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Excess molar enthalpies of the ternary mixtures: methyl tert-butyl ether + 2-methylpentane + (n-decane or n-dodecane) at the temperature 298.15 K
J. Chem. Thermodynamics 36 (2004) 701–706 www.elsevier.com/locate/jct
Excess molar enthalpies of the ternary mixtures: methyl tert-butyl ether + 2-methylpentane + (n-decane or n-dodecane) at the temperature 298.15 K Zhaohui Wang, Benjamin C.-Y. Lu
*
Department of Chemical Engineering, University of Ottawa, Ottawa, Ont., Canada K1N 6N5 Received 26 April 2004; accepted 5 May 2004 Available online 9 June 2004
Abstract Measurements of excess molar enthalpies at the temperature 298.15 K in a flow microcalorimeter are reported for the two ternary mixtures x1 C5 H12 O + x2 (CH3 )2 CHCH2 CH2 CH3 + x3 CH3 (CH2 )m CH3 , where m ¼ 8 and 10. Smooth representations of the results are presented and used to construct constant excess molar enthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the ternary enthalpies can be obtained from the Liebermann and Fried model, using only the physical properties of the components and their binary mixtures. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Excess enthalpy; Ternary mixture; Methyl tert-butyl ether; 2-Methylpentane; n-Decane; n-Dodecane; Liebermann–Fried model
1. Introduction
2. Experimental
Currently, we are studying the thermodynamic properties of (oxygenate + hydrocarbon) mixtures and investigating the applicability of the Liebermann–Fried model to predict the excess enthalpies of ternary mixtures from the properties of the pure components and their binary mixtures. We have reported excess molar enthalpies of ternary mixtures containing methyl tertbutyl ether (MTBE) and hydrocarbons [1,2]. The present paper continues that work by reporting measurements of excess molar enthalpies at T ¼ 298:15 K for the ternary mixtures formed by mixing MTBE with binary mixtures of 2-methylpentane (2MP), and either n-decane (nC10) or n-dodecane (nC12). The binary Liebermann–Fried model parameters obtained from the constituent binaries may also serve the purpose of predicting vapor + liquid equilibria [3].
The OmniSol quality MTBE, with 99.5mol% purity, was obtained from the BDH Inc. The 2MP was Research Grade Reagent from the Phillips Chemical Company. The nC10 and nC12 were obtained from the Aldrich Chemical Company. For the three hydrocarbons, the mole fraction purities, stated by the manufacturers, exceed 0.990. Apart from partial degassing, all of the components were used without further purification. Densities q (T ¼ 298:15 K)/(kg m3 ), measured in an Anton–Paar digital densimeter, were 735.69, 649.78, 726.31 and 745.38 for MTBE, 2MP, nC10 and nC12, respectively. These are comparable with the literature values 735.3 [4], 648.52, 726.35 and 745.18 [5]. Excess molar enthalpies HmE were determined in an LKB flow microcalorimeter (Model 10700-1) at 298.150 K, maintained within 0.003 K. Details of the equipment and the operating procedure have been described previously [6,7]. For the ternary systems, x1 C5 H12 O + x2 (CH 3 ) 2 CHCH 2 CH 2 CH 3 + x3 CH 3 (CH 2 ) m CH 3 , with E m ¼ 8 and 10, the excess molar enthalpy Hm;1þ23 was determined for several pseudo-binary systems in which MTBE was added to a binary mixture of components 2
*
Corresponding author. Tel: +1-613-562-5800-6097; fax: +1-613562-5172. E-mail address: [email protected] (B.C.-Y. Lu). 0021-9614/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2004.05.006
702
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
TABLE 1 Experimental mole fractions x1 and excess molar enthalpies HmE for the binary mixture MTBE(1) + 2MP(2) at 298.15 K x1
HmE
x1
HmE
x1
HmE
x1
HmE
0.0532 0.1063 0.1589 0.2113 0.2633
37.54 89.35 140.48 182.94 218.86
0.3150 0.3658 0.4165 0.4667 0.5174
249.75 271.83 289.29 300.07 303.21
0.5673 0.6165 0.6652 0.7143 0.7628
297.31 291.16 275.87 254.41 226.67
0.8100 0.8548 0.9060 0.9531
193.23 157.51 107.38 57.09
Units: J mol1 .
TABLE 2 Coefficients hk and standard deviations s for the representations of the excess molar enthalpies HmE at 298.15 K by equation (1) h1
Component i
j
MTBE MTBE 2MP MTBE 2MP
2MP nC10 nC10 nC12 nC12
h2
h3
h4
h5
s (J mol1 )
)147.06 )313.32 2.97 )412.37 0.43
1213.98 2000.50 177.32 2279.33 315.03
)145.51 110.94 )5.37 254.78 )11.89
100.36 )2.09 206.70
)87.36 )214.72
2.67a 1.20b 0.05c 1.10b 0.06d
a
This work. Based on data of Wang et al. [1]. c Based on data of Hamam and Benson [8]. d Based on data of Hamam et al. [9]. b
TABLE 3 E at 298.15 K for the addition of methyl tert-butyl ether to a binary mixture of 2-methylpentane and nExperimental excess molar enthalpies Hm;1þ23 E E decane to form x1 C5 H12 O + x2 C6 H14 + x3 C10 H22 and values of Hm;123 calculated from equation (3) using the smooth representation of Hm;23 by equation (2) E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
0.0500 0.1000 0.1499 0.1999 0.2500 0.2999 0.3496
74.07 143.10 205.36 263.16 315.50 359.73 388.13
105.64 173.01 233.61 289.75 340.43 383.00 409.75
0.0500 0.1001 0.1499 0.2001 0.2502 0.3009 0.3501
62.84 122.77 181.14 234.33 279.23 315.48 347.48
104.95 162.66 218.83 269.79 312.47 346.47 376.29
x1
0.0500 0.1000 0.1501 0.2000 0.2499 0.2991 0.3497
45.35 99.40 155.67 202.16 246.06 276.17 302.39
76.46 128.87 183.50 228.36 270.63 299.12 323.69
x1
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
x1
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
E (J mol1 ) ¼ 33.23 x2 =x3 ¼ 0:3332, Hm;23 0.4003 415.42 435.35 0.4497 433.58 451.87 0.4999 444.59 461.21 0.5501 447.70 462.65 0.5998 438.78 452.08 0.6497 424.04 435.68
0.7000 0.7507 0.7996 0.8486 0.9000 0.9499
399.41 362.68 315.62 258.78 184.07 100.21
409.38 370.97 322.28 263.81 187.39 101.88
E x2 =x3 ¼ 0:9998; Hm;23 (J mol1 ) ¼ 44.33 0.3998 367.94 394.55 0.4503 387.71 412.08 0.4998 396.27 418.44 0.5497 397.27 417.23 0.5998 388.65 406.39 0.6500 365.09 380.61
0.7004 0.7500 0.8001 0.8500 0.9014 0.9500
350.71 318.12 274.44 222.82 157.26 83.74
363.99 329.20 283.30 229.47 161.63 85.96
E x2 =x3 ¼ 2:9994; Hm;23 (J mol1 ) ¼ 32.75 0.4000 326.41 346.06 0.4501 337.80 355.81 0.5000 347.11 363.48 0.5498 346.40 361.14 0.5999 340.85 353.95 0.6501 326.58 338.04
0.7004 0.7503 0.8004 0.8497 0.9000 0.9499
303.96 274.28 236.15 190.94 134.70 72.55
313.77 282.46 242.69 195.86 137.97 74.19
E E Ternary term for representation of Hm;1þ23 by equations (3) and (4): Hm;T ðJ mol1 Þ ¼ x1 x2 x3 ð302:47 þ 563:13x1 þ 883:32x2 1024:842x21 407:076x1 x2 1115:156x22 Þ s ¼ 3:48 J mol1 .
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
and 3, having a fixed mole ratio x2 =x3 . For this purpose, binary mixtures with x2 =x3 ¼ 0:3, 1.0 and 3.0 were prepared by weighing. The excess molar enthalpy of the ternary system was obtained from the relation E E E Hm;123 ¼ Hm;1þ23 þ ð1 x1 ÞHm;23 ;
ð1Þ
E is the excess molar enthalpy of the particular where Hm;23 binary mixture of 2MP and either nC10 or nC12. Over most of the mole fraction range of component 1, the E errors of Hm;1þ23 are estimated to be less than 0.5%. Errors in the mole fractions of the final ternary mixtures are estimated to be less than 5 104 .
3. Results and discussion E Excess molar enthalpies Hm;ij ði < jÞ, measured at T ¼ 298:15 K, for four of the constituent binary systems of present interest, have been reported previously: MTBE(1) + nC10(3) [1], MTBE(1) + nC12(3) [1], nC10(3) + 2MP(2) [8] and nC12(3) + 2MP(2) [9]. Excess enthalpies for the MTBE + 2MP binary measured in this study are listed in table 1. Coefficients hk for representation of the results were obtained by the following smoothing function,
E =ðJ mol1 Þ ¼ xi ð1 xi Þ Hm;ij
703 m X
hk ð1 2xi Þ
k1
:
ð2Þ
k¼1
Coefficients hk for the excess enthalpies obtained in this work as well as those reported in the literature for the other four constituent binaries are as listed in table 2. The experimental results for the two ternary mixtures E are reported in tables 3 and 4, where values of Hm;1þ23 are listed against the mole fraction x1 of MTBE. Also included in those tables are the corresponding values of E E Hm;123 , calculated from equation (1), with values of Hm;23 obtained from equation (2) using the coefficients reE ported in table 2. The results for Hm;1þ23 are plotted in figures 1 and 2. Also plotted in those figures are the results given in table 1 and those reported in the literature, corresponding to the cases x2 ¼ 0 [1] and x3 ¼ 0 reported in this work. In all cases, the maximum values E E of Hm;1þ23 and Hm;123 occur near x1 ¼ 0:5. At constant E x1 , Hm;1þ23 increases as x2 =ð1 x1 x2 Þ increases, and the increases are relatively more significant for the E mixtures containing nC12. The values of Hm;1þ23 were represented as a sum of binary terms [10] with an added ternary contribution
TABLE 4 E Experimental excess molar enthalpies Hm;1þ23 at 298.15 K for the addition of methyl tert-butyl ether to a binary mixture of 2-methylpentane and nE E calculated from equation (3) using the smooth representation of Hm;23 by dodecane to form x1 C5 H12 O + x2 C6 H14 + x3 C12 H26 and values of Hm;123 equation (2) x1
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
x1
E Hm;1þ23
(J mol1 ) E Hm;23
0.0499 0.0999 0.1613 0.2002 0.2499 0.3002 0.3505
76.65 151.78 240.11 286.94 342.10 393.10 428.92
132.28 204.48 289.22 333.77 386.02 434.08 466.95
0.0499 0.0999 0.1500 0.1999 0.2502 0.3000 0.3497
61.18 126.16 189.83 245.18 296.20 339.32 367.65
136.01 197.05 256.77 308.19 355.25 394.45 418.87
0.0501 0.1001 0.1501 0.2001 0.2500 0.3002 0.3503
51.47 109.60 163.00 210.53 255.23 287.89 317.55
107.01 162.21 212.69 257.30 299.08 328.80 355.54
E Hm;123
x1
(J mol1 )
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
1
(J mol x2 =x3 ¼ 0:3333, 0.4002 457.07 0.4492 478.21 0.5000 493.23 0.5498 497.77 0.6007 492.09 0.6502 475.51
) ¼ 58.55 492.19 510.46 522.51 524.13 515.47 495.99
0.7000 0.7496 0.8000 0.8502 0.8997 0.9500
448.27 409.44 357.47 292.60 212.18 111.61
465.84 424.10 369.18 301.37 218.05 114.54
E x2 =x3 ¼ 1:0001, Hm;23 (J mol1 ) ¼ 78.76 0.3997 394.91 442.19 0.4500 414.26 457.58 0.5001 424.25 463.62 0.5500 427.77 463.21 0.6004 421.13 452.60 0.6500 406.29 433.85
0.7000 0.7497 0.8000 0.8501 0.8993 0.9500
381.83 347.01 302.01 245.16 178.86 93.76
405.46 366.72 317.76 256.97 186.79 97.70
E x2 =x3 ¼ 3:0000, Hm;23 (J mol1 ) ¼ 58.47 0.3999 339.77 374.86 0.4500 353.37 385.53 0.5003 361.89 391.11 0.5494 363.53 389.87 0.5999 355.10 378.49 0.6503 342.33 362.78
0.7000 0.7502 0.8003 0.8503 0.9000 0.9500
318.76 288.55 248.96 201.44 142.49 76.45
336.30 303.15 260.64 210.19 148.34 79.37
E E by equations (3) and (4): Hm;T ðJ mol1 Þ ¼ x1 x2 x3 ð1185:25 þ 3124:60x1 þ 814:73x2 2947:27x21 Ternary term for representation of Hm;1þ23 1589:67x1 x2 þ 510:43x22 Þ s ¼ 3:74 J mol1 .
704
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706 700
600
600
500
500
-1
(J.mol )
-1
(J.mol )
400
300
H
H
E
E m,1+23
m,1+23
300
400
200 200
100
100
0
0 0.0
0.2
0.4
x1
0.6
0.8
1.0
E FIGURE 1. Excess molar enthalpies, Hm;1þ23 , for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC10 H22 } at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (s), x1 þ x2 ¼ 1; (M), x2 =ð1 x1 x2 Þ ¼ 0:3332; (N), x2 =ð1 x1 x2 Þ ¼ 0:9998; (), x2 =ð1 x1 x2 Þ ¼ 2:9994; (r), x2 ¼ 0 [1]. Curves: (—) calculated from the representation of the results by equations (3) and (4). Using the ternary E term Hm;T given in the footnote of table 3; (- - -) estimated by the Liebermann–Fried model.
E E Hm;1þ23 ¼ fx2 =ð1 x1 ÞgHm;12 þ fð1 x1 x2 Þ= E E ð1 x1 ÞgHm;13 þ Hm;T :
ð3Þ
In the present work, the form E =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þðc0 þ c1 x1 þ c2 x2 þ Hm;T
c3 x21 þ c4 x1 x2 þ c5 x22 þ Þ;
ð4Þ
which was adopted for the ternary contribution, is similar to that employed by Morris et al. [11]. Values of the coefficients ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to the experimental values in tables 3 and 4. The resulting E representations of Hm;T are given in the footnotes of those tables, where the standard deviations s of the representations are also indicated. The solid curves for E Hm;1þ23 in figures 1 and 2 were calculated from equation (3) using these representations. Equations (1), (2), (3) and (4) were also used to calE culate the constant Hm;123 contours plotted on the Roozeboom diagrams in parts a of figures 3 and 4. The general characteristics of these are similar. In both figures, all of the contours extend to the edge of the triangle and there is no indication of an internal maximum. Recent work [12] indicates that an extension of the model of Liebermann and Fried [13,14] can be useful in
0.0
0.2
0.4
x1
0.6
0.8
1.0
E FIGURE 2. Excess molar enthalpies, Hm;1þ23 , for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC12 H26 } at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (s), x1 þ x2 ¼ 1; (M), x2 =ð1 x1 x2 Þ ¼ 0:3333; (N), x2 =ð1 x1 x2 Þ ¼ 1:0001; (), x2 =ð1 x1 x2 Þ ¼ 3:0000; (r), x2 ¼ 0 [1]. Curves: (—), calculated from the representation of the results by equations (3) and (4). Using the ternary E term Hm;T given in the footnote of table 4; (- - -) estimated by the Liebermann–Fried model.
representing the excess enthalpies of binary mixtures and also has the potential for estimating the enthalpies of ternary mixtures from data for the pure components and their binary mixtures. It is therefore of interest to examine how well the Liebermann–Fried model can represent the enthalpies of the present ternary systems. The values of the Liebermann–Fried interaction parameters, Aij and Aji for all the five constituent binaries are given in table 5. These were obtained by fitting the E Liebermann–Fried formula for Hm;ij to the experimental results reported in table 1 for the MTBE + 2MP binary, as well as those evaluated from the literature values for the other four binaries [1,8,9]. Also included in table 5 are values of the standard deviations s achieved in the fitting process, and values [1,8,15] of the isobaric thermal expansivities ap , used in evaluating the contributions due to different sizes of the molecules. E Estimates of Hm;1þ23 , derived from the Libermann– Fried model, are shown as dashed curves in figures 1 and 2. In both cases, the model predicts correctly the order of the three experimental curves and their positions relative to the curves for the two constituent binaries. The root mean square deviations for the 57 points in tables 3 and 4 are 3.48 and 3.74 J mol1 , respectively. E Constant Hm;123 contours, estimated on the basis of the Liebermann–Fried model, are shown on the Rooze-
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
705
E FIGURE 3. Contours for constant values of Hm;123 for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC10 H22 } at the temperature 298.15 K. (a) Calculated E from the footnote of table 3 and (b) estimated by the from the representation of the experimental results by equations (1), (2), (3), (4) with Hm;T Liebermann–Fried model.
E FIGURE 4. Contours for constant values of Hm;123 for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC12 H26 } at the temperature 298.15 K. (a) Calculated E from the footnote of table 4 and (b) estimated by the from the representation of the experimental results by equations (1), (2), (3), (4) with Hm;T Liebermann–Fried model.
TABLE 5 Values of the interaction parameters, Aij and Aji , standard deviations, s, and isobaric thermal expansivities, ap , at 298.15 K Aij
Component i MTBE MTBE 2MP MTBE 2MP
Aji
ap 1
(J mol )
j 2MP nC10 nC10 nC12 nC12
s
1.0086 0.9949 1.0382 1.0107 1.0525
0.7975 0.6952 0.9109 0.6468 0.8631
6.69 1.95 0.11 3.50 0.16
i
j a
1.423 1.423a 1.426b 1.423a 1.426b
1.426b 1.051c 1.051c 0.960c 0.960c
a
Wang et al. [1]. Hamam and Benson [8]. c Benson et al. [15]. b
boom diagrams in parts b of figures 3 and 4. A comparison of the two parts in each figure indicates that the E model provides useful estimates of Hm;123 for both of the present mixtures. Acknowledgements The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.
References [1] L. Wang, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 213 (1993) 83–93. [2] S. Zhu, S. Shen, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 235 (1994) 161–169. [3] Z. Wang, B.C.-Y. Lu, J. Chem. Thermodyn. 32 (2000) 175–186, doi:10.1006/jcht.1999.0580. [4] TRC, Thermodynamic Tables, Non-Hydrocarbons,Thermodynamic Research Center, The Texas A&M University System, College Station, TX 77843-3111, 1996 (Table 23-2-1-(1.2120)-a, dated 30 June 1963).
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Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
[5] TRC, Thermodynamic Tables, Hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996 (Table 23-2-(1.201)-a dated 31 October 1952; Table 23-2-(1.10100)-a, p. 1 dated 31 October 1976; Table 23-2(1.101)-a, p. 2 dated 31 October 1976). [6] R. Tanaka, P.J. D’Arcy, G.C. Benson, Thermochim. Acta 11 (1975) 163–175. [7] F. Kimura, G.C. Benson, C.J. Halpin, Fluid Phase Equilibr. 11 (1983) 245–250. [8] S.E.M. Hamam, G.C. Benson, J. Chem. Eng. Data 31 (1986) 45–47. [9] S.E.M. Hamam, M.K. Kumaran, G.C. Benson, J. Chem. Thermodyn. 16 (1984) 537–542.
[10] C.C. Tsao, J.M. Smith, Chem. Eng. Prog. Symp. Ser. No. 7 (49) (1953) 107–117. [11] J.W. Morris, P.J. Mulvey, M.M. Abbott, H.C. Van Ness, J. Chem. Eng. Data 20 (1975) 403–405. [12] Z. Wang, D.-Y. Peng, G.C. Benson, B.C.-Y. Lu, J. Chem. Thermodyn. 33 (2001) 1181–1191. [13] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 350–354. [14] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 354–355. [15] G.C. Benson, B. Luo, B.C.-Y. Lu, Can. J. Chem. 66 (1988) 531–534.
JCT 04/89
Excess molar enthalpies of the ternary mixtures: methyl tert-butyl ether + 2-methylpentane + (n-decane or n-dodecane) at the temperature 298.15 K Zhaohui Wang, Benjamin C.-Y. Lu
*
Department of Chemical Engineering, University of Ottawa, Ottawa, Ont., Canada K1N 6N5 Received 26 April 2004; accepted 5 May 2004 Available online 9 June 2004
Abstract Measurements of excess molar enthalpies at the temperature 298.15 K in a flow microcalorimeter are reported for the two ternary mixtures x1 C5 H12 O + x2 (CH3 )2 CHCH2 CH2 CH3 + x3 CH3 (CH2 )m CH3 , where m ¼ 8 and 10. Smooth representations of the results are presented and used to construct constant excess molar enthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the ternary enthalpies can be obtained from the Liebermann and Fried model, using only the physical properties of the components and their binary mixtures. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Excess enthalpy; Ternary mixture; Methyl tert-butyl ether; 2-Methylpentane; n-Decane; n-Dodecane; Liebermann–Fried model
1. Introduction
2. Experimental
Currently, we are studying the thermodynamic properties of (oxygenate + hydrocarbon) mixtures and investigating the applicability of the Liebermann–Fried model to predict the excess enthalpies of ternary mixtures from the properties of the pure components and their binary mixtures. We have reported excess molar enthalpies of ternary mixtures containing methyl tertbutyl ether (MTBE) and hydrocarbons [1,2]. The present paper continues that work by reporting measurements of excess molar enthalpies at T ¼ 298:15 K for the ternary mixtures formed by mixing MTBE with binary mixtures of 2-methylpentane (2MP), and either n-decane (nC10) or n-dodecane (nC12). The binary Liebermann–Fried model parameters obtained from the constituent binaries may also serve the purpose of predicting vapor + liquid equilibria [3].
The OmniSol quality MTBE, with 99.5mol% purity, was obtained from the BDH Inc. The 2MP was Research Grade Reagent from the Phillips Chemical Company. The nC10 and nC12 were obtained from the Aldrich Chemical Company. For the three hydrocarbons, the mole fraction purities, stated by the manufacturers, exceed 0.990. Apart from partial degassing, all of the components were used without further purification. Densities q (T ¼ 298:15 K)/(kg m3 ), measured in an Anton–Paar digital densimeter, were 735.69, 649.78, 726.31 and 745.38 for MTBE, 2MP, nC10 and nC12, respectively. These are comparable with the literature values 735.3 [4], 648.52, 726.35 and 745.18 [5]. Excess molar enthalpies HmE were determined in an LKB flow microcalorimeter (Model 10700-1) at 298.150 K, maintained within 0.003 K. Details of the equipment and the operating procedure have been described previously [6,7]. For the ternary systems, x1 C5 H12 O + x2 (CH 3 ) 2 CHCH 2 CH 2 CH 3 + x3 CH 3 (CH 2 ) m CH 3 , with E m ¼ 8 and 10, the excess molar enthalpy Hm;1þ23 was determined for several pseudo-binary systems in which MTBE was added to a binary mixture of components 2
*
Corresponding author. Tel: +1-613-562-5800-6097; fax: +1-613562-5172. E-mail address: [email protected] (B.C.-Y. Lu). 0021-9614/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2004.05.006
702
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
TABLE 1 Experimental mole fractions x1 and excess molar enthalpies HmE for the binary mixture MTBE(1) + 2MP(2) at 298.15 K x1
HmE
x1
HmE
x1
HmE
x1
HmE
0.0532 0.1063 0.1589 0.2113 0.2633
37.54 89.35 140.48 182.94 218.86
0.3150 0.3658 0.4165 0.4667 0.5174
249.75 271.83 289.29 300.07 303.21
0.5673 0.6165 0.6652 0.7143 0.7628
297.31 291.16 275.87 254.41 226.67
0.8100 0.8548 0.9060 0.9531
193.23 157.51 107.38 57.09
Units: J mol1 .
TABLE 2 Coefficients hk and standard deviations s for the representations of the excess molar enthalpies HmE at 298.15 K by equation (1) h1
Component i
j
MTBE MTBE 2MP MTBE 2MP
2MP nC10 nC10 nC12 nC12
h2
h3
h4
h5
s (J mol1 )
)147.06 )313.32 2.97 )412.37 0.43
1213.98 2000.50 177.32 2279.33 315.03
)145.51 110.94 )5.37 254.78 )11.89
100.36 )2.09 206.70
)87.36 )214.72
2.67a 1.20b 0.05c 1.10b 0.06d
a
This work. Based on data of Wang et al. [1]. c Based on data of Hamam and Benson [8]. d Based on data of Hamam et al. [9]. b
TABLE 3 E at 298.15 K for the addition of methyl tert-butyl ether to a binary mixture of 2-methylpentane and nExperimental excess molar enthalpies Hm;1þ23 E E decane to form x1 C5 H12 O + x2 C6 H14 + x3 C10 H22 and values of Hm;123 calculated from equation (3) using the smooth representation of Hm;23 by equation (2) E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
0.0500 0.1000 0.1499 0.1999 0.2500 0.2999 0.3496
74.07 143.10 205.36 263.16 315.50 359.73 388.13
105.64 173.01 233.61 289.75 340.43 383.00 409.75
0.0500 0.1001 0.1499 0.2001 0.2502 0.3009 0.3501
62.84 122.77 181.14 234.33 279.23 315.48 347.48
104.95 162.66 218.83 269.79 312.47 346.47 376.29
x1
0.0500 0.1000 0.1501 0.2000 0.2499 0.2991 0.3497
45.35 99.40 155.67 202.16 246.06 276.17 302.39
76.46 128.87 183.50 228.36 270.63 299.12 323.69
x1
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
x1
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
E (J mol1 ) ¼ 33.23 x2 =x3 ¼ 0:3332, Hm;23 0.4003 415.42 435.35 0.4497 433.58 451.87 0.4999 444.59 461.21 0.5501 447.70 462.65 0.5998 438.78 452.08 0.6497 424.04 435.68
0.7000 0.7507 0.7996 0.8486 0.9000 0.9499
399.41 362.68 315.62 258.78 184.07 100.21
409.38 370.97 322.28 263.81 187.39 101.88
E x2 =x3 ¼ 0:9998; Hm;23 (J mol1 ) ¼ 44.33 0.3998 367.94 394.55 0.4503 387.71 412.08 0.4998 396.27 418.44 0.5497 397.27 417.23 0.5998 388.65 406.39 0.6500 365.09 380.61
0.7004 0.7500 0.8001 0.8500 0.9014 0.9500
350.71 318.12 274.44 222.82 157.26 83.74
363.99 329.20 283.30 229.47 161.63 85.96
E x2 =x3 ¼ 2:9994; Hm;23 (J mol1 ) ¼ 32.75 0.4000 326.41 346.06 0.4501 337.80 355.81 0.5000 347.11 363.48 0.5498 346.40 361.14 0.5999 340.85 353.95 0.6501 326.58 338.04
0.7004 0.7503 0.8004 0.8497 0.9000 0.9499
303.96 274.28 236.15 190.94 134.70 72.55
313.77 282.46 242.69 195.86 137.97 74.19
E E Ternary term for representation of Hm;1þ23 by equations (3) and (4): Hm;T ðJ mol1 Þ ¼ x1 x2 x3 ð302:47 þ 563:13x1 þ 883:32x2 1024:842x21 407:076x1 x2 1115:156x22 Þ s ¼ 3:48 J mol1 .
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
and 3, having a fixed mole ratio x2 =x3 . For this purpose, binary mixtures with x2 =x3 ¼ 0:3, 1.0 and 3.0 were prepared by weighing. The excess molar enthalpy of the ternary system was obtained from the relation E E E Hm;123 ¼ Hm;1þ23 þ ð1 x1 ÞHm;23 ;
ð1Þ
E is the excess molar enthalpy of the particular where Hm;23 binary mixture of 2MP and either nC10 or nC12. Over most of the mole fraction range of component 1, the E errors of Hm;1þ23 are estimated to be less than 0.5%. Errors in the mole fractions of the final ternary mixtures are estimated to be less than 5 104 .
3. Results and discussion E Excess molar enthalpies Hm;ij ði < jÞ, measured at T ¼ 298:15 K, for four of the constituent binary systems of present interest, have been reported previously: MTBE(1) + nC10(3) [1], MTBE(1) + nC12(3) [1], nC10(3) + 2MP(2) [8] and nC12(3) + 2MP(2) [9]. Excess enthalpies for the MTBE + 2MP binary measured in this study are listed in table 1. Coefficients hk for representation of the results were obtained by the following smoothing function,
E =ðJ mol1 Þ ¼ xi ð1 xi Þ Hm;ij
703 m X
hk ð1 2xi Þ
k1
:
ð2Þ
k¼1
Coefficients hk for the excess enthalpies obtained in this work as well as those reported in the literature for the other four constituent binaries are as listed in table 2. The experimental results for the two ternary mixtures E are reported in tables 3 and 4, where values of Hm;1þ23 are listed against the mole fraction x1 of MTBE. Also included in those tables are the corresponding values of E E Hm;123 , calculated from equation (1), with values of Hm;23 obtained from equation (2) using the coefficients reE ported in table 2. The results for Hm;1þ23 are plotted in figures 1 and 2. Also plotted in those figures are the results given in table 1 and those reported in the literature, corresponding to the cases x2 ¼ 0 [1] and x3 ¼ 0 reported in this work. In all cases, the maximum values E E of Hm;1þ23 and Hm;123 occur near x1 ¼ 0:5. At constant E x1 , Hm;1þ23 increases as x2 =ð1 x1 x2 Þ increases, and the increases are relatively more significant for the E mixtures containing nC12. The values of Hm;1þ23 were represented as a sum of binary terms [10] with an added ternary contribution
TABLE 4 E Experimental excess molar enthalpies Hm;1þ23 at 298.15 K for the addition of methyl tert-butyl ether to a binary mixture of 2-methylpentane and nE E calculated from equation (3) using the smooth representation of Hm;23 by dodecane to form x1 C5 H12 O + x2 C6 H14 + x3 C12 H26 and values of Hm;123 equation (2) x1
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
x1
E Hm;1þ23
(J mol1 ) E Hm;23
0.0499 0.0999 0.1613 0.2002 0.2499 0.3002 0.3505
76.65 151.78 240.11 286.94 342.10 393.10 428.92
132.28 204.48 289.22 333.77 386.02 434.08 466.95
0.0499 0.0999 0.1500 0.1999 0.2502 0.3000 0.3497
61.18 126.16 189.83 245.18 296.20 339.32 367.65
136.01 197.05 256.77 308.19 355.25 394.45 418.87
0.0501 0.1001 0.1501 0.2001 0.2500 0.3002 0.3503
51.47 109.60 163.00 210.53 255.23 287.89 317.55
107.01 162.21 212.69 257.30 299.08 328.80 355.54
E Hm;123
x1
(J mol1 )
E Hm;1þ23
E Hm;123
(J mol1 )
(J mol1 )
1
(J mol x2 =x3 ¼ 0:3333, 0.4002 457.07 0.4492 478.21 0.5000 493.23 0.5498 497.77 0.6007 492.09 0.6502 475.51
) ¼ 58.55 492.19 510.46 522.51 524.13 515.47 495.99
0.7000 0.7496 0.8000 0.8502 0.8997 0.9500
448.27 409.44 357.47 292.60 212.18 111.61
465.84 424.10 369.18 301.37 218.05 114.54
E x2 =x3 ¼ 1:0001, Hm;23 (J mol1 ) ¼ 78.76 0.3997 394.91 442.19 0.4500 414.26 457.58 0.5001 424.25 463.62 0.5500 427.77 463.21 0.6004 421.13 452.60 0.6500 406.29 433.85
0.7000 0.7497 0.8000 0.8501 0.8993 0.9500
381.83 347.01 302.01 245.16 178.86 93.76
405.46 366.72 317.76 256.97 186.79 97.70
E x2 =x3 ¼ 3:0000, Hm;23 (J mol1 ) ¼ 58.47 0.3999 339.77 374.86 0.4500 353.37 385.53 0.5003 361.89 391.11 0.5494 363.53 389.87 0.5999 355.10 378.49 0.6503 342.33 362.78
0.7000 0.7502 0.8003 0.8503 0.9000 0.9500
318.76 288.55 248.96 201.44 142.49 76.45
336.30 303.15 260.64 210.19 148.34 79.37
E E by equations (3) and (4): Hm;T ðJ mol1 Þ ¼ x1 x2 x3 ð1185:25 þ 3124:60x1 þ 814:73x2 2947:27x21 Ternary term for representation of Hm;1þ23 1589:67x1 x2 þ 510:43x22 Þ s ¼ 3:74 J mol1 .
704
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706 700
600
600
500
500
-1
(J.mol )
-1
(J.mol )
400
300
H
H
E
E m,1+23
m,1+23
300
400
200 200
100
100
0
0 0.0
0.2
0.4
x1
0.6
0.8
1.0
E FIGURE 1. Excess molar enthalpies, Hm;1þ23 , for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC10 H22 } at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (s), x1 þ x2 ¼ 1; (M), x2 =ð1 x1 x2 Þ ¼ 0:3332; (N), x2 =ð1 x1 x2 Þ ¼ 0:9998; (), x2 =ð1 x1 x2 Þ ¼ 2:9994; (r), x2 ¼ 0 [1]. Curves: (—) calculated from the representation of the results by equations (3) and (4). Using the ternary E term Hm;T given in the footnote of table 3; (- - -) estimated by the Liebermann–Fried model.
E E Hm;1þ23 ¼ fx2 =ð1 x1 ÞgHm;12 þ fð1 x1 x2 Þ= E E ð1 x1 ÞgHm;13 þ Hm;T :
ð3Þ
In the present work, the form E =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þðc0 þ c1 x1 þ c2 x2 þ Hm;T
c3 x21 þ c4 x1 x2 þ c5 x22 þ Þ;
ð4Þ
which was adopted for the ternary contribution, is similar to that employed by Morris et al. [11]. Values of the coefficients ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to the experimental values in tables 3 and 4. The resulting E representations of Hm;T are given in the footnotes of those tables, where the standard deviations s of the representations are also indicated. The solid curves for E Hm;1þ23 in figures 1 and 2 were calculated from equation (3) using these representations. Equations (1), (2), (3) and (4) were also used to calE culate the constant Hm;123 contours plotted on the Roozeboom diagrams in parts a of figures 3 and 4. The general characteristics of these are similar. In both figures, all of the contours extend to the edge of the triangle and there is no indication of an internal maximum. Recent work [12] indicates that an extension of the model of Liebermann and Fried [13,14] can be useful in
0.0
0.2
0.4
x1
0.6
0.8
1.0
E FIGURE 2. Excess molar enthalpies, Hm;1þ23 , for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC12 H26 } at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (s), x1 þ x2 ¼ 1; (M), x2 =ð1 x1 x2 Þ ¼ 0:3333; (N), x2 =ð1 x1 x2 Þ ¼ 1:0001; (), x2 =ð1 x1 x2 Þ ¼ 3:0000; (r), x2 ¼ 0 [1]. Curves: (—), calculated from the representation of the results by equations (3) and (4). Using the ternary E term Hm;T given in the footnote of table 4; (- - -) estimated by the Liebermann–Fried model.
representing the excess enthalpies of binary mixtures and also has the potential for estimating the enthalpies of ternary mixtures from data for the pure components and their binary mixtures. It is therefore of interest to examine how well the Liebermann–Fried model can represent the enthalpies of the present ternary systems. The values of the Liebermann–Fried interaction parameters, Aij and Aji for all the five constituent binaries are given in table 5. These were obtained by fitting the E Liebermann–Fried formula for Hm;ij to the experimental results reported in table 1 for the MTBE + 2MP binary, as well as those evaluated from the literature values for the other four binaries [1,8,9]. Also included in table 5 are values of the standard deviations s achieved in the fitting process, and values [1,8,15] of the isobaric thermal expansivities ap , used in evaluating the contributions due to different sizes of the molecules. E Estimates of Hm;1þ23 , derived from the Libermann– Fried model, are shown as dashed curves in figures 1 and 2. In both cases, the model predicts correctly the order of the three experimental curves and their positions relative to the curves for the two constituent binaries. The root mean square deviations for the 57 points in tables 3 and 4 are 3.48 and 3.74 J mol1 , respectively. E Constant Hm;123 contours, estimated on the basis of the Liebermann–Fried model, are shown on the Rooze-
Z. Wang, B.C.-Y. Lu / J. Chem. Thermodynamics 36 (2004) 701–706
705
E FIGURE 3. Contours for constant values of Hm;123 for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC10 H22 } at the temperature 298.15 K. (a) Calculated E from the footnote of table 3 and (b) estimated by the from the representation of the experimental results by equations (1), (2), (3), (4) with Hm;T Liebermann–Fried model.
E FIGURE 4. Contours for constant values of Hm;123 for {x1 C5 H12 O + x2 C6 H14 + ð1 x1 x2 ÞC12 H26 } at the temperature 298.15 K. (a) Calculated E from the footnote of table 4 and (b) estimated by the from the representation of the experimental results by equations (1), (2), (3), (4) with Hm;T Liebermann–Fried model.
TABLE 5 Values of the interaction parameters, Aij and Aji , standard deviations, s, and isobaric thermal expansivities, ap , at 298.15 K Aij
Component i MTBE MTBE 2MP MTBE 2MP
Aji
ap 1
(J mol )
j 2MP nC10 nC10 nC12 nC12
s
1.0086 0.9949 1.0382 1.0107 1.0525
0.7975 0.6952 0.9109 0.6468 0.8631
6.69 1.95 0.11 3.50 0.16
i
j a
1.423 1.423a 1.426b 1.423a 1.426b
1.426b 1.051c 1.051c 0.960c 0.960c
a
Wang et al. [1]. Hamam and Benson [8]. c Benson et al. [15]. b
boom diagrams in parts b of figures 3 and 4. A comparison of the two parts in each figure indicates that the E model provides useful estimates of Hm;123 for both of the present mixtures. Acknowledgements The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.
References [1] L. Wang, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 213 (1993) 83–93. [2] S. Zhu, S. Shen, G.C. Benson, B.C.-Y. Lu, Thermochim. Acta 235 (1994) 161–169. [3] Z. Wang, B.C.-Y. Lu, J. Chem. Thermodyn. 32 (2000) 175–186, doi:10.1006/jcht.1999.0580. [4] TRC, Thermodynamic Tables, Non-Hydrocarbons,Thermodynamic Research Center, The Texas A&M University System, College Station, TX 77843-3111, 1996 (Table 23-2-1-(1.2120)-a, dated 30 June 1963).
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[5] TRC, Thermodynamic Tables, Hydrocarbons, Thermodynamic Research Center, The Texas A&M University System, College Station, TX, 1996 (Table 23-2-(1.201)-a dated 31 October 1952; Table 23-2-(1.10100)-a, p. 1 dated 31 October 1976; Table 23-2(1.101)-a, p. 2 dated 31 October 1976). [6] R. Tanaka, P.J. D’Arcy, G.C. Benson, Thermochim. Acta 11 (1975) 163–175. [7] F. Kimura, G.C. Benson, C.J. Halpin, Fluid Phase Equilibr. 11 (1983) 245–250. [8] S.E.M. Hamam, G.C. Benson, J. Chem. Eng. Data 31 (1986) 45–47. [9] S.E.M. Hamam, M.K. Kumaran, G.C. Benson, J. Chem. Thermodyn. 16 (1984) 537–542.
[10] C.C. Tsao, J.M. Smith, Chem. Eng. Prog. Symp. Ser. No. 7 (49) (1953) 107–117. [11] J.W. Morris, P.J. Mulvey, M.M. Abbott, H.C. Van Ness, J. Chem. Eng. Data 20 (1975) 403–405. [12] Z. Wang, D.-Y. Peng, G.C. Benson, B.C.-Y. Lu, J. Chem. Thermodyn. 33 (2001) 1181–1191. [13] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 350–354. [14] E. Liebermann, V. Fried, Ind. Eng. Chem. Fundam. 11 (1972) 354–355. [15] G.C. Benson, B. Luo, B.C.-Y. Lu, Can. J. Chem. 66 (1988) 531–534.
JCT 04/89