EXCESS VOLUME OF BINARY MIXTURES OF hWYLS-DECALIN
39 1
The Excess Volume of Binary Mixtures of trans-Decalin with Cyclohexane and with n-Alkanes
by Jo& D. G6mez-Ibanez and Tieh Chu Wang Hall Laboratory of Chemistry, Wesleyan University, Middletown, Connecticut
(Received July IS, 1966)
The excess volume of mixing of binary systems of trans-decalin with some n-alkanes has been determined using both a dilatometric and a pycnometric method. At a given temperature (25.0"),the excess volume increases with increasing length of the alkane chain, from the negative values exhibited by the system trans-decalin n-heptane to the slightly positive value observed for the system of trans-decalin with n-hexadecane. The excess 2), where n is the number of carbons in volume seems to be a linear function of l/(n the aliphatic component. For a given alkane ( i e . , n-heptane and n-nonane), the excess volume increases in magnitude with increasing temperature. Comparison is made with similar alkane-alkane and cyclohexane-alkane binary mixtures previously described. The excess volume of mixtures of trans-decalin with hexadecane is also reported.
+
+
Reports of excess volume measurements of binary, nonpolar systems are not abundant in the literature although such measurements are of particular interest. Modern theories of so1utions1v2 emphasize the importance of the excess volume of mixing and its relation to all other excess thermodynamic functions. Moreover, the theories postulate, when dispersion forces are involved, a sign for VE which depends upon the relative size of the molecular species present in the mixture. As part of a systematic study of the effects of niolecular size and shape on the thermodynamic properties of binary mixtures of nonelectrolytes, we have reported in two previous papers measurements of the excess volumes of binary mixtures of n-alkanes3 and of binary mixtures of cyclohexane with some n-alkane~.~ It seemed of interest to us to extend our study to the binary mixtures of trans-decalin (decahydronaphthalene) with n-alkanes. Such mixtures, differing from the ones previously studied4 by the replacement of cyclohexane by a similar, planar, and nonlinear hydrocarbon, but one which is almost twice as large in one direction, may provide additional and interesting empirical information. We report here the results of measurements of the excess volume of mixing of the following systems: (I) trans-decalin (1) n-
+
heptane (2) at 15.1, 25.0, and 39.5'; (11) trans-decalin (1) n-nonane (2) at 25.0 and 39.5"; (111) trunsn-dodecane (2) at 25.0'; (IV) transdecalin (1) n-hexadecane (2) at 25.0"; (V) transdecalin (1) decalin (1) cyclohexane at 25.0'.
+
+ + +
Experimental Section Procedure. The data here reported were obtained using a dilatometer similar to the one described by van der Waals and De~myter.~The few changes introduced do not modify essentially its design and operation, and reference is made to the original paper for a description of the apparatus. (Details for its operation may be requested from our laboratory.) The errors involved in the dilatometric measurements can be evaluated in terms of temperature fluctuations of the thermostat (*0.005') and the uncertainties in reading the height of the mercury in the measuring capillaries. I n a typical experiment mixing trans(1) I. Prigogine, "The Molecular Theory of Solutions," Interscience Publishers, Inc., New York, N.Y.,1957. (2) R. L.Scott, J . Chem. Phys., 25, 193 (1956). (3) J. D. G(imez-Ib6fiez and T . 4 . Liu, J . Phys. Chem., 67, 1388 (1963). (4) J. D.GBmez-IbBiiez and T.-C. Liu, {bid., 65, 2148 (1961). (5) J. H.van der Waals and A. Desmyter, Rec. Trav. Chim., 77, 53 (1958).
Volume 70, Number 2 February 1966
392
decalin with n-heptane at 25" , the linear contraction of the mercury in the capillary (of volume 0.0769 ~ m . ~ cm. of length) was 1.23 cm. at the first mixing and 6.03 cm. at the last. Since the fluctuation in the meniscus reading was constantly *0.02 em., the relative uncertainty jn the excess volume was reduced from an initial value of about *1.7% to a final value of *0.3$& In terms of ~m.~/rnole, the errors were about k0.007 and *0.002 ~ m . depending ~, on the molecular weights of the hydrocarbons and the amounts being mixed. The uncertainty in the mole fraction varied from about *3% in the first mixing to about h0.401, at the last mixing. Principally for the purpose of checking the reliability of the dilatometric results, pycnometric measurements were carried out with systems I, 11, and V. For this type of measurement, the procedure followed has been described in detail in a previous paper,4 which also discusses the errors involved. Materials. Two samples of trans-decalin were used in our study. The first sample was prepared from a 50% cis-trans mixture obtained from Matheson Coleman and Bell. The mixture was fractionated in a metal-helices-packed column of about 70 theoretical plates, a t a reflux ratio of 5 to 1. The portion boiling between 185 and 187" was collected and fractionated again in the same manner. After four such distillations, final separation was accomplished using a Beckman Megachrome. The purity of the final product was found to be, by V.P.C. analysis, over 99 mole %. The yield was about lo%, and the density of the trans-decalin thus obtained was found to be 0.86584 g . / ~ m .at ~ 25.0'. Later, a sample of pure trans-decalin was obtained from the K & K Laboratories, Inc., which proved to be, by V.P.C. analysis, of about the same purity as the one previously prepared. It had a density of 0.86604 g./cme3. Both densities quoted here show good agreement with the value of 0.86,592 at 25" found in the literature.0 All n-hydrocarbons and the cyclohexane used were Matheson Coleman and Bell reagents. Cyclohexane and n-heptane were spectroquality reagents, n-nonane was chromatoquality reagent, and all others were labeled as "99y0 olefin free" reagents. The purification procedure followed was similar to that described in previous lpapers.3~~The densities of the final materials were determined, and the results, together with those found in the literature,' are summarized in Table
JOSfi
D.
G6MEZ-IBfiEZ AND
TIEHCHU WANG
/ Table I: Densities of Some Hydrocarbons Other values in
d, gJcrn.8
(this
Temp.,
Hydrocarbon
trans-Decalin
Cyclohexane %-Heptane n-Nonane n-Dodecane n-Hexadecane a
work)
OC.
15.1 25.0 39.5 25.0 15.1 25.0 39.5 25.0 39.5 25.0 25.0
the lit. (ref. 7)
0.87363 0.86584 0.86604 0.85509 0.77396 0.68780 0.67969 0.66716 0.71420 0.70305 0.74504 0.76967
dV/dT, cm.*/deg. a X 108, (259 de&-'
0.86592" 0.140
0.876
0.77389 0.67951
0.186
1.26
0.71364
0.203
1.13
0.74515 0.76993
See ref. 6.
measurements and are accurate to within O.OOO1 g./ Comparison is made in the table with ~ mor, better. ~ other values for the densities available in the literature. In columns 5 and 6 values for trans-decalin and for n-heptane are given, respectively, for dV/dT and for CY, the coefficient of thermal expansion at 25'. These values were obtained from a plot of the calculated molar volumes os. the temperature (in both cases yielding a straight line). The values for the excess volume of mixing obtained for all the systems under study, using the dilatometric method, are summarized in Table 11, while in Table 111 we report the values for systems I, 11, and V obtained using the pycnometric method. Using the dilatometric data, equations of the form n
VE
=
x(l
- x)CA,(l - 2xy i=O
(1)
(where x always represents the mole fraction of the component other than trans-decalin) have been computed for each system by the method of least squares. The first three coefficients in the expansion (1) were considered sufficient to represent the data, and their values, together with their variance or mean-square error, are reported in Table IV. In general, we consider the pycnometric values somewhat more reliable, but the difference between the pycnometric values and those computed for the same mole fraction by use of eq. 1 amounted to only
1.
Results The values for the densities of the pure hydrocarbons reported in Table 1 are each the average of several The Journal of Physkal Chemistry
(6) D. L. Camin and F. D. Rossini, J . Phys. Chem., 59, 1173 (1955). (7) "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," American Petroleum Research Project 44, Carnegie Press, Pittsburgh, Pa., 1953.
EXCESS VOLUME OF BINARYMIXTURES O F tmnS-DECALIN
A0.02 to *0.03 ~m.~/rnole.This difference could perhaps be attributed to the "air-free" condition of the components when the dilatometer was used. The dilatometric method offered the additional advantage of providing values for the excess volume of mixing over the whole range of composition in a single operation.
Table 11: Excess of Mixtures of trans-Decalin and Some Hydrocarbons (Dilatometric Measurements) Mole
-VE,
fraction,
om.'/ mole
21
System I trans-decalin (1) n-heptane (2) 15.1" 0,162 0.260 0.288 0.399 0.392 0.465 0.550 0.498 0.606 0.486 0.713 0.434 0.833 0.301 0.860 0.262
+
-VE, cm.a/
Mole fraction,
21
mole
21
om.#/ mole
0.795 0.854
0.519 0.396
0.294 0.368 0.449 0.594 0.730 0.818
0.093 0.101 0.102 0.100 0.083 0.065
System I1 trans-deca1in ( l ) + n-nonane (2) nr
A 0
zr3.u-
0.135 0.238 0.384 0.473 0.620 0.670 0.753 0.845
25.0" 0.171 0.390 0.321 0.572 0.428 0.632 0.535 0.633 0.606 0.626 0.672 0.576 0.733 0.510 0.790 0.440 0.852 0.340 39.5" 0.174 0.490 0.301 0.637 0.385 0.758 0.546 0.777 0.657 0.700 0.714 0.638
Mole fraction,
0.151 0.242 0.321 0.337 0.310 0.292 0.245 0.167
-VE,
Discussion
System IV trans-decalin (1) n-hexadecane (2) 25.0" 0.083 -0.011 0.157 -0.017 0.256 -0.026 0.338 -0.027 0.413 -0.033 0.523 -0.037 0.611 -0.034 0.709 -0.035
+
39.5" 0.140 0.186 0.258 0.298 0.340 0.352 0.434 0.381 0.571 0.382 0.621 0.369 0.771 0.281 0.861 0.188
System V trans-decalin (1) cyclohexane (2) 25.0" 0.208 0.028 0.351 0.038 0.471 0.057 0.554 0.068 0.726 0.084 0.773 0.089 0.847 0.075 0.898 0.061
+
System I11 trans-decalin (1) n-dodecane (2) 25.0" 0.115 0.057 0.214 0.081
+
393
The only values in the literature for the type of systems studied here are those reported by Danusso* for the systems trans-decalin n-heptane, transdecalin n-hexadecane, and trans-decalin cyclohexane at 30'. For the first system Danusso's values at 30" are not far from our values at 25'. For the second system Danusso reports no change in volume on mixing, while we detect a positive, although small, excess volume. For the system trans-decalin cyclohexane Danusso reports a small and positive excess volume while we have observed equally small but negative values. We should mention, in passing, the high value reported by Danusso for the density of the "decalin" used in his work. In Figures 1 and 2 we have represented by full lines eq. 1 obtained for each system. The curves are practically symmetrical about the composition axis, with the minimum (or maximum) about z = 0.5. Systems I and I1 were studied at more than one temperature, and Figure 1 shows the temperature dependence of VE for those systems. The contraction observed on mixing increases in magnitude with increasing temperature, but the variation, as shown by the behavior of system I, is not linear. System I1
+
+
+
+
Mole fraction of trans - deca Iin 0.0
Table I11: Excess Volume of Mixtures of trans-Decalin (1) and Some Hydrocarbons (Pycnometric Measurements)
-VE,
Temp.,
Mole fraction,
System
"C.
22
cm.V mole
I
15.1 25.0
0.54839 0.29408 0.41845 0.56051 0.62618 0.53871
0.489 0.499 0.611 0.612 0.575 0.759
39.5
0.28289 0.41692 0.53773 0.54557 0.62688 0.75327 0.52144
0.299 0.364 0.351 0.356 0.337 0.273 0.418
25.0
0.59901
0.088
39.5
I1
v
25.0
0.01
'
1.0
0.5 I
I
I
I
'
1
I
I
I
I
0 Q,
E. m
E u
W
>
Figure 1. The effect of temperature on the excess volume of mixtures of trans-decalin with n-heptane and with n-nonane. The dots represent pycnometric values (see Table 111). (8) F. Danusso, Atti Accad. NazE. Lincei, Rend., 13, 131 (1952).
Volume 70, Number 2 February 1066
Table IV : Values for the Coefficients and Their Deviations in Eq. 1 for the Excess Volume of Mixtures of trans-Decalin and Some Hydrocarbons Temp., Ao
AAo
Ai
AAI
15.1 25.0 39.5
-1.998 -2.575 -3.098
0.0078 0.0121 0.0524
0.1877 - 0.0467 -0.1103
0.0108 0.0188 0.0733
25.0 39.5
-1.348 -1.564
0.0069 0.0061
-0.0238 0.0214
0.0095 0.0086
I I1 CmHis -tCizHza
25.0
-0.406
0.0087
- 0.0520
0.0081
IV CioHis -t Ci6H34
25.0
0.0040
-0.0456
0.0107
0.0590
0.0192
V
25.0
0.0066
0.2973
0.0108
- 0.2977
0.0237
System
:E CioHis
-t C7Hia I1
CioHu
CioHis
-t CQHZO
OC.
0.138 -0.238
A2
AAa
-0.0972 -0.3166 -0.3794
0.1208 0,00012 -0.1724
0.0204 0.0466 0.1984 0.0238 0.0205 0.0198
-t C-CEHIZ
c16
a 0
E
ro
E
w
>
0.0
0.5
Mole fraction of’ trans- decalin Figure 2. Excess volume of mixtures of trans-decalin with n-alkanes.
1.0
indicates a similar behavior, but the magnitude of the effect shown with this longer paraffin is smaller. All systems were studied at the common temperature of 25.0”, and the results are plotted in Figure 2 so as to show the effect of the length of the paraffin chain on the excess volume. With increasing chain length, VE increases from the relatively large negative value (-0.644 at x = 0.5), exhibited by n-heptane, to the small positive value (+0.035at the same mole fraction) measured for n-hexadecane. The values for n-nonane and for n-dodecane fall between in the appropriate sequence, and the general pattern is similar to that observed in the corresponding cyclohexane systems. This is shown in Figure 3 where the values for the excess volumes a t the maximum (x = 0.5) are plotted against the empirical expression l/(n 2), n being the number of carbons in the paraffin chain. Allowance being made for the experimental errors, the relationship seems to be linear as was the case for the cyclohexane alkane s y ~ t e m s . ~ The analogies and differences observed in the systems so far studied, alkane alkane, cyclohexane alkane, and trans-decalin alkane, are certainly of interest, For the first-mentioned kind of system, the excess volume is shown to be negative, temperature dependent, and increasing in absolute value with increasing difference in the chain length of the two components. The measurements confirmed the fact that the values of VE for mixtures of n-alkanes are consistent with the “principle of congruence”g as shown using the method of representation of Hijmans.lo
+
+
+ +
IC)
E 0
w
>
Figure 3. Relation between excess volume and chain length at z = 0.5.
The Journal of Physical Chemistry
+
(9) J. N. Brpsted and J. Koefoed, Kg1. Danske Videnskab. Selskab., Mat. Fys. Medd., [17]2 2 , 1 (1946). (10) J. Hijmans, Mol. Phys., 1, 307 (1958).
EXCESS VOLUME OF BINARYMIXTURES O F trUns-DECALIN
The behavior of chain-molecule liquids and their mixtures has been the subject of theoretical studies, the most recent one by Flory; Orwoll, and Vrij,” who have derived for n-paraffin hydrocarbons a reduced equation of state in terms of a segment net volume, an interaction parameter, and the number of degrees of freedom per segment. Their treatment leads to the Brprnsted principle of congruence as applied to the excess volume of mixtures of n-alkanes. Mixtures of cyclohexane with n-alkanes exhibit a positive excess volume which (in contrast with the systems reported in this paper) is temperature independent over the measured range (15-35’). The excess volume increases in magnitude with increasing length of the alkane and shows a linear dependence with l/(n 2), as mentioned above. Two main factors will contribute to determine the excess volume of a mixture. On mixing two liquids, changes may take place in both the intermolecular forces and in the geometrical arrangement of the molecules. As a first approximation, qualitatively, no great differences in the interaction energies between the different segments of the molecules must be expected when, in the systems under consideration, cyclohexane is replaced by trans-decalin. Final elucidation of this point requires additional thermodynamic data being gathered.l29l3 The geometrical factor must then play an important role in determining the sign of VE. Any arrangement tending to increase the number of contacts between the segments
+
395
of the molecules (ie., the number of nearest neighbors) will be accompanied by a decrease in the volume of mixing. Such must be the case with the mixtures containing heptane and nonane and, to a lesser extent, with those containing dodecane, suggesting, possibly, a coiling of the flexible hydrocarbon chain on the “surface” of the “flat” truns-decalin molecule. This “adaptation” will become stearically more difficult as the length of the hydrocarbon increases. In paraffins higher than dodecane the effect of the interacting forces will predominate and account for the expansion on mixing. Because of the smaller size of cyclohexane, the system cyclohexane n-hexane already exhibits a positive excess volume. A similar explanation may account for the small contraction observed in the cyclohexane trunsdecalin system. Or perhaps here we are observing a situation which approaches the “monomer-dimer” effect predicted by Prigogine’s corresponding-states theory of mixtures of molecules of different sizes.14
+
+
Acknowledgment. The authors wish to thank the Wesleyan Computer Laboratory and Professor Edward K. Blum for their help with some of the calculations. (11) P. J. Flory, R. A. Orwoll, and A. Vrij, J . Am. Chem. Soc., 86, 3507, 3515 (1964). (12) J. D. G6mer-IbLAes and J. J. C . Shieh, J. Phys. Chem., 69, 1660 (1965). (13) H.Brandt, Z.Physik. Chem. (Frankfurt), 2 , 104 (1954). (14) See ref. 1, Chapter 17.
Volume 70, Number 9 Feebruaw 1966
