Rate constants for the reaction of HO2 radicals with cyclopentane and propane between 673 and 783 K

Article abstract of DOI:10.1039/b108578f

Studies have been made of the separate addition of cyclopentane (c-C₅H₁₀) and propane (C₃H₈) to mixtures of O₂ and tetramethylbutane (TMB) between 673 and 783 K in aged boric-acid-coated vessels to ob

Full text of DOI:10.1039/b108578f

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Rate constants for the reaction of HO radicals with cyclopentane
2
and propane between 673 and 783 K
S. M. Handford-Styring and R. W. Walker*
Department of Chemistry, University of Hull, Hull, UK HU6 7RX
Received 20th September 2001, Accepted 19th November 2001
First published as an Advance Article on the web 21st January 2002
Studies have been made of the separate addition of cyclopentane (c-C
of O and tetramethylbutane (TMB) between 673 and 783 K in aged boric-acid-coated vessels to obtain
kinetic data for the reaction of HO radicals with each of the additives. The contribution by OH radicals to the
5 3 8
H10) and propane (C H ) to mixtures
2
2
5 3 8
removal of c-C H10 and C H has been minimised by use of a total pressure of 15 Torr and by measurements
well within 5% consumption of TMB and the additives. A full product analysis was carried out for each kinetic
data point which shows that at least 85% of the radicals produced from c-C H and C H give conjugate
5
10
3
8
alkene þ HO and which permits a precise correction for the small percentage of OH radicals formed. From
2
1=2
1=2
measurements of the relative rates of consumption of TMB and the additives, values of k12p=k
7
and k12c=k
7
were obtained at each temperature used and were shown by sensitivity analysis to be relatively insensitive to any
other parameter associated with the mechanism.
HO2 þ C3H8 ! H2O2 þ C3H7
HO2 þ c-C5H10 ! H2O2 þ c-C5H9
HO2 þ HO2 ! H2O2 þ O2
ð12pÞ
ð12cÞ
ð7Þ
À1
1=2
3
)=(dm mol
À1 À1 1=2
Values of E12p À 1=2E ¼ 75.6 ± 5.8 kJ mol , log[(A =A
s
)
] ¼ 5.53 ± 0.52 and
7
12p
7
À1
1/2
3
)/(dm mol
À1 À1 1=2
E
12c À 1=2E
7
¼ 71.2 ± 3.9 kJ mol , log[(A12c=A
7
s
)
] ¼ 5.58 ± 0.40 were obtained
9
3
À1 À1
À1
3
which with k
À1 À1
7
¼ 1.87 Â 10 exp(À 775=T) dm mol
s
give E12p ¼ 78.8 ± 6.6 kJ mol , log(A12p=dm
À1
3
À1 À1
s
mol
s
) ¼ 10.17 ± 0.57 and E ¼ 74.4 ± 4.7 kJ mol , log(A12c=dm mol
) ¼ 10.22 ± 0.45. The
À1
1
2c
À1
3
parameters for reaction (12c) are in excellent agreement with E ¼ 73.2 ± 5.0 kJ mol , log(A=dm mol
À1
s
) ¼ 10.23 ± 0.49 obtained in a previous study for the reaction of HO
2
radicals with cyclohexane. For
2
.5
use outside the temperature range of this study, the three-parameter function k ¼ AT exp(ÀB=T ) is
recommended. From a combination of the data obtained for c-C
10 and cyclohexane, values of A ¼ 7.9 dm
radicals of a single secondary
3
5
H
À1 À1
À2.5
mol
s
K
and B ¼ 6970 K are recommended for the abstraction by HO
2
H atom from alkanes with a carbon number larger than 4. Use has been made of all the available
data for HO þ alkane reactions to derive a data base for HO attack at primary, secondary, and tertiary
2
2
C–H sites in alkanes with an accuracy expressed as Dlog ¼ ± 0.15 between 600 and 800 K rising to ± 0.3
at 1200 K.
The importance of H abstraction from alkanes and related
compounds by HO radicals on mid-temperature combustion
2 2
cals react with O to give the conjugate alkene and an HO
radical, thus leaving only 10–20% to react via addition and
decomposition to yield OH radicals. Compared with cyclo-
2
1
chemistry has been stressed in a recent publication concerned
with the kinetics of the HO2 þ cyclohexane reaction. The
hexyl þ O , where only about 60% conjugate alkene is
2
Arrhenius parameters presented therein are unique for
abstraction from a secondary C–H bond. It has been argued
formed, the importance of OH radicals is therefore con-
siderably reduced.
The decomposition of tetramethylbutane (TMB) in the
2
that the absence of strain energy in the ring results in the C–H
bond dissociation energy in cyclohexane being the same to
presence of O
ducible source of HO radicals. Several studies in both KCl-
2
has again been used as a reliable and repro-
À1
5,6
within 2–3 kJ mol as that in linear alkanes. The question
then arises as to the degree to which the cyclohexane kinetic
2
and aged boric-acid-coated Pyrexvessels have established that
the decomposition proceeds in the initial stages via a very
simple mechanism comprising reactions (1–11).
data may be transferred for use with HO
provide an answer and further kinetic data for HO
tion reactions at secondary C–H bonds, experiments have been
carried out with cyclopentane (c-C 10) and propane as sub-
strates between 673 and 783 K. Previous studies
2
þ alkane. In order to
2
abstrac-
C8H18 ! 2 t-C4H9
t-C4H9 þ O2 ! i-C4H8 þ HO2
HO2 ! surface
ð1Þ
ð2Þ
ð3Þ
5
H
3
,4
have
established that their oxidation chemistry in this region is
simpler than that of cyclohexane, for example in particular
that between 80 and 90% of the cyclopentyl and propyl radi-
6
20
Phys. Chem. Chem. Phys., 2002, 4, 620–627
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DOI: 10.1039/b108578f

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HO2 þ C8H18 ! H2O2 þ C8H17
C8H17 ! i-C4H8 þ t-C4H9
H2O2 ! surface
ð4Þ
ð5Þ
down to 0.1 Torr, and the temperature was controlled to better
than 0.2 K along the length and breadth of the reaction vessel.
At the very low rates involved, no temperature changes during
reaction were detectable. The yields of products were measured
by gas chromatography, and particular attention was given to
establishing conditions for excellent peak resolution in order to
achieve highly quantitative analyses. Electronic valves with
response times of less than 0.1 s were used to admit the gases
from the pre-mixing bulb and to sample the products at precise
pre-selected time intervals. In practice, however, time is not a
prime factor in the determination of precise kinetic data.
To avoid complications caused by secondary processes,
when determining rate data the consumption of TMB and of
the additives, c-C H or C H , was never allowed to exceed
ð6Þ
HO2 þ HO2 ! H2O2 þ O2
H2O2 þ M ! 2OH þ M
OH þ C8H18 ! H2O þ C8H17
t-C4H9 þ O2 ! i-C4H8O þ OH
OH þ H2O2 ! H2O þ HO2
ð7Þ
ð8Þ
ð9Þ
ð10Þ
ð11Þ
5
10
3
8
5
%, and was frequently significantly lower.
Experimental results
In boric-acid-coated vessels, HO and H O are not destroyed
2
2
2
at the surface so that k
C H radicals react in reaction (2) to give HO radicals, it is
3
¼ k
6
¼ 0. Further, as 99% of the t-
2 5
TMB 1 O 1 c-C H10 mixtures
4
9
2
clear that the homolysis of H
only source of OH radicals, and the effect of this can be
2
O
2
(reaction (8)) is effectively the
The yields of i-C
10 were measured over the first few % of reaction for
several mixtures at 673, 713, 753, and 783 K. Pressures up to 4
Torr TMB and 2 Torr c-C 10 (not normally exceeded in
order to facilitate good separation of the c-C 10 and c-C
peaks) were used with added O to a total pressure of 15 Torr,
which maintained a very low level of homolysis of H O
4 8
H (from TMB) and of the products from c-
5
C H
minimised by working at low total pressures (typically 15 Torr)
7
and in the very early stages of reaction. By addition of CH ,
4
5
H
8
1
C
2
H
6
and c-C
meters have been obtained for their reaction with HO radi-
6
H
12 to TMB þ O
2
mixtures, Arrhenius para-
5
H
5 8
H
2
2
cals. The fundamentals of the interpretation may be
understood, with c-C H for example, by considering the
2
2
5
10
(
reaction (8)) to give OH radicals. Fig. 1 shows the product
yields for the mixture containing 2, 2, and 11 Torr of TMB, c-
simplest possible mechanism involving reactions (1), (2), (7),
12c), (13), and reaction (OP).
(
1
5 2
C H10 and O , respectively at 753 K. As observed with
TMB þ c-C H þ O mixtures, the product yields tend to
6
12
2
HO2 þ c-C5H10 ! H2O2 þ c-C5H9
ð12cÞ
ð13Þ
increase autocatalytically due to the increased formation of
OH radicals in reaction (8). At 673 K, however, the auto-
catalysis is effectively absent. Further, at all temperatures, the
autocatalysis is less marked for i-C H which is mostly formed
c-C5H9 þ O2 ! c-C5H8 þ HO2
c-C5H9 ! other products
The relative rate of consumption of c-C H and TMB is given
4
8
ðOPÞ
through the homolysis of TMB, and as a consequence the
relative rates of consumption of c-C H and TMB rise slightly
with time. The initial product yields at 20 s, expressed as
5
10
5
10
by eqn. (i).
1=2
1=2
d½c-C H10Š=d½TMBŠ ¼ k12c½c-C H10Š=ðk1k7Þ ½TMBŠ
ðiÞ
5
5
The consumption of TMB may be measured directly from the
4
yield of i-C H (99%), and previous studies have shown that
4
8
ca. 80% of the c-C
c-C H and a regenerated HO radical. Although a consider-
5 9
H radicals undergo reaction (13) to give
5
8
2
able improvement on the yields of c-C
6
6
H
10 þ HO
2
of about
0% in the analogous reaction of c-C H11 radicals, a full
6
product analysis is required for each kinetic datum point in
order first to determine precisely the rate of consumption of c-
C
5
H
10 , and secondly to monitor the loss of c-C
tion with OH radicals. As will be seen later, analysis confirms
that the kinetic data obtained for the reactions of HO radicals
with c-C 10 and C are not particularly sensitive to the
5
H10 by reac-
2
5
H
3 8
H
presence of OH radicals under the carefully chosen conditions
of the present study.
Experimental
1
,5,6
Details of the experimental procedure are given elsewhere.
Reactions were carried out in cylindrical Pyrexvessels, 20 cm
in length and 5.2 cm in diameter. The aged boric-acid-coated
surface was prepared to a totally reproducible state by carrying
9
out repeated runs with H þ O mixtures at 773 K. Once
2
2
established, the rate remained constant to within 1–2% over a
period of years, and with correction for dead volume was
totally independent of vessel diameter between 1.4 and 5.2 cm.
Pressures were measured by transducer to better than 1%
Fig. 1 Products from c-C
5
H
10 mixtures at 753 K. TMB ¼ 2, c-
C H ¼ 2, O ¼ 11 Torr. (a) ꢀ, i-C H ; Â, c-C H ; *, 1,2-c-C H O.
5
10
2
4
8
5
8
5
8
(b) Â, C
2
H
4
; ꢀ, CO; *, C
H ; u, c-pentadiene.
3 6
Phys. Chem. Chem. Phys., 2002, 4, 620–627
621

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Fig. 2 Variation of D([c-C
ent temperatures. TMB ¼ 4, c-C
13 K; (c), 753 K; (d), 783 K.
5
H
8
] þ [OP])=D[TMB] with time at differ-
5
H
10 ¼ 2, O ¼ 9 Torr. (a), 673 K; (b),
2
Fig. 3 Products from C H mixtures at 753 K. TMB ¼ 4, C H ¼ 4,
3
8
3
8
7
O ¼ 7 Torr. ꢀ, i-C H ; Â, C H ; *, C H (Â4); 4, C H O (Â4).
2
4
8
3
6
2
4
3
6
absolute %, for the mixture TMB ¼ 4, c-C ¼ 9
Torr at 753 K are i-butene (1.01), c-C H (0.365), C H
4
5
H
10 ¼ 2, and O
2
5 10 2
Torr of TMB, c-C H and O respectively at 753 K. Again
5
8
2
there is little autocatalysis at 673 K, but it is noticeable at 753
K. Although small yields of oxetane were found as an initial
(
0.0252), C
3 6
H (0.0095), 1,2-c-pentane oxide (0.0283), c-pen-
3
tadiene (0.0065), CH =CHCHO (trace, < 0,002), CO (0.0291).
product when C H was added to H þ O mixtures at 753 K,
2
3
8
2
2
5
is formed uniquely from TMB in yields of 99%, and
,6
i-C
c-C H in yields of 80–90% from c-C H . The yield of 1,2-
4
H
8
in that environment the alkane is removed predominantly by
the non-selective OH radical so the precursor of oxetane,
CH CH CH , is formed in yields well in excess of 50%. In
5
8
5
10
cyclopentane oxide (1,2-c-C
excellent agreement with that found when c-C H10 is added to
5 8
H O) is approximately 10%, in
3
2
2
5
contrast, in the TMB study, C H is consumed mostly by
3
8
4
at 753 K and 500 Torr total pressure. The
mixtures of H
yields of C H , CO, C H and CH =CHCHO all fall as the
2
þ O
2
reaction with the highly selective HO2 radical, so that the
CH CH CH radical is formed in relatively low yield. The
2
4
3
6
2
3
2
2
temperature is lowered, and small amounts of cyclopentadiene
are observed, presumably formed very rapidly as a secondary
3 3 2 3 6
CH CHCH radical reacts with O to give C H and propene
oxide in yields of 99% and 1%, respectively, and the
CH CH CH radical either forms C H or propene oxide by
5 8
product from c-C H . No other products were observed, but
3
2
2
3
6
3
no analysis was made for HCHO. The consumption of TMB,
reaction with O , or undergoes homolysis to give C H .
2
2
4
6
,10
with a 1% correction for the formation of isobutene oxide,
is monitored from the yield of i-C , and that of c-C
from the relationship D[c-C ] þ D[OP], where
10] ¼ D[c-C
OP] ¼ [C ] þ [1,2-c-C O] þ [c-pentadiene]. Previous stu-
dies of c-C 10 oxidation and of allyl radical chemistry
under similar conditions indicate that CH =CHCHO, C
and CO are formed in reaction sequences accompanying C
Consequently the consumption of C H may be measured
3 8
4
H
8
H
5 10
directly, in the absence of secondary reactions, by
D[C H ] ¼ D([C H ] þ [OP]), where [OP] ¼ [C H ] þ [propene
5
H
H
5 8
3
8
3
6
2
4
[
2
H
4
5
H
8
5 10
oxide]. As in a related way with c-C H , the plots of
4
11,12
5
H
D([C H ] þ [OP])=D[TMB] are invariant with time at 673 K but
3
6
2
H
3 6
,
increase slightly with time at the higher temperatures (see
Table 5 further below).
2
H
4
(
see later). If OH attack on c-C
1
5
H
10 is ignored, then the value
=2
of k12c=k
7
may be calculated directly from eqn. (i) because
Determination of rate constants for HO 1 c-C H
10
2
5
6
the value of k
Fig. 2 shows that the values of D([c-C
against time are invariant at 673 K, but increase noticeably at
83 K due to the enhanced effect of OH formation through
homolysis. Allowance for OH attack on c-C 10 is made
1
is accurately known.
8
H ] þ [OP])=D[TMB]
The sub-mechanism, reactions (1)–(11), for TMB decomposi-
tion is given above, and the full mechanism for the initial
5
4
7
H
stages of c-C
5
H
10 oxidation in Table 1. Handford-Styring and
radicals
pressures above
pressures used here, the relative rate
of reactions (13) and (16) would be about 10 : 1, consistent with
the yields of C of about 10% at 753 K. Lodhi and Walker
have studied the reactions of allyl radicals with HO
4
2
O
2
5
H
Walker have shown that the isomerisation of c-C
is only of minor importance at 753 K and O
50 Torr, but at the low O
H
5 9
in two ways. First, the formation of OH radicals is calculated
directly from the product profiles. With FENE defined as the
fraction of c-C H radicals which gives HO radicals (effec-
2
2
5
9
2
tively the fraction which gives c-C
fraction giving OH radicals. At 673 and 713 K, the values of
FENE are almost constant with mixture composition, but at
5
H
8
), then 1 À FENE is the
H
2 4
1
1
2
and with
and application of their data confirms that at the very
high HO concentrations in the TMB system effectively all allyl
radicals will be removed in reactions (18) and (19). Homolysis
of the peroxide bond in CH =CHCH OOH gives OH radicals
and the accompanying CH =CHCH O radical gives either
CH =CHCHO (acrolein) [reaction (21)] or CO, HCHO, and
HO , [reactions (22)–(24)]. Decomposition of the HCO radi-
cals to give CO cannot compete under the present conditions.
1
1,12
O ,
2
7
O
53 and 783 K are both smaller and sensitive to the pressure of
due to the enhanced formation of C and its accom-
panying products. Despite this small complicating factor at the
higher temperatures, the correction for OH attack on c-C
is significantly less than required for the determination of
2
2
2 4
H
2
2
H
5 10
2
2
2
k(HO
C H mixtures.
6 12
2
þ c-C
6
H
12) from related studies with TMB þ O
2
þ c-
2
1
13
4
The H
with an OH radical in the overall sequence (25), although it is
of minor importance at the low pressures of O used here. The
particularly important point that emerges is that in the initial
stages of reaction each molecule of C formed is accom-
2
þ O
2
þ c-C
5 2 4
H10 studies show that C H is also formed
2 3 8
TMB 1 O 1 C H mixtures
2
Similar studies with very low consumptions were carried out
with TMB þ O þ C mixtures at 673, 723, and 753 K and a
total pressure of 15 Torr. Fig. 3 shows the yields of i-C H and
2
H
3 8
2 4
H
panied by an OH radical. As OH radicals are also formed
in the overall reaction (15) which accounts for about 1% of the
4
8
of the C
3 8
H products for the mixture composition 4, 4, and 7
6
22 Phys. Chem. Chem. Phys., 2002, 4, 620–627

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Table 1 Sub-mechanism used for the determination of R12c
HO2 þ c-C5H10 ! H2O2 þ c-C5H9
numerical method used to solve the differential equations
needed to predict the values of D[c-C H ]=D[TMB]. A quan-
titative measure of the production of OH radicals is provided,
as described above, by the parameter 1 À FENE, which is
obtained from the detailed product analysis carried out for
each kinetic point. Minor corrections, such as the allowance
5
10
ð12cÞ
ð13Þ
ð14Þ
ð15Þ
ð16Þ
ð17Þ
ð18Þ
ð19Þ
ð20Þ
ð21Þ
ð22Þ
ð23Þ
ð24Þ
c-C5H9 þ O2 ! c-C5H8 þ HO2
OH þ c-C5H10 ! H2O þ c-C5H9
4 9
for 1% formation of OH radicals from t-C H radicals [reac-
tion (10)], are also carried out by the computer. The values of
FENE and 1 À FENE are constant with time to within 3%
over the very limited extent of reaction (< 5%) utilised for any
particular mixture. With 1 À FENE measured precisely and
6
k =k ¼ 0.010 between 673 and 783 K, and k known to better
1
0
2
1
5
than 10%, the other parameters required for the computer
c-C5H9 þ O2 ! 1; 2-c-C H8O þ OH
5
program are k , R , R , k =k and k =k . R has been
4
8
4
12c
11
9
14
9
5
,6
measured directly under the conditions used here and
4
k =k , of minor importance, is accurately known. The value
1
c-C5H9 ! linear-C5H9
linear-C5H9 ! C2H4 þ CH2CHCH2
HO2 þ CH2CHCH2 ! C3H6 þ O2
1
1
9
of k14=k
9
¼ 3.1 ± 0.5 at 753 K is obtained directly from
2 9 2
k =k(OH þ H ) ¼ 24.6 ± 3 and k =k(OH þ H ) ¼ 8.0 ± 0.9
1
4
4
15
from separate studies of the addition of c-C
5
H10 and TMB
to H þ O mixtures. Variation of k =k with temperature is
2
2
14
9
insignificant between 673 and 783 K, but is taken into account.
1
4
The value of k
, but the high proportions of TMB and c-C
mixtures require relatively accurate values for a and b in eqn.
ii) for M , where 0.35, a, and b are the efficiencies of O
TMB, and c-C 10 , respectively, relative to that of H
8
is accurately known with M ¼ N
2
, O
H12 in the
2
, and
H
2
5
(
8
2
,
HO2 þ CH2CHCH2 ! CH2¼CHCH2OOH
CH2¼CHCH2OOH ! CH2¼CHCH2O þ OH
CH2¼CHCH2O þ O2 ! CH2¼CHCHO þ HO2
CH2¼CHCH2O ! CH2¼CH þ HCHO
CH2¼CH þ O2 ! HCHO þ HCO
5
H
2
.
M8 ¼ 0:35½O Š þ a½TMBŠ þ b½c-C H10Š
ðiiÞ
2
5
A value of a ¼ 2.5 gives an excellent fit to the TMB decom-
1
,6
position data in aged boric-acid-coated vessels and b ¼ 2.0,
1
8
based on values for c-C
6 2 6
H12 , and C H has been adopted for
c-C H10 . The choice is not critical as will be seen from the
sensitivity analysis.
5
The sole remaining parameter is R12c , and the following
procedure was adopted for its evaluation. A range of values
was selected at each temperature and D[c-C H10]=D[TMB]
5
calculated at three times all well within 5% consumption, and
in some cases 1%, and then compared with the experimental
values. The rms and mean deviations were calculated at each
temperature, and the optimum values of R12c isolated. As
shown in Fig. 4, use of both deviations gives the same value.
Table 2 compares the experimental and calculated values of
D[c-C H ]D[TMB] at the three selected times, and gives the
HCO þ O2 ! HO2 þ CO
5
10
c-C5H9 þ O2 +
(
c-C H O ! c-C H OOH !
optimum values of R12c obtained by use of the other para-
meters discussed above.
5
9
2
5
8
ð25Þ
C2H4 þ CH2¼CHCHO þ OH
OH=HO2 þ c-C5H8 ! H2O=H2O2 þ c-C5H7
c-C5H7 þ O2 ! c-C5H6 þ HO2
ð26Þ
ð27Þ
c-C
5
H
9
radicals, the quantity 1 À FENE may be measured
2 4 5 8
directly and precisely from the yields of C H and 1,2-c-C H O.
Use of a computer treatment is necessary, first to facilitate
the incorporation of the parameters FENE and 1 À FENE
into the interpretation, secondly to allow for the non-sta-
tionary formation of OH radicals from H
thirdly to optimise the agreement between the experimental
and calculated values of D[c-C 10]=D[TMB]. Differential
equations are written for reactants and products, and sta-
tionary state equations for the radicals. As previously, [HO
2 2
O homolysis, and
5
H
2
]
1
7
=2
is expressed in the form G ¼ k [HO
2
], as it is the ratios
1
7
=2
1=2
7
R
the computer interpretation.
4
¼ k =k and R12c ¼ k12c=k that are directly involved in
4
Fig. 4 Mean and rms deviations between observed and calculated
values of D[c-C H ]=D[TMB]. Â, mean deviation; ꢀ, rms deviation.
(a), 673 K; (b), 713 K; (c), 753 K; (d), 783 K.
G
stationary state equation for HO
is calculated from the
, and the Runge–Kutta
5
10
2
Phys. Chem. Chem. Phys., 2002, 4, 620–627
623

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Table 2 Calculated and observed values of D[c-C
5
H10]=D[TMB]
Table 3 Summary of sensitivity analysis for R12c
Mixture
composition
D[c-C
D[TMB]
5
H
10]=
% change in R12c
Parameter
changed
Optimum R12c
=
% change
783 K
753 K
713 K
673 K
3
À 1 À 1 1=2
s )
T=K Time=s TMB c-C H O2 Obs. Calc. (dm mol
5
10
k
k
k
k
1
þ 40%
À 40%
þ 40%
À 40%
þ 40%
À 40%
þ 40%
À 40%
To maximum
À 40%
þ 7.8
À 8.4
À 0.4
þ 0.3
À 3.0
þ 3.0
À 2.9
þ 3.5
þ 7.9
À 11.0
þ 6.8
À 7.3
0.0
þ 5.7
À 6.3
À 0.2
þ 0.1
À 1.2
þ 1.0
À 2.4
þ 3.0
þ 5.1
À 6.5
þ 3.5
À 4.2
0.0
6
73 120
4
4
2
4
2
4
1
4
2
4
1
4
2
4
1
4
2
4
2
2
1
2
2
2
1
2
2
2
1
2
7
9
9
9
3.98 3.78 1.22
4.01 3.84
4.05 3.89
2.01 1.87
2.01 1.88
2.01 1.90
6.28 6.71
6.34 6.88
240
360
120
240
360
120
240
360
30
10=k
2
þ 0.4
À 1.4
þ 2.3
À 2.8
þ 3.4
þ 6.3
À 9.0
0.0
8
À 0.8
þ 0.8
À 2.2
þ 3.3
þ 1.5
À 1.5
14=k
9
a
FENE
6.45 7.03 rms dev. ¼ 6.8%
1.14 1.17 2.21
1.18 1.20
7
13
53
83
a
6
9
3
6
9
3
6
9
3
6
9
0
0
0
0
0
0
0
0
0
0
0
Raised to maximum value of unity from values ranging between
about 0.8–0.9.
1.25 1.22
11 2.04 1.96
2.13 2.01
2.30 2.07
10 0.580 0.578
0.605 0.589
0.639 0.601
12 2.87 3.19
3.13 3.28
3.24 3.37 rms dev. ¼ 7.3%
7
10
9
0.803 0.841 4.77
0.835 0.884
0.907 0.922
20
30
10
20
30
10
20
30
10
20
30
3
6
9
3
6
9
3
6
9
3
6
9
11 1.41 1.35
1.46 1.41
1.55 1.48
10 0.435 0.414
0.463 0.433
0.493 0.450
12 1.93 2.11
2.06 2.22
2.23 2.23 rms dev. ¼ 6.1%
7
9
0.552 0.594 6.96
0.620 0.634
0.687 0.672
11 0.902 0.912
1.02 0.969
1.13 1.02
10 0.292 0.293
0.304 0.313
0.330 0.331
12 1.29 1.38
1.40 1.46
Fig. 5 Arrhenius plots for R12c and R12p between 673 and 783 K. u,
R12p (for C H ); ꢀ R (for c-C H ); D, R (for c-C H from ref. 1).
3
8
12c
5
8
12
6
12
is measured directly, the only uncertainty is the role of the CH
radicals formed in reaction (34). Consideration of the values of
k
3
1.57 1.54 rms dev. ¼ 6.0%
35 À k37 at 753 K shows that reaction (35) is their only
1
3
10
3
important reaction. Baulch et al. give k35 ¼ 2.0 Â 10 dm
À1 À1
mol
Westley et al. and by Kerr and Moss,
s
between 300 and 2500 K and, from reviews by
respectively,
1
6
17
The sensitivity analysis is summarised in Table 3 which
shows the effect of a relatively large change of ± 40% in each
of the fixed parameters. The influences on R12c are quite small
under all conditions, and similar to those observed in the
6
3
À1 À1
5
3
À1
k
3
6
¼ 1.0 Â 10 dm mol
s
and k37 ¼ 6.5 Â 10 dm mol
À1
À3
s
at 753 K, so that with [HO ] ¼ 5.0 Â 10 Torr at 10 s for
2
the mixture TMB ¼ 4, C H ¼ 2 and O ¼ 9 Torr, the rate of
3
8
2
1
12 , with the exception that the
related study of HO
2
þ c-C
6
H
reaction (35) relative to the combined rates of reactions (36)
and (37) is about 20. Arising from compensating factors the
relative rate changes little for all conditions used. It should be
further noted that the termolecular reaction CH þ O þ
importance of OH radicals is much reduced at low tempera-
tures with c-C 12 . The values of R12c are plotted in Arrhenius
form in Fig. 5, and the optimum parameters E À 1=2
À1
)=(dm mol
5
H
1
2c
3
2
À1
1=2
3
E
7
¼ 71.2 ± 3.9 kJ mol
and log[(A12c=A
7
M!CH O þ M cannot compete at the low O and total
3
2
2
À1 1=2
s
with 70.0 ± 4.5 and 5.59 ± 0.41, respectively, for the reaction
)
] ¼ 5.58 ± 0.40 are obtained, which may be compared
pressures used here. It may be concluded that the formation of
C H in (34), only a minor reaction anyway, is accompanied
by an OH radical. In confirmation, no CH could be detected
2
4
HO þ c-C H , the data for this reaction having been rein-
2
6
12
4
1
terpreted very slightly from the original. Within experimental
error both reactions have the same activation energy and
A factor.
in the initial products, even at 673 K where the relative rates of
(36) and (37) are slightly higher. Nevertheless, the computer
program makes the very small corrections (<1% effect
on R12p).
The results were interpreted by computer, as described for
c-C H10 . The values of FENE increased slightly with tem-
5
Determination of the rate constants for HO 1 C H
8
2
3
The sub-mechanism used for the interpretation of the
TMB þ O þ C results is given in Table 4. As the yield of
(effectively equivalent to FENE) is about 90% and
propene oxide (C O), which is formed with an OH radical,
perature because of the greater importance of reaction (34),
but were never below 0.90. Consequently, the importance
of OH radicals in removing C H was significantly less than
2
3 8
H
3 6
C H
3
8
1
3
H
6
in the consumption of both c-C
5
H
10 and c-C
6
H10 . A value
6
24
Phys. Chem. Chem. Phys., 2002, 4, 620–627

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Table 4 Sub-mechanism used for the determination of R12p
Table 5 Calculated and observed values of D[C
3
H
8
]=D[TMB]
Mixture
composition
D[C
D[TMB]
3 8
H ]=
HO2 þ C3H8 ! H2O2 þ CH3CH2CH2=CH3CHCH3 ð12pÞ
Optimum R12p
=
s )
3
À1 À1 1=2
T=K Time=s TMB C H O2 Obs. Calc. (dm mol
3
8
OH þ C3H8 ! H2O þ CH3CH2CH2
OH þ C3H8 ! H2O þ CH3CHCH3
CH3CHCH3 þ O2 ! C3H6 þ HO2
CH3CH2CH2 þ O2 ! C3H6 þ HO2
CH3CHCH3 þ O2 ! C3H6O þ OH
CH3CH2CH2 þ O2 ! C3H6O þ OH
CH3CH2CH2 þ M ! CH3 þ C2H4 þ M
CH3 þ HO2 ! CH3O þ OH
ð29aÞ
ð29bÞ
ð30Þ
ð31Þ
ð32Þ
ð33Þ
ð34Þ
ð35Þ
ð36Þ
ð37Þ
6
73 300
4
2
1
4
4
4
2
4
2
1
4
4
4
1
5
2
5
4
4
4
7
9
1.49 1.47 0.468
1.49 1.49
1.49 1.51
2.68 2.58
2.73 2.66
2.76 2.72
6
9
3
6
9
3
6
9
3
00
00
00
00
00
00
00
00
00
10 4.33 4.46
4.45 4.65
4.50 4.87
10 0.342 0.362
0.342 0.364
600
9
00
50
00
50
0.342 0.366 rms dev. ¼ 4.7%
1.29 1.34 1.24
1.38 1.40
1.50 1.49
0.485 0.526
0.521 0.558
0.585 0.597
2.46 2.24
2.59 2.42
2.76 2.65 rms dev. ¼ 5.9%
0.780 0.762 1.96
0.871 0.820
0.943 0.869
1.23 1.21
7
23
6
9
8
7
9
1
1
5
0
1
1
00
50
5
0
1
1
00
50
15
753
3
4
1
3
4
1
3
4
0
5
5
0
5
5
0
5
1.34 1.31
1.45 1.38
10 1.74 1.88
1.88 2.06
CH3 þ C3H8 ! CH4 þ CH3CH2CH2=CH3CHCH3
CH3 þ C8H18 ! CH4 þ C8H17
2.04 2.23 rms dev. ¼ 6.5%
Table 6 Summary of sensitivity analysis for R12p
change in R12p
%
1
8
Parameter changed
% change
7
53 K
723 K
673 K
of k29=k
29=k(OH þ H
The relative efficiency b of C
and applied through eqn. (ii). The values of R12p were
optimised using the same procedure as for R12c from the c-
10 results. Fig. 6 shows that the rms and mean deviations
give the same optimum values of R12p , and Table 5 compares
the experimental and calculated values of D[C ]=D[TMB] at
9
¼ 1.24 ± 0.2 was obtained at 753 K from
1
5
k
2 9 2
) ¼ 9.9 ± 1.2 and
k
=k(OH þ H ) ¼ 8.0 ± 0.9.
k
k
k
k
1
þ 40
þ 6.8
À 8.1
À 0.2
þ 0.2
À 3.2
þ 2.2
À 3.2
þ 4.0
þ 4.5
À 8.3
þ 5.9
À 6.4
À 0.2
þ 0.1
À 2.8
þ 1.6
À 2.3
þ 3.3
þ 2.9
À 3.4
þ 4.2
À 4.6
À 0.0
þ 0.0
À 0.8
þ 0.7
À 1.3
þ 1.8
þ 0.4
À 0.7
3
H
8
as M in reaction (8) is taken as
À 40
2
10=k
2
þ 40
À 40
5
C H
8
þ 40
À 40
3
H
8
29=k
9
þ 40
À 40
the selected times where consumption barely exceeded 1%.
The sensitivity analysis, summarised in Table 6, shows that the
a
FENE
To maximum
À 40
a
Raised to maximum value of unity from about 0.9.
optimum values of R12p are insensitive to all the fixed para-
meters. Although a 40% reduction in FENE would reduce
R12p by about 10%, FENE and 1 À FENE are measured to
better than 10% so that the likely error is less than 3%. The
values of R12p are plotted in Fig. 5 and over the range 673–753
À1
1=2
K, E12p À 1=2E
7
¼ 75.6 ± 5.8 kJ mol and log[(A12p=A
7
)=
3
dm mol
À1 À1 1=2
( ] ¼ 5.53 ± 0.52. A higher activation energy
for the reaction of HO radicals with C H is understandable,
2 3 8
s
)
when compared with those for c-C H and c-C H , because
5
10
6
12
of the presence of primary C–H bonds in C
H
3 8
.
Absolute values of k12c and k12p
The absolute values of k12c and k12p , calculated from the ratios
Fig. 6 Mean and rms deviations between observed and calculated
]=D[TMB]. Â, mean deviation; ꢀ, rms deviation. (a),
1
3
9
3
À1 À1
s
given in Table 7, together with the Arrhenius parameters and
values of D[C
3
H
8
by use of k ¼ 1.87 Â 10 exp(À775=T ) dm mol
7
, are
673 K; (b), 723 K; (c), 753 K.
Phys. Chem. Chem. Phys., 2002, 4, 620–627
625

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a
Table 7 Absolute values of rate constants
1
T=K
k
12p
k
12c
k(HO
2
þ c-C
6
12
H )
4
4
4
4
6
7
7
7
7
7
73
13
23
53
73
83
1.14 Â 10
2.95 Â 10
5.55 Â 10
—
3.79 Â 10
7.25 Â 10
—
4
—
4
4
3.14 Â 10
5.07 Â 10
—
5
5
5
5
1.23 Â 10
1.44 Â 10
1.97 Â 10
—
—
1.84 Â 10
—
3
À1 À1
b
log(A=dm mol
E=kJ mol
s
) 10.17 ± 0.52 10.22 ± 0.45 10.23 ± 0.49
78.8 ± 6.6
À1
b
74.4 ± 4.7
73.2 ± 5.0
a
3
dm mol
À1 À1
b
s
of original data.
1units; accuracy ca. ± 10%. Small re-interpretation
the data determined for HO þ c-C H over a similar tem-
2
6
12
1
perature range. Although the values of k12p lie below those of
k12c and k(HO þ c-C H ), when allowance is made through
2
6
12
the additivity rule for the presence of 6 primary C–H bonds by
8
10.13
3
À1
use of k(HO þ C H ) ¼ 10
exp(À 10330=T ) dm mol
2
2
6
À1
s
, the Arrhenius plot in Fig. 7 shows that on a per C–H bond
Fig. 7 Arrhenius plots for k12 per secondary C–H bond in C
10 and c-C 12 . O, c-C 12 (ref. 1); D, c-C 10 ; u, C
allowance for primary attack–see text).
3
H
8
, c-
basis, the values of the rate constant for reaction at the sec-
ondary C–H bonds in C lie consistently about 45% above
those for c-C H and c-C H . The data for the cyclic com-
C
5
H
6
H
6
H
5
H
H (after
3 8
3
H
8
5
10
6
12
À1
pounds agree extremely well, however, with E ¼ 73.9 kJ mol
3
and log[A(per C–H bond)=(dm mol
À1 À1
À1
À1
s
) ¼ 9.15. For a sec-
estimated difference of about 2 J K mol in the entropies of
activation.
3 8
ondary C–H bond in C H , the data yield 76.1 and 9.53,
respectively.
Accepting that the values for k(HO þ CH CH CH ) are
2
3
2
3
Use of the bond-additivity rule for H=OH þ alkanes with a
accurately placed on a per C–H bond basis at about 45%
above those for attack at the CH positions in c-C H and c-
C H , it is important to establish the validity of the data for
1
9,20
low carbon number has been questioned by Cohen
because the entropy of activation per carbon atom, calculated
by transition state theory, is not constant until C reaches 5. In
an alternative bond additivity approach Atkinson
mainly
2
5
10
6
12
n
modelling purposes. Although values of D(c-C H –H) ¼
5
9
2
1
À1
has
403.5 ± 2.5 kJ mol
and D(c-C H –H) ¼ 399.6 ± 4 kJ
À1
3 2
6
11
À1
allowed for the effect of near-neighbour groups by giving
expressions which effectively modify the activation energy of
mol , compared with D[(CH ) CH–H] ¼ 412 ± 1.6 kJ mol
,
2
2
have been quoted recently, those for the cyclic alkanes were
determined when much lower values were considered ‘estab-
the reaction. Although the use of k(HO
for attack at the primary C–H bonds in C
2
þ C
2 6
H ) to allow
2
3
3
H
8
may introduce
lished’ for C–H bond dissociation energies in alkanes. Given
that there is effectively zero strain energy in the rings, then the
C–H bond dissociation energies in c-C H and c-C H
2
a small error, if the difference in the quoted values of
2
À1
D(C
4
2
H
5
–H) ¼ 423.0 ± 1.6 kJ mol and D(CH
3
CH
2
CH
2
–H) ¼
5
10
6
12
À1 À1
À1
À1
20.0 ± 2.5 kJ mol
s
is taken as 3 kJ mol , then E(HO
2
þ
should differ by no more than 2 kJ mol from that for the
secondary C–H bonds in C H , as strongly argued by
À1
C H ) À E(HO þ CH CH CH ) ꢁ1.5 kJ mol the effect of
2
6
2
3
2
3
3
8
2
McMillen and Golden. Their view will be accepted here and
3
which at 753 K effectively cancels out that caused by the
2
.5
Table 8 Kinetic data for HO
2
þ alkanes in the form k ¼ AT exp(ÀB=T )
3
A=dm mol
À1 À1
À2.5
K
Alkane
Range=K
s
B=K
Ref.
Note
a
b
b
b
b
b
b
b
b
b
CH
4
(total)
(total)
per primary C–H)
Tetramethylbutane (total)
per primary C–H)
c-C 12 (total)
per secondary C–H)
c-C 10 (total)
per secondary C–H)
c-C
12 þ c-C
combined (per secondary C–H)
(total)
per secondary C–H)
10 (total)
per tertiary C–H)
716
47
71
11.8
109
6.0
77
6.4
97
10570
8480
8480
8395
8395
6800
6800
7130
7130
6970
7
8
8
6
6
1
1
C
2
H
6
673–793
673–793
673–793
673–793
673–773
673–773
673–783
673–783
673–783
(
(
6
H
(
5
H
Present
Present
Present
(
9.7
7.9
6
H
5 10
H
b
C
3
H
8
673–753
673–753
753
753
753
753
540–1600
540–1600
99
24.5
7760
7480
Present
Present
26
26
27
27
24
24
b c
d
(
4
i-C
(
4
H
k ¼ 8.7 Â 10
c e
d
15.0
6170
5
2
,3-dimethylbutane (total)
per tertiary C–H)
HCHO (total)
per aldehydic C–H)
k ¼ 1.23 Â 10
10.0
40.8
e f
g
(
6100
5135
5135
(
20.4
a
b
assumed. Obtained from fit to data Additivity rule used with C
c
d
data. Units of rate constant,
Two-thirds of the total A factor for C
.
2
H
6
2
H
6
3
À1 À1
e
f
A factor assumed, based on other values. Additivity rule used with tetramethylbutane data. Based on 4 independent studies,
g
dm mol
see ref. 24.
s
6
26
Phys. Chem. Chem. Phys., 2002, 4, 620–627

View Article Online
if so there must be a further factor contributing to the differ-
ence in the rate constants. As the entropy of activation per C–
3
4
5
6
7
8
9
R. R. Baker, R. R. Baldwin and R. W. Walker, T rans. Faraday
Soc., 1970, 66, 2812, 3016.
S. M. Handford-Styring and R. W. Walker, J. Chem. Soc.,
Faraday T rans., 1995, 91, 1431.
G. M. Atri, R. R. Baldwin, G. A. Evans and R. W. Walker, J.
Chem. Soc., Faraday T rans. 1, 1978, 74, 366.
R. R. Baldwin, M. W. M. Hisham, A. Keen and R. W. Walker, J.
Chem. Soc., Faraday T rans. 1, 1982, 78, 1165.
R. R. Baldwin, P. N. Jones and R. W. Walker, J. Chem. Soc.,
Faraday T rans. 2, 1988, 84, 199.
H bond for HO
significantly, the congruity of the rate constants per CH group
2 5 6
attack on c-C H10 and c-C H12 will not differ
2
is predictable. The higher rate constant for the secondary CH
group in C H probably therefore arises at least partially from
2
3
8
a lower (negative) value for the entropy of activation. The
precise difference is difficult to estimate, but lies in the region
À1
À1
of 4–8 J K mol , which implies that HO
site in C H would be a factor 1.5–2.5 faster than for c-C H
2
attack at the CH
2
R. R. Baldwin, C. E. Dean, M. R. Honeyman and R. W. Walker,
J. Chem. Soc., Faraday T rans.1, 1986, 82, 89.
R. R. Baldwin, P. Doran and R. W. Walker, T rans. Faraday Soc.,
1960, 56, 93.
3
8
5
10
6
and c-C H12 , compared with the figure of 1.45 observed
experimentally. Further discussion at this stage is premature in
the absence of more experimental data.
Based on the Arrhenius expression, values of A(per C–H
10 G. A. Evans and R. W. Walker, J. Chem. Soc., Faraday T rans. 1,
979, 75, 1458.
11 Z. H. Lodhi and R. W. Walker, J. Chem. Soc., Faraday T rans.,
991, 87, 681.
Z. H. Lodhi and R. W. Walker, J. Chem. Soc., Faraday T rans.,
991, 87, 2361.
1
9
3
À1 À1
À1
bond) ¼ 3.0 Â 10 dm mol
s
recommended for HO attack at the CH groups in C H and
and E ¼ 75 kJ mol are
1
2
2
3
8
1
2
4
C H10 between 650 and 800 K, with A(per C–H bond) reduced
1
9
3
À1 À1
s for alkanes where the carbon number
exceeds 4. Outside this temperature range use of the expression
to 1.5 Â 10 dm mol
13 D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, Th.
Just, J. A. Kerr, M. J. Pilling, J. Troe, R. W. Walker and J.
Warnatz, J. Phys. Chem. Ref. Data, 1992, 21, 411.
2
.5
k ¼ AT exp(À B=T ) is preferred, given the clear evidence of
1
4
R. R. Baldwin, D. Jackson, R. W. Walker and S. J. Webster,
T rans. Faraday Soc., 1967, 63, 1676.
R. R. Baldwin, R. W. Walker and Robert W. Walker, J. Chem.
Soc., Faraday T rans. 1, 1979, 75, 1447.
non-Arrhenius behaviour over large temperature ranges for
many radical reactions, the value of
k ¼ 4.1 Â
1
5
1
2.5
3
À1 À1
s determined experimen-
1
tally over the range 540–1600 K for HO
0 T exp(À 5136=T ) dm mol
2
4
2
þ HCHO, and
16 F. Westley, J. T. Herron and R. J. Cvetanovic, Compilation of
Chemical Kinetic Data for Combustion Chemistry, Part 1, NSRDS-
NBS 73, NBS, Washington, DC, August 1987.
2
application of Bozzelli’s methods which suggests that n lies
5
between 2.2 and 3.0. Table 8 summarises all the available data in
1
7
Handbook of Bimolecular and Termolecular Gas Reactions, ed J. A.
Kerr and S. J. Moss, CRC Press, Boca Raton, FL, vol. 1.
R. R. Baldwin and R. W. Walker, J. Chem. Soc., Faraday T rans. 1,
this form. The values of B fall consistently as the HO
approach approximate thermoneutrality (HO
þ HCHO). The
non-Arrhenius A factors per C–H bond fall in the range 6.5–25
2
reactions
2
1
8
1
979, 75, 140.
3
À1 À1
À2.5
and, although perhaps fortuitously, are
view that in abstractions by radicals
dm mol
s
K
consistent with Cohen’s
19 N. Cohen, Int. J. Chem. Kinet., 1991, 23, 683.
20 N. Cohen, Int. J. Chem. Kinet., 1991, 23, 397.
1
9,20
2
2
1
2
R. Atkinson, J. Phys. Chem. Ref. Data, 1997, 26, 217.
CRC Handbook of Chemistry and Physics, ed D. R. Lide, CRC
Press, Boca Raton, FL, 1998, pp. 9–64.
such as H and OH the entropy of activation per C–H bond does
not become constant until the alkane has a carbon number
exceeding 4. The accuracy of the rate constants in the database
may be expressed in the form Dlog k ¼ ± 0.15 between 600 and
2
3
D. F. McMillen and D. M. Golden, Ann. Rev. Phys. Chem., 1982,
3, 493.
3
8
00 K rising to ± 0.3 at 1200 K.
24 B. Eiteneer, C-L. Yu, M. Goldenberg and M. Frenklach, J. Phys.
Chem. A, 1998, 102, 5196.
2
5
C-J. Chen and J. W. Bozzelli, J. Phys. Chem. A, 2000, 104,
9715.
References
2
6
R. R. Baker, R. R. Baldwin and R. W. Walker, Proc. Combust.
Inst., 1971, 13, 291.
1
2
S. M. Handford-Styring and R. W. Walker, Phys. Chem. Chem.
Phys., 2001, 3, 2043.
S. W. Benson, T hermochemical Kinetics, Wiley, New York, 1976.
27 R. R . Baldwin, G. R. Drewery and R. W. Walker, J. Chem. Soc.,
Faraday T rans. 2, 1986, 82, 251.
Phys. Chem. Chem. Phys., 2002, 4, 620–627
627