2): correlation using the UNIQUAC model and prediction using the modified UNI- FAC (Dortmund) model a T (K) UNIQUAC Modified UNIFAC (Dortmund) σ p (kpa) σ rel σ p (kpa) σ rel a σ p is the standard deviations between experimental and calculated vapor pressures and σ rel is the percent ratio of σ p and the maximum value of the vapor pressure. Fig. 4. Activity coefficients against x 1 values for the 2,2-dimethylbutane(1) + TAME(2) system at K: ( ) lnγ 1 ;( ) lnγ 2. Fig. 5. Activity coefficients against x 1 values for the 2,2-dimethylbutane(1) + TAME(2) system at K: ( ) lnγ 1 ;( ) lnγ 2. are: A 12,1 = 140.3K, A 12,2 = , A 21,1 = 101.7K, A 21,2 = A value of 1.6 J mol 1 was obtained for the standard deviation between experimental and calculated molar excess enthalpies, σ H. This leads to a value of 0.7 for the percent ratio of σ H and the maximum molar excess enthalpy value. Values for the standard deviation between experimental and calculated vapor pressures, σ p, and the percent ratio of σ p and the maximum value of vapor pressure, σ rel, are listed in Table 3. The correlation is accurate: values for σ p are lower than 0.4 kpa and values of σ rel are lower than 0.5. The modified UNIFAC (Dortmund) [19,20] model was used to predict VLE data for the 2,2-dimethylbutane + TAME mixtures at , , and K. Values for σ p and σ rel are listed in Table 3. These values are slightly higher than those obtained using the UNIQUAC model. We may conclude that the UNIQUAC model provides a simultaneous description of VLE and Hm E data for the 2,2-dimethylbutane + TAME system and that vapor pressures are accurately predicted for this system using the modified UNIFAC (Dortmund) model. List of symbols A ji UNIQUAC model interaction parameters B second virial coefficient G Gibbs energy H enthalpy p vapor pressure P i Redlich Kister equation parameter V volume x mole fraction in the liquid phase y mole fraction in the vapor phase Greek symbols γ activity coefficient κ isothermal compressibility σ standard deviation Superscripts E excess property Fig. 6. G E m /RT against temperature values for the 2,2-dimethylbutane(1) + TAME(2) system: ( ) x 1 = 0.25; ( ) x 1 = 0.50; ( ) x 1 = Subscripts calc calculated i, j components of binary systems

6 6 A. del Río et al. / Fluid Phase Equilibria 221 (2004) 1 6 H excess enthalpy m molar property p vapor pressure rel relative to maximum value x liquid composition of component 1 Acknowledgements This work was funded by the Spanish Ministry of Science and Technology, PPQ C A. del Río acknowledges the Comunidad Autonoma de Madrid for its support through a predoctoral grant. References [1] B. Coto, C. Pando, R.G. Rubio, J.A.R. Renuncio, J. Chem. Soc., Faraday Trans. 91 (1995) [2] R.E. Gibbs, H.C. van Ness, Ind. Eng. Chem. Fundam. 11 (1972) [3] TRC Thermodynamic Tables, Thermodynamic Research Center, Texas A&M University System, College Station, TX. [4] D.-Y. Peng, G.C. Benson, B.C.-Y. Lu, J. Solut. Chem. 28 (1999) [5] J. Gmehling, U. Onken, W. Arlt, Vapor liquid equilibrium data collection, DECHEMA, Chem. Data Ser. I, Part 6b DECHEMA, Frankfurt Main, Germany, [6] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, McGraw-Hill, Singapore, [7] U.P. Govender, T.M. Letcher, J. Chem. Eng. Data 41 (1996) [8] B. Coto, F. Mössner, C. Pando, R.G. Rubio, J.A.R. Renuncio, J. Chem. Soc., Faraday Trans. 92 (1996) [9] I. Cervenkova, T. Boublik, J. Chem. Eng. Data 29 (1984) [10] M. Palczewska-Tulinska, D. Wyrzykowska-Stankiewicz, J. Cholinski, K. Zieborak, Fluid Phase Equilibria. 54 (1990) [11] F. Mössner, B. Coto, C. Pando, R.G. Rubio, J.A.R. Renuncio, J. Chem. Eng. Data 41 (1996) [12] M.A. Krähenbühl, J. Gmehling, J. Chem. Eng. Data 39 (1994) [13] J.G. Hayden, J.P. O Connell, Ind. Eng. Chem. Process Des. Dev. 14 (1975) [14] R.G. Rubio, J.A.R. Renuncio, M. Diaz Peña, Fluid Phase Equilibria. 12 (1983) [15] A. del Río, B. Coto, C. Pando, J.A.R. Renuncio, Ind. Eng. Chem. Res. 41 (2002) [16] P.J. Maher, B.D. Smith, Ind. Eng. Chem. Fundam. 18 (1979) [17] A. Knezevic-Stevanovic, Z.-L. Jin, G.C. Benson, B.C.-Y. Lu, J. Chem. Eng. Data 40 (1995) [18] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) [19] U. Weidlich, J. Gmehling, Ind. Eng. Chem. Res. 26 (1987) [20] J. Gmehling, L. Jiding, M. Schiller, Ind. Eng. Chem. Res. 32 (1993)