Carbon Kinetic Isotope Effect in the Oxidation of Methane by the Hydroxyl Radical

The reaction of the hydroxyl radical (HO) with the stable cafix)n isotopes of methane has been studied as a function of temperature from 273 to 353 K. The measured ratio of the rate coefficients for reaction with (cid:127)ZCHn relative to (cid:127)3CH(cid:127) (kn(cid:127)/kn3) was 1.0054 (20.0009 at the 95% confidence interval), independent of temperature within the precision of the measurement, over the range studied. The precision of the present value is much improved over that of previous studies, and this result provides important constraints on the current understanding of the cycling of methane through the atmosphere through the use of carbon isotope measurements. steady concentration of 2 to 6 10 cm '3 from the rate of conversion of methane. formaldehyde, subsequently photolyzes or hydroxyl. The extent of conversion of methane and nitrous oxide DA3.01 Fourier transform spectrometer system interfaced the cell. An infrared beam from a heated SiC rod was collimated and White-type internal multiple pass optics total optical 48.6 The the was by a liquid N:-cooled detector. beamsplitter and detector combination of linear relationship between measured and species concentration. The initial spectnnn (100 interferometer scans) was taken before samples were withdrawn for GC and MS analysis. The Beer-Lambert linearity for methane verified for 10


Methane (CH•) is an important trace gas in the atmosphere
. It is a key sink for the tropospheric hydroxyl radical. Methane contributes to greenhouse warming [Donner and Ramanathan, 1980]; its potential warming effects follow only CO 2 and H20. Methane is a primary sink for chlorine atoms in the stratosphere and a major source of water vapor in the upper stratosphere. The concentration of CI-I4 in the troposphere has been increasing at a rate of approximately 1% per year, at least over the past decade [Rasmussen and Khalil, 1981;Blake et al., 1982;Steele et al., 1987;Blake and Rowland, 1988]. Ice core measurements indicate a rapid increase began a few hundred years ago [Craig and Chou, 1982;Rasmussen and Khalil, 1984]. The reasons for this increase have not been established, but it has been suggested that it could be due to an increase in source emissions, a decrease in the atmospheric loss rate, or both. Several approaches have been applied in order to understand the sottrees and sinks of atmospheric methane (see discussion by Cicerone and Oremland [ 1988]). One way to study the methane budget is through the use of stable isotopes of carbon as proposed by Stevens and Rust [1982]. Measurements of in methane in remote background air and in methane sources have been used with data of fluxes from these sources to estimate relative source strengths and to provide input to models of atmospheric methane [e.g., Stevens

CHn + HO ---) CH3 + HzO
The rate coefficient for this reaction has been studied extensively (see review by Ravishankara [1988]), but data indicating the effect of isotope substitution in methane are scarce. Fractionation occurs in the atmosphere because the rate coefficient for reaction (R1) is slightly larger for the •2Hn relative to •3CHn. This secondary (i.e., involving isotopic substitution at a position other than the direct reaction center and involving an atom not split off in the reaction) kinetic isotope effect is expected to be small, and indeed previous studies near room temperature have found an effect of 1% or less [Rust and Stevens, 1980;Davidson et al., 1987]. We attempted to improve the precision of the value for the carbon kinetic isotope effect in reaction (R1) (i.e., the ratio of the rate coefficients for the reaction of •H n with hydroxyl as compared to the reaction of •3CHn) near room temperature.
Additionally, we investigated the temperature dependence of this rate coefficient ratio.
The kinetic isotope effect in reaction (R 1) has been studied in this laboratory previously . Many of the experimental details reported in that study apply here. Differences from our earlier study will be pointed out. The experiment involved the reaction of a mixture of methane containing both stable carbon isotopes, nominally at relative atmospheric abundances, with the hydroxyl radical. We measured the methane concentration and isotopic composition before and after a reaction period. The relation between the amount of methane converted, the change in the ratio of stable carbon composition and the ratio of rate coefficients for reaction (R1) for the two species is given by (see derivation in Davidson et al. [1987]): ln(A) -__.k,, ln(A) + ln{($,+ 1000)/($ o+ 1000)} where/q2 is the rate coefficient for reaction (R1) for methane containing carbon-12 and k•3 is for carbon-13 methane; A is the fraction of methane remaining at time t; and $ is a measure of the ratio of carbon-13 to carbon-12 (in per rail, or parts per thousand difference), at the start of an experiment (•Jo) and the end (•J0, def'med as follows: x 1000 (2) where R, and R,• stand for the ratio of carbon-13 to carbon-12 in a sample, x, and in a standard, respectively. In this case, the standard is PeeDee Belemnite, which is the commonly accepted reference for stable carbon isotope work. The choice of standard has no effect on the final kinetic isotope effect derived. In The accuracy of the measured kinetic isotope effect is sensitive to errors in determining the extent of conversion (A) and the isotope ratios ($). This sensitivity is minimized at relatively large fractional conversions, because of the increased amount of isotopic fractionation which occurs. Hydroxyl radicals were produced in sufficient amount to remove 50-90% of the methane in 24 hours. This design is relatively insensitive to contaminants found in the commercially prepared methane (such as light allcanes) because only the unreacted methane is analyzed (a problem with ethane is possible because it may be cryogenically trapped with methane in the isotope analysis, discussed below).
We used the same hydroxyl radical source as our previous study . Ozone was photolyzed in the Hartley band to produce excited oxygen atoms which react with water vapor.. The cell was illuminated through a quartz window with radiation from a 300-W Xenon arc (ILC Corporation) filtered through a Coming glass •ter 7-54. The [fiter was cooled by circulating tap water through the filter mount. This arrangement minimized possible effects of heating the reaction mixture by the photolysis lamp. The filter inhibited photolysis of ozone in the Chappius bands which produces ground state oxygen atoms. Ground state oxygen does not react with water vapor to produce hydroxyl radical.
The reaction mixture was continuously stirred throughout the course of a run with a stainless steel bellows pump. The volume of the pump and connecting robing was minimized; less than 0.05% of the reaction mixture was outside of the cell at any given time. The entire cell mixture was circulated every 5 to 10 min. The cell was typically circulated for 10 rain before the first sample was extracted, and for 10 rain after the photolysis lamp was turned off before the final sample was taken.
The following procedure was used to prepare a reaction mixture. A volume of liquid water (0.2 to 0.8 cm •) was added through a septurn to an evacuated, temperature regulated stainless steel cell (approximately 48 L volume), which has been describexi previously [Shetter et al., 1987]. Oxygen (Linde UHP, greater than 99.99% purity) was added to the cell in order to insure that methyl radicals (CH3), onc.9 formed, would be converted to stable products (CO or CO o rather than be converted back to methane, o,r be associated:to form ethane.
Back reaction to methane and ethane could provide alternate pathways for isotope fractionation. The methoxy radicals formed react with oxygen to form formaldehyde, which subsequently photolyzes or reacts with hydroxyl.
The extent of conversion of methane and nitrous oxide was monitored by infrared spectroscopy. A BOMEM model DA3.01 Fourier transform spectrometer system was interfaced to the cell. The relative standard deviation of the IR measurements (3-5%) was larger than that for the gas chromatographic determinations. The methane remaining as determined from spectroscopic measurements (FTIR) as compared to GC measurements is shown in Figure 1. The least squares fit of the data yields a slope of 0.98 (+ 0.06), which is not significantly different from unity.

An infrared beam from a heated
The isotope ratio determinations were performed in a fashion similar to that discussed by Tyler [1986;Tyler et al., 1988] and Davidson et al. [1987], using a new high-volume, fast-flow rate combustion train to convert CI-I4 to CO:. A major improvement over the earlier system is in the use of an oven catalyst of platinized alumina (1% loading) at 800øC. Carbon dioxide and water are removed prior to the entry of the sample gas stream into the the oven using a series of four multiple loop traps at liquid nitrogen temperature (77 K). Since Pt-alumina is porous and potentially subject to high blanks, it is conditioned periodically by flushing with dry zero air. Our carbon blank is less that 1 I. tliter of CO: for 300 L of clean zero air processed. The recovery of carbon dioxide produced from the conversion of methane is greater than 99%, even with relatively small samples such as those for this experiment (20 to 50 I. tL). The mass spectrometer used in this study was a Finnigan-Mat Delta-E model, which resulted in overall precision of better than 0.1%o by the use of a specially designed cold finger inlet system. The working standard for this study was Oztech-002 (Oztech Gas Co.) which is--30.011%o relative to PDB carbonate. The values are reported with respect to PDB carbonate, with usual corrections for background, leakage, capillary fractionation, and •70. The separation and combustion procedure would not distinguish carbon originating in ethane from that in methane, therefore a run was chosen for analysis of light allcanes. All alkanes including ethane were below detection limits, and could constitute no more that 0.1% of the methane concentration, and thus present no interference in the isotope ratio analysis.

Temperature and Conversion Dependence of km/kts
The results of this study are analyzed in several ways. First a rate coefficient ratio (k•!k•) was calculated for each experiment from equation (1). These data are presented in Figure 2 and Table 1. The average and 95% confidence intervals for the room temperature recommendations for/q•/k•3 of Davidson et al. [1987] and Rust and Stevens [1980]

Comparison with Previous Measurements
Our new result is about one-half the calculated fractionation of methane carbon isotopes as determined by Davidson et al. [ 1987]. The present result has an uncertainty which is nearly an order of magnitude smaller than Davidson et al. [1987].
Possible reasons for this difference will be discussed below.
The present result is in agreement with the results of Davidson et al. [1987] and Rust and Stevens [1980] within the large uncertainties associated with those studies (•! = 1.010 ñ 0.007 and 1.003 ñ 0.007 at the 95% confidence level; note the confidence interval for Rust and Stevens is calculated from the data, not as reported by them).
It has been pointed out that the individual •! values from the Davidson et al. study fall into two groups [Craig et al., 1988;Stevens and Engelkemeir, 1988]. At least two factors may have contributed to the large spread of values from the study of Davidson et al. [1987] as compared to the present one. The precision of the extent of methane conversion was greatly improved in the present study (less than 1%) as compared to the previous study (about 9%). Also, in this study isotope ratio measurements were performed on the methane at the beginning of every run. In the previous experiment, seven determinations were performed and averaged. While one would expect the isotope ratio of the unreacted methane to be easily characterized and constant, some variability was found in the present study (average initial per value equals -35.9 + 0.5%o). The amount of methane measured in the initial samples was always slightly higher (

Modeling the Carbon Kinetic Isotope Effect
Although Ehhalt et al. [1989] found that primary kinetic isotope effects in simple systems (H 2 and HD with HO) can be calculated quite successfully using the BEBOVIB-IV computer program [Burton et al., 1977], the use of this program for the carbon kinetic isotope effect in the methane-hydroxyl reaction gave a range of values (1.00 to 1.04). These values depend upon the shape assumed for the potential energy surface of the activated complex. A more sophisticated method apparently is required to perform accurate simulations on a secondary kinetic isotope effect such as occurs in this reaction.

Implications for the Atmospheric Methane Budget
What does the value for the ratio of the two rate constants tell us about the 13CH4]1:lCH4 ratio in the sources of atmospheric methane? We performed a simplified calculation following Craig et al. [1988], with an extension to include possible soil sink fractionation as discussed by King et al. [ 1989].

CONCLUSIONS
We performed a study of the temperature dependence of the stable carbon kinetic isotope effect in the oxidation of methane by hydroxyl. The average effect measured in our study is/q•/k•s = 1.0054 (+ 0.0009, 95% confidence interval). This value is larger than that of Rust and Stevens [1980] and lower than that of Davidson et al. [1987], but with much better precision. The ratio is independent of temperature from 273 to 353 K, within the precision of the results. This new value may be used to constrain the atmospheric methane budget using isotope ratio studies, and suggests more measurements of methane sources and sinks are necessary in order to fully understand atmospheric methane.