14N/15N kinetic isotope effect in the association reaction O(3P)+NO+Ar→NO2+Ar

Article abstract of DOI:10.1016/S0009-2614(01)00838-7

The termolecular rate constants for the O(³P)+¹⁴NO+Ar→¹⁴NO₂+Ar and O(³P)+¹⁵NO+Ar→¹⁵NO₂+Ar reactions were determined under room temperature bulk conditions. O(³P) was produced by the pulsed photodissociation of SO₂ at 210.4 nm and was monitored by two-photon laser-induced fluorescence at 225.7 nm. The rate constants for ¹⁴NO and ¹⁵NO were determined to be 5.4±0.2 and 6.1±0.3×10^-32cm⁶s^-1, respectively. The error limits are twice the standard errors (S.E.). This isotope effect is opposite to that expected from a statistical model but is similar to that observed in the O₃ formation reactions from O(³P) and O₂.

Full text of DOI:10.1016/S0009-2614(01)00838-7

7 September 2001
Chemical Physics Letters 345 22001) 44±50
www.elsevier.com/locate/cplett
14N/15N kinetic isotope e€ect in the association reaction
3
Oꢀ P† ‡ NO ‡ Ar ! NO2 ‡ Ar
Hironobu Umemoto *, Kunikazu Tanaka, Shigeki Oguro, Ryoji Ozeki,
Masashi Ueda
Department of Chemical Materials Science, Japan Advanced Institute of Science and Technology, Asahidai, Tatsunokuchi, Nomi,
Ishikawa 923-1292, Japan
Received 10 March 2001; in ®nal form 10 July 2001
Abstract
3
3
The termolecular rate constants for the Oꢀ P† ‡ 14NO ‡ Ar ! 14NO2 ‡ Ar and Oꢀ P† ‡ 15NO ‡ Ar ! 15NO2 ‡ Ar
reactions were determined under room temperature bulk conditions. O23P) was produced by the pulsed photodisso-
ciation of SO2 at 210.4 nm and was monitored by two-photon laser-induced ¯uorescence at 225.7 nm. The rate con-
stants for 14NO and 15NO were determined to be 5:4 Æ 0:2 and 6:1 Æ 0:3 Â 10À32 cm6 sÀ1, respectively. The error limits
are twice the standard errors 2S.E.). This isotope e€ect is opposite to that expected from a statistical model but is similar
to that observed in the O3 formation reactions from O23P) and O2. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction
16O ‡ 18O2 ‡ M, while that for 18O ‡ 16O2 ‡ M
was the smallest. The ratio of the rate constants
was as large as 1.65. This isotope e€ect cannot be
attributed to the di€erence in molecular symmetry
or that in nuclear spin, because the symmetry and
the spin statistics for 16O ‡ 18O2 and 18O ‡ 16O2
are exactly the same [2,3].
Sehested et al. [8,9] have also measured the rate
constants for the O ‡ O2 ‡ M reactions and ex-
amined the isotope e€ect. They employed a pulse
radiolysis technique to produce atomic oxygen
while a time-resolved ultraviolet absorption tech-
nique was used to detect O3 products. The rate
constant for the 18O ‡ 18O2 ‡ M reaction was
measured to be 9.8% larger than that for the
16O ‡ 16O2 ‡ M reaction when CO2 was used as a
third-body, while that was 2.2% smaller when Ar
was used. The presence of a large isotope e€ect
is consistent with the results of Mauersberger
and coworkers, but the third-body dependence
Since the discovery of an isotopic anomaly in
stratospheric ozone [1], Mauersberger and co-
workers have examined the kinetic isotope e€ect in
the ozone formation reactions, Oꢀ P† ‡ O2 ‡ M
3
! O3 ‡ M [2±7]. They photolyzed isotopic O2
mixture to produce ground state atomic oxygen
and detected isotopic O3 products by using a mo-
lecular beam mass spectrometric technique or an
infrared absorption technique. By measuring the
isotopic populations of the produced ozone, they
determined the isotope-speci®c rate constants for
eight 16O/17O/18O combinations [3]. The isotope
e€ect was amazingly large. When N2 was used as a
third body, the rate constant was the largest for
* Corresponding author. Fax: +81-761-51-1655.
E-mail address: umemoto@jaist.ac.jp 2H. Umemoto).
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 2 0 1 ) 0 0 8 3 8 - 7

H. Umemoto et al. / Chemical Physics Letters 345 /2001) 44±50
45
con¯icts with the more recent work by Guenther
et al. [6].
window and the detection zone was 10 cm for the
photolysis laser, while that for the probe laser
beam was 13 cm. Typical pulse energies of the
photolysis and the probe lasers were 0.4 mJ. The
delay time between the two laser pulses was con-
trolled with a delay/pulse generator 2Stanford
Research Systems, DG535). The photomultiplier
signal was monitored and averaged with a digital
oscilloscope 2LeCroy, 9450A). The gas pressures
were measured with capacitance manometers
2MKS Baratron, 122AA and Diavac, SG-133K).
The SO2 pressure was ®xed at 53 Pa. The NO
pressure was changed between 0 and 1.53 kPa. The
bu€er gas pressure was changed between 13.3 and
33.3 kPa. All the measurements were carried out at
room temperature, 295 Æ 2 K.
The question is whether such a large isotope ef-
fect can also be observed in other termolecular
processes, such as 16O ‡ 15N16O ‡ M ! 15N16O2 ‡
M and 16O ‡ 14N16O ‡ M ! 14N16O2 ‡ M reac-
tions. According to Janssen et al. [4] the rate con-
18
stant for the 16O ‡ O16O ‡ M ! 16O18O16O ‡ M
reaction is 8% larger than that for the 16O ‡ 16O2 ‡
M ! 16O3 ‡ M reaction. In the present work, the
absolute rate constants for the above NO2 produc-
tion reactions were determined by employing a
pulsed laser technique.
2. Experimental
The concentration of O atoms just after the
production is estimated to be K 1014 cmÀ3. The
density of excited SO2 molecules produced is cal-
culated to be 3 Â 1014 cmÀ3 from the pulse energy,
the beam diameter, and the absorption coecient
of SO2. It should be noted that 70% of the incident
light is absorbed before reaching the detection
zone. The quenching of excited SO2 by Ar being
taken into account [14], the O atom density is es-
timated to be ꢁ1:5 Â 1014 cmÀ3. This value may be
halved in the presence of NO.
NO 2Sumitomo Seika, 99.9%), 15NO 2Shoko
Tsusho, isotopic purity 99.9%), SO2 2Takachiho
Kako 99.999%), and Ar 2Teisan, 99.9995%) were
used as supplied. The isotopic purity of 15NO was
checked by using a quadrupole mass spectrometer
2Anelva, M-QA200TS). NO we used contains
natural abundance of 15N. However, since the
abundance is 0.36%, the results obtained for nat-
ural abundance NO may be regarded as that for
14NO. In this Letter, natural abundance NO is
sometimes referred to as 14NO.
The experimental apparatus and the procedure
were similar to those described elsewhere [10]. SO2
was photolyzed to produce ground state atomic
oxygen, Oꢀ2p4 3P†, in the presence of NO and a
bu€er gas, Ar. The wavelength was set to 210.4
nm, which is one of the absorption peaks of SO2
[11]. The absorption cross section of SO2 is
9 Â 10À18 cm2, while that of NO at this wavelength
is less than 1 Â 10À20 cm2. The frequency-tripled
output of a YAG laser pumped dye laser 2Quanta-
Ray, GCR-170 and PDL-3) was used for the
photolysis. The frequency tripling was carried out
by using two BBO crystals and a polarization ro-
tator 2Solar) [12]. The temporal dependence of the
Oꢀ2p4 3P† density was measured at various NO
and Ar pressures by using a two-photon laser-in-
duced ¯uorescence technique [13]. Oꢀ2p4 3P† was
3
excited to Oꢀ2p33p P† with the frequency-doubled
output of another YAG laser pumped dye laser
2Quanta-Ray, GCR-170 and PDL-3) at 225.7 nm.
The direct ¯uorescence from this state to the
2p33s3S state around 845 nm, as well as that from
the 2p33p5P state after energy transfer around 777
nm, was monitored. A red-sensitive photomulti-
plier tube 2Hamamatsu Photonics, R636) was used
with a cut-o€ ®lter 2Toshiba, R65) and a lens
system. The two laser beams were aligned collin-
early. The probe laser was tightly focused by using
an iris and a 220 mm focal-length lens, while the
photolysis laser beam was mildly focused to 2 mm
in diameter. The distance between the entrance
3. Results
In the present work, the isotope e€ect in the
termolecular rate constant at the low-pressure
limit is to be measured. For this purpose, the
bu€er gas pressure should not be too low or too
high. At low pressures, the di€usional loss is
dominant and the decay pro®les of the O23P) sig-

46
H. Umemoto et al. / Chemical Physics Letters 345 /2001) 44±50
Table 1
Ar pressure dependence of the decay rate of O23P) in 105 sÀ1
Fig. 1 illustrates the typical photolysis-probe
delay time dependence of the O atom density ob-
tained in the presence of 15NO and 26.7 kPa of Ar.
Similar results were obtained for 14NO. The decay
rates are summarized in Table 2. In order to
evaluate the termolecular rate constant for
[Ar]a
Decay rateb;c
Decay rateb;d
13.3
20.0
26.7
33.3
0.99
0.73
1:15 Æ 0:04
1:43 Æ 0:04
1:66 Æ 0:12
1:02 Æ 0:06
1:28 Æ 0:07
1:52 Æ 0:15
O ‡ NO ‡ Ar,
the
contribution
of
the
a Pressure in kPa. NO pressure was 1.33 kPa.
b Error limits are two S.D.
c Without corrections for di€usional loss.
d With corrections for di€usional loss.
O ‡ NO ‡ NO process must be subtracted. The
rate constant for this reaction has been measured
to be 1:26 Â 10À31 cm6 sÀ1 [15]. The corrected
values are also listed in Table 2. The isotope e€ect
in the O ‡ NO ‡ NO reaction was ignored since
the correction factors were less than 11% of the
measured decay rates.
nal are not exponential. At high pressures, the
decay rate shows saturation against the Ar pres-
sure. The Ar pressure dependence of the decay
rates in the presence of 1.33 kPa of NO is sum-
marized in Table 1. Several measurements were
carried out under the same conditions in order to
evaluate these values. The error limits are two
standard deviations 2S.D.). The non-exponential-
ity was apparent when the Ar pressure was less
than 13.3 kPa. In such a case, only the initial part,
10 ls, was analyzed. This is why the error limits
are not given at 13.3 kPa. The decay rate of O23P)
increased linearly with the increase in the Ar
pressure up to 33.3 kPa after the correction for the
di€usional loss. In other words, the rate constants
obtained below this pressure are those in the low-
pressure limit. Then, the isotope e€ect was mea-
sured in the presence of 26.7 kPa of Ar.
The decay rates of the O23P) density are plotted
in Fig. 2 both for 14NO and 15NO, as a function of
NO pressure. In these plots the contribution of the
O ‡ NO ‡ NO reaction is corrected. The termo-
lecular rate constants evaluated from the slopes of
these plots are listed in Table 3. The error limits
for our results are twice the S.E. calculated by the
formula given in [16]. The value for 15NO is
13 Æ 9% larger than that for 14NO. The literature
values for the natural abundance NO reported
after 1976 listed in Table 3 [17±19] are larger than
the present value. One of the possible reasons for
this discrepancy is the di€erence in local temper-
atures. The local temperature in our system may
have been raised by laser irradiation. The
Fig. 1. Semilogarithmic plots of the decay of O23P) concen-
tration in the presence of 15NO and Ar. The Ar pressure was
26.7 kPa while the 15NO pressure was 0.0 2s), 0.33 2d), 0.67
ꢀM†, 1.00 ꢀN†, 1.33 ꢀÆ, and 1.53 ꢀj† kPa.
Fig. 2. Decay rates of O23P) as a function of 14NO 2d) or 15NO
2s) pressure. The Ar pressure was 26.7 kPa. The contribution
3
of the Oꢀ P† ‡ NO ‡ NO reaction is corrected.

H. Umemoto et al. / Chemical Physics Letters 345 /2001) 44±50
47
Table 2
NO pressure dependence of the decay rate of O23P) in 105 sÀ1
[NO]a
14NOb;c
14NOb;d
15NOb;c
15NOb;d
0.0
0:14 Æ 0:03
0:47 Æ 0:04
0:75 Æ 0:05
1:09 Æ 0:05
1:43 Æ 0:04
1:63 Æ 0:08
0:14 Æ 0:03
0:46 Æ 0:04
0:71 Æ 0:05
1:01 Æ 0:05
1:29 Æ 0:04
1:45 Æ 0:08
0:14 Æ 0:03
0:51 Æ 0:04
0:80 Æ 0:04
1:17 Æ 0:05
1:60 Æ 0:06
1:86 Æ 0:08
0:14 Æ 0:03
0:50 Æ 0:04
0:76 Æ 0:04
1:10 Æ 0:05
1:47 Æ 0:06
1:68 Æ 0:08
0.33
0.67
1.00
1.33
1.53
a Pressure in kPa. Ar pressure was 26.7 kPa.
b Error limits are two S.D.
c Decay rate without corrections for O ‡ NO ‡ NO reaction.
d Decay rate with corrections for O ‡ NO ‡ NO reaction.
O ‡ NO ‡ Ar reaction has a large negative acti-
vation energy [17,19]. The present di€erence can be
explained if the local temperature in our system
was ꢁ40 K higher. The rate constant can also be
evaluated from the Ar pressure dependence. In this
case, however, the pressure dependence of the
di€usional loss rate must be taken into account.
This causes another uncertainty, especially at low
pressures. The measurement of the NO pressure
dependence is more reliable for the evaluation of
the isotope e€ect.
In the present measurements, care must be ta-
ken to the production of O23P) by the probe laser.
The wavelength of the probe laser is near the 20,0)
band of the NO c system. Two-photon dissocia-
tion of NO to produce O23P) cannot be ignored
when the pulse energy of the probe laser is 0.4 mJ.
Therefore, measurements were carried out both in
the presence and in the absence of the photolysis
laser and the contribution of the O23P) production
by the probe laser was subtracted. There is an
isotope e€ect in the absorption coecient of the
probe laser. The coecient for 15NO is larger than
that for 14NO. Then, the O23P) signal intensity for
15NO was weaker than that for 14NO when other
experimental conditions were identical. In the
presence of 1.33 kPa of 14NO, the signal to back-
ground ratio was 100 :ꢁ 6 when the delay time
was 0.1 ls, while it was 60 :ꢁ 7 for 15NO. It may
be suspected that the decay rate depends on the
probe laser intensity. An exact measurement of the
isotope e€ect is dicult in such a case because
the e€ective intensity of the probe laser depends on
isotopic substitution. In order to check this point,
measurements were carried out by changing the
laser energy from 0.2 to 0.5 mJ. No systematic
change was observed in the decay rate of O23P).
Similar measurements of the intensity depen-
dence were performed for the photolysis laser. The
decay pro®les of O23P) density did not change
systematically when the pulse energy was changed
from 0.2 to 0.4 mJ. This independence is consistent
with the estimated initial concentration of O at-
oms. If the concentration is 8 Â 1013 cmÀ3 and all
the O atoms are converted to NO2, which reacts
with O23P) bimolecularly [20], the contribution of
the O ‡ NO2 reaction should be 0.7% of that of
the O ‡ NO ‡ Ar reaction when the NO and Ar
pressures are 1.33 and 26.7 kPa, respectively. The
buildup of NO2 in the reaction vessel should also
be minor. This is supported by the invariance in
the decay rates when the same gas sample was used
succeedingly. It should be noted that the produc-
tion of O23P) by the photodissociation of SO2 was
in the proportional region. When the pulse energy
was reduced from 0.4 to 0.2 mJ, the signal intensity
decreased by 50%.
Table 3
Termolecular rate constants for the Oꢀ P† ‡ NO ‡ Ar !
3
NO2 ‡ Ar reaction
Reaction
Rate constanta
References
O ‡ 15NO ‡ Ar
6:1 Æ 0:3
5:4 Æ 0:2
6:3 Æ 0:1
7:0 Æ 0:7
6:7 Æ 0:1
Present study
Present study
[17]
O ‡ 14NO ‡ Ar
[18]
[19]
a In units of 10À32 cm6 sÀ1 at room temperature.

48
H. Umemoto et al. / Chemical Physics Letters 345 /2001) 44±50
O ‡ NO system can be ignored [23,24]. The above
The present isotope e€ect cannot be attributed
estimate may not be quantitative, but an opposite
isotope e€ect was found between the experimental
and calculated values. Similar results have been
obtained by Kaye for the ozone formation pro-
cesses [25]. According to Smith, the inclusion of an
to the contribution of NO2 impurity. In order to
explain the present di€erence between the rate
constants for 14NO and 15NO, 15NO must have
contained 0.5% of NO2. NO2 can easily be removed
by passing through a trap cooled to ꢁ160 K. Such
puri®cation had no e€ect on the measured rate
constant. NO2 could not be identi®ed by a mass
spectrometric analysis or by a human eye, either.
2
~
excited state NO2, A B1, increases the calculated
low-pressure limiting rate constant by a factor of
1.7 [28]. The production of excited NO2 molecules
is well known as a chemiluminescence reaction.
However, the calculated kinetic isotope e€ect may
not be changed greatly by the inclusion of such
processes. In any case, the isotope e€ect more than
50% observed in the ozone formation reactions
cannot be explained by the di€erence in partition
functions and that in zero-point energies. Of
course, the present isotope e€ect cannot be ex-
plained by symmetry restriction, either.
4. Discussion
The isotope e€ect observed in the present work
cannot be explained by a classical statistical model.
The rate constant for the association, kass, is often
represented by the product of an equilibrium
constant between O ‡ NO and NO2, Keq, and the
rate constant for the thermal unimolecular de-
composition of NO2, kdiss [21,22]
One of the plausible ideas to explain the present
result is the isotope e€ect in the lifetime of the
quasi-bound complex between O and NO. The
termolecular association reactions are usually dis-
cussed in terms of the following energy transfer
mechanism:
kass ˆ Keqkdiss
:
Troe, as well as other investigators, has calculated
the absolute rate constants for the O ‡ NO ‡ M
reactions [22±24]. The kinetic isotope e€ect can
also be evaluated by this statistical approach [25].
In this calculation, the di€erence in partition
functions as well as that in vibrational zero-point
energies was taken into account. The zero-point
energies of the three normal modes of 15NO2 are 8,
5, and 19 cmÀ1 smaller than those of 14NO2 [26],
while that of 15NO is expected to be 17 cmÀ1
smaller than that of 14NO [27]. The di€erence in
translational and rotational partition functions
can easily be calculated from the di€erence in
masses. Numerical calculations employing the
formulas used by Michael and Lee [23] show that
the rate constant for O ‡ 15NO ‡ Ar should be
1.2% smaller than that for O ‡ 14NO ‡ Ar. Here,
the weak collision eciency factor, bc, was as-
sumed to be independent of isotopic substitution.
This small isotope e€ect results from the com-
pensation of the increase in the vibrational state
O ‡ NO ꢀ NOÃ2;
ꢀ1†
ꢀ2†
NOà ‡ Ar ! NO2 ‡ Ar:
2
Here, NOÃ2 is a short-lived collision complex. In
the low-pressure limit, the association rate con-
stant is expressed by
kass ˆ k1k2=k
;
À1
where k1; kÀ1, and k2 are the bimolecular or uni-
molecular rate constants for reactions 21), 2)1),
and 22). If the lifetime of 15NO2Ã, i.e. the inverse of
k
À1, is longer than that of 14NO2Ã, 15NO2Ã has a
larger probability to be stabilized by collisions
during its lifetime. Similar discussions have been
presented by Heidenreich and Thiemens [29] and
by Yang and Epstein [30] in the ozone formation
processes. If the O ‡ NO collision partners have
the correct energy to match one of the energy
levels near the dissociation limit of NO2, the life-
time of NOÃ2 complex should be longer [29]. Heavy
isotopologues may have more vibrational levels
because of their smaller vibrational quanta and
have larger probability for this energy match.
density at the critical energy, which appears in kdiss
,
and the increase in moments of inertia, included in
Keq, in heavy isotopologues. It should also be no-
ted that the Boltzmann factor in Keq cancels with
that in kdiss as far as the activation barrier for the

H. Umemoto et al. / Chemical Physics Letters 345 /2001) 44±50
49
However, such an isotope e€ect is already included
in the above statistical calculations and not su-
cient to explain the present isotope e€ect.
the Ministry of education, science, sports and
culture of Japan.
The isotope e€ects observed in non-adiabatic
transitions, such as predissociation by electronic
transition, are still larger. For example, the pre-
dissociation rate of 16O2ꢀ11Du; v ˆ 2† is 5.4 and 63
times as larger as those of 18O2 and 16O18O, re-
spectively [31]. The transition probability is de-
termined by the Franck±Condon factors, which
may strongly depend on the reduced mass. Apart
from the ground state, NO2 has at least three at-
tractive doublet states below the ON±O dissocia-
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The kinetic isotope e€ect between 14N and 15N
was examined. A signi®cant isotope e€ect was
3
found for the termolecular Oꢀ P† ‡ NO ‡ Ar !
NO2 ‡ Ar reaction. This isotope e€ect cannot be
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