Study of the pressure dependence of the rate constant of the reaction of NO3 with NO2

Article abstract of DOI:10.1016/j.cplett.2011.07.060

We have applied time resolved cavity ring-down spectroscopy to a kinetic study of the reaction of NO₃ with NO₂ in 20-700 Torr of N₂ diluent at 298 and 283 K. By fitting the data to Troe's expression with F_c = 0.6, the low-pressure and high-pressure limiting rate constants of this reaction were determined to be k1low(298 K) = (3.1 ± 0.8) × 10^-30 cm⁶ molecule^-2 s ^-1 and k1high(298 K) = (1.6 ± 0.3) × 10^-12 cm³ molecule^-1 s^-1. These rate constants thus determined were 10-40% larger than those recommend in the NASA/JPL database.

Full text of DOI:10.1016/j.cplett.2011.07.060

Chemical Physics Letters 513 (2011) 27–30
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Study of the pressure dependence of the rate constant of the reaction of NO3
with NO2
b
b
b
Yukio Nakano a, , Kengo Sadamori , Yuichi Hosho , Takashi Ishiwata
⇑
a Department of Environmental Sciences, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei-shi, Tokyo 184-8501, Japan
b Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan
a r t i c l e i n f o
a b s t r a c t
Article history:
We have applied time resolved cavity ring-down spectroscopy to a kinetic study of the reaction of NO3
with NO2 in 20–700 Torr of N2 diluent at 298 and 283 K. By fitting the data to Troe’s expression with
Fc = 0.6, the low-pressure and high-pressure limiting rate constants of this reaction were determined
to be k1low(298 K) = (3.1 0.8) ꢀ 10ꢁ30 cm6 moleculeꢁ2 sꢁ1 and k1high(298 K) = (1.6 0.3) ꢀ 10ꢁ12 cm3
moleculeꢁ1 sꢁ1. These rate constants thus determined were 10–40% larger than those recommend in
the NASA/JPL database.
Received 2 May 2011
In final form 19 July 2011
Available online 23 July 2011
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
where k1low and k1high are low-pressure and high-pressure limiting
rate constants of reaction (1), respectively. The constant of Fc is
Nitrogen trioxide, i.e., nitrate radical NO3, is considered to be
one of the most important oxidizers in urban areas, because NO3
is formed by the reaction of ozone (O3) with nitrogen dioxide
(NO2) included in automobile exhaust emissions. Solar photolysis
suppresses the concentration of NO3 in the daytime resulting in
the mixing ratio of NO3 peaking at nighttime. The NO3 radical
can reversibly combine with NO2 to form dinitrogen pentoxide
(N2O5) by the following equilibrium reaction (1,-1):
the broadening factor, the value of which may be different by each
reaction. In the NASA/JPL database, the value was fixed to Fc = 0.6 in
analyzing the rate constants for reaction (1) reported previously. On
the other hand, the value of Fc = 0.35 was used in the IUPAC data
base in analyzing the different set of rate constants for reaction
(1). Consequently, we can see the difference between the recom-
mendation values of k1low, k1high and Fc by NASA/JPL [1] and IUPAC [2].
In 2000, Burkholder and Ravishankara reported the rate con-
stant for the reaction of O(3P) + NO2 in 20–800 Torr of N2 diluent
[12]. To determine the rate constant, they monitored the time pro-
files of NO3 concentration after the 355-nm pulse laser photolysis
of NO2 in NO2/N2 gas mixture by using the transient long-path
662-nm diode laser absorption method. In their reaction system,
reaction (1) affected the loss of NO3 formed in the reaction of
O(3P) + NO2. In analyzing the data, they included an additional
NO3 first-order loss rate coefficient which depended on [NO2] to
reproduce the fast loss of NO3. They suggested that the increase
of the k1 value by 10–40% from those recommend by NASA/JPL
would have nearly the same effect as introducing an additional rate
coefficient for NO3 first-order loss. This suggestion may indicate
that the value of k1 recommend by NASA/JPL is underestimated
by 10–40% in the total pressure of 20–800 Torr.
NO3 þ NO2 þ M
¢
N2O5 þ M;
ð1; -1Þ
where M implies third bodies [1–10]. This reaction is one of the
chemical reactions that play important roles on chemical transfor-
mation in the earth’s atmosphere and the oxidative capacity of
the troposphere. An atmospheric N2O5 formed in reaction (1) can
react heterogeneously with water to give two molecules of nitric
acid (HNO3) which is a longer-lived reservoir species, and N2O5
can be removed from the atmosphere via wet or dry deposition
[11]. Thus, the equilibrium constant of reaction (1,-1), i.e. the ratio
of the rate constants of reactions (1) to (-1), is important in deter-
mining the oxidative capacity of the troposphere.
Because reaction (1) is a termolecular reaction, its rate constant
is usually characterized in accord with Troe’s expression (2):
0
1
We confirm the results of Burkholder and Ravishankara through
the experiment of 355-nm pulse laser photolysis of NO2 in NO2/N2
gas mixture using time-resolved cavity ring-down spectroscopy
(TR-CRDS). In this study, we determine the rate constant of reac-
tion (1) in 20–700 Torr of total pressure using TR-CRDS, and reveal
the underestimation of k1 in the NASA/JPL data base. Because of the
importance of reaction (1) in the atmospheric chemistry, the re-
sults obtained in this work are valuable for model simulations.
ꢂ
ꢃꢁ1
kl1ow½Mꢂ
h
ꢀ
ꢁi
2
k1 ¼
Fc 1 þ log kl1ow½Mꢂ=k1high
;
@
A
ꢀ
ꢁ
1 þ kl1ow½Mꢂ=kh1igh
ð2Þ
⇑
Corresponding author. Fax: +81 42 329 7518.
E-mail address: nakano@u-gakugei.ac.jp (Y. Nakano).
0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2011.07.060

28
Y. Nakano et al. / Chemical Physics Letters 513 (2011) 27–30
2. Experimental
The TR-CRDS apparatus used in the present study is similar to
that reported previously [13,14]. Two pulsed lasers were em-
ployed. A Nd3+: YAG laser (Continuum Co., Surelite II) was used
to generate the NO3 radicals in the photolysis of N2O5 at 266 nm.
A dye laser (Sirah Co., Cobra-Stretch; DCM Dye) pumped by the
532 nm output of a Nd3+: YAG laser (Continuum Co., Surelite I)
was used to probe the concentration of NO3 at 662 nm. After the
photolysis laser beam traversed a reaction cell nearly collinear to
the axis of the ring-down cavity, the probe laser beam was injected
through one of two high-reflectivity mirrors that made up the ring-
down cavity. The mirrors (Research Electro Optics) mounted
1.04 m apart had a specified maximum reflectivity of 0.999 at
635 nm, a diameter of 7.75 mm, and a radius of curvature of 1 m.
Light leaking from one of the mirrors of the ring-down cavity
was detected by a photomultiplier (Hamamatsu Photonics Co.,
R928) through a broad band pass filter (656 nm, FWHM 10 nm).
The decay of the light intensity was recorded using a digital oscil-
loscope (Tektronix, TDS430A) and transferred to a personal com-
puter. The decay of the light intensity is given by equation:
Figure 1. Typical decay profiles of NO3 in 100 Torr of N2 diluent at 298 K.
[NO2]add = 0 (circles), 9.7 ꢀ 1014 (triangles) and 1.6 ꢀ 1015 molecules cmꢁ3
(squares). The solid curves are the fits of the data to Eq. (5).
IðtÞ ¼ I0expðꢁt=
s
Þ ¼ I0 expfꢁt=s0
ꢁ
r
ncðLR=LÞtg;
ð3Þ
where I(t) is the intensity of light at time t; s0 is the cavity ring-
down time (ꢃ10 s at 662.0 nm) without photolysis laser light; LR
is the length of the reaction region (0.46 m) while L is the cavity
length (1.04 m); is the cavity ring-down time with photolysis
light; and n are the absorption cross section and concentration
l
s
r
of the species of interest, respectively; c is the speed of light.
The reaction cell consisting of a Pyrex glass tube (21 mm i.d.)
was evacuated by an oil rotary pump through a liquid N2 trap.
The volume of the detection region in the reaction cell was
160 cm3. The temperature of the gas flow region was controlled
by the circulation of thermostated water and kept at 298 or
283 K. The difference between the temperatures of the sample
gas at the entrance and exit of the flow region was <0.1 K. The pres-
sure in the cell was monitored by an absolute pressure gauge (MKS,
Baratron). Gas flow rates were regulated and measured by mass
flow controllers (KOFLOC, Model 3660 and Model 3440). A slow
flow of nitrogen diluent gas was introduced at both ends of the
ring-down cavity close to the mirrors to minimize the deteriora-
tion caused by exposure to reactants and products. The total flow
rate was kept constant at 127 cm3 sꢁ1. Experiments were per-
formed with 1 Hz laser operation under the conditions that the
gas mixture in the detection region was replenished every 1–2 la-
ser shots.
The mixtures of N2O5/N2 and NO2/N2 were prepared and stored
in glass bulbs, and were injected into the reaction cell using mass
flow controllers. The concentrations of N2O5 and NO2 in the reac-
tion cell could be calculated by using the flow rates.
We prepared N2O5 in the dehydration of HNO3 in the presence
of P2O5 as described previously [13,15]. Gaseous NO2 was produced
by the reaction of NO with excess O2. The NO2/NO/O2 gas mixture
was passed through a trap at methanol slash temperature, and the
collected NO2 was purified by a trap-to-trap distillation until a
pure white solid was obtained. Other reagents were obtained from
commercial sources. NO (99%), N2 (>99.9995%) and O2 (>99.9995%)
were used without further purification.
Figure 2. Plot of (k0 ꢁ kb0 ase loss) vs. [NO2]add in 100 Torr of N2 diluent at 298 K. The
solid line is a result of the linear least squares fit.
ishankara [12]; the 10–40% larger values of k1 as compared with
those recommended by NASA/JPL were necessary to reproduce
the fast loss of NO3. There are some difficulties for the determina-
tion of the rate constant of reaction (1) in NO2/N2/355 nm experi-
ments because of the existence of the many influences by sub-
reactions.
To minimize the influences of sub-reactions, we performed the
experiments, in which NO3 absorption-time profiles were moni-
tored after the 266-nm photolysis of N2O5 in N2O5/NO2/N2 gas mix-
ture using TR-CRDS for determination of the rate constant reaction
(1). In the N2O5/N2 mixture stored in a glass bulb, N2O5 was gradu-
ally decomposed to NO2 before the N2O5/N2 mixture was flowed
into the reaction cell. The decomposition of a N2O5 molecule gives
two NO2 molecules; NO3 formed in reaction (-1) is converted to
NO2 by a self reaction, a wall reaction, and so on. To check the actual
concentrations of NO2 in a N2O5/N2 mixture, we measured the IR
spectra of the gas mixtures sampled from the N2O5/N2 mixture in
the glass bulb by the FTIR spectrometer. As the result, we experi-
mentally determined the concentration of NO2 and estimated the
decomposition of N2O5 to be about 4% after 30 min and about 16%
after 210 min. Following these results, we have carried out the
experiments under the conditions that the concentrations of NO2
originating from the decomposition of N2O5 were greater than
1 ꢀ 1014 molecules cmꢁ3 in TR-CRDS reaction cell even without
the deliberately-added NO2. Here, >1 ꢀ 1014 molecules cmꢁ3 of
NO2 are required to achieve the pseudo first order conditions where
3. Results and discussion
We performed some experiments where the NO3 absorption-
time profiles were monitored after the 355-nm photolysis of NO2
in NO2/N2 gas mixture using TR-CRDS. In these experiments, we
observed the same phenomena as reported by Burkholder and Rav-

Y. Nakano et al. / Chemical Physics Letters 513 (2011) 27–30
29
Table 1
Pressure effect on the rate constants of NO3 + NO2 at 298 K.
Pressure
(Torr)
[N2O5]0
[NO2]add
[NO3]0
k1
(1014 molecules cmꢁ3
)
(1014 molecules cmꢁ3
)
(1012 molecules cmꢁ3
)
(10ꢁ12 cm3 moleculeꢁ1 sꢁ1
)
20
50
3.3–4.9
3.2–4.9
2.1–8.3
3.2–6.6
1.6–3.2
1.6–3.2
3.2
6.5–32
6.5–32
6.5–32
3.2–65
3.2–16
3.2–16
3.2–16
4.5–14
1.0–1.6
0.6–1.9
0.4–1.5
1.0–2.1
0.4–1.2
0.5–1.2
0.8–1.4
2.3–2.6
0.58 0.07
0.81 0.09
0.98 0.11
1.20 0.13
1.23 0.15
1.32 0.15
1.33 0.14
1.43 0.17
100
200
300
400
500
700
6.8
with NO2 which are produced by the decomposition of N2O5 in
the glass bulb. The concentration of NO2 form N2O5 in the reaction
cell was >1.0 ꢀ 1014 molecules cmꢁ3 from the results of FTIR
experiments as shown above, which was high enough to give the
exponential decay of NO3. Because the concentrations of the sub-
products in reaction (4), such as NO2, NO and O(3P), are three orders
of magnitude less than that of NO2 injected as the contamination
from the N2O5/N2 mixture in the glass bulb, the photolytically-gen-
erated NO2, NO and O(3P) do not have an influence on the loss of
NO3 radical. The influence of reaction (-1) on the NO3 loss could
be neglected for observed NO3 decay because of the small value
of the rate constant of reaction (-1) (kꢁ1 = 0.046 sꢁ1 at 298 K) [19].
To determine the rate constant of the reaction of NO3 with NO2,
temporal profiles of NO3 were measured with deliberately-added
NO2 ([NO2]add = 3.2–32 ꢀ 1014 molecules cmꢁ3) by the introduc-
tion of a gas mixture of NO2/N2 prepared in a glass bulb. Here,
[NO2]add is so much in excess of the NO3 concentration. The NO3
decay could be fitted by Eq. (5):
Figure 3. Plot of rate constants of NO3 with NO2 as a function of N2 diluent pressure
at 298 K (circles) and 283 K (squares). The solid curve and dashed curve are the fits
of the data at 298 and 283 K to Eq. (2), respectively.
½NO3ꢂ ¼ ½NO3ꢂ expðꢁk0tÞ:
ð5Þ
t
0
In Eq. (5), k0 is expressed by the following equation:
the NO3 decay profiles can be fitted by a single exponential decay
without the deliberately-added NO2.
k0 ¼ k1½NO2ꢂadd þ kb0 ase
;
ð6Þ
loss
Then, we started to measure the temporal concentration of NO3
radicals with TR-CRDS by monitoring the electronic transition NO3
(B2E0 X2A02) at 662.0 nm. The absorption of NO3 was converted to
the concentration by using the reported absorption cross section at
where k0base loss is the sum of first order decay components such as the
reaction with NO2 produced by the decomposition of N2O5 in N2O5/
N2 glass bulb, wall loss and diffusion form the detection region. As
described above, kb0 ase
under our experimental conditions con-
662 nm,
r
NO3(662 nm) = 2.25 ꢀ 10ꢁ17 cm2 moleculeꢁ1 [1,16,17].
loss
sists mainly of the reaction of NO3 with NO2 which are produced
by the decomposition of N2O5 in the glass bulb. Here, we can expect
that O(3P) and NO produced from the 266-nm photolysis of NO2 do
not affect the observed NO3 decays. By using absorption cross sec-
tions of NO2 and N2O5, at 266 nm, the concentrations of O(3P) and
NO were estimated to be <1.5 ꢀ 1011 molecules cmꢁ3 under our
experimental conditions. These concentrations are about 3–4 orders
of magnitude less than that of NO2. The rate constants of the reaction
of NO3 with O(3P) and NO is reported to be 1.0 ꢀ 10ꢁ11 cm3 mole-
culeꢁ1 sꢁ1 and 2.6 ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1, respectively [1]. By
considering the concentrations of O(3P) and NO and their reactivity
toward NO3, it is safe to say that the influence of O and NO on the
determination of the rate constant of NO3 + NO2 could be ignored.
The NO3 radicals were produced by the 266 nm photolysis of
N2O5 with the concentration of (2.1–8.3) ꢀ 1014 molecules cmꢁ3
in 100 Torr of N2.
N2O5 þ h
m
ð266nmÞ ! NO3 þ NO2
! NO3 þ NO þ Oð PÞ
N2O5(266 nm) was
ð4aÞ
ð4bÞ
3
The
value
of
r
reported
to
be
2.0 ꢀ 10ꢁ19 cm2 moleculeꢁ1 [1]. The quantum yields of reactions
(4a) and (4b) were reported to be 0.62 and 0.38, respectively
[2,18]. A typical decay profile of NO3 generated by the 266-nm pho-
tolysis of mixtures of N2O5/N2 in the reaction cell at 298 K is shown
by closed circle in Figure 1. The NO3 decay profile shows a single
exponential decay where the NO3 is consumed with about 3.8 ms
of lifetime. This NO3 loss is considered to result from the reaction
The value of k0base
could be determined by the least-squares anal-
loss
ysis of NO3 decay profile measured with [NO2]add = 0 with Eqs. (5)
Table 2
Summary of the reported low-pressure and high-pressure limiting rate constants of the rate constants of NO3 + NO2 at 298 K.
kl1ow
kh1igh
Fc
Temperature
(K)
Reference
(10ꢁ30 cm6 moleculeꢁ2 sꢁ1
)
(10ꢁ12 cm3 moleculeꢁ1 sꢁ1
)
2.0
3.6
3.1
3.3
1.4
1.9
1.6
1.7
0.60
0.35
0.60
0.60
298
298
298
283
NASA/JPL recommendation, 2006 [1]
IUPAC recommendation, 2006 [2]
This work
This work

30
Y. Nakano et al. / Chemical Physics Letters 513 (2011) 27–30
Table 3
Pressure effect on the rate constants of NO3 + NO2 at 283 K.
Pressure
(Torr)
[N2O5]0
[NO2]add
[NO3]0
k1
(1014 molecules cmꢁ3
)
(1014 molecules cmꢁ3
)
(1012 molecules cmꢁ3
)
(10ꢁ12 cm3 moleculeꢁ1 sꢁ1
)
20
50
3.4–6.8
6.6–6.8
6.8
10
6.8
6.8
6.8
9.6
4.7–23
4.9–25
5.1–26
10–30
0.4–1.0
0.5–0.8
0.6–0.8
0.9–1.8
1.5–1.7
1.8–1.9
1.1–1.4
2.8–3.0
0.68 0.09
0.84 0.11
1.08 0.12
1.28 0.17
1.33 0.18
1.44 0.18
1.50 0.23
1.49 0.20
100
200
300
400
500
700
3.4–10
3.4–10
3.4–10
4.8–15
fitting of the data to Troe’s expression (2) with Fc = 0.6, The values
for the low-pressure and high-pressure limiting rate constants of
reaction (1) at 283 K were also determined to be kl1ow(283 K) =
(3.4 1.0) ꢀ 10ꢁ30 cm6 moleculeꢁ2 sꢁ1 and kh1igh(298 K) = (1.7
0.3) ꢀ 10ꢁ12 cm3 moleculeꢁ1 sꢁ1. These results are also summarized
in Table 2. For comparison, the data of k1 at 298 K reported by Kircher
et al. [5], Smith et al. [6], Burrows et al. [7], Wallington et al. [8] and
Orlando et al. [9], which were usedto obtained kl1ow and k1high of NASA/
JPL recommendation, are shown with ours in Figure 4. The falloff
curves of NASA/JPL and IUPAC recommendations are also indicated
in Figure 4. As shown in Figure 4, the values of k1 determined in this
work are in excellent agreement with the falloff curve of IUPAC rec-
ommendations and some of present values are close to some of those
reported previously. The values of k1 determined in this work are
10–40% larger than those recommend by NASA/JPL [1]. This result
is consistent with the suggestion by Burkholder and Ravishankara
in their paper [12]. Because of the importanceof reaction ofNO3 with
NO2 in the atmospheric chemistry, the results of this work are con-
sidered to be valuable for atmospheric model simulations.
Figure 4. Plot of reported rate constants of NO3 with NO2 as a function of N2 diluent
pressure at 298 K. The data of this work (closed circles), Kircher et al. (open
diamonds), Smith et al. (opened down triangles), Burrows et al. (open hexagons),
Wallington et al. (opened up triangles) and Orlando et al. (opened squares) are
shown. The black curve and gray curve are the falloff curves of NASA/JPL and IUPAC
recommendations at 298 K, respectively.
Acknowledgments
This work was supported by the Global Environment Research
Fund of the Ministry of the Environment, Japan (RF-071). Y. Nakano
is grateful to a Grant-in-Aid from the Ministry of Education, Sci-
ence, Sports and Culture of Japan, No. 21710013. T. Ishiwata is
grateful to JSPS Grant-in-Aid for Scientific Research (C) No.
21550009.
and (6). As discussed above, the value of k0base loss gradually increased
during experiments because the N2O5 molecules in glass bulb grad-
ually decomposed to NO2 during the experiments. We measured k0
with [NO2]add = 0 before and after the measurements with [NO2]add
– 0, and corrected the change of k0base loss in determining the rate con-
stant of reaction (1). By this procedure, the term of k1 [NO2]add in Eq.
(6) could be extracted with reasonable accuracy. Figure 2 shows
(k0 ꢁ kb0 ase loss) vs. [NO2]add in 100 Torr of N2 diluent at 298 K. By con-
sidering the relationship of Eq. (5), a linear least-squares analysis
gives k1 = (0.98 0.11) ꢀ 10ꢁ12 cm3 moleculeꢁ1 sꢁ1. The quoted
uncertainty is derived by considering the uncertainties of calibra-
tions of [NO2]add, measurements of pressure, mass flow rates, and
reaction path length, and also the fitting errors.
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experiments were performed in 20, 50, 100, 200, 300, 400, 500 and
700 Torr of N2 diluent at 298 K. As summarized in Table 1, we deter-
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