- Email: [email protected]
Excess enthalpies of the ternary mixtures: {tetrahydrofuran + (2,2,4-trimethylpentane or heptane) + methylcyclohexane} at the temperature 298.15 K
J. Chem. Thermodynamics 2002, 34, 2073–2082 doi:10.1016/S0021-9614(02)00264-1 Available online at http://www.idealibrary.com on
Excess enthalpies of the ternary mixtures: {tetrahydrofuran + (2,2,4-trimethylpentane or heptane) + methylcyclohexane} at the temperature 298.15 K Zhaohui Wang, George C. Benson,a and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, 161 Louis Pasture St., Ottawa, Ont., Canada K1N 6N5
Measurements of excess molar enthalpies at the temperature 298.15 K in a flow microcalorimeter, are reported for the ternary mixtures fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g and fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 ÞC6 H11 CH3 g Smooth representations of the results are described and used to construct constantenthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the ternary enthalpies can be obtained from the Liebermann-Fried model, using only the physical properties of the components and their binary mixtures. Ó 2002 Elsevier Science Ltd. All rights reserved.
KEYWORDS: excess enthalpy; ternary mixture; tetrahydrofuran; 2,2,4-trimethylpentane; n-heptane; methylcyclohexane; Liebermann–Fried model
1. Introduction Adverse concerns regarding the use of methyl tert-butylether as a gasoline additive have provided an incentive to investigate the thermodynamic properties of other (oxygenate + hydrocarbon) mixtures. The present paper reports measurements of excess molar enthalpies at T ¼ 298:15 K for the two ternary mixtures formed by mixing tetrahydrofuran (THF) with binary mixtures of either 2,2,4-trimethylpentane (TMP) and methylcyclohexane (MCH) or n-heptane (nC7), and MCH.
2. Experimental The components, used in the present work, were obtained from the Aldrich Chemical. In all cases the mole fraction purities, stated by the manufacturer, exceeded 0.990. Apart a
To whom correspondence should be addressed (E-mail: [email protected]).
0021-9614/02/$ - see front matter
Ó 2002 Elsevier Science Ltd. All rights reserved.
Z. Wang et al.
2074
from partial degassing, the components were used without further purification. Densities qðT ¼ 298:15 KÞ=ðkg m3 Þ, measured in an Anton–Paar digital densimeter, were 882.09, 688.03, 680.17, and 765.11 for the THF, TMP, nC7, and MCH, respectively. These results agree within <0.1% with values in the literature.ð1;2Þ An LKB flow microcalorimeter (Model 10700-1), thermostatted at T ¼ ð298:150 0:003Þ K, was used to measure the excess molar enthalpies HEm . Details of the equipment and the operating procedure have been described previously.ð3;4Þ In studying the ternary mixtures, the excess molar enthalpy HEm;1þ23 was determined for several pseudo-binary mixtures in which component 1 (THF) was added to binary mixtures of TABLE 1. Mole fractions xi and experimental excess molar enthalpies HEm;ij for four of the constituent-binary mixtures at the temperature 298.15 K xi
E Hm;ij
xi 1
E Hm;ij
xi 1
J mol
E Hm;ij
xi 1
J mol
E Hm;ij
J mol1
J mol
THF(1) + TMP(2) 0.0499
123.43
0.2998
581.00
0.5496
709.07
0.7995
505.96
0.1000
237.71
0.3499
632.84
0.6004
705.19
0.8500
410.94
0.1498
341.65
0.4005
670.99
0.6496
674.81
0.9000
297.22
0.1998
434.35
0.4498
700.62
0.6998
637.42
0.9500
163.16
0.2499
515.59
0.4996
716.27
0.7498
579.91
0.0500
120.56
0.3002
525.15
0.4995
619.46
0.7505
476.60
0.1001
226.82
0.3511
566.26
0.5502
611.18
0.7996
411.87
0.1501
320.98
0.4005
592.62
0.6004
594.91
0.8501
329.37
0.2001
405.08
0.4059
597.00
0.6504
570.89
0.8997
232.36
0.2502
471.61
0.4504
613.41
0.6999
530.57
0.9499
128.04
0.0500
11.36
0.3003
47.39
0.5502
52.97
0.8002
33.57
0.1000
21.63
0.3503
50.86
0.6005
51.30
0.8500
26.75
0.1499
30.12
0.4001
53.04
0.6501
48.32
0.9000
19.33
0.2010
37.36
0.4502
54.29
0.7002
44.26
0.9500
11.57
0.2497
42.93
0.4997
54.39
0.7499
39.38
0.0999
276.82
0.3496
715.86
0.5502
787.82
0.8016
538.96
0.1498
394.01
0.3997
751.58
0.6000
767.97
0.8465
449.52
0.1998
496.73
0.4497
779.78
0.6498
739.63
0.9001
314.81
0.2498
583.62
0.4996
792.71
0.6999
692.93
0.9499
173.59
0.2996
655.69
0.5497
791.94
0.7499
625.67
THF(1) + MCH(3)
TMP(2) + MCH(3)
THF(1) + nC7(2)
Excess enthalpies of the ternary mixtures
2075
components 2 (either TMP or nC7) and 3 (MCH), having fixed compositions. For this purpose, binary mixtures with selected values of x2 =ð1 x1 x2 Þ were prepared by mass from partially degassed samples of the components. Weighings were made on a Mettler balance with a sensitivity of 0.01 mg. The excess molar enthalpy HEm;123 of the ternary mixture was then obtained from the relation E E E Hm;123 ¼ Hm;1þ123 þ ð1 x1 ÞHm;23 ;
ð1Þ
where HEm;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 < 0:005 jHEm j and < 5 104 , respectively.
3. Results and discussion Experimental values of xi and HEm;ij (i < j), measured at T ¼ 298:15 K, for four of the constituent-binary mixtures of present interest, THF(1) + TMP(2), THF(1) + MCH(3), TMP(2) + MCH(3), and THF(1) + nC7(2), are listed in table 1. Our results for THF(1) + nC7(2) are in close agreement with those reported by Inglese et al.ð5Þ The smoothing function E Hm;ij =ðJ mol1 Þ ¼ xi ð1 xi Þ
m X
hk ð1 2xi Þk1 ;
ð2Þ
k¼1
was fitted to the results in table 1 by the method of least-squares with all points weighted equally. The values of the coefficients hk , obtained from the analysis, are listed in table 2, along with the standard deviations s of the representations. Also included in table 2 are the coefficients reported by Wilhelm et al.ð6Þ for the representation of HEm;ij for the fifth constituent-binary, nC7(1) + MCH(3). TABLE 2. Parameters hk and standard deviations sa for the representation of HEm;ij ði < jÞ at T ¼ 298:15 K by equation (2) h1
Component
h2
h3
h4
s J mol1
i
j
THF
TMPb
2857.68
)298.73
210.11
THF
MCHb
2477.38
)37.37
167.34
2.26
TMP
MCHb
216.44
17.74
15.82
0.41
THF
b
nC7
3170.06
)176.85
217.47
MCHc
143.96
32.21
)184.72
)163.64
2.39
2.04
13.79 0.30 Pn 1=2 2 a E E Defined by the form s ¼ , where n is the number of experimental 1 fHm ðcalcÞ Hm ðexptÞg =ðn pÞ values and p is the number of parameters hk . b Present work. c Reference (6). nC7
Z. Wang et al.
2076
The experimental results for the two ternary mixtures are reported in tables 3 and 4, where values of HEm;1þ23 are listed against the mole fraction x1 of THF. Also included in those tables are the corresponding values of HEm;123 , calculated from equation (1), with values of HEm;23 obtained from equation (2) using the coefficients given in table 2. The results for HEm;1þ23 are plotted in figures 1 and 2. Also plotted in those figures are the results given in table 1 corresponding to the cases x2 ¼ 0 and x1 þ x2 ¼ 1. In all cases, TABLE 3. Experimental excess molar enthalpies HEm;1þ23 at the temperature 298.15 K for the addition of THF to (TMP + MCH) mixtures to form fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g, and values of HEm;123 calculated from equation (1) using the smooth representation of HEm;23 by equation (2) x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
E x2 =ð1 x1 x2 Þ ¼ 0:3334; Hm;23 =ðJ mol1 Þ ¼ 42:99
0.0499
125.14
165.98
0.4003
608.33
634.11
0.6996
551.86
564.77
0.1000
225.45
264.14
0.4498
628.88
652.53
0.7497
497.76
508.52
0.1499
325.82
362.37
0.4992
633.93
655.46
0.7998
430.19
438.80
0.2000
407.88
442.27
0.5501
634.74
654.08
0.8500
347.98
354.43
0.2499
475.99
508.24
0.6000
620.47
637.67
0.9004
247.00
251.28
0.2999
533.53
563.63
0.6498
591.96
607.01
0.9500
132.76
134.91
0.3500
576.08
604.02 E =ðJ mol1 Þ ¼ 54:11 x2 =ð1 x1 x2 Þ ¼ 0:9996; Hm;23
0.0501
130.49
181.89
0.4001
627.69
660.15
0.7003
577.91
594.13
0.1002
230.33
279.02
0.4500
648.26
678.02
0.7496
523.70
537.25
0.1501
329.70
375.69
0.5003
659.19
686.23
0.7997
453.26
464.10
0.2000
415.75
459.04
0.5495
662.33
686.71
0.8499
367.79
375.91
0.2501
490.22
530.80
0.6000
644.50
666.14
0.8997
264.54
269.97
0.3002
548.00
585.87
0.6501
620.09
639.02
0.9499
142.27
144.98
0.3499
597.75
632.92 E =ðJ mol1 Þ ¼ 39:67 x2 =ð1 x1 x2 Þ ¼ 2:9990; Hm;23
0.0501
131.83
169.51
0.4005
652.48
676.26
0.7000
607.05
618.95
0.1001
241.39
277.09
0.4501
676.06
697.87
0.7502
552.26
562.17
0.1501
343.12
376.83
0.5003
684.22
704.04
0.7999
480.01
487.95
0.2000
430.77
462.50
0.5504
687.83
705.66
0.8500
390.27
396.22
0.2501
507.15
536.90
0.6000
676.04
691.91
0.9001
280.95
284.91
0.3000
567.33
595.10
0.6503
648.93
662.80
0.9500
151.86
153.84
0.3501
618.15
643.93
a
Ternary term for representation of HEm;1þ23 by equations (3) and (4): HEm;T =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þ ð307:95 125:12x1 þ 794:66x2 Þ, s ¼ 2:37 J mol1 .
Excess enthalpies of the ternary mixtures
2077
the maximum values of HEm;1þ23 and HEm;123 occur near x1 ¼ 0:5. At constant x1 ; HEm;1þ23 increases as x2 =ð1 x1 x2 Þ increases and the increases are relatively more significant for the mixtures containing nC7. The values of HEm;1þ23 were represented as a sum of binary termsð7Þ with an added ternary contribution E E E E Hm;1þ23 ¼ fx2 =ð1 x1 ÞgHm;12 þ fð1 x1 x2 Þ=ð1 x1 ÞgHm;13 þ Hm;T ;
ð3Þ
TABLE 4. Experimental excess molar enthalpies HEm;1þ23 at the temperature 298.15 K for the addition of THF to (nC7 + MCH) mixtures to form fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 Þ C6 H11 CH3 g, and values of HEm;123 calculated from equation (1) using the smooth representation of HEm;23 by equation (2) x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
E x2 =ð1 x1 x2 Þ ¼ 0:3335; Hm;23 =ðJ mol1 Þ ¼ 30:66
0.0500
131.67
160.80
0.4001
640.13
658.52
0.7004
573.11
582.29
0.1000
241.41
269.00
0.4500
659.27
676.13
0.7498
517.25
524.92
0.1503
346.44
372.49
0.5005
669.53
684.84
0.8000
446.23
452.36
0.2001
432.44
456.96
0.5497
657.73
671.53
0.8500
360.12
364.72
0.2500
503.19
526.18
0.6000
647.39
659.65
0.9000
259.64
262.71
0.3001
563.66
585.12
0.6500
616.79
627.52
0.9501
137.77
139.30
0.3502
606.77
626.69 E =ðJ mol1 Þ ¼ 35:99 x2 =ð1 x1 x2 Þ ¼ 0:9996; Hm;23
0.0501
142.69
176.88
0.4004
683.59
705.17
0.7000
615.98
626.78
0.1000
248.86
281.25
0.4498
703.56
723.36
0.7499
555.72
564.72
0.1499
369.55
400.15
0.5001
708.82
726.81
0.8002
479.03
486.22
0.2000
461.86
490.65
0.5506
711.45
727.63
0.8500
386.87
392.27
0.2500
537.90
564.89
0.5998
688.97
703.37
0.9000
281.75
285.35
0.3000
602.98
628.17
0.6502
661.21
673.80
0.9501
148.89
150.69
0.3504
648.78
672.16 E =ðJ mol1 Þ ¼ 24:61 x2 =ð1 x1 x2 Þ ¼ 3:0032; Hm;23
0.0500
145.97
169.35
0.4002
724.48
739.24
0.6998
658.19
665.58
0.0999
276.35
298.50
0.4502
749.06
762.59
0.7502
594.33
600.48
0.1500
388.04
408.96
0.5001
760.08
772.38
0.7998
513.83
518.76
0.1999
491.27
510.96
0.5500
756.99
768.06
0.8500
415.09
418.78
0.2501
567.22
585.67
0.5998
733.90
743.75
0.9000
296.19
298.65
0.3002
634.94
652.16
0.6500
709.10
717.71
0.9500
158.91
160.14
0.3501
684.70
700.69
a Ternary term for representation of HEm;1þ23 by equations (3) and (4): HEm;T =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þð101:12 766:08x1 þ 830:50x2 þ 1474:33xÞ, s ¼ 2:99 J mol1 .
2078
Z. Wang et al.
FIGURE 1. Excess molar enthalpies, HEm;1þ23 , for fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (M) x2 =ð1 x1 x2 Þ ¼ 0:3334; (s) x2 =ð1 x1 x2 Þ ¼ 0:9996; (r) x2 =ð1 x1 x2 Þ ¼ 2:9990; (}) x1 þ x2 ¼ 1; () x2 ¼ 0. Curves: (–––) calculated from the representation of the results by equations (3) and (4), using the ternary term HEm;T given in the footnote of table 3; (- - -) estimated by the Liebermann–Fried model.
where the values of HEm;ij were calculated from the appropriate smoothing functions. The form E Hm;T =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þðc0 þ c1 x1 þ c2 x2 þ c3 x21 þ c4 x1 x2 þ c5 x22 þ Þ;
ð4Þ which was adopted for the latter contribution, is similar to the form used by Morris et al.ð8Þ Values of the coefficients ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to the values of HEm;1þ23 in tables 3 and 4. The resulting forms for HEm;T are given in the footnotes of those tables, along with the standard deviation s for each representation. The solid curves for HEm;1þ23 in figures 1 and 2 were calculated from equation (3) using these representations. Equations (1) to (4) were also used to calculate the constant HEm;123 contours plotted on the Roozeboom diagrams in figures 3a and 4a. In figure 3a, just inside the THF-TMP edge of the triangle, there is a very minor internal maximum to which no real significance should be attached. In figure 4a, all of the contours extend to the edges of the triangle, and there is no indication of an internal maximum.
Excess enthalpies of the ternary mixtures
2079
FIGURE 2. Excess molar enthalpies, HEm;1þ23 , for fx1 C4 H8 O þ x2 C7 H16 Þ þ ð1 x1 x2 Þ C6 H11 CH3 g at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (M) x2 =ð1 x1 x2 Þ ¼ 0:3335; (s) x2 =ð1 x1 x2 Þ ¼ 0:9996; (r) x2 =ð1 x1 x2 Þ ¼ 3:0032; (}) x1 þ x2 ¼ 1; () x2 ¼ 0. Curves: (–––) calculated from the representation of the results by equations (3) and (4), using the ternary term HEm;T given in the footnote of table 4; (- - -) estimated by the Liebermann–Fried model.
Recently,ð9Þ it was found that the Liebermann–Fried model,ð10;11Þ can be extended to provide estimates of the thermodynamic properties of multicomponent mixtures, using only the properties of the pure components and interaction parameters derived from analyses of the excess enthalpies of their constituent-binaries. This approach was investigated for the present ternary mixtures. Reference can be made to the work of Wang et al.ð9Þ for the equations used in this application. The values of the Liebermann–Fried interaction parameters Aij and Aji for the constituent-binaries are given in table 5. These were obtained by fitting the Liebermann– Fried formula for HEm;ij to the primary experimental results for the excess molar enthalpies, as given in table 1 and reference (6). Also included in that table are values of the standard deviations s achieved in the fitting process, and valuesð12;13;14Þ of the isobaric thermal expansivities ap , used in evaluating the contributions due to different sizes of the molecules. Estimates of HEm;1þ23 , derived from the Liebermann–Fried model, are shown as dashed curves in figures 1 and 2. In both cases, it can be seen that the theory predicts correctly
2080
Z. Wang et al.
FIGURE 3. Contours for constant values of HEm;123 =ðJ mol1 Þ for fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CH ðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g at the temperature 298.15 K. Part (a) calculated from the representation of the experimental results by equations (1) to (4) with HEm;T from the footnote of table 3; Part (b) estimated by the Liebermann–Fried model.
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 table 3 and table 4 are 6.8 J mol1 and 6.9 J mol1 , respectively.
Excess enthalpies of the ternary mixtures
2081
FIGURE 4. Contours for constant values of HEm;123 =ðJ mol1 Þ for fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 ÞC6 H11 CH3 g at the temperature 298.15 K. Part (a) calculated from the representation of the experimental results by equations (1) to (4) with HEm;T from the footnote of table 4; Part (b) estimated by the Liebermann–Fried model.
Constant HEm;123 contours, estimated on the basis of the model, are shown on the Roozeboom diagrams in figures 3b and 4b. In the figure 3b, it is interesting that the model also predicts a relatively insignificant internal maximun close to the THF-TMP edge of the
Z. Wang et al.
2082
TABLE 5. Values of the interaction parameters Aij and Aji , standard deviations s, and isobaric thermal expansivities ap at 298.15 K, in Liebermann-Fried model calculations for fx1 C4 H8 Oþ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g and fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 Þ C6 H11 CH3 g Aij
Component i
TMP
ap =kK1
s 1
ðJ mol Þ
j TMP
THF
Aji
MCH MCH
0.8960 0.8236 0.9015
0.6969 0.8002 1.0627
i
j
3.97
1.138a
1.197b
3.75
a
1.187a
b
1.187a
a
0.62
1.138 1.197
THF
nC7
0.8312
0.7219
3.72
1.138
1.256c
nC7
MCH
0.8836
1.1006
1.44
1.256c
1.187a
a
Reference (12). Reference (13). c Reference (14). b
triangle. It is clear from a comparison of the two parts in each figure, that the LiebermannFried model provides useful estimates of HEm;123 for both of the present mixtures. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. REFERENCES 1. TRC—Thermodynamic Tables—Non-Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1996: Table 23-2-1(3.2150)-a, dated 31 December 1985. 2. TRC—Thermodynamic Tables—Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1996: Table 23-2-(1.203)-a, dated 31 October 1990; Table 23-2-(1.10100)-a, page 1, dated 30 April 1995; Table 23-2-(3.1112)-a, dated 31 October 1952. 3. Tanaka, R.; DÕArcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163–175. 4. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245–250. 5. nglese, A.; Wilhelm, E.; Grolier, J.-P.E.; Kehiaian, H. V. J. Chem. Thermodyn. 1980, 12, 217–222. 6. Wilhelm, E.; Inglese, A.; Grolier, J.-P.E. Thermochim. Acta 1991, 187, 113–120. 7. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. 1953, 49(7), 107–117. 8. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403–405. 9. Wang, Z.; Peng, D.-Y.; Benson, G. C.; Lu, B.C.-Y. J. Chem. Thermodyn. 2001, 33, 1181–1191, doi:10.1006/jcht.2001.0831. 10. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 350–354. 11. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 354–355. 12. J.A. Riddick, W.B. Bunger, T.K. Sakano, Techniques of Chemistry, Volume II, Organic Solvents, 4th edition, Wiley, New York, 1986, pp. 100 and 309. 13. Rajagopal, E.; Subrahmanyam, S. V. J. Chem. Thermodyn. 1974, 6, 873–876. 14. Benson, G. C.; Luo, B.; Lu, B.C.-Y. Can. J. Chem. 1988, 66, 531–534. (Received 28 June 2002; in final form 12 August 2002)
WE-359
Excess enthalpies of the ternary mixtures: {tetrahydrofuran + (2,2,4-trimethylpentane or heptane) + methylcyclohexane} at the temperature 298.15 K Zhaohui Wang, George C. Benson,a and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, 161 Louis Pasture St., Ottawa, Ont., Canada K1N 6N5
Measurements of excess molar enthalpies at the temperature 298.15 K in a flow microcalorimeter, are reported for the ternary mixtures fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g and fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 ÞC6 H11 CH3 g Smooth representations of the results are described and used to construct constantenthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the ternary enthalpies can be obtained from the Liebermann-Fried model, using only the physical properties of the components and their binary mixtures. Ó 2002 Elsevier Science Ltd. All rights reserved.
KEYWORDS: excess enthalpy; ternary mixture; tetrahydrofuran; 2,2,4-trimethylpentane; n-heptane; methylcyclohexane; Liebermann–Fried model
1. Introduction Adverse concerns regarding the use of methyl tert-butylether as a gasoline additive have provided an incentive to investigate the thermodynamic properties of other (oxygenate + hydrocarbon) mixtures. The present paper reports measurements of excess molar enthalpies at T ¼ 298:15 K for the two ternary mixtures formed by mixing tetrahydrofuran (THF) with binary mixtures of either 2,2,4-trimethylpentane (TMP) and methylcyclohexane (MCH) or n-heptane (nC7), and MCH.
2. Experimental The components, used in the present work, were obtained from the Aldrich Chemical. In all cases the mole fraction purities, stated by the manufacturer, exceeded 0.990. Apart a
To whom correspondence should be addressed (E-mail: [email protected]).
0021-9614/02/$ - see front matter
Ó 2002 Elsevier Science Ltd. All rights reserved.
Z. Wang et al.
2074
from partial degassing, the components were used without further purification. Densities qðT ¼ 298:15 KÞ=ðkg m3 Þ, measured in an Anton–Paar digital densimeter, were 882.09, 688.03, 680.17, and 765.11 for the THF, TMP, nC7, and MCH, respectively. These results agree within <0.1% with values in the literature.ð1;2Þ An LKB flow microcalorimeter (Model 10700-1), thermostatted at T ¼ ð298:150 0:003Þ K, was used to measure the excess molar enthalpies HEm . Details of the equipment and the operating procedure have been described previously.ð3;4Þ In studying the ternary mixtures, the excess molar enthalpy HEm;1þ23 was determined for several pseudo-binary mixtures in which component 1 (THF) was added to binary mixtures of TABLE 1. Mole fractions xi and experimental excess molar enthalpies HEm;ij for four of the constituent-binary mixtures at the temperature 298.15 K xi
E Hm;ij
xi 1
E Hm;ij
xi 1
J mol
E Hm;ij
xi 1
J mol
E Hm;ij
J mol1
J mol
THF(1) + TMP(2) 0.0499
123.43
0.2998
581.00
0.5496
709.07
0.7995
505.96
0.1000
237.71
0.3499
632.84
0.6004
705.19
0.8500
410.94
0.1498
341.65
0.4005
670.99
0.6496
674.81
0.9000
297.22
0.1998
434.35
0.4498
700.62
0.6998
637.42
0.9500
163.16
0.2499
515.59
0.4996
716.27
0.7498
579.91
0.0500
120.56
0.3002
525.15
0.4995
619.46
0.7505
476.60
0.1001
226.82
0.3511
566.26
0.5502
611.18
0.7996
411.87
0.1501
320.98
0.4005
592.62
0.6004
594.91
0.8501
329.37
0.2001
405.08
0.4059
597.00
0.6504
570.89
0.8997
232.36
0.2502
471.61
0.4504
613.41
0.6999
530.57
0.9499
128.04
0.0500
11.36
0.3003
47.39
0.5502
52.97
0.8002
33.57
0.1000
21.63
0.3503
50.86
0.6005
51.30
0.8500
26.75
0.1499
30.12
0.4001
53.04
0.6501
48.32
0.9000
19.33
0.2010
37.36
0.4502
54.29
0.7002
44.26
0.9500
11.57
0.2497
42.93
0.4997
54.39
0.7499
39.38
0.0999
276.82
0.3496
715.86
0.5502
787.82
0.8016
538.96
0.1498
394.01
0.3997
751.58
0.6000
767.97
0.8465
449.52
0.1998
496.73
0.4497
779.78
0.6498
739.63
0.9001
314.81
0.2498
583.62
0.4996
792.71
0.6999
692.93
0.9499
173.59
0.2996
655.69
0.5497
791.94
0.7499
625.67
THF(1) + MCH(3)
TMP(2) + MCH(3)
THF(1) + nC7(2)
Excess enthalpies of the ternary mixtures
2075
components 2 (either TMP or nC7) and 3 (MCH), having fixed compositions. For this purpose, binary mixtures with selected values of x2 =ð1 x1 x2 Þ were prepared by mass from partially degassed samples of the components. Weighings were made on a Mettler balance with a sensitivity of 0.01 mg. The excess molar enthalpy HEm;123 of the ternary mixture was then obtained from the relation E E E Hm;123 ¼ Hm;1þ123 þ ð1 x1 ÞHm;23 ;
ð1Þ
where HEm;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 < 0:005 jHEm j and < 5 104 , respectively.
3. Results and discussion Experimental values of xi and HEm;ij (i < j), measured at T ¼ 298:15 K, for four of the constituent-binary mixtures of present interest, THF(1) + TMP(2), THF(1) + MCH(3), TMP(2) + MCH(3), and THF(1) + nC7(2), are listed in table 1. Our results for THF(1) + nC7(2) are in close agreement with those reported by Inglese et al.ð5Þ The smoothing function E Hm;ij =ðJ mol1 Þ ¼ xi ð1 xi Þ
m X
hk ð1 2xi Þk1 ;
ð2Þ
k¼1
was fitted to the results in table 1 by the method of least-squares with all points weighted equally. The values of the coefficients hk , obtained from the analysis, are listed in table 2, along with the standard deviations s of the representations. Also included in table 2 are the coefficients reported by Wilhelm et al.ð6Þ for the representation of HEm;ij for the fifth constituent-binary, nC7(1) + MCH(3). TABLE 2. Parameters hk and standard deviations sa for the representation of HEm;ij ði < jÞ at T ¼ 298:15 K by equation (2) h1
Component
h2
h3
h4
s J mol1
i
j
THF
TMPb
2857.68
)298.73
210.11
THF
MCHb
2477.38
)37.37
167.34
2.26
TMP
MCHb
216.44
17.74
15.82
0.41
THF
b
nC7
3170.06
)176.85
217.47
MCHc
143.96
32.21
)184.72
)163.64
2.39
2.04
13.79 0.30 Pn 1=2 2 a E E Defined by the form s ¼ , where n is the number of experimental 1 fHm ðcalcÞ Hm ðexptÞg =ðn pÞ values and p is the number of parameters hk . b Present work. c Reference (6). nC7
Z. Wang et al.
2076
The experimental results for the two ternary mixtures are reported in tables 3 and 4, where values of HEm;1þ23 are listed against the mole fraction x1 of THF. Also included in those tables are the corresponding values of HEm;123 , calculated from equation (1), with values of HEm;23 obtained from equation (2) using the coefficients given in table 2. The results for HEm;1þ23 are plotted in figures 1 and 2. Also plotted in those figures are the results given in table 1 corresponding to the cases x2 ¼ 0 and x1 þ x2 ¼ 1. In all cases, TABLE 3. Experimental excess molar enthalpies HEm;1þ23 at the temperature 298.15 K for the addition of THF to (TMP + MCH) mixtures to form fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g, and values of HEm;123 calculated from equation (1) using the smooth representation of HEm;23 by equation (2) x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
E x2 =ð1 x1 x2 Þ ¼ 0:3334; Hm;23 =ðJ mol1 Þ ¼ 42:99
0.0499
125.14
165.98
0.4003
608.33
634.11
0.6996
551.86
564.77
0.1000
225.45
264.14
0.4498
628.88
652.53
0.7497
497.76
508.52
0.1499
325.82
362.37
0.4992
633.93
655.46
0.7998
430.19
438.80
0.2000
407.88
442.27
0.5501
634.74
654.08
0.8500
347.98
354.43
0.2499
475.99
508.24
0.6000
620.47
637.67
0.9004
247.00
251.28
0.2999
533.53
563.63
0.6498
591.96
607.01
0.9500
132.76
134.91
0.3500
576.08
604.02 E =ðJ mol1 Þ ¼ 54:11 x2 =ð1 x1 x2 Þ ¼ 0:9996; Hm;23
0.0501
130.49
181.89
0.4001
627.69
660.15
0.7003
577.91
594.13
0.1002
230.33
279.02
0.4500
648.26
678.02
0.7496
523.70
537.25
0.1501
329.70
375.69
0.5003
659.19
686.23
0.7997
453.26
464.10
0.2000
415.75
459.04
0.5495
662.33
686.71
0.8499
367.79
375.91
0.2501
490.22
530.80
0.6000
644.50
666.14
0.8997
264.54
269.97
0.3002
548.00
585.87
0.6501
620.09
639.02
0.9499
142.27
144.98
0.3499
597.75
632.92 E =ðJ mol1 Þ ¼ 39:67 x2 =ð1 x1 x2 Þ ¼ 2:9990; Hm;23
0.0501
131.83
169.51
0.4005
652.48
676.26
0.7000
607.05
618.95
0.1001
241.39
277.09
0.4501
676.06
697.87
0.7502
552.26
562.17
0.1501
343.12
376.83
0.5003
684.22
704.04
0.7999
480.01
487.95
0.2000
430.77
462.50
0.5504
687.83
705.66
0.8500
390.27
396.22
0.2501
507.15
536.90
0.6000
676.04
691.91
0.9001
280.95
284.91
0.3000
567.33
595.10
0.6503
648.93
662.80
0.9500
151.86
153.84
0.3501
618.15
643.93
a
Ternary term for representation of HEm;1þ23 by equations (3) and (4): HEm;T =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þ ð307:95 125:12x1 þ 794:66x2 Þ, s ¼ 2:37 J mol1 .
Excess enthalpies of the ternary mixtures
2077
the maximum values of HEm;1þ23 and HEm;123 occur near x1 ¼ 0:5. At constant x1 ; HEm;1þ23 increases as x2 =ð1 x1 x2 Þ increases and the increases are relatively more significant for the mixtures containing nC7. The values of HEm;1þ23 were represented as a sum of binary termsð7Þ with an added ternary contribution E E E E Hm;1þ23 ¼ fx2 =ð1 x1 ÞgHm;12 þ fð1 x1 x2 Þ=ð1 x1 ÞgHm;13 þ Hm;T ;
ð3Þ
TABLE 4. Experimental excess molar enthalpies HEm;1þ23 at the temperature 298.15 K for the addition of THF to (nC7 + MCH) mixtures to form fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 Þ C6 H11 CH3 g, and values of HEm;123 calculated from equation (1) using the smooth representation of HEm;23 by equation (2) x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
x1
E a Hm;1þ23
E Hm;123
J mol1
J mol1
E x2 =ð1 x1 x2 Þ ¼ 0:3335; Hm;23 =ðJ mol1 Þ ¼ 30:66
0.0500
131.67
160.80
0.4001
640.13
658.52
0.7004
573.11
582.29
0.1000
241.41
269.00
0.4500
659.27
676.13
0.7498
517.25
524.92
0.1503
346.44
372.49
0.5005
669.53
684.84
0.8000
446.23
452.36
0.2001
432.44
456.96
0.5497
657.73
671.53
0.8500
360.12
364.72
0.2500
503.19
526.18
0.6000
647.39
659.65
0.9000
259.64
262.71
0.3001
563.66
585.12
0.6500
616.79
627.52
0.9501
137.77
139.30
0.3502
606.77
626.69 E =ðJ mol1 Þ ¼ 35:99 x2 =ð1 x1 x2 Þ ¼ 0:9996; Hm;23
0.0501
142.69
176.88
0.4004
683.59
705.17
0.7000
615.98
626.78
0.1000
248.86
281.25
0.4498
703.56
723.36
0.7499
555.72
564.72
0.1499
369.55
400.15
0.5001
708.82
726.81
0.8002
479.03
486.22
0.2000
461.86
490.65
0.5506
711.45
727.63
0.8500
386.87
392.27
0.2500
537.90
564.89
0.5998
688.97
703.37
0.9000
281.75
285.35
0.3000
602.98
628.17
0.6502
661.21
673.80
0.9501
148.89
150.69
0.3504
648.78
672.16 E =ðJ mol1 Þ ¼ 24:61 x2 =ð1 x1 x2 Þ ¼ 3:0032; Hm;23
0.0500
145.97
169.35
0.4002
724.48
739.24
0.6998
658.19
665.58
0.0999
276.35
298.50
0.4502
749.06
762.59
0.7502
594.33
600.48
0.1500
388.04
408.96
0.5001
760.08
772.38
0.7998
513.83
518.76
0.1999
491.27
510.96
0.5500
756.99
768.06
0.8500
415.09
418.78
0.2501
567.22
585.67
0.5998
733.90
743.75
0.9000
296.19
298.65
0.3002
634.94
652.16
0.6500
709.10
717.71
0.9500
158.91
160.14
0.3501
684.70
700.69
a Ternary term for representation of HEm;1þ23 by equations (3) and (4): HEm;T =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þð101:12 766:08x1 þ 830:50x2 þ 1474:33xÞ, s ¼ 2:99 J mol1 .
2078
Z. Wang et al.
FIGURE 1. Excess molar enthalpies, HEm;1þ23 , for fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (M) x2 =ð1 x1 x2 Þ ¼ 0:3334; (s) x2 =ð1 x1 x2 Þ ¼ 0:9996; (r) x2 =ð1 x1 x2 Þ ¼ 2:9990; (}) x1 þ x2 ¼ 1; () x2 ¼ 0. Curves: (–––) calculated from the representation of the results by equations (3) and (4), using the ternary term HEm;T given in the footnote of table 3; (- - -) estimated by the Liebermann–Fried model.
where the values of HEm;ij were calculated from the appropriate smoothing functions. The form E Hm;T =ðJ mol1 Þ ¼ x1 x2 ð1 x1 x2 Þðc0 þ c1 x1 þ c2 x2 þ c3 x21 þ c4 x1 x2 þ c5 x22 þ Þ;
ð4Þ which was adopted for the latter contribution, is similar to the form used by Morris et al.ð8Þ Values of the coefficients ci were obtained from least-squares analyses in which equations (3) and (4) were fitted to the values of HEm;1þ23 in tables 3 and 4. The resulting forms for HEm;T are given in the footnotes of those tables, along with the standard deviation s for each representation. The solid curves for HEm;1þ23 in figures 1 and 2 were calculated from equation (3) using these representations. Equations (1) to (4) were also used to calculate the constant HEm;123 contours plotted on the Roozeboom diagrams in figures 3a and 4a. In figure 3a, just inside the THF-TMP edge of the triangle, there is a very minor internal maximum to which no real significance should be attached. In figure 4a, all of the contours extend to the edges of the triangle, and there is no indication of an internal maximum.
Excess enthalpies of the ternary mixtures
2079
FIGURE 2. Excess molar enthalpies, HEm;1þ23 , for fx1 C4 H8 O þ x2 C7 H16 Þ þ ð1 x1 x2 Þ C6 H11 CH3 g at the temperature 298.15 K plotted against mole factor x1 . Experimental results: (M) x2 =ð1 x1 x2 Þ ¼ 0:3335; (s) x2 =ð1 x1 x2 Þ ¼ 0:9996; (r) x2 =ð1 x1 x2 Þ ¼ 3:0032; (}) x1 þ x2 ¼ 1; () x2 ¼ 0. Curves: (–––) calculated from the representation of the results by equations (3) and (4), using the ternary term HEm;T given in the footnote of table 4; (- - -) estimated by the Liebermann–Fried model.
Recently,ð9Þ it was found that the Liebermann–Fried model,ð10;11Þ can be extended to provide estimates of the thermodynamic properties of multicomponent mixtures, using only the properties of the pure components and interaction parameters derived from analyses of the excess enthalpies of their constituent-binaries. This approach was investigated for the present ternary mixtures. Reference can be made to the work of Wang et al.ð9Þ for the equations used in this application. The values of the Liebermann–Fried interaction parameters Aij and Aji for the constituent-binaries are given in table 5. These were obtained by fitting the Liebermann– Fried formula for HEm;ij to the primary experimental results for the excess molar enthalpies, as given in table 1 and reference (6). Also included in that table are values of the standard deviations s achieved in the fitting process, and valuesð12;13;14Þ of the isobaric thermal expansivities ap , used in evaluating the contributions due to different sizes of the molecules. Estimates of HEm;1þ23 , derived from the Liebermann–Fried model, are shown as dashed curves in figures 1 and 2. In both cases, it can be seen that the theory predicts correctly
2080
Z. Wang et al.
FIGURE 3. Contours for constant values of HEm;123 =ðJ mol1 Þ for fx1 C4 H8 O þ x2 ðCH3 Þ3 CCH2 CH ðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g at the temperature 298.15 K. Part (a) calculated from the representation of the experimental results by equations (1) to (4) with HEm;T from the footnote of table 3; Part (b) estimated by the Liebermann–Fried model.
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 table 3 and table 4 are 6.8 J mol1 and 6.9 J mol1 , respectively.
Excess enthalpies of the ternary mixtures
2081
FIGURE 4. Contours for constant values of HEm;123 =ðJ mol1 Þ for fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 ÞC6 H11 CH3 g at the temperature 298.15 K. Part (a) calculated from the representation of the experimental results by equations (1) to (4) with HEm;T from the footnote of table 4; Part (b) estimated by the Liebermann–Fried model.
Constant HEm;123 contours, estimated on the basis of the model, are shown on the Roozeboom diagrams in figures 3b and 4b. In the figure 3b, it is interesting that the model also predicts a relatively insignificant internal maximun close to the THF-TMP edge of the
Z. Wang et al.
2082
TABLE 5. Values of the interaction parameters Aij and Aji , standard deviations s, and isobaric thermal expansivities ap at 298.15 K, in Liebermann-Fried model calculations for fx1 C4 H8 Oþ x2 ðCH3 Þ3 CCH2 CHðCH3 Þ2 þ ð1 x1 x2 ÞC6 H11 CH3 g and fx1 C4 H8 O þ x2 C7 H16 þ ð1 x1 x2 Þ C6 H11 CH3 g Aij
Component i
TMP
ap =kK1
s 1
ðJ mol Þ
j TMP
THF
Aji
MCH MCH
0.8960 0.8236 0.9015
0.6969 0.8002 1.0627
i
j
3.97
1.138a
1.197b
3.75
a
1.187a
b
1.187a
a
0.62
1.138 1.197
THF
nC7
0.8312
0.7219
3.72
1.138
1.256c
nC7
MCH
0.8836
1.1006
1.44
1.256c
1.187a
a
Reference (12). Reference (13). c Reference (14). b
triangle. It is clear from a comparison of the two parts in each figure, that the LiebermannFried model provides useful estimates of HEm;123 for both of the present mixtures. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. REFERENCES 1. TRC—Thermodynamic Tables—Non-Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1996: Table 23-2-1(3.2150)-a, dated 31 December 1985. 2. TRC—Thermodynamic Tables—Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1996: Table 23-2-(1.203)-a, dated 31 October 1990; Table 23-2-(1.10100)-a, page 1, dated 30 April 1995; Table 23-2-(3.1112)-a, dated 31 October 1952. 3. Tanaka, R.; DÕArcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163–175. 4. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245–250. 5. nglese, A.; Wilhelm, E.; Grolier, J.-P.E.; Kehiaian, H. V. J. Chem. Thermodyn. 1980, 12, 217–222. 6. Wilhelm, E.; Inglese, A.; Grolier, J.-P.E. Thermochim. Acta 1991, 187, 113–120. 7. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. 1953, 49(7), 107–117. 8. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403–405. 9. Wang, Z.; Peng, D.-Y.; Benson, G. C.; Lu, B.C.-Y. J. Chem. Thermodyn. 2001, 33, 1181–1191, doi:10.1006/jcht.2001.0831. 10. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 350–354. 11. Liebermann, E.; Fried, V. Ind. Eng. Chem. Fundam. 1972, 11, 354–355. 12. J.A. Riddick, W.B. Bunger, T.K. Sakano, Techniques of Chemistry, Volume II, Organic Solvents, 4th edition, Wiley, New York, 1986, pp. 100 and 309. 13. Rajagopal, E.; Subrahmanyam, S. V. J. Chem. Thermodyn. 1974, 6, 873–876. 14. Benson, G. C.; Luo, B.; Lu, B.C.-Y. Can. J. Chem. 1988, 66, 531–534. (Received 28 June 2002; in final form 12 August 2002)
WE-359