1319
Isotope Effect in Diffusion of Benzenes
Isotope Effect in Diffusion of Perdeuteriobenzene and 14C-SubstitutedBenzenes in Unlabeled Benzene at 25' Ian R. Shankland and Peter J. Dunlop* Department of Physical and inorganic Chemistry, Adelaide University, Adelaide, South Australia
(Received November 7, 1974)
Mutual diffusion coefficients, obtained with a Gouy diffusiometer, are reported for the system perdeuteriobenzene-benzene (C6&-C&) at 25'. These results are consistent with tracer diffusion coefficients which have previously been obtained in this laboratory for I4C-substituted benzenes of varying molecular weight in benzene. Because of the small difference in refractive index between C& and C6H6 only a limited range of concentrations was studied, and thus it was not meaningful to extrapolate the mutual data to give tracer diffusion coefficients.
In three previous p a p e r ~ l -tracer ~ diffusion coefficients,
DT,were presented for several 14C-substituted benzenes diffusing in unlabeled benzene. The data in those papers indicated that the tracer diffusion coefficients were a very slight linear function of the molecular weight of the tracer species and were not, as has been sometimes ~ u g g e s t e din,~ versely proportional either to the square root of the mass of the tracer species or to the square root of the reduced mass of the system. The purpose of this article is to present diffusion data for the system perdeuteriobenzene-benzene (C6D&&) which are in agreement with our previous findings.
Experimental Section and Discussion The diffusion coefficients for the system C&-C& were measured with a Gouy d i f f ~ s i o m e t e and r ~ a special diffusion cell which have been previously d e ~ c r i b e d ,as ~,~ have also the experimental techniques and computations which are used to obtain the mutual diffusion coefficients, D. The cell was constructed with a Tiselius-type design but did not have moving surfaces which required lubrication. I t is believed that the data for the system C&-C6H6 are accurate to approximately 0.1-0.2%. The data are summarized in Table I. The C6D6 and C,& samples were analyzed by gpc and found to contain less than 0.4 and 0.01% of impurity, respectively. In Figure 1 the data for the system C6D6-c6H6 are shown as a function of the mole fraction of C&, x 2 . The smooth curve has been drawn through the experimental points and the two limiting points derived from the smoothed data of Allen and Dun1op.l The tracer diffusion coefficient a t x 2 = 0 corresponds to 14C-substituted benzene of mol wt 84 diffusing in C6H6; the tracer diffusion coefficient a t x 2 = 1 was obtained by assuming the StokesEinstein equation8 could be used to correct the self-diffusion coefficient of benzene1 to the tracer diffusion coefficient of unlabeled benzene in C&. The viscosity of C6D6 relative to C6H6 for this calculation was measured with a photoelectric viscometerg so constructed that the kinetic energy correction was negligible. The relative viscosity was found to be 1.0637 and differed by more than our experimental error from the value of 1.069 reported by Dixon and Schiessler.lo Also included in Figure 1 are three diffusion coefficients reported by Birkett and Lyons.ll The two sets of data are in agreement within the error of fl% claimed by those workers. Because of the small difference in refractive index be-
TABLE I: Mutual Diffusion Coefficients for the System CRDR-CRHR at 25"
-
AXZ'
X2a
Jb
105~
2.164 0.356, 44.72 0.178, 2.156 0.234, 0.4684 58 -72 0.7004 87.80 2.141 0.3502 103.33 2.105 0.5879 0.824, 74.03 2.100 0.704, 0.590, and A x 2 are the mean mole fraction and the mole fraction difference, respectively, used in each Gouy experiment. * J is the total number of interferencefringes obtained in each experiment.
20
5 0
02
1 06
04 x2
-
5 08
10
Figure 1. Mutual and tracer diffusion coefficients for the system CeHs-CeDs at 2 5': 0,present results; X , results of Birkett and Lyons;g 0 ,tracer diffusion coefficients from Alien and Dunlop.'
tween C ~ D and G C$&, it was decided not to perform any experiments a t concentrations less than x 2 = 0.18 since the errors in the diffusion coefficients would be greater than 0.2%. Thus although one cannot say that the extrapolated tracer diffusion coefficients agree with the results obtained with l*C-substituted benzenes, it is quite apparent that the two sets of results do not disagree. Acknowledgment. This work was supported in part by a grant from the Australian Research Grants Committee. We wish to thank Dr. B. J. Steel for the use of a photoelectric viscometer. The Journal of Physical Chemistry, Vol. 79, No. 13, 1975
Communications to the Editor
1320
References a n d Notes (1) G. G. Allen and P. J. Dunlop, Phys. Rev. Lett., 30,316 (1973). (2)S.J. Thornton and P. J. Dunlop, J. Phys. Chem., 78, 346 (1974). (3) K. R. Harris, C. K. N. Pua, and P. J. Dunlop, J. Phys. Chem., 74, 3518 (1970). (4) L. B. Eppstein and J. G. Albright, J. Phys. Chem., 75, 1315 (1971). (5)G.Kegeles and L. J. Gosting, J. Am. Chem. SOC., 69, 2516 (1947).
(6) H. D. Ellerton, G. Reinfelds, D. E. Mulcahy, and P. J. Dunlop, J. Phys. Chem., 68, 403 (1964). (7)G. R. Staker and P. J. Dunlop, J. Ch8m. fng. Data, 18, 61 (1973).
(8) H. J. V. Tyrrell, "Diffusion and Heat Flow in Liquids", Butterworths, London, 1961,p 128. (9) C. James, Ph.D. Thesis, Adelaide University, Adelaide, South Australia, 1971. (IO) J. A. Dixon and W. Schiessler, J. Phys. Chem., 58, 430 (1954). (11) J. D. Birketi and P. A. Lyons, J. Phys. Chem., 69, 2782 (1965).
COMMUNICATIONS TO THE EDITOR
Energy Disposal In Unimolecular Reactions. Four-Centered Elimination of HCI
TABLE I: Decomposition Products from Methylchlorocyclobutanes Unimolecular decomposition product
Publication costs assisted by the National Sclence Foundation
Sir: The internal energy released to polyatomic products of unimolecular reactions is difficult to measure and, despite several a t t e m p t ~ , l -the ~ internal energy of the olefin produ_ct from four-centered unimolecular H X elimination reactions has not been established. We wish to report definitive results for the vibrational energy released to methylcyclobutene by the HC1 elimination reactions from l-chloro-lmethyl-, l-chloro-2-methyl-, and 1-chloro-3-methylcyclobutane. The present measurements establish that -57% of the total available energy (corresponding to -28% of the potential energy, which is defined as the threshold energy for H X elimination less the endoergicity for final product formation) was retained by the olefin fragment. These conclusions coupled with data from chemiluminescence and chemical laser which give the vibrational and rotational energy of the H X product, and the kinetic energy released in the elimination of HC1 from polyatomic ionsg provide a rather complete characterization of energy disposal by this unimolecular reaction system. Activation of the methylchlorocyclobutane was provided by the C-H insertion reactions of singlet methylene with chlorocyclobutane; experiments consisted of room temperature photolysis of 0.57 cm3 of ketene, 1.7 cm3 of chlorocyclobutane, and 0.25 cm3 of oxygen in vessels of various size to give the desired pressure. The pressure dependence of the relative product yields was measured by dual pass gas chromatographic analysis. Methylene insertion into the carbon-hydrogen bonds of chlorocyclobutane gave 1-methyl-1-chloro-, l-methyl-2with -109 kcal/ chloro-, and 1-methyl-3-chlorocyclobutane mo13J0 of internal energy (Table I). The vibrationally excited molecules (denoted by an asterisk) are collisionally stablized or, at reduced pressure, react by ring rupture and HC1 elimination to give the products shown in Table I. In this communication we are interested in the energy contents of 1- and 3-methylcyclobutene which were monitored The Journal of Physlcal Chemistry, Vol. 79, No. 13, 1975
Insertion products
transcis.and
'>
HC 1
elimination'
- '0.
Ring rupture
+
CHZ=CHCl
CH3CH=CH2
'Cl
cisand trans.
5
)g+ cis- and
+ CH,=CH2
C1 C1
tvuns-CH,CH=CHCl
- b. -b
CH,=CH,
+
CH,=C
/ 'CH,
The 3-methylcyclobuteneproduct is entered in the table only once, although formed by both 1-methyl-2-chloro-and l-methyl-3chlorocyclobutane, because both processes have the same thermochemistry. Conversely the 1-methylcyclobuteneis entered for each formation pathway because the associated thermochemistry is different. a
by the rate of their isomerization reactions to give substituted pentadienes.
'9 CH3
Over the experimental pressure range (70-0.4 Torr) the cispentadiene yield was -20% of the trans isomer. Although
