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Ultrasonic speeds and isentropic compressibilities of (1,4-dioxane + n-heptane or n-decane or n-tetradecane)
M-2527 J C’henr. Thermodynumir.~ W&22.
1153-I 158
Ultrasonic speeds and isentropic compressibilities of (1,4-dioxane n-heptane or n-decane or n-tetradecane)
+
E. AICART, M. COSTAS,” E. JUNQUERA, and G. TARDAJOS Departamento de Q&mica Fisica I, Facultad de Ciencias Quimicas, Universidad Complutense. 28040-Madrid, Spain {Received I8 June 1990) Ultrasonic speeds u in {xOCH,CH,0CH,CH2 + (1 -x)~-C,H,,+~] for m = 7, 10, and 14 were measured over the whole composition range and at 298.15 K by a pulse-echo-overlap technique of fixed-path type at a frequency of 2.25 MHz. Isentropic compressibilities lis and corresponding excess functions uE and JC:,together with Au values, have been obtained for all measured mole fractions. The rcJ values are negative for m = 7 and positive for m = 10 and 14 {the opposite is true for u’), while the Au values are negative for the three measured mixtures. At 298.15 K all the studied properties have a “normal” behaviour with composition.
1. Introduction There is a wide variety of mixtures for which the excess molar isobaric heat capacity Cz,,, has a striking composition dependence. (r ‘) This is the “W-shaped” curves where two minima occur separated by a maximum. In general those mixtures have components which differ greatly in chemical nature. (‘. lo) This apparently surprising composition dependence is normally associated with a deviation of local from bulk composition. These kinds of mixtures have been studied by measuring several mixing properties”* 3. ‘. ‘* lo 13) like: excess molar enthalpy Hz, excess molar volume VE c;. mt etc. The last is, until now, the only one showing a clear W-shape. Tee ultrasonic speed is a property very sensitive to different kinds of association in the mixtureso 16) and often it is related to some local order. Seeking to know what is the behaviour of the sound speed and the isentropic compressibility for this kind of mixture, we now report experimental values of these properties for some mixtures showing a clear W-shape in CF.,, as is the case for (1,4-dioxane + an n-alkane).“’
2. Experimental The n-heptane, n-tetradecane, and 1,Cdioxane were Fluka puriss, and the n-decane was Fluka purum, all having purities of 99 moles per cent or greater. The substances e Visiting Researcher from ~partamento de Fisica y Quimica Teorica. Division de Ciencias Basicas. Universidad National Autonoma de Mexico. Mexico D.F. 04510. Mexico. 0071-9614/90/121153+06
%02.00/O
#(? 1990 Academic Press Limited
1154 TABLE
E. AICART 1. Densities
/J*. isobaric and isentropic
ET .4L.
expansivities a;, Isobaric molar heat capacities C:, mr speeds of sound II*. compressibilities I$. of pure components at 298.15 K
._____ 1,4-Dioxane n-Heptane n-Decane n-Tetradecane
1028.400 679.810 726.366 759.269
1.135”” 1.256”s) 1.041”9’ o.931”9’
150.77”’ 224.94”O’ 31 5.46’2” 438.50’*”
1343.90 1 129.8S2* 1233.60”” 1311.87’=
538.40 1 152.32’2” 904.69”” 765.28”“’
were used without further purification except that they were carefully dried with Fluka molecular sieves. Densities p *, determined by an Anton-Paar densimeter, are listed in table 1. A pulse-echo-overlap technique with broadband pulses was used to measure the ultrasonic speed at 2.25 MHz. The mixture was formed in a successive-dilution cell. The details of the apparatus and the experimental procedure have been described in previous papers. (22*24) The distance between transducer and reflector was calculated on the basis of the pure-water speed of sound (1496.739 m . s- ‘) as published by Kroebel and Mahrt.“”
3. Results and discussion Results for the excess speed of sound uE and for the excess isentropic compressibility where m = 7, 10, and 14 are $ for {xOCH2CH20CH2CH, + (1 -x)n-C,H2,+,) given in table 2. The rcs and $ have been obtained from the equations: tis = @2-l, KE=K s s -p s9 where ~jid was obtained according to the expression:(14q 23’ & = 4J‘PG.
1 + h%
2 +
4’PiTI/:(a,*,
- T(x,
J2/CX
1 > + 4${
TV@;,
(1) (2)
2)2/Cz,
2}
V;” +x2 T/2*)(4idaz, 1 + &da;, 2)2/(x1 CZ, 1+x2 Ct. 2)r (3)
where ~jd = Xi ~*/(Xl V;C+X2
V;“) =
Xi
r/r*/V~,
(4)
and v*, a;, i, and Cz, i are the molar volume, isobaric expansivity, and molar heat capacity at constant pressure, respectively, of the pure component i. The corresponding values are listed in table 1 together with the values of a* and KS* for pure substances. Densities p of the mixture have been calculated from molar volumes of pure components and literature excess volumes.‘26’ The mixing quantity Au has been calculated as has been common in the literature by Au = u-~,xiu~.
K,{xkH2CH,0CH2CH,+(1
1155
-x)~-C,H~,+~]
TABLE 2. Excess speeds of sound uE and excess isentropic compressibilities KS”of the mixtures at 298.15 K
&
TPa- ’
0.04508 0.08061 0.12146 0.16122 0.20186 0.27591 0.35749 11.39915
0.70 1.39 2.45 3.19 5.26 8.48 12.32 14.51
0.1 123.5 -4.64 0.12545 - 5.09 0.15656 -6.17 0.19659 - 7.33 0.23792 -8.35 0.27961 -9.20 0.32089 -9.85 0.36115 - 10.35 11.39997 - 10.67 0.04018 0.1 1690 0.15891 0.23200 0.29339 0.35992 0.42263 0.47416 0.51724
-2.81 - 7.40 -9.55 - 13.30 - 16.23 -19.00 -21.28 -22.70 -23.91
x
UE --.-i rn,s-
x
TPa-’ ~-~-. ~. .-..-. -_ xOCH*CH~OCH~~H~~(~-x)~-C,H,~ -0.13 0.47565 18.42 - 23.91 -0.62 0.50206 19.75 - 25.48 - 1.78 0.53340 21.34 - 27.29 - 3.54 0.54236 21.96 -28.04 - 5.59 0.56040 22.91 - 29.05 - 10.29 0.56743 23.00 - 29.03 - 15.78 0.60034 24.79 - 30.83 - 18.84 0.64028 26.43 - 32.09 8.98 9.85 11.92
~OCH~~H~O~~*CH~+(l 0.43968 - 10.79 0.47908 - 10.85 0.51923 - 10.70
14.14 16.09 17.70 18.93
0.55862 0.60030
19.85 20.42
0.63703 0.65077
3.84 10.29 13.38 18.67 22.75 26.54 29.56 31.37 32.81
0.60840 0.62725
-x)n-C,,Hz, 20.64 20.69 20.36 19.83
-10.45 -9.96 - 9.64 -9.33
18.88 18.40 17.83 17.77 17.09
- 9.37 - 8.95
kKH,CH,OCH,CH,+(l 0.55604 -- 24.72 0.60021 - 25.34 0.64083 - 25.62 0.65922 - 25.44 0.67986 - 25.62 0.69715 -25.33 0.70148 - 25.36 0.72215 -25.04 0.72894 -25.11
x --.---0.68046 0.72047 0.76055 0.80057 0.8405 1 0.88052 0.92003 0.96030 0.65994 0.67990 0.71935 0.75984 0.79986 0.84024
0.88043 0.92045 0.96047
-.x)n-C,,H,, 33.69 34.21 34.24 33.88 33.86 33.33 33.29 32.65 32.61
0.74554 0.77419 0.80514 0.83432 0.86569 0.89453 0.92535 0.95837 0.97578
us m-s- ’
27.88 28.92 29.39 29.12 27.88 25.21 20.33 12.40
KS --..:?.
TPa ’
-- 32.88 -- 32.99 - 32.24 -- 30.58 -27.85 - 23.82 -- 18.04 -- 10.24
-8.99
-8.48 -1.66 -6.60 - 5.52 -4.18 - 2.84 -1.57 -0.28 - 24.62 - 24.00 -22.91 -21.70 - 19.63 - 17.24 ~ 13.82
-8.75 - 5.56
17.02 16.15 14.58 12.66 10.67 a.35 6.01 3.73 1.44 31.80 30.57 28.69 26.64 23.55 70.14 15.61 9.50 5.87
but taking into account that this quantity is not a real excess function we have preferred to report in table 2 the excess speed of sound gE instead of Au. That excess function has been defined’23’ by the expression: $ = U-uid -- (ptcJ - Ii2 -(f&$?:: + ~~~~~~~~ If2. (61 Excess functions uE and rcg and the mixing polynomial regression of the type: t/?(x) = x(1-x)
f
quantity
$2x-
Iv’.
AU were smoothed
to a
(71
j=O
The coefficients aj and the corresponding standard deviations s are given in table 3. Figures 1 and 2 show plots of the experimental values and calculated curves according to equation (7) for K: and Au against the mole fraction x of 1,4-dioxane. The rc: and AU values increase with the number of carbon atoms in the n-alkane but
1156
E. AICART TABLE
*
3. Parameters
a0
______--
ET AL.
of equation
a1
-
(7) and standard *2 ..--~~.
~~-.-- a3
deviations
~~~-
.S
a4
05
.\
59.144
39.149
0.16 0.12 0.19
xOCH2CH,0CHZCH,+(l-x)n-C,H,, Au/(m.s-‘) uE/(m.sm’) fci/(TPa ‘)
- 255.399 79.245 - 101.239
- 85.849 104.892 - 121.141
- 29.662 56.324 -36.641
xOCH,CH,0CH,CH2 A~/(m.s-‘) ua/{m.s-‘) r&(TPa-
‘)
- 232.682 - 42,242 81.443
- 114.503 6.209 - 15.610
+ (1 -71.633 -7.131 0.212
xOCH,CH,OCH,CH,+(l Au/(m-s-‘) uE/(m.s-‘) $/(TPa-‘)
- 182.306 - 94.605 127.453
0 FIGURE 1. @CH,CHrOCH,CH, ,& m = 14. --,
Excess
- I 13.273 -45.505 55.731
0.2
4.422 41.418 -28.112
-
xWG,H,, -44.037 12.481 -11.193
- i 3.343 31.599 ~ 25.876
0.08 0.15 0.14
-93.52 - 47.627
0.29 0.13 0.28
-x)n-C,.H,, - 64.458 -22.542 47.306
0.4
x
- 99.434 -41.493 25.940
0.6
0.8
isentropic compressibilities ti: against the mole fraction x for } at 298.15 K. Experimental results: 0, m = 7; 0, m = 10; + (1 -x)~-C,,,H~,,,+~ calculated from equation (7) with coefficients from table 3.
k-,{xOCH,CH,OCH,CH,t(l
-x)n-C,Hz,+
2)
1157
FIGURE 2. Mixing functions Au of the speed of sound against the mole fraction T for {xOCHJH,OCH,CH, + (1 -x)n-C,H 2m+2] at 298.15 K. Experimental results: 0, M = 7; 0. m = 10; 1\,. m ~2.14. ---, calculated from equation (7) with coefficients from table 3.
the shape of the curves is quite different. The KS” curves have a change of sign between the mixtures with n-heptane and n-decane, while the Au curves do not show any change of sign. That confirms our previous discussion(23) about the use of Ata as an excess function. On the other hand, the U” curves have the same shape as X: but with opposite sign. For each mixture KS”and uE curves are practically specular images with respect to the x-axis. This is why a plot of the uE curves has been omitted. The mixture of {xOCH,CH20CH,CH, f (1 -x)n-C,H,,) shows a minimum in KS” at x x 0.73 and the curve is highly asymmetric. The mixture with n-C,,H,, has a maximum in K: at x x 0.45, while for that with n-C,,H,, the maximum is shifted to higher x. Although the speed of sound is very sensitive to small changes related to the reorganization or order in the solution, (14 I*) for the three measured mixtures none of the studied functions presents any striking composition dependence like that shown by CF,, at 298.15 K.“2) On the other hand, although the excess molar volume V,” is positive for all the measured mixtures, the excess isentropic compressibility KS”is negative for the first: (1,4-dioxane + n-heptane). That means a lower compressibility for the real mixture than for the ideal one. We have found this feature in many mixtures containing short n-alkanes and it has been discussed previously!21.‘“. “j The authors are grateful to MEC of Spain for financial support through a DGICT grant no. PB86-0568. E.J. thanks MEC of Spain for a scholarship from the FPI programme. M.C. also thanks the MEC of Spain for a scholarship under the Cooperative Cientifica con Iberoamerica programme.
E. AICART
1158
ET AL.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO.
Kimura, F.; D’Arcy, P. J.; Sugamori. M. E.; Benson, G. C. Thermochimicu A<,fu 1983, 64. 149. Inglese, A.; Grolier, J. P. E.; Wilhelm, E. J. Chem. Thermodynamics 1984, 16, 67. Inglese. A.: Grolier. J. P. E. Fluid Phase Equilibria 1984, 15, 287. Grolier, J. P. E.; Benson, G. C. Can. J. Chem. 1984, 62. 949. Lainez. A.: Wilhelm, E.; Roux-Desgranges, G.; Grolier, J. P. E. J. Chem. Thermodynamics 1984, 16. 1154. Lainez, A.; Roux-Desgranges, G.; Grolier, J. P. E.; Wilhelm, E. Fluid Phase Equilibria 1985, 20, 47. Kalali, H.; Kohler, F.; Svejda. P. Fluid Phase Equilibria 1985, 20, 75. Lainez, A.: Grolier, J. P. E.; Wilhelm, E. Thermochimica Acra 1985, 91, 243. Saint-Victor, M. E.; Patterson, D. Fluid Phase Equilibria 1987, 35, 237. Andreoli-Ball, L.; Costas, M.; Patterson, D.; Rubio. R. G.: Masegosa, R. M.; Caceres M. Ber. Bunsenges,
Phvs. Chem.
1989, 93. 882.
1I. Andrews. A. W.; Morcom, K. W. J. Chem. Thermodynamics 1971, 3. 513. 12. Andrews, A. W.; Morcom, K. W. J. Chem. Thermodvnamies 1971, 3, 519. 13. Benson. G. C.; Kumaran. M. K.; Treszczanowicz, T.; D’Arcy, P. J.; Halpin, C. J. Thermochimicu Acta 1985, 95, 59.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
Handa, Y. P.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodynamics 1981, 13, 875. Aicart, E.; Kumaran. M. K.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodynamics 1983, 15, 1989. Zielinski, R.; Ikeda, S.; Nomura, H.; Kato. S. J. Chem. Sot. Faraday Trans. Il989, 85. 1619. Murthy, N. M.: Nagabhushanam, G. Acusfica 1984, 54, 225. Bhnowska. A.; Brostow. W. J. Chem. Thermodynamics 1975, 7, 787. Tardajos. G.; Aicart, E.; Diaz Petia, M. Fluid Phase Equilibria 1985, 20, 87. Messerly, J. F.: Guthrie, G. B.; Todd, S. S.; Finke, H. L. J. Chem. Eng. Data 1967, 12, 338. Tardajos, G.; Aicart, E.; Costas, M.; Patterson, D. J. Chem. Sot. Faraday Tram Il986, 82, 2977. Junquera, E.; Tardajos, G.; Aicart, E. J. Chem. Thermodynamics 1988,20, 1461. Junquera, E.; Aicart, E.; Tardajos, G. J. Chem. Thermodynamics 1989, 21, 1223. Taradajos, G.: Diaz Peiia, M.; Aicart, E. J. Chem. Thermodynamics 1986, 18, 683. Kroebel, N.: Marht, K. H. Acustica 1976, 27, 806. Inglese, A.; Grolier, J. P. E.; Wilhelm, E. J. Chem. Eng. Data 1983, 28, 124. Matilla. A. D.; Aicart, E.; Diaz Peria, M.; Tardajos, G. J. Solution Chem. 1989, 18, 143.
1153-I 158
Ultrasonic speeds and isentropic compressibilities of (1,4-dioxane n-heptane or n-decane or n-tetradecane)
+
E. AICART, M. COSTAS,” E. JUNQUERA, and G. TARDAJOS Departamento de Q&mica Fisica I, Facultad de Ciencias Quimicas, Universidad Complutense. 28040-Madrid, Spain {Received I8 June 1990) Ultrasonic speeds u in {xOCH,CH,0CH,CH2 + (1 -x)~-C,H,,+~] for m = 7, 10, and 14 were measured over the whole composition range and at 298.15 K by a pulse-echo-overlap technique of fixed-path type at a frequency of 2.25 MHz. Isentropic compressibilities lis and corresponding excess functions uE and JC:,together with Au values, have been obtained for all measured mole fractions. The rcJ values are negative for m = 7 and positive for m = 10 and 14 {the opposite is true for u’), while the Au values are negative for the three measured mixtures. At 298.15 K all the studied properties have a “normal” behaviour with composition.
1. Introduction There is a wide variety of mixtures for which the excess molar isobaric heat capacity Cz,,, has a striking composition dependence. (r ‘) This is the “W-shaped” curves where two minima occur separated by a maximum. In general those mixtures have components which differ greatly in chemical nature. (‘. lo) This apparently surprising composition dependence is normally associated with a deviation of local from bulk composition. These kinds of mixtures have been studied by measuring several mixing properties”* 3. ‘. ‘* lo 13) like: excess molar enthalpy Hz, excess molar volume VE c;. mt etc. The last is, until now, the only one showing a clear W-shape. Tee ultrasonic speed is a property very sensitive to different kinds of association in the mixtureso 16) and often it is related to some local order. Seeking to know what is the behaviour of the sound speed and the isentropic compressibility for this kind of mixture, we now report experimental values of these properties for some mixtures showing a clear W-shape in CF.,, as is the case for (1,4-dioxane + an n-alkane).“’
2. Experimental The n-heptane, n-tetradecane, and 1,Cdioxane were Fluka puriss, and the n-decane was Fluka purum, all having purities of 99 moles per cent or greater. The substances e Visiting Researcher from ~partamento de Fisica y Quimica Teorica. Division de Ciencias Basicas. Universidad National Autonoma de Mexico. Mexico D.F. 04510. Mexico. 0071-9614/90/121153+06
%02.00/O
#(? 1990 Academic Press Limited
1154 TABLE
E. AICART 1. Densities
/J*. isobaric and isentropic
ET .4L.
expansivities a;, Isobaric molar heat capacities C:, mr speeds of sound II*. compressibilities I$. of pure components at 298.15 K
._____ 1,4-Dioxane n-Heptane n-Decane n-Tetradecane
1028.400 679.810 726.366 759.269
1.135”” 1.256”s) 1.041”9’ o.931”9’
150.77”’ 224.94”O’ 31 5.46’2” 438.50’*”
1343.90 1 129.8S2* 1233.60”” 1311.87’=
538.40 1 152.32’2” 904.69”” 765.28”“’
were used without further purification except that they were carefully dried with Fluka molecular sieves. Densities p *, determined by an Anton-Paar densimeter, are listed in table 1. A pulse-echo-overlap technique with broadband pulses was used to measure the ultrasonic speed at 2.25 MHz. The mixture was formed in a successive-dilution cell. The details of the apparatus and the experimental procedure have been described in previous papers. (22*24) The distance between transducer and reflector was calculated on the basis of the pure-water speed of sound (1496.739 m . s- ‘) as published by Kroebel and Mahrt.“”
3. Results and discussion Results for the excess speed of sound uE and for the excess isentropic compressibility where m = 7, 10, and 14 are $ for {xOCH2CH20CH2CH, + (1 -x)n-C,H2,+,) given in table 2. The rcs and $ have been obtained from the equations: tis = @2-l, KE=K s s -p s9 where ~jid was obtained according to the expression:(14q 23’ & = 4J‘PG.
1 + h%
2 +
4’PiTI/:(a,*,
- T(x,
J2/CX
1 > + 4${
TV@;,
(1) (2)
2)2/Cz,
2}
V;” +x2 T/2*)(4idaz, 1 + &da;, 2)2/(x1 CZ, 1+x2 Ct. 2)r (3)
where ~jd = Xi ~*/(Xl V;C+X2
V;“) =
Xi
r/r*/V~,
(4)
and v*, a;, i, and Cz, i are the molar volume, isobaric expansivity, and molar heat capacity at constant pressure, respectively, of the pure component i. The corresponding values are listed in table 1 together with the values of a* and KS* for pure substances. Densities p of the mixture have been calculated from molar volumes of pure components and literature excess volumes.‘26’ The mixing quantity Au has been calculated as has been common in the literature by Au = u-~,xiu~.
K,{xkH2CH,0CH2CH,+(1
1155
-x)~-C,H~,+~]
TABLE 2. Excess speeds of sound uE and excess isentropic compressibilities KS”of the mixtures at 298.15 K
&
TPa- ’
0.04508 0.08061 0.12146 0.16122 0.20186 0.27591 0.35749 11.39915
0.70 1.39 2.45 3.19 5.26 8.48 12.32 14.51
0.1 123.5 -4.64 0.12545 - 5.09 0.15656 -6.17 0.19659 - 7.33 0.23792 -8.35 0.27961 -9.20 0.32089 -9.85 0.36115 - 10.35 11.39997 - 10.67 0.04018 0.1 1690 0.15891 0.23200 0.29339 0.35992 0.42263 0.47416 0.51724
-2.81 - 7.40 -9.55 - 13.30 - 16.23 -19.00 -21.28 -22.70 -23.91
x
UE --.-i rn,s-
x
TPa-’ ~-~-. ~. .-..-. -_ xOCH*CH~OCH~~H~~(~-x)~-C,H,~ -0.13 0.47565 18.42 - 23.91 -0.62 0.50206 19.75 - 25.48 - 1.78 0.53340 21.34 - 27.29 - 3.54 0.54236 21.96 -28.04 - 5.59 0.56040 22.91 - 29.05 - 10.29 0.56743 23.00 - 29.03 - 15.78 0.60034 24.79 - 30.83 - 18.84 0.64028 26.43 - 32.09 8.98 9.85 11.92
~OCH~~H~O~~*CH~+(l 0.43968 - 10.79 0.47908 - 10.85 0.51923 - 10.70
14.14 16.09 17.70 18.93
0.55862 0.60030
19.85 20.42
0.63703 0.65077
3.84 10.29 13.38 18.67 22.75 26.54 29.56 31.37 32.81
0.60840 0.62725
-x)n-C,,Hz, 20.64 20.69 20.36 19.83
-10.45 -9.96 - 9.64 -9.33
18.88 18.40 17.83 17.77 17.09
- 9.37 - 8.95
kKH,CH,OCH,CH,+(l 0.55604 -- 24.72 0.60021 - 25.34 0.64083 - 25.62 0.65922 - 25.44 0.67986 - 25.62 0.69715 -25.33 0.70148 - 25.36 0.72215 -25.04 0.72894 -25.11
x --.---0.68046 0.72047 0.76055 0.80057 0.8405 1 0.88052 0.92003 0.96030 0.65994 0.67990 0.71935 0.75984 0.79986 0.84024
0.88043 0.92045 0.96047
-.x)n-C,,H,, 33.69 34.21 34.24 33.88 33.86 33.33 33.29 32.65 32.61
0.74554 0.77419 0.80514 0.83432 0.86569 0.89453 0.92535 0.95837 0.97578
us m-s- ’
27.88 28.92 29.39 29.12 27.88 25.21 20.33 12.40
KS --..:?.
TPa ’
-- 32.88 -- 32.99 - 32.24 -- 30.58 -27.85 - 23.82 -- 18.04 -- 10.24
-8.99
-8.48 -1.66 -6.60 - 5.52 -4.18 - 2.84 -1.57 -0.28 - 24.62 - 24.00 -22.91 -21.70 - 19.63 - 17.24 ~ 13.82
-8.75 - 5.56
17.02 16.15 14.58 12.66 10.67 a.35 6.01 3.73 1.44 31.80 30.57 28.69 26.64 23.55 70.14 15.61 9.50 5.87
but taking into account that this quantity is not a real excess function we have preferred to report in table 2 the excess speed of sound gE instead of Au. That excess function has been defined’23’ by the expression: $ = U-uid -- (ptcJ - Ii2 -(f&$?:: + ~~~~~~~~ If2. (61 Excess functions uE and rcg and the mixing polynomial regression of the type: t/?(x) = x(1-x)
f
quantity
$2x-
Iv’.
AU were smoothed
to a
(71
j=O
The coefficients aj and the corresponding standard deviations s are given in table 3. Figures 1 and 2 show plots of the experimental values and calculated curves according to equation (7) for K: and Au against the mole fraction x of 1,4-dioxane. The rc: and AU values increase with the number of carbon atoms in the n-alkane but
1156
E. AICART TABLE
*
3. Parameters
a0
______--
ET AL.
of equation
a1
-
(7) and standard *2 ..--~~.
~~-.-- a3
deviations
~~~-
.S
a4
05
.\
59.144
39.149
0.16 0.12 0.19
xOCH2CH,0CHZCH,+(l-x)n-C,H,, Au/(m.s-‘) uE/(m.sm’) fci/(TPa ‘)
- 255.399 79.245 - 101.239
- 85.849 104.892 - 121.141
- 29.662 56.324 -36.641
xOCH,CH,0CH,CH2 A~/(m.s-‘) ua/{m.s-‘) r&(TPa-
‘)
- 232.682 - 42,242 81.443
- 114.503 6.209 - 15.610
+ (1 -71.633 -7.131 0.212
xOCH,CH,OCH,CH,+(l Au/(m-s-‘) uE/(m.s-‘) $/(TPa-‘)
- 182.306 - 94.605 127.453
0 FIGURE 1. @CH,CHrOCH,CH, ,& m = 14. --,
Excess
- I 13.273 -45.505 55.731
0.2
4.422 41.418 -28.112
-
xWG,H,, -44.037 12.481 -11.193
- i 3.343 31.599 ~ 25.876
0.08 0.15 0.14
-93.52 - 47.627
0.29 0.13 0.28
-x)n-C,.H,, - 64.458 -22.542 47.306
0.4
x
- 99.434 -41.493 25.940
0.6
0.8
isentropic compressibilities ti: against the mole fraction x for } at 298.15 K. Experimental results: 0, m = 7; 0, m = 10; + (1 -x)~-C,,,H~,,,+~ calculated from equation (7) with coefficients from table 3.
k-,{xOCH,CH,OCH,CH,t(l
-x)n-C,Hz,+
2)
1157
FIGURE 2. Mixing functions Au of the speed of sound against the mole fraction T for {xOCHJH,OCH,CH, + (1 -x)n-C,H 2m+2] at 298.15 K. Experimental results: 0, M = 7; 0. m = 10; 1\,. m ~2.14. ---, calculated from equation (7) with coefficients from table 3.
the shape of the curves is quite different. The KS” curves have a change of sign between the mixtures with n-heptane and n-decane, while the Au curves do not show any change of sign. That confirms our previous discussion(23) about the use of Ata as an excess function. On the other hand, the U” curves have the same shape as X: but with opposite sign. For each mixture KS”and uE curves are practically specular images with respect to the x-axis. This is why a plot of the uE curves has been omitted. The mixture of {xOCH,CH20CH,CH, f (1 -x)n-C,H,,) shows a minimum in KS” at x x 0.73 and the curve is highly asymmetric. The mixture with n-C,,H,, has a maximum in K: at x x 0.45, while for that with n-C,,H,, the maximum is shifted to higher x. Although the speed of sound is very sensitive to small changes related to the reorganization or order in the solution, (14 I*) for the three measured mixtures none of the studied functions presents any striking composition dependence like that shown by CF,, at 298.15 K.“2) On the other hand, although the excess molar volume V,” is positive for all the measured mixtures, the excess isentropic compressibility KS”is negative for the first: (1,4-dioxane + n-heptane). That means a lower compressibility for the real mixture than for the ideal one. We have found this feature in many mixtures containing short n-alkanes and it has been discussed previously!21.‘“. “j The authors are grateful to MEC of Spain for financial support through a DGICT grant no. PB86-0568. E.J. thanks MEC of Spain for a scholarship from the FPI programme. M.C. also thanks the MEC of Spain for a scholarship under the Cooperative Cientifica con Iberoamerica programme.
E. AICART
1158
ET AL.
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