Rate constants for CF3 + H2 → CF3H + H and CF3H + H → CF3 + H2 reactions in the temperature range 1100-1600 K

Article abstract of DOI:10.1021/jp982432q

The shock tube technique coupled with H-atom atomic resonance absorption spectrometry has been used to study the reactions (1) CF₃ + H₂ → CF₃H + H and (2) CF₃H + H → CF₃ + H₂ over the temperature ranges 1168-1673 K and 1111-1550 K, respectively. The results can be represented by the Arrhenius expressions k₁ = 2.56 × 10^-11 exp(-8549K/T) and k₂ = 6.13 × 10^-11 exp(-7364K/T), both in cm³ molecule^-1 s^-1. Equilibrium constants were calculated from the two Arrhenius expressions in the overlapping temperature range, and good agreement was obtained with the literature values. The rate constants for reaction 2 were converted into rate constants for reaction 1 using literature equilibrium constants. These data are indistinguishable from direct k₁ measurements, and an Arrhenius fit for the joint set is k₁ = 1.88 × 10^-11 exp(-8185K/T) cm³ molecule^-1 s^-1. The CF₃ + H₂ → CF³H + H reaction was further modeled using conventional transition-state theory, which included ab initio electronic structure determinations of reactants, transition state, and products.

Full text of DOI:10.1021/jp982432q

7668
J. Phys. Chem. A 1998, 102, 7668-7673
Rate Constants for CF3 + H2 f CF3H + H and CF3H + H f CF3 + H2 Reactions in the
Temperature Range 1100-1600 K
J. Hranisavljevic and J. V. Michael*
Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439
ReceiVed: June 1, 1998; In Final Form: June 29, 1998
The shock tube technique coupled with H-atom atomic resonance absorption spectrometry has been used to
study the reactions (1) CF3 + H2 f CF3H + H and (2) CF3H + H f CF3 + H2 over the temperature ranges
1168-1673 K and 1111-1550 K, respectively. The results can be represented by the Arrhenius expressions
k1 ) 2.56 × 10-11 exp(-8549K/T) and k2 ) 6.13 × 10-11 exp(-7364K/T), both in cm3 molecule-1 s-1.
Equilibrium constants were calculated from the two Arrhenius expressions in the overlapping temperature
range, and good agreement was obtained with the literature values. The rate constants for reaction 2 were
converted into rate constants for reaction 1 using literature equilibrium constants. These data are
indistinguishable from direct k1 measurements, and an Arrhenius fit for the joint set is k1 ) 1.88 × 10-11
exp(-8185K/T) cm3 molecule-1 s-1. The CF3 + H2 f CF3H + H reaction was further modeled using
conventional transition-state theory, which included ab initio electronic structure determinations of reactants,
transition state, and products.
Introduction
being used have been previously described.12,13 Therefore, only
a brief description of the experiment will be presented here.
CF3 abstraction reactions are of importance for establishing
the combustion mechanism of the flame-inhibiting agent
CF3Br.1-4
The apparatus consists of a 7-m (4-in. o.d.) 304 stainless
steel tube separated from the He driver chamber by a 4-mil
unscored 1100-H18 aluminum diaphragm. The tube was
routinely pumped between experiments to less than 10-8 Torr
by an Edwards Vacuum Products model CR100P packaged
pumping system. The velocity of the shock wave was measured
with eight equally spaced pressure transducers (PCB Piezotron-
ics, Inc., model 113A21) mounted along the end portion of the
shock tube, and temperature and density in the reflected shock
wave regime were calculated from this velocity and include
corrections for boundary layer perturbations.14-16 The 4094C
Nicolet digital oscilloscope was triggered by delayed pulses that
derive from the last velocity gauge signal.
CF3 + H2 f CF3H + H
(1)
Reaction 1 is considered to be one of the major routes for the
formation of CF3H in the CF3Br-H2 oxidation system.2-4
Several relative kinetics studies of reaction 1 in the temperature
range 296-1132 K have been carried out,5-9 and a BEBO
calculation of the Arrhenius parameters has also been reported.10
However, no absolute kinetics measurements for this reaction
are available to date. In this work, a direct shock tube kinetics
study of reaction 1 is presented over the temperature range
1168-1673 K.
Rate constants for the reverse reaction,
In the CF3 + H2 experiments, CF3 radicals were produced
by the thermal decomposition of either CF3I or (CF3)2CO.
Thermal decomposition of CF3I has been well documented in
previous work.17 The lower limit of the examined temperature
range was determined by the rate of CF3I decomposition and
the upper limit by the onset of the I + H2 reaction. For CF3
production from (CF3)2CO at the lower temperature end, the
limiting factor is incomplete (CF3)2CO decomposition. How-
ever for this dissociation there are no kinetics data available to
our knowledge. By analogy to (CH3)2CO,18 the assumption was
made that at 1325 K (the lowest temperature for CF3 production
from (CF3)2CO), the first-order rate constant for (CF3)2CO
CF3H + H f CF3 + H2
(2)
have also been measured in the temperature range 1111-1550
K. By use of the two data sets for reactions 1 and 2, equilibrium
constants have been calculated and compared to literature
values11 in the overlapping temperature range. In addition,
conventional transition-state theoretical (CTST) calculations,
which are based on an ab initio potential energy surface, have
been applied to reaction 1 to predict the thermal rate behavior.
These theoretical results help to make a connection between
the present absolute high-temperature measurements and the
low-temperature relative data5-9 and to establish the kinetics
behavior over the entire temperature range for reaction 1, 296-
1673 K.
thermal decomposition would be on the order of ∼1000 s-1
.
To prevent this incomplete thermal decomposition from affecting
the measured rate constants at lower temperatures, the data were
analyzed by excluding the initial 500-µs portion. The limitation
for measuring rate constants at the high-temperature end was
the onset of direct H2 thermal decomposition. In the CF3H +
H experiments H atoms were produced from the thermal
decomposition of C2H5I, as described previously.19,20 The low-
temperature measurements were limited by incomplete thermal
Experimental Section
The present experiments were performed with the shock tube
(ST) technique, and the method and the apparatus currently
* Author to whom correspondence should be addressed, D-193, Bldg.
200. Phone: (630) 252-3171. Fax: (630) 252-4470. E-mail: Michael@
anlchm.chm.anl.gov.
S1089-5639(98)02432-3 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/09/1998

CF3 + H2 f CF3H + H and CF3H + H f CF3 + H2
J. Phys. Chem. A, Vol. 102, No. 39, 1998 7669
Figure 2. Top: transmittance increase for CF3H + H f CF3 + H2.
Bottom: first-order decay plot according to eq 4. k1st ) 2445 ( 40 s-1
for an experiment at P1 ) 15.99 Torr and Ms ) 2.234. T5 ) 1268 K,
and [CF3H] ) 1.612 × 1016 cm-3. The corresponding second-order
Figure 1. Top: transmittance decrease for CF3 + H2 f CF3H + H.
Bottom: first-order buildup plot according to eq 3. k1st ) 2304 ( 128
s-1 for an experiment at P1 ) 15.83 Torr and Ms ) 2.172. T5 ) 1191
K, and [H2] ) 1.324 × 1017 cm-3. The corresponding second-order
rate constant is 1.517 × 10-13 cm3 molecule-1 s-1
.
rate constant is 1.740 × 10-14 cm3 molecule-1 s-1
.
TABLE 1: Rate Data for the CF3 + H2 Reaction
b
dissociation of C2H5I and, at higher temperatures, by the onset
of CF3H thermal decomposition.
P1/Torr
Msa
F5/(1018 cm-3
)
T5/Kb k11st/s-1
XH2 ) 2.050 × 10-2
k1/cm3 s-1 c
X(CF ) CO ) 2.008 × 10-7
3
2
4.531 × 10-14
In both CF3 + H2 and CF3H + H experiments, H-atom atomic
resonance absorption spectrometric (ARAS) detection was used
to follow [H]t, as described previously.21 The photometer
system was radially located at a distance of 6 cm from the
endplate. MgF2 components were used in the photometer optics.
The resonance lamp beam was detected by an EMR G14 solar
blind photomultiplier tube. For the range of [H] used in these
experiments, Beer’s law is valid,19,21 and therefore, [H]t )
(ABS)t/σl where (ABS)t ≡ -ln (It/I0) (It and I0 refer to time-
dependent and incident photometric intensities, respectively, σ
is the effective atomic cross section, and l is the absorption path
length). Hence, only the relative absorbance changes need to
be measured in both experiments, since [H]t is proportional to
(ABS)t.
15.97
15.91
15.91
15.90
15.87
15.87
15.84
10.99
10.96
10.94
10.92
5.98
2.385
2.284
2.411
2.477
2.325
2.351
2.504
2.402
2.529
2.450
2.604
2.570
2.516
2.410
2.524
2.454
2.929
2.790
2.960
3.037
2.836
2.887
3.056
2.034
2.145
2.066
2.198
1.189
1.162
1.107
1.158
1.124
1429
2720
1741
5375
6112
1982
3553
5673
3322
4800
4392
4582
2883
2971
1556
3140
2107
1325
1452
1523
1367
1394
1553
1449
1586
1501
1673
1633
1570
1453
1580
1501
3.045 × 10-14
8.859 × 10-14
9.821 × 10-14
3.410 × 10-14
6.005 × 10-14
9.055 × 10-14
7.969 × 10-14
1.092 × 10-13
1.037 × 10-13
1.017 × 10-13
1.183 × 10-13
1.248 × 10-13
6.859 × 10-14
1.323 × 10-13
9.144 × 10-14
5.97
5.94
5.93
5.92
XCF I ) 3.569 × 10-7
XH2 ) 2.804 × 10-2
For the CF3 + H2 experiment, the H-atom formation rate is
not affected by secondary chemistry, and therefore, H-atom
buildup constants follow the integrated rate law
3
15.98
15.97
15.93
15.92
15.92
15.90
15.89
10.96
10.94
10.93
10.92
10.91
2.232
2.188
2.229
2.221
2.200
2.138
2.300
2.288
2.185
2.194
2.201
2.116
2.753
2.689
2.740
2.727
2.689
2.606
2.828
1.937
1.832
1.832
1.839
1.749
1263
1220
1260
1252
1236
1172
1331
1317
1213
1226
1234
1149
4109
1487
2909
2000
2740
708
4252
2577
1224
2169
1270
610
5.324 × 10-14
1.973 × 10-14
3.787 × 10-14
2.616 × 10-14
3.635 × 10-14
9.696 × 10-15
5.364 × 10-14
4.746 × 10-14
2.383 × 10-14
4.223 × 10-14
2.463 × 10-14
1.244 × 10-14
(ABS)∞ - (ABS)t
ln
) -k1l stt + const
(3)
[
]
(ABS)∞
In the CF3H + H study, the H atoms are formed nearly
instantaneously under the present conditions, and the H-atom
decay constants follow the rate law
ln (ABS)t ) -k12stt + const
(4)
XCF I ) 2.545 × 10-7
XH2 ) 4.953 × 10-2
3
15.96
15.95
15.92
15.90
15.83
2.159
2.184
2.147
2.204
2.172
2.667
2.719
2.651
2.740
2.673
1183
1199
1168
1218
1191
2216
2371
1594
3699
2304
1.678 × 10-14
1.760 × 10-14
1.214 × 10-14
2.726 × 10-14
1.740 × 10-14
The data were analyzed according to eqs 3 and 4 using linear
least-squares methods. Typical results are shown in Figures 1
and 2. The derived values for k1st and k for reactions 1 and 2
at each temperature are reported in Tables 1 and 2, respectively.
Since [H2] and [CF3H] are effectively constant in the two
experiments, the second-order rate constants are given by k1 )
k1st/[H2]0, and k2 ) k1st/[CF3H]0, and these are likewise listed
a The error in measuring the Mach number, Ms, is typically 0.5-
1.0% at the 1 standard deviation level. b Quantities with the subscript
5 refer to the thermodynamic state of the gas in the reflected shock
region. c The rate constants are derived as described in the text.
1
2
in Tables 1 and 2.
Gases. Kr diluent for the experimental mixtures was obtained
from Spectra Gases, Inc. (scientific grade, 99.997%), and was
subjected to further purification by passage through a Gate
Keeper inert gas purifier from Aeronex, Inc. He, used as

7670 J. Phys. Chem. A, Vol. 102, No. 39, 1998
Hranisavljevic and Michael
TABLE 2: Rate Data for the CF3H + H Reaction
T5/Kb k12st/s-1
k2/cm3 s-1 c
b
P1/Torr
Msa
F5/(1018 cm-3
)
XC H I ) 1.594 × 10-6
XCF H ) 6.462 × 10-3
2
5
16.00
15.88
10.97
10.94
10.93
10.92
10.90
10.88
5.98
2.236
2.406
2.156
2.241
2.080
2.077
2.352
2.185
2.240
2.195
2.324
2.761
2.790
1.805
1.893
1.717
1.712
1.987
1.820
1.031
1.006
1.067
12639
1447
1187
1268
1114
1111
1386
1215
1270
1225
1357
3090
7141
1472
2274
1180
1026
4090
1724
1944
965
1.732 × 10-13
3.961 × 10-13
1.262 × 10-13
1.859 × 10-13
1.064 × 10-13
9.270 × 10-14
3.185 × 10-13
1.466 × 10-13
2.919 × 10-13
1.485 × 10-13
2.595 × 10-13
5.98
5.93
1789
XC H I ) 5.848 × 10-7
XCF H ) 5.858 × 10-3
2
5
15.99
15.98
15.97
15.88
15.88
10.93
10.96
10.94
10.90
10.98
2.234
2.088
2.117
2.239
2.130
2.148
2.214
2.359
2.361
2.388
2.751
2.547
2.580
2.740
2.577
1.793
1.867
1.999
1.993
2.033
12638
1124
1155
1274
1172
1177
1242
1396
1398
1427
2445
1002
1128
2912
2109
898
2395
3387
3479
3887
1.517 × 10-13
6.715 × 10-14
7.464 × 10-14
1.817 × 10-13
1.397 × 10-13
8.546 × 10-14
2.190 × 10-13
2.892 × 10-13
2.980 × 10-13
3.264 × 10-13
Figure 3. Arrhenius plot of the data from Table 1. The line is given
by eq 5, and the solid circles are the individual data points.
a The error in measuring the Mach number, Ms, is typically 0.5-
1.0% at the 1 standard deviation level. b Quantities with the subscript
5 refer to the thermodynamic state of the gas in the reflected shock
region. c The rate constants are derived as described in the text.
received as the driver gas and also in the resonance lamp and
atomic filter section, was ultrahigh purity grade (99.995%) and
was obtained from Airco Industrial Gases. In the atomic filter
section, H2 from Airco Industrial Gases (prepurified, 99.995%)
was used as received. (CF3)2CO, CF3I, and CF3H were all
obtained from Aldrich Chemical Co. Inc. and were further
purified by bulb-to-bulb distillation in a greaseless, all-glass,
high-vacuum gas handling system. The middle third was
retained. Mass spectral analyses showed that all samples were
more than 99% pure.
Figure 4. Arrhenius plot of the data from Table 2. The line is given
by eq 6, and the solid triangles are the individual data points. The dashed
line represents the rate constant expression reported by Takahashi and
co-workers,22 and the dotted line represents that reported by Richter et
al.;4 see eq 7.
also been represented by the Arrhenius equation giving the least-
squares expression
Results
For reaction 1, initial curvature in the buildup plots results
from incomplete decomposition, necessitating a long time
analysis in order to obtain the first-order buildup constant. On
the other hand, if H atoms are slowly formed from either I +
H2 or H2 dissociation at higher temperatures, then curvature at
long times results, necessitating an initial time analysis in
buildup plots. In an effort to extend the temperature range, we
carried out experiments at temperatures as low as 1085 K and
as high as 1682 K, but these measurements had to be rejected
due to these complications. Hence, bimolecular rate constants
could only be unambiguously obtained over the limited tem-
perature range 1168-1673 K. The results are given in Table 1
and are plotted in Arrhenius form in Figure 3 along with the
linear least-squares line
k2 ) 6.13 × 10-11 exp(-7364K/T) cm3 molecule-1 s-1 (6)
The data points shown in Figure 4 are within (21% of the line
calculated from eq 6 at the 1σ level.
Unlike reaction 1, there is one previous shock tube study on
reaction 2 by Takahashi et al.22 These workers also used
H-atom ARAS (with H atoms generated from the dissociation
of C2H5I) to measure the rate constants. Hence, the method is
quite similar to this study. The main difference is that the
present experiments were ∼20 times more sensitive in detecting
[H]t, thereby reducing the possibility of secondary reaction
perturbations of decay constants. Even so, these results22 are
higher by only ∼30% than the measurements presented here
and are therefore in good agreement within the error limits of
the two data sets. Richter et al.4 have also estimated k2 in a
flame study, reporting
k1 ) 2.56 × 10-11 exp(-8549K/T) cm3 molecule-1 s-1 (5)
The individual data points in Figure 3 deviate from eq 5 by
(29% at the 1σ level.
k2 ) 1.93 × 10-10 exp(-8800K/T) cm3 molecule-1 s-1 (7)
For reaction 2, the measurements of bimolecular rate constants
are summarized in Table 2 and Figure 4. Similar to the CF3 +
H2 experiments, complications at the highest and lowest
temperatures of the examined temperature range were avoided
by analyzing the plots of ln (ABS)t against t in the initial or
later stages, respectively. The rate constant measurements have
over the temperature range 960-1300 K. Both rate constant
inferences4,22 are shown along with the present data in Figure
4. As seen in the figure, the results summarized by eqs 6 and
7 are nearly superimposable.

CF3 + H2 f CF3H + H and CF3H + H f CF3 + H2
J. Phys. Chem. A, Vol. 102, No. 39, 1998 7671
k1 ) (1.05 × 10-22)T3.0
×
exp(-2667K/T) cm3 molecule-1 s-1 (9)
Equation 9 predicts values only 11% higher and 30% lower
than eq 8 over the present experimental temperature range. Since
the goal of that work was to specify thermodynamic and kinetics
information for modeling flame inhibition,23 it is not necessary
to modify k1 from the value given. However, if eq 9 is used
for temperatures lower than ∼1000 K, the values will undoubt-
edly be incorrect. Also, the values for the implied k2 in that
work will be slightly in error because they suggest ∆H001,2
-2.9 kcal mol-1, in contrast to the present value of -1.564
kcal mol-1
)
.
In anticipation of theoretical rate constant calculations for
reaction 1, we have additionally performed ab initio MP2/
6-31G(d) level electronic structure calculations for both products
and reactants. Similar electronic structure theory calculations
have also been used earlier3 for energy optimization and to find
moments of inertia and vibration frequencies for the CF3 and
CF3H molecules. The present calculations agree with this earlier
work and imply ∆H001,2 ) -2.4 kcal mol-1 from the G2 heats
of formation for CF324 and CF3H.25 Since the Janaf endother-
micity is ∆H001,2 ) -1.564 kcal mol-1, the G2 estimate is
within the (1 kcal mol-1 range usually claimed by the method.
By use of the Janaf endothermicity, harmonic values for Keq
were calculated for 1000-1700 K from the ab initio results.
These values only differed from similarly calculated Janaf
implied Keq values by less than or equal to 1.2%, indicating
that both frequencies and structures for CF3 and CF3H from
the electronic structure calculations are essentially identical
to the experimental values reported in the Janaf tables and
listed in Table 3. This evaluation suggests that ab initio
calculations for the transition state, carried out at the same
level of theory, may also yield accurate values for both struc-
ture and frequencies. We therefore applied the same level of
theory to determine structure, vibration frequencies, and ener-
gy for the transition state. The results, also listed in Table 3,
were again nearly identical to those already presented by
Berry et al.3,26 except for the barrier height. Our calculations
yield a zero-point energy-corrected barrier height for reac-
tion 1 of 16.4, to be contrasted to 12.7 kcal mol-1 from Berry
et al.
Figure 5. Composite Arrhenius plot for k1 obtained by direct
measurements (Table 1) and by the conversion of k2 (Table 2) using
equilibrium constants. The line is given by eq 8.
Discussion
Unlike the previous work on reaction 2,22 the high sensitivity
of the H-atom ARAS detection system used here completely
eliminates the possibility of complications due to the onset of
secondary reactions. This realization and the fact that both rate
constants for reactions 1 and 2 were measured with exactly the
same method, with the same apparatus, and in the same
concentration range allows us to determine an apparatus-specific
value for the equilibrium constants as Keq ) k1/k2. Hence, the
two Arrhenius expressions, eqs 5 and 6, were used to evaluate
the equilibrium constant at the midtemperature range of the two
data sets, 1400 K. The Keq value obtained was 0.18 ( 0.06
(i.e., (36%), in good agreement with the Janaf value of 0.128.11
Hence, the data measured for CF3H + H were transformed into
CF3 + H2 data using the Keq values calculated from the Janaf
tabulation. These transformed data are plotted in Figure 5 along
with direct measurements for reaction 1. This composite set
of data has then been least-squares fitted to an expression of
the Arrhenius form as
k1 ) 1.88 × 10-11 exp(-8185K/T) cm3 molecule-1 s-1 (8)
The individual data points deviate from the line by (28% at
the 1σ uncertainty level. From the plot in Figure 5, the data
from the direct measurements and the data obtained by
transformation through equilibrium constants are evenly scat-
tered about the line calculated from eq 8. Hence, the present
data suggest that the Janaf description is adequate within
experimental error, implying ∆H001,2 ) -1.564 kcal mol-1 for
the equilibrium process CF3 + H2 h CF3H + H. To determine
the error implied by the data, we additionally transformed the
reaction 2 data under the assumption that ∆H001,2 ranged from 1
kcal mol-1 above to 1 kcal mol-1 below the Janaf value. Under
both assumptions, the standard deviations of the combined
sets then significantly increased from the linear least-squares
Arrhenius representations. Values ∼0.6 kcal mol-1 above and
below the Janaf ∆H001,2 could be tolerated and gave similar
least-squares standard deviations. Hence, even though the
present data are consistent with the Janaf endothermicity,
they suggest that the value is only accurate to within (0.6
Berry et al.3 have presented ab initio results and CTST rate
constant calculations with tunneling corrections for the reactions
H + CHnF4-n (0 e n e 4), which includes calculations on
reaction 2 and its reverse, reaction 1. Their results are presented
without energy adjustments and are therefore truly ab initio.
However, we have elected to carry out CTST calculations with
Eckart tunneling, recognizing that the barrier height might have
to be scaled if the present data are to be theoretically rational-
ized. Such adjustments are certainly warranted, since the G2
method for stable molecules is generally accurate to only ∼(1
kcal mol-1 and the G2 method for transition states is accurate
∼(2-3 kcal mol-1
.
The present unadjusted theoretical results (i.e., CTST with
Eckart tunneling, the molecular parameters of Table 3, and
∆E001 ) 16.4 kcal mol-1) are presented in Figure 6 as the
dashed line. This prediction would suggest a 300 K value for
k1 of 1.03 × 10-21 cm3 molecule-1 s-1. As mentioned in the
Introduction, there are several kinetics studies where the
temperature dependence of rate constants for reaction 1 was
measured relative to the rate constants for CF3 self-recom-
bination.5-9 When the highest temperature results are ne-
glected,8 linear least-squares analysis of the composite data
kcal mol-1
.
The experimental results for reaction 1, summarized by eq
8, can be compared to an evaluation given by Burgess et al.23
who suggest

7672 J. Phys. Chem. A, Vol. 102, No. 39, 1998
Hranisavljevic and Michael
TABLE 3: Molecular Parameters Used for Both Equilibrium and CTST/Eckart Theoretical Calculations
CF3
H2
MP2 TS
CF3H
energy in kcal mol-1
0
0
4395
16.4 (MP2) (14.058, adjusted)
266, 266, 478, 647, 989, 1136,
1265, 1700, 1934i
-2.3 (G2), -1.564 (Janaf)
508, 508, 700, 1137, 1152,
1152, 1376, 1376, 3035
9.72 × 10-115
ν in cm-1
500, 500, 701, 1090,
1259, 1259
moment of inertia product
in g cm2 molecule-1
9.61 × 10-115
4.60 × 10-41
1.36 × 10-114
Eckart calculations can recover this value for k1(300 K) if
∆E001 ) 14.058 kcal mol-1. The theoretical prediction of the
temperature dependence is then shown as the solid line in Figure
6 and is reproduced to within ∼(25% by the three-parameter
expression
k1th ) (1.130 × 10-29)T5.259
×
exp(-2564K/T) cm3 molecule-1 s-1 (11)
over the temperature range 300-1700 K. Apparently theory
can agree with both the 300 K and the present high-temperature
experiments simply by adjusting the barrier height. We point
out however that the theoretical values when combined with
the relative expression, eq 10, imply kr values of 4.5, 0.34, 0.26,
and 0.35 × 10-12 cm3 molecule-1 s-1, at the respective
temperatures 300, 400, 500, and 600 K. On the other hand,
we have nonlinear least-squares fitted the k1 value at 300 K,
3.26 × 10-20 cm3 molecule-1 s-1 and the present high-
temperature values summarized by eq 8, obtaining the expres-
sion
Figure 6. Comparison of the present experimental results (b) and
k1(300 K) derived in the text (2) to theoretical and experimental results.
The CTST/Eckart theoretical calculations are for barrier heights of 16.4
kcal mol-1 (- - -) and 14.058 kcal mol-1 ____). Equation 11 is the
(
experimental three-parameter fit (‚‚‚).
k1exp ) (1.244 × 10-24)T3.702
×
sets5-7 (42 points between 295 and 604 K) gives the expression
exp(-3283K/T) cm3 molecule-1 s-1 (12)
k1/k1r /2 ) (8.57 ( 1.89) × 10-7
×
to within (3%. This equation is also plotted in Figure 6 as the
dotted line. When eq 12 is combined with the relative rate
expression, eq 10, respective kr values at 300, 400, 500, and
600 K of 4.5, 1.2, 0.80, and 0.77 × 10-12 cm3 molecule-1 s-1
are obtained.
exp(-5351 ( 92K/T) cm3/2 molecule-1/2 s-1/2 (10)
The 1σ error of the data points from eq 10 is (31%. k1/k1/2 is
r
1.537 × 10-14 cm3/2 molecule-1/2 s-1/2 at 300 K, and this, when
combined with the predicted value from the unadjusted theoreti-
The question arises as to whether the theoretical, eq 11, or
experimental, eq 12, representation is the better description. Of
course, both descriptions strongly depend on the adequacy of
kr and k1(300 K) derived from it; however, assuming that
k1(300 K) is correct, identification of the better description is
still quite ambiguous for several reasons. Regarding theory,
the extent of tunneling with the Eckart method may be
overestimated and the use of CTST may be too simple. Even
if these theoretical strategies are sufficient, the successful
calculation still requires energy scaling. If any of the above
assumptions are incorrect, then vibrational frequency adjust-
ments in the transition state may additionally be required.
Regarding the implied behavior for recombination, both descrip-
tions suggest that kr(T) rapidly decreases with increasing
temperature between 300 and 500 K; however, our theory would
suggest that kr then increases as temperature increases above
500 K. This disagrees with the only study where temperature
was varied (kr apparently increased from 11 to 25 × 10-12 cm3
molecule-1 s-1 between 297 and 457 K).31 By contrast, a recent
theoretical calculation, by Pesa et al.,43 of high-pressure limits
for the recombination using a derived potential energy surface
along with flexible transition state-theory suggests decreasing
values with increasing T (13.42-6.15) × 10-12 cm3 molecule-1
s-1 between 300 and 600 K). This new theoretical estimate
reproduces neither the preferred value at room temperature nor
the steepness of the decrease over the temperature range. Hence,
we find that there is no firm way to decide which representation,
eq 11 or 12, is best.
cal calculation, gives kr ) 4.5 × 10-15 cm3 molecule-1 s-1
.
The reference reaction, CF3 + CF3 (+M) f C2F6 (+M), has
been studied by several workers,27-42 and a value as low as 4.5
× 10-15 cm3 molecule-1 s-1 has never been suggested. In fact,
the room-temperature values span the range (2.2-15) × 10-12
cm3 molecule-1 s-1. This indicates that the present ab initio
barrier height estimate (16.4 kcal mol-1) is too high and must
be scaled in order to agree with experiment.
After review of the extensive database on the CF3 recombi-
nation,27-42 it is clear that there is no consensus agreement on
the rate constant at room temperature. This is due in part to
the use of quite different conditions of pressure and composition
and the subsequent need to extrapolate results to the high-pres-
sure limit. Hence, there have been at least three RRKM calcu-
lations performed on this system.32,36,42 These calculations indi-
cate that under most published experimental conditions of pres-
sure, the recombination should be within 0.74-0.97 of the high-
pressure limit at 300 K.36,42 A simple average of eight room-
temperature values gives kr(300 K) ) (7.0 ( 4.7) × 10-12 cm3
molecule-1 s-1; however, if two of the earlier determinations
are eliminated,28,31 the value becomes (4.0 ( 0.9) × 10-12 cm3
molecule-1 s-1. Allowing for some pressure falloff, we adopt
as a reasonable value for kr∞, 4.5 × 10-12 cm3 molecule-1 s-1
.
k1(300 K) can now be evaluated from the adopted value for
kr∞ and eq 10, giving 3.26 × 10-20 cm3 molecule-1 s-1. This
room-temperature value is shown as the solid triangle in Figure
6. By use of the molecular parameters shown in Table 3, CTST/

CF3 + H2 f CF3H + H and CF3H + H f CF3 + H2
J. Phys. Chem. A, Vol. 102, No. 39, 1998 7673
(14) Michael, J. V.; Sutherland, J. W. Int. J. Chem. Kinet. 1986, 18,
409.
To conclude, even though the relative rate constant data
summarized by eq 10 are really quite accurate and represented
a significant experimental result when they were reported, we
find that they still cannot be used to completely determine either
k1 or kr. The present determination is really the first absolute
determination for reaction 1, and it serves to define only the
rate behavior at higher temperatures. No such absolute data
exist at lower temperatures. Even though absolute data do exist
for kr, these data, undoubtedly for experimental reasons, are not
sufficiently accurate to determine even the room-temperature
rate constant. Clearly what is needed to complete the reactive
description is further accurate and unambiguous experiments
on either k1 or kr in the temperature range 300-600 K.
(15) Michael, J. V. J. Chem. Phys. 1989, 90, 189.
(16) Michael, J. V.; Fisher, J. R. Proceedings of the 17th International
Symposium on Shock WaVes and Shock Tubes; Kim, Y. W., Ed.; American
Institute of Physics: New York, 1990; pp 210-215.
(17) Kumaran, S. S.; Su, M.-C.; Lim, K. P.; Michael, J. V. Chem. Phys.
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Chem. 1976, 80, 645.
(19) Kumaran, S. S.; Su, M.-C.; Lim, K. P.; Michael, J. V. 26th
Symposium (International) on Combustion; The Combustion Institute,
Pittsburgh, PA, 1996; p 605.
(20) Herzler, J.; Frank, P. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 1333.
(21) Lim, K. P.; Michael, J. V. 25th Symposium (International) on
Combustion; The Combustion Institute, Pittsburgh, PA, 1994; p 713 and
references therein.
(22) Takahashi, K.; Inomata, T.; Abe, T.; Fukaya, H. Proceedings of
the 21st International Symposium on Shock WaVes; Houwing, A. F. P.,
Ed.; Panther Publishing: Fyshwick, Australia, 1997; p 163.
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Acknowledgment. This work was supported by the U.S.
Department of Energy, Office of Basic Energy Sciences, Divi-
sion of Chemical Sciences, under Contract No. W-31-109-Eng-
38. The authors thank Drs. S. S. Kumaran, M.-C. Su, and K. P.
Lim for assistance in completing preliminary experiments. We
also thank Dr. B. Ruscic for assistance with ab initio calculations
and helpful discussions.
(24) Ruscic, B. Unpublished G2 result, ∆H0f0,CF ) -114.1 kcal mol-1.
3
(25) Curtiss, L. A.; Raghavachari, K.; Redfern, P.; Pople, J. A. J. Chem.
Phys. 1997, 106, 1063.
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