PHOTOCHEMISTRY OF AZOISOPROPANE
1685
Photochemistry of Azoisopropane in the 2000-A Region1 by M. Louis Arin and Colin Steel* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02164 (Receited August $8,1971) Publication costs assisted by the National Science Foundation
The photochemistry of aeoisopropane (AIP) using light in the 2 0 0 0 4 region (n -+ V * excitation) has been studied and compared with the n -+ T * photochemistry. The data are consistent with the formation of vibrittionally excited isopropyl radicals which, unless collisionally deactivated, undergo unimolecular elimination of either H., reaction 6, or CH3.,reaction 7. The pressure-wavelength data are fitted by As = A7 = loL4sec-', E2 = 41 kcal mol-', and E70 = 46 kcal mol-'. The mean energy of the isopropyl radicals is -35 kcal mol-', but they are formed with a wide energy spread of -40 kcal mol-'. The various radical reactions involving He, CHa., and C3H7. in the system have been studied and compared with the literature values. The ratio of hydrogen abstraction from AIP by H ' to addition of H . to AIP, kl0/k11, has the value of 0.10. The,quantum yield of decomposition = 0.97 & 0.08 and is independent of wavelength or intensity in the 2000-A region; it is also independent of pressure up to at least 400 Torr.
Introduction Azoalkanes exhibit a weak n + T * absorption band (So --t SI) centered in the region 340-360 nm ( E -10 M-' cm-l) and a stronger absorption (So-t Sz) in the 200-nm region (e -1000 M-' cm-l). The nature of the latter band has been the subject of some discussion. A recent spectroscopic investigation assigns it to an n+ --t a* transition.2 Prior investigations into the photodecomposition of azoalkanes were carried out using n -t T:* excitation. For such excitation at room temperature, the reactions involved in the photodecomposition of asoisopropane (AIP) may be written3 AIP -% ---f AIP+ AIP+ X ---f AIP X
+
(1)
+ AIP+ * 2CaH7' + Nz 2CaH7- +C3HO + C3HS
(3)
2C3H7 -+ C6H14 (diisopropyl)
(5)
(2) (4)
At higher temperatures abstraction and addition reactions of the radicals have also to be ons side red.^ Two questions arise. First, in view of the known ability of cyclic azoalkanes to yield vibrationally excited cyclic hydrocarbon^,^-^ can acyclic azoalkanes be used as a source of vibrationally excited radicals? Second, what is the state represented by AIP+? The possible unimolecular reactions of vibrationally excited isopropyl radicals (C3H7'*) are
+ He C3H7. * +CzH4 + CH3. CaH7. * ---f CsHa
+
Nz is endothermic by 15.2 kcal m ~ l - ' . ~ , ~ Thus it is not surprising that light of wavelength 355 nm, which corresponds t o the absorbance maximum of the n --.t T * band and has an energy of 80.5 kcal einstein-l, does not cause the formation of "hot" C3H7. radicals. This, however, should not be a limitation at 200 nm. Of course, even at this wavclcngth, although it is energetically feasible, there may bc mechanistic restrictions to the production of "hot" radicals. Vibrationally excited isopropyl radicals havc been produced by thermal and by chemical activat i ~ n . ~ - 'The ~ results from several laboratorics for reaction 6 have been summarized by Frey and W a l ~ h ' ~ and compared with a calculated value (vix., AB = 1013.4 sec-l and E t = 41.7 kcal mol-'). There are also + 2CaHv.
(6)
(7)
The critical energies Ea0 and E+ for these reactions are about 41 and 46 kcal mol-' (see Discussion). Radicals possessing sufficient energy to carry out these unimolecular reactions we call "hot." The reaction AIP
(1) Abstracted from Ph.D. Thesis of M. L. Arin, Brandeis University, 1971. (2) M. B. Robin, R. R. Hart, and N. A. Keubler, J . Amer. Chem. Soc., 89, 1564 (1967).
(3) R. H. Riem and K. 0. Kutschke, Can. J . Chem., 38, 2332 (1960); R. W. Durham and E. W. R. Steacie, ibid., 31, 377 (1953). (4) T. F. Thomas, C. I. Sutin, and C. Steel, J . Amer. Chem. Soc., 89,
5107 (1967). (5) P. Cadman, H. M. Meunier, and A. F. Trotman-Diekenson, ibid., 91, 7640 (1969). (6) F. H. Dorer, E. Brown, J. Do, and R . Rees, J . Phys. Chem., 75, 1640 (1971); H. M. Frey and I. D. R. Stevens, J . Chem. Soc., 4700 (1964).
(7) J. G. Calvert and J. N. Pitts, Jr., "Photochemistry," Wiley, New York, N. Y., 1966, p 819. (8) G. E. Coates and L. E. Sutton, J . Chem. Soc., 1187 (1948). (9) C. A. Heller and A. S. Gordon, J . Phys. Chem., 62, 709 (1958). (10) K. S. Konar, R. M. Marshall, and J. H. Purnell, Trans. Faraday Soc., 64, 405 (1968).
(11) J. A. Kerr and A. F. Trotman-Dickenson, {bid.,55, 921 (1959). (12) R. A. Back and S. Takamuku, J . Amer. Chem. Soc., 8 6 , 2558 (1964). (13) W. M. Jackson and J. R. MeNesby, J . Chem. Phys., 36, 2272 (1962). (14) W. E. Falconer, B. S. Rabinovitch, and R. J. CvetanoviE, ibid., 39, 40 (1963). (15) H. M. Frey and R. Walsh, Chem. Rev., 69, 103 (1969).
The Journal of Physical Chemistry, Vol. Y6,N o . 12, 1972
1686
M. LOUISARINAND COLINSTEEL
many reports on reaction 7, with E7O ranging from 20 to were not significantly different from those in which the 35 kea1 mol-' and A, from 108.5to 1 0 ' 6 ~~~e c - l . ~ - I ~ monochromator was not employed, the latter was only Nevertheless, although Ey0is reported as being less than used in the quantum yield determinations (vide infra). Eso,Falconer, et al.,14were unable to find any evidence In fact, we found that the simplest way to change the effor (7) when C3H7-* mas produced by chemical activafective wavelength of photolysis was to interpose a filter tion, while Jackson and McNesby13 found that in the consisting of a quartz 1-em cell filled with an aprange 7454323°K an uppcr limit for k7/k6 was 0.06. propriate gaseous olefin in the pressure range 40-200 Frey and Walsh have suggested that the only reasonable Torr. The relative intensities of different frequencies route for (7) is via the n-propyl radical, and on this from the lamp incident on the filter, I @ ) ,were estimated basis have calculated as a lower limit for E70 the value from the published arc spectrum,22the measured trans43 f 4 kea1 mol-1, with A7 = lO13*1 sec-1. mission of the quartz used in fabricating the envelope of Cyclic azoalkanes are known to be able to dissociate the lamp, and the measured absorption spectrum of from both their first singlet (SI) and triplet (TI) oxygen at the pressure and pathlength equivalent to the There is little convincing evidence for air gap between the lamp and the cell.23 If F,(F)is the involvement of vibrationally excited ground states the fraction of light of frequency o transmitted by (Sovib)in their photochemistry. In contrast, although is the probability of absorption by filter i and Paz0(p) it was not generally clearly stated, the implication in the azoisopropane, then the rate of decomposition when early literature on the photochemistry of acyclic azo filter i is used is given by compounds was that dissociation occurred from Sovib. More recently, however, there have been suggestions R t = LmI( p) F i( 7) P a , a (p) a d e c (p) dii (8) that a triplet state may be the one from which dissociation O C C U ~ S . ~ ~ ~ ~ ~ where @deo(p) is the decomposition yield a t frequency V . If @dec(o) is frequency independent, then
Experimental Section
Materials. The preparation and purification of AIP have been described p r e v i o u ~ l y . ~The ~ impurities found in AIP were primarily Ca and c6 hydrocarbons and acetone. The impurities were reduced to less than 0.01% on a preparatory gc column consisting of 10 ft of 0.375-in. 0.d. aluminum tubing packed with Chromosorb W (60/80 mesh) coated with Dow Silicone 710. The level of the impuritics slowly increased with time, although samples were stored at Dry Ice temperature.20 It was therefore necessary to occasionally repurify the samples. Available commercial sources of carbon dioxide were found to contain traces of C1 and Czhydrocarbons which were removed by trap-to-trap vacuum distillation. Prepurified nitrogen was used without further purification. Samples for photolysis were vaporized into photolysis vessels on a greaseless, mercury-free vacuum line which had been evacuated to less than Torr before filling. The photolysis vessel consisted of a quartz cylindrical optical cell (1 = 5 em) fitted with a bellows highvacuum valve. Mixtures of AIP and an added gas were made up by first filling the reaction vessel to the desired azo pressure, then quickly expanding a higher pressure of the added gas into the vessel. Pressures were measured by means of a Texas Instrument quartz spiral pressure gauge calibrated throughout the range 2 X to 5 X lo2 Torr. Light Sources. Most samples were photolyzed by collimated light from a deuterium arc (Sylvania DE50A). In the first experiments this light was passed through a monochromator (Bausch and Lomb high intensity) to isolate the 200-nm region. But since this resulted in a large loss of intensity and since the results The Journal of Physical Chemistry, Vol. 76, N o . 1.9, 1974
R,
Lm
= adec
I(F)Fi(o)P~zo(F)dF
The effective frequency of photolysis, defined by
Teff,
for filter i is
~ffI(o)F,(o)P.,o(o)ds = 0.5
Typical curves are shown in Figure 1. Effective photolysis frequencies, em-' (wavelengths, nm) were as follows: no filter, 51,300 (195); ethylene filter, 50,000 (200) ; propylene filter, 49,020 (204); trans-butene-2 filter, 47,620 (210); cyclohexene filter, 46,300 (216). It is not practical to use any longer wavelength filters since the So + Szabsorption of AIP only commences (16) W. D. K. Clark and C. Steel, J. Amer. Chem. Soc., 93, 6347 (1971); B. S. Solomon, T . F. Thomas, and C. Steel, ibid., 90, 2249 (1968); P. Scheiner, ibid., 90, 988 (1968); S. D. Andrews and A. C. Day, Chem. Commun., 667 (1966); P. S. Engel, J. Amer. Chem. SOC., 89,5731 (1967). (17) I . I. Abram, G. 6. Milne, B. S. Solomon, and C. Steel, ibid., 91, 1220 (1969). (18) S. Collier, D. Slater, and J. Calvert, Photochem. Photobiol., 7, 737 (1968). (19) R. Renaud and L. C. Leitch, Can. J. Chem., 32, 545 (1954). (20) The infrared spectrum of a thin liquid film of AIP which had not been rigorously purified showed a weak absorption at 1572 cm-l. This has been assigned t o a -N=N-- stretching frequency.21 Gas chromatography showed the presence of acetone, which has an absorption at 1572 cm-1. After careful purification, a liquid layer of AIP as thick as 0.05 mm gave no absorption in this region. (21) R. J. LeFBvre, M. F. O'Dwyer, and R. L. Werner, Aust. J. Chem., 14, 315 (1961). (22) K. Watanabe and C. Inn, J. Opt. SOC.Amer., 43, 32 (1953). (23) J. R. McNesby and H. Okabe, Adsan. Photochem., 3, 174 (1964).
PHOTOCHEMISTRY OF AZOISOPROPANE
.-c I)
0.1
I
I
I
I
1687 I
D
2
0.4-
a
? 9
0.2
ci-
0.1
li: -G. Y
Table I: Calculated and Experimental Rates of A I P Photolysis Using Different Filters
I J(cm-l) x
IO-^
Figure 1. Product of light intensity incident on photolysis cell, Ir(s)F&), and fraction of light absorbed by AIP, (1 us. frequency for various hydrocarbon filters. F i (B ) is the fraction of the light transmitted by the filter i : i = 0, no filter; i = 1, ethylene; z = 2, propylene; i = 3, transbutene-2; i = 4, cyclohexene.
at 220 nm. A typical light intensity was such that when the arc was used without an olefin filter 2 X 10l2 photons/(cm3 sec) were absorbed by 0.25 Torr of AIP. When the monochromator was used in the quantum yield experiments, the intensity was reduced so that about 2 X 1Olophotons/(cm3 sec) were absorbed by the same pressure of AIP. Photolyses in the 355-nm region (n --t n*) were carried out as described p r e v i o u ~ l y . ~ ~ Quantum Yields. In the measurement of quantum yields, the monochromator was used to isolate appropriate wavelength regions. The absolute intensity of 254-nm light issuing from the monochromator was determined by ferrioxalate actinometry,26while the intensity at 200 nm relative to that at 254 nm was detcrmined using a sodium salicylate screen as photon counter.26 This enables the absolute intensity of light at 200 nm to be determined. I n determining the effect of wavelength on the quantum yield, the rates of decomposition for different gaseous filters were calculated using eq 8, on the assumption that +dec(p) = constant. The calculated and experimental results are shown in Table I. Considering the uncertainty in the estimation of I ( $ , the agreement may be considered satisfactory. There is certainly no evidence for a significant wavelength dependence for +de0 in the 200-nm region. Unless specifically stated otherwise in the text, photolyses were carried out using the full arc. Product Analyses. AIP and C3 and Cehydrocarbons were analyzed by flame ionization gas chromatography using a 25 ft X ‘/s in. column of 10% SF-9G on Chromosorb W. C1-C4 hydrocarbons were separated on a 10 ft X 0.175 in. column of activated alumina coated Oxygenated hydrocarbons were with 1% 8F-96. separated on a 25 ft X 0.175 in. column of 10% Ucon Polar on Chromosorb W. Hydrogen and nitrogen analyses were carried out by thermal conductivity gas chromatography using Molecular Sieve 13X. The
Effeotive photolysis wavelength, nm
Filter
Exptl
Calod
200 204 210 216
Ethylene Propylene trans-Butene-2 Cyclohexene
1.0 0.60 0.33 0.079
1.0 0.52 0.26 0,077
r-Ri/Rethylene-F
concentration of AIP was also determined spectrophotometrically using a Cary 14. The percentage decomposition was measured in the following ways: (a) change in absorbance of AIP, (b) nitrogen evolution, (c) change in AIP concentration measured by gas chromatography, and (d) total hydrocarbon formation. I n the latter method which is essentially a “carbon count,” we use the fact that 1 mol of C6NzH14 (AIP) is equivalent to 6 mol of CH4, 3 mol of C&, and so on, in calculating the number of moles of AIP consumed. The hydrocarbons observed were CH4, CzH4, CzHB, C3H8,C3H6,i-CdHlo, and C6H14 (diisopropyl). Some data are shown in Table 11. The good agreement among the methods indicates that all the products are being observed and that there is no significant loss due to side reactions such as polymerization, for example. Table I1 : Percentage Decomposition in AIP Photolysis Measured by Different Methods
Run
183 184 186 187 175 177 178 180 196
Type
n+
?F*
n + ?r* n + ?r* n d ?r* n d Q* n + u* n + u* n + u*
n d
u*
,----Method a
51.9 62.8 59.4 38.9 13.3 58.1 52.9 50.4 30.2
of analysis----b
0
d
54.6 64.6 60.4 37.0 10.4 61.5
13.5 59.2
12.8 60.3 52.1
49.1 29.1
Eflect of Extent of Photolysis on Product Distribution. A series of photolyses was carried out to different extents of completion to determine the effect of prolonged photolysis on the rate of AIP consumption and on the product concentrations. If a product P, is formed at a rate proportional to the consumption of AIP, then throughout the range we (24) G. S.Milne and C . Steel, J. Phys. Chem., 72, 3754 (1968). (25) C. G. Hatchard and C. A . Parker, Proc. Roy. Soc., Ser. A , 235,
518 (1956). (26) F. 8. Johnson, K. Watanabe, and R. Tousey, J. Opt. SOC. Amer., 41, 702 (1961). The Journal of Phgsical Chemistry, Vol. 76, No. 16,1976
M. LOUISARIN AND COLINSTEEL
1688 should have [Pt]/A[AIP] = K t , where Kt is a constant and A [AIP] is the change in AIP concentration. I n the range 0-95% completion, we obtain such a constant for diisopropyl, but this was not true for the other products. For propylene, K t tended to decrease slightly as the photolysis proceeded, while the Kt’s for the other products increased. This can be seen from the data given in Table 111, where we tabulate the product concentration normalized on c6 (diisopropyl) at 5 and 50% decomposition. Because of this effect photolyses were generally carried out to [CzHS I, ethyl-ethyl dimerizations and disproportionations can be neglected as a major fate of CzHs. radicals. Using the literature valuezefor the rate constant of (16) and the values given above for All and Ello,we calculate that for PAW = 0.29 Torr and P c ~ H=, 16.0 Torr, 83% of the hydrogen atoms should be consumed by (16). The literature valuea5of k17/k17 kls kls = 0.72; thus, the calculated value of [C5Hlz]/[CaHslxs is (0.83) (0.72) = 0.60. Unfortunately, CQH6could not be measured directly, since the large CzH4 peak swamped the C3H6 peak on the gas chromatogram. We had to estimate its value indirectly by carrying out two experiments, one with CZH4 as the added gas and the second with the same pressure of C 0 2 as added gas. I n the second experiment, the ratio [C3Ha],,/[&] was found to be 0.232. This, together with the known pressure of N2produced in the first experiment, allowed us to estimate the pressure of CBHB,, produced in the first experiment as 0.0151 Torr. The observed pressure of CsH12 was 0.00804 Torr. Thus the experimental value of [ C & I ] / [ C ~ H = B ]0.00804/0.0151 ~~ = 0.53, in good agreement with the calculated value of 0.60. Because ethylene is in such large excess, it did photolyze to a small extent during the photolysis of AIPethylene mixtures even though the photolyses were carried out using the propylene filter. The pertinent data are given in Table IV. It will be seen that after correction for the H2 produced by direct photolysis of CzH4 there is little, if any, H2 produced by the photolysis of AIP in presence of excess ethylene, which is to be expected if most of the H atoms are now reacting by (16). (4) Production of Methyl Radicals. According to the proposed mechanism methyl radicals are produced by
+ +
I '
-1.0
I
1
1
'1
I
I
I
I
I .o
2.0
3.0
0
log Pto+ (Torr)
Figure 4. Relative yields of hydrogen and excess propylene, at various pressures, in the photolysis of AIP: (0)A I P alone, ( 0 )Ptot = 0.27 Torr of A I P 392 Torr of COZ.
+
The Journal of Physical Chemistry, Vol. 76, No. 12, 1972
x
PNa
PHa
PX,
x io*,
Torr
Torr
104, Torr
8.4 0 8.8 8.7
14.3 15.0 9.2 9.5
45.6 45.4 39.5 41.2 2.2
(CzHa) (CzHd) (COz)
(COz)
x
(02)
(7) ; these should then react with isopropyl radicals by combination and disproportionation reactions 12 and 13. The literature values of kla/klz are close to 0.20.aa I n this study, we found (see Table I1 for example) kl3/klZ = [CH.J[i-C4Hlo] = 0.24 f 0.03. The cross combination ratio, C, for methyl and isopropyl radicals is defined by
Several such cross-combination ratios have been found for different radical pairs-the value being close to two in each case.37 In this study we found C = 1.9 f 0.1. However, we should also have [CzHd] = [ C ~ H ~ O ] [CH, J, while we always found that the right-hand side of this equation was about 35% greater than the left-hand side, indicating that there is a source of CH, other than (7). We know that acetone is an impurity in AIP (see Experimental Section). Therefore, samples were carefully purified by gas chromatography so that the acetone was E$, and the good agreement with experiment is further evidence that the activation energy of reaction 7 cannot be less than that of reaction 6. Corresponding to the different gaseous olefin filters, we have diff erent “effective” photolysis wavelengths I n Figures and hence possibly different values of &b. 10 and 11 we have plotted [CIH&,/2A[AIP] and [C,H4]/2A[AIP] against the photon energy for the different filters. The full-line curve is that calculated I 145I I I I \ I by setting E v i b = 90 kcal mol-‘ for Xeff 195 nm, while 140 135 I30 the dashed curve is obtained by setting E v i b = 100 kcal Effective Photon Energy (kcal. einstein-I) mol-1 for the same wavelength. Figure 11. Variation in the yield of ethylene us. photon energy. Because of the very wide dispersion in energy of The symbols have the same meanings as those in Figure 10. the radicals, the fact that nonmonochromatic light was used has little effect on the results. In Figures 7 and 8 we have also shown the results when allowance caused by varying the AIP pressure can be produced was made for nonmonochromaticity. This was done by using a constant AIP pressure and varying the by weighting thef(E) curves for E v i b = 100, 90, and pressure of CO, which acts as an “inert” gas. How80 kcal moly1 by the appropriate values of I(B)F‘~~~ever, when the deactivation efficiency is estimated on a (B) a t 182, 195, and 208 nm, respectively, and generper collision basis, it turns out that COz is only 0.04 ating a new flE]curve. It can be seen that the results times as effective as AIP. From previous work, one do not differ significantly from those assuming monomight have expected a value almoat 10 times energetic excitation. (44) B. Stevens, “Collision Activation in Gases,” Pergamon Press, There remains a puzzling aspect of the pressureOxford, 1967, Chapter 6; G. H. Kohlmaier and B. S. Rabinovitch, dependence studies. Exactly the same effects as are J. Chem. Phgs., 38, 1709 (1963). The Journal of Physical Chemistry, Vol. 76, No. 12, 1972
1694 (7) The Dissociative State. In the previous section we saw that the data were consistent witn isopropyl radicals being formed with a mean energy of -35 kcal mol-' and a significant energy spread (u -40 kcal mol-I). Also, the data were not incorisistcnt with decomposition originating from the ground state. If the bulk of the dissociation in the photolysis of AIP does occur from Sovib,then it should be possible to estimate, using unimolecular theory, the lifetime of the parent AIP molecule. One complication is that because of cis-trans i ~ o m e r i z a t i o n 'dissociation ~,~~ could originate from both trans-AIP (Sovib) and cis-AIP(Sovib). Preliminary evidence indicates that, for a given excess energy, the trans isomer has the longer lifetime.46 We may use a formula such as eq 23 to estimate the lifetime of truns-AIP(Sovib). For E t = 80.5 kcal mol-' (n + r * excitation), we get Ttrans = 0.2 X lo-' However, the variation in a d e c with pressure does not indicate such a long-lived specie^.^^,^^ The data indicate that the longest lived species in the n + T * photolysis of AIP has a lifetime sec. Moreover, from the observed of about 0.8 X curvature of the 1/@&us. pressure plot it may be inferred that species with a range of lifetimes are inv01ved.~* In their study of the photolysis of azoethane, Worsham and Rice49 were also unable to rationalize their @.dec data in terms of decomposition from the ground state, and Wu and observed curvature in the 1/%,, 21s. pressure plots for the photodecomposition of hexafluoroazomethane. Of course, there is always the possibility that the formula given in eq 23 is not valid for representing the lifetimes of vibrationally excited azoalkanes, which would occur, for example, if the energy was not randomized before dissociation, or, if the formula is valid, that we have not chosen the correct values of the parameters A, EO,a , a+, E,,, and Ezp+. In the same vein, we find that for E , = 147 kcal sec. But, as mol-' (Xirr 195 nm), Ttrans = 3.5 X can be seen from Figure 5, we were unable to detect
The Journal of Physical Chemistry, Vol. 76, No. 18,197.9
M. LOUISARIN AND COLINSTEEL any diminution of the decomposition rate up to pressures for which the time between collisions was 1.0 X 10-lo sec. Thus, although the data do not fit well with dissociation occurring from SOVib,the evidence for dissociation from another state is really by default. The observation of cis-trans isomerization certainly indicates that triplet states are involved in the overall photochemistry, but these need not be the states from which dissociation occurs, and we know SO little about the properties of the upper states that we cannot apply any meaningful tests to the data except to rule out dissociation from Sl.'7z's The lack of pressure dependence for %eo obtained for n 4 u* excitation, as opposed to the observed dependence for n + r * excitation, indicates that in the former case the dissociative lifetime is considerably shorter. Therefore, if dissociation originates from a common state(s), its lifetime must decrease markedly as the vibronic energy is increased. Even for irradiation in the n , r * band, Worsham and Rice49found that the lifetime of the dissociative state decreased by a factor of 2 as the exciting wavelength was decreased from 378 to 352. In principle, by carrying out very careful quantum yield measurements of all the processes involved in the photochemistry of both the cis and the trans isomers, it should be possible to resolve some of these problems and to make a more definite statement as to the nature of the dissociative state. We shall report on these studies later.46 Acknowledgment. We are grateful to the National Science Foundation (Grant GP-18808) for support of this work. (45) R. F. Hutton and C. Steel, J. Amer. Chem. Soc., 86, 745 (1964). (46) A. Rennert and C. Steel, unpublished results; ref 17 is a preliminary communication on the subject. (47) The values of A and Eo were taken from ref 42, viz., 0.5 X 1014 sec -1 and 40.8 kcal mol -r, E,, and E,, + were assigned the values 130 and 127 kcal mol-' and a and a + the values 0.95 and 0.90. (48) E. C. Wu and 0. K. Rice, J. Phys. Chem., 72, 542 (1968). (49) W. C. Worsham and 0. K. Rice, J. Chem. Phys., 46, 2021 (1967).
