NOTES
408 1
where the superscripts 1 and 3 represent the multiplicity of the excited electronic state, while an asterisk denotes a molecule with more vibrational energy than a vibrationally equilibrated molecule with superscript zero. The quantum yields obtained here are relative values only. For the purpose of investigating the linearity of l/+os. [A], relative quantum yields are adequate. However, in order to represent these data, we have corrected them so that + = 1 at zero pressure. The fraction of the light absorbed in each cell was always less than 4%; therefore it could be taken as strictly proportional to the pressure in the cell. It is evident that a few per cent of the dissociation takes place by process 8, the dissociation via the triplet state, even below 1 mm. Thus, the quantum yield of dissociation from the singlet excited state directly is obtained by subtracting that via the triplet from the over-all quantum yield, with +" = 0.29. The corrected results are shown in Table I and in Figure 1, where reciprocals of quantum
I
I
0.2
I
I
I
0.4 0.6 0.8 Pressure, m m Hg
1.0
Figure 1.
yields of dissociation via only singlet state are plotted against the pressure. The straight line is drawn by a method of least squares. The experimental error is large at the lowest pressure, but there is no tendency to concavity upward. Therefore, the strong collision deactivation, case ii, is undoubtedly supported in this system.
Acknow2edgmmt' This was supported by a grant from the National Research Council of Canada.
The Isomerization of n-Pentyl and 4-Oxo-l-pentyl Radicals in the
Gas Phase
by L. Endrenyi and D. J. Le Roy Laah Miller Chemical Laboratories, University of Toronto, Toronto, Canada (Received June 18, 1966)
Some years ago Kossiakoff and Rice' suggested that in many cases the activation energy for the isomerization of a long-chain free radical may be much less than the activation energy for its decomposition, and they were able to explain the products of the decomposition of hydrocarbons in terms of intramolecular hydrogen migration in alkyl radicals. Somewhat later, Sefton and Le Roy12in studying the polymerization of ethylene initiated by ethyl radicals labeled in the methylene group with C14, obtained evidence for radical isomerizations involving 1-5 and 1-6 intramolecular hydrogen migration. They showed that most of the product olefins were formed by the decomposition of alkyl radicals and that the molar activity of these was comparable to that of the ethyl radicals which initiated the polymerization. Since a simple decomposition of the long-chain alkyl radicals would have yielded inactive biradicals, and hence inactive olefins, they concluded that the radicals had undergone intramolecular hydrogen migration before decomposition. A number of additional examples have been reported more recently13although quantitative kinetic data are lacking. In the course of a study of the kinetics of the addition of methyl radicals to ethylene it became necessary to follow, in a quantitative way, all of the subsequent reactions of the propyl radicals formed by the addition of methyl radicals (from the photolysis of acetone) to ethylene. From the nature and amounts of certain of the products we were able to obtain kinetic parameters for 1-4 intramolecular hydrogen migration in n-pentyl radicals and somewhat less conclusive data for 1-5 intramolecular hydrogen migration in 4-oxol-pentyl radicals.
Experimental Section Acetone at a concentration of 3.60 X mole was photolyzed in the presence of 0.240 X mole of ethylene (0.300 X mole cm-3 was (1) A. Kossiakoff and F. 0. Rice, J . Am. Chem. SOC.,65,590 (1943). (2) V. B. Sefton and D. J. Le Roy, Can. J . Chem., 34, 41 (1956). (3) E.-A. I. Heiba and R. M. Dessau, J. Am. Chem. SOC.,88, 1589 (1966).
Volume 70,Number IS December 1966
NOTES
4082
used in one of the experiments) using the radiation isolated from a 250-w medium-pressure mercury arc by means of a Corning 9700 filter. The effective radiation consisted mostly of 3130 A. The reaction vessel was a quartz cylinder 6 cmlong and 5 cm in diameter with plane windows. After the removal of GO and CH4 at liquid nitrogen temperature the remaining products were separated into two fractions by pumping the more volatile products through a trap at - 120". Each fraction was analyzed by gas chromatography. Quantitative determinations were based on calibrated relative molar responses using certain reference substances added to the system in accurately measured amounts: one of these, COzJ was added before reaction; the other, isopropyl et)her,was added after reaction. Ethane and butane were determined on a 13-ft, 0.25-in. column containing 35-100 mesh activated silica gel, using elution temperatures of 80 and 130", respectively. The less volatile fraction was analyzed using a 20-ft column containing tri-m-tolyl phosphate (31% by weight on 30-60 mesh firebrick). A more detailed description of the qualitative and quantitative analysis will be presented in a forthcoming publication. The duration of the irradiation ranged from 6 to 21 min, depending on the temperature. The amount of acetone consumed ranged from 4 to 6.3% and the amount of ethylene consumed from 17 to 19%. No studies of the time dependence of the product ratios was made. While the extent of reaction is somewhat greater than one might wish, this was a compromise.
Results and Discussion The portion of the over-all reaction scheme which is relevant to the problem of radical isomerization is shown in Figure 1. Isomerization of n-Pentyl Radicals. If k7 is the rate constant for the isomerization and k-7 is that for the reverse reaction, then in the steady-state d 0 = -(sec-C5Hl1) = k7(n-C5H11) dt
-
k-7(sec-C~H1~)- kg(sec-C5H11)(CH3) (1) or
Thus
-(CHS) ks k7
=
-{ ks Rr[C&&I)"' k3"'k7
k-7 k7
(5) In this development it has been assumed that reactions 7 and 8 are the only ones undergone by secCsHll radicals. Since (CH3) was larger than any other radical concentration, the main additional reaction would be to form C5Hlo by disproportionation. This product was formed, but only in quantities ranging from 0.01 to 0.06 X mole ~ m sec-'. - ~ It has not been taken into account because it could not be measured with very great accuracy. It could be included in eq 5 by multiplying ks by a factor slightly greater than unity. The rates of formation of the various products are given in Table I. Most of the available data on the combination and cross-combination of methyl and npropyl radicals are in substantial agreement with the approximate theoretical estimate that kJ~4/k2~should be equal to l/4, and we have assumed this value in using eq 5.5p6
Table I: Isomerization of n-CaHl1"
502.5 502.9 479.8 457.5 438.5 a
3.10 2.62 2.54 1.97 1.31
1.49 1.27 0.864 0.401 0.203
19.4 22.4 22.1 20.5 15.6
41.9 63.8 79.7 94.2 91.8
12.88 15.60 7.71 4.52 2.99
Rates of formation of products are in moles ern+ sec-* X
1012.
It
to assume that ks
kg
and hence
(n-CSHI1) - ks(n-CaH11)(CHd - Ra4 (SeC-CsHn) ks(sec-CsH11)(CHd R f ti-C.& Also The Journal of Physical Chemistry
1
(3)
(4) We use the terminology Re to indicate the rate of reaction 6 and Rr [i-CeHlc] to indicate the rate of formation of 2-methylpentane. (5) J. A. Kerr and A. F. Trotman-Dickenson, Progr. Reaetion Kinetics,1, 107 (1961). (6) S. W.Benson and W. B. DeMore, Ann. Rev. Phys. Chem., 16, 397 (1965).
NOTES
4083
I
I
I
2.0
2.1
2.2
1000
Figure 1. Reaction scheme for formation and isomerization of O a-CsHsO n-pentyl and 40x0-l-pentyl radicals. Y - C ~ H ~and refer to 40x0-l-pentyl and 2-oxo-l-pentyl, respectively, and EPK, MBK, and MEK refer to ethyl propyl ketone, methyl butyl ketone, and methyl ethyl ketone.
2.3
/ T
Figure 2. Arrhenius plot for the isomerization of n-pentyl radicals.
where
R12 = Rr[MBK] - ki6(CHzCOCH3)(CaH,) Values for k-7/k7 are not available but a reasonably accurate estimate can be made. Thus
where K7 is the equilibrium constant for reaction 7 and AEo is the standard increase in internal energy for the isomeri~ation.~From bond dissociation energy data for the removal of primary and secondary H atoms from normal paraffins A E O can be estimated to be of the order of -5 kcal mole-’, and hence in the temperature range used in these experiments k-7/k7 will be of to 7 X By contrast, the the order of 3 X first term on the right of 5 ranges from 0.51 to 3.2. The quantity k-7/k7 in eq 5 will therefore be neglected. The values of k3ll2k7/ks obtained in this way are given in Table I and in Arrhenius form in Figure 2. A least-squares calculation gave E7 ‘/2E3 - E8 = 10.8 f 0.8 kcal mole-’ and log A7A3’/’/As = 1.58 f 0.35. Assuming A factors of 1013.34 for reaction 3 and 1014 for reaction 8,5 and neglecting their activation energies
+
k7
= 1.4 X lo7 exp(--10.8 X
103/RT)
(7)
Isomerization of 4-0x0-1 -pentyl Radicals. The steadystate treatment of the reaction scheme for this isomerization, shown at the top of Figure 1, is analogous to that which has been given for the isomerization of npentyl radicals. k14
g(CH3) =
k-13 Riz -Rt[EPKl kia
(8)
k3k15
Rt[MEK]Rr[C~Hio] (9) R t [ G H aI
= Rf[MBK]- -
kzkio
The rates of formation of the various products are given in Table 11. The estimation of R12 is subject to error arising from the uncertainty in the value of k3k15/kzk10. A reasonable assumption would be that k15 ‘v klo; if we accept the values k3k4/k2 = 1 / 4 , 5 * 6 k3 = 10ia.34,5 and k4 = 10’4,6it follows that k3k16/k2k~0= k3/k2 = 0.23. These values were used in obtaining the values of Rlz/ Rf[EPK] given in Table 11. The relative constancy of R t [ E P K ] (Rr[CzHs]}l/z/Rizsuggests that this quantity cannot be equated to k13k3~/;lk14, i.e., that k-13/k13 in eq 8 cannot be neglected. Rewriting eq 8 and expressing (CH3) as { R r [CzHs]f‘/z/k31’a
The first term on the right of eq 10 will decrease with increasing temperature while the second term will increase, so that the quantity on the left of eq 10 may be relatively independent of temperature under condi(7) Rigorously, l / K r = e A H ” / R T e - A S ’ / R . However, the number of moles does not change in the reaction A H o = AE’, and the entropies of the two radicals would be expected to differ by very little, 80 that ASo = 0. This is supported by the data for n- and sec-C4H~(J. E. Calvert and J. N. Pitts, Jr., “Photochemistry,” John Wiley and Sons, Inc., New York, N. Y . ,1966, p 819).
Volume 70, Number 19 December 1966
NOTES
4084
Table II: Isomerization of 4-Oxo-1-pentyl" R12 -
a
T,OK
MBK
MEK
EPK
C4HlO
CZH6
RtlEPKl
502.5 502.9 479.8 457.5 438.5
10.77 11.29 8.27 5.07 3.21
36.6 47.5 42.9 34.1 23.8
8.27 9.89 6.58 4.38 2.38
19.4 22.4 22.1 20.5 15.6
41.9 63.8 79.7 94.2 91.8
0.831 0.754 0.840 0.767 0.958
Rates of formation of products are in moles ~ r n sec-1 -~
x
7.8 10.6 10.6 12.6 10.0
lo'*.
tions where k-13 is of the order of magnitude kI4(Rf [CzHs]f"p/k~'p. This suggests that, in the temperature range used, k-13 is of the order of 10'4 X 8 X 10-6/106.7 = 170sec-1.
Discussion Reaction 7 is an intramolecular analog of the reaction R R'H = R H see-R'
+
RrIEPKl {RrlCnHsl)I" _______ Rin x 100
+
Most of the available data when R'H is a paraffin are for R = CHI and indicate that A is of the order of 1011 cms mole-' sec-' and E of the order 8.3 kcal mole-1,6 in comparison with A7 = 1.4 X lo7 and E, = 10.8. The low value of A , cannot be attributed solely to the loss of the entropy of rotation about the three C-C bonds which are incorporated into the cyclic activated complex. The A factor of a unimolecular reaction can be written, in terms of transition-state theory, in the form
The increase of ca. 2.5 kcal mole-' in activation energy above that for an intermolecular hydrogen abstraction can probably be accounted for by the strain energy on forming the cyclic complex. Kaarsemaker and Coops1ohave estimated a strain energy of 6.5 kcal mole-' for cyclopentane, in contrast to the strainfree configuration in cyclohexane. A quantitative comparison of inter- and intramolecular hydrogen abstraction is probably not justified since the dynamics of the two processes are quite different. Acknowledgments. The authors wish to express their appreciation of the assistance of Mr. Frank Safian. The financial assistance of the National Research Council of' Canada is gratefully acknowledged. (8) J. D. Kemp and C.J. Egan, J . Am. Chem. SOC.,60, 1521 (1938). (9) J. G.Aston and G. H. Messerly, ibid., 62, 1917 (1940). (10) S . Kaarsemaker and J. Coops, Rec. Truv. Chim., 71, 125 (1952).
A = K ekTy e AS'/R h
If the transmission coefficient K is assumed to be unity, then A S + = -31 eu at the mean temperature of 470°K. Kemp and Egan8 have estimated an entropy for the restricted rotation of the two methyl groups in propane of 3.84 eu at 298.2"K1 and Aston and Messerlys have estimated an entropy of 1.44 eu for the restricted rotation of the ethyl group in n-butane at 272.66"K. It is evident, therefore, that the removal of internal rotation alone cannot account for an entropy of acti1. I n order to treat the results vation of -31 eu if K in terms of transition-state theory it is necessary to assume that x
