Temperature coefficients of rates of ethyl radical reactions with HBr and Br in the 228-368 K temperature range at millitorr pressures

Article abstract of DOI:10.1021/jp970822r

The rates of the reactions of ethyl radicals with HBr (k₇) and with Br atoms (k₈) have been measured in the temperature range 228-368 K at millitorr pressures using the very low pressure reactor (VLPR) technique. The Arrhenius function for the H atom abstraction reaction is found to be k₇ = (1.43 ± 0.06) × 10^-12 exp[-(444 ± 26)/RT] cm³/(molecule s), while the ethyl radical disproportionation with Br atom shows no temperature dependence. Its average value over the entire temperature range is k₈ = (1.18 ± 0.05) × 10^-11 cm³/(molecule s). Reaction 7 is significantly slower than has been reported in the only other two direct measurements, both finding a negative activation energy for k₇ of from -1.0 to -1.1 kcal/mol. The small positive activation energy found in this work for k₇ fits standard models for H atom metathesis. Combination with all known kinetic information for ethane bromination gives an average reaction enthalpy of ΔH°₇ = 13.0 ± 0.2 kcal/mol using both the second- and third-law thermochemical calculations. It sets the heat of ethyl radical formation to Δ_fH°(C₂H₅) = 28.40 ± 0.25 kcal/mol and the bond dissociation enthalpy, DH°-(C₂H₅-H) = 100.5 ± 0.3 kcal/mol.

Full text of DOI:10.1021/jp970822r

6030
J. Phys. Chem. A 1997, 101, 6030-6042
Temperature Coefficients of Rates of Ethyl Radical Reactions with HBr and Br in the
228-368 K Temperature Range at Millitorr Pressures
Otto Dobis and Sidney W. Benson*
Loker Hydrocarbon Research Institute, UniVersity of Southern California, UniVersity Park,
Los Angeles, California 90089-1661
ReceiVed: March 4, 1997; In Final Form: June 10, 1997X
The rates of the reactions of ethyl radicals with HBr (k7) and with Br atoms (k8) have been measured in the
temperature range 228-368 K at millitorr pressures using the very low pressure reactor (VLPR) technique.
The Arrhenius function for the H atom abstraction reaction is found to be k7 ) (1.43 ( 0.06) × 10-12 exp-
[-(444 ( 26)/RT] cm3/(molecule s), while the ethyl radical disproportionation with Br atom shows no
temperature dependence. Its average value over the entire temperature range is k8 ) (1.18 ( 0.05) × 10-11
cm3/(molecule s). Reaction 7 is significantly slower than has been reported in the only other two direct
measurements, both finding a negative activation energy for k7 of from -1.0 to -1.1 kcal/mol. The small
positive activation energy found in this work for k7 fits standard models for H atom metathesis. Combination
with all known kinetic information for ethane bromination gives an average reaction enthalpy of ∆H°7 )
13.0 ( 0.2 kcal/mol using both the second- and third-law thermochemical calculations. It sets the heat of
ethyl radical formation to ∆fH°(C2H5) ) 28.40 ( 0.25 kcal/mol and the bond dissociation enthalpy, DH°-
(C2H5-H) ) 100.5 ( 0.3 kcal/mol.
Introduction
recombination4
b
Important complex chemical processes, like combustion,
petroleum refining, and hydrocarbon cracking, as well as
atmospheric chemistry, like smog formation, ozone layer
stability, and chemical vapor deposition, are made up of a large
number of elementary steps involving radical-radical and/or
radical-molecule interactions which usually determine the
overall rates or dynamics of these processes. The interpretation
and modeling of these complex processes require a reliable data
base of kinetic parameters for the elementary steps involved,
that is, a large, accurate set of rate constants and also
thermochemical parameters for the reactants, products, and
intermediates. While such a data base is well established for
molecular thermochemistry and has been reviewed recently,1
the thermochemical data base for intermediates, even for simple
organic radicals, is still somewhat elusive in spite of extensive
experimental and theoretical effort for the past few decades.
The lack of broad consensus is mainly related to the very real
experimental difficulties in realizing equilibrium for reversible
chemical reactions involving these short-lived intermediates.
Traditionally, the halogen (X) atom-hydrogen halide chemi-
cal equilibria
R-R′ h R + R′
and the decomposition of alkyl radicals5
c
R h olefin + CH3/H
yielded higher values for ∆fH°(R) by 1-3 kcal/mol. Although
the three different types of equilibria are much more complicated
than the simplified schemes a, b, and c suggest6 and appropriate
experimental conditions were used to minimize the influence
of side reactions and pressure dependence, it was proposed4 to
check the zero backward activation energy assumption for the
halogenation equilibrium by direct measurements of reaction
-a. Using a powerful UV laser flash of 193, 248, or 266 nm
to decompose suitable radical precursors, the kinetics of the
reverse reaction -a was studied in rapid, time-resolved flow
tube experiments.7-9 Investigations were carried out in a
systematic way by generating CH3, C2H5, i-C3H7, s-C4H9, and
t-C4H9 radicals, and the rate constants and their temperature
dependence for the radical consumption rates were measured
in reactions with HBr7,8 and with HI.9 The results were
surprising as all 10 reactions have shown very fast rates
enhanced by negative activation energies of from -0.3 to -1.9
kcal/mol. Except in the case of s-C4H9, these activation energies
are slightly more negative for R + HBr than for R + HI
reactions. It was proposed that, unlike the forward reaction a,
the reverse reaction is not an H metathesis, but a two-step
chemical activation process.10
a
X + RH h HX + R
have been studied2 most extensively and provided the first
systematic set of data on the standard heat of formations of
radicals, ∆fH°(R), and bond dissociation enthalpies DH°(R-
H). From these early studies of the kinetics of bromination
and iodination (X ) Br or I), ∆fH°(R) was calculated assuming
that E-a is very small3 (0-3 kcal/mol) and within the scatter
of the reported values of the activation energy of the forward
reaction.
Without any proof for this two-step mechanism, it was
incorporated into equilibria a, leading to an excessively high
value of ∆H°a when combined with known thermal bromination
rate measurements11-14 for the forward reaction a, which in
terms of ∆fH°(R) actually overshot the targets set by Tsang.5
Therefore, the forward bromination reactions were reinvestigated
using laser flash generation of Br atoms7,15 and it was found
that the forward reaction rates are also faster, mainly due to
Some controversy arose when other chemical equilibrium
studies at higher temperatures such as bond fission-radical
X Abstract published in AdVance ACS Abstracts, August 1, 1997.
S1089-5639(97)00822-0 CCC: $14.00 © 1997 American Chemical Society

Ethyl Radical Reactions with HBr and Br
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6031
lower activation energies by about 1 kcal/mol. Equilibria a were
then described by faster rates in both directions and new “direct”
values for ∆fH°(R) and DH°(R-H) presented16 as free from
earlier zero or low positive activation energy assumptions for
the reverse reaction -a. These new values have been compiled
as critical data in recent editions of CRC Handbook of Chemistry
and Physics (74-76th eds. of 1993-1996).
Apart from the thermochemical consequences derived from
new Ka values of faster opposing reaction rates, the proposed
two-step transition state mechanism for the backward reaction
-a is of special interest by itself. It makes a sharp break with
our conventional understanding of an entire class of H abstrac-
tion reactions, and so far, this new concept has not been
subjected to a thorough experimental or theoretical testing. A
few recent studies, which found positive activation energies,
either did not explore the controversy, like the competitive
bromination of RCl species,17 or arrived at a vague, conciliatory
conclusion, like the combined ab initio calculation of CH3 +
HBr reaction18 and the two-channel RRKM calculation of t-C4H9
+ HI reaction.19 The latter was misinterpreted as a support for
the two-step mechanism10 for that reaction.
in which the 298 K investigations were carried out.22 It has
been described in a series of our kinetic studies.24-26 However,
the temperature control, system parameters, experimental se-
quence, and data handling are briefly summarized in the
following.
The thin-Teflon-coated cylindrical reactor cell of Vr ) 217.5
cm3 has a heating/cooling glass jacket connected to a thermostat
bath circulator. A HAAKE FS2 type circulator was used at
333 and 368 K, but it was replaced by a Neslab ULT-80DD
refrigerated bath circulator for the 265 and 228 K runs. Two
thermocouples are mounted in the heating/cooling jacket, one
at the bottom, the other at the top of the reactor cell, and the
circulation speed of the bath fluid is adjusted to eliminate any
measurable temperature difference between the two thermo-
couples. A heat-insulating cover is also applied to the outer
surface of the reactor jacket to assist the uniform temperature
setting and to protect the glass surface from ice deposition at
low temperatures. This keeps the reactor temperature within
(0.1 °C over the entire temperature range.
The reactor cell operates in the Knudsen flow regime. The
reactor base is sealed to a Teflon-coated, rapidly adjustable slide
mechanism24 having three interchangeable escape orifices with
diameters of 0.193, 0.277, and 0.485 cm. They change the gas
escape unimolecular rate, keM, which permits the variation of
the reactor residence time by a factor of 5 in three steps. The
use of these orifice sizes in different experimental runs is
indicated as φ2, φ3, φ5, respectively, in Tables 1 and 2, and are
marked with different symbols in Figures 2 and 3. With our
reactor volume Vr, the first-order escape rate constant for any
Almost all earlier studies of the relative rate constants for
R + HX -a8 RH + H
R + X2 9
d8 RX + X
have shown that E-a - Ed g 0, but in recent investigations, it
is found only for R ) CH3 in both cases when X ) Cl20,45 or
Br.7,21 In all other cases of radicals from C2H5 to C4H9 and of
X ) Br, E-a - Ed < 0, ranging from -0.27 for R ) C2H5 to
-0.90 kcal/mol for the tert-butyl radical,7,21,23 as Ed is less
negative than E-a. It is difficult to imagine why reaction d
would have any restriction on proceeding by a direct metathesis
path.
gas component of mass M is given by keM ) aφ(T/M)1/2 s-1
,
where T is the absolute temperature and aφ ) 0.258 for φ2,
0.546 for φ3, and 1.321 for φ5 orifices.24 All escape rate
constants appearing in eqs 1-6 were calculated with the above
formula at different temperatures.
Another difficulty not addressed occurs in the case of the
reaction of H atoms with RX (X ) Br, I)44 where the products
are uniquely R + HX. The two-step mechanism10 would predict
the more stable RH + X product channel.
The reactor discharge is an effusive molecular beam through
the selected exit orifice. The beam is chopped by a tuning fork
chopper and further collimated by two pinholes at the entrances
of two successive, differentially pumped chambers to reduce
the background mass signals. This beam is sampled with the
off-axis mass analyzer of a BALZERS QMG 511 quadrupole
mass spectrometer. Its mass signal is fed to a phase sensitive
lock-in amplifier tuned to the chopping frequency. Mass ranges
of kinetic interest are repeatedly scanned, usually 20-30 times
to give a good statistical average, and the mass intensities are
recorded for data acquisition. Each mass signal is corrected
for its small background value recorded prior to start-up of
reaction and remeasured at the end.
In our preceding paper,22 we reported on the investigation of
the C2H5 + HBr reaction rate at 298 K carried out in the very
low pressure reactor (VLPR) system, using as a thermal ethyl
radical source the C2H6 + Cl reaction. This experimental
technique for the first time permits the measurement of all
reaction rates both first and second orders. No side reaction
can escape undetected over the detection limit of our sensitive
mass spectrometric analytical method. Simultaneous measure-
ments of all reactant and product concentrations give excellent
mass balances for all species to 98 ( 2% accuracy.
Gas inlets are affixed on the top of the reactor cell for separate
inlet flows of reactants. They are preceded by resistive capillary
flow subsystems calibrated for regulating the fluxes of initial
gas components24 with the use of Validyne transducers. The
flow of a Cl2/He mixture traverses a phosphoric acid coated
quartz discharge tube centered in the Opthos microwave
generator cavity of a McCarrol antenna before joining at the
tapered capillary inlet of the reactor cell. This strictly controlled
gas inlet and outlet dynamics establish the well-defined steady
state conditions in the reactor. Back-diffusion from the reactor
to upstream gases is prevented by the use of very small
conductance inlet capillaries relative to the conductance of the
exit apertures.
Our rate constant value22 for k7 was found to be 14 times
smaller than those reported over the past 6 years7,23 which
employed laser flash photolysis for radical generation. When
our low rate constant value for k7 is combined with known
thermal rate constant values11-14 of forward reaction a (k-7
)
for the “third law” determination of ∆fH°(C2H5), it agrees well
with currently accepted thermochemistry of the ethyl radical.22
Although the VLPR study of the Cl/C2H6/HBr three-component
system is quite labor consuming when all the system parameters
are employed, we undertook this task to measure the temperature
rate coefficients for the title reactions and to search for the
possible source of fundamental disparities between experimental
techniques.
In typical operation, the chlorine flow is started first using a
4.5% Cl2/He gas mixture (both are Matheson research-grade
gases), and the signal intensities of Cl2 mass isotopes are
repeatedly scanned using 20 V electron energy in the mass range
of m/e ) 70-74 for checking the instrumental reproducibility
Experimental Section
The VLPR system used for current measurements at different
temperatures is the same three-stage, all-turbo-pumped system

6032 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Dobis and Benson
TABLE 1: Initial and Steady State Concentrationsa of Reactants and Ethyl Radical Formed before Introducing HBr into the
System
no./φx
I°Cl/I°Cl + I°HCl × 102
[Cl]0
[C2H6]0
I°Cl/I°Cl + IHCl × 102
[Cl]
[C2H6]
[C2H5]
∑Pib
T ) 368 K
1/φ5
2/φ5
3/φ5
4/φ3
5/φ3
6/φ3
7/φ2
8/φ2
52.72
52.52
53.55
51.21
48.75
50.66
45.75
48.06
3.50
4.10
4.85
12.02
10.67
9.55
19.23
21.90
4.17
5.33
5.92
9.42
8.78
7.85
11.19
13.36
11.04
9.20
8.75
3.80
3.63
4.19
2.31
2.10
0.732
0.718
0.792
0.892
0.794
0.790
0.971
0.946
2.11
2.70
2.92
2.64
2.67
2.38
1.81
2.25
1.62
2.09
2.29
3.49
3.29
2.99
3.30
3.80
0.26
0.31
0.35
0.70
0.65
0.57
1.06
1.18
T ) 333 K
1/φ5
2/φ5
3/φ3
4/φ3
5/φ3
6/φ2
54.28
54.89
45.89
40.91
39.12
41.15
4.45
4.86
7.73
8.11
8.37
18.18
5.92
6.42
7.93
8.90
9.91
11.76
8.35
8.05
3.02
2.27
1.85
1.68
0.685
0.712
0.509
0.450
0.396
0.742
3.06
3.29
3.17
3.87
4.66
2.46
2.21
2.39
2.87
3.03
3.13
3.63
0.30
0.32
0.49
0.56
0.62
1.01
T ) 265 K
T ) 228 K
1/φ5
2/φ5
3/φ3
4/φ3
5/φ3
57.64
58.66
59.11
49.37
50.23
4.89
5.39
13.32
11.84
13.95
7.13
7.51
10.91
11.30
10.15
7.18
6.90
3.53
2.40
2.96
0.610
0.634
0.785
0.576
0.765
3.83
3.98
3.20
4.12
3.02
2.44
2.55
3.70
3.71
3.47
0.27
0.29
0.52
0.55
0.52
1/φ5
2/φ3
3/φ3
4/φ3
5/φ2
6/φ2
69.03
52.67
47.65
62.82
51.32
51.16
6.32
10.72
13.64
13.90
23.61
27.31
7. 56
8. 83
10. 75
10. 36
14. 89
16. 26
8.74
3.64
2.37
4.31
1.91
2.05
0.800
0.741
0.569
0.954
0.877
1.094
3.55
2.65
3.94
2.59
2.50
2.23
2.79
3.07
3.51
3.48
3.73
3.83
0.25
0.39
0.46
0.44
0.77
0.88
a All concentrations are in units of 1011 particles/cm3.
of mass spectral efficiency RCl2. Then the microwave generator
is turned on and its power is adjusted to 100% dissociation of
Cl2, controlled by observing the complete disappearance of Cl2
mass signals. They are replaced with Cl atom and HCl signals
in the mass range 35-38. HCl is produced in Cl atom reaction
with H3PO4 wall coating of the discharge tube. It may constitute
35-60% of the overall Cl content (see column 2 of Table 1),
but it is constant during an experimental run. After the Cl and
HCl signals have reached steady values, the mass range 35-
38 is repeatedly scanned using 20 eV to record the mass signal
intensities of Cl atom isotopes at m/e ) 35 and 37 and those of
HCl at m/e ) 36 and 38.
Next, the flow of ethane is started using 5% C2H6/He mixture
(both are Matheson research-grade gases), and its flow rate is
increased gradually until the mass 35 Cl signal drops to 0.2-
0.04 of its original value. The mass range of 35-38 is scanned
again to record the new signal intensities of Cl and HCl with
20 eV mass spectrometry. The mass range 25-30 is also
scanned to record C2H6 and C2H5 signals and the distribution
of their fragments using 20 eV first and then the more sensitive
40 eV mass spectrometry.
products of surface recombination. No detectable signal
increase of these masses over the background values was ever
found.
Treatment of Data and Results
The measured mass signal intensity, after corrections for its
background signal and fragmentation, is proportional to the
steady state concentration of a given substance in the reactor.
This strictly linear proportionality is established by measuring
the given mass signal intensity (IM) as a function of the specific
flux F(M) according to the relationship: IM ) RMF(M), where
RM is the mass spectral sensitivity for an ion peak of mass M
and F(M) ) (flux)/Vr in molecule/(cm3 s) units. The steady
state concentration of the gas component M can then be
calculated from the relation: [M] ) F(M)/keM, molecule/cm3.
These formulas are universally applied to convert the measured
mass signal intensities of Cl, HCl, C2H6, Br, and HBr into
concentrations given in Tables 1 and 2.
Our mass analyzer is quite sensitive for the specific flux of
each component in the range used. In absolute values they are
RCl ) RHCl ) (2.69 ( 0.06) × 10-11, RRH ) (1.24 ( 0.03) ×
10-11 at the parent mass intensity, where index RH stands for
C2H6, and RHBr ) (8.13 ( 0.18) × 10-11, all with 20 eV mass
spectrometry. Using 40 V electron energy the last two are RRH
As a last step, the flow of pure HBr (Matheson 99.8% purity,
further purified by trap-to-trap vacuum distillation) is started
and increased gradually until some increase of mass signal 30
(and some decrease in mass signal 29) is observed. Mass ranges
of 35-38, 25-30, and 79-82 are scanned to record the mass
signal intensities for the calculation of Cl/HCl, C2H6/C2H5, and
Br/HBr distributions, respectively, in this three-component
reaction system using 20 eV mass spectrometry. Then the mass
ranges of 25-30 and 79-82 are also scanned using the more
sensitive 40 V electron energy.
) (3.91 ( 0.04) × 10-11 and RHBr ) (2.41 ( 0.02) × 10-10
.
The stability of F(M) depends on the upstream pressure reading
which is done with (0.1 Torr accuracy. Its error contribution
is included in the scatter of RM values. Such precision permits
accurate measurements in flow rate changes with very small
fluctuations. The application of these RM values to our complex
system is shown below.
It is found experimentally that ICl + IHCl ) constant within
(2%. This allows the calculation of Cl/HCl distributions given
in columns 2 and 5 of Table 1 and in column 3 of Table 2.
Mass ranges of 114-118 and 158-162 were also checked
regularly for possible traces of BrCl and Br2 side reaction

Ethyl Radical Reactions with HBr and Br
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6033
TABLE 2: Steady State Concentrationsa of Reactants after Introducing the Initial Concentration of [HBr]0 into the Cl + C2H6
Reaction System
no./øx [HBr]0 × 10-12 I°Cl/I°Cl + I°HCl × 102 [Cl] × 10-11 [C2H6] × 10-11 [C2H5] × 10-11 IBr/IBr + IHBr × 102 [HBr] × 10-12 [Br] × 10-11 ∑Pib
T ) 368 K
1/ø5
1a/ø5
2/ø5
2a/ø5
3/ø5
3a/ø5
4/ø3
5/ø3
5a/ø3
6/ø3
6a/ø3
7/ø2
7a/ø2
8/ø2
0.80
1.45
1.65
2.79
4.22
5.57
8.04
4.73
6.43
6.74
9.45
3.07
4.73
4.37
6.74
4.53
3.95
3.51
2.90
3.00
2.29
0.50
0.94
0.80
1.08
0.73
1.65
1.11
1.14
0.91
0.300
0.262
0.274
0.226
0.272
0.203
0.118
0.205
0.175
0.203
0.138
0.694
0.467
0.514
0.410
3.02
3.17
4.05
4.30
4.64
5.01
7.60
5.95
6.33
5.34
6.08
2.26
3.20
3.58
4.09
0.906
0.737
0.908
0.650
0.712
0.504
0.404
0.714
0.525
0.474
0.315
0.715
0.518
0.698
0.461
6.92 ( 0.14
6.37 ( 0.14
6.55 ( 0.26
5.47 ( 0.11
6.52 ( 0.08
5.40 ( 0.18
6.70 ( 0.35
9.28 ( 0.16
8.70 ( 0.05
9.80 ( 0.34
7.66 ( 0.24
27.89 ( 0.77
24.10 ( 0.40
23.41 ( 0.87
22.73 ( 0.05
0.74
1.36
1.54
2.64
3.94
5.27
7.50
4.29
5.87
6.08
8.73
2.21
3.59
3.35
5.21
0.55
0.92
1.07
1.52
2.73
2.97
5.35
4.36
5.56
6.56
7.19
8.50
11.33
10.17
15.22
0.29
0.31
0.37
0.41
0.51
0.56
1.00
0.83
0.89
0.83
0.93
1.18
1.24
1.35
1.44
8a/ø2
T ) 333 K
1/ø5
1a/ø5
2/ø5
2a/ø5
3/ø3
3a/ø3
4/ø3
4a/ø3
5/ø3
5a/ø3
6/ø2
1.63
2.80
4.11
5.48
4.18
6.14
7.08
9.94
8.45
12.81
2.92
4.59
3.84
3.00
3.18
2.55
2.06
1.38
1.11
0.64
0.82
0.65
1.30
0.79
0.315
0.246
0.282
0.226
0.347
0.233
0.220
0.127
0.175
0.140
0.576
0.350
4.29
4.66
4.94
5.24
4.32
5.08
5.74
7.13
6.87
7.67
2.87
4.39
1.129
0.812
0.801
0.617
0.763
0.546
0.507
0.391
0.541
0.325
0.969
0.684
6.68 ( 0.24
5.75 ( 0.10
6.31 ( 0.19
5.37 ( 0.13
12.43 ( 0.35
10.02 ( 0.27
9.07 ( 0.11
7.30 ( 0.15
8.18 ( 0.32
7.41 ( 0.23
20.65 ( 0.42
16.81 ( 0.31
1.52
2.64
3.85
5.19
3.66
5.52
6.44
9.21
7.76
11.86
2.32
3.82
1.08
1.60
2.58
2.93
5.16
6.11
6.39
7.21
6.87
9.43
5.99
7.68
0.36
0.40
0.47
0.51
0.63
0.70
0.81
0.90
0.91
1.06
1.11
1.17
6a/ø2
T ) 265 K
1/ø5
1a/ø5
2/ø5
2a/ø5
3/ø3
3a/ø3
4/ø3
4a/ø3
5/ø3
5a/ø3
1.94
3.60
4.26
5.74
3.62
6.54
8.69
12.02
10.71
12.93
5.26
4.40
5.34
5.27
2.96
1.73
1.47
0.94
1.12
0.84
0.447
0.376
0.491
0.485
0.658
0.384
0.353
0.225
0.290
0.217
4.49
4.94
4.75
4.73
3.71
5.27
5.71
7.22
5.86
6.69
1.573
1.124
1.210
1.095
1.311
0.817
0.649
0.458
0.527
0.421
7.05 ( 0.18
6.54 ( 0.07
7.87 ( 0.07
8.24 ( 0.06
14.20 ( 0.15
11.21 ( 0.22
11.15 ( 0.54
8.56 ( 0.26
8.54 ( 0.31
7.21 ( 0.29
1.80
3.36
3.92
5.27
3.10
5.81
7.72
10.99
9.79
11.10
1.36
2.34
3.33
4.70
5.10
7.29
9.63
10.22
9.09
9.26
0.32
0.37
0.40
0.44
0.62
0.70
0.79
0.88
0.82
0.88
T ) 228 K
1/ø5
1a/ø5
2/ø3
2a/ø3
3/ø3
3a/ø3
4/ø3
5/ø2
5a/ø2
6/ø2
2.92
4.59
3.69
8.20
5.76
3.50
2.39
0.97
0.79
2.15
1.52
1.02
1.52
0.80
0.751
0.527
0.712
0.487
0.233
0.190
0.476
0.699
0.469
0.811
0.430
3.86
4.61
2.76
3.62
6.74
7.34
4.29
2.87
3.99
2.67
4.66
1.696
1.277
1.052
0.697
0.553
0.375
0.434
0.952
0.906
0.681
0.420
8.62 ( 0.08
6.98 ( 0.09
13.95 ( 0.37
11.92 ( 0.13
7.38 ( 0.35
6.71 ( 0.21
13.23 ( 0.21
17.28 ( 0.15
15.67 ( 0.75
22.33 ( 0.17
15.68 ( 0.45
2.67
4.27
3.17
5.59
9.46
13.96
10.42
3.23
4.68
4.04
7.22
2.50
3.18
5.11
7.52
7.49
9.97
15.78
6.69
8.64
11.53
13.34
0.32
0.36
0.48
0.54
0.71
0.82
0.72
0.87
0.90
1.00
1.08
6.35
10.21
14.96
12.01
3.90
5.55
5.20
6a/ø2
8.56
a All concentrations are in units of particles/cm.3 For data at 298 K see ref 22. b ∑Pi is the total pressure in mTorr units of the system calculated
from steady state concentrations of all species including HCl and He.
Since the HCl fragmentation into Cl+ is only 0.24% at 20 V
ionizing electron energy,24,27 corrections are made when the Cl
ratio drops below 6%. With total decomposition of Cl2, the
steady state Cl concentration can be calculated as [Cl] )
2F(Cl2)ICl/(ICl + IHCl)keCl. These Cl concentration values are
given in columns following the data entries of Cl/HCl distribu-
tions in Tables 1 and 2.
with 20 eV mass spectrometry, and
I°25:I°26:I°27:I°28:I°29:I°30 ) 0.36:7.72:15.4:48.7:11.8:16.1
with 40 eV mass spectrometry, where the subscripts of I°M
denote the mass numbers of fragment signals and the upper
index indicates that no chemical reaction is taking place in the
system. The I°30 ratio is directly proportional to F(C2H6)0, that
The mass spectrometry of C2H6 involves a complex mass
fragmentation process27 which reduces the RRH value for the
parent mass intensity measurement. Distributions of C2H6 mass
fragments in the mass range of 25-30 are well studied in our
system.22,27 With the two ionizing electron energies used in
our mass spectral analysis, they are in percentage
is R30 ) RRH, according to the relationship 0.161∑I°M
)
R
RHF(RH)0 with 40 eV and 0.330∑I°M ) R′RHF(RH)0 with 20
eV mass spectrometry. Of course, RM values for mass fragments
can also be calculated with the same type of relationships from
which R29, calculated as 8.05 × 10-2∑I°M/F(RH)0 ) R′29 with
20 eV and 0.118∑I°M/F(RH)0 ) R29 with 40 eV mass
spectrometry, will be used for the derivation of the ethyl radical
mass spectral sensitivity RR.
I°26:I°27:I°28:I°29:I°30 ) 0.12:0.52:58.3:8.05:33.0

6034 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Dobis and Benson
fragment signal contribution from RH; that is ∆I29 ) I29
-
I30R29/RRH
28 and the mass spectral sensitivity of the ethyl radical
,
can be obtained as RR ) ∆I29/[R]keR. These RR values averaged
for all experimental runs of Table 1 are RR(V1)20eV) ) (0.860
( 0.042) × 10-11 and RR(V1)40eV) ) (1.320 ( 0.045) ×
10-11, about the same as we reported earlier.25 Since they are
derived from signal intensity differences, the scatter is about
twice the scatter of RM values for other substances.
We note that the data set of Table 1, besides providing [Cl]0
and [RH]0 concentrations, mainly serve for precise checking of
our system operation and for the exact calibration of RR for
each run. Accurate ethyl radical concentration measurement
depends on an accurate measurement of the parent mass signal
intensity (I30) for the ethane concentration. The most sensitive
fragment signal I28 cannot be used for this purpose, as it is
composed of contributions from fragmentations of RH and R,
as well as of C2H4 product signal.
When pure HBr is introduced into the system with varied
flow rates, which correspond to [HBr]0 concentrations given in
column 2 of Table 2, the Cl, C2H5, and HBr mass signal
intensities decrease, while HCl, C2H6, and C2H4 signals increase,
and Br signal appears in excess over the HBr fragmentation.
These changes in mass signal intensities arise from the following
new reactions:
Figure 1. Arrhenius plot of rate constants of reaction 6.
In the Cl + C2H6 two-component system, the following
elementary reactions are taking place in the millitorr pressure
range given in the last column of Table 1:
Cl + HBr
C2H5 + HBr
Br + C2H5
9
68 HCl + Br
78 C2H6 + Br
Cl + C2H6
9
18 HCl + C2H5
28 HCl + C2H4
9
Cl + C2H5
9
9
88 HBr + C2H4
2C2H5 9
38 C2H6 + C2H4
Usually two different (HBr)0 flow rates are used for each Cl/
C2H6 two-component runs. The second one is marked with “a”
in the run numbering in column 1 of Table 2.
4
Cl + C2H4 h HCl + C2H3
Cl + C2H3
9
58 HCl + C2H2
The new Cl/HCl distributions and the Cl concentrations are
calculated from the corresponding signal intensities in the same
way as was done for the two-component case. These data are
given in columns 3 and 4, respectively, of Table 2. Ethane
and ethyl radical concentrations are calculated from the recorded
I30 and the ∆I29 signal intensities using RRH and RR values
determined in their preceding two-component run. These
concentrations are listed in columns 5 and 6 of Table 2.
Mass fragmentation of HBr was investigated29 as a function
of applied electron voltages between 17 and 65 eV. At the two
electron voltages used in the present mass spectral analysis, the
HBr fragmentation ratios29 are 102I79/(I79 + I80) ) 0.30 ( 0.08
with 20 eV and 25.64 ( 0.19 with 40 eV electron energies,
and they are the same for the 81/82 isotope mass combination.
Correcting the measured mass signal intensities of mass range
79-82 for the above fragmentation ratios, the steady state
distribution of Br/HBr due to reactions 6-8 can be calculated.
With two isotope compositions (79Br and 81Br) and with two
different electron energy measurements, four Br/HBr distribution
data are obtained for each run. Their average is given in column
7 of Table 2. With the known inlet flow rate of HBr, the steady
state concentration of Br atom can be obtained as [Br] )
F(HBr)0IBr/(IBr + IHBr)keBr (column 9 of Table 2), while the use
of the complementary distribution factor with keHBr gives the
steady state HBr concentration (column 8 of Table 2).
This reaction system has been well explored and all rate
constants involved, as well as their temperature dependencies,
are known from our earlier work25,27 using the same VLPR
system.
When the ethane flow is introduced at rates corresponding
to [C2H6]0 concentrations given in column 4 of Table 1, the
I°30 signal decreases to I30, while the intensities of other lower
mass number signals, especially those of I29 and I28, increase.
The new steady state concentration of ethane can be calculated
as [C2H6] ) I30/RRHkeRH using both 20 and 40 eV mass spectral
signal measurements. Since the concentrations calculated from
the two electron voltage measurements are well within the
statistical scatter of the I30 signal, the averages are given in
column 7 of Table 1.
From the steady state kinetic equations of C2H6 and C2H5,
the ethyl radical concentration can be derived25 as
2∆[RH]keRH - k1[RH][Cl]
[R] )
(1)
k2[Cl] + keR
where ∆[RH] ) [RH]0 - [RH]. Using the known rate
constants25 of k1 ) (8.20 ( 0.12) × 10-11 exp[-(170 ( 20)/
RT] and k2 ) (1.20 ( 0.08) × 10-11 cm3/(molecule s), as well
as the tabulated concentrations of [RH] and [Cl] of Table 1, eq
1 can be solved for [R]. Their values are given in column 8 of
Table 1. In turn, these ethyl radical concentrations are
proportional to the excess in I29 signal intensities over the
Data of Table 2, together with [Cl]0 and [C2H6]0 values of
Table 1, provide the detailed numerical data base for kinetic
calculations. All three initial components and the reactor

Ethyl Radical Reactions with HBr and Br
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6035
Figure 2. Dependence of HBr consumption and formation rates on the steady state concentration of HBr according to eq 3 at different temperatures.
Slopes give k7 directly. Symbols indicating the orifices used for given data pairs: ., φ2; _, φ3; ~, φ5.
residence time (escape orifice size change) are varied to
accomplish a multiparametric kinetic study. The overall HBr
consumption is varied between 5.5 and 27.9%, and it is
measured to (2.5%.

6036 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Dobis and Benson
Figure 3. Dependence of Br atom formation and consumption rates on the steady state concentration of Br according to eq 4 at different temperatures.
The slope gives k8 directly. Symbols of orifices are the same as in Figure 2.
Combinations of steady state equations derived for each
substance in the reaction system lead to algebraic equations that
are first order in all rate constants. They may also be solved
for the ethyl radical concentration and for the HBr mass balance
in an explicit way. Detailed steady state algebraic treatment
of this multicomponent kinetic system is given in our preceeding

Ethyl Radical Reactions with HBr and Br
paper.22 The derived equations are
for the ethyl radical steady state concentration:
2∆[RH]keRH - k1[RH][Cl]
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6037
Reaction 6 is about 10 times faster than reaction 7. Even at
low Cl concentration its rate is still high enough to produce Br
atoms in considerable concentrations. Thus the rate of reaction
8 becomes comparable with that of reaction 7 in competition
for ethyl radical consumption with a significant feedback of
HBr. It can be evaluated by solving eq 4 for k8 in a way similar
to the solution of eq 3. Plots of the left side of eq 4 vs [Br] are
presented in Figure 3a-d for four different temperature
measurements, where the slopes give the rate constants k8
directly. Their values calculated with linear regression are
shown in each part of the figure.
All eight linear plots in Figures 2 and 3 have zero intercepts,
and all data of different residence times fit well on each straight
line. This indicates the absence of any side reaction outside
the given mechanism. If there were any wall loss of atoms or
radicals, it would have introduced nonzero intercepts and
produced different k values with the data taken using different
residence times. With the reactor surface area of 222 cm2,
depending on the escape orifice size used, wall collisions are
generally 102 to 103 times more frequent than reactive collisions
in the reactor cell. But the reactor surface is made inert by the
thin Teflon coating. That is why we have excellent mass
balances for Cl and HCl, as well as for Br and HBr, under all
reaction conditions at pressures given in the last columns of
Tables 1 and 2. It is not surprising, since the Teflon surface
has a very low sticking coefficient (γ ) reaction/wall collision)
for Cl atom,32 γCl ) 5 × 10-6, and for Br atom,33 γBr ) 5.3 ×
10-5. These would contribute negligibly to wall removal of X
atoms compared to the escape rate constant keX.
With the knowledge of k7 and k8, the ethyl radical concentra-
tion in the three-component system can now be calculated
according to eq 2 and checked against the radical concentrations
measured directly for each run. This comparison is presented
in Figure 4, where the data for the abscissa are taken from
column 6 of Table 2. Independent of the temperature and
residence time (orifice size) variations, measured [C2H5] values
are in excellent conformity with calculated ethyl radical
concentrations, resulting in a slope of 1.01 ( 0.03. This test
of the entire mechanism indicates that the experimental recovery
of ethyl radical is established within 3% accuracy, leaving no
room for significant wall removal of radicals.
[R] )
(2)
k2[Cl] - k7[HBr] + k8[Br] + keR
where [R] is measured directly (column 6 of Table 2),
for HBr consumption kinetics:
∆[RH]keRH + ∆[HBr]keHBr - k6[HBr][Cl]
k7[HBr] )
-
[R]
{k2[Cl] + k3[R] + keR} (3)
for Br atom kinetics:
k8[Br] )
3∆[RH]keRH + ∆[HBr]keHBr - {k1[RH] + k6[HBr]}[Cl]
-
[R]
{2k2[Cl] + k3[R] + 2keR} (4)
for the mass balance of HBr conversion:
∆[HBr]keHBr ) [Br]keBr
(5)
where ∆[RH] and ∆[HBr] represent the difference between the
initial [RH]0 or [HBr]0 and the steady state concentration of
[RH] or [HBr], respectively. The last two are measured in the
three-component system (Table 2).
Equations 2-5 are all exact, derived directly from the steady
state condition.
Equations 3 and 4 are of primary interest for obtaining rate
constants k7 and k8. For their solution, all concentrations
involved are measured and given in Tables 1 and 2. For k1
and k2 values are given above in connection with eq 1, and k3
) (2.00 ( 0.06) × 10-12 cm3/(molecule s) is taken from our
earlier VLPR study25 of Cl + C2H6 reaction. k6 comes from
our recent study30 of reaction 6 in the same system.
The kinetics of reaction 6 was investigated in parallel with
the present work using the Cl/HBr two-component variant. It
is a simple kinetic system where only the single reaction Cl +
HBr takes place, leading to the steady state equation for both
the Cl atom consumption and the Br atom formation rates as
The observed values of k7 show normal behavior, increasing
with increasing temperature. This is presented as an Arrhenius
plot in Figure 5 with circles. The straight line fitted to these
data is represented by the Arrhenius equation
k7 ) (1.43 ( 0.06) × 10-12 exp [-(444 ( 26)/RT]
∆[Cl]
[Cl]
[Br]
[Cl]
keCl
)
keBr ) k6[HBr]
(6)
cm3/(molecule s)
Measurements of both rates were carried out simultaneously in
the same temperature range with the same temperature steps as
the present study. The Arrhenius plot of measured k6 values is
presented in Figure 1. The linear fit of these data corresponds
to the Arrhenius equation
The precision of both the A-factor and the activation energy is
around 5%, which is consistent with the low scatter of rate
constant measurements (∼1.5%) at each temperature. The
reported results of Seakins et al.7 (hexagons with full line) and
Nicovich et al.23 (squares with broken line) are also shown in
Figure 5. The disagreement with our results is striking.
k6 ) (1.99 ( 0.10) × 10-11 exp[-(710 ( 29)/RT]
cm3/(molecule s)
Discussion
Rate constant k8 shows no temperature dependence which
would exceed the scatter of measurements. The average of five
different temperature measurements, between 368 and 228 K,
including the value reported earlier22 for 298 K, gives
which is in good agreement with the results obtained by laser
flash time-resolved Cl atom fluorescence measurements.31
Having all the necessary input data, eq 3 can be solved for
k7 at each temperature run. Plots of the left side of eq 3 vs
[HBr] are presented in Figure 2a-d for four different temper-
ature measurements, where the slopes give the rate constants
of reaction 7 directly. Their values obtained with linear
regression are shown in each part of the figure.
k8 ) (1.18 ( 0.05) × 10-11 cm3/(molecule s)
which is slightly less than k2 of Cl + C2H5 reaction. Both

6038 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Dobis and Benson
Figure 5. Arrhenius plot of rate constants k7. Circles show present
results taken from Figure 1a-d and the 298 K data from ref 22.
Hexagons with solid line represent the data of ref 7. Squares with broken
line display the data of ref 23.
Figure 4. Comparison of ethyl radical concentrations calculated
according to eq 2 with measured C2H5 concentrations given in column
6 of Table 2 (abscissa).
kinetic data for the forward (7) and reverse (-7) reactions to
derive the enthalpy of reaction, ∆H°7, and the heat of formation
of the ethyl radical ∆fH°(C2H5).
Rate parameters known for the forward reaction 7 are
summarized in Table 3. Since the measured rate constant values
of Seakins et al.7 and Nicovich et al.23 have a reasonable overlap
in their common temperature range (Figure 5), we put their data
into one unified Arrhenius function (line 3a of Table 3), which
resulted in lower scatter for both the A-factor and the activation
energy.
Similarly, the known rate parameters for the reverse reaction
(-7) are collected in Table 4. There is one earlier study36 on
the direct photobromination of ethane in the 308-363 K
temperature range from which only the activation energy E-7
) 13.6 ( 0.5 kcal/mol could be extracted. Its inclusion into
the second law thermochemical calculation would give ∆fH°7
indistinguishable from those obtained from E-7 of lines 3b and
4b (Table 4). We note that the uncertainty in E-7 in line 1b
exceeds our measured activation energy E7 (line 4a of Table
3), while all the rest are about half of that. Since our
experimental investigation of k7 has no temperature overlap with
temperature ranges of the reverse reaction studies, k-7 at 298
K is calculated outside the experimental temperature range using
the modified Arrhenius equation37
reactions are interpreted as proceeding via a recombination to
form an excited singlet (C2H5X)* molecule. Note that the
singlet restriction reduces its rate of formation by a factor of 8
from collision frequencies. Its formation is followed by a rapid
four-center elimination to produce HX. The average lifetime
of the excited molecule is estimated to be <10-7 s, which is
about 300-fold shorter than the time elapse between collisions
in our low-pressure reactor cell. This large time difference
precludes the formation of any measurable atom + radical
recombination product.
Our measured rate constant k7 is about 14 times less at 298
K than those reported7,23 by works with laser flash generation
of ethyl radical. In order for our rate constant to be in error by
a factor of 14, our value of steady-state C2H5 radical concentra-
tion would have to be 14 times smaller than we have reported.
Since the steady state C2H5 radical concentration varies from
25 to 35% of total C2 species, such a gross error would destroy
the very good mass balances (3%) we have found (Figure 4)
for the steady state C2H5 and C2H6 concentrations, the major
C2 species along with C2H4.
This gross discrepancy is mainly accounted for by the
difference of activation energies as vividly presented in Figure
5, while the A7-factors are roughly within the reported scatters
(see Table 3). A similar situation can be found for the t-C4H9
+ HI reaction9,35 and for the comparison of the original
(uncorrected) ab initio calculation18 and experimental9 data of
CH3 + HBr reaction. In both cases the A-factors show
approximate agreements, but positive activation energies18,35 in
contrast with negative activation energies were reported9 for
both reactions.
k-7 ) A′-7(Tm/298)n exp(-E′-7/RT)
(7)
where E′-7 ) E-7 - nRTm and A′-7 ) ATm (Tm/298)-n. Tm is
the mean temperature of experimental measurements calculated
from the 1/T function and Atm is the A-factor at Tm temperature
calculated from the two-parametric Arrhenius equation using
E′-7. They are given in columns 5-7 of Table 4. n ) ∆Cpq /R
) 1.5 since ∆Cpq ) 3.0 cal/(mol K) calculated with a tight
transition state model.22
It is of interest to see how the variations of measured negative
or positive activation energies E7 would affect the thermochem-
istry of reaction 7. Calculations are made using all available

Ethyl Radical Reactions with HBr and Br
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6039
TABLE 3: Rate Parameter of Forward Reaction 7
temperature
range [K]
A7 × 1012
k7(298) × 1013
k7(530) × 1012
no.
[cm3/(molecules s]
E7 [cal/mol]
[cm3/(molecule s)]
[cm3/(molecules)]
ref and notes
1a
2a
3a
4a
297-530
259-427
259-530
228-368
1.70 ( 0.55
1.33 ( 0.33
1.69 ( 0.20
1.43 ( 0.06
-1000 ( 278
-1078 ( 156
-969 ( 82
444 ( 26
91.63 ( 29.65
81.20 ( 20.15
85.90 ( 10.17
6.79 ( 0.28
4.38 ( 1.42
7
23
4.22 ( 0.50
1.20 ( 0.05a
average: 1a,2a
this work
a Calculated using the modified Arrhenius equation 7 fitted to Tm ) 282 K with A1 ) 3.47 × 1013 cm3 (molecule s) and E1 ) -402 cal/mol.
7
7
TABLE 4: Rate Parameters of Reverse Reaction -7
temperature
range [K]
A-7 × 1010
E-7
[kcal/mol]
Tm
[K]
A′-7 × 1011
E′-7
[kcal/mol]
k-7(298) × 1020
no.
[cm3/(molecule s)]
[cm3/(molecule s)]
[cm3/(molecule s)]
ref
1b
2b
3b
4b
5b
473-621
494-592
332-472
312-483
308-363
2.35 ( 1.12
6.61 ( 1.70
1.23 ( 0.20
2.26 ( 0.32
12.74 ( 0.50
14.00 ( 0.24
13.39 ( 0.27
13.67 ( 0.14
13.6 ( 0.5
537
539
390
379
333
2.17 ( 1.03
6.12 ( 1.58
1.83 ( 0.30
3.52 ( 0.50
11.13 ( 0.50
12.38 ( 0.24
12.22 ( 0.27
12.53 ( 0.14
16.89 ( 8.05
5.80 ( 1.49
2.27 ( 0.37
2.59 ( 0.37
7
11
14
34
36
TABLE 5: ∆fH° Ethyl Radical Calculated from Different Combinations of Equilibrium Reactions 7 and -7 at 298 K
combination
no./no.
-∆H°7, 3rd law
(kcal/mol)
-∆fH°(C2H5), 3rd law
-∆H°7, 2nd law
-∆fH°(C2H5), 2nd law
K7(298) × 107
(kcal/mol)
(kcal/mol)
(kcal/mol)
3a/1b
3a/2b
3a/3b
3a/4b
4a/1b
4a/2b
4a/3b
4a/4b
5.09 ( 2.50
14.81 ( 4.19
37.84 ( 7.62
33.17 ( 6.15
0.40 ( 0.19
1.17 ( 0.31
2.99 ( 0.50
2.62 ( 0.39
13.68 ( 0.49
14.31 ( 0.29
14.87 ( 0.23
14.79 ( 0.22
12.16 ( 0.47
12.80 ( 0.27
13.36 ( 0.21
13.28 ( 0.20
29.10 ( 0.49
29.71 ( 0.29
30.27 ( 0.23
30.19 ( 0.22
27.56 ( 0.47
28.20 ( 0.27
28.76 ( 0.21
28.68 ( 0.20
12.99 ( 0.51
14.25 ( 0.25
14.08 ( 0.28
14.40 ( 0.16
11.58 ( 0.50
12.84 ( 0.24
12.67 ( 0.27
12.99 ( 0.14
28.39 ( 0.51
29.65 ( 0.25
29.48 ( 0.28
29.80 ( 0.16
26.98 ( 0.50
28.24 ( 0.24
28.07 ( 0.27
28.39 ( 0.14
A combination of data of Tables 3 and 4 is used for obtaining
the standard enthalpy change of equilibrium 7 according to both
the
equilibrium study of reaction 7. It sets the bond dissociation
enthalpy to DH°(C2H5-H) ) 100.5 ( 0.3 kcal/mol. It is in
excellent agreement with results extracted from shock-tube
decomposition of n-butane4 and from the reversible thermal
decomposition of ethyl radical38 isolated from the high-
temperature pyrolysis of ethane, where the first kinetic method
corresponds to equilibrium b, while the second one to equilib-
rium c given in the Introduction. Both studies report the same
value of ∆fH°(C2H5) ) 28.5 ( 0.5 kcal/mol. This c variant of
the H + C2H4 h C2H5 equilibrium was also studied in a direct
time-resolved system using 193 nm laser flash photodecompo-
sition of C2H4 as an H atom source.39 This system results in
∆fH°(C2H5) ) 28.4 ( 0.4 kcal/mol, or 28.7 ( 0.2 kcal/mol
with high-pressure limiting adjustment for the forward reaction.40
third law:
∆H°7 ) 298(∆S°7 - R ln K7)
second law:
∆H°7 ) E7 - E-7 - nR(298 - Tm)
where K7 ) k7/k-7. ∆S°7 ) 10.4 ( 0.5 cal/(mol K), where the
uncertainty arises from the entropy of the ethyl radical,22 S°-
(C2H5) ) 59.6 ( 0.5 cal/(mol K). This contributes an extra
(0.15 kcal/mol uncertainty to the third law calculation of ∆H°7.
<∆Cp7> is small and negligible22 in the temperature range
298-600 K. From the reaction enthalpy change, the heat of
ethyl radical formation is then calculated in the usual way,
The above survey indicates that the derived thermochemistry
of ethyl radical using positive activation energies in both
directions is in excellent agreement with the thermochemistry
of bond fission and radical decomposition processes. This heat
of formation of ethyl radical and bond dissociation energy of
ethane are also in good agreement with the values suggested
by Walker et al.41 on the bases of general trends found in
oxidation of i-C3H7 and t-C4H9 radicals, as well as with the
value of Miyokawa et al.17 derived from competitive photo-
bromination results of ethane and monohalogenated ethane
derivatives. The laser flash system7 seems to fall in a separate
class. Only the result of flash-flash combination (3a/1b of
Table 5) is in line with present values where the reported
negative activation energy for E7 is compensated by a lower
E-7 activation energy.
∆fH°(C2H5) ) ∆H°7 - ∆fH°(HBr) + ∆fH°(Br) +
∆fH°(C2H6)
taking ∆fH° values of HBr, Br, and C2H6 from JANAF tables.
All the details of the above calculations are summarized in
Table 5, where the first column shows the sequence of data
combinations taken from Tables 3 and 4. The first line of Table
5 gives ∆fH°(C2H5) ) 28.8 ( 0.5 kcal/mol for the average of
the second and third law calculations, the same value as
recommended by Berkovitz et al.16 But the same average with
the next three combinations from 3a/2b to 3a/4b results in ∆H°7
) -14.45 ( 0.30 kcal/mol, and consequently in a higher value
of ∆fH°(C2H5) ) 29.85 ( 0.29 kcal/mol, reflecting the negative
activation energy used for the forward reaction 7. On the other
hand, our measured rate parameters in the combination 4a/1b
of Table 5 give the average of ∆fH°(C2H5) ) 27.3 ( 0.5 kcal/
mol due to the lower activation energy E-7 in line 1b of Table
4. But the last three combinations from 4a/2b to 4a/4b give
∆H°7 ) -12.96 ( 0.22 kcal/mol and ∆fH°(C2H5) ) 28.40 (
0.25 kcal/mol, which we recommend as our updated value for
the heat of formation of ethyl radical obtained from chemical
There are only two absolute rate measurements of reaction
-7. One of them uses the experimental technique of laser flash
photolysis of CF2Br2 for bromine atom source coupled with
time-resolved resonance fluorescence measurement of Br atom
depletion7 upon reaction with ethane on about a 2-12 ms
reaction time scale. The other uses the conventional thermal
bromination of ethane.11 They report different rate parameters,

6040 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Dobis and Benson
TABLE 6: ∆fH°(C2H5) Values of k7 and k-7 at 530 K
combination
no./no.
-∆H°7, 3rd law
(kcal/mol)
-∆fH°(C2H5), 3rd law
-∆H°7, 2nd law
-∆fH°(C2H5), 2nd law
K7(530) × 103
(kcal/mol)
(kcal/mol)
(kcal/mol)
3a/1b
3a/2b
4a/1b
4a/2b
2.97 ( 1.47
3.43 ( 0.98
0.85 ( 0.40
0.98 ( 0.26
14.04 ( 0.57
14.19 ( 0.35
12.71 ( 0.50
12.86 ( 0.28
29.44 ( 0.57
29.59 ( 0.35
28.11 ( 0.50
28.26 ( 0.28
14.37 ( 0.51
14.11 ( 0.25
12.83 ( 0.50
12.91 ( 0.24
29.77 ( 0.51
29.51 ( 0.25
28.23 ( 0.50
28.31 ( 0.24
as shown in lines 1b and 2b, respectively, of Table 4. Over
this temperature range, however, their absolute values agree to
within 20%. At 530 K, k-7 ) (1.42 ( 0.68) × 10-15 of the
flash system7 and (1.23 ( 0.32) × 10-15 cm3/(molecule s) of
the thermal system11 differ by only 7.2%. Combining these
values with forward rate constant data at 530 K given in Table
3, the obtained reaction enthalpies (corrected to 298 K using
the very small ∆Cp correction22) and heats of ethyl radical
formation are summarized in Table 6. A comparison of data
in Tables 5 and 6 indicates that while the combinations of 3a/
2b and 4a/2b remain practically unchanged, the new high-
temperature rate combinations of 3a/1b and 4a/1b in Table 6
are in complete agreement with their respective other (2b-4b)
combinations in Table 5. It also reveals that only the calculation
with 3a/1b combination given in Table 5 agrees with the
enthalpy data reported by Seakins et al.,7 where no combinations
with other known back-reaction rates were made.
ties in the form of
(E-7 - 12)
103 + ln A-7
ln[∆k-7] ) -
(8)
RT
presented in Figure 6b, the disparity becomes very clear. While
the results of the conventional bromination kinetics11 still retain
a good linear Arrhenius relationship within the scatter, the laser
flash bromination7 results display a systematic error that breaks
the Arrhenius function into two parts. The laser flash data
represented by squares in Figure 6b would permit lines of any
slope within the extremes of the two dashed lines shown to be
drawn through them. Thus the experimental points of ref 7
could equally be represented by activation energies varying from
14 to 11.2 kcal/mol. Their A-factor would, of course, vary
appropriately. This error justifies dropping the results of the
4a/1b combination from the 4a series in Table 5. It also shows
that the agreement of the 3a/1b combination in Table 5 with
our thermochemical results is accidental.
From the data of tables 5 and 6, it is seen that the difference
in the heat of formation of ethyl radical between our derived
value and that of Seakins et al.7 is 1.4 kcal/mol, which is equal
to the difference in activation energies E7 given in Table 3. Our
small positive activation energy is plausible on the basis of H
atom metathesis. There is no explanation or precedent for a
negative activation energy for what should be a direct metathesis
reaction. In terms of H atom metathesis, it cannot be negative,
and even the application of a contact transition state mecha-
nism43 (representing the highest rate for a bimolecular H atom
transfer) would result in a rate constant k7 that is about 1 order
of magnitude less than reported by Seakins et al.7 Some of
our reservations concerning the techniques that have been
employed have been discussed in earlier papers,22,29,30 and we
shall not consider them here.
The disparity between the two absolute rate measurements7,11
of reaction -7 is significant, as it can compensate for the
negative activation energy measured7 for the forward reaction
7. We note that the flash photolysis/Br atom resonance
fluorescence system has no radical-scavenging process like the
R + Br2 reaction in the thermal system.11 Therefore, [Br]0
concentration must be kept low to avoid significant Br atom
consumption in the fast reaction 8. From the ethane concentra-
tions given in Table III of ref 7, we estimate that [Br]0 should
be kept below 2 × 1011 atom/cm3 in the experimental runs.
Another experimental problem is the diffusion loss of Br atoms
out of the monitoring zone and its temperature dependence.
According to the original report,7 this diffusion is only a “minor
loss term” of the Br atom removal; therefore no kd data are
provided in Table III of ref 7. However, if kd is as high as
measured directly (25 s-1 at 298 K) in the same experimental
system,42 it may constitute from 30 to 86% of the first order
rate decay of Br atom fluorescence signal in the 473-621 K
range. Inaccurate corrections might lead to higher rate constant
values of k-7 and lower temperature dependence. No data for
such details are reported,7 but the marked concave curvature of
the Arrhenius plot in Figure 2 of ref 7 indicates the influence
of some side processes.
Conclusion
The improved VLPR system is well suited for the measure-
ment of temperature coefficients of the C2H5 + HBr reaction 7
in the temperature range 228-368 K. This experimental system
permits a broad kinetic investigation by allowing concentration
variations of both reactants and of the reactor residence time.
The simultaneous measurement of reactant consumptions and
product formations gives an excellent mass balance for all
species with (3% accuracy. This is a powerful check for the
overall reaction mechanism taking place in the VLPR system.
Such a versatility is not provided by presently existing alterna-
tive techniques, which usually measure either the loss of a single
reactant or the appearance of a single product in time, then fitting
the obtained data to a proposed mechanism by making correc-
tions for the observed extra radical loss such as the wall reaction
of radicals7 with no product identification in the laser flash/
tube flow system or the unidentified “ghost” reaction23 in the
laser flash/Br atom fluorescence system.
A comparison of the two absolute rate measurements7,11 of
reaction -7 is presented as Arrhenius plots of reported data in
Figure 6a. The first four data of laser flash experiments7
between 473 and 546 K give an Arrhenius function of k-7
)
(7.9 ( 4.3) × 10-10 exp[-(13.99 ( 0.80) × 103/RT] cm3/
(molecule s). Although the A-factor is somewhat high, it is in
fair agreement with the result of the thermal system11 (compare
with line 2b of Table 4). Rate constants of the upper
temperature region7 between 523 and 621 K can be described
by an Arrhenius function of k-7 ) (0.60 ( 0.20) × 10-10 exp-
[-(11.21 ( 0.19 × 103/RT. Because of the high activation
energy E-7, the importance of the 2.78 kcal/mol energy change
in the slope of Figure 6a is not very marked. Although both
functions give the same k-7 ) 1.75 × 10-15 cm3/(molecule s)
at Tm ) 537 K, the rate constants at 298 K calculated using the
modified forms of the above Arrhenius equations are different
by a factor of 8. However, using what we called a reduced
Arrhenius plot,46 which emphasizes the experimental uncertain-
Rate constants measured at different temperatures are well
described by an Arrhenius equation, k7 ) (1.43 ( 0.06) × 10-12
exp[-(444 ( 26)]/RT cm3/(molecule s), where the small positive
activation energy is in complete accordance with earlier as-

Ethyl Radical Reactions with HBr and Br
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6041
and with the proposed10 mechanism of a two-step chemical
activation process for H atom abstraction.
When our results are combined with all known kinetic
data,11,14,34 except with that of the laser flash bromination7 of
ethane, for the reverse reaction -7, the heat of ethyl radical
formation deduced from both the second and third law is
obtained as ∆fH°(C2H5) ) 28.40 ( 0.25 kcal/mol, which sets
the bond dissociation enthalpy to DH°(C2H5-H) ) 100.5 ( 0.3
kcal/mol. These thermochemical values agree well with those
obtained from high-temperature bond fission/radical recombina-
tion4 and the reversible thermal decomposition5,39 of the ethyl
radical. The results of these three different chemical equilibria
provide the currently accepted thermochemistry of the ethyl
radical in a remarkable conformity.
The kinetic investigation of the laser flash bromination7 of
ethane involves a systematic error as disclosed in Figure 6a,b.
Its low activation energy E-7 compensates for the the negative
activation energy of the forward reaction, which leads to an
apparent agreement with our thermochemical values. This
agreement is actually an accidental outcome. All other com-
binations of reported kinetic data for the thermal bromination
of ethane11,14,34 with those of laser flash initiated reaction 7 give
higher thermochemical values, reflecting the activation energy
difference for reaction 7 between our value E7 and those of
Seakins et al.7 and Nicovich et al.23
The general trend in the reported7,9 negative activation
energies for R + HX (or X2) type reactions seems, we believe,
to arise from some still undisclosed artifacts of the laser flash
experimental system. We are of the opinion that this problem
may arise from the energy sensitive cross section for near
threshold photoionization of “hot” radicals22 and their quenching
by HBr and HI.
Rate constants obtained for the reaction 8 of C2H5 + Br show
no measurable temperature dependence. Their average gives
k8 ) (1.18 ( 0.05) × 10-11 cm3/(molecule s), which is slightly
less than the rate constant (k2) for the simillar reaction C2H5 +
Cl. Its value is consistent with the proposed mechanism of atom
+ radical disproportionation.
Acknowledgment. Acknowlegement is made to the Donors
of the Petroleum Research Fund administered by the American
Chemical Society, for the support of this research.
References and Notes
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Benson, S. W. Thermochemistry of Alkanes and Cycloalkanes. Chapter 6
In The Chemistry of Alkanes and Cycloalkanes; Patai, S., Rappoport, Z.,
Eds.; John Wiley and Sons: New York, 1992.
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Figure 6. (a) Comparison of absolute rate measurements for reaction
-7 presented as Arrhenius plots of reported data for conventional
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bromination7 (squares with broken lines) of ethane. (b) Reduced
Arrhenius plot (eq 8) of data in part a. This type of plot gives better
presentation of any systematic errors in k. While we have used two
dashed lines to represent the data, a single line of arbitrary slope
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sumptions3 and with direct H atom metathesis. It disagrees with
reported7,23 negative activation energy of about -1 kcal/mol

6042 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Dobis and Benson
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