Pressure dependence and kinetic isotope effects in the absolute rate constant for methoxy radical reacting with NO2

Article abstract of DOI:10.1002/kin.20865

We have investigated the kinetics for the reaction CH₃O ^? + NO₂ in N₂ bath gas. The rate constants are well-fit by the Troe expression over the temperature (250-335 K) and pressure range (30-700 Torr) investigated. The termolecular rate constant is given by k_1a⁰=4.29_-0.37 ^+0.40×10^-29T/298^{-(1.65±1.11)} cm⁶ molecule^-2 s^-1, and the rate constant at the high-pressure limit is given by k_1a^∞=(1. 95±0.03)×10^-11T/298^{-(1.13±0.18)} cm³ molecule^-1 s^-1. We also studied the kinetics of the reaction of CD₃O^? + NO₂ as a function of temperature and pressure under similar conditions as those for CH₃O? + NO₂. The resulting low- and high-pressure limiting rate constants are k_2a⁰=9.97_-0.91 ^+1.00×10^-29T/298^{-(4.79±0.92)} cm⁶ molecule^-2 s^-1 and k_2a ^∞=(1.91±0.02)×10^-11T/298 ^{-(1.11±0.09)} cm³ molecule^-1 s ^-1, respectively. The rate constants for the two isotopologues track each other closely as the high-pressure limit is approached. The present results agree with most previous results at 295 K over a range of pressures, but there is substantial disagreement about the temperature dependence.

Full text of DOI:10.1002/kin.20865

Pressure Dependence and
Kinetic Isotope Effects in
the Absolute Rate Constant
for Methoxy Radical
Reacting with NO2
JIAJUE CHAI, THEODORE S. DIBBLE
Department of Chemistry, State University of New York, College of Environmental Science and Forestry, Syracuse,
NY 13210
Received 19 February 2014; revised 27 April 2014; 7 May 2014; accepted 9 May 2014
DOI 10.1002/kin.20865
Published online 12 July 2014 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: We have investigated the kinetics for the reaction CH3O• + NO2 in N2 bath gas. The
rate constants are well-fit by the Troe expression over the temperature (250–335 K) and pressure
range (30–700 Torr) investigated. The termolecular rate constant is given by k01a = 4.29−+00..4307
×
10−29 (T/298)−(1.65 1.11) cm6 molecule−2 −1, and the rate constant at the high-pressure
s
(1.13 0.18)
limit is given by k1∞a = (1.95 0.03) × 10−11 (T/298)−
cm3 molecule−1 −1. We also
s
studied the kinetics of the reaction of CD3O• + NO2 as a function of temperature and pressure
under similar conditions as those for CH3O• + NO2. The resulting low- and high-pressure
limiting rate constants are k20a = 9.97−+01..9010 × 10−29 (T/298)−(4.79 0.92) cm6 molecule−2 s−1
and k2∞a = (1.91 0.02) × 10−11 (T/298)−(1.11 0.09) cm3 molecule−1 s−1, respectively. The rate
constants for the two isotopologues track each other closely as the high-pressure limit is
approached. The present results agree with most previous results at 295 K over a raꢀCnge of
pressures, but there is substantial disagreement about the temperature dependence.
Wiley Periodicals, Inc. Int J Chem Kinet 46: 501–511, 2014
2014
and atmospheric chemistry [2]. In the atmosphere, it
is primarily produced from the reaction transferring an
oxygen atom from methyl peroxy radical (CH3O2 ) to
INTRODUCTION
•
Methoxy radical (CH3O•) is an intermediate in the ox-
idation of methane for both combustion chemistry [1]
NO, forming NO2 as a coproduct. The major atmo-
spheric fate of methoxy radical is reaction with O2;
however, reaction with NO2 may be important in a
power plant plume [3]. The methoxy radical (CH3O•)
is the prototype for all alkoxy radicals, whose fates
greatly impact ozone formation and gas-particle parti-
tioning of the eventual stable products of oxidation
of volatile organic compounds [4,5]. Similarly, the
Correspondence to: Theodore S. Dibble; e-mail: tsdibble@
esf.edu.
Contract grant sponsor: National Science Foundation.
Contract grant number: ATG-0937626.
Supporting Information is available in the online issue at
www.wileyonlinelibrary.com.
C
ꢀ
2014 Wiley Periodicals, Inc.

502
CHAI AND DIBBLE
methoxy + NO2 reaction (R1a)
k1a
CH3O + NO2(+M) −→ CH3ONO2
(R1a)
(R1b)
k1b
−→ HCHO + HONO(minor)
is the prototype for kinetic and mechanistic studies of
other RO• + NO2 reactions. Early relative rate studies
of the methoxy + O2 reaction had employed (R1) as
the reference reaction [6–8]. One article recently pub-
lished by our group reports similar relative rate studies
together with the absolute rate measurement of (R1)
(and CD3O• + NO2) [9].
Figure 1 Simplified energy diagram for reaction CH3O• +
NO2.
Direct kinetic investigations of (R1) using laser-
induced fluorescence (LIF) detection of CH3O• have
been carried out previously at pressures ranging from
0.6 to 700 Torr over the temperature range 220–473 K,
with Ar, CF4, N2, or He as bath gases. The discharge-
flow method was employed to produce CH3O• for low-
pressure studies by McCaulley et al. (0.6–5 Torr) [10]
and Biggs et al. (1–10 Torr) [11]. Pulsed laser photol-
ysis was used to generate CH3O• for higher-pressure
studies by Frost and Smith (6–125 Torr) [12,13], Wol-
lenhaupt and Crowley (10–200 Torr) [14], Mart´ınez
et al. (50–600 Torr) [15], and ourselves (700 Torr
at 295 K) [9]. All of these studies showed similar
pressure-dependent behavior of k1, except Mart´ınez
et al. [15], whose values are ꢀ30% larger than the
others at all pressures (at room temperature). Reaction
(R1a) proceeds via formation of an activated methyl-
nitrate (CH3ONO2) intermediate, which is quenched
by the bath gas in competition with dissociation to re-
actants. Mart´ınez et al. [15] used He as a bath gas,
and, given that He is expected to be less effective in
deactivating the energized CH3ONO2 than Ar and CF4
[13,16–18], the rate constants determined by Mart´ınez
et al. [15] would be expected to smaller than those de-
termined in the other studies at the same pressure and
temperature. Thus, the results of Mart´ınez et al. [15]
are an anomaly. Also, among the two studies with the
largest pressure range, Mart´ınez et al. [15] showed
a much larger temperature dependence of k0 and a
slightly smaller temperature dependence of kꢁ than
Wollenhaupt and Crowley [14]. It is noteworthy that
(R1a) appears not to have reached the high-pressure
limit at 200 Torr of Ar or 600 Torr of He. There have
been no direct kinetic measurements of (R1) in the
presence of N2 bath gas except at 50 Torr, so previous
experiments did not mimic atmospheric conditions. For
these reasons, it is valuable to reinvestigate k1 at pres-
sures closer to 1 atm and especially to use N2 as a bath
gas, since it is more representative of air than Ar, CF4,
or He.
The reaction between CH3O• and NO2 is known
to proceed via two channels—recombination (R1a)
producing the methyl nitrate (CH3ONO2) and dispro-
portionation (R1b) yielding formaldehyde and nitrous
acid. The disproportionation is found to be a minor
process, and only plays an important role at rather
low pressures (<1 Torr) [10,11]. McCaulley et al. re-
ported a rate constant (independent of pressure) of
ꢀ
ꢁ
ꢂꢃ
+17.3
−2.7
9.6
× 10−12 exp − 1150+−155700 cm3 molecule−1
s−1 for the disproportionation channel [10].
There have been several theoretical investigations
of the energetics and mechanisms of (R1a) and (R1b)
[19–22]. A composite of these energetics is shown
in Fig. 1. Of these studies, only Lesar et al. [20]
found the disproportionation barrier to be higher (by
2–6 kcal/mol depending on levels of theory) than the
reactant energy, yet this seems more consistent than
other reports with the pressure-independent rate con-
stant (k1b) reported by McCaulley et al. [10]. While
all the three theoretical studies were able to find the
transition state for the disproportionation of methyl
nitrate, only Pan et al. [19] reported trying (without
success) to find a transition state for a direct hydrogen
atom-abstraction mechanism for (R1b).
The reaction of methoxy radical with NO2 is a
radical–radical recombination reaction and is anal-
ogous to the very important reaction OH + NO2
[23]. Barker and co-workers took advantage of known
pressure-dependent rate constants at 297 K for various
NO2 addition reactions to constrain Rice–Ramsperger–
Kassel–Marcus (RRKM)/Master Equation (ME) simu-
lations of these reactions [24,25]. This enabled them to
estimate the collisional energy transfer parameters (α)
by fitting to the falloff curves. Although the fitted rate
constants agreed well with the experimental values,
Barker and co-workers concluded that the accuracy of
fitting the collisional energy transfer parameter is sub-
ject to large uncertainties in assumptions for treating
the transition state, which is not a well-defined saddle
point on the potential energy surface. They suggested
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

ABSOLUTE RATE CONSTANT FOR METHOXY RADICAL REACTING WITH NO2
503
that an experimental reinvestigation of the kinetics
of these reactions in extended pressure ranges would
enable validation or refinement of their fitted values
of α.
In this work, we present the experimental kinetics
of (R1) in the temperature range of 250–335 K and
pressure range of 30–700 Torr of N2. We also investi-
gated the kinetics of the perdeuterated isotopologue of
CH3O•, i.e., CD3O• + NO2 (R2). This offers a check
on the kinetic results of (R1) and may facilitate fur-
ther investigations of collisional energy transfer in the
methoxy + NO2 reaction:
EX100H) possessing a pulse energy of 10 mJ and a
repetition rate of 2 Hz. The resulting methoxy radicals
were probed at ꢀ293 nm (0.1 mJ/pulse) by frequency-
doubled (Inrad Autotracker III) narrow band emission
from dye laser (Lambda Physik FL3002). The dye laser
repetition rate was 2 Hz.
The probe and photolysis laser beams counter-
propagate collinearly through the reactor. The size of
the photolysis laser beam was adjusted to be three
times that of the probe laser beam (3 mm × 6 mm).
ꢁ
ꢂ
ꢁ
ꢂ
2
ꢁ
2
ꢁꢁ
˜
˜
The A A1, v 3 = 4 ← X E, v = 0 transition at
3
293.06 nm (CH3O•) and 293.35 nm (CD3O•) were used
for probing the methoxy radicals [31,32]. Emission
from radicals excited by the probe beam was detected
orthogonal to the laser beams by a photomultiplier tube
(PMT) mounted over a window of the cell. Prior to
reaching the PMT, the emission was collimated us-
ing two f = 10 cm convex lenses and passed through
a long-pass filter (>345 nm). The PMT signal was
transmitted to a boxcar averager and then to a com-
puter data acquisition system. The gate (25 ns) of the
boxcar averager was opened 50 ns after the initial rise
of the fluorescence pulse. The fluorescence intensity
was normalized to the energy of the probe laser for
each laser shot. 100–120 laser shots were averaged for
each delay time. A digital delay generator was used to
control the delay time between the two laser pulses.
The shortest delay time was 5 μs, and delay times ex-
tended to 30–260 μs depending on the experimental
conditions. The change of fluorescence intensity as a
function of delay time was used to determine the rate
of disappearance of methoxy radicals.
k2a
CD3 O + NO2(+M) −→ CD3ONO2
(R2a)
(R2b)
k2b
−→ DCDO + DONO(minor)
EXPERIMENTAL
Many of the experimental details appear elsewhere [9].
Methyl nitrites (both CH3ONO and CD3ONO) were
synthesized from the reaction of methyl alcohol with
a saturated aqueous NaNO2 solution upon addition of
concentrated sulfuric acid at 0°C [26]. The gaseous
products were passed over NaOH solution and anhy-
drous CaCl2 before being collected in a dry-ice trap.
The isolated product was purified by freeze–pump–
thaw cycles, resulting in a pale yellow solid, which was
stored at −196°C until it was used. The vapor of the
purified methyl nitrite was characterized by FTIR [27]
to verify the absence of residual alcohol and ultraviolet
(UV) spectroscopy to verify its identity [28]. A 10-L
blackened glass bulb was filled with approximately 3
Torr of methyl nitrite, which was then diluted by N2
(Haun Welding Supply, Syracuse, NY, USA; 99.999%)
to a total pressure of 1000 Torr. NO2 was produced by
mixing NO (American Gas Group, Toledo, OH, USA;
>99.5%) with excess of O2 (MG Welding Products,
Menomenee, WI, USA; 99.999%), followed by purifi-
cation by free–pump–thaw distillation at −196°C until
a pure white solid was obtained. FTIR and UV–visible
spectroscopy were used to verify the identity and purity
of the NO2. NO2 was diluted with N2 to a mole fraction
of about 0.02 in a second glass bulb. Concentrations of
methyl nitrite and NO2 in the bulbs were determined
using UV–visible absorption cross sections [29,30] at
each of six wavelengths in the range of 310–370 and
380–440 nm, respectively, with an uncertainty (2σ) of
5%.
The LIF cell is made of a jacketed and insulated
1.3-L PyrexTM tube. The main body is roughly 28 cm
long by 6 cm diameter with two glass side arms. The
end of each arm has a quartz window attached at Brew-
ster’s angle. The temperature inside the LIF cell could
be controlled between 250 and 335 K. The temper-
ature in the cell was measured in the LIF region at
each pressure and temperature with a calibrated ther-
mocouple thermometer. The flow rate of each gas was
regulated by pressure-based Mass-FLOꢀR controllers.
The reaction pressure in the cell was measured, close
to where fluorescence was being imaged on the PMT,
by absolute pressure transducers.
For a typical concentration of methyl nitrite
(ꢀ3 × 1015 molecule cm−3) and photolysis laser flu-
ence (ꢀ17 mJ pulse−1 cm−2), one pulse of the pho-
tolysis laser can produce approximately 2 × 1013
molecule cm−3 methoxy radicals (CH3O• or CD3O•)
at 295 K. This estimate is based on the cross section
of CH3ONO (ꢀ 3 × 10−19 cm−2) [14], the quantum
yield for the formation of CH3O• (ꢀ1) at the photolysis
wavelength 351 nm [8,33]. NO2 concentrations were
The LIF apparatus is shown elsewhere [9]. Methoxy
radicals were generated by photolyzing methylnitrite
at 351 nm with a XeF excimer laser (GAM Laser,
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

504
CHAI AND DIBBLE
(0.9–6) × 1015 molecule cm−3, sufficient to ensure
pseudo–first-order conditions. Pseudo–first-order rate
constants were measured over the range 250–335 K
and 30–700 Torr.
×
RESULTS AND DISCUSSION
Under pseudo–first-order condition, the temporal pro-
file for the disappearance of methoxy radicals should
be well expressed by a single-exponential decay, e.g.,
for CH3O•:
ꢄ
ꢅ
[CH3O]t
[CH3O]o
ln
= −k1ꢁ t
(E1)
Delay time μ
where kꢁ is the pseudo–first-order rate constant for loss
of the methoxy radical. Under pseudo–first-order con-
ditions, the methoxy radical predominantly reacts with
NO2; other loss processes include side reactions and
diffusion. Hence, kꢁ can be described by
Figure 2 Typical linear decays of ln(LIF intensity) as a
function of the delay time for CH3O• + NO2 at total pressure
700 Torr and 250 K. NO2 concentrations in molecule cm−3
are 6.3 × 1014, 1.19 × 1015, 1.89 × 1015, 2.73 × 1015, and
3.52 × 1015
.
k1ꢁ = k1 [NO2] + kother loss
(E2)
The concentration of NO2 was treated carefully due
to the dimerization of NO2 into N2O4, especially at low
temperatures. The recommended equilibrium constant
[30] as a function of (E3), was used to correct the
concentration of NO2, and all the data shown below
reflect this correction:
[N2O4]
K2NO →N O
=
[NO2]2
2
2
4
ꢄ
ꢅ
6643
= 5.9 × 10−29exp
cm−3
(E3)
T
Figure 3 Plot of kꢁ for CH3O• + NO2 versus [NO2] at
250 K under different pressures. Error bars are 2σ of the
fitted slope of ln(intensity) versus time.
As indicated from Eq. (E3), the extent of the conver-
sion of NO2 to N2O4 increases as the temperature gets
lower and the initial NO2 concentration increases. The
highest dimerization fraction is ꢀ14% (for the highest
NO2 concentration at 250 K). The modest size of this
correction ensures that dimerization causes minimal
error in the determination of k1 and k2.
Figure 2 shows typical plots of the logarithm of
LIF intensity versus delay time between the photoly-
sis laser pulse and probe laser pulse at several NO2
concentrations. The pseudo–first-order rate constants,
kꢁ, for loss of CH3O• were obtained from the absolute
value of the slope of the linear least squares fit to the
data at each [NO2]. Values of kꢁ for each experimental
condition are listed in Tables S1 and S2 in the Support-
ing Information. Figure 3 displays kꢁ versus [NO2] at
five different total pressures at 250 K, along with linear
least squares fits to the data. The slopes of these fits
correspond to the effective bimolecular reaction rate
constants (k1) for the specified temperatures and total
pressures.
The data shown in Figs. 1 and 2 exhibit the high
linearity expected from pseudo–first-order conditions.
The nonzero y intercepts in Fig. 3 can be interpreted
as the sum of the loss rates of CH3O• for all loss pro-
cesses other than reaction with NO2. The y intercepts
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

ABSOLUTE RATE CONSTANT FOR METHOXY RADICAL REACTING WITH NO2
505
in Fig. 3 tend to increase (albeit noisily) with increas-
ing pressure (from 2700 s−1 at 50 Torr to 5300 s−1
at 700 Torr). We do not have a clear explanation for
this effect. Contributions to the intercept are discussed
below.
is only ꢀ0.5% of the volume of the cell) [9]. Losses
of CH3O due to side reactions with other species are
modest, despite often large rate constants for reactions
of (noted here at 298 K): CH3ONO (k = 4.4 × 10−13
cm3 molecule−1
s
−1) [34], O (k = 2.5 × 10−11 cm3
NO is produced by photolysis of CH3ONO and
NO2 with yields of about 0.7% and 1%, respectively.
The values of the rate constants for CH3O + NO and
CH3O + NO2 are very similar, and their ratio has rather
little pressure or temperature dependence [30]. The ra-
tio of these rate constants deviates from unity the most
at 250 K and 30 Torr, where it reaches ꢀ1.4. We con-
clude, therefore, that NO arising from NO2 photolysis
in a single laser shot contributes a negligible error to
the observed rate of loss of CH3O. NO produced from
CH3ONO photolysis in a single laser shot contributes
only modestly to the intercept under the pseudo–first
-order conditions employed here ([NO]0 = [CH3O]0
and k(CH3O + NO) = 3.6 × 10−11 cm3 molecule−1
molecule−1
s
−1) [35], and CH3O• itself (k = (1–4) ×
10−11 cm3 molecule−1 s−1) [36–38]. The rate constants
for CH3O• reacting with CH3ONO2 has only been re-
ported at 750–1000 K (as 5 × 10−12 cm3 molecule−1
s
−1) [39].
Measured absolute rate constants k1 and k2 at dif-
ferent temperatures and pressures over the range 250–
335 K and 30–700 Torr are listed in Table I. As dis-
cussed previously, two channels are known to exist for
the reaction CH3O• + NO2: recombination and dis-
proportionation. Therefore, the measured absolute rate
constants k1 and k2 are the sum of both channels. By
comparing the value of k1b reported by the Arrhenius
expression of McCaulley et al. [10] with the overall rate
constant k1 measured from our experiments, we find the
contribution of k1b to k1 is quite modest. The ratio k1b/k1
increases with increasing temperature and decreasing
pressure, and hence k1b/k1 ranges from ꢀ0.4% at 250 K
and 700 Torr to ꢀ6% at 333 K and 30 Torr. Therefore,
we approximate k1a as equal to the measured k1, so
that all data are included when calculating the falloff
curve. There is no available study of k2b for CD3O•
+ NO2; however, the reaction mechanism is expected
to be similar to the CH3O• + NO2 reaction. Thus we
assumed that the disproportionation channel for (R2)
could also be neglected, i.e., k2a = k2. The effects of
neglecting channel b will be discussed in more detail
below.
s
−1 at 700 Torr and 295 K) [30]. Accumulation of NO
from photolysis of both CH3ONO and NO2 from mul-
tiple laser shots potentially contributes to the slope of
plots of kꢁ versus [NO2], due to the fact that residence
times in the reactor (ꢀ20 s) are much longer than the
0.5 s interval between laser shots. This does not seem
to be the case, as reducing the fluence of photolysis
laser (by 40% at 295 K and 30 Torr) as well as varying
the total gas flow rate while holding the total pres-
sure constant was not found to affect the measured rate
constants by more than 2%. This suggests that accumu-
lation of photolytically produced NO does not occur to
a significant extent, probably because of diffusion of
the NO out of the volume of the photolysis laser (which
Table I Pressure-Dependent Rate Constants k1 and k2 at Different Temperaturesa
k1 (× 10−11 cm3 molecule s−1
)
Pressure (Torr)
250 K
265 K
278 K
295 K
316 K
333 K
700
500
215
100
50
2.16 0.12
2.00 0.11
–
1.54 0.08
1.38 0.08
1.28 0.07
2.01 0.12
1.89 0.10
1.62 0.09
–
1.23 0.07
1.11 0.06
1.89 0.10
1.77 0.09
–
1.36 0.07
1.15 0.06
0.97 0.05
1.70 0.09
1.63 0.09
1.52 0.09
1.23 0.07
1.08 0.06
0.90 0.05
1.62 0.08
1.54 0.08
1.32 0.07
1.17 0.06
1.00 0.05
0.81 0.04
1.47 0.08
1.44 0.08
1.15 0.06
1.04 0.06
0.89 0.05
0.48 0.03
30
k2 (× 10−11 cm3 molecule s−1
)
Pressure (Torr)
250 K
277 K
294 K
319 K
335 K
700
500
215
100
50
2.18 0.13
2.14 0.12
2.06 0.11
1.91 0.10
1.83 0.10
1.72 0.09
1.93 0.10
1.84 0.10
–
1.60 0.08
1.52 0.08
1.40 0.07
1.75 0.10
1.71 0.09
1.53 0.08
1.45 0.08
1.24 0.07
1.15 0.06
1.65 0.09
1.55 0.08
–
1.26 0.07
1.15 0.06
0.98 0.05
1.53 0.08
1.43 0.08
1.29 0.07
1.19 0.06
1.07 0.06
0.86 0.05
30
aError bars represent 2σ statistical error propagated with 5% uncertainty (2σ) in [NO2] concentration determination.
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

506
CHAI AND DIBBLE
Figure 4 Falloff curve showing nonlinear fitting of second-order rate constant k1 measured for CH3O• + NO2 in this study to
Eq. (E4). T = 250–333 K, P = 30–700 Torr. Error bars represent 2σ statistical error propagated with 5% uncertainty in [NO2]
concentration determination.
Figure 5 Falloff curve showing nonlinear fitting second-order rate constant k2 measured for CD3O• + NO2 in this study to
Eq. (E4). T = 250–335 K, P = 30–700 Torr. Error bars represent 2σ statistical error propagated with 5% uncertainty in [NO2]
concentration determination.
ꢄ
ꢅ−1
ꢆ
ꢆ
ꢇꢇ
We plot the pressure-dependent rate constants k1a
and k2a at all temperatures in Figs. 4 and 5, respectively.
The solid lines result from nonlinear fitting to falloff
curves, described by the Troe expression [17]:
2
k0 (T) [M]
k∞ (T)
p = 1 + log10
(E4)
where k0 is the termolecular rate constant in the low-
pressure limit and kꢁ is the bimolecular rate constant
in the high-pressure limit. Values of kꢁ and k0 are
ꢄ
ꢅ
k0 (T ) [M]
1 + k0 (T ) [M] /k∞ (T )
k ([M] , T ) =
Fcpent
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

ABSOLUTE RATE CONSTANT FOR METHOXY RADICAL REACTING WITH NO2
507
Table II High-Pressure and Low-Pressure Limiting Rate Constants Resulted from Fits of Our Data to the Troe
Expression (E4)
CH3O• + NO2
CD3O• + NO2
k0 (×10−29 cm−6
k
ꢁ(×10−11 cm−3
k0 (×10−29 cm−6
k
ꢁ(×10−11 cm−3
T (K)
molecule−2 s−1
)
molecule−1 s−1
)
T(K)
molecule−2 s−1
(24.2 4.02)
)
molecule−1 s−1
)
250
265
278
295
316
333
333a
(6.32 1.66)
(5.45 1.24)
(4.59 0.52)
(4.42 0.66)
(4.15 0.82)
(3.46 0.94)
(2.47 0.68)
(2.35 0.11)
(2.21 0.09)
(2.14 0.05)
(1.96 0.05)
(1.84 0.06)
(1.70 0.09)
(1.75 0.12)
250
(2.32 0.03)
277
294
319
335
(15.4 3.54)
(9.09 1.46)
(7.30 1.19)
(6.99 1.92)
(2.05 0.05)
(1.91 0.04)
(1.81 0.05)
(1.66 0.05)
Quoted errors are 2σ.
aFalloff curve fitting of pure recombination rate constant k1a, each data point being obtained by subtracting k1b (calculated by the Arrhenius
expression of McCaulley et al. [10]) from measured k1 at 333 K in this study.
presented in Table II. Fcent is a parameter that de-
scribes broadening of the falloff curve, which results
from the energy and angular momentum dependen-
cies of k [17,40]. A fixed value of Fcent equal to 0.6
is recommended by Troe in the range of 100–400 K
[18], and this recommendation is adopted by the NASA
Panel for Data Evaluation (although not by the IUPAC
Subcommittee for Gas Kinetic Data Evaluation, which
allows Fcent to vary when fitting experimental data).
Golden [41] pointed out that both the NASA and
IUPAC formulations are adequate to represent
pressure-dependent rate constant as long as the range
of temperature and/or pressure is not too wide. Wol-
lenhaupt and Crowley [14] attempted fitting their data
using (E4) by taking Fcent as a variable, and it was found
Figure 6 Temperature dependence of low-pressure limit
that Fcent was ꢀ0.6 and insensitive to temperature in
their temperature range (233–356 K).
rate constant k10a and k20a for CH3O• + NO2 and CH3O• +
NO2, respectively. Note that the x-axis is linear in log(T).
ꢆ
ꢇ−n
Disregarding the disproportionation channel is ex-
pected to negligibly affect the fitting of the falloff
curve. The largest effect of k1b on k1 occurs at 333 K,
where k1b/k1 is largest (ꢀ2–6%). For this purpose, we
computed k1b from the Arrhenius expression of Mc-
Caulley et al. [10] and subtracted that value from k1
to get k1a. This value of k1a was fitted to the Troe
equation (E4). The resulting parameters are listed in
Table II along with the values computed neglecting re-
action (R1b.) Accounting for k1b reduces k10 (333 K)
by 29%, but increases k1∞ (333 K) by only 3%. The
large uncertainty in k1b [10] and its limited effect on
k1 makes us unwilling to apply this correction to cal-
culating the parameters describing the temperature de-
pendence of k0 and kꢁ.
T
298
The fitting is based on the equation k0 = k2098K
×
.
Error bars are 2σ statistical error from nonlinear fitting.
or 335 K. The temperature dependence of kꢁ is much
smaller over the same temperature range, and only de-
creases by ꢀ20%. As is commonly done [14,15,30],
we fit the temperature dependencies of k0 and kꢁ
ꢁ
ꢂ−n
T
298
to power law expressions: k0 = k2098K
×
and
ꢁ
ꢂ
k∞ = k2∞98K
×
−m , respectively. Figures 6 and 7
T
298
show log–log plots of k versus temperature for k0
and kꢁ, respectively; each figure shows data for both
CH3O• and CD3O•.
A negative temperature dependence is expected for
recombination reactions, and such a temperature de-
pendence can be observed from Figs. 4 and 5, as well
as Tables I and II. k0 decreases by a factor of 2.6 (k10a)
or 3.5 (k20a) as the temperature is raised from 250 to 333
Linear fitting of log(k) versus log(T) leads to expres-
sions for k0 and kꢁ, which are shown in (E5)–(E8). The
intercept of each fit gives the corresponding low- and
high-pressure limiting rate constants at 298 K, whereas
slopes of each fit indicate the temperature-dependent
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

508
CHAI AND DIBBLE
k
k
∞
∞
Figure 7 Temperature∞dependence of high-pressure limit
rate constant k1∞a and k2a for CH3O• + NO2 and CD3O•
+ NO2, respectively. Note that the x-axis is linear in log(T).
Figure 8 Temperature-dependent KIE for k0 and kꢁ. Cited
errors are 2σ.
ꢆ
ꢇ−m
T
The fitting is based on the equation k∞ = k2∞98K
×
.
298
Error bars are 2σ statistical error from nonlinear fitting.
are much smaller than those of the corresponding low-
pressure limiting rate constants. k2∞a is slightly larger
than k1∞a ; however, a t-test of the data in the figure
indicates no significant difference exist between k2∞a
and k1∞a . While k20a is consistently larger than k10a in the
temperature range in our study, the difference between
k20a and k10a decreases with increasing temperature. The
ratio of rate constants for two isotopologues, kH/kD, de-
fines the kinetic isotope effect (KIE). Values of KIE at
each temperature are presented in Table III and Fig. 8
for both k0 and kꢁ. As implied above, the KIE for k0
is quite temperature dependent, ranging from 0.26 to
0.57. However, as indicated in Fig. 8, uncertainties for
these values (20–40%) are large. Linear regression of
log(KIE0) versus log(T) leads to a slope of 3.2 1.7,
and the uncertainty is too large to conclude that a sig-
nificant temperature dependence exists in the KIE for
k0. By contrast, the KIE for kꢁ (1.01–1.04) is equal to
1.00 within the noise and shows no hint of any temper-
ature dependence. Similar temperature dependencies
of k0 and kꢁ have been observed for the reactions
CH3O•/CD3O• + NO [42].
factors n and m
+0.40
k10a = 4.29
× 10−29
−0.37
(T /298)−(1.65 1.11) cm6molecule−2s−1 (E5)
k1∞a = (1.95 0.03) × 10−11
(T /298)−(1.13 0.18) cm3molecule−2s−1 (E6)
+1.00
k20a = 9.97
× 10−29
−0.91
(T /298)−(4.79 0.92) cm6molecule−2s−1 (E7)
k2∞a = (1.91 0.02) × 10−11
(T /298)−(1.11 0.09) cm3molecule−2s−1 (E8)
Figure 6 illustrates that the extent of the temperature
dependence of k20a (n = 4.79 0.92) is greater than for
k10a (n = 1.65 1.11), whereas, as shown in Fig. 7, the
temperature dependencies of k1∞a and k2∞a (m = 1.13
0.18 and 1.11 0.09, respectively) are similar and both
The KIE for methoxy + NO2 can be interpreted us-
ing RRKM theory. The energy-dependent rate constant
Table III KIE Values (kH/kD) at Different Temperatures for k0 and kꢁ
T (K)
Value
250
278
295
316
333
KIE0
0.26 0.08
1.01 0.05
0.30 0.08
1.04 0.03
0.49 0.11
1.02 0.03
0.57 0.15
1.02 0.04
0.50 0.19
1.03 0.06
KIEꢁ
Cited errors are 2σ.
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

ABSOLUTE RATE CONSTANT FOR METHOXY RADICAL REACTING WITH NO2
509
for a unimolecular reaction can be expressed as
CH3ONO2*. This higher density of states may also
increase the rate constant for collisional deactivation
of CD3ONO2* over that for CH3ONO2*. These two
effects result in a larger probability of collisional de-
activation for CD3ONO2* than for CH3ONO2*. This
explains the difference of rate constants especially in
1 Gꢁ (E − E0)
k (E) =
(E9)
h
ρ (E)
where h is Planck’s constant, Gꢁ (E − E0) is the sum
of states of the transition state, and ρ (E) is the density
of states (number of states per energy interval) of the
reactant. Here, the reactant is the energized methyl-
nitrate molecule (CH3ONO2* or CD3ONO2*) formed
from methoxy + NO2, and the reaction is methylnitrate
dissociation back to methoxy + NO2. Since the dissoci-
ation of methylnitrate has no intrinsic barrier other than
the endothermicity of the dissociation reaction, there
is no well-defined saddle point. Instead, there exist
transition states (maxima in Gibbs free energy) whose
positions along the reaction coordinate (CH3O-NO2
distance) vary with energy. As the energized methyl-
nitrate molecules are formed in the thermal reaction
of methoxy + NO2, the energized molecules probably
mostly possess energies that are no more than a few
kBT above the energy of methoxy + NO2. The higher
mass of D than H lowers the frequencies of several vi-
brational modes of CD3ONO2, and so CD3ONO2 pos-
sesses a larger density of states than does CH3ONO2
at the same energy. At the same time, the sum of states
for the transition state does not change significantly,
because the most of the vibrational modes affected
by isotopic substitution have frequencies whose ener-
gies correspond to more than a few kBT. Following
(E9), this larger density of states for CD3ONO2 than
CH3ONO2 leads to a lower rate constant for dissoci-
ation back to methoxy + NO2 for CD3ONO2* than
ꢁ
ꢂ
the low-pressure limit k20a > k10a , shown in Fig. 6.
At the high-pressure limit, all the energized methyl-
nitrate molecules will be quenched rather than dissoci-
ating to reactants, and thus the first step, an association
of radicals to the energized complex, becomes the rate-
limiting step in (R1a) and (R2a). The rates of the as-
sociation step are expected to be very nearly the same
for both isotopologues, and this explains the similarity
of k1∞a and k2∞a at all temperatures.
Displayed in Table IV are the parameters (k0, n,
kꢁ, m) of the temperature-dependent falloff curves de-
rived in this study together with those from previous
investigations. We previously showed [9] that our rate
constants at 295 K coincide well with the results of
the two studies with Ar and N2 being the third body
gas [12,14], upon which the Jet Propulsion Laboratory
(JPL) evaluation is based.
As k0 is expected to differ with the types of third-
body molecule, we first make comparisons between
k10a (298K) in the same bath gas. With He as the third
body, the value of k10a (298K) from Mart´ınez et al. [15]
is ꢀ30% greater than that from McCaulley et al. [10],
but ꢀ30% smaller than that given by Biggs et al. [11].
Note that Mart´ınez et al.’s [15] result was based on
their own data along with the values from the two low-
pressure studies [10,11]. With Ar as the third body
gas, k10a (298K) from Wollenhaupt and Crowley [14]
Table IV Troe Parameters Resulting from Different Studies for the Methoxy + NO2 Reaction
Troe Parameters
Experimental Condition
k0 (298 K)
k
ꢁ(298 K)
P
(×10−29 cm6
(×10−11 cm3
Range
(Torr)
T Range
(K)
molecule−2 s−1
)
n
molecule−1 s−1
)
m
M
Reference
4.29 0.4
9.97 1.0
5.22 0.3
1.65 1.11
4.79 0.92
4.36 0.36
1.95 0.03
1.91 0.02
1.84 0.05
1.13 0.08
1.11 0.09
1.87 0.15
N2
N2
Ar
30–700
30–700
10–200
250–333 This work
250–335 This work (CD3O)
233–356 Wollenhaupt and
Crowley [14]
3.98 0.05
5.3
1.74 0.4
4.0 2.0
4.5 1.3
2.41 0.02
1.9
0.88 0.32
1.8
He
50–600
250–390 Mart´ınez et al. [15]
JPL [30]
220–473 McCaulley et al. [10]
2.68 0.8
5.30 0.2
9.00 1.9
5.20 1.9
11.00 3.0
He
He
Ar
He
CF4
0.6–4.0
1–10
6–100
30–100
30–125
1.4 0.1
1.9 0.3
2.1 0.6
2.0 0.5
298
295
295
295
Biggs et al. [11]
Frost and Smith [12]
Frost and Smith [12]
Frost and Smith [12]
Cited errors are 2σ.
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

510
CHAI AND DIBBLE
is ꢀ70% smaller than that was reported by Frost and
Smith [12], which can be primarily attributed to dif-
ferent value of Fcent (0.44) that Frost and Smith [12]
used in falloff curve fitting. Applying Fcent = 0.6 to
the fitting of Frost and Smith’s data [12] to the Troe
expression (E4) yields a similar value of k10a (298K) as
that of Wollenhaupt and Crowley [14]. Our value of
k10a (298K) is in reasonable agreement with that from
Mart´ınez et al. (in He) [15] and Wollenhaupt and Crow-
ley (in Ar) [14].
The high-pressure limiting rate constant at any one
temperature should be independent of the type of the
third-body molecule. We obtained a very similar value
of k10a (298K) to that from the two measurements in
N2 and Ar bath gas [12,14]. Our value of k10a (298K)
is 42% larger than that of Biggs et al. in He [11].
The pressure (ࣘ10 Torr) use∞d in Biggs et al.’s study is
rather low for an accurate k1a determination, because
the rate constant does not approach the high-pressure
limit until pressures of a few hundred Torr. Our value
of k10a (298K) is 24% smaller than that of Mart´ınez
et al. [15].
Figure 9 Comparison of falloff curves (lines) for k1a cal-
culated using parameters resulted from the current study to-
gether with the absolute T,P-dependent k1a values (symbols)
determined by Wollenhaupt and Crowley in Ar [14], except
for results of Frost and Smith in Ar (noted in the legend) [12].
By comparing the value of the power law expo-
nent, n, in the low-pressure limit from different studies
shown in Table IV, we find that the values of n obtained
fall into two groups: the present results and those of
Mart´ınez et al. [15] agree within 5%, whereas those
from Wollenhaupt and Crowley [14] and McCaulley
et al. [10] agree within 3%. However, the latter pair of
studies yield n 2.6 times larger than the former pair of
studies. The value we derive for the power law expo-
nent, m, in the high-pressure limit (1.13) is 35% larger
than that of Mart´ınez et al. [15]; however, the two re-
sults agree within their errors. Our m value is 65%
smaller than that derived by Wollenhaupt and Crow-
ley [14].
We present a plot comparing rate constants from
our study and previous work to facilitate a global com-
parison. In view of the fact that the temperatures used
in our experiments are different from other studies, we
plot the calculated falloff curves using the Troe expres-
sion (E4) using our fitted parameters at temperatures
that match the available literature data.
Figure 9 illustrates that, despite that our results near
room temperature agree well with those of Wollen-
haupt and Crowley [14], our results show less temper-
ature dependence both above and below room temper-
ature. On the other hand, our falloff curve does a good
job of predicting Frost and Smith’s results [12] at 390 K
in N2 (the only other study carried out in N2).
Neither our work nor previous studies of the
methoxy + NO2 reaction take into account the ex-
tent of formation of methyl peroxy nitrite (CH3OONO)
[19–21]. The absence of direct experimental evidence
for formation of CH3OONO makes such quantifica-
tion impossible. However, there is experimental evi-
dence enabling quantification of the HOONO forma-
tion channel in the HO + NO2 reaction [23,43]. If
formation of CH3OONO (or CD3OONO) occurs to a
similar (large) extent as HOONO formation, the use of
the Troe formula to fit the data would be invalid.
CONCLUSION
We determined rate constants for the reaction of CH3O•
(CD3O•) + NO2 in N2 bath gas over a range for pres-
sures and temperatures. From these results, we derived
the parameters of the Troe expression with Fcent = 0.6:
k0(298 K), n, kꢁ(298 K), and m. Our fitting results are
consistent with all the literature data in Ar bath gas at
room temperature and the limited data in N2 at 390 K.
Wollenhaupt and Crowley [14] reported stronger tem-
perature dependences of k0 and kꢁ than found here,
but we have no explanation for this discrepancy.
The highest pressure investigated in this study (700
Torr) is close to the high-pressure limit for k1a and
k2a, and the third-body gas N2 should reliably mimic
third-body effects in air. Therefore, our results can
be used to reliably interpret chamber studies carried
out in air near 1 atm total pressure. Energy transfer
is increasingly a source of error in ME studies of the
fate of chemically activated species and calculations of
pressure-dependent rate constants. The rate constants
obtained from this study may be valuable to constrain
International Journal of Chemical Kinetics DOI 10.1002/kin.20865

ABSOLUTE RATE CONSTANT FOR METHOXY RADICAL REACTING WITH NO2
511
RRKM/ME studies of collisional energy transfer in
these reactions.
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International Journal of Chemical Kinetics DOI 10.1002/kin.20865