Reaction of hydroxyl radical with nitric acid: Insights into its mechanism

Article abstract of DOI:10.1021/jp002394m

The rate constant for the reaction of hydroxyl radicals with nitric acid has an unusual pressure and temperature dependence. To explore the mechanism for this reaction, we have measured rate constants for reactions of isotopically substituted species OD+DNO₃, OH+DNO₃, OD+HNO₃, and ¹⁸OH+HNO₃ and the yield of NO₃ product. Deuterium substitution on nitric acid results in more than a 10-fold reduction in the rate constant, removes the pressure dependence (over the observed range of 20-200 Torr in He and SF₆), and leads to a strongly curved Arrhenius temperature dependence. Deuterium substitution on hydroxyl increases the rate constant slightly but does not change the pressure dependence. There is no evidence for exchange reactions in the isotopically mixed reactions. Absorption measurements of the NO₃ product yield show that the title reaction produces nitrate radical with unit efficiency over all temperatures and pressures studied. We discuss the implications of the measured rate constants, product yields, and lack of isotopic exchange in terms of a mechanism that involves formation of a hydroxyl radical-nitric acid complex and its subsequent reaction to give NO₃ and H₂O.

Full text of DOI:10.1021/jp002394m

J. Phys. Chem. A 2001, 105, 1605-1614
1605
Reaction of Hydroxyl Radical with Nitric Acid: Insights into Its Mechanism†
Steven S. Brown,*,‡ James B. Burkholder, Ranajit K. Talukdar,§ and A. R. Ravishankara§,|
NOAA Aeronomy Laboratory, R/AL2, 325 Broadway, Boulder, Colorado 80305
ReceiVed: July 5, 2000; In Final Form: October 17, 2000
The rate constant for the reaction of hydroxyl radicals with nitric acid has an unusual pressure and temperature
dependence. To explore the mechanism for this reaction, we have measured rate constants for reactions of
isotopically substituted species OD + DNO3, OH + DNO3, OD + HNO3, and 18OH + HNO3 and the yield
of NO3 product. Deuterium substitution on nitric acid results in more than a 10-fold reduction in the rate
constant, removes the pressure dependence (over the observed range of 20-200 Torr in He and SF6), and
leads to a strongly curved Arrhenius temperature dependence. Deuterium substitution on hydroxyl increases
the rate constant slightly but does not change the pressure dependence. There is no evidence for exchange
reactions in the isotopically mixed reactions. Absorption measurements of the NO3 product yield show that
the title reaction produces nitrate radical with unit efficiency over all temperatures and pressures studied. We
discuss the implications of the measured rate constants, product yields, and lack of isotopic exchange in
terms of a mechanism that involves formation of a hydroxyl radical-nitric acid complex and its subsequent
reaction to give NO3 and H2O.
I. Introduction
for the reaction of OD with DNO3 show a very large kinetic
isotope effect at 298 K (kH/kD ∼ 14).16 Furthermore, a significant
Nitric acid is the most abundant reactive nitrogen species in
the atmosphere, and it is a reservoir for NOx (defined as the
sum of NO and NO2), which plays many critical roles in the
troposphere and stratosphere. The reaction of HNO3 with OH
is a significant pathway for regenerating NOx from this reservoir.
pressure dependence for k(OD + DNO3) was noted at 298 K
but not at other temperatures. A complete understanding of the
mechanism that gives rise to the unusual behavior of k1 is
interesting from a chemical kinetics point of view and is also
an important step in verification of the temperature and pressure
dependence under atmospheric conditions.
There have been a few attempts to elucidate the mechanism
of reaction 1. Margitan and Watson,14 and later Smith et al.,11
showed that the observed pressure dependence requires the
formation of an OH‚HNO3 adduct that can undergo either
dissociation back to OH and HNO3 or react further to give
products. Lamb et al.17 and Marinelli and co-workers10,18 worked
on obtaining a mechanism consistent with the observations
available to them. Marinelli and Johnston10 explained the
negative temperature dependence of k1 by postulating a six
membered ring transition state. Lamb et al.17 suggested that a
transition state in which OH attacks the N atom in HNO3 best
explained the observed temperature dependence.
OH + HNO3 f H2O + NO3
(1)
We recently reported the value of k1, the rate constant for this
reaction, between 200 and 375 K in 10-500 Torr of four
different buffer gases (He, N2, O2, and SF6).1 Our values were
significantly larger at low temperature than the previous
recommendation for atmospheric modeling.2 Our larger values
of k1 have a significant impact on calculated atmospheric
3
partitioning between NOx and NOy (defined as all oxidized
nitrogen species other than N2O), as well as on modeled ozone
destruction rates by different chemical families (i.e., HOx, ClOx,
etc.).4,5 One of the reasons for the difference between our values
and previous recommendations was that k1 increases strongly
with pressure at lower temperatures. Even though the negative
temperature dependence6-13 and pressure dependence14,15 were
known, the strong pressure dependence at low temperature was
unmeasured, and extrapolation of the pressure dependence from
higher temperatures underestimated k1 at low temperatures.
Reaction 1 shows some unusual behavior. Above 300 K, k1
exhibits only a weak temperature dependence and no measurable
pressure dependence. At lower temperatures, the dependence
on pressure increases markedly. Furthermore, the value of k1 is
quite small for a reaction that has a negative temperature
dependence. The limited data available on the rate coefficient
This paper is a more detailed mechanistic study of reaction
1. We present measurements of rate coefficients for reactions
between several different isotopomers.
OD + DNO3 f D2O + NO3
OD + HNO3 f HDO + NO3
f OH + DNO3
(2)
(3a)
(3b)
(4a)
(4b)
OH + DNO3f HDO + NO3
f OD + HNO3
18OH + HN16O3 f H218O + NO3
(5a)
(5b)
† Part of the special issue “Harold Johnston Festschrift”.
‡ NOAA NRC Postdoctoral Fellow.
§ Also affiliated with: Cooperative Institute for Research in the
Environmental Sciences, University of Colorado, Boulder, CO 80309.
| Also affiliated with: Department of Chemistry and Biochemistry,
University of Colorado, Boulder, CO 80309.
f
16OH + HNO3
Measurement of the rate constants for reactions 2-5 explores
10.1021/jp002394m CCC: $20.00 © 2001 American Chemical Society
Published on Web 12/30/2000

1606 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Brown et al.
both the primary and secondary kinetic isotope effects arising
from deuterium substitution on either HNO3 or OH as well as
the possibility for exchange reactions that might indicate the
structure of any reactive complex and the barriers to reaction.
This paper also examines the question of the product yields
from reaction 1. The reaction as written above is the most
initial OH (OD) concentrations, [OH]0 ([OD]0), from the
measured photolysis laser fluence and the known cross-sections
of photolytic precursors (HNO3,23 O3 24). We maintained [OH]0
([OD]0) e 4 × 1011 cm-3 and checked that factor of 4 variation
in photolysis laser fluence did not affect the measured rate
constants. We measured the concentration of the HNO3 (DNO3)
reactant via absorption (213.68 nm Zn line, σ(HNO3) ) (4.52
( 0.19) × 10-19 cm2)23 in either a 100 or 25 cm cell located
either just downstream or upstream of the reactor. Comparison
of ultraviolet spectra of HNO3 and DNO3 from this laboratory
shows the DNO3 cross-section at this wavelength to be within
10% of the HNO3 cross-section. As described previously, we
checked that there was no interference in the measured rate
constants from the pressure dependent OH (OD) + NO2
reaction25 by measuring the NO2 content of the HNO3 (DNO3)
samples via LIF at 532 nm in an external cell. Our previous
paper also described the synthesis and handling of anhydrous
HNO3 in detail.
Measurement of k2, OD + DNO3. Reaction 2 was the most
straightforward of the isotopically labeled variants since the OD
source was the 248 nm photolysis of the DNO3 reactant. As
discussed further below, reaction 2 is considerably slower than
reaction 1, necessitating large concentrations of DNO3 (3 × 1015
to 5 × 1016 cm-3) to observe significant pseudo-first-order OD
loss rate constants. We measured the DNO3 concentration in a
25 cm external absorption cell, taking the 213.86 nm absorption
cross-section for DNO3 to be the same as that for HNO3.
Measurement of k3, OD + HNO3. Measurement of k3 was
somewhat more difficult because the photolytic precursors for
OD tend to undergo H/D exchange (most likely on surfaces)
with the HNO3 reactant, converting it partially into DNO3 prior
to generation of OD. We therefore used the reaction of O(1D),
produced from 248 nm photolysis of O3, with D2 as the OD
source since D2 (unlike, for example, D2O) does not exchange
with HNO3. This source avoided H/D exchange but could also
regenerate OD via the following reaction sequence.
exothermic pathway, with ∆rH°(298) ) -17.3 kcal mol-1 19
.
Production of hydrogen peroxide and NO2 is also slightly
exothermic,19 although there is no direct experimental evidence
for this pathway.
OH + HONO2 f H2O2 + NO2
∆rH°(298) ) -1.8 kcal mol-1 (1b)
Wine et al.,6 who first demonstrated the negative temperature
dependence of k1, suggested that the temperature dependence
might in fact be due to reaction 1b. There have been several
product yield studies of reaction 1.8,9,18,20,21 Husain and Norrish20
were the first to deduce H2O and NO3 as the products of reaction
1 on the basis of NO3 absorption measurements. More recently,
Ravishankara et al.,9 Nelson et al.,18 and Jourdain et al.8 reported
NO3 as the only product, with a yield close to unity. Therefore,
atmospheric modeling studies have assumed that reaction 1 leads
only to H2O + NO3 products.
Further examination of the product yield is warranted for
several reasons. First, it is important to atmospheric modeling
since a significant yield for reaction 1b would impact calcula-
tions of HOx abundance. Reaction 1 is a sink for HOx; reaction
1b may or may not be a HOx sink depending on the fate of
H2O2 (i.e., further reaction with OH or photolysis). Second, there
have been recent revisions and temperature dependence mea-
surements of the recommended absorption cross-sections for
NO3 radicals22 that were the basis for several of the previous
yield studies. For example, Ravishankara et al.9 reported an NO3
yield of unity at both 298 and 251 K at fixed pressures of He
and SF6 bath gases; however, the upward revision of the NO3
absorption cross-section suggests that the NO3 yield from that
study was in fact somewhat smaller than unity. Finally, there
has been no explicit consideration of the pressure dependence
of the product yield since the pressure dependence of k1 was
not widely appreciated at the time of the previous studies.
O(1D) + HNO3 f OH + NO3
OH + D2 f HDO + D
OD + D2 f D2O + D
D + O3 f OD + O2
(6)
(7)
(7b)
(8)
II. Experimental Section
Our previous study of reaction 11 describes the apparatus and
the procedures that are important for accurate, low-temperature
measurement of k1. The first part of this section focuses on the
additional details for measurement of rate constants for isoto-
pically labeled species. The second part describes the apparatus
and methods for measuring NO3 yields.
A. Measurement of k2-k5. The experimental apparatus was
a pulsed-photolysis, laser induced fluorescence (LIF) system.
We produced OH (OD) radicals from a variety of photolytic
precursors (described below) using a 248 nm KrF excimer laser,
and we measured the temporal profile of OH (OD) after their
photolytic production via pulsed LIF. The LIF light source
(280-310 nm) was the frequency doubled output of a Nd:YAG
laser pumped dye laser. All reactions took place under pseudo-
first-order conditions, with [OH]0 ([OD]0) < 10-3[HNO3]
([DNO3]). The LIF/reaction cell was a jacketed Pyrex vessel
with a volume of 150 cm3. The linear gas flow velocity varied
between 5 and 10 cm s-1 at all pressures, fast enough to refresh
the gas mixture in the reaction zone every 1-2 laser shots in
this 10 Hz experiment. Variation of the linear flow velocity
had no effect on the measured rate constants. We calculated
Reaction 7 is rather slow, having a value of k7 ≈ 1.6 × 10-15
cm3 molecule-1 s-1 at 298 K,26 and the contribution to the
observed OD temporal profile can be minimized if the initial
OH concentration is small. We measured the D2 concentration
in the reactor using calibrated mass flow meters, and then we
simulated OD decays to include the effects of reactions (6-
8).2,27-29 For all reported measurements, [O3] was in the range
(1-2) × 1014 molecules cm-3 and [D2] was in the range (1.5-
3.0) × 1016 molecules cm-3, although increasing [D2] by a factor
of 5 did not affect measured rate constants. The corrections,
estimated by numerical simulation of the reaction sequence,
changed the k3 values by 5% or less relative to those obtained
without the correction.
Measurement of k4, OH + DNO3. The source chemistry for
reaction 4 was the most difficult. The reaction of O(1D) with
H2 was not an optimal OH source in this case because the OH
regeneration sequence that is analogous to reactions 7 and 8
contributed significantly to the OH temporal profile. The rate
constant for OH + DNO3 (k4) is more than an order of
magnitude smaller than k3(OD + HNO3), and the rate constant

Reaction of Hydroxyl Radical with Nitric Acid
J. Phys. Chem. A, Vol. 105, No. 9, 2001 1607
for OH + H2 is approximately four times faster than that for
OD + D2.26 Thus, reaction 4 required an OH source that would
neither exchange prior to reaction nor produce H atoms as
byproducts. Therefore, we used the reaction of O(1D) with CF3H
as the OH source. Although the main reaction between these
species is quenching of O(1D),30,31 we found that O3 photolysis
in the presence of CF3H did produce a sufficient amount of
OH and that OH did not significantly react with the CF3H
precursor. The lack of a dependence of measured pseudo-first-
order rate constants on the photolysis laser fluence showed that
the O(3P) produced from quenching of O(1D) by CF3H did not
significantly participate in the reaction. Furthermore, as de-
scribed further below, this source produces some OD from the
reaction of O(1D) with DNO3 and from DNO3 photolysis, and
we were able to simultaneously measure k2 and k4 by monitoring
either OD or OH. The source accurately reproduced k2(OD +
DNO3), further indicating that secondary chemistry was unim-
portant.
Measurement of k5, 18OH + HNO3. The reaction of O(1D)
with H218O was a convenient and straightforward source for
18OH. Since the O3 that served as the O(1D) photolytic precursor
was not isotopically labeled, the source produced approximately
50% each of 16OH and 18OH. We took advantage of the similar
magnitude of LIF signals from both 16OH and 18OH, whose
LIF transitions are adjacent to one another, to measure k1 and
k5 directly in the same gas mixture. For each concentration of
HNO3 we measured the pseudo-first-order loss rate constant for
16OH, then tuned the LIF probe laser wavelength to an 18OH
transition and measured the pseudo-first-order loss rate constant
for that species.
B. NO3 Product Yield. The NO3 yield from reactions 1 and
2 was measured by producing OH (OD) radicals via pulsed laser
photolysis in the presence of HNO3 (DNO3) and monitoring
the temporal profile of NO3 via absorption at 661.9 nm. The
NO3 yield for reaction 1 was measured between 20 and 770
Torr and at a few temperatures in the range 240-330 K.
Reaction 2 was studied at room temperature over the pressure
range 74-360 Torr. The apparatus, data acquisition, and
procedures used to make such measurements have been
described in recent work from this laboratory;32,33 only a brief
outline is given below.
Determination of the NO3 product yield requires a quantitative
measurement of the initial OH radical concentration, [OH]0, and
the NO3 concentration produced by its reaction. Hydroxyl
radicals were produced by the photolysis of HNO3 at 248 nm
(KrF excimer laser).
Figure 1. Variation of k2 (OD + DNO3) on a logarithmic scale vs
1/T. The points are the values of k2 measured in this work, and the
solid line is the sum of two Arrhenius expressions using the E/R values
indicated in the figure, and A1 ) (5.52 ( 0.09) × 10-12 and A2 )
(3.22 ( 0.04) × 10-16 cm3 molecule-1 s-1
.
The apparatus consisted of a long-path absorption cell (path
length of 91 cm), an excimer laser photolysis source (248 nm,
KrF), and absorption light sources and detectors for measuring
photolyte concentrations and monitoring the temporal evolution
of NO3. The jacketed absorption cell (30 mm i.d.) was made of
Pyrex and was temperature regulated by circulating methanol
from a controlled temperature bath through the jacket. A 662
nm diode laser, single mode with 0.5-2 mW output, was used
to measure NO3 transient absorption signals. The diode laser
wavelength was locked at the peak of the NO3 absorption
feature, 661.9 nm, by regulating the laser current (∼40 mA)
and temperature (∼275 K). The signal from the diode laser
detector was sent to a multichannel scalar for digitization and
signal averaging. Data acquisition was initiated approximately
1 ms before the excimer laser fired to provide a baseline from
which changes in absorbance could be calculated. The NO3
detection limit was ∼5 × 109 molecule cm-3 per laser shot.
Absorption by the photolytes were measured using a D2 lamp
(30 W) light source, a 0.5 m spectrograph, and a diode array
detector. The spectrograph was equipped with a 300 grooves/
mm grating and a 1024 element cooled diode array detector.
The wavelength range of 200-365 nm was monitored. Con-
centrations of N2O5 and HNO3 were determined using absorption
cross-sections from the literature.23,35 Wavelength calibration
was made using emission lines from a Hg lamp and a 10 µm
entrance slit.
HNO3 + hν f OH + NO2
(9)
All gases were mixed with the N2 (UHP, 99.9995%) carrier
gas prior to entering the absorption cell. Pressure was measured
with a 1000 Torr capacitance manometer. The linear flow
velocity of the gases in the absorption cell was normally 10 cm
s-1, leading to a transit time through the absorption cell of ∼10
s. The photolysis laser was operated either in single shot mode
or below 0.1 Hz to ensure that a fresh gas mixture was available
for each laser shot.
The OH yield in reaction 9 has been measured to be unity.34
Initial hydroxyl concentration, [OH]0, was calculated from the
excimer laser fluence and the measured HNO3 concentration.
The laser fluence was determined in separate calibration
measurements using N2O5 photolysis at 248 nm
N2O5 + hν f NO2 + NO3
(10)
III. Results
and NO3 transient absorption. The NO3 yield in reaction 10 was
taken as 0.8 in the present analysis.2,35 The calibration was
carried out using N2O5 because NO3 could be measured in both
the calibration and product yield studies. This reduced systematic
error in the product yield determination associated with uncer-
tainties in the wavelength used for monitoring NO3 (diode laser)
and the absorption cross-section of NO3 at that wavelength.
A. Isotopically Substituted Reactions. Figure 1 presents our
measurements of k2, the rate constant for fully deuterated
reactants, OD + DNO3. Since both reactants are deuterated in
this case, direct comparison of k1 with k2 includes both the
primary (arising from D substitution on HNO3) and secondary
(D substitution on OH) kinetic isotope effects, but, as discussed
further below, the primary kinetic isotope effect is by far the

1608 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Brown et al.
TABLE 1: Measured OD + DNO3 Rate Constants (k2)a
T (K)
buffer gas
P (Torr)
k2
Pressure Dependence
296
He
20.1
50.5
100.2
199.5
50.0
100.3
201.1
20.0
1.34 ( 0.08
1.38 ( 0.10
1.38 ( 0.07
1.39 ( 0.08
1.22 ( 0.08
1.22 ( 0.07
1.47 ( 0.07
1.75 ( 0.09
1.75 ( 0.08
1.76 ( 0.08
1.81 ( 0.10
1.64 ( 0.08
1.62 ( 0.08
1.75 ( 0.09
SF6
He
251
50.1
100.1
199.7
50.0
100.1
199.7
SF6
Temperature Dependence
He 100 ( 1
Figure 2. Pressure dependence for k3 (OD + HNO3) at three
temperatures in He buffer gas. The solid points are the k3 values from
this work. The solid lines are fits to the pressure dependence for k3
(OH + HNO3) to the expression k0 + k∆(1 + k∆/kc[M])-1, where k0 is
the bimolecular low-pressure limit, k0 + k∆ is the high-pressure limit,
and kc is a termolecular collisional relaxation rate constant. The dashed
lines are the pressure dependences for k1 (OH + HNO3) in He, fit to
the same form, from our previous study (ref 1).
370.1
360.2
350.1
340.0
330.1
319.9
311.1
296.5
290.0
280.8
269.9
260.0
251.0
239.7
2.17 ( 0.10
2.02 ( 0.09
1.85 ( 0.08
1.62 ( 0.07
1.48 ( 0.07
1.34 ( 0.06
1.38 ( 0.06
1.37 ( 0.08
1.33 ( 0.06
1.41 ( 0.06
1.46 ( 0.06
1.51 ( 0.07
1.76 ( 0.08
2.07 ( 0.09
TABLE 2: Measured Rate Constants for Reactions 3 and 4
in He Buffer Gas (Units of 10-13 cm3 molecule-1 s-1 a
)
1015 [H(D)NO3]
(molecules cm-3
T (K)
)
P (Torr)
k
k 3 (OD + HNO3)
20.0
a The [HNO3] range is 3 × 1015 to 5 × 1016 molecules cm-3. All
rate constants in units of 10-14 cm3 molecule-1 s-1, and the quoted
uncertainties are (2σ.
250
0.4-6
0.9-10
1-14
2.23 ( 0.15
2.67 ( 0.21
3.09 ( 0.23
3.10 ( 0.29
3.40 ( 0.25
1.46 ( 0.08
1.58 ( 0.10
1.73 ( 0.09
1.75 ( 0.09
1.79 ( 0.08
1.05 ( 0.11
1.10 ( 0.08
1.14 ( 0.14
1.21 ( 0.08
50.2
100.2
200.5
498.8
20.0
larger of the two. There are three salient features in Figure 1.
The first is the vertical scale that ranges between 1.2 × 10-14
and 2.4 × 10-14 cm3 molecule-1 s-1, anywhere between a factor
of 5 and 50 times smaller than the rate constant for OH + HNO3
over the same temperature range. The second is that Figure 1
is a plot of temperature dependence only; to within the 7%
uncertainty of the measurement, k2 lacks an observable pressure
dependence over the range that we measured. Table 1 lists
representative pressures over which k2 was measured in both
He and SF6 buffer gases. Our result is in contrast to the study
of Singleton and co-workers,16,36 who found a somewhat
unrealistic pressure dependence for k2 of as much as 40% at
room temperature but no pressure dependence at other temper-
atures. Thus, while we find a temperature dependence that is
similar to the work of Singleton et al.,16 we find no temperature
between 240 and 370 K for which k2 depends on pressure over
the range 20-200 Torr of He and SF6. This result is in marked
contrast to reaction 1; at 250 K, k1 increases by more than 50%
over the same pressure and buffer gas range (see, for example,
Figure 2). Finally, the most obvious feature of Figure 1 is the
curvature in the temperature dependence, with a positive
dependence at high temperature, a negative dependence at low
temperature, and a minimum near 300 K. A fit to the sum of
two separate Arrhenius expressions (solid line) describes the
data in Figure 1, suggesting the presence of two competing
reaction paths.
296
350
49.9
100.3
200.2
500.0
20.5
49.6
100.0
200.0
k4 (OH + DNO3)
297
2-50
100.3
0.108 ( 0.011
a Quoted uncertainties are (2σ.
30% larger than k1 over the temperature and pressure ranges
examined here.
To ascertain if the increase in k3 relative to k1 was due to the
contribution from the exchange, reaction 3b, we measured the
temporal profile of OH during the course of the OD + HNO3
reaction. As noted above, the photolytic OD source produces a
small amount of OH from both the reaction of O(1D) with HNO3
and from the 248 nm photolysis of HNO3 itself. In the case of
OD reacting with HNO3 according to reactions 3a and 3b, and
OH reacting according to reaction 1, the OH temporal profile
is given by the following integrated rate expression.
k3b
0 k3 - k1
[OH]t ) [OH]0 exp(-k1′t) + [OD]
[exp(-k1′t) -
Reaction 3, OD + HNO3, is a test of two different aspects
of the reaction mechanism: the secondary kinetic isotope effect
and the possibility for exchange, i.e., reaction 3b. Figure 2 is a
plot of the pressure dependence of k3 in He buffer gas compared
to that for k1 at 250, 296, and 350 K. (Also see Table 2.)
Reaction 3 exhibits an essentially identical temperature and
pressure dependence to reaction 1, but k3 is consistently 10-
exp(-k3′t)] (11)
Here, k1′ ) k1[HNO3] + kd, k3′ ) k3[HNO3] + kd, and kd is the
first-order rate coefficient for the loss of OH and OD out of the
reaction zone due to diffusion and flow. Also, k3 is the sum of
k3a and k3b; [OH]0 and [OD]0 are initial concentrations. In 100

Reaction of Hydroxyl Radical with Nitric Acid
J. Phys. Chem. A, Vol. 105, No. 9, 2001 1609
Figure 5. Pseudo-first-order rate constants for loss of 18OH (solid
circles) and 16OH (open squares) vs HNO3 concentration at two
temperatures in 100 Torr He. The slopes of both data sets give the
same rate constant to within the uncertainties of the linear least-squares
fits at both temperatures. Solid lines are fits for 18OH losses and dashed
lines for 16OH losses.
Figure 3. Temporal profile of OH (points) when OD is also produced
in the presence of HNO3. The solid and dashed lines are fits to eq 11
with k3b set to zero and to a limiting value of 5 × 10-15 cm3 molecule-1
s-1, respectively. The calculated ratio of [OD]0/[OH]0 was 3.5 for the
data shown in this figure.
TABLE 3: Measured Rate Constants for Reaction 5 in He
Buffer Gas (Units of 10-13 cm3 molecule-1 s-1
)
T
1016 [HNO3]
(K) (molecules cm-3
P
k5
k1
)
(Torr) (18OH+ HNO3) (16OH + HNO3)
295
273
0.13-1.3
0.17-1.0
99.6
100.4
1.33 ( 0.06
1.78 ( 0.13
1.29 ( 0.08
1.83 ( 0.12
the fit to the OH data is approximately 20% smaller. The
observation that OH reacts more slowly with DNO3 than does
OD and the lack of observable OD production at long reaction
times strongly suggest that the exchange, reaction 4b, is not
significant. Rather, the decrease in k4 relative to k2 is consistent
with the secondary kinetic isotope effect described above; OH
reacts slightly more slowly than does OD with either HNO3 or
DNO3. One may surmise, in the absence of such measurements,
that k4 will have a pressure and temperature dependence similar
to k2 but have slightly smaller values.
Figure 4. Plots of measured pseudo-first-order rate constants for loss
of both OH (solid circles) and OD (open squares) as a function of DNO3
concentration at 296 K and 100 Torr He. The slopes of linear least-
squares fits (lines) to the data give the bimolecular rate constant for
the two reactions.
We examined another exchange reaction, the 18OH/16OH
exchange shown in reaction 5b. This experiment tests the
suggestion, noted in the Introduction, that reaction 1 proceeds
via a complex structure in which the hydroxyl O atom attacks
the nitric acid N atom17 (see Figure 10). One would expect a
facile exchange between OH moieties in such a complex and
thus facile 18OH/16OH exchange. Figure 5 displays plots of the
measured pseudo-first-order rate constants for loss of 18OH and
16OH in the presence of HNO3 in 100 Torr of He at 296 and
273 K. Clearly, the bimolecular rate constant for 16OH and
18OH reaction with HNO3 are the same to within experimental
uncertainty (see Table 3). Note that the derived values of k1
agree with our previous data to within 9% at 296 K and 2% at
273 K. Thus, assuming that reaction 5a has the same rate
constant as reaction 1, the rate constant for the exchange reaction
in 5b is smaller than the experimental uncertainty in k5, i.e.,
Torr of He at 298 K, the measured difference between k3 and
k1 is approximately 0.3 × 10-13 cm3 molecule-1 s-1. Measure-
ment of pseudo-first-order OH loss rate constants as a function
of [HNO3] in the presence of OD radicals reproduced (to within
5%) the previously measured value1 for k1 (100 Torr He, 296
K) of 1.40 × 10-13 cm3 molecule-1 s-1. Figure 3 demonstrates
that a fit of the resulting OH temporal profiles to eq 11 sets an
upper limit, k3b < 5 × 10-15 cm3 molecule-1 s-1. The
approximately 20% difference between k3 and k1 is therefore
not due to a contribution from the exchange reaction. The
increase in the rate constant upon deuteration of OH is due solely
to the secondary kinetic isotope effect. (The term “secondary”
means that the O-H(D) bond does not break in the reaction.)
Reaction 4 is similar to reaction 3 in that it is also a test for
H/D exchange, i.e., reaction 4b. In this case, however, it is also
a test of the primary, rather than secondary, kinetic isotope effect
since the deuteration is on HNO3. Because of the experimental
difficulties noted above, we measured k4 only at 296 K and
100 Torr He (see Table 2). Figure 4 shows the plot of the
pseudo-first-order loss rate constants for both OH and OD as a
function of DNO3 concentration under identical pressure and
temperature. We were able to measure both rate constants in
the same reaction mixture as noted earlier. The slope of the fit
to the OD data (dashed line) in Figure 4 gives a k2 value
consistent with that in Table 1 and Figure 1, while the slope of
<1 × 10-14 cm3 molecule-1 s-1
.
B. NO3 Product Yields. To measure the NO3 yield for
reactions 1 and 2, it was necessary to first evaluate the excimer
laser fluence by photolyzing N2O5 and measuring NO3. The
laser fluence is given by the following expression.
laser fluence ) [NO3]t)0/([N2O5]0σ248 nm(N2O5) Φ(NO3))
(12)
Here [NO3]t)0 is the NO3 concentration produced by reaction
10 shortly after the photolysis pulse, [N2O5]0 is the measured

1610 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Brown et al.
Figure 6. Measured temporal profiles (points) at 260 K and 300 Torr
(N2) of the NO3 concentration arising from reaction 1 at five different
HNO3 concentrations. The solid lines are simulated profiles in which
the NO3 yield is the only variable (see text).
Figure 7. Measured NO3 yield from reactions 1 and 2 for several
temperatures (legend) as a function of pressure. To within experimental
uncertainty, the yield does not vary with pressure and is unity at all
temperatures.
initial N2O5 concentration, σ248 nm(N2O5) is the N2O5 cross-
section at the photolysis wavelength, and Φ(NO3) is the NO3
yield in reaction 10. The precision of the laser fluence
measurements was typically ∼5% as determined from the slope
of a plot of [NO3]0 vs [N2O5]. Calibration and product yield
measurements were made in back to back measurements
whenever possible. The laser fluence measured before and after
the product yield experiments agreed to within the precision of
the measurements. The NO3 quantum yield from reaction 10
was observed to decrease slightly, but systematically, in going
from 298 to 240 K (∼3%) after accounting for the temperature
dependences of the NO3 and N2O5 absorption cross-sections.
Although this effect was small, we calibrated the laser fluence
at room temperature (i.e., photolyzed N2O5 at 298 K and then
changed the temperature of the reactor) to minimize systematic
errors in the measured product yields.
Figure 6 shows a representative set of NO3 temporal profiles
measured at 260 K and 300 Torr (N2) upon generation of OH
in the presence of HNO3. The NO3 profiles were typically
measured at five different initial HNO3 concentrations for each
combination of temperature and pressure. Each trace in Figure
6 was obtained from a single excimer laser pulse. The temporal
profiles of NO3 gave the rate coefficients for OH loss. If the
initial concentration of OH is known, then a comparison of NO3
produced (after accounting for its slow loss) with [OH]0 leads
to the yield of NO3 from reaction 1. However, there are small
contributions to OH and NO3 losses due to the following
unavoidable side reactions.
TABLE 4: Measured Yields of NO3 in the Reactions of OH
with HNO3 and OD with DNO3 at Various Temperatures
and Pressures (M ) N2)a
1016[HNO3]
T
P
NO3 yield
((1σ)
no. of
meaurements
(molecules
reaction
(K) (Torr)
cm-3)
OH + HNO3 330 370 0.88 ( 0.05
141 0.90 ( 0.05
296 770 1.02 ( 0.05
600 1.03 ( 0.05
415 1.03 ( 0.03
190 0.94 ( 0.06
50 0.99 ( 0.05
4
3
4
3
3
4
4
4
4
5
5
2
5
4
5
3
3
6
2
2
2
2
2
3
3
3
1.30-2.20
1.94-2.01
0.74-2.04
1.48-1.97
1.40-1.74
0.69-2.18
0.77-1.60
1.57-1.99
1.40-2.05
0.69-2.45
0.78-1.97
0.87, 1.52
0.88-2.40
1.08-1.77
1.08-2.05
1.44-1.59
1.84-2.57
1.09-2.47
0.86, 1.02
0.82, 0.87
0.97, 1.03
0.99, 1.06
1.00, 1.01
2.79-3.33
2.63-3.26
2.33-3.88
100 1.00 ( 0.05
150 0.98 ( 0.05
225 1.03 ( 0.05
370 0.88 ( 0.08
23 0.95 ( 0.05
260 120 0.98 ( 0.05
55 0.95 ( 0.025
300 0.98 ( 0.02
510 0.95 ( 0.02
680 0.89 ( 0.01
300 0.96 ( 0.03
240 334 0.92 ( 0.15
562 0.91 ( 0.2
162 0.94 ( 0.1
65 0.95 ( 0.1
50 0.95 ( 0.1
OD + DNO3 296
74 0.98 ( 0.03
140 0.95 ( 0.03
360 0.97 ( 0.03
OH + NO2 + M f HNO3 + M
NO2 + NO3 + M f N2O5 + M
OH + NO3 f HO2 + NO2
(13)
(14)
(15)
a The rate coefficients for the loss of the hydroxyl radical used in
computing the yield were those determined in this study by following
OH loss or from our previous study.1
the NO3 profiles very well using our recently reported rate
coefficient data for reaction 11 and NO3 product yields near
unity.
Nitrogen dioxide is produced as a photolysis product in reaction
9 and is also present in small amounts (∼100 ppmv) as an
impurity in the HNO3. The NO3 profiles were numerically
simulated for this set of reactions and fit to the observed profiles
by varying only the yield of NO3 in reaction 1. These calculated
profiles are shown as solid lines in Figure 6. The rate coefficients
for the simulations were taken from recent studies in this
laboratory or DeMore et al.2 Under the conditions of our
measurements the secondary chemistry affects the NO3 signal
by less than 2%. As shown in Figure 6 the simulations reproduce
The measured NO3 yields as a function of pressure are
summarized in Figure 7 and Table 4. Under the temperature
and pressure conditions examined in this study, the NO3 yield
is near unity for both reactions 1 and 2. The largest uncertainty
in this value originates from the uncertainty in the NO3 quantum
yield in reaction 10 which we estimate to be accurate to (10%.
We have taken a value of 0.8 for the above analysis. It should
be noted that our absolute product yields are directly propor-
tional to this value, but that our product measurements relative

Reaction of Hydroxyl Radical with Nitric Acid
J. Phys. Chem. A, Vol. 105, No. 9, 2001 1611
Figure 9. Proposed mechanism for reaction 1 showing adduct
formation and subsequent reaction to form NO3 and H2O. Equation 16
in the text gives the overall rate constant that arises from the individual
steps in the mechanism.
following discussion examines the implications of each of these
observations in this order.
Figure 8. Overall variation of rate constants for reactions 1-4 with
temperature and pressure. Reactions 1 (upper solid lines) and 3 (upper
dashed lines) are both pressure dependent and have the same temper-
ature dependence, except that k3 is approximately 20% larger than k1.
A high-temperature value of k1 from Troe37 also appears as the solid
point. Reaction 2 (lower solid line) is pressure independent and has a
curved Arrhenius plot. We assume the same form for reaction 4 (lower
dashed line), but with a 30% decrease in k4 relative to k2.
Previous studies of k1 have established its negative temper-
ature dependence and pressure dependence. Several studies have
also suggested the general features of a reaction mechanism
that includes a complex-forming step followed either by
dissociation of the complex back to reactants or reaction from
the complex to give products (see introduction). Figure 9
outlines such a mechanism. The kinetic scheme in the figure,
combined with a steady-state approximation for the concentra-
tions of the unrelaxed and relaxed intermediates, OH‚HNO3*
and OH‚HNO3, yields the following expression for the overall
rate constant.
to each other (i.e., temperature and pressure dependence) are
independent of the NO3 yield from N2O5 photolysis.
Figure 7 demonstrates clearly that the NO3 yields from
reactions 1 and 2 do not vary with pressure or temperature, and
that they are unity to within the uncertainty of this measurement.
This result is not only important for atmospheric modeling, but
it also shows that reactions 1-5 always give the same set of
products irrespective of the various temperature and pressure
dependences of their rate constants.
-1
kdkc[M]
k ) ka 1 - k-a k-a + kb +
(16)
{
(
) }
k-c[M] + kd
This function gives a sigmoidal dependence on pressure. At both
low and high pressures, eq 16 reaches bimolecular, pressure
independent limits.
IV. Discussion
Figure 8 summarizes the temperature dependence of the rate
constant data for reactions 1-4 in Arrhenius form. Fits from
our previous study of reaction 11 (top solid lines) appear for
both the high pressure and low-pressure behavior of the rate
constant, and include a high-temperature measurement (solid
point) from Troe.37 The fit from the curved Arrhenius plot in
Figure 1 appears as the lower solid line. The dashed lines
represent the smaller magnitude of the secondary kinetic isotope
effect, i.e., k3 (upper) and k4 (lower). Although we have not
directly measured its temperature dependence, in Figure 8 we
assume that k4 (OH + DNO3) has the same behavior as k2 (OD
+ DNO3).
A consistent picture of the mechanism for the reaction of
OH with HNO3 must explain the series of observations described
in the results section and in Figure 8. First, below 300 K, k1
displays a negative temperature dependence and a pressure
dependence that increases with decreasing temperature. Second,
any OH/OD or 16OH/18OH exchange reactions must be a factor
of 10 (or more) slower than the reactions to form products.
Third, the primary kinetic isotope effect (D substitution in
HNO3) decreases the rate constant by an order of magnitude,
makes the rate constant pressure independent (over the 20-
200 Torr range that we measured), and yields a markedly curved
Arrhenius plot. Fourth, the secondary kinetic isotope effect (D
substitution on OH) modestly increases the rate constant but
does not significantly change the overall pressure and temper-
ature dependence. Finally, reaction 1 yields only NO3 and H2O
as products, irrespective of pressure and temperature. The
k-a
kb
kLoP ) ka 1 -
) ka
(17)
(
)
(
)
k-a + kb
k-a + kb
k-a
kb + Keqkd
k-a + kb + Keqkd
kHiP ) ka 1 -
) ka
(
)
(
)
k-a + kb + Keqkd
(18)
To arrive at eq 17, we have assumed k-c[M] , kd and kc[M] ,
k-a + kb, while in eq 18 we have assumed k-c[M] . kd. In eq
18, Keq is the equilibrium constant between the energized and
stabilized adduct, i.e., kc/k-c. We note that the pressure
dependence in eq 16 has a behavior similar to that of the three-
parameter function given by Lamb et al.17 that we used in the
analysis of our previous study1 (see Figure 2). In reality, an
OH‚HNO3 adduct with energies anywhere between the fully
thermalized state (OH‚HNO3 in Figure 9) and the fully energized
state (OH‚HNO3* in Figure 9) will lead to products. Here, for
the sake of simplicity, we have assumed a two state model. A
full RRKM-master equation model is unlikely to give a
different qualitative answer.
The observation that, at low temperature, k1 has a finite value
at low pressures but is pressure dependent over some intermedi-
ate range has two important implications in the context of the
above model. First, the reaction barrier must be sufficiently large
that redissociation of OH‚HNO3* competes with reaction to
products; i.e., k-a cannot be negligible compared to kb in eq

1612 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Brown et al.
acid to hydroxyl radical should have an asymmetric geometry,
just as in complex A. By contrast, the transition state for the
OH/OD exchange reaction should involve a symmetric (i.e., C2V
for the case of two H atoms) six membered ring that does not
resemble the geometry of complex A. Thus, both the calculated
geometry of the adduct and the experimental observations
suggest that the barrier to the exchange reaction is larger than
that for reaction to form NO3 and H2O.
The observation that deuteration of nitric acid dramatically
reduces the rate constant, removes its pressure dependence, and
results in the strongly curved Arrhenius plot of Figure 1 is
consistent with the mechanism of Figure 9. The lack of pressure
dependence comes from the balance between kd and k-c[M] in
eq 16. The first-order rate constants, kb and kd, are likely to be
significantly slower for DNO3 than for HNO3 if tunneling is
involved. Furthermore, the effective barrier height is slightly
larger for the DNO3 than for HNO3 because of zero point energy
stabilization of the reactants relative to the transition state, where
one of the D atom motions has an imaginary frequency.41
Deuterium substitution also increases the density of states in
the adduct near the threshold for dissociation to reactants,
leading to larger collisional rate constants, kc and k-c. Thus, it
is plausible that for DNO3, k-c[M] . kd over the pressure range
examined here, and that eq 18, which is independent of [M], is
a good description of k2 and k4. Since both kb and kd are smaller
for DNO3 than for HNO3, both will be quite small compared to
k-a. Therefore, k2 and k4 should have pressure independent rate
constants that are much smaller than the high-pressure limits
for k1 or k3, in accord with observations. Finally, the rate
expression of eq 18 is consistent with the curved Arrhenius plot
in Figure 1. Both kb and Keqkd will be much less than k-a, so
the overall rate constant from eq 18 will be proportional to their
sum, kb + Keqkd. The positive temperature dependence above
300 K in Figure 1 is most likely determined by kb and gives a
lower limit (because of tunneling) to the barrier height of Ea g
4.3 kcal mol-1. The negative temperature dependence comes
from Keq, with the second term above dominant at lower
temperature. It is noteworthy that the high-temperature measure-
ment of k1 (OH + HNO3)37 in Figure 8 shows that reaction 1
also has a positive temperature dependence at high enough
temperatures, and should thus exhibit a curvature in its Arrhenius
plot similar to that for k2; this is a testable hypothesis. To our
knowledge, there is no published value of a calculated barrier
height for reaction 1.
Figure 10. Two different proposed geometries for the adduct formed
in the reaction of OH with HNO3. Complex A is the doubly hydrogen-
bonded, six membered ring. Complex B is the O-N bonded complex
suggested by Lamb et al.17
16. If kb were much greater than k-a, the overall rate constant
would be equal to the forward association rate constant, ka, and
would be independent of pressure. Second, formation of products
from the stabilized adduct, OH‚HNO3, must compete with
collisional re-excitation that gives back reactants; i.e., kd ≈
k-c[M]. If kd is much less than k-c[M], the overall rate constant
goes to the form of eq 18 and becomes pressure independent.
Since formation of products from the adduct, either stabilized
or unstabilized, clearly must proceed over at least a modest
barrier, kb and (particularly) kd probably have a significant
contribution from tunneling.
Figure 10 shows two plausible proposals for the structure of
the OH‚HNO3 adduct: complex A is a doubly hydrogen bonded,
six membered ring,10,14,15 and complex B is the one resulting
from OH attachment to the N atom in HNO3.17 (The energy of
the adduct shown in Figure 9 comes from ab initio calculations,
as discussed further below.) Experimental observation of any
of the exchange reaction 3b, 4b, or 5b, would have provided
definitive evidence for the existence of one or both of the
adducts in the figure. There is, however, no measurable
exchange in either OH/OD or 16OH/18OH reaction. Thus,
whatever the form of the complex, the barrier to the exchange
reaction, either energetic or entropic, must be larger than that
for reaction to form NO3 and H2O. If, as we argue, the adduct
does form, the transition state leading to NO3 + H2O must be
smoothly connected to the complex. The path connecting
complex A to this transition state would involve elongation of
the H-ONO2 bond. Starting from complex B, the transition
state would require transfer of the nitric acid H to the hydroxyl
O via a four-centered, tight transition state.
The O-N bonded complex structure (B in Figure 10) was
favored by Lamb et al.17 based on calculations showing that
the Arrhenius behavior of k1 for a tight transition state
better matched the available data. Our results showing that
18OH/16OH exchange does not measurably occur suggests that
reaction does not proceed through complex B, although this
observation alone does not disprove this complex. Since the
two OH groups are nearly identical in complex B, elimination
of either to regenerate reactants should be facile, and one expects
to observe both OH/OD and 16OH/18OH exchange.
Formation of the doubly hydrogen-bonded, six membered ring
complex (A in Figure 10) appears to be a more plausible
pathway. Indeed, recent ab initio calculations have predicted it
to be bound by 6.0 kcal mol-1 with respect to OH and HNO3.38
This result is similar to the recent calculations of the nitric acid-
water complex,39 and agrees with other recent, unpublished, ab
initio calculations.40 Complex A is asymmetric, with a strong
hydrogen bond between the H atom of nitric acid and the O
atom of the hydroxyl, and a longer, somewhat weaker bond
between the hydroxyl H atom and one of the nitric acid O atoms.
The transition state for transfer of a single H atom from nitric
The observation that deuteration of hydroxyl radical increases
the rate constant only modestly is consistent with secondary
kinetic isotope effects observed in other OH reactions, i.e., OH
(OD) + H2,26 CH4,41 HCl,42 etc. In these systems, the secondary
kinetic isotope effect comes from the influence of zero point
energy on the effective barrier height, particularly if the
transition state has a bent geometry.
Finally, the fact that NO3 is the only product of reaction 1
means that all of the observed dependences of the rate constant
on temperature and pressure must be due to reactions producing
a single set of products and not due to competition between
pathways that give different products. Clearly, the above model
qualitatively accounts for all observations without invoking any
additional product channels. Furthermore, as Figure 11 dem-
onstrates, eq 16 can reproduce the observed rate constants using
reasonable values for ka, k-a, kb, kc, k-c, and kd. For example,
one may estimate the forward association rate constant, ka, based
on the work of Smith and Williams,43 who measured the
quenching rate constant for OH(V)1) by HNO3 to be 2.5 ×
10-11 cm3 molecule-1 s-1. This quenching rate constant may

Reaction of Hydroxyl Radical with Nitric Acid
J. Phys. Chem. A, Vol. 105, No. 9, 2001 1613
kd, by a factor of 200 relative to the simulation for k1 at the
same temperature. We estimated this factor by calculating the
tunneling transmission probabilities for an asymmetric Eckart
potential45,46 with a barrier height relative to the bottom of the
well of 11 kcal mol-1 (5 kcal mol-1 from separated reactants)
and an exothermicity of -17 kcal mol-1 relative to reactants
(-11 kcal mol-1 from the bottom of the adduct well). We used
a characteristic length for the Eckart potential of 0.7 Å based
on the calculated adduct geometry. We then adjusted kb to match
the observed rate constants (see Table 5). Clearly, reduction in
the tunneling rate constant from the bottom of the well has the
anticipated effect of removing the pressure dependence and
dramatically reducing the overall rate constant. The lack of a
pressure dependence is not sensitive to the value of kd so long
as it is at least a factor of 100 smaller than in the simulation of
k1 at the same temperature. Although it is too small to appear
on the scale of Figure 11, there is a weak pressure dependence
in the simulation of k2, but it occurs only at pressures below
the range of our measurement.
The model presented here is empirical and is not intended as
a rigorous comparison of experiment to theory. It should,
however, provide a framework for further experimental and
theoretical study of reaction 1, and it does qualitatively account
for all observations. As Figure 11 shows, our data, which lie
mainly in the falloff region, may not accurately characterize
either the high- or low-pressure limits of reaction 1, both of
which would aid in a comparison between experiment and
theory. Also, at low enough temperatures, there may be an
observable pressure dependence for OD + DNO3 that would
be very sensitive to the value of the tunneling rate constant, kd.
Finally, this system should provide an excellent test of chemical
kinetics theories in which tunneling plays an important role,
particularly if a reliable potential energy surface connecting both
reactants and products to the adduct can be calculated. Such a
theoretical effort is currently underway.40
Figure 11. Variation of k1 and k2 with bath gas (He) number density
(solid and open points, respectively). The solid and dashed lines are
simulations of k1 and k2, respectively, using eq 16 and the rate constants
in Table 4.
TABLE 5: Rate Constants Used To Simulate Experimental
Data in Figure 11a
T (K)
kc
kb
kd
k1 (OH + HNO3)
296
250
220
0.6
280
450
500
10
5.1
4.0
1.0
2.5
k2 (OD + DNO3)
1.0 33
250
0.025
a The values of ka and k-a are 1 × 10-11 cm3 molecule-1 s-1 and 2.5
× 1010 s-1, respectively, at all temperatures. kc is in units of 10-10 cm3
molecule-1 s-1; kb and kd are in units of 106 s-1
.
have a contribution from resonant energy transer between OH-
(V)1) and HNO3, and we may thus assume ka ≈ 1 × 10-11
cm3 molecule-1 s-1. One may also estimate the value of the
equilibrium constant, Keq ) kc/k-c, from the calculated OH‚
HNO3 binding energy and the density of vibrational states in
the well at the dissociation threshold. To count the vibrational
state density, we used a Beyer-Swinehart algorithm44 and the
harmonic frequencies of Aloisio and Francisco.38 These authors
also give an equilibrium constant for the overall association
reaction, OH + HNO3 a OH‚HNO3. From their equilibrium
constants, our calculated values for kc/k-c and the estimate for
ka, we estimate the first-order rate constant for dissociation of
the energized complex back to reactants, k-a, to be ap-
proximately 2.5 × 1010 s-1. To simulate k1 (solid lines in Figure
11), we used the above values for ka and k-a and, at each
temperature, we adjusted kb to match the observed low-pressure
limit, kd to match the observed high-pressure limit, and kc to
match the observed pressure dependence. Table 5 gives the kc,
kb, and kd values for three different temperatures. The unimo-
lecular/tunneling rate constants, kb and kd, are reasonable,
although the values for kc are rather large. That the collisional
relaxation must be so efficient in order to reproduce the observed
pressure dependence indicates that the simple two-state model
shown in Figure 9 (i.e., consideration only of OH‚HNO3* and
OH‚HNO3) is probably inadequate. For example, collisional
relaxation to states just below the dissociation threshold in the
well will indeed be more efficient. Furthermore, formation of
products via tunneling will occur from any vibrational state
populated within the well.
Acknowledgment. We thank Roberto Bianco and James T.
(Casey) Hynes for many highly valuable discussions. Discus-
sions with I. W. M. Smith, E. R. Lovejoy, and H. Stark were
also very helpful. This work was funded in part by NASA’s
upper atmospheric research program. S.S.B. thanks the National
Research Council for a postdoctoral fellowship.
References and Notes
(1) Brown, S. S.; Talukdar, R. K.; Ravishankara, A. R. J. Phys. Chem.
1999, 103, 3031.
(2) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.;
Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling; JPL Publication, 97-4; Jet Propulsion Laboratory: Pasadena, CA,
1997.
(3) Gao, R.-S.; Fahey, D. W.; DelNegro, L. A.; Donnelly, S. G.; Keim,
E. R.; Neuman, J. A.; Teverovski, L.; Wennberg, P. O.; Hanisco, T. F.;
Lazendorf, E. J.; Proffitt, M. H.; Margitan, J.; Wilson, J. C.; Elkins, J. W.;
Stimpfle, R. M.; Cohen, R. C.; McElroy, C. T.; Bui, T. P.; Salawitch, R.
J.; Brown, S. S.; Ravishankara, A. R.; Portmann, R. W.; Ko, M. K. W.;
Weisenstein, D. K.; Newman, P. A. Geophys. Res. Lett. 1999, 26, 1153.
(4) Portmann, R. W.; Brown, S. S.; Gierczak, T.; Talukdar, R. K.;
Burkholder, J. B.; Ravishankara, A. R. Geophys. Res. Lett. 1999, 26, 2387.
(5) Bru¨hl, C.; Crutzen, P. J. J. Geophys. Res. 2000, 105, 12163.
(6) Wine, P. H.; Ravishankara, A. R.; Kruetter, N. M.; Shah, R. C.;
Nicovich, J. M.; Thompson, R. L.; Wuebbles. J. Geophys. Res. 1981, 86,
1105.
(7) Kurylo, M. J.; Cornett, K. D.; Murphy, J. L. J. Geophys. Res. 1982,
87, 3081.
(8) Jourdain, J. L.; Poulet, G.; Le Bras, G. J. Chem. Phys. 1982, 76,
5827.
(9) Ravishankara, A. R.; Eisele, F. L.; Wine, P. H. J. Phys. Chem.
1982, 86, 1854.
(10) Marinelli, W. J.; Johnston, H. S. J. Chem. Phys. 1982, 77, 1225.
To simulate the data for k2 at 250 K (dashed line and open
circles in Figure 11), we reduced the tunneling rate constant,

1614 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Brown et al.
(11) Smith, C. A.; Molina, L. T.; Lamb, J. J.; Molina, M. J. Int. J. Chem.
Kinet. 1984, 16, 41.
(12) Connell, P. S.; Howard, C. J. Int. J. Chem. Kinet. 1985, 17, 17.
(13) Devolder, P.; Carlier, M.; Pauwels, J. F.; Sochet, L. R. Chem. Phys.
Lett. 1984, 111, 94.
(14) Margitan, J. J.; Watson, R. T. J. Phys. Chem. 1982, 86, 3819.
(15) Stachnik, R. A.; Molina, L. T.; Molina, M. J. J. Phys. Chem. 1985,
90, 2777.
(16) Singleton, D. L.; Paraskevopoulos, G.; Irwin, R. S. J. Phys. Chem.
1991, 95, 694.
(17) Lamb, J. J.; Mozurkewich, M.; Benson, S. W. J. Phys. Chem. 1984,
88, 6441.
(18) Nelson, H. H.; Marinelli, J.; Johnston, H. S. Chem. Phys. Lett. 1981,
78, 495.
(19) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr,
J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data 1997, 26, 521.
(20) Husain, D.; Norrish, R. G. W. Proc. R. Soc. London A 1965, 273,
165.
(21) Glanzer, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 71.
(22) Yokelson, R. J.; Burkholder, J. B.; Fox, R. W.; Talukdar, R. K.;
Ravishankara, A. R. J. Phys. Chem. 1994, 98, 13144.
(23) Burkholder, J. B.; Talukdar, R. K.; Ravishankara, A. R.; Soloman,
S. J. Geophys. Res. 1993, 98, 22, 937.
(29) Dunlea, E. Private communication.
(30) Force, A. P.; Wiesenfeld, J. R. J. Phys. Chem. 1981, 85, 782.
(31) Schmoltner, A. M.; Talukdar, R. K.; Warren, R. F.; Mellouki, A.;
Goldfarb, L.; Gierczak, T.; McKeen, S. A.; Ravishankara, A. R. J. Phys.
Chem. 1993, 97, 8976.
(32) Yokelson, R. J.; Burkholder, J. B.; Goldfarb, L.; Fox, R. W.; Gilles,
M. K.; Ravishankara, A. R. J. Phys. Chem. 1995, 99, 13976.
(33) Yokelson, R. J.; Burkholder, J. B.; Fox, R. W.; Ravishankara, A.
R. J. Phys. Chem. 1997, 101, 6667.
(34) Turnipseed, A. A.; Vaghjiani, G. H.; Thompson, J. E.; Ravishankara,
A. R. J. Chem. Phys. 1992, 96, 5887.
(35) Harwood, M. H.; Burkholder, J. B.; Ravishankara, A. R. J. Phys.
Chem. 1998, 102, 1309.
(36) Bossard, A. R.; Paraskevopoulos, G.; Singleton, D. L. Chem. Phys.
Lett. 1987, 134, 583.
(37) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 74.
(38) Aloisio, S.; Francisco, J. S. J. Phys. Chem. A 1999, 103, 6049.
(39) Tao, F.-M.; Higgins, K.; Klemperer, W.; Nelson, D. D. Geophys.
Res. Lett. 1996, 23, 1797.
(40) Bianco, R.; Hynes, J. T. Manuscript in preparation.
(41) Gierczak, T.; Talukdar, R. K.; Herdon, S. C.; Vaghjiani, G. L.;
Ravishankara, A. R. J. Phys. Chem. 1997, 101, 3125.
(42) Battin-Leclerc, F.; Kim, I.; Talukdar, R. K.; Portmann, R. W.;
Ravishankara, A. R.; Steckler, R.; Brown, D. J. Phys. Chem. 1999, 103,
3237.
(43) Smith, I. W. M.; Williams, M. D. J. Chem. Soc., Faraday Trans.
2 1985, 81, 1849.
(44) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recom-
bination Reactions; Blackwell Scientific Publications: Oxford, U.K., 1990.
(45) Johnston, H. S.; Rapp, D. J. Am. Chem. Soc. 1961, 83, 1.
(46) Johnston, H. S.; Heicklen, J. J. Phys. Chem. 1962, 66, 532.
(24) Molina, L. T.; Molina, M. J. J. Geophys. Res. 1986, 91, 14501.
(25) Brown, S. S.; Talukdar, R. K.; Ravishankara, A. R. Chem. Phys.
Lett. 1999, 299, 277.
(26) Talukdar, R. K.; Gierczak, T.; Goldfarb, L.; Rudich, Y.; Madhava
Rao, B. S.; Ravishankara, A. R. J. Phys. Chem. 1996, 100, 3037.
(27) Yu, H. G.; Varanda, A. J. C. J. Chem. Soc., Faraday Trans. 1997,
93, 2651.
(28) Talukdar, R. K.; Ravishankara, A. R. Chem. Phys. Lett. 1996, 253,
177.