NOTES
July, 1959 is higher than the 530-mp peak, whereas in water the relative peak heights are reversed. Acknowledgments.-Help from Mr. Wayne A. Lavold, who prepared the trans-compound, and Miss Mary E. Burke, who took data during some of the night rate work, is gratefully acknowledged.
1217
b
PENTANE
NORMAL
SELF-DIFPUSION COEFFICIENTS O F ISOMERIC P E N T A N E S BYE. FISHMAN A N D T. VASSILIADES Department o/ Chemistry, Syracuse University, Syracuse, N. Y . Received December 4 , 1968
An earlier paper by one of us2 reported the selfdiffusion coefficients of n-pentane and n-heptane measured over an extended temperature range. Interpretation of the data by the Eyring theory of rate processes3 was undertaken, since normal hydrocarbons provide a direct test of the simple model used in that theory. It was found that the theory correlated the self-diffusion, viscosity and molecular size data quite well. This paper reports an extension of the earlier work to a situation where molecular shape rather than chain length is the variable parameter whose effect is correlated by the Eyring theory. The self-diff usion coefficients of isopentane and cyclopentane were measured over an extended temperature range and found to follow the equ at'ions D = 9.8 X 10-4 e-17881RT for isopentane and D = 3.0 X 10-3e-27600'RT for cyclopentane. These are to be compared with D = 8.1 X 10-4 e-16871RT for n-pentane. As in the previous work, a range of capillary lengths and diffusion times was employed in order to check for systematic error. Coiivincing evidence that the systematic errors in this particular capillary diffusion technique are small is shown by the comparison of the results given in ref. 2 with the self-diffusion data on the same liquids published by Douglass and McCa1L5 Although both the capillary and the spin-echo techniques are open to criticism for possible uncorrected systematic errors, the two methods are completely independent of each other and their close agreement tends to confirm both techniques. Results and Discussion.-The results are shown in Table I ; reported diffusion coefficients are averages of a t least four determinations. Figure 1 iiicludes the data on n-pentane aiid neopeiitaiie for comparison. The straight lines were determined by the method of least squares; equas4
(1) Based on the Master's Thesis of T. Vassiliades, Syracuse University (1958). Presented a t the 134th meeting of the American Chemical Society, Chicago, Ill., September 12, 1958. (2) E. Fishman. THISJOURNAL, 59, 4F9 (1955). (3) S. Glasstone, R. J . Laidler and H. Eyring, "The Theory of Rate Processes,'' McGraw-Hill Book Co., New York, N. Y., 1941. (4) D = 4.6 X 10-8 has been reported for neopentane (private-communication. David W. RlcCall.) ( 5 ) D. C. Dounlabs and D. W. McCnll, T ~ i Js O U R N A L 62, , 1102
(lY58).
CY CLOPENTANE
7,
I
I
\
4.00
3.00
\
Ip
I
io3 .
I 6.08
5.00
"bK
Fig. 1.-The
logarithm of the self-diffusion coefficient reciprocal temperature.
vet.
TABLE I SELF-DIFFUSION COEFFICIENTS OF Iso- AND CYCLOPENTANES' --Isopentane-Teinp., OC.
x 106, cm.a/sec,
D
r-Cyclopentane--Temp., OC
x 106, cm.a/sec.
D
46.2 3.97 4.85 3.20 30.0 3.41 0.0 2.00 3.83 2.31 -22.9 1.09 -78.5 1 .OG -78.5 0.28 a The average error in the incusurements, based OJA CIie average deviation of D from its mean value a t each Uemperature, is about 5%. 25.5
10.0 0.0 -33.9
tions for the lines have been presented above. The frequeiicy factors and the activation energies are in the order cyclo > is0 > normal. Since the activation energy dominates in determining the magnitude of a rate constant a t a given temperature, cyclopentaiie has the lowest diffusion coefficient although the frequency factor is highest. This means that diffusion of the most symmetrical molecule is favored by orientation or entropy factors, but relatively opposed by energy considera-. tions. This idea will be explored quantitatively below. It would be expected that cyclopentane, having the highest energy of vaporization, would also1 have the highest activation energy for diffusion ; however, this alone does not account for the largeness of the activation energy. As may be seen in Table 11, cyclopentane uses a larger fraction of its vaporization energy for diffusion than the less symmetrical pentanes. This ratio has been correlated with the fraction of the intermolecular bonds
Vol. 63
NOTES
1218
TABLE I1 RATIOOF VAPORIZATION TO ACTIVATION ENERGIES AT 0’ E Yap
Liquid
(kcal./mole)
n-Pentane Isopentane Cyclopentane
5.7 5.8 6.9
E*difl
(kcal./mole)
1.6 1.8 2.8
TABLE I11 EVALUATION OF A S * AT 0’ ASSUMING 1.3 A.
Ratio
D X 106
EvapjEdilf
3.6 3.2 2.5
FOR X
X%,AS*/R
Liquid
cm.2/sec:
A.
AS*, e.u.
n-Pentane Isopentane Cyclopentane
4.14 3.83 2.00
0.71 0.82 2.76
-2.4 -1.8 0.59
existing in the liquid lattice for each molecule sequence of AS* values is not changed by any which must be broken in forming the activated reasonable choice of A’s. These relative values of complex for flow. Thus the data of Table I1 AS* indicate a greater need for orientation in the imply that, in moving through the liquid lattice, diffusion of the normal hydrocarbon molecule than the extended chain molecule proceeds with less for the cyclic isomer. Thus the n-pentane, when distortion of the lattice than the more spherical compared to more symmetrical molecules, has a molecule, which requires nearly half of its vapor- lower frequency of properly-oriented jumps (the ization energy to reach the activated state for jump should be along the chain axis) but a much diffusion. larger proportion of the jumps leads to diffusion. If the usual assumptions of the Eyring rate proc- The energy barrier is relatively low in this favored ess theory are accepted, an entropy of activation direction and the over-all diffusion rate is higher. can be calculated from the diffusion coefficients In conclusion, the lattice parameters, XI and and the activation energy using the equation (X2XJ)’/*, defined in the Eyring theory and calculated from the self-diffusion and viscosity coeffiD = eX2 kT - eAS*/R e-AE*/Rl’ cients a t 0” are shown in Table IV. It is obvious h that these parameters do not show the expected Here, all constants have their conventional meaning isomeric trends. and A, with the dimensions of em., is a jump disTABLE IV tance for an individual diffusion step. The freLATTICE PARAMETERS AT 0’ quency factor, then, is the collection of terms eX2 DdkT ( k T / h ) e A s * / R , and a t any one temperature, differ; x : 1 Liquid om. ~(ca.) XI, A. (XnW‘l’ ences in frequency factor from one system to 2.4 8.8 3.0 111.6 another are contained in the term X2eAS*IR. There n-Pentane 2.8 112.5 2.3 9.0 is, a t present, no way of obtaining an independent Isopent ane 2.2 8.3 3.2 91.6 value of A; in order to calculate AS* B value of X Cyclopentane Viscosities taken from Timmcrmans, “Physic0 Chemimust be assumed. Table 111 shows the results for cal Constants of Pure Organic Compounds,” Elsevicr PubA S * calculated a t 0” with the assumption of 1.3 A. lishing Co., New York, N. Y. for A, the length of a methylene group in a satuAcknowledgment.-The authors are grateful to rated hydrocarbon. Other assumptions about A, say using the length of each molecule, lead to the Research Corporation for generous support of different numerical results for A8*, but the this research. 0
\ I
. I
