Kinetics and thermochemistry of the C3H5 + HBr ? C3H6 + Br equilibrium

Article abstract of DOI:10.1039/a905347f

As an accurate heat of formation of the allyl radical is very important for modeling high-temperature combustion, the kinetics of the reaction of the allyl radical with HBr were studied in a tubular reactor coupled to a photoionization MS. The decay of the allyl radical was monitored as a function of HBr concentration under pseudo-first-order conditions. The reaction was studied at 400-523 K and the determined rate constants determined were fitted to an Arrhenius expression, i.e., k = (4.6 ± 3.2) x 10^-13 exp(-(12.6 ± 4.1) kJ/mol/RT). The obtained rate constants were combined with those for the reverse reaction taken from the literature to obtain the enthalpy of formation of the allyl radical as 166.1 ± 4.3 kJ/mol at 298 K, which agreed well with previous measurements. The entropy was 248 ± 15 J/K/mol. The allylic C-H bond energy of propylene derived from the enthalpy of reaction value was 363.9 ± 4.3 kJ/mol, which led to a value of 59.4 ± 4.9 kJ/mol for the resonance stabilization energy of the allyl radical. Ab initio calculations showed that the allylic bond of propene is the weakest bond of the molecule.

Full text of DOI:10.1039/a905347f

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Kinetics and thermochemistry of the C H + HBr ½ C H + Br
3 5
3 6
equilibrium
Jorma A. Seetula
L aboratory of Physical Chemistry, P.O. Box 55 (A.I. V irtasen aukio 1), FIN-00014 University of
Helsinki, Helsinki, Finland
Received 2nd July 1999, Accepted 25th August 1999
The kinetics of the reaction of the allyl radical with HBr has been investigated in a heatable tubular reactor
coupled to a photoionization mass spectrometer. The allyl radical, R, was produced homogeneously in the
reactor by a pulsed 248 nm exciplex laser photolysis of allyl bromide. The decay of R was monitored as a
function of HBr concentration under pseudo-Ðrst-order conditions to determine the rate constants as a
function of temperature. The reaction was studied at temperatures from 400 to 523 K and in this temperature
range the rate constants determined were Ðtted to an Arrhenius expression (error limits stated as
1p ] StudentÏs t values, units in cm3 molecule~1 s~1): k \ (4.6 ^ 3.2) ] 10~13 exp[[(12.6 ^ 4.1) kJ
mol~1/RT ]. The kinetic information was combined with the kinetics of the Br ] propene reaction taken from
the literature to calculate thermodynamic values for the allyl radical at 298 K using a second-law procedure.
The entropy value is 248 ^ 15 J K~1 mol~1 and the enthalpy of formation is 166.1 ^ 4.3 kJ mol~1 in good
agreement with previous measurements. The allylic CÈH bond energy of propene derived from the enthalpy of
reaction value is 363.9 ^ 4.3 kJ mol~1, which leads to a value of 59.4 ^ 4.9 kJ mol~1 for the resonance
stabilization energy of the allyl radical. The resonance stabilization energy calculated by ab initio methods is
59.9 kJ mol~1.
mental apparatus used has been previously described.9,10
Introduction
Pulsed, unfocused 248-nm radiation from a Lambda Physik
EMG 201 MSC exciplex laser operated at 5 Hz was colli-
mated and then directed along the axis of a heatable Pyrex
reactor. The 10.5 mm id reactor was coated with TeÑon to
reduce heterogeneous reactions. Gas Ñowing through the tube
at 5 m s~1 was completely replaced between laser pulses. The
Ñowing gas contained the radical precursor allyl bromide
(\0.1%), HBr in varying concentrations and the carrier gas,
He, in large excess ([93%). Gas 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 it entered the vacuum chamber containing the quadru-
pole mass Ðlter. As the gas beam traversed the ion source, a
portion was photoionized by an atomic resonance lamp radi-
ation and then mass selected. Temporal ion signal proÐles
were recorded from 10È30 ms before each laser pulse and
16È25 ms after the laser pulse with a multichannel scalar.
Data from 3000 to 13 000 repetitions of the experiments were
accumulated before the data were analyzed by a non-linear
least-squares analysis program.
The allyl radical can readily be detected in pyrolysis and com-
bustion processes, which indicates its signiÐcant stability
against carbon centered alkyl radicals.1,2 A possible reason for
this is that the allyl radical is a resonance stabilized free
radical and it has low reactivity with molecules such as Br
2
and Cl compared to alkyl radicals.3 However, the
2
allyl ] O(3P) atom reaction is very fast.4 This implies that
allyl radical reactions with open shell compounds are impor-
tant sinks for this radical in combustion reactions. For model-
ling of high temperature combustion processes, it is very
important to know the accurate heat of formation value of the
allyl radical. This is necessary in order to estimate the kinetics
of the allyl radical reactions with other compounds. Further-
more, conjugation of a CÈC double bond is an important
factor for changing the chemical nature of molecules. In order
to achieve this, it is necessary to have the accurate resonance
stabilization energy of the allyl radical for calculating bond
strengths of allyl-weakened bonds on complex hydrocarbons.
The current study presents a time-resolved experimental
kinetic investigation of the allyl radical with HBr. The reac-
tion has not previously been studied. The approach is the
same as that used for other radical ] HBr studies.5 The study
was carried out to investigate the enthalpy of formation and
the resonance stabilization energy of the allyl radical. The
heat of formation and the resonance stabilization energy of
the allyl radical have been investigated previously.6h8 Here an
ab initio approach was also used in the resonance stabilization
energy calculations for comparison.
The only photolysis wavelength used to generate radicals
was 248 nm. At this wavelength it is practically impossible to
photodissociate the reactant, HBr, to a measurable extent.11
Kinetic results
The chemical kinetics of the following metathetical reaction
was studied in a Ñow reactor:
C H ] HBr ] C H ] Br
(1)
3
5
3 6
The kinetics determined was combined with the kinetics of the
reverse reaction, ([1), in order to calculate the enthalpy of
formation and the experimental entropy value of the allyl
radical studied. The results obtained from the experiments to
measure reaction (1) are given in Table 1.
Experimental and kinetics
Description of experiments
The rate constants of the reaction of C H with HBr were
3
5
measured as a function of the temperature range. The experi-
Phys. Chem. Chem. Phys., 1999, 1, 4727È4731
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4727

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Table 1 Measurements of the rate constant of the C H ] HBr ] C H ] Br reaction
3
6
3 6
T a/K
[He]/1016 cm~3
[HBr]/1015 cm~3
k /s~1
k
b/10~14 cm3 s~1
2
1
400
444
500
523
9.84
9.85
5.87
5.89
1.47È3.48
1.21È2.99
0.54È3.10
1.09È4.54
7.9
3.9
9.6
0.98 ^ 0.25
1.64 ^ 0.36
2.14 ^ 0.18
2.51 ^ 0.10
10.5
k \ (4.6 ^ 3.2) É 10~13 exp [ [ (12.6 ^ 4.1) kJ mol~1/RT ]cm3 molecule~1 s~1
1
a Temperature uncertainty: ^ 3 K. b TeÑon used for wall coating, errors are 1p ] StudentÏs t and based on statistical uncertainties.
Photogeneration of the allyl radical
The allyl radical was photogenerated by photodissociating
allylbromide at 248 nm. Up to 7 quartz plates were used to
diminish laser inÑuence to a very low level. This ensured that
the photon Ñux did not generate Br atoms from HBr to any
measurable extent even though the concentration of HBr was
high in some experiments. The allyl radical was formed from
the precursor by the CÈBr bond rupture. After breaking the
bond, the native 3-propenyl radical formed isomerized to the
resonance stabilized allyl radical.
Data analysis
Experiments were conducted under pseudo-Ðrst-order condi-
tions where HBr existed in great excess compared with the
concentration of radicals. Only the following two reactions
had signiÐcant rates under these conditions:
C H ] HBr ] C H ] Br
3
5
3 6
C H ] heterogeneous loss on the wall
(2)
3
5
In all sets of experiments the initial radical concentration was
adjusted to be so low that radicalÈradical or radicalÈatom
reactions had negligible rates compared to reactions (1) and
(2). This was ensured by comparing the measured Ðrst-order
wall loss decays, k , of the radical with that produced (in the
2
absence of HBr) at di†erent conditions where precursor con-
Fig. 1 Plot of Ðrst-order decay constant k@ vs. [HBr] for one set of
experiments conducted to measure the C H ] HBr rate constant, k ,
centration was held steady but the laser radiation was attenu-
ated by a factor of 3 using quartz and vycor plates (the radical
concentration was changed by the same factor). The decays
from these di†erent experiments were equal with respect to
their statistical error limits.
3
5
1
at 523 K. Inset in the lower right corner is the ion signal proÐle of
C H ` recorded during one of the experiments shown as a solid circle
3
5
([HBr] \ 2.78 ] 1015 molecule~1 cm~3) in the linear regression Ðt.
The line through the data in the insert is an exponential function
Ðtted by a nonlinear least-squares procedure. The Ðrst-order decay
constant for C H ` in the displayed ion signal proÐle is (80.3 ^ 2.0)
Rate constants for reaction (1) were obtained from the
slopes of plots of the exponential radical decay constant k@ vs.
[HBr] Mfrom [R`] \ [R`] exp([k@t)N, where k@ \ k [HBr]
3
5
s~1.
t
0
1
] k . A representative ion signal decay proÐle and a decay
2
constant plot from one set of experiments to measure k are
1
shown in Fig. 1. The results obtained from all the experiments
to measure reaction (1) are given in Table 1.
Accuracy of measurements
The error limits stated in Arrhenius expressions are
1p ] StudentÏs t and they are based only on the statistical
uncertainties. The reactions were studied under pseudo-Ðrst-
order conditions when it was needed to know accurately only
the concentration of HBr. This was measured before and after
the kinetic experiment and the mean value was used for the
rate constant calculation.5 During some experiments a very
large amount of HBr had to be used to obtain large k@ decay
constants. In these conditions [HBr]/[He] was up to 0.07.
However, the gas viscosity of HBr was only 5È15% higher
than the viscosity of the carrier gas He in the temperature
range used in the current study. This caused about 1% addi-
tional error to the large [HBr] (see Fig. 1) when pressure drop
along the reactor is considered. The other errors, such as mea-
sured temperature and gas Ñow rates, were always \ 1%. All
these errors are very small and were thus ignored. The sta-
tistical uncertainties of the decay constants were taken into
Fig. 2 Arrhenius plot of C H ] HBr reactions measured in the
3
5
current study. The line is an Arrhenius expression Ðtted to the rate
constants k . Also shown is the kinetics of Br ] C H reaction taken
1
3 6
from ref. 12.
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Table 2 Heats of formation and entropies used in thermochemical
obtained from the reaction enthalpy and entropy changes at
298 K and the known heats of formation and entropies of the
other reaction species (see Table 2). The values obtained are as
follows:
calculations
Species
* H¡ /kJ mol~1
298
S¡ /J K~1 mol~1
f
298
HBra
Bra
[36.44
111.86
20.2
198.70
175.02
267.1
* H¡ \ 166.1 ^ 4.3 kJ mol~1
f
298
C H b,c
S¡ \ 248 ^ 15 J K~1 mol~1
3
6
298
a Data taken from ref. 13. b Data taken from ref. 15. c Data taken
The enthalpy of formation can be transplanted to the allylic
CÈH bond energy of propene to have a value of 363.9 ^ 4.3 kJ
mol~1.
from ref. 14.
account in data analysis and their e†ects on the rate constants
are shown in Fig. 2. The Arrhenius expression of the reaction
was obtained by weighting the measured rate constants with
reciprocals of their variances for Ðtting procedure.
Computational study
Computation details
Ab initio molecular orbital calculations were carried out with
the GAUSSIAN 94 package of programs.16 All calculations
were carried out on an Indigo2 IMPACT workstation.
Geometries of all open and closed shell species were fully opti-
Reagent sources and puriÐcation procedures
Allylbromide, 99%, and HBr, 99%, were obtained from
Aldrich and helium, 99.995%, from Matheson.
mized using
a second-order MÔller-Plesset perturbation
The carrier gas, He, was used as provided. Allyl bromide
was degassed by using freeze-pump-thaw cycles. HBr was col-
lected to a Ñow trap kept at 77 K and was repeatedly distilled
to remove any traces of bromine. HBr was stored in a dark
Pyrex bulb. The gas handling system, which was used to set
up a known HBr Ñow to the reactor gas inlet, was made from
Pyrex glass and TeÑon tubes.
theory with the frozen core approximation and 6-31G(d,p)
basis set.17 For the free radicals of interest, expectation values,
S2, varied in the range of 0.7911 to 0.9591 depending on the
type of the radical. The S2 value was highest for the resonance
stabilized allyl radical. All optimized structures were shown to
be at the local minimums of the C H potential energy surface
3
5
by frequency calculations at the same level of theory as that
for the optimizations. The zero-point energies of the optimized
compounds for bond energy studies were obtained from fre-
quency calculations. The zero-point energies were scaled by a
factor of 0.9676 as it has been suggested in literature.17
Photoionization energies used
Reactants and products of the photolysis as well as the pre-
cursors were photoionized using atomic resonance radiation.
A chlorine lamp (8.9È9.1 eV) was used to detect C H and an
The energies of the species were calculated at the
MP4(SDTQ)/6-311G(d,p) level of theory. The bond energies
of propene (RX) were calculated from a homolytic bond disso-
3
5
argon lamp (11.6, 11.8 eV) to detect HBr, Br and Br.
2
ciation reaction: RX ] R ] X, where X \ H or open shell C
Thermochemical calculations
1
compound and R can be either a radical or a diradical. The
Both the enthalpy and entropy changes of the reactions were
obtained using a second-law method. This procedure is the
same as used previously.5 BrieÑy, at Ðrst reaction free energy,
enthalpy and entropy were calculated at the mean tem-
perature on a 1/T scale of both reaction directions. Reaction
enthalpy change and entropy value were then recalculated at
room temperature using heat capacity data. Finally, the enth-
alpy of formation and entropy of the free radical of interest
were obtained from the * H¡ and * S¡ values at 298 K.
calculated bond dissociation energies were temperature cor-
rected simply by 4RT where only translational and rotational
contributions have been considered.18
Optimized geometries of free radicals
Energies and symmetries of the free radicals and the other
species are given in Table 3. After photodissociation of the
allylbromide or an H atom abstraction reaction of the reverse
reaction, the formed native 3-propenyl free radical (i.e. perpen-
dicular allyl) will isomerize to the allyl radical, which is a
hybrid of the two resonance structures of 3-propenyl radical.
The allyl radical is by 60 kJ mol~1 lower in energy at
MP4(SDTQ)/6-311G(d,p) level of theory than the 3-propenyl
radical. This di†erence is known as a resonance stabilization
energy or a delocalization energy of the allyl radical.
r
r
The Arrhenius expression for the Br ] C H ] C H
3
6
3 5
] HBr reaction, k \ (8.2 ^ 4.5) ] 10~13 exp[[(10.4 ^ 1.3)
~1
kJ mol~1/RT ] cm3 molecule~1 s~1, was taken from ref. 12.
The ratio of rate constants was used to calculate * G¡ at 322
r
K as 3.8 ^ 1.7 kJ mol~1. A second-law method was then used
to obtain * H¡ to be 2.3 ^ 4.3 kJ mol~1 and * S¡ to be
r
322
r 322
[(5 ^ 14) J K~1 mol~1. These thermodynamic functions
were then recalculated at 298 K using the heat capacities of
the reactant species.13,14 Finally, the enthalpy of formation
and the entropy of the allyl radical at room temperature were
The geometries of the allyl and the 3-propenyl free radicals
di†er drastically. The allyl radical has C symmetry, whereas
2v
the 3-propenyl radical has only a reÑection plane because of
Table 3 Symmetry point groups, total and zero-point energies. The zero-point energy at the MP2/6-31G(d,p) level and total energies at the
MP4(SDTQ)/6-311G(d,p) level are in E
h
Compound
Symmetry
Multiplicity
Total energy
Zero-point energy
H
CH
CH
CH 2CH
CH 2CH-CH
CH --CH--CH
CH -C2CH
K
h
d
t
[0.499 81
[39.053 05
[ 39.730 68
[77.692 12
[116.923 98
[116.944 19
[116.913 91
[116.907 62
[116.908 31
[117.598 73
0.0
C
2v
D
3h
C
s
0.018 149
0.030 702
0.039 094
0.070 943
0.068 222
0.069 097
0.069 420
0.069 219
0.081 924
2
d
d
d
d
d
d
d
s
3
2
C
s
2
2
C
2v
C
s
2
2
3
2
cis-CH -CH2CH
C
s
3
trans-CH -CH2CH
C
C
3
s
CH -CH2CH
3
2
s
Phys. Chem. Chem. Phys., 1999, 1, 4727È4731
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the twisted form of its methylene group. Resonance stabiliza-
tion causes large changes in the CÈC bonds: for the allyl
radical the lengths of the hybrid bonds are 1.38 Ó and for the
3-propenyl radical they are 1.48 and 1.31 Ó, which are typical
for single and double CÈC bonds.
Another VLPP investigation of the reaction of allyl radical
recombination yielded * H¡ to be 163.6 ^ 6.3 kJ mol~1.7
f
300
The allylic CÈH bond energy of propene was calculated as
363.9 ^ 4.3 kJ mol~1. This value is about 17 kJ mol~1 lower
than the ab initio calculated bond energy. A possible reason
for the di†erence is a less accurate temperature correction
method used and the fact that the calculated primary CÈH
bond energies di†er typically from the experimental values by
about 6 kJ mol~1.20
Two geometrical isomers of the 1-propenyl free radical were
considered. The trans-conformer in which the dihedral angle
between the methyl carbon and the H atom at the radical site
is 180¡, is 2.3 kJ mol~1 more stable than the cis-conformer at
the MP4(SDTQ)/6-311G(d,p) level. For comparison the CÈC
double bond length is 1.29 Ó and the CÈC single bond length
is 1.51 Ó for both radicals. The 2-propenyl free radical has the
largest CÈCÈC valence angle of the studied C H radicals. It
Resonance energy
The allyl radical is a resonance stabilized free radical. In the
current study its resonance energy was calculated to be 59.9
kJ mol~1 by ab initio methods at MP4(SDTQ)/6-311G(d,p)
//MP2/6-31G(d,p) level of theory. For comparison more accu-
rate calculations at MP4(SDTQ)/6-311G(2d,2p)//MP3/6-
311G(d,p) level of theory were also used to obtain the reso-
nance energy to be 58.3 kJ mol~1. The resonance energy was
considered as the di†erence of the calculated (zero-point
energy corrected) energies of the allyl and the 3-propenyl free
radicals. For more accurate determinations a slight di†erence
in the stretching frequencies of di†erent CÈH bonds of the
methyl group of propene could be considered. Since frequency
is directly related to the dissociation energy of the bond (for a
harmonic oscillator), one may also expect slightly di†erent
resonance stabilization values for the allyl radical depending
on which of the methyl hydrogens is considered.
3
5
is 138¡ compared to a typical value of 125¡ for the other tau-
tomers studied.
Discussion
Kinetics of the reactions
The kinetics of both reactions are shown in Fig. 2. The Br
atom abstraction reaction is faster than the forward reaction.
Special attention was paid to setting up as low a photon Ñux
as possible to avoid increasing Br atom concentration. If it is
too high during measurement of the forward reaction, it will
cause a displacement on the monitored C H decay signal.
3
5
Because of the very low [Br] used during experiments, all the
exponential decays used for the rate constant measurements
were purely single exponential in shapes.
The calculated allyl resonance energy can be compared to
the experimental value of 59.4 ^ 4.9 kJ mol~1, which is
A Br atom can theoretically abstract one of the four di†er-
ent hydrogen atoms on propene. The equilibrium reaction
studied requires one of the allylic hydrogens on propene to be
abstracted. Concerning this it was shown in the current study
by the ab initio calculations that the allylic CÈH bond is
indeed the weakest bond of propene. Both reaction directions
of the equilibrium reaction are practically thermoneutral, thus
selective Br atom reactions will practically always lead to the
abstraction of the allylic H atom on propene. The ab initio
calculated bond energies of propene are shown in Fig. 3.
E
(n-C H -H) [ E
(allyl-H). The primary CÈH bond
d298
3
7
d298
dissociation energy of propane is taken from literature.21 A
previous experiment yielded the allyl resonance energy to be
51 kJ mol~1.8 However, this value was calculated using
* H¡ (C H ) \ 171 kJ mol~1.
f
300 3 5
Summary
The kinetics of allyl radical reaction with HBr has been char-
acterized. The rate constants obtained were combined with
those for the reverse reaction taken from the literature to
obtain the enthalpy of formation of the allyl radical as
166.1 ^ 4.3 kJ mol~1 at 298 K. The enthalpy of formation
value was used to determine the resonance stabilization
energy of the allyl radical to be 59.4 ^ 4.9 kJ mol~1. The
allylic bond of propene was shown by ab initio calculations to
be the weakest bond of the molecule. Ab initio methods were
used to calculate a value of 59.9 kJ mol~1 for the resonance
stabilization energy of the allyl radical.
Enthalpy of formation of the allyl radical
The enthalpy of formation of the allyl radical was found to be
166.1 ^ 4.3 kJ mol~1. This value is in very good agreement
with the appearance energy measurement of the allyl cation
when various allyl halides and alkenes were used as precur-
sors.19 Traeger combined the information measured with the
adiabatic ionization energy of the allyl radical taken from
another source to calculate the heat of formation of the allyl
radical as 165.2 ^ 3.3 kJ mol~1 at 298 K.
Rossi and Golden derived the heat of formation of the allyl
radical to be 164.8 ^ 6.3 kJ mol~1 at 300 K. The authors
studied the kinetics of C H ] HI reaction using a very low-
Acknowledgements
This research was supported by the University of Helsinki and
the National Science Foundation, Chemistry Division. I also
wish to thank Prof. Irene R. Slagle for kindly lending me the
experimental apparatus for this study. The kinetic experiments
were carried out at the Catholic University of America
(Washington DC, USA).
3
5
pressure pyrolysis (VLPP) technique in a Knudsen cell.6
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2
3
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