J. Phys. Chem. 1993,97,4427-4441
4421
Hydrocarbon Radical Reactions with 0 2 : Comparison of Allyl, Formyl, and Vinyl to Ethyl Joseph W.Bozzelli' and Anthony M. Dean' Corporate Research Labs, Exxon Research and Engineering, Annandale, New Jersey 08801 Received: August 18, 1992
The reactions of allyl, formyl, and vinyl radicals with molecular oxygen have been analyzed as addition reactions, in which the energized adduct has several pathways available for further reaction. Rate constants for each of the reaction channels are estimated using a chemical activation formalism based on the Quantum RiceRamsperger-Kassel theory, along with thermodynamically consistent input rate constants and falloff parameters. Results show good agreement with the limited experimental data available. The well depth of the initially formed adduct is shown to exert a major influence over the preferred reaction channels. In particular, the shallow (- 18 kcal/mol) well for the allyl addition results in very little apparent reaction, and the major channel is simply redissociation to the initial reactants. The deeper wells for formyl and vinyl addition to oxygen (-40 kcal/mol) allow other reaction channels to open up even at low temperatures. Predictions for the vinyl addition indicate HCO and CH2O are major products at lower temperatures, while the vinoxy 0 channel becomes more important at higher temperatures. Formyl addition is shown to produce CO H02 as the major reaction channel. Rate constants for the various reactions are presented over a wide range of temperature and pressure. The good agreement between these calculations and the experimental data support the hypothesis that the reactions between hydrocarbon radicals and oxygen proceed via chemically activated addition and that one does not need to invoke a direct hydrogen abstraction pathway.
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Introduction Important initial products from pyrolysis, oxidation, or photochemical reactions of saturated and unsaturated hydrocarbons are the corresponding radicals. The subsequent elementary reactions of the hydrocarbon radicals with molecular oxygen are complex and difficult to study experimentallyand present a source of controversywith regard to both pathway@)and reaction rates. These reactions, furthermore, represent the principal pathways of the radical conversion in many hydrocarbon oxidation and combustion processes.1.2 There have been several recent studies which show that the reactions of e t h y P and isopropyl? at pressures from 1 to 6000 Torr and temperatures from 300 to 900 K, exhibit a significant negative temperature dependence. The ethyl reaction is the best characterized and is shown to produce CzH4 H02. The rate of ethyl radical loss decreases significantly with temperature3 and increaseswith pressure as expected for the commonly accepted reversible formation of an adduct. The adduct, CzH500*, is readily stabilized at low temperatures, and dissociates back to reactants more rapidly at higher temperature^.^^^ It is this faster dissociationof the adduct back to reactants at higher temperatures that is the origin of the observed negative temperature dependence regime in hydrocarbon oxidation. Walker and co-workers9have also reported similar pressure dependencefor reactions of isopropyl radicals with O2 to produce propene + HO2. The observed pressure and temperature dependence for olefin formation in these reactions is not, however, consistent with a direct hydrogentransfer mechanism, although that is almost always invoked in combustion modeling.'OJI This is an important issue to resolve, since the rate constants one would use for engine or turbine conditions could differ by orders of magnitude, due to the higher pressures. The C2H5 0 2 reaction has been analyzed by Bozzelli and DeanI2 using quantum RRK theory of DeanL3and by Wagner et a1.14using variational RRKM theory for ethylene production and ethyl radical loss at pressures and temperatures relevant to the experimental data of Gutman's g r ~ u p . ~These J analyses postulate the formation of a chemically activated adduct, which can be stabilized or, before stabilization, can dissociate back to C2H5 02, react through a cyclic five-memberring intermediate
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to form a primary hydroperoxy alkyl radical (H shift), which can be stabilized or further react to C2H4 HOz. The formation of epoxide OH in this system is limited by a lower Arrhenius A factor due to the tight transition stateanda slightlyhigher barrier. The results of both modeling studies for loss of ethyl and production of ethylene show excellent agreement with recent experimental data. The results of Bozzelli and Dean also show good agreement with thedata of Kaiser et al.6+7 over a wide pressure range for bath gases of He and N2. An analysis of these results indicated that the ratio of forward to reverse A factors for the initial radical addition as well as the well depth are important. The isomerization A factor (tight transition state) is much lower than that for dissociation of the complex to reactants, but the isomerization barrier height is also lower. The lower barrier to isomerization, 27 kcal/mol, versus dissociation to reactants, 32 kcal/mol, always allows a fraction of the complex to isomerize and subsequently dissociate to C2H4 + HO2. At higher temperatures, increased isomerization relative to stabilization of the activated complex leads to higher C2H4 HO2 formation rates. It should be noted, however, that this approach differs from that used by Walker and co-workers,15J6who suggest that the barrier to epoxide formation is appreciably lower than that to the olefin and HO2. Use of their higher barrier to the olefin H02 channel effectively shuts this channel down, resulting in substantial disagreement with the experimental observations on olefin formation by several groups, including Walkerkg In this study we extend the analysis of these reactions to other types of hydrocarbon radicals. It is shown that the variations in R-OO bond strength ranging from 18 kcal/mol for allyl to over 40 kcal/mol for formyl strongly influence the overall rate constants and product distributions. The vinyl and allyl cases also present the added possibility of cyclization as new pathways to compete with the H-shift reactions. A chemical activation analysis is performed on reactions of allyl, vinyl, and formyl radicals with 0 2 and the predictions compared to the limited literature data. It is difficult to measure each of the products and the specific rate constants to the products of these important reactions over a wide range of both temperature and pressure. We attempt to use the experimental data where available, along with a QRRK analysis incorporating generic rate constants,
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0022-3654/93/2091-4421~04.00/00 1993 American Chemical Society
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4428
The Journal of Physical Chemistry, Vol. 97, No. 17, 19'93
Bozzelli and Dean
calculations are listed in Table 111. The frequency distribution evaluated thermodynamic properties and transition-state theory, for the complexes were approximated by a choice of three to predict the reaction paths as a function of temperature and frequencies and associated degeneracies that were obtained from pressure. We find that the weaker R-OO bond for the allyl case fits to the heat capacity estimates.33 This represents an imsignificantly decreases the energy available for chemically provement over the singlegeometric mean frequencyused earlier;] activated reactions, resulting in substantially lower rate constants the difference is most noticeable at lower temperatures and for than seen for alkyl reactions. Conversely, the increasedwell depths systems where barriers for reaction are comparable to the well in the vinyl and formyl cases provide additional energy, i.e., the depth. Lennard-Jones parameters were obtained from tabulainitially formed adduct has higher energy relative to the barriers tionsj4 and a calculation method based on molar volumes and for unimolecular reactions. This leads to faster rate constants compres~ibility.~~ Collision efficiencies (8) were evaluated using and opens possibilities for new channels. Troe's method,36 with the energy transferred per collision taken The equilibrium between allyl and oxygen has been studied at low temperatures (below 453 K) by Pilling and c ~ - w o r k e r s ~ ~ J ~from Gardiner and TroeS3? Thermodynamic properties were obtained using THERM38 and evaluated bond dissociation and by Slagle et al.,I9 the well depth was measured to be -18 energies from the recent literat~re.3~~40 kcal/mol. Pilling and co-workers also measured the rate of The barriers to the H-shift isomerizations were estimated in productionof theadduct. At higher temperatures, 753 K, Baldwin the usual way, as the sum of the barrier expected for an analogous et al.20 observed that the reaction of allyl with 02 (to produce H transfer in a bimolecular reaction plus the ring strain CO) was orders of magnitude slower than alkyl radical reactions contribution. Here the ring strain was estimated using the with 02.This work was extended by Stothard et a1.,2l who reported concepts developed by Benson,' using the thermodynamic data a rate constant of 1.6 X loll exp(-17.3 kcal/RT) cm3 mol-I s-l of Dorofeeva et al.41 The barriers for cyclization were estimated for formation of a five-member cyclic intermediate which then somewhat differently. Reactions in which the reactants and/or reacted further with 02. Measurements of CO production in products are cyclic have much of the ring strain already contained these systems by Lodhi and WalkerZ2indicated that formation in the enthalpy change. For example, recent calculations by of a four-member cyclic intermediate had a rate constant -2.7 Olivella and calculated the barrier for ring opening in the times that for formationof the five-member intermediate. Lodhi reaction and Walker23 also reported that the rate constant for production of allene and HO2 was 2.5 X lo5 cm3 mol-' s-I at 753 K, much bicyclo[3.1 .O]hex-3-en-2-yl = lower than formation of the cyclic intermediates. Slagle et al.24 cyclopentadienylmethyl radical reported an upper limit for the rate constant of this reaction of 3 X 1010 cm3 mol-' s-1 at 900 K. to be 12.1 kcal/mol. Since this reaction is slightly endothermic The vinyl reaction has been studied by Gutman and co(AH 2 kcal/mol), this implies a barrier of 10 kcal/mol for w o r k e r ~ ,showing ~ ~ , ~ ~slight falloff with increasing temperature, the reverse (cyclization) step. Since the usual activation energy to 650 K, but relatively rapid reaction compared to ethyl. They for alkyl addition reactions is -7 kcal/mol, these findings imply reported formyl radical and formaldehyde as major products. an additional ring strain component (above that contained in the Thesedata alsoagree with the room-temperaturestudy of Krueger heat of formation of the cyclic species) of only -3 kcal/mol for and Weitz.26 Westmoreland2?has analyzed the vinyl + oxygen this reaction, even though it involves formation of a three-member systemusing QRRK analysis, showing agreement with Gutman's ring. We will use this value for the ring strain component for the data. That analysis also predicts that H glyoxal and CzH2 + cyclizations. Our earlier analysisL2of the ethyl + 02 system H 0 2 are important high-temperature channels. suggested a barrier of -8 kcal/mol for HOz addition to ethylene. The formyl radical reaction with 0 2 has been studied by Using an updated value for the heat of formation of H02, that Langford and Moore28over a wide pressure range at 298 K, with value becomes -7 kcal/mol. Thus, we estimate the barrier for data for loss of HCO showing little or no change with pressure; formation of the cyclic peroxide complexes to be 10 kcal/mol they concluded that the mechanism proceeded through an if the reaction is thermoneutral of exothermic. For endothermic energized complex. Lesclaux et al.29330 observed a slight decrease cyclizations, the barrier was assigned to equal AH 10 kcal/ in reaction rate with increase in temperature at pressures of 300mol. 700 Torr, with room-temperature data in good agreement with Details of the rate constant assignments are included in the that of Langford and Moore. Timonen et al.31observed a small tables describing the input data for each of the systems studied. positive temperature dependence for the HCO 0 2 reaction with rate data at 298 in very good agreement with the other work. Results and Discussion
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Calculations Energized complex/QRRK theory as described by Dead3was used to model radical addition reactions to 02.Further details on specifics of the calculation are presented el~ewhere.'~ Preexponential factors ( Afactors) and activation energies (E,) for the bimolecular addition reaction at the high-pressure limit are obtained from the literature and the methods of Bens0n.l A and E, for the unimolecular isomerization reactions are determined using transition-state theory with the appropriate thermodynamic parameters. Kinetic parameters for dissociation to reactants and products are obtained from application of microscopic reversibility. We fit the equilibrium constant to a van? Hoff plot over the temperature range 300-2500 K and use the fitted values to obtain Af/A,,, and Et - E,,,. These values are used in conjunction with the bimolecular rate constants to obtain the dissociation rate constants. Since the van't Hoff plots are generally not exactly linear, the choices of Ar/A,, and Ef - E,,, are somewhat dependent upon the temperature interval chosen. The thermodynamic data used in the equilibrium constant
Allyl + 0 2 . The energy level diagram and input parameters for the chemical activation calculations are shown in Figure 1 and Table I, respectively. The allyl radical combines with Ozto form the chemically activated C=CCOo'* adduct. The reaction channels of C=€COo'* include dissociation back to reactants, stabilization to C=CCOo', isomerization via hydrogen shifts with subsequent8-scissionlstabdization.cyclization to form fouror five-member ring cyclic peroxides with subsequent &scission/ stabilization,and 0 4 bond fission to form C = C C C 0.Figure 1a shows the cyclicisomerization pathways as well as the allyloxy + 0 atom path, while the isomerizations via H shifts are shown in Figure lb. Note in Figure l a that the linear radicals formed after cyclization (C=COOC* and O=CCCO*) will rapidly 8-scission to form CHzO and vinoxy (shown only in the oxy resonance form). These 8-scissionsareincluded in thecalculation. Similarly, in Figure 1b C'HzOOH will rapidly form CHzO and OH. However, this is not included in the calculation since it is not a direct channel from a chemically activated species. Nevertheless, as seen in Table I, the rate of dissociation of C'H2OOH is sufficiently fast than one could effectively write this
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The Journal of Physical Chemistry, Vol. 97, No. 17. 1993 4429
Hydrocarbon Radical Reactions with 02 0 -(
C.CC.+OZ
72
C-XOO.
c.cco0. 23
Kcal/molo
-28
cmcc. + 0 2 C2H2
c-cc. + 0 2
c.ccoo?
+
.CHPOOH
CmC-C C..CCOOH
+
OOH
49
C-C.COOH 44
41
23
cmccoo.
C.CC.OOH 19.6
CCCHO
Koal/moh
+
OH -8.6
Figure 1. Potential energy diagram for the allyl radical + 0 2 reaction: (a) cyclization and 0-0cleavage pathways, (b) H-shift pathways. Note that O=CCCO' will @-scissionto form CHzO + vinoxy, while C'H2OOH will dissociate rapidly to form CH20 + OH. (Although vinoxy is designated for simplicity as a oxygen-centered radical, a more accurate description would include the resonantly stabilized carbon-centered radical.)
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channel with C2H2 + CH2O OH as the products. The parameters in Table I are referenced to the ground (stabilized) state of the complex because this is the formalismused in QRRK theory . The relatively shallow well for this a l l y l 4 0 adduct (- 18 kcal/mol) makes all of the channels to further reaction, with the exception of the one cyclization channel which forms a fivemember ring, at least 10 kcal/mol higher in energy than dissociation back to reactants. Even the cyclic peroxide which can be formed with a low barrier has a very large barrier for the 1,2 H shift needed for further reaction. Thus it will exist in equilibriumwith the allylperoxy radical and the initial reactants. The major reaction channel of the adduct is, therefore, the reverse reaction, Le., reaction back to allyl 0 2 . This pathway not only has the lowest energy, but also a relatively high A factor since this is a simple bond fission. The most likely pathway that would lead toother products is the reactionof the stabilized cyclic peroxy intermediate with another molecule of oxygen to ultimately lead to carbonyls, as discussed by Walker and co-workers.21.22This route is expected to be minor since the steady-state concentration of the cyclic peroxy is very low at combustion temperatures, due to the shallow well. Figure 2 compares the predictions to measurements of the total decay rate. Although the QRRK calculations suggest that stabilization is somewhat larger than actually observed, the temperature dependence is seen to be in good agreement. Given the simple weak-collision model used in these calculations, the offset in predictions versus the observations is hardly surprising; no attempts were made to improve the fit by adjusting the energy transfer parameters. It is encouraging to observe that the predictions are consistent with the measured upper limit at 900 K. Figure 3 compares the predictions to the observations of Walker and co-workers. Here one finds that the QRRK analysis yields results in quite good agreement. Although the channel resulting from formation of the four-member ring is predicted to be faster than observed, that resulting from formation of the
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five-member ring as well the hydrogen shift to product allene + HO2 are in excellent agreement. Thus it seems fair to indicate that, overall, the QRRK predictions capture much of the complexity of this system. In this light, it seems reasonable to expect that the QRRK predictions under other conditions of temperature and pressure are sufficiently accurate to warrant their use in modeling until additional experimental data become available. The predicted effect of temperature at atmospheric pressure is shown in Figure 4. Note the dramatic variation in the total rate constant as the temperature increases. The initial sharp falloff as the temperature is increased is due to the increasing rate of dissociation of energized adducts back out the entrance channel;these complexes do not have enough energy to surmount the barriers separating them from product channels, and one effectively has an equilibrium between the initial reactants and the two adducts C=CCOO* and the five-member ring peroxide (CyCC*COO). These two adducts are separated by a low barrier, and one sees appreciable formation of both adducts. As the temperature increases, the increasing energy of the adducts results in faster dissociation of the adduct relative to stabilization, which is only mildly dependent on temperature. The result is formation of a smaller amount of the stabilized adducts. When the temperature increases above 1500 K the adducts have enough internal energy to begin to reach the other product channels and the overall rate begins to increase. The minimum in the total rate constant depends upon pressure. For example, at lower pressure, 0.01 atm, the lower stabilization rateshifts the minimum down about an order of magnitude and toward lower temperature (- 1200 K). Another effect of pressure is that less of the cyclic adduct is formed at higher pressures, since the increased stabilization rate intercepts the linear adduct before it can cyclize. The C'CyCCOO intermediate provides the lowest energy unimolecular channel for reaction of the C=CCOO' adduct that will not reverse and simply result in reformation of allyl + 0 2 . This channel is 11 kcal/mol above the entrance channel. C*CyCCOO can fi-scissionto form C=COOC', which rapidly leads to C H 2 0 CH2=CHO'. Figure 4 shows that this reaction channel dominates for unimolecular oxidation products up to 1000 K. (For clarity, this radical product is shown in the figure in its [higher energy] oxygen-centered radical form to distinguish this pathway from the dissociation of 0-CCCO', where the products are labeled as CH2O C'H2CHO). While formation of C*=CCOOH also has a barrier which is 11 kcal/mol above the entrance channel, the subsequent reaction of this isomer to form acetylene has a significantly higher barrier. Thus production of the stabilized C*=CCOOH occurs at rates comparable to C H 2 0 C = C O * at the lower temperatures, but acetylene production from this channel occurs only at appreciably higher temperatures. It is important to note that subsequent dissociation of the stabilized adduct to form acetylenecan occur and one must include this dissociation process (as well as the analogous dissociations of all other stabilized complexes) in the overall mechanism. Figures 5 and 6 illustrate the effect of pressure at two temperatures. At 300 K, formation of C=CCOO' and CyCC'COO dominate. Note how the increase in pressuredecreasesthe rate of production of the cyclic adduct, as the increased stabilization rate becomes faster than the unimolecular isomerization. At 1500 K, we can see the overall complexity of this system. The stabilization channels all scale with pressure, with some exhibiting falloff above 10 atm. The chemically activated dissociation channels are generally independent of pressure, although several show effects of competition from stabilization at the highest pressures. At lower pressures, the dominant products arise from the chemically activated isomerization processes; here dissociation products CH2O and vinoxy from the four- and five-membered rings dominate (these two channels are
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Bozzclli and Dean
4430 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
TABLE I: Input Parameters for the QRRK Calculations
_ _+
CIH~ A
reaction 1 -1 2 3 -3 4
5 -5 6 7 -7
8 9
+
C3H5 0 2 C3Hs00' C3H500m+C3Hs 0 2 C3H500' C = C C 0 ' 0 C3Hs00' C4C'OOH C=CC*OOH 4 C1Hs00' C=CC'OOH C=CCHO OH C 3 H 5 0 0 ' C=C'COOH C=C'COOH C3Hs00' C=C'COOH C=C=C HO2 C3H500' C'=CCOOH C'=CCOOH C3HsOO' C'=CCOOH+C2H2 H2C'OOH H2C'OOH CH20 O H
-
+
+
+
+
-+
-
+
E,
(S-I
+
A
reaction
(kcal/mol)
0.0
3.6E+12 1.2E+14 3.68+14 1.8E+13 1.8E+12 1.OE+13 1.1E+12 3.8E+10 3.4E+11 2.2E+12 7.5E+10 1.5E+13 8.OE+12
+
---
or cm3/ (mol s))
0 7-
15.9 56.9 37.0 40.4
C3H500' CyCC'CO04C3H500'
-1 1
CyCCC'OO
12 -1 2 13 14 -14 15
1.o
32.5 11.0 11.2 27.0 5.0 30.0
-c~cc'coo cycc'coo - cyccc'oo cyccc'oo - o=ccc0' o=ccco' - cyccc'oo
10 -10 11
-15 16
1.o
+
1.1E+12 1.5E+13 1.4E+14 1.5E+14 1.3E+13 1.1E+12 5.3E+13 1.1E+12 9.OE+12 1.5E+14 5.6E+11 3.OE+13
CyCC'COO
+ c'c~ccoo
+CCCO'-CH20 C ' C 4 C3Hs00' C'CYCCOO-C~HSOO' C'CyCCOO C=COOC' C=COOC'C'CyCCOO C=COOC*-CH20 C=CO'
-
+
or cm3/ (mol s))
(s-I
+
E, (kcal/mol) 10.0 16.0 39.0 41.7 4.0 47.2 11.4 26.6 10.0 11.0 10.0
1.o
frequencies (from CPFIT3'): 390.7 cm-I (7.69), 1176.8 cm-I (8.47), 2376.7 cm-1 (6.84) Lennard-Jones parameters: u = 5.25 A, r/k = 483 K (est from data on CCCCOH and CCOCC, Ben-Amotz and H e r ~ c h b a c h ) ~ )
+
ki k- I k2 k3 k-3 k4 k5 k-5 k6
Atkinson et al.49for CCC' 0 2 microscopic reversibility, Af/Arsvand E f - E,,, based on fit to van't Hoff plot over range 300-2500 K, hereafter designated MR from MR with k-2 = 2.OE13, based on 0 C H 3 0 , N E T 4 ) A3 = 2(1013.55)(10s/4.6),AS = -2.8 (loss of 1 rotor, gain of optical isomer); E3 = ring strain(26) Eabstraction(l1) MR A4 from A4 = 2.7E12, which is one-half the rate constant for addition of O H to ethylene, Atkinson et al.;49E4 from Soto and Pageso As = 1(1013~55)(10s/4.6), M = -6.9 (loss of 2 rotors, gain of optical isomer); E5 = ring strain(6) Eab,(26.5) MR from MR with k-6 = 2.OE11 exp(-8100/RT), based on CH3 C = C = C , A7 = 2(1013.5S)(10fl/4.6),AS = -6.9 (loss of 2 rotors, gain of optical isomer); E7 = ring strain@) E,a(27) from MR with k-8 = 5.2E11 exp(-7900/RT), based on CH3 C2H2, N E T 4 ) (included for completeness-not used for calculation) A9 from A-9 = 2.7E12, which is one-half the rate constant for addition of O H to ethylene; E9 from Soto and PageSo Alo = (1013.55)(10As/4.6), AS = -6.9 (loss of 2 rotors, gain of optical isomer); El0 = ring strain(3) Eaddilion(7) (cf. text) MR A l l = 4(1013~s5)(10s/4~6), AS = 0 (no loss of rotors), Ell = ring strain(28) Eabs(11) MR MR A-12 = l.lE12 (lose 2 rotors, gain optical isomer); E-12 = rW+ ring strain(3) 1 (from Soto and Pageso) from MR with k-13 = 3.3E11 exp(-7700/RT) for CH, C=C, NIST4) A14 = (1013.55)(10s/4.6),AS = -6.9 (loss of 2 rotors, gain of optical isomer); E14 = AH(16.6) Eadd(7) ring strain(3) (cf. text) MR MR A-15 = 5.6E11 (lose 2 rotors); E-15 = ring strain (3) Eadd(7) from MR with A-16 = 1.6E13, based on CH3O CO, E16 from Soto and Page;5onote that C = C O ' is a higher energy representation of C.C=O; we used the higher energy form here to be consistent with CH3O addition as a surrogate reaction.
+
+
+
+ +
k7
kn k9
kio k-io ki I k-i I k12 k-12 k13 k14 k-14
kl5 k-I5 kl6
+
+
+
+
+
A
reaction
2 3 -3 4
+
-
C2H3 0 2 C2H300' C2H3OO' C2H3 0 2 C2H300' -+ C ' C 4 0 C2H300' -+ C'H=CHOOH C'H=CHOOH C2H3OO' C'H=CHOOH -L C2H2 HO2 +
+
-
+
+
or cm3/ (mols))
(s-l
6.OE+12 5.OE+14 3.3E+14 1.8E+13 5.9E+11 7.2E+11
+
+
+
C2H3 + 0
1 -1
+
2
E,
A
reaction
(kcal/mol)
0.0
5
39.4 36.4 33.0 10.6 12.6
-5 6 -6 7
8
C2H300'
-
CyCC'OO C2H300' CyCC'OO OCHCH2O' OCHCH20'- CyCC'OO OCHCH20' HC'O CH2O OCHCH2O'- H O = C H H C = O
8.7E+12 1.3E+14 6.1E+13 8.7E+12 7.1E+13 3.38+13
c~cc'oo
+
-
+
+
or Cm3/ (mols))
(s-I
+
E, (kcal/mol) 25.4 10.0 4.0 72.0 12.2 29.3
frequencies (from CPFIT33): 374.8 cm-I (4.76), 111 1.3 cm-I (4.09). 2227.8 cm-I (6.14) Lennard-Jones parameters: u = 4.36 A, elk = 451 K (est from data on CCCOH, Ben-Amotz and H e r ~ c h b a c h ~ ~ ) ki ki k2 k3 k-j k4 k5 k-5
k6 k-6 k7 kn
+
this work, adjusted to match data; kl is similar to other R 0 2 systems MR cf. text. A3 = 2(1013.5s)(10s/4~6), AS = -2.8 (loss of 1 rotor, gain of optical isomer); E, = E,b,(27) ring strain (6) MR from k+ = 5.2E 11 exp(-7900/RT), based on CH3 addition to C2H2 (NIST43) A5 = (10~3~5s)(10s~4~6), AS = -2.8 (loss of 1 rotor, gain of optical isomer; Ea = AH(15.4) ring strain(3) E, addition(7) MR MR A 4 = (1013.s5)(10s/4~6), AS = -2.8 (loss of 1 rotor, gain of optical isomer); E d = rW(68) ring strain(3) E a ( l ) (Soto and Pageso) from MR with k-7 = 5.2E+11 exp(-6560/RT), based on CH3 addition to C O (Anastasi and Maw5') from A-8 = 2.9E13, based on H C2H4 (NIST43);E 4 = 4.6 (Sosa and S ~ h l e g e l ~ ~ )
+
+
+
+
+
+
+
Hydrocarbon Radical Reactions with
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4431
0 2
TABLE I (Continued) HCO A
reaction
+
--
HCO 0 2 H(C4)OO' HCO 0 2 H(C=O)OO' H(C=O)OO. H(C=O)O' H(C=O)OO' O=C'OOH +
+
+0
+
(s-I
+ 07
E,
or cm3/
(mol s))
(kcal/mol)
7.OE+12 1.4E+15 1.2E+14 8.7E+ 12
43.8 54.9 34.8
0.0
A (s-1 or cm3/ (mol s))
reaction -3 4 5
WC'OOH O=C'OOH O=C'OOH
-
+ +
H(C=O)OO* CO H02 COz O H
+ +
E,
(kcal/mol)
8.8E+11 6.2E+ 12 5.4E+11
28.4
10.8 10.8
frequencies (from CPFIT33): 343.1 cm-I (3.37), 800 cm-I (0.34), 1547.1 cm-I (5.29) Lennard-Jones parameters: u = 4.38 A, c/k = 450 K (est from data on HCOOH, Ben-Amotz and H e r ~ c h b a c h ~ ~ )
+
this work, adjusted to match data of refs 23-25; similar to other R 0 2 values MR from MR with k-2 = 2.OE13, based on 0 CH30, N E T 4 ) A3 = ( 1 0 ~ 3 ~ 5 5 ) ( 1 0 a s ~A4S~= 6 )-2.8 , (loss of 1 rotor, gain of optical isomer); E3 set 9 kcal/mol lower than well depth, from Langford and Moore28 MR from MR with k-4 = 5.2E+11 exp(-6560/R7'), based on CH3 addition to C O (Anastasi and MawS1) A-4 = 5.OE+11, E-4 = 6.6 from CH3 addition to COsO from MR, with A-5 = 1.OE+12 (cf. text); E5 adjusted to be consistent with experiment (cf. text)
+
C3H5 + 0 2
C3H5 + 0 2
8.0
r
7.0
-
6.0
-
-f
- 5
5.0
0
-F
ton He) Morgan n 01. (1902) (50 ton Ar) A
9.5
9.0
--
//
__
x
Ruiz*.I.(lw1)(2.8
4.0
Shgb M I I (7904) (uppr Ilmit-4 torr
-
He)
3.0
ORRK(2.8tonHe)
-
1-
ORRK 76 1011N2 (AIIen(HH02)
-C- ORRK 76 torr N2 (5
ORRK (54 torr Ai)
m8mb.r Hng)
\
ORRK 76 1011N2 (4-
member rlnp)
I
8.5
I
I
virtually superimposed). Next in importance are the products C-CCHO OH arising from the hydrogen shift to form C=CC'OOH, followed by the other H shifts and formation of allyloxy 0. The two dominant stabilization channels are the linear and five-member ring adducts. Even at this high temperature, stabilization is still the dominant process at atmospheric pressure and above. Again, the main reason that all of the dissociation channels are quite slow in this system is directly traceable to the shallow well. This shallow well has two effects: (1) There is simply not enough energy liberated in formation of the very weak allylic C - 0 0 bond to drive these unimolecular processes. (2) The reverse reaction to allyl + 0 2 is the lowest energy process. This low barrier, combined with the high A factor for this simple bond scission, make this the dominant pathway for dissociation of the allylperoxy adduct, thereby reducing the probability for the isomerizations to occur. As a result, the rate constant for production of allene HOz, as seen in Figure 6,is much slower than the analogous production of CzH4 + H02 from the C2Hs02adduct, where we predicted a rate constant of 2 X 1Olocm3 mol-' s-1 at 1500 K.12 The major difference is that the
+
+
+
appreciably deeper well in the ethyl case brought the shift barrier - 5 kcal/mol below the entrance channel. The predicted rate constants for the various channels, using Nz as the bath gas, were fit to a modified Arrhenius fit [ A P exp(-E,/RT)] and are shown in Table I1 for a extended range of pressures. It was necessary to divide the temperature range to achieve suitable fits, Le., where the deviations between the rate constants obtained from the non-Arrhenius fit and the original values averaged less than 10%. (It was not possible to achieve a suitable low-temperature fit for the C P C C O 0 channel.) Vinyl + 0 2 . Figure 7 illustrates the potential energy diagram. Here the well depth for the vinyl peroxy adduct is 40 kcal/mol, i.e. more than 22 and 8 kcal/mol deeper than the allyl and ethyl additions respectively. The initially formed adduct has significantly more energy to undergo reactions such as isomerizations or dissociations to other products than in the case of allyl or ethyl before stabilization occurs. Table I lists the input parameters for the QRRK calculation. There are two important new features of this potential energy surface. First, the deeper well makes the channel vinoxy + 0 atom less endothermic. This channel is further enhanced by the
+
Bozzelli and Dean
4432 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 C3H5 + 0 2
C3H5 + 0 2 T.1500K
P 760 torr N2
11
9
- .-o---.c.cc.wH - -- *---.C l c U l O +OH x ..- c.c.cwH
-
-0-C.Cd
+ HOI
c..ccww
--a--
1P '' a r
3
3
C"+HK.OW
--.--cycc.cao c.cyCC00
----+-.cycoc.oo - .. ..- O&W. ---+-- 0 1 2 0 .
C.C.0
Figure 6. Plot of the predicted rate constants for the various channels of the allyl + 02 reaction versus pressure of N2 at 1500 K.
C2H3.
0
0.5
1
1.5
2
2.5
3
+
02
3.5
10OOlT (K)
Figure 4. Arrhenius plot of the predicted rate constants for the various channels of the allyl + 0 2 reaction at 760 Torr of Nz. C3H5 + 0 2 T=300K
l5 10
p-=-zz::: r
-- -
--0--c.CEO.+0
-c
lr-
C.OICH20
-23 KoaUmok
0-CH-WOO.
+
Figure 7. Potential energy diagram for the vinyl radical 0 2 reaction. (For completeness, the pathway to dissociation to vinoxy, where vinoxy is considered to be an oxygen-centered radical is also shown.)
peroxy system. It requires a 1,2 H atom shift in order to have any outlet channel other than the reverse reaction. The 1,2 H shift would form CH3CyC*OO,which would rapidly decompose to C02 + CH3. The H shift is, however, a right transition state and has a barrier that is 13 kcal/mol above the inlet vinyl O2 reactants. Thus, like the five-member ring peroxide radical in the allyl case, this isomer reverts back to the vinyl peroxy. Westmoreland has also evaluated this channel, and while our conclusions are similar, i.e., the reaction is unimportant, we determine that the reaction is limited by the H shift, while he concludes the formation of the cyclic C'CyCOO is unfavorable. Given the fact that the vinoxy channel is more accessible, we took particular care in assigning the rate constantfor this channel. One approach was to assume that vinoxy could be represented as the (higher-energy) oxygen-centered radical C 4 0 . Here the reverse reactioncould be described as a radical recombination. Using the measured value43of 2 X 1013for 0 + CH3O as a value representative of the expected rate constant for C 4 0 ' 0, microscopic reversibility yields A = 3.8 X 10'4, E = 44.1 kcal/ mol for the dissociation. Another approach was to assume that vinoxy is best described as the carbon centered radical C'C-0 and that the reverse reaction is an 0-atom addition across the carbonyl bond. Using an A factor for this addition of 7.8 X 1012, observed for 0-atom addition to one obtains a forward A factor of 3.3 X loi4,in very good agreement with the estimate above. Estimation of the barrier for addition of 0 to the oxygen of the carbonyl group is more problematical. To our knowledge, there are no theoretical or experimentalestimates for this barrier. However, molecular beam studies of the translational energy of products formed by multiphoton dissociation of ethyl vinyl ethe+
+
-3
-2
-1
0
1
2
3
4
Log P (atm)
Figure 5. Plot of the predicted rate constants for the various channels of the allyl + 02 reaction versus pressure of N2 at 300 K.
resonance stabilization of vinoxy-the net effect is that this channel is more accessible-approximately 23 kcal/mol lower in energy than the analogous channel (ethoxy 0) in the ethyl + 0 2 reaction. The second feature is the new channel availabledue to intramolecularaddition of the peroxy to the double bond-this can occur with a relatively low barrier as in the allyl case. However, unlike allyl, there is now a low-energy exit channel that allows this to become the dominant reaction at low temperatures. We have also analyzed the reaction of the vinylperoxy radical to cyclize forming the three-member ring C'CyCOO. This isomerization will occur with a similar Arrhenius A factor to formationof the four-member peroxy ring and is only a few kcal/ mol above the four-member ring in energy. This channel is, however, similar to the five-member peroxy ring in the allyl-
+
+
Hydrocarbon Radical Reactions with O2
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4433
.
CZH3 + 0 2
C 2 H 3 t 0 2 T=300K 13
12
11
10
1.0
1.5
2.0
3.0
2.5
-
3.5
lWOfr(K)
7
Figure 8. Comparison of predicted values for rate constants for vinyl +
CZHZ + HOZ
cvcc.00
O2with experiment. Three sets of calculations are included: one (36.4
.- - - A - - - - 0.010110. - -- x ..- Hco +cnm
kcal/mol barrier to vinoxy/25.4 kcal/mol barrier to cyclization) uses the parameters in Table I. The (35.4/25.4) set uses a 1 kcal/mol lower barrier to vinoxy while the (36.4/26.4) set uses a 1 kcal/mol higher barrier to cyclization. Note that the latter two sets predict smaller branching ratios to C H 2 0 HCO.
-- -- H rO.CH4C.O X
+
C2H3 + 0 2
l4
-
aRRK(Iot.1)
P = 7.6 torr N2
-3
I
I
-2
1
I
I
0
2
1
log P(atm)
r
Figure 11. Plot of the predicted rate constants for the various channels of the vinyl
+ 0 2 reaction versus pressure of N2 at 300 K. C2H3 t 0 2 T = 1500K
11
0.5
0
2
1.5
1
2.5
3
3.5
10
1GQOfr (K)
Figure 9. Arrhenius plot of the predicted rate constants for the various 2 reaction at 7.6 Torr of N2. channels of the vinyl 0
+
C2H3 + 0 2
P i 760 tor( N2
7
6
-
5
wm(w)
,2~~-~--CzH300.
-CWI+HOl
-c.cIo.o
-c.=cow
-.-X---CVCC.W
-.-*--0;CHDIZO.
-2
-3
0
1
1
2
log Fi-1 - - - -A&...
HCO+CH20
--C--
-C.QRRK
HI
Figure 12. Plot of the predicted rate constants for the various channels
(10111l
of the vinyl 0.5
0
1
1.5
2
2.5
3
1OOOfr (K)
Figure 10. Arrhenius plot of the predicted rate constants for the various channels of the vinyl
+ 02 reaction at 760 Torr of N2.
and anisole46indicate small (-3 kcal/mol) exit barriers (above the endothermicity) for the dissociation process. In both systems the C-O bond is broken to form a methyl radical as well the oxygen-containing radical (vinoxy and phenoxy, respectively). The barrier is attributed to an electronic rearrangement, leading to considerable double bond character in the remaining C-O bond. Thus methyl addition to either vinoxy or phenoxy would be expected to have a barrier of 3 kcal/mol. One might expect that oxygen-atom addition to vinoxy might occur with a similar barrier. This would lead to an expected barrier for formation of vinoxy 0 from dissociation of C2H300' to be 35.4 kcal/mol,
+
+ 02 reaction versus pressure of N2 at 1500 K.
3.5
substantially smaller than the 44.1 kcal/mol obtained earlier by neglecting any electronic rearrangement. Another estimated of this barrier is based upon hydrogen addition to formaldehyde. Sosa and Schlege14' have calculated that the barrier for H addition to the oxygen in formaldehyde has a barrier 6 kcal/mol higher than that for addition at the carbon end of the carbonyl bond. If one were to assume the same differential were to apply for the oxygen atom addition, one would expect a barrier of -9 kcal/mol, since the barrier has been measured to be -3 kcal/mol for addition to the carbon.48 However, one might expect this estimate to be somewhat high for addition to C*C=O, given that the initially formed diradical can form a C-C double bond by simple rotation, which cannot happen in addition to formaldehyde. Note if there were no
-
4434
TABLE II: Apparent Rate Constants for R A
n
ClHj + 0 2 CIHSOO' CIHS + 0 2 CiHsOO' CIHS 0 2 CiHs00' CIHj 0 2 CiHs00' ClHs + 0 2 CIHSOO' CIH5 0 2 C3Hs00' CIHj + 0 2 CiHjOO' CjH5 0 2 CiHj00' ClHj + 02 CiHsOO' C3Hs 0 2 CIHSOO' ClH5 O2 C=CC'OOH CIH5 + 0 2 C 4 C ' O O H ClH5 0 2 C 4 C ' O O H ClH5 O2 C=CC'OOH CIHS 0 2 C=CC'OOH C3HS+ O 2Q C=CC'OOH CnHS 0 2 C=CC'OOH ClHj + 0 2 C=CC'OOH ClHJ 0 2 C=CC'OOH ClHS + 0 2 I)C=CC'OOH ClH5 O2 C=CCHO + OH C3H5 O2 C=CCHO + OH CIHS O26)C=CCHO + OH C,Hs + O20 C=CCHO + OH ClH5 O2 C-CCHO + OH ClH5 O2 C=CCHO + OH C3Hs O2 C=CCHO + OH ClH5 O2 C=CCHO + OH ClH5 O2 C=CCHO + OH ClH5 O2 C=CCHO + OH ClH5 O2 C=CCOOH ClHS 0 2 C-C'COOH ClH5 O2 C=C'COOH ClHS 0 2 C=C'COOH ClH5 O2 C=C'COOH C3HS 0 2 C=C'COOH CIHJ O2 C=C'COOH CIHJ O2 C 4 ' C O O H C3HS 0 2 C=C'COOH C3H5 O2 C=C'COOH ClHS 0 2 6)C=C% + H02 CIHS 0 2 C=C=C + H02 C3H5 0 2 C = C 4 + H02 ClH5 0 2 C = C 4 + HO2 CIHJ 0 2 C = C 4 + H02 ClH5 0 2 C=C=C + H02 CIHS + 0 2 C=C=C + HO2 CIH5 + 0 2 C = C 4 + H02 ClHS 0 2 6)C=C=C + H02 C3H5 0 2 C=C=C + H02 CIH5 + 0 2 C'=CCOOH CIHs 0 2 0 C'=CCOOH CIHS 02 * C'=CCOOH CIHS + 0 2 C.=CCOOH CIHs O2 C'=CCOOH C3Hs 0 2 C'=CCOOH CIHS 0 2 C'=CCOOH ClHS 0 2 +=+ C'=CCOOH ClH5 O2 C'=CCOOH CnHS 0 2 C'=CCOOH CjHS 0 2 CYCC'COO C3Hs 0 2 w CYCC'COO C3H5 O2 CYCC'COO C3HS + 0 2 CYCC'COO CIH, 0 2 CYCC'COO
8.93E+35 2.03E+37 7,62E+37 7.55E+36 1.29E+35 9.05E+32 2,92E+29 1.81E+25 2,68E+20 1.04E+18 1.15E+13 1.15E+14 1.16E+15 3.59E+15 1.30E+16 4.71E+16 2.14E+17 7.43E+17 6.75E+17 1.01E+17 4.15E+14 4.16E+14 4,22E+14 4.34E+14 4.73E+14 5.71E+14 7.82E+14 9.14E+14 2.548+14 1,94E+13 2.57E+32 3.19E+33 5.93E+29 5.77E+25 5.50E+20 7.35E+l6 3.82E+14 9.98E+12 1.69E+11 2.33E+09 4.34E+12 7.79E+14 2.04E+15 5.55E+12 1.00E+08 2,87E+03 1,01E+00 2.73E-02 9.78E-04 2.87E-05 1.08E+24 2.95E+25 6.60E+26 6.99E+25 5,93E+22 8.38E+18 1.72E+15 4.67E+12 1.358+09 2.36E+06 6.168+38 1.41E+40 5.96E+40 5.618+39 1.64E+37
-9.03 -9.13 -8.95 -8.47 -7.74 -6.90 -5.65 -4.20 -2.59 -1.79 -2.64 -2.64 -2.64 -2.64 -2.65 -2.68 -2.71 -2.72 -2.52 -2.16 -0.94 -0.94 -0.94 -0.94 -0.95 -0.97 -1.01 -1.02 -0.82 -0.46 -8.03 -8.01 -6.47 -5.06 -3.36 -2.06 -1.19 -0.76 -0.17 0.42 -0.67 -1.34 -1.37 -0.53 0.96 2.34 3.34 3.72 4.05 4.45 -5.47 -5.60 -5.65 -5.16 -4.01 -2.67 -1.40 -0.54 0.61 1.48 -9.94 -10.04 -9.87 -9.37 -8.38
CiHs + 0 2 CiHsOO' ClHs + 0 2 CiHsOO' CIHs + 0 2 CiHsOO' ClHS 0 2 * CiHsOO' C3Hs + 0 2 * CjHs00' CIH5 + 0 2 CiHs00' CIHj + 0 2 ClHs00' ClHj + 0 2 C3HsOO' CiH5 + 0 2 C3Hs00' CIHs 0 2 CiH500' ClHj + 0 2 C=CCO' + 0 ClHS 0 2 C 4 C 0 ' + 0 ClHs + 0 2 * C-CCO' + 0 CIHS 0 2 0 C=CCO' + 0 CIHs O2B C-CCO' + 0 ClH5 0 2 C%CO + 0
2.58E+16 3.40E+17 2.29E+19 6.34E+20 6.98E+22 1.28E+25 1.07E+28 1.09E+31 2.198+34 7.798+35 1.54E+39 1.54E+39 1.54E+39 1.54E+39 1.56E+39 1.60E+39
-3.47 -3.50 -3.72 -3.98 -4.38 4.86 -5.49 -6.15 -6.87 -7.18 -6.97 -6.97 -6.97 -6.97 -6.97 -6.97
e)
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Q
Q Q
Q
Q
-Q
C)
Q
Q
Q
Q
--
Q
Q
---
Q
Q
Q
Q Q
Q
Q
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Q Q Q
+ + + + + + + + + + + + + +
Q
Q
e) Q
e) Q
Q
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Q
+
Q
Q
Q
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+ + + + +
Bozzelli and Dean
The Journal of Physical Chemistry. Vol. 97, No. 17, 1993
Q
Q
Q
Q
+ 0 2 (M = N2). k = ATn exp(-&/RZ), press. (atm)
Units in cm3 mol s, & in cal/mol press.
-
A
n
4221 1.00E-03 4515 1.00E-02 5071 l.OOE-O1 5065 3.00E-01 4904 1.00E+00 4659 3.00E+00 4077 l.OOE+Ol 3188 3.00E+01 2040 1.00E+02 1434 2.00E+02 22136 1.00E-03 22136 1.00E-02 22140 1.00E-01 22149 3.00E-01 22178 l.OOE+OO 22247 3.00E+00 22411 1.00E+01 22678 3.00E+01 23008 1.00E+02 23061 2.00E+02 21922 1.00E-03 21922 1.00E-02 21926 1.00E-01 21935 3.00E-01 21964 1.00E+00 22033 3.00E+00 22198 1.00E+01 22466 3.00E+01 22799 1.00E+02 22855 2.00E+02 20506 1.00E-03 21274 1.00E-02 21148 1.00E-01 20410 3.00E-01 19316 l.OOE+OO 18447 3.00E+00 17971 l.OOE+Ol 17963 3.0OE+01 17992 1.00E+02 17787 2.00E+02 17419 l.OOE-03 18726 1.00E-02 20164 I.OOE-O1 20108 3.00E-01 19390 1.00E+00 18557 3.00E+00 18029 1.00E+01 18073 3.00E+01 18357 1.00E+02 18355 2.00E+02 12950 1.00E-03 13254 1.00E-02 14151 I.OOE-01 14348 3.00E-01 14028 1.00E+00 13407 3.00E+00 12877 1.00E+01 12692 3.00E+01 12318 1.00E+02 11857 2.00E+02 4845 1.00E-03 5173 1.00E-02 5975 1.00E-01 6272 3.00E-01 6395 1.00E+00
temu(K) Allyl + O2 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
Products CIHS+ 0 2 CYCC'COO ClHj + 0 2 CYCC'COO C3H5 + 0 2 w CYCC'COO ClH5 + 0 2 CYCC'COO C3H5 + 0 2 - CYCC'COO ClH5 + 0 2 *=) C'CYCCOO C ~ H+J 0 2 C'CYCCOO C3H5 02+C*CYCCOO ClHs + 0 2 C'CYCCOO C I H+ ~ 0 2 C'CYCCOO C3Hs + 0 2 C'CYCCOO CiHs + 0 2 C'CYCCOO CaHs + 0 2 C'CYCCOO CIHS+ 0 2 CCYCCOO CIHS+ 0 2 C'CYCCOO C3H5 + 0 2 CYCCC'OO C3H5 + O~QCYCCC'OO ClH5 + 0 2 CYCCC'OO CIHS+ 0 2 CYCCC'OO CIHS+ 0 2 CYCCC'OO CIHJ + 0 2 CYCCC'OO C3H5 + 0 2 CYCCC'OO CIHS+ 0 2 CYCCC'OO ClH5 + 0 2 w CYCCC'OO C3H5 + 0 2 c* CYCCC'OO C3H5 + 0 2 W C C 0 ' C3H5 + 0 2 M C C 0 ' C3Hs + 0 2 W C C O ' CiH5 + 0 2 W C C O ' C3Hj + 0 2 W C C O ' C3Hs + 0 2 6)o=CCCO' C3H5 + 0 2 W C C O C I H+ ~0 2 MCC0' C I H+ ~0 2 WCC0' ClHS + 0 2 W C O O ' ClHs + 0 2 CH2O + C'C=O CIH, + 0 2 CH20 + C'C=O CiHs + 0 2 * CH20 + C'C=O CiHs + 0 2 CH2O + C ' C 4 ClHs + 0 2 CH20 + C ' C 4 CiHs + 0 2 CH2O + C'C=O ClHs + 0 2 CH2O + C ' C 4 ClHs + 0 2 CH2O + C'C=O CIHs + 0 2 CH2O + C ' C 4 ClHs + 0 2 CH20 + C ' C 4 C3H5 + 0 2 I)C=COOC' CIHs + 0 2 C 4 O O C ' ClHs 0 2 C 4 O O C ' CiH, + 0 2 C 4 O O C ' ClHs 0 2 C 4 O O c ' CiHs + 0 2 ~ C 4 0 O C . CjH5 + 0 2 C 4 O O C ' ClHS + 0 2 C 4 O O C ' CIHS+ 0 2 C 4 O O C ' ClHJ + 0 2 C 4 O O C ' ClHs + 0 2 CH2O + C 4 0 ' ClHs + 0 2 CH2O + C=CO' ClHs + 0 2 CH2O + C 4 0 ' CiHs + 0 2 CH2O + C 4 0 ' CjHs + 0 2 CH2O + C 4 0 ' ClH5 + 0 2 CH2O + C 4 O ' ClHs + 0 2 CH2O + C=CO' C3Hs + 0 2 CH2O + C 4 0 ' C ~ H+S 0 2 CH2O + C=CO' ClHs + 0 2 CHI0 + C=CO'
1.318+33 -6.94 2.32E+26 -4.68 5.10E+ 18 -2.20 1.60E+ IO 0.49 1.80 8.74E+05 6.718+36 -10.28 8.448+37 -10.30 1.578+38 -10.04 1.77E+37 -9.57 1.57E+36 -9.05 1.30E+35 -8.53 I.OOE+33 -7.66 2.68E+29 -6.35 5.04E+22 4 0 7 3.90E+ 17 -2.39 4.31E+ll -2.19 4.35E+12 -2.20 4.75E+13 -2.21 1.71E+14 -2.23 9.708+14 -2.29 6.88E+15 -2.40 2.41E+ 16 -2.37 1.65E+15 -1.82 1.77E+ll -0.40 8.35E+07 0.71 5.39E+1 I -2.29 5.44E+ I2 -2.29 5.94E+ 13 -2.30 2.148+14 -2.33 1.21E+15 -2.39 8.618+15 -2.49 3.04E+ 16 -2.46 2.18E+15 -1.92 2.75E+11 -0.53 1.48E+08 0.57 1.25E+12 -0.21 1.26E+12 -0.21 1.38E+12 -0.22 1.67E+12 -0.24 2.88E+12 -0.31 7.12E+12 -0.41 8.44E+12 -0.40 2.36E+11 0.12 1.04E+07 1.50 2.95E+03 2.59 5.75E+10 -2.40 6.33E+Il -2.41 1.51E+13 -2.52 2.OOE+ 14 -2.71 1.28E+ 16 -3.09 1.05E+18 -3.50 4.28E+19 -3.78 3.938+19 -3.55 1.77E+ 16 -2.27 2.74E+ 12 -0.96 6.66E+ 11 -0.41 7.35E+11 -0.42 1.77E+12 -0.53 7.93E+12 -0.73 1.64E+14 -1.11 5.20E+15 -1.54 8.6lE+16 -1.86 3.84E+ 16 -1.68 8 .WE+ 12 -0.46 7.53E+08 0.82
-8817 -8692 -7822 -6788 -51 19 -3092 -241 2983 7021 9327 70665 70665 70666 70667 70673 70688
1000-2500 1000-2500 1000-2500 100&2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1100-2500 1100-2500 1100-2500 1100-2500 1100-2500 1100-2500
C3Hs + 0 2 C 4 C O ' + 0 ClHS + 0 2 * C=CC0' + 0 C3Hs + 0 2 C 4 C 0 ' + 0 CiHs + 0 2 * C=CC'OOH ClHs + 0 2 0 C 4 C ' O O H CIH, + 0 2 C=CC'OOH C3Hs + 0 2 C=CC'OOH C3H5 + 0 2 w C=CC'OOH ClHs + 0 2 C 4 C ' O O H CIH+ ~ 0 2 C4C'OOH C3H5 + 02 C 4 C ' O O H C3H5 + 0 2 C 4 C ' O O H C3H5 + 0 2 C 4 C ' O O H C3H5 + 0 2 C 4 C H O + OH CsHs + 02 C 4 C H O + OH CIHS+ 0 2 C 4 C H O + OH
2.318+39 5.46E+39 1.58E+40 1.14E+12 1.14E+13 1.14E+14 3.458+14 l.lEE+I 5 3.80E+15 1.61E+16 8.95E+16 1.65E+ 18 2.05E+19 1.758+13 1.758+13 1.76E+13
E,
l.OOE-03 1.00E-02 1.OOE-01 3.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 1.00E+02 2.00E+02 1.00E-03 1.00E-02 1.00E-01 3.00E-01 1.00E+00 3.00E+00
Q
Q
Q
+
Q
Q
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Q Q
Q Q Q
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Q Q Q
-Q
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e)
Q
-
Q
Q Q
-7.02 -7.11 -7.24 -2.22 -2.22 -2.22 -2.23 -2.23 -2.24 -2.26 -2.34 -2.53 -2.74 -0.41 -0.41 -0.41
E.
(atm)
temp(K)
6112 3.00E+00 5130 l.OOE+Ol 3664 3.00E+01 1817 1.00E+02 842 2.00E+02 14691 1.00E-03 14848 1.00E-02 15256 1.00E-01 15322 3.00E-01 15502 I.OOE+OO 15790 3.00E+00 16037 1.00E+01 15945 3.00E+01 15057 1.00E+02 14120 2.00E+02 17809 1.00E-03 17812 1.00E-02 17838 l.OOE-O1 17896 3.00E-01 18073 1.00E+00 18442 3.00E+00 19041 1.00E+01 19407 3.00E+OI 19231 1.00E+02 18854 2.00E+02 17874 I.00E-03 17876 I.00E-02 17903 1.00E-01 17961 3.00E-01 18139 1.00E+00 18510 3.00E+00 19117 I.OOE+OI 19508 3.00E+01 19415 I.OOE+02 19137 2.00E+02 17439 1.00E-03 17442 1.00E-02 17469 1.00E-01 17527 3.00E-01 17707 1.00E+00 18084 3.00E+00 18707 l.OOE+Ol 19121 3.00E+01 19056 1.00E+02 18790 2.00E+02 11719 1.00E-03 11740 1.00E-02 11927 1.OOE-01 12258 3.00E-01 12976 1.00E+00 13942 3.00E+00 15162 1.00E+01 16110 3.00E+01 16360 1.00E+02 15948 2.00E+02 11362 1.00E-03 11383 1.00E-02 11570 l.OOE-O1 11901 3.00E-01 12623 1.00E+00 13603 3.00E+00 14856 I.OOE+Ol 15850 3.00E+01 16161 1.00E+02 15779 2.00E+02
300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300- 1000 300-1000 300-1000 300-1000 300-1000 300-1000 30C-1000 300-1000 300-1000 300-1000 300- 1000 300-1000 300- 1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
70881 71337 71907 23176 23176 23178 23182 23195 23231 23353 23672 24580 25592 22841 22841 22843
1100-2500 1100-2500 1100-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 100C-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500
3.00E+01 1.00E+02 2.00E+02 1.00E-03 1.00E-02 1.00E-01 3.00E-01 l.OOE+OO 3.00E+00 1.00E+OI 3.00E+01 1.00E+02 2.00E+02 1.00E-03 1.00E-02 1.00E-01
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4435
Hydrocarbon Radical Reactions with O2
TABLE II (Continued) ~~
C3H5 + 0 2 C=CCO' + 0 C3Hj + 0 2 c C=CCHO OH C3H5 + 0 2 L.) C X C H O + OH C3H5 0 2 * C=CCHO + OH C3Hj + 0 2 o C-CCHO + OH C3Hj 0 2 C=CCHO + OH C3Hj + 0 2 0 C=CCHO OH C3HS O2o C-C'COOH C3Hj O2o C=C'COOH C3HS O2o C-C'COOH C3Hj O2o C-C'COOH C3Hj O2o C-C'COOH C3Hj + 0 2 C=C'COOH C3HJ O2o C-C'COOH C3Hj+ O2Q C=C'COOH C3Hj O2o C-C'COOH CJHj 02 C=C'COOH HO2 C3Hj 0 2 o C=C=C C3Hj + 0 2 o C=C=C + H02 CjHj 0 2 o C-C-C + H0z C3H5 + 0 2 C=C=C + HOz C3Hj 0 2 o C-C=C + H02 C3Hj + 0 2 C=C=C + H0z C3Hj 0 2 * C-C% + H02 C3Hj 0 2 o C=C=C H02 C3Hj 0 2 C=C=C + H02 CIH, 0 2 C=C% + H02 C3H5+ O2t)C'=CCOOH C3Hs+ O2o C'=CCOOH C3Hj O2 C'=CCOOH C3HS+ O2o C'=CCOOH C3H5 O2o C'=CCOOH ClHj 02 C'=CCOOH C3Hs O2o C'=CCOOH C3H5 0 2 0 C'-CCOOH C3H5+ O2o C'=CCOOH C3Hj O2o C'=CCOOH ClHj 0 2 C2Hz + HzC'OOH C3H5 0 2 C , C2H2 + H2C'OOH CIH5 0 2 C2Hz + H2C'OOH C3H5 + 0 2 c C2H2 + H2C'OOH C3Hs 0 2 o C2H2 + H2C'OOH C3H5 0 2 CI C2H2 + H2C'OOH C3Hs + 0 2 C2H2 + HzC'OOH C3H5 + 0 2 I)C2H2 + H2C'OOH C3H5 + 0 2 C2H2 + H2C'OOH C3H5 + 0 2 o C2H2 + HzC'OOH C3H5 O2Q CYCC'COO C3Hj O2o CYCC'COO C3H5 O2o CYCC'COO C3H5 O2o CYCC'COO C3H5 O2o CYCC'COO C3Hj O2o CYCC'COO C3HJ O2o CYCC'COO C3HJ O2o CYCC'COO C3H5 O2e* CYCC'COO C3Hj O2o CYCC'COO C3HJ O2o C'CYCCOO C3H5 O2o C'CYCCOO Q
+ + + + + + + + + + + + + + + + +
+ + + + + + + + + + +
+
Q
+
Q
+
Q)
Q)
Q)
Q
+ + + + + + + + + + + +
+
A
n
1.77E+39 1.82E+13 1.958+13 2.478+13 4.58E+13 2.53E+14 1.57E+15 2.87E+13 1.29E+15 6.748+18 5.39E+21 4.04E+25 8.358+28 2.02E+30 8.86E+27 5.35E+22 1.41E+20 1.30E+ll 1.65E+ll 1.03E+12 1.678+13 4.998+15 6.668+18 2.188+21 1.75E+20 2.22E+15 2,71E+12 3,64E+19 4,14E+20 1.22E+22 2,07E+23 2.78E+25 1.02E+28 9,72E+29 7.11E+28 5.28E+24 2.79E+22 4.99E+46 5.05E+46 5.76E+46 7.628+46 1.868+47 1.28E+48 2.098+49 4.358+48 3.938+43 3.428+39 8,63E+22 1.31E+24 2,41E+26 2,31E+28 2.22E+31 6.09E+34 1.12E+39 4.80E+42 1.02E+45 7,87E+44 1.21E+04 1.70E+05
-6.98 -0.41 -0.42 -0.45 -0.52 -0.71 -0.92 -2.55 -2.73 -3.45 -4.10 -4.98 -5.71 -5.89 -5.06 -3.47 -2.70 -0.17 -0.20 -0.42 -0.74 -1.40 -2.22 -2.85 -2.50 -1.14 -0.35 -4.04 -4.05 -4.18 -4.38
3.388+23 3.54E+24 5.05E+25 4.70E+26 4.74E+25 6.078+22 2.79E+19 3.27E+17 2.03E+16 1.94E+09 2.088+09 3.73E+09 2.238+10 5.34E+09 6.61E+06 2.27E+02 1.52E-01 8.038-04 5.988+18 6.52E+19 1.34E+21 391E+22
-4.87 -4.88 -4.92 -4.88 -4.41 -3.35 -2.21 -1.56 -1.16 1.03 1.02 0.95 0.74 0.96 1.90 3.29 4.27 4.95 -3.69 -3.70 -3.79 -3.88
-4.80
-5.35 -5.71 -5.23 -3.94 -3.25 -9.26 -9.26 -9.27 -9.31 -9.41 -9.63 -9.93 -9.70 -8.28 -7.17 -5.53 -5.57 -5.91 -6.31 -6.96 -7.74 -8.71 -9.50 -9.90 -9.73 -0.76 -0.80
E.
press. (atm)
70740 l.OOE+Ol 22859 1.00E+00 22896 3.00E+00 23017 1.00E+Ol 23335 3.00E+01 24241 1.00E+02 25251 2.00E+O2 8950 1.00E-03 9627 1.00E-02 12544 l.OOE-O1 15285 3.00E-01 19394 1.00E+00 23589 3.00E+00 26988 l.OOE+Ol 27374 3.00E+01 25403 1.00E+02 24433 2.00E+02 17345 1.00E-03 17455 1.00E-02 18295 1.00E-01 19608 3.00E-01 22428 1.00E+00 26359 3.00E+00 30755 l.OOE+Ol 32465 3.00E+01 31201 1.00E+02 30194 2.00E+02 12175 1.00E-03 12234 1.00E-02 12739 l.OOE-O1 13578 3.00E-01 15468 1.00E+00 18258 3.00E+00 21450 l.OOE+Ol 22502 3.00E+01 21352 1.00E+02 20701 2.00E+02 66514 1.00E-03 66521 1.00E-02 66596 l.OOE-O1 66757 3.00E-01 67278 1.00E+00 68482 3.00E+00 70791 1.00E+01 72268 3.00E+01 70785 1.00E+02 68918 2.00E+02 -7030 1.00E-03 -6833 1.00E-02 -5435 l.OOE-O1 -3717 3.00E-01 -798 1.00E+00 2915 3.00E+00 8071 1.00E+01 13335 3.00E+01 18656 1.00E+02 20916 2.00E+02 -4413 1.00E-03 -4263 1.00E-02 2169 2184 2320 2838 2880 2407 1678 1216 916 -1 10 -92 69 828 1173 977 208 -443 -936 1485 1513 1763 2875
1.00E-03 1.00E-02 l.OOE-O1 1.00E+00 3.00E+00 l.OOE+Ol 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E42 l.OOE-01 1.00E+00
temp(K)
A
+ + + + + +
+
n
E,
press. (atm)
temp(K)
1100-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500 1000-2500
ClH5 O2c)C==CCHO OH C3H5 0 2 *C'CYCCOO C3Hj 0 2 o C'CYCCOO C3Hj 0 2 C'CYCCOO C3Hj 0 2 C'CYCCOO C3Hj 0 2 C'CYCCOO C3H5 + 0 2 c C'CYCCOO C3H5 + 0 2 0 C'CYCCOO C3Hj 0 2 * C'CYCCOO ClHj 0 2 0 CYCCC'OO C3H5 + 02oCYCCC'OO C3H5+ O2o CYCCC'OO C3Hj 0 2 CYCCC'OO C3Hj 0 2 o CYCCC'OO C3H5 0 2 o CYCCC'OO C3Hj + 0 2 o CYCCC'OO C3Hj + 0 2 CYCCC'OO CiHj + 0 2 CYCCC'OO C3Hj + 0 2 * CYCCC'OO C3Hj 0 2 c;* O=CCCO' C3Hj 0 2 M C C O ' C3Hj 0 2 I)o=CCCO' C3H5 0 2 0 M C C O ' C3Hj 0 2 M C C O ' C3Hj + 0 2 w M C C O ' C3Hj 0 2 0 o=CCCO' C3Hj + 0 2 M C C O ' C3H5 + 0 2 * M C C O C3H5 + 0 2 *d O=CCCO' C3H5 + 0 2 CH2O + C ' C 4 C3Hj 0 2 * CH2O + C ' C 4 C3Hj + 02 o CH2O + C ' C 4 C3H5 + 02 0 CH2O + C ' C 4 C3H5 0 2 w CH2O + C'C=O C3H5 + 0 2 o CH2O + C ' C 4 C3H5 0 2 CH20 + C ' C 4 C3Hj + 02 o CH20 + C ' C 4 C3Hj + 02 o CH20 + C ' C 4 C3H5 0 2 * CH2O + C ' C 4 ClHj 0 2 o C=COOC' C3H5 0 2 C 4 O O C ' C3Hj 0 2 o C=COOC' C3H5 0 2 ~3 C-COOC' C3H5 + 0 2 * C--COOC' C3H5 + 0 2 C=COOC' C3Hj 0 2 C=COOC' C3H5 + 0 2 C%OOC' C3H5 0 2 C 4 O O C ' C3H5 + 0 2 C--COOC' C3Hj + 0 2 * CH2O + C=CO' C3H5 + 0 2 B CH2O + C-CO' C3Hj + 0 2 * CH2O + C d O ' C3H5 0 2 CH2O + C=CO' C3Hj + 0 2 CH2O + C d O ' C3Hj + 0 2 CH2O + C-CO' C3Hj + 0 2 CH2O + C = C O C3H5 0 2 CH2O + C = C O C3Hj + 0 2 * CH2O + ' 2 4 0 ' C3H5 02 o CH2O + C=CO'
1.77E+13 2.13E+07 1.28E+09 1.90E+ll 2.08E+13 1.06E+16 1.83E+19 6.66E+23 6.96E+26 8.518+14 8.53E+15 8.708+16 2.73E+17 1.06E+18 4.89E+18 6.47E+19 4.60E+21 1.05E+25 1.74E+27 1.20E+16 1.20E+17 1.23E+18 3.85E+18 1.50E+19 6.92E+19 9.23E+20 6.66E+22 1.558+26 2.688+28 9.58E+14 9.598+14 9.79E+14 1.02E+15 1.19E+15 1.82E+15 7.14E+15 1.70E+17 1.37E+20 1.51E+22 1.15E+09 1.16E+10 1.18E+ll 3.63E+11 1.40E+12 6.05E+12 5.93E+13 1.84E+15 1.13E+18 2.41E+20 5.658+10 5.668+10 5.75E+10 5.97E+lO 6.77E+10 9.47E+10 2.60E+ll 2.40E+12 3.72E+14 3.62E+16
-0.41 22847 3.00E-01 1000-2500 -1.09 -3129 1.00E-01 1000-2500 -1.44 -1773 3.00E-01 1000-2500 -1.88 -30 1.00E+00 1000-2500 -2.30 1633 3.00E+00 1000-2500 -2.88 3998 1.00E+01 1000-2Hw) -3.62 7093 3.00E+01 1000-2500 4 . 6 8 11904 1.00E+02 1000-2500 -5.39 15403 2.00E+O2 1000-2500 -3.11 20376 1.00E-03 1000-2500 -3.11 20378 1.00E-02 1000-2500 -3.11 20388 l.OOE-O1 1000-2500 -3.12 20410 3.00E-01 1000-2500 -3.13 20489 1.00E+00 1000-2500 -3.18 20707 3.00E+00 1000-2500 -3.34 21416 1.00E+01 1000-2500 -3.70 23096 3.00E+Ol 1000-2500 -4.45 26874 1.00E+02 1000-2500 -4.94 29903 2.00E+02 1000-2500 -3.52 20984 1.00E-03 1000-2500 -3.52 20985 1.00E-02 1000-2500 -3.52 20996 1.00E-01 1000-2500 -3.52 21018 3.00E-01 1000-2500 -3.54 21098 1.00E+00 1000-2500 -3.59 21319 3.00E+00 1000-2500 -3.75 22036 1.00E+01 1000-2500 4.11 23735 3.00E+01 1000-2500 -4.86 27563 I.OOE+02 1000-2500 -5.35 30659 2.00E+O2 1000-2500 -0.98 20017 1.00E-03 1000-2500 -0.98 20018 1.00E-02 1000-2500 -0.98 20028 1.00E-01 1000-2500 4 . 9 9 20051 3.00E-01 1000-2500 -1.01 20128 l.OOE+00 1000-2500 -1.06 20343 3.00E+00 1000-2500 -1.21 21046 1.00E+01 1000-2500 -1.58 22724 3.00E+01 1000-2500 -2.34 26566 1.00E+02 1000-2500 -2.86 29726 2.OOE+O2 1000-2500 -1.89 10969 1.00E-03 1000-2500 -1.89 10970 1.00E-02 1000-2500 -1.89 10979 1.00E-01 1000-2500 -1.89 10997 3.00E-01 1000-2500 -1.91 11060 1.00E+00 1000-2500 -1.95 11228 3.00E+00 1000-2500 -2.08 11734 1.00E+01 1000-2500 -2.35 12856 3.00E+01 1000-2500 -2.95 15461 1.00E+02 1000-2500 -3.48 17913 2.00E+02 1000-2500 -0.07 11026 I.00E-03 1000-2500 -0.07 11026 1.00E-02 1000-2500 -0.07 11034 l.OOE-O1 1000-2500 -0.08 11051 3.00E-01 1000-2500 -0.09 11109 1.00E+00 1000-2500 -0.13 11265 3.00E+00 1000-2500 -0.25 11740 1.00E+01 1000-2500 -0.51 12807 3.00E+01 1000-2500 -1.09 15322 1.00E+02 1000-2500 -1.61 17720 2.00E+02 1000-2500
Vinyl + O2 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
Products C2H3 + 0 2 w C'-COOH C2H3 + 0 2 o C'=COOH C2H3 + 02 o C'=COOH C2H3 + 0 2 C'=COOH C2H3 + 0 2 C2H2 + HO2 C2H3 + 0 2 CzHz + H0z C2H3 + 0 2 C2H2 + H02 C ~ H+I 0 2 * CzHz + HOz C2H3 + 0 2 C2H2 + H02 C2H3 + 0 2 * C2H2 + H0z CzH3 + 0 2 C2H2 + H0z CzH3 + 0 2 C2H2 + H0z CzH3 + 0 2 ~4 C2H2 + H02 C2H3 02 CYCC'OO CzH3 + 0 2 * CYCC'OO C2H3 + 0 2 o CYCC'OO czH3 0 2 * CYCC'OO C2H3 + 0 2 CYCC'OO C2H3 + 0 2 CYCC'OO CzH3 + 0 2 e CYCC'OO C2H3 + 0 2 o CYCC'OO C2H3 + 0 2 CYCC'OO
5.91E+15 4.31E+08 1.06E+04 8.60E+00 1.40E+10 1.56E+10 4.04E+10 7.69E+11 7.15E+10 8.40E+05 2.11E-02 9.89E-08 1.72E-11 2.52E+16 2.65E+17 3.99E+18 5.52E+19 7.52E+18 7.95E+15 1.31E+12 5.858+09 1.69E+08
-1.38 0.94 2.40 3.36 0.38 0.37 0.25 -0.09 0.29 1.87 4.22 5.84 6.95 -3.64 -3.65 -3.70 -3.71 -3.27 -2.17
Q
+ + + + +
Q
C)
+ + + + + +
Q)
+
+ + + + + + + + +
+
Q
Q
Q
Q
Q
-
+ +
Q
Q
+
Q
@
Q
2680 1354 374 -313 117 148 423 1765 2447 2249 1049 17 -757 1480 1496 1639 2215 2318 1866 1060 -0.87 509 -0.09 139 0.43
1.00E+01 3.00E+Ol 6.00E+Ol 1.00E+02 1.00E-03 1.00E-02 1.OOE-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02
300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
Bozzelli and Dean
4436 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
TABLE I1 (Continued)
+
A
n
1.21E+21 1.20E+17 1.828+18 2.68E+19 3.898+18 4.27E+15 6.79E+11 2.91E+09 8.20E+07 5.06E+17 5.33E+17 8.158+17 1.26E+18 6.378+16
-3.22 -3.52 -3.57 -3.59 -3.15 -2.06 -0.75 0.04 0.56 -1.70 -1.71 -1.76 -1.79 -1.36
4.73E+33 4.80E+34 5.638+35 2.118+37 4.20E+38 2.12E+40 2.268+41 2.23E+41 8.11E+40 9.09E+14 9.18E+14 l.OlE+lS 2.468+15 1.19E+16 3.818+17 3.85E+19 7.89E+20 5.27E+21 2.34E+23 2.418+24 3.14E+25 2.99E+27 2.75E+29 2.738+32 6.108+34 1.898+35 7.638+34 7.378+14 7.51E+14 9.13E+14 5.19E+15 9.59E+16 3.258+19 1.66E+22 2.27E+23 3.61E+23
-7.90 -7.90 -7.92 -8.07 -8.28 -8.58 -8.70 -8.59 -8.39 -0.66 -0.66 -0.68 -0.78 -0.96 -1.36 -1.89 -2.23 -2.44 -5.09 -5.09 -5.12 -5.38 -5.77 -6.41 -6.87 -6.88 -6.68 -1.03 -1.04 -1.06 -1.26 -1.60 -2.26 -2.96 -3.23 -3.26
HCO 0 2 * HC-0' HCO + 0 2 * HC-0' HCO + 02 H C 4 0 0 ' HCO + 02 * HC-0' HCO + 02 * HC-0' HCO + 0 2 HC=000' HCO + 02 * HC-0' HCO + 0 2 0 H C 4 0 0 ' HCO 0 2 * HC=000' HCO O2 H C 4 0 + 0 HCO + 02 * H C 4 O ' 0 HCO+02*HC+O.+O HCO 02 H C 4 0 ' 0 HCO + Oz HC=OO' + 0 HCO 0 2 * H C 4 O + 0 HCO + 02 * H C 4 O . 0 HCO + 0 2 * HC-' +0 HCO + 0 2 * HC=OO' + 0 HCO + 0 2 * M ' O O H HCO + 0 2 * O=C'OOH HCO + 0 2 * W O O H HCO + 0 2 * O=C'OOH HCO + O2 O=C'OOH
1.51E+23 1.56E+24 2.048+24 3.158+26 1.498+26 2.128+24 4.538+21 6.598+19 3.23E+18 2.36E+06 2.36E+06 2.378+06 2.46E+06 263E+06 2.96E+06 2.21 E+06 6.99E+05 1.11E+05 1.30E+18 1.35E+ 19 1.83E+20 3.85E+21 2.61E+21
HCO + 0 2 * H C 4 0 0 ' HCO + 0 2 * H C 4 0 0 ' HCO + O2 HC=000' HCO + 0 2 HC-0' HCO + O2 HC--000' HCO 0 2 * HC-0' HCO + 02 C. HC-0'
3.778+30 3.81E+31 4.21E+32 9.59E+33 8.84E+34 I . 18E+36 4.738+36
Q
+ + + +
Q Q
+
Q Q
+
+ +
press.
press. (atm)
temp(K)
3243 1428 1571 2157 2270 1829 1030 486 127 1126 1143 1287 1880 2001
3.00E+00 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+Ol 6.00E+OI 1.00E+02 1.00E-03 1.00E-03 l.OOE-O1 1.00E+00 3.00E+00
300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
C2H3 + 0 2 O=CHCHlO' C2H3 0 2 * HCO + CH20 C2H3 + 02 w HCO CH2O C2H3 0 2 HCO + CH2O C2H3 + 0 2 HCO + CH2O C2Hj + 0 2 H O = C H H C 4 C2H3 02 * H + O = C H H C 4 C2H3 0 2 * H + O = C H H C 4 C2H3 + 0 2 H + O = C H H C 4 C2H3 0 2 * H + O=CHHC=O C2H3 + 0 2 H O = C H H C 4 C2H3 0 2 H O=CHHC=O C2H3 + 0 2 H O = C H H C 4 C2H3 0 2 * H + W H H C 4
7144 7153 7236 7951 9057 11010 12927 13852 14274 2676 2680 2725 3135 3875 5580 8065 9931 I1329 3399 3412 3545 4701 6558 10099 14022 16188 17369 2367 2376 2470 3310 4771 7932 12051 14705 16383
1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+O2 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 I.OOE+Ol 3.00E+01 6.00E+01 1.0OE+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+OI 6.00E+OI 1.00E+02
900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500
C2H3 + 0 2 *CYCC'OO C2H3 + 0 2 oCYCC'OO C2H3 + 0 2 * CYCC'OO C2H3 + 02 *CYCC'OO C2H3 + 0 2 * CYCC'OO C2H3 + 0 2 *CYCC'OO C2H3 + 0 2 CYCC'OO C2H3 + 02*CYCC*OO C2H3 + 02*CYCC'OO C I H+ ~ 0 2 * O=CHCH@ C2H3 + 02 * M H C H z O ' C2H3 + 0 2 *O=CHCHzO' CzH3 + O ~ Q O ~ C H C H ~ O . C2H3 + 0 2 * O=CHCH2O' CzH3 + 02 M H C H 2 O ' C2H3 + 0 2 M H C H 2 O ' CzH, + 0 2 * O=CHCHzO' C2H) + 02 b M H C H z O ' C2H3 + 02 HCO CH2O C2H3 + 0 2 * HCO + CH2O C2H3 + 0 2 HCO + CH2O C2H3 + 02 HCO + CH2O C2H3 + 02 HCO + CH2O C2H3 + 0 2 HCO + CH20 C2H3 + 0 2 HCO + CH2O C2H3 + 0 2 HCO CH2O C ~ H+I 0,* HCO + CH,O C;H; + 0; H + O----CHHC=O C2H3 0 2 c=) H + O = C H H C 4 CZH3 + 0 2 H + O=CHHC=O C2H3 0 2 * H + M H H C 4 C2H3 + 0 2 H + O = C H H C 4 C2H3+ O2 H + O=CHHC=O C2H3 + 02 H + M H H C = O C2H3 02 cil H + M H H C 4 C2H3+ 02 H + O=CHHC=O
E,
n
E,
1.14E+ 16 2.05E+13 9.38E+08 1.73E+06 2.57E+04 1.60E+15 1.68E+15 2.61E+15 4.50E+15 2.48E+14 7.78E+10 2.75E+06 3.858+03 4.53E+01
(am) temp (K) -3.51 1412 1.00E-03 300-1000 -0.26 1564 I.OOE+Ol 300-1000 1.07 753 3.00E+01 300-1000 1.89 194 6.00E+01 300-1000 2.42 -179 1.00E+02 300-1000 -1.32 898 1.00E-03 300-1000 -1.33 915 1.00E-02 300-1000 -1.38 1061 1.00E-01 300-1000 -1.42 1669 l.WE+00 300-1000 -1.00 1807 3.00E+00 300-1000 0.10 1378 l.WE+Ol 300-1000 1.47 547 3.00E+01 300-1900 2.33 -38 6.00E+01 300-1000 2.90 -436 1.00E+02 300-1000
1.34E+22 1.36E+23 1.59E+24 5.938+25 1.40E+27 1.78E+29 1.47E+31 9.258+31 1.57E+32 2.18E+22 2.228+23 2.588+24 9.47E+25 2.20E+27 2.85E+29 2.60E+31 1.83E+32 3.468+32 2.52E+22 2.56E+22 2.97E+22 1.09E+23 8.54E+23 3.71E+25 1.49E+27 6.97E+27 1.01E+28 4.51E+17 4.58E+17 5.30E+17 1.91E+18 1.52E+19 7.78E+20 5.058+22 3.898+23 8.90E+23
-5.37 -5.37 -5.39 -5.54 -5.78 -6.19 -6.55 -6.66 -6.64 -5.39 -5.40 -5.41 -5.56 -5.80 -6.21 -6.59 -6.71 -6.71 -3.12 -3.12 -3.14 -3.29 -3.53 -3.96 -4.36 -4.52 -4.54 -2.08 -2.09 -2.10 -2.25 -2.49 -2.94 -3.41 -3.62 -3.70
4048 4056 4131 4787 5859 7957 10402 11882 12800 4343 4350 4424 5068 6125 8213 10674 12185 13139 3177 3185 3257 3892 4942 7043 9574 11166 12197 1706 1713 1782 2398 3429 5541 8180 9912 11082
1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 l.OOE-01 1.00E+00 3.00E+00 I.OOE+Ol 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 l.OOE+Ol 3.00E+01 6.00E+01 1.OOE+O2
900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500
Products HCO 0 2 * W O O H HCO 0 2 M ' O O H HCO + 0 2 L=) O=C'OOH HCO + 0 2 W O O H HCO + 02 CO + H02 HCO + 0 2 CO + HOZ HCO + 0 2 * CO + HO2 HCO + 0 2 * CO + H02 HCO 0 2 CO + H02 HCO + 0 2 CO + H02 HCO + 0 2 * CO + H02 HCO + 0 2 * CO + HO2 HCO + 0 2 * CO + H02 HCO + 0 2 * CO2 + OH HCO + 0 2 * C02 + OH HCO + 0 2 CO2 + OH HCO + 0 2 CO2 + OH HCO + 0 2 * CO2 + OH HCO + 0 2 CO2 + OH HCO + 0 2 * CO2 + OH HCO + 0 2 * C02 + OH HCO + O2 C 0 2+ OH
4.38E+19 5.29E+16 3.16E+14 5.41E+12 1.38E+18 1.43E+18 1.96E+18 4.54E+18 1.15E+18 6.25E+15 2.24E+12 5.45E+09 4.54E+07 1.20E+17 1.25E+17 1.71E+17 3.96E+17 1.00E+17 5.458+14 1.95E+ll 4.748+08 3.95E+06
-3.05 -2.00 -1.24 -0.64 -1.95 -1.95 -1.99 -2.08 -1.87 -1.15 -0.08 0.72 1.36 -1.95 -1.95 -1.99 -2.08 -1.87 -1.15
2326 1917 1565 1284 1129 1140 1246 1781 2062 2018 1613 1249 951 1129 1140 1246 1781 2062 2018 1613 1249 951
1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+Ol 3.00E+OI 6.00E+Ol 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02
300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
HCO + 0 2 H C 4 O ' + 0 HCO + 0 2 * H C 4 O ' + 0 HCO + 0 2 w H C 4 O ' + 0 HCO + 0 2 H C 4 0 + 0 HCO + 02 CI HC=OO' + 0 HCO + 0 2 H C 4 O ' + 0 HCO + O2Q HC=OO' 0
1.41E+12 1.41E+12 1.41E+12 1.458+12 1.538+12 1.86E+12 3.14E+12
-0.10 -0.10 -0.10 -0.11
1578 1578 1579 1592 1620 1717 1980
1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01
900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500
A
+ +
+
Q Q
+ + + + +
Q
+
Q
Q Q
+ + +
Q
Q
Q
+
Q Q
Q Q
Q
+ +
+
Q
Q
c;)
+
-+
Q
Q
+ O2
Formyl 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
-4.89 -4.62 -3.89 -2.94 -2.31 -1.87 1.68 1.68 1.68 1.68 1.67 I .66 1.72 1.89 2.15 -3.89 -3.89 -3.93 -4.01 -3.78
2026 2037 2137 2613 2804 2633 2138 1737 1434 9534 9534 9536 9556 9598 9718 9914 10008 9991 1492 1504 1608 2130 2393
1.00E-03 1.00E-02 1.00E-01 I.OOE+00 3.00E+OO 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1.00E-03 1.00E-02 1.00E-01 1.00E+OO 3.00E+00
300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000 300-1000
-7.02 -7.02 -7.03 -7.13 -7.25 -7.40 -7.41
5597 5603 5662 6170 6948 8292 9619
1.00E-03 1.OOE-02 1.00E-01 1.00E+W 3.00E+00 1.00E+01 3.00E+01
900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500
-4.81
-4.81 -4.85
300-1000
+
Q
Q
Q Q
+
Q Q
Q Q
Q
Q
Q
Q
+
-0.08
0.72 1.36
-0.11
-0.14 -0.20
Hydrocarbon Radical Reactions with O2
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4437
TABLE II (Continued) A
HCO + 02 Q H C 4 0 0 ' HCO 0 2 Q HC-0' HCO + 0 2 0 O-C'OOH HCO + 02 O=C'OOH HCO + 0 2 M ' O O H HCO 0 2 M ' O O H HCO + 0 2 O=C'OOH HCO 0 2 M ' O O H HCO + 0 2 0 O-C'OOH HCO 0 2 M ' O O H HCO 0 2 O-C'OOH HCO + 0 2 c.) CO + H0z HCO + 02 CO + H02 HCO + 02 CO + H02 HCO + 0 2 * CO + H02 HCO + 0 2 CO + HO2
+
Q
+ + + +
C) Q Q
C)
C) C)
Q
Q
Q
n
E.
press. (atm)
temp(K)
-7.32 -7.19 -4.48 -4.48 -4.49 -4.60 -4.76 -5.05 -5.32 -5.45 -5.51 -1.85 -1.85 -1.86 -1.97 -2.14
10343 10777 1979 1985 2041 2534 3340 4927 6879 8244 9282 346 351 406 885 1682
6.00E+01 1.00E+02 1. W E 4 3 1.00E-02 1.00E-01 1.00E+00 3.00E+00 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1. W E 4 3 1 .OOE-02 1.00E-01 1.00E+00 3.00E+00
900-2500 900-2500 900-2500 900-2.500 9W-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500
"penalty" for addition to the oxygen and the barrier was the same as addition to the carbon, the barrier would be the same as that inferred from the molecular beam experiments. Given the direct nature of the molecular beam experiments, we prefer this value, but we recognize the approximation involved in applying it to this particular case. We note that the rate constant for the vinoxy channel, even using the higher barrier of 44.1 kcal/mol, is much higher than that used by Westmoreland,2' and this is one of the reasons for the differences in our results. The experiments of Gutman's group illustrate the importance of the intramolecular addition to ultimately lead to C H 2 0 and HCO. Since the barrier for this addition was assigned by analogy to other systems (cf. discussion in the Calculations section), we also explored the results of adjusting this barrier. Figure 8 compares our calculated results using various combinations of barriers to the available experimental data. All of the combinations predict total rates in good agreement with theobservations, and all predict that the formaldehyde/formyl channel to be dominant. However, use of the 35.4 kcallmol barrier to vinoxy or a 26.4 kcal/mol barrier for cyclization leads to smaller branching ratios for the formaldehyde channel. For example, the branching ratio is predicted to be 64% at 450 K when both the low vinoxy and high cyclization barrier are used. Since Gutman and co-workers report no other products, we consider 35.4 kcal/mol as a lower limit for the vinoxy barrier and 26.4 kcal/mol as an upper limit for the cyclization. Also included in Figure 9 are the results using a 36.4 kcal/mol barrier for the vinoxy channel. This gives a branching ratio of 75% at 450 K. This value seems to represent a suitable compromise between the measurements of Gutman et al. and the barrier inferred from the molecular beam studies of Lee et al. We selected this value as our best estimate and used it for subsequent calculations. A particularly important feature of this reaction system is that the product channels change dramatically with temperature, as illustrated in Figures 9 and 10. At low pressure (Figure 9), we see that the formaldehyde channel is predicted to be dominant below -900 K, above which the vinoxy channel becomes most important. At this low pressure, stabilization is relatively unimportant, even at room temperature. This is in contrast to the allyl system and is directly attributable to the presence of the low-energy exit channel to formaldehyde (and vinoxy). The deeper well here even allows the H-shift channel (C2H2 H 0 2 ) to compete with Stabilization. At higher pressures, as shown in Figure 10, stabilization is much more important at the lower temperatures. The larger contribution from the nonstabilization channels is responsible for the much more gradual decline of the total rate with temperature, as compared with the allyl case. This results in lack of the pronounced minima seen in allyl. The glyoxal H channel, which also occurs via the cyclizationand subsequent 8-scission,is less important than CH2O + HCO, since this channel has a lower A factor as well as a higher barrier for the beta scission of OCHCH20'.
+
+
A
HCO + 0
+ +
n
H C 4 O ' 0 6.378+12 -0.28 HCO HC=OO' 3 1.458+13 -0.37 HCO + 02 CO + H02 9.22E+19 -2.45 HCO + 0 2 CO + H02 1.89E+21 -2.79 HCO + 0 2 * CO + H02 l.lOE+22 -2.98 HCO + 02 CO + H02 3.21E+22 -3.09 HCO + 02 C02 + OH 3.89E+16 -1.85 HCO + 0 2 b C02 OH 3.93E+16 -1.85 HCO + 02 CO2 + OH 4.38E+16 -1.86 HCO + 0 2 CO2 + OH 1.12E+17 -1.97 HCO 0 2 C02 OH 5.00E+17 -2.14 HCO + 0 2 C02 OH 8.03E+18 -2.45 HCO + 02 C02 + OH 1.65E+20 -2.79 HCO + 0 2 0 CO2 OH 9.56E+20 -2.98 HCO 01 COZ + OH 2.80E+21 -3.09
+ 02
2
C)
Q Q
Q
+
Q
+
Q
+ + +
C) Q Q
+
Q
E,
press. (atm)
temp(K)
12339 12766 3294 5357 6846 8002 346 351 406 885 1682 3294 5357 684 8002
6.00E+01 1.00E+02 1.00E+01 3.00E+01 6.00E+01 1.00E+02 1 .DOE43 1. W E 4 2 1 .OOE-O1 1.00E+00 3.00E+00 l.OOE+Ol 3.00E+01 6.00E+01 1.00E+02
900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500 900-2500
Figure 11 illustrates the deceptive apparent simplicity of the vinyl case. The total rate at 300 K is seen to beessentially constant over an enormous pressure range, but this is due to a tradeoff between the stabilization and formaldehyde channels. As seen in Figure 12, a similar plot at 1500 K shows an slightly smaller overall rate constant, due to an increase in the reverse dissociation rate, but here stabilization is unimportant until pressures above 10 atm. At 1500 K, one sees participation of all the channels resulting from chemically activated dissociation of the various adducts. These results suggest that previous attempts to describe the reaction between vinyl and oxygen in combustion models are incomplete. The predicted importance of the vinoxy channel at the higher temperatures suggests that it is especially important to include this channel in combustion models. This new channel for production of atomic oxygen might have substantial effects upon model predictions under certain circumstances. Furthermore, the vinoxy would be expected to quickly split off a hydrogen atom to form ketene. The net effect of this channel would be to convert one reactive radical, vinyl, to both 0 and H while also producing the reactive ketene species; this is really a chainbranching reaction. Our conclusion about the importance of the vinoxy channel differs from that of We~tmoreland,~' where his use of a much lower A factor for the vinoxy channel leads to a substantiallysmaller rateconstant. This differencein assignments emphasizes the need for high-temperature measurements of the branching ratios for this reaction. The predicted rate constants for the various channels, using N2 as the bath gas, were fit to a modified Arrhenius fit [ A P exp(-E,/RT)] over a range of pressures and are shown in Table 11. As with the allyl case, it was necessary to use two temperature ranges to achieve a suitable fit. Formyl + 0 3 . The potential energy level diagram is shown in Figure 13. The well depth of this system is not known, and we have estimated it by comparing R-OO bond energies to R-OH as well R-0 bond energies. The comparison to R-OH is shown in Figure 14. Using the formic acid R-OH bond strength of 110.5 kcal/mol with this correlation gives an HC(O)-OO bond strength of -45 kcal/mol. One estimate for the barrier for the hydrogen shift is based upon an estimate of 16.4 kcal/mol for the analogous bimolecular hydrogen transfer with a ring strain of 22.6 kcal/mol to yield 39 kcal/mol. This ring strain value was recommended by Benson' for cyclobutanone, and this is lower than the 26.2 kcal/mol estimate for cyclobutane. Additional information about this barrier is available from the analysis of Langford and Moore.28 Their chemical activation treatment showed that the isomerization barrier was 9 kcal/mol below the entrance channel. This requires a barrier of 36 kcal/mol, using our estimate of the well depth. (Note in Table I that both the well depth and barrier are 1 kcal/mol lower than these values discussed above; this difference is an illustration of fitting the equilibrium constant data over a wide range-the barriers will
-
4438 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
Bozzelli and Dean
TABLE III: Thermodynamk Dataa spccies
HF(298)
OH H02 HCO HOC0 HC02' HC02H O=CHOO' O-CHOO'A O-C'OOH W H O O H CH3 CH30' C'H20H CH3OO CHzOOH O'CH2OH CH3OOH O=cc=O
9.50 3.80 10.39 49.70 -38.24 -90.52 -34.60 -3 1.30 -29.00 -67.41 34.82 3.96 -6.10 5.70 13.07 44.00 -30.88 -50.60 -1 1.40 -50.60 -18.30 -58.10 -13.80 -22.00 -24.20 -5.40 3.20 14.90 29.23 51.03 49.03 -23.00 44.00 -29.00 -12.58 -73.53 -6.87 0.30 45.92 -16.05 40.97 22.15 23.16 19.39 -28.34 39.70 14.50 39.01 29.87 32.87 18.10 -25.77 -22.17 -12.45 4.81 -9.53 -25.24 70.43 28.66 62.56 60.56 28.09 26.09 43.49 41.49
c=c=o
CHOCHO C'=OCHO HC=OCOOH HC=OC'OOH HC=OCOO' C'=OCOOH CH$'=O C'C-0 C=CO' C=COO. C'=COOH C=C'OOH CO'CHO CYCC'OO C=COH CYCCO COHCHO C=COOH CYCCOO
c=c=c
C=CCHO C=CC' C=CCO' C=CCOO' C=CC'OOH o=CCCO'
c=cooc ' cYc'cc00 C'CY ccoo CCY C'COO CCY CC'OO CY CC'COO
c=coc
CYC30 C=CCOOH
c=cooc
ccYcc00 CYC302 C2H3 CH2=C'OH CC=C* CC'=C C'=CCOH C=C'COH C'=CCOOH C%'COOH a
S(298)
CP300
CP400
CP500
43.88 54.73 53.67 60.13 56.81 59.48 68.51 68.51 70.72 72.53 46.38 54.65 56.31 62.88 65.87 65.35 69.07 65.43 57.82 65.43 66.19 83.13 82.91 79.11 84.19 63.78 63.72 62.12 7 1.62 76.70 74.19 71.33 64.73 64.71 58.07 73.70 75.64 62.80 58.33 67.42 63.04 71.87 80.04 83.40 80.79 84.41 75.16 74.16 73.36 72.18 77.65 73.55 68.56 84.02 85.42 71.63 78.45 56.29 65.78 64.88 64.88 75.52 75.52 85.07 85.07
6.94 8.45 8.39 10.66 9.42 10.89 13.93 13.93 17.17 15.35 9.29 9.09 11.56 13.27 16.33 12.47 14.94 14.91 13.02 14.90 14.19 22.48 22.85 20.13 21.94 12.42 13.60 13.60 16.39 18.24 17.95 14.68 15.57 13.63 11.72 16.14 18.45 14.44 14.17 16.37 14.80 17.14 21.40 22.72 20.91 24.32 18.96 21.71 21.68 23.23 16.16 19.39 17.51 23.36 23.29 22.59 20.1 1 10.08 13.37 15.29 15.29 18.49 18.49 23.34 23.34
6.98 8.98 8.91 12.10 11.07 12.97 15.38 15.38 18.58 17.36 10.09 10.69 13.17 15.31 18.69 14.29 17.44 17.53 15.10 17.51 16.35 25.51 25.61 22.50 25.09 14.55 15.88 15.88 18.85 20.87 20.10 17.49 19.29 16.33 15.15 19.33 21.52 18.68 17.19 20.06 18.55 20.98 25.67 27.16 25.00 28.39 24.23 26.43 26.41 27.68 21.51 23.58 22.17 28.55 27.83 26.83 25.40 12.12 15.27 18.64 18.64 22.14 22.14 27.70 27.70
7.03 9.47 9.43 13.33 12.51 14.72 16.76 16.76 19.74 19.27 10.86 12.22 14.59 17.20 20.69 15.98 19.64 19.71 16.82 19.69 18.06 28.21 27.88 24.77 27.63 16.49 17.81 17.81 21.11 23.06 21.98 19.99 22.42 18.64 18.11 22.15 24.18 22.38 19.77 23.20 21.73 24.37 29.40 30.84 28.56 3 1.92 28.75 30.58 30.57 31.61 26.24 27.32 26.26 33.00 31.88 30.97 30.18 13.85 17.00 21.56 21.56 25.31 25.31 31.33 31.33
CP600
CP800
CPlOOO
CP1500
ref
elements
7.09 9.93 9.95 14.39 13.74 16.19 18.06 18.06 20.68 21.05 11.61 13.66 15.86 18.92 22.36 17.55 21.56 21.50 18.23 21.48 19.39 30.61 29.75 26.9 1 29.70 18.25 19.43 19.43 23.17 24.90 23.60 22.21 25.04 20.63 20.63 24.64 26.47 25.57 21.98 25.86 24.43 27.34 32.66 33.89 3 1.66 34.98 32.60 34.20 34.19 35.05 30.38 30.64 29.82 36.78 35.48 34.93 34.47 15.31 18.54 24.10 24.10 28.04 28.04 34.34 34.34
7.23 10.72 10.91 16.01 15.64 18.44 20.27 20.27 22.06 24.07 12.98 16.23 17.94 21.87 24.92 20.3 1 24.70 24.18 20.33 24.14 2 1.20 34.58 32.56 30.72 32.76 21.22 21.98 21.98 26.66 27.72 26.26 25.86 28.99 23.83 24.61 28.74 30.16 30.64 25.48 29.99 28.63 32.20 37.90 38.50 36.67 39.85 38.64 40.03 40.03 40.61 37.08 36.13 35.62 42.70 4 1.46 42.08 41.59 17.60 21.11 28.18 28.18 32.39 32.39 38.94 38.94
7.38 11.36 11.73 17.10 16.92 20.01 21.91 21.91 22.98 26.30 14.17 18.33 19.53 24.17 26.68 22.56 27.10 25.96 21.74 25.89 22.26 37.55 34.51 33.81 34.93 23.53 23.85 23.85 29.35 29.73 28.28 28.60 31.58 26.26 27.47 3 1.85 32.96 34.23 28.04 32.94 3 1.68 35.86 41.74 41.78 40.43 43.37 42.9 1 44.24 44.24 44.65 41.96 40.26 39.98 46.89 46.03 47.94 46.91 19.26 23.05 31.22 31.22 35.56 35.56 42.21 42.21
7.77 12.39 13.05 18.41 18.38 22.32 23.81 23.81 24.27 28.96 16.30 21.61 21.96 27.56 29.01 26.26 30.99 28.36 23.62 28.10 23.48 41.77 37.36 38.42 38.49 27.06 26.90 26.90 33.19 32.89 3 1.65 32.59 34.63 30.42 3 1.59 36.60 37.47 38.87 3 1.95 37.18 36.40 41.43 47.14 47.00 46.28 48.19 48.76 49.80 49.79 50.00 48.54 46.24 46.62 52.81 52.89 56.58 54.04 21.86 25.92 35.87 35.87 40.31 40.3 1 47.27 47.27
512170 JPC92 512170 SANDIA/89 THERM8191 SWS86 THERM7192 THERM8191 THERM7192 THERM8191 J 6/69 THERM90 THERM90 J WB 10190 THERM90 JB86 JB85 THERM7191 PNK+12/83 6/27/91 T H E R M 6/27/91 T H E R M 6/27/91 T H E R M 6/27/91 T H E R M 6/27/91 6/27/91 BCT1/86 T H E R M 61916 DUPUIS 82 THERM7191 THERM7191 THERM7191 JB86 THERM7191 THERM92 BURCAT JB86 THERM7191 THERM7191 API53 5/8/90 (1) 3/87 11/90 10190 11/7/90 5/8/90 THERM7192 5/8/90 THERM7/92 THERM7192 THERM7192 5/8/90 3/8/91 SWS86 T H E R M 11/90 THERM7/92 THERM7/92 THERM7192 3/5/91 3/5/91 3/5/91 3/5/91 3/5/91 3/5/91 3/5/91 3/5/91
01;Hl H1;02 H 1; C 1; 0 1 Cl;H1;02 Cl;H1;02 C 1; H 2; 0 2 Cl;H1;03 C 1; H l ; O 3 Cl;H1;03 C 1; H 2; 0 3 C1;H3 C 1; H 3; 0 1 C 1; H 3; 0 1 C 1; H 3 ; 0 2 Cl;H3;02 C 1; H 3; 0 2 Cl;H4;02 C2;H2;02 C2;H2;01 C2;H2;02 C2;H 1;02 C 2;H 4;O 3 C 2; H 3; 0 3 C 2; H 3; 0 3 C 2; H 3; 0 3 C 2; H 3; 0 1 C 2; H 3; 0 1 C 2;H 3;O 1 C2;H3;02 C 2; H 3 ; O 2 C 2; H 3 ; O 2 C 2; H 3; 0 2 C2;H3;02 C 2; H 4 ; O 1 C2;H4;01 C2;H4;02 C 2;H 4;O 2 C 2; H 4; 0 2 C3;H4 C 3; H 4; 0 1 C3;H5 C 3; H 5; 0 1 C 3; H 5 ; O 1 C 3; H 5; 0 2 C 3; H 5; 0 2 C 3;H 5 ; 0 2 C 3; H 5 ; O 2 C 3; H 5; 0 2 C 3; H 5; 0 2 C 3; H 5; 0 2 C 3;H 5 ; 0 2 C 3;H 6;O 1 C 3;H 6;O 2 C 3;H 6;O 2 C 3 ; H 6;O 2 C 3;H 6;O 2 C 3; H 6; 0 2 C2;H3 C 2 ; H 3;O 1 C3;H5 C3;HS C 3 ; H 5;O 1 C 3;H 5;O 1 C 3; H 5; 0 2 C 3; H 5; 0 2
Units: AHf (kcallmol), S and C, (cal/(deg mol)).
be somewhat different than the values at 298 K.) We have done calculations with each estimate and find better agreement with the available low temperature data using the Langford-Moore value. The potentialenergydiagram shows two possibleexit channels for dissociation of the O=C'OOH adduct: CO + H 0 2and C 0 2 + OH. Rate constantassignmentswere based upon our estimates of the reverse reactions. We think CHs + CO is an appropriate analog for HOz CO, while we used two approaches to estimate
+
OH addition to CO2. One was the addition of OH to CzH2, with an A factor of 1.2 X 1012 (taken from a review of the data in the NIST database43). A second method was based on the lowtemperature data for OH additionto CO, with an A factor of -4 X loll. This value was doubled to account for the two sites of addition in CO2. The average of these two approaches is 1 .O X this was used with microscopic reversibility to obtain the A factor in the forward direction. The barrier was assigned to be the same as that for the CO channel. Use of appreciably
Hydrocarbon Radical Reactions with O2 HC.0
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4439
02
t
HCO t 0 2
0-CH0.r 0
r
12.7
I
0-
125
-20 -
B4
0-C.OOH O-C(H)OO.
-40-
-60
E
Ie
-
8
X
-g
OH
Kcallmolo
-80 -
12.3
\
-
12.1
A
-- x -- VOyl8bLUCIIUX
-
(1981) (45.5-500 Ion)
Figure 13. Potential energy diagram for the formyl radical t 0 2 reaction. R. R--OH
+
0 2 --’ROO. VS R.
+
...._.... Alklnaonet 01.
11.9
OH --> ROH
Timonen a 11. (1988) (0.51.5 ton)
(1089)
QRRK (total4.70 torr)
Bond Energy
--t QRRK
11.7
(loIn1-7W
torr)
126 -
1
I
1.o
I.5
11.5
2.0
2.5
1
I
3.0
3.5
1000rT(K)
106 -
Figure 15. Comparison of predicted values for rate constants for formyl
+ 0 2 with experiment.
86
-
HCO + 0 2 760 Torr N2
C3H6 13 r I
10
16
20
26
30 35 40 46 R - - 0 0 Bond Energy
60
66
60
Koallmole
Figure 14. Plot of the correlation between the bond energy of R - 0 0 to R-OH. R - 0 0 bond energies: C3H5, C3H7, i-C3H,, CH3, C2H5, Gutman et al.;52CzH3, CIH, Kee et al.,53Boyd et al.;54HCO and CyCsH5, this evaluation.
lower values resulted in too large a branching ratio for C02 production. The predictions are compared to the experimental observations in Figure 15. Note that the predicted pressure effect is very small, in accord with the observations of Langford and Moore. The temperature dependencepredicted is in good agreement with much of the experimental work, the exception being the small positive activation energy reported by Timonen et al. Figure 16 illustrates the predicted effect of temperature at atmospheric pressure. Note that the dominant product at higher temperatures is CO H01, exactly as one would get from a simple abstraction reaction. With the barrier used for the C02 channel, we predict -9% reaction to this channel. This is consistent with most workers,55’56who report 5 19%. However, we hasten to point out that these experimental observations are our only justification for this barrier assignment. The predicted onset of the HCO2 + 0 channel at very high temperatures is not expected to be of importance under typical conditions, since HCO would dissociate at these temperatures before reacting with 02. At lower temperatures, stabilization is an important channel. The predicted pressure effects are illustrated in Figures 17 and 18. As with vinyl, we see little change in the overall rate constant at 300 K, but a dramatic change in product-with all stabilization at high pressures and mostly CO + H 0 2production below 1 atm. At 1200K, one needs much higher pressures to observe significant stabilization. It is interesting to note that the low-temperature, low-pressuredata indicates higher reaction rates to products than the 1200 K data. This is a result of the higher reverse reaction rate (H(C=O)OO* HC’O 02) at higher temperatures,
+
-
+
i
i
’t
6t 0
‘\, \
0.5
1
1.5
2
\
\
2.5
3
3.5
I O O O f f (K)
Figure 16. Arrhenius plot of the predicted rate constants for the various channels of the formyl t 0 2 reaction at 760 Torr of N2.
where the higher Arrhenius A factor overcomes the higher E, for this reverse path. Theisomerization pathway has a lower barrier, but also a lower A factor due to the tight transition state. Non-Arrhenius parameters for the apparent rate constants over a range of pressures are listed in Table 11. It is important to recognize that knowledge of the barriers for reaction from the O=C*OOH isomer to C02 + O H is less quantitative than the other barriers; additional experimental and theoretical studies on this system are needed. Summary The reactionsof allyl, formyl, and vinyl reactionswith molecular oxygen have been analyzed as addition reactions, in which the
Bozzelli and Dean
4440 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 HCO + 0 2 T = 300K
The differences in well depth of the initially formed adduct are shown to exert a major influence over the preferred reaction channels. In particular, the shallow (- 18 kcal/mol) well for the allyl addition results in very little apparent reaction, since the major channel is simply redissociation to the initial reactants. The deeper wells for formyl and vinyl addition (240 kcal/mol) allow reaction channels to open up even at low temperatures. When these results are compared to an earlier analysis for the ethyl radical addition to oxygen, it is possible to develop a framework by which one can estimate the expected product distributionsfor a variety of hydrocarbon radical addition reactions to oxygen. The good agreement between these calculations and the experimental data support the hypothesis that the reactions between hydrocarbon radicals and oxygen proceed via chemically activated addition and that one does not need to invoke a direct hydrogen abstraction pathway.
Y:a
Acknowledgment. We appreciate P. R. Westmoreland's sending us a preprint of his manuscript on the analysis of the vinyl radical 0 2 system. We are also grateful to one of the referees for insights regarding the barrier for formation of vinoxy 0 and the barrier to cyclization.
--C QRRK (total)
5
1
4
1
+
--
------~-------o------o.--o--*---~ --a
+
3 .3
.2
0
1
2
1
References and Notes
log P(m)
Figure 17. Plot of the predicted rate constants for the various channels of the formyl 0 2 reaction versus pressure of Nz a t 300 K.
+
HCO + 0 2 T = 1200K
l3
r
12
11
T
-a
lo
P o
X
8
-
8
I
Y
402-407. (3) Slagle, I. R.; Feng, Q.;Gutman, D. J . Phys. Chem. 1984,88,36483653. (4) McAdam, G. K.; Walker, R. W. J. Chem. Soc., Faraday Trans. 2 1987,83,1509. (5) Plumb, I. C.; Ryan, K. R. Int. J . Chem. Kine?. 1981,13, 1011. (6) Kaiser, E.W.; Rimai, L.; Wallington, T. J. J . Phys. Chem. 1989,93, 4094. (7) Kaiser, E. W.; Rimai, L.; Wallington, T. J. J . Phys. Chem. 1990,94, 3394. (8) Gutman, D. J . Chim. Phys. 1987,84,409. (9) Gulati, S.K.; Walker, R. W. J . Chem. Soc., Faraday Trans 2 1988, 84, 401. (10) Pitz, W. J.; Westbrook, C. K. Combust. Flame 1986,63,113. (11) Cox, R. A.; Cole, J. A. Combust. Flame 1985,60,109. (12) Bozzelli, J. W.; Dean, A. M. J . Phys. Chem. 1990,94, 3313-17. (13) Dean, A. M. J. Phys. Chem. 1985,89,4600-4608. (14) Wagner, A. F.;Slagle, I. R.; Sarzynski, D.; Gutman, D. J . Phys. Chem. 1990.94. 185368. (15) Baldwin, R.R.; Stout, D. R.; Walker, R. W. J . Chem. SOC.,Faraday Trans. 1991,87,2147-2150. (16) Stothard, N.D.; Walker, R. W. J. Chem. SOC.,Faraday Trans. 2 1990,86,2115. (17) Ruiz, R. P.; Bayes, K.D.; Macpherson, M. T.; Pilling, M. J. J . Phys. Chem. 1981,85,1622-1624. (18) Morgan, C. A.; Pilling, M. J.;Tulloch, J. M.J. Chem.Soc., Faraday Trans. 2 1982, 78, 1323-1330. (19) Slagle, I. R.;Ratajczak, E.; Heaven, M. C.; Gutman, D.; Wagner, A. F. J. Am. Chem. SOC.1985,107,1838-1845. (20) Baldwin,R. R.; Lodhi, Z. H.; Stothard, N.; Walker, R. W. In TwentyThird Symposium (International) on Combustion: The Combustion Institute: Pittsburgh, 1990; pp 115-121. (21) Stothard, N. D.;Walker, R. W. 1. Chem.Soc., Faraday Trans. 1991, 87,241-47. (22) Lodhi, Z.H.; Walker, R. W. J. Chem. Soc., Faraday Trans. 1991, 87,2361-2365. (23) Lodhi, 2.H.; Walker, R. W. J . Chem. SOC.,Faraday Trans. 1991, 87,681-689. (24) Slagle, I. R.; Park, J.-Y.; Heaven, M. C.; Gutman, D. J . Am. Chem. SOC.1984,106,4356-4361. (25) Park, J.-Y.; Heaven, M. C.; Gutman, D. Chem. Phys. Lett. 1984, 104, 469-474. (26) Krueger, H.; Weitz, E. J . Chem. Phys. 1988,88, 1608. (27)Westmoreland, P. R. Combust. Sci. Technol. 1992,82, 151-168. Moore, C. B.J. Chem. Phys. 1984,80,4211-4221. (28) Langford, A. 0.; (29) Lesclaux, R.; Roussel, P.; Veyret, B.; Pouchan, C. Ber. Bunsen-Ges. Phys. Chem. 1985,89,330. (30) Lesclaux, R.; Roussel, P.; Veyret, B.; Pouchan, C. J . Am. Chem. Soc. 1986,108,3872. (31) Timonen, R. S. Ratajczak, E.;Gutman, D. J. Phys. Chem. 1988,92, 651655. (32) Dean, A. M.; Bozzelli, J. W.; Ritter, E. R. Combust. Sci. Techno/. 1991,80,63-85. (33) Ritter, E.R. Ph.D. Thesis, New Jersey Instituteof Technology, 1989. ~
---+--.. O=C.OOH
0.
(1) Benson, S. W. ThermochemicalKinetics; John Wileyand Sons: New York, 1976. (2) Slagle, I. R.; Ratajczak, E.; Gutman, D. J. Phys. Chem. 1986,90,
5 1
I"' I
I
I
I
I
-3
-2
1
0
1
2
109 P ( W
Figure 18. Plot of the predicted rate constants for the various channels of the formyl + 0 2 reaction versus pressure of N2 a t 1200 K.
energized adduct has several pathways for further reaction. The various reaction channels are treated using a chemical activation formalism based on the quantum Rice-Ramsperger-Kassel theory. Apparent rate constants are obtained over a wide temperature and pressure range and compared to experiment wherever possible. It was possibleto obtain quitegood agreement to the limited data available using physically reasonable parameters. We feel the calculations serve as useful estimates of the expected rate constants for the various product channels over a wide range of temperature and pressures, where experimental data are not available. It is important to note that inclusion of these reactions in mechanisms must be accompanied by the analogous thermal dissociation rate constants for dissociation of the stabilized adducts.
Hydrocarbon Radical Reactions with O2 (34) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. Properties of Gases and Lbuids. 4th cd.: McGraw Hill: New York. 1987. '(35) 'Ben-Amotz, D.; Herschbach, D. J.'Phys. Chem. 1990, 94, 3393. (36) Troc, J. J . Phys. Chem. 1979,83, 114126. (37) Gardiner, W. C., Jr.; Trce, J. In Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984; pp 173-196. (38) Ritter, E. R.; Bozzelli, J. W .In?.J. Chemical Kinef. 1991,23,767778. (39) Baldwin, A. In The Chemistry of Functional Groups; S.Patal, Ed.; John Wiley and Sons: New York. 1983; Chapter 3. (40) Ervin, K. M.; Gronnert, S.;E., B. S.;Gilles, M.; Harrison, A.; Bierbaum, V.; DePuy, C. H.; Lineberger, W. C.; Ellison, G. B. J . Am. Chem. SOC.1990, 112, 5750. (41) Dorofeeva, 0. V.; Gurvich, L. V.; Jorish, V. S . J . Phys. Chem. Ref. Data 1986, 15. 437464. (42) Olivella, S.;Sole, A. J . Am. Chem. Soc. 1991, 113, 8628-8633. (43) Mallard, W. G.; Wcstley, F.; Herron, J. T.; Hampson, R. F. NIST Chemical Kinetics Database-Ver. 4.0, NIST Standard Reference Data 1992. (44) Mahmud, K.; Marshall, P.; Fontijn, A. J . Phys. Chem. 1987, 91, 1568-1573.
The Journal of Physical Chemistry, Vo1. 97, No. 17. 1993 4441 (45) Huisken, F.; Krajnovich, D.; Zhang, Z.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1983, 78,3806. (46) Schmoltner, A. M.;Anex, D. S.;Lee, Y. T. J. Phys. Chem. 1992,96, 1236-40. (47) Sosa, C.; Schelgel, B. Znf. J. Quantum Chem. 1!386,29,1001-1015. (48) Chang, J. S.;Barker, J. R. J . Phys. Chem. 1979, 83, 3059-3064. (49) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampon, R. F., Jr.; Kerr, J. A,; Troe, J. J . Phys. Chem. Ref. Data 1989, 18,881-1097. (50) Soto, M. R.; Page, M. J. Phys. Chem. 1990, 94, 3242-3246. (51) Anastasi, C.; Maw, P. R. J. Chem. Soc.,Faraday Trans. 1 1982,78, 2423. (52) Seetula, J. A.; Russell, J. J.; Gutman, D. J. Am. Chem. Soc. 1990, 112, 1347. (53) Kee, R. J.; Miller, J. A. The Chemkin Thermodynamic Data Base, SAND87-8215 UC4,Sandia National Laboratory, 1987. (54) Boyd, S.L.; Boyd, R. J.; Ross, L.; Barclay. R. C. J.Am. Chem. Soc. 1990, 112, 572430. ( 5 5 ) Osif, T. L.; Heicklen, J. J . Phys. Chem. 1977, 80, 1526. (56) Nadtochenko, V. A.; Sarkisov, 0. M.;Vedeneev, V. I. Dokl. Akad. Nauk SSSR 1979, 224, 152.
