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Excess enthalpies of {(heptane or decane)+methyl 1,1-dimethylethyl ether+diisopropyl ether} at the temperature 298.15 K
J. Chem. Thermodynamics 1997, 29, 431–439
Excess enthalpies of 4(heptane or decane) + methyl 1,1-dimethylethyl ether + diisopropyl ether5 at the temperature 298.15 K Zhangfa Tong, Dankui Liao, George C. Benson, and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Calorimetric measurements of excess molar enthalpies at the temperature 298.15 K are reported for the ternary mixtures [x1CH3(CH2 )n − 2CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] with n = 7 and 10. Smooth representations of the results are described and used to construct constant-enthalpy contours on Roozeboom diagrams. Comparisons with estimates based on the Flory theory are also presented. 7 1997 Academic Press Limited
KEYWORDS: excess enthalpies; ternary mixtures; n-alkanes; methyl 1,1-dimethylethyl ether; diisopropyl ether; Flory theory
1. Introduction A recent paper(1) from our laboratory described measurements of excess molar enthalpies HmE at T = 298.15 K for ternary mixtures consisting of either heptane (nC7) or decane (nC10), together with methyl 1,1-dimethylethyl ether (MTBE) and methyl 1,1-dimethylpropyl ether (TAME). As a continuation of that investigation, we have made similar measurements for the analogous mixtures in which the isomer diisopropyl ether (DIPE) replaced the TAME used previously.
2. Experimental The nC7 used in the present work was Pure Grade material from the Phillips Chemical Co. The nC10, MTBE (h.p.l.c. Grade), and DIPE were obtained from the Aldrich Chemical Co. In all cases, the mole fraction purities, stated by the manufacturers, exceeded 0.990. Densities r (298.15 K)/(kg·m−3 ), measured in an Anton-Paar densimeter were 679.77, 726.37, 735.58, and 718.71 for nC7, nC10, MTBE, and DIPE, respectively. These results are in reasonable agreement with values in the literature.(2, 3) Excess molar enthalpies HmE were measured in an LKB flow microcalorimeter (Model 10700-1) thermostatted at T = (298.150 2 0.003) K. This equipment and its operating procedure have been described previously.(4, 5) 0021–9614/97/040431 + 09 $25.00/0/ct960170
7 1997 Academic Press Limited
432
Z. Tong et al.
E TABLE 1. Experimental excess molar enthalpies Hm,23 at T = 298.15 K for [x2(CH3 )3COCH3 + (1 − x2 )4(CH3 )2CH52O]
x2
E Hm,23 J·mol−1
0.0500 0.1000 0.1500 0.2001 0.2499
3.97 8.22 11.66 14.93 17.19
x2
E Hm,23 J·mol−1
x2
E Hm,23 J·mol−1
x2
E Hm,23 J·mol−1
x2
E Hm,23 J·mol−1
0.3003 0.3500 0.4003 0.4499
19.55 21.11 22.49 23.07
0.4997 0.5010 0.5492 0.5995
23.62 23.39 23.00 22.87
0.6000 0.6500 0.6998 0.7490
22.57 21.49 20.01 17.93
0.7997 0.8500 0.9001 0.9500
15.22 11.99 8.21 3.83
E The excess molar enthalpies Hm,123 of the ternary mixtures [x1CH3(CH2 )n − 2CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] for n = 7 and 10, were investigated E by measuring the excess molar enthalpies Hm,1 + 23 for some pseudo-binary mixtures in which component 1, the n-alkane (either nC7 or nC10) was added to binary mixtures of components 2 (MTBE) and 3 (DIPE) having fixed compositions. These binaries were prepared by weighing. The excess molar enthalpies of the ternary mixtures were then obtained from the relation: E E E = Hm,1 Hm,123 + 23 + (1 − x1 )Hm,23 ,
(1)
E where Hm,23 is the excess molar enthalpy of the particular binary mixture. Over most of the mole-fraction range, the errors of the excess molar enthalpies and the mole fractions of the final ternary mixtures are estimated to be Q0.005·=HmE = and Q5·10−4 , respectively.
3. Results and discussion E Excess molar enthalpies Hm,ij (i Q j) for four of the five constituent-binary mixtures of present interest have been reported previously: (heptane + methyl 1,1-dimethylethyl ether),(1) (heptane + diisopropyl ether),(6) (decane + methyl 1,1-dimethylethyl ether),(7) and (decane + diisopropyl ether).(8) Experimental values
E TABLE 2. Parameters hk and standard deviations s for the representation of Hm,ij at T = 298.15 K by equation (2)
Component i
j
h1
h2
h3
h4
h5
s/(J·mol−1 )
MTBE nC7 nC7 nC10 nC10
DIPE MTBE a DIPE b MTBE c DIPE d
93.51 1662.94 974.50 2000.50 1357.07
−3.69 70.87 4.55 313.32 109.31
7.83 42.38 −0.71 110.94 162.86
5.08 −58.64 15.48 100.36 58.25
−20.83
0.16 1.06 0.28 1.18 0.88
−87.36 −202.62
a Reference 1. b Reference 6. c Reference 7. d Reference 8. MTBE, methyl 1,1-dimethylethyl ether; DIPE, diisopropyl ether; nC7, heptane; nC10, decane.
JCT 29/4 ISSUE (827284)—MS 0332
HmE of {(heptane or decane) methyl 1,1-dimethylethyl ether + diisoperopyl ether}
433
for the binary ether mixture (methyl 1,1-dimethylethyl ether + diisopropyl ether) at the temperature 298.15 K are summarized in table 1. The smoothing function: m
E Hm,ij /(J·mol−1 ) = xi(1 − xi) s hk (1 − 2xi)k − 1 ,
(2)
k=1
was fitted to these results by the method of least-squares, with all points weighted equally. Values of the coefficients hk are listed in table 2, along with the standard deviation s of the representation. Coefficients for the representations of the four other binary mixtures are also listed in table 2. E E The experimental results for Hm,1 + 23 and the corresponding values of Hm,123 for the E two ternary mixtures are listed in tables 3 and 4. The values of Hm,1 + 23 are plotted in figures 1 and 2, along with curves for the constituent-binary mixtures having E E x2 = 0 and x1 + x2 = 1. In all cases, the maximum values of Hm,1 + 23 and Hm,123 occur near x1 = 0.5, and for comparable x2/(1 − x1 − x2 ), the maximum is larger for E TABLE 3. Experimental excess molar enthalpies Hm,1 + 23 at the temperature 298.15 K for the addition of heptane to methyl 1,1-dimethylethyl ether + diisopropryl ether to form [x1CH3(CH2 )5CH3 + E x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O], and values of Hm,123 calculated from equation (1) using E the smooth representation of Hm,23 by equation (2)
x1
0.0500 0.1000 0.1500 0.2000 0.2506 0.2998 0.3505 0.0501 0.1002 0.1501 0.2003 0.2500 0.3005 0.3506
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
45.5 95.2 138.5 174.8 207.0 231.5 251.9
E x2/(1 − x1 − x2 ) = 0.3331; Hm,23 = 17.4 J·mol−1 62.0 0.3994 265.4 275.9 0.6998 110.9 0.4502 274.5 284.1 0.7499 153.4 0.4999 277.1 285.8 0.8001 188.7 0.5495 274.1 282.0 0.8498 220.1 0.5995 261.7 268.7 0.8999 243.7 0.6495 247.9 254.0 0.9500 263.2
228.9 206.5 174.5 137.5 97.9 51.3
234.2 210.8 178.0 140.1 99.7 52.2
53.3 110.9 161.1 203.8 239.2 268.5 291.5
E x2/(1 − x1 − x2 ) = 1.0158; Hm,23 = 23.4 J·mol−1 75.6 0.3998 306.5 320.5 0.6997 131.9 0.4495 314.1 326.9 0.7499 181.0 0.4998 318.2 329.9 0.7999 222.5 0.5003 316.3 328.0 0.8499 256.8 0.5505 312.2 322.7 0.8999 284.8 0.6000 300.7 310.0 0.9501 306.6 0.6491 286.1 294.3
265.2 241.3 204.5 162.6 112.6 57.9
272.2 247.2 209.1 166.1 115.0 59.1
300.7 271.4 234.4 182.4 129.3 66.7
306.0 275.8 238.0 185.0 131.0 67.6
x1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
x1
E x12/(1 − x1 − x2 ) = 2.9874; Hm,23 = 17.9 J·mol−1
0.0500 0.1000 0.1502 0.1999 0.2495 0.2998 0.3493
60.2 125.1 181.8 230.6 270.3 303.1 328.6
77.2 141.3 197.1 244.9 283.7 315.7 340.3
0.4003 0.4500 0.4996 0.4999 0.5494 0.6001 0.6498
347.1 357.8 359.7 359.7 355.6 345.0 325.5
357.8 367.7 368.7 368.7 363.7 352.1 331.8
0.6999 0.7500 0.8001 0.8500 0.8999 0.9501
E E a −1 Ternary contribution term for representation of Hm,1 )= + 23 by equations (2) and (3): Hm,T/(J·mol x1x2(1 − x1 − x2 )(−1621.68 + 5410.55x1 + 3367.02x2 − 8652.72x12 − 3313.80x1x2 − 3889.40x22 + 3687.02x13 ), s = 2.0 J·mol−1 .
434
Z. Tong et al.
E TABLE 4. Experimental excess molar enthalpies Hm,1 + 23 at the temperature 298.15 K for the addition of decane to methyl 1,1-dimethylethyl ether + diisopropryl ether to form [x1CH3(CH2 )8CH3 + E x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O], and values of Hm,123 calculated from equation (1) using E the smooth representation of Hm,23 by equation (2)
x1
0.0500 0.1000 0.1499 0.1998 0.2502 0.2998 0.3503 0.0500 0.1000 0.1500 0.2007 0.2501 0.3005 0.3504 0.0502 0.1001 0.1501 0.2000 0.2502 0.3000 0.3508
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
75.3 144.2 203.5 253.4 293.1 324.8 346.9
E x2/(1 − x1 − x2 ) = 0.3416; Hm,23 = 17.6 J·mol−1 92.1 0.3990 361.7 372.3 0.6999 160.1 0.4504 368.4 378.1 0.7497 218.5 0.4993 370.0 378.9 0.7999 267.5 0.5002 368.4 377.3 0.8499 306.3 0.5500 362.9 370.8 0.9000 337.2 0.6005 347.8 354.9 0.9500 358.3 0.6497 326.5 332.7
303.6 269.0 225.6 177.3 123.8 65.8
308.9 273.4 229.1 180.0 125.6 66.7
86.0 161.4 229.4 283.1 324.9 359.0 383.4
E = 23.4 J·mol−1 x2(1 − x1 − x2 ) = 1.0179; Hm,23 108.2 0.4000 399.7 413.7 0.6998 182.4 0.4503 406.8 419.7 0.7499 249.3 0.4997 407.1 418.8 0.8000 301.8 0.5001 405.9 417.6 0.8498 342.5 0.5503 399.7 410.2 0.9001 375.4 0.5999 381.5 390.9 0.9500 398.6 0.6496 358.3 366.4
329.5 290.9 245.2 191.6 133.9 71.8
336.6 296.8 249.9 195.1 136.3 73.0
95.7 179.3 253.3 312.2 360.3 396.8 425.0
E = 17.8 J·mol−1 x2/(1 − x1 − x2 ) = 3.0209; Hm,23 112.7 0.4002 440.1 450.8 0.6999 195.4 0.4496 447.7 457.5 0.7499 268.4 0.5002 446.9 455.8 0.8000 326.5 0.5005 447.9 456.8 0.8500 373.7 0.5500 437.2 445.2 0.9000 409.2 0.6004 417.2 424.3 0.9500 436.6 0.6504 389.8 396.0
359.3 320.3 264.7 207.9 147.0 75.9
364.6 324.8 268.3 210.6 148.8 76.8
x1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
x1
E a Ternary contribution term for representation of Hm,1 by equations (2) and (3): + 23 E /(J·mol−1 ) =x1x2(1 − x1 − x2 )(−1342.28 + 2732.42x1 + 3135.19x2 − 2409.74x12 − 3711.56x1x2 − Hm,T 3316.90x22 ), s = 1.4 J·mol−1.
the mixture with decane. For both mixtures at constant x1 , the excess molar enthalpies increase as x2/(1 − x1 − x2 ) increases. E (9) The values of Hm,1 with an added + 23 were represented as a sum of binary terms ternary contribution term: E E −1 Hm,1 ) = 4x2/(1 − x1 )5·Hm,12 + + 23/(J·mol E E 4(1 − x1 − x2 )/(1 − x1 )5·Hm,13 + Hm,T ,
(3)
E where values of the Hm,ij were calculated from the appropriate smoothing functions. Following Morris et al.(10) the ternary contribution term was assumed to have the form: E Hm,T /(J·mol−1 ) =
x1x2(1 − x1 − x2 )(c0 + c1x1 + c2x2 + c3x12 + c4x1x2 + c5x22 + . . .),
(4)
HmE of {(heptane or decane) methyl 1,1-dimethylethyl ether + diisoperopyl ether}
435
E FIGURE 1. Excess molar enthalpies Hm,1 for [x1CH3(CH2 )5CH3 + x2(CH3 )3COCH3 + + 23 (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K. Experimental results: r, x2/(1 − x1 − x2 ) = 2.9874; w, x2/(1 − x1 − x2 ) = 1.0158; t, x2/(1 − x1 − x2 ) = 0.3331. Curves: · — · —, x2 = 0, reference 6; ...., x1 + x2 = 1, reference 1; ——, calculated from the representation of the results by equations (2) and E (3), using the ternary contribution term Hm,T given in the footnote of table 3; ----, estimated from the Flory theory.
Values of the parameters ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to the experimental results in tables 3 and 4. These representations are given in the footnotes of the tables, along with their standard deviations s. The solid curves in figures 1 and 2 were calculated from these representations. E Some constant Hm,123 contours, calculated from equations (1) to (4), are plotted on the Roozeboom diagrams shown in figures 3 and 4. The general characteristics of these are similar to those found previously for the mixtures containing TAME.(1) All of the contours extend to the edges of the triangle. E The maximum value of Hm,123 is located in the edge of the plot for the constituent binary comprising MTBE and the n-alkane. The two figures are very similar,
436
Z. Tong et al.
E FIGURE 2. Excess molar enthalpies Hm,1 for [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + + 23 (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K. Experimental results: r, x2/(1 − x1 − x2 ) = 3.0209; w, x2/(1 − x1 − x2 ) = 1.0179; t, x2/(1 − x1 − x2 ) = 0.3416. Curves: · — · —, x2 = 0, reference 8; ...., x1 + x2 = 1, reference 7; ————, calculated from the representation of the results by equations (2) E and (3), using the ternary contribution term Hm,T given in the footnote of table 4; ----, estimated from the Flory theory.
and in both cases contours which terminate only on the (methyl 1,1-dimethylethyl ether + n-alkane) edge are skewed towards the (diisopropyl ether + n-alkane) edge of the triangle. Previously,(7) for mixtures of alkanes and ethers, it was found that the Flory theory,(11, 12) as applied to multicomponent mixtures by Brostow and Sochanski(13) provided reasonable estimates of the ternary excess molar enthalpies, when only properties of the pure components and their binary mixtures were used. The same approach was investigated for the present mixtures. Since the treatment closely follows our previous work,(7) the equations are not repeated here. The characteristic values of the pressure p*, the molar volume V* m , and the temperature T* are listed in table 5 for each component. These were taken from
436
Z. Tong et al.
E FIGURE 2. Excess molar enthalpies Hm,1 for [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + + 23 (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K. Experimental results: r, x2/(1 − x1 − x2 ) = 3.0209; w, x2/(1 − x1 − x2 ) = 1.0179; t, x2/(1 − x1 − x2 ) = 0.3416. Curves: · — · —, x2 = 0, reference 8; ...., x1 + x2 = 1, reference 7; ————, calculated from the representation of the results by equations (2) E and (3), using the ternary contribution term Hm,T given in the footnote of table 4; ----, estimated from the Flory theory.
and in both cases contours which terminate only on the (methyl 1,1-dimethylethyl ether + n-alkane) edge are skewed towards the (diisopropyl ether + n-alkane) edge of the triangle. Previously,(7) for mixtures of alkanes and ethers, it was found that the Flory theory,(11, 12) as applied to multicomponent mixtures by Brostow and Sochanski(13) provided reasonable estimates of the ternary excess molar enthalpies, when only properties of the pure components and their binary mixtures were used. The same approach was investigated for the present mixtures. Since the treatment closely follows our previous work,(7) the equations are not repeated here. The characteristic values of the pressure p*, the molar volume V* m , and the temperature T* are listed in table 5 for each component. These were taken from
438
Z. Tong et al.
E FIGURE 4. Contours for constant values of Hm,123 /(J·mol−1 ) for [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K, calculated from the E evaluated from the footnote representation of the experimental results by equations (1) to (3) with Hm,T of table 4.
smooth representations of the results for the mixtures in tables 3 and 4. The results of the calculations for the nC7 mixture are shown on the Roozeboom diagram in figure 5. It is clear from a comparison of this with figure 3 that the Flory theory E provides useful estimates of Hm,123 without requiring the direct investigation of any ternary mixtures. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. TABLE 5. Pressure p*, molar volume V* m , and temperature T* used in Flory theory calculations at the temperature 298.15 K for [x1CH3(CH2 )5CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] a and [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] b Component
p*/MPa
3 −1 V* ) m /(cm ·mol
T*/K
Reference no.
Heptane Decane Methyl 1,1-dimethylethyl ether Diisopropryl ether
431.9 447.0 442.9 447.9
113.60 155.75 90.20 106.50
4648.1 5091.4 4385.0 4335.2
Benson et al.(14) Benson et al.(14) Wang et al.(7) Zhu et al.(8)
Interchange-energy parameters Xij/(J·cm−3 ): 15.6509; X13 = 10.4782; X23 = 0.9228.
a
X12 = 15.0620; X13 = 8.4433; X23 = 0.9228;
b
X12 =
HmE of {(heptane or decane) methyl 1,1-dimethylethyl ether + diisoperopyl ether}
439
E FIGURE 5. Contours for constant values of Hm,123 /(J·mol−1 ) for [x1CH3(CH2 )5CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K, estimated from the Flory theory.
REFERENCES 1. Tong, Z.; Benson, G. C.; Wang, L. L.; Lu, B. C.-Y. J. Chem. Eng. Data 1996, 41, 865–869. 2. TRC—Thermodynamic Tables—Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station, TX 77843-3111. 1988: Table 23-2-(1.101)-a, dated 31 October 1977. 3. TRC—Thermodynamic Tables—Non-Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station, TX 77843-3111. 1988: Tables 23-2-1-(1.2120)-a and 23-2-1-(1.2121)-a, dated 30 June 1963. 4. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163–175. 5. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245–250. 6. Oba, M.; Murakami, S.; Fujishiro, R. J. Chem. Thermodynamics 1977, 9, 407–414. 7. Wang, L.; Benson, G. C.; Lu, B. C.-Y. Thermochim. Acta 1993, 213, 83–93. 8. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1994, 26, 415–420. 9. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. Ser. No. 7 1953, 49, 107–117. 10. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403–405. 11. Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833–1838. 12. Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838–1846. 13. Brostow, W.; Sochanski, J. S. J. Mater. Sci. 1975, 10, 2134–2145. 14. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531–534.
(Received 4 September 1996; in final form 18 October 1996)
WE-075
Excess enthalpies of 4(heptane or decane) + methyl 1,1-dimethylethyl ether + diisopropyl ether5 at the temperature 298.15 K Zhangfa Tong, Dankui Liao, George C. Benson, and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Calorimetric measurements of excess molar enthalpies at the temperature 298.15 K are reported for the ternary mixtures [x1CH3(CH2 )n − 2CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] with n = 7 and 10. Smooth representations of the results are described and used to construct constant-enthalpy contours on Roozeboom diagrams. Comparisons with estimates based on the Flory theory are also presented. 7 1997 Academic Press Limited
KEYWORDS: excess enthalpies; ternary mixtures; n-alkanes; methyl 1,1-dimethylethyl ether; diisopropyl ether; Flory theory
1. Introduction A recent paper(1) from our laboratory described measurements of excess molar enthalpies HmE at T = 298.15 K for ternary mixtures consisting of either heptane (nC7) or decane (nC10), together with methyl 1,1-dimethylethyl ether (MTBE) and methyl 1,1-dimethylpropyl ether (TAME). As a continuation of that investigation, we have made similar measurements for the analogous mixtures in which the isomer diisopropyl ether (DIPE) replaced the TAME used previously.
2. Experimental The nC7 used in the present work was Pure Grade material from the Phillips Chemical Co. The nC10, MTBE (h.p.l.c. Grade), and DIPE were obtained from the Aldrich Chemical Co. In all cases, the mole fraction purities, stated by the manufacturers, exceeded 0.990. Densities r (298.15 K)/(kg·m−3 ), measured in an Anton-Paar densimeter were 679.77, 726.37, 735.58, and 718.71 for nC7, nC10, MTBE, and DIPE, respectively. These results are in reasonable agreement with values in the literature.(2, 3) Excess molar enthalpies HmE were measured in an LKB flow microcalorimeter (Model 10700-1) thermostatted at T = (298.150 2 0.003) K. This equipment and its operating procedure have been described previously.(4, 5) 0021–9614/97/040431 + 09 $25.00/0/ct960170
7 1997 Academic Press Limited
432
Z. Tong et al.
E TABLE 1. Experimental excess molar enthalpies Hm,23 at T = 298.15 K for [x2(CH3 )3COCH3 + (1 − x2 )4(CH3 )2CH52O]
x2
E Hm,23 J·mol−1
0.0500 0.1000 0.1500 0.2001 0.2499
3.97 8.22 11.66 14.93 17.19
x2
E Hm,23 J·mol−1
x2
E Hm,23 J·mol−1
x2
E Hm,23 J·mol−1
x2
E Hm,23 J·mol−1
0.3003 0.3500 0.4003 0.4499
19.55 21.11 22.49 23.07
0.4997 0.5010 0.5492 0.5995
23.62 23.39 23.00 22.87
0.6000 0.6500 0.6998 0.7490
22.57 21.49 20.01 17.93
0.7997 0.8500 0.9001 0.9500
15.22 11.99 8.21 3.83
E The excess molar enthalpies Hm,123 of the ternary mixtures [x1CH3(CH2 )n − 2CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] for n = 7 and 10, were investigated E by measuring the excess molar enthalpies Hm,1 + 23 for some pseudo-binary mixtures in which component 1, the n-alkane (either nC7 or nC10) was added to binary mixtures of components 2 (MTBE) and 3 (DIPE) having fixed compositions. These binaries were prepared by weighing. The excess molar enthalpies of the ternary mixtures were then obtained from the relation: E E E = Hm,1 Hm,123 + 23 + (1 − x1 )Hm,23 ,
(1)
E where Hm,23 is the excess molar enthalpy of the particular binary mixture. Over most of the mole-fraction range, the errors of the excess molar enthalpies and the mole fractions of the final ternary mixtures are estimated to be Q0.005·=HmE = and Q5·10−4 , respectively.
3. Results and discussion E Excess molar enthalpies Hm,ij (i Q j) for four of the five constituent-binary mixtures of present interest have been reported previously: (heptane + methyl 1,1-dimethylethyl ether),(1) (heptane + diisopropyl ether),(6) (decane + methyl 1,1-dimethylethyl ether),(7) and (decane + diisopropyl ether).(8) Experimental values
E TABLE 2. Parameters hk and standard deviations s for the representation of Hm,ij at T = 298.15 K by equation (2)
Component i
j
h1
h2
h3
h4
h5
s/(J·mol−1 )
MTBE nC7 nC7 nC10 nC10
DIPE MTBE a DIPE b MTBE c DIPE d
93.51 1662.94 974.50 2000.50 1357.07
−3.69 70.87 4.55 313.32 109.31
7.83 42.38 −0.71 110.94 162.86
5.08 −58.64 15.48 100.36 58.25
−20.83
0.16 1.06 0.28 1.18 0.88
−87.36 −202.62
a Reference 1. b Reference 6. c Reference 7. d Reference 8. MTBE, methyl 1,1-dimethylethyl ether; DIPE, diisopropyl ether; nC7, heptane; nC10, decane.
JCT 29/4 ISSUE (827284)—MS 0332
HmE of {(heptane or decane) methyl 1,1-dimethylethyl ether + diisoperopyl ether}
433
for the binary ether mixture (methyl 1,1-dimethylethyl ether + diisopropyl ether) at the temperature 298.15 K are summarized in table 1. The smoothing function: m
E Hm,ij /(J·mol−1 ) = xi(1 − xi) s hk (1 − 2xi)k − 1 ,
(2)
k=1
was fitted to these results by the method of least-squares, with all points weighted equally. Values of the coefficients hk are listed in table 2, along with the standard deviation s of the representation. Coefficients for the representations of the four other binary mixtures are also listed in table 2. E E The experimental results for Hm,1 + 23 and the corresponding values of Hm,123 for the E two ternary mixtures are listed in tables 3 and 4. The values of Hm,1 + 23 are plotted in figures 1 and 2, along with curves for the constituent-binary mixtures having E E x2 = 0 and x1 + x2 = 1. In all cases, the maximum values of Hm,1 + 23 and Hm,123 occur near x1 = 0.5, and for comparable x2/(1 − x1 − x2 ), the maximum is larger for E TABLE 3. Experimental excess molar enthalpies Hm,1 + 23 at the temperature 298.15 K for the addition of heptane to methyl 1,1-dimethylethyl ether + diisopropryl ether to form [x1CH3(CH2 )5CH3 + E x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O], and values of Hm,123 calculated from equation (1) using E the smooth representation of Hm,23 by equation (2)
x1
0.0500 0.1000 0.1500 0.2000 0.2506 0.2998 0.3505 0.0501 0.1002 0.1501 0.2003 0.2500 0.3005 0.3506
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
45.5 95.2 138.5 174.8 207.0 231.5 251.9
E x2/(1 − x1 − x2 ) = 0.3331; Hm,23 = 17.4 J·mol−1 62.0 0.3994 265.4 275.9 0.6998 110.9 0.4502 274.5 284.1 0.7499 153.4 0.4999 277.1 285.8 0.8001 188.7 0.5495 274.1 282.0 0.8498 220.1 0.5995 261.7 268.7 0.8999 243.7 0.6495 247.9 254.0 0.9500 263.2
228.9 206.5 174.5 137.5 97.9 51.3
234.2 210.8 178.0 140.1 99.7 52.2
53.3 110.9 161.1 203.8 239.2 268.5 291.5
E x2/(1 − x1 − x2 ) = 1.0158; Hm,23 = 23.4 J·mol−1 75.6 0.3998 306.5 320.5 0.6997 131.9 0.4495 314.1 326.9 0.7499 181.0 0.4998 318.2 329.9 0.7999 222.5 0.5003 316.3 328.0 0.8499 256.8 0.5505 312.2 322.7 0.8999 284.8 0.6000 300.7 310.0 0.9501 306.6 0.6491 286.1 294.3
265.2 241.3 204.5 162.6 112.6 57.9
272.2 247.2 209.1 166.1 115.0 59.1
300.7 271.4 234.4 182.4 129.3 66.7
306.0 275.8 238.0 185.0 131.0 67.6
x1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
x1
E x12/(1 − x1 − x2 ) = 2.9874; Hm,23 = 17.9 J·mol−1
0.0500 0.1000 0.1502 0.1999 0.2495 0.2998 0.3493
60.2 125.1 181.8 230.6 270.3 303.1 328.6
77.2 141.3 197.1 244.9 283.7 315.7 340.3
0.4003 0.4500 0.4996 0.4999 0.5494 0.6001 0.6498
347.1 357.8 359.7 359.7 355.6 345.0 325.5
357.8 367.7 368.7 368.7 363.7 352.1 331.8
0.6999 0.7500 0.8001 0.8500 0.8999 0.9501
E E a −1 Ternary contribution term for representation of Hm,1 )= + 23 by equations (2) and (3): Hm,T/(J·mol x1x2(1 − x1 − x2 )(−1621.68 + 5410.55x1 + 3367.02x2 − 8652.72x12 − 3313.80x1x2 − 3889.40x22 + 3687.02x13 ), s = 2.0 J·mol−1 .
434
Z. Tong et al.
E TABLE 4. Experimental excess molar enthalpies Hm,1 + 23 at the temperature 298.15 K for the addition of decane to methyl 1,1-dimethylethyl ether + diisopropryl ether to form [x1CH3(CH2 )8CH3 + E x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O], and values of Hm,123 calculated from equation (1) using E the smooth representation of Hm,23 by equation (2)
x1
0.0500 0.1000 0.1499 0.1998 0.2502 0.2998 0.3503 0.0500 0.1000 0.1500 0.2007 0.2501 0.3005 0.3504 0.0502 0.1001 0.1501 0.2000 0.2502 0.3000 0.3508
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
75.3 144.2 203.5 253.4 293.1 324.8 346.9
E x2/(1 − x1 − x2 ) = 0.3416; Hm,23 = 17.6 J·mol−1 92.1 0.3990 361.7 372.3 0.6999 160.1 0.4504 368.4 378.1 0.7497 218.5 0.4993 370.0 378.9 0.7999 267.5 0.5002 368.4 377.3 0.8499 306.3 0.5500 362.9 370.8 0.9000 337.2 0.6005 347.8 354.9 0.9500 358.3 0.6497 326.5 332.7
303.6 269.0 225.6 177.3 123.8 65.8
308.9 273.4 229.1 180.0 125.6 66.7
86.0 161.4 229.4 283.1 324.9 359.0 383.4
E = 23.4 J·mol−1 x2(1 − x1 − x2 ) = 1.0179; Hm,23 108.2 0.4000 399.7 413.7 0.6998 182.4 0.4503 406.8 419.7 0.7499 249.3 0.4997 407.1 418.8 0.8000 301.8 0.5001 405.9 417.6 0.8498 342.5 0.5503 399.7 410.2 0.9001 375.4 0.5999 381.5 390.9 0.9500 398.6 0.6496 358.3 366.4
329.5 290.9 245.2 191.6 133.9 71.8
336.6 296.8 249.9 195.1 136.3 73.0
95.7 179.3 253.3 312.2 360.3 396.8 425.0
E = 17.8 J·mol−1 x2/(1 − x1 − x2 ) = 3.0209; Hm,23 112.7 0.4002 440.1 450.8 0.6999 195.4 0.4496 447.7 457.5 0.7499 268.4 0.5002 446.9 455.8 0.8000 326.5 0.5005 447.9 456.8 0.8500 373.7 0.5500 437.2 445.2 0.9000 409.2 0.6004 417.2 424.3 0.9500 436.6 0.6504 389.8 396.0
359.3 320.3 264.7 207.9 147.0 75.9
364.6 324.8 268.3 210.6 148.8 76.8
x1
E a Hm,1 + 23 J·mol−1
E Hm,123 J·mol−1
x1
E a Ternary contribution term for representation of Hm,1 by equations (2) and (3): + 23 E /(J·mol−1 ) =x1x2(1 − x1 − x2 )(−1342.28 + 2732.42x1 + 3135.19x2 − 2409.74x12 − 3711.56x1x2 − Hm,T 3316.90x22 ), s = 1.4 J·mol−1.
the mixture with decane. For both mixtures at constant x1 , the excess molar enthalpies increase as x2/(1 − x1 − x2 ) increases. E (9) The values of Hm,1 with an added + 23 were represented as a sum of binary terms ternary contribution term: E E −1 Hm,1 ) = 4x2/(1 − x1 )5·Hm,12 + + 23/(J·mol E E 4(1 − x1 − x2 )/(1 − x1 )5·Hm,13 + Hm,T ,
(3)
E where values of the Hm,ij were calculated from the appropriate smoothing functions. Following Morris et al.(10) the ternary contribution term was assumed to have the form: E Hm,T /(J·mol−1 ) =
x1x2(1 − x1 − x2 )(c0 + c1x1 + c2x2 + c3x12 + c4x1x2 + c5x22 + . . .),
(4)
HmE of {(heptane or decane) methyl 1,1-dimethylethyl ether + diisoperopyl ether}
435
E FIGURE 1. Excess molar enthalpies Hm,1 for [x1CH3(CH2 )5CH3 + x2(CH3 )3COCH3 + + 23 (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K. Experimental results: r, x2/(1 − x1 − x2 ) = 2.9874; w, x2/(1 − x1 − x2 ) = 1.0158; t, x2/(1 − x1 − x2 ) = 0.3331. Curves: · — · —, x2 = 0, reference 6; ...., x1 + x2 = 1, reference 1; ——, calculated from the representation of the results by equations (2) and E (3), using the ternary contribution term Hm,T given in the footnote of table 3; ----, estimated from the Flory theory.
Values of the parameters ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to the experimental results in tables 3 and 4. These representations are given in the footnotes of the tables, along with their standard deviations s. The solid curves in figures 1 and 2 were calculated from these representations. E Some constant Hm,123 contours, calculated from equations (1) to (4), are plotted on the Roozeboom diagrams shown in figures 3 and 4. The general characteristics of these are similar to those found previously for the mixtures containing TAME.(1) All of the contours extend to the edges of the triangle. E The maximum value of Hm,123 is located in the edge of the plot for the constituent binary comprising MTBE and the n-alkane. The two figures are very similar,
436
Z. Tong et al.
E FIGURE 2. Excess molar enthalpies Hm,1 for [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + + 23 (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K. Experimental results: r, x2/(1 − x1 − x2 ) = 3.0209; w, x2/(1 − x1 − x2 ) = 1.0179; t, x2/(1 − x1 − x2 ) = 0.3416. Curves: · — · —, x2 = 0, reference 8; ...., x1 + x2 = 1, reference 7; ————, calculated from the representation of the results by equations (2) E and (3), using the ternary contribution term Hm,T given in the footnote of table 4; ----, estimated from the Flory theory.
and in both cases contours which terminate only on the (methyl 1,1-dimethylethyl ether + n-alkane) edge are skewed towards the (diisopropyl ether + n-alkane) edge of the triangle. Previously,(7) for mixtures of alkanes and ethers, it was found that the Flory theory,(11, 12) as applied to multicomponent mixtures by Brostow and Sochanski(13) provided reasonable estimates of the ternary excess molar enthalpies, when only properties of the pure components and their binary mixtures were used. The same approach was investigated for the present mixtures. Since the treatment closely follows our previous work,(7) the equations are not repeated here. The characteristic values of the pressure p*, the molar volume V* m , and the temperature T* are listed in table 5 for each component. These were taken from
436
Z. Tong et al.
E FIGURE 2. Excess molar enthalpies Hm,1 for [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + + 23 (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K. Experimental results: r, x2/(1 − x1 − x2 ) = 3.0209; w, x2/(1 − x1 − x2 ) = 1.0179; t, x2/(1 − x1 − x2 ) = 0.3416. Curves: · — · —, x2 = 0, reference 8; ...., x1 + x2 = 1, reference 7; ————, calculated from the representation of the results by equations (2) E and (3), using the ternary contribution term Hm,T given in the footnote of table 4; ----, estimated from the Flory theory.
and in both cases contours which terminate only on the (methyl 1,1-dimethylethyl ether + n-alkane) edge are skewed towards the (diisopropyl ether + n-alkane) edge of the triangle. Previously,(7) for mixtures of alkanes and ethers, it was found that the Flory theory,(11, 12) as applied to multicomponent mixtures by Brostow and Sochanski(13) provided reasonable estimates of the ternary excess molar enthalpies, when only properties of the pure components and their binary mixtures were used. The same approach was investigated for the present mixtures. Since the treatment closely follows our previous work,(7) the equations are not repeated here. The characteristic values of the pressure p*, the molar volume V* m , and the temperature T* are listed in table 5 for each component. These were taken from
438
Z. Tong et al.
E FIGURE 4. Contours for constant values of Hm,123 /(J·mol−1 ) for [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K, calculated from the E evaluated from the footnote representation of the experimental results by equations (1) to (3) with Hm,T of table 4.
smooth representations of the results for the mixtures in tables 3 and 4. The results of the calculations for the nC7 mixture are shown on the Roozeboom diagram in figure 5. It is clear from a comparison of this with figure 3 that the Flory theory E provides useful estimates of Hm,123 without requiring the direct investigation of any ternary mixtures. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. TABLE 5. Pressure p*, molar volume V* m , and temperature T* used in Flory theory calculations at the temperature 298.15 K for [x1CH3(CH2 )5CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] a and [x1CH3(CH2 )8CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] b Component
p*/MPa
3 −1 V* ) m /(cm ·mol
T*/K
Reference no.
Heptane Decane Methyl 1,1-dimethylethyl ether Diisopropryl ether
431.9 447.0 442.9 447.9
113.60 155.75 90.20 106.50
4648.1 5091.4 4385.0 4335.2
Benson et al.(14) Benson et al.(14) Wang et al.(7) Zhu et al.(8)
Interchange-energy parameters Xij/(J·cm−3 ): 15.6509; X13 = 10.4782; X23 = 0.9228.
a
X12 = 15.0620; X13 = 8.4433; X23 = 0.9228;
b
X12 =
HmE of {(heptane or decane) methyl 1,1-dimethylethyl ether + diisoperopyl ether}
439
E FIGURE 5. Contours for constant values of Hm,123 /(J·mol−1 ) for [x1CH3(CH2 )5CH3 + x2(CH3 )3COCH3 + (1 − x1 − x2 )4(CH3 )2CH52O] at the temperature 298.15 K, estimated from the Flory theory.
REFERENCES 1. Tong, Z.; Benson, G. C.; Wang, L. L.; Lu, B. C.-Y. J. Chem. Eng. Data 1996, 41, 865–869. 2. TRC—Thermodynamic Tables—Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station, TX 77843-3111. 1988: Table 23-2-(1.101)-a, dated 31 October 1977. 3. TRC—Thermodynamic Tables—Non-Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station, TX 77843-3111. 1988: Tables 23-2-1-(1.2120)-a and 23-2-1-(1.2121)-a, dated 30 June 1963. 4. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163–175. 5. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245–250. 6. Oba, M.; Murakami, S.; Fujishiro, R. J. Chem. Thermodynamics 1977, 9, 407–414. 7. Wang, L.; Benson, G. C.; Lu, B. C.-Y. Thermochim. Acta 1993, 213, 83–93. 8. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1994, 26, 415–420. 9. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. Ser. No. 7 1953, 49, 107–117. 10. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403–405. 11. Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833–1838. 12. Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838–1846. 13. Brostow, W.; Sochanski, J. S. J. Mater. Sci. 1975, 10, 2134–2145. 14. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531–534.
(Received 4 September 1996; in final form 18 October 1996)
WE-075