J. Phys. Chem. 1985,89, 2013-2019
2013
A Shock Tube Investigation of Major Pathways in the High-Temperature Pyrolysis of Benzene J. H. Kiefer,* L. J. Mizerka, M. R. Patel, and H.-C.Wei Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60680 (Received: November 30, 1984)
The high-temperature pyrolysis of benzene, 1 and 2 mol % in krypton, has been studied in the shock tube with the laser-schlieren technique over 1900-2400 K and 0.2-1 .O atm. A completely successful modeling of the density gradient profiles and some time-of-flight mass spectra is achieved with a simple radical chain mechanism consisting of essentially just four reactions. The dissociation is solely CH bond scission (M) + C6H6 C6H5+ H + (M) whose rates are strongly dependent on both temperature and pressure in this range; this reaction is near second order for T > 2300 K. An RRKM fit to these data suggests a barrier of 112 f 2 kcal/mol, which corresponds to " p 2 9 8 = 80 2 kcal/mol for the phenyl radical heat of formation, and an average collisional energy transfer of (-AE)au = 70 cm-I. The extrapolated k , for this reaction is 2 X 10'' exp(-118000 (cal)/RT) s-I (1900-2400 K). The model also indicates a rate constant of 2.5 X lOI4 exp(-16000 (cal)/RT) cm3/(mol s) (1900-2200 K) for the abstraction H + CsH6 C6H5 + H2.
-
*
-
Benzene pyrolysis has an obvious importance deriving from the molecule's common appearance in fuels, as well as in the products and feedstocks of pyrolytic olefin production. The aromatic ring also carries a unique stability and may well play a major role in soot f0rmation.l As a consequence this pyrolysis has been extensively studied over a rather broad range of conditions and by a variety of methods. For the lower temperatures, below about 1300 K, the primary pyrolysis products are biphenyl and other p o l y a r ~ m a t i c s , ~al-- ~ though even here some ring opening can occur.4 There is little agreement as to reaction order or rate among the studies in this the reaction evidently a radical chain which may not be completely homogeneous.6 This work has been reviewed by Brooks and Peacock: Asaba and F ~ j i iand , ~ V a ~ g h n .A ~ rather complete listing of papers is given by Smith and Johnson.8 Pyrolysis at higher temperatures has been observed in flow react0rs,63~a Knudsen and the shock t ~ b e . ~ * Here ~ 9 ' the ~~~ product distribution seems quite well defined, there being only minor disagreement among analyses. The dominant product species are C2H2and C4H2, produced in approximate equality for moderate temperat~res.~-'OAt higher temperatures, above about 1400-1 500 K, depending on benzene concentration, C2H2begins to dominate. Numerous minor products are also seen; a most complete listing is provided by Smith and Johnson.8 They are concerned over possible heterogeneous reactions in their Knudsen cell, but their essential findings are well confirmed by the homogeneous shock tube analyses.'JO At the lower temperatures small quantities of biphenyl and other large aromatics persist, whereas substantial quantities of the polyacetylenes C&2 and C8H2 appear as the temperature is raised. Trace quantities of
C4H4(vinyl acetylene), C4H3,C3H3,and C6H4were also identified. There would seem to be some disagreement regarding the quantity of vinyl acetylene produced,7,8J0but the amount is certainly small. A rather surprising result in the dynamic analyses is the absence of measurable phenyl radical.8v'0 Both Smith and Johnson8 and Singh and Kernlo have also investigated the pyrolysis of chlorobenzene under similar conditions, producing substantial phenyl, thus indicating that instability cannot account for the near absence of this radical in the benzene pyrolysis. Another anomaly in the shock tube product analyses is the observation of styrene as a major product in the single-pulse study of Vaughn.' Styrene was not detected in any other reported product analysis. The high-temperature studies also disagree on both rate and reaction order. Several a ~ t h o r s ~report * ~ ~rates ' ~ second order in benzene with very low effective activation energies (30-38 kcal/mol). However, those studies using very low initial benzene c o n c e n t r a t i ~ n s suggest ~ J ~ ~ ~first-order ~ rates with much greater E,. The results obtained at high benzene concentration probably reflect secondary radical chain decomposition. Two very recent papers reporting rates at very high temperatures and low benzene concentration are of particular interest here.I2*l3 The first is an atomic resonance absorption (ARAS) study of D-atom formation rates in shock waves from C6D6 highly dilute in argon.I2 Rates were corrected for the isotope effect with the result k = 7 X 1013exp(-95000/RT) s-l (1630-1900 K) for the first-order rate constant of C6H6 dissociation. The second is again a shock tube study, this time monitoring C O production in the very fuel-lean oxidation of benzene.13 Here the suggestion is that the unimolecular dissociation CsH6 C6H5 4- H (1) -+
(1) S. C. Graham, J. B. Homer, and J. L. J. Rosenfeld, Proc. R. SOC. London, Ser. A , 344,259 (1975);Tenth International Shock-Tube Sympo.~ sium, Kyoto, 1975,p 621. (2)G. M. Badger and J. Novotny, J . Chem. SOC.,3400 (1961). (31 R. Louw and J. H. Lucas. Recl. Trav. Chim. Paw-Bas. 92.55 (1973). (4)C.T.Brooks, S. J. Peacock, and B. G. Reuben, Chem. Soc.,Furadiy Trans. I , 75, 652 (1979). (5) T. Asaba and N. Fujii, Symp. (Int.) Combust. [Proc.],13th, 1971, 155
(1972). (6)K.C.Hou and H. B. Palmer, J. Phys. Chem., 69,863 (1965). (7)S. N.Vaughn, Ph.D. Thesis, Kansas State University, 1980. (8) R. D.Smith and A. L. Johnson, Combust. Flame, 51, 1 (1983). (9)R. S. Slysh and C. R. Kinney, J. Phys. Chem., 65, 1044 (1961). (10)R.D.Kern, H. J. Singh, H. J. Esslinger,and P.W.Winkeler, Symp. (Int.) Combust., [Proc.],19th, 1982, 1351 (1983);H. J. Singh and R. D. Kern, Combust. Flame, 54,49 (1983). ( 1 1) I. L.Mar'yasin and A. Z . Nabutovskii, Kinet. Katal., 10,983 (1969). (12)V. S . Rao and G. B. Skinner, J . Phys. Chem., 88, 5990 (1984). (13) D.S. Y. Hsu, C. Y.Lin, and M. C. Lin, Symp. (Int.) Combust., [Proc.],ZOth, 1984, in press, and private communication. (14)R.D. Kern,C. H. Wu, G. B. Skinner, V. S. Rao, J. H. Kiefer, J. A. Towers, and L. J. Mizerka, Symp. (Int.) Combust., [Proc.],ZOth, 1984, in press.
0022-3654/85/2089-2013$01.50/0
is effectively rate controlling, and a rate constant, k = 5 X 10l5 exp(-108000/RT) s-' (1600-2300 K), is then derived for this reaction. Both experiments used pressures near 2 atm, yet these rates differ by a factor 2-3 where they overlap. A preliminary, initial-rate analysis of laser-schlieren data on benzene p y r ~ l y s i salso ' ~ indicated endothermic rates too large to be compatible with the ARAS measurements. Here a parallel molecular channel, C6H6 CzHz + C4H4,was proposed as a possible explanation for the low H-atom formation rate. In the present paper, a partly new and more complete set of laserschlieren data is presented and fully analyzed. Confinement of dissociation to the C H bond scission, reaction 1, is now found to be completely successful in modeling the density gradient profiles, and the notion of a parallel molecular channel is no longer supported.
-
Experimental Section The apparatus and methods used in the measurement of density gradients by the laser-schlieren method have been described in 0 1985 American Chemical Society
2014
The Journal of Physical Chemistry, Vol. 89, No. 10, 1985
TABLE I: Initial rod Frozen Reaction Conditions shock PI, VI p23 T2, no. torr mm/ps torr K 2.00% CnH,-Kr f
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
14.12 12.30 1 1.06 25.23 27.40 26.25 26.63 32.43 29.83 22.63 11.69 14.46 11.50 15.17 14.03 13.04 12.24 11.29 10.51 10.03 9.15 10.76 9.51 8.25 8.57 8.11 4.97 3.60 4.31 4.10
1.004 1.027 1 .OS9 1.028 0.999 1.026 1.004 0.995 1.011 0.994 1.053 1.014 1.063 0.994 1.004 1.030 1.047 1.063 1.093 1.089 1.118 1.074 1.104 1.151 1.135 1.143 1.073 1.149 1.110 1.117
382 348 333 714 731 741 719 859 816 599 346 396 347 399 376 369 358 340 335 318 305 33 1 309 292 295 283 153 127 142 137
31 32 33 34 35 36 37 38 39 40 41 42 43
12.68 14.09 10.97 11.59 11.99 10.95 5.53 4.91 4.88 4.85 4.80 4.72 13.35
1 .oo% C6H6-KT 1.032 352 1.003 369 1.072 327 1.081 352 1.049 342 1.092 338 1.053 158 1.108 156 1.111 156 1.097 151 1.090 147 1.116 153 1.023 363
Kiefer et al. This same program was also used in the modeling of some time-of-flight (TOF) mass spectra of benzene pyrolysis.I0 For these calculations thermodynamic data were estimated by standard methodsSz0 Heats of formation of all acetylenes, polyacetylenes, and their radicals are those of ref 21. The C4H3radical is assumed to be the less stable isomer CH==CH-C=CH, with an estimated = 126 kcal/mol. Since this radical will be assumed to dissociate rapidly, this estimate is not critical. The one radical whose properties are significant is the phenyl radical. The equilibrium constant for the initiation reaction
P21
pmollcm)
1921 1993 2101 1999 1905 1993 1924 1895 1946 1892 2081 1955 2114 1890 1921 2006 2064 2114 2216 2205 2303 2153 2255 2422 2365 2393 2148 2415 2276 2302
3.18 2.80 2.54 5.73 6.15 5.96 5.99 7.27 6.72 5.07 2.66 3.25 2.63 3.38 3.14 2.95 2.78 2.58 2.42 2.31 2.12 2.46 2.20 1.93 2.00 1.89 1.14 0.85 0.96
2132 2032 2276 2311 2193 2352 2207 2413 2425 2371 2344 2444 2101
2.64 2.91 2.30 2.44 2.50 2.31 1.15 1.04 1.03 1.02 1.01 1 .oo 2.77
1 .oo
detail.I5*l6Benzene (Fisher spectroanalyzed) was vacuum distilled, and a middle fraction introduced to a 50-L glass vessel. G C analysis found the benzene better than 99.9% pure, in accord with the maker’s specifications. Proportions of krypton (Spectra-Gases U.H.P.) and benzene vapor were set manometrically and the mixtures stirred for more than 1 h before use. Two mixtures, one of 1.00% C6Hsin Kr, the other 2.00% C6H6 in Kr, were prepared. Preshock conditions for a11 the experiments are listed in Table I. Calculations Thermodynamic properties for benzene were calculated from the frequencies given by Shimanouchi,I7 with results agreeing with the API tabulationI8 for T I 1500 K. Frozen reaction conditions were calculated with these properties and are displayed in Table I. Density gradient profiles were modeled with a Gear-integrator kinetics routine with imposed ideal shock conservation re1ati0ns.I~
C6H6
+
C6H5
+H
(1)
is small even at very high temperatures, and this reaction is rapidly equilibrated under nearly all present conditions. The results are then sensitive to the value of this equilibrium constant and thus to the properties of phenyl radical. Entropies and enthalpies (heat capacities) for phenyl were estimated with the methods of ONeal and Benson,z2 and its heat of formation was taken as AHf0z98 = 81 kcal/m01.~~ Over the range 1800-2500 X, the derived equilibrium constant is K 1 = 128 exp(-55850/T) mol/cm3. Although the modeling results are indeed sensitive to K 1 , any variation of this can be nearly compensated by an opposing change in the rate constant for phenyl dissociation, a much more uncertain parameter, so this sensitivity is of little real consequence. In this paper a new RRKM program is used, the program incorporating a Beyer-Swinehart vibrational state countz4with a classical treatment of active rotations2s for the transition state. The Whitten-Rabinovitch approximationz5 is retained for the molecular state density. The correction factor for the adiabatic rotations is that suggested by Troe,z6 and the calculation also includes his anharmonic correction. This program has been constructed to be in complete accord with Troe’s formulation of the second-order rate constant in the low-pressure limit. Results and Analysis Experimental density gradient profiles are shown in Figures 1-3. Also in these figures are the results of modeling with the mechanism of Table I1 which is discussed below. The observed density gradients show a distinct local maximum, broad and comparatively late at low temperatures and narrow, early, and only partially resolved at high temperatures. This maximum shows there is a strong initial acceleration of the net endothermic rate in benzene pyrolysis, an observation usually indicative of radical chain decomposition. The presence of a strong initial rise in density gradient makes the usual procedure of extrapolation to zero time for an initial ratel6 quite uncertain, and rates for the initiation, here taken to be solely reaction 1, were determined by interpolation between computed profiles after the rest of the mechanism had been established. The rate constants for (1) thus derived are exhibited in Figure 4. Also shown here are the results of an RRKM model whose parameters were chosen to fit these rates, and the highpressure limit rate constant kl”, obtained from this model. The data of Figure 4 are actually more precise than they appear; the scatter at high temperatures is in large part a result of the strong pressure dependence of the first-order rate in this range. The pressures cited in Figure 4 are mean values for three groups of experiments with similar pressures, and, as indicated, there is significant variation within these groups. When the high-temperature rate constants are plotted second order, as they are in Figure 5 , the scatter is much reduced and the rates very nearly (20)S. W. Benson, ‘Thermochemical Kinetics”, 2nd ed.,Wiley, New York 1976.
(15)J. H.Kiefer in ‘Shock Waves in Chemistry”, A. Lifshitz, Ed., Marcel Dekker, New York, 1981,p 59. (16)M.Z.AI-Alami and J. H. Kiefer, J. Phys. Chem., 87, 499 (1983). (17) T. Shimanouchi, Narl. Stand. Ref. Data Ser., Narl. Bur. Srand., No. 39 (1972). (18)‘Selected Values of Properties of Hydrocarbons and Related Compounds”, American Petroleum Institute Research Project 44, 1975. (19)W. C.Gardiner, Jr., B. F. Walker, and C. B. Wakefield in “Shock Waves in Chemistry”, A. Lifshitz, Ed., Marcel Dekker, New York, 1981,p 319.
~
(21)J. H.Kiefer, S. A. Kapsalis, M. Z.AI-Alami, and K. A. Budach,
Combust. Flame, 51, 79 (1983). (22)I H. E. O”ea1 and S. W. Bensim, Int. J . Chem. Kiner., 1, 221 (1969). (23) G. A. Chamberlain and E.Whittlle, Trans. Faraday SOC.,61, 2077 (1971). (24)S . E.Stein and B. S. Rabinovitch, J. Chem. Phys., 58,2438 (1973). (25)P. J. Robinson and K. A. Holbrook, ‘Unimolecular Reactions”, Wiley, New York, 1972. (26)J. Troe, J. Chem. Phys., 66,4745,4758(1977);J . Phys. Chem., 83, 114 (1979).
The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 2015
High-Temperature Pyrolysis of Benzene
"(E) dx
cm4
T ' 4
.t
1
2
3
4
Figure 1. Semilog plots of measured density gradients (X) for experiments 12 (2% C6H6-Krr1955 K, 396 torr) and 32 (1% C6H6-Kr, 2032 K, 369
torr). The lines indicate the results of modeling with the mechanism of Table 11. The rapidly falling initial points are caused by residual beam-shock front interaction. TABLE E W t i c Mechanism for Benzene Pyrolysis
reaction no. 1 2 3 3a
3b
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
- +
reaction'
log A,b cgs
n
E,, kcal/mol
C& + (M) C6H5 + H + (M)' C6H6 + H C6H5 + H2 CsH5 C4H3 C2H2(P2 740 torr) C6H5+ M C4H3+ C2H2+ M (Pz 350 torr) C6H5 M C4H3+ C2H2+ M (P2 150 torr) C4H3 + M C4H2 H + M C6H2 C6H + H H2 + M + 2 H + M C2H2 + M C2H + H + M C2H + H2 H + C2H2 C2H + C2H2 C4H2 + H C4H2 C4H H C2H + C4H2 C6H2 + H C4H C2H2 C6H2 + H C6H + C2H2 CsHz + H C2H + C6H2 C8Hz + H C4H2 + C4H C8H2 + H C4H + H2 H + C,H2 C6H + H2 H + C6Hz C8H + H2 H C8H2 C2H + H --* C2 + H2 C4H + H C4 + H2 C4H C4 + H C4 C(so1id) C2H + C6H.5 C6H5 + C2H2 C4H + CsH6 C6H5 C4H2 C.5H C6H6 C6H5 + C6H2 CsH + C6H6 C6H5 + C8Hz
14.40 15.20 15.60 15.78 5 1.52 14.89 12.35 16.62 12.87 13.60 14.89 13.60 13.60 13.60 13.60 13.60 13.30 13.30 13.30 12.00 13.48 13.90 8.00 13.30 13.30 13.30 13.30
0.0 0.0 0.0 0.0
16.0 82.0 37.0 37.0 63.0 120.0 92.5 107.0 0.0 0.0 120.0
+
-
---+ --
+
+
+
--
+
+
+
+
+
+
-
+
-
+
+
--
+
+
+
source PWd
10.0
0.0 -0.5 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 116.6 0.0 0.0
0.0 0.0 0.0
PW
PW PW
PW
est 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21
est
est est est
'The reverse of each reaction is included through detailed balance. bThe rate constants have the form A T " exp(-E,/RT). 'Pressure dependent, see text. dPresent work. coalesce a t 2400 K. This dissociation is close to second order for T > 2300 K and P < 0.5 atm. One complication in these experiments is the formation of substantial soot, which is reflected in serious attenuation of the He-Ne laser radiation at late time. This attenuation was monitored in selected experiments by recording the sum signal from the divided ph~todetector.'~In some of the low-temperature, high-pressure experiments, attenuation reached 30%by the end of the 45-ps recorded period, but in no case was there any overlap of this attenuation with measurable differential signal. In all cases the density gradient had dropped to less than 5% of its initial value before the appearance of detectable attenuation. The measurements of density gradient are then unaffected by soot formation and its attendant beam attenuation. This observation also suggests that the reactions ultimately leading to soot formation play little
if any role in the initial endothermic decomposition. The mechanism used for modeling both the density gradient profiles and the TOF data of Kern et a1.I0 is given in Table 11. The important reactions here are the first four, which essentially constitute the chain mechanism originally proposed by Bauer and Aten.27 Reactions 5-22 and their assigned rates were taken from ref 21 without modification. The rates for the four abstraction reactions, 23-26, are estimates. These reactions are then found to be of almost no consequence. The rate of (4) is an estimate, this decomposition assumed to be near second order under present conditions. Rate constants for the remaining three reactions, 1-3, were then the only parameters varied in fitting the density gradient profiles. Reactions 1 and 3 have rates dependent on both pressure (27) S. H.Bauer and C. F. Aten, J. Chem. Phys., 39, 1253 (1963).
Kiefer et al.
2016 The Journal of Physical Chemistry, Vol. 89, No. 10, 1985
4
4
2
-U--J 1
10-5
2
3
I
4
t (PSI
Figure 2. Semilog plots of measured density gradients ( X ) for experiments 6 (2% C6H6-Kr, 1993 K, 741 torr) and 1 1 (2% C6H6-Kr, 2081 K, 346 torr). The lines indicate the result of modeling with the mechanism of Table 11.
6
6
t
4t *i-. I
4
n
.
\
1
2
Figure 3. Semilog plots of measured density gradients (X) for experiments 23 (2% C6H,-Kr, 2255 K, 309 torr) and 38 (1% C6H,-Kr, 2413 K, 156 torr). The lines indicate the result of modeling with the mechanism of Table 11.
and temperature, and different rate expressions were used for each pressure group. The three expressions used for reaction 3 are given in Table 11; for reaction 1, the rates were those shown in Figures 4 and 5. To account for the variation in rate of (1) from pressure and temperature changes within an experiment, an Arrhenius function was used which fit the data of these figures in the immediate vicinity of each experimental temperature. For initial temperatures in excess of 2150 K, reaction 1 was taken as second order. A sensitivity analysis for two representative experiments is given in Table 111. What is shown here are “rms sensitivities”, which are defined as
for the rth reaction. Here the sum covers calculated gradients over 0.5-2 ps, the portion of the gradient profiles emphasized in the derivation of rate constants. The reason for using rms values is the tendency for different rates of (1) to produce profiles which cross one another in this time period. In this case, calculation
of a sensitivity at a single point in time could be quite misleading. The sensitivities of Table I11 quantify an earlier statement: the important reactions in the early endothermic decomposition are (1)-(4). The sensitivity to (4) is too low to establish rate, and the rate constant for this was estimated. The choice here seems reasonable, but is obviously quite uncertain. If this reaction were much slower than assumed here, its exact rate would be of far greater significance. However, such a slow rate would delay the chain decomposition and any such delay would not be consistent with the shape of the gradient profiles. The gradients are almost equally sensitive to reactions 2 and 3, an observation easily understood through consideration of a simple steady-state treatment of reactions 1-4. The effective rate constant for benzene disapand the effects of k2, pearance in steady state is then (kzk3Kl)’/2 k3, and the equilibrium constant for reaction 1 are inseparable. Of course this process is not in steady state or there would be no sensitivity to the rate of ( l ) , but variations in the rates of (2) and (3) do have a somewhat similar effect on the profiles. For this reason the rate constant for reaction 2, derived here, is most solid at the lower temperatures where steady state is delayed to beyond 4 M, and an independent measure of the rate for (3) is available.”
The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 2017
High-Temperature Pyrolysis of Benzene
i
T x lop2 (K)
ps x 10-2
T-1 x 104 (K-1) Figure 4. Rate constants for first-order reaction 1 as determined from
the density gradient profiles. The symbols denote various concentrations and mean pressures: 0,1% C&,-Kr, 154 4 torr; 0 , 1% CsH6-Kr, 349 15 torr; 0 , 2% Cs&-Kr, 141 13 torr; 0, 2% C&-fi, 341 34 torr 4 2% C6H6-Kr, 741 i 83 torr. The lines show the results of RRKM calculations described in the text: (- - - -) 150 torr; (- - -) 350 torr; (- -- - - -) 740 torr.
*
*
*
Tx \
8-
torr. The lines show calculated profiles for the same conditions, also referred to initial neon, using the mechanism of Table 11. The lines indicate: (-) 1942 K; (---) 2192 K.
*
1-
(K)
24
23
22
I
I
I
'
Figure 6. TOF profiles of CsH6concentration, relative to initial Ne,10914 from pyrolysis of 2.1% C6H6-Ne: 0,1942 K, 326 torr; A, 2192 K, 392
,'A:b
h
A
'
I 1
~
I 2
~ 3
I
'
I
4 ps x
' 5
I 6
'
I
'
7
10-2
Figure 7. TOF profiles of C2H2concentrati~n.l~~'~ The lines and symbols are identified as in Figure 6.
&-
2-
T-1 x 104 ( K - ~ )
Figure 5. Rate constants for second-order reaction 1. The symbols are defined as in Figure 4. The lines are RRKM calculations for (-) 350 torr (-- -) 150 torr.
The rate of reaction 3, phenyl dissociation, has been measured by Rao and Skinnerlz by observing H-atom formation in the pyrolysis of chlorobenzene. Implicitly assuming reaction 4 is rapid, they obtain the rate constant expression k3 = 1.2 X exp(-82000/RT) s-I for 1570-1790 K and pressures of 2-3 atm. As seen in Table 111, a rate constant very close to this has been used for the highest pressure experiments, the slight increase lying well within their expressed uncertainty. The modeling requires significant falloff of this rate for lower pressures, and the reaction was taken as second order in this range. This may not be the optimum choice for T < 2000 K, but since the gas density varies but slightly during decomposition for these experiments, the chosen order has almost no effect on the results. This reaction is clearly well into unimolecular falloff for present conditions, and no single choice of order or temperature dependence can be expected to apply at all pressures.
Figure 8. TOF profiles of C4H2con~entration.l~-'~ The lines and symbols are identified as in Figure 6 .
An additional testjof the kinetic mechanism of Table I1 is provided by a modeling of some TOF species profiles of Kern and coauthor^.'^.'^ The pressures and temperatures of these experiments are similar to the laser-schlieren experiments, and the rates for reactions 1 and 3 could be selected for near identical conditions.
I
Kiefer et al.
2018 The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 TABLE III: Rms Gradient Sensitivities" reactionb shock 12d 1 0.88 2 0.29 3 0.23 4 0.09 5 C 6 7 8 9 x 10-5 9 3 x lo-' 10 11 12
Tx
shock 23' 0.70 0.21 0.18 0.05
(K)
w
C
7 x 10-4 7 x 10-3
13 14 15 16 17 18 19 20
.L1.
22 23 24 25 26 "See text for definition. bReactionsnumbered as in Table 11. cThe unspecified sensitivities are all smaller than that of reaction 8. "2% C6H6, 1955 K, 397 torr. '2% C6H6, 2255 K, 310 torr.
The results of this modeling for the two higher temperatures presented by Kern et al. are shown in Figures 6-8. For benzene the results are excellent, while the two major products, CzH2and C4H2, are very slightly overestimated. Since there is a small defect of the carbon balance in these data, very likely a consequence of soot formation over such a long observation time, a prediction of e x a s product is than inevitable for a mechanism which does not include any adequate path to soot. Another observation of Kern et al., the absence of detectable phenyl radical, is also predicted by this mechanism. For these two experiments the calculated phenyl concentration remains below 6 X mol/cm3 over the entire time of observation, and this should be well below TOF detection threshold. The reasons for such low phenyl concentration are evidently early equilibration of (1) with small KI for low to moderate temperatures and rapid dissociation of this radical at the higher temperatures. For the RRKM calculations whose results are shown in Figures 4 and 5 , the frequencies of the transition state were merely those of the molecule which remain, lowered by about 100 cm-' (the grain size for the state count is 10 crn-l). The lowest frequencies were then adjusted to give the desired high-pressure A factor. That this A factor is the only feature sensitive to transition-state frequency assignment is well-known, and this crude model should give results adequate for extrapolation. The only other parameters adjusted to fit the experimental rate constants are the barrier Eo and (-PE)allr26 the average energy transfer per collision, which was assumed constant. = 70 an-'and Eo = 112 kcal/mol, the fit is quite For good as shown in Figures 4 and 5 . At no point do the measurements and calculations differ by more than 10%. The highpressure limit rate constant from this model is
Although the A factor may seem excessively large here, it should be apparent that this merely reflects the considerable difference between the activation energy of k," and the barrier, Eo. Obviously this difference arises from a slight preexponential temperature dependence in kl", and it will decrease markedly at low temperature along with the A factor. The primary quantity of interest from the RRKM fit is the barrier, here found to be 112 kcal/mol, with an uncertainty of
T-1 x 104 (K-1)
Figure 9. Comparison of the rates predicted by the RRKM model (see text) for 2.3 atm (-- -) with the expressions given by Hsu,Lin, and Lid3 and Rao and Skinner.I2 Also shown is the k," predicted by this model.
f2 kcal/mol. The error here is that suggested by the fitting process, but there is of course also an indeterminate uncertainty associated with the RRKM model. With no barrier to recombination the heat of formation for phenyl radical is then AHf0298 = 80 f 2 kcal/mol, which is very near that assumed at the outset. The RRKM model also allows an extrapolation to 2.3 atm, the mean pressure used by both Hsu et al.I3 and Rao and Skinner.I2 Figure 9 compares the rates predicted for this pressure with the results of these authors. The agreement with the expression offered by Hsu et al. is truly excellent; even the slight rolloff from their line for T > 2100 K is actually in accord with their data. However, the calculations are a factor 2-3 higher than the measurements of Rao and Skinner. This discrepancy is discussed below.
Discussion The simple radical chain mechanism of Bauer and Aten,27as represented here by the first four reactions of Table 11, is a completely successful model for the net endothermic rate in benzene pyrolysis. Agreement of calculated with measured density gradients is excellent over the entire set of experiments performed. This mechanism, with the kinetic parameters of Table 11, also provides a very good description of major species concentration profiles from TOF mass spectra.1° There is then every reason to believe the first four reactions of Table I1 represent a correct description of the major path in benzene pyrolysis at high temperature. In a previous paper,I4 a preliminary analysis of some of the data presented here led to the suggestion of a parallel molecular channel, perhaps C6H6 C2H2+ C4H4. The primary motivation for this suggestion lay in a disagreement between the rate of dissociation suggested by the laser-schlieren data and that determined from the H-atom formation rates of Rao and Skinner.I2 This notion is no longer supported here for the following reasons: (i) the success of the radical chain mechanism as a model of the laser-schlieren data (Should a molecular channel be involved, it must delay H-atom formation, and any substantial delay would cause serious problems in matching the density gradiept profiles.); (ii) the excellent agreement of the extrapolated rate for benzene dissociation at 2.3 atm with the independent measurements of Hsu et al.;" (iii) the close agreement between the barrier for benzene dissociation obtained from the present RRKM model and the Moo expected for C H bond scission; (iv) the large highpressure frequency factor, typical of bond fission, and the absence of any rational path for a molecular channel which would show this
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J. Phys. Chem. 1985,89, 2019-2021 feature; and (v) a consistency of disagreement between laserschlieren and ARAS measurements of dissociation rate. Laserschlieren rates on propaneI6 are about a factor three higher than the ARAS values,z8 and some recent measurements on toluene pyrolysisz9are similarly distant from ARAS ratesM There would seem to be some problem in extracting rate constants from the ARAS measurements. The RRKM model used here, although crude, has at least no prior prejudice in favor of any particular channel for dissociation. The parameters required to fit the measurements seem quite reasonable, although an average energy transfer of 70 cm-' may be a bit small. This could reflect the high temperatures of this study, since there are indications a slight negative temperature dependence for (-AE)," would improve the fit. The rate constant (28) C. Chiang and G. B. Skinner, Symp. (Inr.) Combust., [Proc.],18rh, 1981,915 (1982). (291 H.-C. Wei and J. H. Kiefer, unpublished laser-schlieren measure-
ments o n toluene pyrolysis. (30) V. S. Rao and G. B. Skinner, J. Phys. Chem., 88, 4362 (1984).
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for reaction 2 is only well established for the lower temperatures, so the assigned activation energy is rather uncertain. However, extrapolation of this expression to 800 K gives 1 X 1Olocm3/(mol s), close to the upper limit of 9 X lo9 cm3/(mol s) suggested by Nicovich and R a ~ i s h a n k a r a . ~ ~ The experiments and analysis presented here define the major pathways and their kinetic parameters in high-temperature benzene pyrolysis. The remaining problems in this pyrolysis concern the paths to minor products, about which laser-schlieren measurements provide no information.
Acknowledgment. We thank Profs. R. D. Kern and G. B. Skinner for helpful discussion and transmission of their results prior to publication. This research was supported by the Department of Energy under Contract No. DE AC02-78ER,4759. Registry NO. C6H6,71-43-2; C6H5,2396-01-2. (31) J. M. Nicovich and A. R. Ravishankara, J. Phys. Chem., 88, 2534 (1984).
Gallium Dicarbonyi: Matrix Isolation ESR Study Paul H. Kasai* and Paul M. Jones IBM Instruments, Inc.,-Orchard Park, Danbury, Connecticut 06810 (Received: December 3, 1984)
ESR spectra of a gallium carbonyl generated in argon matrices by co-condenstation of gallium atoms and carbon monoxide were observed and analyzed. It is shown that the carbonyl consists of one gallium atom and two CO molecules. It has a bent planar structure OC-Ga-CO, and a semifilled orbital representing the back-donation from the Ga pr orbital into the antibonding x orbitals of the CO moiety.
Introduction Many mononuclear transition-metal atom carbonyls M(CO), have been prepared by co-condensation of metal atoms and carbon monoxide molecules in inert-gas matrices.' All of these carbonyls have been identified and examined by their vibrational spectra (IR and Raman). For C O ( C O ) ~C, U ( C O ) ~and , Ag(C0)3, ESR (electron spin resonance) spectra have also been Ogden and his co-workers5 reported that co-condensation of aluminum atoms and carbon monoxide in a krypton matrix led to formation of an aluminum carbonyl. Based on the effect of CI8O upon the I R spectrum, they demonstrated that the species had the formula Al,(CO)z, but refrained from asserting the number of aluminum atoms involved. Ozin et ale4suggested that it might be A12(C0)z. Detection by I R of similarly generated Ga,(CO)z has also been reported.6 Recently we reported on our ESR study of an aluminum carbonyl generated in argon matrices.' The study showed that the carbonyl involved one aluminum atom and two carbon monoxide molecules. It also showed that the carbonyl had a bent, planar structure and its semifilled orbital represented the backdonation from the A1 pI orbital into the antibonding x orbitals of the CO molecules. (1) See,for example, Moskovitz, M.; Ozin,G. A. 'Cryochemistry"; Wiley: New York, 1976; Chapters 7 and 8. (2) Hanlan, L. A.; Huber, H.; Kiindig, E. P.; McGarvey, B. R.; Ozin, G. A. J. Am. Chem. Soc. 1975, 97,1054. (3) Ozin, G. A. Appl. Specrrosc. 1976, 30, 573. (4) McIntosh, D.; Ozin, G. A. J. Am. Chem. Soc. 1976, 98, 3167. (5) Hinchcliffe, A. G.; Ogden, J. S.; Oswald, D. D. J. Chem. Soc., Chem. Commun. 1972, 338. (6) Ogden, J. S.,ref 1, p 247. (7) Kasai, P. H.; Jones, P. M. J. Am. Chem. Soc. 1984, 106, 8018.
0022-3654/85/2089-2019$OlSO/O
We report in this paper ESR spectra of a gallium carbonyl generated in argon matrices. The spectra unequivocally demonstrated the presence of one gallium atom and two carbon monoxide molecules in the complex. They also revealed that the structure and the bonding scheme of Ga(CO)z were essentially identical with those of Al(CO)z.
Experimental Section A liquid helium cryostat that would enable trapping of vaporized species in an inert-gas matrix and examination of the resulting matrix by ESR has been described earlier.8 In the present series of experiments, gallium atoms were generated from a resistively heated (- 1400 "C) tantalum cell and were trapped in argon matrices containing a controlled amount of carbon monoxide (-20%). The ESR spectrometer used was an IBM Model ER2OOD system. A low-frequency (375 Hz) modulation was employed for the signal detection. All the spectra reported here were obtained while the matrix was maintained at -4 K, and the spectrometer frequency locked to the sample cavity was 9.4275 GHz. Research grade argon and CP grade carbon monoxide were obtained from Matheson, while 13C-enriched (enrichment > 90") carbon monoxide was obtained from MSD Isotopes. Gallium metal (99.999%) was obtained from Ventron Corp. Results The ground-state electronic configuration of Ga atoms is 4s2 4p'. Thus, owing to the degeneracy of the p orbitals, the ESR signal of the Ga atoms situated at sites with a cubic symmetry would be broadened beyond detection. However, it has been shown (8) Kasai, P. H. Acc. Chem. Res. 1971, 41, 329.
Q 1985 American Chemical Society
