2374
J. Phys.
Chem. 1980, 84, 2374-2381
We thank Dr. S. Misumi for a sample of the compound and Dr. Kokubun for helpful discussions.
References and Notes (1) L. R. Fauikner, MTPInt. Rev. Sci.: Phys. Chem., Ser. Two, 9, 213 (1976). (2) L. R. Fauikner and A. J. Bard, Electroanal. Chem., 10, 1 (1977). (3) K. Itaya and S. Toshima, Kagaku no Ryoiki, 31, 1024, 1133 (1977). (4) R. E. Visco and E. A. Chandross, J . Am. Chem. Soc., 86. 5350 (1964). (5) D. M. Hercules, Science, 145, 808 (1964). (6) Su. M. Park and A. J. Bard, J. Am. Chem. Soc., 97, 2978 (1975). (7) C. P. Keszthelyi and A. J. Bard, Chem. Phys. Lett ., 24, 300 (1974). (8) Su. M. Park, M. T. Paffett, and G. H. Daub, J. Am. Chem. Soc., 99, 5393 (1977). (9) K. Itaya and S. Toshima, Chem. Phys. Lett., 51, 447 (1977). (10) K. Itaya, Ph.D. Dissertation, Tohoku University, 1977. (1 1) T. Okada, T. Saito, N. Mataga, Y. Sakata, and S. Misumi, Bull. Chem. SOC.Jpn., 50, 331 (1977), and references cited therein. (12) M. Kawai, Ph.D. Dissertation, Tohoku University, 1979. (13) C. A. Mann, Electroanal. Chem., 3, 57 (1969). (14) K. Itaya, M. Kawai, and S. Toshima, J. Am. Chem. Soc., 100,5996 (1978).
(15) R. Bezman and L. R. Faulkner, J. Am. Chem. Soc., 94, 6317 (1972). (16) E. T. Seo, R. F. Nelson, J. M. Fritsch, L. S. Marcoux, 0. W. Leady, and R. N. Adams, J . Am. Chem. Soc., 88, 5498 (1966). (17) L. S. Marcoux, J. M. Fritsch, and R. N. Adams, J. Am. Chem. Soc., 89, 5766 (1967). (18) R. S.Nicholson and I. Shain, Anal. Chem., 38, 706 (1964). (19) S. W. Feldberg, J. Am. Chem. Soc., 88, 390 (1966). (20) R. Bezman and L. R. Fauikner, J. Am. Chem. Soc., 94,3699 (1972). (21) L. R. Faulkner, J . Electrochem. Soc., 124, 1724 (1977). (22) P. R. Michael and L. R. Faulkner, J . Am. Chem. Soc., 99, 7754 (1977). (23) R. Bezman and L. R. Faulkner, J. Am. Chem. Soc., 94,3699 (1972). (241 R. Bezman and L. R. Faulkner. Anal. Chem.. 43. 1749 (19711. (25) T. Okada, T. Fujita, and N. Mataga, 2.Phys. &em: (Frankiurtah Main), 101, 57 (1976). (26) J. T. Maioy and A. J. Bard, J. Am. Chem. SOC..93. 5968 119711. ’ (27) C. P. Keszthlyi and A. J. Bard, Anal. Chem., 47, 249 (1975). (28) N. E. Tokel-Takvoryan, R. E. Hemlngway, and A. J. Bard, J. Am. Chem. SOC.,95, 6582 (1973). (29) A. Weiler and K. Zachariasse, Chem. Phys. Lett., 10, 590 (1971). (30) K. Zachariasse, “The Exciplex”, M. Gordon and W. R. Ware, Eds., Academic Press, New York, 1975. (31) R. A. Marcus, J. Chem. Phys., 4 3 2654 (1965); 52, 2803 (1965). (32) D. Rehm and A. Weiier, Tsr. J. Chem., 8, F5Sc197T).
Reactlons of Thermal Hydrogen Atoms at Cryogenic Temperature below 77 K as Studled by ESR. Isotope Effect in Hydrogen Abstraction from Ethane in Xenon Matrices Kazumi Toriyama, Kelchi Nunome, and Machlo Iwasakl” Government Industrial Research Instkute, Nagoya, Hirate, Kiia, Nagoya, Japan (Received: August 7, 1979; I n Final Form: March 12, 1980)
Previously we have reported that thermal H atoms easily abstract H from CzH6 at 10-30 K probably by the tunnel process. To characterize the hydrogen atom reactions in the low-temperature solids, we have studied kinetic isotope effects in hydrogen abstraction from CzH6 and CzDs by using H atoms trapped after 4.2 K photolysis of HI in Xe matrices containing a small amount of ethane. The kinetic isotope ratio kH/kD was found to be temperature dependent, giving k H / k D = 1-2 at -35 K and 60 at -50 K. The results suggest that the reactions in the low-temperature solids are diffusion controlled and the k H / k D ratio becomes larger as the diffusion velocity of H atoms increases with increasing temperature. The fact that the larger k H / k D ratio such as 60 is obtained at -50 K even under partial diffusion control may give further evidence that the reactions proceed by the tunnel effect. A simple model of hydrogen-atom reactions in low-temperature solids is given to interpret the experimental results. The efficiency of this reaction depends upon the relative concentration of CzH6 and CzD, as well as the annealing temperature. This is due to the involvement of the competitive reaction of H atoms with HI, giving k H I / k H = 2-3.
In hydrocarbon radiolysis, hydrogen atoms are formed as one of the most important primary species and play an important role in the radiation-induced reactions. In this field, however, hydrogen atoms have been postulated to be unreactive with alkanes if they are thermalized, especially in the low-temperature solids, because the activation energies of hydrogen-abstraction reactions by hydrogen atoms at ordinary temperatures are of the order of kcal/mol. Contrary to this postulate, we have recently obtained ESR evidence that thermal H atoms can abstract H from C-H bonds even at 10-20 K;lp2that is, it has been shown that H atoms are trapped in CHI containing 0.5 mol 940 of CzH6 X irradiated at 4.2 K, and upon warming to 10-20 K the trapped H atoms (HtJ are released to react selectively with dilute solutes forming C2H6radicals with an efficiency of about 50%. The reaction of thermal H atoms a t cryogenic temperatures has been further confirmed by using Ht, produced by the 4.2 K photolysis of HI (0.15 mol %) in Xe matrices containing C2H6 (0.75 mol %). In this case, Ht, is released at 35-50 K and reacts with
C2H6 forming C2H5with an efficiency of about 70%. In the chemical reactions which proceed at such cryogenic temperatures, the tunnel effect must play an important role.3a Several examples of intermolecular H-atom transfer below 77 K68 have been reported for the reactions which take place between the two neighboring reactants in the rigid solids. For example, CH3 radicals in CHBOH abstract .an H atom from the neighboring CH3 group forming CHzOH even at 4.2 K.8 Although these reactions are interpreted in terms of the tunnel process, there might be some particular situations such as preferential orientations and geometries which accelerate the reactions to proceed even at cryogenic temperatures. In this sense, the behaviors and the reactions of diffusive H atoms in the solid phases may be of considerable importance to characterize the features of chemical reactions a t cryogenic temperatures. For these reasons we have studied deuterium isotope effects in the abstraction reaction from CZH6 and in Xe matrices, since a large isotope effect is thought to be
0022-3654/80/2084-2374$0 1.0010 tQ 1980 American Chemical Society
Reactions of Thermal Hydrogen Atoms
The Journal of Physical Chemistry, Vol. 84, No. 19, 1980 2375
indicative of the involvement of the tunnel proce~s.~n~ The results giving a relatively small kinetic isotope ratio indicate that the reactions of thermal H atoms in Xe matrices are strongly diffusion controlled. This is in marked contrast to the extremely large kinetic isotope ratio reported for the hydrogen-abstraction reaction by CH3 radicalsa6 However, the present results are consistent with our previous conclusion that the low-temperature irradiation effect in the solid-phase radiolysis of some alkanes2i9 and their mixtures’*l2 is due to the suppression of hydrogen-atom migration and the reactivity of thermal hydrogen atoms at temperatures below 77 K. Experimental Section The samples of (&D6 (>99%) obtained from Merck Sharp and Dohme and those of CzH6 (>99.7%) and Xe (>99.9%) obtained from Takachiho Shoji were used without further purification. The samples of HI obtained from Tokyo Kasei Kogyo as aqueous solutions were distilled in a vacuum line after being treated with phosphorus pentoxide. Gaseous mixtures of Xe, ethane, and HI were prepared by using a vacuum line and then frozen into a Suprasil ESR tube a t 77 K by repeated depositions of a small amount of gaseous mixtures on the cold surface. The frozen mixtures prepared at 4.2 K to ensure more rapid condensation gave the same results, suggesting that the samples are homogeneously frozen. The concentration of ethane and HI in the gaseous mixtures are 1and 0.1 mol % , respectively, throughout the experiments. The fractions of C&G to the total ethane in the samples examined are 0, O.O2,, 0.10, 0.13, 0.50, and 1.0. To ensure good thermal conduction and equilibrium during the thermal annealing and the successive ESR measurements, we filled the sample tubes with helium to about 0.5 atm at 77 K before sealing them offal1 The photolysis were performed with 2537-A light from a low-pressure mercury lamp for 8 min by using an insertion type ESR Dewar at 4.2 K. The ESR measurements were made by a Varian E-12 spectrometer with 100-kHz field modulation. The signals from a single crystal of ruby mounted on the cavity wall were used as a monitor of the spectrometer conditions. All of the spectra were digitized by a Nicolet signal averager Model 1070 and transferred into an on-line computer (HP-9825A),by which the double integration and other spectral analyses were performed. The thermal annealing of the samples below 77 K was performed in the liquid-helium Dewar used by pulling the sample tube up above the liquid-helium level. The annealing temperatures were measured by a digital thermometer (Scientific Instrument Model 1875CK) equipped with an iron-chromel-gold thermocouple. Because of the temperature gradient above the liquid-helium level, the specimen temperature during the thermal annealing has a range of ca. *3 K at, -30-50 K. The annealing at 77 K was performed by transferring the sample tube to the liquid-nitrogen Dewar. The time required to transfer the sample from the one to the other Dewar was less than 1 9.
Results Abstraction Reactions during Photolysis at 4.2 K. H atoms produced by photolysis of HI in Xe matrices are efficiently trapped at 4.2 K.lJ3 They are detrapped at 35-50 K1* and migrate through the crystals to react with ethane forming ethyl radicals. A typical example obtained for the sample with the CzH6fraction of 0.02, is shown in Figure 1. Spectrum (a) is obtained immediately after the photolysis a t 4.2 K. The outer signals are from H,, and exhibit superhyperfine structures due to lZ9Xeand 131Xe
Figure 1. ESR spectra obtained from 4.2 K photolysis of Xe/ethane (1 mol %)/HI (0.1 mol % ) with the C2H6fraction of 0.02,: (a) immediately after 4.2 K photolysis; (b) after annealing at -50 K for 1 min. The spectrometer gains are the same for (a) and (b) except for the hydrogen-atom signal in (a). The arrows indicate signals from the trapped D atoms. Microwave power is 0.01 mW; f i i M modulation width is 2 G.
Figure ESR spectra of ethyl radicals produced by 4. K photolysis of Xe/ lane (1 mol %)/HI (0.1 mol % ) with the C2H6fraction of (a) 0,(b) O.02,, (c) 0.10, (d) 0.50, and (e) 1.00. Microwave power is 0.01 mW; field modulation width is 2 G.
n~c1ei.l~ The central signal is mainly due to C2D5radicals. The very weak signals shown by the arrows are from Dt, which also exhibit superhyperfine structures of Xe nuclei. The yield of D,, is about 1% of Ht,. Although the source of D, is evidently C2D6, the process of producing D from c2D6 is not clear. One of the possibilities is decomposition of CzD5into CzD4and D.15 The cross section of the displacement of D by H may be very small for hot H atoms photochemically produced by 2537-A light. Similar observations are reported by Willard and his co-workers16in the photolysis of HI in 3-methylpentane-d14and other glasses. As shown in Figure lb, the spectrum of the ethyl radicals grows with a concomitant decrease of Htr. Since a part of the H atoms react with ethane during the 4.2 K photolysis of HI, information about H-atom reactions during the photolysis can be obtained as well, although hot H-atom reactions may be involved. Figure 2 shows the comparison of the spectra of ethyl radicals obtained immediately after the 4.2 K photolysis for the five samples with the different CzHG contents. The hyperfine structure of CzH5 shown in Figure 2e can be interpreted in terms of the CH! group which undergoes tunneling rotation at 4.2 K giving a
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The Journal of Physical Chemistry, Vol. 84, No. 19, 1980
Toriyama et ai.
A
C)
n
-
I\
f)
20
30
40
50
60
m
77
TYK)
50 G
Flgure 3. The firstderivative (a) and integrated (d) ESR spectra of ethyl radicals obtained from 4.2 K photolysis of Xe/ethane (1 mol %)/HI (0.1 mol %) with the CH , , fraction of 0.5 and their decomposition into the spectral contributions from C2H5(b and e) and C,D, (c and f). The spectra of C2H, and Cp, used in the decomposition are obtained from 4.2 K photolysis of Xe/C2H,/HI and Xe/C,D,/HI mixtures. Microwave power is 0.01 mW; field modulation width is 2 G for (a) and 1.2 G for (b) and (c).
Figure 4. The decay of trapped hydrogen atoms and the growth of ethyl radicals and iodine atoms vs. annealing temperature for the sample with the CpH, fraction of O . i O .
TABLE I: Fractions of the C,H, Radicals Trapped during 4.2 K Photolysis of Xe/C,H,:C,D,/HI and Those after Thermal Annealings at 35 and 60 KC
-
-
fractions of C,Hs radicalsb fraction of C,H,'"
during 4.2 K photolysisd
0.02,
0.03 k 0.01 (0.024) 0.17t 0.03 (0.11) 0.19 f 0.03 (0.14) 0.60f 0.05 (0.52)
0.10 0.13 0.50
after thermal annealing at 35 K
0.04
f
0.02
at 50 K 0.33k 0.02
0.20f 0.03
0.60i 0.03
0.20 f 0.03
0.60f 0.03
0.65 f 0.05
0.95 t 0.05
? [C2H61/([C2H61
[CZD61)* [c2HSl/([c2HS1 The contents of ethane and HI are 1and 0.1 mol %. respectivelv. The numbers in Darentheses are calculatedfrom e i 6 and 7, assuming n 1 and N = 14.
[C,D,]).
typical splitting of the A and E lines.17a The spectral assignment of C2D5 will be given in a later section. The amount of the ethyl radicals trapped after the 4.2 K photolysis is approximately the same for all of the samples and is estimated to be 10 f 3% of the total yield of H, and ethyl radicals. On the other hand, the relative yield of C2H5 to CzD5proportionally increases with increasing C2H6 content. The fractional yields of C2H5to the total ethyl radicals were determined by the following method. Using the neat spectra of C2H5and C2D5, we have made the simulations of the first derivative and the integrated spectra with varying of the abundance ratio, and then we have compared them with the observed spectra. A typical example is given in Figure 3. As shown in Table I the fraction of C2H5 to the total ethyl radicals is nearly the same as that of for all of the samples. From eq 1the kH/kD ratios of 1-2 are obtained for the El-atom reactions during the 4.2 K photolysis. Abstraction Reactions by Detrapped H Atoms. The reactions of detrapped H atoms have been studied by measuring the spectral changes at 4.2 K after successive annealings of the samples at temperatures from 25 to 77 K. At each temperature the samples were annealed for 0.5-2 min. In Figure 4 the decay of H, and the growth of ethyl radicals are plotted against the annealing temperature for the sample with the C2H6fraction of 0.10. The concomitant increase of the ethyl radicals with the decrease of H,, was observed at around 35 and 50 K. Most of the
Flgure 5. The changes of the ESR spectra of ethyl radicals caused by the thermal annealing of the sample wtth the CPHBfraction of 0.02,: (a) immediately after 4.2 K photolysis: (b) after annealing at -35 K for 1 min; (c) after the subsequent annealing at -50 K for 1 min; (d) difference spectrum between (b) and (a); (e) difference spectrum between (c) and (b). The spectrometer gain settings are the same for all of the spectra. Microwave power is 0.01 m W field modulation width is 2 G.
H,, disappeared upon warming up to 50 K, while the ethyl radicals were stable up to 77 K. Shown in Figure 5 is a typical example of the spectral change after the thermal annealing of the sample with the C2H6 fraction of 0.023. Upon annealing at 35 K for 1min, the ethyl radicals are increased, giving a spectrum shown in Figure 5b. The subsequent annealing at 50 K for 1min results in further increase of the ethyl radicals, giving a spectrum shown in Figure 5c. The difference spectra after and before the thermal annealing at 35 and 50 K are shown in Figure 5, d and e, respectively. These spectra are due to the ethyl radicals produced by the reaction of detrapped H atoms at 35 and 50 K, respectively. It is clear from the structureless line shape of spectrum (d) that C2D5 is mainly formed at 35 K. The fraction of C2H5 in spectrum (d) was estimated to be 0.05, giving k H / k D= 2.2 for the reaction at 35 K. On the other hand, as is evident from spectrum (e), C2H5 is efficiently formed in the reaction at 50 K. The fraction of C2H5 in spectrum (e) was 0.58. This greatly exceeds the fraction of C2H6in the sample, giving kH/kD = 60 for the reaction at 50 K. Shown in Figure 6 are similar spectral changes of the sample with the CzH6 fraction of 0.13. The C2H5fraction in the difference spectrum (d) was estimated to be 0.22, giving k H / k D= 1.7 at 35 K. The C2H5 fraction formed a t 50 K was estimated to be 0.91 from the difference spectrum (e), giving k H / k D= 60, which is consistent with the value obtained from the sample with the C2H6 fraction of 0.023. Similar resulta have been obtained from the other samples, as is tabulated in Table I. In Figure 7 the CzH5 fractions measured after annealing at 35 and 50 K are plotted against the C2H6 fractions. The k H / k Dratios thus estimated are summarized in Table 11. I t 1s interesting that k H / k Dat 35 K is nearly the same as that of the re-
The Journal of Physical Chemistty, Vol. 84, No. 19, 1980 2377
Reactions of Thermal Hydrogen Atoms a)
E 0.81
I . . . . . . , . . .
0.0
02
0.4
0.6
0.8
1.0
[CzHd/( [CZHd iCZD61) +
Figure 6, The changes of the ESR spectra of ethyl radicals caused by the thermal annealing of the sample with the C2H6fraction of 0.10: (a) immediately after 4.2 K photolysis; (b) after annealing at -35 K for 1 min; (c) after the subsequent annealing at -50 K for 1 min; (d) difference spectrum between (b) and (a); (e) difference spectrum between (c) and (b). The spectrometer gain settings are the same except for (d). Microwave power is 0.01 mW; field modulation width is 2 G.
Figure 8. The conversion efficiency of hydrogen atoms into ethyl radicals at -50 K vs. C2H6 fractions in the samples.
Figure 9. The ESR spectra of (a) CpH5and (b) C2D, radicals. The solid lines are the observed spectra at 77 K, and the dotted lines the simulated spectra by the parameters given in the text. [CZH6i/i[CZHd'[CZD61)
Flgure 7. The fractions of CpH5radicals (A) after 4.2 K photolysis, (0) after annealing at -35 K, and (0)at -50 K vs. C2H, fractions in the samples.
TABLE 11: Kinetic Isotope Ratio KH/KD of Hydrogen Abstraction Reaction&by Thermal H Atoms from C,H, and C,D, in Xe Matrices below 77 K b thermal H atom reactions during 4.2 K at at -50 K photolysisa -35 K
-
kH/kD 1-2 -2 60 a Both hot and thermal H atoms may be involved. The contents of ethane and HI in Xe matrices are 1 and 0.1 mol %, respective1:y.
actions during the 4.2 K photolysis. Efficiency of Abstraction Reaction from Ethane. The efficiency of the reaction, that is, the ratio of the increase of ethyl radicals and the decrease of Ht,, was as high as 0.7 at 50 K for the sample with the CzH6 fraction of 1.0, indicating that 70% of the detrapped H atoms reacted with CzH& However, the efficiency was decreased with increasing CzD6 content as shown in Figure 8. The efficiency was also dependent upon temperature, giving a lower value with increasing temperature especially in the samples with the high CzD6fraction. For example, the sample with the C&H6fraction of 0.10 gave efficiencies of 0.70 and 0.35 a t around 35 and 50 K, respectively. Spectral Identification of CzD5. Since the hyperfine structure of CzD5 was not well resolved, the spectral identification was carefully made on the basis of the spectra observed at 77 K. The CH3 group in CzH5vndergoes tunneling rotation at 4.2 K and classical hopping rotation at 77 K. As shown in Figure 9a, the six-line spectrum of CzH5obeierved at 77 K can be simulated by
the two equivalent a-proton coupling (22.0 G) and the three equivalent P-proton couplings (26.7 G), using the = 5 G. The spectrum of Gaussian line shape with AHmB1 CzD5 simulated by the deuterium hyperfine couplings equivalent to these proton couplings shows excellent agreement with the observed spectrum as shown in Figure 9b. If partially protiated ethyl radicals are formed from H addition to ethylenic impurities, the observed spectrum must exhibit a hyperfine splitting of about 27 G. For these reasons the structureless spectrum obtained from the Xe/C2D6/HI mixtures is attributed to CZD5.
Discussion Reaction of the Detrapped H Atoms with Ethane. Our experiments show that ethyl radicals are increased with the concomitant decrease of Ht, upon annealing a t 35-50 K. Since the activation energy of hydrogen-atom addition to ethylene is lower than hydrogen abstraction from ethane,18one might be suspicious that the ethyl radicals are formed from ethylene which might be contained in ethane as impurities or formed by the photolysis.16 However, formation of CzD6cannot be expected from H-atom addition. It is also hard to believe that scrambling of H and D gives mainly CzD5 without forming partially protiated ethyl radicals. We have also examined the Xe/CH3CD3/HI mixtures, and in this case it was observed that CHzCD3radicals are increased with the decrease of H,, at 50 K.19 It is not possible to interpret this in terms of H addition. We have also studied the CD4/CzH6mixtures X-irradiated at 4.2 K and have observed formation of CzH5 with the decrease of Dt, at 10-20 K.19 In this case, one cannot expect that CZH5 is formed from D addition. All of these observations in the different systems support our previous conclusion that the detrapped hydrogen atoms abstract a hydrogen atom from ethane at temperatures below 50 K.1~2 The detrapped H atoms might possess extra kinetic energy liberated from the strained lattice. In this sense,
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The Journal of Physical Chemistry, Vol. 84, No. 79, 7980
the detrapped H atoms might be quasithermal. However, our previous shows that the detrapped H atoms in CHI matrices do not react with CH4forming CH3 so that the extra kinetic energy, if they have any, is not sufficient to undergo hot abstraction from CH4. This is further confirmed by the experiments on Xe/CH4/HI mixtures in which the detrapped H atoms did not abstract H from CHI a t In addition, the temperature change of the k ~ / ratio k ~ and its high value of 60 at 50 K cannot be explained in terms of such hot processes. For these reasons, we presume that the detrapped H atoms possess nearly thermal energy when the abstraction reaction takes place at 35-50 K. Initial Yield of Ethyl Radicals during 4.2 K Photolysis. The efficient trapping of H atoms and a relatively small initial yield (-10%) of ethyl radicals during the 4.2 K photolysis suggest that the H atoms which escape from the cage recombination are trapped without traveling a long distance. Otherwise, they would have encountered and reacted with ethane and HI before the thermal annealing. H atoms produced by photolysis (2537 A) of HI have initially excess kinetic energies (at most 1.8 eV) so that the abstraction during photolysis may involve the hot process. Suppose that H atoms escaped from the cage recombination are thermalized after n collisions as an average. If the collisions with ethane or HI are not involved in these n collisions, the H atoms may be thermalized, whereas, if they are involved, the H atoms may be converted into ethyl radicals or I atoms by hot reactions with ethane or HI. If this is the case, the probability of thermalization is (1 F)", whereas the probability of forming solute radicals (ethyl radicals plus I atoms) is 1- (1- F)",where F is the total fraction of ethane and HI. Thus, the numbers of the ethyl radicals. produced by the hot reactions are given by eq 2, where [HI, is the total number of H atoms produced [fitlhot
=
[fi10[1 -
(1 - F)"](f/F)
(2)
and f is the fraction of ethane. Next, it is assumed that at 4.2 K the thermalized H atoms are immobilized in the trapping sites and that they can react with ethane or HI if they find these solutes in the cage wa11.12 The probability of finding no solute so molecules in the N surrounding neighbors is (1that the numbers of H,, are given by eq 3. If ethane [H,] = [H]O(l - F)n+N
(3)
molecules are involved without HI in the N surrounding neighbors, ethyl radicals may be exclusively formed, and thus the number of ethyl radicals formed by the thermal reaction is given by12 eq 4, where i is the number of ethane
molecules of the N surrounding molecules. The contribution to the total ethyl radicals from the cage involving both the ethane and HI molecules is neglected since the probability of finding both of the molecules is very small, and in addition the reaction with HI would be more favorable for such a case because the activation energy (0.5 kcal/mol) of this reaction at ordinary temperature is very much lower than that of the reaction with ethane.21 Thus, the realtive yield of the ethyl radicals to Ht, can be obtained from eq 2-4 and for small solute concentrations it becomes (5) [EtI/(tH,l + [ktl) = ( n + W f have reported that the Very recently Morton et photochemically produced H atoms from HI are mainly
Toriyama et al.
trapped in the octahedral interstitial site in the Xe matrices. Since the crystal lattice of Xe is a face-centered cubic,13the cage wall consists of the six nearest and the eight second-nearest neighbors. The ethane or HI molecule may occupy the substitutional site so that N = 6 if the H atoms only react with the nearest neighbors and N = 14 if they react with the second nearest as well. If n is tentatively assumed to be 1, [Et]/([Ht,] t [Et]) is found to be 0.07 for N = 6 and 0.14 for N = 14, in which the hot contribution is 0.01. Therefore, the observed yield of 0.10 f 0.03 can be expected statistically from the solute concentrations without assuming a long-range migration of H atoms. If thermal H atoms cannot react with ethane in the cage wall at 4.2 K, the initial ethyl radical yield has to be attributed to hot abstraction with n = 10. However, a much lower initial yield of CH3 in the Xe/CH4/HI mixturesz0suggests that the initial ethyl radical yield is considerably contributed from the reaction of H,, with the cage wall. Kinetic Isotope Effect in the Reaction during 4.2 K Photolysis. When both C!& and C2H6 are contained in the mixtures, the initial yields of C2D5 and C2H5 are given by eq 6 and 7, where f is the fraction of the total ethane; [czD51 = N
[filo{[l- (1- F)"](fD/F)
t (1- F)" zNCifD'(1 - qN-') i= 1
(6)
[CzHsl = [fi]o([l - (1 - F)"] (fH/F)
+ (1 - F)"
X N cNci(f - fD')(1
i=l
-
nN-') (7)
and f H are the fractions of CzD6 and C&&, respectively. For the hot process the probabilities of H and D abstractions are assumed to be equal. In the thermal process C2D6or C2H5 is exclusively formed in the sites where either CZD6 or CzH6is involved in the surroundings. The small contribution to [C2D5]from the cage involving both C2D6 and C2H6 is neglected, assuming that C2H5is exclusively formed in such cages. Thus, the relative yield of C2H5 to CzD5can be obtained from eq 6 and 7, and for small solute concentrations it becomes as follows regardless of the values of n and N
fD
[CZH5I / [cZD51
fH/fD
(8)
It is clear that the above-mentionedmodel gives the k ~ / k D ratio close to unity, as is observed since the situation assumed for the thermal reactions is essentially equivalent to the reaction with the diffusion-controlled limit. The fractional yields of C2H5 obtained from eq 6 and 7 are in reasonable agreement with the observed values as shown in Table I. Kinetic Isotope Effect i n Reactions at 35 and 50 K. The decay of H atoms starts at around 35 K and becomes prominent at around 50 K in the Xe matrices both with and without ethane. The decay temperature is also independent of the C2H6-to-C2D6 ratio. As is previously reported, H,, in CH4 matrices are detrapped at a lower temperature, 10-20 K, forming C2H5.1,2 These results suggest that the reaction of H atoms takes place when they are detrapped and mobilized at a temperature which is dependent upon the matrices. For these reasons it may be reasonably assumed that Ht, is in the cage involving no ethane or HI, and upon warming some of the H, migrates into a neighboring cage where there is a probability of finding ethane. The preliminary experiments on Xe/ CH4/HI mixturesmmentioned in the foregoing section also support this assumption.
Reactions of Thermal Hydrogen Atoms When UH and uD are defined as the probabilities that the detrapped H atoms abstract from C2H6 and C2D6, respectively, during their stay in a new cage, the ratio of C2H5and C2D6 formed by the reaction of the detrapped H atoms is given by eq 9, where it is assumed that the H N
i=l
atoms in a cage involving both C2H6 and C2D6 abstract exclusively from C2HG. Although strictly speaking the value of u must be different from cage to cage with different i, a constant value is assumed for u because the contribution from a cage with i 1 2 is very small. For small solute concentrations eq 9 becomes [C2H5I/[C2D6] zz %fH/'DfD (10) Thus, the k H / k D ratio experimentallyobtained is physically equivalent to the (rH/UD ratio in this model. If the jumping rate of the detrapped H atoms from cage to cage is sufficiently slow at 35 K, they may be able to abstract from ethane during their stay in a cage giving uH and uD close to unity. With increasing temperature the jumping rate may become faster, making the u value shaller than unity. Since the actual abstraction rate from C2D6 must be slower than that from C2H6, the decrease of uD from unity may be more prominent than that of UH. Thus, the kH/kD ratio increases with increasing temperature and finally reaches a ratio of the actual abstraction rates in the non-diffusion-control limit. Although the actual kH/kI) ratio is not known for the reactions of H atoms below 77 K, a considerably large isotope effect may be expected, as is reported in our previous papers5 If the actual kH/kDratio is as high as lo4-lo5,which is reported for the abstraction reactions by CH,,& the reactions at 50 K with kH/kD = 60 may be still strongly diffusion controlled. The fact that a kH/kD ratio as large as 60 is observed under the condition of diffusion control may support the idea that the abstraction reaction proceeds by the tunnel process. The present results suggest that the kinetic isotope ratio of hydrogen abstraction reaction by thermal H atoms in low-temperature solids is strongly dependent upon the mobility of € I atoms and thus depends upon the nature of the matrix as well as the temperature. The kinetic isotope ratio is sometimes used to discriminate between the reaction of hot and thermal H atoms.23 For the reactions in the low-temperature solids, however, our results indicate that a small kH/kD ratio itself does not always mean that the reaction proceeds by a hot process. Absolute Rate of Tunneling Abstraction. It is to be noted here that abstraction of D from C-D bonds by CH3 is too slow to be observed at 77 K in the experimental time scale,6ewhile that by H atoms proceeds very fast within a time scale on the order of seconds, resulting in the diffusion-controlled reaction. On the basis of our previous observation,la2 Willard and his co-workers have recently interpreted decay properties of trapped hydrogen atoms in 3-methylpentane-d14glass1&and in 3-methylheptane-dI8 and methylcyclohex.ane-dI4glassePb at
