Low-Temperature Kinetics of Reactions of OH Radical with Ethene, Propene, and 1-Butene

Article abstract of DOI:10.1021/jp030230a

The kinetics of the reactions of the OH radical with ethene (k ₁), propene (k₂), and 1-butene (k₃) are studied over a temperature range of T = 96-296 K. The low-temperature environment is provided by a pulsed Laval nozzle supersonic expansion of nitrogen with admixed radical precursor and reactant gases. The OH radicals are produced by pulsed photolysis of H₂O₂ at 248 nm. Laser-induced fluorescence of the OH radicals excited in the (1,0) band of the A²σ⁺-X²∏_i transition is used to monitor the OH decay kinetics to obtain the bimolecular rate coefficients. At T = 296 K, the rate constants k₁, k₂, and k₃ are also measured as a function of total pressure. The room-temperature falloff parameters are used as the basis for extrapolation of the low-temperature kinetic data, obtained over a limited range of gas number density, to predict the high-pressure limits of all three rate coefficients at low temperatures. The temperature dependence of the measured high-pressure rate constants for T= 96-296 K can be expressed as follows: k_1,∞ = (8.7 ± 0.7) × 10^-12(T/300) ^{(-0.85±0.11)} cm³ molecule^-1 s ^-1; k_2,∞ = (2.95 ± 0.10) × 10 ^-11(T/300)^{(-1.06±0.13)} cm³ molecule ^-1 s^-1; k_3,∞ = (3.02 ± 0.15) × 10^-11(T/300)^{(-1.44±0.10)} cm³ molecule^-1 s^-1. All three high-pressure rate constants show a slight negative temperature dependence, which is generally in agreement with both low-temperature and high-temperature kinetic data available in the literature. Implications to the atmospheric chemistry of Saturn are discussed. Incorporating the new experimental data on k₁ in photochemical models of Saturn's atmosphere may significantly increase the predicted rate of photochemical conversion of H₂O into C-O containing molecules.

Full text of DOI:10.1021/jp030230a

J. Phys. Chem. A 2003, 107, 10055-10062
10055
Low-Temperature Kinetics of Reactions of OH Radical with Ethene, Propene, and 1-Butene
Andrei B. Vakhtin,† James E. Murphy,‡ and Stephen R. Leone*,§
JILA, National Institute of Standards and Technology and UniVersity of Colorado, and Department of
Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0440
ReceiVed: February 20, 2003; In Final Form: June 30, 2003
The kinetics of the reactions of the OH radical with ethene (k1), propene (k2), and 1-butene (k3) are studied
over a temperature range of T ) 96-296 K. The low-temperature environment is provided by a pulsed Laval
nozzle supersonic expansion of nitrogen with admixed radical precursor and reactant gases. The OH radicals
are produced by pulsed photolysis of H2O2 at 248 nm. Laser-induced fluorescence of the OH radicals excited
in the (1,0) band of the A2Σ+-X2Πi transition is used to monitor the OH decay kinetics to obtain the bimolecular
rate coefficients. At T ) 296 K, the rate constants k1, k2, and k3 are also measured as a function of total
pressure. The room-temperature falloff parameters are used as the basis for extrapolation of the low-temperature
kinetic data, obtained over a limited range of gas number density, to predict the high-pressure limits of all
three rate coefficients at low temperatures. The temperature dependence of the measured high-pressure rate
constants for T ) 96-296 K can be expressed as follows: k1,∞ ) (8.7 ( 0.7) × 10-12(T/300)(-0.85(0.11) cm3
molecule-1 s-1; k2,∞ ) (2.95 ( 0.10) × 10-11(T/300)(-1.06(0.13) cm3 molecule-1 s-1; k3,∞ ) (3.02 ( 0.15) ×
10-11(T/300)(-1.44(0.10) cm3 molecule-1 s-1. All three high-pressure rate constants show a slight negative
temperature dependence, which is generally in agreement with both low-temperature and high-temperature
kinetic data available in the literature. Implications to the atmospheric chemistry of Saturn are discussed.
Incorporating the new experimental data on k1 in photochemical models of Saturn’s atmosphere may
significantly increase the predicted rate of photochemical conversion of H2O into C-O containing molecules.
Introduction
this paper we report new kinetic data on the reactions of OH
with ethene, propene, and 1-butene:
In a previous paper we reported measurements of the rate
constants of the reactions of hydroxyl radical OH with propene
and 1-butene at T ) 103 and 298 K using a pulsed Laval nozzle
apparatus.1 Both measured rate constants agreed well with
available low-temperature and high-temperature kinetic data,
showing a slight negative temperature dependence. At low and
moderate temperatures, reactions of OH with alkenes proceed
by addition;2-9 therefore, in general, the corresponding rate
constants should be pressure-dependent. In the initial study1 we
assumed that the rate constants for the OH + propene and
OH + 1-butene reactions measured at T ) 103 K and a total
gas number density of about 2 × 1016 molecule cm-3 are at, or
very close to, the high-pressure limit. This assumption is
reasonable in view of the considerable complexity of the species
involved in the reactions. Moreover, comparison of the rate
constants measured at room temperature and similar total gas
densities with literature data shows that the 2 × 1016 molecule
cm-3 gas number density provides essentially high-pressure
conditions for these two reactions even at room temperature.
However, our estimates indicate that the high-pressure limit
would not be the case for the reaction of OH with ethene. For
this reaction, analysis of the pressure dependence of the rate
constant is required even at temperatures as low as 100 K. In
k1
OH + C2H4 (+ M)
OH + C3H6 (+ M)
OH + C4H8 (+ M)
98 C2H4OH (+ M)
(R1)
(R2)
(R3)
k2
98 C3H6OH (+ M)
k3
98 C4H8OH (+ M)
obtained over a temperature range of T ) 96-296 K. As
indicated by the reaction equations, we assume that all three
reactions proceed by addition at low temperatures. The rate
constants k1, k2, and k3 are measured as a function of total
pressure at T ) 296 K, and the room-temperature falloff
parameters are used to extrapolate the low-temperature data for
k1, k2, and k3 (obtained for a limited range of total gas number
densities) to the high-pressure limit. The obtained rate constants
are compared to the available literature data and are also
discussed in terms of possible applications to the photochemical
models of the atmospheres of the outer planets.
Experimental Section
The apparatus used in this work has been described previ-
ously.1,10 Therefore, only a brief description will be given here.
The low-temperature environment is created by supersonic
expansion of gas through a Laval nozzle. The Laval nozzle block
is mounted inside a stainless steel chamber. The nozzle block
can be translated about 30 cm along the chamber axis. Two
homemade pulsed valves driven by piezo disk translators supply
a gas pulse of approximately 5-ms duration (nitrogen with
* Corresponding author.
† Present address: Southwest Sciences, Inc., Santa Fe, NM 87544.
E-mail: avakhtin@swsciences.com.
‡ Present address: National Renewable Energy Laboratory, Golden, CO
80401. E-mail: murphyje@mail.colorado.edu.
§ Present Address: Departments of Chemistry and Physics, and Lawrence
Berkeley National Laboratory, University of California, Berkeley, CA
94720. E-mail: srl@cchem.berkeley.edu.
10.1021/jp030230a CCC: $25.00 © 2003 American Chemical Society
Published on Web 11/04/2003

10056 J. Phys. Chem. A, Vol. 107, No. 47, 2003
Vakhtin et al.
TABLE 1: Characterization of the Three Laval Nozzles, Used in the Kinetic Experiments, by Different Methods
OH LIF
excitation spectra
direct measurements
of the flow velocity
Pitot tube measurements
gas number density,
nozzle
Mach number
molecules cm-3
temp, K
flow velocity, cm/s
temp, K
flow velocity, cm/ s
1
2
3
2.01 ( 0.19
2.93 ( 0.14
3.24 ( 0.10
(3.5 ( 0.7) × 1016
(2.65 ( 0.45) × 1016
(1.9 ( 0.2) × 1016
165 ( 14
110 ( 7
96 ( 4
(5.34 ( 0.30) × 104
(6.24 ( 0.12) × 104
(6.48 ( 0.07) × 104
152 (14
109 ( 16
94 ( 8
(5.34 ( 0.10) × 104
(6.21 ( 0.12) × 104
(6.47 ( 0.09) × 104
admixed radical precursor and reactant gases) to the preexpan-
sion chamber of the nozzle block. The gas expands through the
Laval nozzle to the chamber pumped by a mechanical pump
(60 L/s). The expansion results in a collimated supersonic gas
flow, which is characterized by uniform Mach number, gas
number density, and temperature along the flow axis for about
20 cm.1,10 The variable opening of a gate valve is used to control
the pumping speed in order to optimize the background pressure
for the appropriate collimation of the supersonic flow. The
background pressure in the chamber is measured by a capaci-
tance manometer. With three different Laval nozzles used in
the present work, the kinetic measurements can be performed
in a temperature range of 96-165 K. The Mach number,
temperature, gas number density, and static pressure in the
supersonic flow are characterized by Pitot tube measurements,11
as described earlier.1,10 The static pressure of the flow obtained
from the Pitot tube measurements is in reasonably good
agreement with the background pressure in the chamber adjusted
to obtain a collimated supersonic flow. For the three nozzles
used in the experiments, the difference was not more than 13%.
The temperature in the flow can also be tested independently
by analysis of the rotational structure of laser-induced fluores-
cence (LIF) excitation spectra of the OH radical.1 In this paper,
we use an additional means of flow diagnostics, namely, direct
measurement of its velocity, based on measurements of the OH
radical LIF signal versus distance between the nozzle and
photomultiplier (see Results).
The chamber and the nozzle block have quartz windows,
which makes it possible to introduce laser beams along the axis
of the gas flow to generate radicals photolytically (an excimer
laser) and for laser-based diagnostics (tunable frequency-doubled
dye laser). In this work, LIF from OH is used as a probe. The
output flange of the chamber is equipped with a baffle arm
ending in a quartz Brewster angle window to minimize the
scattered light.
The OH radicals are produced by pulsed photolysis of H2O2
at 248 nm with the unfocused beam of a KrF excimer laser (up
to 100 mJ/pulse at a repetition rate of 10 Hz). The frequency-
doubled output radiation of a pulsed dye laser operating on
Rhodamine 590 dye and pumped by the second harmonic of a
Nd:YAG laser is used for excitation of LIF in the Q1(1) line of
the (1,0) band of the A2Σ+-X2Πi transition of OH. LIF from
OH is detected on the (1,1) and (0,0) bands of the A-X
transition by a photomultiplier tube (PMT) equipped with a UG-
11 UV band-pass filter and a narrow-band interference filter
(310 ( 10 nm). The PMT, mounted 15 cm downstream of the
nozzle, detects the light that is collected by a quartz lens (5 cm
in diameter and 5-cm focal length). The lens focuses the image
of a segment of the irradiated zone, which is about 2 cm long,
to the PMT photocathode. The optics are appropriately shielded
to minimize the effect of scattered light.
background subtraction is performed by setting the photolysis-
probe delay to a negative value for every other triggering pulse
and subtracting the background from the signal. Normally, each
OH decay profile is obtained as an average of 20-100
experimental kinetic curves. Each kinetic curve consists of 20
points (signal minus background) covering a probe delay time
interval of 10-200 µs in 10-µs steps and takes 4 s to be acquired
(at 10-Hz pulse repetition rate). The triggering of all units and
devices is provided by a four-channel digital delay/pulse
generator. Both the boxcar integrator and the pulse generator
are GPIB-interfaced to a PC computer, which is used to control
the experiment and for data acquisition.
The gas flows, supplied from cylinders through stainless steel
lines and controlled by mass flow controllers, are mixed in a
150-cm3 stainless steel cylinder on their way to the nozzle block.
A controlled flow of N2 is bubbled through a sample of a
concentrated (>90%) aqueous solution of hydrogen peroxide
and then mixed into the main flow of the carrier gas. The total
gas number density in the collimated supersonic flow is
measured by the Pitot tube method,11 as described in the earlier
work.1 The gas number densities for individual components are
calculated from the total density and the known relative mass
flows. The flow controllers are calibrated for individual gases
by measuring the rate of filling a known volume to a known
pressure.
The gases used are as follows: N2 (99.999%); ethene
(99.999%); propene (99.97%); 1-butene (99.9%). All gases are
used as supplied without purification.
Results and Discussion
Characterization of the Supersonic Flow: Direct Mea-
surement of Flow Velocity. In this work, three Laval nozzles
are used to provide different low-temperature environments at
different temperatures. The supersonic flows produced by the
nozzles are characterized by Pitot tube measurements and LIF
spectroscopy of OH radicals. The characterization procedures
have been described in detail elsewhere.1 The results of these
measurements for the three nozzles are summarized in Table 1.
As seen from Table 1, uncertainties in temperature and gas
number density are relatively high (especially for nozzle no.
1). These uncertainties are caused mainly by inhomogeneity of
the collimated supersonic flow and are treated as systematic
errors in evaluating the final uncertainties reported for the
measured rate constants.1
We also use a direct method of determination of the flow
velocity, which provides complementary information. To mea-
sure the flow velocity we take advantage of a spike in the OH
concentration time profile that is produced by the photolysis of
H2O2 in the preexpansion chamber of the Laval nozzle block
(see Figure 1a). The preexpansion chamber is relatively small,
and most of its volume is irradiated by the photolysis laser beam.
When the portion of the gas irradiated in the preexpansion
chamber expands through the nozzle, the OH radicals fill the
whole aperture of the flow (in contrast to the OH produced in
the supersonic flow, where OH radicals are formed only within
the laser beam aperture diameter). Since the gas flow diameter
The kinetics of the OH decay are traced by monitoring the
OH LIF intensity versus delay between the photolysis and probe
laser pulses. Typically, the signal from the photomultiplier is
integrated over a 200-ns gate after a delay of 200 ns with respect
to the excitation laser pulse by a boxcar averager. Active

Low-Temperature Kinetics of Reactions
J. Phys. Chem. A, Vol. 107, No. 47, 2003 10057
Figure 2. Reciprocal OH decay time versus reactant concentration
for the OH + C4H8 reaction obtained at T ) 110 K. For each
concentration, the error bars indicate two standard deviations of the fit
of the experimental kinetic curves by a single-exponential function.
The line shows the 1/σ2-weighted linear fit. The inset shows representa-
tive examples of the OH decay profiles obtained at different 1-butene
concentrations: 1.0 × 1014 molecule cm-3 (open circles); 2.4 × 1014
molecule cm-3 (filled squares); 4.4 × 1014 molecule cm-3 (open
triangles).
Figure 1. (a) Points show the OH time profiles obtained in the
photolysis of H2O2 in supersonic expansion through Laval nozzle no.
3 (Mach number 3.24) at different nozzle-PMT distances. For each
data set, lines represent the parabolic fits to the seven points closest to
the maximum of the spike. Arrows show the positions of the maxima
of the spikes in OH time profiles that correspond to OH produced in
the preexpansion chamber (see text). The time window for kinetic
studies (which are performed at a nozzle-PMT distance of 15 cm) is
indicated as the “working range”. (b) The arrival times of the spikes
in OH time profiles plotted in time-distance coordinates for the three
nozzles used in this study. The flow velocities obtained from the slopes
are indicated.
from Pitot tube measurements are considered the most reliable.
The direct OH LIF flow velocity measurements have smaller
uncertainty for the no. 1 nozzle but give excellent agreement
with the Pitot tube measurements. The Pitot measurements are
used to characterize the experimental conditions for the kinetic
studies described in the following sections.
Rate Constants for the Reactions of OH with Ethene,
Propene, and 1-Butene. The low-temperature rate constants
of the reactions R1, R2, and R3 are measured using the pulsed
Laval nozzle expansion method and LIF detection of the
disappearance of the OH radicals. The inset in Figure 2 shows
representative examples of OH decay profiles obtained at
different concentrations of 1-butene at T ) 110 K. Similar results
have been obtained for OH decay kinetics in the presence of
ethene and propene. In all cases, the kinetic curves are well
described by a single-exponential decay function. To ensure that
the OH rotational relaxation effects14,15 do not interfere with
the OH reactive decay kinetics, we neglect the first two points
of the experimental kinetic curves in the fitting procedure; i.e.,
we fit only the tails of the OH time profiles, starting at a 30-µs
photolysis-probe delay (the fitted data range is shown by the
horizontal arrow in the inset in Figure 2). To obtain the rate
constants, the OH decay time is measured as a function of alkene
concentration, which is varied over at least a factor of 10. A
representative example of the pseudo-first-order plot for reaction
R3 is shown in Figure 2. The corresponding rate constant can
be obtained from the slope of the straight line that fits the
experimental dependence. The intercept is primarily due to the
diffusion loss of the OH radicals out of the detection zone. We
estimate the OH concentration immediately after the photolysis
pulse to be <3 × 1010 molecule cm-3, which is about 3 orders
of magnitude less than the smallest alkene concentration used
in kinetic measurements. Therefore, self-reaction of OH can
probably be neglected. However, a certain contribution of the
reaction of OH with H2O2 cannot be excluded. The rate constant
for this reaction at room temperature is 1.7 × 10-12 cm3
is 2-4 times larger than the laser beam diameter, the radial
diffusion of the radicals from the center of the flow (where the
OH radicals are detected by LIF) is different (slower) for the
portion of the flow where the radicals are formed before the
expansion. This leads to the appearance of a spike in the OH
radical profile. Another reason for the OH spike formation could
be a difference in the absorption cross-section of H2O2 at 248
nm at low temperatures (in the supersonic flow) and at room
temperature (in the preexpansion region).12,13 Note that only the
uniform part of the OH profile (with nozzle-PMT distance
equal to 15 cm) is used for kinetic studies (marked as the
“working range” in Figure 1a). The portion of the OH profile
with the spike is used only for the flow velocity measurements.
To measure the flow velocity, the OH time profiles are
recorded at different distances between the Laval nozzle and
the PMT (see Figure 1a). The arrival time of the maximum of
the spike is determined for each nozzle-PMT distance by fitting
the seven points closest to the maximum of the spike by a
second-order polynomial for each data set (lines in Figure 1a).
Then the data are plotted in distance-time coordinates. Figure
1b shows the results obtained for the three nozzles. The slopes
of the linear fits of the experimental data give the flow velocities
directly. The results of the direct velocity measurements are
presented in Table 1 and are seen to be in excellent agreement
with both the Pitot tube data and the OH rotational temperatures
obtained by LIF. In this work we use a simplified procedure to
estimate the OH rotational temperature that involves consider-
ation of relative intensities of the rotational lines belonging to
only two branches, R1 and Q21, of the LIF excitation spectra of
the OH radical in the (1,0) band of the A2Σ+-X2Π transition
(obtained at the photolysis-probe delay of 30 µs). This
procedure produces higher uncertainty, compared with the Pitot
tube measurements. The supersonic flow parameters derived
molecule-1 s-1 16
and low-temperature measurements of this
,
rate constant are underway in this laboratory. The rate constants
for reactions R1, R2, and R3 measured at different temperatures
and gas number densities, as well as the details of the
experimental conditions, are presented in Tables 2-4. The

10058 J. Phys. Chem. A, Vol. 107, No. 47, 2003
Vakhtin et al.
TABLE 2: Rate Constants for the OH + C2H4 Reaction
(k1). Buffer Gas N2
total gas density,
molecule cm-3
[C2H4],
rate constant,a
T, K
molecule cm-3 cm3 molecule-1 s-1
96 ( 4 (1.9 ( 0.2) × 1016
(0-6.3) × 1014 (1.99 ( 0.33) × 10-11
110 ( 7 (2.65 ( 0.45) × 1016 (0-7.2) × 1014 (1.74 ( 0.40) × 10-11
165 ( 14 (3.5 ( 0.7) × 1016
(0-1.6) × 1015 (7.20 ( 1.80) × 10-12
(0-1.6) × 1015 (1.54 ( 0.19) × 10-12
(0-2.6) × 1015 (2.03 ( 0.21) × 10-12
(0-4.3) × 1015 (2.72 ( 0.30) × 10-12
(0-5.8) × 1015 (3.04 ( 0.33) × 10-12
(0-9.6) × 1015 (3.60 ( 0.46) × 10-12
(0-6.5) × 1015 (4.43 ( 0.54) × 10-12
(0-6.6) × 1015 (5.09 ( 0.59) × 10-12
(0-5.1) × 1015 (5.02 ( 0.62) × 10-12
(0-4.2) × 1015 (5.48 ( 0.58) × 10-12
(0-3.5) × 1015 (5.59 ( 0.59) × 10-12
(0-6.6) × 1015 (6.17 ( 0.67) × 10-12
(0-7.1) × 1015 (6.80 ( 0.76) × 10-12
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
2.85 × 1016
4.74 × 1016
8.06 × 1016
1.07 × 1017
1.68 × 1017
2.34 × 1017
3.27 × 1017
4.85 × 1017
7.11 × 1017
9.72 × 1017
1.65 × 1018
3.25 × 1018
a The indicated uncertainties are represented as (2σc, where σc is a
“combined standard uncertainty” that accumulates both statistical and
systematic errors (see text).
Figure 3. Room-temperature rate constants of reactions R1, R2, and
R3 obtained in this work and taken from the literature, plotted as a
function of total gas density. Legend: Vakhtin01, Vakhtin et al. (M )
N2);1 Zellner84, Zellner and Lorenz (M ) Ar);3 Klein84, Klein et al.
(M ) Ar and synthetic air);4 Nielsen90, Nielsen et al. (M ) Ar);5
Kuo91, Kuo and Lee (M ) N2);7 Becker91, Becker et al. (M ) synthetic
air);6 Fulle97, Fulle et al. (M ) He);8 Atkinson75, Atkinson and Pitts
(M ) Ar);44 Ravishankara78, Ravishankara et al. (M ) He);49 Tully85,
Tully and Goldsmith (M ) He);45 Biermann82, Biermann et al. (M )
He).50 Solid lines show the fitted falloff curves (see text).
TABLE 3: Rate Constants for the OH + C3H6 Reaction
(k2). Buffer Gas N2
total gas density,
molecule cm-3
[C3H6],
rate constant,a
T, K
molecule cm-3
cm3 molecule-1 s-1
96 ( 4 (1.9 ( 0.2) × 1016 (0-4.6) × 1014 (1.29 ( 0.29) × 10-10
103 ( 9
2.1 × 1016
(0-3.8) × 1014 (8.1 ( 1.8) × 10-11 b
165 ( 14 (3.5 ( 0.7) × 1016 (0-1.4) × 1015 (5.10 ( 1.31) × 10-11
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
2.88 × 1016
(0-9.4) × 1014 (1.56 ( 0.18) × 10-11
(0-9.2) × 1014 (1.93 ( 0.21) × 10-11 b
(0-9.2) × 1014 (1.79 ( 0.19) × 10-11 b
(0-1.6) × 1015 (1.78 ( 0.19) × 10-11
(0-2.7) ×1015 (1.85 ( 0.19) × 10-11
(0-1.9) × 1015 (1.90 ( 0.21) × 10-11
(0-1.5) × 1015 (2.06 ( 0.23) × 10-11
(0-6.9) × 1014 (2.00 ( 0.21) × 10-11 b
(0-1.2) × 1015 (2.12 ( 0.22) × 10-11
(0-1.1) × 1015 (2.30 ( 0.28) × 10-11
(0-7.8) × 1014 (2.29 ( 0.23) × 10-11
(0-1.3) × 1015 (2.39 ( 0.34) × 10-11
(0-1.1) × 1015 (2.41 ( 0.29) × 10-11
(0-3.3) × 1015 (2.30 ( 0.29) × 10-11
(0-2.7) × 1015 (2.33 ( 0.29) × 10-11
nozzle is not possible, due to certain technical difficulties and
also to the fact that each nozzle is designed for a particular gas
density. Therefore, the low-temperature measurements have been
performed at a single total gas number density for each
temperature. However, at room temperature, we obtained the
kinetic data for reactions R1, R2, and R3 over a relatively wide
range of total pressure (more than 2 orders of magnitude). The
information about the falloff behavior of the rate constants at
room temperature is helpful in estimating the importance of the
falloff effects for lower temperatures. The solid points in Figure
3 show the room-temperature rate constants for reactions R1,
R2, and R3 measured in this work as a function of total gas
density (with nitrogen used as a buffer gas). The rate constants
obtained by other groups are also shown. For reaction R1, only
the data obtained with buffer gases similar to nitrogen (Ar, N2,
synthetic air) are presented. The only exception is the point at
a total gas density of 1021 molecules cm-3 indicating a recent
very-high-pressure measurement by Fulle et al. with M ) He.8
To obtain the room-temperature falloff parameters, we fitted
the experimental data by the Troe expression:18,19
4.8 × 1016
4.8 × 1016
4.83 × 1016
8.35 × 1016
1.08 × 1017
1.66 × 1017
1.76 × 1017
2.34 × 1017
3.28 × 1017
4.85 × 1017
7.20 × 1017
1.03 × 1018
1.65 × 1018
3.32 × 1018
a The indicated uncertainties are represented as (2σc, where σc is a
“combined standard uncertainty” that accumulates both statistical and
systematic errors (see text). b Taken from our previous paper.1
TABLE 4: Rate Constants for the OH + C4H8 Reaction
(k3). Buffer Gas N2
total gas density,
molecule cm-3
[C4H8],
rate constant,a
T, K
molecule cm-3
cm3 molecule-1 s-1
96 ( 4 (1.9 ( 0.2) × 1016
(0-2.1) × 1014 (1.74 ( 0.28) × 10-10
103 ( 9
2.1 × 1016
(0-2.9) × 1014 (1.24 ( 0.27) × 10-10 b
k ) [k0[M]/(1 + k0[M]/k∞)]F
(1)
110 ( 7 (2.65 ( 0.45) × 1016 (0-4.5) × 1014 (1.68 ( 0.40) × 10-10
165 ( 14 (3.5 ( 0.7) × 1016
165 ( 14 (3.5 ( 0.7) × 1016
(0-6.8) × 1014 (5.80 ( 1.51) × 10-11
(0-1.1) × 1015 (8.13 ( 2.10) × 10-11
(0-7.5) × 1014 (3.03 ( 0.34) × 10-11
(0-4.6) × 1014 (3.18 ( 0.37) × 10-11 b
(0-5.7) × 1014 (2.94 ( 0.37) × 10-11
(0-1.6) × 1015 (3.03 ( 0.34) × 10-11
(0-2.5) × 1015 (2.88 ( 0.46) × 10-11
where
296 ( 2
296 ( 2
296 ( 2
296 ( 2
296 ( 2
2.88 × 1016
4.90 × 1016
1.57 × 1017
6.96 × 1017
3.34 × 1018
log F ) log Fcent/[1 + (log(k0[M]/k∞))2]
(2)
In eqs 1 and 2, k0 and k∞ are the limiting low-pressure and high-
pressure rate constants, respectively; F is the “broadening”
correction factor, which takes into account the energy distribu-
tion of the back-dissociating adducts and weak collision
effects.18,19 Fcent is the value of F at the “center” of the falloff
curve (i.e., where k0[M] ) k∞). Equation 1 was used to fit our
data for reactions R1 and R2 alone and also combined with the
literature data shown in Figure 3a,b. For the data obtained in
a The indicated uncertainties are represented as (2σc, where σc is a
“combined standard uncertainty” that accumulates both statistical and
systematic errors (see text). b Taken from our previous paper.1
uncertainties of the measured rate constants are reported as 2σc,
where σc’s are the “combined standard uncertainties” calculated
according to NIST recommendations,17 as described in a
previous paper.1
Although it would be desirable, a large variation in the total
gas number density in the supersonic flow produced by a Laval
this work, the following parameters were obtained: k1,0
)
(11.6 ( 1.8) × 10-29 cm6 molecule-2 s-1, k1,∞ ) (7.5 ( 0.4) ×
10-12 cm3 molecule-1 s-1, with Fcent ) 0.65 for reaction

Low-Temperature Kinetics of Reactions
J. Phys. Chem. A, Vol. 107, No. 47, 2003 10059
R1; k2,0 ) (9.0 ( 3.6) × 10-27 cm6 molecule-2 s-1, k2,∞
)
(2.6 ( 0.2) × 10-11 cm3 molecule-1 s-1, with Fcent ) 0.5 for
reaction R2. When all the data shown in Figure 3a,b were fitted,
the following falloff parameters were obtained: k1,0 ) (8.6 (
1.4) × 10-29 cm6 molecule-2 s-1, k1,∞ ) (8.7 ( 0.4) × 10-12
cm3 molecule-1 s-1, with Fcent ) 0.65 for reaction R1; k2,0
)
(6.2 ( 2.0) × 10-27 cm6 molecule-2 s-1, k2,∞ ) (3.0 ( 0.1) ×
10-11 cm3 molecule-1 s-1, with Fcent ) 0.5 for reaction R2.
The broadening factors Fcent were estimated as recommended
by Troe and co-workers18,19 (see below). Since the fitted low-
and high-pressure rate constants showed good agreement with
the latest recommended values,16,20,21 we adopted the following
recommended falloff parameters: k1,0 ) 9 × 10-29 cm6
molecule-2 s-1, k1,∞ ) 9 × 10-12 cm3 molecule-1 s-1, Fcent
)
,
0.65 for reaction R1;21 k2,0 ) 8 × 10-27 cm6 molecule-2 s-1
k2,∞ ) 3.0 × 10-11 cm3 molecule-1 s-1, Fcent ) 0.5 for reaction
R2.21 The falloff curves constructed with these parameters are
shown in Figure 3a,b.
Figure 4. Solid points: experimental rate constants for reaction (R1)
measured in this work at temperatures of 296, 165, 110, and 96 K
plotted as a function of total gas density. Open points: room-
temperature data obtained by other groups: Zellner84: Zellner and
Lorenz (M ) Ar);3 Klein84: Klein et al. (M ) Ar and synthetic air);4
Nielsen90: Nielsen et al. (M ) Ar);5 Kuo91: Kuo and Lee (M ) N2);7
Becker91: Becker et al. (M ) synthetic air);6 Fulle97: Fulle et al.
(M ) He).8 For T ) 296 K, the line shows the fit of all the experimental
data by the Troe expression.18,19 The lines for T ) 165, 110, and 96 K
are the extrapolations of the experimental data obtained at a single total
gas density to the high-pressure limit, using calculated low-pressure
limiting rate constants (see text).
Reaction R3 does not show any noticeable pressure depen-
dence; thus its rate constant is considered to be in its high-
pressure limit under the experimental conditions employed in
this work, for both low-temperature and room-temperature
measurements. Simple averaging of the data shown in Figure
3c yields the following rate constants: k3,∞ ) (3.0 ( 0.2) ×
10-11 cm3 molecule-1 s-1 (data from this work only) and
k3,∞ ) (3.1 ( 0.4) × 10-11 cm3 molecule-1 s-1 (this work and
the literature data). The latter value, which is in good agreement
with the recommendation by Atkinson,20 was adopted as k3,∞
and is shown as the solid line in Figure 3c.
taken into account to obtain the high-pressure limiting rate
constants at these temperatures. Note, however, that at low
temperatures (96-165 K) and gas number densities of (1.9-
3.5) × 1016 molecule cm-3, k1 is close to its high-pressure limit,
and the extrapolation of the experimental data to infinite pressure
is not very sensitive to the uncertainties of the falloff model.
Figure 4 shows the results of fitting each experimental low-
temperature data point for reaction R1 by eq 1. During fitting,
the calculated low-pressure rate constant k0 and the falloff central
broadening factor Fcent were fixed at the values described below,
and k∞ was allowed to float. In calculations of k0 at low
temperatures, we assumed that the average energy transferred
per collision - ∆E does not depend on temperature. Based on
the room-temperature âc value, the - ∆E value was estimated
to be equal to 115 cm-1, using the following expression: âc/(1
- âc1/2) ) - ∆E /(FEkT), where FE is the correction factor for
the energy dependence of the vibrational density of states at
the adduct dissociation threshold.22,31 Then the âc values for
For reaction R1, the strong-collision low-pressure rate
SC
constants k0 were calculated by using the Troe formulas for
barrierless association reactions,22,23 and the collision efficien-
cies, âc, were obtained as âc ) k0/k0SC. To calculate k0SC, we
used the vibrational frequencies and structural parameters of
the C2H4OH adducts reported by Villa et al.24 and the OH +
C2H4 f C2H4OH reaction enthalpy ∆H0° ) -123 kJ/mol that
was recently measured by Fulle et al.8 This experimental value
agrees well with the earlier experimental data25 and ab initio
calculations.9,24,26,27 For reaction R2, the k0SC values were also
estimated. In view of the lack of spectroscopic and thermody-
namic information on the C3H6OH adduct, only approximate
SC
estimates of k0 could be made. To get estimates of the
vibrational frequencies, the structure of C3H6OH, and the
enthalpy of reaction R2, we performed Gaussian-9828 quantum
chemical calculations for C3H6OH and also C2H4OH for
comparison, using the CBS-QB3 compound method developed
by Montgomery et al.29,30 For C2H4OH, our calculations resulted
in vibrational frequencies and structures similar to those reported
by Villa et al.24 The reaction enthalpy was calculated as -113
kJ/mol at 0 K, showing a reasonable agreement with the
experimental value. As expected, the CBS-QB3 calculations for
reaction R2 gave essentially the same reaction enthalpy as for
reaction R1, which encouraged us to use the experimental ∆H0°,
obtained for the OH + C2H4 f C2H4OH reaction,8 for
lower temperatures were calculated for - ∆E ) 115 cm-1
The central broadening factor Fcent was represented as a product
of “strong-collision” and “weak-collision” factors: Fcent
.
)
SC
WC 18,19
SC
Fcent
F
.
The Fcent factor was estimated as recom-
cent
mended by Troe,18 with the vibrational frequencies of the
transition state taken from ab initio calculations by Villa et al.24
WC
The weak-collision broadening factor Fcent was obtained by
using the expression log Fcent ) 0.14 log âc.19 The falloff
WC
parameters for reaction R1 are shown in Table 5.
The resulting high-pressure rate constants for reactions R1-
R3 are plotted as a function of temperature in Figure 5. The
error bars for k1,∞ include the systematic error, in addition to
the statistical error. The systematic error arises from the
uncertainty of the extrapolation of the kinetic data to the high-
pressure limit, which is dominated by the uncertainty in the
calculated k1,0 values. Under a rather conservative assumption
that the calculated k1,0 values are accurate to a factor of 2, we
estimated the systematic error as the range of the k1,∞ variation
when the low-pressure rate constant was varied from 0.5k1,0 to
2k1,0. Then the combined uncertainty that includes the systematic
SC
calculations of k0 for reaction R2. It was found that, for
reaction R2, the falloff effects, although important at room
temperature, are essentially negligible under the low-temperature
conditions of the Laval nozzle supersonic expansions employed
in our experiments. That is, the rate constants obtained at T )
96-165 K and at total gas densities of (1.9-3.5) × 1016
molecule cm-3 (see Tables 2-4) are at or very close to the
high-pressure limit.
For reaction R1 the situation is more complicated. The falloff
effects are important even at low temperatures and need to be

10060 J. Phys. Chem. A, Vol. 107, No. 47, 2003
Vakhtin et al.
TABLE 5: Falloff Parameters for the OH + C2H4 (+ N2) f C2H4OH (+ N2) Reaction
k0SC,a cm6 molecule-2 s-1
âc
Fcent
Fcent
Fcent
k0, cm6 molecule-2 s-1
k∞, cm3 molecule-1 s-1
SC
WC
T, K
296
165
110
96
3.7 × 10-28
2.9 × 10-27
1.2 × 10-26
2.0 × 10-26
0.24
0.36
0.46
0.49
0.79
0.93
1.0
0.82
0.65
0.81
0.90
0.90
9.0 × 10-29
1.0 × 10-27
5.7 × 10-27
9.8 × 10-27
9.0 × 10-12
1.1 × 10-11
2.1 × 10-11
2.4 × 10-11
0.87
0.90
0.90
1.0
a Calculated by the Troe method.22,23
of T ) 200-300 K. For higher temperatures (T ) 290-525
K), the rate constant k1,∞ ) 9 × 10-12(T/298)-1.1 cm3 molecule-1
s-1 with a slight negative temperature dependence is recom-
mended by Atkinson.20,35 The latter expression extrapolated
down to T ) 90 K describes the experimental low-temperature
data reasonably well, overestimating k1,∞ by a factor of ≈1.5 at
T ) 100 K. The IUPAC21 and NASA16 evaluations significantly
underestimate k1,∞ at low temperatures.
For reaction R2, IUPAC evaluation21 recommends a temper-
ature-independent value of 3.0 × 10-11 cm3 molecule-1 s-1
(T ) 200-300 K), while for higher temperatures (T ) 290-
525 K) the following rate constant is suggested by Atkinson:20
k2,∞ ) 2.8 × 10-11(T/298)-1.3 cm3 molecule-1 s-1. Again, the
extrapolated higher temperature expression20 is the most ap-
propriate. The IUPAC evaluation21 underestimates k2,∞ at low
temperatures, while the earlier evaluations by Atkinson33 and
Tsang,34 when extrapolated down to T ) 90 K, yield very high
rate constants that are not physically reasonable.
For reaction R3, the available reviews by Warnatz32 and
Atkinson33 recommend the Arrhenius expression with a negative
activation energy of about -3.8 kJ/mol (-0.9 kcal/mol), which
is obviously inadequate for extrapolation to low temperature.
Figure 5. High-pressure rate constants of reactions R1, R2, and R3
plotted as a function of temperature. Filled points are the results of the
present measurements. Open triangles in (a) are the experimental high-
pressure rate constants reported by Fulle et al.8 Open circles and dash-
dot line in (c) are the low-temperature data for reaction R3 obtained in
the CRESU apparatus.15 Thick solid lines show the fits of the data
obtained in this work by the empirical expression k ) A(T/300)n (see
eqs 3-5). Thin lines represent the recommended high-temperature rate
constants: Warnatz84, Warnatz;32 Atkinson85, Atkinson;33 Tsang91,
Tsang;34 Atkinson97, Atkinson;20 DeMore97, DeMore et al.;16 Atkin-
son99, Atkinson et al.21 Dashed lines show the extrapolations of the
recommended high-temperature rate constants to low temperatures.
The negative temperature dependence of the rate constants
for reactions of OH radical with alkenes has been a matter of
extensive discussions.24,33,36-38 Some of the explanations involve
an assumption of the formation of an intermediate weakly bound
complex36,38 followed by competing forward and backward
dissociation of the complex.39-41 Villa et al.24 applied variational
transition state theory on the calculated potential energy surface
for the OH + C2H4 reaction and managed to reproduce the
experimental negative temperature dependence of k1 without
any assumptions about the intermediate complex formation. It
could be also possible that, at low temperatures, the reaction
rate is controlled by adiabatic capture on the attractive part of
the barrierless potential energy surface that is determined by
long-range electrostatic interactions.37 As the temperature is
lowered, the inter-reagent distance, corresponding to the transi-
tion state, increases, until eventually the reaction rate is
and statistical contributions was calculated.17 The three rate
constants each show an apparent negative temperature depen-
dence. For reactions R2 and R3, the rate constants measured in
this work agree well with our earlier results1 and the CRESU
low-temperature data set (for reaction R3).15 Thick solid lines
in Figure 5 represent the results of the 1/σ2-weighted fitting of
the present data together with the data from the previous work1
by the empirical expression k ) A(T/300)n used in the IUPAC21
and NASA16 evaluations, with two fitting parameters A and n.
The temperature dependence of the high-pressure rate constants
of reactions R1-R3 can be expressed as follows (for T ) 96-
296 K):
2
determined by the capture.37 For reaction of a Π dipole with
1
a Σ quadrupole, for moderately low temperatures, adiabatic
k1,∞ ) (8.7 ( 0.7) × 10-12(T/300)(-0.85(0.11)
capture theory predicts rate constants independent of temper-
ature.37,42,43 The experimental k1,∞, k2,∞, and k3,∞ each show a
trend of increasing value with decreasing temperature; however,
there are signs of leveling-off at the lowest temperatures,15 which
could indicate approaching the capture limit.37
Fulle et al.8 performed measurements of k1 at very high
pressures (total gas densities of He up to 1021 molecule cm-3).
They succeeded in approaching high-pressure conditions for this
reaction for temperatures as high as 800 K. Their data show
essentially no temperature dependence of k1,∞ for T ) 300-
800 K. These results disagree with many earlier measurements
that show a negative temperature dependence for k1,∞. In view
of the experiments by Fulle et al.,8 it could be argued that the
apparent negative temperature dependence of k1,∞ is the result
of improper extrapolation of the data, obtained in the intermedi-
ate pressure range, to the high-pressure limit. However, this
cm3 molecule-1 s-1 (3)
k2,∞ ) (2.95 ( 0.10) × 10-11(T/300)(-1.06(0.13)
cm3 molecule-1 s-1 (4)
k3,∞ ) (3.02 ( 0.15) × 10-11(T/300)(-1.44(0.10)
cm3 molecule-1 s-1 (5)
The literature data for reactions R1-R3, represented by the
evaluated rate constants from the reviews,16,20,21,32-35 are also
presented in Figure 5. For reaction R1, DeMore et al. (NASA
evaluation)16 and Atkinson et al. (IUPAC evaluation)21 recom-
mend temperature-independent values of 8.8 × 10-12 and 9 ×
10-12 cm3 molecule-1 s-1, respectively, for the temperature range

Low-Temperature Kinetics of Reactions
J. Phys. Chem. A, Vol. 107, No. 47, 2003 10061
Figure 7. Pressure dependence of k1 calculated for T ) 110 K with
the falloff parameters obtained in this work for M ) N2 (solid line)
and with those used in the photochemical model of Saturn’s atmosphere
by Moses et al.46 (dashed line). The shaded area represents the gas
density range that is relevant to Saturn’s stratosphere.
Figure 6. Low-pressure limiting rate constant for reaction R1. Filled
circles show k1,0 calculated in this work. Filled triangles and dashed
line are the experimental k1,0 obtained by Fulle et al.8 Solid lines, marked
as k0SC, are the strong-collision rate constants calculated in this work
by the Troe method22,23 for M ) N2 and M ) He. Also shown are the
temperature dependence of k1,0, recommended for T ) 200-300 K by
DeMore et al.16 (solid line) and its extrapolation to low temperatures
(dashed line) that is used in the photochemical model of Saturn’s
atmosphere by Moses et al.46
the most abundant gas in the Saturn’s atmosphere is hydrogen,
it would be more appropriate to use k1,0 for M ) H2 to construct
the falloff curve. Our estimates show that k1,0 for M ) H2 will
be about 60% larger than k1,0 for M ) N2, thus making the
difference between the falloff curve based on the experimental
data and that used in the photochemical model46 even more
dramatic.
argument can hardly be applied to reactions R2 and R3, which
should be at or close to the high-pressure limit at room
temperature and moderately elevated temperatures, within the
range of total pressures typically used in experimental kinetic
studies. The available experimental data on reactions R2 and
Although it is difficult to predict the detailed impact of the
new low-temperature experimental rate constant for reaction R1
on the Saturn atmospheric models, rough estimates can be made.
According to the photochemical model by Moses et al.,46 in
Saturn’s stratosphere, about 96% of the water that is photodis-
sociated into H and OH efficiently recycles (mostly through
the OH + H2 reaction). The remaining 4% of photochemical
loss of water results in permanent conversion of H2O into CO
and CO2 (70%) and condensation (30%). The most important
primary processes that are responsible for the conversion of
water to carbon oxides are the OH + C2H2 and OH + C2H4
reactions. In the calculated reaction rate profiles,46 the rate of
OH + C2H2 is about an order of magnitude higher than that of
the OH + C2H4 reaction. However, if the experimental low-
temperature rate constant for the OH + C2H4 reaction were used,
the two reaction rates would be approximately the same. This
would probably lead to about a 2-fold increase in the overall
rate of permanent photochemical conversion of H2O to CO and
CO2 and would therefore affect the calculated balance of
conversion/condensation of water. This example shows the
importance of direct kinetic measurements at low temperatures
for adequate photochemical modeling of planetary atmospheres.
R3 support a negative temperature dependence of k2,∞ and
3,44,45
k3,∞
.
It seems that it would be valuable to have further
theoretical and experimental studies of the kinetics of the
reactions of OH radical with alkenes that may involve measure-
ments under extreme conditions including very low temperatures
and very high pressures.
Applications to Photochemical Modeling of Saturn’s
Atmosphere. In Saturn’s atmosphere, reactions of the OH
radical with unsaturated hydrocarbons play the key role in
conversion of water, introduced mostly by comets and meteors,
to molecules containing C-O bonds, ultimately CO and CO2.46
According to the model by Moses et al.,46 the two most
important reactions following dissociation of H2O by photolysis
are OH + C2H2 and OH + C2H4. In view of the lack of
experimental data, the most straightforward way to obtain
estimates for low-temperature rate constants is extrapolation of
the literature high-temperature rate constants to the temperature
and pressure range that are important for Saturn’s stratosphere.
In many cases, however, these extrapolations lead to significant
errors.47 To estimate the low-temperature rate constants of the
OH + C2H4 reaction, Moses et al.46 extrapolated the expressions
for k1,∞ and k1,0 evaluated by DeMore et al.48 Thus, k1,∞ was
Acknowledgment. The support of this research by the
National Aeronautics and Space Administration (Grants NAG5-
8923 and NAG5-13339) is gratefully acknowledged.
considered temperature-independent and equal to k1,∞
)
8.79 × 10-12 cm3 molecule-1 s-1 48
.
For the low-pressure rate
constant, the following expression was adopted: 9.59 × 10-27
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