Kinetics and thermochemistry of the R + HBr ? RH + Br (R = n-C3H7, isoC3H7, n-C4H9, isoC4H9, sec-C4H9 or tert-C4H9) equilibrium

Article abstract of DOI:10.1039/a608224f

The kinetics of the reactions of n-C₃H₇, isoC₃H₇, n-C₄H₉, isoC₄H₉, sec-C₄H₉ and tert-C₄H₉ radicals, R, with HBr have been investigated in a beatable tubular reactor coupled to a photoionization mass spectrometer. The reactions were studied by a time-resolved technique under pseudo-first-order conditions, where the rate constants of R + HBr reactions were obtained by monitoring the decay of the radical as a function of time. The radical was photogenerated in situ in the flow reactor by pulsed 248 nm exciplex laser radiation. All six reactions were studied separately over a wide range of temperatures and, in these temperature ranges, the rate constants determined were fitted to an Arrhenius expression (error limits stated are 1σ + Students t values, units cm³ molecule^-1 s^-1): k(n-C₃H₇) = (1.6 ± 0.2) × 10^-12 exp[+(5.4 ± 0.2) kJ mol^-1/RT], k(isoC₃H₇) = (1.4 ± 0.2) × 10^-12 exp[+(6.9 ± 0.2) kJ mol^-1/RT], k(n-C₄H₉) = (1.3 ± 0.2) × 10^-12 exp[+(6.4 ± 0.4) kJ mol^-1/RT], k(isoC₄H₉) = (1.4 ± 0.2) × 10^-12 exp[+(6.1 ± 0.2) kJ mol^-1/RT], k(sec-C₄H₉) = (1.4 ± 0.3) × 10^-12 exp[+(7.5 ± 0.3) kJ mol^-1/RT] and k(tert-C₄H₉) = (1.2 ± 0.3) × 10^-12 exp[+(8.3 ± 0.3) kJ mol^-1/RT]. The kinetic information was combined with the kinetics of the Br + RH reactions to calculate the entropy and the heat of formation values for the radicals studied. The thermodynamic values were obtained at 298 K using a second-law procedure. The entropy values and enthalpies of formation are (entropy in J K^-1 mol^-1 and enthalpy in kJ mol^-1): 284 ± 5, 100.8 ± 2.1 (n-C₃H₇); 281 ± 5, 86.6 ± 2.0 (isoC₃H₇); 329 ± 5, 80.9 ± 2.2 (n-C₄H₉); 316 ± 5, 72.7 ± 2.2 (isoC₄H₉); 330 ± 5, 66.7 ± 2.1 (sec-C₄H₉) and 315 ± 4, 51.8 ± 1.3 (tert-C₄H₉). The C-H bond strength of analogous saturated hydrocarbons derived from the enthalpy of reaction values are (in kJ mol^-1): 423.3 ± 2.1 (primary C-H bond in propane), 409.1 ± 2.0 (secondary C-H bond in propane), 425.4 ± 2.1 (primary C-H bond in n-butane), 425.2 ± 2.1 (primary C-H bond in isobutane), 411.2 ± 2.0 (secondary C-H bond in n-butane) and 404.3 ± 1.3 (tertiary C-H bond in isobutane). The enthalpy of formation values are used in group additivity calculations to estimate Δ_f H₂₉₈^○ values of six pentyl and four hexyl free radical isomers.

Full text of DOI:10.1039/a608224f

View Article Online / Journal Homepage / Table of Contents for this issue
Kinetics and thermochemistry of the R + HBr ¢ RH + Br (R = n-
C H , isoC H , n-C H , isoC H , sec-C H or tert-C H )
3 7 3 7 4 9 4 9 4 9 4 9
equilibrium
Jorma A. Seetula*a and Irene R. Slagleb
a L aboratory of Physical Chemistry, P.O. Box 55 (A. I. V irtasen aukio 1), FIN-00014 University
of Helsinki, Finland
b Department of Chemistry, T he Catholic University of America, W ashington, DC 20064, USA
The kinetics of the reactions of n-C H , isoC H , n-C H , isoC H , sec-C H and tert-C H radicals, R, with HBr have been
3
7
3
7
4
9
4
9
4
9
4 9
investigated in a heatable tubular reactor coupled to a photoionization mass spectrometer. The reactions were studied by a
time-resolved technique under pseudo-Ðrst-order conditions, where the rate constants of R ] HBr reactions were obtained by
monitoring the decay of the radical as a function of time. The radical was photogenerated in situ in the Ñow reactor by pulsed 248
nm exciplex laser radiation. All six reactions were studied separately over a wide range of temperatures and, in these temperature
ranges, the rate constants determined were Ðtted to an Arrhenius expression (error limits stated are 1p ] Students t values, units
cm3 molecule~1 s~1): k(n-C H ) \ (1.6 ^ 0.2) ] 10~12 exp[](5.4 ^ 0.2) kJ mol~1/RT ], k(isoC H ) \ (1.4 ^ 0.2) ] 10~12
3
7
3 7
exp[](6.9 ^ 0.2) kJ mol~1/RT ], k(n-C H ) \ (1.3 ^ 0.2) ] 10~12 exp[](6.4 ^ 0.4) kJ mol~1/RT ], k(isoC H ) \ (1.4 ^ 0.2)
4
9
4 9
] 10~12 exp[](6.1 ^ 0.2) kJ mol~1/RT ], k(sec-C H ) \ (1.4 ^ 0.3) ] 10~12 exp[](7.5 ^ 0.3) kJ mol~1/RT ] and k(tert-
C H ) \ (1.2 ^ 0.3) ] 10~12 exp[](8.3 ^ 0.3) kJ mol~1/RT ]. The kinetic information was combined with the kinetics of the
4
9
4
9
Br ] RH reactions to calculate the entropy and the heat of formation values for the radicals studied. The thermodynamic values
were obtained at 298 K using a second-law procedure. The entropy values and enthalpies of formation are (entropy in J K~1
mol~1 and enthalpy in kJ mol~1): 284 ^ 5, 100.8 ^ 2.1 (n-C H ); 281 ^ 5, 86.6 ^ 2.0 (isoC H ); 329 ^ 5, 80.9 ^ 2.2 (n-C H );
3
7
3
7
4 9
4 9
316 ^ 5, 72.7 ^ 2.2 (isoC H ); 330 ^ 5, 66.7 ^ 2.1 (sec-C H ) and 315 ^ 4, 51.8 ^ 1.3 (tert-C H ). The CwH bond strength of
4
9
4
9
analogous saturated hydrocarbons derived from the enthalpy of reaction values are (in kJ mol~1): 423.3 ^ 2.1 (primary CwH
bond in propane), 409.1 ^ 2.0 (secondary CwH bond in propane), 425.4 ^ 2.1 (primary CwH bond in n-butane), 425.2 ^ 2.1
(primary CwH bond in isobutane), 411.2 ^ 2.0 (secondary CwH bond in n-butane) and 404.3 ^ 1.3 (tertiary CwH bond in
isobutane). The enthalpy of formation values are used in group additivity calculations to estimate * H¡ values of six pentyl and
f
298
four hexyl free radical isomers.
In organic chemistry nearly all chemical processes seem to
proceed through a set of reaction steps which involve radicals
and/or other neutral reaction intermediates.1,2 Such is espe-
cially the case in combustion chemistry.3 The formation of
soot particles in the burning of organic materials is the result
of very complex free radical chemistry which involves the
reactions of these species with themselves and with other free
radicals and molecules. A combination of the kinetics and
dynamics of these reactions under known fuel/oxidant condi-
tions determines the rate of the overall process and the Ðnal
products. Under unknown reaction conditions product forma-
tion could be problematic. For example, soot production
reduces combustion efficiency and increases maintenance
demands in combustion vehicles and other devices. For eco-
nomic reasons it is imperative to determine the conditions
where the presence of soot particles in a combustion process
are minimized but the combustion beneÐts are maximized. To
do so requires knowledge of rate constants and activation
parameters for those elementary reactions involved in the
process. These activation parameters are related to the ther-
mochemical parameters of reaction species.
The reaction thermochemistry of alkyl radicals is of wide-
ranging importance.4 This information establishes the magni-
tudes of the primary, secondary and tertiary CwH bond
strengths which are associated with the enthalpy change of the
following reaction: RH ] R ] H. This, and other bond
strengths, are of immeasurable value in attempts to estimate
the heats of formation of stable molecules and, in particular,
labile reaction species. Furthermore, accurate thermochemical
information of reaction species will make it possible to conÐne
or even establish plausible reaction paths and identify short-
lived reaction intermediates.
The current study presents an experimental kinetic investi-
gation of propyl and butyl free radical isomers with HBr.
Three of these reactions have not previously been studied. The
kinetics of these polyatomic radicals is studied here in order to
obtain thermochemical properties for the radicals. The ther-
modynamic data determined are used to compare di†erent
bond energies in small hydrocarbons and free radicals and to
estimate the heats of formation of some pentyl and hexyl
radical isomers. The kinetic and thermodynamic method is
similar to that used previously for chlorinated methyl and
ethyl radical reactions with HBr.5
Experimental and Kinetics
Description of experiments
The rate constants of the reactions of propyl and butyl free
radicals with HBr were measured as a function of temperature
and pressure. The reactions were studied in a tubular-Ñow
reactor which ensures that there is no mixing of the Ñowing-
gas components in the direction of the Ñow but complete
mixing perpendicular to the direction of the Ñow. Therefore,
radial di†usion must be very efficient, which is the case at low
pressures. Details of the experimental apparatus and condi-
tions used have been described previously.5h7 BrieÑy, pulsed
unfocused 248 nm radiation from a Lambda Physik EMG 201
MSC exciplex laser was collimated and then directed through
a quartz window along the axis of a Pyrex or quartz reactor.
J. Chem. Soc., Faraday T rans., 1997, 93(9), 1709È1719
1709

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The laser operated at 5 Hz. The reactor, 10.5 mm id, was
coated with halocarbon wax,¤ poly(dimethylsiloxane)” or
boric oxide to reduce heterogeneous radical reactions on the
reactor wall. Gas Ñowing through the reactor at 5 m s~1 was
completely replaced between laser pulses. The Ñowing gas
contained the radical precursor (typically below 0.03%), HBr
in varying concentrations (see Table 1) and the carrier gas, He,
in large excess ([99.5%). The radical precursor and HBr were
directed into the reactor through di†erent gas inlets and were
mixed with helium inside the upstream portion of the reactor.
An estimate for the mixing time of di†usion to reduce the
radial concentration, under typical conditions, to 5% of its
initial value was 0.3 ms.8,9 This means that the length of the
reactor needed to develop a homogeneous gas mixture and a
parabolic velocity proÐle of the gas8 was only a few mm, i.e.
short compared with the distance, ca. 40 cm, from the gas
inlets to the sampling oriÐce. A portion of the gas mixture was
sampled through a 0.44 mm id hole located at the end of a
nozzle in the wall of the reactor and was formed into a beam
by a conical skimmer before entering the vacuum chamber
containing the quadrupole mass Ðlter. A portion of the gas
beam was then photoionized by VUV light just above the
skimmer. Selectively ionized species were mass selected and
temporal ion signal proÐles recorded, from 10È30 ms before
and 16È25 ms after the laser pulse, with a multichannel scalar.
Data from 1500 to 16 000 repetitions of the experiments were
accumulated and analysed by a non-linear least-squares
program.
dependence was found. The results of these tests and all the
other experiments to measure reactions (1)È(6) are given in
Table 1.
Photogeneration of free radicals
The radicals were generated by photolysing alkyl halides at a
wavelength of 248 nm; typically, 1È3% photodissociation
occurred. For primary isomers, special attention is needed to
ensure that any radical generated with excess internal energy
does not isomerize to a more stable form during the timescale
(50 ms) of the kinetics measurement. The possibility of isomer-
ization was investigated by studying the products of the
unimolecular decomposition of the radical as a function of
temperature. Di†erent products from the unimolecular
decomposition of radical isomers and a clear di†erence in
temperatures at which the decomposition begins are evidence
that a less stable radical isomer can be isolated for kinetic
studies.
The n-C H radical was generated by photolysis of n-
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C H Br, which gives, as primary products, n-C H and Br.
3
7
3 7
The n-C H radical begins to decompose unimolecularly at
3
7
ca. 620 K (at a gas density of 6 ] 1016 molecule cm~3)
whereas its more stable form, isoC H , begins to decompose
3
7
at 750 K. This can be seen by comparing the measured Ðrst-
order wall reactions of the n-C H radical with that of the
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7
isoC H radical in Table 1 at 667 K. The decay of the n-C H
3
7
3 7
radical at this temperature is already almost 200 s~1 while the
isoC H radical shows no sign of unimolecular decomposi-
tion. The products of unimolecular decomposition of the
The radicals were generated only at 248 nm. At this wave-
length HBr was not photodissociated to any measurable
extent. This was ensured by monitoring the Br atom mass
number with only HBr in the reactor; no measurable signal of
Br atoms was detected. It is important to avoid photogenerat-
ing reactive H and Br atoms during the reaction since these
species can interfere with the observed kinetics by reacting
with the radical under study and the product of the reaction.5
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propyl radicals are quite di†erent: n-C H decomposes to
3
7
ethylene and methyl radical and isoC H decomposes to
3
7
propene and hydrogen atom. These products have also been
veriÐed elsewhere under conditions similar to those in the
current study.12,13
The isoC H radical was photogenerated from isopropyl
3
7
bromide whose major photolysis channel at 248 nm is the dis-
sociation of the CwBr bond. The yields of C H and HBr
Kinetic results
3
6
from either propyl bromide were negligible.
The kinetics of six polyatomic free radical reactions with HBr
were studied separately:
The n-C H radical was photogenerated from n-C H Br,
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9
4 9
again, possible isomerization of the primary butyl radical to a
more stable form had to be investigated separately. n-C H
n-C H ] HBr ] C H ] Br
(1)
(2)
(3)
(4)
(5)
(6)
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9
3
7
3 8
begins to decompose unimolecularly at 550 K (at a gas density
of 6 ] 1016 molecule cm~3), i.e. at an even lower temperature
than for n-C H . In contrast, the sec-C H radical
isoC H ] HBr ] C H ] Br
3
7
3 8
3
7
4 9
n-C H ] HBr ] n-C H ] Br
(photogenerated from sec-C H Br) begins to decompose at ca.
4
9
4
10
4
9
600 K under similar conditions. Moreover, the decomposition
products from these butyl radicals are di†erent: ethyl radical
and ethylene from the n-C H radical, and propylene and
methyl radical from the sec-C H radical.
The primary isoC H radical was generated from isoC H I.
Again the thermal stability of the radical was tested as a func-
tion of temperature at the gas densities used in the kinetic
investigations. The isoC H begins to decompose unimole-
cularly at ca. 570 K. The products are the same, C H
] CH , as for the sec-C H radical. Isomerization of
isoC H to sec-C H requires an intramolecular shift of the
CH group to occur, which would be more difficult than an
isomerization of the isoC H radical to the tert-C H radical
since the latter process requires only a 1,2-shift of the hydro-
gen atom. It was concluded that isomerization of isoC H to
tert-C H did not occur in the experimental timescale (50 ms).
The absence of this isomerization was ensured by monitoring
the mass numbers of C H and isoC H , as a function of
time, at temperatures from 570 to 800 K. At 700 K the signal
of the isoC H radical decays very fast showing no sign of any
displacement (which should appear if isomerization is
occurring) on the ion signal. At the temperature of 730 K the
tert-C H radical begins to decompose unimolecularly. Above
isoC H ] HBr ] isoC H ] Br
4
9
4
10
sec-C H ] HBr ] n-C H ] Br
4
9
4 10
4
4
9
9
tert-C H ] HBr ] isoC H ] Br
4
9
4
10
4
9
4 9
The rate constants of the forward reactions were combined
with the rate constants of the reverse, Br ] RH, reactions10,11
in order to calculate the heats of formation and the experi-
mental entropy values. All the rate constants, including both
forward and reverse reaction, were determined in time-
resolved studies. No ratio of rate constant values was needed
in order to calculate the Arrhenius expressions for the reverse
reactions. The forward reactions were studied over a wide
temperature range (296È667 K) with the upper limit of tem-
perature determined by the onset of unimolecular decomposi-
tion of the radical of interest. The e†ect of pressure on the rate
constant was tested for each free radical reaction investigated
at room temperature, where the reaction intermediate should
have the longest lifetime. The pressure was changed by up to a
factor of 4.3 during these tests. As expected, no pressure
4
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3
6
3
9
4 9
4
4 9
3
4
9
4 9
4
9
4
9
4
9
4 8
4
9
¤ Halocarbon Wax is a product of the Halocarbon Wax Corp.
Hackensack, NJ.
” Poly(dimethylsiloxane), 200 Ñuid was obtained from Aldrich.
4
9
this temperature no signal of isoC H was detected. This
4
8
1710
J. Chem. Soc., Faraday T rans., 1997, V ol. 93

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Table 1 Conditions and results of experiments used to measure the rate constant of the reaction R ] HBr ] RH ] Br (R \ n-C H , isoC H ,
3
7
3 7
n-C H , isoC H , sec-C H and tert-C H )
4
9
4
9
4
9
4 9
T a
/K
[He]
/1016 cm~3
[HBr]
/1013 cm~3
k
wall
coatingb
k c
7
i
/s~1
/10~12 cm3 s~1
n-C H ] HBr ] C H ] Br (k )
3
7
3
8
1
296
297
348
412
457
511
512
667
5.80
17.8
5.82
5.83
5.84
5.89
5.88
5.89
0.44È3.05
0.73È3.28
0.54È2.77
0.52È3.02
0.87È3.43
0.52È3.28
1.28È3.74
1.53È19.9
84
83
65
65
41
15
45
PDMS
PDMS
PDMS
PDMS
PDMS
B O
13.3 ^ 1.01
14.1 ^ 0.37
10.7 ^ 0.27
7.70 ^ 0.73
6.82 ] 0.25
5.89 ^ 0.12
5.42 ] 0.17
4.07 ^ 0.23
2
3
PDMS
B O
194
2
3
k \ (1.6 ^ 0.2) ] 10~12 exp[ ] (5.4 ^ 0.2) kJ mol~1/RT ] cm3 molecule~1 s~1
1
isoC H ] HBr ] C H ] Br (k )
3
7
3
8
2
304
304
348
414
414
511
667
5.79
24.7
5.82
5.88
5.81
5.85
5.87
0.53È1.90
0.71È2.10
0.88È2.97
0.85È4.76
0.54È2.68
1.07È5.33
1.22È5.42
23
37
21
16
21
11
HW
HW
HW
20.3 ^ 1.07
20.4 ] 0.74
15.7 ] 0.51
10.7 ^ 0.28
10.9 ^ 0.26
7.01 ^ 0.10
4.88 ^ 0.18
PDMS
B O
2
3
PDMS
B O
8.8
2
3
k \ (1.4 ^ 0.2) ] 10~12 exp[ ] (6.9 ^ 0.2) kJ mol~1/RT ] cm3 molecule~1 s~1
2
n-C H ] HBr ] n-C H ] Br (k )
4
9
4
10
3
303
303
319
348
348
414
414
511
550
5.81
24.8
0.79È3.12
0.72È1.93
0.44È1.31
0.77È4.61
0.64È2.36
0.96È3.82
0.85È3.13
0.64È4.82
1.38È4.90
39
HW
HW
HW
15.0 ^ 2.04
16.3 ^ 0.93
16.3 ^ 1.62
12.5 ^ 1.71
12.6 ^ 1.49
8.44 ^ 0.57
8.39 ^ 0.34
5.70 ^ 0.41
5.32 ^ 0.21
41
28
36
36
31
27
30
39
5.81
5.81
5.83
5.85
5.81
5.86
5.89
HW
PDMS
PDMS
B O
2
3
PDMS
B O
2
3
k \ (1.3 ^ 0.2) ] 10~12 exp[ ] (6.4 ^ 0.4) kJ mol~1/RT ] cm3 molecule~1 s~1
3
isoC H ] HBr ] isoC H ] Br (k )
4
9
4
10
36
4
301
303
348
378
378
414
459
511
550
5.80
24.8
0.76È2.34
0.86È2.38
0.65È4.92
1.21È4.54
1.20È4.94
1.42È4.66
1.01È6.53
1.42È6.94
1.82È7.09
PDMS
PDMS
PDMS
PDMS
B O
17.8 ^ 0.95
16.2 ^ 0.37
12.1 ^ 0.81
10.5 ^ 0.44
10.2 ^ 0.35
8.82 ^ 0.44
7.34 ^ 0.50
5.94 ^ 0.13
5.72 ^ 0.21
31
35
30
37
31
36
37
38
5.82
5.84
5.84
5.81
5.84
5.84
5.89
2
3
PDMS
PDMS
PDMS
B O
2
3
k \ (1.4 ^ 0.2) ] 10~12 exp[ ] (6.1 ^ 0.2) kJ mol~1/RT ] cm3 molecule~1 s~1
4
sec-C H ] HBr ] n-C H ] Br (k )
4
9
4
10
39
5
302
305
348
414
414
511
610
24.9
0.56È1.88
0.56È1.22
0.65È1.99
0.88È4.12
1.29È4.25
1.35È4.98
1.18È6.83
HW
HW
HW
27.7 ^ 0.91
27.3 ^ 1.81
20.5 ^ 1.02
13.3 ^ 0.85
13.1 ^ 0.58
7.92 ^ 0.57
5.90 ^ 0.41
5.78
5.82
5.85
5.83
5.84
5.88
36
32
20
24
17
87
PDMS
B O
2
3
PDMS
B O
2
3
k \ (1.4 ^ 0.3) ] 10~12 exp[ ] (7.5 ^ 0.3) kJ mol~1/RT ] cm3 molecule~1 s~1
5
tert-C H ] HBr ] isoC H ] Br (k )
4
9
4
10
6
301
303
348
414
511
511
667
25.0
0.42È1.45
0.40È1.20
0.56È1.93
0.84È3.79
1.47È5.28
1.14È5.95
0.61È7.79
47
46
37
25
15
22
26
HW
HW
HW
30.7 ^ 2.61
31.3 ^ 2.04
22.0 ^ 0.91
13.8 ^ 0.61
8.06 ^ 0.32
8.92 ^ 0.40
5.39 ^ 0.48
5.80
5.86
5.86
5.85
5.87
5.89
PDMS
PDMS
B O
2
B O
2
3
3
k \ (1.2 ^ 0.3) ] 10~12 exp[ ] (8.3 ^ 0.3) kJ mol~1/RT ] cm3 molecule~1 s~1
6
a Temperature uncertainty: ^1
K (296È348 K), ^2 K (378È512 K) and ^4 K (550È667 K). b HW (halocarbon wax), PDMS
[poly(dimethylsiloxane)]. c Errors are 1 p ] StudentÏs t and based on statistical uncertainties.
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1711

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alkene and H atom are the decomposition products of tert-
C H .14 Special attention was paid to the isoC H radical. Of
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9
4 9
the radicals studied it was the only species which was gener-
ated from alkyl iodide. This precursor is more sensitive to
background radiation from a Cl atom resonance lamp than
alkyl bromides. To prevent fragmentation of the precursor at
the radical mass number in the vacuum chamber the com-
bination of a BaF salt window with a Cl resonance lamp was
2
used to photoionize the radical. BaF is transparent to VUV
2
radiation above 135 nm. This is almost 15 nm above the
transmittance threshold of a CaF crystal. A drawback of the
2
more selective ionization radiation of a BaF /Cl lamp light
2
source is its lower radiation yield compared to that of a
CaF /Cl lamp. Nevertheless, a BaF /Cl lamp was used suc-
2
2
cessfully to monitor the isoC H radical with a very good
4
9
signal/noise ratio.
The tert-C H was generated from tert-C H Br. As with
the other alkyl bromides used in the current study, tert-
4
9
4 9
C H Br seems to be photodissociated at 248 nm almost exclu-
4
9
sively by CwBr bond rupture. Even though a competitive
photolysis channel in alkyl bromides, and especially alkyl
iodides, could exist at 248 nm (such as the formation of C H
3
6
] HBr or C H ] HBr/HI), such channels did not interfere
4
8
with the detection of propyl or butyl radicals because of the
selective ionization method used in the current study. Propene
or butene cannot be ionized by 8.9È9.1 eV radiation from a
chlorine resonance lamp. In addition, the mass numbers of
these alkenes are di†erent than those of the propyl and butyl
radicals.
Fig. 1 First-order decay constant k@ vs. [HBr] for set of experiments
conducted to measure the isoC H ] HBr rate constant, k , at 348 K.
4
9
4
Insert is the ion signal proÐle of isoC H ` recorded during one of the
4
9
experiments, shown as a solid circle in the linear regression Ðt. The
solid line through the data points in the insert is an exponential func-
tion Ðtted by a non-linear least-squares procedure. The Ðrst-order
decay constant for isoC H ` in the displayed ion signal proÐle is
Measurement of R + HBr rate constants
Experimental conditions were chosen such that the initial con-
centration of radicals was always negligible compared with
the concentration of the other reactant, HBr. Estimates of the
initial radical concentrations were determined from the mea-
sured extents of depletion of the known concentration of
radical precursors. The initial radical concentrations were
typically \1 ] 1011 cm~3. Under these pseudo-Ðrst-order
conditions only reactions (1)È(6) and (7) had signiÐcant rates.
4
9
(402.5 ^ 4.1) s~1 ([HBr] \ 3.22 ] 1013 molecule cm~3).
when a Ñow of HBr is added to the reactor. Evidence for such
a phenomenon is a non-linear decay constant plot of k@ vs.
[HBr] in which the slope becomes smaller at high HBr con-
centrations (see Fig. 2 in ref. 16). Such a phenomenon was not
present in the experiments which were used to determine the
rate constants of reactions (1)È(6). If such heterogeneous
bimolecular reactions exist during experiments, they would
appear as part of the homogeneous bimolecular R ] HBr rate
constant making it higher than normal. To minimize any
inÑuence of heterogeneous wall reactions, di†erent wall-
coating materials were used (see Table 1). While the coatings
did reduce the unimolecular heterogeneous wall loss of free
radical, they did not a†ect the value of the R ] HBr rate con-
stant. The coatings have a tendency also to minimize the
decomposition of HBr on the wall of the reactor.
R ] Heterogeneous loss on the wall
(7)
Low initial radical concentrations ensured that any side reac-
tions had negligible rates compared to reactions (1)È(7). This
was easily veriÐed by measuring the heterogeneous Ðrst-order
rate constant, k , of the radical under di†erent conditions
7
where the radical precursor concentration was held steady but
the radical concentration was changed by a factor of 2. This
was achieved by attenuating the laser radiation with quartz
plates. The rate constants from these di†erent experiments
were equal within their statistical error limits.
Bimolecular rate constants, k , for reactions (1)È(6) were
obtained from the slopes of plots of the exponential radical
i
Accuracy of measurements
decay constant k@ vs. [HBr] Mfrom [R`] \ [R`] exp([k@t),
The error limits stated in the rate constants of reactions (1)È
(6) are 1 p ] StudentÏs t and are based only on the statistical
uncertainties. The bimolecular rate constants of measured
R ] HBr reactions, weighted by their error limits, were Ðtted
to the two-parameter Arrhenius expression. The error limits
stated in Arrhenius expressions are also 1 p ] StudentÏs t. The
reactions were studied under pseudo-Ðrst-order conditions
and hence it was necessary to know only the concentration of
HBr accurately; the mean value of [HBr] before and after the
kinetic experiment was used (see more details in ref. 5). Other
errors including temperature and Ñow rate were always \1%
and were thus ignored.
t
0
where k@ \ k
[HBr] ] k . An example of such a
1, 2, 3, 4, 5 or 6
7
plot is shown in Fig. 1, together with a representative ion
signal decay proÐle of the radical. The products of reactions
(1)È(6) could not be detected. This is because the appearance
potential of the radicals from their precursors and from the
products of these metathetical reactions are lower in energy
than the ionization energy available from suitable resonance
lamps needed to detect the stable reaction products.15
Heterogeneous reactions
There is always a possibility of heterogeneous bimolecular
reactions occurring during HBr experiments in a Ñow reactor.
On the other hand, the heterogeneous unimolecular reaction
is taken into account in the data analysis (see above). The
inÑuence of heterogeneous bimolecular reactions could exist
Reagents
Helium (Matheson, 99.995%) was used without further puriÐ-
cation. Hydrogen bromide (99%) and the liquids (1-bromo-
1712
J. Chem. Soc., Faraday T rans., 1997, V ol. 93

View Article Online
propane, 99%; 2-bromopropane, [99%; 1-bromobutane,
98%; 2-bromobutane, 98%; 1-iodo-2-methylpropane, 97%
and 2-bromo-2-methylpropane, 98%) were obtained from
Aldrich. The free-radical precursors were degassed by using
freezeÈpumpÈthaw cycles. HBr was collected in a Ñow trap
kept at 77 K and was distilled several times to remove any
traces of bromine. HBr was stored in a dark Pyrex bulb. HBr
Ñows were measured in a gas-handling system made from
Pyrex glass and TeÑon tubes.
should inÑuence the overall rate constant by only a few per
cent.10
Furthermore, Washida and Bayes have shown, in their
time-resolved discharge Ñow-photoionization mass spectro-
meter experiments, that there is a large di†erence in the rates
of abstracting di†erent hydrogens from deuterium-labelled
isobutane by oxygen atoms.17 The Arrhenius expression for
reaction ([1) was taken from ref. 10 to be
k
\
~1
k
\ (2.4 ^ 1.1) ] 10~10 exp[[(53.3 ^ 2.1) kJ mol~1/
Br`ethane
RT ] cm3 molecule~1 s~1.
In the thermochemical calculations, Ðrst the enthalpy of
Photoionization energies
reaction (*H¡) at T , the middle of the overlapping tem-
m
A selective photoionization of reactants and products of the
photolysis and reactions was achieved by atomic resonance
radiation. Three resonance lamps with di†erent salt windows
were used. An argon lamp (11.6, 11.8 eV; with LiF window)
was used to ionize HBr, Br , Br and C H . A hydrogen lamp
perature ranges (on a 1/T scale) of the forward (f) and reverse
(r) reactions was determined: *H¡ at T \ E (1) [ E ([1)
m
a
a
] *nRT . At the same temperature the Gibbs energy and
¡ \ [RT [ln(k /k
entropy of reaction were calculated: *G
)
m
T
1
~1
] *n ln(R@T )] and *S¡ \ (*H¡ [ *G¡ )/T . Next, both
2
2 4
Tm
Tm
Tm
m
(10.2 eV; with MgF window) to ionize all radical precursors,
the reaction enthalpy and entropy changes were recalculated
at 298 K by using the heat capacities of the reactant
species.18,19 Finally, the enthalpy of formation and entropy of
the n-C H radical at room temperature were obtained from
2
propene, butene and CH and a chlorine lamp (8.9È9.1 eV;
with either CaF or BaF window) to ionize ethyl, propyl and
3
2
2
butyl radicals.
3
7
the reaction enthalpy and entropy changes using the values
for other reaction species listed in Table 2. See Table 3 for
results.
Thermochemical calculations
Both the enthalpy and entropy changes associated with reac-
tions (1)È(6) were obtained using a second-law method. This
procedure requires knowledge of the temperature dependences
of the rate constants of both the forward and reverse reactions
but the accuracy of the rate constants is not important. In
contrast, a third-law method requires knowledge of the absol-
ute values of the rate constants of both the forward and
reverse reactions at the same temperature. Although the ther-
mochemical parameters in the current study were principally
obtained by the second-law method, the third-law method was
also used, for comparison. The procedure of thermochemical
calculations is the same for all six free radicals studied. The
methods are described brieÑy in the next section.
The experimental entropy value of 284 ^ 5 J K~1 mol~1
for n-C H radical is quite close to the value of 289.41 J K~1
3
7
mol~1 calculated by Tsang.21 This value can be used in a
third-law procedure to obtain a value of 103.9 ^ 2 kJ mol~1
for the heat of formation of the n-C H radical. Here the
3
7
Gibbs energy change is calculated directly from the thermody-
namic equilibrium constant value: *G¡ \ *G¡ ] *S¡ (T
298
Tm
298 m
[ 298) [ *C¡(T [ 298) ] *C¡ ] T ln(T /298).
p
m
p
m
m
isoC H . The Arrhenius expression for reaction ([2) was
3
7
taken from ref. 10. In this time-resolved investigation Seakins
et al. measured the rate constant of Br ] C H ] HBr
3
8
] isoC H
to be
k
\ (8.8 ^ 3.0) ] 10~11 exp[[(36.0
3
7
~2
^ 2.0) kJ mol~1/RT ] cm3 molecule~1 s~1 from 476 to 667 K.
This rate equation was then used in thermochemical calcu-
lations. Results for the thermochemical parameters calculated
are shown in Table 3. Tabulated thermochemical functions
needed for calculations are from ref. 18, 19 and 22, and from
Table 2.
n-C H . The Arrhenius expression for the reverse reaction,
3
7
Br ] C H ] HBr ] n-C H , is not, and most likely cannot
3
8
3 7
be, measured directly. A selective bromine atom will always
abstract a secondary hydrogen atom much more easily than a
primary hydrogen atom from propane. However, there is
reason to believe that the Arrhenius expression for reaction
([1) [the reverse of reaction (1)] is as large as the Arrhenius
expression for the reaction of Br ] C H . Both these hydro-
Chen et al. calculated the entropy of the isoC H radical to
3
7
be 288.28 J K~1 mol~1 at room temperature.22 Use of this
2
6
carbons have six primary hydrogens. Proof for the kinetics of
abstracting the same kind of hydrogen atoms by a bromine
atom from hydrocarbons can be found in the literature.
Seakins et al. measured the reactions of Br ] propane and
Br ] n-butane as a function of temperature using a laser Ñash
photolysis resonance-Ñuorescence apparatus.10 They found
the rate of Br ] n-C H reaction to be about twice as fast as
Table 2 Enthalpies of formation and entropies used in thermochemi-
cal calculations
* H¡
S¡
f
298
298
species
/kJ mol~1
/J K~1 mol~1
HBra
Bra
[36.44
111.86
[104.5
[126.5
[134.5
198.70
175.02
270.18
310.68
295.31
4
10
the rate of Br ] C H reaction. The activation energies of
3
6
C H b
these reactions were essentially the same. Both these reactions
should proceed by Br atom abstraction of a secondary hydro-
gen from butane or propane. A competitive abstraction
process involving primary hydrogen atoms in these molecules
3
8
b
n-C H
4
10
b
isoC H
4
10
a Ref. 18. b Enthalpy from ref. 20 and entropy from ref. 19.
Table 3 Second-law determinations of * H¡ (R) based on the R ] HBr ¢ RH ] Br equilibrium
f
298
radical
T
*G¡
Tm
*H¡
Tm
*S¡
*H¡
298
*S¡
298
* H¡
S¡
298
m
Tm
f
298
n-C H
537
556
509
509
516
415
503
[(36.5 ^ 1.8)
[(23.8 ^ 1.5)
[(37.7 ^ 1.7)
[(36.2 ^ 1.7)
[(22.5 ^ 1.4)
[(19.7 ^ 0.7)
[(16.6 ^ 1.5)
[(58.7 ^ 2.1)
[(42.9 ^ 2.0)
[(59.7 ^ 2.1)
[(59.4 ^ 2.1)
[(45.2 ^ 2.0)
[(37.0 ^ 1.0)
[(37.1 ^ 1.5)
[(41.4 ^ 5.2)
[(34.4 ^ 4.5)
[(43.3 ^ 5.4)
[(45.7 ^ 5.3)
[(44.1 ^ 4.8)
[(41.7 ^ 2.9)
[(40.6 ^ 4.3)
[(57.0 ^ 2.1)
[(42.8 ^ 2.0)
[(59.1 ^ 2.1)
[(58.8 ^ 2.1)
[(44.9 ^ 2.0)
[(37.2 ^ 1.0)
[(38.9 ^ 1.5)
[(37.2 ^ 5.2)
[(34.1 ^ 4.5)
[(41.5 ^ 5.4)
[(44.2 ^ 5.3)
[(43.2 ^ 4.8)
[(42.4 ^ 2.9)
[(45.4 ^ 4.3)
100.8 ^ 2.1
86.6 ^ 2.0
80.9 ^ 2.2
72.7 ^ 2.2
66.7 ^ 2.1
51.0 ^ 1.1
52.7 ^ 1.6
284 ^ 5
281 ^ 5
329 ^ 5
316 ^ 5
330 ^ 5
314 ^ 3
317 ^ 4
3
isoC H
3
7
7
n-C H
4
isoC H
4
9
9
sec-C H
4
9
tert-C H
4
tert-C H
4
9
9
Energies and entropies in kJ mol~1 and J K~1 mol~1 and temperature in K.
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1713

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Table 4 Recommended enthalpies of formation on radicals studied and CwH bond energies of corresponding hydrocarbons
* H¡
S¡
E
other results
f
298
298
d 298
R
/kJ mol~1
/J K~1 mol~1
/kJ mol~1
* H¡ /kJ mol~1
f
298
n-C H
100.8 ^ 2.1
86.6 ^ 2.0
80.9 ^ 2.2
72.7 ^ 2.2
66.7 ^ 2.1
51.8 ^ 1.3d
284 ^ 5
281 ^ 5
329 ^ 5
316 ^ 5
330 ^ 5
315 ^ 4d
423.3 ^ 2.1a
409.1 ^ 2.0b
425.4 ^ 2.1a
425.2 ^ 2.1a
411.2 ^ 2.0b
404.3 ^ 1.3c,d
100.2,e 95.4f
90.0,g 87.9,h 82.2,i 86.8,i 79.9,j 80.3f
84.1,k 75.7j
66.1,j 70l
67,i 69È72,e 58.2,f 64.0j
48.6,m 48.1,n 50.6o
3
7
isoC H
3
7
n-C H
4
9
isoC H
4
9
sec-C H
4
9
tert-C H
4
9
50.9,p 51.3,g 47È50,i 49.5,q 39.3,f 39.7j
a Primary CwH bond energy. b Secondary CwH bond energy. c Tertiary CwH bond energy. d Weighted arithmetic mean value. e Ref. 21. f Ref.
37. g Ref. 10. h Ref. 40. i Ref. 7, 33. j Ref. 41. k Ref. 42. l Ref. 20. m Ref. 11. n Ref. 30. o Ref. 28. p Ref. 29. q Ref. 21 (a rotational barrier of 6.3 kJ
mol~1 used).
value results in a value of 90.9 ^ 2 kJ mol~1 for the heat of
314.64 J K~1 mol~1 shown in ref. 24. Accordingly, the third-
law calculation gives, within experimental error the same
value (72.0 kJ mol~1) for the enthalpy of formation of the
isoC H radical.
formation of isopropyl radical in the third-law method.
n-C H . The Arrhenius expression for the reverse reaction
4
9
4
9
([3) was taken to be as large as that of reaction ([1). The
reverse reaction is very difficult to measure because bromine
atoms will abstract secondary hydrogen atoms much more
readily than primary hydrogen atoms. Any possible errors in
the assumed A factor will reÑect its uncertainty only in the
entropy value of the radical. The thermochemical calculations
were carried out similarly to those for n-C H and the results
sec-C H . The kinetics of Br ] n-C H was measured as a
4
9
4 10
function of temperature in ref. 10 giving k \ (2.9 ^ 0.9)
~5
] 10~10 exp[[(37.7 ^ 2.0) kJ mol~1/RT ] cm3 molecule~1
s~1. Results from thermochemical calculations are shown in
Table 3 (tabulated thermochemical functions needed for calcu-
lations are from ref. 18, 19 and 25, and from Table 2).
3
7
are shown in Table 3 (for tabulated thermochemical functions
see ref. 18, 19 and 23 and Table 2).
The calculated entropy value of 334.43 J K~1 mol~1 for
sec-C H radical was taken from a study by Chen et al.25 This
A value of 327.0 J K~1 mol~1 for the calculated entropy of
n-butyl radical can be found in ref. 23. This is nearly identical
to the experimental entropy value of 329 ^ 5 J K~1 mol~1
shown in Table 3. A similar small di†erence between these two
values is also reÑected in the third-law calculation: * H¡ (n-
4
9
entropy value corresponded to a value of 68.9 ^ 2 kJ mol~1
for the enthalpy of formation of a secondary butyl radical in a
third-law procedure.
f
298
C H ) \ 80.1 kJ mol~1.
tert-C H . The reaction between Br atom and isobutane
4
9
4
9
has been studied by two di†erent research groups using a
resonance-Ñuorescence technique with either laser photolysis
or Ñash lamp photolysis.10,11 The Arrhenius expressions di†er
only slightly. However, the thermochemical functions for tert-
C H were calculated using both kinetic data values for the
isoC H . The rate constant of the reverse reaction again
4
9
had to be assumed and was taken to be exactly 1.5 times that
of the Br ] ethane reaction. The constant was simply deter-
mined from the ratio of primary hydrogen atoms in isobutane
and ethane. Although there are nine primary hydrogen atoms
as compared with one tertiary hydrogen atom in isobutane,
the Br atom will still react about 1000 times more readily with
the tertiary hydrogen atoms, making it virtually impossible to
investigate the kinetics of reaction ([4) directly. The Arrhe-
4
9
reverse reaction. Nava et al. determined the kinetics of reac-
tion ([6) to be k \ (1.8 ^ 0.2) ] 10~10 exp[ [ (28.7 ^ 0.9)
~6
kJ mol~1/RT ] cm3 molecule~1 s~1 from 298 to 478 K.11
Seakins et al. measured reaction ([6) from 423 to 621 K
and found: k \ (1.6 ^ 0.6) ] 10~10 exp[ [ (28.8 ^ 1.5) kJ
~6
nius expression used for the reverse reaction ([4) was k
\
mol~1/RT ] cm3 molecule~1 s~1.10
~4
(3.5 ^ 1.7) ] 10~10 exp[[(53.3 ^ 2.1) kJ mol~1/RT ] cm3
molecule~1 s~1. Thermochemical functions for the radical
were then calculated using the second-law method. Results are
shown in Table 3 (tabulated thermochemical functions are
taken from ref. 18, 19 and 24, and Table 2).
Results from the thermochemical calculations are shown in
Table 3 (thermochemical functions are from ref. 14, 18 and 19,
and from Table 2). Weighted arithmetic mean values from
these calculations for thermochemical parameters at 298 K are
shown in Table 4.
The experimental entropy value found in the current study
for isoC H is nearly the same as the calculated value of
A calculated entropy value of 314.01 J K~1 mol~1 from ref.
14 was used in a third-law method. This procedure gave prac-
tically the same enthalpy of formation value, 51.0 kJ mol~1
for tert-C H using the determined reaction Gibbs energy
4
9
Table 5 Calculated * H¡ of large alkyl free radicals using group
298
additivity and experimental * H¡ values
298
4
9
f
change at either 415 or 503 K.
f
radical
* H¡
NIST23
f
298
CwH and CwC bond energies. The reaction enthalpy
change found at 298 K was used to calculate the CwH bond
1-C H (pentyl)
11
isoC H (butyl, 2-methyl)
11
3-C H (propyl, 1-ethyl)
11
2-C H (butyl, 1-methyl)
11
2-C H (CH ) (propyl, 1,2-dimethyl)
61.0 ^ 3.8
52.8 ^ 3.8
46.8 ^ 3.6
46.8 ^ 3.7
38.6 ^ 3.6
31.9 ^ 3.2
26.9 ^ 3.7
59.1
5
strength of
a corresponding hydrocarbon according to:
5
E
\ [*H¡ (R ] HBr ¢ RH ] Br) ] E
(HBr). The
5
44.8
29.7
d 298
298
d 298
5
set of free radical isomers studied here makes it possible to
determine all CwH bond strengths of small saturated hydro-
carbons (see Table 4). The enthalpies of formation data deter-
mined in the current study and elsewhere26 were also used to
calculate CwC bond strengths in saturated hydrocarbons and
to estimate bond strengths of alkyl free radicals. A compari-
son of di†erent bond strengths between molecules and free
radicals is shown in Chart 1.
4
8
3
tert-C H (propyl, 1,1-dimethyl)
11
3-C H (butyl, 1-ethyl)
13
5
6
sec-C H (CH ) (propyl,
4
7
3 2
1-ethyl-2-methyl)
18.7 ^ 3.7
tert-C H(CH ) (propyl,
2
3 4
1,1,2-trimethyl)
3.8 ^ 3.3
tert-C H (CH ) (butyl, 1,1-dimethyl)
12.0 ^ 3.3
4
7
3 2
1714
J. Chem. Soc., Faraday T rans., 1997, V ol. 93

View Article Online
procedure can now be used to calculate * H¡ values for six
f
298
pentyl and four hexyl free radicals (all * H¡ values of free
f
298
radicals needed for the calculations are taken from the current
study and from ref. 26). The calculated values are shown in
Table 5.
Discussion
Kinetics of the R + HBr (R = propyl or butyl) reaction
The kinetics of the reactions of n-C H , n-C H and isoC H
3
7
4
9
4 9
have not been measured previously. The results obtained for
the reactions of isoC H and tert-C H with HBr are in good
3
7
4 9
accord with the most recent study of Seakins et al.10 A slight
di†erence appears in the activation energies. The current
results for both reactions (1) and (4) are ca. 0.5 kJ mol~1 more
negative than the activation energies found in ref. 10. A pos-
sible reason lies in the di†erent wavelengths used to generate
the free radicals, 193 nm in ref. 10 cf. 248 nm in this study. As
was pointed out in ref. 5, the shorter photolysis wavelength
can dissociate HBr, forming reactive H and Br atoms. The
reactions of these atoms could interfere with the observed free
radical kinetics.
The kinetics of the sec-C H ] HBr reaction have been
4
9
studied previously in ref. 27. The rate constants from this
study are ca. 140% lower at 298 K but only 50% lower at 533
K than the rate constants found in the current study. Wide
error limits of reaction (5) in ref. 27 will decrease the di†erence
at 298 K to 80% but still the disparity is large. The only
obvious di†erence lies in the material of the gas-handling
system. In ref. 27 stainless-steel pipes were used cf. glass pipes
and TeÑon tubes in the current investigation and in ref. 5, 10
and 26. Stainless-steel walls are e†ective in catalysing the het-
erogeneous decomposition of HBr. Comparing the kinetics of
sec-C H with HBr with the other alkyl radical kinetics in
4
9
Fig. 2, it is unrealistic to expect that its kinetics should be
much slower. It is more likely that the accuracy of the kinetics
Chart 1 Experimental bond strengths (in kJ mol~1) of saturated
hydrocarbons and alkyl free radicals
Enthalpy of formation values from group additivities. A
method such as group additivity24 may be used to estimate
thermochemical properties of unknown molecules. Here it is
tested and used to estimate * H¡ for 10 polyatomic alkyl free
f
radicals. First, the principle of group additivity requires that
the following equation is valid:
* H¡(sec-C H ) ] * H¡(C H )
f
4
9
f
2 5
\ * H¡(isoCH H ] * H¡(n-C H )
f
3
7
f
3 7
Fig. 2 Arrhenius plot of R ] HBr reactions measured in the current
Using this equation with values found in the current study at
298 K conÐrms the validity of the current results. The same
study. The lines are two-parameter Arrhenius expressions Ðtted to the
rate constants k
.
1h6
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1715

View Article Online
of reaction (5) claimed in ref. 27 is much worse than was
thought.
Hyperconjugation e†ects can explain alkyl radical stabilities
among a family of radicals with the same number of carbon
atoms. The hyperconjugation e†ect increases with the number
of a-H atoms. In such cases, delocalization of an unpaired
electron becomes more e†ective, hence tert-C H is more
Temperature dependence of the R + HBr (R = propyl or butyl)
reaction
4
9
stable than n-C H ; their unimolecular decomposition thresh-
4
9
The rate constants of the reactions of alkyl radicals with HBr
as a function of temperature, measured in the current study,
are shown in Fig. 2 on an Arrhenius plot. All show a small
negative temperature dependence with the most negative
being for tert-C H . Such a phenomenon has been observed
old temperatures support this conclusion.
The alkyl radicals increase in stability in the order: methyl
\ ethyl \ isopropyl \ tertiary butyl. This has been explained
historically by a parallel trend of the weakening RwH bond
energies in alkanes. However, a clearly decreasing trend in
CwH bond energies in alkanes seems to be an exceptional
case. This anomalous situation is shown in Fig. 3. Further-
more, the trend is not so obvious if the set of free radicals is
expanded to include all small alkyl radicals from C to C .
4
9
by many research groups since its Ðrst observation in 1988.11
In all these time-resolved investigations negative activation
energies were determined by monitoring either the products,
using
a
laser Ñash photolysis resonance-Ñuorescence
1
4
method28,29 or a tunable IR diode laser probe,30 or the reac-
tants, using laser photolysis photoionization mass spectrom-
etry.10,11,27,31 In general, negative activation energies are
associated with a complex reaction mechanism involving two
transition states: a loose one, near the entrance channel,
associated with complex-formation and a tight one leading to
the formation of Ðnal products via intramolecular rearrange-
ment. The second transition state is lower in energy than the
Ðrst32 and the energy di†erence increases with the complexity
of the radical (see Table 1).
The radicals are arranged on the x-axis in Fig. 3 by increasing
“steric hindranceÏ in the ground state of the RwX bond,
where X is H, OH, CH , NH or Cl. The primary radicals
3
2
from ethyl to isobutyl have almost the same CwH bond
strength in alkanes. A very similar e†ect can be seen in larger
alkanes where X is a methyl group. Contrary to the more or
less decreasing RwX bond strength in alkanes from methane
to isobutane the RwX bond strength in alcohols increases
from methyl to tert-butyl. In addition, the RwX bond energy
in amines and alkyl chlorides seems not to be at all a†ected by
di†erent alkyl groups. More likely the RwX bond strength is
inÑuenced by mutual repulsion of the nucleus, the bonding
electrons, bond length and in particular, by the polarity of the
RwX bond. The RwX bond energy does not necessarily
reveal anything about the stability of R.
Thermal stability of the radical
The degree of complexity of radicals with the same number of
carbon atoms also seems to control the thermal stability of
the radical. For the butyl radicals, n-butyl and isobutyl start
to decompose unimolecularly at 550 and 570 K, whereas sec-
butyl withstands temperatures up to 600 K and tert-butyl up
to 730 K, at pressures of a few torr. This correlates with the
bond energy of the weakest bond of butyl radicals shown in
Chart 1. A similar conclusion results from comparing the
strength of the weakest bond of propyl radicals. Not only
radical complexity, but also the size of the radical, a†ects the
thermal stability of the species. Small alkyl radicals such as
ethyl will survive even higher temperatures than tert-C H or
Thermodynamic properties
n-C H radical. The enthalpy of formation of n-C H
3
7
3 7
radical was found to be 100.8 ^ 2.1 kJ mol~1 in the current
study. This can be compared with the kinetic study of
4
9
isoC H and, if the a-carbon of this radical is substituted by
3
7
chlorine atom(s), its thermal stability is even higher.5
Reactivity explanation
Radical complexity appears to control the reactivity of the
species. Alkyl radical reactivity or nucleophilicity (although
this tendency is relatively small compared with the nucleo-
philicity of a negative ion) increases in parallel with its com-
plexity in the order: CH \ primary \ secondary \ tertiary
3
(see also the results in ref. 26 for CH , C H and n-C H ). A
3
2
5
3 7
similar trend can be found in the reactions of alkyl radicals
with HI,33 O ,34 and O .35 It cannot be explained by steric
2
3
e†ects alone. Comparing the kinetics of the tert-C H radical
4
9
with that of n-C H radical in Fig. 2 one would expect a
reverse order in reactivity if only steric e†ects were involved.
3
7
The radical centre in tert-C H is shielded by three methyl
4
9
groups, and yet the rate constant, k , is more than twice k at
6
1
298 K (the comparison between tert-C H and CH is even
4
9
3
more striking). It is more likely that intramolecular electronic
e†ects such as inductive and hyperconjugation36 e†ects deter-
mine p-radical reactivity,5 the former being expected to be
stronger than the latter. An increasing number of alkyl sub-
stituents directly connected to the a-carbon increases, by a
positive inductive e†ect, the electron density at the radical
centre, thus making the alkyl radical more nucleophilic. If the
substituent is located far from the centre carbon, one could
expect a smaller electron repulsion e†ect, as can be seen by
comparing the rate constants of primary and secondary
propyl radicals in their reactions with HBr.
Fig. 3 RwX bond energies at 298 K in alkanes, alkohols, amines
and alkyl chlorides. * H¡ values for H, Cl, OH and NH radicals,
f
298
2
X, and molecules, RX, are taken from ref. 18 and 20. * H¡ of alkyl
f
298
free radicals are from ref. 38 and 46 (methyl), 26 (ethyl) and the
current study (propyl and butyl).
1716
J. Chem. Soc., Faraday T rans., 1997, V ol. 93

View Article Online
Tsang.21 An average value of 100.2 ^ 4.2 kJ mol~1 can be
calculated from the following dissociationÈrecombination
equilibria from eight di†erent investigations shown in ref. 21:
Holmes et al. used a monoenergetic electron impact method
to determine an average value of 79.9 kJ mol~1 for the heat of
formation of isoC H .41 They measured the appearance
3
7
energy for ionic reactions such as:
n-C H ] CH ] C H
3
7
3
2 4
isoC H [ X ] e~ ] 2e~ ] isoC H ] X`
n-C H ] C H ] n-C H
3
7
3 7
6
12 3 7
3
5
Here X \ CH NH , CH(CH )OH or C(CH ) OH. From
The calculations are based on a third-law method, where a
calculated value of 289.41 J K~1 mol~1 was used for the
entropy of the radical.
2
2
3
3 2
three di†erent investigations they obtained values of 79.1, 77.0
and 83.7 kJ mol~1. The enthalpies of formation of counter-
ions, X`, formed are also needed for thermochemical calcu-
lations. These values were determined from certain
appearance energy measurements where accuracy between dif-
ferent experiments has been typically 4.2 kJ mol~1. Another
0.4 kJ mol~1 must be added to their value for the accuracy of
the * H¡ of the precursor molecules used in the determi-
nations for the heat of formation values of ions. The Ðnal
error limits, estimated on the basis of the range of determined
* H¡ values of isoC H 41 and the inaccuracies mentioned
above, are ^4.2 kJ mol~1. The enthalpy of formation value
determined by Holmes et al. still remains lower than that
obtained in the current study. However, if the error limits
from both studies are taken into account, the values may be
considered to be in satisfactory agreement.
Another comparison can be made with the radical bu†er
investigation of Castelhano and Griller, where the exchange
reactions between radicals and alkyl iodides were studied in
solution by EPR.37 They determined * H¡ (n-C H ) \ 95.4
f
300
3 7
^ 4.2 kJ mol~1, using enthalpy of formation of the methyl
radical, 143.9 kJ mol~1, as a standard. If the most recent
determination38 of * H¡ (CH ) is used then the heat of for-
f
298
f
298
3
mation of n-C H would be increased by 2.1 kJ mol~1 to a
value of 97.5 kJ mol~1 in good accord with our result.
3
7
f
298
3 7
isoC H radical. The enthalpy of formation of isoC H
3
7
3 7
found in this study is 86.6 ^ 2.0 kJ mol~1 cf. 90.0 ^ 1.7 kJ
mol~1 reported in ref. 10. Both reaction directions were mea-
sured in ref. 10 under time-resolved conditions using either a
tubular Ñow reactor coupled to a mass spectrometer or the
Ñash photolysis resonance-Ñuorescence technique. The
kinetics of reaction (2) used for the thermochemical calcu-
lations of isoC H radical in ref. 10 is essentially the same as
A radical bu†er investigation of Castelhano and Griller
yielded * H¡ (isoC H ) \ 80.3 ^ 4.2 kJ mol~1.37 However,
f
298
3 7
a value of 84.7 ^ 4.2 kJ mol~1 can be calculated from their
experiments if the more recent entropy value22 of isoC H
3
7
3
7
that determined in the current study but this is not the case
for reaction ([2). The Arrhenius expression of the Br
] C H reaction used by Seakins et al. is not the one they
radical and the enthalpy of formation26 of ethyl radical are
used.
3
8
n-C H radical. The value for * H¡ (n-C H ) determined
determined, instead they used the old ratio of rate constants of
k(isobutane ] Br)/k(propane ] Br) determined by Fettis et al.
in 1960,39 combined with the activation energy of the reaction
of Br ] isoC H measured in ref. 10. However, the current
4
9
f
298
4 9
in this study is 80.9 ^ 2.2 kJ mol~1. Knyazev et al. have
studied unimolecular decomposition of n-C H under time-
4
9
resolved experimental conditions.42 The experimental
approach, combined with ab initio calculations for the struc-
tures of all the reaction species and a master equation model-
ling of the reaction fall-o† behaviour, yielded an energy
barrier for both reaction directions. These energy barriers
were then used to determine the enthalpy of reaction at room
temperature. * H¡ (n-C H ) was then determined to be 84.1
kJ mol~1, using a second-law method.42 The uncertainty in
this value was estimated to be ^4.2 kJ mol~1, leading to
good agreement with the current result.
4
10
study uses precisely the Arrhenius expression of reaction ([2)
measured by Seakins et al. with the measured Arrhenius
expression of reaction (2) to calculate the thermochemical
functions of isoC H radical. This is the main reason for the
3
7
di†erence in the values of * H¡ . There seems not to be any
f
298
unexpected systematic error in the resonance-Ñuorescence
measurements; the Arrhenius expression determined in ref. 10
for the reaction of Br ] isoC H is in excellent agreement
f
298
4 9
4
10
with the study of Nava in ref. 11. Moreover, a value of
An appearance energy measurement by Holmes et al. pro-
duced an average value of 75.7 ^ 4.2 kJ mol~1,41 again in
satisfactory agreement, within error limits.
86.0 ^ 2.2 kJ mol~1 can be calculated for * H¡ (isoC H ) if
f
298
3 7
the kinetics measured in ref. 10 for reactions (2) and ([2) are
used.
Tschuikow-Roux and Chen re-evaluated TsangÏs study of
the third-law method for the dissociationÈrecombination equi-
libria of isoC H .40 Tsang treated21 the two methyl tops of
isoC H radical. Experimental thermodynamic studies of
4
9
isoC H seem quite rare. The study of Holmes et al. using
4
9
electron impact measurements yielded an average value of
66.1 ^ 4.2 kJ mol~1,41 clearly below the value of 72.7 ^ 2.2 kJ
mol~1 found in the current study. On the other hand Tsang
determined the enthalpy of formation of isoC H to be ca. 70
3
7
the isopropyl radical as free rotors, whereas Tschuikow-Roux
and Chen incorporated a computed barrier with a value of ca.
1 kJ mol~1 for the internal rotation of CH groups in
3
4
9
isoC H . This partly hindered rotation reduces the calculated
kJ mol~1 using shock-tube experiments.20
3
7
entropy value of the radical which, in the third-law procedure,
translates to a lower * H¡ value. Tschuikow-Roux and Chen
sec-C H radical. sec-C H is a more stable isomer than
f
4
9
4 9
obtained a value of 87.9 kJ mol~1 which is, within the esti-
n-C H and has been the subject of many kinetic and ther-
4
9
mated error limits, in very good agreement with the current
value.
modynamic investigations. Here * H¡(sec-C H ) was found to
f
4 9
be 66.7 ^ 2.1 kJ mol~1. Practically the same value, with larger
error limits, was determined from the sec-C H ] HBr ¢ n-
The kinetic study of the reaction of isoC H radical with HI
3
7
4
9
as a function of temperature used with the Arrhenius expres-
sions of the two iodination studies for the reverse reaction,
I ] C H , yields values of 82.2(^8.0) and 86.8(^4.2) kJ
C H ] Br equilibria in ref. 27, also by a second-law method.
4
10
As was pointed out earlier, the kinetics of the sec-C H
4
9
] HBr reaction in ref. 27 turned out to be less accurate than
was thought. This was also true for the reverse reaction ([5).
Fortuitously, the errors cancelled out leading to an accurate
3
8
mol~1 from the second-law procedure for isoC H .7,33 The
3
7
determinations are in good agreement with the value of 86.6
kJ mol~1 found in the current study after taking into con-
sideration the large error limits in the isoC H ] HI ¢ C H
] I studies. The kinetics of I atoms reacting with propane
have a very strong temperature dependence which makes it
difficult to measure the activation energies of I atom reactions
precisely.
value for * H¡
.
f
298
A second-law method was also used to give a value of
67 ^ 9 kJ mol~1 from a kinetic study of the equilibrium of
sec-C H ] HI ¢ n-C H ] I.33 The large error limits were
3
7
3 8
4
9
4 10
caused mainly by the inaccuracy of the measured temperature
dependency for the reverse reaction.
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
1717

View Article Online
TsangÏs studies gave values from 68.6 to 72.0 kJ mol~1 at
300 K.21 The experimental data which he used in a third-law
procedure are from the dissociationÈrecombination equilibria
of sec-C H . The entropy value of 336.69 J K~1 mol~1 used
ionization potential of the tert-C H radical. The value of
4
9
6.70 ^ 0.03 eV has been determined from the band onset of
the tert-C H radical ionization potential spectrum.44 This
4
9
yields * H¡ \ 47.3 ^ 3 kJ mol~1, when the enthalpy of for-
4
9
f
298
by Tsang is 2.26 J K~1 mol~1 larger than the most recently
calculated value by Chen et al.25
mation for the cation is taken from ref. 20.
In general, for large radicals the ionization process from a
free radical to a cation may involve a large change in molecu-
lar geometry. This is especially true for tetrahedral or octa-
hedral molecules. For such molecules the (0 ^ 0) transition
could be difficult to observe or distinguish from a hot band.
Other phenomena which may occur during appearance energy
measurements of polyatomic species include fragmentation
and autoionization.45
A radical bu†er method involving ethyl and sec-butyl rad-
icals yielded * H¡ \ 58.2 ^ 4.2 kJ mol~1.37 Such a low
f
298
value can easily be explained by comparing the entropy and
* H¡ values used in this study with the most recently deter-
f
mined values.25,26 A recalculation of the data from ref. 37
with these new thermodynamic values gives * H¡ (sec-
f
298
C H ) \ 64.1 ^ 4.2 kJ mol~1.
4
9
The electron impact study of Holmes et al. yielded an
average value of 64.0 ^ 4.2 kJ mol~1.41
Bond strengths in free radicals and molecules. Chart 1 com-
pares the bond strengths in alkyl radicals and in saturated
hydrocarbons. For the bond strength calculations the enth-
alpies of formation of molecules are taken from ref. 20 and
those of methylene and the H atom from ref. 18, respectively.
The * H¡ values of free radicals are taken from the current
study, ref. 26 (ethyl) or a mean value of 146.0 kJ mol~1 for
methyl from ref. 38 and 46. The value in parentheses is calcu-
lated by assuming that the product forming in a homolytic
bond Ðssion is a cyclo compound.
tert-C H radical. The tert-C H radical has been the most
4
9
4 9
intensively studied by time-resolved techniques. The study of
Russell et al. gave the Ðrst proof of “higherÏ enthalpy of forma-
tion values in contrast to the “lowerÏ ones.11 They found a
value of 48.6 ^ 1.7 kJ mol~1 using photoionization mass spec-
trometry and a second-law method. Later, Richards et al.
determined * H¡ (tert-C H ) to be 48.1 ^ 3.3 kJ mol~1,
f
298
f
298
4 9
using a tunable IR diode laser technique.30 Nicovich et al.
obtained a value of 50.6 ^ 3.3 kJ mol~1 using a resonance-
Ñuorescence technique.28 The same technique was used in the
study of Seakins and Pilling, yielding a value of 50.9 ^ 3.5 kJ
mol~1 from a third-law method.29 Later Seakins et al. studied
both reaction directions of the tert-C H ] HBr ¢ isoC H
The weakest bond in saturated hydrocarbons is the CwC
bond. For n-butane the weakest bond is found as a non-
terminal CwC bond. CwH bond strengths in saturated
hydrocarbons increase as: tertiary \ secondary \ primary \
H-CH . Such a trend is also very reasonable in view of the
4
9
4 10
3
] Br equilibrium by time-resolved techniques and concluded
that * H¡ (tert-C H ) was 51.3 ^ 1.8 kJ mol~1 using both a
activation barriers of Br atom abstracting H atom from satu-
rated hydrocarbons.10 The reaction is fastest and the barrier is
smallest, 29 kJ mol~1, for abstracting a tertiary H atom, and
the reaction is slowest and the barrier is highest, 76 kJ mol~1,
for abstracting the H atom on methane.39 However, such a
trend is not as obvious in the case of alkyl radicals. Here, the
weakest bond is the CwC bond which is not connected
directly to the radical centre, whereas a terminal CwC bond
at the radical site seems to be the strongest. This is well
demonstrated in the case of primary radicals. It can also be
seen that in alkyl radicals which have only one CwC bond
type, the weakest bond is the CwH bond. Finally, a corre-
lation between the weakest bond of alkyl radicals and the
thermal stability of the radical can be seen. This is well
demonstrated among the radicals which contain the same
number of carbons. As is expected from C radicals, tert-C H
f
298
4 9
second-law and a third-law method.10 Furthermore, a photo-
ionization mass spectrometric study of the three tert-C H
4
9
] HI ¢ isoC H ] I equilibria yielded 47.2 ^ 2.9, 48 ^ 5
4
10
and 49.8 ^ 2.5 kJ mol~1 by a third-law method.33 The
current result, 51.8 ^ 1.3 kJ mol~1, seems to conÐrm the
upper limit of the previously determined values to be the most
likely one.
Tsang has published an analysis of kinetic studies of
dissociationÈrecombination equilibria involving tert-C H
4
9
radical.21 He calculated * H¡ (tert-C H ) values from 42.3
f
298
4 9
to 50.2 kJ mol~1 assuming a rotational barrier of 10 kJ mol~1
for the internal methyl group rotation and values from 47 to
55.2 kJ mol~1 if the methyl groups are free for rotation. A
barrier of 6.3 kJ mol~1 has been used in a study of
unimolecular decomposition by Knyazev et al.14 If such a
barrier height is accepted then TsangÏs assessment will be ca.
49.5 ^ 3 kJ mol~1.
4
4 9
has the highest thermal stability, since its weakest bond is
stronger than the bonds of the other isomers.
The study of Castelhano and Griller produced a value of
39.3 ^ 4.2 kJ mol~1.37 The radical bu†er method can be used
to measure enthalpy of formation values which are related to
a certain standard value. However, the estimated * H¡
Enthalpy of formation of C and C radicals
5
6
Group additivity was used to calculate * H¡ values for six
f
298
f
298
(isoC H ) used by Castelhano and Griller was only 80.3 kJ
pentyl and four hexyl free radicals. The values obtained are
shown in Table 4. Also shown are three enthalpy of formation
values taken from the NIST database.23
3
7
mol~1, based on an old iodination equilibrium study,37 and
the entropy value of tert-C H radical which they used in
4
9
their calculation was 8.61 J K~1 mol~1 lower than the most
recent calculated value in ref. 14. A recalculated value of 49.9 J
K~1 mol~1 can be obtained if the * H¡ (isoC H ) from the
Determinations of experimental enthalpy of formation for
large alkyl free radicals are exceptional. A Ðnal product
analysis by Seres yielded the enthalpy of formation of the
propyl, 1,1,2-trimethyl radical to be [1.6 ^ 8 kJ mol~1.47
This value is in good agreement with the current value of
3.8 ^ 3.3 kJ mol~1.
f
298
3 7
current study and S¡ (tert-C H ) from ref. 14 are used.
298
4 9
Holmes et al. used an electron impact method to measure
appearance energies from several precursors to generate the
tert-C H radical and an ion. Their value of 39.7 ^ 4.2 kJ
mol~1 41 is much lower than the current value. Appearance
energy measurements seem to yield lower appearance poten-
tials values for the cations formed compared with photoion-
ization measurements.43 The di†erence may be as large as 13.5
kJ mol~1. It is interesting to compare the low value obtained
in their study with that from a photoelectron spectroscopic
study. This technique has been used to measure an adiabatic
Stocker and Pilling have also used group additivity to esti-
mate the enthalpy of formation of the butyl, 1,1-dimethyl
radical to be 12.7 kJ mol~1.48 A value of 12.0 ^ 3.3 kJ mol~1
was found in the current study.
As is demonstrated in Table 5 the enthalpy of formation of
the radical decreases as: primary [ secondary [ tertiary. This
trend is the same as found for the butyl radical isomers. The
enthalpies of formation of both unbranched secondary pentyl
4
9
1718
J. Chem. Soc., Faraday T rans., 1997, V ol. 93

View Article Online
18 M. W. Chase Jr., C. A. Davies, J. R. Downey Jr., D. J. Frurip,
R. A. McDonald and A. N. Syverud, J. Phys. Chem. Ref. Data,
1985, 14, Suppl. No. 1.
19 A. Burcat, in Combustion Chemistry, ed. W. C. Gardiner Jr., New
York, 1984, ch. 8.
radicals (3-C H and 2-C H ) seem to be equally large, indi-
cating that all secondary CwH bonds in n-pentane have the
same strength.
5
11
5 11
This research was supported by the Division of Chemical Sci-
ences, Office of Basic Energy sciences, office of Energy
Research, U.S. Department of Energy under Grant DE-FG02-
94ER1446 and by the Finnish Combustion Research Program
LIEKKI.
20 S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D.
Levin and W. G. Mallard, J. Phys. Chem. Ref. Data, 1988, 17,
Supplement No. 1.
21 W. Tsang, J. Am. Chem. Soc., 1985, 107, 2872.
22 Y. Chen, A. Rauk and E. Tschuikow-Roux, J. Phys. Chem., 1990,
94, 2775.
23 S. G. Lias, J. F. Liebman, R. D. Levin, S. A. KafaÐ and S. E.
Stein, ST RUCT URES AND PROPERT IES, NIST database 25,
1994.
Registry No. n-C H , 2143-61-5; isoC H , 2025-55-0; n-
3
7
3 7
C H , 2492-36-6; isoC H , 4630-45-9; sec-C H , 2348-55-2;
4
9
4
9
4 9
tert-C H , 1605-73-8; 1-C H , 2672-01-7; isoC H , 7419-
23443-59-6; 2-C H
C H (CH ), 2679-30-3; tert-C H
19414-29-0; sec-C H (CH ) , 18971-87-4; tert-C H(CH ) ,
24436-98-4; tert-C H (CH ) , 21058-26-4; HBr, 10035-10-6;
4
9
5
11
5
11
24 S. W. Benson, T hermochemical Kinetics, Wiley, New York, 2nd
85-4; 3-C H
,
,
2492-34-4; 2-
5
11
5
11
edn., 1976.
,
4348-35-0; 3-C H
,
4
8
3
5
11
6
13
3 4
25 Y. Chen, A. Rauk and E. Tschuikow-Roux, J. Phys. Chem., 1992,
96, 6854.
26 J. A. Seetula and I. R. Slagle, 13th Int. Symp. On Gas Kinetics,
University College Dublin, Dublin, 1994, p. 148.
27 J. A. Seetula and D. Gutman, J. Phys. Chem., 1990, 94, 7529.
28 J. M. Nicovich, C. A. van Dijk, K. D. Kreutter and P. H. Wine, J.
Phys. Chem., 1991, 95, 9890.
29 P. W. Seakins and M. J. Pilling, J. Phys. Chem., 1991, 95, 9874.
30 P. D. Richards, R. J. Ryther and E. Weitz, J. Phys. Chem., 1990,
94, 3663.
31 J. J. Russell, J. A. Seetula and D. Gutman, J. Am. Chem. Soc.,
1988, 110, 3092.
32 Y. Chen and E. Tschuikow-Roux, J. Phys. Chem., 1993, 97, 3742.
33 J. A. Seetula, J. J. Russell and D. Gutman, J. Am. Chem. Soc.,
1990, 112, 1347.
34 R. P. Ruiz and K. D. Bayes, J. Phys. Chem., 1984, 88, 2592.
35 R. Paltenghi, E. A. Ogryzlo and K. D. Bayes, J. Phys. Chem.,
1984, 88, 2595.
36 M. C. R. Symons, T etrahedron, 1962, 18, 333.
37 A. L. Castelhano and D. Griller, J. Am. Chem. Soc., 1982, 104,
3655.
4
4
7
7
3 2
3 2
2
Br, 10097-32-2.
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