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Excess enthalpies of (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane or cyclohexane + decane) at the temperature 298.15 K
M-3117 J. Chem. Thermodynamics 1995, 27, 531–539
Excess enthalpies of (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane or cyclohexane+ decane) at the temperature 298.15 K Andjela Knezˇevic´-Stevanovic´, George C. Benson, and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
(Received 26 November 1994) Microcalorimetric measurements of excess enthalpies at the temperature 298.15 K are reported for the two ternary mixtures (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane + decane) and (methyl 1,1-dimethylpropyl ether + cyclohexane + decane). Smooth representations of the results are presented and used to construct constant-enthalpy contours on Roozeboom diagrams. Comparisons of the experimental results with estimates based on the Flory theory of mixtures are also described.
1. Introduction The thermodynamic properties of mixtures of {methyl 1,1-dimethylpropyl ether (tert-amyl methyl ether) + a hydrocarbon} are of interest, in view of the use of the ether as a blending agent in oxygenated gasolines. A recent paper(1) from our laboratory described microcalorimetric measurements of the excess enthalpies of the ternary mixture (methyl 1,1-dimethylpropyl ether + hexane + decane) at the temperature T=298.15 K. As an extension of that earlier investigation, we have now measured excess enthalpies at T=298.15 K for the two ternary mixtures (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane + decane) and (methyl 1,1-dimethylpropyl ether + cyclohexane + decane), in which different C6-hydrocarbons replace the hexane used previously.
2. Experimental Pure-Grade CH3CH(CH3 )CH(CH3 )CH3 and Research-Grade c-(CH2 )6 from the Phillips Chemical Co., were used in the present work. The CH3(CH2 )8CH3 was obtained from the Aldrich Chemical Co. The stated mole-fraction purities of all of the hydrocarbons were at least 0.990. The CH3 OC(CH3 )2 C2 H5 (Fluka, purum) had a stated mole-fraction purity exceeding 0.970. All of the components were used without further 0021–9614/95/050531+09 $08.00/0
7 1995 Academic Press Limited
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purification. Values of r(T=298.15 K)/(kg·m−3 ), where r denotes density, measured in an Anton-Paar densimeter, were 657.14, 774.01, 726.40, and 765.91 for CH3CH(CH3 )CH(CH3 )CH3 , c-(CH2 )6 , CH3(CH2 )8CH3 , and CH3 OC(CH3 )2C2 H5 , respectively. These values are in reasonable agreement with the values compiled by the TRC.(2, 3) The excess molar enthalpy HmE was measured in an LKB flow microcalorimeter (Model 10700-1), thermostatted at T=(298.1520.002) K. Previous publications(4, 5) have described this equipment and the operating procedure. In studying the ternary mixtures [x1 CH3 OC(CH3 )2C2 H5 + x2 {CH3CH(CH3 )CH(CH3 )CH3 or c-(CH2 )6 } + E (1−x1−x2 )CH3(CH2 )8CH3 ], the excess molar enthalpies Hm, 1+23 were measured for several pseudo-binary mixtures in which the ether (compound 1) was added to binary mixtures of components 2 (2,3-dimethylbutane or cyclohexane) and 3 (decane) having a fixed mole ratio x2 /(1−x1−x2 ). These binaries were prepared by weighing. The
E TABLE 1. Experimental excess molar enthalpies Hm, 1+23 at the temperature 298.15 K for the addition of CH3 OC(CH3 )2 C2 H5 to {x2 CH3 CH(CH3 )CH(CH3 )CH3 + (1−x2 )CH3 (CH2 )8 CH3 } to form {x1 CH3 OC(CH3 )2 C2 H5+x2 CH3 CH(CH3 )CH(CH3 )CH3+(1−x1−x2 )CH3 (CH2 )8 CH3 }, and values of E E Hm, 123 calculated from equation (1) using Hm, 23 from reference 6
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
0.0500 0.1000 0.1500 0.2004 0.2501 0.3000 0.3498
61.0 114.5 163.8 205.0 243.0 274.7 298.0
E −1 x2 /(1−x1−x2 )=0.3266, Hm, )=33.9 23 /(J·mol 93.2 0.3999 317.1 337.4 0.7004 144.9 0.4497 329.2 347.8 0.7499 192.6 0.5003 335.1 352.0 0.8001 232.1 0.5500 335.2 350.5 0.8500 268.4 0.6003 327.5 341.1 0.9042 298.4 0.6503 314.2 326.0 0.9500 320.0
292.6 265.0 228.4 182.4 124.3 68.2
302.8 273.4 235.1 187.5 127.5 69.9
0.0499 0.1000 0.1500 0.2000 0.2501 0.2998 0.3500
56.9 106.3 150.3 188.8 221.9 250.5 271.6
E −1 x2 /(1−x1−x2 )=0.9739, Hm, )=46.7 23 /(J·mol 101.3 0.4002 287.4 315.4 0.6997 148.4 0.4501 297.4 323.1 0.7497 190.0 0.4996 300.4 323.8 0.8001 226.1 0.5501 299.0 320.0 0.8500 257.0 0.6001 290.9 309.6 0.9000 283.3 0.6498 277.1 293.4 0.9500 302.0
256.9 231.0 197.7 157.5 111.8 58.1
270.9 242.7 207.0 164.6 116.4 60.4
0.0500 0.1000 0.1500 0.2000 0.2498 0.3002 0.3506
52.8 99.4 140.7 174.7 204.5 227.9 246.6
E −1 x2 /(1−x1−x2 )=2.9968, Hm, )=36.0 23 /(J·mol 87.0 0.4002 258.9 280.4 0.7001 131.8 0.4500 266.4 286.2 0.7500 171.3 0.5000 269.2 287.2 0.8001 203.5 0.5505 265.6 281.8 0.8500 231.5 0.6000 257.6 272.0 0.9000 253.1 0.6500 243.6 256.2 0.9500 270.0
224.6 200.1 169.4 135.4 95.8 49.8
235.4 209.0 176.6 140.8 99.4 51.6
E E a −1 Ternary term for representation of Hm, by equations (2) and (3): Hm, )= 1+23 T /(J·mol x1 x2(1 − x1 − x2 )(−904.8 + 1193.8x1 + 2137.5x2 − 166.1x12 − 4991.0x1 x2 − 1257.2x22 − 2577.1x13 + 8387.3x12 x2), s=1.1.
533
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5
E TABLE 2. Experimental excess molar enthalpies Hm, 1+23 at the temperature 298.15 K for the addition of CH3 OC(CH3 )2 C2 H5 to {x2 c-(CH2 )6 + (1−x2 )CH3 (CH2 )8 CH3 } to form {x1 CH3 OC(CH3 )2 C2 H5 + E E x2 c-(CH2 )6 + (1−x1−x2 )CH3 (CH2 )8 CH3 }, and values of Hm, 123 calculated from equation (1) using Hm, 23 from reference 7
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
0.0500 0.1000 0.1499 0.2001 0.2501 0.2986 0.3503
61.3 112.9 159.9 201.5 237.4 266.9 290.2
E −1 x2 /(1−x1−x2 )=0.3340, Hm, )=203.5 23 /(J·mol 254.7 0.3999 308.4 430.6 0.7001 296.1 0.4499 320.4 432.4 0.7500 332.9 0.4997 326.0 427.8 0.8009 364.3 0.5501 325.1 416.7 0.8500 390.0 0.6000 317.8 399.2 0.9000 409.6 0.6508 304.0 375.1 0.9500 422.4
283.8 256.3 219.2 176.1 124.9 65.3
344.8 307.1 259.8 206.7 145.3 75.4
0.0500 0.1000 0.1500 0.2000 0.2499 0.3000 0.3500
57.9 108.2 154.1 192.4 225.4 251.2 272.6
E −1 x2 /(1−x1−x2 )=0.9504, Hm, )=316.0 23 /(J·mol 358.1 0.4002 287.9 477.4 0.6997 392.6 0.4502 297.2 470.9 0.7498 422.6 0.5000 300.4 458.4 0.8001 445.1 0.5499 297.7 439.9 0.8501 462.4 0.5999 289.5 415.9 0.8999 472.3 0.6502 274.4 384.9 0.9500 478.0
254.4 230.3 195.3 155.6 109.6 57.5
349.2 309.3 258.5 202.9 141.2 73.3
0.0499 0.1000 0.1500 0.1999 0.2500 0.2998 0.3504
60.9 115.9 162.8 202.4 236.3 263.0 283.0
E −1 x2 /(1−x1−x2 )=2.8339, Hm, )=296.8 23 /(J·mol 342.9 0.3999 296.7 474.9 0.6996 383.0 0.4498 304.5 467.8 0.7524 415.0 0.4997 305.4 453.8 0.8000 439.9 0.5502 301.0 434.5 0.8500 458.9 0.6004 291.3 409.9 0.9000 470.8 0.6495 275.2 379.2 0.9500 475.8
253.5 222.2 191.6 151.7 106.2 55.4
342.6 295.7 250.9 196.2 135.8 70.3
E E a −1 Ternary term for representation of Hm, by equations (2) and (3): Hm, )= 1+23 T /(J·mol x1 x2 (1 − x1 − x2 )(12.2 − 20610.9x1 − 2008.9x2 + 56460.2x12 + 34090.1x1 x2 − 840.5x22 − 50319.4x13 − 2 2 51771.1x1 x2−26240.1x1 x2 ), s=4.0.
E excess molar enthalpy Hm, 123 of the ternary mixture was then obtained from the relation: E E E Hm, 123=Hm, 1+23+(1−x1 )Hm, 23 ,
(1)
E m, 23
where H is the excess molar enthalpy of the particular binary mixture. E Values of Hm, 23 for {x2CH3CH(CH3 )CH(CH3 )CH3 + (1−x2 )CH3(CH2 )8CH3 } and {x2 c-(CH2 )6 + (1−x2 )CH3(CH2 )8CH3 } were taken from the literature.(6, 7) 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 E The experimental results for Hm, 1+23 and the corresponding values of Hm, 123 are listed E in tables 1 and 2 for the two ternary mixtures. Plots of the values of Hm, 1+23 against
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A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
x1 for the various constant values of x2 /(1−x1−x2 ) are shown in figures 1 and 2. Also included in these figures are curves for the constituent binaries having x2=0 and (x1+x2 )=1, taken from our previous work.(8, 9) E The Hm, 1+23 results for the mixtures containing CH3CH(CH3 )CH(CH3 )CH3 in figure 1 are nearly symmetric about x1=0.5, and fall between the curves for x2=0 and E (x1+x2 )=1. Hm, 1+23 for a fixed x1 increases as the ratio x2 /(1−x1−x2 ) decreases. In figure 2, the behaviour of the results for the mixtures containing c-(CH2 )6 is quite E different. All of the Hm, 1+23 values fall below the curves for the two constituent binaries, E and Hm, 1+23 does not vary monotonically with x2 /(1−x1−x2 ). Apart from
E FIGURE 1. Excess molar enthalpies Hm,1+23 for {x1 CH3 OC(CH3 )2 C2 H5 + x2 CH3 CH(CH3 )CH(CH3 )CH3 + (1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K. Experimental results: r, x2 /(1−x1−x2 )=0.3266; w, x2 /(1−x1−x2 )=0.9739; t, x2 /(1−x1−x2 )=2.9968. ····, x2=0 (reference 9); ·–·–·–, (x1+x2 )=1 (reference E 8); ——, calculated from the representation of the results by equations (2) and (3), using the ternary term Hm,T given in the footnote of table 1; ----, estimated from the Flory theory.
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5
535
E FIGURE 2. Excess molar enthalpies Hm, for {x1 CH3 OC(CH3 )2 C2 H5 + x2 c-(CH2 )6 + 1+23 (1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K. Experimental results: r, x2 /(1−x1−x2 )= 0.3340; w, x2 /(1−x1−x2 )=0.9504; t, x2 /(1−x1−x2 )=2.8339. ····, x2=0 (reference 9); ·–·–·–, (x1+x2 )=1 (reference 8); ——, calculated from the representation of the results by equations (2) and (3), using the E ternary term Hm,T given in the footnote of table 2; ----, estimated from the Flory theory.
this unusual variation, the characteristics of the present results in figures 1 and 2 are qualitatively similar to those found previously(10) for the analogous mixtures containing methyl 1,1-dimethylethyl ether (methyl tert-butyl ether) in place of methyl 1,1-dimethylpropyl ether. E (11) The values of Hm, with an added 1+23 were represented as a sum of binary terms ternary contribution: E E E E Hm, 1+23={x2 /(1−x1 )}Hm, 12+{(1−x1−x2 )/(1−x1 )}Hm, 13+Hm, T ,
(2)
E where the values of Hm, 1j were calculated from the smoothing functions reported
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A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
previously.(8, 9) Following Morris et al.,(12) the ternary term was assumed to have the form: E −1 Hm, )=x1 x2(1−x1−x2 )(c0+c1 x1+c2 x2+c3 x12+ T /(J·mol
c4 x1 x2+c5 x22+c6 x13+c7 x12 x2+c8 x1 x22+··· ).
(3)
Values of the parameters ci were obtained from least-squares analyses in which E equations (2) and (3) were fitted to the experimental results for Hm, 1+23 in tables 1 and 2. These representations are given in the footnotes of the tables, along with their standard deviations s. The continuous curves in figures 1 and 2 were calculated from these representations. The value of s for the cyclohexane mixture is larger than that for the 2,3-dimethylbutane mixture; nevertheless the representation given in the E footnote of table 2 should provide useful estimates of the variation of Hm, 123 with composition for that mixture. E Equations (1) to (3) were used to calculate the constant-Hm, 123 contours plotted on the Roozeboom diagrams shown in figures 3 and 4. All of the contours
E −1 FIGURE 3. Contours for constant values of Hm, ) for {x1 CH3 OC(CH3 )2 C2 H5 + 123 /(J·mol x2 CH3 CH(CH3 )CH(CH3 )CH3+(1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K, calculated from E the representation of our experimental results by equations (1) to (3) with Hm, T from the footnote of table 1.
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5
537
E −1 FIGURE 4. Contours for constant values of Hm, ) for {x1 CH3 OC(CH3 )2 C2 H5 + 123/(J·mol x2 c-(CH2 )6+(1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K, calculated from the representation E of our experimental results by equations (1) to (3) with Hm, T from the footnote of table 2.
for the 2,3-dimethylbutane mixture in figure 3 extend to the edges of the triangle, E and the maximum value of Hm, 123 is located in the x2=0 edge. Previously for the analogous mixture containing methyl 1,1-dimethylethyl ether(10) instead of methyl 1,1-dimethylpropyl ether, the maximum was inside the triangle but close to the corresponding edge. The shapes of the contours in figure 3 are more similar to those found for {x1CH3 OC(CH3 )2C2 H5 + x2CH3(CH2 )4CH3 + (1−x1−x2 )CH3(CH2) 8CH3 }.(1) For the mixture containing c-(CH2 )6 in figure 4, the maximum is located near the centroid of the triangle, and the general characteristics of the diagram resemble those of the corresponding mixture containing CH3 OC(CH3 )2CH3 . (10) In the case of [x1CH3 OC(CH3 )2CH3 + x2 {CH3CH(CH3 )CH(CH3 )CH3 or c-(CH2 )6 } + (1−x1−x2 )CH3(CH2 )8CH3 ], (10) the Flory theory,(13, 14) as applied to ternary mixtures by Brostow and Sochanski,(15) provided reasonable estimates of the ternary 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 equations for this treatment have been outlined in a previous publication,(16) they will not be repeated here.
538
A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
TABLE 3 Parameters used in Flory-theory calculations at T=298.15 K for {x1 CH3 OC(CH3 )2 C2 H5 (1) + x2 CH3 CH(CH3 )CH(CH3 )CH3 (2)a or x2 c-(CH2 )6 (2)b + (1−x1−x2 )CH3 (CH2 )8 CH3 (3)} Component CH3 OC(CH3 )2 C2 H5 CH3 CH(CH3 )CH(CH3 )CH3 c-(CH2 )6 CH3 (CH2 )8 CH3
p*/(J·cm−3 )
3 −1 V* ) m /(cm ·mol
T*/K
Ref.
456.1 405.3 532.0 447.0
103.32 99.16 84.23 155.75
4714.8 4430.2 4715.0 5091.4
9 17 18 19
Interchange-energy parameters Xij /(J·cm−3 ): X12=8.988, from fit of HmE ;(8) X13=12.699;(9) X23=2.302.(10) b X12=15.718, from fit of HmE ;(8) X13=12.699;(9) X23=12.474.(10)
a
The parameters used in the calculations are summarized in table 3. The values of the characteristic pressures p*, molar volumes V* m , and temperatures T* were taken from our previous publications.(9, 17–19) In estimating the ratios sij of molecular surface areas of contact per segment for components i and j, the spherical approximation was again assumed for the shapes of the molecules. The values of the interchange-energy parameters X12 for {xCH3 OC(CH3 )2CH3 + (1−x)CH3CH(CH3 )CH(CH3 )CH3 } and {xCH3 OC(CH3 )2CH3 + (1−x)c-(CH2 )6 } were obtained by fitting the Flory formula for HmE to the smooth representations of the experimental results for those mixtures.(8) The values of X13 and X23 were the same as reported by Zhu et al.(9, 10) E The dashed curves for Hm, 1+23 in figures 1 and 2 were estimated for the extended Flory theory using the values of the parameters in table 3. For the 57 points of the mixture containing CH3CH(CH3 )CH(CH3 )CH3 in table 1, the root-mean-square deviation E −1 between the estimated and experimental values of Hm, and the mean 123 is 5.7 J·mol absolute relative deviation is 2.4 per cent. The deviations of the points of the mixture containing c-(CH2 )6 in table 2 are larger, amounting to 13.8 J·mol−1 and 4.1 per cent, respectively. However, it is noteworthy that the relative positions of the curves for different values of x2 /(1−x1−x2 ) are predicted correctly. Thus for the present type of mixtures, it again appears that the Flory treatment can provide estimates of the excess molar enthalpies within less than 5 per cent. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. REFERENCES 1. Knezˇevic´-Stevanovic´, A.; Jin, Z.-L.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1995, 27, 423–430. 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, page 1; Table 23-2-(1.201)-a; Table 23-2-(3.100)-a. 3. TRC-Thermodynamic Tables-Non-Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1988: Table 23-2-1(1.2121)-a. 4. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163. 5. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245. 6. Hamam, S. E. M.; Benson, G. C. J. Chem. Eng. Data 1986, 31, 45. 7. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1993, 25, 909.
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
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Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Eng. Data 1994, 39, 302. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1994, 26, 35. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. Thermochim. Acta 1994, 235, 161. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. Ser. No. 7 1953, 49, 107. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403. Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833. Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838. Brostow, W.; Sochanski, J. S. J. Mater. Sci. 1975, 10, 2134. Wang, L.; Benson, G. C.; Lu, B. C.-Y. Thermochim. Acta 1993, 213, 83. Kimura, F.; Benson, G. C. J. Chem. Eng. Data 1983, 28, 387. Treszczanowicz, A. J.; Benson, G. C. Thermochim. Acta 1991, 179, 39. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531.
Excess enthalpies of (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane or cyclohexane+ decane) at the temperature 298.15 K Andjela Knezˇevic´-Stevanovic´, George C. Benson, and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
(Received 26 November 1994) Microcalorimetric measurements of excess enthalpies at the temperature 298.15 K are reported for the two ternary mixtures (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane + decane) and (methyl 1,1-dimethylpropyl ether + cyclohexane + decane). Smooth representations of the results are presented and used to construct constant-enthalpy contours on Roozeboom diagrams. Comparisons of the experimental results with estimates based on the Flory theory of mixtures are also described.
1. Introduction The thermodynamic properties of mixtures of {methyl 1,1-dimethylpropyl ether (tert-amyl methyl ether) + a hydrocarbon} are of interest, in view of the use of the ether as a blending agent in oxygenated gasolines. A recent paper(1) from our laboratory described microcalorimetric measurements of the excess enthalpies of the ternary mixture (methyl 1,1-dimethylpropyl ether + hexane + decane) at the temperature T=298.15 K. As an extension of that earlier investigation, we have now measured excess enthalpies at T=298.15 K for the two ternary mixtures (methyl 1,1-dimethylpropyl ether + 2,3-dimethylbutane + decane) and (methyl 1,1-dimethylpropyl ether + cyclohexane + decane), in which different C6-hydrocarbons replace the hexane used previously.
2. Experimental Pure-Grade CH3CH(CH3 )CH(CH3 )CH3 and Research-Grade c-(CH2 )6 from the Phillips Chemical Co., were used in the present work. The CH3(CH2 )8CH3 was obtained from the Aldrich Chemical Co. The stated mole-fraction purities of all of the hydrocarbons were at least 0.990. The CH3 OC(CH3 )2 C2 H5 (Fluka, purum) had a stated mole-fraction purity exceeding 0.970. All of the components were used without further 0021–9614/95/050531+09 $08.00/0
7 1995 Academic Press Limited
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A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
purification. Values of r(T=298.15 K)/(kg·m−3 ), where r denotes density, measured in an Anton-Paar densimeter, were 657.14, 774.01, 726.40, and 765.91 for CH3CH(CH3 )CH(CH3 )CH3 , c-(CH2 )6 , CH3(CH2 )8CH3 , and CH3 OC(CH3 )2C2 H5 , respectively. These values are in reasonable agreement with the values compiled by the TRC.(2, 3) The excess molar enthalpy HmE was measured in an LKB flow microcalorimeter (Model 10700-1), thermostatted at T=(298.1520.002) K. Previous publications(4, 5) have described this equipment and the operating procedure. In studying the ternary mixtures [x1 CH3 OC(CH3 )2C2 H5 + x2 {CH3CH(CH3 )CH(CH3 )CH3 or c-(CH2 )6 } + E (1−x1−x2 )CH3(CH2 )8CH3 ], the excess molar enthalpies Hm, 1+23 were measured for several pseudo-binary mixtures in which the ether (compound 1) was added to binary mixtures of components 2 (2,3-dimethylbutane or cyclohexane) and 3 (decane) having a fixed mole ratio x2 /(1−x1−x2 ). These binaries were prepared by weighing. The
E TABLE 1. Experimental excess molar enthalpies Hm, 1+23 at the temperature 298.15 K for the addition of CH3 OC(CH3 )2 C2 H5 to {x2 CH3 CH(CH3 )CH(CH3 )CH3 + (1−x2 )CH3 (CH2 )8 CH3 } to form {x1 CH3 OC(CH3 )2 C2 H5+x2 CH3 CH(CH3 )CH(CH3 )CH3+(1−x1−x2 )CH3 (CH2 )8 CH3 }, and values of E E Hm, 123 calculated from equation (1) using Hm, 23 from reference 6
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
0.0500 0.1000 0.1500 0.2004 0.2501 0.3000 0.3498
61.0 114.5 163.8 205.0 243.0 274.7 298.0
E −1 x2 /(1−x1−x2 )=0.3266, Hm, )=33.9 23 /(J·mol 93.2 0.3999 317.1 337.4 0.7004 144.9 0.4497 329.2 347.8 0.7499 192.6 0.5003 335.1 352.0 0.8001 232.1 0.5500 335.2 350.5 0.8500 268.4 0.6003 327.5 341.1 0.9042 298.4 0.6503 314.2 326.0 0.9500 320.0
292.6 265.0 228.4 182.4 124.3 68.2
302.8 273.4 235.1 187.5 127.5 69.9
0.0499 0.1000 0.1500 0.2000 0.2501 0.2998 0.3500
56.9 106.3 150.3 188.8 221.9 250.5 271.6
E −1 x2 /(1−x1−x2 )=0.9739, Hm, )=46.7 23 /(J·mol 101.3 0.4002 287.4 315.4 0.6997 148.4 0.4501 297.4 323.1 0.7497 190.0 0.4996 300.4 323.8 0.8001 226.1 0.5501 299.0 320.0 0.8500 257.0 0.6001 290.9 309.6 0.9000 283.3 0.6498 277.1 293.4 0.9500 302.0
256.9 231.0 197.7 157.5 111.8 58.1
270.9 242.7 207.0 164.6 116.4 60.4
0.0500 0.1000 0.1500 0.2000 0.2498 0.3002 0.3506
52.8 99.4 140.7 174.7 204.5 227.9 246.6
E −1 x2 /(1−x1−x2 )=2.9968, Hm, )=36.0 23 /(J·mol 87.0 0.4002 258.9 280.4 0.7001 131.8 0.4500 266.4 286.2 0.7500 171.3 0.5000 269.2 287.2 0.8001 203.5 0.5505 265.6 281.8 0.8500 231.5 0.6000 257.6 272.0 0.9000 253.1 0.6500 243.6 256.2 0.9500 270.0
224.6 200.1 169.4 135.4 95.8 49.8
235.4 209.0 176.6 140.8 99.4 51.6
E E a −1 Ternary term for representation of Hm, by equations (2) and (3): Hm, )= 1+23 T /(J·mol x1 x2(1 − x1 − x2 )(−904.8 + 1193.8x1 + 2137.5x2 − 166.1x12 − 4991.0x1 x2 − 1257.2x22 − 2577.1x13 + 8387.3x12 x2), s=1.1.
533
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5
E TABLE 2. Experimental excess molar enthalpies Hm, 1+23 at the temperature 298.15 K for the addition of CH3 OC(CH3 )2 C2 H5 to {x2 c-(CH2 )6 + (1−x2 )CH3 (CH2 )8 CH3 } to form {x1 CH3 OC(CH3 )2 C2 H5 + E E x2 c-(CH2 )6 + (1−x1−x2 )CH3 (CH2 )8 CH3 }, and values of Hm, 123 calculated from equation (1) using Hm, 23 from reference 7
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
x1
E Hm, 1+23 J·mol−1
a
E Hm, 123 J·mol−1
0.0500 0.1000 0.1499 0.2001 0.2501 0.2986 0.3503
61.3 112.9 159.9 201.5 237.4 266.9 290.2
E −1 x2 /(1−x1−x2 )=0.3340, Hm, )=203.5 23 /(J·mol 254.7 0.3999 308.4 430.6 0.7001 296.1 0.4499 320.4 432.4 0.7500 332.9 0.4997 326.0 427.8 0.8009 364.3 0.5501 325.1 416.7 0.8500 390.0 0.6000 317.8 399.2 0.9000 409.6 0.6508 304.0 375.1 0.9500 422.4
283.8 256.3 219.2 176.1 124.9 65.3
344.8 307.1 259.8 206.7 145.3 75.4
0.0500 0.1000 0.1500 0.2000 0.2499 0.3000 0.3500
57.9 108.2 154.1 192.4 225.4 251.2 272.6
E −1 x2 /(1−x1−x2 )=0.9504, Hm, )=316.0 23 /(J·mol 358.1 0.4002 287.9 477.4 0.6997 392.6 0.4502 297.2 470.9 0.7498 422.6 0.5000 300.4 458.4 0.8001 445.1 0.5499 297.7 439.9 0.8501 462.4 0.5999 289.5 415.9 0.8999 472.3 0.6502 274.4 384.9 0.9500 478.0
254.4 230.3 195.3 155.6 109.6 57.5
349.2 309.3 258.5 202.9 141.2 73.3
0.0499 0.1000 0.1500 0.1999 0.2500 0.2998 0.3504
60.9 115.9 162.8 202.4 236.3 263.0 283.0
E −1 x2 /(1−x1−x2 )=2.8339, Hm, )=296.8 23 /(J·mol 342.9 0.3999 296.7 474.9 0.6996 383.0 0.4498 304.5 467.8 0.7524 415.0 0.4997 305.4 453.8 0.8000 439.9 0.5502 301.0 434.5 0.8500 458.9 0.6004 291.3 409.9 0.9000 470.8 0.6495 275.2 379.2 0.9500 475.8
253.5 222.2 191.6 151.7 106.2 55.4
342.6 295.7 250.9 196.2 135.8 70.3
E E a −1 Ternary term for representation of Hm, by equations (2) and (3): Hm, )= 1+23 T /(J·mol x1 x2 (1 − x1 − x2 )(12.2 − 20610.9x1 − 2008.9x2 + 56460.2x12 + 34090.1x1 x2 − 840.5x22 − 50319.4x13 − 2 2 51771.1x1 x2−26240.1x1 x2 ), s=4.0.
E excess molar enthalpy Hm, 123 of the ternary mixture was then obtained from the relation: E E E Hm, 123=Hm, 1+23+(1−x1 )Hm, 23 ,
(1)
E m, 23
where H is the excess molar enthalpy of the particular binary mixture. E Values of Hm, 23 for {x2CH3CH(CH3 )CH(CH3 )CH3 + (1−x2 )CH3(CH2 )8CH3 } and {x2 c-(CH2 )6 + (1−x2 )CH3(CH2 )8CH3 } were taken from the literature.(6, 7) 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 E The experimental results for Hm, 1+23 and the corresponding values of Hm, 123 are listed E in tables 1 and 2 for the two ternary mixtures. Plots of the values of Hm, 1+23 against
534
A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
x1 for the various constant values of x2 /(1−x1−x2 ) are shown in figures 1 and 2. Also included in these figures are curves for the constituent binaries having x2=0 and (x1+x2 )=1, taken from our previous work.(8, 9) E The Hm, 1+23 results for the mixtures containing CH3CH(CH3 )CH(CH3 )CH3 in figure 1 are nearly symmetric about x1=0.5, and fall between the curves for x2=0 and E (x1+x2 )=1. Hm, 1+23 for a fixed x1 increases as the ratio x2 /(1−x1−x2 ) decreases. In figure 2, the behaviour of the results for the mixtures containing c-(CH2 )6 is quite E different. All of the Hm, 1+23 values fall below the curves for the two constituent binaries, E and Hm, 1+23 does not vary monotonically with x2 /(1−x1−x2 ). Apart from
E FIGURE 1. Excess molar enthalpies Hm,1+23 for {x1 CH3 OC(CH3 )2 C2 H5 + x2 CH3 CH(CH3 )CH(CH3 )CH3 + (1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K. Experimental results: r, x2 /(1−x1−x2 )=0.3266; w, x2 /(1−x1−x2 )=0.9739; t, x2 /(1−x1−x2 )=2.9968. ····, x2=0 (reference 9); ·–·–·–, (x1+x2 )=1 (reference E 8); ——, calculated from the representation of the results by equations (2) and (3), using the ternary term Hm,T given in the footnote of table 1; ----, estimated from the Flory theory.
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5
535
E FIGURE 2. Excess molar enthalpies Hm, for {x1 CH3 OC(CH3 )2 C2 H5 + x2 c-(CH2 )6 + 1+23 (1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K. Experimental results: r, x2 /(1−x1−x2 )= 0.3340; w, x2 /(1−x1−x2 )=0.9504; t, x2 /(1−x1−x2 )=2.8339. ····, x2=0 (reference 9); ·–·–·–, (x1+x2 )=1 (reference 8); ——, calculated from the representation of the results by equations (2) and (3), using the E ternary term Hm,T given in the footnote of table 2; ----, estimated from the Flory theory.
this unusual variation, the characteristics of the present results in figures 1 and 2 are qualitatively similar to those found previously(10) for the analogous mixtures containing methyl 1,1-dimethylethyl ether (methyl tert-butyl ether) in place of methyl 1,1-dimethylpropyl ether. E (11) The values of Hm, with an added 1+23 were represented as a sum of binary terms ternary contribution: E E E E Hm, 1+23={x2 /(1−x1 )}Hm, 12+{(1−x1−x2 )/(1−x1 )}Hm, 13+Hm, T ,
(2)
E where the values of Hm, 1j were calculated from the smoothing functions reported
536
A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
previously.(8, 9) Following Morris et al.,(12) the ternary term was assumed to have the form: E −1 Hm, )=x1 x2(1−x1−x2 )(c0+c1 x1+c2 x2+c3 x12+ T /(J·mol
c4 x1 x2+c5 x22+c6 x13+c7 x12 x2+c8 x1 x22+··· ).
(3)
Values of the parameters ci were obtained from least-squares analyses in which E equations (2) and (3) were fitted to the experimental results for Hm, 1+23 in tables 1 and 2. These representations are given in the footnotes of the tables, along with their standard deviations s. The continuous curves in figures 1 and 2 were calculated from these representations. The value of s for the cyclohexane mixture is larger than that for the 2,3-dimethylbutane mixture; nevertheless the representation given in the E footnote of table 2 should provide useful estimates of the variation of Hm, 123 with composition for that mixture. E Equations (1) to (3) were used to calculate the constant-Hm, 123 contours plotted on the Roozeboom diagrams shown in figures 3 and 4. All of the contours
E −1 FIGURE 3. Contours for constant values of Hm, ) for {x1 CH3 OC(CH3 )2 C2 H5 + 123 /(J·mol x2 CH3 CH(CH3 )CH(CH3 )CH3+(1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K, calculated from E the representation of our experimental results by equations (1) to (3) with Hm, T from the footnote of table 1.
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5
537
E −1 FIGURE 4. Contours for constant values of Hm, ) for {x1 CH3 OC(CH3 )2 C2 H5 + 123/(J·mol x2 c-(CH2 )6+(1−x1−x2 )CH3 (CH2 )8 CH3 } at the temperature 298.15 K, calculated from the representation E of our experimental results by equations (1) to (3) with Hm, T from the footnote of table 2.
for the 2,3-dimethylbutane mixture in figure 3 extend to the edges of the triangle, E and the maximum value of Hm, 123 is located in the x2=0 edge. Previously for the analogous mixture containing methyl 1,1-dimethylethyl ether(10) instead of methyl 1,1-dimethylpropyl ether, the maximum was inside the triangle but close to the corresponding edge. The shapes of the contours in figure 3 are more similar to those found for {x1CH3 OC(CH3 )2C2 H5 + x2CH3(CH2 )4CH3 + (1−x1−x2 )CH3(CH2) 8CH3 }.(1) For the mixture containing c-(CH2 )6 in figure 4, the maximum is located near the centroid of the triangle, and the general characteristics of the diagram resemble those of the corresponding mixture containing CH3 OC(CH3 )2CH3 . (10) In the case of [x1CH3 OC(CH3 )2CH3 + x2 {CH3CH(CH3 )CH(CH3 )CH3 or c-(CH2 )6 } + (1−x1−x2 )CH3(CH2 )8CH3 ], (10) the Flory theory,(13, 14) as applied to ternary mixtures by Brostow and Sochanski,(15) provided reasonable estimates of the ternary 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 equations for this treatment have been outlined in a previous publication,(16) they will not be repeated here.
538
A. Knezˇevic´-Stevanovic´, G. C. Benson, and B. C.-Y. Lu
TABLE 3 Parameters used in Flory-theory calculations at T=298.15 K for {x1 CH3 OC(CH3 )2 C2 H5 (1) + x2 CH3 CH(CH3 )CH(CH3 )CH3 (2)a or x2 c-(CH2 )6 (2)b + (1−x1−x2 )CH3 (CH2 )8 CH3 (3)} Component CH3 OC(CH3 )2 C2 H5 CH3 CH(CH3 )CH(CH3 )CH3 c-(CH2 )6 CH3 (CH2 )8 CH3
p*/(J·cm−3 )
3 −1 V* ) m /(cm ·mol
T*/K
Ref.
456.1 405.3 532.0 447.0
103.32 99.16 84.23 155.75
4714.8 4430.2 4715.0 5091.4
9 17 18 19
Interchange-energy parameters Xij /(J·cm−3 ): X12=8.988, from fit of HmE ;(8) X13=12.699;(9) X23=2.302.(10) b X12=15.718, from fit of HmE ;(8) X13=12.699;(9) X23=12.474.(10)
a
The parameters used in the calculations are summarized in table 3. The values of the characteristic pressures p*, molar volumes V* m , and temperatures T* were taken from our previous publications.(9, 17–19) In estimating the ratios sij of molecular surface areas of contact per segment for components i and j, the spherical approximation was again assumed for the shapes of the molecules. The values of the interchange-energy parameters X12 for {xCH3 OC(CH3 )2CH3 + (1−x)CH3CH(CH3 )CH(CH3 )CH3 } and {xCH3 OC(CH3 )2CH3 + (1−x)c-(CH2 )6 } were obtained by fitting the Flory formula for HmE to the smooth representations of the experimental results for those mixtures.(8) The values of X13 and X23 were the same as reported by Zhu et al.(9, 10) E The dashed curves for Hm, 1+23 in figures 1 and 2 were estimated for the extended Flory theory using the values of the parameters in table 3. For the 57 points of the mixture containing CH3CH(CH3 )CH(CH3 )CH3 in table 1, the root-mean-square deviation E −1 between the estimated and experimental values of Hm, and the mean 123 is 5.7 J·mol absolute relative deviation is 2.4 per cent. The deviations of the points of the mixture containing c-(CH2 )6 in table 2 are larger, amounting to 13.8 J·mol−1 and 4.1 per cent, respectively. However, it is noteworthy that the relative positions of the curves for different values of x2 /(1−x1−x2 ) are predicted correctly. Thus for the present type of mixtures, it again appears that the Flory treatment can provide estimates of the excess molar enthalpies within less than 5 per cent. The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. REFERENCES 1. Knezˇevic´-Stevanovic´, A.; Jin, Z.-L.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1995, 27, 423–430. 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, page 1; Table 23-2-(1.201)-a; Table 23-2-(3.100)-a. 3. TRC-Thermodynamic Tables-Non-Hydrocarbons. Thermodynamic Research Center: The Texas A&M University System, College Station TX 77843-3111. 1988: Table 23-2-1(1.2121)-a. 4. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163. 5. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245. 6. Hamam, S. E. M.; Benson, G. C. J. Chem. Eng. Data 1986, 31, 45. 7. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1993, 25, 909.
HmE for ternary mixtures containing CH3 OC(CH3 )2 C2 H5 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
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Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Eng. Data 1994, 39, 302. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1994, 26, 35. Zhu, S.; Shen, S.; Benson, G. C.; Lu, B. C.-Y. Thermochim. Acta 1994, 235, 161. Tsao, C. C.; Smith, J. M. Chem. Eng. Prog. Symp. Ser. No. 7 1953, 49, 107. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403. Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1833. Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 87, 1838. Brostow, W.; Sochanski, J. S. J. Mater. Sci. 1975, 10, 2134. Wang, L.; Benson, G. C.; Lu, B. C.-Y. Thermochim. Acta 1993, 213, 83. Kimura, F.; Benson, G. C. J. Chem. Eng. Data 1983, 28, 387. Treszczanowicz, A. J.; Benson, G. C. Thermochim. Acta 1991, 179, 39. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531.