J . Chem. SOC., Faraday Trans. 1, 1982, 78, 3187-3202 Pyrolysis of Ethylbenzene BY C. TERENCE BROOKS? AND STANLEY J. PEACOCK British Gas Corporation, London Research Station, Michael Road, London SW6 2AD AND BRYAN G. REUBEN* Department of Chemical Engineering, Polytechnic of the South Bank, Borough Road, London SEI OAA Received 3rd December, 198 1 The pyrolysis of ethylbenzene has been studied using a static reactor. At low conversion hydrogen and styrene are the major products together with methane, toluene, ethylene, ethane and benzene plus traces of higher molecular-weight hydrocarbons. The pyrolysis is a chain reaction with a chain length of the order PhC,H, -+ PhCH, + CH, of 10 initiated by for which k/s-' = 1014.4*1.1 exp (- 293 k 18 kJ mol-'/RT) based on an average of toluene and methane yields.This agrees well with previous work involving toluene and aniline carriers. The results may be explained by a complex mechanism involving free radicals, CH,, PhCH,, PhCHCH,, PhCH,CH,, C,H,, Ph and H. Termination appears to occur mainly by the reaction 2PhCHCH, + PhCH: CH, +PhC,H,. PhCHCH, -+ PhCH : CH, + H For the reaction a rate constant k/s-' = 1015.9 exp (-217 kJ mol-'/RT) was deduced. The hydrogenation of coal and oil is a potentially important route to substitute natural gas. In these processes the cracking and subsequent hydrogenation of aromatic compounds, such as ethylbenzene, play a part. Although there have been many studies of the pyrolyses of aromatic hydrocarbons, their mechanism is still uncertain. Studies of the pyrolysis of ethylbenzene date back to Szwarc's work' in 1949.Szwarc suggested that the reaction be described by a free-radical chain mechanism. Initiation occurs by fission of the aliphatic C-C bond to yield benzyl and methyl radicals. PhCH,CH, --+ PhCH, + CH,. CH, + PhCH,CH, -, CH, + PhCHCH, CH, + PhCH,CH, -+ CH, + PhCH,CH, PhCHCH, -, H + PhCHCH, H + PhCH,CH, + H, + PhCH,CH, H + PhCH,CH, -+ H, + PhCHCH, H + PhCH,CH, -, PhH + C,H, H + PhCH,CH, -+ CH, + PhCH, (1) (2 4 (2) ( 5 ) (6) (6 4 (6 b) (6 c ) This was followed by the propagation reactions Present Address: British Gas Corporation, Westfield Development Centre, Cardenden, Fife. 31873188 PYROLYSIS OF ETHYLBENZENE C2H5 + PhCHZCH, -+ C2H6 + PhCHZCH, C,H, + PhCH,CH, -+ C2H6 + PhCHCH,. (8) (8 a) Possible chain-termination processes were H + PhCH, -+ PhCH, 2C2H5 --* C2H4 -t- C2H6 H+H+M-+H,+M.Szwarc suggested that the reaction was too complicated to be suitable for a conventional study and proposed a technique employing an excess of toluene as a carrier. Thus the reaction was modified to PhCH,CH, + PhCH, + CH, PhCH, + CH, -+ PhCH, + CH, 2 PhCH, -, (PhCH,),. Szwarc obtained a rate constant for reaction (I) k/s-l = lo1, exp (-263.3 kJ mol-l/RT). The carrier method has been widely used in one form or another in subsequent Estban et al., used aniline as a carrier in a plug flow apparatus. They obtained the rate constant for reaction (1) from the methane yield. Crown et aL3 used a stirred flow reactor to study the pyrolysis in the presence of an excess of toluene. Their findings show that the experimental first-order rate constant is dependent on the pressure of toluene and that the rate of methane production falls with a reduction in carrier pressure for a given partial pressure of reactant.k/s-l = 1014a6 exp (- 292.6 kJ mol-l/RT) The rate constant for reaction (1) was Clarke and Price4 have carried out a detailed investigation using a toluene carrier and have suggested that the pyrolysis occurs between 910 and 1089 K by 3 main reactions k/s-l = exp (- 289.2 kJ mol-l/RT). PhCH,CH, -+ PhCH, + CH, PhCHZCH, + PhH + C2H4 PhCH,CH, -+ PhC,H, + H,. (1) (13) (14) For the initiation reaction (1) a rate constant of k/s-l = exp (- 293 kJ mol-l/RT) was obtained. quartz vessel a rate constant of for reaction (1 3) was obtained. Experiments showed ethylene yield to be surface-dependent but in a conditioned k/s-l = exp (-216.1 kJ mol-l/RT)C. T.BROOKS, S. J. PEACOCK A N D B. G. REUBEN 3189 A rate constant for reaction (14) of k/s-l = exp (-267.5 kJ mol-l/RT) was obtained from styrene yield. Experiments without a carrier gas have been performed by Lee and Oliver5 and Hausmann and Kings who found the order of reaction for styrene formation to be one-half. A rate expression k:/mol: dm-g s-l = 1015 exp (-292.6 kJ mol-lRT) where was proposed. Considerable scatter on the Arrhenius plot makes the value unreliable. The following chain mechanism was proposed d[styrene]/dt = k+[PhCH,CH,]g (9 PhCH,CH, -+ PhCH, +CH, (1) CH, + PhCH,CH, -+ PhCHCH, + CH, (2 4 PhCHCH, -+ PhCHCH, + H ( 5 ) H + PhCH,CH, -+ PhCHCH, + H, (6 a) 2 PhCHCH, -+ various products.( W For long chains the expression d[styrene]/dt = (k, k: /2k,,,)~[PhCH,CH,]~ (ii) was found to be consistent with the experimental results. Thus the bulk of the kinetic studies have been carried out with carriers in flow systems. As better experimental techniques became available the limitations of these techniques became apparent. For a more complete investigation from which a reaction mechanism can be proposed it is desirable that the pyrolysis be carried out in the absence of carriers. Modern methods enable accurate results to be obtained for vapours in a static system.' This paper sets out (a) to confirm that the rate data obtained for the initiation reaction by carrier techniques also apply to the system in the absence of a carrier and (b) to obtain a satisfactory reaction mechanism.EXPERIMENTAL A conventional static system described previously was used.' RESULTS PRELIMINARY EXPERIMENTS The major reaction products are hydrogen and styrene. To minimise side reactions and secondary product formation, the reaction was studied at low conversions. A typical experiment at 783 K with 4 min residence time gave ca. 3% conversion. Thus ca. 0.55 Torrt of hydrogen and styrene were produced from an initial concentration of 30 Torr of ethylbenzene. The other products are methane and toluene formed in t 1 Torr = 101 325/760 Pa.3190 PYROLYSIS OF ETHYLBENZENE approximately an order of magnitude lower concentration together with ethylene, ethane and benzene. At these low conversions no other gaseous or liquid products were seen. After evaporating a sample of the condensate only trace quantities of solid products were identified by mass spectrometry.Hence we assume that only the primary pyrolysis reactions are taking place and accordingly for most of the kinetic experiments conversions were kept at these low levels. Reaction (12) giving bibenzyl is an attractive chain termination step but repeated attempts to detect it in the reaction products were unsuccessful. This was surprising but it is significant that the most recent study of the pyrolysis in the absence of carrier gas also failed to detect bibenzyl.* It is possible that it is unstable at the temperatures of these experiments. Oxygen impurity has a profound effect on hydrocarbon pyrolysis.Rates of pyrolysis were measured from samples of ethylbenzene which had been degassed a different number of times. The rate was independent of the number of degassing cycles which suggests that the ethylbenzene is oxygen-free. The variation of gaseous product yield with time is shown in fig. 1. For all products a linear relationship is obtained and hence initial rate was taken as the yield after 4 min divided by time. 0 2 4 6 8 10 residence time/min FIG. 1.-Progress of reaction with time. Hydrogen 0, methane 0, ethane and ethylene (> yield at 788 K for a mixture of 30 Torr of ethylbenzene and 300 Torr of nitrogen. Most experiments were carried out with a 6 cm diameter, 20 cm long silica reaction vessel with a surface-to-volume ratio of 0.077 mm-l. Initial rates were methane 2.5 x Torr s-l, hydrogen 2.29 x Torr s-l, ethylene 3.54 x Torr s-l and ethane 3.75 x lou4 Torr s-l for a reaction temperature of 792 K and ethylbenzene concentration of 34 Torr.Under similar conditions in a reaction vessel packed with silica tubes (1.105 mm-l surface-to-volume ratio) initial rates were methane 3.12 x Torr s-l, hydrogen 2.17 x Torr s-l, ethylene 3.96 x Torr s-l and ethane 3.12 x Torr s-l. Therefore under the conditions of our experiments the effects of surface were assumed to be insignificant.C. T. BROOKS, S. J. PEACOCK AND B. G. REUBEN 3191 Fig. 2 shows the effect of added nitrogen on reaction rate. Varying amounts of nitrogen were added to 30 Torr of ethylbenzene with a reaction temperature of 788 K and residence time of 4 min.Nitrogen increases ethylene yield and may decrease the benzene yield slightly but the other products are apparently unaffected. 0.7 0-5 k - O Q A 8 Q - 00 0'0 0" U U 0 0.31 I I I I , , 2- t- ; 2 0-08 0.06 2 5 0.07 2 a a 0.05 0.03 I : 0 I I I 1 I I B O m m o # U Y 0 0 0 0 n o - 8 B -. I I I I 1 1 100 200 3 00 4 00 500 600 nitrogen pressure/Torr FIG. 2.-Effect of added nitrogen on rate. Hydrogen 0, methane 0, ethane a, styrene 0, toluene D, ethylene c) and benzene A yields after 4 min. FORMATION OF METHANE AND TOLUENE If methane and toluene are formed only in an initiation reaction then their yields should be equal and the rate constant derived from both products should be the same. The rates of formation of these products showed a first-order dependence on ethylbenzene concentration (fig.3). The temperature dependences for methane and toluene formation are shown in fig. 4. The slopes of the lines yield values of k / s s 1 = 1014.48+1.1 exp (-293.8+ 18 kJ mol-l/RT) k/s-l = 1014.35*1.2 exp (-291.8+ 19 kJ mol-l/RT) and3192 PYROLYSIS OF ETHYLBENZENE 0 10 20 30 40 50 ethylbenzene pressure/Torr FIG. 3.-Dependence of methane 0 and toluene yield on ethylbenzene pressure. Reaction - 4.2 - 4 . 4 -4.6 h -1.8 . - 5 0 b~ -5.0 - - 5 . 2 - 5 . 4 -5.6 temperature = 719 K, residence time = 4 min. a 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 103 KIT FIG. 4.-Temperature dependence of methane 0 and toluene m yield. respectively, which are identical within experimental error. These rate data agree well with those obtained by carrier techniques and we conclude that methane and toluene are indeed produced only in an initiation stage.FORMATION OF HYDROGEN A N D STYRENE Hydrogen and styrene account for 90 % of the total reaction products. Fig. 5 shows the dependence of these products on ethylbenzene pressure and a least-squares analysis of a log-log line yields 0.6 reaction order for both products. The temperature dependence plot (fig. 6) yields a rate expression (in mol dme3 s-l) of d[H,]/dt = 1019.8*0.5 exp (- 377.4_+ 16.8 kJ rnol-'/RT) [PhC,H5]o-6 d[styrene]/dt = 1018.2+0.3 exp (-359.5 16.0 kJ mol-l/RT) [PhC,H5]o.6.0.6 t 0 . 5 0 + ---. 22 0 . 4 2 0.3 2 a 0.2 0 . 1 .- x I -0 0 3. T. BROOKS, S. J . PEACOCK A N D B. G. REUBEN 3 193 I 1 I I e t hy 1 benzene pressu re/Torr 10 20 30 LO FIG. 5.-Dependence of hydrogen 0 and styrene @ yield on ethylbenzene pressure.Reaction temperature = 719 K, residence time = 4 min. - 7.0 h ? -7.2 E a 0 - .g -7.L 1” E: -7.6 0 - I a a 3 v w 2 - 7 . 8 -7.0 I I 1 I I 1.24 1.25 1.26 1.27 1.28 1.29 103 K I T FIG. 6.-Temperature dependence of hydrogen 0 and styrene 0 yield. Ethylbenzene concentration = 6.05 x mol drnw3, residence time = 4 min. FORMATION OF ETHANE, ETHYLENE A N D BENZENE Fig. 7 shows the effect of ethylbenzene pressure on the yields of ethane, ethylene and benzene and reaction orders of 1 . 1 , 0.9 and 1 .O, respectively, are obtained. The temperature dependences (fig. 8) give rise to the rate expressions (all in mol dm-3 s-l) d[C,H,]/dt = l Ozl.osf 0-4 exp ( - 389.9 f 16.4 kJ ~ o ~ - ~ ) / R T [ P ~ C , H , ] ~ .~ d[C,H,]/dt = 1021-48*0.2 exp (-405.5 f 6.0 kJ ~ O ~ - ~ ) / R T [ P ~ C , H , ] ~ . ~ d[PhH]/dt = 1016.59*0-2 exp (- 321.4+ 18.0 kJ ~ o ~ - ~ ) / R T [ P ~ C , H , ] .3194 PYROLYSIS OF ETHYLBENZENE I 0.30 0.20 0.10 0 10 20 30 4 0 ethyl benzene pressure/Torr FIG. 7.-Dependence of ethane 0 , ethylene 0 and benzene A yield on ethylbenzene pressure. Reaction temperature = 719 K, residence time = 4 min. - 4 . 4 - 4 . 6 h T - 4 , 8 c, c - 5 . c m -0 Q) 2) ;h W - 5 -5.2 s. Y w " 5 . 4 - - 5 . 6 - 5.E 0 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1 0 3 K I T - 4 . 4 - 4 . 5 -4.6 n -4.7 v al N P -4.8 5 s. u 0 -4.9 2 -5.0 -5.1 FIG. 8.-Temperature dependence of ethane ethylene 0 and benzene yield. Ethylbenzene concentration = 6.05 x lo-* mol dm-3, residence time = 4 min.C. T.BROOKS, S. J. PEACOCK A N D B. G. REUBEN 3195 TABLE 1 .-SOLID COMPOUNDS FOUND BY MASS SPECTROMETRIC ANALYSIS OF THE RESIDUE FROM THE PYROLYSIS OF ETHYLBENZENE AT HIGH CONVERSIONS accurate mass relative molecular (measured) molecular intensity weight formula (%I compounda 128 142 152 154 166 168 178 180 192 194 202 204 206 216 228 230 252 254 278 280 300 302 304 330 342 3 50 378 380 402 502 - 142.0770 (CllHlo) 154.0793 (CI2Hl0) 166.0782 (C13Hlo) 168.0939 (C13H12) 178.0782 (C14Hlo) 180.0939 (CI4Hl2) 192.0939 (C15H12) 194.1095 (C15H14) 202.078 3 ( C16Hlo) 204.0939 (C16H12) 206.1096 (C16H14) 216.0938 (Cl,Hl2) - - 5 trace 1 1 4 5 2 100 20 14 2 26 29 5 4 4 5 10 17 9 6 trace 2 2 3 trace trace trace trace trace trace naphthalene methylnaphthalene biphenylene biphenyl fluorene biphenylmethane anthracene stilbene met hylan t hracene ethylfluorene pyrene dihydropyrene ethylanthracene methylpyrene chr y sene p-terphenyl benzop yrene dihydrobenzopyrene benzochrysenes dihydrobenzochrysenes coronene benzopery lenes di hydrobenzopery lenes methylbenzonaphthoperinaphthenes methyldibenzochrysene pyrenopyrene dibenzopicenes dihydro benzopicenes tetrabenzopyrene benzanthracenopyrene a Other isomeric forms are possible.FORMATION OF HIGHER MOLECULAR WEIGHT PRODUCTS Samples of the solid products of reaction in the condensate were prepared in a simple flow apparatus operating at 778 K and 833 K with 2 min residence time. The electron impact mass spectrum of the volatile matter in the sample was obtained using a Varian MAT 31 1 A mass spectrometer linked to an on-line data system.At low conversions obtained from the experiment carried out at 778 K, very few products other than styrene, toluene and benzene are observed. However, at higher conversions a range of polynuclear aromatic hydrocarbons was found. The m/z values for the parent peaks together with relative abundance and possible structures are shown in table 1 . It also shows examples of some of the components of the solid products identified by accurate mass measurements.3196 PYROLYSIS OF ETHYLBENZENE DISCUSSION STOICHIOMETRY A N D ANALYTICAL ERROR The reaction products obtained by all workers suggest that the integrity of the benzene ring is retained in all reactions in this system at temperatures up to ca. 800 K.If multi-ring products are discounted, then stoichiometry demands that styrene yield must equal hydrogen + methane + ethane yields, methane yield must equal toluene yield and benzene yield must equal ethane +ethylene yields. Previous workers, for example Shirazi,* have not concentrated on this point, presumably because of analytical difficulties that were also observed in this work. Toluene and methane yields were found to be identical within experimental error, as mentioned earlier and shown in fig. 4. Hydrogen yields typically appeared 1 5 % higher than styrene yields as illustrated in fig. 6, though at the low temperature used for the run shown in fig. 5 they appear equal as would be expected in view of the methane and ethane yields being small compared with the styrene yield.The styrene peak on the gas chromatograph trace occurred on the side of a very large ethylbenzene peak and though its size was estimated by a consistent technique, we are inclined to attribute the discrepancy largely to a systematic error in this measurement. Nonetheless, note that formation of coking precursors such as polynuclear aromatic hydrocarbons would lead to an excess of hydrogen over styrene and that this would increase with temperature. Yields of benzene were approximately in balance with ethane + ethylene (fig. 7) considering the errors involved in measurement of such small concentrations. The activation energy for benzene production (fig. 8) is slightly less than for ethane and ethylene which would be consistent with a loss of benzene at higher temperatures to give polynuclear aromatic hydrocarbons.The effect of added nitrogen is most difficult to explain (fig. 2) in that benzene yields drop while ethane remains constant and ethylene increases. This would also be consistent with the formation of polynuclear aromatic hydrocarbons and the amounts that would need to be formed are very small. There is no obvious reason, however, why added nitrogen should have this effect. POSSIBLE REACTION MECHANISMS To account for all the products, any reaction mechanism is necessarily complicated. Initiation is via reaction (1) followed in Szwarc’s scheme by reactions (2) and (20) which give rise to PhCH,CH, and PhCHCH,. Whether both these radicals are involved in the mechanism is open to discussion. On the one hand, abstraction reactions between free radicals and olefins containing allylic hydrogen atoms are generally accepted to involve only the latter.Reaction (2a) might thus be expected to be at least an order of magnitude faster than reaction (2) and subsequent reactions of PhCH,CH, might reasonably be ignored. On the other hand, the added stability of the PhCHCH, radical which makes it the preferred product also leads to its being less reactive. ShirazP has calculated that in certain cases PhCH,CH, reacts lo7 times as fast as PhCHCH, and we have consequently felt it justifiable to retain both species in our mechanism. Formation of toluene and methane in equal amounts suggests that the benzyl radical is more reactive than originally proposed by Szwarc and suggests the need for reactions (3) and ( 3 a ) : PhCH, + PhCH,CH, + PhCH,CH, + PhCH, PhCH, + PhCH,CH, --+ PhCHCH, + PhCH,.(3) (3 4C. T. BROOKS, S. J. PEACOCK A N D B . G. REUBEN 3197 Szwarc suggested that toluene might also be formed by the reaction We have not felt it necessary to include it because our rate constants for toluene formation agree with those involving carriers where reaction (1 5 ) is not thought to take place. Decomposition of PhCHCH, was proposed to account for styrene formation in reaction ( 5 ) . The radical PhCH,CH, might similarly react as in reaction (4) to give ethylene CH,+PhC,H, -+ C,H5+PhCH,. (15) PhCH,CH, -+ Ph + C2H4. (4) The phenyl radical can then react as in reactions (7) and (7a) to yield benzene Ph + PhC,H, ---* PhH + PhCH,CH, Ph + PhC,H, + PhH + PhCHCH,.C2H5 + PhCZH, -+ PhCHZCH, + C2H6 C,H, + PhC,H, -+ PhCHCH, + C2H6. (7) (7 4 (8) (8 4 Ethylene formation is dependent on nitrogen concentration and under the conditions (9) Ethane, the remaining product, can be formed by attack of an ethyl radical on e thy1 benzene of this work the reaction C,H,+M -+C,H,+H+M is in its pressure-dependent region and hence it probably also occurs. The mechanism is therefore made up of a number of cycles. The major cycle yields hydrogen and styrene and this accounts for 90% of the reaction product. Benzene and ethylene are formed in another cycle whilst ethane is formed in the third cycle. In addition some ethylene is formed separately by the decomposition of ethyl radicals. Fig. 9 represents the scheme diagrammatically. It illustrates the interlocking cyclic nature of the reactions.The solid circles represent reactions and reactants are shown as entering and products as emerging from them. Free radicals are shown as molecular formulae and neutral molecules as names. The ‘crossroads’ at the open circle reflect the fact that reactions generating PhCH,CH, might also generate PhCHCH,. To summarise, the propagation reactions considered are reactions (2)-(9) below : PhCH,CH, -+ PhCH, + CH, (11 (2) (2 4 (3) (3 4 (4) ( 5 ) (6) (6 4 (6 4 CH, + PhCH,CH, -+ PhCH,CH, + CH, CH, + PhCH,CH, -+ PhCHCH, + CH, PhCH, + PhCH,CH, -+ PhCH,CH, + PhCH, PhCH, + PhCH,CH, -+ PhCHCH, + PhCH, PhCH,CH, -+ Ph + C,H, PhCHCH, -+ H + PhCH :CH, H + PhCH,CH, -+ PhCH,CH, + H, H + PhCH,CH, -+ PhCHCH, + H, H + PhCH,CH, -+ C,H, + PhH3198 PYROLYSIS OF ETHYLBENZENE ethylbenzene I I G PhCHCH, I\ 5 styrene I 1 11 ethylbenzene 1 I I H Ph \ ethylbenzene ethylene + M b 6b benzene M FIG.9.-Diagrammatic representation of the proposed ethylbenzene pyrolysis mechanism. Ph + PhCH,CH, + PhCH,CH, + PhH Ph + PhCH,CH, -, PhCHCH, + PhH C,H, + PhCH,CH, -+ PhCH,CH, + C,H, C,H, + PhC,H, + PhCHCH, + C,H, C2H5 + (M) -+ H + C2H.4 + (M) (7) ( 7 4 ( 8 ) ( 8 4 (9) (10) 2 PhC,H, -+ PhCH,CH, + PhCH : CH,. Szwarc reported a chain length of ca. 15. The ratio initiation/overall rate in this work suggests a chain length of just over 10. No single high-molecular-weight product predominates in the mass spectrometric analysis of the solid products and hence we assume that the major termination reaction is via disproportionation 2 PhCHCH, -+ PhCH,CH, + PhCHCH,.(10) The rate expression for styrene is d[PhCH : CH,]/dt = 2k,[PhC2H5] + k5(k1/k10)' [PhC2H,]g. (iii) Hence a plot of rate of styrene formation/[ethylbenzene] against [ethylbenzene$ should be a straight line with the intercept equal to k,. Fig. 10 shows that this is approximately true. From the methane and toluene yield 2k, = 19.42 x lop8 s-l. The least-squares intercept is 2.5 x s-' but there is considerable scatter and the line inC. T. BROOKS, S. J. PEACOCK A N D B. G. REUBEN 3199 effect goes through the origin. If 2k1 [PhC,H,] is assumed to be small compared with k5( k 1 / k 10); [ PhC , H ,I+ then d[PhCH : CH,]/dt = k,(kl/kl,)~[PhC,H5]~ (iv) and half-order kinetics are predicted.In fact the chain length is ca. 10; so the first term cannot be neglected and hence an order slightly greater than 0.5 is predicted by the mechanism. Experiment gives a value of ca. 0.6. 3 1 . 4 v1 . h c ; 1.2 $ 1.0 N OJ 2 c) Y . h c .s 0.8 2 2 J 5 a 0 - € c x c) 0.4 - E v X 5 0.2 v I I I I 0 0.1 0.2 0.3 0.4 0.5 [ ethylbenzene 1 -4 FIG. 10.-Function plot to test the proposed mechanism. If a value for the rate constant of the termination reaction (10) is assumed, then it is possible to estimate a value for the rate constant for reaction ( 5 ) PhCHCH, + H + PhCH : CH,. Now kstyrene = k5(k1/k10)t (v) k5ls-l = (Astyrene) (~lo/AA'ex~ [( -Estyrene +iQ/RTI ( 5 ) (vi) where kstyrene and Astyrene are the experimentally measured rate constants and Arrhenius parameters.Substituting for k, and kstyrene and assuming a value for k,, allows k, to be estimated. Benson9 suggests that termination reactions involving large radicals have a rate constant of ca. k5/s-l N 1015.9 exp (-217 kJ mol-l/RT). The high value for the activation energy is a result of the resonance stabilisation of the radical PhCHCH,. Thermochemical calculation suggests a value of ca. 205 kJ mol-1 for the activation energy. The rate expression for hydrogen yield is more complicated as hydrogen is produced in reactions ( 6 ) and (6a) and hydrogen atoms are consumed in reactions (6), (6a) and dm3 mol-1 s-l. Hence using this figure (6 b).3200 PYROLYSIS OF ETHYLBENZENE Eqn (vii) describes hydrogen yield (vii) where 8 = (k, + kau) [PhC2H5] + k,. If ksb 6 (k, + k6u) then an expression identical to that for styrene yield is obtained.d[H,]/dt = k,(kl/klo)g [PhC,H,]g. (viii) By carrying out an analysis as described earlier a further check of the rate constant for reaction ( 5 ) can be obtained. This yields k5/s-l = 1016.5 exp (-229.9 kJ mol-l/RT). This value is less accurate than that obtained from styrene yield because in addition to the assumptions made there it also assumes that k6b is very small compared with (k6 + k6~). A comparison of hydrogen yield with ethane yield gives the rate expression (ix) d[H21/dt - - (k6 + k6U) + (k6 + '6U) kg [phC,H5]-1. d[C2H61/dt k6b (kt3 + '8U) k6b A plot of (d[H,]/dt)/(d[C,H,]/dt) against [PhC,HJ1 should yield a straight line with an intercept of (k6 + k,,)/k,b and a gradient of (k6 + k6J k,/(k, + kau) kSb.Fig. 1 1 shows that this holds true for a number of temperatures between 758 and 945 K. The ratio of gradient to intercept gives a value of k,/(k, + k8u). Thus an Arrhenius plot of log(gradient/intercept) against inverse temperature will yield an activation energy and pre-exponential factor for this ratio of rate constants. However a small .: 2 -: M E O 1 I 1 I I 1 I 0 0.02 0.04 0.06 0.08 0.10 0.12 [ethylbenzene] -1 /Tom-' FIG. 11.-Comparison of hydrogen and ethane yields with [ethylbenzene]-' at 845 K 0 , 8 1 5 K 0, 791 K 0, 764 K 0, 825 K 0, 798.5 K and 758 K A.C. T. BROOKS, S. J. PEACOCK AND B. G. REUBEN 320 1 error in the value of the intercept has a large effect on the function (gradient/intercept) and leads to a meaningless plot.A more productive approach is to plot log(gradient) against inverse temperature to yield Arrhenius parameters for the function (k,+k6,)kg/(k,+k,,)k6b. The plot is shown in fig. 12. It yields a value of 47.2 1 1.7 kJ mol-l for the activation energy. This is equal to &, 6a + E, - E,, - E6b where &, 6, and E,, 8a are approximate activation energies applicable to reactions (6) and (6a) and (8) and @a), respectively. The scattered intercepts in fig. 11 suggest that &, 6a - &b is Ca. 0. If so Eg - E,, = 47.2 kJ m01-l. c 2 -3.2 % 2 +, -3.0 2, % Y . m 3 - 2 . 8 + - 2 . 4 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1 O3 KIT FIG. 12.-Arrhenius plot for the function (k, + k6u) k,/(k, + kEU) kBb derived from the pyrolysis reaction scheme. Arrhenius parameters for reaction (9) are well documented.Lin and Backlo suggest kco/s-l = 1013-6 exp (- 158.8 kJ mol-l/RT). Arrhenius parameters for the ethane-forming reactions (8) and @a) are more difficult to obtain. However, by analogy with ethyl radical reactions an activation energy of 58.5 kJ mol-l seems reasonable. This means that Eg-E,,8u is ca. 100 kJ mol-l compared with the experimental value of 47+ 11 kJ mol-l. Reaction (9) is, however, in its pressure-dependent region and Lin and Back report the activation energy for the bimolecular limit to be 135.4 kJ mol-l. Using this value E, - Fa, ,, becomes 76.1 kJ mol-l giving better but still only moderate agreement with experiment where 0 = (k, + kaa) [PhC,H5] + k,. If k, b (k,+k,,) [PhC,H,] then an order of 2 is predicted if reaction (9) is taken as second order. In this pressure region its order will be 2 so an order of $ is predicted. If the reverse is true and k , is small then3202 PYROLYSIS OF ETHYLBENZENE and an order of $ is predicted. This does not agree with the experimental value of 1.1 and suggests that the two terms are of similar value, and if anything reaction (9) is the more important. If so, a considerable quantity of ethylene is produced via reaction (9) and its inclusion in the mechanism is justified. We thank the referees for helpful and constructive comments. M. Szwarc, J. Chem. Phys., 1949, 17, 431. G. L. E. Estban, J. A. Kerr and A. F. Trotmann-Dickenson, J . Chem. SOC., 1963, 3873. C. W. P. Crowne, V. J. Grigulis and J. J. Throssell, Trans. Faraday Soc., 1969, 65, 1051. W. D. Clark and S. J. Price, Can. J. Chem., 1970, 48, 1059. E. H. Lee and G. D. Oliver, Ind. Eng. Chem., 1959, 51, 1351. 13 E. D. Hausmann and C. J. King, Ind. Eng. Chem., Fundam., 1966, 5, 295. ’ C. T. Brooks, S. J. Peacock and B. G. Reuben, J . Chem. SOC., Faraday Trans. I , 1979, 75, 652. Z. H. Shirazi, Ph.D. Thesis (University College of Wales, Swansea, 1973). S. W. Benson, Thermochemical Kinetics (Wiley, New York, 1967). lo M. C. Lin and M. H. Back, Can. J. Chem., 1966, 44, 2357. (PAPER 1 / 1879)