The reinvestigation of the kinetics of the metathesis reactions t-C 4H9?+ HBr (HI) → i-C 4H10+ Br?(I?) and of the t-C4H9?free radical thermochemistry

Article abstract of DOI:10.1021/jp500724r

A reinvestigation of the absolute rate constant of the metathesis reactions t-C₄H₉^?+ HBr → i-C₄H ₁₀+ Br^?(1) and t-C₄H₉ ^?+ HI → i-C₄H₁₀+ I ^?(2) was performed thanks to a recently developed apparatus consisting of a Knudsen reactor coupled to detection based on single-photon (VUV) photoionization mass spectrometry (SPIMS). It enables the generation of thermalized hydrocarbon free radicals owing to a source upstream of and external to the Knudsen reactor. The following Arrhenius expressions were obtained: k₁= 5.6(±1.4) × 10^-12exp(-6.76(±0.94)/ (RT)) and k₂= 2.0(±0.6) × 10^-11exp(-8. 48(±0.94)/(RT)) with R = 8.314 J mol^-1K^-1over the range 293 to 623 K. The mass balance of the reaction system based on closed shell product detection (CSPD) was checked in order to ensure the accuracy of the used reaction mechanism and as an independent check of k₁and k₂The wall-loss rate constants of the t-butyl free radical, _kwC₄H₉ were measured and found to be low compared with the corresponding escape rate constant, _keC ₄H₉for effusion of t-C₄H₉ ^?out of the Knudsen reactor. On the basis of the present results, the free radical standard heat of formation Δ _fH298°t-C₄H₉^?44.3 ± 1.7 kJ mol^-1was obtained when combined with the kinetics of the inverse halogenation reaction taken from the literature and using S298° (t-C₄H₉^?) = 322.2 J K^-1mol ^-1following a "Third Law" evaluation method. The standard enthalpy for t-butyl free radical is consistent for both the bromination and iodination reactions within the statduncertainties.

Full text of DOI:10.1021/jp500724r

Article
pubs.acs.org/JPCA
The Reinvestigation of the Kinetics of the Metathesis Reactions
t‑C4H9 + HBr (HI) → i‑C4H10 + Br• (I•) and of the t‑C4H9 Free Radical
Thermochemistry
•
•
N. Leplat and M. J. Rossi*
Laboratory of Atmospheric Chemistry (LAC), Paul Scherrer Institute (PSI), CH-5232 Villigen PSI, Switzerland
S
* Supporting Information
ABSTRACT: A reinvestigation of the absolute rate constant of the metathesis
reactions t-C4H9 + HBr → i-C4H10 + Br• (1) and t-C4H9 + HI → i-C4H10 + I• (2)
was performed thanks to a recently developed apparatus consisting of a Knudsen
reactor coupled to detection based on single-photon (VUV) photoionization mass
spectrometry (SPIMS). It enables the generation of thermalized hydrocarbon free
radicals owing to a source upstream of and external to the Knudsen reactor. The
following Arrhenius expressions were obtained: k1 = 5.6( 1.4) × 10−12
exp(−6.76( 0.94)/(RT)) and k2 = 2.0( 0.6) × 10−11 exp(−8.48( 0.94)/(RT))
with R = 8.314 J mol−1 K−1 over the range 293 to 623 K. The mass balance of the
reaction system based on closed shell product detection (CSPD) was checked in order
•
•
to ensure the accuracy of the used reaction mechanism and as an independent check of k1 and k2. The wall-loss rate constants of
C4H9
the t-butyl free radical, kCw H , were measured and found to be low compared with the corresponding escape rate constant, ke
,
4
9
for effusion of t-C4H9• out of the Knudsen reactor. On the basis of the present results, the free radical standard heat of formation
ΔfH2°98(t-C4H9 ) = 44.3 1.7 kJ mol−1 was obtained when combined with the kinetics of the inverse halogenation reaction taken
•
from the literature and using S°298(t-C4H9 ) = 322.2 J K−1 mol−1 following a “Third Law” evaluation method. The standard
•
enthalpy for t-butyl free radical is consistent for both the bromination and iodination reactions within the stated uncertainties.
•
INTRODUCTION
t‐C4H9 + HBr → i‐C4H10 + Br•
(1)
(2)
■
In the past, the chemical kinetics of halogenation equilibria of
the type R• + HX ⇄ RH + X•, where X is a halogen atom, was
thoroughly investigated with the goal to determine the standard
enthalpy of formation of hydrocarbon free radicals, ΔfH°298(R•).
Indeed, if the rate parameters of both the forward and the
reverse reactions are known, this thermochemical quantity may
simply be derived using the so-called “Second Law” or “Third
Law” treatments. Whereas acceptable agreement between the
many previous investigations of the kinetics for the reverse
reaction was obtained, two opposite sets of data for the forward
reaction exist, for example, for the halogenation reactions
•
t‐C4H9 + HI → i‐C4H10 + I•
Table1 presents a review of the literature in past investigations
of reactions 1 and 2. In all studies, the free radical was
generated by UV-laser photolysis of different suitable
precursors: photodissociation of 4,4-dimethyl-1-pentene at
193 nm,3,4,7,10 2,2,4,4-tetramethyl-3-pentanone at 193 nm,3,10
3,3-dimethyl-2-butanone at 248 nm,7 t-C4H9Br at 248 nm,8 t-
C4H9I at 266 nm,5 or 2,2′-azoisobutane at 351 nm.6,9,11 For the
reaction with HBr, all previous studies reported rather elevated
rate constants coupled to a negative temperature dependence.
The rate constants were measured by monitoring the temporal
decay of the t-butyl free radical at selected conditions,3,7,8 with
the exception of three measurements, for which the rate
constants were derived either from the accumulation of atomic
Br, the open-shell reaction product in reaction 1,5,6 or the
corresponding closed shell product, namely, isobutane (i-
C4H10).4 The oldest investigation3 reported a rate constant for
reaction 1 at ambient temperature that is approximately three
times lower than the more recent studies.4−8 In the case of the
results published by Russell et al.,3 a problem of contamination
of HBr with a substantial amount of H2 was later judged to be
•
•
•
involving C2H5 , n-C3H7 , or i-C3H7 summarized in two
recent papers.1,2 Indeed, some investigators measured a low
rate constant at ambient temperature associated with a positive
activation energy, whereas other workers obtained the opposite
trend in experimental studies, namely, rate constants higher by
as much as a factor of 50 or more associated with negative
activation energies. The source of these discrepancies has so far
never been satisfactorily explained. This leaves open the debate
about the kinetics of these halogenation reactions as well as
some unacceptably large uncertainties about the standard
enthalpy of formation of some prototypical hydrocarbon free
radicals.
Part of a larger measurement campaign, the present paper
focuses on the results obtained for two halogenation reactions
involving the transfer of a hydrogen atom to the t-C4H9
Received: January 21, 2014
Revised: June 13, 2014
•
radical:
© XXXX American Chemical Society
A
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
Table 1. Obtained Rate Parameters for t-C4H9• + HX (X = I, Br) → i-C4H10 + X• and Recommended Value for ΔfH°(R•) Based
on the Rate Constants for the Inverse Reaction X• + C4H10 from the Corresponding References
•
authors
A (cm3 molecule−1 s−1
)
Ea (kJ mol−1
)
k298 (cm3 molecule−1 s−1
)
ΔfH°298(t-C4H9 ) (kJ mol−1
)
t-C4H9 + HBr → i-C4H10 + Br•
•
a
Russell et al.3
9.86 × 10−13
1.07 × 10−12
−5.8
1.0 × 10−11
1.0 × 10−11
2.7 × 10−11
3.2 × 10−11
3.2 × 10−11
3.4 × 10−11
2.6 × 10−13
48.6 1.7
Richards et al.4
Nicovich et al.5
Seakins and Pilling6
Seakins et al.7
b
−8.0
50.6 2.9
c
50.9 3.5
d
1.37 × 10−12
1.2 × 10−12
−7.8
−8.3
51.3 1.8
e
Seetula and Slagle8
Muller-Markgraf et al.11
51.8 1.3
f
38.5 2.1
̈
t-C4H9 + HI → i-C4H10 + I•
•
g
Rossi and Golden9
Richards et al.4
Seetula et al.10
8.92 × 10−12
1.98 × 10−12
3.10 × 10−12
7.0
−6.3
−6.3
5.3 × 10−13
2.5 × 10−11
3.9 × 10−11
6.0 × 10−13
38.5 5.0
h
48.1 3.3
i
48.3 2.0
j
Muller-Markgraf et al.11
44.2 2.1
̈
a
•
“Second Law” value. The “Third Law” value yields ΔfH°(t-C4H9 ) = 47.8 3.0 kJ mol−1 at 300 K using S°(298) = 313 10 J mol−1 K−1 computed
b
from data of ref 12. Average of “Second” and “Third Law” values using the Arrhenius parameters of k−1 from ref 3. The individual “Second Law”
•
•
result is ΔfH°(t-C4H9 ) = 49.4 2.3, S°(298) = 311.2 6.9 evaluated at Tm = 375 K, the “Third Law” yields ΔfH°(t-C4H9 ) = 50.8 4.0 kJ mol−1,
c
S°(298) = 315.7 11.3 J K−1 mol−1. “Third Law” value using S°(298) = 314 10 J K−1 mol−1 (refs 12 and 13) and the equilibrium constant k1/k−1
•
at 298 K. When combined with measurements at 573 K (44.2 4.0 kJ mol−1) and 641 K (48.1 4.0 kJ mol−1), the average value is ΔfH°(t-C4H9 )
d
= 47.3 3.5 kJ mol−1. “Third Law” value using S°(298) = 313 6 J K−1 mol−1 evaluated at Tm = 359 K (listed) is identical to “Second Law” value
•
(ΔfH°(t-C4H9 ) = 51.3 1.7 kJ mol−1, S°(298) = 313 5 J K−1 mol−1 at Tm = 359 K). The extensive reinvestigation of both forward and reverse
rate constants presented in ref 3 yields identical results for the free radical thermochemical parameters except for the absolute rate constants, which
e
are higher by a factor of 2 or 3 across the investigated temperature range. “Second Law” value obtaining S°(298) = 315 4 J K−1 mol−1. Listed
f
•
value of ΔfH°(t-C4H9 ) is the average of 51.0 1.1 and 52.7 1.6 kJ mol−1 using refs 3 and 7 at Tm = 415 and 503 K, respectively, for k−1. “Third
•
Law” value using k−1 of ref 3 at 298 K and S°(298) = 313 10 J K−1 mol−1 (refs 12 and 13). ΔfH°(t-C4H9 ) = 41.4 2.5 kJ mol−1 is obtained when
k−1 of ref 14 is used at 298 K. The measured rate constant k1 has been multiplied by (3)0.5 = 1.73 in order to account for the measured primary H/D
g
isotope effect at T = 298 K according to ref 9. “Second Law” approach using data for k−2 of ref 15 after correction of k2 with the measured primary
isotope effect for H/D abstraction at 600 (k2H/k2D = 20.5 = 1.41, assumed) and 300 K (k2H/k2D = 1.75, measured, see ref 16) resulting in S°(298) =
310.4 4 J K−1 mol−1. In comparison, Weitz and co-workers (ref 4) measure a primary H/D isotope effect for the reaction t-C4H9• + HBr/DBr of
1.25 in contrast to a false claim by Seetula et al. (ref 10) reporting 4.0. The results based on the measurements of k−2 in refs 17 and 18 were rejected
•
on the basis that they resulted in unrealistically low values of S°(298). The significant uncertainty in the displayed value of ΔfH°(t-C4H9 ) stems
from the small T-range for the measurement of k−2 published in ref 37 and the uncertainty in the H/D primary isotope effect. “Second Law” value.
h
i
•
Inverse rate constant k−2 taken from refs 15, 17, and 18 and averaging of values of ΔfH°(t-C4H9 ). “Third Law” value using k−2 from refs 15
•
•
•
(ΔfH°(t-C4H9 ) = 50.0 3.0 kJ mol−1), 17 (ΔfH°(t-C4H9 ) = 47.0 3.0 kJ mol−1), and 18 (ΔfH°(t-C4H9 ) = 48.0 3.0 kJ mol−1) using S°(298) =
j
•
313 10 J K−1 mol−1 (ref 12). “Second Law” treatment obtains ΔfH°(t-C4H9 ) = 50.0 5.0 kJ mol−1 evaluated at Tm in midrange of k−2. k2 has
been multiplied by a factor of (3)0.5 = 1.73 in order to account for the primary H/D isotope effect at T = 298 K using the measured value from ref 9
(see also footnote g). “Third Law” value displayed uses extrapolation to 300 K of log k−2 = −(9.18 0.1) − (99555 1255)/(2.303RT) (R = 8.314
kJ mol−1) of unpublished work of Bracey and Walsh (ref 15) cited and used in refs 9 and 10 with S°(298) = 322.2 2.1 J K−1 mol−1 (Millennium
•
database). Using S°(298) = 310.4 2.1 J K−1 mol−1 as a lower limit, we obtain ΔfH°(t-C4H9 ) = 40.7 2.5 kJ mol−1 at 300 K. Using the same
•
procedure at T = 300 K for k−2 published in refs 17 and 18 yields values in the brackets of 34.3−37.8 and 37.4−40.9 kJ mol−1 for ΔfH°(t-C4H9 ) at T
= 300 K.
responsible for this difference5 and led to a thorough
reinvestigation of both k1 and k−1 by Seakins et al.7 However,
no sound explanation has been proposed for the disagreement
between the referenced kinetic results3 and the results of
Richards et al.4 whose experiments were moreover carried out
under nominally identical experimental conditions compared
with recent investigations,5,7,8 with the exception that the gas
mixture used as a buffer gas by Richards et al.4 contained a
significant fraction of efficient collisional quencher SF6. The
buffer gas absolute pressure typically was on the order of 5
mbar in addition to 0.5 mbar HBr used in 100−300-fold excess
over the free radical concentration at 1% decomposition of its
corresponding precursor. This study is characterized by an
exceptionally large concentration of t-butyl free radicals in the
range (0.2−1.0) × 1014 cm−3 compared with most other studies
listed in Table 1.
rate constant initially obtained by Rossi and Golden9 is
opposite to the later, more recent measurements performed by
Richards et al.4 and Seetula et al.10 The reaction between t-
butyl free radical and HI is one for which the extent of the
disagreement is the largest among hydrocarbon free radical
metathesis reactions of this kind. The discrepancy is a factor 75
at ambient temperature between the two extreme values of k−1
or k−2, namely, the “low” values presented in ref 9 vs the “high”
values highlighted in refs 4 and 10. The difference between the
previously used experimental approach and the present study
essentially lies in the free radical generation scheme and in the
type of reactor. A laminar flow reactor was used by both
Richards et al.4 and Seetula et al.,10 whereas Rossi and Golden9
and Muller-Markgraf et al.11 conducted their experiments using
̈
a Knudsen flow reactor. The results obtained on the R• + HX
reaction by Rossi and Golden9 also differ from all other recent
measurements leading to a negative activation energy of k−1 and
k−2 by the fact that the used photon energy was the least
energetic at a wavelength of 351 nm, in comparison to the 193,
248, and 266 nm wavelengths used in other studies with the
The previous investigations of the kinetics of the reaction t-
C4H9• + HI are also presented in Table 1. These data constitute
another explicit example of two opposite trends obtained for
such reactions. Indeed, a positive activation energy and a small
B
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
exception of the study by Seakins and Pilling.6 As we have
already emphasized in our previous publications,1,2 the large
rate constants at ambient temperature, associated with small,
but significant negative activation energies, were exclusively
obtained under conditions of UV photolysis (<266 nm) of a
free radical precursor for all investigations of the kinetics of the
reaction of the type R• + HX ⇄ RH + X•. Notable exceptions
are two experiments on CH3• + HBr and C2H5• + HBr, each at
ambient temperature, in which the free radical was generated
using H-abstraction by atomic chlorine from the corresponding
hydrocarbons upon laser irradiation at 355 nm.5 Owing to the
weak exothermicity of H-abstraction from CH4 and C2H6 by
atomic chlorine, we expect no or at best only a minor degree of
molecular excitation in the resulting free radical. The same is
true for the reaction Br + i-C4H10 → t-C4H9• + HBr performed
by Seakins and Pilling mentioned above.6
C4H9 ) = 39.3
4.2 kJ mol−1 using the free radical buffer
•
technique by measuring the equilibrium constants for the
•
•
exchange reaction CH3 + t-C4H9I ⇄ CH3I + t-C4H9 in
solution. From an extensive shock tube study on t-butyl free
radical using different precursors, Tsang reported ΔfH2°98(t-
•
C4H9 ) = 45.6 3.0, 50.6 4.0, and 47.7 3.0 kJ mol−1 using
the “Third Law” approach from experiments involving the
•
•
23,24
equilibria (t-C4H9)2 ⇄ 2 t-C4H9 , C(CH3)4 ⇄ CH3 + t-
C4H9 , and t-C4H9 ⇄ t-C4H8 + H•, respectively.
The
•
•
“Third Law” treatment performed by Benson et al.14 based on
the experimental measurement of the equilibrium constant HBr
•
+ t-C4H9 ⇄ Br• + i-C4H10 and the kinetics of the forward
•
reaction led to a value of ΔfH2°98(t-C4H9 ) = 45.1 kJ mol−1. This
•
value is in good agreement with ΔfH2°98(t-C4H9 ) = 44.2 4.0
and 48.1 4.0 kJ mol−1 from similar studies of the bromination
equilibrium after generation of atomic Br• from a suitable
precursor (CF2Br2) using pulsed 193 nm laser radiation at 573
and 641 K reported by Seakins and Pilling.6 As briefly
mentioned above, these authors managed to separately measure
both reaction rate constants (k1 and k−1) using resonance
fluorescence detection of atomic Br•, once as the open-shell
product of the forward reaction (k1) and once as the reactant
This is a remarkable exploratory study of reaction 1
combining ambient temperature kinetics of photolytically
•
generated t-C4H9 with HBr leading to the measurement of
k1, with an equilibration study at 573 and 641 K leading to the
extraction of both k1 and k−1 using the time-dependent
relaxation rate of a pulse of atomic bromine generated through
excimer laser photolysis from a suitable atomic bromine
precursor (CF2Br2). It is the only study combining photolytic
generation of the radical followed by reaction with HBr at
ambient temperature with direct equilibration/relaxation at
high temperature initiated by reaction −1, namely, H-
abstraction from i-C4H10 by atomic Br•. The measurement of
the relaxation kinetics enables the measurement of both high-
temperature rate constants, k1 and k−1, over a narrow
for the backward reaction (k ). Muller-Markgraf et al.11
̈
−1
•
investigated the kinetics of t-C4H9 + DX (X = Br, I) → i-
•
C4H9D + X•, and derived the rate constant for t-C4H9 + HBr
→ i-C4H10 + Br• from their results using DI after application of
a correction for the primary H/D kinetic isotope effect based
on experimental data.9 A “Third Law” treatment led to the
•
recommended value ΔfH2°98(t-C4H9 ) = 38.5
2.1 kJ mol−1
•
and ΔfH2°98(t-C4H9 ) = 41.4 2.5 kJ mol−1 by using the results
temperature range. It is obvious that the mode of t-C4H9
of Russell et al.3 and Benson et al.,14 respectively, for the inverse
•
formation is very different at ambient and high temperatures,
namely, photolysis of the free radical precursor (azo-isobutane,
t-C4H9−NN−C4H9-t) vs thermal H abstraction by atomic
Br• from the corresponding hydrocarbon, i-C4H10.
reaction (k−i).
•
In contrast, a high value ΔfH2°98(t-C4H9 ) = 53.1
12 kJ
mol−1 was obtained by Kiral
of the group additivity value for ΔfH2°98(C−(C)3) by means of
́
y et al.25 thanks to a new evaluation
•
The thermochemical calculations from the studies associated
experimental measurements of the equilibrium process CH3 +
•
with a negative activation energy result in ΔfH2°98(t-C4H9 )
(CH3)2CCH(CH3) ⇄ (CH3)2C•CH(CH3)2. This higher value
lying in the range 48.1−51.8 kJ mol−1 associated with a high
value of k1 at ambient temperature. The value of the standard
of the standard heat of formation of t-C4H9 is consistent with
the results of several theoretical ab initio electronic structure
•
enthalpy of formation ΔfH2°98(t-C4H9 ) = 38.5 kJ mol−1
calculations with the used quantum-chemical method given
•
obtained by Rossi and Golden9 and Muller-Markgraf et al.11
inside the parentheses: ΔfH2°98(t-C4H9 ) = 52.3 18.0 kJ mol−1
•
̈
is affected by the Arrhenius parameters of the measured rate
constant for reaction i, namely, ki with i = 1, 2, which is
associated with a positive activation energy and a low value of ki
(CBS-q),26 54.4
8.5 kJ mol−1 (G3),27 57
7 kJ mol−1
(variety of theoretical methods),28 ΔfH2°98(t-C4H9 ) = 44.8 kJ
•
29
mol−1 (CBS-4), and ΔfH2°98(t-C4H9 ) = 51.4 kJ mol−1 (CBS-4
corrected by using an empirical expression in order to deal with
the experimental results of Seetula and Slagle8) and 55.3 kJ
mol−1 (G3MP2B3).30
•
•
at ambient temperature. This renders the free radical of t-C4H9
more stable in the above equilibrium, everything else being
equal, compared with studies proposing high values of ki. This
has been recognized a number of times by the proponents of
the high values of ki in the past who attributed the disparity of
•
A review of literature relevant to ΔfH2°98(t-C4H9 ) reveals
that this thermochemical quantity remains quite uncertain.
Most of the experimental measurements of ΔfH2°98(t-C4H9 )
•
•
ΔfH2°98(t-C4H9 ) between high and low values exclusively to
that fact, namely, the absolute magnitude of ki.3−5,10,19
Nevertheless, the above range of 38−52 kJ mol−1 for the
standard heat of formation of t-C4H9• lies in the middle of the
are based on kinetic results of photolytic studies in the recent
past leading to high values of the rate constants k1 or k2
associated with negative activation energies3−8,10 that have been
questioned as a result of our recent invesigations1,2 as well as
the results previously published by Rossi and Golden9 and
•
extremes of other results for ΔfH2°98(t-C4H9 ) obtained by other
nonkinetic experimental techniques and ab initio electronic
structure calculations. Indeed, lower values were measured,
Muller-Markgraf et al.11 In fact, the opposite, namely a positive
̈
•
such as the recommended value of ΔfH2°98(t-C4H9 ) = 35.1
temperature dependence of k1 was obtained in these two
studies for t-C4H9• + HI by using a softer photolytic generation
of the radical coupled to a high frequency of hard-sphere
collisions of t-C4H9• against the vessel walls inside the Knudsen
flow reactor. Qualitatively similar results have been obtained in
our recent investigations pertaining to reactions involving a
number of other hydrocarbon free radicals. The most recent
4.6 kJ mol−1 obtained by Houle and Beauchamp20 from a
photoelectron spectroscopic study of t-butyl free radical.
•
However, this value has been superseded by ΔfH2°98(t-C4H9 )
= 43.1 5.0 kJ mol−1 resulting from a reevaluation of the same
spectroscopic data11 using more recent ancillary thermochem-
istry.21 Castelhano and Griller22 obtained a value of ΔfH2°98(t-
C
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
studies have been performed using a newly developed
experimental apparatus, which notably enables a novel method
of generation of the free radical in question external to the
Knudsen flow reactor. Therefore, the remaining uncertainties of
99.998%, H2 ≥ 99.995%, HBr ≥ 99.98%, and i-C4H8
99.00%), by the Fairfield Chemical Company (2,2,3,3-
tetramethylbutane (C8H18)) and by Carbagas (i-C4H10
≥
≥
100%) and liquid t-C4H9I of purity ≥95% whose gas phase
above the liquid t-C4H9I was stabilized with copper (Sigma-
Aldrich). Gas phase HI was set free from concentrated solution
(Sigma-Aldrich) according to the method described by Dillon
and Young.32 All condensable gases (HI, HBr, and t-C4H9I)
were purified and degassed by using several freeze (77.36 K)−
pump−thaw cycles.
The experiments were performed in two different Knudsen
reactors between 293 and 623 K. The main properties of the
two reactors are listed in Table 2. These reactors and the close
•
the rate constant and ΔfH°298(t-C4H9 ) motivated the use of this
new tool for the reinvestigation of the kinetics of the reactions
•
t-C4H9 with HBr or HI reported in the present manuscript.
EXPERIMETAL METHODOLOGY
■
The main features of the recently developed experimental
apparatus were detailed in a recent publication.31 Additional
information about the experiment, as well as the used data
treatment, was also described in both papers on the reactions
between ethyl and the propyl free radicals reacting with
hydrogen halides HX (X = Br, I).1,2 Therefore, only a brief
overview focusing on t-butyl free radical is presented here.
Experimental Apparatus. Briefly, the experiment consists
of a Knudsen flow reactor coupled to single-photon (VUV)
photoionization mass spectrometry (SPIMS) in “line-of-sight”
Table 2. Important Parameters of the Knudsen Reactor
reactor a
213
reactor b
286
volume (cm3)
internal area (cm2)
256
3.5
275.5
7.0
Φ exit aperture (mm), nominal
•
geometry. The t-C4H9 free radicals were generated before
diameter
introduction into the Knudsen reactor thanks to a reactor
consisting of two glass tubes in series. A flow of 20% H2/Ar
mixture was established across the first tube excited by a 2.45
GHz (λ = 12.2 cm) microwave discharge. When the μ-wave
discharge was turned on and powered at 40 W, approximately
50% H2 underwent bond scission and generated H• atoms.
Subsequently, these H• atoms flowed into the second tube
across a 1 mm diameter Teflon capillary and reacted with the
radical precursor flowing into the tube from a separate inlet. In
the present case, the used precursor was t-C4H9I, so that the
chemical generation scheme consisted of the two following
reactions:
ke (s−1) (measured)
ω (s−1) (calculated)
1.034(T/M)1/2
4386(T/M)1/2
2.367(T/M)1/2
3509(T/M)1/2
upstream tube where the radicals are generated were FEP-
Teflon coated in order to minimize wall losses of the t-butyl
free radical. The upper limiting temperature of 623 K was
chosen in order to prevent significant depolymerization of the
thin FEP-Teflon coating. The duplication of experiments in two
reactors of differing escape rate constants (ke) and therefore gas
residence or reaction times, enabled the measurement of small
radical wall losses (see below). Finally, the gases flowed out of
the reactor in an effusive molecular beam across an orifice of 3.5
or 7 mm diameter into the ionization volume of the mass
spectrometer and were identified and quantitatively analyzed
using single-photon VUV photoionization mass spectrometry,
VUV-SPIMS.31 Photoionization was obtained thanks to VUV
photons emitted from a pure H2 discharge lamp (Lyman-α
radiation at 10.20 eV).
This experimental apparatus embodies some major improve-
ments compared with previously used techniques because it
enables, without any doubt, thermal generation of t-C4H9• free
radicals for essentially two reasons: (i) the precursors of the
radical, namely, t-C4H9I, never interacted with the diffuse
microwave plasma in the first tube of the external free radical
H2 + hν(μ‐wave) → 2H•
(3)
H• + t‐C4H9I → t‐C4H•9 + HI
°
(ΔrH298 = − 75.2 kJ/mol)
(4)
It was experimentally verified that no products other than t-
•
C4H9 and HI were present in the radical generation tube in
order to exclude parasitic reaction pathways. This ascertained
that no unwanted reactions occurred in this part of the
apparatus and that the performed experiments were thus safe
from potential artifacts, especially when t-butyl iodide or HI
were used.
•
Subsequently, all the gases, namely, the t-C4H9 free radical
•
generation system, and (ii) the numerous collisions of t-C4H9
with the wall of the second tube, as well as with the internal
walls of the Knudsen reactor, removed the potential excess of
internal energy in t-C4H9 . It is therefore expected that all
radicals are thermalized.
Data Treatment. The data treatment must consider all
reactions occurring in the reactor, namely:
but also the remaining t-C4H9I and H2 as well as Ar and the
product HI from reaction 4, flowed from the second tube into
the Knudsen reactor across another 1 mm diameter Teflon
capillary. The t-C4H9I flow was always kept in excess compared
with the H• atom flow, typically higher by a factor of 7−10, in
order to prevent the admission of significant quantities of H• to
•
•
the reactor. Finally, the t-C4H9 reacted in the Knudsen
•
t‐C4H9 + HBr → i‐C4H10 + Br•
reaction vessel with controlled amounts of the titrant
introduced directly using a separate inlet. We note that
[HI]0, the concentration of HI in the absence of titrant, which
comes from its production in reaction 4, was at least 80 times
lower than the smallest HI concentration used for titration in
(1)
or
•
t‐C4H9 + HI → i‐C4H10 + I•
(2)
•
•
t‐C4H9 → wall loss
the case of the investigation of the t-C4H9 + HI reaction. All
(5)
operating conditions, including the inlet flow of each chemical
compound, for each individual rate constant measurement are
given in Tables A1 and A2 in the Supporting Information. The
used gases and liquids were provided by Messer (Ar ≥
•
•
t‐C4H9 + t‐C4H9 → i‐C4H8 + i‐C4H10
(6)
(7)
•
•
t‐C4H9 + t‐C4H9 → (CH3)3CC(CH3)3
D
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
Table 3. Kinetic Parameters Obtained in the Two Reactors a and b and the Evaluation of kw and Ratio kw/ke
kw (s−1
)
reactor
A (cm3 molecule−1 s−1
)
Ea (kJ mol−1
t-C4H9 + HBr → i-C4H10 + Br•
6.68 1.22
)
298 K
373 K
473 K
0.31
623 K
0.38
kw/ke min−max
0.086−0.11
•
a
(5.05 1.94) × 10−12
(5.42 2.62) × 10−12
0.20
0.25
b
6.12 2.92
t-C4H9 + HI → i-C4H10 + I•
•
a
(1.73 0.78) × 10−11
(2.02 1.04) × 10−11
7.98 1.42
8.64 0.67
<0
<0
<0
0.16
<0−0.048
b
In addition to the two reactions of interest, reactions 1 and 2,
the t-C4H9• may be consumed by disproportionation (reaction
6, kd), recombination (reaction 7, kr), and first-order loss on the
recombination product are expected here because kr,ethyl = 1.42
× 10−11 cm3 molecule−1 s−1,33 whereas the corresponding rate
constant is ten times lower for t-butyl radical with kr,t‑butyl = 1.66
× 10−12 cm3 molecule−1.34 Therefore, eq 8 may be simplified as
follows:
reactor surface (reaction 5, kCw H ). Two data procedures were
used to derive the rate constants of interest. The first is based
on the measured decay of the free radical MS signal and enables
4
9
0
⎛
⎝
⎞
⎟
⎠
the determination of the free radical wall-loss constant, kwC H
I
I
4
9
;
ki
C4H9
⎜
= 1 +
[HX]
9
kwC H + keC H
4
9
4
the second uses the quantitative measurement of the
accumulated closed shell products (i-C4H8, i-C4H10, and
(CH3)3CC(CH3)3) in the presence of HX. This is tantamount
to measuring the perturbation of the closed shell product
concentration in the presence of increasing concentrations of
HX, or in other words, the increasing competition of reactions
1 or 2 for t-butyl free radicals compared with reactions 6 and 7.
The first method uses the MS signals of the radical as a
function of the concentration of titrant, [HX]. This was the
signal measured at m/z 57 corrected for the contribution from
the fragmentation of i-C4H10 and t-C4H9I at m/z 57. Using the
flow balance equations, it may be shown1 that the ratios
between the MS signals of t-C4H9• in the absence and presence
of titrant HX (I0C H /IC H ) and for any concentration of HX,
C4H9
(10)
If for one given operating condition the experimental
measurement of I0C H /IC H is plotted as a function of HX
4
9
4
9
concentration, a linear regression line is obtained with a slope
C4H9
(S) equal to ki/(kwC H + kwC H ). Because ke , the escape rate
4
9
4
9
constant of t-C4H9• out of the Knudsen reactor, is known from
a previous calibration, two unknowns remain, namely, kCw H and
ki. Therefore, ki, the rate constant of interest, may be
determined together with the wall-loss rate constant by using
two different sets of data. These two sets are the measurements
obtained in the two reactors, namely, reactors a and b. These
4
9
two reactors differ by their respective values of kCe H , and at a
given temperature, the obtained slopes for reactors a or b are
equal to
4
9
4
9
4
9
depend on [HX] according to
ki
⎛
⎞
⎟
⎟
kd
kr
in
out,0
0
Sa =
R
R
− 2 1 +
R
R
keC H ,a + kwC H
C4H9
C8H18
I
I
⎜
⎜
(
)
)
4
9
4
9
C4H9
(11)
=
kd
kr
in
C4H9
out
C8H18
C4H9
⎜
⎝
⎟
⎠
− 2 1 +
ki
(
Sb =
keC H ,b + kwC H
4
9
4
9
(12)
⎛
⎞
⎟
⎠
ki
⎜
⎝
1 +
[HX]
i = 1, 2
Using Sa, Sb, and kCe 4H9 measured experimentally, one can
kwC H + keC H
4
9
4
9
(8)
calculate kCw H and ki using eqs 13 and 14 derived from eqs 11
4
9
where Rin and Rout are the specific flows of the chemical
compounds mentioned in the subscript into or out of the
Knudsen reactor and are expressed in molecules s−1 cm−3. The
superscript 0 refers to initial conditions, namely, in the absence
of titrant. Moreover, it was verified in the study involving ethyl
radical1 that the first term in the brackets on the right-hand side
of the equation remains close to unity at the prevailing
experimental conditions. This is the case because either Rin of
the radical significantly exceeds 2Rout of the recombination
products or the experimental conditions were kept within a
range for which Rout of the recombination product did not vary
significantly. The first cited condition is in any case constrained
by the mass balance equation governing the present system:
and 12:
SbkeC H ,b − SakeC H ,a
4
9
4
9
kwC H
=
4
9
Sa − Sb
(13)
(14)
SaSb
(keC H ,b − keC H ,a
)
4
9
4
9
ki =
Sa − Sb
Table 3 reports results of obtained values of kCw H for the four
investigated temperatures and the two reactions of interest. It
appears that the wall-losses are rather small in all cases, thus
4
9
reaching 11% of the value of kCe H in reactor a (note that kea <
keb) at most. This parameter is even slightly negative in the
range 298−473 K, according to the measurements performed
in the t-C4H9• + HI experiments. These negative terms have no
physical reality and are set to zero. This means that the wall
losses are too small to be accurately determined because the
small random variations of the measurement may lead to
4
9
out
C8H18
in
C4H9
out
C4H9
out
C4H8
out
C4H10
2R
= R
− R
− R
− R
(9)
Several checks of the accuracy of this assumption were made
in the case of the ethyl study,1 which are also valid in the
present case in view of the similarity of the operating
conditions. It must be even more accurate in the present case
in view of the smaller recombination rate constant compared
with ethyl free radical. Indeed, smaller concentrations of the
unphysical values of kwC H
4
9
.
Because the wall-loss measurements reveal that the numerical
value of kCw H is very small, Table 3, columns 2 and 3, displays
the Arrhenius parameters for k1 and k2 that may be individually
4
9
E
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Table 4. Main Experimental Conditions and Measured Rate Constants for t-C4H9 + HBr → i-C4H10 + Br•
Article
a
•
b
c
d
T
(K)
inlet flow of t-C4H9
[t-C4H9]0
[total]0
[HBr]max
e
(molecules s−1
)
(molecules cm−3
)
(molecules cm−3
)
(molecules cm−3
)
k1 (cm3 s−1 molecule−1
)
error (%)
Reactor a (V = 213 mL, exit aperture = 3.5 mm, kesc (s−1) = 1.034(T/M)1/2
)
293
293
293
373
473
623
623
623
5.79 × 1013
1.86 × 1013
1.62 × 1014
6.05 × 1013
6.10 × 1013
3.90 × 1013
3.32 × 1013
6.00 × 1013
1.16 × 1011
3.73 × 1010
3.24 × 1011
1.07 × 1011
9.62 × 1010
5.35 × 1010
4.56 × 1010
8.24 × 1010
1.71 × 1012
9.81 × 1011
5.40 × 1012
1.47 × 1012
1.27 × 1012
7.84 × 1011
7.53 × 1011
2.85 × 1012
6.55 × 1012
5.15 × 1013
3.72 × 1013
2.62 × 1013
2.47 × 1013
1.60 × 1013
1.71 × 1013
2.37 × 1013
3.52 × 10−13
3.58 × 10−13
60
57
33
53
62
41
29
19
f
2.80 × 10−13
7.87 × 10−13
1.05 × 10−12
1.75 × 10−12
1.34 × 10−12
f
1.26 × 10−12
Reactor b (V = 287 mL, exit aperture = 7.0 mm, kesc (s−1) = 2.367(T/M)1/2
)
293
293
293
373
373
373
373
473
473
473
623
1.28 × 1014
1.63 × 1013
1.93 × 1013
1.38 × 1014
1.31 × 1014
1.27 × 1014
8.90 × 1013
6.80 × 1013
1.38 × 1014
1.25 × 1014
2.09 × 1013
8.34 × 1010
1.06 × 1010
1.26 × 1010
7.97 × 1010
7.58 × 1010
7.35 × 1010
5.14 × 1010
3.49 × 1010
7.08 × 1010
6.41 × 1010
9.34 × 109
1.09 × 1012
5.16 × 1011
5.10 × 1011
1.01 × 1012
1.00 × 1012
1.10 × 1012
8.07 × 1011
7.33 × 1011
9.36 × 1011
9.39 × 1011
3.19 × 1011
3.23 × 1013
2.26 × 1013
1.35 × 1013
1.03 × 1013
1.55 × 1013
2.64 × 1013
1.76 × 1013
5.58 × 1012
7.15 × 1012
1.11 × 1013
6.33 × 1012
3.19 × 10−13
3.46 × 10−13
3.79 × 10−13
5.71 × 10−13
8.54 × 10−13
6.39 × 10−13
5.50 × 10−13
1.09 × 10−12
9.10 × 10−13
1.22 × 10−12
1.40 × 10−12
44
88
53
36
80
74
64
59
33
42
46
a
Arrhenius expressions for the whole data set: k1 = 5.62( 1.41) 10−12 exp(−6.761( 0.936)/(RT)); A in cm3 molecule−1 s−1 and Ea in kJ mol−1.
b
•
•
•
Obtained by dividing the inlet flow of t-C4H9 by Vkw. The steady state concentration, [t-C4H9 ]ss, is lower due to consumption of t-C4H9 by
c
disproportionation and recombination reactions. Initial total concentration (without any titrant) based on the measured initial inlet flows of stable
species and the known decays of the radical precursors when the μ-wave discharge is switched on ([total]0 = [t-C4H9 ]0 + [t-C4H9I]0 + [HI]0 +
•
d
e
[H2]0 + [Ar]0). Maximum [HBr] in the investigated range. Relative error in the rate constants in % of the absolute value of the rate constants.
f
Rate constant based on the detection of closed shell products (CSPD).
calculated in each reactor by making the assumption that kwC H
reactor. Therefore, for a given experiment, a plot of the ratio
4
9
out
out
out
1/2
= 0. It appears that for both investigated reactions, the obtained
Arrhenius parameters for the two reactors are quite close to
R
/R
C4H10
as a function of [HX]/(kd/√kr)(R
)
results
C4H8
C4H18
in a straight line whose slope is equal to the rate constant ki of
each other which is an indication of the small value of kwC H
.
4
9
interest according to eq 15.
Equation 15 shows that the independent variable R
The rate constants ki determined from eq 14 are given and
discussed below in Results and Discussion, together with the
combined set of Arrhenius parameters (Tables 4 and 5).
The second method of data evaluation used to determine the
rate constants of interest is based on the observation of the
closed shell products of reactions 1 or 2 and 6 and 7, namely, i-
C4H8, i-C4H10, and (CH3)3CC(CH3)3. This method will be
called “closed shell product detection” or CSPD. Using the
steady-state equations that describe the production and the
reactive as well as nonreactive (effusive) loss of these closed-
shell compounds in the reactor, the following expression has
been derived:1
out
C4H10
/
out
C4H8
R
depends on the ratio s = kd/(kr)0.5 for t-butyl free radical
disproportionation (reaction 6) and recombination (reaction
7), which have been repeatedly measured in the past using a
variety of experimental techniques. We are making a choice in
that we adopt the values from molecular modulation spectros-
copy (MMS)35−37 that are consistent with the corresponding
values from the Warnatz review.34 The ratio s has the following
values in units of cm1.5 s−0.5 molecule−0.5: 3.22 × 10−6,34 4.96 ×
10−6,35 3.75 × 10−6,36 and 3.60 × 10−6,37 which are all based on
the ratio r = kd/kr of 2.338 except for the Warnatz value, which
returned r = 2.5. The value r = 2.3 originates from the review by
Kerr,38 is based mostly on the analysis of stable hydrocarbon
products from radical recombination and disproportionation
and is considered a consensus value that is independent of
temperature in the range of most experiments. Taking the most
recent MMS results36,37 with r = 2.3, we obtain satisfactory
agreement of the resulting rate constant of interest, ki, when
using the values of the Warnatz review that uses r = 2.5. If we
take the Warnatz kinetics as a baseline, the Arthur36 and
Anastasi and Arthur37 s ratios increase the measured rate
constant ki by 12−14%. The increase in ki based on the Arthur
and Anastasi and Arthur data36,37 is lower than the calculated
uncertainties of the measurements. However, the Parkes and
Quinn data35 lead to an increase of ki by a factor of 1.54 and
1.74 using r = 2.3 from Kerr38 and their measured r of 2.8,35
respectively. In conclusion, we take the Warnatz34 values of kd
out
R
R
ki[HX]
C4H10
= 1 +
out
C4H8
⎛
⎜
⎞
kd
out
C8H18
⎟
⎠
R
kr
⎝
(15)
The Rout terms are the specific flows of the closed shell
recombination and disproportionation products out of the
Knudsen reactor that were determined using a suitable
calibration of the MS signal of authentic chemical compounds.
The rate constant of disproportionation (kd) and recombina-
tion (kr) were previously determined in several studies. The
following values given in the review of Warnatz34 were used in
the present study: kd,t‑butyl = 4.15 × 10−12 cm3 molecule−1,
k
r,t‑butyl = 1.66 × 10−12 cm3 molecule−1.34 The steady state value
of [HX] may also be easily calculated from the measured inlet
flow using its escape rate constant, kHe X and the volume V of the
F
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Table 5. Main Experimental Conditions and Measured Rate Constants for t-C4H9 + HI → i-C4H10 + I•
Article
a
•
b
c
d
T
(K)
inlet flow of t-C4H9
[t-C4H9]0
[total]0
[HI]max
e
(molecules s−1
)
(molecules cm−3
)
(molecules cm−3
)
(molecules cm−3
)
k2 (cm3 s−1 molecule−1
)
error (%)
Reactor a (V = 213 mL, exit aperture = 3.5 mm, kesc (s−1) = 1.034(T/M)1/2
)
293
293
293
373
473
623
623
623
3.93 × 1013
3.16 × 1013
8.92 × 1013
6.19 × 1013
4.85 × 1013
2.02 × 1013
3.74 × 1013
1.40 × 1014
7.87 × 1010
6.32 × 1010
1.79 × 1011
1.10 × 1011
7.65 × 1010
2.77 × 1010
5.13 × 1010
1.92 × 1011
1.75 × 1012
1.64 × 1012
5.00 × 1012
1.88 × 1012
1.42 × 1012
6.41 × 1011
9.00 × 1011
3.57 × 1012
3.12 × 1013
4.23 × 1013
3.84 × 1013
2.90 × 1013
1.20 × 1013
8.32 × 1012
7.08 × 1012
7.08 × 1012
5.66 × 10−13
6.42 × 10−13
69
67
73
27
29
27
34
48
f
7.45 × 10−13
1.28 × 10−12
2.66 × 10−12
5.08 × 10−12
3.37 × 10−12
f
3.49 × 10−12
Reactor b (V = 287 mL, exit aperture = 7.0 mm, kesc (s−1) = 2.367(T/M)1/2
)
293
373
373
473
473
623
7.65 × 1013
5.27 × 1013
1.01 × 1014
3.92 × 1013
1.09 × 1014
4.53 × 1013
4.99 × 1010
3.04 × 1010
5.82 × 1010
2.01 × 1010
5.59 × 1010
2.02 × 1010
9.95 × 1011
8.03 × 1011
7.79 × 1011
5.16 × 1011
8.22 × 1011
4.96 × 1011
4.34 × 1013
2.66 × 1013
2.83 × 1013
2.36 × 1013
2.72 × 1013
1.85 × 1013
6.34 × 10−13
1.17 × 10−12
1.13 × 10−12
2.53 × 10−12
2.07 × 10−12
4.20 × 10−12
18
60
28
61
53
73
a
Arrhenius expressions for the whole data set: k2 = 2.02( 0.58) 10−11 exp(−8.483( 0.940)/(RT)); A in cm3 molecule−1 s−1 and Ea in kJ mol−1.
b
•
•
•
Obtained by dividing the inlet flow of t-C4H9 by Vkw. The steady state concentration, [t-C4H9 ]ss, is lower due to consumption of t-C4H9 by
c
disproportionation and recombination reactions. Initial total concentration (without any titrant) based on the measured initial inlet flows of stable
species and the known decays of the radical precursors when the μ-wave discharge is switched on ([total]0 = [t-C4H9 ]0 + [t-C4H9I]0 + [HI]0 +
•
d
e
[H2]0 + [Ar]0). Maximum [HBr] in the investigated range. Relative error in the rate constants in % of the absolute value of the rate constants.
f
Rate constant based on the detection of closed shell products (CSPD).
Figure 1. Functional dependence of t-C4H9• SPIMS signals (left) and ratio I0/I as a function of HI concentration (reactor a, 293 K, entry 1 in Table
5). Correlation line parameters: y = (2.39 × 10−13)x + 0.9312.
and kr as the most suitable values with the understanding that it
constitutes a lower limiting value of ki. The most recent MMS
measurements36,37 support this contention. Both rate constants
(kd, kr) have been independently evaluated using the resulting r
= 2.534 being close to the consensus value of 2.3.38
accurate within the uncertainty limits of the experiment. This
means that no major chemical reaction is missing or has failed
to be taken into account in the corresponding reaction
mechanism.
In comparison to the first, this second method presents the
RESULTS AND DISCUSSION
■
advantage that the measurement of ki is independent of the
The Absolute Value of the Measured Rate Constants.
Tables 4 and 5 present the results of all individual rate constant
determinations obtained using the data evaluation procedure
described above. For the two investigated reactions, the rate
constants were measured at four different temperatures in the
range 293−623 K in several individual measurements based on
determination of the radical wall-loss rate constant, kwC H
4
9
.
However, this second method requires the additional
calibration of the evaluated MS signals of two closed shell
products (i-C4H8 and 2,2,3,3-tetramethylbutane or hexamethyl-
ethane, C8H18) in terms of exit flows. The main advantage of
the dual data evaluation method is the welcome opportunity to
check the mass balance between the loss of the free radical and
the closed-shell product formation in the same experiment,
which has never been performed to date. Indeed, if the rate of
disappearance of the radical with increasing amounts of titrant
agrees with the accumulation or reaction yield of the products
for the considered reactions involving this radical, we may claim
that the reaction mechanism is completely understood and
•
the disappearance of the t-C4H9 SPIMS signals. Figure 1
displays an example of typical data on t-butyl free radical decay
with increasing HI concentration leading to a rate constant
determination. Results such as these are relevant for the rate
constant measurement of the reaction of t-C4H9 with HI at
293 K in reactor a, for which the operating conditions are listed
•
in the first data row in Table 5. It clearly appears that the t-
•
C4H9 MS signal decreases when the amount of HI increases.
G
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
Figure 2. Functional dependence of i-C4H8, i-C4H10, and C8H18 calibrated exit flows as a function of the concentration of HBr in the Knudsen flow
reactor (reactor a, 293 K, entry 3 in Table 4), and the linear fit for the measurement of the rate constant based on the closed shell products (CSPD)
method. Correlation line parameters: y = (2.80 × 10−13)x + 0.8082.
Moreover, as shown on the right panel of Figure 1, a plot of
which corresponds to results displayed in entry 3 of Table 4
corresponding to data measured at 293 K for the reaction t-
C4H9• with HBr. When the concentration of HBr increases, the
exit flows of i-C4H8 and C8H18 decrease, whereas the exit flow
of i-C4H10 becomes more important due to the production of
I0C H /IC H as a function of HI concentration leads to a linear
4
9
4
9
regression line whose slope is equal to ki/(kCw H + keC H ),
according to the data treatment procedure described above.
Taking these results as an example, the obtained slope is equal
to 2.39 × 10−13. Multiplying this value by the known values of
ke and kw leads to a rate constant of 5.66 × 10−13 cm3 s−1
molecule−1 for the conditions of the example. It may be noted
that the linear regression line has an intercept close to unity as
expected for eq 10.
4
9
4
9
•
this chemical compound in the reaction t-C4H9 + HBr. The
linear fit obtained for a rate constant determination using the
closed shell product method (see above) is shown at the
bottom right of Figure 2 and led to a rate constant of 2.80 ×
10−13 cm3 s−1 molecule−1 in the present case. Once again, it
may be noted that the intercept is close to unity as expected in
view of eq 15. The errors listed in the last column to the right
of Tables 4 and 5 are given in terms of a percentage of the rate
constant and were determined by means of an appropriate 2σ
least-squares analysis of the slopes of the experimental fits of
each individual rate constant determination.
In both cases, two additional measurements were also
performed based on the observations of the closed shell
products (isobutene, hexamethylethane) for two different
temperatures. These closed-shell products experiments were
always performed in reactor a characterized by a larger
residence time compared with reactor b and, therefore, at
•
•
In addition to the t-C4H9 , i-C4H8, i-C4H10, and (CH3)3CC-
equivalent inlet flows, by a greater value of [t-C4H9 ] and
(CH3)3 MS signals required for the evaluation of the rate
constants k1 and k2, the MS signals of Ar, t-C4H9I, HBr, and HI
were also monitored. The Ar MS signals were always constant
over a set of experiments and therefore validate the fact that the
H2/Ar flows in the discharge tube were always maintained at a
constant rate. Moreover, this observable served as an internal
standard and is a good indication that each set of experiments
higher importance of the radical−radical reaction compared
with reactions 1 or 2. As expected, a MS signal for the
recombination product that clearly stands out above the
baseline could not be measured in reactor b owing to its lower
free radical concentration at equal or comparable inlet flow of t-
butyl free radicals. An example of an experiment performed for
a measurement of the rate constant is presented in Figure 2,
H
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
was performed under controlled and stable photoionization
conditions. The MS signals for the free radical precursor, t-
C4H9I, also remained constant. This ensures that the rate of
free radical generation by the reaction t-C4H9I + H• was kept
constant during each individual set of experiment. This notably
indicates that there was no HX counterflow from the Knudsen
•
reactor into the t-C4H9 generation tube. Indeed, if this would
not have been the case, HX would react with the H• atoms in
the rather fast H• + HX → H2 + X• reactions (k298,H+HBr = 6.31
× 10−12 cm3 molecule−1 s−1 and k298,H+HI = 2.09 × 10−11 cm3
molecule−1 s−1)39,40 and therefore compete with the t-C4H9
•
generation reaction. This may finally lead to a lower decrease of
the t-C4H9I MS signal and therefore decreasing initial t-butyl
free radical concentration with increasing HX. Such behavior
has never been observed. Another conclusion that may be
reached from this observation is that there was no additional
consumption of the precursor in the Knudsen reactor with X•
atoms released from the titration by the reaction t-C4H9I + X•
Figure 4. Arrhenius plot (solid line) of current data in comparison
with previously published results for k2 (t-C4H9• + HI → i-C4H10 + I•)
under the experimental conditions presented in Table 5 (experimental
uncertainties of individual data points). Dark blue squares, light blue
diamonds, and black crosses correspond to the present work for radical
decay in reactor a, radical decay in reactor b, or closed shell product
analysis, respectively; pink triangles, Richards et al.;4 brown circles,
Rossi and Golden;9 dark green diamonds, Seetula et al.;10 light green
•
→ t-C4H9 + XI, as expected from the slow kinetics of this
reaction (k298,t‑C4H9I+I = 2.41 × 10−20 cm3 molecule−1 s−1).17
Finally, the titrant signals were also monitored, and it appears
that HI flowing out the radical generation tube was negligible in
comparison to the flow of HI used as titrant. Recombination
and disproportionation of t-butyl free radicals taking place
already in the upstream free radical generation tube could be
ruled out because the analysis of the closed-shell reaction
products in reactor b revealed the complete absence of the
corresponding reaction products, namely, 2,2,3,3-tetramethyl-
butane and isobutylene. The t-C4H9• concentration in reactor b
circles, Muller-Markgraf et al.11
̈
and 5. On each graph, the dark and light blue points are all
measurements of individual rate constants obtained using the
free radical detection method and the black crosses are the
results of the closed shell product analysis. The latter method
was used for two sets of experiments located at the two
extremes of the investigated temperature range for both
reactions. The kinetic results obtained from the two data
treatments are in good agreement with each other. This ensures
a mass balance check of the used chemical system to which we
attach great importance.
is expected to be lower by the factor keC H ,b/keC H ,a = 2.3,
which sufficiently slows these radical−radical reactions 6 and 7
compared with reactions 1 and 2. All the observations discussed
in this paragraph are regarded as an additional check of the
used experimental procedure.
4
9
4
9
Figures 3 and 4 display the experimental results as an
Arrhenius plot using the rate constants presented in Tables 4
The two sets of measurements exhibit linearity in the
Arrhenius plot for both studied reactions and may be correlated
to the following Arrhenius expressions:
k1 = 5.6( 1.4) × 10−12 exp(−6.76( 0.94)/(RT))
(16)
k2 = 2.0( 0.6) × 10−11 exp(−8.48( 0.94)/(RT))
(17)
where the units are cm3 molecule−1 s−1 for preexponential
factors and kJ mol−1 for the activation energies with R = 8.314 J
mol−1 K−1. The uncertainties reported in the two Arrhenius
expressions were obtained from a 2σ statistical evaluation of the
random errors, enabling the determination of the standard
deviation associated with the slope and intercept of the linear
Arrhenius plot.
These Arrhenius expressions clearly indicate that the two
reactions of interest are occurring with a rather low rate
constant associated with a positive temperature dependence
when the present experimental apparatus was used. This is
obviously in distinct contrast with most of the previous
determinations, which are also shown in Figures 3 and
4.3−5,7,8,10 Indeed, the high rate constants and negative
activation energies obtained in studies in which the free radical
was generated by highly energetic photolysis of a suitable
precursor at 193, 248, or 266 nm are not obtained in the
present case. However, for the reaction with HI, the present
results are in rather good agreement with the previous
measurements performed by Rossi and Golden,9 as well as
Figure 3. Arrhenius plot (solid line) of current data in comparison
•
with previously published results for k1 (t-C4H9 + HBr → i-C4H10
+
Br•) under the experimental conditions presented in Table 4
(experimental uncertainties of individual data points). Dark blue
squares, light blue diamonds, and black crosses correspond to the
present work for radical decay in reactor a, radical decay in reactor b,
or closed shell product analysis, respectively; purple diamonds, Russell
et al.;3 pink triangle, Richards et al.;4 orange triangles, Nicovich et al.;5
red circles, Seakins et al.;7 dark green diamonds, Seetula and Slagle;8
brown diamonds, Seakins and Pilling;6 light green circles, Muller-
̈
Markgraf et al.11
Muller-Markgraf et al.,11 both in terms of the absolute rate
̈
I
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
Table 6. Thermochemical Parameters of t-Butyl Free Radical from t-C4H9 + HX ⇆ i-C4H10 + X• Equilibria Using k1 and k2
•
a
from This Work and k−1 and k−2 from Work of Listed Authors
b
Second Law
Third Law
c
d
authors for k−i
Fettis et al.42
Islam and Benson43
Choo and Choe44
Benson et al.14
Russell et al.3
Seakins et al.7
average
T range for k−i (K)
ΔfH2°98
i-C4H10 + Br•
38.8 1.2
S2°98
ΔfH2°98 (Ki at Tm)
ΔfH2°98 (Ki at 298 K)
423−483
295−305
299−328
298−363
298−478
423−621
286 0.8
311 0.5
292 0.5
288 2.0
301 0.6
299 1.1
296 11.6
53.2 2.0
33.9 1.7
44.6 1.7
45.2 1.7
42.9 1.9
45.9 2.2
44.3 7.7
48.0 1.9
33.9 1.6
44.2 1.5
44.1 1.7
41.1 1.9
41.5 2.0
42.1 5.9
30.6 2.7
35.3 0.9
34.2 2.7
35.4 1.2
37.1 1.7
35.2 3.5
i-C4H10 + I•
Teranishi and Benson17
Knox and Musgrave18
Bracey and Walsh15
525−583
503−618
573−614
29.8 8.0
34.0 8.3
36.6 2.3
31.1
285 1.4
293 2.9
299 2.5
288.8
44.9 3.6
44.8 6.1
41.7 2.8
44.8
38.1 2.9
39.9 4.7
43.6 3.5
39.0
e
average
total average
34.4 2.7
294 7.9
44.4 4.7
41.3 3.8
a
b
Units of ΔfH2°98 in kJ mol−1 and S2°98 in J K−1 mol−1. Thermochemical quantities for other products and reactants, including S2°98 of t-C4H9• = 322.2
J K−1 mol−1 for the “Third Law” calculations, are based on data from the Millennium database.37 From the listed maximum least-squares error of
•
•
Cp(t-C4H9 ) of 0.64% at 1300 K, we obtain an uncertainty in S2°98 of t-C4H9 of 2.1 J K−1 mol−1 assuming that the error in Cp is independent of
c
temperature. Calculation based on the equilibrium constant Ki at the mean temperature (Tm) using the measured inverse reaction rate constant, k−i.
Tm is the algebraic (unweighted) average over the given temperature range. Calculation based on the equilibrium constant Ki at 298 K using the
extrapolated rate constant k−1 or k−2. The thermochemical parameters obtained by using k−2 of Bracey and Walsh (ref 15) have not been used to
establish the displayed average for ΔfH°(t-C4H9 ) at 300 K.
d
e
•
constant and its temperature dependence. This precursor study
also used photolytic generation of the free radical albeit using
less energetic photons (351 nm). These authors even added a
caveat at the end of the more recent publication regarding the
use of 248 nm radiation when an azo precursor of t-butyl free
radical was used.11 The study performed by Rossi and Golden9
presents another important common feature with the present
work, namely, the use of a Knudsen flow reactor in contrast to
the flow tube reactors used in most other investigations. The
good agreement between the current data set and the results of
was generated through photolysis of azoisobutane at 351 nm.
The two high-temperature rate constants have a positive
temperature dependence (Figure 2 in ref 6; see also Figure 3)
akin to our present results. In the analysis of Seakins and
Pilling, all kinetic data are treated using a common Arrhenius
line and result in a significant negative temperature dependence
by virtue of the large value of k1 at ambient temperature. Future
work will reveal whether there are systematic errors not
accounted for when comparing two sets of rate constants
obtained from very different experimental techniques. It may be
speculated that a potential excess of internal energy in the free
radical may significantly affect the absolute value of the
obtained rate constant in cases characterized by a low reaction
barrier.
Rossi and Golden9 and Muller-Markgraf et al.11 displayed in
̈
Figure 4, the latter after correction of ki for the measured
primary H/D isotope effect, does perhaps not come as a
surprise in view of the similar experimental technique used in
both investigations.
However, as mentioned in our previous papers1,2 that
showed similar discrepancies for identical H-transfer reactions
involving ethyl and propyl radicals, an unambiguous explan-
ation about the origin of this disagreement cannot be proposed
with certainty at this point. We can only underline our
confidence in our results owing to the major improvement
brought about by resorting to an advanced experimental
technique, mainly the external and “soft” chemical generation
of the free radicals used in the present case. Moreover, the
current study is the only one that investigated the effect of the
HX addition on both the radical and the closed shell products,
which clearly leads to consistent results.
It is well-known that the Knudsen reactor is a system
characterized by many “hard” collisions of the molecules with
the vessel wall, as is the case here, at collision frequencies of ω
(s−1) = 4386(T/M)1/2 and ω (s−1) = 3509(T/M)1/2 in reactors
a and b, respectively. This may ensure efficient removal of any
•
potential excess internal energy in the t-C4H9 free radical
before reaction with HX. The thermalization by numerous wall
collisions achieved in such a reactor is in distinct contrast to
collisions with weak colliders such as He and N2 used as bath
gases in flow reactors used in other studies.3−5,7,8,10 Regarding
the role of collisions, it is interesting to note that the study
performed by Richards et al.,4 in which the hard collider SF6
was used at a significant partial pressure in the buffer gas
mixture leads to a lower rate constant among the photolytic
studies conducted in tubular reactors. This observation may be
interpreted as an indication that the thermalization of the
radical is a key feature in such a kinetic study. By the same
token, the two high temperature experiments of Seakins and
Pilling6 addressing the generation of t-butyl free radical using
H-abstraction by atomic bromine may not be comparable to
their ambient temperature experiments where t-butyl radical
•
Thermochemical Consequences for t-C4H9 Free
Radical. The present Arrhenius parameters may be used with
those previously published for the inverse reactions to perform
thermochemical calculations. Two methods may be used in this
regard that enable the calculation of the enthalpy of reaction,
from which the t-C4H9• standard enthalpy of formation may be
derived if this parameter is known for the other chemical
compounds involved in the reaction. The first is called the
“Second Law” method and uses the difference between the
J
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
activation energy (Ea) of the forward and reverse reaction in
order to obtain the enthalpy of the reaction:
the “Second Law” entropy S°298 = 314
6 kJ mol−1 K−1
mentioned in footnotes c, d, and f of Table 1, which agrees with
both measurement and numerical calculation of the structure of
t-butyl free radical,12,13 and the value from the Millennium
Tm
°
ΔrH298 = Ea,i − Ea,−i
−
(∑ Cp,prod−∑ Cp,react) dT
∫
41
database of S°(298) = 322.2 2.1 kJ mol−1 K−1 (footnote b
298
(18)
of Table 6). In the present work, we have preferred to use the
value given in the Millennium database in order to use heat
capacities (Cp) that are consistent with the absolute entropy of
t-butyl. It seems, however, that the uncertainty limits of S°298(t-
where Tm is the mean temperature of the smallest investigated
temperature range corresponding to the inverse reaction (k−1
and k−2) in the present case. This “Second Law” method also
enables the determination of the entropy of reaction from the
ratio between the two preexponential terms according to
•
C4H9 ) may be unduly optimistic in this case.
Following the approach taken in our recent publications,1,2
•
our preferred value for ΔfH2°98(t-C4H9 ) will be based on the
⎛
⎜
⎝
⎞
⎟
⎠
Tm
(∑ Cp,prod − ∑ Cp,react
)
Ai
results obtained by the “Third Law” method at Tm. The
“Second Law” calculations are discarded because the reliability
of the results obtained using this method greatly depends on
the accuracy of the measured activation energies. The accuracy
of these parameters will essentially depend on the size of the
investigated temperature ranges, more specifically, the 1/T
ranges. These ranges are often quite narrow for the inverse
reaction k−i as listed in the second column of Table 6.
Therefore, it may be assumed that in most cases, the activation
energies are more uncertain than the rate constants measured
within a given temperature range, which leads us to prefer the
“Third Law” approach. Another reason to reject the “Second
Law” approach, is that the resulting entropy is inconsistent with
commonly accepted values for this thermochemical parameter,
ΔrS298 = R ln
−
dT
∫
A
298
T
−i
(19)
The alternative treatment, named “Third Law” method,
enables the calculation of the enthalpy of reaction at a given
temperature (T) from the rate constants measured in both
directions and thus from the equilibrium constant Keq = ki/k−i
at some temperature Tm:
T
⎛
⎞
⎟
⎠
ki
k−i
°
°
ΔrH298 = T ΔS − R ln
−
( ∑ Cp,prod
−
⎜
∫
r
298
⎝
∑ Cp,react) dT
(20)
such as S2°98(t-C4H9 ) = 322.2 2.1 J K−1 mol−1 listed in the
•
This second method requires knowledge of the entropy of
reaction, ΔSr°, either from a measurement or from an a priori
estimate or guess. Both methods obtain the thermochemical
quantities at a given temperature (Tm or T) and must be
corrected to 298 K for the calculation of the standard
thermochemical parameters by using the known heat capacities
of each chemical compound. From the so obtained enthalpy of
Millennium database, which seems to be agreed upon by
many.41
Between the two “Third Law” calculations displayed in Table
6, the one performed at Tm is preferred over the one at 298 K,
because the extrapolation of the rate constants k−i using the
measured Arrhenius parameters from Tm down to ambient
temperature is fraught with larger uncertainties (see above)
than the extrapolation of the equilibrium constant Ki from Tm
to 298 K. The reader is reminded of the limited accuracy of the
Arrhenius parameters of the inverse reaction (k−1) owing to a
rather restricted temperature range in most cases over which
k−1 could be measured owing to a substantial activation energy
for k−1 in the case of iodination. Therefore, it seemed more
suitable to perform the thermochemical calculations by using
the rate constants obtained at high temperatures (Tm), and to
subsequently apply the correction down to 298 K by using the
well-accepted and tabulated heat capacities of the involved
chemical compounds including the free radical in question
listed in the Millennium database.41
•
reaction, the t-C4H9 enthalpy of formation is calculated by
using known enthalpies of formation for the other chemical
species:
°
°
°
°
Δf H298(t‐C4H9) = −ΔrH298 − Δf H298(HX) + Δf H298(X)
°
+ Δf H298(i‐C4H10)
(21)
For the calculations presented below, all required thermo-
chemical parameters except for t-butyl free radical were taken
from the Millennium database.41 Table 6 presents the results of
“Second Law” and “Third Law” calculations using all available
measurements for the kinetics of the inverse reaction, which are
referred to in the first column of Table 6. Two “Third Law”
treatments were performed, the first at Tm, the mean
temperature of the investigated ranges for the inverse reaction
that are listed in second column of Table 6, and the second at
298 K. The results presented in Table 6 show that a general
agreement between all of these evaluations cannot be obtained
within reasonable uncertainty limits. The “Second Law”
A further argument for the justification of a “Third Law”
recommendation of a result obtained at Tm may be the
agreement between the evaluation of the bromination and
iodination system as has been commented on several times.10,19
•
The preferred value is therefore ΔfH2°98(t-C4H9 ) = 44.3 1.7
kJ mol−1, which is the average value among all “Third Law”
evaluations at Tm with the exception of the two older
bromination studies.42,43 Both studies seem to be outliers
•
treatment often leads to smaller values of ΔfH2°98(t-C4H9 )
compared with the “Third Law” method for reasons that are
well and widely known. One exception is the work of Seakins et
al.,7 which leads to perfect agreement of the thermochemical
parameters obtained using the “Second Law” and “Third Law”
methods. These authors apparently have managed a flawless
separation of the reaction entropy from enthalpy from the
temperature dependence of the equilibrium constant K = k−1/
k1, which leads to identical values of the thermochemical
parameters as mentioned in footnote d of Table 1. An open but
perhaps a minor problem is the apparent disagreement between
•
whose results for ΔfH2°98(t-C4H9 ) are symmetrically located
around the average value. In any case, its inclusion in the global
average does not significantly affect the preferred value but
rather extends its uncertainty limits. Fettis et al.42 overestimate
the standard enthalpy of t-butyl free radical by approximately
10 kJ mol−1, whereas Islam and Benson43 underestimate it by
the same amount. This latter work has been superseded by a
more recent study14 because of the significant lifetime of the
upper spin state of Br (2P1/2) in the VLPR system.45 This
K
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
excited state of atomic bromine lies 3685.4 cm−1 over its
ground state (Br(2P3/2))46 and is generated together with its
ground state in the microwave discharge of a dilute Br2/He
mixture. The preferred value displayed in Table 6 is notably in
perfect agreement with some previous experimental determi-
ment: (a) The role and nature of the “loss” processes needed to
describe either the real-time decay of the free radical3,7,8,10 or
the accumulation of the atomic Br product.5 In the first case
(molecular beam sampling), we have significant first-order
losses in excess of 50 s−1; in the second type of experiments
(optical detection using resonance fluorescence), we have
diffusion out of the viewing region on the order of 25 s−1.5 It is
clear that radical loss rate constants on the order encountered
in Knudsen flow reactors (kw < 1 s−1) cannot be measured in
laminar flow tube and slow-flow optical experiments. At this
point, we have to strongly oppose an attempted “explanation”
for the shortcomings of the Knudsen flow reactor experiments
in terms of the magnitude of kw.10,19 Owing to the influence of
wall-deactivation processes of free radicals at low pressure
conditions all Knudsen flow reactor studies have been
conducted under strict inclusion of wall effects of the radical
(kw), which means that redundant experiments have been
systematically performed in order to separate ki from kw,
without exception. This is standard procedure in the application
of a method where molecules and radicals predominantly
undergo wall collisions except for the fastest gas-phase reactions
such as radical−radical recombination and disproportionation.
(b) Although the buffer gas pressures in UV-laser photolytic
experiments range from a few Torr of He up to 300 Torr of N2,
it would be desirable to learn more about the details of
vibrational cooling and energy transfer, especially the seemingly
rate-controlling V−T energy transfer at low levels of internal
energy as well as its temperature dependence47 in hydrocarbon
free radicals other than methyl free radical. Methyl free radical
energy transfer and deexcitation have been investigated as far as
its VUV absorption at 216 nm is concerned, but nothing is
known about the sensitivity of detection at low internal
energies of polyatomic free radicals. It would be beneficial to
learn more about low-level energy transfer in complex
hydrocarbon free radicals in order to enable the solution of
this experimental conundrum or at the very least eliminate a
potential problem. In parallel, theoretical methods have to be
investigated thoroughly as to their robustness regarding the
chemical kinetic significance of stable complexes of the type
HX·R•.
•
nations, such as ΔfH2°98(t-C4H9 ) = 45.1 kJ mol−1 recom-
mended by Benson et al.14 and ΔfH2°98(t-C4H9 ) = 44.2 4.0
•
or 48.1 4.0 kJ mol−1 reported by Seakins and Pilling6 (see
also Table 1, as well as Figure 3, for the kinetic results), both
studies dealing with experiments involving the equilibrium Br•
•
•
+ i-C4H10 ⇆ HBr + t-C4H9 . ΔfH2°98(t-C4H9 ) = 45.6 3.0 and
47.7 3.0 kJ mol−1 obtained by Tsang23,24 from data involving
the equilibrium (t-C4H9)2 ⇆ 2 t-C4H9 and t-C4H9 ⇆ C4H8
•
•
•
+ H, respectively, also strongly support the present results. The
ab initio CBS-4 calculations published by Marsi et al.29 leading
to ΔfH°298(t-C4H9 ) = 44.8 kJ mol−1 is also in perfect agreement
•
with the present results when the empirical correction post
factum is dropped. However, we are aware that the preferred
value supported by the present measurements is a few kJ mol−1
smaller than some other preferred experimental and theoretical
thermochemical parameters as alluded to in the Introduction. It
seems that the present results lie at the lower end of the
consensus range proposed by W. Tsang,24 namely, ΔfH2°98(t-
C4H9 ) = 48.0 3.0 kJ mol−1 under conditions where both
•
uncertainties overlap. The same may be said for the proponents
of the “high” values of the thermochemical parameters for t-
butyl free radical: their uncertainty range certainly overlaps
Tsang’s, and their preferred value is located at the upper end of
Tsang’s consensus value. However, we would like to stress that
this is the first time the halogenation method leads to values as
close as they are to the consensus value in terms of overlapping
uncertainties across the time history of thermochemical studies.
In retrospect, we have embarked on a program to
reinvestigate a couple of fast halogenation reactions, namely,
reactions 1 and 2 that have been disputed over the years and for
which a consensus on a high value of the rate constant k1 and k2
as well as a negative energy of activation seems to have been
firmly established. On the other hand, a serious reinvestigation
using a different experimental setup has been performed of
which the present paper is a part. The disagreement first and
foremost concerns the kinetics, much less so the thermochem-
•
CONCLUSIONS
ical consequences, of ΔfH2°98 (t-C4H9 ), the change of which
■
The kinetics of the reactions t-C4H9 + HBr → i-C4H10 + Br•
•
may be regarded as modest for reasons mentioned above.
Obviously, a specific reason for this profound disagreement
between the two sets of the halogenation kinetics cannot be
given at this time. We first will restrict ourselves to point out
areas that apparently do not constitute the likely cause of the
problem. In both “camps”, kinetic experiments have been
performed on both the disappearance of the t-butyl free radical
and the appearance of products, either atomic bromine,
isobutene, or the change in the closed-shell products upon
HBr or HI addition as performed in this work. Therefore, the
kinetics seems confirmed from a mass balance point of view
owing to consistent results. The obvious difference between
both camps arise apparently in the manner in which the free
radicals are generated and the collisional environment: The
group observing fast kinetics exclusively generates the radicals
using UV-laser photolysis at pressures of He or N2 ranging into
the hundred millibar regime except for two experiments in
which the free radical was generated through H-abstraction
from a hydrocarbon precursor by atomic chlorine.5
(1) and t-C4H9 + HI → i-C4H10 + I• (2) were reinvestigated
•
by using a newly developed apparatus. This enabled a novel
generation of the t-C4H9• radical by soft chemical reaction in an
ancillary flow reactor upstream of the Knudsen flow reactor,
which constitutes a major improvement in comparison to past
experimental techniques. The treatment of the obtained
experimental data enabled the verification that the chemical
mechanism takes into account all reactions occurring in the
reactor thanks to a suitable mass balance check involving both
•
the decay of the t-C4H9 free radical and the accumulation of
the closed shell products isobutylene, isobutane, and
hexamethylethane generated in reactions of the t-butyl free
radical with either HBr or HI or by recombination and
disproportionation. The obtained rate parameters led to low
absolute values of the rate constants associated with a positive
temperature dependence for both HBr and HI reactions, as well
as to low but expected wall loss rate constants for t-butyl free
radical. The results may be expressed in the following Arrhenius
expressions: k1 = 5.6( 1.4) × 10−12 exp(−6.76( 0.94)/(RT));
k2 = 2.0( 0.6) × 10−11 exp(−8.48( 0.94)/(RT)). These new
Two areas need to be addressed more closely in future
experiments designed to shed light on this profound disagree-
L
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
(9) Rossi, M. J.; Golden, D. M. Laser-Induced Kinetics: Arrhenius
Parameters for t-C4H9 + XI ⇆ i-C4H9X + I (X = H, D) and the Heat
of Formation of the t-Butyl Radical. Int. J. Chem. Kinet. 1983, 15,
1283−1300.
kinetic results enabled a thermochemical evaluation of the
standard enthalpy of formation of t-butyl free radical based on
the “Third Law” approach, which led to the following preferred
•
value: ΔfH2°98(t-C4H9 ) = 44.3
1.7 kJ mol−1 using S2°98(t-
•
(10) Seetula, J. A.; Russell, J. J.; Gutman, D. Kinetics and
Thermochemistry of the Reactions of Alkyl Radicals (CH3, C2H5, i-
C3H7, s-C4H9 and t-C4H9) with HI: A Reconciliation of the Alkyl
Radical Heats of Formation. J. Am. Chem. Soc. 1990, 112, 1347−1353.
C4H9 ) = 322.2 J K−1 mol−1. In view of the tenacious and
persistent disagreement with the results of some other
experiments resulting in very different chemical kinetics, we
forego at this time a recommended value in favor of a preferred
(11) Muller-Markgraf, W.; Rossi, M. J.; Golden, D. M. Rate
̈
•
value of ΔfH2°98(t-C4H9 ).
Constants for the Reaction t-C4H9 + DX → i-C4H9D + X (X = Br,
I), 295 < T (K) < 384: Heat of Formation of the tert-Butyl Radical. J.
Am. Chem. Soc. 1989, 111, 956−962.
ASSOCIATED CONTENT
■
(12) Pacansky, J.; Chang, J. S. Infrared matrix isolation studies on the
t-butyl radical. J. Chem. Phys. 1981, 74, 5539−5546.
S
* Supporting Information
Detailed experimental conditions for reactions 1 and 2. This
material is available free of charge via the Internet at http://
pubs.acs.org.
(13) Pacansky, J.; Yoshimine, M. J. Theoretical Studies on the
Barriers for internal Rotation of the Methyl Groups in the tert-Butyl
Radical. J. Phys. Chem. 1986, 90, 1980−1983.
(14) Benson, S. W.; Kondo, O.; Marshall, R. M. Absolute Rate
Constants for the Reaction of Br Atoms with i-C4H10. Int. J. Chem.
Kinet. 1987, 19, 829−839.
(15) Bracey, J.; Walsh, R. Unpublished results on the kinetics of I + i-
C4H10, cited and used in refs 9 and 10, 1983.
AUTHOR INFORMATION
■
Notes
The authors declare no competing financial interest.
(16) Rossi, M. J.; Golden, D. M. The Absolute Rate Constant for the
Metathesis t-C4H9 + DI → i-C4H9D + I and the Heat of Formation of
the t-Butyl Radical. Int. J. Chem. Kinet. 1979, 11, 969−976.
(17) Teranishi, H.; Benson, S. W. The Kinetics of Dehydrogenation
of Isobutane by Iodine and the Heat of Formation of the t-Butyl
Radical. J. Am. Chem. Soc. 1963, 85, 2887−2890.
ACKNOWLEDGMENTS
■
Generous support by the Swiss State Secretariat for Education,
Research and Innovation (SERI) through Contract No. SBF
Nr. C11.0052 in the framework of COST project CM0901
(Detailed Chemical Kinetic Models for Cleaner Combustion) is
gratefully acknowledged. We enjoyed substantial and insightful
discussions with John Barker and David Golden on our favorite
subject. We also would like to sincerely thank our Italian master
craftsman Mr. Flavio Comino for whom no challenge is large
enough regarding the construction of the experimental
apparatus.
(18) Knox, J. H.; Musgrave, R. H. Iodination of Alkanes: Ethane,
Propane and Isobutane. Trans. Faraday Soc. 1967, 63, 2201−2216.
(19) Gutman, D. The Controversial Heat of Formation of the t-
•
C4H9 Radical and the Tertiary C-H Bond Energy. Acc. Chem. Res.
1990, 23, 375−380.
(20) Houle, F. A.; Beauchamp, J. L. Photoelectron Spectroscopy of
Methyl, Ethyl, Isopropyl, and tert-Butyl Radicals. Implications for the
Thermochemistry and Structures of the Radicals and Their
Corresponding Carbonium Ions. J. Am. Chem. Soc. 1979, 101,
4067−4074.
REFERENCES
■
(1) Leplat, N.; Wokaun, A.; Rossi, M. J. Reinvestigation of the
(21) Schultz, J. C.; Houle, F. A.; Beauchamp, J. L. Photoelectron
Spectroscopy of 1-Propyl, 1-Butyl, Isobutyl, Neopentyl, and 2-Butyl
Radicals: Free Radical Precursors to High-Energy Carbonium Ion
Isomers. J. Am. Chem. Soc. 1984, 106, 3917−3927.
(22) Castelhano, A. L.; Griller, D. Heats of Formation of Some
Simple Alkyl Radicals. J. Am. Chem. Soc. 1982, 104, 3655−3659.
(23) Tsang, W. The Stability of Alkyl Radicals. J. Am. Chem. Soc.
1985, 107, 2872−2880.
•
Elementary Chemical Kinetics of the Reaction C2H5 + HBr (HI) →
C2H6 + Br• (I•) in the Range 293−623 K and Its Implication on the
•
Thermochemical Parameters of C2H5 Free Radical. J. Phys. Chem. A
2013, 117, 11383−11402.
(2) Leplat, N.; Rossi, M. J. The Measurement of the Rate Parameters
•
•
for the Reactions i-C3H7 and n-C3H7 + HI → C3H8 + I• over the
Temperature Range 293 − 623 K: Implications for the Standard Heat
of Formation of the Propyl Radicals. Int. J. Chem. Kinet. 2014, 46,
305−320, DOI: 10.1002/kin.20832.
(24) Tsang, W. Heat of Formation of Organic Free Radicals by
Kinetic Methods. In Energetics of Organic Free Radicals; Martinho
Simoes, J. A., Greenberg, A., Liebman, J. F., Eds.; Chapman & Hall:
London, 1996; pp 22−58.
(3) Russell, J. J.; Seetula, J. A.; Timonen, R. S.; Gutman, D.; Nava, D.
F. Kinetics and Thermochemistry of t-C4H9 Radical. Study of the
Equilibrium t-C4H9 + HBr ⇆ i-C4H10 + Br. J. Am. Chem. Soc. 1988,
110, 3084−3091.
(4) Richards, P. D.; Ryther, R. J.; Weitz, E. Diode Laser Probes of
tert-Butyl Radical Reaction Kinetics: Reaction of C(CH3)3• with HBr,
DBr, and HI. J. Phys. Chem. 1990, 94, 3663−3667.
(5) Nicovich, J. M.; van Dijk, C. A.; Kreutter, K. D.; Wine, P. H.
Kinetics of the Reactions of Alkyl Radicals with HBr. J. Phys. Chem.
1991, 95, 9890−9896.
(6) Seakins, P. W.; Pilling, M. J. Laser Flash Photolysis Study of the
Br + i-C4H10 ⇆ HBr + t-C4H9 Reactions. Heat of Formation of t-
C4H9. J. Phys. Chem. 1991, 95, 9874−9878.
(7) Seakins, P. W.; Pilling, M. J.; Niiranen, J. T.; Gutman, D.;
Krasnoperov, L. N. Kinetics and Thermochemistry of R + HBr ⇆ R-H
+ Br Reactions: Determinations of the Heat of Formation of C2H5, i-
C3H7, sec-C4H9 and t-C4H9. J. Phys. Chem. 1992, 96, 9847−9855.
(8) Seetula, J. A.; Slagle, I. R. Kinetics and Thermochemistry of the R
+ HBr ⇆ RH + Br (R = n-C3H7, i-C3H7, n-C4H9, i-C4H9, sec-C4H9 or
t-C4H9) Equilibrium. J. Chem. Soc., Faraday Trans. 1997, 93 (9),
1709−1719.
́ ́
(25) Kiraly, Z.; Kortvelyesi, T.; Seres, L. Thermal Reaction of 2-
̈
methyl-2-butene in the Presence of Azomethane: Enthalpy of
•
Formation of the Radicals (CH3)2C•CH(CH3)2 and tert-C4H9 .
Phys. Chem. Chem. Phys. 2000, 2, 349−354.
(26) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Stefanov, B. B.
Assessment of Complete Basis Set Methods for Calculation of
Enthalpies of Formation. J. Chem. Phys. 1998, 108, 692−697.
(27) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.;
Pople, J. A. Gaussian-3 (G3) Theory for Molecules Containing First
and Second-Row Atoms. J. Chem. Phys. 1998, 109, 7764−7776.
(28) Smith, B. J.; Radom, L. Heat of Formation of the tert-Butyl
Radical. J. Phys. Chem. A 1998, 102, 10787−10790.
(29) Marsi, I.; Viskolcz, B.; Seres, L. Application of the Group
Additivity Method to Alkyl Radicals: An ab Initio Study. J. Phys. Chem.
A 2000, 104, 4497−4504.
(30) Janoschek, R.; Rossi, M. J. Thermochemical Properties of Free
Radicals from G3MP2B3 Calculations. Int. J. Chem. Kinet. 2002, 34,
550−560.
M
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A
Article
(31) Leplat, N.; Rossi, M. J. Effusive Molecular Beam-Sampled
Knudsen Flow Reactor Coupled to Vacuum Ultraviolet Single Photon
Ionization Mass Spectrometry Using an External Free Radical Source.
Rev. Sci. Instrum. 2013, 84, No. 114104, DOI: 10.1063/1.4829879.
(32) Dillon, R. T.; Young, W. G. The Preparation of Anhydrous
Hydrogen Iodide. J. Am. Chem. Soc. 1929, 51, 2389−2391.
(33) Dobis, O.; Benson, S. W. Temperature Coefficients of the Rates
of Cl Atom Reactions with C2H6, C2H5 and C2H4. The Rates of
Disproportionation and Recombination of Ethyl Radicals. J. Am. Chem.
Soc. 1991, 113, 6377−6386.
(34) Warnatz, J. Rate Coefficients in the C/H/O System. In
Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New
York, 1984; pp 197−360.
(35) Parkes, D. A.; Quinn, C. P. Study of the Spectra and
Recombination Kinetics of Alkyl radicals by Molecular Modulation
Spectrometry. J. Chem. Soc., Faraday Trans. I 1976, 72, 1952−1971.
(36) Arthur, N. L. Absorption Cross-Sections and Mutual Reaction
Rate Constants for C2H5 and t-C4H9 Radicals. J. Chem. Soc., Faraday
Trans. II 1986, 82, 1057−1065.
(37) Anastasi, C.; Arthur, N. L. Rate Constants for the Reactions of
CH3 Radicals with C2H5, i-C3H7 and t-C4H9 Radicals. J. Chem. Soc.,
Faraday Trans. II 1987, 83, 277−287.
(38) Kerr, J. A. Rate Processes in the Gas Phase. In Free Radicals,
Kochi, J. K., Ed.; John Wiley & Sons, New York, 1973; Vol. I
(Dynamics of Elementary Processes), pp 1−36.
(39) Mitchell, T. J.; Gonzalez, A. C.; Benson, S. W. Very Low
Pressure Reactor Study of the H + HBr = H2 + Br Reaction. J. Phys.
Chem. 1995, 99, 16960−16966.
(40) Vasileiadis, S.; Benson, S. W. Kinetics of the Reaction: H + HI =
H2 + I at 298 K and Very Low Pressures. Int. J. Chem. Kinet. 1997, 29,
915−925.
(41) Burcat, A.; Ruscic, B. Third Millennium ideal Gas and
Condensed Phase Thermochemical Database for Combustion with
Updates from Active Thermochemical Tables, Argonne National
Laboratory. Report ANL-05/20 and Technion Report TAE 960 2005.
See also: http://garfield.chem.elte.hu/Burcat/burcat.html.
(42) Fettis, G. C.; Knox, J. H.; Trotman-Dickenson, A. F. The
Reaction of Bromine Atoms with Alkanes and Methyl Halides. J. Chem.
Soc. A 1960, 4177−4185.
(43) Islam, T. S. A.; Benson, S. W. Rates and Equilibria in the
Reaction System Br + i-C4H10 = HBr + t-C4H9. The Heat of
Formation of the t-Butyl Radical. Int. J. Chem. Kinet. 1984, 16, 995−
1008.
(44) Choo, K. Y.; Choe, M. H. A Kinetic Study of Br Atom Reactions
with Trimethylsilane by the VLPR (Very Low Pressure Reactor)
Technique. Bull. Korean Chem. Soc. 1985, 6, 196−202.
(45) Muller-Markgraf, W.; Rossi, M. J. Interaction of Br (2P3/2) and
̈
Br (2P1/2) with PTFE and Polycrystalline Ni Surfaces. Int. J. Chem.
Kinet. 1995, 27, 403−418.
(46) Moore, C. E. Atomic Energy Levels. NBS Monogr. 1971, 467, 2.
(47) Yardley, J. T. Vibration-to-Translation (V-T) Energy Transfer.
Introduction to Molecular Energy Transfer; Academic Press, Inc.: New
York, 1980; Chapter 4.
N
dx.doi.org/10.1021/jp500724r | J. Phys. Chem. A XXXX, XXX, XXX−XXX