Kinetics and activation energy of the oxidation of para-tolyl radical by cobalt(III) in acetic acid: Competition kinetics

Article abstract of DOI:10.1002/kin.20116

The title reaction gives rise to a benzylic cation that is rapidly transformed to its bromide in competition with the reaction of the radical with carbon tetrachloride. Experiments were carried out over 17-69°C in acetic acid containing cobalt(II) acetate, para-xylene, hydrobromic acid, carbon tetrachloride, and meta-chloroperoxybenzoic acid. The product ratio, ArCH ₂Cl/ArCH₂Br, in combination with other pertinent rate constants, was used to determine the rate constant for the step of interest: log script k sign (L mol^-1 s^-1) = 19.9 - (75 ± 11 kJ mol^-1/2.303 RT). The large pre-exponential factor, which gives ΔS? = 128 J K^-1 mol^-1, signals an unusual transition state, because a negative value of ΔS? would be expected for a simple bimolecular reaction. The production of the ion pair ArCH ₂⁺||OAc^- in HOAc, which has the same dielectric constant as benzene, may be responsible, at least in part. Furthermore, inner sphere reorganization of cobalt may also contribute.

Full text of DOI:10.1002/kin.20116

Kinetics and Activation
Energy of the Oxidation
of para-Tolyl Radical by
Cobalt(III) in Acetic Acid:
Competition Kinetics
JAMES H. ESPENSON, DOUGLAS TAK-YEUNG YIU
Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011
Received 21 October 2004; accepted 28 April 2005
DOI 10.1002/kin.20116
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The title reaction gives rise to a benzylic cation that is rapidly transformed to
its bromide in competition with the reaction of the radical with carbon tetrachloride. Exper-
◦
iments were carried out over 17–69 C in acetic acid containing cobalt(II) acetate, para-xylene,
hydrobromic acid, carbon tetrachloride, and meta-chloroperoxybenzoic acid. The product ratio,
ArCH Cl/ArCH Br, in combination with other pertinent rate constants, was used to determine
2
2
−
1
−1
−1
the rate constant for the step of interest: log k (L mol
s
) = 19.9 – (75 ± 11 kJ mol /2.303
‡
−1
−1
RT ). The large pre-exponential factor, which gives ꢀS = 128 J K mol , signals an unusual
‡
transition state, because a negative value of ꢀS would be expected for a simple bimolecular
+
−
reaction. The production of the ion pair ArCH ||OAc in HOAc, which has the same dielectric
2
constant as benzene, may be responsible, at least in part. Furthermore, inner sphere reorganiza-
tion of cobalt may also contribute. ꢀC 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 599–604,
2
005
INTRODUCTION
and HBr as catalysts. The reaction is run in aque-
ous acetic acid at 190–210 C. Several transient inter-
◦
The commercial process for the autoxidation of para-
xylene (pX) to terephthalic acid (TA) is well estab-
lished. It occurs by a complex and multistep free radi-
cal chain reaction that requires Co(OAc)2, Mn(OAc)2,
mediates are involved, including ArCH2˙, ArCH2OO˙,
ArCH2O˙, Mn(III), Co(III), and HBr2˙. Much is known
about the steps involved in the overall reaction which
need not be repeated here except as pertinent to this
investigation [1–16].
For most applications, it is desirable that the
product (purified terephthalic acid, PTA) be color-
less. Minor levels of intensely colored intermedi-
ates can be deleterious if they have high molar
absorptivities at visible wavelengths. Among these is
Correspondence to: J. H. Espenson; e-mail: espenson@
iastate.edu.
Contract grant sponsor: National Science Foundation.
Contract grant number: #CHE-020409.
2,6-dicarboxyanthraquinone, which is formed by oxi-
Contract grant sponsor: BP-Amoco Chemicals.
ꢀ
c 2005 Wiley Periodicals, Inc.
dation of a benzylic cation as in this sequence:

600
ESPENSON AND YIU
(
(
MCPBA) (77% max.), 4-methylbenzyl bromide
97%), 4-methylbenzyl chloride (98%), carbon tetra-
chloride (99.9+%, HPLC grade), and glacial acetic
acid (ACS plus) were used as received. The purity of
the MCPBA (75.0%) was determined by iodometric
titration.
(1)
Kinetics Measurements
The benzylic cation may result from the oxidation of
The Co(III) oxidation of 4-methylbenzyl radical was
evaluated by competition with the Cl-atom abstrac-
tion from carbon tetrachloride as the monitoring re-
action (3b) [20]. Separate acetic acid solutions of the
aradicalprecursorbyanactivecobalt(III)intermediate,
∗
in competition with its very rapid reaction [17] with
oxygen:
(Co(II)/HBr/CCl4/pX) and MCPBA were sealed in cu-
vettes with serum caps and purged with argon. Both
solutions were then equilibrated at the desired temper-
ature before initiating the reaction by transferring the
MCPBA into the (Co(II)/HBr/CCl4/pX) solution via
the septum.
(2a)
(2b)
The 4-Methylbenzyl Radical
The first of these reactions has not been examined
independently, and our objective has been to do so, not
only for its relevance to the practice of catalytic chem-
istry but because it is of fundamental interest [18,19].
We are particularly seeking to evaluate the activation
energy for kCo, as this will determine the importance of
that reaction at the elevated temperatures used commer-
The radical transient was produced in situ from the
oxidation of pX by HBr2˙via H-atom abstraction (p-
C6H4Me2 + HBr2˙→ ArCH2˙+ 2 HBr) with the rate
5
−1 −1
s [5]. The HBr2 radi-
constant 1.6 × 10 L mol
cal was generated from Co(OAc)2 (10 mM) and HBr
(15 mM), and the external oxidant that converts Co(II)
to Co(III) was 0.5 mM MCPBA. MCPBA is a two
electron oxidant and its oxidation rate of Co(II) to
Co(III) is about 1000 times faster than the rate at which
◦
cially, which are well in excess of the 17–70 C range
used in this study. A direct investigation did not seem
feasible because the steps preceding reaction (2a) are
slower. Thus we have employed a competition method
in the absence of oxygen, using the reaction between
the radical and carbon tetrachloride as the reference.
Thus the competition scheme is
−
MCPBAoxidizeswithBr [2]. TheCo(II)-MCPBAre-
action does not involve radicals. It proceeds at a rate
2
d[Co(III)]/dt = 2k1[Co(II)] [MCPBA] [21].
RESULTS AND INTERPRETATION
Product Analysis
(
3a)
The oxidation products were analyzed by HPLC (Wa-
ters 501 solvent delivery system, Waters 996 photodi-
ode array detector and a Novapak C18 3.9 mm × 150
mm column). The chromatographic separations were
performedinisocraticmodeusingmobilephaseof37%
H2O, 61% CH3CN, 1.2% CH3OH, and 0.5% HOAc
with a flow rate of 0.9 mL min . The wavelength of
product detection was 254 nm. The analytes were iden-
tified by comparing the retention time of the chromato-
graphic peaks with those of the authentic samples (4-
methylbenzyl bromide, 4-methylbenzyl chloride, and
p-xylene), and their concentrations were obtained from
the precalibrated plots of peak area against concentra-
tion for each reference. The products (4-methylbenzyl
(3b)
EXPERIMENTAL SECTION
Materials
−
1
Cobalt(II) acetate tetrahydrate (98+%, ACS grade),
p-xylene (99+%, HPLC grade), hydrobromic acid
(48%, ACS grade), meta-chloroperoxybenzoic acid
∗
9
−1 −1
◦
The value of kO2 is 2.8 × 10 L mol
s
at 25 C.

KINETICS AND ACTIVATION ENERGY OF THE OXIDATION OF PARA-TOLYL RADICAL
601
chloride and 4-methylbenzyl bromide) were analyzed
by HPLC after 1–2 min of reaction, which corre-
sponded to completion. No other product was detected.
The Co(III) so produced gives rise to HBr2˙, which then
rapidly oxidizes pX to ArCH2˙, as in reaction (6) [5].
|||
HOAc
||
·
Co + CoBr2 −→ 2 Co + HBr
2
k2
Product Ratios
·
·
HBr + pX −→ 2HBr + ArCH
(6)
The concentration ratio, R = ArCH2Cl/ArCH2Br, was
2
f ast
2
determined over a range of CCl4 concentrations, 70–
5
20 mM. Lower concentrations could not be used be-
With these two reactions and two in Eq. (3), one has all
the steps that establish the steady-state concentrations
cause too little of the chloride was formed for an accu-
rate analysis. A control experiment lacking CCl4 pro-
duced no detectable amount of ArCH2Cl. These de-
terminations were carried out at four temperatures in
the range 17–70 C. At each temperature, the plot of
R against [CCl4] is linear with a small positive inter-
cept, as illustrated by Fig. 1. The slopes S of the lines
·
of ArCH and Co(III), as in Eqs. (7) and (8).
2
d[Co(III)]
2
◦
= 2k [Co(II)] [ArCO H] − k [Co(II)]
1
3
2
dt
·
×[Co(III)] − kCo[ArCH ][Co(III)] = 0
(7)
2
◦
◦
are 8.1 ± 0.5 (17.5 C), 7.6 ± 0.4 (25.0 C), 6.1 ± 0.3
◦
◦
(50.8 C), and 4.38 ± 0.01 (69.0 C).
·
d[ArCH ]
2
From the reactions in Eq. (4), the product ratio can
=
k2[Co(II)] − kCo
dt
be expressed as
·
·
2
×
[ArCH ][Co(III)] − kCl[ArCH ][CCl4] = 0
2
ArCH2Cl
kCl
[CCl4]
R =
=
×
(4)
(8)
ArCH2Br
kCo
[Co(III)]
Conditions were set with [Co(II)] >> [P]0, where P
represents ArCO3H. Given that [Co(III)] << [Co(II)]
by the steady-state approximation, these equations will
simplify further. The simultaneous solution of Eqs. (7)
and (8) affords the expression for [Co(III)]ss, which
is needed for the further interpretation of the product
ratio R in Eq. (4). The Appendix gives this solution
with further approximations to obtain a tractable form.
By this method, the slope S of the plot of R versus
Provided, therefore, that [Co(III)] can be taken as a
constant (say, by the steady-state approximation), one
can verify that R should vary linearly with [CCl4],
thus providing the value of the desired rate constant
kCo, because reactions between carbon-centered radi-
cals and carbon tetrachloride have been widely stud-
ied [22–25]. The reaction is initiated by addition of
meta-chloroperoxybenzoic acid to cobalt(II). The rate
of cobalt(III) generation from this very rapid reaction
[CCl4] is
2
is d[Co(III)]/dt = 2k1[Co(II)] [ArCO3H], according to
Eq. (5).
2
k2kCl
S =
(9)
TP0k1kCo
||
|||
2
Co + ArCO3H → 2Co + ArCO2H
(5)
Activation Parameters
Because S is a quantity composed of the products and
quotients of individual rate constants, the values of the
term (S × T × P0/2) can be expected to conform to
the Arrhenius equation,
ꢀ
ꢁ
TP0
2
ES
S ×
= AS × exp −
(10)
RT
The graphical analysis of the data according to
Eq. (10) is presented in Fig. 2. It leads to these ap-
parent activation parameters, log10 AS = −6.36 ± 0.26
−
7
−1
(
or A = 4.4 × 10 mol L ) and ES = −9.3 ± 1.5 kJ
−
1
Figure 1 Plots of the ratio of the aralkyl halide products
against [CCl4] at different temperatures.
mol . To use these values to determine the activation
parameters for kCo, one must use the established values

602
ESPENSON AND YIU
Calculation of kCo
One has this equation
k2kCl
k1 × AS × e−
kCo =
(10)
(ES/RT )
From it, ECo = E2 + ECl − E1 − ES = 75 ± 11 kJ
−
1
19
−1 −1
s . Thus at 298
mol and ACo = 8 × 10 L mol
6
−1 −1
K, kCo = 6 × 10 L mol
s . From Eq. (11), the stan-
dard entropy of activation is
ꢀ
ꢁ
ACoh
∗
= 128 J K−1 mol−1 (11)
ꢀ
S
= R ln
Co
e × kB T
Figure 2 Analysis of the temperature dependence of S
according to the Arrhenius equation.
Mechanism of the kCo Reaction
Does the kCo reaction proceed by “simple” outer-sphere
electron transfer?
or estimates for the other rate constants in Eq. (9). This
is the subject of the next sections.
·
+
Co(III) + ArCH → Co(II) + ArCH
(12)
2
2
One approach to providing an answer is to use the
Marcus cross relation to estimate the rate constant
kCo. For the couple ArCH /ArCH2˙, the value of E is
Estimation of kCl
+
o
2
Therateconstantforthisreactionhasnotbeenreported,
but values of the reactions of several other alkyl radicals
with CCl4 have been summarized in Table I. They can
form the basis for the estimation of kCl. The closest pri-
mary radical other than methyl, which is nonrepresen-
tative, is the 5-hexenyl radical, CH2 CH(CH2)3CH2˙.
This specific reaction will be used to represent kCl in
this work. Also, the trends for the set of radical reac-
tions shown in Table I parallel those for the reactions
of the same alkyl radicals with BrCCl3 [20].
5
+
0.75 V [26] and the electron exchange rate is 3 × 10
−
1
−1
[27]. For the Co(III)/Co(II) couple, E
o
L mol
s
2
1
is 2.0 V [1], giving the value K12 = 1.3 × 10 . The
electron exchange rate constant k11 between Co(IIIa)
and Co(II) in acetic acid is apparently unknown. The
3+/2+
5
−1 −1
value of Co(en)3
is used, 9.3 × 10 L mol
s
in aqueous solution, then the Marcus cross relation al-
lows the calculation the rate constant for reaction 12
8
−1 −1
s . Compared with the
as kCo = 3.6 × 10 L mol
6
−1 −1
experimental value, kCo = 6 × 10 L mol
s , the
agreement is not particularly convincing. The use of
k11 for aqueous [Co(en)3] is, however, a serious draw-
back to the calculation, as it seems to be an unrealistic
model to use a rate constant for reactions between two
positive ions in a solvent of high dielectric constant to
model an electron exchange between two uncharged
species in a medium of very low dielectric constant. It
appears that the matter cannot be taken further.
Other Rate Constants
The value of k1 and its activation parameters have been
reported by Jones [2,3]
1
2
2
−2 −1
A1 = 4.5 × 10 L mol
s
−
1
E1 = 40 ± 4 kJ mol
In addition, there is the matter as to whether elec-
tron transfer, which creates ionic species, can be re-
garded as an appropriate mechanism is a solvent such
as acetic acid with a dielectric constant the same as
that of benzene. The octahedral coordination of cobalt
in both oxidation states will be maintained, but with
three acetates for Co(IIIa) and two for Co(II). This is
one reason to question the electron exchange model
based on [Co(en)3]. Likewise, the aralkyl cation will
really exist as an ion pair in acetic acid.
5
2
−2 −1
k1,298 = 1 × 10 L mol
s
The same author reports this information for k2
17
−1 −1
s
A2 = 2.4 × 10 L mol
−1
E2 = 80 ± 4 kJ mol
3
−1 −1
s
k2,298 = 2.3 × 10 L mol

KINETICS AND ACTIVATION ENERGY OF THE OXIDATION OF PARA-TOLYL RADICAL
603
Table I Rate Constants (k ) for the Reactions of Alkyl Radicals with CCl
Cl
4
log10(A)
ECl
k298
−1 −1
−1
−1
−1
(kJ mol )
Radical
(L mol
s
)
(L mol
24.7
s
)
Ref.
·
CH
3
8.8(3)
8.4(3)
9.4(1)
7.0
42.3(21)
25.9(17)
28.8
[23]
[22]
[24]
[25]
·
3
4
4
CH2 CH(CH2)3CH
Cyclo-C6H
Tert-butyl
7.2 × 10
2.3 × 10
3.8 × 10
2
·
1
1
·
13.8(42)
The reaction can thus more properly be written as
With further rearrangement, one arrives at this
quadratic equation,
·
[
Co(HOAc) (OAc) ] + ArCH + HOAc
3
3
2
2
+
2
−
2
k1T P{kCo X + kClC} − k2TX{kCo X + kClC}
→
[Co(HOAc) (OAc) ] + [ArCH ]||OAc
4
2
2
−kCok2TX = 0
(A3)
(13)
‡
−1
−1
The large and positive value of ꢀS , 128 J K mol ,
Dividing through by k2kCoT and collecting terms by
powers of X,
is a strong indication that the reaction with the rate
constant kCo is not an example of “simple” bimolec-
ular electron transfer. Bimolecular reactions are cus-
tomarily characterized by substantially negative values
of their entropies of activation, reflecting the union of
two separate reactants in the transition state. Exami-
nation of reaction (13) suggests that opposing factors
come into play. The principal ones are the substantial
inner-sphere reorganization accompanying the change
in oxidation state of cobalt and in particular the creation
of an ion pair in a very nonpolar solvent.
ꢂ
ꢃ
kCl
2k1TP
k2
2k1kClTPC
k2kCo
2
2X + X
C −
+
= 0
(A4)
kCo
The quadratic formula gives this solution,
ꢀ
ꢄ
ꢅ
2
k1
kCl
X =
TP −
k1
C
k2
kCo
ꢆ
ꢁ
ꢇ
ꢄ
ꢅ
2
2
kCl
16k1kCl
k2kCo
Some experiments were conducted with the use of the fa-
cilities of the Ames Laboratory, which is operated by Iowa
State University of Science and Technology under contract
W-7405-Eng-82.
+
TP −
C
+
TPC
4k2
k2
kCo
(A-4)
where only the positive root gives a physically mean-
ingful answer.
APPENDIX: DERIVATION OF AN
EXPRESSION FOR [CO
(III)]SS
Because the general expression is intractable, we
have examined the limits at t = ∞ (where x = 0 be-
cause P∞ = 0) and at t = 0. Further all terms in C have
been dropped from Eq. (A4) because S shows a linear
dependence on C, but no further variation. Thus
Abbreviations: T = [Co(II)] = [Co]T; C = [CCl4];
X = [Co(III)]
From Equation (8),
k2TX
ꢆ
·
ꢈ
ꢉ
ꢈ
ꢉ
[
ArCH ] =
(A1)
2
2
2
k1
2k1
k2
kCo X + kClC
TP +
TP
k2
k1TP
k2
Substitution of Eq. (A1) into Eq. (7) gives
X =
=
(A-5)
4
k2
dx
2
·
−
= 2k1T P − k2TX − kCo[ArCH ]X = 0
2
Our solution to the problem of the too-complex form
for x is to use an average concentration,
dt
ꢂ
ꢃ
k2T X
2
=
2k1T P − k2TX − kCo X
kCo X + kClC
X0 + X∞
k1TP0
2k2
Xav =
=
(A6)
(A2)
2

604
ESPENSON AND YIU
The slope of the plot of R versus [CCl4] is, from
Eq. (4),
10. Saha, B.; Koshino, N.; Espenson, J. H. J Phys Chem A
2004, 108, 425–431.
1
1
1
1
1. Zakharov, I. V.; Muratov, V. M. Dokl Akad Nauk SSSR
1971, 196, 1125–1128.
2. Zakharov, I. V.; Geletii, Y. V.; Adamyan, V. A. Kinet
Catal 1988, 29, 924–929.
3. Zakharov, I. V.; Geletii, Y. V.; Adamyan, V. A. Kinet
Catal 1991, 32, 31–37.
4. Zakharov, I. V.; Kumpan, Y. V. Kinet Catal 1993, 23,
kCl
1
S =
S =
×
(A7)
(A8)
kCo
[Co(III)]ss
2k2kCl
k1kCoTP0
922–927.
1
1
5. Zakharov, I. V. Kinet Catal 1998, 39, 485–492.
6. Partenheimer, W.; Gipe, R. K. In ACS Symposium Series
no. 523; Oyama, S. T.; Hightower, J. W. (Eds.), 1993.
7. Neta, P.; Grodkowski, J.; Ross, A. B. J Phys Chem Ref
Data 1996, 25, 955.
BIBLIOGRAPHY
1
1
. Jiao, X.; Espenson, J. H. Inorg Chem 2000, 39,
549–1554.
1
18. Eberson, L. Adv Phys Org Chem 1982, 18, 79.
19. Lande, S. S.; Kochi, J. K. J Am Chem Soc 1968, 90,
5196.
20. Rollick, K. L.; Kochi, J. K. J Am Chem Soc 1982, 104,
1319.
2
3
4
. Jones, G. H. J. Chem Res (M) 1981, 2814–2818.
. Jones, G. H. J. Chem Res 1982, 207.
. Metelski, P. D.; Adamian, V. A.; Espenson, J. H. Inorg
Chem 2000, 39, 2434–2439.
5
. Metelski, P. D.; Espenson, J. H. J Phys Chem 2001, 105,
21. Jones, G. H. J Chem Soc, Chem Commun 1979,
536–537.
5
881–5884.
6. Partenheimer, W. In Catalysis of Organic Reactions;
Blackburn, D. W. (Ed.); Marcel Dekker: New York,
22. Jewell, D. R.; Mathew, L.; Warkentin, J. Can J Chem
1987, 65, 311.
1
990, pp. 321–346.
23. Macken, K. V.; Sidebottom, H. W. Int J Chem Kinet
1979, 11, 511–527.
24. Alfassi, Z. B. Int J Chem Kinet 1980, 12, 217–223.
25. Frith, P. G.; McLauchlan, K. A. J Chem Soc, Faraday
Trans 2 1976, 72, 87–103.
7
. Partenheimer, W.; Gipe, R. K. In Nature of the Cobalt-
Manganese-Bromine Catalyst in the Methylaromatic
Compounds Process; Oyama, S. T.; Hightower, J. W.
(Eds.); ACS Symposium Series, 1993.
8
9
. Partenheimer, W. Catal Today 1995, 23, 69–157.
. Saha, B.; Espenson, J. H. J Mol Catal A 2004, 207,
26. Sim, B. A.; Milne, P. H.; Griller, D.; Wayner, D. D. M.
J Am Chem Soc 1990, 112, 6635.
1
23–129.
27. Eberson, L.; Springer-Verlag: New York, 1987.