Investigation of the thermal decomposition of ketene and of the reaction CH2 + H2 ? CH3 + H

Article abstract of DOI:10.1524/zpch.2001.215.12.1601

Using frequency modulation (FM) spectroscopy singlet methylene radicals have been detected for the first time behind shock waves. The thermal decomposition of ketene served as source for metylene radicals at temperatures from 1905 to 2780 K and pressures around 450 mbar. For the unimolecular decomposition reaction, (1) CH₂CO+M → CH₂ +CO+M, the rate constants obtained are: k₁ = (9.5±5.7) · 10¹⁵ · exp[(-244±25) kJ mol^-1/RT] cm³mol^-1 s^-1. As a first study of a methylene reaction at high temperatures by diretly tracing methylene the reaction of methylene with hydrogen, (8+9) ^1.3CH₂ + H₂ → CH₃ + H, was investigated at temperatures from 1930 to 2455 K and pressures around 500 mbar. For the total rate constant of the singlet and triplet methylene reaction a temperature independent value was obtained: log(k_g+9/(cm³mol^-1s^-1)) = 13.89±0.26. A comparison with low temperature literature data and the systematics of activation energies of triplet methylene reactions allowed a consistent description of singlet and triplet contributions and of the forward and reverse reaction. by Oldenbourg Wissenschaftsverlag, Muenchen.

Full text of DOI:10.1524/zpch.2001.215.12.1601

Zeitschrift für Physikalische Chemie, 215, 12, 1601–1623 (2001)
by Oldenbourg Wissenschaftsverlag, München
Investigation of the Thermal Decomposition of
Ketene and of the Reaction CH2 +H2 ꢀ CH3 +H
∗
By Gernot Friedrichs and Heinz Gg. Wagner
Georg-August Universität Göttingen, Institut für Physikalische Chemie,
Tammannstraße 6, D-37077 Göttingen, Germany
Dedicated to Prof. Dr. Dr. h.c. mult. Fritz Peter Schäfer
on the occasion of his 70th birthday
(Received October 23, 2000; accepted in revised form November 6, 2000)
Chemical Kinetics / Elementary Reactions / Shock Waves /
Frequency Modulation Spectroscopy / CH2 Radicals
Using frequency modulation (FM) spectroscopy singlet methylene radicals have been
detected for the first time behind shock waves. The thermal decomposition of
ketene served as source for metylene radicals at temperatures from 1905 to 2780 K
and pressures around 450 mbar. For the unimolecular decomposition reaction, (1)
CH2CO+M → CH2 +CO+M, the rate constants obtained are:
k1 = (9.5 5.7)·1015 ·exp [(−244 25) kJ mol−1/RT ] cm3 mol−1 s−1
.
As a first study of a methylene reaction at high temperatures by diretly tracing methylene
the reaction of methylene with hydrogen, (8+9) 1,3CH2 +H2 → CH3 +H, was investigated
at temperatures from 1930 to 2455 K and pressures around 500 mbar. For the total rate
constant of the singlet and triplet methylene reaction a temperature independent value
was obtained:
log (k8+9/(cm3 mol−1 s−1)) = 13.89 0.26.
A comparison with low temperature literature data and the systematics of activation
energies of triplet methylene reactions allowed a consistent description of singlet and
triplet contributions and of the forward and reverse reaction.
1. Introduction
The kinetics of the methylene radical is of interest in combustion chemistry. It
is an important intermediate in hydrocarbon flames where it is mainly formed
by the reaction of oxygen atoms with acetylene. Also the stepwise decompo-
sition of higher hydrocarbon radicals can form methylene. Consecutive reac-
tion products of methylene reactions strongly influence the product distribution
*
Corresponding author. E-mail:gfriedr@gwdg.de

1602
G. Friedrichs and H. Gg. Wagner
of the combustion process. For example, the reaction CH2 +O2 is an important
chain branching reaction [1, 2] and the reaction CH2 +H → CH+H2 is a main
source for CH radicals, which may contribute to the prompt-NO formation via
the consecutive reactions CH+N2 → HCN+N and N+O2 → NO+O [3].
Methylene also plays a role in forming C3 and C4 hydrocarbons [4].
An interesting feature of methylene reactions results from the existence of
two electronic states of methylene, the triplet ground state (3CH2 ) and the first
excited singlet state (1CH2 ). Since the singlet state lies only 37.6 kJ/mol [5]
higher than the ground state the population of the singlet state at combustion
temperatures is not negligible. At 2000 K in thermal equilibrium around 4.6%
of the methylene is present as 1CH2 . The reactivity of both states is very differ-
3
ent. CH2 reacts with hydrocarbons non-stereospecific under H atom abstrac-
1
tion, whereas CH2 inserts in single bonds and undergoes stereospecific add-
ition to double bonds [6]. Normally, 3CH2 reactions show rather high activation
energies, while 1CH2 reactions often proceed with no or very low energy barri-
ers and the rate coefficients are comparable to the collision number. Therefore,
especially at lower temperatures, the rate coefficients of the 1CH2 reactions of-
ten surmount the homologous 3CH2 reactions by several orders of magnitude.
Direct spectroscopic measurements of methylene reactions were performed
rather extensively near ambient and elevated temperatures up to 730 K by
means of Laser induced fluorescence (LIF, singlet methylene), e.g. [7–9], and
Laser magnetic resonance (LMR, triplet methylene), e.g. [10–13]. However,
at temperatures higher than 1000 K, which are relevant for the combustion
process, studies of methylene reactions are very rare. In fact, due to low ab-
sorption coefficients and the high reactivity of methylene which results in low
concentration levels of methylene, no high temperature kinetic study by di-
rectly tracing the methylene radical is found in the literature yet. Furthermore,
it is just ten years ago when Sappey et al. [14] reported the first optical spec-
troscopic detection of singlet methylene at a temperature higher than 1000 K.
They succeeded to detect methylene in a premixed methane/oxygen flame by
means of LIF. Recently, Lozovsky et al. [15] and McIllroy [16] detected sing-
let methylene in premixed methane flames with good signal-to-noise ratios by
means of Intracavity laser absorption spectroscopy (ICLAS) and Cavity ring-
down spectroscopy (CRDS), respectively.
Here we report the first investigation of 1CH2 reactions behind shock waves
by means of frequency modulation (FM) spectroscopy which was shown to be
one and a half orders of magnitude more sensitive than the normal dual beam
absorption technique using narrow bandwidth laserlight [17, 18].
2. Experimental
All experiments were carried out behind incident shock waves. An aluminium
shock tube with an inner diameter of 20 cm [19], equipped with a ring dye

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1603
laser (Coherent, 899–21) pumped by an Ar+ laser (Coherent, Innova 200–15)
1
provided a sensitive means to detect CH2 using FM spectroscopy. The FM
spectrometer used is described in detail in [18]. The electronic bandwidth of
the FM spectrometer was 2.5 MHz, high enough for a time resolution of sev-
eral microseconds due to the spatial extent of the laser beam. In order to adjust
1
the laser wavelength to the b B1(0, 14, 0)404 ← a˜ 1A1(0, 0, 0)414 transition of
˜
1CH2 at 590.707 nm and to check the FM spectrometer settings, the laser beam
passed a photolysis cell as a stationary radical source. The photolysis of gas
mixtures of 5% ketene in argon at 308 nm was used to generate (quasi-) sta-
1
tionary CH2 concentrations in the photolysis cell. In most experiments the
laser beam passed three times through the shock tube to extend the absorp-
tion length to 60 cm. The multipassing was achieved by two small adjustable
mirrors built into the shock tube wall [20]. A detection limit of approximately
2·10−12 mol/cm3 for 1CH2 at 2200 K was achieved.
Gas mixtures of 6000 ppm ketene in argon were prepared in a stainless
steel cylinder which could be evacuated to pressures lower than 10−7 mbar and
heated up to a temperature of 500 K. A magnetic stirrer in the cylinder allowed
experiments to be performed 15 min after preparation. UV absorption measure-
ments showed that these mixtures were stable for several days. By using a flow
system with calibrated mass flow controllers (Tylan, MKS) the gas mixture
could be further diluted with argon or a 1% hydrogen/argon mixture, respec-
tively. Before each experiment the shock tube was flushed with the particular
mixture for about 10 min in order to reduce any influence of wall absorption.
Ketene was prepared by pyrolysis of acetone at T = 600 ◦C on Cr/Ni
wires and was purified by trap to trap distillation. The purity of samples
stored at 77 K was periodically checked by FTIR spectroscopy. Small impuri-
ties of ethylene (< 2.5%) were found. Numerical simulations of the reaction
system showed that such small amounts of ethylene did not enter critically
into the evaluation. Other substances used were argon (99.998%) and hydro-
gen (99.999%).
For all computer simulations of the complex reaction mechanism given in
Table 1 and for sensitivity analysis the Chemkin-II package [21] was used. The
sensitivity coefficients σo were normalized with respect to the maximum con-
centration of the particular species over the time history. Except for CH2, which
will be discussed in the next section, all thermochemical data were taken from
Konnov [22].
3. Evaluation
For the decomposition of ketene the following channels may be considered:
3
(1a) CH2CO+Mꢀ CH2 +CO+M
r H2◦98K = 328 kJ/mol
366 kJ/mol
1
(1b)
ꢀ CH2 +CO+M

1604
G. Friedrichs and H. Gg. Wagner
(1c)
ꢀ C2O+H2 +M
ꢀ HCCO+H+M
ꢀ C2H+OH+M
ꢀ C2 +H2O+M
ꢀ HCO+CH+M
433 kJ/mol
443 kJ/mol
634 kJ/mol
637 kJ/mol
687 kJ/mol.
(1d)
(1e)
(1f)
(1g)
Because of the high endothermicity the three channels (1e)–(1g) should
not contribute to the decomposition, whereas the other channels might get
some influence especially at high temperatures. Channel (1b) yields singlet
methylene which is rapidly quenched under the experimental conditions ap-
plied:
3
(2)
1CH2 +Mꢀ CH2 +M
r H2◦98 K = −37.6 kJ/mol.
1
Carstensen [23] determined the quenching rate of CH2 by argon at tem-
peratures from 206 to 547 K. Using his expression for k2, 2.41 ·1010 · T 0.9
,
and assuming an average total density of 2.5·10−6 mol/cm3 the thermal equi-
librium should be reached within 250 ns which is much faster than the time
resolution of the shock tube apparatus (7 s). As a result of the thermal equi-
librium between singlet and triplet methylene on the one hand the experimental
1CH2 concentration time profiles could be taken as a measure for the total
methylene concentration in the reaction system. On the other hand it was not
possible to distinguish between singlet and triplet reactions in general and be-
tween channel (1a) and (1b) in particular.
Channel (1c) would yield C2O which decomposes fast to C atoms and
CO [24]. Markus et al. [25] investigated the thermal decomposition of ketene
by means of C-Atomic resonance absorption spectroscopy (C-ARAS) and
ruled out channel (1c) to be a direct decomposition channel. Frank et al. [26]
also investigated the thermal decomposition of ketene at temperatures from
1650 to 2800 K by means of resonant detection of H atoms and CO. At
temperatures from 2000 to 2300 K channel (1d) was found to show a 10%
contribution. At higher temperatures a possible influence of channel (1b) on
the measured H atom profiles could not be distinguished from other H atom
forming secondary reactions. Bauerle et al. [27] inferred channel (1d) to be less
significant (< 5%) from their H atom measurements up to temperatures of
2700 K.
For a quantitative evaluation of the singlet methylene profiles the equi-
librium constant and with it the energy difference between singlet and triplet
methylene (singlet triplet splitting ST) had to be known accurately [5, 28–
30]. In this work
= 3147 cm−1 = 37.6 kJ/mol was used which is in
ˆ
ST
good agreement with the data of [5] and [30]. For the enthalpies of for-
mation of methylene values of f H2◦98 K(3CH2 ) = 391.0 kJ/mol [31, 32] and
f H2◦98 K(1CH2 ) = 428.6 kJ/mol were used. The temperature dependence of
the enthalpies and entropies of formation were taken from the thermodynamic

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1605
1
Fig. 1. Experimental and simulated CH2 concentration profiles. T = 2315 K, ꢀ = 2.58 ·
10−6 mol/cm3, 1195 ppm ketene; solid lines: experiment and best fit; dashed lines: simula-
tions with k1 ×2 and k3/2; (1) CH2CO+M CH2 +CO+M and (3a+3b) CH2 +CH2
1
C2H2 +2H resp. C2H2 +H2. The maximum of the CH2 concentration profile corres-
1
ponds to 13 ppm CH2 .
database of GRI-Mech 3.0 [33]. Using these values equilibrium constants for
reaction (2) of K = 23.2, 14.9, 11.0 and hence singlet methylene fractions
1
([ CH2 ]/[CH2]tot) of 4.1%, 6.3%, 8.4% at 1900, 2350 and 2800 K were ob-
tained, respectively.
The thermal decomposition of ketene was investigated behind incident
shock waves in the temperature range from 1905 to 2780 K and densities
ranging from 1.6 to 3.4·10−6 mol/cm3 which correspond to pressures of
370 – 530 mbar. Most experiments were performed by multipassing the de-
tection laser three times through the shock tube (3×20 cm). Control experi-
ments with a single path of the laser beam were performed. These experi-
ments provided consistent results. The initial mole fraction of ketene varied
from 395 – 2605 ppm (multipass) and 1200 – 5400 ppm (single pass), respec-
tively.
In Fig. 1 an experiment at a temperature of 2315 K, a total density of
2.58·10−6 mol/cm3 and an initial ketene mole fraction of 1195 ppm is shown.
1
The CH2 concentration reaches its maximum value after 7–8 s and is near
zero again after 100 s. The initial increase is determined by the unimolecu-
lar decomposition of ketene (reaction (1)). For the evaluation it was assumed
3
to proceed via channel (1a) yielding quantitatively CH2 which rapidly equili-
brates with 1CH2 .
The following decrease of CH2 is due to fast consecutive reactions of
methylene with itself, with ketene and with other species, e.g.
(3) CH2 +CH2 → products
(3a) CH2 +CH2 ꢀ C2H2 +H+H
r H2◦98 K = −119 kJ/mol
−555 kJ/mol.
(3b)
ꢀ C2H2 +H2

1606
G. Friedrichs and H. Gg. Wagner
Here and within the following text CH2 is used instead of 3CH2 and 1CH2
in cases where no seperate literature data are available. For numerical analysis
in these cases CH2 was set equal to 3CH2 . That should be a good approximation
since 3CH2 is the excess species (see above).
Frank et al. [26] concluded that from 2100 to 2700 K reaction (3) pro-
ceeds via channel (3a) yielding two H atoms with a rate constant of 1·1014
cm3 mol−1 s−1. Such a quantitative H atom yield is in disagreement with meas-
urement of Dombrowsky et al. [2] who investigated the reaction CH2 +O2 →
products by tracing OH radicals. Assuming a quantitative H atom yield of
the side reaction (3) would have resulted in a much higher OH concentration
and faster OH formation via the reaction H +O2 → O+OH than measured.
Bauerle et al. [27] also investigated the thermal decomposition of ketene and
diazomethane behind shock waves by means of H-ARAS and concluded that
channel (3a) contributes 10–20% to the total reaction (3) at temperatures from
1100 to 2700 K. They reported a total rate constant of 1.3·1014 cm3 mol−1 s−1
at 2300 K which is in good agreement with the rate constant reported by
Frank et al.
Other channels like
(3c) CH2 +CH2 ꢀ C2H4
r H2◦98 K = −730 kJ/mol
−264 kJ/mol
(3d)
(3e)
ꢀ C2H3 +H
ꢀ CH+CH3
−38 kJ/mol,
are of minor importance for the experimental conditions used here. C2H3 which
would be formed via channel (3d) decomposes fast yielding C2H2 and H. Thus,
channel (3d) is indistinguishable from channel (3a). The formation of CH3
via channel (3e), as proposed by Frank and Just [34], could not be verified
by Dombrowsky [35] during the thermal decomposition of diazomethane at
temperatures from 900 to 1400 K. Markus et al. [25] measured CH radical pro-
files during the thermal decomposition of ketene at temperatures from 2200 to
3400 K and they concluded that approximately 6% of reaction (3) proceed via
channel (3e).
Next to reaction (3) the reactions of methylene with ketene and the reaction
of methylene with H atoms shall be considered.
For the reactions
(4) 3CH2 +H ꢀ CH+H2
r H2◦98 K = −12 kJ/mol
r H2◦98 K = −50 kJ/mol
(5) 1CH2 +H ꢀ CH+H2
several investigations are reported in the literature. For reaction (4) we re-
fer to the publication of Hippler et al. [36] who recently compared their new
experimental results with literature data and SACM calculations. We used
a temperature independent value of k4 = 1.1·1014 cm3 mol−1 s−1. In addition,
reaction (5) was taken into account with k5 = 7·1013 cm3 mol−1 s−1 based on an
estimation of Peeters et al. [37].

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1607
There are some bimolecular reactions of ketene which might have some
influence especially at lower temperatures, e.g.
(6a) 3CH2 +CH2CO ꢀ C2H4 +CO
(6b) 3CH2 +CH2CO ꢀ CH3 +HCCO
(7a) 1CH2 +CH2CO ꢀ C2H4 +CO
(7b) 1CH2 +CH2CO ꢀ CH3 +HCCO
r H2◦98 K = −401 kJ/mol
−19 kJ/mol
−439 kJ/mol
−57 kJ/mol.
1
Carstensen [23] determined the rate of the reaction CH2 +CH2CO →
products at temperatures from 240 to 510 K to be (1.5 0.2) · 1014·
0.45
(T/293 K)−0.45
cm3 mol−1 s−1. This rate constant represents the sum of the
3
quenching process (→ CH2 +CH2CO) and the reactive process. Thus, this
expression, which has been used here for the evaluation, gives an upper limit
for this rate. On the basis of the quantum yield of CO and C2H4 following the
photodissociation of CH2CO (φCO/φC H = 2.2 [38]) Böhland et al. [11] con-
2
4
cluded that the quenching process should be of minor importance. The reaction
of triplet methylene with ketene should be relatively slow. Based on estima-
tions of this reaction in [26, 27], k6 was estimated to be 1·1012 cm3 mol−1 s−1.
In thermal equilibrium at 2000 K (4.6% 1CH2 ) approximately 75% of the total
methylene consumption by reaction (6) and (7) is due to the singlet reaction (7).
The individual product channels (a) and (b) are assumed to contribute equally
to the total rate constants of reactions (6) and (7).
Next to the reactions just mentioned several other reactions can influence
the measured 1CH2 concentration profiles. In Table 1 the mechanism used for
the simulations is given.
It is devided into five groups. Reactions (1) and (2) represent the start reac-
tions, reactions (3)–(16) take into account bimolecular reactions of both singlet
and triplet methylene, reactions (17) and (18) specify reactions of ketene with
H and H2, reactions (19)–(27) summarize bimolecular reactions of other re-
active species and finally reactions (28)–(39) list unimolecular decomposition
reactions of the intermediate species.
In some cases singlet (1CH ) and triplet (3CH = CH ) reactions are taken
ˆ
2
2
2
into account seperately. In all other cases the triplet reactions hold for the sum
of singlet and triplet reaction.
1
For a first evaluation of the experimental CH2 profiles only the rate con-
stant of reaction (1) and a scaling factor, which converts the measured signal
1
level to CH2 concentration, were used as free parameters. The scaling was
needed because the absorption coefficient of 1CH2 was unknown. In Fig. 1 the
influence of reaction (1) on the simulated profile is shown. Next to the solid line
(best fit) a simulation with k1 ×2 is shown, which results in a maximum 1CH2
concentration at a shorter reaction time and a subsequent faster decrease. Scal-
ing the signal to this new maximum would have resulted in a worse fit. Thus,
with all other rate coefficients held constant, a reliable determination of k1 and
the scaling factor was possible.

1608
G. Friedrichs and H. Gg. Wagner
Table 1. Reaction mechanism: Rate constants are given in ki = A·T n ·exp (Ea/RT ) (units
3
kJ, cm3, mol, s and K). CH2 is equal to CH2 .
No.
Reaction
A
n
Ea
Ref.
Start Reactions
1
2
CH2CO + M
CH2
CH2
+ CO
+ M
+ M 9.5·1015
2.4·1010
0
0.9
244
0
**
[23]
1CH2 + M
1
Reactions CH2 +X and CH2 +X
3a CH2
3b CH2
+ CH2
+ CH2
+ H
C2H2
C2H2
CH
CH
C2H4
CH3
C2H4
CH3
CH3
+ H
+ H 3.8·1014
0
0
0
0
0
0
29.5 **
29.5 **
+ H2
3.8·1014
4
5
CH2
+ H2
1.1·1014
0
0
0
[36, 39]
[37], est.
est.
1CH2 + H
+ H2
7.0·1013
6a CH2
6b CH2
+ CH2CO
+ CH2CO
+ CO
+ HCCO
+ CO
+ HCCO
+ H
5.0·1011
5.0·1011
0
est.
7a 1CH2 + CH2CO
7b 1CH2 + CH2CO
9.5·1014 −0.45
0
0
[23] ***
[23] ***
**, ****
**, ****
[40] ***
[40] ***
[40] ***
[40] ***
[27], est.
[41]
9.5·1014 −0.45
8
9
CH2
+ H2
1.0·1013
6.8·1013
6.0·1012
6.0·1012
1.1·1014
1.1·1014
1.0·1014
3.2·1012
1.1·1014
4.2·1013
1.8·1013
0
0
0
0
0
0
0
0
0
0
0
51
0
28
28
0
0
0
22
0
1CH2 + H2
CH3
C3H3
+ H
10a CH2
10b CH2
+ C2H2
+ C2H2
+ H
→ AC3H4*
11a 1CH2 + C2H2
11b 1CH2 + C2H2
C3H3
+ H
+ H
→ AC3H4*
C2H2
12 CH2
13 CH2
+ CH
+ C2H4
C3H6
C3H6
C2H4
C2H4
14 1CH2 + C2H4
[8]
15 CH2
+ CH3
+ H
+ H
0
[40]
16 1CH2 + CH3
0
[42]
Suppl. Ketene Reactions
17a H
17b H
18a H
18b H
18c O
+ CH2CO
+ CH2CO
+ CH3CO
+ CH2HCO
+ C2H4
CH3
+ CO
1.8·1013
5.0·1013
3.3·1013
2.0·1013
6.7·105
0
0
0
0
14
33
0
[40]
[43]
[44]
[45]
HCCO + H2
CH2CO + H2
CH2CO + H2
CH2CO + H2
0
1.88
0.8 [46]
Suppl. Bimolecular Reactions
19
20
21 CH
H
H
+ C2H2
+ C2H4
+ C2H2
H2
H2
H
C3H3
C2H2
C2H
+ C2H
6.0·1013
0
0
0
0
0
0
0
0
0
116
62
0
13
0
0
57
0
[40]
[40]
[47]
[4, 48]
[4]
[49]
[40]
[40]
[51]
+ C2H3
+ C3H2
+ CO
+ CO
+ H
5.4·1014
1.3·1014
22 HCCO + C2H2
1.0·1011
23 HCCO + HCCO
+ CO 1.0·1013
24 CH
25 CH3
+ CH
+ CH3
+ C2H5
+ H2
1.5·1014
→ C2H5
C2H4
CH4
+ H
3.0·1013
26
27 CH3
H
+ H
2.0·1012
+ H
2.0·1013
60
continued on the next page →
However, using the rate expressions for the important reactions (3a)
and (3b) given in [27] for the first evaluation, rate constants k1 were obtained
which showed an unexpected but obvious deviation from a linear Arrhenius be-

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1609
Table 1. continued.
No.
Reaction
A
n
Ea
Ref.
Suppl. Unimolecular Decompositions
28
CH
+ M → C
+ M → C
+ H
+ M
1.9·1014
1.6·1014
5.6·1015
1.9·1016
4.2·1015
2.0·1017
8.0·1014
4.0·1016
4.2·1041
2.6·1017
2.6·1017
2.0·1048
1.1·1021
6.0·1015
6.0·1018
0
0
0
0
0
0
0
0
280
268
375
383
345
368
342
447
190
332
404
410
409
246
437
[50]
[25]
[27]
[52]
[53]
[54]
[55]
[56]
[40]
[56]
[56]
[57], est.
[58]
[59]
[60]
29a CH2
29b CH2
30a CH3
30b CH3
31
32
33
34
+ H2 + M
CH + H + M
+ M
+ M
+ M
+ M
1CH2 + H
+ M
CH + H2 + M
CH4
C2H
CH3 + H
+ M
+ M
+ M
+ M
+ M → C2
+ H
C2H + H
C2H2 + H
C2H2 + M
C2H3 + M
−7.5
35a C2H4 + M
C2H2 + H2 + M
0
35b C2H4 + M
C2H3 + H
C3H2 + H
C2H3 + CH3
+ M
+ M
0
36
37
38
39
C3H3 + M
C3H6
HCCO + M
−8.5
−1.2
0
−1.1
CH + CO + M
H2
+ M
H
+ H
+ M
*
Allen (H2C = C = CH2).
** this work.
*** channel distribution estimated.
**** k8+9 = 7.8·1013 cm3 mol−1 s−1
est.: estimated.
.
havior at lower temperatures. Furthermore, the absorption coefficient, which
could be calculated from the obtained scaling factors, showed a pronounced
maximum at a temperature around 2200 K whereas a simple population analy-
sis predicts a uniform increase of the absorption coefficient with decreasing
temperature at the experimental conditions used. Both effects clearly indicate
that, at low temperatures in particular, bimolecular reactions have a more pro-
nounced influence on the profiles than predicted from the mechanism used for
this first evaluation.
In Fig. 2 two experiments at a temperature of 1965 K and 2535 K are
shown, respectively. For sensitivity analysis, which is shown in the upper and
lower part of Fig. 2, only the most sensitive reactions are shown. At both
temperatures the reactions (1) and (3) are the dominant reactions, but also reac-
tion (4) has a noticeable influence, whereas reaction (7) is important only at low
temperatures. The high sensitivity coefficients of reaction (3a) and (3b) suggest
these reactions to be responsible for the observed deviations in k1 and the ab-
sorption coefficient. It was found in a second evaluation that the following rate
expressions for reaction (3a) and (3b) allow a good description of the experi-
mental methylene profiles and, beyond it, result in consistent data for k1 and the
absorption coefficient:
k3a = k3b = 3.8·1014 ·exp (−29.5 kJ/mol/ RT ) cm3 mol−1 s−1.

1610
G. Friedrichs and H. Gg. Wagner
Fig. 2. 1CH2 concentration profiles and sensitivity analysis for two experiments. T =
1965 K, ꢀ = 3.22 · 10−6 mol/cm3, 1500 ppm ketene and T = 2535 K, ꢀ = 1.87 · 10−6
1
mol/cm3, 1245 ppm ketene. Middle: experimental CH2 profils and best fits (solid lines).
The dashed lines refer to simulations using a reduced mechanism (reactions (1–4)
and (7)). Upper and lower: sensitivity analysis. (1) CH2CO+M
CH2 +CO+M,
(2) 1CH2 +M
(4) 3CH2 +H
C2H4 +H.
3CH2 +M, (3a) 2 CH2
C2H2 +2 H, (3b) 2 CH2 C2H2 +H2,
CH+H2, (7a + 7b) 1CH2 +CH2CO
products, (15) 3CH2 +CH3
Compared to the rate constants of Bauerle et al. [27] this expression gives
a 1.5 times larger rate constant k3 at 1900 K, but the same value at 2800 K.
The channel distribution is changed from 10–20% in [27] to 50%. The resulting
higher H atom yield also increases the importance of reaction (4) (3CH2 +H).
It should be mentioned here that higher values of k3 without changing
the channel distribution did not result in consistent data. However, an in-
crease of the rates of reactions (4), (7) or choosing a higher rate for ketene
decomposition channel (1d) result in a tendency of the evaluated data quite
similar to the performed change of k3a and k3b. As expected from the sen-
sitivity analysis shown in Fig. 2 these variations would however have been
more pronounced than the changes introduced here. Overall, H atom yields

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1611
Table 2. Experimental conditions and results: Unimolecular decomposition of ketene and
1CH2 calibration function ζ (scaling factor).
No.
T / K
106 ·ꢀ
x(CH2CO)
[ppm]
k1
10−8 ·ζ(T )
[cm3/mol]
[mol cm−3
]
[cm3 mol−1 s−1
]
l = 20 cm, single pass (ζ(T) is adjusted to l = 60 cm)
k24
k23
k27
k33
k25
k45
k44
k37
k20
k19
2085
2090
2135
2145
2280
2290
2315
2350
2400
2430
2.78
2.79
2.80
2.80
2.75
2.55
2.55
2.28
2.28
2.28
5400
3240
3090
3090
3090
1200
2600
2800
1680
5400
7.5·109
7.0·109
5.5·109
6.0·109
1.7·1010
2.4·1010
2.7·1010
2.8·1010
5.5·1010
6.0·1010
2.97
2.25
2.09
2.36
2.04
2.25
2.47
1.89
1.95
1.73
l=60 cm, multipass
k72
k93
k74
k91
k83
k98
k89
k70
k71
k99
k77
k92
k64
k61
k60
k97
k84
k94
k52
k81
k87
k95
k56
k58
k57
k85
k88
k86
k80
1905
1940
1965
1975
1990
1995
2030
2060
2065
2085
2125
2175
2185
2185
2195
2255
2280
2300
2315
2330
2365
2415
2460
2485
2500
2535
2620
2640
2780
3.35
3.45
3.22
3.44
3.06
3.34
3.03
2.82
3.11
2.88
3.04
2.54
2.58
2.59
2.56
2.56
2.20
2.55
2.58
2.56
2.36
2.29
1.94
1.94
1.92
1.87
1.88
1.88
1.61
1000
1115
1500
1045
1245
1500
975
1.6·109
4.5·109
1.9·109
5.0·109
4.5·109
5.0·109
8.0·109
8.0·109
6.7·109
9.0·109
6.5·109
1.8·1010
1.4·1010
1.7·1010
1.6·1010
2.3·1010
2.6·1010
2.6·1010
2.1·1010
2.4·1010
3.2·1010
4.3·1010
8.0·1010
9.0·1010
1.1·1011
8.5·1010
1.6·1011
1.1·1011
2.5·1011
2.83
2.45
2.47
2.67
2.38
2.74
2.76
2.90
2.47
2.25
2.11
2.54
2.61
2.25
2.54
2.11
1.91
2.38
(3.41)
1.89
2.00
1.59
1.80
1.73
1.95
1.46
1.37
1.24
1.12
1000
1000
2605
1000
1045
955
950
950
1500
1245
1115
1195
1245
1215
1115
1195
395
1195
1245
730
750
1000
higher than those reported by Bauerle et al. seem very probable. The experi-
mental conditions, obtained values for k1 and the scaling factors are listed in
Table 2.

1612
G. Friedrichs and H. Gg. Wagner
Fig. 3. Experimental profile and sensitivity analysis. T = 2210 K, ꢀ = 2.41·10−6 mol/cm3,
1550 ppm ketene, 6120 ppm hydrogen, [H2]o : [CH2CO]o = 4 : 1. Upper: solid lines –
experiment and best fit; dashed lines – simulations with k8+9 ×2 and k8+9/2. Lower: sen-
sitivity analysis of same experiment; (1) CH2CO+M
CH2 +CO+M, (2) 1CH2 +M
3CH2 +M, (3a) CH2 +CH2
C2H2 +H+H, (3b) CH2 +CH2 C2H2 +H2, (8+9)
1,3CH2 +H2 → CH3 +H, (15) 3CH2 +CH3
C2H4 +H.
Having once established the ketene decomposition mechanism, H2 was
added to the intitial gas mixture to increase the influence of the reaction of
methylene with hydrogen:
(8) 3CH2 +H2 ꢀ CH3 +H
r H2◦98 K = −26.0 kJ/mol
−63.6 kJ/mol.
(9) 1CH2 +H2 ꢀ CH3 +H
Experiments were performed behind incident shock waves in the tempera-
ture range 1930–2455 K and densities ranging from 2.3 to 3.2·10−6 mol/cm3
which correspond to pressures of 458 to 515 mbar. Initial mixtures of
1115–1495 ppm ketene in argon served as methylene source. The mole frac-
tion of H2 was chosen to be 6360–14450 ppm, thus a factor of 4 – 10 higher
than ketene.
In the upper part of Fig. 3 an experiment at a temperature of 2210 K and
a hydrogen excess of 4 is shown. The partly negative signal during the first
6 s is due to the passage of the shock wave through the detection plane of the
laser beam (Schlieren signal). The thick solid line was obtained by numerical

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1613
simulation of the reaction system. As 1CH2 and 3CH2 were not distinguishable,
reaction (8) was neglected and reaction (9) was used as an adjustable param-
eter. Therefore the obtained rate constant represents the total rate constant k8+9
.
The scaling factor was varied within its error limits.
1
The influence of the reaction (8 + 9) on the CH2 profile is illustrated
in Fig. 3. In the upper part two simulations are shown with k8+9 chosen
twice and half of the best fit value. In the lower part the sensitivity an-
alysis reveals that reaction (8 + 9) has become as sensitive as reactions (3a)
or (3b). Thus a reliable determination of this rate constant should be pos-
sible. Due to the methyl radicals formed via reation (8 +9) at longer reaction
3
times reaction (15), CH2 +CH3 ꢀ C2H4 +H, becomes important. Further-
more, at these long reaction times the sensitivity coefficient of reaction (8+9)
changes its sign from negative to positive values. This could be interpreted in
a way that reaction (8+9) becomes a methylene source, thus mainly taking
place in the reverse direction due to a strong H formation via several con-
secutive reactions. In contrast to the pure ketene decomposition reaction (2),
3
1CH2 +M ꢀ CH2 +M, shows little influence on the detected profiles. Due
1
to the fast reaction of CH2 with hydrogen the thermal equilibrium of singlet
and triplet methylene is not fully established. However, in the example given
in Fig. 3 1CH2 still reaches at least 96% of its equilibrium concentration. Such
small deviations were negligible for the evaluation.
Next to the experimental conditions the obtained values for k8+9 are listed
in Table 3.
4. Results and discussion
Reaction (1)
The obtained values for the rate constant of the unimolecular decomposition of
ketene
3
(1) CH2CO+M → CH2 +CO+M
r H2◦98 K = 328 kJ/mol
are plotted as function of temperature (filled circles) and are compared to other
literature values in Fig. 4. At temperatures from 1905 to 2780 K and densities
from 1.6 to 3.4·10−6 mol/cm3 they can be represented by the expression (thick
solid line):
k1 = (9.5 5.7)·1015 ·exp [(−244 25) kJ mol−1 / RT ] cm3 mol−1 s−1.
Wagner and Zabel [61] investigated the thermal decomposition of ketene
at temperatures from 1300 to 2000 K at total densities from 5.0·10−5 to
2·10−3 mol/cm3 behind reflected shock waves. Ketene profiles were meas-
ured by means of UV absorption at 220 and 230 nm. As expected for a five-
atom molecule the unimolecular decomposition took place in the fall-off

1614
G. Friedrichs and H. Gg. Wagner
Table 3. Experimental conditions and results: (8+9) CH2 +H2
CH3 +H.
106 ·ꢀ
x(CH2CO) x(H2)
k8+9 ·10−13
[H ]
o
2
No.
T / K
[mol cm−3
]
[ppm]
[ppm]
[cm3 mol−1 s−1
]
[CH CO]
o
2
kh01
kh04
kh05
kh06
kh07
kh10
kh11
kh13
kh14
kh15
kh16
kh17
2160
2310
2455
2395
2125
1930
2110
1990
2210
2185
2020
2110
2.54
2.56
2.31
2.30
2.84
3.21
3.06
3.07
2.41
2.56
2.81
2.55
1115
1115
1115
1115
1115
1115
1115
1550
1550
1285
1285
1495
6360
6360
6360
6360
6360
6360
6360
6130
6130
10850
10850
14450
5.7
5.7
5.7
5.7
5.7
5.7
5.7
4.0
4.0
8.4
8.4
9.7
7
7
11
12
12
5
10
8
8
6
7
5
region. For a total density of 6 ·10−5 mol/cm3, the low density range of
their experiments, they reported an Arrhenius expression of k1 = 3.6·1015·
exp (−247 kJ mol−1/RT) cm3 mol−1 s−1 which is shown in Fig. 4 as solid line
marked with open triangles. Frank et al. [26] investigated the thermal decom-
position of ketene behind shock waves by means of Molecular resonance
absorption spectroscopy (MolRAS) of carbon monoxide. For temperatures of
1650 to 1850 K and an average total density of 1.2·10−5 mol/cm3 they ob-
tained k1 = 2.3·1015 ·exp (−241 kJ mol−1/RT) cm3 mol−1 s−1 (open squares)
which is in very good agreement with the expression given in [61]. An extrap-
olation of the expressions of Frank et al. and Wagner and Zabel towards higher
temperatures would result in lower values for k1 than measured in this work.
Since our expression is obtained at 5–25 times lower total densities (ꢀ ∼ 2.5·
10−6 mol/cm3) this is an indication, that the rate of the thermal decomposition
of ketene has not yet reached its low pressure limit value at densities of 6 ·
10−5 mol/cm3 used in [61]. Generally, a second order evaluation of a unimolec-
ular reaction, which takes place in the fall off region, yields too low second
order rate constants.
In the GRI-Mechanism [33] the rate k−1 of the recombination reaction (−1)
is given as a function of temperature and pressure. The reported expression is
based on a RRKM calculation assuming a recombination barrier of 18.8 kJ/mol.
The calculation was fitted to reproduce the experimental values of Wagner
and Zabel and Frank et al. In Fig. 4 the corresponding values for an average
total density of 6 · 10−5 mol/cm3 (dashed line marked with crosses) and 2.5 ·
10−6 mol/cm3 (dashed line marked with stars) are shown, respectively. The
GRI-Mech data result in merely 30% lower values than measured in this work.
As the GRI-Mech data were also fitted to the high pressure experimental
values of [61] (not shown in Fig. 4), they are in good agreement with all ex-

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1615
Fig. 4. Arrhenius plot of reaction (1) CH2CO+M → CH2 +CO+M.
perimental data over a wide range of temperatures (1300–2780 K) and total
densities (1.6·10−6 − 2·10−3 mol/cm3). The assumed recombination barrier
of 18.8 kJ/mol might be somewhat too high. Recently published results are
from Kim et al. (15.3 kJ/mol, experimental value [62]) and from King et al.
(17.8 kJ/mol, theoretical value [63]).
Reaction (8+9)
The obtained values for the total rate constant k8+9 of the reaction of methylene
with hydrogen
(8) 3CH2 +H2 → CH3 +H
(9) 1CH2 +H2 → CH3 +H
r H2◦98 K = −26.0 kJ/mol
−63.6 kJ/mol
are given in Table 3. Within the scatter of the data no temperature dependence
was found for 1930 – 2455 K. The mean value of log (k8+9) with its error bars
(double standard deviation) is
log (k8+9/(cm3 mol−1 s−1)) = 13.89 0.26.
Due to the short reaction time scale a possible influence of the vibra-
tional relaxation of hydrogen on the measured 1CH2 concentration time profiles
should be considered first. The mole fraction of hydrogen is sufficiently low to

1616
G. Friedrichs and H. Gg. Wagner
Fig. 5. Arrhenius plot of k8+9. Estimation of the triplet reaction contribution by compar-
ison with literature data. — and −·− : k8+9 this work, : temperature independent ex-
◦
1
1
trapolation of CH2 reaction, : temperature dependent extrapolation of CH2 reaction,
3
and : estimation of CH2 reaction on the basis of k8+9, ꢀ : k8 [65], - - - : interpola-
•
3
3
tions of CH2 reaction, ∗ and dotted line: estimation of CH2 reaction given in [33], × :
k9 calculated on the basis of the reverse reaction [66].
have no effect on the temperature behind the shock wave. On the other hand its
vibrational relaxation time in argon (10 s at 1900 K, 4 s at 2500 K) [64] is
comparable to the characteristic reaction times of 50–100 s observed in this
work. Therefore an influence of the hydrogen relaxation especially during the
first few microseconds can not be ruled out. However, in thermal equilibrium,
which could not be reached during these early reaction times, only 5% of the
whole hydrogen is in its first vibrational excited state at 2200 K. It is very im-
probable that a short deviation from this low equilibrium value should have
a great influence on the determined rate constant.
In Fig. 5 the obtained temperature independent rate constant is plotted
in Arrhenius form and is compared to other literature data. The thick ho-
rizontal line represents the determined value of k8+9 = 7.8·1013 cm3 mol−1 s−1
in its error bars (dash-dotted lines). Other experimental data both for the
singlet and the triplet forward reactions (8) and (9) are not available for
temperatures higher than 700 K. Wagener [7, 67] investigated the reaction
1
of CH2 with hydrogen at temperatures from 210 to 475 K by means of
3
LIF. For the total rate constant, quenching process (kQ, → CH2 ) and re-
active channel (9) (k9, → products), he reported kQ+9 = (7.3 1.0) · 1013 ·
0.6)
(T/295 K)(−0.5
cm3 mol−1 s−1. The slightly inverse temperature dependence
is consistent with ab initio calculations that predict a reaction without en-
ergy barrier [68]. The value of Wagener at room temperature (kQ+9 = 8.1·
1013 cm3 mol−1 s−1) is in good agreement with measurements of Ashfold et al.

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1617
(7.8 · 1013 [69]) and Langford et al. (6.3 · 1013 [70]). Taking into account
a quenching ratio of 16% [11, 71] the value of k9 = 6.8·1013 cm3 mol−1 s−1
was used for the reactive singlet channel (9) at room temperature in this work.
Starting from this value two different extrapolations were made toward high
temperatures. In Fig. 5 the solid line marked with open circles represents a tem-
perature independent extrapolation whereas the solid line marked with open
squares represents a temperature dependent extrapolation based on the tem-
perature dependence reported in [67]. In the latter case the expression k9 = 6.8·
1013 ·(T/295 K)−0.5 cm3 mol−1 s−1 was used, a possible additional temperature
dependence of the quenching ratio [67] was not taken into account. Using the
extrapolated values for k9 at high temperatures and the value for k8+9 obtained
in this work the rate constant of the triplet reaction (8) could be estimated
applying the formula:
1
[ CH2]
1
k8 = (k8+9 −k9)·
= (k8+9 −k9)·
.
(1)
3
[ CH2]
K(T )
3
K(T)representstheequilibriumconstantofreaction (2) 1CH2 +Mꢀ CH2 +M.
By this means for the rate of the triplet reaction k8 the solid lines marked with
solid circles and solid squares were obtained for the temperature independent
and temperature dependent extrapolation of the singlet reaction, respectively.
Thus, 13% (T-independent k9) or 68% (T-dependent k9) of the whole reaction
proceeds via the triplet reaction. However, the exact values strongly depend on
the used value for k8+9
.
The only measurement of reaction k8 was performed at a temperature of
700 K and is shown in Fig. 5 by the open triangle [65]. Simple linear in-
terpolations between this single point and the estimated k8 values at higher
temperatures (dashed lines) yield an activation energy for the triplet reac-
tion of Ea = 66 or 51 kJ/mol and a preexponential factor of 1.1·1014 or 1.0·
1013 cm3 mol−1 s−1, respectively. The obtained activation energies can be com-
pared with estimations reported by Do´be´ et al. [10] and Böhland et al. [12].
On the basis of a linear correlation of activation energy and dissociation
3
energy (Evans-Polanyi) which holds for the reactions of CH2 with several
hydrocarbons both authors give an estimation for the activation energy of re-
action (8). Do´be´ et al. extrapolated Ea ≈ 49 kJ/mol, whereas Böhland et al.
reported Ea ≈ 42 kJ/mol.
The dotted line in Fig. 5 refers to an estimation of the triplet reaction rate
taken from GRI-Mech [33]. This estimation is based on the rate of the reaction
3CH2 +CH4 ꢀ 2CH3 and on reactions of the isoelectronic oxygen atom. The
H atom abstraction reactions of oxygen show a good correlation with homol-
ogous methylene reactions. In general, the activation energies of O(3P) atom
reactions are roughly 7 kJ/mol and the preexponentials factor are about 5−15
times lower [12, 72].
Taking altogether, the interpolation of the triplet reaction which yields 13%
3
triplet contribution fits better into the overall picture of CH2 abstraction re-

1618
G. Friedrichs and H. Gg. Wagner
actions than the interpolation yielding a 68% triplet contribution. Thus, the
temperature independent interpolation of the singlet reaction (9) between room
temperature and about 2200 K seems to be more probable.
Bhaskaran et al. [66] investigated the thermal decomposition of methane
and determined the rate of the reaction CH3 +H ꢀ CH2 +H2 by means of
H-ARAS behind shock waves. The reported rate expression, k = 1.8·1014 ·
exp (−63 kJ mol−1/RT ) cm3 mol−1 s−1, was obtained by fitting the H atom pro-
files using a complex reaction mechanism. The activation energy of Ea =
63 kJ/mol is equal to the reaction enthalpy of the reverse reaction (−9).
As the forward reaction proceeds without energy barrier and as the activa-
tion energy of the homologous triplet reaction can be estimated to be about
71 kJ/mol (reaction enthalpy 26 kJ/mol + activation energy of forward reac-
tion ≈ 45 kJ/mol) the expression obtained by Bhaskaran et al. can be assumed
to describe the rate of the reverse singlet reaction (9). In Fig. 5 the dotted line
marked with crosses represents the rate of the forward singlet reaction cal-
culated via the equilibrium constant (K(1000 K) = 538, K(2500 K) = 7.55)
on the basis of the expression given by Bhaskaran et al. The obtained curve
is nearly temperature independent and the agreement with the temperature
independent extrapolation of the singlet reaction at high temperatures is very
good1.
Taking altogether, the measurements and estimations both of the singlet re-
action (9) and the triplet reaction (8) provide a consistent data set assuming
a (nearly) temperature independent singlet reaction.
Mechanism and scaling factor
With regard to the sensitivity analysis shown for the two experiments in Fig. 2
it should be possible to reduce the complex mechanism given in Table 1 to
the most important reactions (1–4) and (7). Singlet methylene profiles cal-
culated using this reduced mechanism are also shown in the middle part of
Fig. 2 as dashed lines. Whereas the initial increase and the reached maximum
is still reproduced well, towards longer reaction times the agreement gets
worse. The deviation is due to small but similar contributions of several other
reactions which overall could not be neglegted, e.g. (6) 3CH2 +CH2CO ꢀ
C2H4 +CO, (9) 1CH2 +H2 ꢀ CH3 +H, (12) CH2 +CH ꢀ C2H2 +H and (15)
3CH2+ CH3 ꢀ C2H4 +H.
The scaling factors ζ, which convert the measured FM signal level to 1CH2
concentration, are shown as function of temperature in Fig. 6. It was shown
1
Baulch et al. [40] calculated the rate of the reverse reaction (−9) on the basis of
a temperature independent value of k9 =7.2·1013 cm3 mol−1 s−1 and obtained a value for
k
which is 6 times lower than the corresponding value of Bhaskaran et al. In contrast to
−9
that in this work forward and reverse reaction are consistent. This discrepancy is probably
due to a typing error in the reported expression for the equilibrium constant in [40].

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1619
1
Fig. 6. Calibration function obtained for CH2 . Experimental conditions: modulation in-
dex = 1.45, modulation frequency = 965 MHz, experimental pressure = 640 mbar (T =
1500 K) to 320 mbar (T = 3100 K). — Fit, - - - Fit 25%.
in [18] that the following simple relation holds for FM measurements:
max
FM
I
= Io ·c·ζ.
max
FM
I
refers to the measured FM signal intensity, Io is the total intensity of
the laser beam, c is the species concentration and ζ refers to the calibration
function. ζ describes the temperature (and pressure) dependence of the scaling
factor and varies with modulation frequency (here 965 MHz) and modulation
index (here 1.45). Thus, ζ comprises the temperature and pressure dependence
of the absorption coefficient, the temperature and pressure dependence of the
FM factor (which takes into account some extra lineshape effects relevant for
FM spectroscopy) and an apparatus constant of the used FM spectrometer. It
is possible to convert the calibration function to the absorption coefficient and,
vice versa, to calculate the calibration function on the basis of a known absorp-
tion coefficient. For further details see [18].
In Fig. 6 the obtained calibration function ζ (solid line) is shown with
its 25% error bars (dashed lines). If the calibration function should be used
1
to determine the absorption coefficient of CH2 an additional influence of
the reaction mechanism should be taken into account. Due to fast con-
secutive reactions the CH2 concentration does not reach a maximum value
max
of [CH2]tot = [CH2CO]o. For example, at a temperature of 2500 K and
at 500 mbar total pressure only 31% of an initial ketene mole fraction of
1000 ppm could be detected as CH2. It can be seen from Fig. 1 that a varia-
tion of the rate constants of the most sensitive reactions (1) and (3) by a factor
1
of two results in a change of the simulated maximum CH2 concentration
(and with it the scaling factor and the calibration function) of approximately
30%.

1620
G. Friedrichs and H. Gg. Wagner
5. Conclusions
The formation of CH2 during the thermal decomposition of ketene has been in-
vestigated at temperatures from 1905 to 2780 K and pressures around 450 mbar
and could be described by a complex reaction mechanism. For the unimolecu-
lar decomposition reaction, (1) CH2CO+M → CH2 +CO+M, the rate con-
stants obtained in that range of pressure and temperature are
k1 = (9.5 5.7)·1015 ·exp [(−244 25) kJ mol−1/RT] cm3 mol−1 s−1.
For the reaction (3a) and (3b), CH2 +CH2 → C2H2 +2 H and → C2H2 +H2
a channel distribution of 50% and a rate expression of
k3a = k3b = 3.8·1014 ·exp (−29.5 kJ mol−1/RT ) cm3 mol−1 s−1
allows a consistent description of the experimental data.
The high temperature methylene reaction (8+9) 1,3CH2 +H2 → CH3 +H
was investigated at temperatures from 1930 to 2455 K at pressures around
500 mbar. For the total rate constant a temperature independent value was
obtained:
log (k8+9/(cm3 mol−1 s−1)) = 13.89 0.26.
On the basis of low temperature literature data and the systematics of ac-
tivation energies of triplet methylene reactions the rate constants of the singlet
and triplet reactions could be estimated to be
k9 = 6.8·1013 cm3 mol−1 s−1
k8 = 1.0·1013 ·exp (−51 kJ mol−1/RT) cm3 mol−1 s−1.
This corresponds to a triplet reaction contribution of 13% at 2200 K.
1
The quantitative detection of CH2 as described in this paper allows the
determination of the absorption coefficient of 1CH2 at high temperatures. The
conversion procedure of the calibration function to the absorption coefficient is
described in [18].
1
Quantitative detection of CH2 enables further direct investigations of
methylene reactions at high temperatures and could serve as a verification
of complex hydrocarbon combustion mechanisms which were developed in
1
recent years. Measurements of CH2 profiles during the thermal decompos-
ition of methane and ethane behind shock waves have already been per-
formed [73].
Acknowledgement
The active help of J. Deppe and the support by DFG and Fonds der Chemie are
gratefully acknowledged.

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1621
References
1. J. Warnatz, 18th Symp. (Int.) on Combust., The Combustion Institute, Pittsburgh
(1981), p. 369.
2. Ch. Dombrowsky and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem. 96 (1992)
1048, p. 373.
3. C. P. Fenimore, 13th Symp. (Int.) on Combust., The Combustion Institute, Pittsburgh
(1971).
4. J. A. Miller and C. F. Melius, Combust. Flame 91 (1992) 21.
5. P. Jensen and P. R. Bunker, J. Chem. Phys. 89 (1988) 1327.
6. P. P. Gaspar and G. S. Hammond, R. A. Moss and M. Jones (eds.), Carbenes, vol. 2,
New York (1975), p. 207.
7. M. Koch, F. Temps, R. Wagener and H. Gg. Wagner, Z. Naturforsch. 44a (1989)
195.
8. W. Hack, M. Koch, R. Wagener and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem.
93 (1989) 165.
9. H.-H. Carstensen and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem. 99 (1995)
1539.
10. S. Do´be´, T. Böhland, F. Temps and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem.
89 (1985) 432.
11. T. Böhland, F. Temps and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem. 89 (1985)
1013.
12. T. Böhland, S. Do´be´, F. Temps and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem.
89 (1985) 1110.
13. U. Bley, F. Temps, H. Gg. Wagner and M. Wolf, Ber. Bunsenges. Phys. Chem. 96
(1992) 1043.
14. A. D. Sappey, D. R. Crosley and R. A. Copeland, Appl. Phys. B 50 (1990) 463.
15. V. A. Lozovsky, I. Derzy and S. Cheskis, 27th Symp. (Int.) on Combust., The Com-
bustion Institute, Pittsburgh (1998), p. 445.
16. A. McIlroy, Chem. Phys. Lett. 296 (1998) 151.
17. J. Deppe, G. Friedrichs, H.-J. Römming, A. Ibrahim and H. Gg. Wagner, Ber. Bun-
senges. Phys. Chem. 102 (1998) 1474.
18. G. Friedrichs and H. Gg. Wagner, Z. Phys. Chem. 214 (2000), 1723.
19. K. Holzrichter and H. Gg. Wagner, 18th Symp. (Int.) on Combust., The Combustion
Institute, Pittsburgh (1981), p. 769.
20. G. Friedrichs, Frequenzmodulierte Spektroskopie zur Untersuchung von Reaktionen
des Amino- und Methylenradikals hinter Stoßwellen, Cuvillier-Verlag, Göttingen
(1999), ISBN 3-89712-741-5, Ph.D. thesis, Universität Göttingen.
21. R. J. Kee, F. M. Ruply and J. A. Miller, Chemkin-II: A Fortran Chemical Ki-
netics Package for the Analysis of Gas-Phase Chemical Kinetics, Sandia Re-
port SAND89-8009, Sandia National Laboratories, Livermore, California (1989),
http://www.ca.sandia.gov/chemkin/.
22. A. A. Konnov, Detailed reaction mechanism for small hydrocarbons combustion.
Release 0.3 (1997), http://homepages.vub.ac.be/∼akonnov/.1997.
23. H. Carstensen, Untersuchungen von Elementarreaktionen des Singulett-Methylens
CH2(a˜1A1) mit Hilfe der Laser-Induzierten-Fluoreszenz, Ph.D. thesis, Universität
Göttingen (1995), MPI für Strömungsforschung Bericht 4/1995.
24. G. Friedrichs and H. Gg. Wagner, Z. Phys. Chem. 203 (1998) 1.
25. M. W. Markus, P. Roth and A. M. Tereza, 25th Symp. (Int.) on Combust., The Com-
bustion Institute, Pittsburgh (1994), p. 705.
26. P. Frank, K. A. Bhaskaran and T. Just, J. Phys. Chem. 90 (1986) 2226.
27. S. Bauerle, M. Klatt and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem. 99 (1995)
870.

1622
G. Friedrichs and H. Gg. Wagner
28. P. R. Bunker, P. Jensen, W. P. Kraemer and R. Beardsworth, J. Chem. Phys. 85
(1986) 3724.
29. A. R. W. McKellar, P. R. Bunker, T. J. Sears, K. M. Evenson, R. J. Saykally and S. R.
Langhoff, J. Chem. Phys. 79 (1983) 5251.
30. D. G. Leopold, K. K. Murray, A. E. S. Miller and W. C. Lineberger, J. Chem. Phys.
83 (1985) 4849.
31. M. Litorja and B. Ruscic, J. Chem. Phys. 108 (1998) 6748.
32. I.-C. Chen, W. H. Green, Jr. and C. B. Moore, J. Chem. Phys. 89 (1988) 314.
33. G. P. Smith, D. M. Golden, M. Frenklach, N. W. Moriarty, B. Eiteneer, M. Gol-
denberg, C. T. Bowman, R. Hanson, S. Song, W. C. Gardiner Jr., V. Lissianski and
Z. Qin, GRI-Mech Version 3.0 (1999), http://www.me.berkeley.edu/gri_mech.
34. P. Frank and T. Just, Symp. Int. Shock Tubes Proc. 14 (1984) 706.
35. Ch. Dombrowsky, Universität Göttingen, unpublished results.
36. D. Fulle and H. Hippler, J. Chem. Phys. 106 (1997) 8691.
37. W. Boullart and J. Peeters, J. Phys. Chem. 96 (1992) 9810.
38. H. Okabe, Photochemistry of Small Molecules, John Wiley & Sons, New York (1978).
39. T. Böhland, F. Temps and H. Gg. Wagner, J. Phys. Chem. 91 (1987) 1205.
40. D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, T. Just, J. A. Kerr, M. J.
Pilling, J. Troe, R. W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data 21 (1992)
411.
41. T. Böhland, F. Temps and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem. 90 (1986)
468.
42. W. Tsang and R. F. Hampson, J. Phys. Chem. Ref. Data 15 (1986) 1087.
43. J. A. Miller and C. T. Bowman, Prog. Energy Combust. Sci. 15 (1989) 287.
44. M. Bartels, J. Edelbüttel-Einhaus and K. Hoyermann, 23th Symp. (Int.) on Com-
bust., The Combustion Institute, Pittsburgh (1991), p. 131.
45. A. A. Konnov, Detailed reaction mechanism for small hydrocarbons combustion.
Release 0.4 (1998), http://homepages.vub.ac.be/∼akonnov.
46. D. L. Baulch, C. J. Cobos, R. A. Cox, P. Frank, G. Hayman, T. Just, J. A. Kerr,
T. Murrells, M. J. Pilling, J. Troe, R. W. Walker and J. Warnatz, Combust. Flame 98
(1994) 59.
47. A. J. Dean and R. K. Hanson, J. Quant. Spectrosc. Radiat. Transfer 42 (1989) 375.
48. K. H. Homann and C. Wellmann, Ber. Bunsenges. Phys. Chem. 87 (1983) 609.
49. M. Röhrig, E. L. Petersen, D. F. Davidson, R. K. Hanson and C. T. Bowman, Int. J.
Chem. Kin. 29 (1997) 781.
50. A. J. Dean and R. K. Hanson, Int. J. Chem. Kinet. 24 (1992) 517.
51. R. Möller, E. Mozzhukhin and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem. 90
(1986) 854.
52. P. Roth, U. Barner and R. Löhr, Ber. Bunsenges. Phys. Chem. 83 (1979) 929.
53. M. W. Markus, P. Roth and T. Just, Int. J. Chem. Kinet. 28 (1996) 171.
54. R. Hartig, J. Troe and H. Gg. Wagner, 13th Symp. (Int.) on Combust., The Combus-
tion Institute, Pittsburgh (1971), p. 147.
55. T. Kruse, Untersuchungen zu Hochtemperaturreaktionen von Kohlenwasserstoff-
radikalen mit atom- und molekülspektroskopischen Methoden, Ph.D. thesis, Univer-
sität - Gesamthochschule - Duisburg (1999).
56. J. Warnatz, W. C. Gardiner Jr. (ed.), Combustion Chemistry, chap. 5, Springer Ver-
lag, New York (1985).
57. J. H. Kiefer and S. S. Kumaran, J. Phys. Chem. 97 (1993) 414.
58. W. Tsang, J. Phys. Chem. Ref. Data 20 (1991) 221.
59. P. Frank, K. A. Bhaskaran and T. Just, 21th Symp. (Int.) on Combust., The Combus-
tion Institute, Pittsburgh (1986), p. 885.
60. N. Cohen and K. R. Westberg, J. Phys. Chem. Ref. Data 12 (1983) 531.
61. H. Gg. Wagner and F. Zabel, Ber. Bunsenges. Phys. Chem. 75 (1971) 114.

Investigation of the Thermal Decomposition of Ketene and of the Reaction ...
1623
62. S. K. Kim, E. R. Lovejoy and C. B. Moore, J. Chem. Phys. 102 (1995) 3202.
63. R. A. King, W. D. Allen, B. Ma and H. F. Schaefer III, Faraday Discuss. 110 (1998)
23.
64. J. E. Dove and H. Teitelbaum, Chem. Phys. 6 (1974) 431.
65. H. Gg. Wagner, unpublished results.
66. K. A. Bhaskaran, P. Frank and T. Just, A. Lifshitz and J. Rom (eds.), Proc. 12th
Int. Symp. Shock Tubes and Waves, The Magnes Press, The Hebrew University of
Jerusalem (1980), p. 503.
67. R. Wagener, Untersuchung von Reaktionen der Singulett-Carbene CH2(a˜1A1) und
1
ꢁ
˜
CHCl(X A ) in der Gasphase, Ph.D. thesis, Universität Göttingen (1990), MPI für
Strömungsforschung Bericht 4/1990.
68. C. Sosa and H. B. Schlegel, J. Am. Chem. Soc. 106 (1984) 5847.
69. M. N. R. Ashfold, M. A. Fullstone, G. Hancock and G. W. Ketley, Chem. Phys. 55
(1981) 245.
70. A. O. Langford, H. Petek and C. B. Moore, J. Chem. Phys. 78 (1983) 6650.
71. B. Himme, Reaktionen von Sauerstoffatomen und Methylenradikalen mit ungesät-
tigten Kohlenwasserstoffen. Erprobung der Hg-Sensibilisierten N2O Photolyse bei
hohen Drucken, Ph.D. thesis, Universität Göttingen (1977).
72. R. E. Huie and J. T. Herron, Prog. Reaction Kinetics 8 (1975) 1.
73. J. Deppe, Reaktionskinetik kleiner Moleküle hinter Stoßwellen unter Verwendung
empfindlicher spektroskopischer Methoden, Cuvillier Verlag, Göttingen (2000),
ISBN 3-89712-986-8, Ph.D. thesis, Universität Göttingen.