Rate coefficients and products of ethyl and vinyl cross-radical reactions

Article abstract of DOI:10.1021/jp021497x

Rate constants and products for cross-radical reactions of vinyl (C₂H₃) and ethyl (C₂H₅) radicals have been determined at T = 298 K and a total pressure (predominately helium) of 93.3 kPa (700 Torr). C₂H₃ and C₂H₅ were produced simultaneously through the 193-nm excimer laser photolysis of dilute mixtures of C₂H₅COC₂H₃ (EVK)/He. This is the first report of direct rate determination for the C₂H₅ + C₂H₅ reaction and using the photolysis of EVK as a precursor for producing a nearly 1:1 ratio of C₂H₅/C₂H₃. Time-resolved UV absorption spectroscopy and gas chromatographic/mass spectroscopic (GC/MS) product analysis methods were employed for kinetics and product studies. Major reaction products consisted of n-butane, 1,3-butadiene, and 1-butene which are formed, respectively, through the combination reactions: C₂H₅ + C₂H₅ → n-butane (1c), C₂H₃ + C₂H₃ → 1,3-butadiene (2c,) and C₂H₅ + C₂H₃ → 1-butene (3c). Minor products, ethane, ethylene, and acetylene, result from disproportionation reactions. Analysis of the temporal absorptions at 230 and 235 nm through kinetic modeling of the reaction system resulted in an overall rate constant of k₃ = 9.6 × 10^-11 cm³ molecule^-1 s^-1 for the C₂H₅ + C₂H₃ cross-radical reaction. A detailed error analysis with estimates of both random error and systematic errors for each parameter in the model was performed; the resulting combined uncertainty on the rate constant k₃ is ±1.9 × 10^-11 cm³ molecular^-1 s^-1. Using previously published rate constants for the combination reactions 1c and 2c [2.0 × 10^-11 and 9.3 × 10^-11 cm³ molecule^-1 s^-1, respectively], and relative yields of the combination products the rate constant for the cross-combination reaction k_3c [C₂H₃ + C₂H₅] c alculated to be (6.5 ± 1) × 10^-11 cm³ molecule^-1 s^-1.

Full text of DOI:10.1021/jp021497x

J. Phys. Chem. A 2002, 106, 11135-11140
11135
Rate Coefficients and Products of Ethyl and Vinyl Cross-Radical Reactions
Askar Fahr*
Physical and Chemical Properties DiVision, National Institute of Standards and Technology,
Gaithersburg, Maryland 20899-8381
Dwight C. Tardy
Department of Chemistry, The UniVersity of Iowa, Iowa City, Iowa 52242
ReceiVed: June 26, 2002; In Final Form: August 22, 2002
Rate constants and products for cross-radical reactions of vinyl (C2H3) and ethyl (C2H5) radicals have been
determined at T ) 298 K and a total pressure (predominately helium) of 93.3 kPa (700 Torr). C2H3 and C2H5
were produced simultaneously through the 193-nm excimer laser photolysis of dilute mixtures of C2H5COC2H3
(EVK)/He. This is the first report of direct rate determination for the C2H5 + C2H5 reaction and using the
photolysis of EVK as a precursor for producing a nearly 1:1 ratio of C2H5/C2H3. Time-resolved UV absorption
spectroscopy and gas chromatographic/mass spectroscopic (GC/MS) product analysis methods were employed
for kinetics and product studies. Major reaction products consisted of n-butane, 1,3-butadiene, and 1-butene
which are formed, respectively, through the combination reactions: C2H5 + C2H5 f n-butane (1c), C2H3 +
C2H3 f 1,3-butadiene (2c,) and C2H5 + C2H3 f 1-butene (3c). Minor products, ethane, ethylene, and acetylene,
result from disproportionation reactions. Analysis of the temporal absorptions at 230 and 235 nm through
kinetic modeling of the reaction system resulted in an overall rate constant of k3 ) 9.6 × 10-11 cm3 molecule-1
s-1 for the C2H5 + C2H3 cross-radical reaction. A detailed error analysis with estimates of both random error
and systematic errors for each parameter in the model was performed; the resulting combined uncertainty on
the rate constant k3 is (1.9 × 10-11 cm3 molecular-1 s-1. Using previously published rate constants for the
combination reactions 1c and 2c [2.0 × 10 -11 and 9.3 × 10-11 cm3 molecule-1 s-1, respectively], and relative
yields of the combination products the rate constant for the cross-combination reaction k3c [C2H3 + C2H5]
calculated to be (6.5 ( 1) × 10-11 cm3 molecule-1 s-1.
I. Introduction
cm3 molecule-1 s-1 for the combination channel and a branching
ratio of k1c/k1d ) 7.9
Knowledge of the termination rates together with the yield
and nature of the termination products for reactions of hydro-
carbon radicals are of great importance in understanding and
modeling of hydrocarbon combustion1-3 as well as planetary
atmospheric reactions.4-6 The role of small unsaturated hydro-
carbon radicals are particularly significant. Despite their sus-
pected importance, little is known about the kinetics and reaction
mechanism of unsaturated radicals. It is also known that both
vinyl and ethyl radicals are observed in hydrocarbon combustion
and photochemical processes. The self-reactions of ethyl and
vinyl radicals have, directly and indirectly, been studied in a
number of laboratories.7-10 Nonetheless, no experimentally
determined rate coefficient for ethyl-vinyl cross-radical reaction
has previously been reported. Thus one of the objectives of this
paper is to measure the rate constant for the bimolecular reaction
of vinyl and ethyl radicals. In addition, the contribution of the
combination (c) and disproportionation (d) channels for the
vinyl-ethyl cross-radical reaction will be determined.
The reaction C2H3 + C2H3 has previously been studied in
our laboratory using a number of methods and radical
precursors.8-10 The first direct and absolute kinetic measurement
of vinyl self-reaction employed vacuum-UV flash photolysis
in conjunction with vacuum-UV absorption detection of vinyl
radicals and GC product analysis. In later studies excimer laser
photolysis-UV kinetic absorption spectroscopy and GC/MS
product analysis methods were used to determine the rate
constant and product channels for the vinyl self-reaction.8,9
C2H3 + C2H3
9
M8 C4H6 (1,3-butadiene)
M8 C2H4 + C2H2
(2c)
(2d)
C2H3 + C2H3
9
These studies established an overall rate constant of k2 ) (12
( 2) × 10-11 cm3 molecule-1 s-1 at ambient temperature and
the pressure range of about 6.6-53 kPa. In addition, the product
yield determinations indicated that the combination channel 2c
producing 1,3-butadiene is the dominant channel at pressures
higher than about 6.6 kPa with relative rates k2c/k2d ) 3.0.8,9
In a later study, Thorn et al.10 employing a flow discharge
and direct mass spectroscopic detection of vinyl radicals
determined, at a nominal pressure of 0.13 kPa and T ) 298 K,
a total rate constant of (14 ( 6) × 10-11 cm3 molecule-1 s-1
for vinyl self-reaction, which is in good agreement with the
total rate constant value (12 ( 2) × 10-11 cm3 molecule-1 s-1
determined in our laboratory at higher pressures. But under the
Baulch et al.7 have critically reviewed the published data on
the self-reaction of ethyl radicals and recommended a high-
pressure rate constant value of k1c ) (1.9 ( 0.3) × 10-11
C2H5 + C2H5
9
M8 C4H10
(1c)
(1d)
C2H5 + C2H5
9
M8 C2H4 + C2H6
* Corresponding author. E-mail: askar.fahr@nist.gov.
10.1021/jp021497x CCC: $22.00 © 2002 American Chemical Society
Published on Web 10/24/2002

11136 J. Phys. Chem. A, Vol. 106, No. 46, 2002
Fahr and Tardy
experimental conditions of Thorn et al., the major products are
reported to be ethylene and acetylene rather than 1,3-butadiene,
i.e., no combination products were observed. Thus high pres-
sures are required to measure contributions of both combination
and disproportionation reactions.
193-nm photolysis of dilute mixtures of diethyl ketone (C2H5-
COC2H5) and divinyl ketone (C2H3COC2H3) in He. The
photolysis samples consisted of a small amount of the radical
precursor, typically in the range of about (6-13) × 1015
molecule cm-3, in an excess amount of He (93 kPa). The
photolyzed sample was admitted to an evacuated injection loop
and directly injected onto two separate Al2O3-coated capillary
columns (HP-19095P) by admitting the carrier gas into the
collection loop. Temperature programming of the oven was
required to separate the products. The retention times and
response of the FID and MS were calibrated by injection of
standard samples with concentrations similar to those produced
from the laser photolysis. The uncertainty of our quantitative
GC analysis, determined from repetitive measurements of known
samples, is typically 15% or less for C2-C6 hydrocarbons.
Radical precursor molecules were obtained commercially, at the
highest purity available (99.5%) and were used after successive
freeze-pump-thaw cycles. Ultrahigh purity He (99.999%) was
used for sample preparations and as carrier gas for GC/MS.
Here we report the rate constants and products of the vinyl-
ethyl cross-radical reactions, determined at relatively high
pressures (93.3 kPa or 700 Torr) and at a temperature of 298
K. Excimer laser photolysis, UV-kinetic absorption spectros-
copy, and quantitative GC/MS product analysis have been used
for these studies. We also report on the photolysis of ethylvinyl
ketone (EVK) as a simultaneous source for producing ethyl and
vinyl radicals. Our preliminary results on the pressure depen-
dence of the product channels and rate coefficients for the C2H5
and C2H3 mixed radical system suggest very complex and
interesting behavior. The complexity is the result of the large
exoergicity for the combination process and the competition of
collisional quenching with unimolecular decomposition and
isomerization. The detailed results of the pressure effect on C2H5
and C2H3 mixed radical reactions will be reported soon.
III. Results and Discussion
II. Experimental Procedures
Production of C2H5 and C2H3 Radicals. Ethyl and vinyl
radicals were produced from the 193-nm photolysis of dilute
mixtures of EVK in He. Although there are no previously
reported studies on the photolysis of EVK, it appeared to be a
worthwhile choice since the primary decomposition channel for
small ketones is C-C rupture. For example, the 193-nm
photolysis of methylvinyl ketone (CH3COC2H3), diethyl ketone
(C2H5COC2H5), and acetone have been used, in our and a
number of other laboratories, as photolytic sources of methyl,
vinyl, and ethyl radicals.8-10,12-14 In the present studies the
formation of ethyl and vinyl radicals from the193-nm photolysis
of EVK are confirmed through product analysis determinations
and also direct optical detection.
Product Analysis. The reaction mixtures following photolysis
of the radical precursor in He were analyzed employing an on-
line gas chromatograph coupled to a flame ionization detector
and a quadrupole mass spectrometer. The nature and yields of
the final reaction products, at a total pressure of about 93.3 kPa
(700 Torr) and at ambient temperature, were determined. The
major final reaction products consisted of n-butane, 1,3-
butadiene, and 1-butene (products of combination reactions) and
ethane, ethylene, and acetylene (products of disproportionation
reactions). A major photolytic product, CO, is not detectable
by FID method, and the corresponding MSD peak overlapped
with a background air peak thus could not be quantified. No
oxygenated hydrocarbon products were detected suggesting that
the 193-nm photolysis of EVK primarily produces CO and ethyl
and vinyl radicals.
Two isomers of C4H8 (1-butene and 2-butene), with a relative
yield of [2-butene]/[1-butene] = 0.04, were identified. In
addition to 1,3-butadiene, a small quantity of 1,2-butadiene was
also detected ([1,2-butadiene]/[1,3-butadiene] = 0.05); also,
several C3, C5, and C6 hydrocarbon products were identified.
The yield of these later products appear to increase when the
total reaction pressure was decreased. The preliminary results
on the pressure dependence of the product channels for the C2H5
and C2H3 mixed radicals system suggest very complex mecha-
nistic behavior involving reactions of the chemically activated
combination adducts. The pressure dependence of the C6
products is an indicator of sequential reaction of the energetic
combination adduct. Similarly, significant pressure effects on
product channels of the reaction CH3 + C2H3 have been recently
reported by Fahr et al.12 Thorn et al.13 and Stoliarov et al.14
Ethyl and vinyl radicals were produced by the 193-nm
photolysis of EVK. Time-resolved UV absorptions of both ethyl
and vinyl radicals were monitored and used for kinetic
determinations. The final products of the ethyl-vinyl mixed
radical reactions were identified and quantified through gas-
chromatographic and mass-spectroscopic (GC/MS) analysis of
the reaction products.
A summary of our methods is presented here. More detailed
descriptions of the procedures can be found in previous
publications from our laboratory.12 The output radiation of an
excimer laser is expanded uniformly by a cylindrical lens and
fills the reaction cell side-on through a Suprasil11 flat window
over the cell length (l ) 10 cm). For optical determinations, a
monitoring light from a 75-W xenon arc lamp is rendered nearly
parallel using a condenser and two long-focal-length lenses. An
interposed fast electromechanical shutter, normally closed, is
located between the xenon lamp and the reaction cell. The
shutter is electronically opened shortly before the photolysis
laser pulse and closed at a preset time following the photolysis
event. Thus photolysis by the monitoring light is minimized.
The monitoring light traverses the cell four times, is deflected
by a prism, and then focused on the slit of a monochromator.
The signal from the photomultiplier is fed into a multi-time base
waveform digitizer through a differential comparator. The
transient signal is recorded by the digitizer and then transferred
to a computer for storage and signal averaging. A self-enclosed
gas circulating pump was used to flow the gas mixture through
the reaction cell so that the cell contents were replaced between
the photolysis pulses of 0.5-Hz repetition rate. A total system
volume of about 2000 times that of the active photolysis volume
was used. Because of the significant product dilution, secondary
reactions due to product photolysis is unimportant. The effect
of photodissociation energy on the kinetics was examined by
varying the excimer laser output energies between about 200
and 70 mJ (as monitored at the source).
Identification and quantification of final reaction products
were performed using an on-line HP-4890 gas chromatograph
equipped with a flame ionization detector (FID), and a HP-
5973 mass-selective detector (MSD).11 In most experiments
ethyl and vinyl radicals were simultaneously produced from the
193-nm photolysis of EVK. Ethyl and vinyl radicals were also
produced, in a limited number of test experiments, from the

Ethyl and Vinyl Cross-Radical Reactions
J. Phys. Chem. A, Vol. 106, No. 46, 2002 11137
TABLE 1: Experimental Conditions and Yields of the
Major Final Products (1013 molecule cm-3) Following the
193-nm Photolysis of Mixtures of EVK in He at T ) 298 K
and a Total Pressure of 93.3 KPa
[C2H4]3d1 ) [C2H4]total - [C2H4]1d - [C2H4]2d
)
[C2H4]total - [C4H10]/8-[C4H6]/3.0 (3)
[C2H6]3d2 ) [C2H2]3d2 ) [C2H6]total - [C2H6]1d
)
laser
[EVK]a energyb [C2H2]a [C2H4]a [C2H6]a [C4H6]a [C4H8]a [C4H10]a
[C2H6]total - [C4H10]/8 (4)
6.5 × 1015 ∼200 1.31
8.0 × 1015 ∼130 0.82
6.5 × 1015 ∼70 0.54
13 × 1015 ∼75 1.21
2.54
2.08
1.0
0.89
0.78
0.46
0.82
2.77
2.14
1.13
2.30
3.72
2.80
1.40
3.36
3.62
2.75
1.28
2.98
Thus the ratios of disproportionation/combination channels for
ethyl-vinyl cross-radical reactions can be determined from the
product ratios
1.87
a Concentration unit in molecule cm-3
.
b ArF laser pulse energy (mJ)
k3d1/k3c ) [C2H4]3d1/2[C4H8] )
as monitored at the source.
{[C2H4]total - [C4H10]/8-[C4H6]/3.0 }/2[C4H8] (5)
The pressure dependent studies of the C2H5 and C2H3 mixed-
radicals reactions are currently in progress in our laboratory and
the results will be reported soon.15
k3d2/k3c ) [C2H6]3d2/[C4H8] )
{[C2H6]total - [C4H10]/8}/[C4H8] (6)
Table 1 lists a number of experimental conditions and the
absolute yield of the major final products at a pressure of 93.3
kPa as derived from the calibrated GC/MS product analysis.
Based on the previous studies of the self-reactions of ethyl
radicals, C2H5 + C2H5, and vinyl radicals, C2H3 + C2H3, and
in conjunction with the results of the present final product
analysis, for the mixed C2H5 and C2H3 reactions, the following
reaction sequences at high-pressure conditions are expected upon
the 193-nm photolysis of EVK:
It should be noted that the values of k3d1/k3c and k3d2/k3c derived
from eqs 5 and 6 are expected to have large uncertainties due
to the propagation of measurement uncertainties on various
parameters affecting the ratios. Estimates of the ratio of the
combination/disproportionation channels derived from eqs 5 and
6 suggest the disproportionation channels, at conditions of P )
93.3 kPa and T ) 298 K, are about 10% to 20% of the
combination channel.
Kinetic Absorption Spectroscopy at 230 and 235 nm.
Time-resolved absorption spectroscopy of the mixed ethyl and
vinyl radical reaction system was performed by monitoring
absorptions at wavelengths of 230 and 235 nm. Analysis of the
time-resolved absorption data requires knowledge of the absorp-
tion characteristics of the transient radical species and the stable
reaction products and their absorption cross sections at the
monitoring wavelength(s). The UV absorption spectrum and
cross sections for vinyl radicals, in the spectral range of 225-
238 nm, have previously been determined in our laboratory.16
The vinyl UV absorption exhibits a relatively broad feature with
C2H5COC2H3 193 nm8 C2H5 + C2H3 + CO
C2H5 + C2H5
M8 C2H4 + C2H6
M8 C4H6 (1,3-butadiene)
M8 C2H4 + C2H2
M8 C4H8 (1-butene)
M8 C2H4 + C2H4
M8 C2H6 + C2H2
9
M8 C4H10
(1c)
(1d)
(2c)
(2d)
(3c)
C2H5 + C2H5
9
C2H3 + C2H3
9
cross sections of σC H ) 5.3 × 10-18 cm2 molecule-1 at 230
C2H3 + C2H3
9
2 3
nm and σC H ) 3.1 × 10-18 cm2 molecule-1 at 235 nm.16
2
3
Ethyl radicals also have a broad absorption feature between
about 200-260 nm17,18 due to a number of transitions; some
structures develop further into the UV. Absorption cross sections
for ethyl radicals in the spectral range 200-260 nm have been
reported by Munk et al.17 At the monitoring wavelengths of
this study, the cross sections are σC H ) 1.7 × 10-18 cm2
C2H5 + C2H3
9
C2H5 + C2H3
C2H5 + C2H3
9
(3d1)
(3d2)
2
5
9
molecule-1 at 230 nm and σC H ) 2.5 × 10-18 cm2 molecule-1
2
5
at 235 nm.
Among the reaction products, only 1,3-butadiene has a
significant absorption at the monitoring wavelengths of this
study.19 All other final reaction products have appreciable
absorptions at considerably shorter wavelengths.20 To confirm
the absorption characteristics of the reaction products, known
samples of the expected products of the mixed ethyl-vinyl
radical reactions (excluding 1,3-butadiene) with concentrations
similar to those expected in experiments were introduced into
the reaction cell. The monitoring light intensity was monitored
before and after the introduction of the sample. No detectable
variations of the monitoring light level were observed.
The temporal UV absorption traces, following the 193-nm
photolysis of EVK samples, were averaged and recorded at the
selected monitoring wavelengths. Figure 1 displays one such
trace obtained at 235 nm. No variations of the monitoring light
intensity were detected when the cell containing only He was
irradiated by ArF laser pulses. Thus the observed signal is a
result of the photolysis and not of optical or electrical interfer-
ences.
Each of the final disproportionation products, ethane, ethylene
and acetylene, are formed through multichannel reactions. To
assess the relative rates of the combination and disproportion-
ation channels for the C2H5 + C2H3 reaction, it is necessary to
determine the contribution of each reaction channel to the
production of the final disproportionation products.
The contribution of the disproportionation channels involving
self-reactions of ethyl radicals and vinyl radicals (channels 1d
and 2d), on the formation of ethane, ethylene and acetylene,
can be determined from the known ratios of the combination/
disproportionation for these reactions.8-10
[C2H6]1d ) [C2H4]1d ) [C4H10]/8
[C2H4]2d ) [C2H2]2d ) [C4H6]/3.0
(1)
(2)
The contribution of the cross-radical reaction C2H5 + C2H3
on the formation of ethane, ethylene, and acetylene can be
assessed as follows:

11138 J. Phys. Chem. A, Vol. 106, No. 46, 2002
Fahr and Tardy
Figure 1. Time-resolved absorption trace at 235 nm after the 193-nm
photolysis of a mixture of 1.3 × 1016 molecule cm3 of C2H5COC2H3
in 93 kPa He. The trace is an average of 1000 sweeps.
Figure 2. Time-resolved absorbance at 235 nm determined experi-
mentally (circles) and from fitting (solid line) using modeling parameters
-11
in Table 2 and with derived values of k3 ) (9.5 ( 0.4) × 10
cm3
molecule-1 s-1, [C2H5] ) (10.5 ( 0.5) × 1013 molecule cm-3, and
TABLE 2: Rate Constants Used in the Analysis of the
Time-Resolved Absorption Data
[C2H3] ) (11.1 ( 0.4) × 1013 molecule cm-3
.
reaction
parameter
ref
The time-resolved absorption data cannot distinguish various
product channels which lead to nonabsorbing products such as
those for the reactions C2H5 + C2H5 and C2H5 + C2H3. Thus,
the overall k1 rate constant (k1 ) k1c + k1d) was used as a fixed
parameter and the overall k3 rate constant (k3 ) k3c + k3d) was
evaluated through the modeling and fitting procedures.
The Acufit kinetic simulation program is specifically designed
for analysis of time-resolved absorption data; it uses the
experimental data file, the model information generated by
Acuchem and user selected values for input parameters. Known
parameters are held at their input values. An iterative procedure
is used to adjust the values of parameter(s) of interest until the
“best” fit of the experimental data to the assumed model is
achieved. The initial ethyl and vinyl radical concentrations is
calculated from the Beer-Lambert law by using the absorbance
immediately following the photolysis event, the known absorp-
tion cross sections for the ethyl and vinyl radicals and the optical
path length of the absorption cell. However, the values for the
initial radical concentrations along with the k3 value were
determined from the fitting procedures. In this way the relative
and absolute values for the initial radical concentrations were
allowed to vary until best fit was obtained. The quality of the
fit and adequacy of the mechanism was assessed using the chi
square (ψ2) statistic.22 The Acufit iterative least-squares pro-
cedure, through the ψ2 minimization, returns the value of the
searched parameters, their error estimates and ψ2 value for the
fit. The error estimates of the searched parameter(s) depend on
the signal/noise ratio of the experimental trace and the number
of the searched parameters.
C2H5 + C2H5 f products
C2H3 + C2H3 f C4H6
C2H3 + C2H3 f C2H4 + C2H2
C2H5 + C2H3 f products
[C2H5]0 and [C2H3]0
k1 ) 2.2 × 10 -11 (fixed)
k2c ) 9.3 × 10-11 (fixed)
k2d ) 3.1 × 10-11 (fixed)
k3 ) adjusted
7
8, 9
8, 9
adjusted
The trace in Figure 1 shows an instant absorption rise due to
nascent vinyl and ethyl radicals produced from the EVK
photolysis. The contribution of each radical to this absorption
is proportional to its corresponding absorption cross section and
concentration. The second absorption component is a decay to
a nonzero baseline which is a composite absorption due to loss
of vinyl and ethyl radicals and the absorption rise due to
formation of the 1,3-butadiene product. The third absorption
component at long observation times (the “absorption tail”) is
primarily due to the product 1,3-butadiene. The absorbance at
any time At can be related, by the Beer-Lambert law (eq 7), to
concentrations of the absorbing species ni, absorption cross
section σi, and the absorption path length labs
At ) Σniσi(labs
)
(7)
Data Analysis. Kinetic modeling and simulation were used
for analysis of the time-resolved absorption data and deriving
the overall rate constant for the C2H5 + C2H3 reaction. Acuchem
and Acufit packages of modeling and analysis programs11,21,22
were used here.
The reaction sequences 1-3 were modeled at high-pressure
conditions. A listing of the reactions and rate constants is
provided in Table 2. The following absorption coefficients (σ,
10-18 cm2 molecule-1) were fixed in the modeling calculation:
Table 3 lists the experimental conditions and the values for
the measured parameters from such fits of the modeled signals
to different time-resolved absorption signals at λ ) 230 nm and
λ ) 235 nm.
At 230 nm: σC H ) 5.3,16 σC H ) 1.7 17, and σ1,3-C H
)
2
3
2
5
4
6
11.0.19
At 235 nm: σC H ) 3.1,16 σC H ) 2.5 17, and σ1,3-C H
)
These results suggest an overall rate constant of about 9.6 ×
2
3
2
5
4
6
3.7.19
10-11 cm3 molecule-1 s-1 for the C2H5 + C2H3 cross-radical
TABLE 3: The Overall Rate Constant, k3, for the C2H5 + C2H3 Reaction and the Initial Radical Concentrations Derived from
the Modeling of Time-Resolved Absorption Data
EVK/He,
laser energy,a
mJ
monitoring λ,
k3,b 10 -11
[C2H5]0,b 1013
molecule cm-3
[C2H3]0,b 1013
molecule cm-3
% dissociation
molecule cm-3/kPa
nm
cm3 molecule-1 s-1
13 × 1015/93
6.5 × 1015/93
13 × 1015/93
6.5 × 1015/93
8.0 × 1015/93
∼70
∼130
∼75
230
230
235
235
235
9.3 ( 0.3
10.1 ( 0.3
10.9 ( 0.4
8.0 ( 0.6
9.5 ( 0.4
11.1 ( 0.3
10.1 ( 0.2
16.2 ( 0.4
12.3 ( 0.3
11.1( 0.4
10.5 ( 0.3
9.6 ( 0.3
15.4 ( 0.4
10.9 ( 0.3
10.5 ( 0.5
∼0.9
∼1.4
∼1.2
∼1.9
∼1.3
∼200
∼140
a ArF excimer laser energy as read at the source. b Error estimates derived from modeling fits.

Ethyl and Vinyl Cross-Radical Reactions
J. Phys. Chem. A, Vol. 106, No. 46, 2002 11139
TABLE 4: Biases on Measured k3 Due to Uncertainties of the Known Parameters Used in Analysis of Absorption Dataa
parameter:
central value:
k1c + k1d
k2c
k2d
σC H
σC H
σC H
3.47f
measured k3
9.6 ( 0.4g
bias on k3
2
3
2
5
6
2.2b
9.3c
3.1c
3.1d
2.5e
0.0
+0.3
-0.3
9.1
9.8
1 0.6
8.4
0.5
0.2
1.0
1.2
0.6
0.4
1.0
1.1
0.5
0.7
0.6
0.9
3
4
5
6
7
8
+1.5
-1.5
+0.5
-0.5
9.0
10.0
10.6
8.5
10.1
8.9
10.2
8.7
+0.7
-0.7
+0.1
-0.1
+0.2
-0.2
a The units are σ × 1018 cm2 molecule and k × 1011 cm3 molecule-1 s-1
.
b Rate constant value and error from ref 7. c From ref 8. d From ref 16.
e From ref 17. f From ref 19. g Measurement (random) error.
TABLE 5: Product Yields Derived from Modeling of the
C2H5 and C2H3 Mixed Radical System for Various k3c
Values and by Using the Rate Parameters Listed in Table 2a
reaction. The results of the analysis, within the measurement
uncertainties, agree with a one-to-one production of ethyl and
vinyl radicals through the 193-nm photolysis of EVK. The
calculated initial radical concentrations relative to the radical
precursor concentrations at various experimental conditions
suggest a photodissociation efficiency of about 1% to 2%
depending upon the photolysis energy.
As unknown parameters are extracted from a relatively
complex, multicomponent reaction scheme, it is essential to
quantify a realistic uncertainty for the derived parameter(s). In
general, both systematic (inaccurate value for known param-
eter(s) or faulty calibration) and random (unpredictable varia-
tions in the measurement) errors must be included. Systematic
errors are often called biases in the measurement.22,23 In the
present work we have assessed the contribution of uncertainties
of each known parameter used in the modeling of the ethyl-
vinyl reaction system toward the combined uncertainty of the
measured k3 rate constant.
Table 4 lists the parameters used in the data analysis (first
row), their central values (second row) and corresponding error
limits (rows 3-8). By using the central values for known
parameters a rate constant value of k3 ) 9.6 × 10-11 has been
determined from analysis of an absorption trace obtained at 235
nm. The random error for determining k3, derived by the analysis
program, is (0.4 (listed in the second row). The random error
primarily is due to the level of signal/noise on the data and
also depend on the number of measured parameters.
k3
[C2H2]b [C2H4]b [C2H6]b [C4H6]b [C4H8]b [C4H10]b
2.0 × 10-11
4.0 × 10-11
6.5 × 10-11
8.0 × 10-11
2.2
1.8
1.4
1.1
6.3
4.9
3.2
2.2
1.6
1.3
0.9
0.6
2.7
2.7
2.7
2.7
1.0
2.1
3.4
4.1
3.2
3.2
3.2
3.2
a [C2H5]0 ) [C2H3]0 ) 1.2 × 1014 molecule cm-3, k3 ) 9.6 cm3
molecule-1 s-1, and k3D1/k3D2 ) 2. b Concentrations in units of 1013
molecule cm-3
.
The contribution of the biases from each fixed parameter is taken
as the average of the upper and lower biases determined at the
uncertainty limits of each known parameter.
The vector addition (eq 8) assumes that the errors in the fixed
parameters are not correlated. Since values of known parameters
are obtained from independent experiments, they are thus
uncorrelated errorwise and they are as likely to have a positive
as a negative error associated with them.
Therefore, the overall rate constant value for the ethyl and
vinyl cross-radical reaction, with a combined uncertainty as
derived from these measurements can best be presented as:
k3 ) (9.6 ( 1.9) × 10-11 cm3 molecule-1 s-1
.
Evaluation of the Combination Rate Constant k3c Using
Comparative Methods. In mixed radical systems, the major
product yields and the known rate coefficients can be used to
determine an unknown radical-radical rate coefficient. Here,
through use of the kinetic modeling and comparison of the
experimental product yields with the numerical simulations, we
have determined the k3c rate constant for the combination
reaction C2H5 + C2H3 f C4H8. The reaction sequences 1-3
were modeled, at high-pressure conditions, using known rate
coefficients for the self-reactions of ethyl radicals and vinyl
radicals as given in Table 2. The kinetic modeling was
performed using the Acuchem21,22 numerical integration routine.
Initial radical concentrations similar to those of the experimental
conditions were used. The product yields determined experi-
mentally were compared with the modeling results for a range
of k3c values between 1 × 10-11 and 9.6 × 10-11 cm3
molecule-1 s-1. The total k3 value (k3 ) k3c+ k3d) was kept
constant at 9.6 × 10-11 cm3 molecule-1 s-1, and a ratio of
k3d1/k3d2 ) 2 was used. Table 5 lists the product concentrations
derived when [C2H5]0 ) [C2H3]0 ) 1.2 × 1014 molecule cm-3
was used.
In developing rows 3-8 of Table 4, the known parameters
are fixed either at their best known (central) values, as given
on the second row of the Table 4, or at the upper or lower limits
of values as dictated by the corresponding uncertainties. If a
cell is blank the central value for that parameter is employed.
The k3 value is then derived for the corresponding set of known
parameters. All rows involve the analysis of the same absorption
trace obtained at 235 nm. The biases on k3, listed in the last
column of Table 4, are the difference of the k3 values when the
central and noncentral values for known parameters are used.
The results of the error analysis suggest that biases on k3 are
largest (∼10%) when k2c and σC H are fixed at “noncentral”
2
3
values. Variations of other parameters, within their correspond-
ing uncertainties, each result in about a 5% bias on k3 value.
The combined uncertainty on the measured k3 value can be
estimated through the vector addition of the biases (systematic
errors) and the random error.22, 23
The best agreement between the yield of the products
determined experimentally and through the modeling was
achieved when k3c ) 6.5 × 10-11 cm3 molecule-1 s-1. A 20%
δ2k3 ) (0.35)2 + (1.1)2 + (0.5)2 + (1.0)2 + (0.55)2 +
(0.8)2 + (0.4)2 ) (1.9)2 (8)

11140 J. Phys. Chem. A, Vol. 106, No. 46, 2002
Fahr and Tardy
variation of the k3c from the central value, (6.5 ( 1.3) × 10-11
cm3 molecule-1 s-1, resulted in variations of the simulated
product yields which were within about the 15% uncertainties
of the experimental product analysis measurements.
Acknowledgment. The authors thank Drs. Stephen Stein,
Robert Huie, Allan Laufer, and Vladimir Orkin for helpful
comments that improved this manuscript.
The rate constant of k3c ) 6.5 × 10-11 cm3 molecule-1 s-1
References and Notes
for the combination reaction C2H5 + C2H3 f C4H8 is nearly a
factor of 2 slower than a previously reported rate constant of
(1) Westmoreland, P. R.; Dean, A. M.; Howard, J. B.; Longwell, J. P.
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references therein.
-11
12 × 10
cm3 molecule-1 s-1 for the combination reaction
CH3 + C2H3 f C3H6.9,14 The difference in collision cross
sections of the ethyl and methyl radicals account for about 25%
reduction in rate constant for C2H5 + C2H3. However, additional
factors such as energetics of the reactions and products may
also play significant roles in the efficiency of the radical-radical
combination reactions. Deviations from hard sphere collision
rate constants have recently been presented.25
(6) Romani, N. P.; Bishop, J.; Bezard, B.; Atreya, S. Icarus 1993, 106,
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(11) Certain commercial instruments, materials and computational
programs are identified in this paper to adequately specify the experimental
or computational procedures. In no case does such identification imply
recommendation or endorsement by NIST, nor does it imply that the
instruments, materials, and computational programs identified are necessarily
the best available for the purpose.
The geometric mean rule24 kAB ) 2(kAAkBB 0.5 also has often
)
been used to estimate rate constants for cross-radical combina-
tion reactions kAB when rate constants for the radical self-
combination reactions kAA and kBB are known. Using k1c
)
2.0 × 10-11 cm3 molecule-1 s-1 and k2c ) 9.3 × 10-11 cm3
molecule-1 s-1, a value of k3c ) 8.6 × 10-11 cm3 molecule-1
s-1 is calculated from the geometric mean rule. This value is
about 30% higher than the k3c value derived through kinetic
modeling but within the uncertainties of two measurements.
IV. Conclusions
(12) Fahr, A.; Laufer, A. H.; Tardy, D. C. J. Phys. Chem. 1999, 103,
8433,
The cross-radical reactions of ethyl and vinyl radicals have
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rate constant of (9.6 ( 1.9) × 10-11 cm3 molecule-1 s-1 for
the C2H5 + C2H3 cross-radical reaction. The reported uncertainty
was calculated from contributions of both random and systematic
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at high-pressure conditions with a rate constant of about 6.5 ×
-11
10
cm3 molecule-1 s-1 The analysis of the time-resolved
absorption data and product analysis agree with the 1:1
production of ethyl and vinyl radicals upon 193-nm photolysis
of EVK. Under the experimental conditions of this study a
photodissociation yield of about 1% to 2% for EVK has been
achieved.