The 13C and D Kinetic
Isotope Effects in the
Reaction of CH4 with Cl
KAREN L. FEILBERG,1 DAVID W. T. GRIFFITH,2 MATTHEW S. JOHNSON,1 CLAUS J. NIELSEN3
1
Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen OE, Denmark
Department of Chemistry, University of Wollongong, Wollongong, NSW 2522, Australia
3
Department of Chemistry, University of Oslo, Pb. 1033 – Blindern, 0315 Oslo, Norway
2
Received 7 June 2004; accepted 28 September 2004
DOI 10.1002/kin.20058
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The kinetic isotope effects in the reaction of methane (CH4 ) with Cl atoms
are studied in a relative rate experiment at 298 ± 2 K and 1013 ± 10 mbar. The reaction rates of 13 CH4 , 12 CH3 D, 12 CH2 D2 , 12 CHD3 , and 12 CD4 with Cl radicals are measured
relative to 12 CH4 in a smog chamber using long path FTIR detection. The experimental
data are analyzed with a nonlinear least squares spectral fitting method using measured
high-resolution spectra as well as cross sections from the HITRAN database. The relative reaction rates of 12 CH4 , 13 CH4 , 12 CH3 D, 12 CH2 D2 , 12 CHD3 , and 12 CD4 with Cl are determined as kCl+12 CH4 /kCl+13 CH4 = 1.06 ± 0.01, kCl+12 CH4 /kCl+12 CH3 D = 1.47 ± 0.03, kCl+12 CH4 /
kCl+12 CH2 D2 = 2.45 ± 0.05, kCl+12 CH4 /kCl+12 CHD3 = 4.7 ± 0.1, kCl+12 CH4 /kCl+12 CD4 = 14.7 ± 0.3.
C 2004 Wiley Periodicals, Inc. Int J Chem Kinet 37: 110–118, 2005
INTRODUCTION
Methane is the most abundant hydrocarbon in the atmosphere and as it absorbs well in the atmospheric infrared
window, it is one of the primary greenhouse gases contributing as much as 20% of the anthropogenic radiative
forcing of the modern atmosphere. The main anthropogenic sources of methane are biogenic, from various
aspects of land use such as enteric fermentation, rice
paddies, and biomass burning. These sources are estimated at 275 Tg(CH4 )/Yr; fossil fuel use contributes
about 100 Tg(CH4 )/Yr. The main natural source is
emissions from wetlands estimated at 115 Tg(CH4 )/Yr
Correspondence to: Karen Feilberg; e-mail: [email protected].
Contract grant sponsor: Nordic Network for Chemical Kinetics
supported by the Nordic Academy for Advanced Study (NorFA).
Contract grant sponsor: Danish Natural Science Research
Council.
c 2004 Wiley Periodicals, Inc.
[1]. Although its abundance is less than 0.5% that of
CO2 , methane is about 21 times more effective on a
per molecule basis in perturbing climate than CO2 .
The average atmospheric mixing ratio of methane is
1.8 ppm which has increased from about 0.7 ppm in
pre-industrial times. The last few decades have seen
methane growth rates of nearly 1% per year and so
it is of concern in relation to global climate change.
In addition to its role as a greenhouse gas, methane is
one of the main sinks for the OH radical, which is the
primary oxidant in the troposphere, and together with
its oxidation product CO, methane regulates the oxidative capacity of the troposphere. In the stratosphere,
methane accounts for about half of the 50% increase in
water vapor seen over the past 50 years and is a source
of HOx species which contribute to ozone destruction
[2].
Measurements of the isotopic composition of atmospheric trace gases are used to infer the photochemical
THE
13 C
AND D KINETIC ISOTOPE EFFECTS IN THE REACTION OF CH4 WITH Cl
history of sampled air masses leading to a better understanding of the sources and sinks of these compounds [3,4]. For methane, a variety of 13 C and D measurements have been performed to elucidate emission
sources and atmospheric chemistry [5–9]. An accurate
description of the global methane budget is essential
to evaluate its global impact and its anthropogenic and
biogenic sources, most of which are poorly quantified
[10]. The main loss process for methane is reaction
with OH radicals in the troposphere, however, a significant fraction is removed in the stratosphere by reaction
with Cl and O(1 D) and in the marine boundary layer by
reaction with Cl. The Cl + CH4 reaction has a measurable effect on the 13 C content of tropospheric CH4 , and
has indicated a global average tropospheric Cl concentration of ca. 3 × 103 cm−3 [11]. Microbial uptake in
soils is another important sink which removes 5–10%
of atmospheric methane [12].
The reaction of methane with chlorine atoms is thus
an important removal process, and the 12 CH4 /13 CH4
and 12 CH4 /CH3 D kinetic isotope effects (KIEs) in the
CH4 + Cl → CH3 + HCl reaction add to constraints
to the methane isotope budgets [10]. The 12 CH4 /CD4
isotopic signature is important as it has been used as
an atmospheric tracer [13]. The KIEs in the chlorine
reaction are different from the KIEs associated with
the OH and O(1 D) reactions and therefore knowledge
of these effects can be used to distinguish stratospheric
removal processes [14]. Cl + CH4 is the only significant source of HCl in the stratosphere, and is responsible for limiting chlorine-catalyzed ozone depletion
[2]. Recently, the 12 CH4 /12 CH3 D KIE in the reaction
with chlorine has been the subject of renewed interest
because it affects the concentrations of H2 and HD in
the troposphere. The atmospheric hydrogen budget is
needed to assess the atmospheric implications of a possible future hydrogen-based economy. The oxidation of
methane and other hydrocarbons leads to the production of formaldehyde (HCHO). Photolysis of formaldehyde is the only chemical source of molecular hydrogen in the troposphere, in the stratosphere it is the only
source. The deuterium isotope signature in methane is
transported via formaldehyde photolysis to H2 [15].
The CH4 + Cl reaction has attracted the attention of
theoretical chemists and various levels of theory have
been applied to calculate the rate coefficients as well
as the KIEs [16–19]. The reaction is an activated hydrogen abstraction reaction with an absolute rate constant of ∼10−13 cm3 s−1 at 298 K [20]. It exhibits a
non-Arrhenius behavior which is attributed to a combination of tunneling and enhancement of the rate by
excitation of the C H vibrational modes, the same effects that are thought to account for the large KIEs
associated with this reaction [21].
111
In this study, we present data for the rate of reaction of chlorine atoms with 13 CH4 , 12 CH3 D, 12 CH2 D2 ,
12
CHD3 , and 12 CD4 relative to 12 CH4 . It is the first
study in which all of these KIEs are determined simultaneously, and we employ a newly developed fullspectrum fitting procedure which constitutes a considerable improvement compared to standard spectral
subtraction methods for the quantitative analysis of
FTIR spectra.
EXPERIMENTAL
The kinetic study was carried out by the relative rate
method in a static gas mixture, in which the decays of
the concentrations of the reacting species are measured
simultaneously as a function of reaction time. Consider
two simultaneous bimolecular reactions with the rate
coefficients kA and kB :
kA
A + X −→ Products
kB
B + X −→ Products
(1)
(2)
Assuming that there are no other loss processes than
these reactions, then the following relation is valid:
[A]0
ln
[A]t
kA
[B]0
=
ln
kB
[B]t
(3)
where [A]0 , [A]t , [B]0 , and [B]t denote the concentrations of the compounds A and B at times zero and t,
respectively. A plot of ln([A]0 /[A]t ) vs. ln([B]0 /[B]t )
will thus give the relative reaction rate coefficient
= kA /kB as the slope, or in terms of the fractionation constant, ε = − 1. In these experiments, A
is 12 CH4 and B represents the 13 C and D-substituted
isotopologues.
The experiments were carried out in a 250 L electropolished stainless steel smog chamber equipped
with a White type multiple reflection mirror system
with a 120 m optical path length for FTIR detection. The chamber was equipped with UV photolysis lamps mounted in a quartz tube inside the chamber, and all experiments were carried out in synthetic
air (AGA 99.9990% purity; CO and NOx < 100 ppb)
at 298 ± 2 K and 1013 ± 10 mbar. The temperature
was monitored on the outside of the chamber and
it remained constant for the duration of the experiments. The Cl atom source in the chamber was photolysis of Cl2 employing Philips TLD-08 fluorescence
lamps (max ∼ 370 nm) leading to the production of
ground state chlorine atoms. The initial mixing ratio
of each methane isotopologue was 3 ppm and the Cl2
112
FEILBERG ET AL.
mixing ratio was 15 ppm. All methane isotopomers
used were from Sigma-Aldrich with an isotopic purity
of 99 atom%, and the Cl2 was a standard laboratorygrade chemical purified by two freeze-pump-thaw procedures. The methane isotopomers and Cl2 gas were
flushed into the reaction chamber with synthetic air
via a Pyrex gas handling system, and the chamber
was subsequently filled to 1013 mbar. The pressures
of the reactants were measured in a standard volume on the gas line by a 10 mbar range capacitance
manometer. Prior to experiments the chamber was passivated by photolyzing Cl2 to eliminate impurities in the
system.
The infrared spectra were recorded with a Bruker
IFS 88 FTIR instrument equipped with a liquid nitrogen cooled InSb detector and an 1800–4000 cm−1 band
pass filter. A total of 128 scans were co-added, each
with a nominal resolution of 0.125 cm−1 (OPD = 8 cm)
and using boxcar apodization. Infrared spectra were
recorded at regular intervals during a ca. 1.5 h to monitor the relative decay of the methane isotopomers. The
experiment consisted of 10–14 steps of 30 s photolysis
followed by 10 min of data collection with the lamps
off. The experiments were stopped when about half
of the CH4 initially present had been consumed. The
chemistry initiated by photolysis is
Cl2 + h → 2Cl
(4)
Cl + CH4 → CH3 + HCl
(5)
CH3 + O2 → CH3 O2
(6)
CH3 O2 + Cl → CH3 O + ClO
CH3 O + Cl → HCHO + HCl
HCHO + Cl + O2 → CO + HCl + HO2
(7)
(8)
(9)
resulting in the destruction of CH4 and ultimately
the production of CO. HCHO was not observed in
the spectra as it reacts very quickly with Cl atoms
(k298 = 7.3 × 10−11 cm3 molecule−1 s−1 ) to form HCl,
HO2 , and CO (reaction (9)) [22]. The reaction system
was examined in a FACSIMILE kinetic model including 49 reactions in order to investigate the possibility of competing chemical reactions [23]. The model,
given as supporting information, showed no reactants
that could possibly compete with the Cl atoms in removing methane. The other possible methane oxidants
are O(1 D) and OH radicals and their maximum concentrations in the model were ∼0 (1 × 10−14 cm−3 )
and 8.76 × 103 cm−3 respectively, and the minimum
Cl concentration is 6.14 × 109 cm−3 .
The experimental spectra were analyzed using a
nonlinear least squares spectral fitting procedure, de-
veloped by D. W. T. Griffith and coworkers [24–27].
In this method, the spectrum of the mixture of absorbing species is first simulated by calculation from
initial estimates of the absorber concentrations [28].
The calculation is then iterated to minimize the residual between the measured and simulated spectrum.
In the spectrum calculation, true absorption coefficients are normally calculated from HITRAN line parameter data, the transmission spectrum is computed,
and then convolved with the FTIR instrument function to simulate the measured spectrum. If HITRAN
line parameter data are not available, a scaled quantitative laboratory spectrum measured at high resolution can be used as a good approximation to the absorption coefficients. The iterative fitting follows the
Levenberg–Marquardt algorithm [29] to adjust the calculation parameters (absorber concentrations, continuum level, and instrument lineshape parameters) and
achieve a least squares minimum residual between
measured and simulated spectra in typically 5–10 iterations. Figure 1 shows an illustrative example of such
a fit for a reaction mixture including of all CHn D4−n
isotopomers.
The spectral features used in the analyses were the
C H stretching bands in the 2800–3200 cm−1 region
and the C D stretching bands in the 2100–2300 cm−1
region. The spectral data needed in the least squares
algorithm were taken from the HITRAN database for
12
CH4 , 13 CH4 , and 12 CH3 D; for 12 CH2 D2 , 12 CHD3 , and
12
CD4 experimental high-resolution IR spectra were
used. These spectra were recorded with a Bruker IFS
120 FTIR instrument at 0.01 cm−1 resolution in a
10 cm Pyrex gas cell equipped with CaF2 windows.
The partial pressures of methane isotopomers were
in the range 10–15 mbar, and the cell was filled to
1013 mbar with synthetic air (Air Liquide, dry technical air). A Ge on KBr beam splitter and 1800–4000
cm−1 band pass filter were used in the interferometer
and a globar (SiC2 ) was used as the MIR light source.
The detector was a liquid N2 cooled InSb semiconductor, and 128 scans were co-added to achieve an acceptable signal/noise ratio in the resulting spectra. The
spectral simulation was also carried out using highresolution IR spectra to calculate the absorption coefficients for all six methane isotopomers; the results
of this analysis agreed within 3% with the analysis in
which HITRAN data was used for 12 CH4 , 13 CH4 , and
12
CH3 D. However, the root mean square errors of the
fit residuals using only high-resolution spectra were on
average 25% larger, which is most likely due to the
additional noise from the experimental high-resolution
spectra. For this reason the analysis employing only
three high-resolution spectra and HITRAN data is
preferred.
THE
13 C
AND D KINETIC ISOTOPE EFFECTS IN THE REACTION OF CH4 WITH Cl
113
Figure 1 An experimental IR spectrum of a mixture of 12 CH4 , 12 CH3 D, 12 CH2 D2 , and 12 CHD3 in the CH stretching region,
2800–3200 cm−1 high-resolution spectra of all isotopomers used to fit the spectrum, and the residual of the fit (expanded ×2).
RESULTS AND DISCUSSION
An experimental spectrum of one of the reaction mixtures is shown in Fig. 1, along with the spectra of individual isotopomers used in the fitting procedure and
the residual spectrum after fitting. The concentrations
of the methane isotopomers thus obtained were subsequently analyzed according to Eq. (3) using a general weighted least squares regression method, which
includes uncertainties in both reactant concentrations
[30]. The relative rate method relies on the fact that
only Cl atoms consume the methane isotopomers and
the reference compound (CH4 ), and that no CH4 is reformed by secondary reactions. This was corroborated
by kinetic modeling and a “dark” experiment in which
the reaction mixture was allowed to sit for 2 h without
photolysis with no resulting change in isotopic composition. To test for systematic errors—either due to
chemistry or to the spectral analyses—we also carried
out linear regression analyses allowing a zero-point offset to ascertain that the intercepts of the linear regressions were not significantly different from zero. For
all data sets the differences were within 2 statistical
error suggesting that such errors were of no importance. The relative rate plots for the five isotopomers
are shown in Fig. 2. The values for the reaction rates of
13
CH4 , 12 CH3 D, 12 CH2 D2 , 12 CHD3 , and 12 CD4 relative
to 12 CH4 are summarized in Table I. Each experiment
was carried out 2–3 times to ensure experimental reproducibility. The values for individual runs agree to
within 1% for all experiments. In addition, the concentrations of 12 CH3 D, 12 CH2 D2 , and 12 CHD3 were
Table I Summary of Measured Fractionation Factors, α, at 298 K
Reaction Mixture
12 CH , 13 CH , 12 CH D
4
4
3
Spectral region analyzed 12 CH4 /13 CH4
2850–3025 cm−1
1.0582 (0.0021)
1.0585 (0.0011)
1.0584 (0.0012)
–
2150–2262 cm−1
Weighted mean (2)
ε
1.058 (0.002)
58‰
+ Cl
12 CH , 12 CH D, 12 CH D , 12 CHD , 12 CD
4
3
2 2
3
4
12 CH /12 CH D
4
3
+ Cl
12 CH /12 CH D 12 CH /12 CHD 12 CH /12 CD
4
2 2
4
3
4
4
1.446 (0.006)
1.459 (0.006)
2.422 (0.008)
2.417 (0.011)
4.71 (0.03)
4.70 (0.04)
–
–
2.438 (0.015)
2.455 (0.017)
2.430 (0.012)
1430‰
4.74 (0.04)
4.75 (0.04)
4.73 (0.04)
3730‰
14.7 (0.1)
14.7 (0.2)
14.7 (0.2)
13700‰
1.460 (0.004)
1.468 (0.005)
1.459 (0.006)
459‰
Two reaction mixtures were used for the CH4 + Cl system: 12 CH4 , 13 CH4 , 12 CH3 D + Cl and 12 CH4 , 12 CH3 D, 12 CH2 D2 , 12 CHD3 , 12 CD4 +
Cl. Each experiment was carried out at least twice. 12 CH3 D, 12 CH2 D2 , and 12 CHD3 were analyzed in both the C H and C D stretching regions.
An additional experiment was carried out for 13 CH4 and 12 CH4 . The relative rates are based on weighted least squares linear regression, and the
weighted means are given as the recommended values. The errors indicated are 2 and do not include possible systematic errors.
114
FEILBERG ET AL.
Figure 2 Relative rate plots showing the decays of 13 CH4 , 12 CH3 D, 12 CH2 D2 , 12 CHD3 , 12 CD4 during reaction with chlorine
atoms. The slopes correspond to the enrichment = k(Cl + CH4 )/k(Cl + isotopologue); the 2 errors on the slopes are given
in brackets. (a)–(d) show the results obtained from the 2800–3200 cm−1 region, and (e) shows results obtained in both spectral
regions. The relative rate plots are shown together in (f ) for comparison. The error bars on both axes correspond to 1 errors.
THE
13 C
AND D KINETIC ISOTOPE EFFECTS IN THE REACTION OF CH4 WITH Cl
obtained from both the C H stretch and C D stretch
spectral regions and the values obtained differed by less
than 1.5%. The CH4 /CD4 relative rates were obtained
from the 12 CH4 /12 CH3 D and 12 CD4 /12 CH3 D ratios to
eliminate any systematic differences between simulating the different spectral regions. Also, an additional
experiment was carried out for the 12 CH4 /13 CH4 KIE
to ensure that no effects from spectral overlap with the
deuterated species interfered with this result. Strong
spectral overlap can in some cases introduce systematic error in the fitting procedure, however this value
was in complete agreement with the values obtained
from the 12 CH4 , 13 CH4 , and 12 CH3 D mixture.
A comparison of the results obtained in this study
with previous experimental and theoretical work is
shown in Table II. As can be seen, some of the results
fall outside the mutual statistical errors of the respective
determinations. The 12 CH4 /13 CH4 KIE has been determined by the relative rate method by Tyler et al. using
isotope ratio mass spectrometry [31], by Saueressig
115
et al. using tunable diode laser absorption spectroscopy
(TDLAS) [32], and by Crowley et al. using FTIR detection [33]. There is reasonably good agreement between
these studies on a value for the 12 CH4 /13 CH4 KIE of
1.06 (0.002). While similar, our value of 1.058 (0.002)
is lower than the 1.066 (0.002), value found by both
Saueressig et al. [32] and Crowley et al. [33]. However,
different linear regression methods were employed to
obtain the results in these studies and ours.
The 12 CH4 /12 CH3 D KIE has been determined by the
relative rate method by Wallington and Hurley [34] and
Boone et al. [17] using FTIR detection, by Saueressig
et al. [35] using TDLAS, and by Tyler et al. [31] using isotope ratio mass spectrometry. These studies are
in fair agreement, and values for the KIE are reported
from 1.47 to 1.54. Originally Wallington and Hurley
reported a value of 1.36 (0.02) for this KIE [34]. However, they subsequently reanalyzed their data and revised their result to 1.47 (0.09) [35]. Our result for the
12
CH4 /12 CH3 D KIE of 1.459 (0.006) is, again, slightly
Table II A Comparison of the Results of This Study with Experimental and Theoretical Literature Values for Methane
KIEs
Relative Reaction
Rates 298 K
This work
Wallington et al. [34]
Wallington et al. [35]
Tyler et al. [31]
Boone et al. [17]
Saueressig et al. [32,35]
Crowley et al. [33]
Matsumi et al. [36]
Clyne et al. [37]
Chiltz et al. [38]
Corchado et al. [16]
12 CH /13 CH
4
4
12 CH /12 CH D
4
3
12 CH /12 CH D
4
2 2
12 CH /12 CHD
4
3
12 CH /12 CD
4
4
1.058 (0.002)
–
1.459 (0.006)
1.36 (0.02)
1.47 (0.09)
1.474 (0.020)
1.54 (0.05)
1.518 (0.041)
–
2.43 (0.01)
2.18 (0.02)
4.73 (0.04)
4.31 (0.005)
14.7 (0.2)
16.4 (0.007)
–
2.38 (0.05)
–
–
1.4 (0.2)
–
5.26 (0.3)
–
–
2.93b
2.16d
2.24c
2.40g
–
3.93d
4.28c
4.83g
–
–
–
–
–
18.52 (0.4)
–
–
12 (2.0)
13.6 (1.0)
11 (1.0)
(T = 304 K)
7.8a
14.0b
12.3d
16.8c
22.6g
12.8d
16.9c
10.0e
11.1 f
–
1.0621 (0.0001)
–
1.066 (0.002)
1.066 (0.002)
1.057a
1.141b
Boone et al. [17]
Roberto-Neto et al. [18]
Gupta et al. [19]
1.021d
1.028c
1.049e
1.057 f
1.034c
1.35a
1.93b
1.41d
1.43c
1.48g
1.42d
1.43c
1.44e
1.38 f
–
All values given are for room temperature unless otherwise indicated. All errors are 2 errors. The data by Matsumi et al. [36] are converted
into relative rate data from absolute rate data.
a
CVT/OMT using the AM1-SRP4[MP2]-IC direct dynamics method of [24].
b
CUS/OMT.
c
Conventional transition state theory including Wigner tunneling correction.
d
Conventional transition state theory.
e
Variational transition state theory.
f
CVT/OMT using the AM1-SRP4[MP2]-IC direct dynamics method.
g
Conventional transition state theory including the Eckart tunneling correction.
116
FEILBERG ET AL.
lower than those obtained previously. The experiment
by Saueressig et al. [35] was carried out at a range of
temperatures between 223 K and 296 K and they provide an expression to calculate the KIE as a function of
temperature. Their value at 296 K is 1.508 (0.041) and
using their expression (KIE(CH3 D + Cl)(T ) = 1.278
exp (51.308/T )), we obtain a value at 298 K of 1.518
(0.041). Any small variation in temperature between
different experiments is thus insufficient to explain the
slight discrepancies between our result and previous
experiments.
The available data for the KIEs of the multiply
deuterated methane species do not agree with one another within their respective uncertainties. Experimental studies of the 12 CH4 /12 CH2 D2 , 12 CH4 /12 CHD3 , and
12
CH4 /12 CD4 KIEs using the FTIR relative rate technique have been published by Wallington and Hurley
[34] and Boone et al. [17]. These results differ by
as much as 20% in the case of the 12 CH4 /12 CHD3
KIE. An absolute rate study of the 12 CH4 /12 CH2 D2
and 12 CH4 /12 CD4 KIEs has been published by Matsumi
et al. [36] showing results that differ significantly from
the results obtained in the relative rate studies. The
trend obtained in the present study follows the same
general trend as other studies, however, the values differ
by more than the quoted experimental errors. Our data
are supported by internal cross-checks with the values
for 13 CH4 and 12 CH3 D, which match earlier studies.
Boone et al. [17] have obtained a value that is significantly larger for the 12 CH4 /12 CD4 ratio, however this
result was obtained with 13 CO + Cl as the reference
reaction making a direct comparison difficult. Also,
their experiments were based on the analysis of a few
FTIR absorption lines whereas ours rely on a global
fit of the entire methane absorption band. In addition,
the global fit method in principle extracts all available information from the available data, in contrast
to the smaller spectral features used in other studies.
Wallington and Hurley [34] have not communicated
revised results for the multiply deuterated methanes,
as they did for 12 CH4 /12 CH3 D. The absolute rate determinations by Matsumi et al. [36] are in poor agreement
with the relative rate studies; Boone et al. suggest that
this may be due to impurities in the chemicals [17].
Table II includes the results of theoretical models ranging from transition state theory [17,19] based
upon quantum chemical computations (with or without tunneling corrections) which reproduce most of
the variation in the KIEs, through canonical variation theory [16,18] to complex direct dynamics calculations [16,18]. The theoretical investigations of
the KIEs in the CH4 + Cl reaction have been successful at predicting observed trends in the KIEs
but none of the models are in satisfactory agree-
ment with all the experimental data. Gierczak et al.
have reported an empirical algebraic relationship between the rate constants for reactions of deuterated methanes with OH radicals: k(OH + CHx D y ) =
x(k(OH + CH4 )/4) + y(k(OH + CD4 )/4) [37]. They
conclude that this relationship is a result of tunneling
being the main factor in the KIE, and our reaction rates
for Cl + CHx D y are in excellent agreement with this.
A clear trend in the data, shown in Fig. 3, is that
the dependence of the 12 CH4 /12 CHx D4−x KIE on the
degree of deuteration is nonlinear. This has been observed previously by Boone et al. [17] who discuss the
nonlinearity in terms of the effect of deuteration on the
exponential and pre-exponential terms in the transition
state theory rate expression for the reaction. They note
that the largest contributor to this “nonlinearity” is the
rotational partition function, the change in which is due
to the change in mass when substituting D for H. Further, they find that tunneling contributes to the “nonlinearity” to a lesser extent although it has a large effect
on the magnitudes of the KIEs. A possible interpretation of the “nonlinearity” is that there is a primary KIE,
which is linear with the number of deuterium atoms,
and a secondary KIE, which is not.
CONCLUSIONS
We provide new data for the 13 C and D kinetic isotope
effects in the reaction of methane with chlorine atoms
using the global-fitting procedure for FTIR spectra. Our
Figure 3 The dependence of the 12 CH4 /12 CHx D y KIE on
the number of substituted deuterium atoms. The experimental values are indicated with 2 error bars and a straight line
is drawn between CH4 and CD4 . The curvature of the experimental data indicates a nonlinear dependence on deuterium
substitution. Data by Boone et al. [17] and Wallington et al.
[34] are indicated for comparison.
THE
13 C
AND D KINETIC ISOTOPE EFFECTS IN THE REACTION OF CH4 WITH Cl
data closely match results from previous studies of the
KIE of the atmospherically important species 13 CH4
and the KIE in CH3 D is in fair agreement with previous studies, but with a smaller statistical error. A
recent study by M. C. McCarthy et al. of the sensitivity of atmospheric chemistry and transport models
to KIEs suggests that the 13 C KIE in the chlorine reaction is adequately determined for modeling purposes
at ground level temperatures [10]. However the 4.5%
difference between previously determined values for
the 12 CH4 /12 CH3 D KIE is large enough to influence
model results significantly. The value of 1.459 (0.006)
found in the present study constrains this important
KIE. We propose revised KIEs for the multiply deuterated methane isotopomers. The values determined in
the present work for 12 CH2 D2 , 12 CHD3 , and 12 CD4 +
Cl follow the same trend as in other studies, however
they differ outside experimental error. Following the
present study, the 13 CH4 and CH3 D KIEs in the Cl reaction with methane are now sufficiently accurate to
satisfy the requirements of sophisticated atmospheric
modeling studies at tropospheric temperatures. Further
work is needed to constrain the KIEs at stratospheric
temperatures. The systematic differences for the full
series of deuterated methanes are useful for theoretical
studies.
The authors would like to thank Flemming M. Nicolaisen
for his valuable assistance in recording the high resolution
spectra of the methane isotopomers.
BIBLIOGRAPHY
1. Houghton, J. T.; Ding, Y.; Griggs, D. J.; Noguer, M.; van
der Linden, P. J.; Dai, X.; Maskell, K.; Johnson, C. A. Climate Change 2001: The Scientific Basis. Contribution of
Working Group I to the Third Assessment Report of the
Intergovernmental Panel on Climate Change, 2001.
2. Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and
Physics: From Air Pollution to Climate Change, Wiley:
New York, 1998.
3. Quay, P.; Stutsman, J.; Wilbur, D.; Snover, A.;
Dlugokencky, E.; Brown., T. Global Biogeochem Cycles
1999, 13, 445–461.
4. Röckmann, T.; Jöckel, P.; Gros; V.; Bräunlich, M.;
Possnert, G.; Brenninkmeijer, C. A. M. Atmos Chem
Phys 2002, 2, 147–159.
5. Bergamaschi, P.; Brenninkmeijer, C. A. M.; Hahn, M.;
Röckmann, T.; Scharffe, D. H.; Crutzen, P .J.; Elansky,
N. F.; Belikov, I. B.; Trivett, N. B. A.; Worthy, D. E. J.
J Geophys Res 1998, 103, 8227.
6. Gupta, M. L.; Tyler, S.; Cicerone, R. J Geophys Res
1996, 101, 22923.
117
7. Ridal, M.; Siskind, D. E. J Geophys Res 2002, 107,
4807–4814.
8. Ridal, M. J Geophys Res 2002, 107, 4285–4290.
9. Rice, A. L.; Tyler, S. C.; McCarthy, M. C.; Boering,
K. A.; Atlas, E. J Geophys Res 2003, 108, 4460–4477.
10. McCarthy, M. C.; Boering, K. A.; Rice, A. L.; Tyler,
S. C.; Connell, P.; Atlas, E. J Geophys Res 2003, 108,
4461.
11. Allan, W.; Lowe, D. C.; Cainey, J. M. Geophys Res Lett
2001, 28, 3239–3242.
12. Bull, I. D.; Parekh, N. R.; Hall, G. H.; Ineson, P.;
Evershed, R. P. Nature 2000, 405, 175–178.
13. Mroz, E. J.; Alei, M.; Cappis, J. H.; Guthals, P. R.;
Mason, A. S.; Rokop, D. J. J Geophys Res 1989, 94,
8577.
14. Bergamaschi, P.; Brühl, C.; Brenninkmeijer, C. A. M.;
Saueressig, G.; Crowley, J. N.; Grooss, J. U.; Fischer, H.;
Crutzen, P. J. Geophys Res Lett 1996, 23, 2227–2230.
15. Rahn, T.; Eiler, J. M.; Boering, K. A.; Wennberg, P. O.;
McCarthy, M. C.; Tyler, S.; Schauffler, S.; Donnelly, S.;
Atlas, E. Nature 2003, 424, 918–921.
16. Corchado, J. C.; Truhlar, D. G.; Espinosa-Garcia, J.
J Chem Phys 2000, 112, 9375–9389.
17. Boone, G. D.; Agyin, F.; Robichaud, D. J.; Tao, F.-M.;
Hewitt, S. A. J Phys Chem A 2000, 105, 1456–1464.
18. Roberto-Neto, O.; Coitino, E. L.; Truhlar, D. G. J Phys
Chem A 1998, 102, 4568–4578.
19. Gupta, M. L.; McGrath, M. P.; Cicerone, R. J.; Rowland,
F. S.; Wolfsberg, M. Geophys Res Lett 1997, 24, 2761–
2764.
20. Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.;
Hampson, R. F., Jr.; Kerr, J. A.; Rossi, M. J.; Troe, J.
Summary of Evaluated Kinetic and Photochemical Data
for Atmospheric Chemistry, 2001.
21. Michelsen, H. A. J Geophys Res 2001, 106, 12267–
12274.
22. DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson,
R. F.; Kurylo, M. J.; Howard, C. J.; Kolb, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use
in Stratospheric Modeling. Evaluation Number 14, JPL
Publication 02-25, 2003.
23. FACSIMILE. AEA Technology Plc, Abingdon, UK
1998.
24. Esler, M. B.; Griffith, D. W. T.; Wilson, S. R.; Steele,
L. P. Anal Chem 2000, 72, 215.
25. Esler, M. B.; Griffith, D. W. T.; Wilson, S. R.; Steele,
L. P. Anal Chem 2000, 72, 216–221.
26. Griffith, D. W. T.; Esler, M. B.; Steele, L. P.; Reisinger,
A. Poster, 2nd International Conference on Advanced
Vibrational Spectroscopy, Nottingham, 2003.
27. Feilberg, K. L.; Sellevåg, S. R.; Nielsen, C. J.; Griffith,
D. W. T.; Johnson, M. S. Phys Chem Chem Phys 2002,
4, 4687–4693.
28. Griffith, D. W. T. Appl Spectroc 1996, 50, 59–70.
29. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.;
Flannery, B. P. Numerical Recipes; Cambridge University Press: Cambridge, UK, 1992.
30. York, D. Can J Phys 1966, 44, 1079–1086.
118
FEILBERG ET AL.
31. Tyler, S. C.; Ajie, H. O.; Rice, A. L.; Cicerone, R. J.;
Tuazon, E. C. Geophys Res Lett 2000, 27, 1715–
1718.
32. Saueressig, G.; Bergamaschi, P.; Crowley, J. N.; Fischer,
H.; Harris, G. W. Geophys Res Lett 1995, 22, 1225–
1228.
33. Crowley, J. N.; Saueressig, G.; Bergamischi, P.; Fischer,
H.; Harris, G. W. Chem Phys Lett 1999, 303, 268–
274.
34. Wallington, T. J.; Hurley, M. D. Chem Phys Lett 1992,
189, 437–442.
35. Saueressig, G.; Bergamaschi, P.; Crowley, J. N.; Fischer,
H. Geophys Res Lett 1996, 23, 3619–3622.
36. Matsumi, Y.; Izumi, K.; Skorokhodov, V.; Kawasaki, M.;
Tanaka, N. J Phys Chem A 1996, 101, 1216–1221.
37. Gierczak, T.; Talukdar, R. K.; Herndon, S. C.; Vaghjiani,
G. L.; Ravishankara, A. R. J Phys Chem A 1997, 101,
3125–3134.