Kinetics of hydroxyl radical reactions with isotopically labeled hydrogen

Article abstract of DOI:10.1021/jp9518724

The rate coefficients for the reactions of hydroxyl radical (OH) with H₂ (k₁), HD (k₂), and D₂ (k₃) were measured between ～230 and ～420 K to be k₁ = 7.21 × 10^-20T^2.69

Full text of DOI:10.1021/jp9518724

J. Phys. Chem. 1996, 100, 3037-3043
3037
Kinetics of Hydroxyl Radical Reactions with Isotopically Labeled Hydrogen
Ranajit K. Talukdar,† Tomasz Gierczak,†,‡ Leah Goldfarb,§ Yinon Rudich,|
B. S. Madhava Rao, and A. R. Ravishankara*,§
National Oceanic and Atmospheric Administration, Aeronomy Laboratory, 325 Broadway,
Boulder, Colorado 80303
ReceiVed: July 7, 1995; In Final Form: NoVember 7, 1995X
The rate coefficients for the reactions of hydroxyl radical (OH) with H2 (k1), HD (k2), and D2 (k3) were
measured between ∼230 and ∼420 K to be k1) 7.21 × 10-20T2.69 exp(-1150/T), k2 ) 5.57 × 10-20T2.7
exp(-1258/T), and k3 ) 5.7 × 10-20T2.73 exp(-1580/T) cm3 molecule-1 s-1 using pulsed photolysis to generate
OH and laser-induced fluorescence to detect it. Using the same method, the rate coefficients for the reactions
of OD with H2 and D2 were measured to be equal to k1 and k3, respectively. In reaction 2, the yield of H was
measured to be 0.17 ( 0.03 and 0.26 ( 0.05 at 250 and 298 K, respectively, by detecting it using CW
Lyman-R resonance fluorescence. k2 was found to be half the sum of k1 and k3 over the entire temperature
range of this study. The quoted uncertainties are at the 95% confidence level and include estimated systematic
errors. On the basis of these findings it is suggested that most, if not all, of the reaction in the range of
temperatures studied here may be occurring via tunneling of H/D atoms through the barrier.
Introduction
reactants. Therefore, in addition to reactions 1 and 2, the rate
coefficient for the reaction
The reaction of OH with H2,
k3
k1
OH + D2
98 HDO + D
(3)
OH + H2
98 H2O + H
(1)
was measured to provide a consistent set of low-temperature
rate coefficients for comparison with calculations.
Reaction 2 has an added feature in that it can lead to
distinguishable products, H and HDO (reaction 2a) or D and
H2O (reaction 2b),
plays a significant role in atmospheric chemistry because of
the large abundance, ∼0.5 ppmv, of H2 in Earth’s atmosphere.
It is a significant contributor to the conversion of OH to HO2
in the troposphere. H2 is produced, at least in part, from the
oxidation of methane and non-methane hydrocarbons and is
primarily removed via reaction 1. Since the isotopic abundance
of D in hydrogen is related to that in methane, knowledge of
the atmospheric flux of H2 and HD will help elucidate the
sources of CH4. The flux calculation requires the rate of
removal of HD, which is also expected to be controlled by OH
reaction. Therefore, the rate coefficients for the reaction
k2a
OH + HD
OH + HD
9
k2b
8 HDO + H
(2a)
(2b)
98 H2O + D
The product yields in reaction 2 should also be calculable from
the ab initio PES. We have measured the branching ratio for
H atom production in reaction 2 to provide experimental data
for comparison with calculations.
k2
OH + HD
98 H2O + D or HDO + H
(2)
Isotopic substitution of the hydroxyl radical, i.e., OH vs OD,
should not significantly alter the rate coefficient for the hydroxyl
radical reaction with hydrogen because such a substitution
involves a secondary kinetic isotope effect. To estimate the
secondary kinetic isotope effect, we have also studied the
reactions
are needed.
Reaction 1 is a key reaction in the combustion of H2.
Therefore, there are numerous measurements of k1 as a function
of temperature up to ∼3000 K.1 Because the reaction of
hydroxyl radicals with hydrogen is one of the simpler radical-
molecule reactions, it is amenable to theoretical investigations.
The potential energy surfaces (PES’s) for the reaction of
hydroxyl radical with hydrogen have been computed,2-5 and
the rate coefficients have been calculated using these surfaces.1,5-7
The accuracy of the PES and the calculated rate constants can
be evaluated by varying the isotopic composition of the
k4
OD + H2
9
k5
8 HDO + H
(4)
(5)
OD + D2
98 D2O + D
Experiments and Results
* Address correspondence to this author at: NOAA/ERL, R/E/AL2, 325
Broadway, Boulder, CO 80303.
During this study, k1-k5 were measured by observing the
temporal profiles of OH/OD detected via pulsed laser induced
fluorescence (LIF) in known concentrations of H2, D2, or HD.
The branching ratio in reaction 2, k2a/k2, was measured by
detecting H atoms via CW Lyman-R resonance fluorescence.
The apparatus and the data acquisition/ analysis methodology
for such measurements have been used extensively and are
described elsewhere.8-12 The major difference between the
current and previous methodology was the use of a circulation
† Also associated with the Cooperative Institute for Research in
Environmental Sciences, University of Colorado, Boulder, CO.
‡ Permanent address: Department of Chemistry, Warsaw University, ul.
Zwirki i Wigury 101, 02-089, Warszawa, Poland.
§ Also associated with the Department of Chemistry and Biochemistry,
University of Colorado, Boulder, CO 80309.
| NOAA/NRC postdoctoral research associate.
Permanent address: Department of Chemistry, University of Pune, Pune
411 007, India.
X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-3037$12.00/0 © 1996 American Chemical Society

3038 J. Phys. Chem., Vol. 100, No. 8, 1996
Talukdar et al.
TABLE 1: Values of k1, k2, and k3 (in Units of 10-15 cm3
system to minimize the use of expensive HD in some experi-
ments. k1 and k2 were also determined while measuring the
yield of H atoms in reaction 2 by monitoring H atom temporal
profiles.
molecule-1 s-1) Measured by Monitoring the Temporal
Profile of OHa
T, K
k1 ( 2σb
T, K
k2 ( 2σc
T, K
k3 ( 2σd
238
252
267
297
1.46 ( 0.04 248
2.09 ( 0.12 258
3.10 ( 0.10 263
6.50 ( 0.13 268
1.07 ( 0.04f 242
1.38 ( 0.04f 242
1.57 ( 0.14 242
1.79 ( 0.03f 243
1.99 ( 0.09 243
2.78 ( 0.14 254
3.94 ( 0.26 258
5.16 ( 0.28f 263
6.14 ( 0.18 268
6.48 ( 0.42 285
9.35 ( 0.18 297
0.265 ( 0.020g
0.331 ( 0.015
0.332 ( 0.02
0.316 ( 0.024
0.251 ( 0.037
0.428 ( 0.03
0.484 ( 0.04g
0.59 ( 0.03
0.66 ( 0.04
1.08 ( 0.04
1.69 ( 0.10e
1.57 ( 0.04d
1.72 ( 0.10g
1.80 ( 0.07
2.12 ( 0.15
3.29 ( 0.15
6.85 ( 0.16
Materials and Sample Handling. Samples of H2, HD, and
D2 were analyzed for the presence of impurities using a gas
chromatograph (GC) equipped with capillary columns (DB-5
and GS-AL columns from J & W Scientific) and a flame
ionization detector. H2 was obtained from Scott Specialty Gases
(99.99%) and contained <1 ppmv of hydrocarbons. D2,
obtained from Matheson Gas Products with an isotopic purity
of 99.9%, contained less than 0.5 ppmv of impurity, which was
mostly ethane. HD, obtained from Cambridge Isotope labora-
tories, had an isotopic purity of 97% and contained an unknown
impurity which condensed at liquid N2 temperature. This HD
sample was transferred to a 5 L Pyrex bulb which was connected
through a Teflon stopcock to a cold finger maintained at liquid
N2 temperature. After 15 h of exposure to the cold finger, the
HD sample was withdrawn and was found to contain <10 ppmv
of small saturated hydrocarbons, presumably methane and
ethane. As shown later, these impurities did not lead to
significant errors in the measured rate coefficients.
323 11.8 ( 0.50
348 18.0 ( 0.20
373 27.3 ( 0.60
400 40.3 ( 0.70
273
286
298
313
315
323
337
PP-RF
245
263
273
300
323 10 ( 1
348 16 ( 2
373 23 ( 7
2.05 ( 0.20 355 11.92 ( 0.68 298
2.85 ( 0.45 373 16.18 ( 0.12 299
3.8 ( 0.2
7.4 ( 2.1
398 24.53 ( 0.40 301
418 29.38 ( 1.52f 315
334
PP-RF
363
401 14.1 ( 0.16
298
5 ( 1
a Rate coefficients measured by following H atom growth are listed
under PP-RF. The error bar includes 2σ precision only. The pressure
in the reaction cell was 100 Torr for most experiments and 300 Torr
in a few cases. b Photolysis of H2O2 at 248 nm was used as the OH
source except where noted. c Photolysis of H2O by Xe flash lamp (165-
185 nm) was used as the only OH source. d Photolysis of N2O at 193
nm to generate O(1D) followed by reaction with H2O/D2O to produce
OH/OD except where noted. e Photolysis of H2O2 at 193 nm was used
The closed-loop circulation system employed in measuring
k2 was equipped with a ∼3-L ballast volume, a Teflon
circulation pump, throttle valves, and inlets in tandem with the
reactor. Water was used as the photolyte because it is a stable
compound, does not isotope exchange with HD at the temper-
atures of this study, and photolyzes at wavelengths where
hydrogen does not absorb. The concentrations of HD in the
circulating mixtures were determined from the known pressure,
concentration of the premade mixtures, and dilution factors. As
a test of the reliability of the circulation system, the rate
coefficient for the OH + CH4 reaction was measured at 298 K
and found to be in excellent agreement with the recommended
value.13,14 Further, k1 measured using the circulation system
was the same as that obtained in the conventional flow system.
Lastly, the value of k2 measured at 298 K using the conventional
pump-out configuration was the same as that determined using
the circulation system.
to generate OH. The flash lamp energy was 1/4 of the maximum energy.
f
g Photolysis of H2O2 at 248 nm.
(ArF laser), or (3) photolysis of N2O at 193 nm (ArF laser) to
generate O(1D), which reacted with H2O (D2O). OH and OD
were detected by pulsed LIF as described elsewhere.9 The de-
tection limit for OH was 1 × 108 cm-3 for integrating 100 laser
shots in the presence of 3 × 1016 cm-3 of H2O and 100 Torr of
He. The detection limit for OD was similar to that for OH.
Reactions 1-5 are highly temperature sensitive. Therefore,
the temperature of the gas mixture in the reaction zone, defined
by the intersection of the photolysis and probe laser beams, was
directly measured by a shielded thermocouple prior to and after
the acquisition of a rate coefficient and was estimated to be
accurate to (0.5 K.
All experiments were carried out under pseudo-first-order
conditions in OH or OD. The initial concentrations of OH and
OD were <3 × 1011 cm-3, while concentrations of H2, HD, or
D2 were 105-106 times larger. Therefore, the temporal profiles
of [OH] or [OD] followed the equation
After exposure to air, there were often reactive impurities on
the inside surfaces of the circulation system that enhanced the
decay rate of OH. To remove these impurities, at the beginning
of an experiment, a gas mixture containing H2O was circulated
through the system while the photolysis lamp was pulsing. The
OH decay rates measured after this procedure did not change
with time. To make sure that the gases were well mixed, each
gas mixture was circulated in the system for approximately 15
min before acquiring kinetic data. During the course of
determining k2, many pseudo-first-order rate coefficients were
remeasured using the same concentrations of HD; the obtained
values of k2 did not change. The reaction mixture circulating
through the system was subjected to many photolysis pulses
and then analyzed by GC. No new impurities were detected.
It is worth noting that photolysis of a mixture of hydrogen and
water does not change the composition. It is possible that small
amounts of H2O2 were produced; however, H2O2 was not a
significant stable product, since the measured decay rates of
OH did not change with photolysis duration. Also, there was
no significant buildup of O2, which would have led to OH
regeneration at long times via the formation of HO2 and its
subsequent reaction with H/D atoms.
d ln S
dt
) -ki[Xi] + kb ) -k′
(I)
where i ) 1-5, Xi refers to H2/HD/D2 (as appropriate) in
reaction i, k′ ) ki[Xi] + kb, S is the LIF signal from OH or OD,
and kb is the first-order rate coefficient for the loss of OH/OD
in the absence of the reactant. The concentration of the
photolyte (H2O, H2O2, or N2O) and the photolysis energy were
held constant during the course of measuring a particular
bimolecular rate constant. Keeping the concentration of H2O2
constant was particularly important because it reacts with OH
and contributes to the measured value of kb; if [H2O2] changed,
kb would change. Weighted (according to the signal to noise)
least squares fits of the LIF signals at various reaction times to
eq I yielded k′. The second-order rate coefficients, k1-k5, were
obtained from weighted linear least squares analyses of the
measured values of k′ at various concentrations of H2, HD, and
D2. Results of such measurements, repeated at different
temperatures, are listed in Table 1.
OH/OD Kinetics. The OH (OD) radicals were generated
by one or more of the following methods: (1) photolysis of
H2O (D2O) by a Xe flash lamp (165 nm < λ < 185 nm), (2)
photolysis of H2O2 (D2O2) at 248 nm (KrF laser) or at 193 nm

Hydroxyl Radical Reactions with Hydrogen
J. Phys. Chem., Vol. 100, No. 8, 1996 3039
All OH kinetic studies (including those using the circulator)
were carried out under a slow steady flow of the gas mixture.
The linear gas flow velocity in the reaction zone was ∼5-15
cm s-1. The total pressure in the reactor was usually in the
range 50-300 Torr. Experimental conditions, such as [OH]0,
total pressure, lamp energy, and linear gas flow rates were varied
to check for possible errors due to secondary reactions; no
dependence on any of these variables was observed.
The measured values of k1-k3 are plotted as a function of
1/T in Figure 1. They were fitted to the conventional Arrhenius
form, k ) Ae-E/RT, as well as to a three-parameter form, k )
ATne-E/RT. The obtained values of A, E/R, and n are listed in
Table 2 along with k(298 K). The quoted uncertainties in the
values of A and E/R from this study are at the 95% confidence
limit. The uncertainties in the E/R values presented in the format
adapted by NASA/JPL13 and IUPAC/CODATA14 evaluations
were chosen to represent the uncertainties in the values of the
rate constants at temperatures not equal to 298 K.
Also shown in Table 2 are the rate coefficients for the
reactions of OD with H2 (k4) and D2 (k5). The value of k4
measured at 302 K was (7.4 ( 0.4) ×10-15 cm3 molecule-1
s-1, which leads to k4(298 K) ) (6.8 ( 0.4) × 10-15 cm3
molecule-1 s-1 by assuming that the E/R value for k4 is the
same as that for k1. The measured value of k5 at 302 K was
(1.84 ( 0.13) × 10-15 cm3 molecule-1 s-1, which translates to
k5(298 K) ) (1.65 ( 0.13) × 10-15 cm3 molecule-1 s-1 by
Figure 1. Plot of the second-order rate coefficients, k1, k2, and k3, on
a logarithmic scale, as a function of 1/T. The solid lines are the fit of
the data to a three-parameter modified Arrhenius form (ki ) ATn e-E/RT).
The dashed line traced along the HD data (k2) is the average of k1 and
k3, i.e., k2 ) (k1 + k3)/2.
TABLE 2: Comparison of Measured k1-k5 with Those from Previous Worksa
k(298 K)b
A
n
E/R ( ∆E/R (K)
T range (K)
commentc
ref
OH + H2 (k1)
6.7 ( 1.5
7.7
5.5
5.44 ( 0.27
7.21 × 10-8
5.4
2100 ( 200
2000 ( 400
1983 ( 17
1150
200-450
200-300
238-400
238-400
238-400
14
13
6.7 ( 1.2
6.65 ( 0.36d
PP-LIF
this work
2.69
PP-LIF
this work
6.65
2000 ( 25
f(298 K) ) 1.08
this work rece
OH + HD (k2)
3.95 ( 0.12
3.96 ( 0.32d
relative
32
4.98 ( 0.32
5.57 × 10-8
5.00
2121 ( 21
1258
2130 ( 25
248-418
248-418
248-418
FP-LIF
this work
this work
this work rece
2.7
FP-LIF
f(298 K) ) 1.08
3.96
OH + D2 (k3)
2.1 ( 0.18
2.05 ( 0.31
1.99 ( 0.26f
1.83 ( 0.12
FP-RA
30
39
40
24
24
VUV FP-RF
FP-RA
12.1 ( 5.2
2671 ( 147
2332
250-470
FP-RF
FP-RF
FP-RF
PP-LIF
PP-LIF
4.37 × 10-3
1.18
250-1050
+6.0
12.5
2.2 ( 0.4
1.64 ( 0.13d
2587 ( 181
2456 ( 19
1324
2420 ( 16
1580
2456 ( 20
210-460
29
-4.0
6.21 ( 0.33
3.43 × 10-10
5.64 ( 0.27
5.7 × 10-8
6.21
242-401
242-401
242-401
this work
this work
ref 24
3.47
2.73
+ this work
1.64
242-401
f(298 K) ) 1.08
this work rece
OD + H2 (k4)
6.8 ( 0.40f
this work
OD + D2 (k5)
1.88 ( 0.30
2.21 ( 0.22
1.65 ( 0.13f
PP-LIF
FP-RA
PP-LIF
31
30
this work
a Our quoted error bars are at the 95% confidence level and include estimated systematic errors. k and A are in the units of 10-15 and 10-12 cm3
molecule-1 s-1, respectively. b The 298 K values quoted here were obtained from an average of k(298 K) calculated from the Arrhenius expression
and the measured values of k at T in the range 295 e T e 300 K. Data close to 298 K were normalized to 298 K using E/R measured here.
c FP-LIF: Flash photolysis (H2O using Xe flash lamp)-laser-induced fluorescence detection of OH. PP-LIF: Pulsed (laser) photolysis-laser-
induced fluorescence detection of OH. FP-RF: Flash photolysis-resonance fluorescence detection of OH. FP-RA: Flash photolysis-resonance
absorption detection of OH. d Includes estimated systematic error of 5% in concentrations of H2, HD, and D2. e These are our values in the format
used in NASA and IUPAC/CODATA recommendations. Uncertainty at temperature T is given by f(T) ) f(298 K) exp|(∆E/R)((1/T) - (1/298))| .
f This value was obtained by transforming the measured data at temperatures other than room temperature by using activation energy E/R for
reactions 1 and 3 determined in this work.

3040 J. Phys. Chem., Vol. 100, No. 8, 1996
Talukdar et al.
assuming E/R ) 2460 K. The quoted error bars include an
estimated 5% uncertainty in concentrations of D2 and H2.
H Atom Kinetics. The yield of H atoms in the reaction of
OH with HD (reaction 2) was measured relative to that in
reaction 1. They were placed on an absolute scale by assuming
the H atom yield in reaction 1 to be unity. The Lyman-R lines
of H and D atoms are very close to each other. D atoms are
produced in reaction 2b. If D atoms are detected by the H atom
lamp, the measured temporal profiles cannot be attributed to
only H atoms. Therefore, we checked to see if D atoms were
detected by the H atom detection system by generating only D
atoms via the O(1D) + D2 reaction; D atoms were not detected.
OH radicals (<1 × 1012 cm-3) were produced via 248 nm
photolysis of H2O2 (∼5 × 1014 cm-3) or of ozone (2-5 × 1012
cm-3); O(1D) from O3 photolysis reacted with H2 to make OH
or with HD to make OH and OD. The concentration of H2 and
HD were in the range (2-20) × 1017 cm-3. Postphotolysis
reactions are illustrated for the H2O2 source and HD reactant:
H2O2
9
k7
hν8 2OH
(6)
(7)
OH + H2O2
98 H2O + HO2
k2a
Figure 2. H atom temporal profiles in the reactions of OH with HD
and H2 at 250 K and 60 Torr pressure. The concentrations of H2 and
HD were 5.6 × 1017 and 5.3 × 1017 molecule cm-3, respectively. The
solid lines are the biexponential fits to eq II (see text for details). The
rate coefficients, k1 and k2, and the yields of H atom in reaction 2a
were determined from the fitted parameters.
OH + HD
OH + HD
9
8 HDO + H
(2a)
(2b)
k2b
98 H2O + D
kOH
OH 8 loss
(8)
(9)
kH
H
D
98 loss
The parameters R, â, γ, and δ were obtained by fitting the H
atom temporal profiles to eq II. Examples of the measured H
atom temporal profile and the fit of this data to eq II are shown
in Figure 2. During the course of these measurements, [H2O2]
was kept constant and concentrations of H2 and HD were varied.
kD
9
8 loss
(10)
The temporal profile of H atoms is given by
[H]t ) (R × e-ât) - (γ × e-δt
)
(II)
The obtained values of δH and δHD were plotted against [H2]
2
and [HD] to obtain, respectively, the bimolecular rate coef-
ficients k1 and k2.
where
Using the above procedure, the value of k2 determined at 298
RHD ) {k2a[OH]0[HD]}/
K was k2 ) (5 ( 1) × 10-15 cm3 molecule-1 s-1
. At
{k7[H2O2] + k2[HD] + kOH - kH} ) γHD (IIIa)
temperatures other than 298 K, the δHD parameter was not
determined at many HD concentrations, because very large
amounts of HD would have been required for these experiments.
âHD ) kH
(IIIb)
However, δH was measured as a function of [H2] at various
and
2
temperatures, and the obtained values of k1 are listed in Table
1. In general, they agree with the values obtained by observing
OH profiles. Determining rate coefficients from the temporal
profile of a product, by fitting to an eq such as eq II, is less
precise than the values obtained by monitoring an exponential
decay of a reactant. Therefore, we used only the data obtained
by monitoring OH profiles for deriving the Arrhenius parameters
reported in Table 2.
To determine the yield of H atoms in reaction 2, we carried
out back-to-back experiments where HD was replaced with H2
while maintaining all other parameters constant. The H atom
resonance fluorescence signals were normalized for small
changes in the resonance lamp output by using the background
signal obtained before generating OH radicals. The signal for
a given concentration of H atoms did not change significantly
with H2 concentration (<5% decrease for doubling [H2]).
Because comparable concentrations of H2 and HD were used,
it was assumed that H atom detection sensitivity was the same
in the two back-to-back experiments where HD was replaced
by H2. By assuming that [H2O2], laser fluence, kOH, and
detection sensitivity of H atom remained unchanged between
the back-to-back experiments and by using eqs III and IV, we
δHD ) {k7[H2O2] + k2[HD] + kOH
}
(IIIc)
The H + HD f H2 + D (k(298 K) ) 4.5 × 10-17 cm3
molecule-1 s-1) and D + HD f D2 + H (k(298 K) ) 4.3 ×
10-17 cm3 molecule-1 s-1) reactions are too slow at the
temperatures used in our measurements to cause any interfer-
ence. Therefore, these reactions were not included in deriving
the above rate expression. Rate coefficients for the H + HD
and D + HD reactions were estimated from the experimentally
determined rate constants of the reverse reactions, D + H2 and
H + D2,15,16 and the known thermodynamic quantities.17 In
the presence of H2, the parameters in eq II are given by
RH ) {k1[OH]0[H2]}/
2
{k7[H2O2] + k1[H2] + kOH - kH} ) γH (IVa)
2
âH ) kH
(IVb)
2
and
δH ) {k7[H2O2] + k1[H2] + kOH
}
(IVc)
2

Hydroxyl Radical Reactions with Hydrogen
J. Phys. Chem., Vol. 100, No. 8, 1996 3041
TABLE 3: Branching Ratio, k2a/k2, in OH + HD Reaction
branching ratios determined using the two different methods
are in excellent agreement.
branching ratio (k2a/k2)
estimated from
Discussion
source of OH
H2O2/248 nm
temp (K)
measured
k1 and k3 k2 and k3
The major sources of error in our measured values of k1-k5
are the uncertainties in the concentrations of H2, HD, or D2,
which are conservatively estimated to be 5% at the 95%
confidence level, and the presence of reactive impurities. The
latter possibility is important because k1-k5 are small and, hence,
very small amounts of impurities can lead to large errors. We
have already mentioned that the level of impurities in H2 and
D2 samples was too small to affect the measured values of k1
and k3. Our purified sample of HD contained <10 ppmv of
small hydrocarbons (CH4 and C2H6). Even if we assume this
impurity to be all C2H6, it would contribute less than 0.1% to
the measured rate coefficient even at 245 K, the lowest
temperature of our measurements. Since the same gas handling
procedures were employed at different temperatures, systematic
errors in the concentrations of the excess reagent, i.e., H2, D2,
or HD, are the same at all the temperatures. Therefore, the
uncertainties in E/R values shown in Table 2 are primarily
determined by the measured temperature and the precision of
k1-k3. The A factors, of course, are affected by the uncertainties
in measuring concentrations of H2, HD, and D2.
250
298
298
0.17 ( 0.03
0.28 ( 0.05
0.24 ( 0.03
0.15
0.20
0.20
0.17
0.21
0.21
O3/248 nm/H2 (HD)
obtain the following expression for the branching ratio:
k2a RHD k1[H2] δHD - âHD
k2
)
×
×
δ - â
H2 H2
(V)
R
k2[HD]
H2
All parameters on the right-hand side of eq V can be obtained
from the biexponential fits (eq II), the derived values of k1 and
k2, and the known concentrations of H2 and D2. Alternatively,
the k1[H2] and k2[HD] values can be obtained from the
differences in the δ parameters measured with H2 and HD and
the intercepts of plots of δH vs [H2] and δHD vs [HD]. Since
2
only a limited number of HD concentrations were used and since
the values of k1 and k2 measured by observing OH temporal
profiles are more accurate, we used the computed values of k1-
[H2] and k2[HD]. The intercept of a plot of δ vs [H2] or [HD]
is δint ) k7[H2O2] + kOH. The measured values of δint in back-
to-back experiments involving H2 and HD were, within the
experimental uncertainty, the same. This constancy showed that
the concentration of H2O2 and, hence, [OH]0, did not change
during these experiments. The obtained values of the branching
ratio are shown in Table 3 as the mean of a large number of
back-to-back measurements. The quoted error bars are the
standard deviation of the mean.
In a second series of experiments at 298 K, a small amount
of O3 (<5 × 1012 cm-3) was photolyzed to generate O(1D) in
the presence of a large concentration of HD (∼1 × 1018 cm-3).
O(1D) reacted with HD to make OH and OD. The sum of the
concentration of OH and OD was equal to the initial concentra-
tion of O(1D) that reacted with HD. The concentration of O3
was small enough to prevent any significant loss of H or D
atoms via the reactions
Table 2 lists the parameters obtained by fitting our data to
Arrhenius expressions and three-parameter forms, k ) ATne-E/RT
.
Such parameters from previous studies are also shown in the
table. The average value of k1(298 K) measured here, (6.65 (
0.36) × 10-15 cm3 molecule-1 s-1, is in excellent agreement
with the current recommendations.13,14 The quoted error bar
includes an estimated systematic uncertainty of 5% in measuring
the concentration of H2 and 2σ precision in k1 obtained from
the fits of k′ vs [H2] data to a straight line. The Arrhenius
parameters from our data are in excellent agreement with the
recommenations.13,14 Oldenberg et al.23 measured k1 in the
temperature range 800-1500 K. They combined their data with
those of Ravishankara et al.,24 Tully et al.,25 Michael and
Sutherland,26 Frank and Just,27 and Davidson et al.28 and derived
the expression k1 ) 3.56 × 10-16T1.52 exp[-1736/T] cm3
molecule-1 s-1, to cover 250-2581 K. This fit agrees well
with our measured values, except at temperatures less than ∼250
K, where it deviates by ∼20%.
k11
H + O3
D + O3
9
8 OH + O2
(11)
(12)
The k3 values between 250 and 1050 K reported by Ravi-
shankara et al.24 are in excellent agreement with those from
the present study in the overlapping temperature range. The
data of Smith and Zellner29 appear to be systematically higher
than those measured here and of Ravishankara et al. Neverthe-
less, the three sets of data agree within the combined error limits.
We have combined Ravishankara et al.’s data with those from
the present study to extract the recommended values of k3(298
K) and its temperature dependence, which are also shown in
Table 2.
To check for a secondary isotope effect, we measured the
rate coefficients for reactions 4 and 5. The 297 K value of k5
measured by Paraskevopoulos and Nip30 is 35% higher than
our value at 298 K. Their measured value of k3 is also ∼30%
higher than that measured here and by Ravishankara et al. The
difference is likely due to the presence of impurities in the D2
sample used by Paraskevopoulos and Nip. Our previously
reported value31 of (1.88 ( 0.30) × 10-15 cm3 molecule-1 s-1
at 298 ( 2 K is in good agreement with the present measure-
ments. Because of the greater care taken here to analyze the
samples, the present value supersedes our previously reported31
rate coefficient. Our observation that k4 ) k1 and k5 ) k3 shows
the minimal amount of secondary kinetic isotope effect in the
k12
9
8 OD + O2
and subsequent H atom production via reactions of OH and OD
with HD, even though k11 and k12 are rapid,13 ∼3 × 10-11 cm3
molecule-1 s-1. The rate coefficients for the reaction of HD
with OD should be equal to k2, and the branching ratio for H
atom production in the two reactions should also be the same.
Hence, the concentration of H atoms produced will depend on
the sum of the concentrations of OH and OD. There was an
instantaneous production of H atoms via the reaction of O(1D)
with HD. Following this jump, there was a slower production
of H atoms via the reactions of OD and OH with HD. The
temporal profiles of H atom were again fit to a biexponential
expression, which was essentially the same as eq II with the
exception that it included a term for the initial H atom produced
by the O(1D) + HD reaction. By comparing the signal due to
the reaction of OD/OH with HD to that due to the reaction of
O(1D) with HD, the H atom yield was calculated. This method
requires knowledge of the fractional yield of H atom in the
O(1D) + HD reaction, which was independently measured18 to
be 0.57 ( 0.03, in agreement with previously reported values.19-22
The obtained value of k2a/k2 is also listed in Table 3. The

3042 J. Phys. Chem., Vol. 100, No. 8, 1996
Talukdar et al.
reaction of hydroxyl radical with hydrogen. This is to be
expected because the H or D atom in the hydroxyl group is
merely a spectator and the mass difference between OH and
OD is very small. Of course, this finding is consistent with
theoretical calculations.1, 6
There are no previous absolute measurements of k2. Ehhalt
et al.32 measured k1/k2 at 298 K to be 1.65 ( 0.05 using a
relative rate technique. The ratio of our measured k1 and k2 at
298 K yields k1/k2 ) 1.68 ( 0.11, if we assume that the
systematic errors in our measurements of k1 and k2 are the same.
The agreement between these two studies is excellent. The
activation energy for reaction 2 is closer to that for reaction 1
than for reaction 3. This is to be expected if H atom abstraction
is the major channel in reaction 2 (see below).
Table 3 shows the branching ratio, k2a/k2, measured at 298
and 250 K. The ratio was measured at 298 K using two very
different methods, and the values were found to agree with each
other; this agreement enhances our confidence in this value. It
can be easily shown that secondary reactions are not significant
in our system. Attempts to measure this branching ratio at
higher temperatures were not successful; they yielded incon-
sistent values and were not pursued further. The low H atom
yield is consistent with a large fraction of reaction 2 proceeding
via H atom abstraction.
To a zeroth order approximation, a reaction with a barrier
such as that between OH and H2 can be roughly divided into
three energy regimes: (1) reactions at energies much higher
than the barrier, where dynamical effects are dominant; (2)
reactions at energies comparable to the barrier height, where
the rate coefficients are sensitive to the height of the barrier;
and (3) reactions at energies where passing over the barrier is
essentially impossible and, hence, tunneling through the barrier
is the most likely pathway. The third regime is particularly
important for H atom transfer processes, such as the reaction
under consideration here. Usually, dynamical calculations
address the first two regimes, where the height of the barrier is
of major importance. It appears that our data mostly refer to
the third regime, where the width/shape of the barrier is likely
to play a major role.
A large number of investigators have calculated the thermal
rate constants for reactions 1 and 3 with varying degrees of
agreement with measured values (see Clary5 and references
therein). Most of these calculations are based on the ab initio
PES of Walch and Dunning.3 Recently, Fisher and Michael33
used the PES of Kraka and Dunning, which is believed to be
better than the Walch and Dunning surface, to calculate k1 and
k3 using transition state theory. They obtained remarkably good
agreement between experimental data and their calculations over
a very wide range of temperatures, 250-2500 K. Because rate
coefficients in the temperature range ∼500-2500 K are sensitive
to the height of the barrier, Fisher and Michael could estimate
this parameter well. In all these calculations, except the “exact
quantum” methodologies,6,34-36 tunneling through the barrier
was added a posteriori using a correction, such as the Wigner
correction (see, e.g., ref 1). Therefore, comparison of our low-
temperature data with theoretical calculations is not a very good
test of the PES or the dynamics.
channels (reactions 2a and 2b) in the OH + HD reaction,
attributed the low branching ratios for H atom production at
low collision energies (below threshold) to the preferential
tunneling of H over D atoms. The lowest collision energy used
in their calculations, 2.8 kcal/mol, is much higher than the
average collision energy in the temperature range of our
experiments. The calculations of Zhang and Zhang36 are
qualitatively consistent with our results. Calculation of the
thermal rate constants from reactive cross sections would be
useful. Calculation of low-temperature rate constants requires
cross sections at low collision energies, which are not always
available.
In Figure 1, we compare the measured values of k2 with those
calculated by assuming them to be equal to half the sum of k1
and k3. The agreement over the entire temperature range is
amazing! With the same assumption, we can calculate the
branching ratios for H atom production at different temperatures,
which are also shown in Table 3. Again the agreement between
the measured and the calculated values is excellent. These two
observations suggest that when OH reacts with hydrogen, the
identity of the uninvolved atom does not matter. If OH
approaches an H atom, it abstracts the H atom as efficiently
from H2 as from HD. If it approaches the D atom of HD, it
abstracts it with the same efficiency as from D2. The OH +
H2 reaction is not a heavy-light-heavy system of the A +
B-C type reaction. Yet it appears to behave as one! One
simple (simplistic?) explanation for these observations is that
the majority of the reaction proceeds via tunneling, as suggested
by the calculations noted above. Measurements of k1, k2, k3,
and k2a/k2 at much lower temperatures would be very useful to
find out the cause(s) for our observations. However, such
measurements are difficult to make. In the interim, our
measured values of k1-k3 should provide a consistent data set
for testing the theoretical calculations.
Atmospheric Implications. The tropospheric lifetimes of
HD, τHD, and H2, τH , due to reaction with OH can be estimated
2
using the formulation of Prather and Spivakovsky37 by using
the expression
277 K
τ
HD or τ
k
CH3CCl3
H2
)
(VI)
277 K
k
HD
CH3CCl3
or k2H77 K
τ
2
277 K
CH3CCl3
where k
is the rate coefficient for the reaction of OH
with CH3CCl3 at 277 K, the weighted average temperature of
the troposphere for removal of species via reaction with OH.
k2H7D7 K and kH277 K are the rate constants at 277 K for the reactions
of OH with 2HD and H2, respectively. Using the tropospheric
lifetime of CH3CCl3 due to reaction with OH, τCH CCl , of 4.9
3
3
years,38 we obtain tropospheric lifetimes for removal via OH
for HD and H2 of 14.5 and 8.5 years, respectively. Equation
VI is a good approximation because hydrogen and CH3CCl3
are both well mixed and activation energies for the OH + CH3-
CCl3 and OH + H2/HD reactions are not too different. In the
above analysis, we assumed that the only loss process for H2
and HD is reaction with OH in the troposphere. The atmo-
spheric lifetimes of H2 and HD would be ∼8 and 14 years when
stratospheric removal of these compounds is considered. Again,
we are assuming that the only loss process for these two species
in the stratosphere is via reaction with OH.
The reaction of OH with H2 has been extensively studied
theoretically as a “prototype” for quantum scattering calcula-
tions. Absolute rate coefficients, as well as kinetic isotope
effects, have been calculated (see, e.g., Clary5) with varying
levels of agreement between calculations and between calcula-
tions and experiments.
There would be a large isotopic fractionation if the primary
loss of atmospheric hydrogen is due to its reaction with OH.
Microbial uptake of hydrogen by soil is known to be isotope
nonselective.32 However, if the microbial uptake is a major
loss process for hydrogen, the ratio of HD/H2 in the atmosphere
Zhang and Zhang,36 in their time dependent quantum me-
chanical calculations of the reaction probabilities for the two

Hydroxyl Radical Reactions with Hydrogen
J. Phys. Chem., Vol. 100, No. 8, 1996 3043
M. J. Chemical Kinetics and Photochemical Data for use in Stratospheric
Modeling; JPL publication 94-26; Jet Propulsion Laboratory: 1994.
(14) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J.
A.; Troe, J. J. Phys. Chem. Ref. Data 1992, 21, 1125.
(15) Michael, J. V. J. Chem. Phys. 1990, 92, 3394.
(16) Michael, J. V.; Fisher, J. R. J. Phys. Chem. 1990, 94, 3318.
(17) Benson, S. W. Thermochemical Kinetics; John Wiley and Sons
Inc.: New York, 1976; p 292.
(18) Talukdar, R. K.; Ravishankara, A. R. Chem. Phys. Lett., in press.
(19) Matsumi, Y.; Tonokura, K.; Kawasaki, M.; Kim, H. L. J. Phys.
Chem. 1992, 96, 10622.
(20) Tsukiyama, K.; Katz, B.; Bersohn, R. J. Chem. Phys. 1985, 83,
2889.
(21) Satyapal, S.; Park, J.; Bersohn, R.; Katz, B. J. Chem. Phys. 1989,
91, 6873.
(22) Laurent, T.; Naik, P. D.; Volpp, H.-R.; Wolfrum, J.; Arusi-Parpar,
T.; Bar, I.; Rosenwaks, S. Chem. Phys. Lett. 1995, 236, 343.
(23) Oldenberg, R. C.; Loge, G. W.; Harradine, D. M.; Winn, K. R. J.
Phys. Chem. 1992, 96, 8426.
(24) Ravishankara, A. R.; Nicovich, J. M.; Thompson, R. L.; Tully, F.
P. J. Phys. Chem. 1981, 85, 2498.
(25) Tully, F. P.; Ravishankara, A. R. J. Phys. Chem. 1980, 84, 3126.
(26) Michael, J. V.; Sutherland, J. W. J. Phys. Chem. 1988, 92, 3853.
(27) Frank, P.; Just, T. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 181.
(28) Davidson, D. F.; Chang, A. Y.; Hanson, R. K. Proc. Int. Symp.
Combust. 1988, 1877.
will be much smaller than that seen in the absence of a soil
sink. Therefore, measurement of HD/H2 ratios in the atmo-
sphere and estimation of its sources can place limits on the
microbial sink. Measuring the D/H ratio in atmospheric
molecular hydrogen in conjunction with the measured values
of k1 and k2 and the isotopic abundances of CH3D is likely to
help constrain the methane budget.
Acknowledgment. This work was funded in part by
NOAA’s Climate and Global Change Program and was carried
out while Yinon Rudich held a National Research Council-
NOAA Research Associateship and Leah Goldfarb held a
NASA-Climate and Global Change Doctoral Fellowship. We
are grateful to one of the reviewers for very insightful comments.
References and Notes
(1) Michael, J. V. The measurement of thermal bimolecular rate
constants by the flash photolysis-shock tube (FP-ST) technique: Com-
parison of experiment to theory. In AdVances in chemical kinetics and
dynamics; Barker, J. R., Ed.; JAI Press Inc.: Greenwich, CT, 1992; p 47.
(2) Schatz, G. C.; Elgersma, H. Chem. Phys. Lett. 1980, 73, 21.
(3) Walch, S. P.; Dunning, T. H., Jr. J. Chem. Phys. 1980, 72, 1303.
(4) Dunning, T. H., Jr. Harding, L. B.; Kraka, E. In Supercomputer
algorithms for reactiVity, dynamics, and kinetics of small molecules; Lagana,
A., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1989;
p 57.
(29) Smith, I. W. M.; Zellner, R. J. Chem. Soc., Faraday Trans. 2 1974,
70, 1045.
(30) Paraskevopoulos, G.; Nip, W. S. Can. J. Chem. 1980, 58, 2146.
(31) Vaghjiani, G. L.; Ravishankara, A. R.; Cohen, N. J. Phys. Chem.
1989, 93, 7833.
(5) Clary, D. C. J. Phys. Chem. 1994, 98, 10678.
(6) Clary, D. C. J. Chem. Phys. 1992, 96, 3656.
(32) Ehhalt, D. H.; Davidson, J. A.; Cantrell, C. A.; Friedman, I.; Tyler,
S. J. Geophys. Res. 1989, 94, 9831.
(33) Fisher, J. R.; Michael, J. V. J. Phys. Chem. 1990, 94, 2465.
(34) Clary, D. C. J. Chem. Phys. 1991, 95, 7298.
(35) Zhang, D. H.; Zhang, J. Z. H. J. Chem. Phys. 1994, 101, 1146.
(36) Zhang, D. H.; Zhang, J. Z. H. Chem. Phys. Lett. 1995, 232, 370.
(37) Prather, M.; Spivakovsky, C. M. J. Geophys. Res. 1990, 95, 18723.
(38) Prinn, R. G.; Weiss, R. F.; Miller, B. R.; Huang, J.; Alyea, F. N.;
Cunnold, D. M.; Fraser, P. J.; Hartley, D. E.; Simmonds, P. G. Science
1995, 269, 187.
(7) Schatz, G. C.; Walch, S. P. J. Chem. Phys. 1980, 72, 776.
(8) Talukdar, R. K.; Burkholder, J. B.; Schmoltner, A.-M.; Roberts, J.
M.; Wilson, R.; Ravishankara, A. R. J. Geophys. Res. 1995, 100, 16.
(9) Vaghjiani, G. L.; Ravishankara, A. R. J. Phys. Chem. 1989, 93,
1948.
(10) Talukdar, R. K.; Warren, R. F.; Vaghjiani, G. L.; Ravishankara,
A. R. Int. J. Chem. Kinet. 1992, 24, 973.
(11) Talukdar, R.; Mellouki, A.; Gierczak, T.; Burkholder, J. B.;
McKeen, S. A.; Ravishankara, A. R. Science 1991, 252, 693.
(12) Warren, R. F.; Gierczak, T.; Ravishankara, A. R. Chem. Phys. Lett.
1991, 183, 403.
(39) Stuhl, F.; Niki, H. J. Chem. Phys. 1972, 57, 3671.
(40) Greiner, N. R. J. Chem. Phys. 1968, 48, 1413.
(13) 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,
JP9518724