addition of toluene and ethylbenzene to mixtures of h2 and o2 at 772 k: part 2: formation of...

Addition of toluene and ethylbenzene to mixtures of H2

and O2 at 772 K: Part 2: Formation of products anddetermination of kinetic data for H� additive and for

other elementary reactions involved

Colin Ellis, Michael S. Scott, Raymond W. Walker*Chemistry Department, Hull University, Hull HU6 7RX East Yorkshire, UK

Received 13 May 2002; received in revised form 19 July 2002; accepted 26 July 2002

Abstract

A detailed product analysis was carried out at 773 K when toluene (TOL) and ethylbenzene (EB) were addedseparately in small amounts to H2 � O2 � N2 mixtures at 500 Torr total pressure. Benzaldehyde is the majorinitial product from TOL, formed in reaction (26) and in the overall reaction (31).

C6H5CH2 � HO23 OH � C6H5CH2O (� O23 C6H5CHO) (26)

C6H5CH2 � O23 C6H5CHO � OH (31)

The electron-delocalised benzyl radical reacts very slowly with O2, and the importance of radical-radicalreactions is confirmed by the observation that bibenzyl is formed in relatively high yields.

Values of k26 � (5.1 � 1.5) � 109 dm3 mol�1 s�1 and k29 � 2.8 � 103 s�1 (for the 1,3 Hatom transferinvolved in (31)) are obtained.

C6H5CH2OO3 C6H5CHOOH (29)

Styrene is the major initial product from EB. The electron-localised radical C6H5CH2CH2 reacts almostcompletely in a fast reaction (k � 2 � 108 dm3 mol�1 s�1) with O2 to give styrene, but the more stableelectron-delocalised C6H5CHCH3 radicals also undergo radical-radical reactions to give benzaldehyde with k38 �(7.3 � 3.0) � 109 dm3 mol�1 s�1.

C6H5CHCH3 � HO23 C6H5CH(OOH)CH3 (38)

Measurements of the yields of benzene from TOL and EB gave rate constants for the reaction H � TOL/EB3C6H6 � CH3/C2H5, and combination with independent data gives k � 950T2exp(�475) dm3 mol�1 s�1 for the TOLreaction. Rate expressions are given in non-Arrhenius form for all H abstractions by H atoms from TOL and EB.Further evidence is provided that H abstraction from the �-carbon atom in alkyl benzenes is considerably slowerthan expected on thermochemical grounds. It is, however, concluded that abstraction from the benzene ring byH atoms is significantly more important than hitherto suggested. © 2003 The Combustion Institute. All rights reserved.

Keywords: aromatic oxidation, kinetics, mechanism

1. Introduction

In Part 1 [1], attention was focussed on the deter-mination of kinetic data for the reactions of H and

* Corresponding author. Tel.: �01482-465549; fax:�01482-466410.

E-mail address: [email protected] (R.W. Walker).

Combustion and Flame 132 (2003) 291–304

0010-2180/03/$ – see front matter © 2003 The Combustion Institute. All rights reserved.doi:10.1016/S0010-2180(02)00439-X

HO2 radicals with toluene (TOL) and ethylbenzene(EB); very few of the data having been previouslydetermined experimentally. In particular, a databasewas established for H abstraction reactions by HO2

radicals from aromatics, alkanes, alkenes and relatedcompounds. In Part 2, the results of detailed productanalysis are reported, a number of mechanistic fea-tures elucidated, and rate constants determined for anumber of important elementary reactions. Unlikemany studies where attempts are made to model thewhole reaction through to the final products, hereconditions and experiments are selected to facilitate arelatively simple interpretation of the results. Twokey features of the additive approach merit emphasis.

The radical environment is controlled almostentirely by the H2 � O2 mixture, providingvery small amounts of additive are used;here the concentration is typically 1–2 Torrof additive in 70–360 Torr of O2 and 140–430 Torr of H2.

Attention is focussed most strongly on theinitial stages of reaction, in terms of bothproduct analysis and interpretation of thedata. The radical environment and relativeradical concentrations remain effectivelyconstant and the consumption of any inter-mediate is minimal, as may be confirmed byadding the intermediate with the confidencethat the radical environment is unchanged.

Barnard and Ibberson [2] reported in 1965 that therewas little detailed information on the homogeneous ox-idation products of TOL, and their study between 733and 788 K contributed significantly to establishing mostof the major products and the basic mechanism of ox-idation. However, a very important feature of theirproduct profiles was that CO and CO2 were formed inalmost equal amounts in the early stages of reaction,with the relative yield of CO2 falling as the temperatureincreased. These observations are common features ofoxidations where surface effects are prominent. An in-teresting aspect of their product analysis, although notdiscussed, was the product ratio [benzene]/[H2] � 2 at759 K. In the early stages, reactions (22ta) and (22tm)are the only plausible major sources of these com-pounds, so that k22ta � 2k22tm; these two reactions willbe discussed later in the context of the present work.

H � C6H5CH33 [adduct]3 C6H6 � CH3 (22ta)

H � C6H5CH33 H2 � C6H5CH2 (22tm)

Benzaldehyde was the only other major initial prod-uct reported by Barnard and Ibberson. It is also a majorproduct when TOL is oxidised in the range 1000–1200K [3,4], and it is generally accepted that reactions of thebenzyl radical with O, OH and HO2 radicals are the

main source at high temperatures. There is also a con-sensus view that initial attack occurs largely at the CH3

group, although O atom addition to the ring, H atomaddition to the carbon atom attached to the CH3 group,and H-abstraction by OH radicals from the ring prob-ably contribute about 40% to the overall consumptionof TOL at temperatures in excess of 1000 K.

Radical-radical reactions are important in the con-sumption of benzyl radicals because unlike most al-kyl radicals and many aromatic radicals, where theodd electron is localised on the side group, the benzylradical has no easy reaction with O2 to give a conju-gate alkene and the HO2 radical [5], for example C2H4

from C2H5 and C6H5CH¢CH2 from C6H5CH2CH2.Further, the benzyl radical has no facile homolysis re-actions. In these respects, the benzyl radical has much incommon with the CH3 radical the oxidation chemistryof which is deeply influenced by radical-radical reac-tions at almost all temperatures. Consequently, even invery oxygen-rich environments between 600 and 1000K, relatively high yields of the recombination productC2H6 are found [6], together with high yields of CH4

formed from CH3 radicals by H-abstraction [6,7]. Habstraction by benzyl radicals is normally uncompeti-tive because of their enhanced stability due to elec-tron-delocalisation. In consequence radical-radicalrecombination to give 1,2-diphenylethane (bibenzyl)is likely, and this product has been observed in sig-nificant yield in the initial stages of the oxidation ofTOL between 1000 and 1200 K [3,4].

Although the oxidation of ethylbenzene has re-ceived considerably less attention, Litzinger et al. [8]carried out a detailed study at 1060 K. Not surpris-ingly, styrene was the major initial product togetherwith high yields of benzene, C2H4, CH4, benzalde-hyde and acetylene. A number of other unsaturatedcompounds and CO, undoubtedly formed from thebreakdown of the benzene ring, were also observed.Of particular significance, no 2,3-di-phenylbutane wasreported in the products, and this is fully understandablebecause both C6H5CH2CH2 (very rapid) andC6H5CHCH3 (relatively rapid) radicals have fast re-actions with O2 to give the conjugate alkene, styrene.

2. Experimental

The apparatus and general procedure are extremelywell established [9]. Absolute pressures and pressuredifferences were measured by use of a transducer capa-ble of better than 1% accuracy down to 0.01 Torr.Concentrations of reactants and products were mea-sured by gas chromatography, using a flame ionizationdetector for organic species and a helium ionizationdetector for CO and CO2. Very careful attention waspaid to good peak resolution to ensure a high level of

292 C. Ellis et al. / Combustion and Flame 132 (2003) 291–304

precision in measurements of concentration. Productswere identified by retention times and by gc-ms.Formaldehyde was measured colorimetrically. No anal-ysis was made for H2O or peroxides; H2O2 is the onlyperoxide likely to be present in measureable quantitiesat 773 K. In some experiments where higher molec-ular weight species were being analysed, particularlybibenzyl, the lines and the glass sampling bulbs wereheated to about 350 K to avoid condensation/adsorp-tion of the involatile products on the surface.

A cylindrical Pyrex vessel, 20 cm in length and5.2 cm in diameter, and aged by carrying out repeatedreactions between H2 and O2 (approximately 60) wasused at 773 K. Once aged, the reactions rates andproducts yields were extremely reproducible over aperiod of years and from one aged vessel to another.Electromagnetic valves with response times of lessthan 0.1 s were used to admit gases to the vessel fromthe pre-mixing bulb and to sample the products atprecise pre-determined time intervals. Toluene(99.9% purity) and ethylbenzene (�99.5% purity)were used in the experimental work. None of theproducts observed in the oxidation studies were iden-tified in the starting materials.

3. Results and discussion

3.1. Product yields from toluene

Two series of experiments were carried out.

3.1.1. Benzaldehyde, benzene, CH4, CO and CO2

Attention was focussed on the lower molecularweight products which could be measured accuratelywithout heating reaction lines and sample bulbs.Some of the data were presented in a previous pub-lication [10], and Fig. 1 shows new results for themixture containing 2.5, 427.5, and 70 Torr of TOL,H2, and O2, respectively. Essentially similar resultswere obtained for the low H2 mixture (2.5, 140, 70,and 287.5 Torr of TOL, H2, O2, and N2, respectively)and the high O2 mixture (2.5, 140, and 357.5 Torr ofTOL, H2, and O2, respectively), although the yieldsof benzene and CH4 were noticeably lower. A peakwas identified with the same retention time as ethyl-benzene, but was too small to measure quantitatively,which indicates that the concentration of CH3 radi-cals is too small to compete with benzyl and HO2

radicals in removing benzyl radicals. This is consis-tent with the mechanism adopted. No other productswere observed in this series of experiments.

When the bibenzyl yields are included (see later),carbon balances of TOL consumed and productsformed of about 98% are obtained over the first 25%reaction showing that all major products have beendetected. A 1–2% yield of cresol, found by Litzinger

et al. [8] at about 1200 K, because of the difficultiesof measurement cannot be excluded. Benzyl alcohol,from the C6H5CH2 � OH reaction, can be excludedbecause of the very low concentration of OH radicalsin the present study.

With the exception of CO2, all the products ob-served are formed in primary processes directly fromradicals directly produced from TOL. It is apparentthat the yields of both CH4 and benzene relative tothe consumption of TOL remain effectively constantover a very wide range of reaction; as also found forthe other two mixtures. This feature arises from theconsiderably greater stability of CH4 and benzenerelative to that of TOL. The yields of CH4 and ben-zene are clearly linked through the generally ac-cepted mechanism of formation, (22ta) and (25) [3,5,10].

H � C6H5CH33 adduct3 CH3 � C6H6 (22ta)

CH3 � H23 CH4 � H (25)

Table 1 compares the ratio [CH4]/[benzene] at 5%reaction with the fraction of CH3 radicals convertedinto CH4, determined previously [7] for the threemixtures used here, and the agreement provides firmevidence that 1 CH3 radical is produced for eachbenzene produced in the early stages of reaction. Thehomolysis reaction C6H5CH3 3 C6H5 � CH3 maybe discounted, first because it is highly endothermic(�H � �420 kJ mol�1) with k � 9 � 10�13 s�1 [4],and secondly because whereas the majority of CH3

radicals give CH4 in the H2 � O2 mixtures used, only

Fig. 1. Variation of product yields with consumption ofTOL at 773 K. TOL � 2.5, H2 � 430, O2 � 70 Torr. (a) F,benzaldehyde; X, benzene; E, CH4; ‚, HCHO (�5). (b) �,CO; ƒ, CO2.

293C. Ellis et al. / Combustion and Flame 132 (2003) 291–304

10–20% of phenyl radicals react with H2 to givebenzene [10].

The ratios k21t/k1 � 6.1, k22t/k2 � 78, k23t/k3 �44, and k24t/k10

1/2 � 2.10 (dm3 mol�1 s�1)1/2 at 773 K,obtained in Part 1 [1], determine the % of TOLremoved by H atoms. Use of the computer program[1] with the benzene yields gives k22ta/k2 � 41 � 5,and comparison with k22t/k2 � 78 shows that theaddition reaction (22ta) accounts for approximately50% of the total reaction of H atoms with TOL at 773K.

OH � C6H5CH33 products (21t)

H � C6H5CH33 products (22t)

O � C6H5CH33 products (23t)

HO2 � C6H5CH33 products (24t)

OH � H23 H2O � H (1)

H � O23 OH � O (2)

O � H23 OH � H (3)

HO2 � HO23 H2O2 � O2 (10)

Using k(H � C2H6) as the reference reaction [12]with k(H � C2H6)/k2 � 39 � 4 at 773 K [1] then,from the ratios above, k22t � (5.05 � 0.8) � 108

(overall reaction with H atoms) and k22ta � (2.65 �0.35) � 108 dm3 mol�1 s�1. As H-atom addition tothe benzene ring is unimportant above 500 K, andabstraction from the ring is considered negligible at773 K [11,12], then k22t � k22ta � k22tm, so thatk22tm � (2.4 � 0.5) � 108 dm3 mol�1 s�1. Otherdata reported specifically for reaction (22tm) aresummarised in Arrhenius form in Fig. 2; the agree-ment is unsatisfactory with a band of uncertainty of afactor of 2–3 across the entire temperature range.Baulch et al. [12] have reviewed the kinetic data forthe specific abstraction reaction (22tm) and empha-sised that most of the evaluations have been obtainedby computer modelling with models accepted by theauthors as plausible. In arriving at recommended pa-rameters of k22tm � between 600 and 2800 K, they

relied heavily on an expression given by Rao andSkinner [13] for the range 600–1700 K which wasdetermined by combining their own data between1410 and 1730 K with unpublished low-temperaturedata obtained by Ravishankara and Nichovich. FromFig. 2 it is clear however that the line based on theRao and Skinner expression is above the best linedrawn through the remaining data (with the exceptionof that determined by Robaugh and Tsang [14]) at alltemperatures with a difference in k22tm of a factor ofabout 2.

A brief examination of the individual studies isjustified in an attempt to arrive at the best parametersfor k22tm. Rao and Skinner pyrolysed toluene-d8 be-hind reflected shock waves in both the presence(1200–1460 K) and absence (1410–1730 K) of Hatoms [13]. In addition to doubts in the modeling,

Table 1Initial yields* of methane, ethylene and benzene from toluene and ethylbenzene

Mixture/torr Toluene** Ethylbenzene**

H2 O2 N2 [CH4]/[C6H6] f(CH33CH4)† 103C2H4/% 103C6H6/% [CH4]/[C6H5CHO]

140 70 290 0.75 0.75 � 0.03 1.17 1.11 0.67140 360 0 0.53 0.46 � 0.02 0.70 0.71 0.51430 70 0 0.89 0.88 � 0.04 1.49 1.60 0.91

* Yields at 5% consumption; ** Results for 0.5% and 0.25% toluene and ethylbenzene, respectively; † Fraction of CH3

radicals converted to CH4 through CH3 � H2.

Fig. 2. Arrhenius plot for the reaction H � TOL 3 ben-zyl � H2. �, Pamidimukkala et al. [23]; Œ, Astholz et al.[20]; �, Kiefer and Mizerka [11]; �, Rao and Skinner [13];F, Hippler et al. [18]; ƒ, Braun-Unkhoff et al. [19]; X,Robaugh and Tsang [14]; E, Mkryan et al. [21]; ‚, presentwork. Full line from the expression given by Baulch et al.[11,12]. Broken line derived from the expression recom-mended here (Table 5).


which they concede give uncertainty factors of 1.6and 1.8 in the rate constants for H and D attack ontoluene-d8, respectively, transition state theory wasthen used to allow for the isotope effects and thus tocalculate k22tm. Rao and Skinner attribute a totaluncertainty in k22tm of a factor of 2, but this is almostcertainly a conservative estimate [13]. Robaugh andTsang [14] used a single-pulse shock tube and givek22tm � 1.2 � 1011exp(�4138/T) dm3 mol�1 s�1

between 950 and 1100 K, which gives values notice-ably above those recommended by both Baulch et al.[12] and by Rao and Skinner [13]. The homolysis ofsmall amounts of tetramethylbutane in the presenceof considerably larger quantities of TOL was used asa source of H atoms. With abstraction from the ringconsidered negligible, from measurements of theyields of isobutene and benzene they were able tomeasure the ratio k22tm/k22ta, the only unknown beingthe rate constant for the homolysis of tetramethylbu-tane which is known with an accuracy of about 30%[15,16]. On addition of large quantities of CH4

(12%), the formation of benzene is reduced by theenhanced loss of H atoms due to the reaction H �CH4 3 CH3 � H2 and the yields of i-butene andbenzene remeasured. The value of k22tm/k(H � CH4)is obtained by difference from the two sets of mea-surements in the presence and absence of methane,but unfortunately the larger only exceeds the smallerquantity by about 60%, so that the ratio k22tm/k(H �CH4) is susceptible to serious error. When coupled todoubts first about the basic mechanism in the pres-ence of very large amounts of CH4, and secondly theuncertainty (50%) in k(H � CH4) and in the tetram-ethylbutane homolysis rate constant (30%) in thistemperature range [12], then an uncertainty factor of3 must be assigned to Robaugh and Tsang’s value fork22tm. By comparison their value of k22tm/k22ta �9.8exp(�1560/T) is probably reliable to a factor of1.4 between 950 and 1100 K.

Consideration of the data shown in Fig. 2 and thearguments above suggest the data of both Rao andSkinner, and Robaugh and Tsang, are too high by afactor of 2–3. In the present study at 773 K, the ratiosk22t/k2 and k22ta/k2 are determined directly, by use ofa method which for many H � alkane reactions hasbeen confirmed by Cohen [17] as extremely reliable.Although the ratio k22tm/k2 is obtained by difference,it is doubtful whether the derived value of k22tm is inerror by more than 25% because of the establishedreliability of the approach used. The most reliabledetermination of k22tm at higher temperatures is thatby Hippler et al. [18] who used reflected shock waveswith ethyl iodide as a source of H atoms and mea-sured the concentration of benzyl radicals directly at260 nm where the absorption coefficient of benzylrelative to that of TOL exceeded 100, so that very

small consumptions of TOL could be used. Theirresults are in good agreement with those from ashock-tube study of TOL pyrolysis by Just and co-workers [19], where [H] was measured by atomicresonance absorption spectroscopy and when mod-elled was very sensitive to the value of k22tm, andwith the rate constants (if not the temperature coef-ficient) from a much earlier shock-tube study of TOLpyrolysis by Astholz et al. [20]. It is more difficult tocomment critically on the flow reactor study carriedout by Mkryan et al. [21]. It is pertinent to emphasisethat their data fit in well with the full line in Fig. 2which effectively ignores the data of Rao and Skin-ner, Robaugh and Tsang, and the unpublished data ofRavishankara and Nichovich, and which is based onthe expression k22tm � 5.0 � 104T2exp(�3830/T)dm3 mol�1 s�1 and preferred to the recommendedexpression given by Baulch et al. [11,12].

Fig. 3 summarises the limited data available forreaction (22ta). Although an old investigation, Bar-nard and Ibberson’s [2] measurement of the yields ofthe very stable products benzene and H2 in the oxi-dation of TOL at 759 K gives a direct and reliablemeasurement of k22ta/k22tm � 2.0, because in theinitial stages of reaction benzene and H2 are formeduniquely in reactions (22ta) and (22tm) (abstractionfrom the ring is too slow to compete). Using theexpression recommended above for k22tm, thenk22ta � 3.7 � 108 dm3 mol�1 s�1. Values of k22ta

may also be calculated from Robaugh and Tsang’srelatively reliable expression for k22tm/k22ta for therange 950–1100 K (see above). Based on the unpub-lished data of Ravishankara and Nicovich, Rao and

Fig. 3. Arrhenius plot for the reaction H � C6H5CH3 3C6H6 � CH3. �, Kiefer and Mizerka [11]; ƒ, Rao andSkinner [13]; ‚, Robaugh and Tsang [14]; F, Barnard andIbberson [2]; E, present work. � dashed line, k(H � C6H6

3 C6H5 � H2)/6 from Nicovich and Ravishankara [24].Full line derived from expression recommended here (Table5).


Skinner [13] quote an expression for k(H �C6D5CD3 3 C6D5H � CD3) for the range 1200–1460 K, which should be very similar to k22ta, butwhich predicts a slightly negative temperature coef-ficient as shown in Fig. 3. Although Pamidimukkalaet al. [22] report a value of k22ta � 1.25 � 109 exp(�1862/T) between 1600 and 2150 K from shock-tube studies of toluene pyrolysis, they do not refer tothis expression in later modelling [23] of this reactionbut prefer to use estimates given by Rao and Skinner[13]. In consequence the values of k22ta obtained inthe present work and from the studies of Barnard andIbberson [2] and of Robaugh and Tsang [14] areconsidered the most reliable. Fig. 3 also emphasisesthat these data are in excellent agreement with therate constant for the addition of H atoms to benzenefrom k � 4.0 � 1010exp(�2170/T) dm3 mol�1 s�1,allowing for a path degeneracy of 6, given by Nico-vich and Ravishankara [23] for the range 300–1000K and recommended by Baulch et al. [12]. Based onthe data and the consistency with the H � benzenereaction, k22ta � 3.7 � 109exp(�1880/T) dm3 mol�1

s�1 is recommended for the range 300–1250 K. Al-ternatively, the data give a good fit to the non-Arrhe-nius expression k22ta � 9.5 � 102T2exp(�475/T)dm3 mol�1 s�1, which defines the curve shown inFig. 3.

Benzaldehyde is an important primary productboth at 773 K and at temperatures up to 1200 K [3,4],albeit considerably more reactive than CH4 and ben-zene. Glassman and co-workers [3,4] propose that itis formed in reactions of benzyl radicals with O, OHand HO2 radicals, but at 773 K in H2 � O2 mixturesO and OH radicals will be unable to compete withHO2 even to a minor degree. Further, in a recentstudy of the decomposition of neopentylbenzene inthe presence of O2 at 753 K, Ellis and Walker [25]were able to show that the peroxy radical isomerisa-tion and decomposition sequence made a substantialcontribution to the formation of benzaldehyde in ad-dition to the HO2 � benzyl route (26) and (27)

C6H5CH2 � HO23 OH � C6H5CH2O (26)

C6H5CH2O � O23 C6H5CHO � HO2 (27)

C6H5CH2 � O2ª C6H5CH2O2 (28)

C6H5CH2O23 C6H5CHOOH (29)

C6H5CHOOH3 C6H5CHO � OH (30)

Although the equilibrium position in (28) is highlyunfavourable compared with those found in alkylradical systems [26,27], reaction (29) is rapid be-cause a very labile H atom is transferred, and thesequence can compete with reaction (26) due to therelatively low concentration of HO2 radicals (and

other radicals). These reactions will be discussedlater.

3.1.2. Benzaldehyde and bibenzylA second set of analyses were carried out using a

Supelco SP2100 column specially adapted to give agood peak for bibenzyl. Benzaldehyde was also wellseparated, but not benzene and toluene. After consid-erable testing it was shown that bibenzyl could beanalyzed quantitatively by heating all sample deliv-ery lines and the sample bulbs to about 350 K. Anal-yses were carried out immediately following reac-tion. The yields of the two products were monitoredcarefully against both pressure change and time;those of benzaldehyde were in very good agreementwith the yields obtained from the first set of analyses(above). Due to the relatively high reactivity of bothproducts, considerable attention was paid to the first5–10% reaction. Fig. 4 shows the yields against timefor the 5 mixtures used. All the data fit smoothcurves, which are markedly autocatalytic due to sec-ondary initiation caused by the homolysis of H2O2.

H2O2 � M3 2OH � M (7)

As seen in Fig. 1, the yield of benzaldehyde reachesa maximum at about 50% consumption of TOL, dueto removal by secondary reactions; a similar situation

Fig. 4. Variation of the yields of benzaldehyde and bibenzylwith time and O2 pressure at 773 K. TOL � 2.5 Torr; totalpressure with N2 � 500 Torr; (a) bibenzyl; (b) benzalde-hyde. X, H2 � 430, O2 � 70 Torr; ƒ, H2 � 280, O2 � 70Torr; E, H2 � 140, O2 � 70 Torr; �, H2 � 140, O2 � 360Torr; F, H2 � 140, O2 � 210 Torr.


exists with the bibenzyl yields. In consequence thedata shown in Fig. 4 have been interpreted by con-sidering the rates of formation at about 5% reactionwhich can be identified accurately by computer anal-ysis of the data, which also shows that less than 2–3%of benzaldehyde and bibenzyl have been consumed atthis point. This approach differs from that used byother groups where the complete oxidation is studiedand modeled, and reliance is placed on sensitivityanalysis to obtain rate data for important primaryelementary reactions. However, in many cases, theoverall complexity and lack of reliable kinetic datafor secondary processes either precludes any deter-mination of data for primary processes or results invalues which are of doubtful validity.

Accepting that benzaldehyde is formed in the twosequences above [26,27,28–30] and that bibenzyl isformed uniquely in reaction (32), then their rates offormation RBZ and RBB, respectively, are related byequation (i), where (31) is the overall process for theformation of benzaldehyde in the sequence (28)–(30).

RBZ/[O2](RBB)1/2 � k31/k321/2 � k26[HO2]/k32

1/2[O2]

(i)

C6H5CH2 � O23 C6H5CHO � OH (31)

C6H5CH2 � C6H5CH23 (C6H5CH2)2 (32)

The HO2 concentration is controlled almost totally bythe kinetics of the H2 � O2 reaction and hence can becalculated precisely for any mixture and time, andallowance made (�5%) for the presence of smallamounts of TOL [28]. Table 2 gives values for RBZ,RBB and [HO2] at times for each mixture whichcorrespond to 5% consumption of TOL. If k26 � 0,then RBZ/[O2](RBB)1/2 should be constant, but asshown varies by a factor about 3. If k31 � 0, thenRBZ/[HO2](RBB)1/2 should be constant, but experi-mentally varies by a factor of about 3.5. With bothroutes involved, as shown by the plot in Fig. 5,equation (i) gives a very good fit to the data, provid-ing confirmation of the proposed mechanisms forbenzaldehyde and bibenzyl. The intercept gives k31/

k321/2 � 0.33 � 0.04 (dm3 mol�1 s�1)1/2, and from the

gradient k26/k321/2 � (8.5 � 1.1) � 104 (dm3 mol�1

s�1)1/2 at 773 K. Absolute values of k26 and k32 maybe calculated from a knowledge of k32, which hasbeen the subject of three investigations. Muller-Markgraf and Troe [29] used a shock tube with UVspectroscopy to monitor [benzyl] between 700 and1500 K, and when they include a value of 2.9 � 109

dm3 mol�1 s�1 at 300 K obtained by Pagsberg andTroe [30] by use of pulse radiolysis give k32 �109.6�0.1(T/1000K)0.4 dm3 mol�1 s�1 between 300and 1500 K. This expression gives values signifi-cantly lower than k32 � (2.8 � 1.5) � 1010 dm3

mol�1 s�1 reported by Fenter et al. [26] who usedflash photolysis/UV absorption methods between 400and 450 K. In analyzing their data, they acknowledgethat their values are probably too high, and thereforethe expression given by Muller-Markgraff and Troewill be adopted, leading to k26 � 5.1 � 109 andk31 � 1.97 � 104 dm3 mol�1 s�1 at 773 K. Anumber of other values have been obtained for k26

Table 2Rates of formation of benzaldehyde (RBZ) and bibenzyl (RBB) at 5% consumption

Mixture/Torr*H2 O2

107RBZ/mol�1 dm�3 s�1

109RBB/mol�1 dm�3 s�1

108[HO2]/mol dm�3

RBZ/[O2]RBB1/2/

dm3/2 mol�1/2 s�1/2RBZ/[HO2]RBB

1/2/dm3/2 mol�1/2 s�1/2

140 70 1.35 8.3 1.08 1.02 1.37 � 105

140 210 1.34 2.9 1.28 0.57 1.94 � 105

140 360 1.60 1.87 1.45 0.49 2.55 � 105

280 70 1.45 6.1 1.63 1.29 1.14 � 105

430 70 1.99 8.5 2.00 1.49 1.07 � 105

* Contains 2.5 Torr toluene; total pressure 500 Torr with N2.

Fig. 5. Plot of RBZ/[O2]RBB1/2 against [HO2]/[O2] at 5% con-

sumption of TOL.


and they are summarized in Table 3. The consistencyis striking, and a value of k26 � (5 � 2) � 109 dm3

mol�1 s�1 is recommended for the range 500–1500K. The good agreement also provides convincingevidence for the validity of the expression adoptedfor k32.

The overall reaction (31) proceeds through thesequence (28), (30), and with (28) fully equilibratedunder the conditions used [5], then k31 � K28k29, aseffectively all the hydroperoxide radicals will un-dergo reaction (30). Fenter et al. [26] from their flashphotolysis study measured the equilibrium constantof reaction (28) and give K28 � 1.05 �10�5exp(10366/T) dm3 mol�1 between 398 and 525K, in excellent agreement with the individual pointsdetermined by Elmaimouni et al. [27] who reportK28 � 1.67 � 10�4exp(9221/T) dm3 mol�1 between393 and 433 K. Given the agreement at low temper-atures and the wider range used by Fenter et al., theirexpression is used for K28. Extrapolation to 773 Kgives K28 � 7.0 dm3 mol�1 with an uncertainty ofbetter than a factor of 2, so that k29 � 2.8 � 103 s�1

for a 1,3 transfer of a secondary benzyl-type of Hatom in C6H5CH2OO radicals (30). No other valuesare available in the literature, and it will be discussedfurther later.

3.2. Product yields from ethylbenzene

Fig. 6 shows the product profiles for the mixturecontaining 1.25, 140, 70, and 288.7 Torr of EB, H2,O2 and N2, respectively. The number of products issomewhat greater than from TOL, and it is clear thatstyrene, benzene, acetophenone, C2H4, CH4 and COare all formed in primary processes. Styrene has noother source than EB and, as its reactivity is consid-erably greater than that of benzene and of CH4 and atleast equal to that of EB, its profile reaches a maxi-mum at about 40% consumption. Benzene, C2H4,and particularly CO show evidence of secondary for-mation as does benzaldehyde which has an almostlinear profile despite its undoubted reactivity and the

distinct fall-off observed when benzaldehyde isformed from TOL (Fig. 1). Benzaldehyde is almostcertainly formed as a secondary product via OH ad-dition to styrene, either by direct decomposition ofthe adduct or following further addition of O2.

C6H5CH¢CH2 � OH3 C6H5CH(OH)CH2

3 C6H5CHO � CH3

C6H5CH(OH)CH2 � O23 C6H5CH(OH)CH2O2

3 C6H5CHO � HCHO � OH

C6H5CHCH2(OH) � O23 C6H5CH(O2)CH2(OH)

3 C6H5CHO � HCHO � OH

Good carbon balances (ca 96%) were obtained up toabout 25% consumption of EB, but small yields of

Table 3Rate constants for the reaction HO2 � R 3 X

R X T/K k/dm3 mol�1 s�1 Reference

C6H5CH2 C6H5CHO 773 (5.1 � 1.5) � 109 presentC6H5CH2 C6H5CHO 990–1100 (3.2 � 1.5) � 109 3C6H5CH2 Products 1180–

1450(5 � 1.5) � 109 31

CH2CHCH2 CO � products 753 (5.8 � 1.9) � 109 32CH2CHCH2 Products 300–2500 9.6 � 109 33C6H5CHCH3 CH5CHO � CH3 773 (7.3 � 3.0) � 109 present*

* See text under ‘rate constants involved in the ethylbenzene studies.’

Fig. 6. Variation of product yields with consumption of EBat 773 K. EB � 1,25, O2 � 70, H2 � 140, N2 � 289 Torr.(a) F, CO; X, C6H5COCH3; E, styrene oxide. (b) F, sty-rene; E, benzaldehyde; ‚, benzene; �, CH4; X, C2H4.


ethyl-substituted phenols cannot be excluded due tothe difficulty of their analysis.

3.2.1. Product balancesThe formation of the initial products directly from

EB may be fully explained by the mechanism givenin Scheme I. Davis [34] gives k33 �1015.1exp(�36290/T) s�1 between 700 and 1100 K,which indicates that homolysis of EB accounts foronly 0.020% of the EB consumed at 5% consump-tion, so that reaction (33) may be disregarded interms of product formation, including the formationof benzaldehyde from benzyl radicals in the se-quences (26), (27), (28)–(30). Justification for thebasic mechanism arises in several ways.

1. The type of chemistry involved is well estab-lished in alkane oxidation systems [5].

2. As will be discussed later, reaction (46) is fast(k46 � 2 � 108 dm3 mol�1 s�1) so that reac-tion (50) cannot compete at the levels of O2

and HO2 used here. Consequently, as a pri-mary product, benzaldehyde is formeduniquely in the sequence (38)–(40) (k34 �10�2k46) together with a CH3 radical. Table 1shows the ratio of the initial yields of CH4 andbenzaldehyde from EB and the % of CH3 rad-icals that undergo reaction (25) in the particu-

lar mixture used [7]. The excellent agreementconfirms the validity of the mechanism of for-mation of CH4 and benzaldehyde.

3. Table 1 and Fig. 6 show that the initial yieldsof C2H4 and benzene are effectively identical.There are two possible routes for the formationof C2H4 as a primary product, either from thehomolysis of C6H5CH2CH2 radicals (45), orvia specific H addition in (52), discussed lateras the adduct step (22ea), followed by reaction(53). As earlier studies [10] indicate that only15–20% of C6H5 react with H2 to give benzenein a stoichiometric H2 � O2 mixture at 500Torr and 773 K, then clearly (45) is not thesource of equal yields of the two products. Incontrast, reactions (52) and (53) lead directlyto equal yields because it has been firmly es-tablished [5,35] that 99% of C2H5 radicals areconsumed in (53) under the conditions used.Further, given that �H45 � 150 kJ mol�1 (sothat k45 is unlikely to exceed 100 s�1) andk46 � 2 � 108 dm3 mol�1 s�1, reaction (45)cannot compete. Later in the reaction, C2H4 isprobably formed as a secondary product via Hatom addition to styrene and homolysis of the‘hot’ adduct.

H � C6H5CH¢CH23 C6H5CH2CH*23 C6H5

� C2H4

3.2.2. Reactions of the C6H5CH2CH2 radicalWith k46 � 2.0 � 108 dm3 mol�1 s�1 [5] at 773

K, competing reactions of (46) will be of lower im-portance even though the sequence (47–49) givingstyrene oxide involves a ‘normal’ R � O2 3 RO2

equilibrium and a 1,4 transfer of a weakly boundbenzyl-type H atom. From a computer calculation of[HO2], discussed earlier, the radical-radical process(50) leading to benzaldehyde cannot compete withthe formation of styrene and styrene oxide, whichtherefore, with (45) already shown to be of negligibleimportance, are the only initial products from theC6H5CH2CH2 radical.

Validation of the proposed mechanism and deter-mination of rate constants for the elementary reac-tions may be simply achieved. Calculation of the %of C6H5CH2CH2 radicals formed in the primary at-tack on EB is simple given an accurate knowledge ofthe ratios k21e/k1, k22e/k2, k23e/k3 and k24e/k10

1/2 ob-tained in Part 1 of his paper [1] for OH, H, O, andHO2 attack on EB. Small allowances (10%) aremade through the computer program for OH attack atthe ring, H atom addition to give benzene (reactions(52) and (54)), and O atom addition to the ring (4%),although these corrections have a negligible effecton the relative amounts of C6H5CH2CH2 and

Scheme IBasic mechanism for the initial consumption ofethylbenzene

C6H5CH2CH3 3 C6H5CH2 � CH3 (33)C6H5CHCH3 � O2 3 C6H5CH¢CH2 � HO2 (34)C6H5CHCH3 � O2 3 C6H5CH(O2)CH3 (35)C6H5CH(O2)CH3 3 C6H5C(OOH)CH3 (36)C6H5C(OOH)CH3 3 C6H5COCH3 � OH (37)C6H5CHCH3 � HO2 3 C6H5CH(OOH)CH3 (38)C6H5CH(OOH)CH3 3 C6H5CH(O)CH3 � OH (39)C6H5CH(O)CH3 3 C6H5CHO � CH3 (40)CH3 � H2 3 CH4 � H (25)C6H5CH(O)CH3 � O2 3 C6H5COCH3 � HO2 (41)C6H5CH(O)CH3 3 C6H5COCH3 � H (42)C6H5CH(O2)CH3 3 C6H5CH(OOH)CH2 (43)C6H5CH(OOH)CH2 3 C6H5CHCH2 � OH (44)

{ }O

C6H5CH2CH2 3 C6H5 � C2H4 (45)C6H5CH2CH2 � O2 3 C6H5CH¢CH2 � HO2 (46)C6H5CH2CH2 � O2 3 C6H5CH2CH2O2 (47)C6H5CH2CH2O2 3 C6H5CHCH2OOH (48)C6H5CHCH2OOH 3 C6H5CHCH2 � OH (49)

{}O

C6H5CH2CH2 � HO2 3 C6H5CH2CH2OOH (50)C6H5CH2CH2OOH 3 C6H5CH2 � HCHO � OH (51)H � C6H5C2H5 3 C6H6 � C2H5 (52)C2H5 � O2 3 C2H4 � HO2 (53)


C6H5CHCH3 radicals produced. Formation of sty-rene oxide through the peroxy radical isomerizationand decomposition sequence from C6H5CHCH3 rad-icals via reactions (35), (43) and (44) is negligiblebecause with K35 � 7 dm3 mol�1, taken as the same‘low’ allyl-type value as for the C6H5CH2O2 � O2

3 C6H5CH2O2 equilibrium (given earlier as K28

when discussing the yields of benzaldehyde andbibenzyl from TOL) and the ‘normal’ value of k �2.0 � 102 s�1 for a 1,4 H primary H atom transfer inalkylperoxy radicals [5] then K35k48 � 1.4 � 103

dm3 mol�1 s�1 compared with a value of k34 � 3 �105 dm3 mol�1 s�1 at 773 K [5].

Based on their relative total yields (Fig. 7) and the% of C6H5CH2CH2 radicals formed, the initial valuesof [C6H5CH¢CH2]46/[styrene oxide] for formationfrom this radical are given in Table 4. The values arealmost constant for the three mixtures used, and ac-cording to the mechanism are given by equation (ii).

[C6H5CH¢CH2]46/[styrene oxide] � k46/K47k48

(ii)

From the data in Table 4, k46/K47k48 � 13 � 3 at 773K and will be discussed later.

3.2.3. Reactions of the C6H5CHCH3 radicalsThe distinguishing feature of the chemistry of the

C6H5CHCH3 radical is the absence of a facile reac-tion with O2. With the standard heats of formation ofC6H5CHCH3 and HO2 taken as 168 and 16 kJ mol�1,then �H34 � �4 kJ mol�1, compared with a typicalvalue of 55–60 kJ mol�1 for the analogous reactionsof alkyl radicals [5]. From a well-established rela-tionship between the rate constant for the formationof the conjugate alkene and the enthalpy of reactionfor alkyl and alkenyl radicals (including both electronlocalized and delocalised species), k34 � 2.5 � 105

dm3 mol�1 s�1 at 773 K, compared with k46 � 2.0 �108, as discussed above. Radical-radical reactionssuch as (38) become more likely and, as shown by thesequence (38)–(40), there exists a plausible route forbenzaldehyde formation which moreover producesCH4 (via CH3 � H2) in the correct proportion, as

discussed earlier. The product ratios of styreneformed in (35) to total benzaldehyde at 5% consump-tion of EB are given in Table 4, and from the mech-anism the ratio is given by equation (iii).

[C6H5CH¢CH2]34/[C6H5CHO] � k34[O2]/k38[HO2]

(iii)

As the HO2 concentration is determined almost com-pletely by the H2 � O2 mixture used it may becalculated precisely, as indicated in Table 2 for theTOL results. The derived values of k34/k38 are satis-factorily invariant with mixture composition with amean value of (3.4 � 0.4) � 10�5.

Methylphenylketone is clearly formed as a pri-mary product in yields of 2–3%, and may be formedin both the sequence (35–37) and via HO2 addition tothe C6H5CHCH3 radical, reactions (38), (39), (41),and (42). However, there is no increase in the yield ofmethylphenylketone at high H2 pressure where[HO2] is significantly greater (see Table 2). Almostcertainly the HO2 addition route may be excluded, asmight be anticipated given the high value of k41 �1 � 108 s�1 which implies that C6H5CH(OOH)CH3

molecules uniquely decompose to give benzaldehydeas discussed above. The formation of methylphenylk-etone competes with that of styrene in reaction (34),so that the product ratio is given by equation (iv) withthe justifiable assumption that reaction (35) is fullyequilibrated. As seen from Table 4, the values ofk34/K35k36 are effectively constant with a mean valueof 28 � 5. This value and similar ones derived abovewill be discussed in a later section in terms of rateconstants for the elementary reactions involved.

[C6H5CH¢CH2]34/[C6H5COCH3] � k34/K35k36

(iv)

3.3. Rate constants involved in the ethylbenzenestudies

3.3.1. Rate constants for the reactions of H atomswith ethylbenzene

There are five types of reaction of H atom withEB.

Table 4Products ratios from the addition of ethylbenzene*

Mixture/torrH2 O2

C6H5CH2CH2

formed/%**[styrene]46/[styr. oxide]†

[styrene]34/[C6H5CHO]†

105k34/k38 [styrene]34/[CH3COC6H5]†

140 70 21.9 12.5 4.6 3.4 30.9140 360 25.6 15.8 13.6 3.0 29.7430 70 16.0 11.0 2.73 3.8 23.7

* Yields at 5% reaction; ** Calculated as the percentage of C6H5CH2CH2 radicals formed from radical attack on the C2H5

group; † [styrene]34 and [styrene]46 refer to styrene formed in reactions (34) and (46), respectively.


H � C6H5C2H53 C6H6 � C2H5 (22ea)

H � C6H5C2H53 C6H6C2H5 (22ear)

H � C6H5C2H53 C6H5CH2CH2 � H2 (22em)

H � C6H5C2H53 C6H5CHCH3 � H2 (22es)

H � C6H5C2H53 C6H4C2H5(3 isomers) � H2

(22er)

As reported in Part 1 [1], a value of k22e/k2 � 168 �18 at 773 K was obtained from the kinetic studies,where k22e � k22ea � k22ear � k22em � k22es � k22er.No other value is available for k22e except at roomtemperature [12] where addition to the ring will bethe dominant reaction.

H � O23 OH � O (2)

99% of C2H5 radicals formed in reaction (22ea) reactwith O2 to give C2H4 under the present conditions[5,35], and its yields in the three mixtures used overthe first 8% reaction may be fitted very well (rmsdeviation 4.5%) with k22ea/k2 � 49 � 5. In theabsence of further information, it will be assumedthat the CH3 group behaves as in C2H6, so thatk22em/k2 � 0.5 k(H � C2H6)/k2 � 20 [28]. All theevidence supports the view that addition to the ring(22ear) is totally reversible above 550 K [12], andabstraction from the ring is generally regarded asnegligible below 1500 K [11,12]. It is, however,pertinent to re-examine the latter view, in part toanalyse fully the reaction of H atoms with EB atcombustion temperatures, and additionally becausestrong evidence was presented earlier that the expres-sion given by Baulch et al. [12] gives rate constantsfor the reaction of H atoms with TOL to form benzylradicals too high by a factor of about 2.

H � C6H63 C6H5 � H2 (22br)

OH � C6H63 C6H5 � H2O (21br)

Fig. 8 shows a plot of the data quoted by Baulch et al.[12] for abstraction from benzene by H atoms (22br).Kiefer and co-workers [36] used the shock tube-laserschlieren technique to investigate the pyrolysis ofbenzene, and fitted their data with a 24-step mecha-nism. Between 1900 and 2200 K, they give k22br �2.5 � 1011exp(�8050/T) dm3 mol�1 s�1. Fujii andAsaba [37] also studied benzene pyrolysis, using gaschromatography and light absorption to follow theproducts, and give k22br � 7.8 � 1010exp(�5032/T)dm3 mol�1 s�1. The results of their earlier study,which give considerably higher values of k22br, willbe ignored here because the authors do not refer tothem in later work. Nicovich and Ravishankara [24]effectively studied the low temperature addition re-

action and give only estimates of the maximum valueof k22br up to about 1000 K. Rao and Skinner [38]pyrolysed deuterated benzene, and for their modelingpurposes effectively used the maximum values ofk22br suggested by Nicovich and Ravishankara.Mkryan et al. [39] studied the overall reaction be-tween H atoms and benzene in the range 883–963 K,and give k22br � 2.05 � 1010exp(�4380/T) dm3

mol�1 s�1, if it is assumed that the addition reactionis negligible and that the correct reaction stoichiom-etry was adopted. As can be seen from Fig. 8, thevalues discussed above lie on a reasonable Arrhenius

Fig. 7. Plots of [styrene]/[styrene oxide] against consump-tion of EB for different mixture compositions. 773 K, EB �1.25 Torr. ‚, H2 � 430, O2 � 70 Torr; E, H2 � 140, O2 �360 Torr; X, H2 � 140, O2 � 70 Torr.

Fig. 8. Arrhenius plot for the reaction H � C6H63 C6H5 �H2. E, Kiefer et al. [36]; X, Fujii and Asaba [37]; ‚,Mkryan et al. [39]; F, estimates (see text). Full line derivedfrom expression recommended here (Table 5).


line, and although no other experimental data areavailable, a relatively reliable estimate of k22br maybe made as follows. Using data recommended byBaulch et al. [11,12], but for consistency values ob-tained by Tully and co-workers [11,12] for the OHreactions, values of k(OH � C2H6)/k(H � C2H6) �11 � 3, k(OH � CH4)/k(H � CH4) � 19 � 5 andk21br � 7.7 � 108 dm3 mol�1 s�1 are obtained at 773K. The difference in enthalpies of reaction for theC2H6 and CH4 reactions is 20 � 1 kJ mol�1 and thatfor the CH4 and C6H6 reactions is 25 � 1 kJ mol�1,so that k22br/k21br can be reasonably estimated fromthe two known ratios as 40 � 10 and hence k22br �(1.9 � 0.7) � 107 dm3 mol�1 s�1. Similar calcula-tions at 1500 K give k22br � (3 � 1) � 109. Thesetwo estimated values are included in Fig. 8, and takeninto account when determining expressions for thetemperature coefficient. Use of the Arrhenius equa-tion gives k22br � 2.15 � 1011exp(�7050/T) dm3

mol�1 s�1 between 700 and 2200 K, and the curvedrawn is based on the expression 2.3 �104T2exp(�4880/T) dm3 mol�1 s�1. Although theremay be significant error in the rate expression, thereis considerable evidence that abstraction from thering by H atoms is considerably more important thansuggested hitherto. Using the expression given earlierfor H � C6H5CH3 3 C6H5CH2 � H2, and taking5/6ths of k22br for abstraction from the ring in TOLby H atoms, then this pathway contributes about 4%of total abstraction at 773 K. At 1000 K and 2000 K,the predicted percentages are 8% and 15%, respec-tively.

Table 5 gives the relative rate constants based onthe discussion above for the 4 identified pathways ofthe H � EB reaction at 773 K. As in previous studies,

absolute values are obtained by combining the rateconstant ratios with k(H � C2H6)/k2 � 39 � 4 andk(H � C2H6) � 1.44 � 106T1.5exp(�3730/T) dm3

mol�1 s�1 [12]. Also given are estimates of A, B andn for the expression k � ATnexp(�B/T), based onadditivity rules. Casual examination of the A factorssuggests that A22er is too low, and this could becaused by either underestimating the errors in k22br orperhaps because k22tr has been overestimated at hightemperatures due to a contribution from abstractionfrom the ring. The parameters for the overall reaction(22e) are derived by summing the rate constants foreach specific pathway. The parameters fit the calcu-lated values of k22e to within 5% between 600 and2000 K. An Arrhenius plot for the overall rate con-stant for H � TOL (k22t) shows marked curvaturemainly because the addition reaction (22ta), with itslow temperature coefficient, dominates at low tem-peratures. In consequence a much higher value of n isrequired for the empirical expression. The fit to thecalculated value of k22t is almost exact at 600 and1600 K and better than 7% at all intermediate tem-peratures, but over predicts at 2000 K by about 12%.

3.3.2. Absolute rate constants for elementaryreactions involving C6H5CH2CH2 and C6H5CHCH3

radicals3.2a. k48. The value of k46/K47k48 � 13 � 3 has beendetermined earlier on the basis that reaction (47) isfully equilibrated under present conditions [5] and(49) sufficiently rapid that alternative products or thereverse reaction are unimportant.

C6H5CH2CH2 � O23 C6H5CH¢CH2 � HO2

(46)

Table 5Summary of kinetic data for H � C6H5CH3 and H � C6H5C2H5 reactions*

Product k22/k2** k at 773 K/dm3 mol�1 s�1

A/dm3

mol�1 s�1

K�n

n B/K note

H � C6H5CH3

C6H5CH2 (22tm) 34 2.2 � 108 5.0 � 104 2.0 3830 –C6H4CH3 (22tr) 3.0 1.9 � 107 1.9 � 104 2.0 4880 †C6H6 � CH3 (22ta) 41 2.6 � 108 9.5 � 102 2.0 475 –total products above 78 5.0 � 108 2.22 � 10�7 5.2 �675 ‡H � C6H5C2H5

C6H5CHCH3 (22es) 96 6.1 � 108 3.3 � 104 2.0 2690 –C6H5CH2CH2 (22em) 19.5 1.25 � 108 7.2 � 105 1.5 3730 –C6H4C2H5 (22er) 3.0 1.9 � 107 1.9 � 104 2.0 4880 †C6H6 � C2H5 (22ea) 49 3.1 � 108 1.0 � 103 2.0 475 §total products above 168 1.07 � 109 1.53 � 101 3.0 1580 ‡

* Based on the expression k � ATnexp(�B/T); ** k22 refers to the general reaction H � RH; † Parameters obtained for H �C6H6 3 C6H5 � H2, with allowance for path degeneracy difference; ‡ Calculated from the parameters given for the specificpaths; § As note c, with a small increase in the A factor.


C6H5CH2CH2 � O2ª C6H5CH2CH2O2 (47)

C6H5CH2CH2O23 C6H5CHCH2OOH (48)

C6H5CHCH2OOH3 C6H5CHCH2{}

O

� OH (49)

As indicated earlier, k46 � 2.0 � 108 dm3 mol�1 s�1

[5]. K47 has not been measured, but its value isequated to that (5.50 � 103 dm3 mol�1) for the(CH3)3CCH2 � O2 ª (CH3)3CCH2O2 equilibrium[40] but reduced by a factor of 2 to allow for theenhanced electron-pulling power of the C6H5CH2

group. Substitution of these values gives k48 �(1.2 � 0.6) � 104 s�1 at 773 K, compared with avalue of 5.0 � 103 s�1 (recalculated using morerecent data from the original value [41]) for thetransfer of the single tertiary H atom in(CH3)2CHCH2O2 radicals. A somewhat larger differ-ence in the two values might be expected given thatthe 1,4 transfer (benzyl-type) in C6H5CH2CH2O2

radicals will be less endothermic by about 35 kJmol�1. However, Scott and Walker [1] have shownthat H abstractions by HO2 radicals at the �-positionin alkyl benzenes have A factors lower by a factor ofabout 3.5 and activation energies higher by about 10kJ mol�1 when compared on a thermochemical andC™H bond basis with abstraction by HO2 radicalsfrom alkanes. On the assumption that these differ-ences are carried forward to internal H abstractionfrom the �-position in arylperoxy radicals, then k48

will be reduced by a factor of about 20. Althoughalternative products from C6H5CHCH2OOH radicalare unlikely to be important, it is conceivable that K47

is still too high despite the allowance made above.Further although, if directly reflected in the differ-ence in the activation energy, the enthalpies of reac-tion for (48) and for a 1,4t H atom transfer in alky-lperoxy radicals indicate k48 � 200 k(1,4t), (48) isactually exothermic by about 25 kJ mol�1, and thedifference in the activation energies may be closer to25 kJ mol�1 with a difference in the rate constants ofa factor of about 50. Further discussion is premature.

3.2b. k38. Combination of the value of k34/k38 �(3.4 � 0.4) � 10�5 given earlier with k34 � 2.5 �105 dm3 mol�1 s�1 [5] gives k38 � 7.3 � 105 dm3

mol�1 s�1 at 773 K. No other independent determi-nation is available, but the value may be comparedwith k26 � 5.1 � 109 dm3 mol�1 s�1 obtained fromthe toluene product studies for the related reactionbetween benzyl and HO2 radicals.

C6H5CH2 � HO2

3 C6H5CH2OOH3 OH � C6H5CH2O2O2

C6H5CHO � HO2

(26)

C6H5CHCH3 � O23 C6H5CH¢CH2 � HO2 (34)

C6H5CHCH3 � HO23 C6H5CH(OOH)CH3

3 C6H5CHO � OH � CH3 (38)

3.2c. k36. With reaction (35) assumed to be fullyequilibrated and k36 effectively irreversible then k34/K35k36 � 28 � 5 was derived earlier. As above k34 �2.5 � 105 dm3 mol�1 s�1 and taking K35 � 3.5 dm3

mol�1, from K28 � 7.0 dm3 mol�1 for the analogousC6H5CH2 � O2 equilibrium but with a factor of 2reduction due to branching in the radical [42], thenk36 � 2.5 � 103 s�1 in comparison with a value of2.8 � 103 s�1 for the structurally related 1,3 H atomtransfer in C6H5CH2O2 radicals. In the two cases,path degeneracy and enthalpy of reaction differenceswill work in opposite directions and their effects willto a considerable degree cancel. Table 6 summarisesthe rate constants for isomerisations in the arylperoxyradicals and compares them with the values for re-lated alkylperoxy radicals [5]

C6H5CHCH3 � O2ª C6H5CH(O2)CH3 (35)

C6H5CH(O2)CH33 C6H5C(OOH)CH3 (36)

Table 6Rate constants for Hatom transfer in arylperoxy and alkyperoxy radicals at 773 K*

RO2 ROOH Type** k/s�1 k(per C™H)/s�1

C6H5CH(O2)CH3 C6H5C(OOH)CH3 1,3tb 2.5 � 103 2.5 � 103

C6H5CH2CH2O2 C6H5CHCH2OOH 1,4sb 1.2 � 104 6.0 � 103

C6H5CH2O2 C6H5CHOOH 1,3sb 2.8 � 103 1.4 � 103

CH3CH(OO)CH2CH3 CH3C(OOH)CH2CH3 1,3t 1.8 � 102 1.8 � 102

(CH3)2CHCH2OO (CH3)2CCH2OOH 1,4t 1.2 � 104 1.2 � 104

* See ref [5] for full data on alkylperoxy radicals; ** tb and sb refer to the transfer of tertiary and secondary benzyl type Hatoms in arylperoxy radicals.


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