Initiation and Abstraction Reaction in the Pyrolysis of Acetone

Article abstract of DOI:10.1021/jp9520613

The rates of the reactions, (CH3)2CO -> CH3 + CH3CO (1) and CH3 + (CH3)2CO -> CH4 + CH2COCH3 (3) have been studied in the flow pyrolysis of acetone at 825-940 K and 10-180 Torr.Yields of products were mesured by gas chromatography.The rate constant, k₁, for the initiation reaction, determined from the sum of the yields of the termination products, was observed to be pressure dependent at 928 K.The Arrhenius expression for this reaction at the high-pressure limit (obtained from a nonlinear least-squares fit to the experimental data using the Troe factorization procedure) was found to be k_1infinite (s^-1) = 10^17.9+/-0.8 exp(-353 +/- 14 kJ mol^-1/RT).The Troe method has also been used to find the high-pressure limits of the cross-combination ratio for CH3 and CH3COCH2 radicals (1.9 +/- 0.1) and of the qoutient k₅/k₃², where reaction 5 is 2CH3 -> C2H6.Calculated rate constants for reaction 3, when combined with values reported from photolysis experiments at lower temperatures, were found to exhibit a curved Arrhenius plot.A transition state theory model was fitted to the data for k₃ to determine the average transitional vibrational term value in the transition state (279 +/- 8 cm^-1), the effective activation barrier height (46 +/- 1 kJ mol^-1), and the full width of the barrier at half its height (52 +/- 3 pm).

Full text of DOI:10.1021/jp9520613

J. Phys. Chem. 1996, 100, 3573-3579
3573
Initiation and Abstraction Reactions in the Pyrolysis of Acetone
S. Hosein Mousavipour and Philip D. Pacey*
Department of Chemistry, Dalhousie UniVersity, Halifax, NoVa Scotia, Canada B3H 4J3
ReceiVed: July 21, 1995; In Final Form: NoVember 17, 1995X
The rates of the reactions, (CH3)2CO f CH3 + CH3CO (1) and CH3 + (CH3)2CO f CH4 + CH2COCH3 (3)
have been studied in the flow pyrolysis of acetone at 825-940 K and 10-180 Torr. Yields of products were
measured by gas chromatography. The rate constant, k1, for the initiation reaction, determined from the sum
of the yields of the termination products, was observed to be pressure dependent at 928 K. The Arrhenius
expression for this reaction at the high-pressure limit (obtained from a nonlinear least-squares fit to the
experimental data using the Troe factorization procedure) was found to be k1∞ (s-1) ) 1017.9(0.8 exp(-353 (
14 kJ mol-1/RT). The Troe method has also been used to find the high-pressure limits of the cross-combination
2
ratio for CH3 and CH3COCH2 radicals (1.9 ( 0.1) and of the quotient k5/k3 , where reaction 5 is 2CH3 f
C2H6. Calculated rate constants for reaction 3, when combined with values reported from photolysis
experiments at lower temperatures, were found to exhibit a curved Arrhenius plot. A transition state theory
model was fitted to the data for k3 to determine the average transitional vibrational term value in the transition
state (279 ( 8 cm-1), the effective activation barrier height (46 ( 1 kJ mol-1), and the full width of the
barrier at half its height (52 ( 3 pm).
ss
Introduction
Here Ress, Rbss, and Rh are the steady state rates of formation
of the termination products ethane, butanone, and 2,5-hexanedi-
“The photolysis of acetone is undoubtedly the most studied
reaction in gas kinetics,” according to a review.1 The objective
of at least 36 of these studies has been to measure the rate
constant for the reaction of methyl radicals with acetone or other
organic molecules. However, such studies have been limited
to the temperature range 300-750 K. It is the purpose of the
present work to build on this firm foundation, extending the
temperature range up to 940 K, generating methyl radicals not
by photolysis, but by the pyrolysis of acetone.
one, respectively.
Again applying the steady state approximation, k5/k3 may
2
be calculated as
ss 2
k5/k32 ) Ress[(CH3)2CO]2/(Rm
)
(9)
ss
where Rm is the steady state rate of formation of methane.
This equation has been the basis of the determination of k3 in
most photolysis experiments.1 Reaction 5 has been studied
many times, and the pressure and temperature dependence of
its rate constant are reasonably well-known.4 In this work we
will attempt to apply eqs 8 and 9 to the pyrolysis of acetone
for the first time.
Rice and Herzfeld2 proposed that the pyrolysis of acetone
proceeds by a free radical mechanism
(CH3)2CO f CH3 + CH3CO
CH3CO f CH3 + CO
(1)
(2)
The present experiments employed a flow reactor system.
Acetone entered the reactor cold, and the steady rates of product
formation would only have been achieved after a delay, τh, in
transferring heat to the flowing gas and after a delay, τc, as
reaction 1 increased the concentrations of radicals toward their
steady state values. During the delay caused by incomplete
radial heat transfer, the observed chordal or average rate of
CH3 + (CH3)2CO f CH4 + CH3COCH2
CH3COCH2 f CH2CO + CH3
2CH3 f C2H6
(3)
(4)
(5)
(6)
(7)
app
methane formation, Rm ()[CH4]/t), would have been given
by the following expression5
CH3 + CH3COCH2 f CH3COC2H5
2CH3COCH2 f (CH3COCH2)2
Rmapp/Rmss ) 1 - (τh/t)
(10)
During the establishment of the steady state for radicals, the
observed rate of formation of methane would have been given
It has been confirmed that CH4 and CH2CO are the major
products of the reaction,3 but there do not appear to have been
any experimental studies of all the minor products.
Applying the steady state approximation to the radicals in
this mechanism, the rate of the initiation reaction, step 1, would
be equal to the sum of the rates of the termination reactions,
steps 5-7. This assumption would allow the calculation of the
rate constant, k1, for reaction 1 as
by6
Rmapp/Rmss ) (τc/t ln 2) ln cosh(t ln 2/τc)
(11)
Any pressure dependence of the rate constants k1 and k5 can
be analyzed using the factorization method of Troe:7
WC
k1/k1∞ ) FLHFCSCFC
(12)
(13)
ss
k1 ) (Ress + Rbss + Rh )/[(CH3)2CO]
(8)
FLH ) (k1,0[M]/k1∞)/(1 + k1,0[M]/k1∞)
X Abstract published in AdVance ACS Abstracts, February 1, 1996.
Here k1∞ and k1,0 are the limiting, high-pressure, first-order and
0022-3654/96/20100-3573$12.00/0 © 1996 American Chemical Society

3574 J. Phys. Chem., Vol. 100, No. 9, 1996
Mousavipour and Pacey
limiting, low-pressure, second-order rate constants, respectively,
for reaction 1. Parallel expressions are available for reaction
5, but the rate constants are second and third order, respectively.
SC
FC corrects for strong collision effects. The weak collision
factor, FCWC, is a function of the collision efficiency, âc, and
was calculated using eqs 79-81 in ref 7. The effective number
of vibrational modes, Sk, was calculated from experimental
vibrational frequencies, as listed in the Appendix in the
supporting information.
The steady rate of formation of the cross-combination product,
butanone, should be approximately twice the square root of the
product of the other termination rates, provided all reactions
are at their high-pressure limits.8 At lower pressures, this
relationship could be generalized as follows:
ss 1/2
Rbss ) m(RessRh )
(14)
Figure 1. Chordal rate of formation of CH4 at 20 Torr and 876 K in
a reactor with a surface-to-volume ratio of 14.0 cm-1: 9, experimental
data; lines, nonlinear least-squares fits of eqs 10 (dashed) and eq 11
(solid) to the data.
We will make use of this relationship to estimate rates of
termination reactions in conditions where direct measurements
were not possible.
Experimental Section
Acetone (Burdick & Jackson, 99.9%) was degassed by
condensing with liquid nitrogen, evaporated, and was again
degassed in liquid nitrogen. Methane and ethane of 99% purity
(Matheson CP Grade) were used to prepare a mixture to calibrate
the gas chromatograph. Butanone (Fisher) and 2,5-hexanedione
(Eastman Kodak Co.) with less than 1% acetone as impurity
were used individually for the same purpose.
The flow system was similar to that used previously in this
laboratory.5,6 The pressures in the storage bulbs and reactor
were monitored by two pressure transducers (Bell & Howell,
Type 4-366-0006-03Mo, 0-50 and 0-15 psi). The flow rate
into the reactor was controlled by a needle valve (Edwards,
Model LBlB). Three 1-m cylindrical quartz reactors were
used: two with internal radii of 4.0 and 3.0 mm and inside
thermocouple wells of 2.1 mm external radius and the third with
a 1.4 mm internal radius and an outside thermocouple compart-
ment. The surface-to-volume ratios (s/v) for these reactors were
calculated to be 10.3, 20.4, and 14.0 cm-1, respectively. During
an experiment, a 43 cm long section was heated by a resistive
furnace. The reactor temperature was controlled by a platinum/
platinum-13% rhodium thermocouple. An automatic control-
ler, which consisted of a pressure transducer (MKS-122AA-
01000AB), a programmable temperature controller (Omega CN
2000), and an outlet selenoid valve (MKS-0248A-50000SY),
was used to control the pressure in the reactor.
Figure 2. Ketene absorbance at 2150 cm-1 as a function of residence
time at 876 K and 125 Torr with an s/v of 14.0 cm-1
.
Results
The reaction was studied in the temperature range 825-940
K, the pressure range 10-180 Torr, and the residence time range
0.01-3 s. The main products observed were methane and
ketene, and the minor products were hydrogen, carbon mon-
oxide, ethylene, ethane, propylene, propane, butanone, and 2,5-
hexanedione. Conversions were less than 1%.
Figure 1 shows the chordal rate of formation of methane at
876 K and 20 Torr. There was an initial rise in the rate,
followed by a plateau at times longer than 0.3 s. Both eqs 10
and 11 were fitted to the data from this experiment and similar
experiments by nonlinear least squares;10 the difference between
the steady state rates obtained from one set of data with the
two equations was always less than 5%. At conditions where
no induction period was observed, the average rate of formation
in the plateau region was taken as the steady state rate of
formation.
Figure 2 shows the absorbance by ketene at 2150 cm-1 as a
function of residence time at 876 K and 125 Torr. Similar
experiments were performed at temperatures from 834 to 929
K and pressures between 85 and 176 Torr. The ketene infrared
absorbance was always proportional to the methane gas
chromatographic peak size, independent of reaction pressure and
temperature. Assuming the steady rates of formation of methane
A six-way linear gas sampling valve (Varian 57-000034-00)
was used to take samples in a 10 cm3 sample loop, and a gas
chromatograph (Tracor 550) was used to analyze the samples.
Methane, ethane, and ethylene were separated on a 1-m silica
gel column (mesh 100/120) at room temperature, CO and
hydrogen on a 1.2 m alumina column (type F1) at 0 °C,
butanone on a 1.2 m Porapak column (type Q) at 160 °C, and
2,5-hexanedione on a 1.0 m 10% carbowax-20M on chromosorb
column at 110 °C. Nitrogen was used as carrier gas. A flame
ionization detector was used to detect the hydrocarbon and
ketone products, and a zirconia sensor9 was used to detect CO
and hydrogen. Typically three samples were analyzed at each
flow condition; reproducibility was between 0.5% and 3%,
except for the smallest peaks. Ketene peaks at 2150 cm-1 were
detected with a (Nicolet 510P FT-IR) spectrometer with a
resolution of 4 cm-1. All analytical techniques were not applied
to all samples.

Reactions in the Pyrolysis of Acetone
J. Phys. Chem., Vol. 100, No. 9, 1996 3575
TABLE 1: Steady State Rates and Rate Constants from Experiments at Several Pressures and Temperatures in Three
Reactors
Rm × 105,
Re × 107,
Rb × 107,
Rh × 107,
k5/k3 × 104,
k1 × 104 ,
2
P, Torr
mol L-1 s-1
mol L-1 s-1
mol L-1 s-1
mol L-1 s-1
mol s L-1
s-1
928 K, s/v ) 20.4 cm-1
10.3
20.9
41.4
82.2
126.0
182.0
1.37
3.67
11.0
25.7
46.
7.0
15.8
39.
73.
107.
161.
3.2
7.2
0.21
0.49
1.23
4.1
12.0
17.0
1.18 ( 0.08
1.53 ( 0.08
1.65 ( 0.07
2.2 ( 0.2
58 ( 2
65 ( 1
79 ( 2
82 ( 2
92 ( 2
91 ( 1
16.3
39.4
81.
2.4 ( 0.2
76.
109.
2.8 ( 0.2
876 K, s/v ) 10.3 cm-1
10.3
20.6
30.6
41.3
0.22
0.62
0.99
1.40
0.40
1.08
1.62
1.81
0.41
0.78
1.13
1.54
3.0 ( 0.3
4.0 ( 0.2
5.2 ( 0.3
5.3 ( 0.2
4.6 ( 0.2
5.2 ( 0.1
4.7 ( 0.1
876 K, s/v ) 20.4 cm-1
20.5
30.8
41.0
82.0
0.61
0.95
1.49
3.27
1.05
1.33
1.89
2.92
4.0 ( 0.4
4.7 ( 0.3
4.8 ( 0.1
6.1 ( 0.2
1.60
3.7
4.9 ( 0.1
5.1 ( 0.1
876 ( 2 K, s/v ) 14.0 cm-1
10.3
20.6
41.3
81.4
124.0
176.0
0.059
0.090
0.223
1.03
1.81
2.92
0.62
1.43
3.70
5.9
1.13
1.79
3.3
3.9
5.9
4.2 ( 0.8
5.0 ( 0.2
5.4 ( 0.2
5.7 ( 0.2
6.8 ( 0.3
5.5
8.8
4.9 ( 0.1
5.5 ( 0.1
9.5
834 ( 2 K, s/v ) 10.3 cm-1
10.3
21.0
41.5
80.6
126.9
183.6
0.039
0.098
0.24
0.44
0.88
1.46
0.039
0.072
0.122
0.163
0.238
0.361
0.087
0.190
0.323
10 ( 2
13 ( 1
14 ( 2
20 ( 2
18 ( 2
21 ( 2
0.81 ( 0.04
0.84 ( 0.03
0.74 ( 0.02
a Rm, Re Rb, and Rh are the rates of formation of methane, ethane, butanone, and 2,5-hexanedione, respectively. s/v is the reactor surface-to-
volume ratio.
TABLE 2: Results of Experiments Carried out at 15.5 Torr at Several Temperatures with s/v Equal to 10.3 cm-1
Rm × 106,
Re × 108,
Rb × 108,
Rh × 108,
k5/k3 ,
2
T, K
mol L-1 s-1
mol L-1 s-1
mol L-1 s-1
mol L-1 s-1
mol s L-1
k1, s-1
940
897
854
825
45.4
9.23
1.63
0.44
230
108
9.4
7.8 × 10-5
2.57 × 10-4
6.3 × 10-4
1.49 × 10-3
1.31 × 10-2
1.77 × 10-3
2.12 × 10-4
28.5
1.97
0.32
18.7
3.35
1.06
and ketene were equal, as predicted by the mechanism (reactions
3 and 4) provided chains are long, the molar absorption
coefficient of ketene was calculated to be 535 ( 36 L mol-1
cm-1. Here the quoted uncertainty is the standard deviation of
29 individual ketene/methane measurements.
parameters, Sk, BT, and FCSC, for reaction 5 are given in the
Appendix. The Troe expression (12) for the pressure depen-
dence was fitted to the data by nonlinear least squares,10 to
2
estimate the high- and low-pressure limits for k5/k3 . The high-
pressure limits for this quotient at 928, 876, and 834 K, assuming
unit collision efficiency, are presented in Table 3. Changing
the fixed value of âC from unity to 0.1 changed these values by
only 15%. The uncertainties in these numbers in Table 3 are
standard deviations determined by the least-squares program.10
The low-pressure limits for k5/k32 were calculated to be 8 ( 2,
25 ( 3, and 66 ( 17 s at 928, 876, and 834 K, respectively.
Hydrogen, ethylene, propane, and propylene were secondary
products, with yields proportional to the square of the residence
time. Hydrogen was detected in clean reactors only at pressures
higher than 80 Torr, but was also detected at lower pressures
when the reactor surface was partially covered by carbon.
Experiments were carried out at 876 K in each of the three
reactors to test for any surface reaction. Carbon deposition on
the reactor wall increased the yield of ethylene but, as Table 1
shows, with clean quartz reactors at identical pressures; there
was no trend evident in the steady state rates of formation of
methane, ethane, and butanone on changing s/v. The last digit
quoted in each rate is the first digit of the standard deviation.
Table 2 shows the results of experiments at different
temperatures at a constant pressure of 15.5 Torr.
2
2
The ratios of (k5/k3 )∞ to k5/k3 at 15.5 Torr were calculated to
be 2.75, 2.66, and 2.62 at 928, 876, and 834 K, respectively.
2
Values of (k5/k3 )∞ at 940, 897, 854, and 825 K were calculated
2
by multiplying the values of k5/k3 at 15.5 Torr in Table 2 by
the ratios at the nearest temperature in the preceding sentence.
It was not possible to separately determine k3 and k5 from
the present experiments, so a value of k5∞ was taken from the
literature,11 (k5∞ (L mol-1 s-1) ) 9.05 × 1013(T/K)-1.18 exp-
(-2.74 (kJ mol-1)/RT)). The values of k3 in Table 3 were
calculated by substituting these values of k5∞ into the values of
2
Equation 9 was used to calculate the values of k5/k3 for
several conditions. Figure 3 shows the pressure and temperature
dependences of this quotient. The value of k5 is known to be
affected by changing the pressure.4 Values of the Troe input
2
(k5/k3 )∞ in the preceding column. The results are shown as
the filled squares in Figure 4.

3576 J. Phys. Chem., Vol. 100, No. 9, 1996
Mousavipour and Pacey
Figure 4. Overall temperature dependence of k3: 9, this work; 1, ref
25a; ×, ref 25b; 4, ref 25c; b, ref 25d; 0, ref 25e; 3, ref 14; s,
nonlinear least-squares fit of eq 16 to the experimental data.
2
Figure 3. Dependence of the ratio, k5/k3 , on temperature and acetone
concentration: 9, experimental data; a, 834 K; b, 876 K; c, 928 K; s,
nonlinear least-squares fits of eq 12 with unit collision efficiency.
TABLE 3: Limiting Rate Constants at Several
Temperatures
(k5/k3 )∞ × 104,
k3 × 10-6
,
2
T, K
k1∞, s-1
mol s L-1
L mol-1 s-1
940
928
897
876
854
834
825
(2.4 ( 0.2) × 10-2
(1.2 ( 0.1) × 10-2
(2.7 ( 0.2) × 10-3
(5.8 ( 0.3) × 10-4
(2.5 ( 0.1) × 10-4
(8.8 ( 0.6) × 10-5
2.2 ( 0.2
3.7 ( 0.3
7.4 ( 0.6
9.3 ( 0.5
17 ( 1
9.5 ( 0.5
7.4 ( 0.3
5.3 ( 0.2
4.8 ( 0.1
3.6 ( 0.1
2.8 ( 0.2
2.4 ( 0.2
29 ( 3
39 ( 4
The butanone and 2,5-hexanedione peaks were not measured
at some experimental conditions, represented by blanks in Tables
1 and 2. Where peaks were reliably measured for all three
termination products (if necessary, including data from two
reactors), eq 14 was applied to calculate values of the cross-
combination ratio, m. This ratio was found to be weakly
dependent on pressure, as predicted in the Introduction because
Figure 5. Dependence of k1 on acetone concentration: a, 928 K; b,
876 K (raised 1 log unit); 9, experimental data; s, nonlinear least-
squares fit of eq 12 to the data with âC ) 1.0.
of the known pressure dependence of k5. Accordingly, m-2
,
which is proportional to k5, was plotted in graphs like Figure 3.
The pressure dependence was found to be similar to, but slightly
2
weaker than, that for k5/k3 . The results were treated by the
2
Troe factorization method as described for k5/k3 . The limiting
high-pressure values of m were found to be 1.9 ( 0.1 at both
928 and 876 K.
For conditions where one termination product was not
measured, a value of m determined at the nearest possible
temperature and pressure was inserted in eq 14, which was then
solved for the missing rate. This was not done at 825 K, where
it appeared that the missing rate could have been the major
radical recombination. The rate constant for reaction 1 was
calculated using the sum of the rates of formation of termination
products as in eq 8. Values of this rate constant listed in Table
1 and shown in Figure 5 have a clear dependence on pressure
at 928 K and a slight dependence at 876 K. Troe input
parameters for this reaction are also given in the supporting
information. The Troe expression, eq 12, was fitted to the
experimental data by nonlinear least squares10 to estimate the
low- and high-pressure limits, k1,0 and k1∞. The results showed
Figure 6. Dependence of the high-pressure limit of k1 on tempera-
ture: 9, experiment; s, linear least-squares fit.
WC
that k1∞ was not sensitive to FC and that changing âc, the
measurements were made at only a single pressure, values of
k1/k1∞ at 15.5 Torr were taken from the curves at the nearest
temperature or temperatures in Figure 5.
An Arrhenius plot for k1∞ is shown in Figure 6. The
Arrhenius expression for this rate constant from the present work
collision efficiency, from unity to 0.1 again changed k1∞ by only
15%. The value of k1,0 at 928 K was found to be (1.0 ( 0.2)
× 103 L mol-1 s-1, but the value at 876 K could not be reliably
determined. The high-pressure limits for k1 are given in Table
3. To calculate k1∞ at the temperatures in Table 2, where

Reactions in the Pyrolysis of Acetone
was found by least squares to be
J. Phys. Chem., Vol. 100, No. 9, 1996 3577
of the yield of CO from reaction 2, and the latter reaction was
found to have a rate only 10% or less of the rates of formation
of methane and ketene in the present work. Thus, a direct,
unimolecular production of ketene and methane from acetone
(without the participation of radicals) could only account for
1% of the methane observed in this work.
k1∞ (s-1) ) 1017.9(0.8 exp(-353 ( 4 kJ mol-1/RT)
Discussion
Fits of both eqs 10 and 11 to the data obtained during the
induction periods gave consistent values of the plateau rates
within 5%. At most experimental temperatures and pressures,
we were able to make measurements in the steady state regime.
It is necessary to consider whether reactions in addition to
(1) to (7) could have contributed to the observed products. A
possible competitor to the initiation reaction 1 is the rupture of
a carbon-hydrogen bond in acetone. However, the dissociation
The value of 1.9 ( 0.1 found in this work for the cross-
combination quotient of CH3 and CH3COCH2 radicals is similar
to the values of 2.4, 2.0, 1.8 ( 0.1, 1.9 ( 0.2, and 2.4 ( 0.2
found in photolysis experiments14 at temperatures of 473, 523,
578, 638, and 708 K, respectively. It is also similar to values
of 1.86-2.08 determined for various alkyl radicals at room
temperature.8 According to simple collision theory, this quotient
would be equal to the product of a factor of 2 from symmetry,
a factor of 1.11 from the quotient of relative velocities, and an
undetermined factor close to unity from the quotient of collision
diameters. It is not possible to determine these three rate
constants separately from the present results.
enthalpy for this bond is 411 kJ mol-1 12 72 kJ mol-1 greater
,
than that calculated for reaction 1. Such a difference would
lead to a ratio of 4 orders of magnitude in the exponential factors
at the present experimental temperatures.
It is also necessary to consider possible competing termination
processes. It has been suggested13 that there is a dispropor-
tionation reaction (CH3 + CH3COCH2 f CH4 + CH2COCH2)
with a rate about one-quarter the rate of reaction 6. However,
one suggested product was a diradical, which seems improbable.
Another suggestion,14 (CH3 + CH3COCH2 f C2H4 + CH4 +
CO), can be ruled out because C2H4 was not a primary product
in the present study. The CH3CO radical could participate in
termination. Using a value of k2 from the literature,15 we
estimate that the concentration of this radical is always at least
4 orders of magnitude less than that of CH3 under the present
experimental conditions. Addition of CH3 to acetone would
produce the (CH3)3CO radical. Using reported rate constants
for the forward and reverse processes,16,17 we predict that the
concentration of this radical would be several orders of
magnitude lower still.
Our Arrhenius parameters for k1∞, log A ) 17.9 ( 0.8, and
EA ) 353 ( 14 kJ mol-1, are similar to the values reported by
Ernst and Spindler21 from shock tube experiments, log A ) 16.4
and EA ) 342 ( 12 kJ mol-1. These authors also noted that
the rate constant was pressure dependent. The preexponential
factors, log A ) 14.4 and 14.1, reported20 from toluene carrier
experiments, are lower than expected for a unimolecular
decomposition reaction.
If we assume that the temperature dependence of the reverse
of reaction 1 is between +RT/2 and -RT/2, its activation energy
would be 0 ( 4 kJ mol-1. Combining this with the present
activation energy for reaction 1, we obtain 353 ( 15 kJ mol-1
as the internal energy change for reaction 1 and 360 ( 15 kJ
mol-1 as the enthalpy change. Taking heat capacities from the
literature, the latter value may be adjusted to 358 ( 15 kJ mol-1
at 298 K. Combining this with the heats of formation of
acetone22 and CH3,23 we obtain -6 ( 15 kJ mol-1 as the heat
of formation of CH3CO. This may be compared with the recent
Variation, like that observed in Figure 3, of the quotient, k5/
2
k3 , with changing acetone concentration has previously been
observed in photolysis experiments. Brinton14 performed the
most detailed study and criticized previous investigations,
particularly those at temperatures above 600 K. In order to
determination of -10.0 ( 1.2 kJ mol-1 24
.
The experimental data for k3 from Table 3 were combined
in Figure 4 with data at lower temperatures from the literature,
consistently taking k5∞ from ref 11. There is good agreement
among the results of photolysis experiments in the temperature
range 400-550 K,1 so only three such studies25a-c have been
selected. Between 550 and 750 K, only the data from the most
detailed study14 have been included.
The Arrhenius plot for reaction 3 in Figure 4 is curved.
Similar curvature has been observed previously in a number of
reactions involving hydrogen transfer.4,26 For several reactions
it has been possible to fit a transition state theory model to the
experimental data.26
2
explain values of m as low as 0.3 and variations of k5/k3 by a
factor of 7 with only a 4-fold pressure change (but a 25-fold
photolysis intensity change), the following additional reaction
was postulated:
CH3 + CH3COCH3 f C2H6 + CH3CO
(15)
We need to carefully consider the pressure dependence of m
2
and k5/k3 to determine whether reaction (15) could have an
effect under the present conditions.
The values of P1/2, the pressure at which k5 has fallen to half
its high-pressure limiting value, were found from the variation
of k5/k32 in Figure 3 to be 39, 42, and 49 Torr at 834, 876, and
928 K, respectively, and, from m-2, to be 12 and 10 Torr at
876 and 928 K, respectively. These may be compared with a
value of 17 Torr found for reaction 5 at 822 K,18 and values
between 10 and 60 Torr in the present temperature range from
a survey of the literature for the reverse reaction.19
We have fitted a model in which C2H6 is formed by both
reactions 5 and 15 to the pressure dependence of the present
measurements of Ress[(CH3)2CO]2/(Rmss)2 (the right-hand side
of eq 9), as listed in the second last column in Table 1. The
pressure dependence of reaction 5 was assumed to follow refs
18 and 19. The fitted rates of reaction 15 were small enough
to affect the quoted values of k3 by 10% or less.
k ) κ(T/T*, Vb)(kBT/h)δQTS(I,ωb,T)/QAQB exp(-Vb/RT)
(16)
where κ(T/T*,Vb) is the tunneling factor, δ is the reaction path
degeneracy, kB is Boltzmann’s constant, T is the absolute
temperature, h is Planck’s constant, QTS, QA, and QB are partition
functions for the transition state (TS) and reactants (A and B),
and Vb is the effective barrier height including zero-point energy.
The characteristic tunneling temperature, T*, is the temperature
at which the average reacting pair has energy approximately
equal to half the barrier height. QTS(I,ωb,T) depends on the
product of moments of inertia, I, of the transition state and on
the average term value, ωb, for six transition state vibrational
degrees of freedom which are significantly different from the
corresponding motions in the reactants. The moments of inertia
Addition of toluene, a radical scavenger, to the pyrolysis of
acetone20 suppressed the formation of ketene to only 10-15%

3578 J. Phys. Chem., Vol. 100, No. 9, 1996
Mousavipour and Pacey
in the transition state were calculated from the results of a
semiempirical bond energy-bond order (BEBO) calculation.27
General features of the transition state theory method have
been described elsewhere. Details specific to reaction 3 are
given in the Appendix in the supporting information.26-33 The
three parameters Vb, T*, and ωb, in eq 16 were fitted to the
experimental data by nonlinear least squares.10 The parameters
were found to be equal to 46.0 ( 1.0 kJ mol-1, 375 ( 17 K,
and 279 ( 8 cm-1, respectively.
ethane, CO, butanone, and 2,5-hexanedione. The relative rates
of formation of the termination products are in good agreement
with the simple predictions of collision theory, provided a small
adjustment is made for the pressure dependence of at least one
of these rate constants. The initiation rate constant, determined
from the sum of the termination rates, depends weakly on
pressure and has an activation energy in reasonable agreement
with recent thermochemistry. The abstraction of hydrogen from
acetone by methyl radicals has a strongly curved Arrhenius plot,
which has been interpreted to provide new insights into the role
of tunneling and of six low-frequency vibrations in the transition
state.
These results could be compared with those for reaction 17:
26
CH3 + H2 f CH4 + H
(17)
Acknowledgment. The authors thank the Natural Sciences
and Engineering Research Council of Canada for financial
support, the Ministry of Culture and Higher Education of Iran
for a scholarship to S.H.M., N. Burford for the use of the
infrared spectrometer, and V. Knyazev for sending results prior
to publication.
Parameters for this reaction, updated by including recent
experimental results,34 are 58.5 ( 1.2 kJ mol-1, 395 ( 36 K,
and 806 ( 33 cm-1, respectively. Reaction 3 is exoergic by
27 kJ mol-1 and would be expected to have a lower activation
barrier than reaction 17, which is almost thermoneutral.26 Half
the difference in exoergicity is reflected in the barrier height in
the forward direction and half, in the reverse barrier height.
The values of T*, defined in terms of the second derivative
of potential energy with respect to the reaction coordinate at
Supporting Information Available: A description of the
Troe model and input parameters for reactions 1 and 5 and a
description of the transition state theory treatment of reaction 3
with a table of input parameters (5 pages). Ordering information
is given on any current masthead page.
the barrier top, are similar to each other. The full widths, ∆s1/2
,
of the Eckart barriers at half their heights26 were calculated from
Vb and T* to be 52 ( 3 pm for reaction 3 and 58 ( 5 pm for
reaction 17.
References and Notes
The average vibrational term value in the transition state for
reaction 3 could have been predicted to be lower than that for
reaction 17 because of the heavier CH3COCH2 replacing a
hydrogen atom and because of the contribution of a hindered
internal rotation in the TS for reaction 3. However, the more
than 2-fold drop is surprising. In fact, the present value of ωb
is the lowest we have found for any reaction.26
(1) Kerr, J. A.; Parsonage, M. J. EValuated Kinetic Data on Gas Phase
Hydrogen Transfer Reactions of Methyl Radicals; Butterworths: London,
1976; p 171.
(2) Rice, F. O.; Herzfeld, K. F. J. Am. Chem. Soc. 1934, 56, 284.
(3) Rice, F. O.; Vollrath, R. E. Proc. Natl. Acad. Sci., 1929, 15, 702.
Rice, F. O.; Varnerin, R. E. J. Am. Chem. Soc. 1955, 77, 221. McNesby, J.
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(4) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just,
Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J.
Phys. Chem. Ref. Data 1992, 21, 655.
The barrier height is within 10% of the value of 51 kJ mol-1
estimated by the BEBO method in the supporting information.
It is only about two-thirds of the experimental activation energy
of 72 kJ mol-1 found in the present work between 825 and 940
K. This difference may be explained in terms of the low
-frequency vibrations in the activated complex. We consider
that three translational degrees of freedom of the reactants, plus
two rotations and two vibrations (a C-H stretch and a hindered
methyl internal rotation) transform in the complex to the reaction
coordinate and six low-frequency vibrations (the symmetric
stretch, a similar hindered internal rotation, two CHC bends,
and two CH3 rocks). (The rotation of the reactant CH3 about
its 3-fold axis is considered to remain effectively free in the
complex.) The above seven degrees of freedom will each
contribute thermal energy close to RT in the activated complex.
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or 25 kJ mol-1, just enough to account for the difference
between the observed activation energy and the barrier height
fitted to the data.
On the other hand, in photolysis experiments at 400-500 K,
the observed activation energy was 40 ( 1 kJ mol-1, which is
less than the present barrier height. At such temperatures
tunneling allows significant amounts of reaction by species with
less energy than the barrier height.
The curvature of the Arrhenius plot can thus be understood
in terms of the contribution of tunneling at low temperatures
and of the low-frequency vibrations at higher temperatures. It
is anticipated that similar statements will apply to reactions of
methyl radicals with other organic molecules.
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Reactions in the Pyrolysis of Acetone
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