Rate constant for the recombination reaction CH3 + CH3 → C2H6 at T = 298 and 202 K

Article abstract of DOI:10.1021/jp014044l

The recombination of methyl radicals is the major loss process for methyl in the atmospheres of Saturn and Neptune. The serious disagreement between observed and calculated levels of CH₃ has led to suggestions that the atmospheric models greatly underestimated the loss of CH₃ due to poor knowledge of the rate of the reaction CH₃ + CH₃ + M → C₂H₆ + M at the low temperatures and pressures of these atmospheric systems. In an attempt to resolve this problem, the absolute rate constant for the self-reaction of CH₃ has been measured using the discharge-flow kinetic technique coupled to mass spectrometric detection at T = 202 and 298 K and P = 0.6-2.0 Torr nominal pressure (He). CH₃ was produced by the reaction of F with CH₄, with [CH₄] in large excess over [F], and detected by low energy (11 eV) electron impact ionization at m/z = 15. The results were obtained by graphical analysis of plots of the reciprocal of the CH₃ signal vs reaction time. At T = 298 K, k₁(0.6 Torr) = (2.15 ± 0.42) × 10^-11 cm³ molecule^-1 s^-1 and k₁(1 Torr) = (2.44 ± 0.52) × 10^-11 cm³ molecule^-1 s^-1. At T = 202 K, the rate constant increased from k₁(0.6 Torr) = (5.04 ± 1.15) × 10^-11 cm³ molecule^-1 s^-1 to k₁(1.0 Torr) = (5.25 ± 1.43) × 10^-11 cm³ molecule^-1 s^-1 to k₁(2.0 Torr) = (6.52 ± 1.54) × 10^-11 cm³ molecule^-1 s^-1, indicating that the reaction is in the falloff region. Klippenstein and Harding had previously calculated rate constant falloff curves for this self-reaction in Ar buffer gas. Transforming these results for a He buffer gas suggest little change in the energy removal per collision, -<ΔE>_d, with decreasing temperature and also indicate that -<ΔE>_d for He buffer gas is approximately half of that for Argon. Since the experimental results seem to at least partially affirm the validity of the Klippenstein and Harding calculations, we suggest that, in atmospheric models of the outer planets, use of the theoretical results for k₁ is preferable to extrapolation of laboratory data to pressures and temperatures well beyond the range of the experiments.

Full text of DOI:10.1021/jp014044l

6060
J. Phys. Chem. A 2002, 106, 6060-6067
Rate Constant for the Recombination Reaction CH3 + CH3 f C2H6 at T ) 298 and 202 K
Regina J. Cody,*,† Walter A. Payne, Jr.,† R. Peyton Thorn, Jr.,‡ Fred L. Nesbitt,§
Mark A. Iannone,| Dwight C. Tardy, and Louis J. Stief†
Laboratory for Extraterrestrial Physics, NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771,
Department of Natural Sciences, Coppin State College, Baltimore, Maryland 21216, Department of Chemistry,
MillersVille UniVersity, MillersVille, PennsylVania 17551, and Department of Chemistry, UniVersity of Iowa,
Iowa City, Iowa 52242
ReceiVed: NoVember 2, 2001; In Final Form: March 19, 2002
The recombination of methyl radicals is the major loss process for methyl in the atmospheres of Saturn and
Neptune. The serious disagreement between observed and calculated levels of CH3 has led to suggestions
that the atmospheric models greatly underestimated the loss of CH3 due to poor knowledge of the rate of the
reaction CH3 + CH3 + M f C2H6 + M at the low temperatures and pressures of these atmospheric systems.
In an attempt to resolve this problem, the absolute rate constant for the self-reaction of CH3 has been measured
using the discharge-flow kinetic technique coupled to mass spectrometric detection at T ) 202 and 298 K
and P ) 0.6-2.0 Torr nominal pressure (He). CH3 was produced by the reaction of F with CH4, with [CH4]
in large excess over [F], and detected by low energy (11 eV) electron impact ionization at m/z ) 15. The
results were obtained by graphical analysis of plots of the reciprocal of the CH3 signal vs reaction time. At
T ) 298 K, k1(0.6 Torr) ) (2.15 ( 0.42) × 10-11 cm3 molecule-1 s-1 and k1(1 Torr) ) (2.44 ( 0.52) × 10-11
cm3 molecule-1 s-1. At T ) 202 K, the rate constant increased from k1(0.6 Torr) ) (5.04 ( 1.15) × 10-11
cm3 molecule-1 s-1 to k1(1.0 Torr) ) (5.25 ( 1.43) × 10-11 cm3 molecule-1 s-1 to k1(2.0 Torr) ) (6.52 (
1.54) × 10-11 cm3 molecule-1 s-1, indicating that the reaction is in the falloff region. Klippenstein and Harding
had previously calculated rate constant falloff curves for this self-reaction in Ar buffer gas. Transforming
these results for a He buffer gas suggest little change in the energy removal per collision, - ∆E , with
d
decreasing temperature and also indicate that - ∆E for He buffer gas is approximately half of that for
d
Argon. Since the experimental results seem to at least partially affirm the validity of the Klippenstein and
Harding calculations, we suggest that, in atmospheric models of the outer planets, use of the theoretical
results for k1 is preferable to extrapolation of laboratory data to pressures and temperatures well beyond the
range of the experiments.
Introduction
1969-1980. They determined k∞ (296 K) ) 6.5 × 10-11 cm3
molecule-1 s-1 with a small negative temperature dependence
given by k∞ ) 4.1 × 10-11 exp(137/T); values for k0 were also
reported. To obtain more detailed knowledge of this reaction
in the falloff region, Slagle et al.4 (1988) employed two
techniques. In laser photolysis-photoionization mass spectrom-
etry (LP-PIMS) studies, the rate constant was measured at T
) 296-906 K, P ) 1.2-10.6 Torr Ar and at T ) 296-810 K,
P ) 2.5-10.7 Torr He. In LP-UVA studies, the experimental
conditions were T ) 296-906 K and P ) 5.4-493 Torr Ar.
Analytical expressions for k0 as a function of temperature and
pressure (M ) Ar) and k∞ as a function of temperature were
presented. Both sets of measurements suggest k∞ (296 K) )
6.0 × 10-11 cm3 molecule-1 s-1. Walter et al.5 (1990) reported
measurements at T ) 200, 300, and 408 K in Ar buffer gas. In
LP-UVA experiments at T ) 200 K and P ) 9.6-401 Torr,
the high-pressure limiting rate constant k∞ (200 K) ) 6.9 ×
10-11 cm3 molecule-1 s-1. In discharge flow-mass spectrometry
(DF-MS) experiments they reported pressure dependent k
values in the range (1.7-4.1) × 10-11 cm3 molecule-1 s-1 at T
) 300 K, P ) 0.15-2.2 Torr Ar and in the range (1.1-2.9) ×
10-11 cm3 molecule-1 s-1 at T ) 408 K, P ) 0.3-3.2 Torr Ar.
The methyl radical recombination reaction is one of the most
studied in the field of chemical kinetics. The experimental and
theoretical studies are far too numerous to list individually. The
NIST 1998 Kinetics Data Base1 lists more than 60 references
for this reaction. Noteworthy is the classic 1951 paper by Gomer
and Kistiakowsky2 using the rotating sector technique in a
photodecomposition experiment that may be considered the first
reliable quantitative measurement of the high-pressure rate
constant k∞.
For present purposes we mention three extensive experimental
studies which are frequently cited. Macpherson, Pilling, and
Smith3 (1983, 1985) measured the rate constant at T ) 296-
577 K and P ) 5.4-500 Torr Ar in laser photolysis-UV
absorption (LP-UVA) experiments; Table IV of the 1985 paper
gives a good summary of experimental results for the period
* Corresponding author. Mailing address: NASA/Goddard Space Flight
Center, Code 691, Greenbelt, MD 20771. Tel: 301-286-3782. Fax: 301-
286-0212. E-mail: regina.cody@gsfc.nasa.gov
† Goddard Space Flight Center.
‡ Present address: The Midland Certified Reagent Company, 3112-A
W. Cuthbert Ave., Midland, TX 79701.
Among the many theoretical studies of the methyl recombi-
nation reaction are those by Wardlaw and Marcus6 (1986),
Wagner and Wardlaw7 (1988), Forst8 (1991), Robertson et al.9
§ Coppin State College.
| Millersville University.
University of Iowa.
10.1021/jp014044l CCC: $22.00 © 2002 American Chemical Society
Published on Web 06/01/2002

CH3 + CH3 Recombination Reaction
J. Phys. Chem. A, Vol. 106, No. 25, 2002 6061
(1995), and Klippenstein and Harding10 (1999). The RRKM
calculations of Wardlaw and Marcus6 are able to account for
the experimentally observed negative temperature dependence
of k∞ at T ) 300-2000 K. At T ) 300 K, k∞ ) 7.1 × 10-11
cm3 molecule-1 s-1. The Wagner and Wardlaw7 variational
RRKM theory calculations were performed in conjunction with
the experimental study by Slagle et al.4 In the Wagner and
Wardlaw7 calculations as well as the microcanonical variational
theory calculations of Forst,8 good agreement is observed
between the Slagle et al.4 experiments and the calculations in
the range T ) 296-906 K and P ) 5.4-493 Torr Ar. The
calculations by Robertson et al.9 include results for k∞ at T )
200 K but not for k0. Extensive master equation calculations
using an ab initio potential energy surface and the RRKM model
by Klippenstein and Harding10 provide values for k over a wide
pressure range (P ) 0.1-1000 Torr Ar) and at T ) 200-1700
K. Although they find that k∞ decreases with increasing
temperature for T > 296 K, the value for k∞ between T ) 296
and 200 K is essentially constant at 6.4 × 10-11 cm3 molecule-1
calculations by Klippenstein and Harding10 on the pressure
dependence of k1 at T ) 200 K when modified from M ) Ar
to M ) He.
Experimental Section
Discharge Flow Reactor. The experiments were performed
in a Pyrex flow tube about 60 cm in length and 2.8 cm in
diameter. The inner surface of the flow tube was lined with
Teflon FEP. The flow tube was fitted with a Pyrex movable
injector whose position could be varied between a distance d
) 2 and 44 cm from the sampling pinhole. The system has
been described in previous publications.17,18
The flow tube was used at ambient temperature or cooled by
circulating ethanol from a cooled reservoir through the jacket
surrounding the tube. At T ) 202 K the temperature profile is
flat (( 2 K) from d ) 10 to 44 cm. However, there is a gradual
increase in temperature in the region d ) 1-10 cm where the
flow tube is coupled to the MS sampling system. Modeling
calculations show that the higher temperatures in this region
have little or no effect on the reaction chemistry since we are
studying a rather fast reaction. However, the flow velocity varies
directly with T, and thus the time scale is distorted in this region
close to the sampling pinhole. This time perturbation has been
shown to have little effect on the exponential decay of signal
under the usual pseudo-first-order conditions. But in the present
experiments with signal decay under mostly second-order
conditions, the distortion of the decay profile was evident and
the decay was difficult to fit with either a pure second-order
plot of 1/[CH3] vs time or the numerical simulation program
described in the results section. Corrected reaction times were
obtained by numerically integrating the inverse of the position-
dependent flow velocity from the pinhole to each injector
position. When analyzed in this way, all the T ) 202 K
experiments gave signal profiles free of distortion.
s-1
.
The impetus for the present study was the recent detection
of the methyl free radical in the atmospheres of Saturn11 and
Neptune.12 These are the first observations of any free radical
in the atmospheres of the outer planets. The levels of CH3
observed were much lower than predicted by atmospheric
models, especially for Saturn. It has been suggested11-14 that
the models greatly underestimated the loss of CH3 due to poor
knowledge of the rate of the self-reaction
CH3 + CH3 + M f C2H6 + M
(1)
at the low temperatures and pressures of these atmospheric
systems. For the atmospheric models, appropriate conditions
would be T ) 140-200 K, P < 0.2 Torr, and M ) H2/He.
Laboratory data used in the models came essentially from
the studies of Slagle et al.4 With few exceptions, most laboratory
studies have been performed at higher temperatures (T g 296
K) or higher pressures (P g 5 Torr) or with inappropriate bath
gases M (usually Ar). Only two reports are available of studies
below room temperature and both are at the high-pressure limit
(k∞): the results of Walter et al.5 at T ) 200 K, P ) 9.6-401
Torr Ar and those of Parkes et al.15 at T ) 253 and 273 K, P
) 760 Torr N2. We are aware of only a few published studies
at pressures below 5 Torr. They include the extensive DF-MS
results of Walter et al.5 at P ) 1.1-4.1 Torr Ar and the LP-
PIMS results of Slagle et al.4 at P ) 1.2-10.6 Torr Ar and P
) 2.5-10.7 Torr He. There are also studies in which results
for reaction 1 were a byproduct of the main study of the reaction
of CH3 with a free radical R with [CH3] > [R]. These include
the discharge flow-laser magnetic resonance (DF-LMR)
results of Deters et al.16a,b at P ) 0.5-3.0 Torr He and the recent
LP-PIMS results of Stoliarov et al.16c at P ) 0.94-3.8 Torr
He. Finally, the only published studies employing He as a bath
gas are those of Slagle et al.,4 Deters et al.,16a,b and Stoliarov et
al.16c The paucity of data at low temperatures and low pressures
reflects both experimental convenience and the importance of
the CH3 + CH3 reaction in hydrocarbon combustion chemistry.
In addition to the effect on reaction chemistry and flow
velocity, the effect of the temperature gradient on the number
density or concentration of CH3 is a potential problem. Extensive
calculations using a simple model were performed in which the
temperature from d ) 10 cm to the mass spectrometer sampling
pinhole at d ) 0 cm was increased linearly at 2 cm intervals as
observed in our system. For the conditions of our experiments,
the calculations showed that for d g 10 cm, the slope of the
1/[CH3] vs time plot was the same as that for the case of no
temperature gradient but the line was slightly displaced down-
ward. For d ) 10 cm, the line showed slight upward curvature.
For several reasons, this effect was rendered negligible under
the conditions and practices of our experiments. First, the
deviation at d ) 8 or 9 cm from the straight line is small and
well within the scatter of the data. In addition, we did not attempt
to record data for d ) 2 cm due to end effects and flow
perturbations in the pump out region near the sampling pinhole.
For the remaining two or three points in the interval d ) 3 to
7 cm, we frequently observed upward curvature in the 1/[CH3]
vs time plot and neglected these data points. The observed
upward curvature looked very much like that predicted in the
temperature gradient region. The significant conclusion is that,
under the conditions of our experiments and with the routine
neglect of two or three data points in the interval d ) 3 to 7
cm, there is no measurable effect of the change in [CH3] on the
slope of the 1/[CH3] vs time plots, and hence no measurable
effect on the derived value of k1.
We report here on measurements of k1 using the DF-MS
technique. Experiments at T ) 298 K and P ) 0.6 and 1.0 Torr
He may be compared with the few previous low-pressure studies
with M ) He. We have also measured k1 at T ) 202 K and P
) 0.6-2.0 Torr He (the limits of our system), which provides
the first measurements of this rate constant in the falloff region
at T < 296 K. This allows for verification of the recent
The flow tube was coupled via a two-stage stainless steel
collision-free sampling system to a quadrupole mass spectrom-
eter (ABB Extrel). The CH3 reactant, whose production is

6062 J. Phys. Chem. A, Vol. 106, No. 25, 2002
Cody et al.
discussed below, was monitored at low electron energies (11
eV) in order to avoid formation of CH3 from dissociative
by measuring the decrease in the Cl2+ signal (m/z ) 70, electron
energy ) 14 eV) when the microwave discharge was initiated.
The dilute Cl2/He mixture was admitted to the flow tube via
the movable injector. The position of the injector was chosen
to ensure that reaction 3 went to completion and that the position
was close to the middle of the decay range for the CH3 reactant.
Separate experiments showed that the absolute value of [F]0
was invariant for injector positions of 10 to 40 cm from the
sampling pinhole. The absolute F concentration is given by
+
ionization of CH4 that was present in great excess. The low
electron energy of 11 eV also precludes formation of CH3+ from
dissociative ionization of the equilibrated C2H6 product. Ions
were detected by an off-axis channeltron multiplier (Burle
Electro-Optics).
Helium carrier gas was flowed into the reaction flow tube
through ports at the rear end of the flow tube. All gas flows
were measured and controlled by mass flow controllers (MKS
Instruments). The linear flow velocity ranged from about 2400
to 2700 cm s-1 for the kinetic experiments at nominal pressures
of 1.0 and 2.0 Torr and about 2100 cm s-1 for a pressure of 0.6
Torr. In the calculation of the linear flow velocity, the plug
flow assumption was made. The flow velocity is calculated from
the gas constant, temperature, cross-sectional area of the flow
tube, total gas flow, and total pressure. A sidearm, at the
upstream end of the flow tube, contained a microwave discharge
for the production of F atoms. The discharge region consisted
of a 3/8 in. i.d. ceramic tube coupled via Teflon Swagelok
connectors to a glass discharge arm.
Production and Monitoring of CH3. Fluorine atoms were
produced at the upstream end of the flow reactor by passing
molecular F2 diluted in He through a microwave discharge (50
W, 2450 MHz). For [F2] g 1 × 1012 molecule cm-3, about
50-90% of the F2 was dissociated in the discharge. The CH4
reactant was admitted via a Pyrex movable injector. At the tip
of the movable injector CH3 was produced via the reaction
[F]0 ) [Cl2]disch. off - [Cl2]disch. on
≡ ∆[Cl2] signal × [Cl2]disch. off
where ∆[Cl2] signal is the fractional decrease in the Cl2+ signal,
(Sdisch. off - Sdisch. on)/Sdisch. off. The uncertainty in [F]0 is estimated
to be (10%. At low [F]0 levels, the procedure was modified as
described in the next section.
MS Scaling Factor for CH3. The scaling factor for CH3 is
the ratio of the absolute [CH3] to the mass spectrometer signal
at m/z ) 15. However, the absolute [CH3] comes from the F
atom titration and hence gives [CH3] at t ) 0 while the signal
is recorded at t ) about 3 ms and beyond due to the limitation
of finite time for mixing at the tip of the injector and
perturbations in the flow near the end of the flow tube. For the
case of a first-order signal decay, this is readily handled by a
short, linear extrapolation of the signal back to t ) 0 in a plot
of ln(signal) vs t. This is not an option in the present experiments
since the signal decay is mostly second order (CH3 + CH3) but
with some first-order components (CH3 + F2, CH3 + wall; see
results section). After trying several less satisfactory options to
obtain [CH3] and CH3 signal at the same time (not necessarily
t ) 0), we adopted the following procedure. We reduced [CH3]
to the lowest signal level where it was still possible to
quantitatively record signal decay. For the present conditions
this was [CH3] ) (2-4) × 1011 molecule cm-3. Under these
conditions, the signal appears to exhibit good first-order decay
although modeling shows that there is a substantial second-
order contribution. To verify the correctness of this procedure,
we also performed more than half of these experiments with
[Cl2] ) (2-3) × 1013 molecule cm-3, i.e., [Cl2] . [CH3]. Under
these conditions, CH3 decays largely by the reaction
F + CH4 f CH3 + HF
(2)
where k2 (298 K) ) 6.7 × 10-11 and k2 (202 K) ) 4.4 × 10-11
,
both in units cm3 molecule-1 s-1 (ref 19). Methane was in large
excess with concentrations in the range (0.5-1.0) × 1015
molecule cm-3. These conditions ensured rapid and quantitative
conversion of F to CH3. Thus the large excess of CH4 prevented
secondary loss of CH3 via reaction with F. In addition, the
subsequent reaction of CH3 with residual F2 to form CH3F + F
is followed by very rapid regeneration of CH3 via reaction 2.
The large concentrations of CH4 required to achieve these
desirable features were only possible in the present experiments
due to the complete absence of dissociative ionization of CH4
+
to yield CH3
.
CH3 + Cl2 f CH3Cl + Cl
(4)
Methyl radicals were detected at m/z ) 15 following low-
energy electron ionization. Mass scans were recorded for the
region 14.5-15.5 amu and signals were taken as the integrated
area of the m/z ) 15 peak. Signals were typically averaged for
30-60 s for each injector position and several scans were
recorded for each position. The observed signal was corrected
for a small (e1%) background signal measured with the
microwave discharge off. The background signal and the
background pressure in the ionization region were reduced by
the use of a cold shroud (77 K) that surrounded the mass
spectrometer.
(See ref 21.) Thus the signal decay is strictly first-order and we
determine the CH3 signal at t ) 0 directly by a short linear
extrapolation. A small correction (5%) was made to allow for
the occurrence of F + Cl2 in competition with F + CH4. For
experiments at T ) 202 K, we also applied a correction for the
effect of increasing flow velocity due to increasing temperature
in the region near the sampling pinhole as described above for
the second-order decay of CH3. As expected, the slope is not
affected but the intercept is. Regeneration of CH3 via the slow
reaction of Cl with CH4 was entirely negligible. We found that
the CH3 signal level at t ) 0 was the same within (10% in
both the presence and absence of Cl2. At these lower signal
levels, the CH3 background signal was more significant but
could be reduced to ∼10% of the observed signal as needed by
pretreating the system under conditions similar to those em-
ployed for the decay of CH3 in the presence of excess Cl2.
The potential effect of the change in [CH3] due to the
temperature gradient near the sampling pinhole, discussed in a
previous section for the measurement of k1 from the second-
order decay of CH3, must also be considered for the determi-
Determination of [F]0. The absolute concentration of fluorine
atoms used to generate CH3 was determined by measuring the
consumption of Cl2 in the fast titration reaction:
F + Cl2 f Cl + FCl
(3)
where k3 ) 6.2 × 10-11 cm3 molecule-1 s-1 at T ) 298 and
202 K.20 The F + Cl2 reaction system is ideal for this purpose.
There is complete absence of complicating secondary chemistry
such as Cl + residual F2 or F + FCl since these reactions are
negligibly slow. The initial F atom concentration was determined

CH3 + CH3 Recombination Reaction
J. Phys. Chem. A, Vol. 106, No. 25, 2002 6063
nation of the MS scaling factor via the first-order decay of low
levels of CH3 in the presence of excess Cl2. Also, since the
reaction CH3 + Cl2 (4) is slower than CH3 + CH3 (2) and has
a stronger temperature dependence,21 allowance must be made
for the effect of the varying temperature near the pinhole on
k4. As described above, the measurement of interest here is the
intercept of the ln(CH3 signal) vs time plot, which provides the
CH3 signal at t ) 0. Since the decay under these conditions
was quite slow, we usually recorded only one or two data points
in the temperature gradient region (d ) 1-10 cm) and these
were frequently neglected because they fell measurably below
the trend of the other points (d ) 10-44 cm). We saw no
evidence for deviation from linearity in these plots for the
constant temperature region. Extensive calculations, similar to
those described for the k1 determination, were performed using
a simple model. For the conditions of our experiments,
calculations showed that the CH3 signal at t ) 0 was lowered
by only 2-3% due to the effect of changing [CH3] and k4 with
temperature. As expected for a pseudo-first-order reaction, the
slope is unchanged. The difference between the intercept with
and without a temperature gradient is just the difference in the
amount of reaction that occurs over the 10 cm length with and
without the temperature gradient. This difference is small since
there are two compensating terms in the reaction rate with the
temperature gradient: increasing the temperature decreases
[CH3] and increases k4. Thus the compensation gives a rate
which is close to the amount of reaction that would have taken
place if there was not a temperature gradient.
Figure 1. Plot of CH3 signal vs reaction time at T ) 202 K and P )
1.0 Torr He. [CH3]0 ) 4.35 × 1012 molecule cm-3
.
Results
Figure 1 shows a typical experimental temporal profile of
CH3 signal at T ) 202 K and P ) 1 Torr He measured at m/z
) 15. The reaction time (t) was derived from the measured
distance (x) between the tip of the movable injector to the
sampling pinhole, and the linear velocity (V) calculated from
the measured pressures and gas flows:
distance (x)
time (t) )
(5)
velocity (V)
Each experiment consisted of two parts: (1) the high [CH3]
({1-10} × 1012 molecule cm-3) decay measurement to
determine the rate constant k1 and the measurement of [CH3]0
via F-atom titration with Cl2; (2) the low [CH3] (∼ 3 × 1011
molecule cm-3) decay measurement to determine the scaling
factor (SF) along with its F-atom titration. In the majority of
the experiments, the low methyl decay measurement to deter-
mine SF was performed both before and after the high methyl
decay experiment. For the SF determination, the ln(CH3 signal)
versus time was fitted by the linear regression analysis in the
Excel spreadsheet program to determine the intercept. The SF
is the [CH3]0 from the titration divided by the intercept. For
the rate constant decay curve at high [CH3], the inverse of the
CH3 signal versus time was similarly fitted in Excel according
to the second-order rate equation
To relate the signal at t ) 0 to [CH3]0 we need to determine
[F]0 at this lower level via the procedure outlined above for
higher levels of [F]0. However, determination of the consump-
tion of Cl2 in the fast titration reaction F + Cl2 is not
straightforward at low levels of [F]. If there is sufficient Cl2 to
ensure complete removal of F by the middle of the CH3 decay
range (d ) 20 cm), then the consumption of Cl2 will be
immeasurably small (<1%). By moving the injector out to d )
44 cm, we were able in many instances to achieve essentially
complete removal of F. In some instances in which [Cl2] was
rather low, a 10-15% correction for undertitration was made.
Separate experiments showed that, when corrected for under-
titration of F by Cl2, the derived [F] was constant to (5%
between d ) 20 and 44 cm.
By combining the signal level at t ) 0 with the value for
[F]0 as determined by F atom titration at the low level of (2-
4) × 1011 molecule cm-3, we obtain the desired scaling factor
SF ) [CH3]0/CH3 signal. This scaling factor is then used in the
graphical analysis of the CH3 + CH3 decay experiments at high
[CH3] as described below in the Results section. This of course
makes the assumption that the scaling factor is the same at both
high [CH3] ) (1-10) × 1012 molecule cm-3 and low [CH3] )
(2-4) × 1011 molecule cm-3. This requires a linear dependence
of signal on concentration, which is inherent in the extraction
of a rate constant from the signal decay in this as well as most
kinetic experiments and has been well established for mass
spectrometric detection.
1
1
) 2k1t +
(6a)
[CH3]
[CH3]0
Since [CH3] is the product of the CH3 signal and the scaling
factor SF, this can be written as
1
1
) 2k1SFt +
(6b)
CH3 signal
CH3 signal (t ) 0)
The second-order plots using eq 6b were essentially linear at
both T ) 298 and 202 K; Figure 2 shows a second-order plot
of the data displayed in Figure 1 for an experiment at T ) 202
K and P ) 1 Torr He. The slopes of these second-order plots
provided a value for k1, but the small intercepts were poor
estimates of the CH3 signal at t ) 0. Since this treatment neglects
first-order removal of CH3 via wall loss and reaction with
residual F2 (see below), such graphs provided an indication that
these first-order processes are small and the experiment had
predominately second-order behavior.
Materials. Helium (99.9995%, Air Products) was passed
through a trap containing a molecular sieve before entering the
flow system or before use in the preparation of mixtures. The
molecular sieve was periodically heated to about 220 °C under
vacuum. F2 (99.9%, Cryogenic Rare Gases, 5% in He) and CH4
(99.9995%, MG Industries) were used as provided without
further purification. Cl2 (VLSI 4.8 grade, Air Products) and C2H6
(99.95%, MG Industries) were degassed at liquid nitrogen
temperature.
As a check on the simple graphical method, the rate constant
k1 for the methyl self-recombination was derived by a one-

6064 J. Phys. Chem. A, Vol. 106, No. 25, 2002
Cody et al.
TABLE 1: Summary of Experimental Conditions and Rate
Data for the CH3 + CH3 Reaction at T ) 298 K and P ) 0.6
and 1.0 Torr He
[CH3]0/1012
k1/10-11
pressure/Torr molecule cm-3 [CH4]0/[F]0 cm3 molecule -1 s -1
0.6
1.0
6.33
7.60
138
119
1.95
2.35a
<2.15 ( 0.42>b
2.34
2.64
2.60
2.23
2.35
2.93
2.38
1.82
2.66
2.43
2.85
5.89
6.07
6.77
7.18
7.35
7.58
7.66
7.66
7.97
9.24
9.49
9.74
90
105
123
110
97
91
98
115
84
89
95
92
Figure 2. Plot of the reciprocal of the CH3 signal vs reaction time at
T ) 202 K and P ) 1.0 Torr He. Data from Figure 1.
2.45
<2.44 ( 0.52>b
parameter fitting of the rate constant decay curve to a numerical
simulation of the reaction system using the Facsimile program.22
The absolute concentrations of CH3 were calculated from the
net CH3 mass spectrometric signals multiplied by the scaling
factor (SF). The reaction mechanism used in the numerical
simulation was the following:
a Value of k1 at P ) 0.6 Torr measured relative to average value of
k1 at P ) 1.0 Torr for this experiment only; all other experiments are
absolute measurements of k1. b Mean central value of k1 at each pressure;
error is one standard deviation ((1σ) plus an additional 10% for
systematic errors.
+
reaction 1 and subsequent dissociative ionization to CH3 in
F + CH4 f CH3 + HF (ref 19)
CH3 + CH3 + M f C2H6 + M
CH3 + wall f products
(2)
(1)
(7)
(8)
the ionization region. The relative cracking patterns were
measured at an ionization energy of 15 eV for ethane formed
in situ from reaction 1 and then for a comparable concentration
of ethane introduced from a 1% C2H6 in He mixture. Relative
ratios were determined for m/z of 30, 29, 28, and 26 and were
the same whether ethane arose from reaction 1 or from the
prepared gas mixture. We thus have no evidence for any
contribution from stabilized, nonequilibrated ethane.
CH3 + F2 f CH3F + F (ref 23)
According to the numerical simulation, reaction 1 accounted
for >90% of the loss of CH3 while reactions 7 and 8 contributed
<10% and <1%, respectively. This confirms the expectation
from the simple graphical analysis using eq 6b. The rate constant
for the first-order wall loss is very small and a temperature
independent value k7 ) 10 s-1 was estimated from prior work24
as well as a two-parameter fit (k1 and k7) to a typical experiment.
The final value for k1 is very insensitive to the value chosen
for k7.
At T ) 298 K the graphical method using eq 6b and the
numerical simulation using reactions 2, 1, 7, and 8 gave average
k1 values that agreed to within a few percent. However, at T )
202 K, the numerical simulation always led to values of k1 that
were on average 25% lower than the graphical method. A very
likely explanation is that, at the lower temperature, diffusional
mixing of CH4 into the F/He flow is slower and formation of
CH3 via reaction 2 is considerably longer than the 0.1 ms
calculated from k2 and [CH4]. Based on a rough estimate, the
time scale for mixing was estimated to be at least 1 ms. When
this was incorporated into the Facsimile numerical simulation,
the residual sum of squares for the fit decreased substantially
and the distribution of the residuals with reaction time was much
flatter. Equally significant was the fact that, for a typical
experiment, the fitted value for k1 was now in much better
agreement (better than 10%) with the graphical determination.
We also showed that, for the plot of typical data using eq 6b,
a shift in t ) 0 by +1 ms had no effect on the slope and hence
on the value of k1. Because of this mixing complication, we
prefer the simple graphical method using eq 6b to determine k1
at both temperatures.
CH3 + CH3 Rate Constant at T ) 298 K. Although there
are numerous measurements of k1 at room temperature, there
are only a few published studies at P ) 1 Torr with He as the
bath gas.16 We measured k1 at T ) 298 K partly to fill in this
gap and partly to test our experimental technique before
performing measurements at lower temperatures. The ratio of
[CH4] to [F] was =100 to ensure rapid formation of CH3 via
reaction 2 and to eliminate secondary chemistry such as the
reaction of F with CH3. The rate constant was invariant with
[CH3] between (5.9-9.7) × 1012 molecule cm-3, but was not
invariant above this concentration limit. Table 1 presents the
results for T ) 298 K and P ) 0.6 and 1.0 Torr He. The rate
constant k1 was determined to be (2.15 ( 0.20) × 10-11 cm3
molecule-1 s-1 at P ) 0.6 Torr He and (2.44 ( 0.28) × 10-11
cm3 molecule-1 s-1 at P ) 1.0 Torr He where the quoted errors
are one standard deviation ((1σ). To allow for systematic errors
we add an additional 10%. Therefore, the recommended values
are k1 (0.6 Torr) ) (2.15 ( 0.42) × 10-11 cm3 molecule-1 s-1
and k1 (1.0 Torr) ) (2.44 ( 0.52) × 10-11 cm3 molecule-1 s-1
.
The results suggest a slight positive dependence of k1 on pressure
over this narrow range, consistent with most previous studies
with M ) He or Ar.
CH3 + CH3 Rate Constant at T ) 202 K. At T ) 202 K,
the rate constant for methyl recombination k1 was measured at
pressures of 0.6, 1.0, and 2.0 Torr as shown in Table 2. At this
temperature, [CH4]/[F] ) 100-600. For P ) 1 Torr, k1 is
invariant for initial methyl concentrations in the range (1.2-
8.6) × 1012 molecule cm-3. The average value is k1 ) (5.25 (
1.43) × 10-11 cm3 molecule-1 s-1 where the error is 1σ
(statistical) + 15% (systematic). This result is ∼2 times higher
than that at 298 K. Because of the temperature gradient in the
region near the sampling pinhole (d ) 1-10 cm) described in
A factor that would adversely affect the CH3 decay experi-
ments is formation of stabilized but not equilibrated C2H6 in

CH3 + CH3 Recombination Reaction
J. Phys. Chem. A, Vol. 106, No. 25, 2002 6065
TABLE 2: Summary of Experimental Conditions and Rate
Data for the CH3 + CH3 Reaction at T ) 202 K and P )
0.6, 1.0 and 2.0 Torr He
TABLE 3: Lennard-Jones Parameters and Calculated
Collision Numbers
k12(T) /cm3 molecule-1 s-1, Ω(2,2)*
collision partners
[CH3]0/1012
k1/10-11
(σ, ꢀ)a
T ) 200 K
T ) 296 K
pressure/Torr molecule cm-3 [CH4]0/[F]0 cm3 molecule -1 s -1
Ar(3.42, 124) +
C2H6(4.42, 230)
He(2.58, 10.2) +
C2H6(4.42, 230)
3.47 × 10-10 b, 1.45
4.06 × 10-10, 0.97
3.58 × 10-10 b, 1.23
4.55 × 10-10, 0.89
0.6
1.0
5.73
7.23
8.56
142
119
98
4.62
5.38
5.12
< 5.04 ( 1.15 >a
1.21
1.86
2.69
3.57
4.35
5.84
6.42
6.99
7.60
8.21
8.62
589
384
272
199
105
97
107
129
117
99
5.98
5.44
5.53
5.26
5.00
5.37
4.25
5.74
a Units of Angstroms and Kelvin, respectively. b Present calculated
values in agreement with those used by ref 10.
T ) 298 K and P ) 1 Torr He which yields k1 ) 2.6 × 10-11
cm3 molecule-1 s-1, in excellent agreement with our determi-
nation. At T ) 298 K and P ) 0.55 Torr He, the Deters et
al.16a result of k1 ) (1.8 ( 0.7) × 10-11 cm3 molecule-1 s-1 is
in good agreement with our value k1 ) (2.2 ( 0.4) × 10-11
cm3 molecule-1 s-1 at P ) 0.6 Torr He.
Of more interest is the data at T ) 202 K that provides the
first measure of the pressure dependence of k1 for a temperature
below T ) 298 K. Qualitatively, our results demonstrate that
the reaction is in the falloff region. Moreover, the measured
value of the rate constant at P ) 2.0 Torr He, k1 ) (6.5 ( 1.5)
× 10-11 cm3 molecule-1 s-1, is very close to the previously
measured value5 of the high-pressure limit at T ) 200 K, k∞ )
(6.9 ( 0.2) × 10-11 cm3 molecule-1 s-1. This suggests that at
P ) 2.0 Torr He the measured k1 is very close to or has reached
k∞. Other than this reference to the value for k∞, comparison
with previous data at T ) 202 K is not an option. So we turn
to a comparison with calculations of the rate constant under
the conditions of our experiment.
4.52
6.24
100
4.45
< 5.25 ( 1.43>a
2.0
3.11
6.26
10.3
234
115
97
6.68
5.89
6.98
< 6.52 ( 1.54 >a
a Mean central value of k1 at each pressure; error is one standard
deviation (( 1σ) plus an additional 15% for systematic errors.
the Experimental Section and because of the complications from
the corrections applied, we made two additional measurements
of k1 at T ) 202 K, P ) 1.0 Torr He using a recently installed
flow tube in which the jacketed region went all the way to the
end of the flow tube. The design of the new flow reactor, to be
described in a future publication, resulted in a uniform tem-
perature profile. Thus there was complete absence of the
previously discussed corrections due to the temperature gradient.
The values of k1 at P ) 1.0 Torr were 5.51 and 5.21 in units
10-11 cm3 molecule-1 s-1. These are within 5% of the central
value of 5.25 × 10-11 cm3 molecule-1 s-1 for the 11 experi-
ments (Table 2) obtained after correction for the effect of the
temperature gradient. This demonstrates the essential validity
of the corrections applied.
The measured value at P ) 0.6 Torr is k1 ) (5.04 ( 1.15) ×
10-11 cm3 molecule-1 s-1 and at P ) 2.0 Torr, k1 ) (6.52 (
1.54) × 10-11 cm3 molecule-1 s-1 with the same error estimate
of 1σ + 15%. The systematic error was increased somewhat
compared to that at T ) 298 K to allow for the additional
difficulties of the measurements at T ) 202 K. Over this small
pressure range the results suggest a slight increase with
increasing pressure which indicates that, as expected, the
reaction is in the falloff region.
Calculations for the “observed” rate coefficients for the
combination of methyl radicals in an argon bath (T ) 200-
1600 K) have been reported by Klippenstein and Harding10 (KH)
as a function of the energy removed per collision. In the
following discussion the numerical value associated with the
average energy removed per collision is defined as a positive
quantity, i.e., - ∆E . As shown below, the argon pressures
d
can be transformed to the equivalent helium pressures using
the appropriate Lennard-Jones parameters (σ, Ω(2,2)* and ꢀ)26
for the collision partners. Bimolecular collision rate coefficients
(cm3 molecule-1 s-1) are determined by temperature, collision
cross section (σ), well depth (ꢀ), masses (m1 and m2), and the
collision integral (Ω(l,s)*). For vibrational energy transfer it has
been assumed that l,s ) 2,2. Thus the collision frequencies,
k12(T), between substrate (1) and deactivator (2) are calculated
from the expression
k12(T) ) π[σ1/2 + σ2/2 ]2 [8kT(m1 + m2)/(πm1m2)]0.5 Ω(2,2)*
[T/(ꢀ1 ꢀ2)0.5] (9)
Discussion
A tabulation of k1,2(T) and the appropriate constants for the
Lennard-Jones 6-12 potential are presented in Table 3. The
equivalent helium pressure is calculated by
The only published experimental measurements with which
our results at T ) 298 K and P ) 1 Torr He may be directly
compared are those of Deters et al.16a,b and Stoliarov et al.16c
These studies were designed to measure the rate constant for
the radical-radical reactions CH3 + OH,16a CH3 + CH2,16b and
p(He) ) cp(Ar)
(10)
16c
CH3 + C2H3 with [CH3] > [OH, CH2 or C2H3], and thus
where c ) [(σ1 + σAr)2/(σ1 + σHe)2] [(m1 + mAr)/(m1 + mHe)]0.5
[mHe/mAr]0.5 [Ω(T/(ꢀ1 ꢀAr)0.5)/Ω(T/(ꢀ1ꢀHe)0.5)]. The conversion
factor, c, changes from 0.856 to 0.787 as the temperature
increases from 200 to 296 K. To be noted is that the bracketed
σ and mass factors, which are independent of temperature, give
a factor of 0.562 while the bracketed Ω factor is 1.49 at 200
and decreases to 1.38 at 296 K. Thus, the assumed values for
the parameters of k12(T) and its temperature dependence will
systematically displace the k vs pressure “falloff” curves.
these determinations of k1 for CH3 + CH3 were a byproduct of
the measurements. Nevertheless, their results of k1 ) (2.9 (
0.8),16a (2.9 ( 0.8),16b and (3.5 ( 0.5)16c × 10-11 cm3
molecule-1 s-1 are in reasonable agreement with our value k1
) (2.4 ( 0.5) × 10-11 cm3 molecule-1 s-1 given the quoted
uncertainties. All other published studies at room temperature
are at higher pressures of He4 or with the bath gas M ) Ar.3-5
We recently learned of an unpublished DF-MS study25 at

6066 J. Phys. Chem. A, Vol. 106, No. 25, 2002
Cody et al.
transfer model and the excess energy is more important than
the excitation energy.27 In the ethyl radical system28 the collision
efficiency, âc, decreases from 0.37 to 0.26 as the temperature
increases from 195 to 300 K; - ∆E d values were not reported
for this system. The deactivation of butyl radicals29 formed by
the addition of H atoms to cis-2-butene has been studied with
both helium and argon as the deactivators at T ) 195 and 300
K; this system has ∼40 kcal mol-1 of internal energy and an
excess energy of ∼7 kcal mol-1. The results from those
experiments indicate that âc for helium decreases from 0.55 to
0.35 as the temperature increase from 195 to 300 K; similarly,
âc for argon decreases from 0.59 to 0.41 over the same
temperature range. The values for - ∆E d for helium decreased
from 2.1 to 1.5 kcal mol-1 as the temperature increased from
195 to 300 K. Over the same temperature range - ∆E for
d
argon increased from 2.1 to 2.6 kcal mol-1. The decrease in âc
with increase in temperature is due to the increase of the “up”
transitions with increasing temperature. These results suggest
a weak or negligible (within experiment error) temperature
Figure 3. Plots of calculated k1 vs pressure of He at T) 200 K for
values of - ∆E (cm-1): long dashed line (800), dash-dot-dot line
d
(400), short dashed line (200), dot-dot line (100), solid line (50).
Experimental results (filled circles) at P ) 0.6, 1.0, and 2.0 Torr He
and T ) 202 K are from this study (Table 2).
dependence for - ∆E and a small difference between argon
d
and helium deactivators. The energy transfer information
reported in the combination of substituted methyl radicals30 was
not considered pertinent. Although they have comparable
average excitation energies these systems have average excess
energies in excess of 20 kcal mol-1 (substantially greater than
the available thermal energy). These large excess energies
require a multicollision cascade for stabilization, which produces
large nonlinearities on the yield of stabilization with pressure.27
The KH plots at T ) 200 K indicate that the reported
experiments5 with argon as the deactivator are in the high-
pressure limit so that energy transfer parameters cannot be
extracted. However, at T ) 296 K the lowest pressure
experimental rate coefficient for argon has decreased by more
than a factor of 3 from its high-pressure limit; the measured
falloff for argon is consistent with - ∆E between 100 and
d
200 cm-1. Values for - ∆E can also be extracted from the
d
Figure 4. Plots of calculated k1 vs pressure of He at T ) 296 K for
present experiments with helium by assuming the same high-
pressure rate coefficients as calculated by KH. At T ) 200 K
the lowest pressure rate coefficient (∼0.8 times the rate
values of - ∆E (cm-1): long dashed line (800), dash-dot-dot line
d
(400), short dashed line (200), dot-dot line (100), solid line (50).
Experimental results (filled circles) at P ) 0.6 and 1.0 Torr He and T
) 298 K are from this study (Table 1). Experimental results (filled
triangles) at P ) 2.5, 5.2 and 10.7 Torr He and T ) 296 K are from
ref 4.
coefficient for the high-pressure limit) is consistent with - ∆E
d
∼100 cm-1 as shown in Figure 3. Similar reasoning for the T
) 296 K helium experiments indicates a value of - ∆E
d
between 50 and 100 cm-1 as shown in Figure 4. Thus the present
The falloff curves in Figures 3 and 4 are the results of
helium experiments suggest a slight increase in - ∆E with
transforming the KH curves10 as a function of - ∆E from
d
d
decreasing temperature, with - ∆E d being approximately half
argon to helium at T ) 200 and 296 K, respectively. The new
of that for argon. These values of - ∆E for helium are also
d
plots exhibit the same information as those with argon as the
2 to 4 times smaller than those observed for the H + cis-2-
butene system.29 However, it is difficult to uniquely identify
the experimental points displaced from the calculated curves
deactivator; the falloff extends to higher pressure as - ∆E
d
decreases and/or the temperature increases. Also to be noted is
that for a given - ∆E the falloff curves are shifted to lower
d
as due to either a change in - ∆E or to the temperature
d
pressure when the deactivator changes from argon to helium,
dependence of Ω(2,2)*. Likewise, an error in σ2 would also
since c < 1.
produce a displacement in the pressure curves.
Since the exact value for - ∆E for this reaction and its
d
Finally, a brief consideration may be given to the implication
of these results for the modeling of the hydrocarbon chemistry
in the atmospheres of the planets Saturn and Neptune. As
mentioned in the Introduction, attempts to compare the observed
concentration of the methyl radical in the atmospheres of these
planets11,12 with those predicted by atmospheric models have
led to the suggestion11-14 that the loss of CH3 via the reaction
CH3 + CH3 (1) was significantly underestimated due to
inappropriate values for k1 based on the limited laboratory data
available for this reaction at low temperatures and low pressures.
The danger of extrapolating laboratory data to temperatures and
pressures far beyond the range of the experiments is widely
temperature dependence are not known, other systems must be
used to get some insight. The decomposition of ethyl radicals
formed by the addition of H atoms to ethene is a system
comparable to the methyl radical combination. The similarity
is that both systems have nearly the same number of atoms and
the excess energy (average thermal energy of the chemically
activated species minus the critical energy for the reverse of
the formation) is very small, comparable to the available thermal
energy. The differences are the level of excitation (∼40 kcal
mol-1 for the ethyl radicals and ∼85 kcal mol-1 for the ethane)
and the unpaired electron. Data from other systems suggest that
the unpaired electron does not affect the vibrational energy

CH3 + CH3 Recombination Reaction
J. Phys. Chem. A, Vol. 106, No. 25, 2002 6067
(11) Bezard, B.; Feuchtgruber, H.; Moses, J. I.; Encrenaz, T. Astron.
Astrophys. 1998, 334, L41.
(12) Bezard, B.; Romani, P. N.; Feuchtgruber, H.; Encrenaz, T.
Astrophys. J. 1999, 515, 868.
(13) Atreya, S. K.; Edington, S. G.; Encrenaz, T.; Feuchtgruber, H. The
UniVerse as Seen by ISO, Eur. Space Agency Spec. Publ., ESA SP-427,
1999; p 149.
(14) Lee, A. Y. T.; Yung, Y. L.; Moses, J. J. Geophys. Res. 2000, 105,
20207.
recognized. The present experiments at T ) 202 K over a limited
range of low pressures seems to affirm the validity of the
Klippenstein and Harding calculations10 in the falloff region as
extended here for M ) He. This suggests that, in models of the
hydrocarbon chemistry of the outer planet atmospheres, use of
this theoretical calculation for k1 is preferable to extrapolating
the limited laboratory data available.
(15) Parkes, D. A.; Paul, D. M.; Quinn, C. P. J. Chem. Soc., Faraday
Trans. I 1976, 72, 1935.
(16) (a) Deters, R.; Otting, M.; Wagner, H. Gg.; Temps, F.; Laszlo, B.;
Dobe, S.; Berces, T. Ber. Bunsen-Ges. Phys. Chem. 1998, 102, 58. (b)
Deters, R.; Otting, M.; Wagner, H. Gg.; Temps, F.; Dobe, S. Ber. Bunsen-
Ges. Phys. Chem. 1998, 102, 978. (c) Stoliarov, S. I.; Knyazev, V. D.;
Slagle, I. R. J. Phys. Chem. A 2000, 104, 9687.
(17) Brunning, J.; Stief, L. J. J. Chem. Phys. 1986, 84, 4371.
(18) Nesbitt, F.; Payne, W. A.; Stief, L. J. J. Phys. Chem. 1988, 92,
4030.
(19) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.;
Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling: Evaluation Number 12, NASA Panel for Data Evaluation, JPL
Publication 97-4, 1997.
Acknowledgment. This work was supported by the NASA
Planetary Atmospheres Research Program. R.P.T., Jr. thanks
the National Academy of Sciences for the award of a postdoc-
toral research associateship. We thank Stephen Klippenstein and
Larry Harding for their generosity in sharing with us their
calculated falloff curves for argon. We thank Jozef Peeters for
informing us of the unpublished measurement of k1(298 K) at
P ) 1.0 Torr He. We thank Paul Romani for bringing this
problem to our attention and for helpful discussions. Informative
discussions with Sushil Atreya, Yuk Yung, and Julie Moses
are also gratefully acknowledged.
(20) Unpublished results from CNRS, Orleans and GSFC, Greenbelt to
be submitted to J. Phys.Chem.
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