Communicationsto the Editor
1317’
Comment on the Communication, “Thermal Decomposition of Cyclobutanone,”by A. T. Blades and H. S. Sandhu
Sir: I n the above-mentioned communication Blades and Sandhu indicate a possible discrepancy in previously published data on the activation energy for the formation of cyclopropane in the thermal decomposition of cyclobutanone. I n results published by Blades1 the activation energy for cyclopropane formation obtained from relative rate 0.5 kcal/mol measurements was determined to be 6.0 higher than that for the formation of ethylene. The data of McGee and Schleifer2 indicate activation energies of 51.9 f 0.8 and 56.3 1.2 kcal/mol for ethylene and cyclopropane, respectively, resulting in a difference of 4.4 A 2.0 kcal/mol. The relative rates’have been graphed on an Arrhenius type plot (Figure 1) to resolve this problem3 since such an analysis should be inherently more accurate. A value of 5.5 0.3 kcal/mol for the difference in activation energies is calculated from this plot. We feel that within experimental conditions, this result is in agreement with that previously published by Blades. Along with our reported value of 51.9 kcal/mol for the activation energy for ethylene formation this results in an activation energy of 57.4 kcal/mol for the cyclopropane formation. This slightly revised figure does not alter any of the mechanistic conclusions already published.2
ligible, but not zero. The analysis of Blades and Sandhu supports this in that their results indicate propylene formation to the extent of less than l%of the cyc1opropane.l Unfortunately, this amount was not detectable with accuracy under our experimental conditions. The formation of propylene does not conflict with the conclusion that cyclopro. pane and carbon monoxide are formed in the decomposition of cyclobutanone via a concerted mechanism. The forma. tion of propylene to such a small extent substantiates the conclusion that the trimethylene diradical is not formed1 during the reaction.
*
*
*
(1) A. T. Blades, Can. J. Chem., 47, 615 (1969). (2) T. H. McGee and A. Schleifer, J. Phys. Chem., 76, 963 (1972) (3) The authors thank Dr. Blades for this suggestion.
York College of The City University of New York Jamaica, New York 11432
T. Howard McGee* A. Schleifer
Received March 12, 1973
Chemical Relaxation of Aqueous Rhodamine B1
Sir: The concentration-jump relaxation method has recently been applied to studying the kinetics of fast reaction$ and bonding in dye aggregates.3 In the present work we used the technique to the dimerization of the laser dye rhodamine B in aqueous solution. Knowledge of the spectroscopic properties, as well as the kinetics of the aggregation of the dyes involved, is basic to the understanding of organic dye lasers, since dimer formation is detrimental to laser action in most cases.* The single relaxation times T of the monomer (M+)dimer (D2+) equilibrium 2Mf
-
A D2+
(1)
ob-1
2.05
L ‘I
1.40
1.50
1-45
I/PX
1.55
1.60
103
Figure 1. Plot of log [ R ( C Z H ~ ) / R ( &vs. ] t h e reciprocal of the absolute temperature.
A larger disagreement exists between theoretical and experimental values of the C3 ring-closing activation energy as discussed above by Blades and Sandhu. These discrepancies are not resolved and clearly additional studies are required in this area. It should be noted, however, that using 1.0 kcal/mol as a lower limit for the C3 ringclosing activation energy results in a calculated Ea = 69.6 kcal/mol for the formation of cyclopropane via the . C O C H ~ C H ~ C H Zdiradical. . The observed Ea = 57.4 kcal/mol (as recalculated above) remains significantly lower. Thus, the concerted decomposition of cyclobutanone into c-CsH6 and CO is still favored as the dominant reaction mechanism. Finally, the calculations of McGee and Schleifer indicated that within the experimental conditions employed the rate of propylene formation from cyclopropane is neg-
of the dye we measured a t 9 and 22“, range from 0.67 to 3.65 msec if the total concentration CT is between 1.82 X 10-5 and 5.45 X 10-6 M (Figure 1).At larger CT the relaxation is too fast for the method used, and a t smaller CT the dimer concentration CD is too low. Due to large OD changes, as well as to sufficiently large perturbations caused by sudden 11-fold dilution, we were able to measure shorter relaxation times than the ca. 1.5-msec dead time of our Gibson-Milnes type stopped flow apparatus. In such a case, while the system is far from equilibrium, the nonlinear part of the relaxation occurs during the dead time. The linear end of the relaxation, that would correspond to a small perturbation, is observed after stopping. The experiments were performed at natural ionic strength of the dye solutions, where the square of the reciprocal relaxation time 7 - 2 of equilibrium 1 is given in terms of total concentration CT by Taken in part from M. M. Wong’s Ph.D. Thesis, to be submitted at the University of Georgia. 2 . A. Schelly, R. D. Farina, and E. M. Eyring, J. Phys. Chem., 74, 617 (1970). 2. A . Schelly, D.J. Harward, P. Hemmes, and E. M. Eyring, J. Phys. Chem., 74, 3040 (1970). J. E. Selwyn and J. I. Steinfeld, J. Phys. Chem., 76, 762 (1972). The Journal of Physical Chemistry, Voi. 77, No. 10, 1973
Communications to the Editor
1318
I
T
lim
-2 N
I0 u)
-'
: 0 X III
-O
.I C,
x
1
I
I
2
IO',
0
M
Figure 1. 7-* vs. CT at 9" ( 0 )and 22" (0).
Equation 2 is obtained from the expression for the reciprocal relaxation time 7-1 of equilibrium 1 5
(3) by using the relationships o k l / o k - l = cDfD/cM2fiv2 and CT = CM 2cD. Since the activity coefficients fi 1 as CT 0 , the ionic strength independent forward okl and reverse 012-1 rate constants were determined from (2) using
-
+
The Journai of Physicai Chemistry, Voi. 77, No. 10, 1973
+
7-2
=
ok-12
(4)
CT-0
and K = o k i / o k - i , based on non-linear least-squares fitting of the experimental data. The equilibrium constants K = C D / C Mwere ~ computed from the absorption spectra taken at 9 and using an iterative method previously described.6 At the two temperatures, Kg. = 1.55 X 103 M - l and K229'= 1.44 X lo3 M-1. At 9" the forward and reverse rate constants are okl = 3.1 x lo5 M-1 sec-1 and ok-1 = 2.0 X lo2 sec-I; at 22" okl = 4.5 x 105 M-1 sec-1 and ok-l = 3.2 X 102 sec-1. The activation energy for association is El = 4.9 kcal mol-1, and for the dissociation reaction E-1 = 5.8 kcal mol-1. These values are in good agreement with AH" = -935 cal mol-1 of the equilibrium. Other laser dyes in different solvents are also being studied at the present time, and a comparative analysis will be presented later.
Acknowledgment. This work has been supported in part by the Research Corporation and the National Science Foundation. The authors are indebted to R. Sexton, R. E. Morton, M. W. Williams, and R. J. Krusberg for technical assistance. (5) 2. A. Schelly, R . D. Farina, and E. M. Eyring, Monatsh. Chem., 101, 493 (1970), (6) A. R. Monahan and D. F. Blossey, J. Phys. Chem., 74,4014 (1970)
(7) NSF-URP participant. Department of Chemistry University of Georgia Athens, Georgia 30602 Received February 14. 1973
M. M. Wong
R. A. Heckman' 2 . A. Schelly"
