Infrared Frequency-Modulation Probing of Product Formation in Alkyl + O2 Reactions: I. the Reaction of C2H5 with O2 between 295 and 698 K

Article abstract of DOI:10.1021/jp0024874

The production of HO₂ in the reaction of ethyl radicals with molecular oxygen has been investigated using laser photolysis/cw infrared frequency modulation spectroscopy. The ethyl radicals are formed by reaction of photolytically produced Cl atoms with ethane, initiated via pulsed laser photolysis of Cl₂, and the progress of the reaction is monitored by frequency-modulation spectroscopy of the HO₂ product. The yield of HO₂ in the reaction is measured by comparison with the Cl₂/CH₃OH/O₂ system, which quantitatively converts Cl atoms to HO₂. At low temperatures stabilization to C₂H₅O₂ dominates, but at elevated temperatures (> 575 K) dissociation of the ethylperoxy radical begins to contribute. Biexponential time behavior of the HO₂ production allows separation of prompt, direct HO₂ formation from HO₂ produced after thermal redissociation of an initial ethylperoxy adduct. The prompt HO₂ yield exhibits a smooth increase with increasing temperature, but the total HO₂ yield, which includes contributions from the redissociation of ethylperoxy radicals, rises sharply from ～10% to 100% between 575 and 675 K. Because of the separation of time scales in the HO₂ production, this rapid rise can unambiguously be assigned to ethylperoxy dissociation. No OH was observed in the reaction, and an upper limit of 6% can be placed on direct OH formation from the C₂H₅ + O₂ reaction at 700 K. The time behavior of the HO₂ production is at variance with the predictions of Wagner et al.'s RRKM-based parameterization of this reaction (J. Phys. Chem. 1990, 94, 1853). However, a simple ad hoc correction to that model, which takes into account a recent reinterpretation of the equilibrium constant for C₂H₅ + O₂ ? C₂H₅O₂, predicts yields and time constants consistent with the present measurements. The reaction mechanism is further discussed in terms of recent quantum chemical and master equation studies of this system, which show that the present results are well described by a coupled mechanism with HO₂ + C₂H₄ formed by direct elimination from the C₂H₅O₂ adduct.

Full text of DOI:10.1021/jp0024874

J. Phys. Chem. A 2000, 104, 11549-11560
11549
Infrared Frequency-Modulation Probing of Product Formation in Alkyl + O2 Reactions: I.
The Reaction of C2H5 with O2 between 295 and 698 K
Eileen P. Clifford,†,‡ John T. Farrell,†,§ John D. DeSain,† and Craig A. Taatjes*
Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories,
LiVermore, California 94551-0969
ReceiVed: July 12, 2000; In Final Form: October 3, 2000
The production of HO2 in the reaction of ethyl radicals with molecular oxygen has been investigated using
laser photolysis/cw infrared frequency modulation spectroscopy. The ethyl radicals are formed by reaction of
photolytically produced Cl atoms with ethane, initiated via pulsed laser photolysis of Cl2, and the progress of
the reaction is monitored by frequency-modulation spectroscopy of the HO2 product. The yield of HO2 in the
reaction is measured by comparison with the Cl2/CH3OH/O2 system, which quantitatively converts Cl atoms
to HO2. At low temperatures stabilization to C2H5O2 dominates, but at elevated temperatures (> 575 K)
dissociation of the ethylperoxy radical begins to contribute. Biexponential time behavior of the HO2 production
allows separation of prompt, “direct” HO2 formation from HO2 produced after thermal redissociation of an
initial ethylperoxy adduct. The prompt HO2 yield exhibits a smooth increase with increasing temperature, but
the total HO2 yield, which includes contributions from the redissociation of ethylperoxy radicals, rises sharply
from ∼10% to 100% between 575 and 675 K. Because of the separation of time scales in the HO2 production,
this rapid rise can unambiguously be assigned to ethylperoxy dissociation. No OH was observed in the reaction,
and an upper limit of 6% can be placed on direct OH formation from the C2H5 + O2 reaction at 700 K. The
time behavior of the HO2 production is at variance with the predictions of Wagner et al.’s RRKM-based
parameterization of this reaction (J. Phys. Chem. 1990, 94, 1853). However, a simple ad hoc correction to
that model, which takes into account a recent reinterpretation of the equilibrium constant for C2H5 + O2 T
C2H5O2, predicts yields and time constants consistent with the present measurements. The reaction mechanism
is further discussed in terms of recent quantum chemical and master equation studies of this system, which
show that the present results are well described by a coupled mechanism with HO2 + C2H4 formed by direct
elimination from the C2H5O2 adduct.
Reactions of alkyl radicals with oxygen molecules are critical
in understanding many combustion systems and play an
especially important role in autoignition phenomena. At low
temperatures, stabilization to the alkylperoxy radical dominates
the reaction. At higher temperatures, thermal dissociation of the
alkylperoxy radical becomes more rapid and only bimolecular
product channels remain. This change in mechanism is respon-
sible for the negative temperature coefficient region in hydro-
carbon oxidation. Depending on the size of the alkyl radical,
reaction with O2 can lead to either HO2 radicals and the
conjugate alkene or to the more reactive OH radical and an
epoxide. The precise mechanism of these reactions has been a
source of puzzlement, with apparently contradictory conclusions
arising from investigations of the forward and the reverse (HO2
+ alkene) reactions. The reaction of ethyl radicals with O2 has
been the most extensively studied of all the R + O2 reactions,
with a wealth of theoretical and experimental investigations.
Ethyl + O2 has been regarded as prototypical for the set of R
+ O2 reactions, a position gained mainly from its relative
theoretical tractability; it is the smallest R + O2 system for which
HO2 + alkene and OH + epoxide formation are possible.
Previous experiments on the ethyl + O2 reaction have
determined that at low temperatures the ethyl radical forms an
adduct with the oxygen which may be collisionally stabilized.
At higher temperatures and lower pressures the bimolecular
product channels, principally to ethylene + HO2, increase in
importance.
C2H5 + O2 7[M]8 C2H5O2
f C2H4 + HO2
(1a)
(1b)
(1c)
f c - C2H4O(oxirane) + OH
Much of the investigation of ethyl + O2 has concentrated on
unraveling the mechanism of the reaction.1-3 Proposed mech-
anisms have generally fallen into two categories, a parallel
mechanism and a coupled mechanism. The parallel mechanism
typically postulates an activated direct abstraction mechanism
for the production of C2H4, which would occur as a parallel
path to stabilization. The coupled mechanism proposes that
formation of a vibrationally excited ethylperoxy adduct is the
initial step toward formation of all of the observed products.
Reactions 1b and 1c therefore occur by rearrangement and
† Sandia National Laboratories Postdoctoral Associate.
‡ Present address: Therma-Wave Inc., 1250 Reliance Way, Fremont, CA
94539.
§ Present address: Exxon Mobil Research and Engineering Company,
1545 Route 22 East, LH386, Annandale, NJ 08801.
* To whom correspondence should be addressed.
10.1021/jp0024874 CCC: $19.00 © 2000 American Chemical Society
Published on Web 11/17/2000

11550 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Clifford et al.
dissociation of the ethylperoxy adduct, and all product channels
are coupled through reaction 1a. These two types of reaction
mechanism imply different effects of temperature and pressure
on the rate coefficient and branching fractions for reaction 1.
reactants, in good agreement with the -4.3 kcal mol-1 they
infer from comparison of the master equation results to
experimental data. While this transition state may account for
the behavior of the C2H5 + O2 reaction, an explanation which
also predicts the preferential production of C2H4OOH from the
C2H4 + HO2 reaction, with a sizable activation barrier, remains
elusive. Recent ab initio and density functional calculations yield
a smaller activation energy (∼13.5 kcal mol-1) for HO2 addition
to ethylene than that deduced by Walker’s group.18 The apparent
disharmony between measurements of the forward and reverse
reaction may be alleviated by recent proposals involving the
participation of excited electronic surfaces.1-3
The available experimental evidence appears to favor some
form of the coupled mechanism for reaction 1 at temperatures
below 1000 K. The reaction produces C2H4 + HO2 even at room
temperature, with a yield that decreases with increasing pressure.
Early measurements by Plumb and Ryan suggested a pressure-
independent component to C2H4 formation,4 as would be
observed in a parallel mechanism. However, more recent
measurements by Kaiser, Wallington, and co-workers have
shown a (pressure)-0.8 dependence of the C2H4 yield over nearly
4 orders of magnitude and have demonstrated that the pressure-
independent contribution to C2H4 is negligible.5-7 Slagle, Feng,
and Gutman showed that the consumption of C2H5 in reaction
1 exhibits a negative temperature dependence from 298 to 1000
K,8 even at temperatures > 700 K where the yield of C2H4 is
essentially unity, a result which has been corroborated by
McAdam and Walker.9 McAdam and Walker found that
formation of C2H4 dominates the C2H5 + O2 reaction between
673 and 813 K, with only a small branching to OH + c-C2H4O
products. The observed negative temperature dependence pre-
cludes an activated direct abstraction mechanism for reaction
1b. Significant abstraction contributions are to be expected only
at still higher temperatures.
Several experimental investigations of the ethyl + O2 reaction
have concentrated on describing the fate of the ethylperoxy
radical in the coupled mechanism. Slagle et al. have studied
the kinetics and probable mechanism of the C2H5 + O2 reaction
in a series8,19,20 of papers, observing production of ethylene and
HO2 as well as the C2H5O2 adduct, and measuring thermo-
chemical bond strengths and kinetic rate coefficients. A detailed
analysis of this experimental data, along with a fit to an RRKM
model, forms the basis for the parameterization of Wagner et
al.11 Recently, Kaiser has studied the ethylene branching fraction
as a function of temperature and pressure.21 In these experiments,
the total yield of C2H4 is determined using end-product analysis
from photolysis of Cl2/C2H6/O2 mixtures in a smog chamber
apparatus. The yield of C2H4 as a function of temperature
displays a slow increase with temperature from ambient up to
∼400 K, followed by a more rapid increase around 500 K. The
rapid increase is attributed to the onset of thermal decomposition
of the ethylperoxy radical, and Kaiser is able to fit his data using
a 12-reaction model, employing the Wagner et al. parameteriza-
tion for the ethyl + O2 reaction.
In the present investigation, infrared frequency-modulation
spectroscopy is used to monitor the time behavior of HO2
production from reaction 1 as a function of pressure and
temperature. Using the time resolution in these experiments, it
is possible to discern the kinetic signature of the equilibration
in reaction 1a. Redissociation of the C2H5O2 regenerates the
reactants after some delay, resulting in a biexponential profile
of HO2 production. The difference in time scales permits a
separation between “prompt” HO2 and HO2 which is produced
after ethylperoxy redissociation. The time behavior of HO2
production from ethylperoxy dissociation has also been mea-
sured as a function of temperature and pressure. These observa-
tions are complementary to the lower pressure measurements
of reactant disappearance by Slagle, Gutman, and co-work-
ers8,11,19,20 and the final product measurements of Kaiser et
al.,5-7,21 and provide an additional level of detailed experimental
characterization of this critical combustion reaction. The present
total yield measurements can be qualitatively modeled using
the parameterization of Wagner et al.,11 with modifications to
account for recent improvements in the equilibrium constants
for reaction 1a.19 The detailed time behavior is in excellent
agreement with recent master equation calculations.17
The details of the coupled reaction mechanism have been a
source of greater controversy. Reaction of the C2H5O2 radical
is thought to pass through a cyclic five membered transition
state before forming products. It was initially proposed that
isomerization to an ethyl hydroperoxy radical is the initial step
in the formation of HO2 and C2H4. To account for the negative
temperature dependence, the transition state for this isomeriza-
tion must lie below the energy of C2H5 + O2. A QRRK
calculation by Bozzelli and Dean predicted that isomerization
to the ethylhydroperoxy radical (C2H4OOH) would be followed
rapidly by dissociation to C2H4 + HO2.10 Wagner et al.
developed a model in 1990 which parameterizes the experi-
mental evidence for the forward reaction using a similar
mechanism, with a transition state for isomerization lying 2.4
kcal mol-1 below ethyl + O2.11 The exact nature of the pathway
from C2H5OO to HO2 + C2H4 is not constrained by the
experimental measurements used in Wagner et al.’s RRKM fits,
except for requiring rapid irreversible dissociation of any
intermediate species to products.
However, investigations by Walker and co-workers of the
reverse reaction, HO2 + C2H4, suggested a barrier of 17 kcal
mol-1 for the addition to form C2H4OOH, and a still higher
barrier for the isomerization to C2H5OO. Further, the HO2 +
C2H4 reaction was observed to form principally c-C2H4O + OH
instead of C2H5 + O2.12,13 These measurements appeared to rule
out C2H4OOH as an intermediate species in the formation of
C2H4 and HO2 in reaction 1. An alternative mechanism for
reaction 1b has been proposed, with a cyclic transition state
leading to direct HO2 elimination from C2H5O2. Calculations
at various levels of theory have confirmed this proposal,14-16
with recent density functional calculations producing a cyclic
transition state for HO2 elimination 1.9 kcal mol-1 below the
reactants. Miller, Klippenstein, and Robertson have performed
time-dependent master equation simulations of reaction 1 using
ab initio theory to characterize the important stationary points
on the potential energy surface.17 They calculate the HO2
elimination transition state as -3.0 kcal mol-1 relative to the
Experiment
The reaction of C2H5 with O2 is investigated using a
modification of the laser photolysis/continuous wave (CW)
infrared long-path absorption (LP/CWIRLPA) method, similar
to that employed in previous experiments.22-26 The reaction is
initiated by pulsed photolysis of Cl2 at 355 nm. The Cl atoms
react rapidly with a large excess of ethane (99.995% purity) to

IRFrequency-Modulation Probe of Product Formation
J. Phys. Chem. A, Vol. 104, No. 49, 2000 11551
Figure 1. Diagram of the experimental apparatus.
produce the corresponding C2H5 radical in a nearly thermo-
neutral reaction. The thermal C2H5 subsequently reacts with O2.
reactions 4 and 5 by comparing signal strengths.
Cl2 hν(355 nm)8 2Cl•
(2)
(4)
(5)
Cl2 hν(355 nm)8 2Cl•
Cl + C2H6 f C2H5 + HCl
C2H5 + O2 f products
(2)
(3)
(1)
Cl + CH3OH 100%8 CH2OH + HCl
CH2OH + O2 100%8 HO2+ CH2O
The yield of OH can be determined using the same reference
reaction, by completely reacting HO2 with NO to form OH
radicals.35
The progress of reaction 1 is monitored by infrared absorption
of the overtone of the O-H stretch in HO2 near 6686 cm-1
using a tunable diode laser.27-29 Possible OH production is
monitored by absorption on the P(2.5)1- line of the vibrational
fundamental30 at 3484.6 cm-1 using an F-center laser. Two-
tone frequency modulation of the infrared lasers is sometimes
employed26,31 to increase the signal-to-noise ratio. The sensitivity
decreases at higher temperatures due to increases in the
vibrational and rotational partition functions. The infrared probe
beams are passed multiple times through the reactor using a
Herriott-type multipass cell.32,33 The optical arrangement is
depicted in Figure 1. Both infrared beams are placed on the
same path through the reactor using polarizing prisms to
combine and separate the beams. The Nd:YAG photolysis laser
(2-3 mJ cm-2) travels along the axis of the cell, and the pump-
probe overlap is confined to the center of the cell, where the
temperature can be precisely controlled.
HO2 + NO 100%8 OH + NO2
(6)
Comparison of the signal amplitudes of HO2 or OH from
reaction with ethane to that of the reference reaction with
methanol gives a phenomenological yield of the products. To
relate the observed quantities to characteristics of the reaction,
corrections must be made for removal reactions of OH and HO2,
as well as for certain side reactions, as discussed below.
The individual gas flows are controlled by calibrated mass
flow controllers, and the chosen total pressure is maintained
by a butterfly valve at the exit of the cell which operates under
feedback from a capacitance manometer. The reactor is heated
by three resistive elements, each under microprocessor control
from a separate K-type thermocouple. The pressure using the
present yield measurement method is limited to about 100 Torr,
above which the neat methanol vapor does not produce a stable
The relative yield of HO2 in the reaction of C2H5 with O2 is
determined by comparison with the reference reaction of CH2-
OH with oxygen, which produces one HO2 for each CH2OH.34
Signals are acquired using the same amount of Cl2 and the same
photolysis conditions, but replacing the ethane flow by a similar
flow of methanol. The initial Cl concentration is the same in
both cases, and the amount of HO2 produced from the ethane
reaction can be scaled to the 100% conversion of Cl to HO2 in
flow. Typical concentrations are [O2] ) 1017 molecules cm-3
;
[Cl2] ) 1015 molecules cm-3; and [C2H6] or [CH3OH] ) 5 ×
1015 molecules cm-3, with the remainder He (99.9999%). In
the reference system for OH detection NO concentrations of
∼4 × 1014 cm-3 are typically used. The reaction of ethyl with
Cl2 can affect the production of HO2 by sequestering radical
density in the Cl2/C2H6 chain reaction, causing incorrect yield

11552 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Clifford et al.
Figure 2. Time-resolved HO2 signals taken at 423 K. The larger
amplitude trace in blue is the HO2 signal from the reference reaction;
the smaller amplitude trace in red is the HO2 signal from the Cl2/C2H6/
O2 system.
Figure 3. Time-resolved infrared FM signals for HO2 taken at 648 K.
The larger amplitude trace in blue is the HO2 signal from the reference
reaction; the smaller amplitude trace in red is the HO2 signal from the
Cl2/C2H6/O2 system.
transfer.36-38 The decay of the reference signal is dominated
by the HO2 self-reaction
measurements. Keeping the concentration of O2 approximately
30 times higher than that of Cl2 gives a yield that does not vary
as the O2/Cl2 ratio increases further. The O2 number density is
maintained at 30-100 times the Cl2 number density in order to
minimize contributions from the C2H5 + Cl2 side reaction. At
the concentrations used, the reaction of Cl with ethane or
methanol is complete in a few microseconds.
HO2 + HO2 f products
(7)
and the time profile of the HO2 signal from the reference
reaction is therefore given by
R[HO2]0
Iref(t) ) R[HO2]t )
(8)
1 + 2k7[HO2]0t
Results and Data Analysis
with R a constant relating HO2 concentration to FM signal
amplitude. A plot of the inverse of the reference HO2 signal vs
time therefore gives a line with slope 2k7/R. The differential
equation governing the HO2 concentration in the ethyl + O2
reaction can be written
Yields of HO2. The time-resolved production of HO2 in
reaction 1b has been measured as a function of pressure and
temperature. Figure 2 shows a typical time-resolved FM signal
of HO2 at low temperature. The HO2 FM signal from the
reference reactions 4 and 5 is the larger-amplitude trace; the
smaller-amplitude signal represents the smaller HO2 yield for
reaction 1 at this temperature and pressure. The reference
reaction of CH2OH with O2 proceeds rapidly and produces HO2
directly, and the decay of the HO2 concentration is dominated
by self-reaction. At temperatures below 550 K, the time profile
of the HO2 production from reaction 1 is similar to that from
the reference reaction, that is, essentially instantaneous at the
high O2 concentrations used. Under these conditions, where the
production of HO2 is much faster than its removal, the HO2
yield is straightforwardly calculable as the ratio of the prompt
signal amplitudes.
d
dt
[HO2] ) Rproduction - 2k7[HO2]2 - Rremoval[HO2]
(10)
where Rproduction and Rremoval are the effective time-dependent
rate of HO2 production and the effective time-dependent rate
coefficient for removal of HO2 by processes besides self-
reaction. Under the conditions of the present experiments,
Rremoval reflects principally reactions of HO2 with C2H5O2
radicals,
HO2 + C2H5O2 f products
(11)
Figure 3 shows an analogous pair of traces taken at higher
temperature (648 K). The time behavior of the HO2 produced
in the reference reaction is similar to that observed at lower
temperatures. Once again the HO2 is produced rapidly and the
decay is second order, principally by self-reaction. However,
the production of HO2 from reaction 1 now displays two clearly
separated components. The prompt HO2 observed at lower
temperatures remains, but a slower “delayed” production of HO2
begins to appear. The separation of time scales between
production and removal of HO2, which simplifies the prompt
yield analysis, is no longer valid. Determining the fraction of
HO2 that appears via this delayed mechanism requires correction
for the ongoing removal of HO2 by self-reaction and reaction
with other radical species.
so that Rremoval ≈ k11[C2H5O2]t. Determining the time-resolved
production of HO2 from reaction 1, denoted Rproduction, is the
aim of the measurement. Equation 10 has the formal solution
t
[HO ] ) tR
(x)dx - 2k [HO ] 2dx -
∫
∫
2 t
production
7
2 x
0
0
tRremoval(x)[HO2]xdx (12)
∫
0
So the time-dependent FM signal from HO2 produced in reaction
1 can be described by
t
I(t) ) R tR
(x)dx - 2Rk [HO ] 2dx -
∫
∫
production
7
2 x
0
0
R
tRremoval(x)[HO2]xdx (13)
∫
0
This correction is accomplished using a modification of
Yamasaki’s integrated profiles method, originally developed to
extract rate coefficients for state-to-state vibrational energy
The integrated profiles method uses this formal solution along
with the measured time-resolved relative concentrations to

IRFrequency-Modulation Probe of Product Formation
J. Phys. Chem. A, Vol. 104, No. 49, 2000 11553
TABLE 1: Yields and Time Constants for HO2 Production
a
from C2H5 + O2
temp (K)
total density
Φprompt
Φraw
Φtotal
τ
294
294
294
294
423
523
523
523
523
573
573
598
598
598
608
623
623
623
623
623
623
623
623
643
643
643
643
643
643
648
648
648
648
648
658
663
663
663
663
673
673
673
673
698
3.3 × 1017 cm-3
8.2 × 1017 cm-3
1.6 × 1018 cm-3
2.5 × 1018 cm-3
1.1 × 1018 cm-3
4.6 × 1017 cm-3
9.2 × 1017 cm-3
1.1 × 1018 cm-3
1.4 × 1018 cm-3
7.7 × 1017 cm-3
1.1 × 1018 cm-3
7.8 × 1017 cm-3
9.0 × 1017 cm-3
1.1 × 1018 cm-3
9.0 × 1017 cm-3
3.8 × 1017 cm-3
5.3 × 1017 cm-3
6.8 × 1017 cm-3
7.8 × 1017 cm-3
8.3 × 1017 cm-3
9.0 × 1017 cm-3
1.1 × 1018 cm-3
1.6 × 1018 cm-3
1.5 × 1017 cm-3
3.8 × 1017 cm-3
7.5 ×1017 cm-3
8.3 × 1017 cm-3
9.8 × 1017 cm-3
1.1 × 1018 cm-3
3.7 × 1017 cm-3
7.5 × 1017 cm-3
7.8 × 1017 cm-3
9.0 × 1017 cm-3
1.1 × 1018 cm-3
8.5 × 1017 cm-3
3.6 × 1017 cm-3
6.6 × 1017 cm-3
8.0 × 1017 cm-3
1.1 × 1018 cm-3
5.7 × 1017 cm-3
7.8 × 1017 cm-3
9.3 × 1017 cm-3
1.2 × 1018 cm-3
7.8 × 1017 cm-3
0.08
0.06
0.032
0.025
0.06
0.10
0.08
0.07
0.05
0.12
0.06
0.15
0.08
0.08
0.10
0.18
0.13
0.09
0.16
0.10
0.15
0.12
0.09
0.44
0.26
0.16
0.13
0.09
0.07
0.29
0.18
0.21
0.16
0.15
0.21
0.31
0.26
0.16
0.15
0.32
0.24
0.22
0.17
0.29
0.08
0.06
0.032 0.03
0.025 0.025
0.08
0.06
0.06
0.10
0.08
0.07
0.05
0.12
0.06
0.15
0.08
0.15
0.12
0.15
0.13
0.17
0.25
0.12
0.22
0.37
0.61
0.90
0.22
0.40
0.28
0.45
0.32
0.30
0.50
0.23
0.38
0.88
0.42
0.23
0.40
0.56
0.59
0.76
0.35
0.96
0.98
0.47
0.06
0.10
0.08
0.07
0.05
0.35
0.23
0.50
0.36
0.43
0.56
0.64
0.62
0.70
0.69
0.72
0.76
0.73
0.90
0.93
0.76
0.85
0.66
0.84
0.87
0.82
0.84
0.75
0.85
1.00
0.80
0.69
0.78
0.88
0.81
0.93
0.77
1.02
0.99
0.81
32 s-1
88 s-1
42 s-1
49 s-1
48 s-1
64 s-1
47 s-1
Figure 4. Correction of HO2 FM signals from Figure 3 using the
integrated profiles method. The largest-amplitude trace in blue is the
HO2 signal from the reference reaction after correction for the HO2
self-reaction; since the decay of HO2 in this system is dominated by
the self-reaction, the signal after this correction is nearly a step function
at the time of the photolysis pulse. The red trace is the HO2 signal
from the C2H5 + O2 reaction after correction for the self-reaction; the
green trace represents the signal after accounting for both the self-
reaction and the reaction with C2H5O2 radicals as described in the text.
This signal represents the time-resolved production of HO2 correspond-
ing to the observed time-resolved FM signal.
35 s-1
91 s-1
22 s-1
65 s-1
70 s-1
67 s-1
74 s-1
88 s-1
105 s-1
36 s-1
144 s-1
127 s-1
89 s-1
correct for known rate processes.37 In the present case, 2k7/R is
known from the reference reaction, and the time profile of the
HO2 FM signal from reaction 1 has been measured: I(t) ) R
[HO2]t. The self-reaction term in the expression for the FM
signal amplitude, the second term on the right in eq 13, is thus
simply related to the time integral of the observed signal
156 s-1
149 s-1
121 s-1
214 s-1
139 s-1
183 s-1
101 s-1
131 s-1
180 s-1
367 s-1
247 s-1
403 s-1
338 s-1
421 s-1
2k7
t
2Rk [HO ] 2dx )
tI(x)2dx
0
(14)
∫
∫
7
2 x
0
R
The contribution of self-reaction is readily removed from the
observed signals by this method. Figure 4 shows the application
of this method to the raw data traces displayed in Figure 3.
The reference signal now displays a rapid rise which abruptly
levels off, since the production of HO2 is extremely rapid and
self-reaction is the dominant removal mechanism. The signal
from reaction 1 maintains its biexponential behavior, but now
also reaches a plateau at long times. If self-reaction would
dominate HO2 removal in the ethyl + O2 system, the yield
would simply be the ratio of the amplitudes of these two signals
at long-time. The raw yields of HO2 Φraw, calculated after
correction for self-reaction in this manner, are listed in Table 1
along with the prompt HO2 yields Φprompt, i.e., the ratio of the
amplitudes for the fast initial rise in the ethane and methanol
systems.
a Numbers are averages for several measurements at each listed set
of conditions. Estimated relative uncertainties are ( 10% for yields,
( 20% for time constants.
increase the yield extracted from the data. An upper limit can
be constructed by assuming that all ethyl radicals react promptly
to produce either HO2 or C2H5O2. This assumption is good if
the steady-state for reaction 1a favors the products, which is
the case under the high-[O2] conditions of the present experi-
ments. Then, immediately after the fast establishment of the
steady-state concentration [C2H5O2] ≈ [C2H5]0 - [HO2]. Using
reactions 1, 7, 11, and the self-reaction of the ethylperoxy
radical,
While the data necessary for removing the contributions of
HO2 self-reaction are inherent in the measurements themselves,
relating the phenomenological yields to the time-dependent HO2
production rate requires additional modeling. For example, under
conditions where ethylperoxy and HO2 are both present (i.e.,
at intermediate yields of HO2), an additional correction is needed
for the C2H5O2 + HO2 reaction. Correction for removal of HO2
by the reaction with C2H5O2 requires the relative value for the
rate coefficients k11/k7, as well as information on the concentra-
tion of C2H5O2. While literature values are available for rate
coefficients of the relevant reactions, there is no direct measure
of the time behavior of the ethylperoxy radical concentration.
The inclusion of an additional loss channel will serve to slightly
C2H5O2 + C2H5O2 f products
(15)
a formal solution to the kinetic equations can be constructed
which allows recursive extraction of a corrected HO2 profile:
d[C2H5O2]
) -Rproduction(t) - k15[C2H5O2]2 -
dt
k11[HO2][C2H5O2] (16)
[C H O ] ) [C H ] - tRproduction(x)dx -
∫
2
5
2 t
2
5 0
0
t
k15 [C H O ]2dx - k
t[C H O ][HO ]dx (17)
∫
∫
2
5
2
11
2
5
2
2
0
0

11554 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Clifford et al.
The equation for the observed HO2 FM signal is modified to
reflect that kremoval is dominated by reaction with ethylperoxy
radicals:
t
I(t) ) R tR
(x)/dx - 2Rk [HO ] 2dx -
∫
∫
production
7
2 x
0
0
Rk11 t[C H O ] [HO ] dx (18)
∫
2
5
2 x
2 x
0
Recognizing that the peak HO2 signal from the methanol
reference system is Iref(0) ) R[C2H5]0 and the quantity 2k7/R is
known from fitting the second-order decay of the reference
signal, it is straightforward to recast the kinetic equations as
equations using the observed signals (i.e., effectively using signal
amplitude as a concentration unit)
R[C H O ] ) I (0) - R tRproduction(x)dx -
∫
2
5
2 t
ref
0
Figure 5. Measured total HO2 yields as a function of temperature for
total densities of 1.1 × 1018 cm-3 (solid circles) and 7.5 × 1017 cm-3
(open circles). The circles with the crosses represent experiments with
higher initial Cl atom concentrations (2-3 × 1014 cm-3). The reduction
in yield at high temperatures for higher radical densities occurs because
of increased removal of C2H5O2 by radical-radical reactions before
dissociation can occur.
2k15
k11
tR2[C H O ]2dx -
tR[C H O ]I(x)dx ≡ A (19)
∫
∫
2
5
2
2
5
2
0
0
R
R
2k7
R
tRproduction(x)dx ) I(t) +
tI(x)2dx +
∫
∫
0
0
R
k11
tR[C H O ] I(x)dx ≡ B (20)
∫
2
5
2 x
0
R
We initially assume A(0) ) 0, and then calculate the nth
approximations to the quantities A and B using the following
equations:
2k7
k11
B(n) ) I(t) +
tI(x)2dx +
tA I(x)dx (21)
∫
∫
(n)
0
0
R
R
2k15
A(n+1) ) (Iref(0) - B(n)) -
t(I (0) - B )2dx -
∫
ref
(n)
0
R
k11
t(I (0) - B )I(x)dx (22)
∫
ref
(n)
0
R
Iteration of these equations converges to a solution for B which
represents the production of HO2 from reaction 1 which would
give rise to the observed signal under the conditions of the
model. The yields extracted from this procedure are necessarily
larger than the raw yields taken directly from the data (corrected
only for self-reaction). Yield estimates based on both methods
are given in Table 1.
Figure 6. Pressure dependence of prompt HO2 yields for several
temperatures. The yield measurements of Wagner et al. (ref 11) are
shown as the open symbols. The inverse pressure dependence of the
prompt yields persists even at higher temperatures where the pressure
dependence of the total yields, which include redissociation of C2H5O2,
are negligible.
The temperature dependence of the HO2 yields for a constant
total density is shown in Figure 5. The biexponential HO2
production allows separation of prompt HO2 from the remainder
of the HO2 product. The total yield, which includes the slower
rise in HO2, rises slowly at low temperatures but abruptly
increases from 10% to 100% between 548 and 648 K. The
prompt yield smoothly increases with temperature over the entire
temperature range; the rapid increase is entirely from the delayed
production of HO2. This increase occurs at significantly higher
temperatures than observed by Kaiser; however, the competing
removal mechanisms for C2H5O2 in this system are radical-
radical reactions. The radical densities in Kaiser’s smog chamber
experiments are much lower than the ∼3-4 × 1013 cm-3 in
the present system, so the thermal dissociation does not
overcome the competing reactions until higher temperatures in
the current work. The circles with crosses in Figure 5 are yield
measurements made at radical densities approximately 5 times
higher (∼2-3 × 1014 cm-3) than for most of the other
experiments; the yield at high temperatures is significantly
reduced for higher radical concentrations.
The change in prompt HO2 yield with total pressure is shown
in Figure 6. As observed in previous experiments, the yield of
HO2 is inversely dependent on pressure in the low temperature
regime, because stabilization of the ethylperoxy radical becomes
increasingly dominant as the pressure is raised. At higher
temperatures, stabilization becomes more difficult and thermal
dissociation of the ethylperoxy radical begins to occur, and the
dependence of the yield on pressure lessens. At the highest
temperatures of the present studies the total HO2 yield displays
little or even a slight positive pressure dependence, due entirely
to the pressure dependence of the delayed HO2 production.
However, the prompt yield retains its inverse pressure depen-
dence even at the highest temperatures observed. The present
results are in good agreement with extrapolation of published
results at lower pressures, as can be seen in Figure 6.
Upper Limits on OH Yields. Detection of OH products from
reaction 1 was attempted using infrared absorption on the
P(2.5)1- line. A clear absorption signal could be detected from
the reference system of CH2OH + O2 + NO (reactions 4-6
above), which is used as a calibration for possible OH

IRFrequency-Modulation Probe of Product Formation
J. Phys. Chem. A, Vol. 104, No. 49, 2000 11555
TABLE 3: Time Constants for Delayed HO2 Production as
a Function of O2 Concentration
temp (K)
643
[O2]
τ
2.7 × 1015 cm-3
5.3 × 1015 cm-3
1.1 × 1016 cm-3
1.1 × 1016 cm-3
1.1 × 1016 cm-3
2.1 × 1016 cm-3
3.2 × 1016 cm-3
4.3 × 1016 cm-3
5.3 × 1016 cm-3
6.4 × 1016 cm-3
5.1 × 1015 cm-3
6.9 × 1015 cm-3
1.1 × 1016 cm-3
1.9 × 1016 cm-3
6.7 × 1016 cm-3
1.3 × 1017 cm-3
1.8 × 1017 cm-3
84 s-1
96 s-1
107 s-1
94 s-1
118 s-1
138 s-1
91 s-1
100 s-1
93 s-1
93 s-1
658
129 s-1
114 s-1
86 s-1
140 s-1
204 s-1
140 s-1
157 s-1
Figure 7. Simultaneous OH and HO2 detection in the Cl2/CH3OH/
O2/NO system and attempted detection of OH from C2H5 + O2. No
OH is observed under the conditions of the present study.
ethane to reacting H2/O2 and 2,2,3,3-tetramethylbutane/O2
mixtures and have deduced branching fractions for production
of oxirane relative to ethylene.12 The initial [C2H4]/[C2H4O]
ratios in those experiments, which range from 127 at 673 K to
87 at 813 K, are consistent with the upper limits to OH
production observed at the lower temperatures of the present
experiments.
TABLE 2: Upper Limits for OH Yields from C2H5 + O2
prompt
delayed
temp
OH yield
OH yield
523
573
700
e0.02
e0.03
e0.06
e0.1
e0.1
e0.15
Time Behavior of HO2 Production. The time-resolved FM
signal shown in Figure 4, after the correction for HO2 self-
reaction, is related to the production of HO2 in reaction 1:
production in reaction 1. Figure 7 illustrates the simultaneous
detection of HO2 and OH in the reference system. The time
behavior of the HO2 and OH signals can be modeled by a
mechanism which contains reactions 2, 4-6, and additional
reactions of OH with methanol and HO2:
Icorrected(t) ) R tR
(x)dx - R tRremoval(x)[HO2]xdx
∫
∫
production
0
0
OH + CH3OH f H2O + CH2OH (or CH3O) (23)
(27)
OH + HO2 f H2O + O2
(24)
(25)
The effective time-resolved production and removal rates are
composites of elementary rate processes. Under the conditions
of our experiments Rremoval is dominated by the reaction of HO2
with C2H5O2, as discussed above. The approximate correction
for this reaction, made using the assumption that the steady-
state of reaction 1a lies far to the right, is accomplished using
the recursive solution of eqs 21 and 22, to extract an effective
HO2 profile which reflects only the production from reaction
1:
CH3O + O2 f CH2O + HO2
Figure 7 also shows an attempted measurement of OH produc-
tion from reaction 1 at 623 K. Measurements at temperatures
from 573 to 700 K and pressures of 25 and 50 Torr failed to
produce observable OH within the noise limits of the experi-
ment.
Assuming reactions 4-6 convert 100% of the initial Cl atoms
to OH, the signal which would be observed for various OH
yields in reaction 1 can be predicted. The mechanism is identical
to that for the reference system, except that reaction 23 is
replaced by reaction 26,
I (t) ≈ R tRproduction(x)dx
(28)
∫
eff
0
The present experiments require relatively large concentrations
of O2, because the signal size is determined by the initial Cl
concentration (and hence the Cl2 concentration), and [O2] is
maintained at 30-100 [Cl2]. As a result, the initial rise of HO2
from the reaction of ethyl with O2 is rapid and unresolved.
However, the slower time constant, τ, in the production of HO2
can be measured, and time constants are listed in Tables 1 and
3. Figure 8 shows the slow time constant, extracted from the
effective signals after correction for self-reaction and the HO2
+ C2H5O2 reaction (reaction 11), as a function of temperature.
The time constant displays a rapid increase from approximately
30 s-1 at 573 K to several hundred per second at 698 K. The
lowest temperature time constants are slightly affected by the
correction for reaction 11, but at higher temperatures this
correction is less important and the time constants are inde-
pendent of the details of the HO2 removal mechanism. At 623
K, a change of 50% in the assumed rate coefficient for reaction
11 changes the extracted time constant by approximately 5%.
OH + C2H6 f H2O + C2H5
(26)
and the NO concentration is zero. Upper limits to the OH yield
are determined by considering the signal-to-noise ratio of the
reference OH signal and the relative sensitivity to OH in the
reference system and in the Cl2/C2H6/O2 system. The main
determinant of the relative sensitivity is the production rate of
OH relative to the removal by OH + ethane or OH + methanol
reactions. A slower production of OH, as may occur after
isomerization of thermalized ethylperoxy radicals, would pro-
duce smaller peak OH concentrations than immediate production
from a direct reaction. Two separate upper limits for OH
production are therefore listed in Table 2, one for prompt OH
production, and a higher limit for delayed production on a time
scale matching the slow rise in HO2 signals. Walker and co-
workers have measured stable products from the addition of

11556 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Clifford et al.
Figure 10. Pressure dependence of the time constant τ for delayed
production of HO2. The dot-dashed line shows the predictions of the
parameterization of the C2H5 + O2 reaction published by Wagner et
al. (ref 11). The solid line is the predictions of the same model after an
ad hoc correction to account for recent equilibrium constant measure-
ments. See text for details.
Figure 8. Time constant τ for delayed production of HO2 as a function
of temperature. The dot-dashed line shows the predictions of the
parameterization of the C2H5 + O2 reaction published by Wagner et
al. (ref 11). The solid line is the predictions of the same model after an
ad hoc correction to account for recent equilibrium constant measure-
ments. See text for details.
for the reaction can be constructed using only the species in
reactions 1a and 1b:
ka
C2H5 + O2 98 C2H4 + HO2
k1a
C2H5 + O2 7 [M]8 C2H5O2 k [M]8 C2H4 + HO2 (29)
e
V
removal
where ke represents elimination from C2H5O2 and ka represents
a direct production of HO2 and ethylene from the reactants. The
direct reaction does not necessarily represent an abstraction
reaction, but any immediate production of HO2 and C2H4,
including rapid dissociation of an incipient C2H5O2 complex
before collisional stabilization. A similar scheme has been used
by Wagner et al.11
In general, the kinetics of Scheme 29 give a biexponential
production of HO2 products, where the time constants and
amplitudes depend on all the rate coefficients of the system.
The parameterization of reaction 1 using phenomenological rate
coefficients for the mechanism 29 allows a qualitative under-
standing of the reaction mechanism. The measured HO2
production can be described by the rapid establishment of a
steady state in reaction 1a, followed by a slow production of
HO2 with a time constant reflecting the removal rate of C2H5O2.
Using the coupled mechanism for reaction 1, as depicted in
Figure 11, the significance of the experimentally accessible
quantities can be described. The fast time constant, reflecting
the establishment of the steady state between addition and
redissociation, is governed by the transition state for addition,
TS1. The prompt yield, which is the fraction of HO2 at the
establishment of the steady-state, reflects the competition
between collisional stabilization and elimination via the second
transition state TS2. The slow time constant depends on the
escape of radicals from the C2H5 + O2 T C2H5O2 quasi-
equilibrium through TS2, both by the “direct” reaction with rate
coefficient ka and by thermal elimination. Recently, Miller et
al. performed detailed master equation calculations that give a
physically rigorous description of the competition between
stabilization and elimination.17 Their results demonstrate the
dominance of the second transition state in determining the rate
coefficient above 700 K, where the stabilization channel ceases
to play a role.
Figure 9. Time constant τ as a function of O2 concentration at 658 K.
The dot-dashed line shows the predictions of the parameterization of
the C2H5 + O2 reaction published by Wagner et al. (ref 11). The solid
line is the predictions of the same model after an ad hoc correction to
account for recent equilibrium constant measurements. See text for
details.
Time constants have been measured as a function of oxygen
concentration (Table 3) and total pressure. Figure 9 shows the
time constants measured for various partial pressures of O2 at
658 K and total density of 8.5 × 1017 cm-3. The time constant
shows no dependence on the oxygen concentration at the
relatively high [O2] used in these experiments. The effect of
total pressure on the slow time constant is also observed to be
small in the 25-85 Torr pressure range of the present experi-
ments, as shown in Figure 10 for 643 K.
Discussion
The description of reaction 1 must reflect the complex
dependences of the time behavior and the HO2 yields on pressure
and temperature. The main features of the reaction can be made
plain by first applying a simplified analytical model to the
reaction, where the measured quantities can be related to explicit
convolutions of elementary kinetic steps. This is the strategy
employed by Wagner et al. in their parameterization of the C2H5
+ O2 reaction.11 Reaction 1 is known to proceed through the
intermediate C2H5O2, and a simplified formal kinetic scheme

IRFrequency-Modulation Probe of Product Formation
J. Phys. Chem. A, Vol. 104, No. 49, 2000 11557
predict time constants in excellent agreement with the present
measurements.40 Both the high-temperature rate coefficient and
the slow time constant are sensitive to the energy of the
elimination transition state TS2. The agreement between the
present experiments and the master equation calculations
therefore demonstrates consistence between the time constant
measurements and the literature values for the high-temperature
rate coefficient. By extension, the time constant measurements
also provide further evidence for the direct elimination mech-
anism used in the master equation calculations.
Analysis of the HO2 yields is somewhat more problematic.
The parameterization does not include any irreversible removal
of ethyl radicals except by reaction to form HO2 and ethylene.
The yield as t f ∞ is therefore always unity. Comparison to
experimental results requires estimation of the competing
reactions of the stabilized C2H5O2 radical, designated “removal”
in eq 29. This can be accomplished, as in the original Wagner
et al. work, by introducing a “cutoff” time, corresponding to
some experimental limiting time scale, at which the yield will
be evaluated. Unless this time is unambiguously defined by the
experiments, this approach essentially introduces an arbitrary
fitting parameter, which determines the temperature at which
the rapid rise in yield is predicted. In the evaluation of his smog
chamber measurements of C2H4 yields in reaction 1, Kaiser
employed a more detailed modeling of the chemistry, using a
12-reaction kinetic mechanism. Application of a similar mech-
anism enables a relatively direct comparison between the
experimental measurements and the parameterization used to
model the C2H5 + O2 reaction. The model presently employed,
given in Table 4, assumes no production of C2H4OOH radical
as a precursor to C2H4 + HO2, which is consistent with recent
calculations of a direct pathway for HO2 elimination from
C2H5O2.14-17
Figure 11. Simplified schematic representation of the reaction
mechanism for C2H5 + O2. Several other potential wells and transition
states exist in the C2H5O2 system, but do not affect the present
experiments.
The parameterization of reaction 1 provided by Wagner et
al.11 is readily applied to modeling the present results. Kaiser
has also used this parameterization to describe his measurements
of ethylene yields as a function of temperature.21 However, the
equilibrium constants which formed part of the basis of this
model have recently been substantially revised.19 The time
constant for the delayed production of HO2 is sensitive to the
dissociation pathways of the ethylperoxy radical. Figure 8 shows
the measured effective time constants for the slow production
of HO2 as a function of temperature in the present experiments.
The predictions of the original Wagner et al. parameterization
are shown as the dot-dashed line. (Note that the activation
energies of k0 and k∞ for C2H5O2 f C2H4 + HO2 should be
positive, not negative as printed in Table 6 of ref 11)39 This
model predicts a far more rapid dissociation of the C2H5O2
radical at these temperatures than is experimentally observed.
However, this overestimation is not completely unexpected,
given that the equilibrium constants predicted by the Wagner
et al. model have since been shown to be in error by up to a
factor of 5. An ad hoc modification to the Wagner et al.
parameterization can be constructed by simply correcting the
rate coefficient for the reverse reaction to match the reevaluated
equilibrium constants. As the simplest approximation, we have
simply fit the correction factors Keq,new/Keq,old from the reana-
lyzed equilibrium data19 to an Arrhenius form and used this
expression to modify the rate coefficient k-1a (k-4a in ref 11).
This fit yields k-1a,new/k-1a,old ) 1.16 × 10-3 e3480/T; the
experimental equilibrium constants and the predictions of the
modified parameterization are shown in Figure 12. Application
of this ad hoc correction to the calculation of the slow time
constant yields predictions which are in much better agreement
with the experimentally observed quantities, as shown by the
solid line in Figure 8. The negligible dependence of the time
constant on O2 concentration is duplicated by the analytic model,
as shown in Figure 9. The modified parameterization also
predicts a very shallow pressure dependence, in agreement with
the observations shown in Figure 10.
Because the removal of C2H5O2 is dominated by radical-
radical reactions, the predictions of the chemical kinetic model
in Table 4 depend sensitively on the initial radical density,
[C2H5]0 ) [Cl]0. This dependence is manifested experimentally
in the dependence of the yield on initial Cl concentration, as
shown in Figure 5. The initial radical density is measured in
the present experiments via the second-order decay of the
reference signal. Using literature values for k7, the initial HO2
density can be calculated for the reference system, which is equal
to the initial ethyl radical density in the ethyl + O2 measurement.
The time-resolved HO2 signal can then be calculated, using
literature values for the rate coefficients and the experimentally
determined radical density. Figure 13 shows a comparison
between calculated signals (with the HO2 self-reaction removed)
and the experimental signals corrected only for HO2 self-
reaction. The calculated time trace is completely specified by
the model and the initial radical density from the reference
reaction measurement, leaving no adjustable parameters. Once
again the overestimation of C2H5O2 dissociation in the original
model of Wagner et al. is evident in the comparison to the
experimental data. The ad hoc correction for the reevaluated
equilibrium constants yields predictions that are in much better
agreement with the experiments.
Master equation calculations have been carried out recently
by Miller, Klippenstein, and Robertson, on the basis of quantum
chemical calculations of the transition state for HO2 elimination
from the ethylperoxy radical.17 These calculations employ a
transition state TS2 which is -4.3 kcal mol-1 from the energy
of the C2H5 + O2 reactants, an energy which was adjusted to
fit the high-temperature rate coefficient measurements of
Gutman and co-workers. The second transition state completely
determines the high-temperature rate coefficient as stabilization
becomes negligible. Calculations using this transition state
The correspondence between the experimental [HO2] vs time
profiles and the predictions of the ad hoc model which is shown
in Figure 13 is typical of the agreement for measurements in
the transition region between 600 and 650 K, where the total
HO2 yields are intermediate between the low prompt yields
observed at lower temperatures and the ∼100% yields observed
at higher temperatures. Slight systematic differences persist as
evident in the figure; the prompt yields are slightly underpre-

11558 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Clifford et al.
ref
TABLE 4: Kinetic Model for Cl2/C2H6/O2 System
reaction
rate coefficient
Cl + C2H6 f C2H5 + HCl
C2H5 + Cl2 f C2H5Cl + Cl
HO2 + HO2 f H2O2 + O2
8.5 × 10-11 e-113/T cm3 molecule-1 s-1
24
41
42
11
1.26 × 10-11 e152/T cm3 molecule-1 s-1
1.2 × 10-33 [M] e1150/T + 3.8 × 10-13 e580/T cm3 molecule-1 s-1
2
φ ) 1 - {(1 + e2.3c +c c
)
} ;
a
0.621 -1
3
4 3
C2H5 + O2 f C2H5O2
c3 ) log([M]) - 15.53 - 3.11 × 10-4
T
-1.54 × 10-6T2
c4 ) 0.367 - 7.09 × 10-4T + 3.23 × 10-7T2
k∞ ) 3.67 × 10-14T0.772e287/T
;
k0 ) 1.96 × 10-5T-8.24e-2150/T
;
Fcent ) 0.580e-T/1250 + 0.420e-T/183
2
C2H5 + O2 f C2H4 + HO2
φ ) {(1 + e2.3c +c c
)
}
;
11
a
0.621 -1
3
4 3
c3 ) log([M]) - 15.53 - 3.11 × 10-4
T
-1.54 × 10-6T2
c4 ) 0.367 - 7.09 × 10-4T + 3.23 × 10-7T2
k∞ ) 3.67 × 10-14T0.772e287/T
;
k0 ) 1.96 × 10-5T-8.24e-2150/T
;
Fcent ) 0.580e-T/1250 + 0.420e-T/183
C2H5O2 f C2H5 + O2
φ ) 1.16 × 10-3e3480/T
11
a
(ad hoc correction);
φ ) 1(original model);
k∞ ) 6.17 × 1017T-0.835e-17160/T
;
k0 ) 3.29 × 1026T-9.85e-19600/T
;
Fcent ) 0.580e-T/1250 + 0.420e-T/183
φ ) 1;
a
C2H5O2 f C2H4 + HO2
11,39
k∞ ) 6.92 × 1014T-0.634e-15800/T
;
;
k0 ) 2.04 × 1035T-12.86e-20100/T
Fcent ) 2.72e-T/220 + e-7270/T
C2H5O + O2 f HO2 + CH3CHO
C2H5O2 + C2H5O2 f 2C2H5O + O2
C2H5O2 + C2H5O2 f CH3CHO + C2H5OH + O2
C2H5O2 + HO2 f C2H5O2H + O2
C2H5O2H f C2H5O + OH
6.0 × 10-14 e-550/T cm3 molecule-1 s-1
(1.33 e-207/T) 8.5 × 10-14 e-125/T cm3 molecule-1 s-1
(1-1.33 e-207/T) 8.5 × 10-14 e-125/T cm3 molecule-1 s-1
2.7 ×10-13 e1000/T cm3 molecule-1 s-1
4.0 × 1015 e-21600/T s-1
43
44
44
43
45
a Rate coefficient is parameterized using the listed parameters in the expressions
2
k0[M]
log
- 0.4 - 0.67 log[Fcent
k0[M]
]
[
]
k∞k0[M]
k∞
k ) φ
(Fcent)c; c-1 ) 1 +
k∞ + k0[M]
0.75 - 1.27 log[Fcent] - 0.14 log
- 0.4 - 0.67 log[Fcent]
{
}
(
)
[
]
k∞
with the values for the parameters as given.
Figure 13. Comparison of time-resolved HO2 signal with predicted
signals based on the analytic model for the Cl2/C2H6/O2 system (Table
4). The initial radical density (equal to the initial Cl atom concentration)
is fixed by the second-order decay of the associated reference reaction
signal, leaving no adjustable parameters for the model signal. The dot-
dashed line shows the predictions of the parameterization of the C2H5
+ O2 reaction published by Wagner et al. (ref 11). The solid line is the
predictions of the same model after an ad hoc correction to account
for recent equilibrium constant measurements. See text for details.
Figure 12. Comparison of equilibrium constants for reaction 1a
reported by Knyazev and Slagle (ref 19) with those predicted by the
Wagner et al. parameterization after adjustment of the rate constant
k1a. See text for details.
dicted and the time constant is still on average somewhat
overpredicted, even by the corrected model. At higher temper-
atures the model fails to predict yields reaching 100%, probably
because the kinetic significance of the ethylperoxy adduct is
overestimated in the model; in particular the extrapolation of
the C2H5O2 + HO2 reaction rate coefficient may be unreliable.
However, the general agreement obtained from a simple
modification to the Wagner et al. parameterization is good.

IRFrequency-Modulation Probe of Product Formation
J. Phys. Chem. A, Vol. 104, No. 49, 2000 11559
from formation via thermal dissociation of the C2H5O2. This
kinetic signature demonstrates unambiguously that the rapid rise
in HO2 yields with temperature arises from the redissociation
of the ethylperoxy radical. The prompt yields rise slightly with
temperature from 298 to 700 K and show an inverse pressure
dependence over the entire temperature range. The pressure
dependence of the prompt yield derives from the competition
between elimination and collisional stabilization in the initially
formed excited adduct. Neither the rapid rise in total HO2 yield
nor the rise in prompt yield at elevated temperatures appears to
be a result of the emergence of the direct abstraction pathway.
The master equation calculations of the high-temperature rate
coefficient, the HO2 yields, and the slow time constant for HO2
formation by Miller and co-workers display a high degree of
sensitivity to the energy of the transition state to elimination.17,40
Their transition state energy of -4.3 kcal mol-1, chosen to
match the high temperature rate measurements, produces nearly
exact agreement with the present yield and time constant
measurements. The level and scope of the conformity of theory
and experiment provide strong evidence of the accuracy of this
description. While the understanding of the C2H5 + O2 reaction
may appear complete in this temperature region, further
experimental and theoretical studies aimed at the reverse
reaction, C2H4 + HO2, and at temperatures above 1000 K may
provide information concerning other areas of the potential
energy surface and could help resolve remaining questions about
this complex chemical reaction.
Figure 14. Predictions of HO2 yields at a total density of 1.1 × 1018
cm-3 as a function of temperature from the parameterization of the
C2H5 + O2 reaction. The experimental yields are shown as the solid
circles. The master equation calculations of Miller and co-workers (ref
17) are shown as the open squares. The dot-dashed line shows the
predictions of the parameterization of the C2H5 + O2 reaction published
by Wagner et al. (ref 11). The solid line is the predictions of the same
model after an ad hoc correction to account for recent equilibrium
constant measurements. See text for details.
Finally in Figure 14 the experimental HO2 yields are
compared to predictions based on the analytic parameterization.
The cutoff time has been chosen to be 17 ms to best match the
predictions of the corrected model with the measured HO2
yields. As can be seen in Figure 13, the delayed production of
HO2 is largely complete in 15-20 ms at the temperatures that
characterize the rapid increase in HO2 yield. For comparison,
the predictions of the original Wagner et al. model are also
shown. The agreement of the measured yields with the model
predictions is quite satisfactory, although, as mentioned above,
there is an element of arbitrariness in the comparison arising
from the choice of cutoff times. The comparisons of model
predictions to experimental time constants and to the actual data
traces are a more reliable indicator of the success of the corrected
parameterization.
Also shown in Figure 14 are comparisons with calculated
yields reported by Miller et al. and based on master equation
simulations.17 The results of their calculations are once again
in outstandingly good agreement with the experimental mea-
surements. The master equation analysis rigorously describes
the competition between stabilization and elimination without
recourse to a phenomenological effective kinetic scheme. Miller
et al. have provided expressions for the high and low pressure
limiting rate coefficients for reaction 1 as a function of
temperature. The results of master equation calculations could
also be used, possibly in conjunction with additional experi-
mental measurements, to construct a new parameterization for
the falloff behavior of reaction 1 in the transition temperature
region. Such an undertaking is, however, far beyond the scope
of the present work. The ad hoc correction to the falloff
parameterization of Wagner et al. appears to acceptably model
the present experimental data in the temperature region up to
approximately 700 K. At higher temperatures the reaction should
be described well by the pressure-independent bimolecular
expression given by Miller et al.
Conclusions
The reaction of ethyl radicals with O2 has been investigated
as a function of temperature between 293 and 698 K using laser
photolysis/CW frequency modulation spectroscopy. The yield
of HO2 in the reaction shows a rapid increase between 600 and
650 K, which is attributable to the onset of thermal dissociation
of the ethylperoxy radical. The experimental results can be
successfully modeled using the parameterization of Wagner et
al. if a modification is made to correct the predicted equilibrium
constants. Recent master equation calculations are in excellent
agreement with the present experimental results, consistent with
the C2H5 + O2 f C2H4 + HO2 reaction proceeding via a
concerted elimination with a transition state ∼4.3 kcal mol-1
below the reactants.
Acknowledgment. The experiments described here were
made possible by the able technical support of Leonard E.
Jusinski. The authors thank Dr. James A. Miller and Prof.
Stephen J. Klippenstein for illuminating discussions regarding
master equation modeling of the ethyl + O2 reaction and for
sharing results of their calculations prior to publication. This
work is supported by the Division of Chemical Sciences, the
Office of Basic Energy Sciences, the U.S. Department of
Energy.
References and Notes
(1) Robertson, S. H.; Seakins, P. W.; Pilling, M. J. In Low-Temperature
Combustion and Autoignition; Pilling, M. J., Ed.; Elsevier: Amsterdam,
1997; Vol. 35, p 125.
(2) Walker, R. W. In Research in Chemical Kinetics; Compton, R.,
Hancock, G., Eds.; Elsevier: Amsterdam, 1995; Vol. 3, p 1.
(3) Walker, R. W.; Morley, C. In Low-Temperature Combustion and
Autoignition; Pilling, M. J., Ed.; Elsevier: Amsterdam, 1997; Vol. 35, p 1.
(4) Plumb, I. C.; Ryan, K. R. Int. J. Chem. Kinet. 1981, 13, 1011.
(5) Kaiser, E. W.; Lorkovic, I. M.; Wallington, T. J. J. Phys. Chem.
1990, 94, 3352.
The present data appear in excellent agreement with the
predictions of a coupled kinetics model where the formation of
an ethylperoxy radical is the antecedent to ethylene + HO2
formation. The separation of time scales for HO2 production in
the present results permits separation of prompt HO2 formation
(6) Kaiser, E. W.; Wallington, T. J.; Andino, J. M. Chem. Phys. Lett.
1990, 168, 309.

11560 J. Phys. Chem. A, Vol. 104, No. 49, 2000
Clifford et al.
(7) Kaiser, E. W.; Rimai, L.; Wallington, T. J. J. Phys. Chem. 1989,
93, 4094.
(8) Slagle, I. R.; Feng, Q.; Gutman, D. J. Phys. Chem. 1984, 88, 3648.
(9) McAdam, K. G.; Walker, R. A. J. Chem. Soc., Faraday Trans. 2
1987, 83, 1509.
(10) Bozzelli, J. W.; Dean, A. M. J. Phys. Chem. 1990, 94, 3313.
(11) Wagner, A. F.; Slagle, I. R.; Sarzynski, D.; Gutman, D. J. Phys.
Chem. 1990, 94, 1853.
(12) Baldwin, R. R.; Pickering, I. A.; Walker, R. W. J. Chem. Soc.,
Faraday Trans. 1 1980, 76, 2374.
(28) Hunziker, H. E.; Wendt, H. R. J. Chem. Phys 1974, 60, 4622.
(29) Johnson, T. J.; Wienhold, F. G.; Burrows, J. P.; Harris, G. W.;
Burkhard, H. J. Phys. Chem. 1991, 95, 6499.
(30) Amano, T. J. Mol. Spectrosc. 1984, 103, 436.
(31) Janik, G. R.; Carlisle, C. B.; Gallagher, T. F. J. Opt. Soc. Am. B
1986, 3, 1070.
(32) Herriott, D.; Kogelnik, H.; Kompfner, R. Appl. Opt. 1964, 3, 523.
(33) Pilgrim, J. S.; Jennings, R. T.; Taatjes, C. A. ReV. Sci. Instrum.
1997, 68, 1875.
(34) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.;
Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling; Jet Propulsion Laboratory: Pasadena, CA, 1997.
(35) Howard, C. J. J. Am. Chem. Soc. 1980, 102, 6937.
(36) Yamasaki, K.; Watanabe, A.; Kakuda, T.; Ichikawa, N.; Tokue, I.
J. Phys. Chem. A 1999, 103, 451.
(37) Yamasaki, K.; Watanabe, A. Bull. Chem. Soc. Jpn. 1997, 70, 89.
(38) Yamasaki, K.; Watanabe, A.; Kakuda, T.; Tokue, I. Int. J. Chem.
Kinet. 1998, 30, 47.
(39) Wagner, A. F.; Slagle, I. R.; Sarzynski, D.; Gutman, D. J. Phys.
Chem. 1991, 95, 1014.
(40) Miller, J. A., private communication.
(41) Timonen, R. S.; Gutman, D. J. Phys. Chem. 1986, 90, 2987.
(42) Lightfoot, P. D.; Veyret, B.; Lesclaux, R. J. Phys. Chem. 1990,
94, 708.
(43) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr,
J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data 1997, 26, 521.
(44) Wallington, T. J.; Dagaut, P.; Kurylo, M. J. Chem. ReV. 1992, 92,
667.
(13) Baldwin, R. R.; Stout, D. R.; Walker, R. W. J. Chem. Soc., Faraday
Trans. 1991, 87, 2147.
(14) Quelch, G. E.; Gallo, M. M.; Schaefer, H. F., III J. Am. Chem.
Soc. 1992, 114, 8239.
(15) Quelch, G. E.; Gallo, M. M.; Shen, M.; Xie, Y.; Schaefer, H. F.,
III; Moncrief, D. J. Am. Chem. Soc. 1994, 116, 4953.
(16) Ignatyev, I. S.; Xie, Y.; Allen, W. D.; Schaefer, H. F., III J. Chem.
Phys. 1997, 107, 141. Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H.
F., III J. Phys. Chem. A 2000, 104, 9823.
(17) Miller, J. A.; Klippenstein, S. J.; Robertson, S. H. Proc. Symp.
(International) Combust. 2000, 28, in press.
(18) Chen, C.-J.; Bozzelli, J. W. J. Phys. Chem. A 2000, 104, 4997.
(19) Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. A 1998, 102, 1770.
(20) Slagle, I. R.; Ratajczak, E.; Gutman, D. J. Phys. Chem. 1986, 90,
402.
(21) Kaiser, E. W. J. Phys. Chem. 1995, 99, 707.
(22) Pilgrim, J. S.; Taatjes, C. A. J. Phys. Chem. A 1997, 101, 5776.
(23) Pilgrim, J. S.; Taatjes, C. A. J. Phys. Chem. A 1997, 101, 4172.
(24) Pilgrim, J. S.; McIlroy, A.; Taatjes, C. A. J. Phys. Chem. A 1997,
101, 1873.
(25) Pilgrim, J. S.; Taatjes, C. A. J. Phys. Chem. A 1997, 101, 8741.
(26) Farrell, J. T., Taatjes, C. A. J. Phys. Chem. A. 1998, 102, 4846.
(27) Becker, K. H.; Fink, E. H.; Langen, P.; Schurath, U. J. Chem. Phys.
1974, 60, 4623.
(45) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Frank, P.; Hayman, G.;
Just, T.; Kerr, J. A.; Murrells, T.; Pilling, M. J.; Troe, J.; Walker, R. W.;
Warnatz, J. J. Phys. Chem. Ref. Data 1994, 23, 847.