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High-temperature pyrolysis of ketene in shock waves
COMBUSTION AND FLAME 99: 18-28 (1994)
18
High-Temperature Pyrolysis of Ketene in Shock Waves YOSHIAKI HIDAKA,* KENICHI KIMURA, and HIROYUKI KAWANO Department of Chemistry, Facultyof Science, Ehime University,Bunkyo-cho,Matsuyama 790,Japan The high temperature pyrolysis of ketene was studied behind reflected shock waves using both a time-resolved UV-absorption method (200 nm) and a single-pulse method (reaction time between 1.7 and 2.1 ms). The studies were done for the mixtures of 0.26% ketene and 2.2% ketene diluted with Ar in the temperature range 1102-1921 K at a total pressure range of 1.2-2.7 atm. From a computer-simulation study, a 38-reaction mechanism for the high temperature pyrolysis of ketene was developed. The mechanism and the rate-constant expressions were arrived at that could explain all our current data and previously reported data. It was found that the reactions 1-7 played a role in the ketene consumption. The rate constant expressions of the following six reactions except reaction 4 over the temperature range 1102-1921 K were estimated by using simulation. CH2CO + M -~ CH 2 + CO + M,
(1)
CH2CO + H ~ CH 3 + CO,
(2)
CH2CO + H ~ CHCO + H2,
(3)
CH2CO + CH z ~ C2H 4 + CO,
(4)
CH2CO + CH 2 --~ CHCO + CH3,
(5)
CH2CO + CH 3 --~ C2H 5 + CO,
(6)
CH2CO + CH 3 --~ CHCO + CH 4.
(7)
INTRODUCTION Ketene (CH 2CO) a n d / o r ketyl radical (CHCO) are produced in a combustion reaction of acetylene and they play a role in the combustion reaction of acetylene [1-4]. Acetylene is also formed as an intermediate in a combustion of higher-molecular-weight hydrocarbon and plays an important role in the overall processes, so that the mechanism of the acetylene combustion is indispensable in explaining the combustion reaction of the hydrocarbon. The mechanism of ketene pyrolysis is also an essential part of the mechanism of ketene oxidation. Because of the above, it is considered to be necessary to understand the mechanism of ketene pyrolysis at temperatures above 1000K in order to clarify the combustion mechanisms of ketene and hydrocarbons in detail.
*Corresponding author. 0010-2180/94/$7.00
The pyrolysis of ketene at the high temperatures was first studied at temperatures from 1140 to 1530 K by Tsuda and Kuratani [5] by using a single pulse shock tube. They reported that the disappearance of ketene followed a kinetic order of 1.5 with respect to ketene and its rate constant was represented by 1.6 x 1014 exp(-65.6 kcal/RT) l 1/2 m o 1 - 1 / 2 S -1. They also explained their results by using a 8-reaction mechanism. Wagner and Zabel [6] investigated the thermal decomposition of ketene behind reflected shock waves over the temperature range of 1300-2000 K. They proposed the reaction CH2CO + Ar ~ C H 2 + C O + Ar with the rate constant of k 1 = 3.6 × 1015exp(-59.3 k c a l / R T ) c m 3 tool -1 s -1 (the density of the gas mixture used was 6 x 10 -5 mol/cm 3) as the initiation step. Frank et al. [7] also investigated the reaction of ketene with H and CH z behind reflected shock waves using atomic and molecular absorption spectrometry. For temperatures between 1650 and 1850 K, the value of (1.8 _+ 0.6) x 1013 c m 3 mol- 1 s- 1 was deduced for the reaction of ketene with the H atom. However, the mechanism of ketene Copyright © 1994 by The Combustion Institute Published by Elsevier Science Inc.
HIGH-TEMPERATURE PYROLYSIS OF KETENE IN SHOCK WAVES pyrolysis at the high temperatures has not been studied in detail and is thus vague. So, we studied the ketene pyrolysis at the high temperatures by employing both techniques and arrived at the mechanism and the rate constant expressions. EXPERIMENTAL SECTION Two shock tubes of 4.1 cm i.d. were used in these experiments. The first shock tube is a standard-type connected an absorption apparatus [8]. An absorption measurement at 200 nm was used to monitor the CH2CO concentrations as follows. The transmitted intensity of a D 2 lamp (Hamamatsu-L544) through a 4.1 cm path in the shock tube and through a RicoMC-20 grating monochromator (with a halfwidth of 25 A) was monitored by a photomultiplier (Hamamatsu R-955). The response time of the optical-electrical system was about 2 /zs. The second shock tube is a magic-hole-type, which was described in detail previously [9, 10]. Within 20 s after shock heating, reacted gas mixtures were extracted into a preevacuated vessel (50 cm 3) through a valve near the end plate. The reacted mixtures were analyzed on three gas-chromatographs (Shimazu GC-3BT1, Shimazu GC-3BT2, Shimazu GC-8AT), which have thermal-conductivity detectors. The gaschromatographs were serially connected. A column of 2-m-long sebaconitrile at 40°C in the GC-3BT1 was used to determine ketene concentration and hydrocarbon concentrations above C a. A column of 2 m-long Porapak Q and 2 m-long Unibeads 1S in the GC-8AT was employed to determine the concentrations of carbon dioxide, ethane, ethylene, acetylene, propane, propylene, allene, and propyne: the rate of increasing temperature from 50 to 130 °C was 3 °C/min. A 2-m-long Molecular Sieve 5A column in the GC-3BT2 was employed at 50 °C to determine the concentration of hydrogen, methane, and carbon monoxide. The carrier gas used for the gas analysis was helium gas. The signal obtained from the gaschromatograph was introduced into data processors (Shimazu Chromatopac C-R3A1, Shimazu Chromatopac C-R3A2, and Shimazu Chromatopac C-R1B) and was automatically treated. An effective heating time was deter-
19
mined using the same method as that described previously [9, 10]. The reaction was assumed to be frozen perfectly at the effective heating time (reaction time), which was defined as the time between the arrival point of the reflected shock-front and 80% point of the reflected shock-front pressure. The effective heating time was used as the reaction time in a simulation. The relationship between the effective heating time and temperature showed a simple curve: the effective heating time increased with a decrease in temperature as seen in Fig. 2 of Ref. 9. The effective heating times at 1200, 1300, 1400 and 1500 K were determined as 1.97, 1.89, 1.80, and 1.71 ms, respectively. The gas compositions used were 0.26% CH2CO, 99.74% Ar (mixture a), and 2.2% CH2CO, 97.8% Ar (mixture b). The CH2CO was prepared by heating vapor of acetic anhydride at 500 °C in a quartz tube. The crude CHzCO was purified by trap to trap distillation. The CHzCO purity was examined with the gas chromatograph and was confirmed to be above 99%. The impurity included in it was only carbon dioxide. The purified ketene usually contained about 1% carbon dioxide. The carbon dioxide is considered to exert no influence upon the reaction rate and product distribution [5]. The Ar (Teisan Co.), specified to be 99.999% pure, was used. The computer calculations used in this study are essentially the same as described previously [9-11]. The computer routine used was Gear-type integration of the set of differential equations describing the chemical kinetics under constant density conditions for reflected shock waves. Reverse reactions were automatically included in the computer program through equilibrium constants computed from polynomial fits to standard thermochemical data. The computer program which contained the expressions relating the temperature change to the reaction progress was used for the simulations: the computations for concentration-time variations were carried out by making the rateconstant values of each elementary reaction change every 0.001 K. The time variations of absorption curves were also calculated with the program considering both the concentration change of each species during the reaction
20
Y. HIDAKA ET AL.
progress and the dependence of the absorption intensity on temperature. All references to temperature herein refer to the full vibrational relaxation, no-reaction shock front value. Assuming that the reaction was frozen perfectly at the effective heating time, the hydrocarbon-concentrations analyzed by gas chromatographs were compared with the simulated ones. The details for these have also been represented previously [9, 10]. The basic thermochemical data source was the JANAF table [12] and the table of coefficients sets for NASA polynomials [13] with the following alterations. The heats of formation used for the species, C 2 H , C 2 H 3 , C 3 H 3 , and C4H 5 are 135.3 kcal/mol [14], 71.7 kcal/mol [14], 83.6 kcal/mol [15] and 72.3 kcal/mol [15], respectively. RESULTS AND DISCUSSION The pyrolysis of CH2CO was studied over the temperature range 1102-1921 K and over the pressure range of 1.2-2.7 atm, by both tracing the time variation of absorption at 200 nm and analyzing concentrations of reacted mixtures on the gas chromatograph. The product distribution determined by the gas chromatograph is shown in Fig. 1. Under our experimental conditions, the main pyrolysis products detected on the gas chromatograph were CO, H2, CH4, C2Hz, and C2H 4. These are in a good agreement with the results of Tsuda and Kuratani [5]. The species C 2 H 6 , C 3 H 6 , a - C 3 H 4 (allene), P-Call 4 (propyne), C4H 4 (vinylacetylene), and 1,3-C4H 6 were detected in smaller quantities. Only a slight mass deficit for carbon was observed below 1200 K, but at 1400 and 1500 K was about 5% and 7%, respectively. Typical time-profiles of absorption at 200 nm are shown in Fig. 2. A t is defined as A t = log(If/It)/log(If/Io)
,
where If is the signal voltage corresponding to the full intensity and I 0 and I t are the signal voltages corresponding to the absorption intensity at the reflected shock front (t = 0) and at time t, respectively. The absorption intensity using the mixture, 0.26% CH2CO, 99.74% Ar, increased rapidly at the reflected shock front,
1,0
0.5
0'0L10'00' T / K
1500
0 0'' 10'00 _
1500
¢ /c O /
O
0.0 10'00 '
1500 T/K
' T/K
(e)
(d)
i
0.01 •Z
t
0:0, O O
,
10'00'
1500
1000'
1500 T/K T/K Fig. 1. Comparison of observed with calculated product distribution with mixture (2.2% ketene, 97.8% Ar), where C O is the initial concentration of CH2CO and C is the concentration of each species. The calculation was carried out with Table 1. (a) ©, [CH2CO] observed; 0 ; [CO] observed; O, [C2H 4] observed; , [CH2CO] calculated; - - - - - , [CO] calculated; . . . . . , [C2H4] calculated. (b) A, [CH4] observed; - - , [CH 4] calculated. (c) A; [C2H2] observed; ®; [H 2] observed; - - , [C2H 2] calculated; . . . . . , [H 2] calculated. (d) It; [a-C3n4] observed; v, [P-C3H 4] observed; ©, [C3H 6] observed; - - , [a-C3n 4] calculated: - - - - - , [p-C3H4] calculated; . . . . . , [C3H6] calculated. (e) 0, [ c 4 n 4] observed; ©, [1,3-C4H 6] observed; ~, [C2H 6] observed; - - - - - : [C4H 4] calculated, . . . . . : [1,3-C4H6] calculated; , [C2H 6] calculated.
and then was constant for about 1 ms at temperatures below 1500 K. At temperatures between 1500 and 1921 K, it decreased with time. The relationship between the total absorption data, A t, and temperature T with mixture, 0.26% CH2CO, 99.74% Ar, is shown in Fig. 3. In order to calculate the absorption intensity of each product, extinction coefficients of ketene and main products at 200 nm were measured with each mixture, 0.26% CH2CO, 5% CO, 1% H2, 1% CH 4, 1% C2H4, or 1% C 2 H E diluted in Ar. The extinction coefficients were calculated from the reflected shock front absorbance. The relationship between the extinction coefficient E c and temperatures is
H I G H - T E M P E R A T U R E PYROLYSIS OF K E T E N E IN S H O C K WAVES
1.0
1.0
1.0 0
0
A
<
0
~" 0.5
0.5
0.5
i
i
i
i
0.0
I
i
500
i
1000
0.0
I
k
i
i
I
0.0
2000
I
shown in Fig. 4. The equations, log E C = 2.27 X 10 -4 T + 5.74 cm 2 mo1-1, log E c = 4.20 × 10 -4 T + 4.57 cm 2 mo1-1 and log E c = 8.61 × 10 -4 T + 3.94 cm 2 mo1-1 for CHzCO, C2H 2 and C e l l 4 w e r e obtained, respectively. These equations were used for simulations. Extinction coefficients of CH4, He, and CO were also below 10 3 c m 2 mol 1: the extinction coefficients of CH 4, H e, and CO were below one thousandth of ketene. Hence, extinction coefficients of CH4, H2, and CO were neglected in simulation. The reaction mechanism adopted for explaining the data of CH2CO pyrolysis is shown in Table 1. The initial step in the thermal decomposition of CH2CO was studied in detail by Wagner and Zabel [6]. From the absorption results at 230 nm, they showed that reaction 1 was the initiation step and played an important role in the C H z C O pyrolysis: 2+CO+M (1)
We also adopted reaction 1 as the initiation step. Reaction 1 is very sensitive to the consumption of ketene and the production of carbon monoxide, as shown in Table 2. Reaction 1 is also very sensitive to the absorption curve because the absorption mainly comes from reactant ketene: the extinction coefficient of main products, CO, H2, CH4, C2H2, and C2H 4 are below one tenth of that of ketene, as men-
1.0
8
8 <~
,g
0.5
0.5
J
i
+
1500
L
i
I
2000 T/K
i
+
i
I
2000 T/K
1.0
0.0
i
1500
T/K
Fig. 2. Comparison of the observed UV-absorption curves at 200 nm with the calculated ones at low, middle and high temperatures using mixture (0.26% ketene, 99.74% Ar). O, observed at 1575 K; zx, observed at 1669 K; t2, observed at 1721 K; and - - , calculated with Table 1.
A H 0 = 75.8 kcal/mol.
i
500
t /as
CH2CO+M~CH
21
~
c~b
0.0 1500
2000 T/K
Fig. 3. Relationship between absorption data A t and temperature T using mixture (0.26% ketene, 99.74% At). As0 , AI00, A300, and As00 are A t values observed at 50, 100, 300, and 500 /zs, respectively. O, observed; , calculated with Table 1.
tioned above. To explain all our experimental data consistently, this reaction with k I = 3.96 × 1015exp(-59.3 k c a l / R T ) cm 3 mo1-1 s -1 was indispensable: the activation energy - 5 9 . 3 k c a l / m o l was adopted from a value proposed by Wagner and Zabel [6] though the activation energy of reaction 1 was inferred to be somewhat lower than 59.3 k c a l / m o l because reaction 1 was considered to be in the falloff range under our experimental conditions [6] and the density we used is about a fourth of Wagner and Zabel's. The rate-constant value evaluated is by a factor of 1.1 higher than that of Wagner and Zabel [6] evaluated at the density of 6 x 10 -5 mol/cm3: the density we used was 1.2 x 10 -5 - 1.7 × 10 -5 m o l / c m 3. This k 1 value can predict our data well, as shown in Figs. 1-3. This value can also predict the data of Tsuda and Kuratani [5] and Frank et al. [7] within an experimental error, as shown in Figs.
22
Y. H I D A K A ET AL. TABLE 1 Elementary Reactions and Rate Constant Expressions a No.
Reaction
(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) (31) (32) (33) (34) (35) (36) (37) (38)
C U e C O + M = CH 2 + CO + M C H 2 C O + H = CH 3 + CO CH2CO + H = CHCO + H 2 C H 2 C O + CH 2 = C2H 4 q" CO C H 2 C O + CH z = C H C O + CH 3 C H 2 C O + CH 3 = C 2 H 5 + CO C H 2 C O + CH 3 = C H C O + CH 4 C H C O + H = CH 2 + CO C H C O + CH 2 = C 2 H 3 + CO C H C O + CH 3 = C2H 4 -1- CO C H C O + C H C O = C2H 2 + CO + CO CH 4 + CH 2 = CH 3 + CH 3 CH 4 + H = CH 3 + H 2 CH 3 + M = CHe + H + M CH 3 + H = CH 2 + H 2 CH 3 + CH 2 = C2H 4 + H CH 3 + CH 3 = C2H 5 + H CH 2 + CH~ = C2H 2 + H + H C2H 6 = CH 3 + CH 3 C2H5 = C2H 4 + H C2H 4 + M = C2H 2 + H 2 + M C2H 4 + H = C 2 H 3 + H 2 C 2 H 4 + CH 2 = a-C3H 5 + H C 2 H 3 + M = C2H 2 + H + M C 2 H 2 + CH 2 = P-C3H 4 C3H 6 + H = C 2 H 4 + CH 3 a-C3H 4 + H = a-C3H 5 a-C3H 4 + CH 2 = i - C a l l 5 + H a-C3H 4 + CH 3 = 1,2-C4H 6 + H P-C3H 4 + M = C3H 3 + H + M P-C3H 4 + CH 2 = 2-C4H 5 + H p-C3 H 4 = a-C3H 4 1,3-C4H 6 = C2H 4 + C2H 2 1,2-C4H 6 = 1,3-C4H 6 1,2-C4H 6 = C3H 3 + CH 3 2-C4H 5 = C4H 4 + H i-C4H 5 = C4I~I4 "~ H C4H 4 = C2H 2 + C2H2
A 3.96 1.11 1.80 1.00 3.60 9.00 7.50 1.50 3.00 2.00 1.00 6.00 3.80 1.90 7.00 4.20 2.80 1.20 7.00 1.20 3.30 5.00 3.00 2.31 1.20 3.40 4.00 1.00 8.75 4.70 1.00 2.10 1.00 2.50 2.00 3.00 5.00 3.40
X x x x × × × × X × × × × × × × × x × × × × × × × × × x x × × × × × × × x x
n 1015 107 10 TM 1012 1013 101° 1012 1014 1013 1012 1013 1014 106 1016 1013 10 j3 1013 10 TM 1014 1012 1017 1015 1012 10 TM 1013 1013 1012 1013 1011 10 TM 1013 1012 1014 1013 1015 1013 1013 1013
0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.1 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
E
References
59300 2000 8600 0 11000 0 13000 0 0 0 0 14000 7750 91400 15100 0 13600 795 80000 35000 81260 22850 0 28000 6617 3500 2700 0 14900 80000 0 60000 75000 63000 75000 45000 44000 77140
see text this work this work 7 this work this work this work 16 3 assumed 3 17 18 19 17 16 20 16 9 9 21 b 21 c assumed 21 d 16 22 22 assumed 23 10 assumed 10 23 23 23 23 23 24
"Rate constants in the form, AT" exp(-E/RT), in cm, mol, cal, and K units. bThis value, which was very similar to the value k = 2.95 × 1017exp(-81.3 kcal/RT)cm 3 mo1-1 s -1 reported by Tanzawa and Gardiner [25], was evaluated from data in C 2 H 4 pyrolysis and oxidation. CThis value, which was very similar to the value k = 1.32 × 106T 2"53 e x p ( - 1 2 . 2 kcal/RT) cm 3 m o l - 1 s-1 reported by Tsang and Hampso n [26], was evaluated from data in C z H 4 pyrolysis and oxidation. dThis value, which was very similar to the value k = 7.9 x 10 TM exp( - 31.5 kcal/RT) cm 3 m o l - 1 s - 1 reported by Benson and Haugen [27], was evaluated from data in C 2 H 4 pyrolysis and oxidation.
5 and 6, respectively, which were obtained with a density similar to ours. The value we evaluated for reaction 1 is roughly consistent with Wagner and Zabel's within an experimental error. However, since reaction 1 was considered to be in the fall-off range under our experimental conditions [6] and the density we
used is about a fourth of Wagner and Zabel's, the value k 1 w e evaluated should be lower than Wagner and Zabel's. However, our value is somewhat higher than Wagner and Zabel's. We cannot explain this. For consumption reactions of CH2CO except reaction 1, there are six reactions which
HIGH-TEMPERATURE PYROLYSIS OF KETENE IN SHOCK WAVES
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24
Y. H I D A K A ET AL. 1.0
(a)
/
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1300 T I K 1500
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T/K Fig. 4. Comparison of the extinction coefficients of ketene, acetylene and ethylene at 200 nm. - - , ketene; - - - , acetylene; . . . . . . . , ethylene.
now to us seem possible. CH2CO
+ H --, C H 3 + C O ,
AH 0 = -32.5 kcal/mol, CH2CO+H~CHCO+H
(2) 2,
A H 0 = - 0.7 kcal/mol, CH2CO
+ CH 2 ~
(3)
+ CH 2 -~ CHCO
(4) + CH3,
A H o = - 4 . 3 kcal/mol, CH2CO
(5)
+ C H 3 --+ C 2 H 5 + C O ,
A H o = - 2 3 kcal/mol, CH2CO
1500 T/K
1300
1500 T/K
Fig. 5. Comparison of reported (symbols) with computed product distribution using Table 1 for the mixture of 2% ketene, 98% Ar, where [C]0 is the initial concentration of CH2CO and C is the concentration of each species. (a) O, [CO] observed; [3, [C2H4] observed; - - - - - , [CO] calculated; . . . . . . . , [C a H 4 ] calculated. (b) A, [CH 4 ] observed; - - , [CH4] calculated. (c) A, [C2H2] observed; ®, [H 2] observed; . . . . . . . . , [C2H2] calculated; , [H 2] calculated. (d) v , [P-C3n4] observed; O, [C3H 6] observed; - - - - - , [P-C3H4] calculated; . . . . . . . , [C3H6] calculated. (e) O, [C2H6] observed; , [C2H6] calculated• Experimental data are taken from Table 2 of Ref. 5.
C2H 4 + CO,
A H 0 = - 94.2 kcal/mol, CH2CO
I
1300
+ C H 3 --~ C H C O
& H o = 0.7 kcal/mol.
(6) + CH4, (7)
The reaction of atomic hydrogen with ketene has been studied at temperatures below 500 K [28-30]. Carr et al. [28] used a discharge flow-mass spectrometric technique and showed that the major reaction products in the reaction of atomic hydrogen with ketene w e r e C H 3 and CO. This was corroborated by Slemr and
Warneck [29]. Reaction 2 was proposed for the reaction of atomic hydrogen with ketene. Michael et al. [30] also have reported k 2 = 1.10 X 1 0 13 e x p ( 3.44 kcal/RT) c m 3 mol-1 s-1 for reaction 2 over the temperature range of 298-500 K. For temperatures between 1650 and 1850 K, Frank et al. [7] also deduced k 2 = (1.8 q- 0.6) × 1013 c m 3 m o l s -~ for reaction 2 from a shock tube study. Under our experimental conditions, reaction 2 also played an important role for the ketene consumption and the formation of CO and C H 3. As long as we used an extrapolated value of Michael et al. [30] for reaction 2, computed ketene concentration was larger than the observed one at a given time and the yield of methane was always lower than the observed one. One way to match the computed concen-
H I G H - T E M P E R A T U R E PYROLYSIS O F K E T E N E IN S H O C K WAVES 3.0
25
3.0 11
1013
e}
2.0 oE
'E z0 o
o
o ~
0 1.0 0
1.0
0.0
0.0
200
400
600
800
~
O....
t / ~s
Fig. 6. Comparison of reported [HI and [CO] concentrations [7] with computed ones at 1670 K and at 1.74 bar for mixture (50 ppm ketene in At). A, reported [H] concentration; O, reported [CO] concentration; - - - - - , [H] calculated with Table 1; - - - , [CO] calculated with Table 1; . . . . . . , [H] calculated with k t × 0.91; - - , [CO] calculated with k 1 x 0.91.
trations to the observed ones was to increase the k 2 value by a factor of about 3. This shows that the value of reaction 2 at the high temperatures is larger than extrapolated one at the low temperatures. This result was consistent with that obtained by Frank et al. [7]. The e x p r e s s i o n k 2 = 1.11 × 1 0 7 T 2 e x p ( - 2 kcal/RT) c m 3 mo1-1 s - I was evaluated for the rate constant of reaction 2. The extrapolated value of k 2 = 1.11 × 1 0 7 T 2 e x p ( - 2 kcal/RT) c m 3 m o l - 1 s- 1 is in good agreement with the value of Michael et al. [30] at low temperatures, as shown in Fig. 7. This k2 value is also very consistent with Frank et al.'s, as shown in Fig. 7. When we used reaction 2 only for the reaction of atomic hydrogen with ketene, the computed yield of H 2 was much lower than the observed one. This shows that reaction 3 cannot be ignored under our experimental condition because the species H 2 is mainly produced by reaction 3. Reaction 3 also affected on the absorption curves observed at 200 nm. The best fit for our data and Tsuda and Kuratani's data [5] (Fig. 5) was obtained by using k 3 = 1.80 X 1014 e x p ( - 8 . 6 0 k c a l / R T ) cm 3 m o l - 1 s- 1. We assumed two channels for the reaction of CH 2 with CH2CO. Reaction 4 plays a role for the formation of C 2 H 4 together with reactions 6, 10 and 16, as may be seen in Table 2: the intermediate product C2H5 was rapidly
1010
10aK/T Fig. 7. Comparison of the rate constant k 2 derived in this study with those reported. - - - , present work; - - -, Michael et al. [30]; . . . . . . . , Slemr and Warneck [29]; 0 , Cart et al. [28]; O, Frank et al. [7].
decomposed to ethylene by reaction 20. When reaction 16 only with k16 -- 4.2 × 1013 c m 3 mol - t s -1 [16] reported for C a n 4 formation was used for calculations, the calculated yield of C2H 4 was always smaller t h a n the observed one. Hence, it was necessary to adopt reaction 4 with k4 = 1.0 × 1012 c m 3 mo1-1 s -1 to predict the observed yield of C E H 4 together with reactions 6 and 10: the C2H 5 was rapidly decomposed to ethylene by reaction 20. While, reaction 5 plays a role for the formation of C H 3. We assumed k s = 3.6 × 1013 e x p ( - 1 1 kcal/RT) c m 3 mol-1 s-1 for reaction 5. This value can predict well the C H 4 yield, as shown in Fig. 1. If we omitted this reaction in simulation, the calculated yield of CH 4 was much smaller than the observed one. To achieve an agreement between the calculated yield and the observed one without reaction 5, we needed to increase the rate constants of reactions 2 a n d / o r 7. The k2 value used in Table 1 is consistent with that reported by Frank et al. [7] as described above. Furthermore, our k 2 value used in Table 1 is 1.3 × 1013 cm 3 mol-1 s - 1 at 1500 K. A k 2 value larger than our value is not acceptable. On the other hand, o u r k 7 value used in Table 1 is 9.6 x 101° cm 3 mo1-1 s -1 at 1500 K. This value is similar to the rate constant, 9.9 × 101° cm 3 mo1-1 s -1 of a similar
26 reaction, c2n
Y. H I D A K A ET AL. 4 + C H 3 ---* C 2 H 3 + C H 4 A H 0
= 0.8 kcal/mol, which was recommended by Baulch et al. [16]. However, the rate constant of reaction 7 is inferred to be half that of reaction C 2 H 4 + C H 3 ~ C 2 H 3 + C H 4 because the number of C-H bond of ketene is half that of ethylene and A H 0 value of reaction 7 is similar to reaction C2H 4 + C H 3 --* C 2 H 3 + C H 4. Hence, o u r k 7 value used in Table 1 is larger than that inferred from the similar reaction. Because of the above, we did not increase the rate constants of reactions 2 and 7. We assumed two channels for the reaction of C H 3 with C H : C O . Initially, we tried to model our data without reaction 6. When we used a mechanism without reaction 6, which could explain the absorption data in mixture 0.26% ketene, 99.74% Ar, the calculated yields of carbon monoxide and ethylene, etc, in mixture 2.2% ketene, 97.8% Ar, were always lower than the observed ones. One way to solve this problem was to introduce reaction 6. Reaction 6 plays an important role for the formation of CO and C 2 H 4 : the C e l l 5 rapidly decomposes t o C 2 H 4. The species C H 3 is more at risk in a steric structure than the CH 2 species when they carried out an addition reaction to ketene. Furthermore, the A H 0 value of reaction 6 is about a fourth of that of reaction 4. Thus, the rate c o n s t a n t k 6 --= 9.0 × 101° c m 3 mo1-1 s -1 of reaction 6 was assumed to be about a tenth of that of reaction 4. This value gave a best fit for both the product yields and the time-profiles. Methane is one of the major products in the pyrolysis of ketene. The methane is produced by reaction 7 only. The rate constant k 7 = 7.50 × 1012 e x p ( - 1 3 . 0
kcal/RT)
cm 3
mo1-1 s -1 was evaluated from the CH 4 yield. Its value can also predict well the yield of CH 4 reported by Tsuda and Kuratani [5], as shown in Fig. 5. The reaction between ketyle radical and hydrogen atomic was studied in O + C2H 2 mixtures. It has been proposed that reaction 8 produced CO and CH 2 [31, 32]. The values evaluated for reaction 8 is 3.00 × 1012 c m 3 mo1-1 s -1 - 1.5 × 10 TM cm 3 mo1-1 s -1 [31, 32]. W e a d o p t e d k 8 = 1.50 × 1014 cm 3 mol-1 s-1 because its value was evaluated
at temperatures to be similar to ours [32] and was recommended [16]. E v e n had k s = 3.00 × 1013 c m 3 mo1-1 s -1 been used instead of k 8 = 1.50 × 10 TM c m 3 mo1-1 s -1, the computed results would scarcely have varied from those shown in Figs. 1-3. Furthermore, reaction 8 is not sensitive in our experiment, as shown in Table 2. Hence, this rate constant was not discussed in detail. Reaction 9 is less sensitive to all the products. We used k 9 = 3.0 × 1013 c m 3 mo1-1 s -1 assumed by Miller et al. [3]. Very little is known about reaction of the ketyle radical with the methyl radical. Reaction 10 is somewhat sensitive to the consumption of ketene and the formation of methane and ethylene, as may be seen in Table 2. Reaction 10 plays a role in the formation of ethylene: ethylene was mainly produced by reactions 4, 10, 16, and 20. Reaction 10 with kl0 = 2.0 × 1012 c m 3 mo1-1 s -1 was assumed to predict our results. Reaction 11 is somewhat sensitive to acetylene and carbon monoxide yield, as may be seen in Table 2. A few acetylene and carbon monoxide molecules were produced from reaction 11 in our calculations, so reaction 11 with k l l = 1.0 × 1013 c m 3 mol-1 s-1 [3] was added to Table 1. In order to predict the yields of allene, propyne, propylene, vinylacetylene, and 1,3butadiene, reactions 23 and 25-38 were introduced in Table 1. In order to account for allene production, reaction 23 was assumed. The species a-C 3H 5 ( CH 2= CH(~H 2 ) formed by reaction 23 decomposes to allene by reaction - 2 7 . Propyne was produced by reactions 25 and - 3 2 . The yield of vinylacetylene was predicted by assuming reactions 28 and 31: the i - C 4 H 5 (CH2=CCH~----CH 2) formed may produce vinylacetylene by reaction 37 and the 2 - C 4 H s ( C H z C ~ C C H 3) formed is expected to produce vinylacetylene via 1,2,3-butatriene [23]. The 1,3-butadiene was expected to be formed via raction 34: the 1,2-butadiene was assumed to be formed by reaction 29. The yield of propylene was predicted by reaction 26. Figure 5 shows the comparison of reported product yields [5] with those modeled using Table 1. The mechanism and the rate constant expressions shown in Table 1 can nearly pre-
H I G H - T E M P E R A T U R E PYROLYSIS O F K E T E N E IN S H O C K WAVES
I
~,
E
4.
4.0
0
5.
0
6. 0
2.0
7. o
8.
V
0.0 0
1 O0
200
300
t/IJs
Fig. 8. Comparison of reported ketene concentrations [7] with computed one at 1725 K and at 7.35 bar for mixture (1620 ppm ketene in Ar). ~7, reported ketene concentration; - - - - - , calculated with Table 1; - - , calculated with Table 1 changing k 1 = 3.96 × 1015 exp(-59.3 kcal/RT) cm 3 mo1-1 s -1 to k~ = 2.30 × 1015exp(-57.6 kcal/RT) cm 3 mol- 1 s - 1 132].
9. 10.
11.
12.
dict Tsuda and Kuratani's data, as shown in Fig. 5. Figure 6 shows a comparison of reported H atom and CO molecule concentrations [7] with calculated results. The mechanism and the rate constant expressions shown in Table 1 can predict Frank et al.'s data within an experimental error, as shown in Fig. 6. Figure 8 shows a comparison of reported ketene concentration [7] with calculated result. The mechanism and the rate constant expressions shown in Table 1 can predict it well. The pressure used was 7.35 bar and it was by a factor of about 3 larger than our pressure. Thus, the value of k t = 2.3 × 1015 e x p ( - 5 7 . 6 kcal/RT) cm 3 mol -~ s -1 reported by Frank et al. was used instead of k 1 = 3.96 x 1015exp(-59.3 k c a l / R T ) c m 3 mo1-1 s -1 shown in Table 1. This mechanism and the rate constant expression can also predict well Fig. 8.
13. 14.
15.
16.
17. 18. 19.
20.
21. 22.
REFERENCES 1. Lange, W., and Wagner, H. G., Ber. Bunsenges. Phys. Chem. 79:165-170 (1975). 2. Vandooren, J., and Van Tiggelen, P. J., Sixteenth Symposium (International) olt Combustion, The Combustion Institute, Pittsburgh, 1976, pp. 1133-1144. 3. Miller, J. A., Mitchell, R. E., Smooke, M. D., and Kee, R. J., Nineteenth Symposium (International) on
23.
24.
25.
27
Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 181-196. Hidaka, Y., Gardiner, W. C., Jr., and Eubank, C. S., J. Mol. Sci. 2:141-153 (1982). Tsuda, M., and Kuratani, K., Bull. Chem. Soc. Jpn. 41:53-60 (1968). Wagner, H. G., and Zabel, F., Ber. Bunsenges. Phys. Chem. 75:114-118 (1971). Frank, P., Bhaskaran, K. A., and Just, Th., J. Phys. Chem. 90:2226-2231 (1986). Hidaka, Y., Kataoka, T., and Suga, M., Bull. Chem. Soc. Jpn. 47:2166-2170 (1974). Hidaka, Y., Chiori, T., and Suga, M., Chem. Phys. Lett. 119:435-437 (1985). Hidaka, Y., Shiba, S., Takuma, H., and Suga, M., Int. J. Chem. Kinet. 17:441-453 (1985). Hidaka, Y., Nakamura, T., Miyauchi, A., Shiraishi, T., and Kawano, H., Int. J. Chem. Kinet. 21:643-666 (1989). Hidaka, Y., Takahashi, S., Kawano, H., Suga, M., and Gardiner, W. C. Jr., J. Phys. Chem. 86:1429-1433 (1982). Stull, D. R., and Prophet, H., JANAF Thermochemical Tables, 2nd ed., NSRDS-NBS 37, 1971. Bureat, A., in Combustion Chemistry (W. C. Gardiner, Jr., Ed.), Springer-Verlag, New York, p. 456. Ervin, K. M., Gronert, S., Barlow, S. E., Gilles, M. K, Harrison, A. G., Bierbaum, V. M., Depuy, C. H,, Lineberger, W. C. and Ellison, G. B., J. Am. Chem. Soc. 112:5750-5759 (1990). Lias S. G., Bartmess, J. E., Liebman, J. F,, Holmes, J. L. Levin, R. D., and Mallard, W. G., J. Phys. Chem. Ref. Data 17:1-861 (1988). Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., J. Phys. Chem. Ref. Data 21:411-734 (1992). Just, Th., Thirteenth Symposium (International) on Shock Tubes and Waves, 1981, pp. 54-68. Rabinowitz, M. J., Sutherland, J. W., Patterson, P. M., and Klemm, R. B., J. Phys. Chem, 95:674-681 (1991), Markus, M. W., Woiki, D., and Roth, P., Twenty. Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 581-588, Frank, P., and Braun-Unkhoff, M., Sixteenth Symposium (International) on Shock Tubes and Waves, 1987, pp. 379-385. Hidaka, Y., Higashihara, T., Inami, K., and Kawano, H., in preparation. Hidaka, Y., Nakamura, T., Tanaka, H., Jinno, A., Kawano, H., and Higashihara, T., Int. J. Chem. Kinet. 24:761-780 (1992). Hidaka, Y., Higashihara, T., Ninomiya, N., Oshita, H., and Kawano, H., J. Phys. Chem. 97:10977-10983 (1993). Braun-Unkhoff, M., Kurz, A., and Frank, P., Seventeenth Symposium (International) on Shock Tubes and Waves, 1989, pp. 493-498. Tanzawa, T., and Gardiner, W. C., Jr., Combust. Flame 39:241-253 (1980).
28 26. Tsang, W., and Hampson, R. F., J. Phys. Chem. Ref. Data 15:1087-1279 (1986). 27. Benson, S. W., and Haugen, G. R , J. Phys. Chem. 71:1735-1746 (1967). 28. Carr, R. W., Jr., Gay, I. D., Glass, G. P., and Niki, H., J. Chem. Phys. 49:846-853 (1968). 29. Slemr, F., and Warneck, P., Ber. Bunsenges. Phys. Chem. 79:152-158 (1975). 30. Michael, J. V., Nava, D. F., Payne, W. A., and Stief, L. J., J. Chem. Phys. 70:5222-5227 (1979).
Y. HIDAKA ET AL. 31. Lohr, R., and Roth, P., Ber. Bunsenges. Phys. Chem. 85:153-158 (1981). 32. Frank, P., Bhaskaran, K. A., and Just, Th., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 885-893. 33. Homann, K. H., and WeUmann, Ch., Bet. Bunsenges. Phys. Chem. 87:609-616 (1983).
Received 15 October 1993; revised 20 April 1994
18
High-Temperature Pyrolysis of Ketene in Shock Waves YOSHIAKI HIDAKA,* KENICHI KIMURA, and HIROYUKI KAWANO Department of Chemistry, Facultyof Science, Ehime University,Bunkyo-cho,Matsuyama 790,Japan The high temperature pyrolysis of ketene was studied behind reflected shock waves using both a time-resolved UV-absorption method (200 nm) and a single-pulse method (reaction time between 1.7 and 2.1 ms). The studies were done for the mixtures of 0.26% ketene and 2.2% ketene diluted with Ar in the temperature range 1102-1921 K at a total pressure range of 1.2-2.7 atm. From a computer-simulation study, a 38-reaction mechanism for the high temperature pyrolysis of ketene was developed. The mechanism and the rate-constant expressions were arrived at that could explain all our current data and previously reported data. It was found that the reactions 1-7 played a role in the ketene consumption. The rate constant expressions of the following six reactions except reaction 4 over the temperature range 1102-1921 K were estimated by using simulation. CH2CO + M -~ CH 2 + CO + M,
(1)
CH2CO + H ~ CH 3 + CO,
(2)
CH2CO + H ~ CHCO + H2,
(3)
CH2CO + CH z ~ C2H 4 + CO,
(4)
CH2CO + CH 2 --~ CHCO + CH3,
(5)
CH2CO + CH 3 --~ C2H 5 + CO,
(6)
CH2CO + CH 3 --~ CHCO + CH 4.
(7)
INTRODUCTION Ketene (CH 2CO) a n d / o r ketyl radical (CHCO) are produced in a combustion reaction of acetylene and they play a role in the combustion reaction of acetylene [1-4]. Acetylene is also formed as an intermediate in a combustion of higher-molecular-weight hydrocarbon and plays an important role in the overall processes, so that the mechanism of the acetylene combustion is indispensable in explaining the combustion reaction of the hydrocarbon. The mechanism of ketene pyrolysis is also an essential part of the mechanism of ketene oxidation. Because of the above, it is considered to be necessary to understand the mechanism of ketene pyrolysis at temperatures above 1000K in order to clarify the combustion mechanisms of ketene and hydrocarbons in detail.
*Corresponding author. 0010-2180/94/$7.00
The pyrolysis of ketene at the high temperatures was first studied at temperatures from 1140 to 1530 K by Tsuda and Kuratani [5] by using a single pulse shock tube. They reported that the disappearance of ketene followed a kinetic order of 1.5 with respect to ketene and its rate constant was represented by 1.6 x 1014 exp(-65.6 kcal/RT) l 1/2 m o 1 - 1 / 2 S -1. They also explained their results by using a 8-reaction mechanism. Wagner and Zabel [6] investigated the thermal decomposition of ketene behind reflected shock waves over the temperature range of 1300-2000 K. They proposed the reaction CH2CO + Ar ~ C H 2 + C O + Ar with the rate constant of k 1 = 3.6 × 1015exp(-59.3 k c a l / R T ) c m 3 tool -1 s -1 (the density of the gas mixture used was 6 x 10 -5 mol/cm 3) as the initiation step. Frank et al. [7] also investigated the reaction of ketene with H and CH z behind reflected shock waves using atomic and molecular absorption spectrometry. For temperatures between 1650 and 1850 K, the value of (1.8 _+ 0.6) x 1013 c m 3 mol- 1 s- 1 was deduced for the reaction of ketene with the H atom. However, the mechanism of ketene Copyright © 1994 by The Combustion Institute Published by Elsevier Science Inc.
HIGH-TEMPERATURE PYROLYSIS OF KETENE IN SHOCK WAVES pyrolysis at the high temperatures has not been studied in detail and is thus vague. So, we studied the ketene pyrolysis at the high temperatures by employing both techniques and arrived at the mechanism and the rate constant expressions. EXPERIMENTAL SECTION Two shock tubes of 4.1 cm i.d. were used in these experiments. The first shock tube is a standard-type connected an absorption apparatus [8]. An absorption measurement at 200 nm was used to monitor the CH2CO concentrations as follows. The transmitted intensity of a D 2 lamp (Hamamatsu-L544) through a 4.1 cm path in the shock tube and through a RicoMC-20 grating monochromator (with a halfwidth of 25 A) was monitored by a photomultiplier (Hamamatsu R-955). The response time of the optical-electrical system was about 2 /zs. The second shock tube is a magic-hole-type, which was described in detail previously [9, 10]. Within 20 s after shock heating, reacted gas mixtures were extracted into a preevacuated vessel (50 cm 3) through a valve near the end plate. The reacted mixtures were analyzed on three gas-chromatographs (Shimazu GC-3BT1, Shimazu GC-3BT2, Shimazu GC-8AT), which have thermal-conductivity detectors. The gaschromatographs were serially connected. A column of 2-m-long sebaconitrile at 40°C in the GC-3BT1 was used to determine ketene concentration and hydrocarbon concentrations above C a. A column of 2 m-long Porapak Q and 2 m-long Unibeads 1S in the GC-8AT was employed to determine the concentrations of carbon dioxide, ethane, ethylene, acetylene, propane, propylene, allene, and propyne: the rate of increasing temperature from 50 to 130 °C was 3 °C/min. A 2-m-long Molecular Sieve 5A column in the GC-3BT2 was employed at 50 °C to determine the concentration of hydrogen, methane, and carbon monoxide. The carrier gas used for the gas analysis was helium gas. The signal obtained from the gaschromatograph was introduced into data processors (Shimazu Chromatopac C-R3A1, Shimazu Chromatopac C-R3A2, and Shimazu Chromatopac C-R1B) and was automatically treated. An effective heating time was deter-
19
mined using the same method as that described previously [9, 10]. The reaction was assumed to be frozen perfectly at the effective heating time (reaction time), which was defined as the time between the arrival point of the reflected shock-front and 80% point of the reflected shock-front pressure. The effective heating time was used as the reaction time in a simulation. The relationship between the effective heating time and temperature showed a simple curve: the effective heating time increased with a decrease in temperature as seen in Fig. 2 of Ref. 9. The effective heating times at 1200, 1300, 1400 and 1500 K were determined as 1.97, 1.89, 1.80, and 1.71 ms, respectively. The gas compositions used were 0.26% CH2CO, 99.74% Ar (mixture a), and 2.2% CH2CO, 97.8% Ar (mixture b). The CH2CO was prepared by heating vapor of acetic anhydride at 500 °C in a quartz tube. The crude CHzCO was purified by trap to trap distillation. The CHzCO purity was examined with the gas chromatograph and was confirmed to be above 99%. The impurity included in it was only carbon dioxide. The purified ketene usually contained about 1% carbon dioxide. The carbon dioxide is considered to exert no influence upon the reaction rate and product distribution [5]. The Ar (Teisan Co.), specified to be 99.999% pure, was used. The computer calculations used in this study are essentially the same as described previously [9-11]. The computer routine used was Gear-type integration of the set of differential equations describing the chemical kinetics under constant density conditions for reflected shock waves. Reverse reactions were automatically included in the computer program through equilibrium constants computed from polynomial fits to standard thermochemical data. The computer program which contained the expressions relating the temperature change to the reaction progress was used for the simulations: the computations for concentration-time variations were carried out by making the rateconstant values of each elementary reaction change every 0.001 K. The time variations of absorption curves were also calculated with the program considering both the concentration change of each species during the reaction
20
Y. HIDAKA ET AL.
progress and the dependence of the absorption intensity on temperature. All references to temperature herein refer to the full vibrational relaxation, no-reaction shock front value. Assuming that the reaction was frozen perfectly at the effective heating time, the hydrocarbon-concentrations analyzed by gas chromatographs were compared with the simulated ones. The details for these have also been represented previously [9, 10]. The basic thermochemical data source was the JANAF table [12] and the table of coefficients sets for NASA polynomials [13] with the following alterations. The heats of formation used for the species, C 2 H , C 2 H 3 , C 3 H 3 , and C4H 5 are 135.3 kcal/mol [14], 71.7 kcal/mol [14], 83.6 kcal/mol [15] and 72.3 kcal/mol [15], respectively. RESULTS AND DISCUSSION The pyrolysis of CH2CO was studied over the temperature range 1102-1921 K and over the pressure range of 1.2-2.7 atm, by both tracing the time variation of absorption at 200 nm and analyzing concentrations of reacted mixtures on the gas chromatograph. The product distribution determined by the gas chromatograph is shown in Fig. 1. Under our experimental conditions, the main pyrolysis products detected on the gas chromatograph were CO, H2, CH4, C2Hz, and C2H 4. These are in a good agreement with the results of Tsuda and Kuratani [5]. The species C 2 H 6 , C 3 H 6 , a - C 3 H 4 (allene), P-Call 4 (propyne), C4H 4 (vinylacetylene), and 1,3-C4H 6 were detected in smaller quantities. Only a slight mass deficit for carbon was observed below 1200 K, but at 1400 and 1500 K was about 5% and 7%, respectively. Typical time-profiles of absorption at 200 nm are shown in Fig. 2. A t is defined as A t = log(If/It)/log(If/Io)
,
where If is the signal voltage corresponding to the full intensity and I 0 and I t are the signal voltages corresponding to the absorption intensity at the reflected shock front (t = 0) and at time t, respectively. The absorption intensity using the mixture, 0.26% CH2CO, 99.74% Ar, increased rapidly at the reflected shock front,
1,0
0.5
0'0L10'00' T / K
1500
0 0'' 10'00 _
1500
¢ /c O /
O
0.0 10'00 '
1500 T/K
' T/K
(e)
(d)
i
0.01 •Z
t
0:0, O O
,
10'00'
1500
1000'
1500 T/K T/K Fig. 1. Comparison of observed with calculated product distribution with mixture (2.2% ketene, 97.8% Ar), where C O is the initial concentration of CH2CO and C is the concentration of each species. The calculation was carried out with Table 1. (a) ©, [CH2CO] observed; 0 ; [CO] observed; O, [C2H 4] observed; , [CH2CO] calculated; - - - - - , [CO] calculated; . . . . . , [C2H4] calculated. (b) A, [CH4] observed; - - , [CH 4] calculated. (c) A; [C2H2] observed; ®; [H 2] observed; - - , [C2H 2] calculated; . . . . . , [H 2] calculated. (d) It; [a-C3n4] observed; v, [P-C3H 4] observed; ©, [C3H 6] observed; - - , [a-C3n 4] calculated: - - - - - , [p-C3H4] calculated; . . . . . , [C3H6] calculated. (e) 0, [ c 4 n 4] observed; ©, [1,3-C4H 6] observed; ~, [C2H 6] observed; - - - - - : [C4H 4] calculated, . . . . . : [1,3-C4H6] calculated; , [C2H 6] calculated.
and then was constant for about 1 ms at temperatures below 1500 K. At temperatures between 1500 and 1921 K, it decreased with time. The relationship between the total absorption data, A t, and temperature T with mixture, 0.26% CH2CO, 99.74% Ar, is shown in Fig. 3. In order to calculate the absorption intensity of each product, extinction coefficients of ketene and main products at 200 nm were measured with each mixture, 0.26% CH2CO, 5% CO, 1% H2, 1% CH 4, 1% C2H4, or 1% C 2 H E diluted in Ar. The extinction coefficients were calculated from the reflected shock front absorbance. The relationship between the extinction coefficient E c and temperatures is
H I G H - T E M P E R A T U R E PYROLYSIS OF K E T E N E IN S H O C K WAVES
1.0
1.0
1.0 0
0
A
<
0
~" 0.5
0.5
0.5
i
i
i
i
0.0
I
i
500
i
1000
0.0
I
k
i
i
I
0.0
2000
I
shown in Fig. 4. The equations, log E C = 2.27 X 10 -4 T + 5.74 cm 2 mo1-1, log E c = 4.20 × 10 -4 T + 4.57 cm 2 mo1-1 and log E c = 8.61 × 10 -4 T + 3.94 cm 2 mo1-1 for CHzCO, C2H 2 and C e l l 4 w e r e obtained, respectively. These equations were used for simulations. Extinction coefficients of CH4, He, and CO were also below 10 3 c m 2 mol 1: the extinction coefficients of CH 4, H e, and CO were below one thousandth of ketene. Hence, extinction coefficients of CH4, H2, and CO were neglected in simulation. The reaction mechanism adopted for explaining the data of CH2CO pyrolysis is shown in Table 1. The initial step in the thermal decomposition of CH2CO was studied in detail by Wagner and Zabel [6]. From the absorption results at 230 nm, they showed that reaction 1 was the initiation step and played an important role in the C H z C O pyrolysis: 2+CO+M (1)
We also adopted reaction 1 as the initiation step. Reaction 1 is very sensitive to the consumption of ketene and the production of carbon monoxide, as shown in Table 2. Reaction 1 is also very sensitive to the absorption curve because the absorption mainly comes from reactant ketene: the extinction coefficient of main products, CO, H2, CH4, C2H2, and C2H 4 are below one tenth of that of ketene, as men-
1.0
8
8 <~
,g
0.5
0.5
J
i
+
1500
L
i
I
2000 T/K
i
+
i
I
2000 T/K
1.0
0.0
i
1500
T/K
Fig. 2. Comparison of the observed UV-absorption curves at 200 nm with the calculated ones at low, middle and high temperatures using mixture (0.26% ketene, 99.74% Ar). O, observed at 1575 K; zx, observed at 1669 K; t2, observed at 1721 K; and - - , calculated with Table 1.
A H 0 = 75.8 kcal/mol.
i
500
t /as
CH2CO+M~CH
21
~
c~b
0.0 1500
2000 T/K
Fig. 3. Relationship between absorption data A t and temperature T using mixture (0.26% ketene, 99.74% At). As0 , AI00, A300, and As00 are A t values observed at 50, 100, 300, and 500 /zs, respectively. O, observed; , calculated with Table 1.
tioned above. To explain all our experimental data consistently, this reaction with k I = 3.96 × 1015exp(-59.3 k c a l / R T ) cm 3 mo1-1 s -1 was indispensable: the activation energy - 5 9 . 3 k c a l / m o l was adopted from a value proposed by Wagner and Zabel [6] though the activation energy of reaction 1 was inferred to be somewhat lower than 59.3 k c a l / m o l because reaction 1 was considered to be in the falloff range under our experimental conditions [6] and the density we used is about a fourth of Wagner and Zabel's. The rate-constant value evaluated is by a factor of 1.1 higher than that of Wagner and Zabel [6] evaluated at the density of 6 x 10 -5 mol/cm3: the density we used was 1.2 x 10 -5 - 1.7 × 10 -5 m o l / c m 3. This k 1 value can predict our data well, as shown in Figs. 1-3. This value can also predict the data of Tsuda and Kuratani [5] and Frank et al. [7] within an experimental error, as shown in Figs.
22
Y. H I D A K A ET AL. TABLE 1 Elementary Reactions and Rate Constant Expressions a No.
Reaction
(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) (31) (32) (33) (34) (35) (36) (37) (38)
C U e C O + M = CH 2 + CO + M C H 2 C O + H = CH 3 + CO CH2CO + H = CHCO + H 2 C H 2 C O + CH 2 = C2H 4 q" CO C H 2 C O + CH z = C H C O + CH 3 C H 2 C O + CH 3 = C 2 H 5 + CO C H 2 C O + CH 3 = C H C O + CH 4 C H C O + H = CH 2 + CO C H C O + CH 2 = C 2 H 3 + CO C H C O + CH 3 = C2H 4 -1- CO C H C O + C H C O = C2H 2 + CO + CO CH 4 + CH 2 = CH 3 + CH 3 CH 4 + H = CH 3 + H 2 CH 3 + M = CHe + H + M CH 3 + H = CH 2 + H 2 CH 3 + CH 2 = C2H 4 + H CH 3 + CH 3 = C2H 5 + H CH 2 + CH~ = C2H 2 + H + H C2H 6 = CH 3 + CH 3 C2H5 = C2H 4 + H C2H 4 + M = C2H 2 + H 2 + M C2H 4 + H = C 2 H 3 + H 2 C 2 H 4 + CH 2 = a-C3H 5 + H C 2 H 3 + M = C2H 2 + H + M C 2 H 2 + CH 2 = P-C3H 4 C3H 6 + H = C 2 H 4 + CH 3 a-C3H 4 + H = a-C3H 5 a-C3H 4 + CH 2 = i - C a l l 5 + H a-C3H 4 + CH 3 = 1,2-C4H 6 + H P-C3H 4 + M = C3H 3 + H + M P-C3H 4 + CH 2 = 2-C4H 5 + H p-C3 H 4 = a-C3H 4 1,3-C4H 6 = C2H 4 + C2H 2 1,2-C4H 6 = 1,3-C4H 6 1,2-C4H 6 = C3H 3 + CH 3 2-C4H 5 = C4H 4 + H i-C4H 5 = C4I~I4 "~ H C4H 4 = C2H 2 + C2H2
A 3.96 1.11 1.80 1.00 3.60 9.00 7.50 1.50 3.00 2.00 1.00 6.00 3.80 1.90 7.00 4.20 2.80 1.20 7.00 1.20 3.30 5.00 3.00 2.31 1.20 3.40 4.00 1.00 8.75 4.70 1.00 2.10 1.00 2.50 2.00 3.00 5.00 3.40
X x x x × × × × X × × × × × × × × x × × × × × × × × × x x × × × × × × × x x
n 1015 107 10 TM 1012 1013 101° 1012 1014 1013 1012 1013 1014 106 1016 1013 10 j3 1013 10 TM 1014 1012 1017 1015 1012 10 TM 1013 1013 1012 1013 1011 10 TM 1013 1012 1014 1013 1015 1013 1013 1013
0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.1 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
E
References
59300 2000 8600 0 11000 0 13000 0 0 0 0 14000 7750 91400 15100 0 13600 795 80000 35000 81260 22850 0 28000 6617 3500 2700 0 14900 80000 0 60000 75000 63000 75000 45000 44000 77140
see text this work this work 7 this work this work this work 16 3 assumed 3 17 18 19 17 16 20 16 9 9 21 b 21 c assumed 21 d 16 22 22 assumed 23 10 assumed 10 23 23 23 23 23 24
"Rate constants in the form, AT" exp(-E/RT), in cm, mol, cal, and K units. bThis value, which was very similar to the value k = 2.95 × 1017exp(-81.3 kcal/RT)cm 3 mo1-1 s -1 reported by Tanzawa and Gardiner [25], was evaluated from data in C 2 H 4 pyrolysis and oxidation. CThis value, which was very similar to the value k = 1.32 × 106T 2"53 e x p ( - 1 2 . 2 kcal/RT) cm 3 m o l - 1 s-1 reported by Tsang and Hampso n [26], was evaluated from data in C z H 4 pyrolysis and oxidation. dThis value, which was very similar to the value k = 7.9 x 10 TM exp( - 31.5 kcal/RT) cm 3 m o l - 1 s - 1 reported by Benson and Haugen [27], was evaluated from data in C 2 H 4 pyrolysis and oxidation.
5 and 6, respectively, which were obtained with a density similar to ours. The value we evaluated for reaction 1 is roughly consistent with Wagner and Zabel's within an experimental error. However, since reaction 1 was considered to be in the fall-off range under our experimental conditions [6] and the density we
used is about a fourth of Wagner and Zabel's, the value k 1 w e evaluated should be lower than Wagner and Zabel's. However, our value is somewhat higher than Wagner and Zabel's. We cannot explain this. For consumption reactions of CH2CO except reaction 1, there are six reactions which
HIGH-TEMPERATURE PYROLYSIS OF KETENE IN SHOCK WAVES
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Y. H I D A K A ET AL. 1.0
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now to us seem possible. CH2CO
+ H --, C H 3 + C O ,
AH 0 = -32.5 kcal/mol, CH2CO+H~CHCO+H
(2) 2,
A H 0 = - 0.7 kcal/mol, CH2CO
+ CH 2 ~
(3)
+ CH 2 -~ CHCO
(4) + CH3,
A H o = - 4 . 3 kcal/mol, CH2CO
(5)
+ C H 3 --+ C 2 H 5 + C O ,
A H o = - 2 3 kcal/mol, CH2CO
1500 T/K
1300
1500 T/K
Fig. 5. Comparison of reported (symbols) with computed product distribution using Table 1 for the mixture of 2% ketene, 98% Ar, where [C]0 is the initial concentration of CH2CO and C is the concentration of each species. (a) O, [CO] observed; [3, [C2H4] observed; - - - - - , [CO] calculated; . . . . . . . , [C a H 4 ] calculated. (b) A, [CH 4 ] observed; - - , [CH4] calculated. (c) A, [C2H2] observed; ®, [H 2] observed; . . . . . . . . , [C2H2] calculated; , [H 2] calculated. (d) v , [P-C3n4] observed; O, [C3H 6] observed; - - - - - , [P-C3H4] calculated; . . . . . . . , [C3H6] calculated. (e) O, [C2H6] observed; , [C2H6] calculated• Experimental data are taken from Table 2 of Ref. 5.
C2H 4 + CO,
A H 0 = - 94.2 kcal/mol, CH2CO
I
1300
+ C H 3 --~ C H C O
& H o = 0.7 kcal/mol.
(6) + CH4, (7)
The reaction of atomic hydrogen with ketene has been studied at temperatures below 500 K [28-30]. Carr et al. [28] used a discharge flow-mass spectrometric technique and showed that the major reaction products in the reaction of atomic hydrogen with ketene w e r e C H 3 and CO. This was corroborated by Slemr and
Warneck [29]. Reaction 2 was proposed for the reaction of atomic hydrogen with ketene. Michael et al. [30] also have reported k 2 = 1.10 X 1 0 13 e x p ( 3.44 kcal/RT) c m 3 mol-1 s-1 for reaction 2 over the temperature range of 298-500 K. For temperatures between 1650 and 1850 K, Frank et al. [7] also deduced k 2 = (1.8 q- 0.6) × 1013 c m 3 m o l s -~ for reaction 2 from a shock tube study. Under our experimental conditions, reaction 2 also played an important role for the ketene consumption and the formation of CO and C H 3. As long as we used an extrapolated value of Michael et al. [30] for reaction 2, computed ketene concentration was larger than the observed one at a given time and the yield of methane was always lower than the observed one. One way to match the computed concen-
H I G H - T E M P E R A T U R E PYROLYSIS O F K E T E N E IN S H O C K WAVES 3.0
25
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0 1.0 0
1.0
0.0
0.0
200
400
600
800
~
O....
t / ~s
Fig. 6. Comparison of reported [HI and [CO] concentrations [7] with computed ones at 1670 K and at 1.74 bar for mixture (50 ppm ketene in At). A, reported [H] concentration; O, reported [CO] concentration; - - - - - , [H] calculated with Table 1; - - - , [CO] calculated with Table 1; . . . . . . , [H] calculated with k t × 0.91; - - , [CO] calculated with k 1 x 0.91.
trations to the observed ones was to increase the k 2 value by a factor of about 3. This shows that the value of reaction 2 at the high temperatures is larger than extrapolated one at the low temperatures. This result was consistent with that obtained by Frank et al. [7]. The e x p r e s s i o n k 2 = 1.11 × 1 0 7 T 2 e x p ( - 2 kcal/RT) c m 3 mo1-1 s - I was evaluated for the rate constant of reaction 2. The extrapolated value of k 2 = 1.11 × 1 0 7 T 2 e x p ( - 2 kcal/RT) c m 3 m o l - 1 s- 1 is in good agreement with the value of Michael et al. [30] at low temperatures, as shown in Fig. 7. This k2 value is also very consistent with Frank et al.'s, as shown in Fig. 7. When we used reaction 2 only for the reaction of atomic hydrogen with ketene, the computed yield of H 2 was much lower than the observed one. This shows that reaction 3 cannot be ignored under our experimental condition because the species H 2 is mainly produced by reaction 3. Reaction 3 also affected on the absorption curves observed at 200 nm. The best fit for our data and Tsuda and Kuratani's data [5] (Fig. 5) was obtained by using k 3 = 1.80 X 1014 e x p ( - 8 . 6 0 k c a l / R T ) cm 3 m o l - 1 s- 1. We assumed two channels for the reaction of CH 2 with CH2CO. Reaction 4 plays a role for the formation of C 2 H 4 together with reactions 6, 10 and 16, as may be seen in Table 2: the intermediate product C2H5 was rapidly
1010
10aK/T Fig. 7. Comparison of the rate constant k 2 derived in this study with those reported. - - - , present work; - - -, Michael et al. [30]; . . . . . . . , Slemr and Warneck [29]; 0 , Cart et al. [28]; O, Frank et al. [7].
decomposed to ethylene by reaction 20. When reaction 16 only with k16 -- 4.2 × 1013 c m 3 mol - t s -1 [16] reported for C a n 4 formation was used for calculations, the calculated yield of C2H 4 was always smaller t h a n the observed one. Hence, it was necessary to adopt reaction 4 with k4 = 1.0 × 1012 c m 3 mo1-1 s -1 to predict the observed yield of C E H 4 together with reactions 6 and 10: the C2H 5 was rapidly decomposed to ethylene by reaction 20. While, reaction 5 plays a role for the formation of C H 3. We assumed k s = 3.6 × 1013 e x p ( - 1 1 kcal/RT) c m 3 mol-1 s-1 for reaction 5. This value can predict well the C H 4 yield, as shown in Fig. 1. If we omitted this reaction in simulation, the calculated yield of CH 4 was much smaller than the observed one. To achieve an agreement between the calculated yield and the observed one without reaction 5, we needed to increase the rate constants of reactions 2 a n d / o r 7. The k2 value used in Table 1 is consistent with that reported by Frank et al. [7] as described above. Furthermore, our k 2 value used in Table 1 is 1.3 × 1013 cm 3 mol-1 s - 1 at 1500 K. A k 2 value larger than our value is not acceptable. On the other hand, o u r k 7 value used in Table 1 is 9.6 x 101° cm 3 mo1-1 s -1 at 1500 K. This value is similar to the rate constant, 9.9 × 101° cm 3 mo1-1 s -1 of a similar
26 reaction, c2n
Y. H I D A K A ET AL. 4 + C H 3 ---* C 2 H 3 + C H 4 A H 0
= 0.8 kcal/mol, which was recommended by Baulch et al. [16]. However, the rate constant of reaction 7 is inferred to be half that of reaction C 2 H 4 + C H 3 ~ C 2 H 3 + C H 4 because the number of C-H bond of ketene is half that of ethylene and A H 0 value of reaction 7 is similar to reaction C2H 4 + C H 3 --* C 2 H 3 + C H 4. Hence, o u r k 7 value used in Table 1 is larger than that inferred from the similar reaction. Because of the above, we did not increase the rate constants of reactions 2 and 7. We assumed two channels for the reaction of C H 3 with C H : C O . Initially, we tried to model our data without reaction 6. When we used a mechanism without reaction 6, which could explain the absorption data in mixture 0.26% ketene, 99.74% Ar, the calculated yields of carbon monoxide and ethylene, etc, in mixture 2.2% ketene, 97.8% Ar, were always lower than the observed ones. One way to solve this problem was to introduce reaction 6. Reaction 6 plays an important role for the formation of CO and C 2 H 4 : the C e l l 5 rapidly decomposes t o C 2 H 4. The species C H 3 is more at risk in a steric structure than the CH 2 species when they carried out an addition reaction to ketene. Furthermore, the A H 0 value of reaction 6 is about a fourth of that of reaction 4. Thus, the rate c o n s t a n t k 6 --= 9.0 × 101° c m 3 mo1-1 s -1 of reaction 6 was assumed to be about a tenth of that of reaction 4. This value gave a best fit for both the product yields and the time-profiles. Methane is one of the major products in the pyrolysis of ketene. The methane is produced by reaction 7 only. The rate constant k 7 = 7.50 × 1012 e x p ( - 1 3 . 0
kcal/RT)
cm 3
mo1-1 s -1 was evaluated from the CH 4 yield. Its value can also predict well the yield of CH 4 reported by Tsuda and Kuratani [5], as shown in Fig. 5. The reaction between ketyle radical and hydrogen atomic was studied in O + C2H 2 mixtures. It has been proposed that reaction 8 produced CO and CH 2 [31, 32]. The values evaluated for reaction 8 is 3.00 × 1012 c m 3 mo1-1 s -1 - 1.5 × 10 TM cm 3 mo1-1 s -1 [31, 32]. W e a d o p t e d k 8 = 1.50 × 1014 cm 3 mol-1 s-1 because its value was evaluated
at temperatures to be similar to ours [32] and was recommended [16]. E v e n had k s = 3.00 × 1013 c m 3 mo1-1 s -1 been used instead of k 8 = 1.50 × 10 TM c m 3 mo1-1 s -1, the computed results would scarcely have varied from those shown in Figs. 1-3. Furthermore, reaction 8 is not sensitive in our experiment, as shown in Table 2. Hence, this rate constant was not discussed in detail. Reaction 9 is less sensitive to all the products. We used k 9 = 3.0 × 1013 c m 3 mo1-1 s -1 assumed by Miller et al. [3]. Very little is known about reaction of the ketyle radical with the methyl radical. Reaction 10 is somewhat sensitive to the consumption of ketene and the formation of methane and ethylene, as may be seen in Table 2. Reaction 10 plays a role in the formation of ethylene: ethylene was mainly produced by reactions 4, 10, 16, and 20. Reaction 10 with kl0 = 2.0 × 1012 c m 3 mo1-1 s -1 was assumed to predict our results. Reaction 11 is somewhat sensitive to acetylene and carbon monoxide yield, as may be seen in Table 2. A few acetylene and carbon monoxide molecules were produced from reaction 11 in our calculations, so reaction 11 with k l l = 1.0 × 1013 c m 3 mol-1 s-1 [3] was added to Table 1. In order to predict the yields of allene, propyne, propylene, vinylacetylene, and 1,3butadiene, reactions 23 and 25-38 were introduced in Table 1. In order to account for allene production, reaction 23 was assumed. The species a-C 3H 5 ( CH 2= CH(~H 2 ) formed by reaction 23 decomposes to allene by reaction - 2 7 . Propyne was produced by reactions 25 and - 3 2 . The yield of vinylacetylene was predicted by assuming reactions 28 and 31: the i - C 4 H 5 (CH2=CCH~----CH 2) formed may produce vinylacetylene by reaction 37 and the 2 - C 4 H s ( C H z C ~ C C H 3) formed is expected to produce vinylacetylene via 1,2,3-butatriene [23]. The 1,3-butadiene was expected to be formed via raction 34: the 1,2-butadiene was assumed to be formed by reaction 29. The yield of propylene was predicted by reaction 26. Figure 5 shows the comparison of reported product yields [5] with those modeled using Table 1. The mechanism and the rate constant expressions shown in Table 1 can nearly pre-
H I G H - T E M P E R A T U R E PYROLYSIS O F K E T E N E IN S H O C K WAVES
I
~,
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4.
4.0
0
5.
0
6. 0
2.0
7. o
8.
V
0.0 0
1 O0
200
300
t/IJs
Fig. 8. Comparison of reported ketene concentrations [7] with computed one at 1725 K and at 7.35 bar for mixture (1620 ppm ketene in Ar). ~7, reported ketene concentration; - - - - - , calculated with Table 1; - - , calculated with Table 1 changing k 1 = 3.96 × 1015 exp(-59.3 kcal/RT) cm 3 mo1-1 s -1 to k~ = 2.30 × 1015exp(-57.6 kcal/RT) cm 3 mol- 1 s - 1 132].
9. 10.
11.
12.
dict Tsuda and Kuratani's data, as shown in Fig. 5. Figure 6 shows a comparison of reported H atom and CO molecule concentrations [7] with calculated results. The mechanism and the rate constant expressions shown in Table 1 can predict Frank et al.'s data within an experimental error, as shown in Fig. 6. Figure 8 shows a comparison of reported ketene concentration [7] with calculated result. The mechanism and the rate constant expressions shown in Table 1 can predict it well. The pressure used was 7.35 bar and it was by a factor of about 3 larger than our pressure. Thus, the value of k t = 2.3 × 1015 e x p ( - 5 7 . 6 kcal/RT) cm 3 mol -~ s -1 reported by Frank et al. was used instead of k 1 = 3.96 x 1015exp(-59.3 k c a l / R T ) c m 3 mo1-1 s -1 shown in Table 1. This mechanism and the rate constant expression can also predict well Fig. 8.
13. 14.
15.
16.
17. 18. 19.
20.
21. 22.
REFERENCES 1. Lange, W., and Wagner, H. G., Ber. Bunsenges. Phys. Chem. 79:165-170 (1975). 2. Vandooren, J., and Van Tiggelen, P. J., Sixteenth Symposium (International) olt Combustion, The Combustion Institute, Pittsburgh, 1976, pp. 1133-1144. 3. Miller, J. A., Mitchell, R. E., Smooke, M. D., and Kee, R. J., Nineteenth Symposium (International) on
23.
24.
25.
27
Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 181-196. Hidaka, Y., Gardiner, W. C., Jr., and Eubank, C. S., J. Mol. Sci. 2:141-153 (1982). Tsuda, M., and Kuratani, K., Bull. Chem. Soc. Jpn. 41:53-60 (1968). Wagner, H. G., and Zabel, F., Ber. Bunsenges. Phys. Chem. 75:114-118 (1971). Frank, P., Bhaskaran, K. A., and Just, Th., J. Phys. Chem. 90:2226-2231 (1986). Hidaka, Y., Kataoka, T., and Suga, M., Bull. Chem. Soc. Jpn. 47:2166-2170 (1974). Hidaka, Y., Chiori, T., and Suga, M., Chem. Phys. Lett. 119:435-437 (1985). Hidaka, Y., Shiba, S., Takuma, H., and Suga, M., Int. J. Chem. Kinet. 17:441-453 (1985). Hidaka, Y., Nakamura, T., Miyauchi, A., Shiraishi, T., and Kawano, H., Int. J. Chem. Kinet. 21:643-666 (1989). Hidaka, Y., Takahashi, S., Kawano, H., Suga, M., and Gardiner, W. C. Jr., J. Phys. Chem. 86:1429-1433 (1982). Stull, D. R., and Prophet, H., JANAF Thermochemical Tables, 2nd ed., NSRDS-NBS 37, 1971. Bureat, A., in Combustion Chemistry (W. C. Gardiner, Jr., Ed.), Springer-Verlag, New York, p. 456. Ervin, K. M., Gronert, S., Barlow, S. E., Gilles, M. K, Harrison, A. G., Bierbaum, V. M., Depuy, C. H,, Lineberger, W. C. and Ellison, G. B., J. Am. Chem. Soc. 112:5750-5759 (1990). Lias S. G., Bartmess, J. E., Liebman, J. F,, Holmes, J. L. Levin, R. D., and Mallard, W. G., J. Phys. Chem. Ref. Data 17:1-861 (1988). Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., J. Phys. Chem. Ref. Data 21:411-734 (1992). Just, Th., Thirteenth Symposium (International) on Shock Tubes and Waves, 1981, pp. 54-68. Rabinowitz, M. J., Sutherland, J. W., Patterson, P. M., and Klemm, R. B., J. Phys. Chem, 95:674-681 (1991), Markus, M. W., Woiki, D., and Roth, P., Twenty. Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 581-588, Frank, P., and Braun-Unkhoff, M., Sixteenth Symposium (International) on Shock Tubes and Waves, 1987, pp. 379-385. Hidaka, Y., Higashihara, T., Inami, K., and Kawano, H., in preparation. Hidaka, Y., Nakamura, T., Tanaka, H., Jinno, A., Kawano, H., and Higashihara, T., Int. J. Chem. Kinet. 24:761-780 (1992). Hidaka, Y., Higashihara, T., Ninomiya, N., Oshita, H., and Kawano, H., J. Phys. Chem. 97:10977-10983 (1993). Braun-Unkhoff, M., Kurz, A., and Frank, P., Seventeenth Symposium (International) on Shock Tubes and Waves, 1989, pp. 493-498. Tanzawa, T., and Gardiner, W. C., Jr., Combust. Flame 39:241-253 (1980).
28 26. Tsang, W., and Hampson, R. F., J. Phys. Chem. Ref. Data 15:1087-1279 (1986). 27. Benson, S. W., and Haugen, G. R , J. Phys. Chem. 71:1735-1746 (1967). 28. Carr, R. W., Jr., Gay, I. D., Glass, G. P., and Niki, H., J. Chem. Phys. 49:846-853 (1968). 29. Slemr, F., and Warneck, P., Ber. Bunsenges. Phys. Chem. 79:152-158 (1975). 30. Michael, J. V., Nava, D. F., Payne, W. A., and Stief, L. J., J. Chem. Phys. 70:5222-5227 (1979).
Y. HIDAKA ET AL. 31. Lohr, R., and Roth, P., Ber. Bunsenges. Phys. Chem. 85:153-158 (1981). 32. Frank, P., Bhaskaran, K. A., and Just, Th., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 885-893. 33. Homann, K. H., and WeUmann, Ch., Bet. Bunsenges. Phys. Chem. 87:609-616 (1983).
Received 15 October 1993; revised 20 April 1994