Absolute rate constants for the β-scission and hydrogen abstraction reactions of the tert-butoxyl radical and for several radical rearrangements: Evaluating delayed radical formations by time-resolved electron spin resonance

Article abstract of DOI:10.1021/ja990837y

An analysis is presented for the determination of absolute rate constants for radical transformation reactions in complex reaction systems by time-resolved ESR during intermittent photochemical radical production. The technique is applied to obtain absolu

Full text of DOI:10.1021/ja990837y

J. Am. Chem. Soc. 1999, 121, 7381-7388
7381
Absolute Rate Constants for the â-Scission and Hydrogen Abstraction
Reactions of the tert-Butoxyl Radical and for Several Radical
Rearrangements: Evaluating Delayed Radical Formations by
Time-Resolved Electron Spin Resonance
Matthias Weber and Hanns Fischer*
Contribution from the Physikalisch-Chemisches Institut der UniVersit a¨ t Z u¨ rich, Winterthurerstrasse 190,
CH-8057 Z u¨ rich, Switzerland
ReceiVed March 15, 1999
Abstract: An analysis is presented for the determination of absolute rate constants for radical transformation
reactions in complex reaction systems by time-resolved ESR during intermittent photochemical radical
production. The technique is applied to obtain absolute rate constants in large temperature ranges for the
â-scission of the tert-butoxyl radical in various solvents and its hydrogen abstraction from cyclohexane,
cyclopentane, tert-butylbenzene, and anisole. Kinetic studies of the neophyl and the 2-methyloxiran-2-yl
rearrangements and the decarboxylation of the tert-butoxycarbonyl radical also demonstrate the versatility of
the method. Further, rate data are given for the addition of the methyl radical to benzene and fluorobenzene,
as well as for the hydrogen abstraction of methyl from di-tert-butyl peroxide.
Introduction
Lower rate constants can be derived from the time dependence
of the radical concentrations in kinetic systems with competing
reactions. Then, all competing reactions must be known, and
the time profiles must be sufficiently exact so that several rate
parameters can be extracted simultaneously by numerical fits
of rate equations to the experimental data. Here, as in previous
work, we use this technique in combination with radical
detection by electron spin resonance. Transient radicals are
produced photochemically from suitable precursors with inter-
mittent generation. Kinetic traces of their concentrations are
taken during the on- and off-periods, are coherently accumulated
to increase the signal-to-noise ratio, and are analyzed. Full
analyses of the complete traces are possible but tedious and
Reactions which convert transient radicals A‚ into other forms
B‚ are ubiquitous. They include conformational and configu-
rational isomerizations, structural rearrangements by internal
atom, and group migrations or cyclizations, fragmentations, and
bimolecular reactions by electron, atom, or group transfer as
well as additions to unsaturated compounds. Many of these
processes are synthetically and technically useful, and hence,
much effort has been devoted to determine their rate constants
1
both in the gas and in the liquid phase. Depending on radical
and reaction, the rate constants vary by many orders of
magnitude. Ideally, for their determination one would apply
kinetic isolation conditions, that is, generate the primary species
A‚ in a short pulse and then follow its conversion to B‚ by a
spectroscopic technique, eventually in competition with the
formation of an indicator radical. However, most direct detection
techniques require appreciable initial radical concentrations of
2
a
were performed earlier for a fragmentation and several
2b
hydrogen abstractions competing with self- and cross-termina-
tions. However, a simpler analysis is sufficient if the desired
radicals B‚ are formed rapidly from A‚ or other precursors, and
if their first- or pseudo-first-order reactions contribute only little
to the total decay; that is, they are slow compared to the
terminations. Then, the rate parameters follow from fits of
approximate analytical formulas to the decay profiles in the off-
period of radical generation. This procedure yielded rate
constants for various hydrogen and chlorine atom transfer
-6
-5
about 10 -10 M. For transient radicals the bimolecular self-
and cross-terminations are close to diffusion or collision control
9
-1 -1
1c
(
2kt ≈ (1-10) × 10 M
s
for usual conditions), and thus
interfere with the radical transformation in times longer than
about 10-1000 µs after the pulse. Hence, the reactions of
interest can only be isolated if the rate constants are fairly large.
3
reactions and radical additions to alkenes, alkynes, and aromatic
4
(1) (a) Kerr, J. A.; Moss, S. J. Handbook of Bimolecular and Termo-
compounds.
lecular Gas Reactions; CRC Press: Boca Raton, FL, 1981, Vol. 1, p 2. (b)
de Mayo, P. Rearrangement in Ground and Excited States; Academic
Press: New York, 1980, Vol. 1-3. (c) Landolt-B o¨ rnstein, Radical Reaction
Rates in Liquids; Fischer H., Ed.; New Series, Springer: Berlin, Germany,
(2) (a) R u¨ egge, D.; Fischer, H. Int. J. Chem. Kinet. 1986, 18, 145-158.
(b) R u¨ egge, D.; Fischer, H. J. Chem. Soc., Faraday Trans. 1 1988, 84,
3187-3205.
(3) (a) D u¨ tsch, H.-R.; Fischer, H. Int. J. Chem. Kinet. 1981, 13, 527-
541. (b) D u¨ tsch, H. R.; Fischer, H. Int. J. Chem. Kinet. 1982, 14, 195-
200.
(4) (a) Fischer, H. in Free Radicals in Biology and EnVironment; Minisci,
F., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1997l;
pp 63-78 and references given therein. (b) Rubin, H.; Fischer, H. HelV.
Chim. Acta 1996, 79, 1670-1682. (c) Zytowski, T.; Fischer, H. J. Am.
Chem. Soc. 1996, 118, 437-439. (d) Zytowski, T.; Fischer, H. J. Am. Chem.
Soc. 1997, 119, 9, 12869-12878. (e) Weber, M.; Fischer, H. HelV. Chim.
Acta 1998, 81, 770-780.
1
983-1997, Vol. II/13, II/18. (d) Baulch, D. L.; Cobos, C. J.; Cox, R. A.;
Esser, C.; Frank, P.; Just, T.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker,
R. W.; Warnatz, J. J. Phys. Chem. Ref. Data 1992, 21, 411-734. (e) Baulch,
D. L.; Cobos, C. J.; Cox, R. A.; Frank, P.; Hayman, G.; Just, T.; Kerr, J.
A.; Murrells, T.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J.
Phys. Chem. Ref. Data 1994, 23, 847-1033. (f) Neta, P.; Grodkowski, J.;
Ross, A. B. J. Phys. Chem. Ref. Data 1996, 25, 709-1050. (g) Fossey, J.;
Lefort, D.; Sorba, J. Free Radicals in Organic Chemistry; John Wiley &
Sons: New York, 1995. (h) Scaiano, J. C. CRC Handbook of Organic
Photochemistry; CRC Press: Boca Raton, FL, 1989, Vol. I, II.
1
0.1021/ja990837y CCC: $18.00 © 1999 American Chemical Society
Published on Web 07/29/1999

7382 J. Am. Chem. Soc., Vol. 121, No. 32, 1999
Weber and Fischer
e-t/τA
+ t/τ2
Now, we extend this analysis to cases where the observed
[
A‚] ) [A‚]0‚
(9)
species are formed not only during the photolysis but also
thereafter from an instantly formed precursor. Then, in the
beginning of the off-period the concentration vs time profiles
have a sigmoid shape. This effect of delayed radical formation
1
e-t/τA - e-t/τB
[B‚]0
B
[
B‚] )
e-t/τ + τ ‚(1 + τ /τ )‚
0
A
B
2
+ t/τ2{
τA - τ
B
}
1
5
was already observed by Bennett et al. in 1974. However, it
(
10)
has not yet been exploited to obtain rate constants for radical
reactions.
[
C‚]0
τB
1 + ‚(1 - e
-t/τB
In the following, we provide the appropriate analytical
formulas in short. These are then applied to the formation of
the methyl radical by â-scission of the tert-butoxyl radical and
to its competing hydrogen abstraction reactions from several
[C‚] )
) +
{
1
+ t/τ2
τ2
-t/τB
-t/τA
τ
τ ‚e
- τAe
A
B
‚
(1 + τ /τ )
+ 1 (11)
B
2
(
)}
τ2
τA - τ
B
1
substrates. These reactions are well-known but especially, for
In the following we concentrate on the behavior of radical
the â-scission reliable absolute rate constants, are still missing.
To show the versatility of the method, we also restudy several
radical rearrangements. Moreover, rate data are given for
processes which accompany the reactions of major interest.
B‚ and on the determination of its formation (τA) and decay
(
τB) parameters with eq 10. When A‚ converts instantly to B‚,
3
,4
this simplifies to the previously used relation
e-t/τB
+ t/τ2
Reaction Kinetics
[
B‚] ) [B‚]0
(12)
1
We consider the sequence of reactions 1-4 which corre-
sponds to the studied systems
For a fast conversion obeying τA , τB and 1 + τA/τB ≈ (1 -
-1 τ /τ
A B
τA/τB) ≈ e
, it can be rewritten for t . τA as
I
source
98 A‚
(1)
(2)
(3)
(4)
-(t-τ )/τ
A
B
e
[
B‚] ) [B‚]0
(13)
kA
1
+ (t - τ )/(τ + τ )
A 2 A
A‚
B‚
9
kB
9
8 B‚
In essence, this relation was applied earlier to determine the
fragmentation rate constant of the cumyloxyl radical. For a
pure second-order decay of B‚ it becomes
8 C‚
4d
2kt
X‚ + Y‚
98 products
[
B‚]0
X‚, Y‚ ) A‚, B‚, C‚
[B‚] )
(14)
1
+ (t - τ )/(τ + τ )
A
2
A
In the on-period of photolysis, radical A‚ is produced from a
suitable precursor with a constant rate I (1). It then transforms
to radical B‚ by a first- or pseudo-first-order process 2 with
rate constant kA. Radical B‚, in turn, reacts with first- or pseudo-
first-order kinetics in reaction 3 to radical C‚ (rate constant kB).
All radicals self- and cross-terminate to nonradical products (4).
The rate constants of these termination reactions are assumed
to be equal, and deviations therefrom are considered below.
Further, the radicals shall reach their steady-state concentrations
in the on-period. The rate equations for reactions 1-4 yield for
the steady state
Basically, eqs 13 and 14 show that a sufficiently fast delayed
formation causes a simple shift of the onset of the radical decay
by the precursor lifetime τA.
To check the influence of unequal terminations on rate
constants kA and kB obtained by fits of eq 10 to experimental
6
data, we solved the rate equations for reactions 1-4 numerically
-
3
-1
B
9
-1 -1
3
-1
5
8
for I ) 10 M s , 2kt ) 10 M s , 10 s e kA e 10
-
1
-1
-1
AA
CC
s , 10 s e kB e 200 s , and 2kt and 2kt set as 2 × 10
-
1
-1
9
-1 -1
7a
M
s
and/or 5 × 10 M
s
using the geometric mean
for the cross-terminations. The fits to the numerical results
retrieved the inputs kA and kB with less than 20% deviations
for most cases and a maximum deviation of about a factor of 2
for extremely different termination constants. Hence, if the
radicals have similar sizes and terminate diffusion-controlled,
that is, have similar termination constants in the order of
for usual solvent viscosities,
applications of eq 10 to kinetic traces should provide rather
reliable results. For the carbon-centered radicals encountered
I
2 k
[
A‚] + [B‚] + [C‚] )
) I‚τ2
(5)
0
0
0
x
t
-
1
where τ2 ) (2 kt([A‚]0 + [B‚]0 + [C‚]0)) is the second-order
9
-1 -1
magnitude of 1-10 × 10 M
s
lifetime of the total radical concentration, and
I‚τA
[
A‚] )
(6)
(7)
(8)
7b
0
in this work, this is expected to be well fulfilled, and there is
1
+ τ /τ2
A
some evidence that the self-termination constant of the tert-
I‚τB
butoxyl radical occurs also with a rate close to the diffusion-
[
B‚] )
1c
0
controlled limit.
(
1 + τ /τ )‚(1 + τ /τ )
A
2
B
2
Experimental Section
I‚τ2
[
C‚] ) [B‚] ‚τ /τ )
Most of the chemicals were obtained commercially in the purest
available forms and used as received. Water, tert-butylbenzene, and
di-tert-butyl peroxide were purified by repeated distillation. Benzene,
0
0
2
B
(
1 + τ /τ )‚(1 + τ /τ )
A 2 B 2
where τA ) kA- and τB ) kB-1. Equations 6-8 are useful to
extract relative lifetimes from steady-state radical concentrations
and have widely been applied.1 For the off-period starting at t
1
(6) MATLAB 4.2c.1 using the Gear algorithm for integrating the stiff
differential equations. To take account of the closure condition in the
repetitive sampling, we repeated the integrations several times and, for each
repetition, we set the initial concentrations to the final concentrations of
the previous one. The method converged after three to four iterations.
(7) (a) Paul, H.; Segaud, C. Int. J. Chem. Kinet. 1980, 12, 637-647. (b)
Fischer, H.; Paul, H. Acc. Chem. Res. 1987, 20, 200-206.
c
)
0 one obtains the following:
(5) Bennett, J. E.; Eyre, J. A.; Rimmer C. P.; Summers, R. Chem. Phys.
Lett. 1974, 26, 69-71.

Absolute Rate Constants for the tert-Butoxyl Radical
J. Am. Chem. Soc., Vol. 121, No. 32, 1999 7383
solvents were presented by Walling and co-workers.10 They
found an astonishing large variation with the solvent and
concluded that this is due to a solvent dependence of the
fragmentation and not of the hydrogen abstraction. Later, similar
product studies provided many rate constants for addition and
abstraction processes of the tert-butoxyl radical relative to the
â-scission and/or the hydrogen abstraction from cyclohexane
fluorobenzene, cyclopentane, and cyclohexane were passed through an
alumina column, and all solutions were freed from oxygen by at least
3
0 min of purging with argon or helium before use. The arrangements
and procedures for steady-state and time-resolved electron spin
resonance spectroscopy have been described earlier.2-4 In principle,
the signal s(n) of a radical is monitored with repetition times of 5-10
ms. Individual signal vs time profiles (100000-500000) are coherently
accumulated and provide 500 data points in the n channels of a transient
recorder. The s(n) obey s(n) ) c[R(t)], with [R(t)] representing the
radical concentration at time t ) nτ. Here, τ is the channel time width
and c is a sensitivity constant which has not been determined since it
does not influence the extraction of first-order rate constants.
1
c
and other donors.
The strong solvent dependence of the â-scission and the
solvent independence of the hydrogen abstraction reaction were
1
1
confirmed more recently by Ingold et al. in direct time-
resolving studies of product formation and radical decay at 30
The decay parts of the time profiles were analyzed by fits using the
simplex algorithm and either eq 9 if radical A‚ was observed, eq 12 or
°C. These authors also discussed the solvent dependence in detail
9
if the transformation to B‚ was very fast, or eq 10. The fitting
but used the cumyloxyl radical as the model alkoxyl because
tert-butoxyl decayed too slowly for their optical detection
methods. Since our technique allows the study of slower
processes, we applied it here to tert-butoxyl and also present
the temperature dependence of the rate constants. The tert-
butoxyl radical cannot be directly detected in the liquid phase
procedure required the definition of the effective time t at which the
0
photochemical radical generation ends. Actually, the sector edge does
not cut off the light beam instantly but in a sigmoid type fashion2
extending over 10-20 µs. This variation was measured by recording
the signal amplitude of tert-butyl radicals during continuous photolysis
of 4 vol % di-tert-butyl ketone in tetradecane and at room temperature
as a function of the sector angle position φ. In this system, tert-butyl
is generated in about 1-2 µs after ketone excitation, that is, practically
12
by electron spin resonance. Therefore, the kinetic probe is the
methyl radical and its delayed formation from tert-butoxyl after
the scission reaction. 1,1,2-Trichloro-1,2,2-trifluoroethane (Fri-
gen 113), benzene, and fluorobenzene were used as fairly inert
solvents, and the tert-butoxyl radicals were generated by
photolysis of 10 vol % di-tert-butyl peroxide. The dissociative
excited state of the peroxide ensures an instant tert-butoxyl
formation. As further medium, neat di-tert-butyl peroxide was
employed. It is known that tert-butoxyl abstracts a hydrogen
atom from the peroxide. The resulting radical ‚CH2CMe2-
OOCMe3 undergoes rapid fragmentation to 2,2-dimethyl oxirane
8
9
instantly, and shows a pure second-order decay. Hence, the square
of the signal amplitude is proportional to the generation rate I. In the
transition region from the on- to the off-period, this rate followed the
relation I(φ) ∝ (1 - tanh[b(φ - φ
but fixed) origin of the angular scale and the parameter b depends on
the slit width. t was then defined by the position of the inflection point
and was determined in kinetic experiments involving the di-tert-
0 0
)])/2, where φ is the (arbitrarily set
0
φ
0
butyl ketone system and simulations of the tert-butyl trace including
the sigmoid generation. Interestingly, the location of the inflection point
resulted also and more simply from fits of pure second-order decays
to eq 15
5
-1
13
and tert-butoxyl with k ) 7 × 10 s at 298 K in benzene.
r
Since this reaction regenerates tert-butoxyl and is fast in the
temperature range employed here, it should not influence the
methyl formation kinetics.
[
B‚]0
[B‚] )
(15)
1
+ (t - t )/τ2
0
In accord with expectation, ESR spectra taken during
continuous photolysis of the peroxide in the four solvents
revealed the presence of methyl in high predominance. Solvent-
derived radicals and the peroxide-derived species ‚CH2CMe2-
OOCMe3 were not observed, but there were very weak signals
of radicals which are formed from products of the major
reactions. Thus, the acetonyl radical ‚CH COCH arises by
which is very similar to eq 14. This is not surprising, since the sigmoid
drop of the radical generation and a delayed formation of the radical
from its precursor must lead to a similar behavior of the concentration
in the on-off transition region. Hence, t
the simpler procedure. In analyses of the various kinetic experiments,
was taken as time origin and defined the channel number for the
0
was mostly determined by
t
0
2
3
on-off transition. This number was held constant as long as the optical
arrangement remained unchanged. More details justifying the procedures
are given as Supporting Information. The upper limiting value of a
hydrogen abstraction from the scission product acetone, the
-hydroxyprop-2-yl radical (CH3)2 C˙ OH by photoreduction of
2
acetone, and the tert-butoxymethyl radical, ‚CH2CO(CH3)3, by
hydrogen abstraction from the cross-termination product of
methyl and tert-butoxyl. The total concentration of the additional
radicals was less than about 8% of methyl and was neglected
in the analysis.
Figure 1 shows kinetic traces of the methyl radical in Frigen
113 containing 10 vol % di-tert-butyl peroxide at two temper-
atures. Overlayed are fits of eq 10 to the data, and the bottom
traces are the fit residuals. After the end of the photolysis the
delayed formation of methyl is clearly visible, in particular in
the enlarged inset. Table 1 gives the lifetimes obtained from
first- or pseudo-first-order rate constant k
A
measurable with the
5
-1
technique is about 10 s . Rate constants given in the figures and tables
are averages from 5 to 15 individual determinations. ESR spectra
obtained during continuous photolysis demonstrate the reactions and
are included in the Supporting Information, and all radicals mentioned
were identified by their known g factors and hyperfine coupling
constants.
â-Scission and Hydrogen Abstractions of the tert-Butoxyl
Radical and Reactions of the Methyl Radical with
Solvents
The â-scission of the tert-butoxyl radical into acetone and
the methyl radical is well-known. In liquids it often occurs in
competition with hydrogen abstraction by tert-butoxyl from
solvent or substrates. Early extensive product studies on the ratio
of rate constants for the â-scission and for the hydrogen
abstraction from cyclohexane and other substrates in various
(
10) (a) Walling, C.; Pawda, A. J. Am. Chem. Soc. 1963, 85, 1593-
1
1597. (b) Walling, C.; Pawda, A. J. Am. Chem. Soc. 1963, 85, 1597-1601.
(
c) Walling, C.; Wagner, P. J. Am. Chem. Soc. 1963, 85, 2333-2334. (d)
Walling, C.; Wagner, P. J. J. Am. Chem. Soc. 1964, 86, 3368-3375. (e)
Walling, C. Pure Appl. Chem. 1967, 15, 69-80, and further references
therein.
(11) Avila, D. V.; Brown, C. E.; Ingold, K. U.; Lusztyk, J. J. Am. Chem.
Soc. 1993, 115, 466-470.
(12) (a) Ingold, K. U.; Morton, J. R. J. Am. Chem. Soc. 1964, 86, 3400-
3402. (b) Symons, M. C. R. J. Am. Chem. Soc. 1969, 91, 5924, and
references given therein.
(13) Bloodworth, A. J.; Davies, A. G.; Griffin, I. M.; Muggleton, B.;
Roberts, B. P. J. Am. Chem. Soc. 1974, 96, 7599-7601.
(
8) (a) Tsentalovich, Y. P.; Fischer, H. J. Chem. Soc., Perkin Trans. 2
994, 729-733. (b) Neville, A. G.; Brown, C. E.; Rayner, D. D. M.;
Lusztyk, J.; Ingold, K. U. J. Am. Chem. Soc. 1991, 113, 1869-1870.
9) Schuh, H.-H.; Fischer, H. Int. J. Chem. Kinet. 1976, 8, 341-356;
HelV. Chim. Acta 1978, 61, 2130-2164.
1
(

7384 J. Am. Chem. Soc., Vol. 121, No. 32, 1999
Weber and Fischer
Figure 2. Rate constants and fits to the Arrhenius equation for the
reaction of methyl radicals with benzene (closed circles) and fluo-
robenzene (open circles) and di-tert-butyl peroxide in Frigen 113 (open
squares).
Figure 1. Methyl concentrations vs time in Frigen 113 at (a) 298 (
1
K and (b) 307 ( 1 K and fits of eq 10 to the data. Bottom traces are
residuals of fits, and the inset shows an expansion of the traces around
t ) 0 s.
Table 1. Lifetimes τ
2
, τ
A
B
, and τ Obtained by Fits of Equation 10
to Kinetic Traces of the Methyl Radical in Frigen 113 at Different
a
Temperatures
T, K
τ
2
, µs
τ
A
, µs
B
τ , ms
2
2
2
2
2
3
3
78
83
89
93
98
02
07
424 (50)
409 (51)
383 (31)
374 (24)
370 (19)
363 (19)
350 (32)
394 (23)
338 (30)
215 (11)
164 (9)
125 (6)
85 (3)
60 (20)
33 (8)
23 (10)
17 (2)
14 (2)
11 (3)
8.3 (2)
59 (2)
a
Standard deviations are given in brackets in units of the last quoted
digit.
the fits. Obviously, several lifetimes are significant, are of similar
orders of magnitude, and can be determined simultaneously,
though with different confidence. The second-order lifetime τ2
is due to terminations and is not evaluated here. τA is interpreted
as the lifetime of tert-butoxyl, and since no solvent-derived
radicals are observed, it is identified as the inverse rate constant
of the â-scission. τB reflects reactions of the methyl radical with
some constituent of the Frigen 113 solution. It was found that
Figure 3. Rate constants and fits to the Arrhenius equation for the
â-scission of the tert-butoxyl radical in Frigen 113 (open squares), di-
tert-butyl peroxide (closed squares), benzene (closed circles), and
fluorobenzene (open circles).
Table 2. Absolute Rate Constants and Arrhenius Parameters for
the â-Scission of the tert-Butoxyl Radicala
1
a
E )
, kJ/mol log(A/s-1
solvent
T, K
k
â,298, s-
-
1
τB increases linearly with the concentration of di-tert-butyl
peroxide and passes through the origin of a corresponding
pseudo-first-order plot, whereas τA decreases only very slightly.
Hence, the reaction leading to τB is very probably and
exclusively the hydrogen abstraction of methyl from the
peroxide. From the slope of the pseudo-first-order plot, we
Frigen 113 278-312
8050 (400)
52.7 (19)
50.5 (18)
48.7 (9)
13.2 (5)
12.9 (5)
12.8 (2)
12.7 (3)
DTBPO
283-323 12000 (2900)
284-318 20300 (3500)
263-308 21400 (1800)
C
C
6
H
H
6
6
5
F
47.5 (11)
a
Standard deviations are given in brackets in units of the last quoted
digit. DTBPO ) di-tert-butyl peroxide.
-1 -1
obtained kMe,298 ) 132(37) M s , and experiments at different
-
1
-1
Figure 2 shows the temperature dependence of the rate constants
for the reactions of the methyl radical with the solvents.
temperatures gave log(kMe/ M s ) ) 9.3(3) - 41.0(15)/
.303RT with the activation energy expressed in kilojoules per
2
The temperature dependence of the rate constants kâ for the
â-scission of the tert-butoxyl radical is shown in Figure 3, and
the activation parameters are given in Table 2. As concluded
mole and standard deviations given in units of the last quoted
digit. The frequency factor is in the normal range for hydrogen
atom abstractions, and the rate constants are small enough to
be compatible with the undetectably low concentration of ‚CH2-
CMe2OOCMe3.
1
0
by Walling et al. for tert-butoxyl and found by Ingold et al.
1
1
for cumoxyl, kâ varies with the solvent and for our solvents
at room temperature by a factor of 2.6. The frequency factors
are normal for the elimination of a small group, and the above-
mentioned decrease of τA with increasing peroxide concentration
is explained by the increasing scission rate.
Kinetic traces taken with the other solvents benzene, fluo-
robenzene, and neat di-tert-butyl peroxide closely resembled
those given in Figure 1. For benzene and fluorobenzene, the
lifetime τB was shorter than predicted by the reaction of methyl
with the peroxide alone. This is due to the well-known methyl
addition to aromatic compounds. From τB the rate constants kadd
of this process were obtained using τB-1 ) kDTBPO[peroxide] +
kadd[solvent] with kDTBPO as given above. In Arrhenius form they
Reliable absolute values for kâ of tert-butoxyl in liquid media
are still missing. From relative values kâ/kH and various absolute
14a
rate constants for the hydrogen abstraction kH, Scaiano
-1
deduced kâ ) 29 000 s for 295 K and aromatic solvents. This
is strongly supported by our findings. Wong’s estimate of kâ
) 300 s in di-tert-butylperoxide at room temperature is much
too low, and Ingold’s early Arrhenius parameters also lead
-
1
-1
14b
are presented by log(kadd(benzene)/M s ) ) 8.3(2) - 36.7-
-1
-1
(
3
10)/2.303RT and log(kadd(fluorobenzene)/M-1 s ) ) 8.7(7) -
4d
14c
9.5(2)/2.303RT, in excellent agreement with our earlier data.

Absolute Rate Constants for the tert-Butoxyl Radical
J. Am. Chem. Soc., Vol. 121, No. 32, 1999 7385
to very small values. For aqueous solution and at room
temperature, Bors et al.14d reported kâ ) 1.4 × 10 s . This is
6 -1
larger than our data but compatible with an earlier estimate of
6
7
-1
14e
1
0 < kâ < 10 s by Gilbert et al. If the data for the aqueous
phase are correct, the solvent dependence is even larger than
indicated by the results found for organic solvents alone. Gas-
phase rate constants are also available. By a combination of
earlier data, Choo and Benson15 obtained log(A/s ) ) 14.1 and
Ea ) 64 kJ/mol. Using a calculated frequency factor for the
-1
16
combination of tert-butoxyl with NO, Batt et al. determined
-
1
log(A/s ) ) (14.04 ( 0.37) and Ea ) (62.5 ( 0.6) kJ/mol for
03-443 K. The rate constants at 300 K are at least 10 times
3
smaller in the gas phase than in solution, and both the frequency
factors and the activation energies are significantly lower for
the liquid phase. The lower activation energies point to
considerable solvation effects, which are already clear from the
solvent dependence. They are likely due to the fact that the
transition state for the â-scission from the unpolar radical to
the polar acetone is more polar than the radical. Hence, it is
more stabilized by interactions with polar and polarizable
solvents than the radical. Our small selection of solvents does
Figure 4. Rate constants and fits to the Arrhenius equation for the
hydrogen abstraction of the tert-butoxyl radical from cyclohexane in
Frigen 113 (open squares), benzene (closed circles), and fluorobenzene
(open circles).
in Figure 4 renders the small differences of the activation
parameters insignificant. This again supports Walling’s and
1
0,11
Ingold’s conclusion
of solvent-independent abstractions.
not allow us to quantify this point, and we refer to the earlier
Moreover, our absolute rate constants and activation parameters
agree very well with the few previous data. Thus, Howard and
discussions.1
0,11
Further, the lower activation energies for the
solutions may also mean earlier transition states, and this may
lead to the lower frequency factors. Our data in Table 2 confirm
this correlation of the activation parameters. In comparison to
cumyloxyl11 the â-scission of tert-butoxyl is about a factor of
1
7a
6
-1 -1
Scaiano report an absolute value of kH ) 1.6 × 10 M
at 300 K whereas we find about 1.0 × 10 M s . For Frigen
13, benzene, and fluorobenzene, Walling’s relative data10 led
to Ea,â - Ea,H ) 40.0, 36.2, and 32.8 kJ/mol and log(Aâ/AΗ/M)
s
6
-1 -1
1
2
0 slower at 30 °C, in agreement with known structural effects
)
)
5.04, 4.63, and 4.15, and our absolute data yield Ea,â - Ea,H
40.8, 36.8, and 32.9 kJ/mol and log(Aâ/AΗ/M) ) 5.2, 4.7,
10
on the cleavage.
In inert solvents the hydrogen abstraction reaction of the tert-
butoxyl radical with suitable added substrates will compete with
the â-scission. If not too fast, its rate constant can also be
determined using eq 10. In principle, one can kinetically follow
either the substrate-derived species or the methyl radical. In both
and 4.2. Further, we note that the rate constants for hydrogen
abstraction from cyclohexane are very similar for tert-butoxyl
11
5
6
-1 -1
and cumyloxyl radicals (9.1 × 10 vs 1.2 × 10 M
s
at
3
0 °C); that is, there are only small structural effects of the
alkoxyl radical residues on the hydrogen abstraction.
10,11
Our
-
1
cases the lifetime τA obeys τA ) kâ + kH[substrate], where
kâ is the rate constant for the â-scission. The choice of the radical
will depend on the ease of its detection.
rate constants kH also provide a coarse re-estimate of the self-
termination constant 2kt of the tert-butoxyl radical at about room
temperature and in low viscous solvents from known ratios 2kt/
Here, we investigate the hydrogen abstractions from cyclo-
hexane, cyclopentane, tert-butylbenzene, and anisole. For all
of these substrates, the radical formed by the hydrogen abstrac-
tion was observed besides methyl. Methyl has less ESR-line
groups than the cycloalkyl species but more than the primary
radicals from tert-butylbenzene and anisole. Therefore, in the
first two cases, methyl was followed whereas in the latter the
kinetics of the substrate-derived radicals was analyzed.
2
17b
2
kH . Walling et al. reported 2 kt/kH ) 0.01, which leads to
10
-1 -1
2
14c
an acceptable 2kt ≈ 10
M
s . Ingold’s 2 kt/kH ) 0.35
gives a value that is too high, but both results confirm a fast
self-termination.
The same procedure was applied to the hydrogen abstraction
of tert-butoxyl from cyclopentane (22-124 mM) in fluoroben-
zene and provided the rate parameters also displayed in Table
3
. For this substrate various absolute hydrogen abstraction rate
1
8
Cyclohexane was added in 11.5 and 24.4 mM concentrations
constants are available, and a comparison of our data shows
again good general agreement.
to solutions of di-tert-butyl peroxide (10 vol %) in Frigen 113,
-
1
benzene, and fluorobenzene. Plots of τA vs the cyclohexane
concentrations were linear. Experiments at different temperatures
led to the data shown in Figure 4, and the activation parameters
of the abstraction constant for the individual solvents are given
in Table 3.
For tert-butylbenzene (1.0-5.2 M) and methylphenyl ether
(anisole, 0.5-1.5 M) in di-tert-butyl peroxide, the kinetic traces
of the substrate-derived primary radicals were analyzed. As
-1
before, plots of τA vs the substrate concentrations were linear.
The rate constants kH and the activation parameters (Table 3)
again agree with some earlier data. The hydrogen abstraction
from tert-butylbenzene was measured in benzene relative to the
For the three solvents the rate constants are nearly equal, and
the fit of one Arrhenius equation to the combined data shown
1
9
â-scission. With kâ from Table 2 the reported ratios convert
4
-1 -1
19a
4
(14) (a) Scaiano, J. C. in Landolt-B o¨ rnstein, Radical Reaction Rates in
to kH ) 1.8 × 10 M
s
at 313 K and to kH ) 8.8 × 10
Liquids; Fischer H., Ed.; New Series, Springer: Berlin, Germany, 1984,
Vol. II/13d, p 8. (b) Wong, S. K. Int. J. Chem. Kinetics 1981, 13, 433-
(17) (a) Baign e´ e, A.; Howard, J. A.; Scaiano, J. C.; Stewart, L. C. J.
Am. Chem. Soc. 1983, 105, 6120-6123. (b) Walling, C.; Kurkov, V. P. J.
Am. Chem. Soc. 1967, 89, 4895-4901.
(18) (a) Paul, H.; Small, R. D., Jr.; Scaiano, J. C. J. Am. Chem. Soc.
1978, 100, 4520-4527. (b) Wong, S. K. J. Am. Chem. Soc. 1979, 101,
1235-1239. (c) Wong, P. C.; Griller, D.; Scaiano, J. C. J. Am. Chem. Soc.
1982, 104, 5106-5108. (d) Jackson, R. A.; Ingold, K. U.; Griller, D.;
Nazran, A. S. J. Am. Chem. Soc. 1985, 107, 208-211. (e) Baban, J. A.;
Goddard, J. P.; Roberts, B. P. J. Chem. Soc., Perkin Trans. 2 1986, 1269-
1274.
4
4
1
44. (c) Carlsson, D. J.; Ingold, K. U. J. Am. Chem. Soc. 1967, 89, 4891-
894. (d) Erben-Russ, M.; Michel, C.; Bors, W.; Saran, M. J. Phys. Chem.
987, 91, 2362-2365. (e) Gilbert, B. C.; Marshall, P. D. R.; Norman, R.
O. C.; Pineda, N.; Williams, P. S. J. Chem. Soc., Perkin Trans. 2 1981,
1
8
2
392-1400.
15) Choo, K. Y.; Benson, S. W. Int. J. Chem. Kinet. 1981, 13, 833-
44.
(
(16) Batt, L.; Hisham, M. W. M.; Mackay, M. Int. J. Chem. Kinet. 1989,
1, 535-546, and references given therein.

7386 J. Am. Chem. Soc., Vol. 121, No. 32, 1999
Weber and Fischer
Table 3. Absolute Rate Constants k
Substrate
H
and Arrhenius Parameters for the Hydrogen Abstraction of the tert-Butoxyl Radical from Different
a
substrate
solvent
Frigen 113
T, K
k
H,298, M-1s-1
5
E
a
, kJ/mol
log(A/ M-1s-1
)
ref
C
6
H
12
10
263-302
283-302
253-298
8.3 (5) × 10
9.6 (5) × 10
11.9 (7)
12.1 (19)
14.6 (11)
13.0(10)
14.8 (7)
8.0 (2)
8.1 (6)
8.5 (2)
8.2(2)
8.5 (1)
5
C
C
6
H
H
6
5
5
6
5
F
9.8 (12) × 10
7.2 (17) × 10
average
C
5
H
C
H
6 5
F
253-298
295
253-303
236-344
298
5
DTBPO
DTBPO or C
DTBPO/C H
6
8.8 × 10
18a
18b
18c
18d
18e
18e
5
5
5
5
5
4
4
4
b
6
H
6
4.3 × 10
8.5 × 10
10.7 × 10
12.8 × 10
10.6 × 10
3.9 × 10
9.5 × 10
9.3 × 10
25.5 (13)
14.5 (25)
10.1 (2)
8.5 (5)
b
6
6 6
C H
b
b
b
b
b
c-C
CF CCl
C(CH
DTBPO
3
H
6
149-216
150-205
247-283
231-293
14.8 (15)
14.7 (15)
25.7 (25)
21.8 (8)
8.7 (3)
8.6 (3)
9.1 (8)
8.8 (2)
9.3 (2)
2
2
C
C
6
H
H
5
C(CH
OCH
3
)
3
C
H
6 5
3 3
)
6
5
3
2
53-303
24.7 (13)
18b
a
b
Standard deviations are given in brackets in units of the last quoted digit. DTBPO ) di-tert-butyl peroxide From the Arrhenius parameters.
-
1
s-1 at 318 K,19b whereas we find kH,313 ) 6.5 × 10 M
4
-1
M
s
-1
4
-1 -1
18b
and kH,318 ) 7.6 × 10 M s . For anisole, Wong also
measured rate constants kH directly which are close to ours
Table 3). Further, Schwetlick et al.20a obtained a ratio of the
rate constants for hydrogen abstraction and â-scission of 0.235
(
-1
M
in anisole at 408 K. Assuming that kâ is the same in anisole
5
-1
as in fluorobenzene, the ratio yields kH,408 ) 9.8 × 10 M
-1
5
s , which is equal to our prediction of kH,408 ) 10.2 × 10
-1
-1
20b
M
s . Sakurai et al. reported the same ratio in Frigen 113
-
1
5
-1
as 6.0 M at 318 K, which leads to kH,318 ) 2.1 × 10 M
-1 -1
-1
5
s , also very similar to our result kH,318 ) 1.7 × 10 M s .
Besides the desired lifetime τA, the analysis via eq 10 yielded
the lifetimes τ2 and τB. τ2 was always in the diffusion-controlled
regime. For the solutions containing cyclohexane and cyclo-
pentane, the lifetimes τB of the methyl radical were as found
for the substrate free solutions; that is, the reaction of methyl
with the substrates is slow. For the anisole-containing solutions,
the lifetime τB of the anisyl radical was about 10-15 ms and
not interpreted. The radical resulting from tert-butylbenzene
rearranges, and its τB is treated in detail below.
Figure 5. 2-Benzylprop-2-yl concentrations vs time at (a) 319 ( 1 K
and (b) 333 ( 1 K and fits of eq 10 to the data. Bottom traces are
residuals of fits, and the inset shows an expansion of the traces around
t ) 0 s.
order rate constant for the hydrogen abstraction of about 3.8 ×
4
-1
10
s
(from the activation parameters and a substrate
concentration of 5 M). At higher temperatures the neophyl
radical is increasingly replaced by the rearranged species. Methyl
stays minor, and there is an additional weak quartet belonging
to an unidentified radical. In the analysis these contaminations
were neglected.
The rate constants measured in this work for the â-scission
1
0,11
and hydrogen abstractions not only confirm earlier views
but also extend the knowledge of tert-butoxyl radical kinetics.
1c
They allow the conversion of many additional relative rate data
to the absolute scale.
At lower temperatures of 264-298 K, the rate constants of
the rearrangement kr were determined from the time-dependent
concentration of the neophyl radical. To allow for the noninstant
Other Radical Rearrangements and Fragmentations
The reactions considered in this section have been kinetically
studied before to different degrees of precision. We reinvestigate
them here to provide additional absolute rate data and to confirm
that the analysis of the concentrations of both the rearranging
and the rearranged species yields the same information.
Neophyl Rearrangement. The primary alkyl radical (neo-
phyl) formed by the hydrogen abstraction from a methyl group
of tert-butylbenzene (vide supra) undergoes a 1,2-phenyl shift
5
-1
hydrogen abstraction (kH,280[tert-butylbenzene] ) 1 × 10 s ),
we used eq 10 for temperatures between 264 and 275 K, and kr
-
1
was obtained as τB . For 287-298 K the neophyl formation
is practically instantaneous on the observation time scale, so
-
1
that eq 9 was fitted to the data (kr ) τA ). For still higher
temperatures of 303-363 K, the concentration of the rearranged
radical was followed, and the analysis used eq 10 with kr )
-1
τA . Figure 5 shows two kinetic traces obtained for the
1
to the 2-benzylprop-2-yl radical. Steady-state ESR spectra taken
rearranged radical in the high-temperature range together with
fits to eq 10. At the onset of the dark period the delayed
formation is again clearly visible.
during photolysis of 20 vol % di-tert-butyl peroxide in tert-
butylbenzene at 258 K show strong features of neophyl and
very little contamination by methyl radicals stemming from the
â-scission. In fact, the rate constant of the â-scission is estimated
The lifetime τB of the rearranged species was large (τB > 15
ms); that is, it is kinetically insignificant, and the second-order
lifetime was about 900 µs. Measurements at various tempera-
tures of the concentrations of both the rearranging and the
rearranged radical lead to the data shown in Figure 6, to kr,298
-
1
as kâ,258 ) 870 s (from the activation parameters for the
solvent benzene) and is much smaller than the pseudo-first-
(
19) (a) Dulog, L.; David, K.-H. Makromol. Chem. 1976, 177, 1717-
724. (b) Niki, E.; Kamiya, Y. J. Org. Chem. 1973, 38, 1403-1406.
20) (a) Schwetlick, K.; Karl, R.; Jentzsch, J. J. Prakt. Chem. 1963, 22,
-
1
1
) 402 s , and to the activation parameters
(
1
3
13-124. (b) Sakurai, H.; Hosomi, A.; Kumada, M. J. Org. Chem. 1970,
5, 993-996.
-1
log(k /s ) ) (12.7 ( 0.3) - (57.6 ( 1.5)/2.303RT (16)
r

Absolute Rate Constants for the tert-Butoxyl Radical
J. Am. Chem. Soc., Vol. 121, No. 32, 1999 7387
This is indicated also by the absence of methyl in steady-state
spectra and is in accord with the high rate constant k273 ) 5.2
5
-1 -1
×
10 M
s
for the hydrogen abstraction which follows from
our average activation parameters for cyclohexane (Table 2)
and relative abstraction rate constants measured by Walling et
2
2d
al. For higher temperatures (263-306 K), the concentration
-
1
of the acetonyl radical was analyzed with eq 10 (kr ) τA ).
The results from both radicals are displayed in Figure 6, lead
4
-1
to kr,298 ) 3.1 × 10 s and are expressed by
-1
log(k /s ) ) (13.8 ( 0.3) - (53.1 ( 1.3)/2.303RT (17)
r
Our earlier estimate from steady-state radical concentrations
-
1
22b
was log(kr/s ) ) (15 ( 1) - (62.7 ( 8.4)/2.303RT, but the
frequency factor is too high. Other data seem not available. The
decay of acetonyl showed an appreciable first- or pseudo-first-
order decay component τB. This may be due to the reaction
with the methyloxirane solvent, which was inferred by Wallace
Figure 6. Rate constants and fits to the Arrhenius equation for the
neophyl (squares) and of the 2-methyloxiran-2-yl (circles) rearrange-
ments: open symbols, observation of the rearranging radical; closed
symbols, observation of the rearranged radical.
2
3
et al. to explain the formation of 5-hydroxy-2-hexanone in
the reaction system
where the activation energy is again given in kJ/mol and the
errors are standard deviations.
In early work, we estimated an activation energy in the
temperature range from 290 to 340 K of Ea ) (43 ( 9) kJ/
(
18)
21a
21b
mol. Ingold et al. combined steady-state concentrations with
directly determined second-order lifetimes and obtained the more
-
1
The temperature dependence of τB ) k[2-methyloxirane]
-
1 -1
leads to log(k/M s ) ) (5.4 ( 0.8) - (25.2 ( 2.1)/2.303RT
for this reaction, but the low-frequency factor sheds doubt on
the interpretation.
-1
exact relation log(kr/s ) ) (11.7 ( 1.0) - (56.8 ( 4.2)/2.303RT
for 283-307 K. From product yields, Franz et al.2 deduced kr
relative to the trapping of the neophyl radical by tri-n-
butylstannane. With the known temperature dependence of the
1c
Decarboxylation of the tert-Butoxycarbonyl Radical. Pho-
tolysis of 20 vol % di-tert-butyl peroxide in n-heptane containing
.0 M tert-butyl formate generates tert-butoxycarbonyl
by hydrogen abstraction of tert-butoxyl radicals
from the substrate. For ethyl formate an absolute rate constant
-1
latter reaction, they arrived at log(kr/s ) ) (11.6 ( 0.3) - (45.5
2.0)/2.303RT for 393-492 K, and this relation was accepted
1
(
2
a,18e,24
radicals
2
1d
by Ingold et al. When more exact data for the reaction of
alkyl radicals with the stannane became available, these results
5
-1 -1
for the hydrogen abstraction k ) 5.1 × 10 M
s
at 297 K
-
1
21e
were corrected to log(kr/s ) ) 11.0-45.3/2.303RT.
Our
24b
is available, and the high value ensures again instant formation
of the alkoxycarbonyl species. Decarboxylation of tert-butoxy-
carbonyl gives tert-butyl, and both radicals can be monitored
activation parameters agree best with the earlier results of Ingold
et al.2 and hold for a large temperature range. In comparison
1b
21c,e
to the more recent other determinations,
both our frequency
2
a,18e
by ESR spectroscopy.
The rate constants of the decarboxy-
factor and our activation energy are higher, and the frequency
lation were determined at low temperatures (219-244 K) from
the time-dependent concentration of the tert-butoxycarbonyl
radical analyzed with eq 9 and for higher temperatures (242-
2
1c
factor appears even too high in view of earlier discussions.
However, it should be noted that, because of error compensation
effects, the different Arrhenius parameters yield rather similar
3
1
02 K) from the signal profile of tert-butyl analyzed with eq
4
-1
rate constants, for example, at 343 K kr ) 12.5 × 10 s from
4
-1
0. They are shown in Figure 7, give kr,298 ) 8.1 × 10 s ,
the latest literature data2 vs kr ) 8.5 × 10 s from eq 16,
1e
4
-1
and follow the relation
their difference being within the error limits.
Ring Opening of the 2-Methyloxiran-2-yl Radical. Di-tert-
butyl peroxide (20 vol %) photolyzed in (()-2-methyloxirane
-
1
log(k /s ) ) (13.6 ( 0.2) - (49.6 ( 0.7)/2.303RT (19)
r
yields the 2-methyloxiran-2-yl radical as the major and the
-methyloxiran-3-yl radical as the minor species,2 in accord
2a,b
In our earlier work2a the tert-butoxycarbonyl radicals were
produced by photolysis of tert-butylpivalate in the range 225
K < T < 253 K, and the rate constants were determined by a
simultaneous multiparameter fit of numerically integrated rate
equations to the traces of both radicals. This avoided the
assumption of equal termination constants, which were found
to differ by a factor of 2. The decarboxylation obeyed log(kr/
2
2
2c
with quantum chemical calculations of the radical stabilities.
The former radical undergoes a facile ring opening to the
acetonyl radical. Steady-state ESR spectra taken during the
reactions agreed with those given earlier.22a,b Under neglect of
the minor species, the rate constants of the ring opening were
determined for low temperatures (229-253 K) from the time-
dependent concentration of 2-methyloxiran-2-yl via eq 9 (kr )
-
1
s ) ) (13.8 ( 0.2) - (49.0 ( 1.2)/2.303RT, in perfect
agreement with the present results which confirms the validity
of the new much simpler analysis. Good agreement is also
observed with the results of Roberts et al. obtained by laser
flash electron spin resonance under kinetic isolation conditions
-1
τA ). The formation of this radical is practically instantaneous.
(
21) (a) Hamilton, E. J., Jr.; Fischer, H. HelV. Chim. Acta 1973, 56, 795-
7
1
1
99. (b) Maillard, B.; Ingold, K. U. J. Am. Chem. Soc. 1976, 98, 1224-
226. (c) Franz, J. A.; Barrows, R. D.; Camaioni, D. M. J. Am. Chem. Soc.
984, 106, 3964-3967. (d) Lindsay, D. A.; Lusztyk, J.; Ingold, K. U. J.
Am. Chem. Soc. 1984, 106, 7078-7090. (e) Burton, A.; Ingold, K. U.;
Walton, J. C. J. Org. Chem. 1996, 61, 778-3782.
-
1
18e
as log(kr/s ) ) (13.2 ( 0.3) - (45.2 ( 1.5)/2.303RT.
(23) (a) Gritter, R. J.; Wallace, T. J. J. Org. Chem. 1961, 26, 282-283.
(b) Wallace, T. J.; Gritter, R. J. Tetrahedron 1963, 19, 657-665.
(24) (a) Griller, D.; Roberts, B. P. J. Chem. Soc., Perkin Trans. 2 1972,
747-751. (b) Chatgigliaglu, C.; Lunazzi, L.; Macciantelli, D.; Placucci,
G. J. Am. Chem. Soc. 1984, 106, 5252-5256.
(
22) (a) Behrens, G.; Schulte-Frohlinde, D. Angew. Chem. 1973, 85, 993-
9
94. (b) Itzel, H.; Fischer, H. HelV. Chim. Acta 1976, 59, 880-900. (c)
Caballol, R.; Canadell, E. J. Mol. Struct. 1988, 168, 93-104. (d) Walling,
C.; Mintz, M. J. J. Am. Chem. Soc. 1967, 89, 1515-1519.

7388 J. Am. Chem. Soc., Vol. 121, No. 32, 1999
Weber and Fischer
reactions and has proven its versatility. Measurable first- or
pseudo-first-order lifetimes range from 10 µs to about 10 ms,
2
5
-1
which means that rate constants of 10 -10 s for first-order
8
-1 -1
processes or 10-10 M
s
for pseudo-first-order reactions
are accessible. The requirement of similar termination constants
for different radicals involved in the competing reactions is
expected to be fulfilled in most realistic cases.
Acknowledgment. This work is dedicated to Dr. Keith U.
Ingold on the occasion of his 70th birthday, to the pioneering
promotor of quantitative free radical chemistry. We acknowledge
financial support by the Swiss National Foundation for Scientific
Research. H.F. thanks the Research School of Chemistry,
Australian National University, Canberra, and especially Prof.
L. Radom for the kind hospitality during a sabbatical leave.
Figure 7. Rate constants and fits to the Arrhenius equation for the
decarboxylation of the tert-butoxycarbonyl in n-heptane: open symbols,
observation of the rearranging radical; closed symbols, observation of
the rearranged radical.
Supporting Information Available: Two tables with results
of fits to numerically integrated kinetic equations, five figures
with ESR spectra, two figures on the importance of the sector
error, and one figure showing the temperature dependence of
the hydrogen abstractions from tert-butylbenzene and anisole.
This material is available free of charge via the Internet at
http://pubs.acs.org.
In summary, in this work we have extended the analysis of
the time dependence of radical concentrations observed during
intermittent photochemical radical generation and during com-
peting reactions to delayed radical formations in the off-period
of generation. The technique was applied to obtain absolute rate
constants and their activation parameters for a variety of
JA990837Y