(Vapour + liquid) equilibria for binary and ternary mixtures of 2-propanol, tetrahydropyran, and 2,2,4-trimethylpentane at P = 101.3 kPa

J. Chem. Thermodynamics 47 (2012) 260–266

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(Vapour + liquid) equilibria for binary and ternary mixtures of 2-propanol, tetrahydropyran, and 2,2,4-trimethylpentane at P = 101.3 kPa Dun-Yi Lin, Chein-Hsiun Tu ⇑ Department of Applied Chemistry, Providence University, Shalu 43301, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 5 September 2011 Received in revised form 26 October 2011 Accepted 28 October 2011 Available online 3 November 2011 Keywords: Experiments Isobaric VLE 2-Propanol Tetrahydropyran 2,2,4-Trimethylpentane

a b s t r a c t (Vapour + liquid) equilibrium (VLE) at P = 101.3 kPa have been determined for a ternary system (2-propanol + tetrahydropyran + 2,2,4-trimethylpentane) and its constituent binary systems (2-propanol + tetrahydropyran, 2-propanol + 2,2,4-trimethylpentane), and (tetrahydropyran + 2,2,4-trimethylpentane). Analysis of VLE data reveals that two binary systems (2-propanol + tetrahydropyran) and (2-propanol + 2,2,4-trimethylpentane) have a minimum boiling azeotrope. No azeotrope was found for the ternary system. The activity coefficients of liquid mixtures were obtained from the modified Raoult’s law and were used to calculate the reduced excess molar Gibbs free energy (gE/RT). Thermodynamic consistency tests were performed for all VLE data using the Van Ness direct test for the binary systems and the test of McDermott–Ellis as modified by Wisniak and Tamir for the ternary system. The VLE data of the binary mixtures were correlated using the three-suffix Margules, Wilson, NRTL, and UNIQUAC activity-coefficient models. The models with their best-fitted interaction parameters of the binary systems were used to predict the ternary (vapour + liquid) equilibrium. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Certain oxygenated compounds are usually added to gasoline in order to improve the octane number and reduce pollution. This work has been carried out as part of the project to study the thermophysical behaviour of hydrocarbon liquid mixtures including oxygenated compounds. The present paper is concerned with an experimental determination of (vapour + liquid) equilibrium (VLE) for the system formed by the oxygenated compounds of the type (cyclic ether or aliphatic alcohol) with a hydrocarbon liquid. Such data of oxygenated mixtures are important for predicting the vapour-phase composition that would be in equilibrium with different hydrocarbon liquids. The knowledge is useful in the reformulation of gasoline for the anti-knocking and environmentally friendly purposes. For this reason, we measured VLE data for a ternary system (2propanol + tetrahydropyran + 2,2,4-trimethylpentane) and three binary systems (2-propanol + tetrahydropyran), (2-propanol + 2,2,4-trimethylpentane), and (tetrahydropyran + 2,2,4-trimethylpentane) at P = 101.3 kPa. The oxygenated compounds, such as tetrahydropyran and 2-propanol, were chosen for the present study because they are two potential candidates as blending agents for the reformulated gasoline. The third added compound, 2,2,4trimethylpentane, represents the hydrocarbons in the gasoline. In ⇑ Corresponding author. Tel.: +886 4 26328001x15214; fax: +886 4 26327554. E-mail address: [email protected] (C.-H. Tu). 0021-9614/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2011.10.025

the past, isobaric VLE data were measured at six pressures from P = (40.00 to 98.66) kPa for (tetrahydropyran + 2-propanol) [1]. Experimental VLE data were reported at P = 101.3 kPa for (2-propanol + 2,2,4-trimethylpentane) [2,3]. However, we are not aware of any other data in the literature for the systems presented in this study.

2. Experimental 2.1. Materials The chemicals used were of analytical grade and were used without further purification. The sources and mass fraction purities of the chemicals employed are as follows: 2-propanol (Merck, >0.995); tetrahydropyran (Acros, >0.99); and 2,2,4-trimethylpentane (Merck, >0.99). The purity of the chemicals was checked by gas chromatography (GC) analysis, and no impurity peak was detected. The purity levels of these pure compounds are listed in table 1. The purity of each component was further ascertained by comparing its boiling temperature, density, and refractive index with the corresponding literature values [3–11] as shown in table 1. The density q was measured at T = (298.15 ± 0.01) K using a DMA-5000 vibrating-tube densimeter (Anton-Paar; Graz, Austria) with an accuracy of ±0.01 kg  m3. The refractive index nD was measured at (298.15 ± 0.05) K using an automatic Anton Paar RXA-156 refractometer with an accuracy of ±0.00002.

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TABLE 1 Provenance, purity and comparison of the measured boiling temperature (T) at P = 101.3 kPa, density (q), and refractive index (nD) at T = 298.15 K with literature values for pure components. Compounds

Mass fraction purity

q/(kg  m3)

T/K

nD

Expt.

Lit.

Expt.

Lit.

Expt.

Lit.

2-Propanol

>0.995

355.39

355.42 [3] 355.392 [4]

781.04

781.02 [4] 781.26 [5]

1.37518

1.3751 [4] 1.3752 [6]

Tetrahydropyran

>0.99

361.09

361.00 [4] 361.17 [9]

878.84

878.82 [7] 878.85 [10]

1.41864

1.41865 [8]

2,2,4-Trimethylpentane

>0.99

372.37

372.40 [3] 372.388 [4]

687.75

687.81 [4] 687.67 [11]

1.38904

1.38898 [4] 1.3890 [11]

Standard uncertainties u ate u(P) = 0.1 kPa, u(T) = 0.05 K, u(q) = 0.01 kg  m3, and u(nD) = 0.00002.

2.2. Apparatus and procedure The VLE measurements were carried out by circulation for both vapour and liquid in an all-glass equilibrium still (NGW, Wertheim, Germany) of the Hunsmann type [12] connected to a manostat as used by Fowler and Hunt [13]. The boiling temperature was measured with a precision thermometer (Hart Scientific, Model 1560/ 2560) with a platinum RTD probe to within ±0.01 K, the uncertainty of the measurement being estimated at ±0.05 K. Constant pressure was maintained by the manostat within ±0.1 kPa. The equilibrium pressures were determined comparatively via the boiling temperature of pure water, measured in a S´wie˛tosławski type ebulliometer [14] connected to the system. The equilibrium still was insulated by an oil jacket and its temperature was maintained at a temperature of approximately 6 K above the boiling temperature of the mixture in the boiling chamber to ensure that no phase change occurred. Equilibrium compositions of sampled liquid and condensed vapour phases were analysed with a Perkin–Elmer Autosystem gas chromatograph (GC). A flame ionisation detector (FID) was used along with a capillary column packed (60 m long, 0.25 mm i.d., 0.5 lm film) with Petrocol DH (SUPELCO, PA/USA). High purity (mass fraction) nitrogen (0.99995) was used as the carrier gas with a flow rate of 5 cm3  min1. The injector and FID were maintained at T = 473 K. The column of the GC was kept between 348 K and 388 K using a temperature program (initial temperature 348 K, temperature ramp 8 K  min1 to 388 K; temperature maintained at 388 K for another 4 min, giving a total run time of 9.0 min). The GC response peaks were integrated by using Perkin–Elmer Turbochrom software. Calibration analyses using gravimetrically prepared standard solutions were carried out to convert the peak area ratios to mole fractions of the sample. Three or four analyses were performed for each sample in order to obtain a mean mass fraction value with repeatability better than 0.1%. To know the possible errors involved in using these calibration curves, several ternary mixtures of well-known concentrations were examined. Based on these analyses, we estimated the uncertainty of the equilibrium concentration in mole fraction to be within ±0.003. 3. Results and discussion The VLE data for three binary systems (2-propanol + tetrahydropyran), (2-propanol + 2,2,4-trimethylpentane), and (tetrahydropyran + 2,2,4-trimethylpentane) at the pressure of 101.3 kPa are presented in tables 2 to 4, respectively. The activity coefficients of pure liquid i (ci) were calculated from the equality of component fugacity in both liquid and vapour phase under the assumptions of an ideal vapour-phase and an unity in the Poynting factor, i.e.

ci ¼ fyi ðP=PaÞg=fxi ðP i =PaÞg;

ð1Þ

TABLE 2 VLE data for the binary system of {2-propanol (1) + tetrahydropyran (2)} at 101.3 kPa. T/K

x1

y1

c1

361.09 358.71 357.30 356.49 355.94 355.50 355.25 355.04 354.89 354.80 354.78 354.79 354.80 354.86 354.91 354.98 355.05 355.11 355.17 355.30 355.39

0.000 0.082 0.162 0.235 0.301 0.373 0.428 0.487 0.549 0.613 0.656 0.709 0.747 0.792 0.827 0.861 0.891 0.916 0.946 0.977 1.000

0.000 0.135 0.234 0.306 0.367 0.425 0.471 0.518 0.569 0.622 0.658 0.704 0.739 0.782 0.815 0.850 0.883 0.910 0.942 0.976 1.000

1.442 1.338 1.246 1.193 1.134 1.107 1.079 1.058 1.039 1.028 1.017 1.013 1.009 1.005 1.004 1.005 1.005 1.005 1.003 1.000

c2

gE/RT

1.000 1.012 1.025 1.043 1.059 1.087 1.105 1.130 1.155 1.183 1.205 1.233 1.250 1.268 1.291 1.300 1.290 1.286 1.286 1.245

0.000 0.041 0.068 0.084 0.093 0.099 0.100 0.100 0.096 0.089 0.082 0.073 0.066 0.056 0.048 0.040 0.032 0.025 0.018 0.008 0.000

Standard uncertainties u ate u(P) = 0.1 kPa, u(T) = 0.05 K, and u(x1) = u(y1) = 0.003.

TABLE 3 VLE data for the binary system of {2-propanol (1) + 2,2,4-trimethylpentane (3)} at 101.3 kPa. T/K

x1

y1

c1

372.37 361.23 358.96 356.86 354.77 353.35 351.80 350.57 350.23 349.99 349.96 349.93 349.65 349.69 349.85 349.95 350.17 350.39 351.74 353.17 355.39

0.000 0.053 0.073 0.098 0.138 0.175 0.246 0.366 0.432 0.521 0.533 0.549 0.608 0.640 0.693 0.735 0.787 0.805 0.911 0.953 1.000

0.000 0.310 0.360 0.416 0.468 0.499 0.549 0.581 0.597 0.609 0.613 0.617 0.627 0.634 0.648 0.668 0.692 0.715 0.793 0.875 1.000

4.640 4.276 4.001 3.478 3.098 2.584 1.935 1.708 1.459 1.438 1.407 1.306 1.252 1.174 1.137 1.090 1.091 1.011 1.005 1.000

c3

gE/RT

1.000 1.009 1.025 1.026 1.045 1.075 1.113 1.280 1.390 1.611 1.638 1.680 1.899 2.027 2.274 2.476 2.838 2.848 4.337 4.737

0.000 0.090 0.129 0.159 0.210 0.258 0.315 0.398 0.418 0.425 0.424 0.421 0.414 0.398 0.364 0.334 0.290 0.274 0.140 0.078 0.000

Standard uncertainties u ate u(P) = 0.1 kPa, u(T) = 0.05 K, and u(x1) = u(y1) = 0.003.

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TABLE 4 VLE data for the binary system of {tetrahydropyran (2) + 2,2,4-trimethylpentane (3)} at 101.3 kPa. T/K

x2

y2

c2

372.37 371.17 370.70 370.27 369.62 368.68 368.31 367.40 366.82 366.41 366.02 365.20 364.78 364.33 363.75 363.47 362.91 362.42 362.02 361.45 361.09

0.000 0.078 0.112 0.144 0.192 0.268 0.299 0.376 0.427 0.463 0.499 0.576 0.617 0.662 0.720 0.748 0.805 0.855 0.897 0.951 1.000

0.000 0.110 0.151 0.188 0.247 0.333 0.365 0.447 0.498 0.535 0.569 0.652 0.690 0.730 0.777 0.800 0.847 0.886 0.916 0.962 1.000

1.051 1.017 1.002 1.002 0.996 0.989 0.986 0.986 0.988 0.986 1.001 1.002 1.002 0.996 0.996 0.996 0.995 0.992 1.000 1.000

c3

gE/RT

1.000 0.998 1.002 1.006 1.008 1.012 1.016 1.022 1.027 1.027 1.033 1.010 1.007 1.007 1.024 1.027 1.033 1.050 1.104 1.074

0.000 0.002 0.004 0.005 0.007 0.007 0.008 0.009 0.009 0.009 0.009 0.005 0.004 0.003 0.004 0.004 0.003 0.003 0.003 0.003 0.000

ate measure in the root mean square (RMS) value of d ln(c1/c2). The residual in the logarithms of the activity-coefficient ratio d ln(c1/c2) is calculated between two sets of activity coefficients coming from the experimental data and from the correlation. For this direct test, the values of gE/RT in this study were calculated from experimental activity coefficients and were correlated with the three-suffix Margules equation. With constants from this fit, the RMS values of d ln(c1/c2) were determined. The consistency-index values for (2propanol + tetrahydropyran), (2-propanol + 2,2,4-trimethylpentane), and (tetrahydropyran + 2,2,4-trimethylpentane) systems were found to be 2, 3, and 2, respectively, suggesting that all binary VLE data are acceptable. The new binary VLE data were then correlated with the various activity coefficient models, including three-suffix Margules [19], Wilson [20], NRTL [21], and UNIQUAC [22] through a bubble temperature calculation procedure [23]. Estimation of energy parameters of all the models studied was based on the least square errors between the calculated (calc) and experimental (expt) c values as the following objective function (OF):

OF ¼

n h X

i 2 2 expt ðcexpt  ccalc  ccalc ; 1 Þ þ ðc2 2 Þ 1

ð4Þ

i

i¼1

Standard uncertainties u ate u(P) = 0.1 kPa, u(T) = 0.05 K, and u(x2) = u(y2) = 0.003.

where xi and yi are the liquid and vapour mole fractions at equilibrium for pure component i, P° is the vapour pressure for pure component, and P is the total pressure. Equation (1) is also known as the modified Raoult’s law. The temperature dependence of the vapour pressure for pure component was calculated from:

lnðP =PaÞ ¼ A þ B=ðT=KÞ þ C lnðT=KÞ þ DðT=KÞE ;

ð2Þ

where A, B, C, D, and E are the component specific coefficients for vapour pressure and T is the equilibrium temperature. The values of A, B, C, D, and E for 2-propanol and tetrahydropyran were derived from the literature vapour pressure data [15,16]. Those for 2,2,4trimethylpentane were obtained directly from CHEMCAD Data Bank [17]. The results are listed in table 5. The reduced excess molar Gibbs free energy (gE/RT) was calculated according to the equation:

g E =RT ¼

N X

xi ln ci ;

ð3Þ

i¼1

where N is the number of components. The thermodynamic consistency for the three binary systems was treated using the direct test proposed by Van Ness [18]. In the direct test, a proposed consistency index associated with the test characterises the degree of departure of a data set from consistency. The consistency index starts at 1 for highly consistent data and goes to 10 for data of very poor quality based on an appropri-

where n is the number of data points. The liquid molar volume (vL) of pure component for the Wilson equation was evaluated using the relation: d

v L =ðm3  kmol1 Þ ¼ a1  bf1þ½1ðT=KÞ=c g ;

where a, b, c, and d are the component specific coefficients for liquid molar volume and T is the equilibrium temperature. Our experimental density data were used to derive the values of a, b, c, and d for tetrahydropyran and those for the remaining components were obtained directly from CHEMCAD Data Bank. These values are also shown in table 5. The binary parameters (Aij and Aji) of the activity coefficient models along with the average deviations between calculated and measured values (RMS dT and RMS dy) are shown in table 6. All binary systems yield similar deviations in T and y (less than 0.26 K and 0.007, respectively). It can be concluded that all the four

TABLE 6 VLE data reduction for the three binary systems with the three-suffix Margules, Wilson, NRTL, and UNIQUAC models.

TABLE 5 The parameters of vapour pressure and liquid molar volume for the pure components used in this study. Parameters A B C D E

2-Propanol

Tetrahydropyran

2,2,4-Trimethylpentane

73.032 7215.9 7.1145 4.62  106 2.0

Po/(Pa) 59.2735 5775.14 5.41244 9.29  107 2.0

120.81 7550 16.111 1.71  102 1.0

1.18 0.26475 508.31 0.243

2.85898 0.454476 572.2 0.658587

Models

Aija

Ajia

Margules Wilson NRTL UNIQUAC

2-Propanol (1) + tetrahydropyran (2) 0.498 0.273 797.83 383.92 119.08 230.43 0.241 160.48 271.00

aij

0.5886 0.27373 543.96 0.2846

dyi

0.08 0.15 0.14 0.14

0.002 0.003 0.002 0.002

Margules Wilson NRTL UNIQUAC

2-Propanol (1) + 2,2,4-trimethylpentane (3) 1.708 1.657 0.18 1340.70 259.83 0.17 172.42 182.94 0.313 0.13 98.65 387.21 0.26

0.006 0.007 0.006 0.005

Margules Wilson NRTL UNIQUAC

Tetrahydropyran (2) + 2,2,4-trimethylpentane (3) 0.039 0.041 0.18 245.20 226.15 0.13 160.36 236.20 0.338 0.17 37.00 27.19 0.19

0.004 0.006 0.004 0.007

Pn RMS dyi ¼ a

RMS dT/K

RMS: root mean square deviation, defined as: RMS dT ¼

vL/(m3  kmol1) a b c d

ð5Þ

ðyexpt ycalc Þ2 i;j j¼1 i;j n

Pn

j¼1

ðT expt T calc Þ2 j j n

1=2

;

1=2 .

The binary adjustable parameters for Wilson: Aij = (kij  kii)/R, Aji = (kji  kjj)/R; NRTL: Aij = (gij  gjj)/R, Aji = (gji  gii)/R; UNIQUAC: Aij = (Uij  Ujj)/R, Aji = (Uji  Uii)/R.

D.-Y. Lin, C.-H. Tu / J. Chem. Thermodynamics 47 (2012) 260–266

263

362.0

T/K

360.0

358.0

356.0

354.0

0.0

0.2

0.4

0.6

0.8

1.0

x 1 ,y 1 FIGURE 1. Experimental T–x1–y1 diagram of {2-propanol (1) + tetrahydropyran (2)} at P = 101.3 kPa: (d, s) this work at P = 101.3 kPa; () Uno et al. at P = 98.66 kPa [1]; (d, ) liquid phase; and (s) vapour phase. Solid and dashed curves were calculated from our NRTL equation respectively for P = 101.3 kPa and P = 98.66 kPa.

FIGURE 3. Experimental T–x2–y2 diagram of {tetrahydropyran (2) + 2,2,4-trimethylpentane (3)} at P = 101.3 kPa: (d, s) this work; (d) liquid phase; (s) vapour phase; and (–) NRTL equation.

375.0

370.0

T/K

365.0

360.0

355.0

350.0

345.0 0.0

0.2

0.4

0.6

0.8

1.0

x 1 ,y 1 FIGURE 2. Experimental T–x1–y1 diagram of {2-propanol (1) + 2,2,4-trimethylpentane (3)} at P = 101.3 kPa: (d, s) this work; (N, 4) Bures et al. [2]; (j, h) Hiaki et al. [3]; (d, N, j) liquid phase; (s, 4, h) vapour phase; and (–) NRTL equation.

FIGURE 4. Experimental ci and cj vs. xi plots for the binary systems at P = 101.3 kPa: (N, 4) {2-propanol (1) + 2,2,4-trimethylpentane (3)}, i = 1, j = 3; (d, s) {2-propanol (1) + tetrahydropyran (2)}, i = 1, j = 2; (j, h) {tetrahydropyran (2) + 2,2,4-trimethylpentane (3)}, i = 2, j = 3; (d, N, j) ci; (s, 4, h) cj; and (–) NRTL.

equations show a good performance in correlating the activity coefficients. Although all equations fit experimental data quite satisfactorily, the NRTL equation has been arbitrarily chosen in VLE calculations to prepare T–x–y diagrams. The calculated T–x–y curves for the binary systems are compared with the experimental VLE data in figures 1 to 3, showing the correlated results from NRTL model agree satisfactorily with the experimental values over the entire experimental conditions. Figure 1 contains the experimental T–x values reported by Uno et al. [1] for (2-propanol + tetrahydropyran) at 98.66 kPa. As shown in figure 1, the T–x curve was also plotted at this pressure using our NRTL equation for comparison purpose. For the case of (2-propanol + 2,2,4-trimethylpentane) in figure 2, our T–x–y data agree well with Hiaki et al. [3], while a significant difference between our data and those from Bures et al. [2] was found. The VLE results for (tet-

rahydropyran + 2,2,4-trimethylpentane) are shown in figure 3. These diagrams are indicative that two binary systems (2-propanol + tetrahydropyran) and (2-propanol + 2,2,4-trimethylpentane) show azeotropic behaviour. The azeotropic compositions were obtained by determining the xi values that make the function ((xi  yi) = f(xi)) zero. The azeotropic temperature was computed from the experimental result around the azeotropic point, using the xi value previously determined. The azeotropic points are Taz = 354.78 K and xaz 1 = 0.668 for {2-propanol (1) + tetrahydropyran (2)} and Taz = 349.66 K (349.58 K) and xaz 1 = 0.632 (0.635) for {2-propanol (1) + 2,2,4-trimethylpentane (3)}. The values shown in the parentheses are literature data [3]. The experimental activity coefficients (c) and those calculated from the NRTL model for these binary systems are plotted as a function of the liquid-phase mole fraction in figure 4. The variation

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D.-Y. Lin, C.-H. Tu / J. Chem. Thermodynamics 47 (2012) 260–266 0.50

TABLE 7 VLE Data for the ternary system of {2-propanol (1) + tetrahydropyran (2) + 2,2,4trimethylpentane (3)} at 101.3 kPa.

0.40

E

g /RT

0.30

0.20

0.10

0.00 0.0

0.2

0.4

0.6

0.8

1.0

xi FIGURE 5. Experimental gE/RT vs. xi diagram for the binary systems at P = 101.3 kPa: (4) {2-propanol (1) + 2,2,4-trimethylpentane (3)}, xi = x1; (s) {2propanol (1) + tetrahydropyran (2)}, xi = x1; (h) {tetrahydropyran (2) + 2,2,4-trimethylpentane (3)}, xi = x2; and (–) NRTL equation.

of gE/RT with liquid-phase composition also for binary systems is shown in figure 5. It can be seen that all these systems exhibit a positive deviation from ideal behaviour but larger in the case of mixtures with 2-propanol. The gE/RT values of the (tetrahydropyran + 2,2,4-trimethylpentane) system are close to zero, indicating that ideal behaviour is essentially formed on the system. The gE/RT values increases in the sequence as: 0 < (tetrahydropyran + 2,2,4trimethylpentane) < (2-propanol + tetrahydropyran) < (2-propanol + 2,2,4-trimethylpentane). The values of gE/RT (x = 0.5) vary from 0.01 through 0.09 to 0.42 approximately. The VLE data for the ternary system of (2-propanol + tetrahydropyran + 2,2,4-trimethylpentane) at P = 101.3 kPa are reported in table 7. Similarly, equation (1) was applied to calculate the activity coefficients for each component and equation (3) was utilised to obtain the gE/RT values. Figure 6 shows the experimental tie-lines between the saturated vapour and liquid phases, indicating the absence of ternary azeotrope. The thermodynamic consistency of the ternary system was tested using the McDermott–Ellis method [24] as modified by Wisniak and Tamir [25]. According to this method, two adjacent data points a and b are considered to be thermodynamically consistent if D < Dmax where D is a local deviation and Dmax is a maximum deviation, both related to the equilibrium data a and b. The values of calculated Dmax  D in this study were greater than zero with a mean value of 0.103, indicating the thermodynamic consistency. Table 8 presented the average deviations of the bubble points and vapour compositions for the ternary system using the three-suffix Margules, the Wilson, the NRTL, and the UNIQUAC models with the pre-determined binary parameters in table 6. The Wilson, the NRTL, and the UNIQUAC models predict equally well while the Margules model yields somewhat higher deviations. The experimental T–x data were also used to calculate the deviations in boiling temperature, DT, according to the following equation:

DT=K ¼ T=K 

N X

xi ðT i =KÞ;

ð6Þ

i¼1

where xi and T i are the liquid-phase mole fraction and boiling temperature of pure component i, respectively. N is the number of components and T is the boiling temperature of the mixture. The

T/K

x1

x2

y1

y2

c1

c2

c3

gE/RT

350.93 351.03 351.26 351.67 352.10 352.20 352.25 352.47 353.07 353.10 353.22 353.27 353.28 353.52 354.10 354.13 354.29 354.33 354.44 354.83 354.88 354.99 355.03 355.45 355.96 355.97 356.33 356.37 356.38 356.56 356.64 357.32 357.41 357.52 357.65 358.86 358.87 359.15 359.56 359.78 359.84 359.88 360.00 360.29 360.70 360.95 361.75 362.67 363.08 364.02 364.19

0.613 0.487 0.723 0.276 0.506 0.818 0.621 0.369 0.720 0.493 0.289 0.903 0.381 0.618 0.391 0.503 0.804 0.281 0.700 0.293 0.600 0.187 0.386 0.513 0.290 0.169 0.286 0.393 0.295 0.187 0.160 0.180 0.186 0.197 0.207 0.102 0.096 0.099 0.087 0.091 0.092 0.042 0.093 0.044 0.044 0.046 0.048 0.052 0.042 0.039 0.035

0.053 0.048 0.055 0.046 0.154 0.056 0.157 0.144 0.156 0.251 0.148 0.054 0.244 0.252 0.357 0.357 0.153 0.250 0.251 0.340 0.349 0.164 0.463 0.435 0.452 0.150 0.559 0.557 0.656 0.347 0.250 0.456 0.541 0.636 0.743 0.848 0.745 0.644 0.352 0.443 0.276 0.898 0.548 0.784 0.696 0.619 0.530 0.113 0.220 0.194 0.047

0.634 0.601 0.680 0.541 0.604 0.747 0.652 0.556 0.712 0.592 0.520 0.852 0.542 0.658 0.524 0.585 0.786 0.488 0.715 0.471 0.644 0.449 0.496 0.577 0.439 0.437 0.405 0.475 0.380 0.388 0.392 0.348 0.329 0.311 0.285 0.156 0.175 0.203 0.255 0.237 0.287 0.074 0.216 0.094 0.105 0.119 0.138 0.250 0.186 0.180 0.216

0.030 0.025 0.037 0.025 0.096 0.046 0.108 0.086 0.125 0.175 0.091 0.057 0.162 0.199 0.266 0.283 0.147 0.171 0.225 0.250 0.303 0.113 0.376 0.374 0.360 0.105 0.473 0.484 0.583 0.273 0.192 0.382 0.465 0.563 0.678 0.807 0.706 0.606 0.323 0.412 0.245 0.882 0.514 0.778 0.698 0.624 0.535 0.108 0.225 0.201 0.049

1.240 1.473 1.112 2.283 1.363 1.040 1.193 1.694 1.086 1.318 1.966 1.028 1.549 1.148 1.411 1.223 1.023 1.816 1.061 1.644 1.095 2.436 1.302 1.122 1.476 2.523 1.360 1.160 1.236 1.978 2.326 1.787 1.629 1.447 1.259 1.334 1.596 1.761 2.488 2.194 2.620 1.464 1.928 1.747 1.936 2.079 2.215 3.620 3.246 3.334 4.318

0.793 0.720 0.910 0.731 0.818 1.076 0.906 0.772 1.025 0.892 0.780 1.340 0.844 0.997 0.923 0.981 1.180 0.839 1.097 0.888 1.049 0.831 0.978 1.021 0.930 0.819 0.978 1.002 1.024 0.903 0.879 0.937 0.961 0.985 1.011 1.017 1.013 0.996 0.962 0.965 0.923 1.018 0.969 1.015 1.014 1.011 0.990 0.914 0.965 0.950 0.933

1.923 1.535 2.423 1.195 1.633 3.019 1.979 1.344 2.343 1.622 1.229 3.763 1.401 1.934 1.441 1.631 2.660 1.247 2.109 1.285 1.762 1.135 1.419 1.549 1.275 1.096 1.273 1.338 1.249 1.163 1.125 1.162 1.173 1.178 1.159 1.091 1.107 1.105 1.094 1.090 1.068 1.062 1.082 1.066 1.068 1.071 1.056 1.019 1.046 1.026 1.017

0.338 0.372 0.267 0.334 0.292 0.175 0.246 0.301 0.170 0.231 0.274 0.098 0.252 0.170 0.198 0.163 0.086 0.227 0.101 0.197 0.100 0.218 0.145 0.091 0.143 0.189 0.113 0.074 0.089 0.163 0.172 0.129 0.113 0.090 0.063 0.048 0.070 0.079 0.116 0.096 0.108 0.036 0.072 0.047 0.056 0.064 0.056 0.072 0.075 0.056 0.063

Standard uncertainties u ate u(P) = 0.1 kPa, u(T) = 0.05 K, u(x1) = u(y1) = 0.003, and u(x2) = u(y2) = 0.003.

gE/RT and DT for binary mixtures were represented mathematically by the following type of the Redlich–Kister equation [26] for correlating the data:

DQ ij ¼ xi xj

m X

ak ðxi  xj Þk ;

ð7Þ

k¼0

where DQij refers to gE/RT or DT for each i + j system. The variables xi and xj are the liquid-phase mole fractions of pure component i and j, respectively. The values of the binary coefficients ak for each binary system were determined by a nonlinear regression analysis based on the least-squares method and are summarised along with the standard deviations between the experimental and calculated values of the respective functions in table 9. The standard deviation (r) is defined by:

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tetrahydropyran

tetrahydropyran 0.0 1.0

0.0 1.0

0.2

0.8

0.2

0.02

0.8 0.07

0.4

0.6

0.6

0.12

x2

x3

x2

x3

0.4

0.16

0.6

0.6

0.4

0.4 0.20

0.8

0.24

0.8

0.2

0.2

0.29 0.33

1.0 0.0

0.2

0.4

x1

2,2,4-trimethylpentane

0.6

0.8

0.37

1.0 0.0

0.0 1.0

0.2

0.4

2-propanol

FIGURE 7. Curves of constant reduced Gibbs free energy (g /RT) for the ternary {2propanol (1) + tetrahydropyran (2) + 2,2,4-trimethylpentane (3)} system at P = 101.3 kPa.

tetrahydropyran 0.0 1.0

RMSa dT/K

dy1

dy2

dy3

0.77 0.55 0.52 0.51

0.018 0.006 0.007 0.007

0.017 0.003 0.004 0.004

0.011 0.005 0.005 0.005

0.2

0.8

359.8 358.3

0.4

RMS dT and dyi as defined in table 6.

363.2 357.0

0.6 355.6

0.6

TABLE 9 Binary coefficients ak of the Redlich–Kister equation and ternary coefficients Ck of the Cibulka equation and their standard deviations r for gE/RT and DT.

DQij

a0

a1

a2

a3

a4

2-Propanol (1) + tetrahydropyran (2) 0.108 0.048 0.020 6.020 6.182 4.300

0.2

352.4

gE/RT DT/K

2-Propanol (1) + 2,2,4-trimethylpentane (3) 1.704 0.039 0.099 0.140 55.698 21.822 32.593 57.297 79.148

0.003 0.29

gE/RT DT/K

Tetrahydropyran (2) + 2,2,4-trimethylpentane (3) 0.031 0.041 0.024 0.066 0.055 2.896 1.027 0.442 0.147 0.222

0.001 0.02

0.001 0.03

2-Propanol (1) + tetrahydropyran (2) + 2,2,4-trimethylpentane (3) C0 C1 C2 r 1.430 0.802 0.926 0.012 127.510 266.075 31.763 0.45

" #1=2 n X calc 2 ðDQ expt  D Q Þ =ðn  pÞ ; i i

353.6

0.8

0.394 12.824

r¼

0.4 354.6

r

gE/RT DT/K

DQ123 gE/RT DT/K

x2

x3

a

2-propanol E

TABLE 8 VLE prediction for the ternary system of {2-propanol (1) + tetrahydropyran (2) + 2,2,4-trimethylpentane (3)} from the determined binary parameters in table 6.

Margules Wilson NRTL UNIQUAC

0.0 1.0

0.8

2,2,4-trimethylpentane

FIGURE 6. Tie-lines for the ternary {2-propanol (1) + tetrahydropyran (2) + 2,2,4trimethylpentane (3)} system at P = 101.3 kPa: (d) liquid phase and (s) vapour phase.

Models

0.6

x1

ð8Þ

i¼1

where n is the number of experimental points and p is the number of fitting parameters. The largest standard deviations occurred at (2-propanol + 2,2,4-trimethylpentane) system with 0.003 for gE/RT and 0.29 K for DT. The derived properties, gE/RT and DT/K, for the ternary system of {2-propanol (1) + tetrahydropyran (2) + 2,2,4-trimethylpentane (3)} were correlated using the equation:

1.0 0.0

350.9

0.2

2,2,4-trimethylpentane

0.4

x1

0.6

0.8

1.0

0.0

2-propanol

FIGURE 8. Curves of constant boiling temperature (T/K) for the ternary {2-propanol (1) + tetrahydropyran (2) + 2,2,4-trimethylpentane (3)} system at P = 101.3 kPa.

DQ 123 ¼ DQ 12 þ DQ 13 þ DQ 23 þ x1 x2 x3 D123 ;

ð9Þ

where DQ123 refers to gE/RT or DT for ternary mixture, x3 = 1  x1  x2, and DQij is given by equation (7) with the parameters shown in table 9. The ternary contribution term D123 was correlated using the expression suggested by Cibulka [27]:

D123 ¼ C 0 þ C 1 x1 þ C 2 x2 :

ð10Þ

The ternary parameters C0, C1, and C2 were determined with the optimisation algorithm similar to that for the binary parameters. The parameters C0, C1, and C2 and the corresponding standard deviations are also given in table 9. The standard deviations for the ternary system are 0.012 in gE/RT and 0.45 K in DT. The curves of constant gE/RT and boiling temperature (T) at P = 101.3 kPa for the ternary mixtures were calculated from Eqs.

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(9), (10) and are plotted in figures 7 and 8, respectively. As can be expected from the behaviour of binary mixtures, the ternary system of (2-propanol + tetrahydopyran + 2,2,4-trimethylpentane) shows the positive gE/RT values at all equilibrium compositions (figure 7). The maximum gE/RT value is located at x  0.5 of 2propanol near the (binary 2-propanol + 2,2,4-trimethylpentane). Figure 8 shows the curves of constant boiling temperature for the ternary mixtures with a minimum value close to the (2-propanol + 2,2,4-trimethylpentane) side at x  0.6 of 2-propanol. All this indicates that an increase in the amount of tetrahydropyran will decrease the values of gE/RT but increase the boiling temperatures of the mixtures.

4. Conclusion Isobaric VLE data of binary and ternary mixtures formed by 2propanol, tetrahydropyran, and 2,2,4-trimethylpentane were determined experimentally at P = 101.3 kPa. The ternary system reported here, for which no data have been published, constitutes an example of the oxygenated compound with hydrocarbon mixtures. The values of gE/RT for the three binary systems are all positive over the entire composition range. The minimum boiling azeotropes were found for two binary systems (2-propanol + tetrahydropyran) and (2-propanol + 2,2,4-trimethylpentane). The ternary system (2-propanol + tetrahydropyran + 2,2,4-trimethylpentane) did not show azeotropic behaviour according to our ternary VLE data. The activity coefficients of pure liquids in the mixtures were obtained from the modified Raoult’s law. The binary VLE data were shown to be acceptable using the Van Ness direct test. The ternary VLE data adequately fulfilled the thermodynamic consistency test of McDermott–Ellis as modified by Wisniak and Tamir. Reduction of the binary VLE data using the three-suffix Margules, Wilson, NRTL, and UNIQUAC models showed that all four models gave satisfactory correlations. Using the interaction parameters of the constituent binaries, the Wilson, NRTL, and UNIQUAC models gave a better prediction than the Margules model for the ternary VLE equilibrium. The values of gE/RT and boiling temperature (T) for the ternary mixtures were successfully correlated in terms of liquid-phase composition using the Redlich–Kister equation and the Cibulka equation.

Acknowledgement The authors wish to extend their deep gratitude for the support by the National Science Council of Republic of China under Grant NSC 95-2221-E-126-010-MY3. References [1] S. Uno, H. Matsuda, K. Kurihara, K. Tochigi, Y. Miyano, S. Kato, H. Yasuda, J. Chem. Eng. Data 53 (2008) 2066–2071. [2] E. Bures, C. Cano, A. De Wirth, J. Chem. Eng. Data 4 (1959) 199–200. [3] T. Hiaki, K. Takahashi, T. Tsuji, M. Hongo, K. Kojima, J. Chem. Eng. Data 39 (1994) 602–604. [4] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents, fourth ed., Physical Properties and Methods of Purifications, Wiley-Interscience, New York, 1986. [5] TRC Thermodynamics, Thermodynamic Research Center, Texas A&M University, College Station, TX, 1994. [6] I. Nagata, K. Tamura, K. Miyai, Fluid Phase Equilib. 170 (2000) 37–48. [7] A. Villares, L. Sanz, B. Giner, C. Lafuente, M.C. Lopez, J. Chem. Eng. Data 50 (2005) 1334–1337. [8] P. Brocos, Á. Piñeiro, R. Bravo, A. Amigo, A.H. Roux, G. Roux-Desgranges, J. Chem. Eng. Data 48 (2003) 712–719. [9] S. Rodriguez, C. Lafuente, H. Artigas, F.M. Royo, J.S. Urieta, J. Chem. Thermodyn. 31 (1999) 139–149. [10] P. Brocos, E. Calvo, R. Bravo, M. Pintos, A. Amigo, A.H. Roux, G. RouxDesgranges, J. Chem. Eng. Data 44 (1999) 67–72. ~ a, V. Marti´nez-Soria, J.B. Monto´n, Fluid Phase Equilib. 166 (1999) 53– [11] M.P. Pen 65. [12] W. Hunsmann, Chem.-Ing.-Tech. 39 (1967) 1142–1145. [13] A.R. Fowler, H. Hunt, Ind. Eng. Chem. 33 (1941) 90–96. [14] E.J. Hála, V. Fried, J. Pick, O. Vilím, Vapour–Liquid Equilibrium, second ed., Pergamon Press, New York, 1967. p. 255. [15] D. Ambrose, C.H.S. Sprake, J. Chem. Thermodyn. 2 (1970) 631–645. [16] Y. Miyano, S. Uno, K. Tochigi, S. Kato, H. Yasuda, J. Chem. Eng. Data 52 (2007) 2245–2249. [17] CHEMCAD Software, Version 4.1.6, Chemstations Inc., Houston, 1998. [18] H.C. Van Ness, Pure Appl. Chem. 67 (1995) 859–872. [19] M. Gess, A.R.P. Danner, M. Nagvekar, Thermodynamic Analysis of Vapour– Liquid Equilibria: Recommended Models AND A Standard Data Base, DIPPR, AIChE, 1991, p. 19. [20] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127–130. [21] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [22] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116–128. [23] J.M. Smith, H.C. Van Ness, Introduction to Chemical Engineering Thermodynamics, fourth ed., McGraw-Hill, NY, 1987. [24] C. McDermott, S.R.M. Ellis, Chem. Eng. Sci. 20 (1965) 293–295. [25] J. Wisniak, A. Tamir, J. Chem. Eng. Data 22 (1977) 253–260. [26] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [27] I. Cibulka, Collect. Czech. Chem. Commun. 47 (1982) 1414–1419.

JCT-11-361