6. GAS KINETICS By J. A. Kerr (Department of Chemistry The University Birmingham 15) THIS Report is based on publications that appeared between the 1 st November, 1966 and the 15th November 1967. The output of papers on gas kinetics continues unabated ; over 400 were published during this period. Drastic pruning is required to produce a Report of manageable size. Priority has been given to papers concerned with quantitative data on elementary reactions. Processes that are difficult to interpret such as complex pyrolyses and com-bustions are not considered. Unfortunately it has also been necessary to omit ion-molecule and molecular-beam reactions which warrant substantial treatments. The Reporter’s task in gas kinetics has been considerably lightened by the publication of three series of books ; ‘Progress in Reaction Kinetics’ ‘Advances in Photochemistry’ and ‘Progress in Free Radical Chemistry’.So far a total of ten volumes has appeared and their value is orientating the vast literature on kinetics cannot be overestimated. An International Journal of Chemical Kinetics edited by S. W. Benson (Stanford Research Institute) is being started in 1968. After surveying the gas kinetics literature for 1 9 6 6 4 7 this Reporter is convinced of the justification for such a publication. 1. Atomic Reactions.-Over the past few years atomic reactions have constituted one of the most rapidly expanding sections of gas kinetics. The main impetus has been obtained from the discovery of new methods for deter-mining concentrations of atoms. The discharge-flow method has been par-ticularly fruitful in yielding absolute rate constants for combination addition, and transfer reactions of atoms.This topic was reviewed in the 1965 Annual Report by Thrush and Campbell and more recently Thrush’ has written an excellent summary of the method. The production of atoms in discharge-tubes has long been known but their application to quantitative studies of the kinetics of elementary atomic reactions has had to await the development of specific methods for measuring the concentrations of the atoms. In a flow-discharge experiment atoms are produced by pumping metered flows of purified diatomic gases through an electrodeless discharge to give about 1 % dissociation into atoms. In the absence of added reactant gas the atoms decay by recombining either on the surface of the down-stream reaction tube or in the gas-phase.The walls of the reaction vessel can be treated to reduce wall combination. From a knowledge of the flow-rate of the gas and measurement of the decay of atoms down the flow tube the kinetics of the atom decay can ’ B. A. Thrush Science 1967,156,470 74 J . A. Kerr be deduced. The addition of a reactant gas causes an acceleration of the atom decay and the rate constant for the reaction of the atom with the reactant can be obtained from the rate of this acceleration. Several methods for measur-ing the absolute concentrations of reactive species have been devised. Elec-tronic-absorption spectroscopy is particularly suitable for small free radicals such as hydroxy and cyano whereas chemiluminescent recombination reactions have been widely applied for atoms.Mass spectrometry is also suitable provided a molecular-beam inlet system is used to select species that have not undergone wall collisions. More recently e.s.r. techniques have been used successfully to measure absolute concentrations of atoms. Westenberg and Haas have described a method for measuring the rate constants of atom-molecule reactions over the temperature range 300-1000"K by combining a flow-discharge reaction with an e.s.r. spectrometer located at a fixed position outside the reaction zone. Detailed kinetic and dynamic arguments have been put forward in support of the method and the first results (Tables 1 and 2) look most encouraging. Brown and Thrush,6 almost simultaneously with Westenberg and Haas also reported temperature coefficients for atom-molecule reactions involving the determination of atom concentrations by e.s.r.techniques. We can look forward to a wealth of quantitative information on atomic reactions from this important development. Atomic Recombination Reactions.-The experimental results are listed in Table 3. The mechanism of the recombination of nitrogen atoms has been investigated in detail,'"17 and the following reactions established : N + wall =$N, N + N = N2 (3) N + N + M = N2 + M (4) Reaction (3) which was thought to be partly heterogene~us'~ was later shown to be entirely heterogeneous.17 Values of the rate constants (k and k3) have been measured for a variety of surfaces and it has been clearly demonstrated that the homogeneous three-body recombination of nitrogen atoms does not obey a power-law dependence of the type k4 = AT-".A. A. Westenberg and N. De Haas J . Chem. Phys. 1967,46,490; 1967,47 1393. J. V. Michael and H. Niki J . Chem. Phys. 1967,46,4969. J. V . Michael and R. E. Weston J . Chem. Phys. 1966,45 3632. K . Hoyermann H. G. Wager and J. Wolfrum Z . phys. Chem. (Frankfurt) 1967,55,72. J. M. Brown and B. A. Thrush Trans. Faraday SOC. 1967,63,630. A. B. Callear and W. J; R. Tyerman Trans. Faraday SOC. 1966,62,2760. E. L. Wong and A. E. Potter Canad. J . Chem. 1967,45367. l o W. K. Stuckey and J. Heicklen J . Chem. Phys. 1967,46,4843. G. Marsh and J. Heicklen J . Phys. Chem. 1967,71 250. '* R. D. Cadle and J. W. Powers J .Phys. Chem. 1967,71 1702. A. Kato and R. J. CvetanoviC Canad. J . Chem. 1967,45 1845. l4 K. M. Evenson and D. S. Burch J . Chem. Phys. 1966,45,2450. I. M. Campbell and B. A. Thrush Proc. Roy. SOC. 1967 A 296,201. l6 I. M. Campbell and B. A. Thrush Trans. Faraday SOC. 1966,62,3366. M. A. A. Clyne and D. H. Stedman J . Phys. Chem. 1967,71 3071. ' N. Niki and B. Weinstock J . Chem. Phys. 1966,45 3468 Gas Kinetics 75 Campbell and Thrush'6. determined the rates of recombination of oxygen and nitrogen atoms by extending the flow-discharge method to active nitrogen systems in which NO was added resulting in the partial formation of oxygen atoms. The atom concentrations were determined from the intensities of the N2 First Positive and NO p-emissions. The activation energy for the N + 0 + M reaction (E = -270 cal.mole-') is abnormally low for this type of process. Rate constants have been reported for the iodine atom recombination reaction from the rotating-sector photolysis of CF31 in which the parent molecule was the third body.Ig The rate constant was shown to be second-order with a value of 5.1 x 10'' mole-' C.C. set.-' at 3 7 3 " ~ within CF31 concentrations 2-9 x lov6 mole c.c.-l. This result is difficult to reconcile with the many known third-order recombination rate constants for iodine atoms but might be explained if CF31 is a very efficient third body. Table 4 lists the results of shock-tube measurements on the dissociations of diatomic molecules i.e. the reverse of atomic recombination reactions. Benson and De More2' have pointed out the difficulties of deriving rate constants for the recombination process (k,) from measurements of the dis-sociation reaction ( k - 1) via the equilibrium constant K = k,/k - '.In particular, calculation of the activation energy El from shock-tube measurements of E - is likely to lead to large errors since El is a small number and E - a large number with considerable errors. Carabetta and Palmer" were able to follow the kinetics of the dissociation of C12 in a shock-tube by measuring the light emission from the radiative recombination of chlorine atoms : The emission reaction is the reverse of photodissociation and is a two-body process as distinct from normal third-order atomic recombination. Atomic Addition Reactions.-Recent data are summarised in Table 1.The rates of addition of hydrogen atoms to unsaturates have long been sources of contention.22 Examination of Table 1 shows that even for the simplest reactions such as addition to acetylene and ethylene there is still little detailed agreement on the magnitude of the rate constants. The addition of hydrogen atoms to acetylene proceeds through the following mechanism :3 CI + c1 = c1 + hv H + C2H2 = C2H3* C2H3* = C2H2 + H C2H3* + M = C2H3 + M l 8 I. M. Campbell and B. A. Thrush Proc. Roy. SOC. 1967 A 296,222. l9 G. S. Laurence Trans. Faraday Soc. 1967,63 1155. 2o R. A. Carabetta and H. B. Palmer J . Chem. Phys. 1967 46 1325 1333; H. B. Palmer ibid., 1967,47,2116. S. W. Benson and W. B. De More Ann. Rev. Phys. Chem. 1965,16,397. 22 R.J. CvetanoviC Ado. Photochem. 1963,1 11 5 ; B. A. Thrush Progr. Reaction Kinetics 1965, 3,63 TABLE 1 Atomic addition log k (mole-' C.C. set.-') Method (298 K) Atom Substrate H Acetylene Flow discharge, mass spectrometer 9 , 10.34 H Acetylene - d4 Acetylene Acetylene 10.86 D H 10.56 11.56 9 , Flow discharge, [HI by photometry Flow discharge, e.s.r. Flow discharge, [HI by photometry Flow discharge, e.s.r. Flow discharge, e m . Flow discharge, NO2 titration, Thermal probe H H Acetylene 1 0 10 Ethylene 11.29 Ethylene 11.08 H H Methyl-acetylene Isobutene 11.38 Acetylene Ethylene Propyne Isobutene But-1-ene Diacetylene Ethylene Propene But-1-ene cis But-2-ene trans But-2-ene Isobutene Buta-l,3-diene Pent-1-ene Vinyl Chloride Acry lonitrile Flow discharge, e.s.r.99 99 Flash photolysis Flow discharge, mass spectrometer Flash photolysis, CSe, 99 99 99 9 9 9 9 99 ,? 9 9 99 ,, 3, 10.96 11-51 1 1 *60 11.61 a Ref. 3; ref. 4; ref. 5 ; ref. 6; J. M. Brown P. B. Coates and B. A. Thrush Chem. Comm., Comm. 1966,917; A. B. Callear and I. W. M. Smith Nature 1967,213,382; ' ref. 7; ref TABLE 2 Transfer reactions of H N and Reaction Temp. (OK) System H + D2 = HD + D H + N2H4 = NH + NH3 D + H2 = HD + H H + H2S = H + HS H + CH,CHO = CH + CHO D + DNO = D + NO N + 0 = NO + 0 N + CO = NO + CO l80 + 0 = l8OO + 0 l80 + co = l80c + 0 l80 + CO + l8OCO + 0 I 8 0 + N,O = N,I80 + 0 0 + HNO = OH + NO3 l80 + COCl = c'80c1 4- 0 Flow-discharge e.s.r.Flow-discharge e.s.r. Flow-discharge NH, emission Photolysis H,S, in presence CO, Flo w-discharge mass spectrometer mass spectrometer Flow-discharge e.s.r. Flow-discharge indirect, product analysis Photolysis N1802, mass spectrometer Photolysis N1802 mass spectrometer Dz + Hg(3p), 99 7, 99 Photolysis NO, 450-750 450-750 293-349 3 2 3 4 297 298 300-910 291-523 2 9 8 298-391 298-395 298-358 298 29 O + O + O + O + O + O + O + O + O-l-ot ot ot ot ot O + ot O + O + C302 = 3CO H2 = OH + H CH = OH + Me CH = OH + Me CH = OH + Me EtOH = OH + MeCHOH MeOMe = OH + CH20Me Photolysis C302 Flow discharge e.s.r. 9, 9, Static system, mass spectrometer Flow discharge e.s.r.competitive N,O + Hg(3P) competitive N 2 0 + Hg(3P) competitive N*O + Wd3P), 298 300-1000 4 5 0 4 300-1000 375-576 300-1000 298-398 298-398 298-398 7 9, 9 307-398 9 97 Flow-discharge detailed 2 9 9 4 analysis N,O + Hg(3P) 298 detailed analysis Flow-discharge 303 mass spectrometer " Ref. 2; P. K. Ghosh and E. J. Bair J. Chem. Phys. 1966,45,4738; R. L. Wadlinger and B. de R. L. Wadlinger and M. J. Allard ibid. p. 2346; a R. M. Lambert M. I. Christie and W. J. Linnett, J. Chem. Pkys. 1967,46,4075; W. E. Wilson J. Chem. Phys. 1967,46 2017; 'JL. I. Avramenko and 1967,516;' S. Jaffe and F. S. Klein Trans. Faraday SOC. 1966,62,3135; S. Jaf€e and H.W. -ord J. Phys. J.Amer. Chem. Soc. 1967 89 3390; ' ref. 6; ref. 9; ref. 10; ' ref. 11; ref. 12; ref. 13; Y. Takezaki, 1966,44,341 TABLE 3 Atomic recombination reactions A + A + M = A + M dL-A,l/dt = k,CAI2 [MI Reaction Method Temp. (" K) H + H + M = H2 + M Shock tube dissociation HCl, infrared emission Pulsed discharge, afterglow emission Flow and static discharge e.s.r. Flow discharge, NO titration He + He + M = He + M N + N + M = N + M N + N + M = N 2 + M 4000 366 298 29 N + N + M = N + M Flow discharge, NO titration N + N + M = N + M N + 0 + M = N O + M Flow discharge, NO titration Flow discharge, NO titration N + 0 + M = N O + M Flow discharge, NO titration 0 + 0 + M = 0 + M Flow discharge, NO titration 196 298 196 298 298 298 196 298 196 298 298 'T.A. Jacobs R. R. Giedt and N. Cohen J . Chern. Phys. 1967.47 54; K. M. Phys. 1967,46 127; ref. 14; ref. 15; ref. 16; ref. 17; g ref. 18 TABLE 4 Diatomic dissociation reactions A2 + M = A + A+ M (--d[A,lldt = k-l[A,ICMI Reaction Method Temp. (OK) HCI + Ar = H + C1 + Ar Shock tube infrared 3300-5400 emission from HCI HCI + Ar = H + CI + Art Shock tube infrared 2800-4600 emission from HC1 F + Ar = F + F + Ar Shock tube absorption ? spectroscopy Shock tube absorption Kr spectr~scopy Shock tube emission 1735-2582 from radiative recombination C1 ? C1 F + k r = F + F + + Ar = C1 + C1 + (Ar Ar ~~ ~ ~~~~ t Similar results were obtained with DCI. a E. S. Fishburne J . Chem. Phys. 1966,45,4053; Phys. 1967,46,1958.' D. J. Seery and D. Britton J . Phys. Chem. 1966,70,4074; ref. 20 Gas Kinetics 83 The initial addition reaction produces a chemically-activated vinyl radical and hence there is the possibility of collisional stabilisation and pressure-dependent kinetics. This explains some of the discrepancies in the rate constants for the addition reaction since there have been conflicting reports on the pressure-dependence of the reaction. Michael and Niki3 investigated the reaction in a fast discharge-flow system coupled to a time-of-flight mass spectrometer and from the pressure effect on the apparent overall bimolecular rate constant confirmed that the system undergoes a unimolecular reaction that could be treated satisfactorily by the Rice-Ramsperger-Kassel-Marcus theory.Of the isotopic modifications studied by Michael and Niki only the H + C2D2 system reached the unimolecular high-pressure condition within the pressure region 1-2 torr. The previous results of Michael and Weston4 for the H + C2H2 reaction have been rationalised in terms of the pressure-dependent kinetics of the system and the more recent results of Hoyermann, Wager and Wolfrum’ would appear to have been measured in the pressure-sensitive region. The kinetics of the addition of hydrogen atoms to ethylene are also com-plicated by the production of a chemically-activated radical. The additions of hydrogen atoms to acetylene and ethylene produce activated vinyl and ethyl radicals containing approximately the same excess energy but since there are six more degrees of freedom in the ethyl than in the vinyl radical, the pressure-sensitive region will be lower for the hydrogen atom addition to ethylene.Michael and Weston4 deduced a high-pressure limiting value of log k = 11.29 mole- C.C. set.- for the addition of hydrogen atom to ethylene from a discharge-flow system in which the concentration of hydrogen atoms was determined by a photometric method based on the Lyman-cL absorption. On the other hand Brown and Thrush6 obtained log k = 11.08 with e.s.r. detection of the atom concentration. Since both systems were studied below the second-order limit for the addition reaction and the high-pressure values were obtained by rather crude extrapolations the agreement is reasonable. It is clear however, that extended pressure studies are required to obtain reliable rate constants for this type of system.Much information is available on the reactions of carbon atoms mainly with hydrocarbons in condensed phases.23 The first gas-phase reactions of carbon atoms with benzene have now been reported.24 The “C-atoms (t.& 20-5 min.) were produced by nuclear techniques and were thermally equi-librated with added neon. Product analysis revealed that the C6H6-l lC adduct undergoes bimolecular reactions leading to polymer formation rather than fragmentation processes which although energetically possible appeared to require too much internal rearrangement. Active nitrogen systems continue to attract several workers and the reactions of nitrogen atoms have been re~iewed.~’ Arrhenius parameters for the second-23 C .MacKay and R. W. Wolfgang Science. 1965. 148 899 A. P. Wolf. A h . Phvs. Orq. Chm 24 T. Rose C. MacKay and R. W. Wolfgang J . Amer. Chem. SOC. 1967,89 1529. ’’ B. Brocklehurst and K. R. Jennings Progr. Reaction Kinetics 1967,4 1. 1964 2 2 10 84 J . A. Kerr order reaction of nitrogen atoms with ethylene and propene have been de-termined as follows :26 log kCzH4 = 10-2 - (700/2*3 RT) and log kC3H6 = 11.2 - (1,700/2-3RT) mole-1 C.C. set.-'. The mechanism of the reaction of nitrogen atoms with propene has been investigated in detail with I4C-labelled propene and product analysis. 27 Of several mechanisms considered the most likely seems to be the reversible addition of the nitrogen atom to the double bond followed by reversible rearrangement of the excited adduct to an excited azocyclobutyl radical : 4 C H ! /"\ ,CH21* N + MeCH=CH + [MeCH-CH2]* 'N' CH2 The experimental results could be correlated in terms of the decomposition of the two intermediates and the attack of methyl carbene (a decomposition product) or a nitrogen atom on the intermediates.Brown and Thrush6 have studied the additions of oxygen atoms to acetylene, ethylene and propyne in a flow-discharge system with e.s.r. detection of the atom concentrations. The mechanism for the 0 + C2H2 reaction is thought to be 0 + C2H2 = CH + CO 0 + CH2 = CO + 2H CH2 + C2HZ = C3H4 while the initial attack of an oxygen atom on propyne is proposed to be 0 + MeC=CH = MeCH + CO which is a much faster reaction than with acetylene. The initial reaction for the addition of oxygen atom to ethylene has been deduced from the overall stoicheiometry and the hydrogen atom yield to be 0 + C2H4 = Me + HCO and that for diacetylene is proposed to be :7 0 + C4H2 = C3H2 + CO The Arrhenius parameters for a number of reactions of selenium atoms with olefins have been determined by flash photolysis of CSe in the presence of the olefin and the observations of intense-banded systems in the far U.V.which are ascribed to the (olefin-Se)* adduct.* The rates of addition of selenium atoms were measured relative to the rate of addition to ethylene which had previously been determined.28 There is a good correlation between the activation energies for the selenium-atom additions and the ionisation potentials of the olefins.z6 G. Paraskevopoulos and C. A. Winkler J . Phys. Chem. 1967,71 947. '' P. T. Hinde Y. Titani and N. N. Lichtin J . Amer. Chem. SOC. 1967,89 1411 z8 A. B. Callear and W. J. R. Tyerman Trans. Faraday SOC. 1966,62,371 Gus Kinetics 85 Gunning and S t r a u ~ z ~ ~ have comprehensively reviewed the reactions of of sulphur atoms and have continued their investigations3' of these reactions from the photolysis of COS. With light of 2537 A triplet (3P) and singlet ('D) sulphur atoms are produced in the ratio 3 1. The rates of addition of triplet sulphur atoms to a series of olefins have been determined relative to the addition to ethylene at 298"~. It is deduced that triplet sulphur atoms are electrophilic, while a few results on the relative rates of singlet sulphur atoms to olefins indicate that this species is also electrophilic but generally less selective than S( P).Table 5 contains data obtained from fast-flow systems on atom-addition reactions which reveal third-order kinetics. Atomic Transfer Reactions. As seen from Tables 6 and 7 many results have been determined for this type of reaction particularly for reactions of triplet oxygen atoms [O('P)]. The flow-discharge method of studying oxygen atoms involving e.s.r. de-termination of the atom concentrations has already been mentioned. The agreement between the results for the reaction of oxygen atoms with CH4 from the two e.s.r. studies2* is reasonably satisfactory although the results of Westenberg and Haas' are probably to be preferred on the grounds that their temperature range was considerably larger.The rate constants of Wong and Potterg for the 0 + CH4 reaction from a stirred-flow reactor and mass-spectrometric analysis are in excellent agreement with those of Westenberg and Haas although the Arrhenius parameters from a much shorter temperature range are somewhat higher. Heicklen"? '' has devised a neat competitive method for studying the re-actions of O( 3P) atoms produced from the mercury-photosensitised decompo-sition of N 2 0 : Hg* + N 2 0 = Hg + N2 + O(3P) The only oxygen-containing product from the reaction of O(3P) with C2F is CF20 which can be determined by in situ i.r. analysis. Thus when the oxygen atoms are produced in the presence of a mixture of C2F4 and a hydrocarbon the reactions of interest are 0 + CpF4 = CF2O + .0 + RH = products (6) (7) and the ratio of rate constants can be calculated from the expression - RCF,O) [c2H41 RCF2O [RHI kdks = where R is the rate of formation of product X and square brackets denote 29 H. E. Gunning and 0. P. Strausz Adv. Photochem. 1966,4,143. 'O E. M. Lown E. L. Dedio 0. P. Strausz and H. E. Gunning J . Amer. Chem. SOC. 1967,89, 1056; 0. P. Strausz J. Font. E. L. Dedio P. Kebarle and H. E. Gunning ibid. p. 4805 86 J. A. Kerr rc, m N 0" z + z 0 z + Q0" 2 2 + + no" n o II 0 + 0 +so + M = so + M 0 + SO + M = SO + M c1+ co + M = ClCO + M C l + N O + M = C l N O + M 0 + SO2 + M = SO3 + M 0 + SO + M = SO + M Flow discharge 298 air afterglow * Flow discharge 300 SO2 afterglow Flow discharge 300 C1 afterglow Flow discharge 293 C1 afterglow Flow discharge 300 SO2 afterglow Flow discharge 299 e.s.r.D. B. Hartley and B. A. Thrush Proc. Roy. SOC. 1967 A 297 520; F. Kaufman 4541; A. Sharma J. P. Padur and P. Warneck J. Phys. Chem. 1967,71 1602; M. A. A. Proc. Roy. SOC. 1966 A 295 355; C. J. Halstead and B. A. Thrush ibid. pp. 363 380; C. Ward J . Phys. Chem. 1967,71 2124; B. T. Clarke M. A. A. Clyne and D. H. Stedman TABLE 6 Transfer reactions of halogen Reaction System Temp. (OK) C1 + EtCl = HC1 + CH2CH2C1 C1 + MeCHC1 = HCl + CH2CHCl C1 + MeCC1 = HCl + CH,CCl, C1 + EtCl = HCl + MeCHCl C1 + CH2C1CH2C1 = HCl + CHC1CH2C1 C1 + CH2ClCC13 = HCl + CHClCCl, C1 + MeCHC1 = HC1 + MeCCl, C1 + CH2ClCHCl2 = HCl + CHClCHCl, C1 + CHZClCHCl = HCl + CH2ClCC12 C1 + CHC12CHC12 = HCl + CHC12CC1, C1 + C2HC1 = HC1 + C2C1, I + C2H6 = HI + Et I + C3H = HI + Pr" I + C3H8 = HI + Pr' I + isoC,H, = HI + But I + PhI = I + Ph I + CF3H = HI + CF3 I + CF31 = I + CF, Competitive with CHCl or MeCl 77 99 97 99 77 97 77 97 79 Competitive with CHC1 or CH,Cl Thermal iodination 79 99 99 99 79 Thermal reaction with HI Thermal and photochemical iodination 3 2 3 99 79 77 99 77 99 99 99 79 3 2 3 4 97 589-503-77 77 77 648-773 373-Ref.31 ; * C. A. Goy A. Lord and H. 0. Pritchard J . Phys. Chem. 1967,71 1086; ' J. H. Knox 32; ' ref. 19 Gas Kinetics 89 TABLE 7 Cross-combination ratios (@) 'a 'b Me Me Me Me Me Et Et Pr" CF3 cyclo-C,Hej Et Pr" CH,F CHF, CHF, Pr" Pr' Pr' CH2CH=CH2 CYC~O-C~H~~ 2.00 2.02 1.4 2.4 2.4 1.8 2.08 2-04 1.87 2.0 298" 298" 447b 329-585' 564-636* 298" 298" 298" 3 1 3-523f 299-560" ~~ ~ ~ Ref.33; * G. Greig and J. C. J. Thynne Trans. Faraday SOC. 1966,62 3338; G. 0. Pritchard and R. L. Thommarson J. Phys. Chem. 1967,71 1674; R. D. Giles L. M. Quick and E. Whittle, Trans. Faraday SOC. 1967 63 662; ref. 34; G. Greig and J. C. J. Thynne Trans. Faraday SOC., 1967 63 1369. concentration. Hexafluoropropene which is some thirty-times less reactive than C2F4 can also be used in similar competitive experiments since the only important products are CF20 and small amounts of CF,CFO. While such experiments yield rate factors for the reaction of O(jP) with hydrocarbons they do not provide unequivocal evidence as to the mechanism of the reaction.Although it seems reasonable to suppose that the reaction involved is hydrogen abstraction by the oxygen atoms this is not the view held by Avramenko and his co-w~rkers.~ They have studied oxygen atom reactions with hydrocarbons in a flow-discharge system where the rate constants are derived by an indirect method based on product analysis and have consistently proposed that the initial reaction of oxygen atoms with higher alkanes involves C-C rupture. Likewise for the reactions with EtOH and EtCHO they suggest :35 0 + EtOH = MeCHO + H 2 0 = CH,O + H,O + CH, and 0 + EtCHO = Me + CH,O + CHO whereas Kato and C v e t a n ~ v i c ~ ~ and Cadle and Powers" propose the simpler hydrogen abstraction reactions : 3 1 C.Cillien P. Goldfinger G. Huybrechts and G. Martens Trans. Faraday SOC. 1967,63 1631. 32 A. S. Rogers D. M. Golden and S. W. Benson J. Amer. Chem. SOC. 1967,89,4578. 33 J. 0. Terry and J. H. Futrell Canad. J. Chem. 1967 45,2327. 34 J. T. Bryant and G. 0. Pritchard J . Phys. Chem. 1967,71,3439. 3s L. I. Avramenko R. V. Kolesinkova and G. I. Savinova Zzvest. Akad Nauk. S.S.S.R. Ser. Khim. 1967 22 253 90 J. A. Kerr 0 + EtOH = OH + MeCHOH 0 + EtCHO = OH + EtCO A comprehensive study of hydrogen abstractions by chlorine atoms from chloro-ethanes has been rep~rted.~ ' The results (see Table 6) show that chlorine atom attack is faster at the most chlorine-substituted carbon atom.The de-crease in A-factor as the chlorine-substitution is increased is predicted by transition-state theory but the parallel increase in activation energy is not explained by a Polanyi relation since D(C-Cl) = 96 f 2 kcal. mole-' throughout the series of chloro-ethanes. It is apparent that polar effects play an important part in these reactions. The classic example of a 'bimolecular' reaction the H + I reaction, has now been shown to take place entirely by an atomic mechanism. Sullivan36 has photolysed (5780 A) iodine in the presence of hydrogen between 418 and 5 2 0 " ~ and shown that the rate of formation of HI is proportional to the square of the iodine-atom concentrations. The concentrations of iodine atoms were determined photochemically and for the termolecular reaction 21 + H = 2HI a rate constant of log k = 13.88 - (5310/2.3 RT) mole- c.c.set.-' was deduced. Previous thermal data (633-738"~) when treated with the ter-molecular reaction in place of the bimolecular reaction H2 + I = 2HI gave rate constants for reaction (8) corresponding to the same Arrhenius parameters. It was not possible to distinguish between the two kinetically identical mechanisms : H + 21 = 2HI or H 2 + I + M = H 2 1 + M H21 + I = 2HI Several important papers have been published on the kinetics of hot-atom reactions. In particular Wolfgang3' and his group3* have studied the reactions of F* and T* atoms produced by nuclear reactions with various simple molecules such as H, CH4 and CF4 and have successfully analysed their results in terms of the kinetic theory of hot-atomic reactions.2. Radical Reactions.-Several reviews of free-radical reactions have been published. Friswell and G o w e n l ~ c k ~ ~ have critically compiled kinetic and thermochemical data and information on inorganic hydrogen- and alkyl-36 J. H. Sullivan J . Chem. Phys. 1967,46 73. 3' R. Wolfgang Progr. Reaction Kinetics 1965 3,97. 38. J. F. J. Todd N. Colebourne and R. Wolfgang J . Phys. Chem. 1967,71,2875; D. Seewald and 3y N. J. Friswell and B. G. Gowenlock. A h . Frc~c~-Reiclic~ciI Chc~r 1965. 1 39 1967. 2. 1 R. Wolfgang J . Chem. Phys. 1967.46 1207 Gas Kinetics 91 containing radicals of the elements of groups 11-VI. Although the amount of quantitative kinetic information on these radicals is small there is now a sub-stantial body of related thermodynamic data including heats of formation of the radicals and compounds and bond-dissociation energie~.~' The reactions of halog~nomethyl~' and a l k o ~ y ~ ~ radicals have also been rcviewed.There has been much discussion concerning the addition of iodine atoms to olefins giving rise to planar or tetrahedral radicals. The present position has been summarised in a joint paper,43 in which it is agreed that either the planar radical configurations are more stable than the tetrahedral or the barrier to in-version of tetrahedral carbon atoms is much less than that for tetrahedral nitrogen compounds. Crosley and B e r ~ o h n ~ ~ claim to have made the first actual detection of radicals or hydrogen atoms during a steady-state gas-phase photolysis.Their system consisted of applying the principles of optical pumping to the vacuum U.V. (1048 and 1067 A) photolysis of ethane in the presence of rubidium. The pumped gas atoms spin-orientated rubidium were produced in a magnetic field via the selective absorption of polarised light. In the presence of unpaired electrons the spin polarisation is lost and hence the atoms or radicals can be detected. Combination and Disproportionation Reactions. Since the general features and patterns of reactivity of radical-radical reactions are now reasonably well established interest in these systems seems to have waned. Most of the available information4' on combination reactions R + R = R, (9) has been derived from rotating-sector experiments although other methods are also available.The results show that the A-factors (A,) correspond approxi-mately to the collision numbers and the activation energies (E,) are close to zero. A much simpler experimental problem is to measure the cross-combina-tion ratio of rate constants (4) for a pair of radicals: R + R = R, (9) This ratio is defined as +(Ra,Rb) = kll/(k9kl,,)k and for a large number of radical pairs + has been observed2'F4' to be close to two indicating that the combinations are occurring on every collision with zero activation energies. 40 J. A. Kerr Chem. Rev. 1966,66,475. 41 J. M. Tedder and J. C. Walton Progr. Reaction Kinetics 1967,4 37. 42 P. Gray R. Shaw and J. C. J. Thynne Progr. Reaction Kinetics 1967,4 63. 43 R. M. Noyes D.E. Applequist S. W. Benson D. M. Golden and P. S. Skell J . Chem. Phys., D. R. Crosley and R. Bershon J . Chem. Phys. 1966 45 4353; D. R. Crosley ibid. 1967,47 1967,46 1221. 1361. 44 4s J. A. Kerf and A. F. Trotman-Dickenson Progr. Reaction Kinetics 1961 1,107. 92 J . A. Kerr Disproportionation reactions are usually considered with combination reactions since unlike other metathetical reactions their rates are comparable with combination reactions. For like radicals the reaction is R + R = R,H + olefin R + R = R,H + olefin (12) and the autodisproportionation-combination ratio of rate constants is given by A(R,,R,) = ki,/kg while for unlike radicals we have (13) and the cross-disproportionation-combination ratio is defined as A(Ra,R,,) = k13/k11.Many A values for alkyl and other radicals have been de-termined21.45,46 and as a general rule A shows little or no variation with temperature. For alkyl radicals A values can be reasonably well predicted from their relation with the entropy differences of the products of dispropor-tionation and the product of ~ombination.~~ There has been much speculation on the structures of the transition states in disproportionation and combination reactions and particularly whether they are identical or different. The issue is not yet clear although the weight of opinion seems to favour different com-plexes.21 Controversy has arisen regarding the rate constant for the reaction : 2cc13 = C2C1 (14) A preliminary p ~ b l i c a t i o n ~ ~ on the photochlorination of CHCl by the rotating-sector method reports log k = 8-55 mole-' C.C.set.-' at 345°K for the reaction CCI + C1 = CCI + C1 and hence from the previously determined ratio log(k1,/k14+) = 2.24 it follows that log k14 = 12-62 mole-' C.C. see.-'. This result is considerably lower than the value log k14 = 13.9 mole- C.C. set.-' determined by Tedder and W a l t ~ n ~ ~ from rotating-sector experiments on the addition of CC1,Br to C2H4 at 350-446 OK. The self-consistency of the latter experiments is remarkably good consider-ing the experimental difficulties of the technique while it is difficult to assess the results on the photochlorination of CHC13 since full experimental details are still to be published. It has been pointed that the higher value of log A14 leads to more reasonable A-factors for the addition and transfer reactions of CCl radicals and that the c$ values for CCl radicals do not indicate an ab-normally-low rate constant for reaction (14).On these grounds the higher value of kI4 is to be preferred. An interesting application of the toluene-carrier method for studying pyrolytic reactions has been made to determine the rate of the combination reaction4' (16) Me + PhCH = PhEt A F. Trotnian-Dickcnson Proc. Clicrii Soc 1964 249. 4 7 G. R. De Mart and G. H. Huybrechts Chrm. Phys. Letters 1967,1,64. 48 J. M. Tedder and J. C. Walton Trans. Faraday Soc. 1967 63 2464; J. M. Tedder and J. C. 49 Walton Chem. Comm. 1966 140. R . J. Kominar. M. G. Jacko. and S. J. Price. Ccrncrd. J . Ch~rii 1967. 45. 575 Gas Kinetics 93 By analysing for the methane ethane and ethylbenzene in the products of the pyrolyses of gallium and thallium trimethyls and mercury dimethyl it has been shown that log k = 11.20 - 200/2.3 RT mole-' c.c set.-' at 529-799"~.The concentration of benzyl radicals was monitered by the rate of formation of methane and the known rate constant for methyl attack on toluene. The value of A16 is in excellent agreement with that calculated from the relation log ( A / A - 16) = AS/2.3 R and the experimental A-factor for the pyrolysis of ethyl benzene. O Cross-combination ratios 4 are listed in Table 7. The value @(Me,cyclo-propyl) = 1.4 is somewhat lower than the expected result of about two but the difference is probably due to the difficulty of obtaining quantitative data on cyclo-alkyl radicals.The latest results for fluorinated alkyl radicals are quite normal whereas the early results on 4 values were anomalous since allowance was not made for the fact that the activated fluoro-alkanes formed in the combination reaction can undergo an elimination reaction under certain conditions to give HF and an olefin51 (see section on activated molecules). Table 8 summarises the data on disproportionation-combination reactions. A(Bu",Bu") has been shown to be 0.14 independent of temperature from a careful study of the photolysis of a~o-n-butane.~~ This result is in keeping with TABLE 8 Disproportionation-combination reactions R + R' = RH + Olefin (d) R + R' = RR' (4 k,/k = A(R,R') R R' A(R,R') Temp. ( O K ) R R' A(R,R') Temp. (OK) Me Me Me Et Et Et Pr' Pr' Pr' Pr' Et Pr' Pr" Et Pr' Pr" Et Pr' Pr' Pr" 0.036 0.163 0-058 0.135 0.180 0.066 0- 124 0.687 0.58 0-409 298" 298" 298" 298" 298" 298" 298" 298" 295-339' 298" Pr" Pr" Bun Me Me Me0 NO NO H S Me Et Pr" Bun HCO Me0 Me0 Pr' Pr' HS Me 0.057 0-1 54 0.14 5.8 1.9 0.17 0.22 0.04 67 0 * 1 5 4 3 0 298" 298" 300-400' 303-376d 3 14-365" 314" 4 2 3 - ~ l 5 3 ~ 378-422g 3 h 298' Ref.33; S. E. Braslavsky J. Grotewold and E. A. Lissi J . Chem. SOC. (B) 1967 414; ' ref. 52; ref. 53; M. J. Yee Quee and J. C. J. Thynne Trans. Faraday SOC. 1966,62,3154. f B. E. Ludwig and G. R. McMillan J . Phys. Chem. 1967,71,762.gG. A. Hughes and L. Phillips J . Chem. SOC. (A) 1967,894; P. Fowles M. De Sorgo A. J. Yarwood 0. P. Strausz and H. E. Gunning J . Amer. Chem. SOC. 1967,89 1352; A. Good and J. C. J. Thynne, Trans. Faraday SOC. 1967,63,2708. G. L. Esteban J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. 1963 3873. " R. D. Giles and E. Whittle Trans. Faraday SOC. 1965,61 1425. 5 2 W. E. Morganroth and J. G. Calvert J . Amer. Chern. SOC. 1966,88 5387. 53 M. J. Yee Quee and J. C. J. Thynne Trans. Faraday SOC. 1967,63 1656 94 J. A. Kerr other n-alkyl radicals and obeys the A relation with the entropy differences of the products. The previously reported higher values for A(Bu" and the temperature coeficient for this ratio would now appear to be in error owing to complications with the sources of the radicals.The radical-radical reactions of methyl ethyl n- and iso-propyl radicals have been studied from the high-intensity photolyses of the corresponding azo-compounds at room temperat~re.~~ Under these conditions the concen-trations of the radicals are very high and the radical-radical reactions pre-dominate. The results summarised in Table 8 in the main confirm the previous 'best available' values of these ratios.46 The A values reported for oxygenated radicals are considerably higher than for the analogous alkyl radicals and furthermore the results do not fit the A relation with the differences in entropies of the products.42 The autodispropor-tionation of formyl radicals has been suggested to go via the reaction 2HC0 = H2 + 2CO and although no quantitative results were available it was clear from the product analyses that A(HC0 HCO) is very high.53 Radical Transfer Reactions.As usual most of the free-radical transfer reactions reported are concerned with the abstraction of a hydrogen atom. These reactions have been reviewed," and the general features are well established. The activation energies which seldom exceed 15 kcal. mole- are governed by the enthalpy change of the reaction and by polar effects. Un-fortunately there are no quantitative methods for dealing satisfactorily with these effects. The A-factors however can be calculated reasonably well from the transition-state theory and for hydrogen atom abstraction by Me the expec-ted range is log A = 11.5 rf 0.5 mole-' C.C. set.-'.The results for hydrogen atom abstraction reactions are summarised in Table 9. The reaction of methyl radicals with benzene is of interest, The most recent results were obtained at high temperatures in a flow sy~tem.~' Under these conditions the rate of combination of methyl radicals was in the pressure-dependent region but when this was taken into account the results for reaction (17) were in good agreement with previous determinations. EI7 has been taken62 in conjunction with the activation energy for the reverse 54 J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. 1960 1602; J. C. J. Thynne Trans. 5 5 A. F. Trotman-Dickenson Adv. Free-Radical Chem. 1965 1. 1. 56 R. J. CvetanoviC and R. S. Irwin J . Chem. Phys. 1967,46 1694. 57 M. Krech and S. J. W.Price Canad. J . Chem. 1967,45 157. 58 J. A. Kerr D. H. Slater and J. C. Young J . Chem SOC. (A) 1967 134. 5 9 T. N. Bell and B. B. Johnson Austral. J . Chem. 1967 20 1545. 6o D. G. Home and R. G. W. Norrish Nature 1967,215 1373. 61 A. J. Dijkstra J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1967 105,864. Faraday SOC. 1962,58 1533. F. J. Duncan and A. F. Trotman-Dickenson J . Chem. SOC 1962,4672; W. Fielding and H. 0. Pritchard J . Phys. Chem. 1962 66 821 Gas Kinetics 95 TABLE 9 Abstraction of H atoms by radicals R + HS = RH + S (a) 2R = R (b) ( E - 9%) log A,? Temp. (OK) R HS* kcal (mole-' C.C. mole - sec. - ' Me Propene But-1-ene cis-But-2-ene trans-But-2-ene Isobutene Benzene Acetone CH,FCOMe MeOCOOMe PhOCH, CF,CHO C,F,CHO C,F,CHO CFzHCOCFzH CYC~O-C 3H 5 C H 0 NH,CH,CH,NH, NH2CH2CH2NH, ND,CH,CH,ND, Me,SiH SiHF, SiHCl, MeSiHCl, Me3SiC1 Me,SiCl, MeSiC1, CF MeF CH2F2 CF,Me CF,HCF,H SiHC1, C A H CH,F CH,FCOMe CF,H MeCOMe CCl CH,CH==CH, CH3CF=CH2 Me0 MeOCOOMe 7.2 7.3 7.6 8-2 7.9 9.3 9.4 4.6 4.3 7.4 10.5 8.7 9-8 10.3 8.7 7.3 6.8 7.9 7.0 8.7 8.5 7.2 11.5 11.6 11.5 11-2 11.2 13.5 12.4 11.5 6.9 6.7 9-0 - 6.3 - 6.6 5.9 10.3 11.0 11.1 11.4 11.0 10.8 11.4 10.1 10.3 10.2 11.7 12-1 12.9 13.2 12.3 10.9 10.3 10.3 11.1 12.4 13.4 11.8 13.4 13.2 12.9 12.2 11.9 12.2 12.0 11-3 12.1 10.0 10.9 - 12.0 - 12.0 10.8 353453" a a a a 99 97 9 ) 9 ) 744--8Wb 329-Wd 299-560' 3 14--366f 453-5399 40 1-444h 398-43gh 373-473' 360-450' j i 403-503' 99 99 330-445k 34347ok 303-393k 3 1 5-395k 337-47 1 361455k 3 7 8 4 7 g k 469-632' 448436' 566478' 5 10-683' 507-724' 329-585d 395483" 3 6 2 4 5 4 3 14--366f 83-563" 299-560 J .A. Kerr TABLE 9-continued Temp. ( E - +&J log 43 ( O K ) R HS* kcal (mole- ' C.C. mole - ' sec. -Pr" MeCOMe 8.4 10.7 403-503' Bun (Bu"N) 7.1 11.2 377-520' OH CH4 5.0 13.7 ? P C2H6 3.6 14.1 2 9 8 4 2 3 P NF cyclo-C,H1 13.4 9.1 334-3914 * Atom in italics is abstracted; t based on log k = 13.34 (mole-' C.C. set.-'); ref. 56; ref. 57; ' L. Endrenyi and D. J. Le Roy J . Phys. Chem. 1967 71 1334; * G.0. Pritchard and R. L. Thom-marson J . Phys. Chem. 1967,71,1674; ref. 34; M. J. Yee Quee and J. C. J. Thynne Trans. Faraday SOC. 1966,62,3154; M. F. R. Mulcahy B. G. Tucker D. J. Williams and J. R. Wilmshurst Austral. J . Chem. 1967 20. 1155; E. R. Morris and J. C. J. Thynne Trans. Faraday SOC. 1967 63 2470; G. Greig and J. C. J. Thynne Trans. Faraday Soc. 1966,62,3338; P. Gray and A. A. Herod Trans. Faraday SOC. 1967,63,2489; Ir ref. 58; ' R. D. Giles L. M. Quick and E. Whittle Trans. Faraday SOC., 1967,63 662; ref. 59; J. M. Tedder and J. C. Walton Trans. Faraday SOC. 1967,63 2678; ' ref. 52; P ref. 60; ref. 61. reaction E - 7 to obtain values of the bond strength D(Ph-H) = 102 and 105 kcal. mole- '. Rogers Golden and B e n ~ o n ~ ~ have subsequently determined D(Ph-H) = 112 PhI + HI + C,H + I2 and since this is now a well-established method for yielding reliable bond-dissociation energies it is clear that the previous determinations based on the hydrogen atom abstraction reactions are seriously in error.It has been suggested that the reaction of a methyl radical with benzene in the gas-phase does not involve hydrogen atom abstraction as shown by reaction (17) but that the radicals add to the benzene ring to give a resonance-stabilised cyclohexadienyl radical that subsequently reacts with another methyl radical to form methane :32 1 kcal. mole-' from an equilibrium study of the system 0 + Me = CH4 + Me Me If this mechanism is correct the products of the reaction of methyl radicals with benzene should contain toluene.The reactions of methyl and CF radicals with organosilicon com~oundsS8- 5 9 are among the first quantitative kinetic results for this class of substrates. The A'-factors for some of the methyl reactions are abnormally high and they 9 Gas Kinetics 97 have been explained by invoking ionic participation in the transition state, ofthe type previously suggested to be involved in disproportionation reactions.,' It is also very difficult to reconcile the reported Arrhenius parameters for methyl and CF radical attack on SiHC1,. More work is obviously needed on these systems. The rates of reaction of hydroxy radicals with methane and ethane have been studied by flash photolysing the hydrocarbons in mixtures with water and argon.60. 6 3 The rate of disappearance of the radicals was followed spectro-scopically ; so-called kinetic spectroscopy.The Arrhenius parameters listed in Table 9 for methane and ethane are not in very good agreement with rate constants reported by Greiner63using the same method or with other published data on these reactions.64 Comparatively few results have been reported on radical reactions involving the transfer of atoms other than hydrogen. King and S ~ i n b o u r n e ~ ~ have pointed out the difficulties of obtaining quantitative data on the halogen abstractions Me + RX = MeX + R where X = C1 or Br arising from complications involving the generation of radicals by hydrogen atom abstraction. A competitive study of the reactions CF3 + I2 = (3'31 + I CF + HI = CF3H + I (18) (19) has been carried out by Amphlett and Whittle.66 From the previously de-termined rate constant for reaction (18) they deduce log k = 11.73 - (500/ 2.3RT) mole-' C.C.set.-'. Whittle and c o - ~ o r k e r s ~ ~ have now completed studies of the reactions CF3 + X2 = CF,X + X CF3 + HX = CF3H + X where X = C1 Br and I and have discussed the results in terms of thermo-dynamic data available on these systems. A rate constant of log kZ0 = 12-17 - (23,500/2.3 RT) mole- C.C. set.-' has been obtained for the reaction (20) by generating the NF radicals from the equilibrium dissociation of N2F4 and observing the pressure change in the presence of C1F,.67 NF + ClF = NF + ClF, 6 3 N. R. Greiner J . Chem. Phys. 1967 46 2795 3389. 64 L. I. Avramenko and R. V. Kolesnikova Adv.Photochem. 1964 2,25; P. Gray and A. Jones, Canad. J . Chem. 1967,45 333. K. D. King and E. S. Swinbourne J . Phys. Chem. 1967,71,2371. 66 J. C. Amphlett and E. Whittle Trans. Faraday SOC. 1967 63 2695. '' G. von Ellenmeder E. Castellano and H. I. Schumacher Z . phys. Chem. (Frankfurt) 1967, 56 20 98 J . A. Kerr Radical Addition Reactions. As for transfer reactions the general features of free-radical addition reactions to multiple bonds seem to be well established. The activation energies usually fall within the range 5-15 kcal. mole' and the A-factors within the range predicted by transition-state theory, mole- ' C.C. set.- Unfortunately compared with hydrogen atom abstraction reactions there is much less quantitative data available on addition reactions.The experimental difficulties are much greater with addition reactions since the initial product is a free radical which may undergo a variety of further re-actions. Even for simple systems such as Me + C2H = Pr" the accuracy of the rate constants is not very good as shown by the data in Table 10 which includes two recent determinations. Since there are no obvious TABLE 10 Arrhenius parametersfor the reaction Me + C2H = Pr" Source of Me Temp. E log A and system (OK) (kcal. mole-') (mole-' C.C. set.-') (Me,CO)2 397-43 1 8-7 product analysis (Me,C0)2 395-432 7.8 product analysis Me2C0 403-503 6.8 product analysis (MeCO), 353-453 7-9 mass balance 12.1" 1 Mb 11.1' ll.9* ~~ ~~ ~ R. K. Brinton J. Chem. Phys. 1958,29 781; A. M. Hogg and P.Kebarle J . Arner. Chem. Soc., 1964,86,4558; L. Endrenyi and D. J. Le Roy J. Phys. Chem. 1967,71,1334; ref. 56. reasons for selecting one result in preference to the others it would seem best to take the average Arrhenius parameters and obviously significant errors should be attached to such values. This lack of accuracy in determining rate constants for free-radical addition reactions means that caution should be exercised in making deductions on the detailed mechanisms of these reactions based on small differences in Arrhenius parameters. CvetanoviC and Irwins6 have developed a useful variant of the mass-balance method for studying the addition reactions of methyl radicals to olefins. Small amounts of biacetyl were photolysed in the presence of the olefin and a reference hydrocarbon isobutane.Under the experimental conditions the important reactions are MeCOCOMe + hv = 2MeCO (A Gas Kinetics 99 MeCO = Me + CO (B) Me + Me3CH = CH + Me,C (21) Me + 0 1 = R' (22) Me + 0 1 = CH + R" (23) Radical-radical reactions can be neglected provided the concentrations of olefin (01) and isobutane are far in excess of the methyl concentration. A steady-state treatment yields so that plots offversus [RH]/[Ol] yield values of k,,/k, and k 2 1 / k 2 2 . In the limiting case with [Ol] = 0 the expression becomes (&O/&H4) - 1 = 0 and this was confirmed experimentally although minor corrections were necessary for addition methyl reactions at low temperatures and low RH concentrations. The advantage in using biacetyl as a methyl source in preference to acetone is that the ratio CO/CH is unity with biacetyl even although all the MeCO radicals do not decompose by reaction (B).Accordingly it is possible to work at lower temperatures with biacetyl than with acetone. Temperature coefficients of the ratios k 2 ~ / k Z 2 and k z l / k Z 2 were obtained and the Arrhenius parameters for reactions (22) and (23) listed in Tables 11 and 9 were deduced TABLE 11 Radical additions to unsaturates R + S = R S Radical Substrate Temp. E log A mole - ') sec - l ) (OK) (kcal. (mole-' C.C. Me Propene But- 1 -ene cis-But-2-ene trans-But-2-ene Is0 butene 2-Methyl but-2-ene 2,3-Dimethylbut-2-ene Buta-1,3-diene Allene Propyne Sulphur Dioxide Et Allene 353-453 3 5 3 4 5 3 3 5 3 4 5 3 353-453 3 5 3 4 5 3 3 5 3 4 5 3 3 5 3 4 5 3 353-453 3 7 3 4 8 3 3 7 9 4 6 5 298-437 374-471 7.4 7.2 7.5 8.1 6.9 -6 -7 4.1 8-1 8.8 1.5 9.2 11-5" 11-3" 11.0" 11.5" 11.5" - 10.5" - 10.3" 11.2" 11.3' 11-7' 1 0*8d 1 1.5' D 100 J .A. Kerr TABLE 1 1-continued Radical Substrate Temp. E log A mole- I ) sec. - l ) (" K) (kcal. (mole- C.C. Pr' Pr' Pr" But CH,COMe CCl, Allene Prop yne Ethylene Prop yne Ethylene Propene 2-Fluoropropene Hexafluoropropene Ethylene Propene But-1-ene cis-But-2-ene trans-But -2-ene Isobutene 2-Me t hyl bu t -2-ene 2,3-Dimethylbut-2-ene Cyclopentene Vinyl chloride Vinyl bromide Ethylene Isobutene 36-73 36-39 385-439 403-503 395-483 362-454 415-485 3 5 1 4 2 8 334-391 334-391 334-39 1 314-373 314-373 314-373 334-39 1 351-405 351-405 403-503 334-391 245-333 245-333 7.2 5.7 5.1 6.6 3.4 3.2 6.2 15.5 13.7 13.6 11.9 11.9 11-8 10.1 8.3 11.0 12.9 13.2 1-1 1.7 -6 10.7' 9.7' 10.1' - 9.3' 11.1' 10.2f 9*8f 9.5f 1 0*6g 10.28 10.18 9-58 9.58 9.8g 9.08 8*3g 8.98 9.49 9.6g 1 1.Oh 12.5' ~ ~~~ Ref.56; * ref. 68 ; ' R. R. Getty J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1967, 1360; * A. Good and J. C. J. Thynne Trans. Faraday SOC. 1967,63 2708; L. Endrenyi and D. J. Le Roy J . Phys. Chem. 1967,71 1334; J. M. Tedder and J. C. Walton Trans. Faraday SOC. 1967, 63 2678 ; 8 ref. 61 ; L.I. Avramenko L. M. Evlashkina and R. V. Kolesnikova Izvest. Akad. Nauk. S.S.S.R. Ser. Khim. 1967 259. from the known rate constant for reaction (21). The outstanding advantage of the method is that it yields reliable relative rates of addition of methyl even in cases such as 2 methyl and 2,3-dimethylbut-2-ene where the abstrac-tion of hydrogen atoms predominates over the addition reaction. There is reasonable agreement between the k 2 2 / k 2 values and the corresponding ratios obtained in iso-octane solution,69 on the assumption that the A-factors for the various olefins are approximately the same. CvetanoviC and Irwin have also drawn up a useful summary of relative rate constants for additions of atoms radicals and biradicals to unsaturate^.^^ It is interesting to note that the additions of alkyl radicals to allene occurred exclusively at the terminal carbon atoms.68 Meunier and Abel17* have shown R.R. Getty J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1967 979; 6 9 M. Feld and M. Szwarc J . Am. Chem. SOC. 1960,82 3791 and references cited therein. 70 H. G. Meunier and P. I. Abell J . Phys. Chem. 1967,71 1430 Gas Kinetics 101 that in the additions of CF,I and Me1 to allene the CF and methyl radicals also add exclusively to the terminal atoms. There has been considerable dis-cussion over the years regarding the orientations of free radical and atomic additions to allene." The results on the methyl and CF additions have been interpreted as indicating that polar effects are not important. While the electro-philic CF radical would be expected to add to the point of highest electron density i.e.the terminal carbon atom the 'slightly nucleophilic' methyl radical should add to the central carbon atom if polar effects were the only consideration. NF radicals have been added to olefins by generating the radicals from the equilibrium dissociation of tetrafluorohydrazine :61 NZF4 + 2NF, Since D(NF,-NF,) is only 20 kcal. mole-' the concentration of NF is appreciable at low pressures and temperatures above 3 7 3 " ~ . For the series of NF additions listed in Table 11 a general mechanism has been established : NF + 01 = NF,OI* NF,Ol* + Mol = NF,O1 + Mol NF + NF,Ol = 01(NF2), (24) ( 2 5 ) (26) (27) (28) NF,OI* = NF + 01 NF,Ol = NF + 0 1 The concentration of NF2 radicals is known from the total pressure of N,F4 and NF radicals and the dissociation constant of N,F4.0 1 is the olefin of known initial concentration NF,Ol* is a vibrationally-excited radical and Mol is any molecule in the system capable of removing the excess energy. A steady-state treatment yields : where kobs is defined by d[Ol(NF,),]/dt = kob,[O1][NF,] and OI(NF,) is the bis-difluoro-amine product that is analysed. Less than 5 % of hydrazine and olefin were consumed and hence their concentrations were taken to be constant during the run. Two series of experiments were carried out for each compound at each temperature. In one series [Moll was kept constant and [NF,] varied; l/kobs was plotted against l/[NF,] and the intercept on the l/k,,bs axis gave (l/kz4)(l + k,,/k,,[Mol]) while the slope gave (1/kz4){l + k,5/k,,[Mol])(k27/k,8).Thus k,,/k,* was obtained by dividing the slope by the intercept. Similarly k,5/k,6 was determined from plots of 1 kobs against l/[Mol] with [NF,] constant and k24 could then be derived from either set of observations by substituting the appropriate value of kZ5/k2 or k27/k28. H. G. Kuivila W. Rahman and R. Fish J An~rr. Chew. Soc. 1965 87 2835 TABLE 12 Radical elimination reactions Reaction Temp. (OK) C2H6 = 2Me CH2:CH(CH2),CH:CH2 = 2CH2:CHCH2 MeCMe,CH,CH CH = But + CH,CH CH, EtOOEt = 2Et0 Me,CHOOCH(Me) = 2Me,CHO Me,CHOOCH(Me) = 2Me2CH0 N-F,* = CF + N, MeN:NMe = 2Me + N, Me,NN:NNMe = N + 2Me,N Me,Hg = 2CH + Hg Me,SiSiMe = 2SiMe, Me,SiSiMe = 2SiMe, Et = H + C2H4 Pr" = Me + C2H, CH,:CH(CH,),CH:CH = 2CHz:CHCHz ~ ~ ~~~~ 9 13-999 850-950 1000-1 130 407-458 4 0 7 4 5 8 3 7 8 4 2 2 3 9 6 4 4 3 5 5 3 4 2 3 4 0 0 4 8 585-4574 977-1070 628-796 93 5- 1044 9 13-999 53 3-5 7 Bu" = Et + C2H4 BUS = Me + C3H6 EtCO = Et + CO PhOCH = PhCHO + H MeSO = Me + SO2 CF,CO = CF3 + CO NFZC2H4 = NF2 + C2H4 NF2C3H6 = NF2 + C3H6 NF2C4H8 = NF2 + MeCH:CHMe 432-520 533-4513 300-523 303-353 45 3-5 39 298-43 7 3 7 3 4 2 8 334-39 1 334-39 1 Second-Order Reactions (A - mole-' C.C.C,H + M = 2Me + M 9 13-999 Et + M =C2H4 + H + A4 9 13-999 EtCO + M = Et + CO + M 303-3 5 3 Ref. 72; * R. J. Akers and J. 3. Throssell Trtrus. Ftrrtrtltrv Sot,. 1967 63. 124 J. Chem. 1966,44,2211; ref. 73 ; C.Leggett and J. C. J. Thynne Truns. Faraday SOC., L. Phillips J. Chem. SOC. (A) 1967 894; E. W. Neuvar and R. A. Mitsch J . Phys. and K. J. Laidler Canad. J. Chem. 1966,44 2927; A. Good and J. C. J. Thynne, Waring and R. Pellin J. Phys. Chem. 1967,71 2044; ref. 74; [ref. 75; ref. 52; J. Chem. 1967,45,1315; J. C. Amphlett and E. Whittle Trans. Faraday SOC. 1967,63,80; Trans. Faraday SOC. 1967.63 2480; M. F. R. Mulcahy B. G. Tucker. D. J. Williams, Chem. 1967 20 1155; A. Good and J. C. J. Thynnc Trtrtis. Furtrcltrj Soc. 1967 63, fall-off region. 'I2 M. C. Lin and M. H. Back Canad. J. Chem. 1966,44,2357; 1967,45,2115. 'I3 W. Tsang J. Chem. Phys. 1967,46,2817. l4 S. J. Band I. M. T. Davidson C. A. Lambert and I. L. Stephenson Chem. ' I 5 J. A. Connor R. N. Haszeldine G.J. Leigh and R. D. Sedgwick J. Chem 104 J . A. Kerr Temperature coefficients yielded the Arrhenius parameters for the addition reactions (24) listed in Table 11. The results for the decompositions of the ther-mally equilibrated radicals [reaction (27)] which are given in Table 12 have been deduced on the assumption of zero activation energy and an arbitrary A-factor for reaction (28). show a regular trend with the structure of the olefin : The activation energies for the addition reactions, E24 = 15.5 - 1.8 (number of alkyl substituents on double bond) By comparison with other radical additions the results indicate that the NF, radical is an electrophilic species. Thus if the addition of the radicals was at a specific carbon atom attack would occur on the most substituted carbon atom to form a o-complex.It would also be expected on this basis that Eethylene > Epropene * Ebut-Zene > Ejsobutene. Since these predictions were not confirmed it was concluded that the initial radical attack was on the double bond forming a n-complex rather than at a specific carbon atom. Support for this conclusion was taken from the fact that the pattern of reactivity of NF additions to olefins closely resembles that for oxygen atoms where a n-complex appears to be involved. The issue regarding o- or n-complexes between NF2 and olefins is not,’however so clear cut. Additional important evidence concerns the addi-tions of NF to cis- and trans-but-2-ene. The cis-isomer is found in the products of the addition of NF to trans-but-2-ene and conversely the trans-isomer is produced from NF addition to cis-but-2-ene.This is in accord with the pro-posed mechanism involving the reversible formation of the adduct radical and is good evidence in support of the mechanism. At the same time it would seem to indicate the formation of a o-complex from addition to the butenes since the isomerization would be less likely from a n-complex. The idea of relating the activation energy for a free-radical addition reaction to the localisation energy or the difference in n-energy between the adduct radical and the parent olefin has been extended76 to include addition re-actions to unsymmetrical olefins. R + CH,=CHR’ = RCH,CHR’ R + CHR’-LH = RCHR’CH, (29) (30) For such a pair of reactions the A-factors have been assumed to be equal and the activation-energy difference (E29-E,,) which is then a measure of the relative rates of addition have been compared with the differences in localisa-tion energies [E,(29) - E,(30)] calculated by a Huckel LCA0‘-MO technique.The experimental activation energies for CCl additions to fluoroethylenes,” correlate well with the calculated localisation energies and the general con-clusion has been reached that the direction of addition in these reactions is determined mainly by the relative stabilities of the adduct radicals. 3. Unimolecular Reactions.-A notable feature of unimolecular reactions 7 6 J. B. Flannery J . Phys. Chem. 1966,70 3707. 77 J. M. Tedder and J. C . Walton Trans. Faraday SOC. 1966,62 1859 TABLE 13 Unimoiecular isomerisation Reaction cis-FN NF = trans-FN NF n-c.,H = s-c,Hl CH,CCl,CH = CH,ClCCl CH, r---l I Me,CCH CHCH = Me,C CHCH CH2 Me,CCH:CMeCH = Me,C:CHCMe:CH, CH,CMe:CMeCH = CH,:CMeCMe:CH, kF,C(CF3) C(CF3)CF2 = CF C(CF3)C(CF,) CF, cis-CH CHCH CHCH,Me = cis,trans-MeCH CHCH CHMe CH CHCH CHCHMeCH CH = CH,CH CHCMe CHCH CH CH,:C:CHCH,CH,CH:CH = CH,:CHC(CH,)CH,CH:CH, I I I * In dimethyl phthalate solution; * J.Binenboym A. Burcat A. Lifshitz and J. Shamir, ref. 84; ref. 85; J. P. Chesick J. Amer. Chem. SOC. 1966,88,4800; H. M. Frey and B. D. H. Lister J. Chem. SOC. (A) 1967 26; K. W. Egger J . Amer. Chem. SOC. 1967,89,3688 106 J . A. Kerr is the increasing application of the Rice-Ramsperger-Kassel-Marcus (RRKM) theory as exemplified in the treatment of Wieder and Marcus.78 The theory is not readily explained in a short space but several summaries have been made.’l* 79 Continuing success is still being met however with the classical Rice-Ramsperger-Kassel (RRK) theory” of unimolecular reactions in cases where the information for RRKM calculations is not readily available.Isomerisation Reactions. These reactions were considered by Frey in the 1960 Annual Report and cis-trans isomerisations were reviewed in 1 964.81 Brief summaries have also appeared in the Annual Reviews of Physical Chemistry. Over the past five or six years however such a volume of work on unimolecular structural and geometric isomerisations has appeared that a separate review and assessment seems highly desirable. Unfortunately limitations of space preclude mention here of all but the most recent data which are summarised in Table 13.The first Arrhenius parameters for the thermal isomerisation of a simple alkyl radical have been determined by Endrenyi and Le Roy.8’ The activation energy 10.8 kcal. mole-’ for the isomerisation of n- to sec-pentyl is reasonable but the A-factor lo7 set.-' is abnormally low. Much of the interest in studying isomerisations of small ring compounds lies in elucidating the transition states in these reactions. While it is now generally accepted that cyclopropane and cyclobutane compounds undergo structural and geometric isomerisations via biradical intermediates,’ ‘3 86 the evidence is not conclusive in all cases. Interesting results have been reportedS3 on the isomerisation of 1,l-dichlorocyclopropane which yields 2,3-dichloro-propene.The reaction is proposed to occur via chlorine atom migration, *.q “t€g involving the intermediate H,C-CCl on the basis that the most stable biradical CCl,CH,CH, would not give the observed product. The results are quite different however for the isomerisations of fluorocyclopropanes,87 where it has been established that fluorine atom migration does not occur. Thus with 1,l-difluorocyclopropane the products were CF,=CHMe and CH,=CHCF,H.88 Biradical formation seems probable with fluorocyclo-7 8 G. M. Wieder and R. A. Marcus J . Chem. Phys. 1962,37 1835. ’’ B. S. Rabinovitch and D. W. Setser Adu. Photochem 1964 3 1. S. W. Benson ‘The Foundations of Chemical Kinetics’ Mc-Graw-Hill New York 1960.A. S. Cundal1,Progr. Reaction Kinetics 1964 3 165. L. Endrenyi and D. J. Le Roy J. Phys. Chem. 1966,70,4081. K. A. W. Parry and P. J. Robinson Chem. Comm. 1967 1083; R. Fields R. N. Haszeldine, and D. Peter ibid. p. 1081. 84 H. M. Frey B. M. Pope and R. F. Skinner Trans Faraday SOC. 1967,63 1166. 85 H. M. Frey D. C. Montague and I. D. R. Stevens Trans. Faraday SOC. 1967,,63 372. 86 D. W. Setser and B. S. Rabinovitch J . Amer. Chem. SOC. 1964 86 564; R. J. Ellis and H. M. Frey J . Chem. Soc. 1964 5578. B. Grzybowska J. H. Knox and A. F. Trotman-Dickenson J . Chem. SOC. 1963,746. F. Casas J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. 1965 1141. 8 Gus Kinetics 107 propanes. Since chlorine atom migration occurs at some stage in the isomerisa-tion and fluorine atom migration does not it may be that quite different mechanisms operate for fluoro- and chloro-compounds.The temperature- and pressure-dependence of the ’ 3C isotope-effect on the isomerisation of cyclopropane have been in~estigated.~’ At a pressure of 1 atmos. the effect can be expressed by the relation log (k12c,Jk12c,13cH 1 = -0003 + (19.1/2.3 RT). 13C isotope labelling had the same effect up02 the isomerisation as deuterium labelling and it was concluded that the isomerisa-tion involves considerable ring relaxation or in other words supports a biradical intermediate. Isotopic labelling has also been appliedg0 in the case of the isomerisation of vinyl cyclopropane to cyclopentene. With vinylcyclopropane labelled with D in the C2 ring position loss of stereospecificity was about five-times faster than isomerisation to cyclopentene.This was interpreted in terms of a biradical mechanism although the evidence was not conclusive. Frey and co-worker~~~* 85 have studied the isomerisations of cyclobutene and a variety of methylcyclobutenes to 1,3-dienes. These reactions are thought to proceed via a ‘conrotary’ mechanism in which there is rotation of the C3 and C4 atoms on the ring coupled with appreciable stretching of the C3-C4 bond. Benson and De More2’ have suggested an alternative transition state involving partial ion-pair formation. A distinct pattern of reactivity in the isomerisations of methyl-substituted cyclobutenes can now be discerned.84 The activation energy can be increased or decreased depending upon the posi-tion of methyl substitution but owing to the significant spread of A-factors the effect of methyl substitution on E is not additive.On the other hand a good correlation is achieved by comparing the effect of methyl substitution for each carbon atom in the ring on the free energy of activation (AGS) calculated from the rate constant at a fixed temperature. This is simply an alternative way of expressing the effect of substitution on the rate constant. Thus the average changes in AGS for substituting a methyl group in the 1,2 and 3 positions are 1.17,0.83 and - 1.76 kcal. mole- ’. The correlation is such that it is now possible to predict AGS and hence rate constants for the isomerisations of methyl-substituted cyclobutenes that have not yet been studied.Molecular Elimination Reactions. Recent data are summarised in Table 14. Some years ago Maccoll and Thomasg3 suggested that the mechanisms of dehydrohalogenations of alkyl chlorides and bromides in the gas-phase could involve heterolytic character. It was subsequently suggested that these gas phase reactions were somewhat analogous to SN1 or E l reactions in solution. 89 L. B. Sims and P. E. Yankwich J . Phys. Chem. 1967,71 3459. 90 M. R. Willcott and V. H. Cargle J . Amer. Chem. SOC. 1967,89 723. 91 K. A. Holbrook and A. R. W. Marsh Trans. Faraday SOC. 1967,63,643. 92 N. Capon A. Maccoll and R. A. Ross Trans. Faraday SOC. 1967,63 1152. ’’ A. Maccoll and P. J. Thomas Nature 1955 176 392 TABLE 14 Molecular elimination reactions Reaction Temp.(OK) Cyclohexa-1,3-diene = benzene + H 6 3 5 Cyclohexa- 1,Cdiene = benzene + H 603-663 1 Methylcyclohexa-l,4-diene = toluene + H 587435 3 Methylcyclohexa-1,4-diene = toluene + H 56-14 Me3CC02Et = Me3CC02H + C2H4 62-94 Me,SiCH,CH,Cl = Me,SiCl + C2H4 573-6 Et3SiCH,CH2Cl = Et,SiCl + C2H4 573-659 Me2CCH20cH2 = Me,C:CH + CH,O 673-723 Bu”OCH:CH = MeCH,CH:CH + MeCHO 590-4550 ClCOOH = HCl + CO 288-343 EtCl = CH2:CH2 + HCl 675-794 Me(CH,),CHClMe = Me(CH2)4CH CHMe + HCl 598-658 MeCH(0Et)Cl = CH,:CHOEt + HCl 4 3 7 MeCH,CHBrCH,Me = MeCH CHCH,Me + HBr 558-621 a S. W. Benson and R. Shaw J. Amer. Chem. SOC. 1967,89 5351 ; S. W. Benson and H. M. Frey and D. H. Lister J. Chem. SOC. (A) 1967 509; H. M. Frey and D. H. Cross and V. R. Stimson Austrul.J . Chem. 1967,20 177; I. M. T. Davidson M. R. g G. F. Cohoe and W. D. Waters J. Phys. Chem. 1967,78 2326; * T. 0. Barnkole and R. J. Jensen and G. C. Pirnentel J. Phys. Chem. 1967,71 1803; j ref. 91 ; li C. J. Harding, 1967 289; ’ R. L. Failes and V. R. Stirnson Austrul. J. Chem. 1967,20 1553; ref. 92 Gas Kinetics 1 09 The transition state was formulated as R R I I H X with the P-H atom playing a part analogous to that of the solvent in SN1 or El reactions in solution. This idea of a ‘quasi-heterolytic’ transition state has been extended to include other types of molecular elimination reactions and the situation has been reviewed.94 One of the most striking applications of the ‘quasi-heterolytic’ hypothesis is that the activation energy for the elimination of HX from an alkyl halide RX can be estimated from the equation E(HX) = 0*29D(R+X-) where D(R ‘X-) is the heterolytic bond-dissociation energy corresponding to the process RX = R+ + X-.Benson and B o ~ e ~ ~ have also considered the energetics of the transition state in gas-phase HX eliminations and the reverse additions of HX to olefins and have successfully calculated activation energies in terms of a ‘semi-ion pair’ model in which the double bond is partially polarised with formal charges of +* at each carbon atom and there is cor-responding parallel polarisation at H and X. The question of whether the decomposition of neopentyl chloride involves a molecularg6 or free-radicalg7 mechanism appears to have been largely resolved. By studying the reaction in a vessel from which bromides had been excluded the products of the reaction were showng8 to include (i) 2 methylbut-1-ene and (ii) 1,l-dimethylcyclopropane and 2-methylbut-2-ene.Product (i) was unaffected by the presence of added olefin whereas products (ii) were greatly reduced by the olefin. It was thus inferred that the dimethyl cyclo-propane and 2-methylbut-2-ene are formed from a free-radical split while the 2 methylbut-1-ene arises from a molecular process. Capon Maccoll and Rossg2 have made a careful study of the pyrolysis of 3-bromopentane in the presence of cyclohexene. The dehydrobromination reaction was shown to be homogeneous first-order and consistent with a molecular elimination. The free-radical chain mechanism for the pyrolysis of bromides proposed by Wojciechowski and Laidler,99 is not valid under the fully inhibited conditions.Holbrook and Marsh” have made a detailed investigation of the effect of pressure upon the elimination of HCl from EtCl. The limiting high-pressure 94 A. Maccoll and P. J. Thomas Progr. Reaction Kinetics 1967 4 119; A. Maccoll ‘Studies in 95 S. W. Benson and A. N. Bose J . Chem. Phys. 1963,39,3463. 96 A. Maccoll and E. S. Swinbourne Proc. Chem. SOC. 1960,409. 97 K. H. Anderson and S. W. Benson J . Chem. Phys. 1963,39 1673. 98 J. S. Shapiro and E. S. Swinbourne Chem. Comm. 1967,465. 99 B. W. Wojciechowski and K. J. Laidler Trans. Faraday SOC. 1963,59 369. Structure and Reactivity’ Ed. J. Ridd Methuen London 1966 110 J . A. Kerr rate constant (see Table 14) is in reasonable agreement with previous results.The pressure fall-off curves fitted those calculated from RRK theory with the number of effective oscillators taken as S = 12. Fall-off curves calculated from RRKM theory were displaced towards higher values of k/k than the experimental curves. In the later case all vibrational modes were taken to be active and the calculations were relatively insensitive to the structure of the activated complex. Other RRKM calculations on the rates of decomposi-tion of ethyl and t-butyl chlorides have suggested that not all vibrational modes are effective in intramolecular energy transfer. O0 Radical Elimination Reactions. Over the years much attention has been focussed on this type of unimolecular reaction because of its application to the determination of bond-dissociation energie~.~' It is usually assumed that E for the reverse radical-combination reaction is zero and hence E for the radical-elimination reaction can be equated with the dissociation energy of the bond broken.At one time it was thought that the A-factors for radical elimination reactions should be close to 1013 set.-' i.e. of the order of a vibrational frequency and there is sometimes a tendency for this notion to persist. In accord with transition-state theory it is now well established that the A-factors for these reactions can be several powers of ten in excess of lo1 3 particularly if two large radical fragments result from the decomposition.21 One of the most interesting developments for many years in the field of pyrolysis has been described by Benson and Spokes.'" The reactions were carried out at very low pressures (- lob6 torr.) by passing the gas through a cylindrical reaction vessel with a small exit aperture at carefully-controlled temperature and analysing the products and unreacted parent molecules in a quadrupole mass spectrometer.At the very low pressures energy transfer occurred mainly through collisions between the gas and the walls of the reaction vessel. The average number of gas-wall collisions (Z,) was determined from the ratio of internal surface-area of the reaction vessel to the area of the exit aperture. A number of reaction vessels were used with values of 2, from 90-9000. Of several reactions the decomposition Pr'I = C,H + HI has been most extensively studied.The extent of decomposition was obtained from the mass-spectral analyses of the products and reactants and kinetic equations have been derived pertaining to the low-pressure pyrolysis condi-tions from which the rate constants were obtained. It was noted from a com-parison of the observed rate constants with the known high-pressure limiting rate constants (k,) that the rate of decomposition was limited by the rate of energy transfer even in the 9000-collision reaction vessel. Good agreement was obtained between the observed rate constants and the values derived from k , by an RRK treatment involving 15 or 18 effective oscillators. The low-pressure pyrolysis method lends itself to extensive temperature variation and thus gives loo H. Heydtmann Chem. Phys. Letters 1967 1 105.S. W. Benson and G. N. Spokes J . Amer. Chem. SOC. 1967,89,2525 Gas Kinetics 111 a large range of rate constants extending well into the pressure fall-off region for many molecules. It should also prove useful in obtaining information on energy transfer with walls and added gases. In addition the products of pyrolytic reactions can be directly determined. Quantitative results on radical elimination reactions are given in Table 12. There seems at last to be some measure of agreement between the A-factors, or rate constants for the pyrolysis of ethane and those calculated from the reverse radical-recombination reaction via the equilibrium constant. For the reaction 2Me = C2H (31) the corrected pyrolysis data72 lead to log k 3 1 = 12.58 mole-' C.C.set.-' at 5 0 0 " ~ which is about a factor of six lower than the value directly determined at lower temperatures. Tsang7 has developed a competitive shock-tube method of studying pyroly-tic reactions and has reported Arrhenius parameters for a number of elementary hydrocarbon radical- elimination and other reactions. As a general rule the activation energies determined by Tsang for C-C fission in hydrocarbons have been in reasonable agreement with the bond-dissociation energies, whereas the A-factors have been 1-3 powers of ten lower than the values calculated from the entropy change for the reaction and the known or assumed rate constants for the reverse radical recombination reactions. The latest results on the shock-tube pyrolysis of 4,4'-dimethylpent-l-ene are given in Table 12.The activation energy (E = 65.5 kcal. mole-') leads to a value of ca. 9 kcal. mole-' for the allylic resonance energy based on the accepted value4' of ABF (But). There are good reasons for believing that the allylic resonance energy is nearer to 13 kcal. mole-' which implies that E for the pyrolysis of 4,4'-dimethylpent-l-ene has been overestimated. If this is the case the reported A-factor is also high and hence the divergence between the A-factor of the decomposition reaction and that estimated from the reverse re-combination reaction is even greater than suggested. There seems no prospect of reconciling the A-factors for the shock-tube pyrolyses of hydrocarbons with the A-factors for radical recombination reactions. Two determinations of the rate constant for the pyrolysis of hexamethyl-disilane have been reported.74* Haszel'dine and ~ o - w o r k e r s ~ ~ have studied the reaction in a flow system at pressures less than torr by measuring the rate of disappearance of the disilane mass-spectrometrically.The mechanism d the reaction was by no means established however and a range of Arrhenius parameters was determined as given in Table 12. A-factors as low as 10" sec. - for this type of process are quite incompatible with transition-state theory and furthermore at the low pressures of the experiments it is possible that the reaction was in the pressure fall-off region. For these reasons the value of D[(Me),Si-Si(Me),] reported by Haszeldine and co-workers would seem to be a gross underestimate and the results of Davidson et al.74 are much to be preferred 11 2 J .A. Kerr Activated Molecule Reactions. For the present purposes activated molecules are considered to be in their electronic ground-states but contain excess vibrational energy over and above that due to their ambient temperature. Such molecules are most conveniently produced by exothermic chemical reactions, or by dissociation of a molecule following the absorption of a quantum of light. The general features of chemically-activated molecules have been described by Rabinovitch and Flowers,lo2 and Rabinovitch and S e t ~ e r ~ ~ have sum-marised recent data on the unimolecular decompositions of activated alkanes and alkyl radicals. Activated molecules formed by the reaction of CH with olefins have also been discussed.' O3 Emphasis has subsequently switched to studying molecular elimination reactions from chemically-activated alkyl chlorides and fluorides.So far three methods of forming chemically-activated alkyl halides have been studied. The combination of alkyl radicals gives rise to activated molecules containing excess energy equivalent to the C-C bond dissociation energy i.e. in the range 85-90 kcal. mole-' : Me + CH,CF,H =EtCF,H* Me + CH,Cl =EtCI* The fluoroalkyl radicals can be produced from the photolysis of the correspond-ing or from the reaction of CH radicals from ketene or diazo-methane with a f l u ~ r o a l k a n e ' ~ ~ CH + MeCF,H = Me + CH2CF2H Chloroalkyl radicals are produced from the CH reaction with chloroalkanes,'06 CH + MeCl = Me + CH,C1 Alkyl fluorides of much higher energy-content can be generated by the insertion of singlet CH (photolysis of ketene in the presence of 0,) into C-H bonds of fluor~alkanes,'~~* ' 0 5 CH + MeF = EtF* Here the excess energy in the EtF* is estimated to be 115 kcal.mole-'. Activated ethyl fluoride has also been formed by the reaction Et + F2 = EtF* +F which occurs when fluorine is reacted with ethane. '04 The enthalpy change of reaction (32) is 69 kcal. mole-' and it has been argued that this mostly resides in the ethyl fluoride. B. S. Rabinovitch and M. C. Flowers Quart. Rev. 1964 18 122. H. M. Frey Progr. Reaction Kinetics 1964 2 131 ; H. M. Frey in 'Carbene Chemistry' by J. A. Kerr A. W. Kirk B. V. O'Grady and A. F. Trotman-Dickenson Chem.Comm. 1967,365. J. C. Hassler D. W. Setser and R. L. Johnson J . Chem. Phys. 1966,45 3231; J. C. Hassler and D. W. Setser ibid. pp. 3237 3246; D. W. Setser and J. C. Hassler J . Phys. Chem. 1967 71, W. Kirmse Academic Press London 1964 p. 2 17. lo' J. A. Kerr B. V. O'Grady and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1966 1621. 1364 Gas Kinetics 113 TABLE 15 Elimination of hydrogen halides @om activated alkyl halides at room temperature Alkyl Halide System kelk (cm.) EtF MeCHF, CH,FCH,F MeCF, CF,HCF2H EtCF,H EtCF,H MeCF,Me MeCF,Me EtCl CH,C1CH2C1 MeCHCl, CHCl ,CH ,C1 Fluorides CH + MeF Me + CH,F Me + CH,F Et + F2 CH + CHZF, Me + CHF, 2CH,F 2CH,F Me + CF3 2CF,H Me + CH2CF2H* CH + MeCF,H Me + CF,Me* CH + MeCF,H Chlorides Me + CH2C1* Me + CH2C1* Me + CH2Cl* 2CH2C1* 2CH2C1* Me + CHC12* CHCl + CH2C1* CHCl + CH2C1* 351a 14" 7tb 0.07" N 10C.d 5.t' 2f.s 5 b - 1.4h v.low' < 0.47' 1.24' <4*1" 19' 2 9 27Tj 28ti 1.8' 1.6t' 2.2' 3.51' 116i * Radicals produced from abstraction by CH,; t results obtained under different conditions of M from other results for same molecule; Ref. 104; * G. 0. Pritchard and R. L. Thommarson J . Phys. Chem 1967,71 1674; ref. 105; ref. 107; ref. 34; re6 108; ref. 109; W. G. Alcock and E. Whittle Trans. Faraday SOC. 1965 61, 244; R. D. Giles and E. Whittle $id. p. 1425; G. 0. Pritchard and J. T. Bryant, J . Phys. Chem. 1965,69 1085; j ref. 106. Since theenergy contents ofthealkyl halides produced by these three methods, are considerably in excess of the activation energies for the dehydrohalo-genation reaction the molecules react in this way unless collisionally deacti-vated : EtX* -+ CH2=CH + HX (e) lo' G.0. Pritchard J. T. Bryant and R. L. Thommarson J. Phys. Chem. 1965,69,2804. lo' G. 0. Pritchard M. Venugopalan and T. F. Graham J. Phys. Chem. 1964,68,1786. lo9 S . W. Benson and G. Haugen J. Phys. Chem. 1965,69 3898 114 J . A. Kerr EtX*+ M - Etx + M A steady state treatment yields the expression REt X I R C Z H 4 = (ks/ke)CMl and thus k$k can be determined by plotting the ratio of alkyl halide to olefin, i.e. stabilisation to elimination products against the concentration or pressure. Some allowance ,is usually made for the variations in collisional efficiencies of different moecules in the system.Since k,/k is given by (alkyl halide/olefin) (l/[M]) it is convenient to express the ratio in pressure units and a summary of results for eliminations from various activated alkyl halides is given in Table 15. It follows from this convention that the k,/k values denote the pressure at which k = k,. Benson and Haugenlo9 have interpreted the results'08 on the reactions of activated alkyl fluorides from the combination of radicals in terms of RRK theory. The rate constant of the elimination is related to the energy content ( E ) of the molecule by the equation : k = A [ ( E - E,)/E]"-' where A and E are the Arrhenius parameters for the thermal-elimination re-action and n is the number of effective oscillators.On the assumption that stabilisation occurs in a single collision the rate constant can be expressed as k = Z where Z is the number of collisions and the probability of complete deactiva-tion on collision is assumed to be unity. It follows that ks/ke = Z / A . ( E / E - E,)"-l Owing to experimental difficulties values of E for the thermal elimination of HF from alkyl halides have not been measured and hence the above rela-tions can be applied to obtain E from the data on the activated alkyl fluorides. Benson and Haugen"' have shown that the energy content ( E ) at different temperatures can be calculated from the equation E = E + ACg'b(T- 298) where E is the energy change on the recombination of the radicals taken to be 85.4 kcal. mole- at 2 9 8 " ~ for fluoralkyl radicals and ACVb is the difference in vibrational specific heat of the two radicals and the activated molecule.The A-factor of the HF elimination reaction is assumed to be 1013*5 set.-' in line with other HX eliminations from alkyl halides and the number of effective oscillators n is usually taken to be two-thirds of the total number of vibrational modes or it can be estimated by comparison with similar rea~ti0ns.l'~ For one particular type of activated molecule formed say from the combination of radicals k,/k is measured over a range of temperatures and the results are interpreted in terms of a plot (see Figure). Theoretical values of k,/k, calculated from Z / A . ( E / E - I?,)"- ' are plotted against temperature resulting in a serie Gas Kinetics 115 of lines one for each of the selected values of E,.By comparing the experimental values of k$k, from plots of halide/olefin versus P with the theoretical lines it is possible to select the value of E which gives the best fit. Benson and Haugen'" and Pritchard and c o - ~ o r k e r s ~ ~ have thus deduced activation energies for HF elimination from alkyl fluorides in the range 5 3 - 6 2 kcal. mole-'. -0.8, 54 53 \ 52 \ 51 '0 -28 300 i 400 5 0 0 6 0 0 700 T O K FIGURE Results for reactions CH2FCH2F* + M + CH2FCH2F + M (s) and CH2FCH2F* + CH2=CHF + HF ( e ) re$ 110). Lines are calculated from log (kJk,) = log (Z/A. (E/E-EJ- ' ) f o r activation energies (E,) between 49 and 54 kcal. mole-' assuming A = set.-' n = 14 and E29 = 85.4 kcal.mole-'. Experimental pointsfrom log (k,/k,) = log ((l/P) (CH2FCH2F/CH2=CHF)} open circles ref 110 filled circles ref 108. An alternative approach involves measuring k,/k values at room tempera-ture for a chemically-activated alkyl fluoride with different energy contents, formed by the three previously described methods. The RRK equation can again be applied to determine which value of E gives the best agreement between calculated and observed kJk; values with assumed values of A and n and estimated values of the different energy contents E. In this way the acti-vation energy for the elimination of HF from EtF has been c a l ~ u l a t e d ' ~ ~ to be 51 kcal. mole-' which is considerably lower than the other estimates. It has been pointed out however that the use of the non-quantised RRK model for a unimolecular reaction leads to an underestimate of E,.Subsequent treatment of more extensive data'" according to the RRKM theory supports a value of 110 J A. Kerr A. W. Kirk B. 1'. O'Grady D. C. Phillips and A. F. Trotman-Dickenson Discuss. Faraday SOC. 1967,44,263 116 J . A. Kerr about 60 kcal. mole-' for HF elimination from alkyl fluorides which is in agreement with the value predicted by the quasi-heterolytic approach.'" The formation of vibrationally-excited molecules by photochemical reac-tions offers some advantages over the chemical-activation approach in that the range of energies is more controllable and.may be more extensive. Thomas, Sutin and Steel112 have carried out an elegant study of the distribution and exchange of vibrational energy in the products of the photolysis of 2,3-diazo-bicyclo[2.2.l]hept-2-ene (I) The primary photochemical split gives activated bicyclo[2.1.O]pentane (11) which can either be collisionally stabilised or rearranges to cyclopentene and penta-1,4-diene.The effects of wavelength pressure and added gases on the relative yields of the hydrocarbon products have been studied in detail. The energy-dependence of the rate constants for the reactions of the activated molecule (11) as determined by wavelength variations were treated success-fully by RRK theory. It was further deduced that the activated molecules were produced with a distribution of energies having a standard deviation of 6-7 kcal. and in consequence the photochemical production of activated molecules may not prove to be a very sensitive test of theories of unimolecular reactions.4. Molecule-molecule Reactions.-There are two general types of reaction, addition and transfer. Addition reactions are the reverse of molecule-elimina-tion reactions e.g. Olefin + HX = RX Since the equilibrium constants tend to favour the elimination reactions, addition reactions are not easy to study although Benson and his collabora-tors,21,113 have made a systematic study of the additions of HI to olefins. Transfer or disproportionation reactions of molecules e.g. 2C2H4 = Et + C2H3 are equally difficult to study being the reverse of radical-radical reactions and highly endothermic. It has become increasingly apparent that molecule-molecule transfer reactions can be important in the initiation of complex high-temperature pyrolyses.'I4 Recent data on molecule-molecule and misiellaneous radical-molecule reactions are given in Table 16. Benson1'6 has made a kinetic analysis of the Diels-Alder reactions of buta-'I1 A. Maccoll Discuss. Faraday SOC. 1967,44,274. Ii2 T. F. Thomas C. I. Sutin and C. Steel J . Amer. Chem. SOC. 1967,89 5107. 'I3 K. W. k g e r and S. W. Benson J . Phys. Chem. 1967,71,1933. S. W. Benson and G. R. Haugen J . Phys. Chem. 1967,71,1735. R. M. Marshall J. H. Purnell and B. C. Shurlock Canud. J . Chem. 1966,44 2778. 116 S. W. Benson J . Chem. Phys. 1967,46,4920 TABLE 16 M olecule-molecule and miscellaneous Reaction Temp log ( O K ) (mole-sec. CO + NO = C 0 2 + NO COCl + NO = C 0 2 + NO + C1 0 + 2N0 = 2N02 HNO + HNO = N20 + H 2 0 SO + NO2 = SO3 + NO SO + 0 = SO2 + O2 MeCHO + NO = MeCO + HNO, CH CHOEt + HCI = MeCH(0Et)Cl Pr‘OH + HI = C3H + H,O + HI trans-but-2-ene + HI = BuI but-1-ene + HI = BuI pent-1-ene + HI = C5H,,I penta-1,4-diene + HI = C5H91 penta-1,3-diene + HI = C5H91 666-746 666-746 478 298 298 223-300 3 8 3 4 5 3 4 3 7 4 9 4 3 5 6 4 5 7 46 1 483 46 1 4 2 1 4 6 1 432 9.5 12.7 * Units mole-’ c.c.’ sec-’; t estimated A-factor; * J.H. Thomas and G. R. Woodman, J. Morecroft and J. H. Thomas J . Phys. Chem. 1967,71 1543; F. C. Kohout and F. A. A. Clyne C. J. Halstead and B. A. Thrush Proc. Roy. SOC. 1966 A 295 355; C. M. I. Christie and M. A. Voisey Trans Faraday SOC. 1967 63 2702; f R. L. Failes 1553; @ R.L. Failes and V. R. Stimson Austral. J. Chem. 1967,20 1143; ’ ref. 113 118 J. A. Kerr diene. It is proposed that the reactions involve a common biradical intermediate and the following competing systems have been considered The results of the kinetic analysis are consistent with independent studies of the rates of individual reactions in the above scheme (i) the pyrolysis of cyclo-octa-l$diene to 4-vinyl cyclohexene and butadiene (ii) the dimerization of butadiene to 4-vinyl cyclohexene (iii) the reverse pyrolysis of 4-vinyl cyclo-hexene to butadiene and (iv) the reaction of 1,4-divinyl cyclobutane in solution to give 4-vinyl cyclohexene cyclo-octa-1,5-diene and lesser amounts of butadiene. Benson's treatment of the data is based on steady-state approxi-mations and the application of thermodynamics to kinetics.Equilibrium constants and rate constants are derived from the thermodynamic expression : log K = log (kf,/k,) = AS12.3 R - AH12.3 RT Where experimental enthalpies and entropies are not available or are con-sidered to be unreliable they are calculated by the group-additivity method,' l7 which is estimated to give A H f to f 1 kcal. mole- ' and So and Ci to f 1 cal. mole-' deg-'. For the reaction scheme or mechanism to be considered valid, there should be good agreement between the observed rate constants and those calculated from the equilibrium constants. 5. Biradicals and Related Species.-The most studied biradical is methylene, CH, and although its reactions and properties are well d o ~ u m e n t e d ' ~ ~ ~ '18 several recent papers have considerably clarified and extended our knowledge.It has been accepted for some time that the ground state of CH is the triplet state (3E,) and that there is a low-lying singlet state ('Al). The commonest sources of CH are the photolyses of ketene (CH,CO) and diazomethane (CH,N,) and it now appears that both give rise to mixtures of 3(CH2) and '(CH,). As a general rule the proportion of '(CH,) increases as the wavelength of the photolysis is decreased and there have been many attempts to determine the exact proportions of '(CH,) and 3(CH,) for given conditions of photolysis. 'Chemical' evidence for the existence of '(CH,) came from a study of the stereo-chemistry of the CH addition reactions to cis- and trans-butene,"9 where it was argued that the stereospecific additions were due to '(CH,) adding across 11' S.W. Benson and J. H. Buss J . Chem. Phys. 1958,29 546. I t * W. B. De More and S. W. Benson Adu. Photochern. 1964 2,219. P. S. Skell and R. C. Woodworth J . Amer. Chem. Soc. 1956 78 4496; R. C. Woodworth and P. S. Skell ibid. 1959,81 3383 Gas Kinetics 119 the double bond in a concerted manner without formation of an intermediate biradical. The additions of 3(CH2) on the other hand have been shown to be non-stereospecific presumedfo arise from the formation of a biradical with rotation around the original double bond.',' It should be pointed out that Benson and De More2' have put an entirely different interpretation on the above experiments based on the different energy contents of '(CH,) and 3(CH2), although the original interpretations are still widely accepted.The reactions of CH with CO',' and with C3H,"2 have both been studied to determine the proportions of '(CH,) and 3(CH,) from the photolysis of CH,CO but the most encouraging results have been derived from the reactions of CHT with C2H4.123 The CHT biradicals were generated from the 3120 A photolysis of CHTCO in the presence of C2H4 with and without added oxygen and over ranges of pressure. From the analysis of the [3H]cyclopro-pane and the C3H]propene it was deduced that the following reactions occurred with the percentages of 3(CHT) and '(CHT) as shown: '(CHT)(17%) + CH2=CH2 = CH2TCH=CH2 CHT / \ '(CHT)(54%) + CH2=CH = CH,-CH, 3(CHTX29%) + CH,=CH2 = CH,-CH2 There was also subsequent isomerisation of the [3H]cyclopropane to [3H] propene.In these as in other experiments use was made of the fact that oxygen suppresses the formation of products from 3(CH,) reactions thereby making it possible to study the '(CH,) reactions alone. NO has been used for the same purpose.' 24 '(CH,) radicals react with alkanes mainly by insertion reactions : '(CH,} + MeCH,Me = MeCH,CH,Me MeCHMe, and it has now been shown that the insertion occurs indiscriminately the rates for primary secondary and tertiary C-H bonds being equal for '(CH,) produced from CH2C0'24 115 and from CH2N2.125 3(CH,) radicals react with alkanes mainly by abstracting hydrogen atoms : 3(CH2) + MeCH,Me = Me + MeCHMe lZo F. A. L. Anet R. F. Bader and A. M. Van der Auwera J.Amer. Chem. SOC. 1960,82 3217; H. M. Frey ibid. p. 5947. B. A. De Graff and G. B. Kistiakowsky J. Phys. Chem. 1967.71 1553. 12' Shih-Yeng Ho and W. A. Noyes J. Amer. Chem. SOC. 1967,89 5091. lZ3 C. McKnight E. K. C. Lee and F. S. Rowland J. Amer. Chem. SOC. 1967,89 469. lZ4 M. L. Halberstadt and J. R. McNesby J. Amer. Chem. SOC. 1967,89 3417. 12' R. W. Carr J. Phys. Chem. 1966,70 1970; B. M. Herzog and R. W. Carr ibid. 1967,71 2688; G. Z. Whitten and B. S. Rabinovitch. ihid 1965 69. 4348 120 J. A. Kerr and while there is no data on the relative reactivities of C-H bonds the usual order of reactivities tertiary > secondary > primary appears to prevail. Both 3(CH,) and '(CH,) add to olefins to give activated cyclopropanes. As previously mentioned the additions of 3(CH,) are believed to proceed via the formation of biradical intermediates and a recent study of the addition of 3(CD,) (from the mercury-photosensitised decomposition of CD,CO) has confirmed this mechanism and further revealed that there is some decomposition of the trimethylene biradical to give ally1 radicals.' 26 Krzyzanowski and CvetanoviC' 2 7 have determined the relative rates of reaction of 3(CH,) (mercury-photosensitised decomposition of CH,CO) and '(CH,) (direct photolysis of CH2C0 at 2660 A) with a series of olefins at room temperature.With 3(CH,) the rate of the principal reaction of addition to give the cyclopropanes depends relatively little on the structure of the olefin, although the addition to butadiene was somewhat faster than to mono-olefins.The additions of '(CH,) to olefins were complicated mainly by insertion but when this was taken into account the relative rates of addition were again essentially equal throughout the olefin series. CH from the photolysis of CH2C0 has been shown to react with MeCl by abstraction,'06' 128 while CH from CH,N2 is believed to react with SiH4 both by abstraction and insertion.'" It was not entirely clear from these systems whether 3(CH,) or '(CH,) was taking part in the reactions. The above summary of the reactions of CH is intended to describe the broad features of the radical although it undoubtedly presents an over-simplified picture. Rate constants for the reactions of methylidene CH with CH, H, and N2 have been determined by flash photolysis of CH4 with vacuum U.V.radiation.' 30 The concentrations of CH radicals were determined by kinetic spectroscopy involving the absorption by CH at 3143 A. From the product analyses and kinetics of the reactions it is proposed that CH radicals react by insertion reactions : CH -!- H,=Me CH + CH4 = C2H4 + H with rate constants of 1.5 x 10' and 6.2 x 10' ' mole- ' C.C. set.- ' respectively. Carbonyl carbene (CCO) has been generated from the photolysis of carbon suboxide (C302) and shown to react with olefins to yield allenes and lesser amounts of alkynes. ' '- ' With ethylene the products are allene and propyne : R. J. CvetanoviC H. E. Avery and R. S. Irwin J . Chem. Phys. 1967,46 1993. lZ7 S. Krzyzanowski and R. J. CvetanoviC Canad. J . Chem. 1967,45 665.lZ8 R. S. B. Johnstone and R. P. Wayne Photochem. and Photobiol. 1967 6 531. l Z 9 J. W. Simons and C. J. Mazac Canad. J . Chem. 1967,45 1717. 13' W. Braun J. R. McNesby and A. M. Bass J . Chem Phys. 1967,46,2071. lJ1 K. D. Bayes J . Amer. Chem. SOC. 1961,83 3712; 1962,84,4077; 1963,85 1730. 132 R. T. K. Baker J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1966,975; 1967, 1641 Gas Kinetics 121 CCO + C2H4 = C H 2 X X H 2 + CO = M e C d H + CO so that CCO radicals function effectively as carbon atoms. The relative rates of reaction of CCO radicals with a series of methyl-substituted ethylenes have been determined by Baker Kerr and Trotman-Dickenson 132 by comparison with the reaction: CCO + C302 = polymer + CO These results showed that methyl substitution on the double bound reduced the reactivity of the alkene regularly.Willis and Bayes', have found exactly the opposite effect for CCO adding to methyl-substituted ethylenes using a different method based on comparisons of the efficiency of oxygen quenching of the allene yields. A major discrepancy obviously exists and until it is resolved the effect of olefin structure on the reactivity of CCO is uncertain. 6. Theory.-Aromic Recombinations. The question of non-attainment of a Boltzmann distribution of energy states in atomic recombination and diatomic-dissociation reactions has received further theoretical consideration. ' 34 For the general system A + A + M $ A + M k d it has been demonstrated that provided the concentration of atoms is small it is valid to apply the phenomenological equation dn,,/dt = -&dn,/dt) = -kdnA2nM + k,nA 2nM which implies an equilibrium distribution of internal states.It appears that all the systems so far studied have sufficiently low concentrations of atoms to fulfil this condition. The temperature-dependence of the rate of termolecular atomic-recombina-tion reactions has been calculated on the basis of the 'radical-molecule complex mechanism' ' A + M + A M (33) A M + A + A 2 + M (34) The equilibrium constant K,, was calculated assuming a Lennard-Jones (12-6) potential between A and M and the rate of reaction (34) was calculated from the collision rate between A and AM. For the reaction I + I + Ar = I2 $- Ar (35) the rate constant was deduced to be log k, = 14.5 + 1400/2.3RTmole-2 C.C.sec. - ' in good agreement with experimental values. 1 3 3 C. Willis and K. D. Bayes J . Amer. Chem. SOC. 1966 88 3203; C. Wiliis and K. D. Bayes, 134 N. S. Snider J . Chem. Phys. 1966,45 3299. 13' Shoon Kyung Kim J . Chem. Phys. 1967,46 123. J . Phys. Chem. 1967,71 3367 122 J . A. Kerr Unimolecular Reactions. O’Neal and B e n ~ o n l ~ ~ have described a method for estimating A-factors for four- and six-centre unimolecular reactions based on transition state theory: A = (ekT/h) exp(ASz/R) The problem is to calculate ASz the entropy of activation. For a unimolecular reaction contributions to ASz arise from changes in the vibrational frequencies, internal rotations and from symmetry changes. In forming the transition-state transitional entropy is unchanged rotational entropy changes are small, and it is assumed that there is no change in electronic degeneracy.By drawing up rules for assigning bending stretching and torsional frequencies A-factors have been calculated with an estimated uncertainty of +O-3 in log A(sec.-’). It was deduced that the most important factors in determining AS$ are the losses in hindered internal rotations in forming the cyclic transition states which are ‘looser’ than the analogous cyclic compounds. A-factors have been calculated for a large number of unimolecular reactions and good agree-ment obtained with experimental values. Experimental A-factors for four- and six-centre unimolecular reactions can now be examined for ‘reasonableness’ by comparison with the values calculated by the application of the empirical rules to transition-state theory.The problems of intermolecular and intramolecular energy transfer in unimolecular reactions have been considered. Current theories of thermal unimolecular reactions have overcome the difficulty of inefficient intermolecular internal-energy transfer either (i) by making the Lindemann strong-collision assumption that all inelastic collisions of the activated molecules lead to deacti-vation or (ii) by making the equilibrium-assumption that the distribution of states with insufficient energy to react is given by the equilibrium Boltzmann distribution at ambient temperature. Tardy and Rabin~vitch’~ have made calculations based on a number of different models for deactivation to test these assumptions in the second-order pressure region for five simple uni-molecular reaction systems.Intramolecular energy-flow is a necessary postulate of the RRK theory of unimolecular reactions whereas in Slater’s model vibrations are assumed to be strictly harmonic and there is no transfer between them. solc has extended Slater’s theory by considering the effect on the unimolecular rate constant of allowing rapid intramolecular-energy transfer between some of the normal vibrational modes of the m01ecule.l~~ Theories of unimolecular reactions usually make the assumption that the time scale for reaction is controlled by vibrational processes and that other degrees of freedom reach a rapid equilibrium. In the RRKM theory since the H. E. O’Neal and S.W. Benson J. Phys. Chem. 1967,71,2903. 13’ D. C. Tardy and B. S. Rabinovitch J . Chem. Phys. 1966 45 3720. B. S. Rabinovitch D. C. 138 M. solc Mol. Phys. 1966 11 579; 1967 12 101; M. solc Chem. Phys. Letters 1967 1 160; Tardy and Y. N. Lin J . Phys. Chem. 1967,71 1549. N. B. Slater Mol. Phys. 1967 12 107 Gas Kinetics 123 reaction time is long compared with the time to reach vibrational equilibrium, the reaction is considered as being only a function of the total vibrational energy so that the total unimolecular rate constant has a simple additive con-tribution from all the initial vibration states. Valence and Schlag have now derived a theoretical rate constant for thermal unimolecular reactions in a multi-quantum-level system. 13' It has been shown that the unimolecular rate constant is the lowest eigenvalue of a relaxation matrix that describes all microscopic processes occurring in the reaction system. In a second paper the eigenvalue problem has been solved without the usual assumption of uni-molecular reaction-rate theory that there is an equilibrium distribution of non reactive states. BimoZecuZar Reactions. These will be only briefly mentioned since there have been several comprehensive reviews.140 Theoreticians in this field have received a considerable stimulus from the detailed information on the molecular dynamics of bimolecular processes that has been obtained from molecular-beam studies. Light and co-worker~'~' have developed a statistical or phase-space theory of chemical reactions which was initially applied to ion-molecule reactions re-quiri'ng no activation energy e.g. A+ + BC = AB' + C A + BC+ = AB+ + C Each reaction path was allotted a probability proportional to the amount of phase-space available to it. The theory has subsequently been extended to three-body reactions with activation energies. For systems such as K + HBr, H + C12 and H + HX (X = C1 Br and I) excellent agreement has been ob-tained between calculated and experimental rate constants reaction cross-sections isotope ratios and product excitations. The theory of chemical-reaction cross-sections as applied to molecular-beam studies has been extended by Marcus.142 A statistical-dynamical model has been formulated for total chemical-reaction cross-section as a function of the relative velocity and the vibrational and rotational state of the reactants. The model has been applied to the H + H2 reaction and the reaction cross-sections shown to agree reasonably well with those derived from three-dimen-sional classical-mechanical computer calculations. Marcus has also considered the analytical mechanics of chemical reactions dealing with both the classical and quantum mechanics of linear collision^.'^^ 139 W. G. Valence and E. W. Schlag J . Chem. Phys. 1966,445,216; 1966,45,4280. 140 K. J. Laidler and J. C. Polanyi Progr. Reaction Kinetics 1965,3 1 ; D. L. Bunker 'Theory of Elementary Gas Reaction Rates' (Internation-a1 Encyclopaedia of Physical Chemistry and Chemical Physics Topic 19 Vol. 1) Pergamon Press New York 1966; J. Ross ed. Adv. Chem. Phys. 1966 10, J. Lin and J. Light J . Chem. Phys. 1966,45,2545; and references therein. 142 R A. Marcus J . Chem Phys. 19645,2630; 1967,46,959. 143 R. A. Marcus J . Chem Phys. 1966,45,4493,4500.