Kinetic and thermodynamic parameters for the equilibrium reactions of phenols with the dpph. radical

Article abstract of DOI:10.1039/b606322e

The kinetics and energetics of the reversible reaction of phenols with the dpph^. radical have been studied; steric shielding of the divalent N by the o-NO₂ in dpph^. seems to be the main cause of the entropic barriers of this reaction. The Royal Society of Chemistry 2006.

Full text of DOI:10.1039/b606322e

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COMMUNICATION
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Kinetic and thermodynamic parameters for the equilibrium reactions of
phenols with the dpph? radical
Mario C. Foti* and Carmelo Daquino
Received (in Cambridge, UK) 5th May 2006, Accepted 7th June 2006
First published as an Advance Article on the web 27th June 2006
DOI: 10.1039/b606322e
The kinetics and energetics of the reversible reaction of phenols
with the dpph? radical have been studied; steric shielding of the
divalent N by the o-NO2 in dpph? seems to be the main cause of
the entropic barriers of this reaction.
Reactions of phenols (ArOH) with the dpph? (2,2-diphenyl-1-
picrylhydrazyl) radical continue to be the focus of intense
investigation1 because they serve as a prototypical model for the
reactions of peroxyl radicals, RO?2, with ArOH which are
extremely important, both in biology and chemistry, for their
inhibitory effect on the autoxidation processes of organic
materials.2
ArOH + RO?2 A ArO? + RO2–H
(1)
ArOH + dpph? P ArO? + dpph–H
(2)
Scheme 1 Phenols investigated in the present study.
The analysis of a large number of experimental rate constants
determined at 303 K with non-hindered phenols reveals, in fact,
that the rate constants of reaction 1, k1, for polystyrylperoxyl
radicals correlate almost linearly with the rate constants relative to
reaction 2, k2, being k1 # 4000 6 kO2 .3 This equation also shows
that the RO?2 radicals are about 3 orders of magnitude more
reactive than dpph? in the abstraction of the hydrogen atom from
ArOH. In fact, reaction 1 is exothermic and essentially irreversible
(DS1 # 0), since the O–H bond enthalpy (DH298) of hydroper-
oxides varies in the range 86–884 kcal mol21, whereas the
DH298(O–H) of ArOH with antioxidant activity are confined in
the range 78–863 kcal mol21. In contrast, reaction 2 is endothermic
for most phenols since the DH298(N–H) in dpph-H is compara-
tively low, being 78.9 kcal mol21 (vide infra). Reaction 2 is
therefore expected to be reversible (DS2 # 0, vide infra) with a rate
constant for the forward reaction slower than that of the reverse
step, i.e. k2 % k22. In this paper, we report on the kinetics and
energetics of ArOH/dpph? reactions which may help in clarifying
the intimate mechanism of the formal H-atom transfer from
ArOH to dpph?. We chose for this study almost exclusively
methoxyphenols (see Scheme 1) because for a few of them,
reaction 2 is manifestly an equilibrium process. To avoid the
undesirable complications of the so-called ‘‘sequential proton loss
electron transfer’’5 and the kinetic solvent effects,6 all reactions
were exclusively studied in cyclohexane or n-hexane which are
not hydrogen-bond acceptor solvents and inhibit phenol
deprotonation. The course of the reaction was followed by
monitoring spectrophotometrically at 512 nm the loss of dpph?
over time. Despite all reactions being almost exclusively studied in
pseudo-first order conditions, i.e. with [ArOH] & [dpph?] # 0.02–
0.1 mM, the dpph? loss very rarely followed first-order kinetics over
the entire reaction time. In many cases the k2 values, shown in
Table 1, were therefore calculated from the initial rates at 298 K.
We observed a substantial reduction of the rate of dpph? loss when
the reactions were carried out in the presence of 0.1–1 mM dpph–
H, and this confirmed the reversibility of reactions 2. However,
with the exception of the phenols 3, 8 and 13, these reactions,
either in the absence or in the presence of dpph–H, proceeded to
completion, i.e., to a total consumption of dpph?.
This is because the aryloxyl radicals produced in reaction 2 were
in turn quenched by irreversible processes such as reactions 2a and
2b.
ArO? + dpph? A products
(2a)
(2b)
In a few instances, these two radical–radical processes are,
however, equilibrium reactions themselves. The aryloxyl radicals
of 3, for instance, dimerize reversibly with rate constants 2k2b and
k22b of 8.6 6 108 M21 21 and 11 s21, respectively, in n-hexane at
s
ambient temperature.7 Actually, the reaction of dpph? with 3 did
not proceed to complete consumption of dpph? even with a
concentration ratio [3]:[dpph?] of 52:1 but reached an equilibrium
position. Kinetic simulations{ of the decay traces of dpph? + 3
showed that reaction 2a had no role in the overall process, i.e. the
2,6-(MeO)2C6H3O? radicals are quenched by the dpph? radical too
slowly for this reaction to compete with the dimerization 2b. The
Istituto di Chimica Biomolecolare del CNR, Via del Santuario 110,
95028 Valverde (CT), Italy. E-mail: mario.foti@icb.cnr.it;
Fax: +39 095 7212141; Tel: +39 095 7212136
3252 | Chem. Commun., 2006, 3252–3254
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Table 1 Values of DH298(ArO–H) (benzene solution) and rate constants in cyclohexane or n-hexane at 298 K for 1–13
ArOH
DH298(O–H)/kcal mol21
Ref.
k2/M21 21
s
k22/104 M21 21
s
k2a/105 M21 21
s
k2b/108 M21 21
s
k22b/s21
1
2
87.2
8a
0.10
0.92
a
85.3 ¡ 0.9
88.6
82.1
81.7
81.7
83.3
84.6
81.3
80.5
82.1 ¡ 0.6
83.4 ¡ 0.6
81.8b
81.2 ¡ 0.6
83.5 ¡ 0.6
80.1
4e
0.01–1e
17g
4.3g
8d
8b
8d
8b
8d
8c
8c
3
4
50
1.1e
11g
238
5
6
7
8
9
3
90c
990d
68
3.0f
0.73f
0.52e
1.0f
2e
¡ 1.5a
0.8–4e
2h
50–100e
8d
a
a
11
1.8f
10
11
12
13
a
8e
1900
226
10
10g
a
0.70f
1.9f
a
8a
c
0.91
b
d
Present work. In isooctane solution. The rate constant from the initial rates was divided by 2 (stoichiometric factor). See the text.
Obtained from kinetic simulations. See the text. From ref. 7. From ref. 12.
e
f
g
h
in fairly good agreement with an additive contribution of 22 kcal
recently reported for 2CHLCH–COOH.9 Kinetic simulations{ of
the dpph? decay in the presence of phenols 2, 3 and 7 allowed us to
estimate the corresponding k22 for reaction 22, see Table 1. These
three values correlate linearly with the DH298(O–H), as shown in
Fig. 1, and the corresponding equation was used to estimate the
values of k22 at ambient temperature for the remaining
o-methoxyphenols reported in Table 1. We also determined the
N–H bond enthalpy DH298(N–H) in dpph–H by monitoring the
position of the equilibria dpph?/2,4,6-tri-tert-butylphenol 13 and
GO?/dpph–H (GO? denotes the galvinoxyl radical) in the absence of
O2 at various temperatures (range 283–348 K) by UV-vis
spectroscopy. The equilibrium constant at 295 K with 13 was
determined to be 0.1378 ¡ 0.0013 whereas the van’t Hoff plot
yielded DH2 = 1.4 ¡ 0.5 kcal mol21 and DS2 = 0.6 ¡
2 cal mol21K21. Therefore, according to these data we can
calculate that DH298(N–H) = 80.1 2 1.4 = 78.7 ¡ 0.5 kcal mol21
where 80.1 is the DH298(O–H) in 13. In the case of the GO? radical,
the equilibrium constant at 295 K was determined to be 0.094 ¡
simulations also yielded for the reverse step of reaction 2 a rate
constant k22 of (1.2 ¡ 0.1) 6 104 M21 21
at 298 K. The
s
equilibrium constant K2 can therefore be calculated to be (50 ¡ 5)/
(1.2 ¡ 0.1) 6 104 = (4.2 ¡ 0.5) 6 1023 at 298 K, in satisfactory
agreement with the value of (6 ¡ 2) 6 1023 obtained from the
infinity-time absorbances and initial concentrations of reactants.
The average value of 5.1 6 1023 allows us to calculate (DS2 # 0)
that the DH298(O–H) in 3 is 82.0 kcal, in excellent agreement with
the data reported in the literature, see Table 1.
Most of the DH298(ArO–H) reported in Table 1 are taken from
the literature.8 The values determined by EPR techniques in
benzene solution, based on 13 as a reference compound, were
adjusted downward by 1.1 kcal because of a recent revision of the
DH298(O–H) in 13.8a We also revised the O–H bond enthalpy of 2
reported in the literature8d as 88.6 kcal mol21 to a value of ca. 85.3
¡ 0.9 kcal mol21.{ The O–H bond enthalpies of 5 and 6 were
instead estimated by using the group additivity rule8c and
subtracting 1.18a kcal from the final values. The DH298(O–H) in
o-methoxyphenols 2, 3, 5–7 correlate linearly with the correspond-
ing log k2 (see Fig. 1). The equation obtained was used to estimate
the DH298(O–H) in the o-methoxyphenols 8, 9, 11 and 12 on the
basis of their k2 values measured at 298 K. The DH298(O–H) in 11
(81.2 kcal mol21) and 12 (83.5 kcal mol21) so obtained allow us to
calculate that the para 2CHLCH–COOMe group, according to
our data, reduces the DH298(O–H) in phenols by only ca. 1.4 kcal,
0.019 whereas the van’t Hoff plot provided the values of DS22
=
1 ¡ 2 cal mol21 K21 and DH22 = 1.4 ¡ 0.4 kcal mol21. Given
that the correct DH298(O–H) in GOH is 77.7 ¡ 0.310,8a kcal mol21
we can calculate that the DH298(N–H) in dpph–H is 77.7 + 1.4 =
79.1 ¡ 0.5 kcal mol21. In conclusion, our measurements indicate
that the DH298(N–H) in dpph–H is 78.9 ¡ 0.5 kcal mol21, in quite
remarkable agreement with the value of 78.5 kcal mol21 obtained
from Mahoney et al.’s data11 after correcting by 1.18a kcal.
Ubiquinol-0, QH2, reacts with dpph? with an observed rate
constant of ca. 990 M21s21 (see Table 1). The interpretation of this
value depends upon the quenching reactions of the semiquinone
radical QH? which follow reaction 2. We can envisage two possible
quenching processes for QH? (Q represents ubiquinone-0):
QH? + dpph? A Q + dpph–H
2QH? A Q + QH2
(2c)
(2d)
If reaction 2c is faster than reaction 2d then k2 = kobs/2 =
495 M21s21; in the opposite case, i.e. 2d & 2c, k2 # kobs
990 M21 21
whereas in the intermediate case, i.e. 2c # 2d, 495 ,
k2 , 990 M21 21
Fig. 1 Linear free-energy relationships between k2 (&) or k22 ($) and
DH298(O–H) for o-methoxyphenols 2, 3, 5–7. The linear equations are:
DH298(O–H) = 85.172 2 (1.701 6 log k2) (R = 0.98) and DH298(O–H) =
=
s
60.608 + (5.354 6 log k22) (R = 0.999) in kcal mol21
.
s
. The temperature dependence of k2 followed the
Chem. Commun., 2006, 3252–3254 | 3253
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hydrogen-bonded complex and the hydrogen-bond donor X–H
and the hydrogen-bond acceptor (HBA) Y?.4a
Table 2 Activation parameters of phenols for their reactions with the
dpph? and RO?2 radicals
a
dpph?
ArOH Ab/M21 21
RO?2
(3)
s
Eab/kcal mol21 A/M21 21
s
Ea/kcal mol21
With a large excess of the XH reactant, the first step follows
first-order kinetics and, if its time scale is much shorter than the
second, i.e. ka[XH] + k2a & kb, then it can be regarded as being at
equilibrium. The observed rate constant for the overall process will
therefore be equal to kobs = Keq,a 6 kb/(1 + Keq,a [XH]) y Keq,a
6 kb for comparatively low [XH]. We can therefore calculate that,
1
2
3
4
7
1.6 6 106
1.7 6 105
2.9 6 105
2.1 6 106
1.5 6 105
1.3 6 105
7.3 6 105
4.5 6 103
b
9.8
7.2
4.9
5.4
3.3
4.5
3.5
5.0
1.59 6 107 5.2
8
10
13
a
log(Aobs/M21 21
s
) y log(Ab/s21) + DSa/2.303R, that is, the
1.6 6 104
0.5
observed A-factor will be smaller than the value4a of Ab because
of the loss of freedom caused by formation of the HB-complex
(DSa , 0). Furthermore, it is important to realize that the dpph?
radical has several HBA centres but a few of them, e.g. the p-NO2,
hold the H-atom of ArOH molecules in a non-productive
neighbourhood because they are far apart from the divalent N.
These HB-complexes must therefore re-dissociate and associate to
an HBA centre suitable for product formation, a process that may
require a long time scale.
From ref. 15. Experimental error ca. ¡10%.
Arrhenius law with an A-factor of 1.5 6 105 M21 21
and an
s
activation energy of 3.3 kcal mol21 (see Table 2). Our results
indicate that the A-factors of all phenols 1–13 are confined in the
range, log(A/M21s21) = 3.6–6.3. QH? being still a ‘‘phenol’’, its
A-factor in reaction 2c may be similar or even identical to that of
QH2 in reaction 2, i.e. 1.5 6 105 M21 21
energy is expected to be small. We can therefore conclude that k2c
may be ¡1.5 6 105 M21 21
. In contrast, the process of
s
while the activation
s
disproportionation of two semiquinone radicals derived from
ubiquinol-2 has been reported to occur rapidly, the reported rate
References
{ We used the ‘‘Chemical Kinetics Simulator’’ by IBM, version 1.01 (1995).
{ Table 2 shows that the Ea for phenol 2 in reaction 2 is 7.2 ¡ 0.7 kcal.
Since for most phenols the activation energy for the reverse step of reaction
2 is on average ca. 1 ¡ 0.5 kcal we can calculate that the DH298(O–H) in 2
is 78.9 + 7.2 2 1 = 85.1 ¡ 0.9 kcal, that in benzene solution becomes ca.
85.3 ¡ 0.9 kcal because of the enthalpy of hydrogen-bonding between
benzene and 2 (see ref. 8a).
constant being 2.2 6 108 M21 21
in acetonitrile solution at
s
ambient temperature.12 Kinetic simulations{ of reactions 2, 2c and
2d using the above-mentioned rate constants and [dpph?] y 2 6
1024 M showed that ca. 90% of the QH? radical disappears by self-
reacting, i.e. reaction 2d is largely predominant over reaction 2c
and thus k2 # kobs = 990 M21 21
s . Finally, this rate constant can
be split into a contribution of ca. 764 and 226 M21s21 for the O–H
groups at the 1- and 4-positions, respectively, of ubiquinol-0 on the
basis of the difference in their bond enthalpies (ca. 0.9 kcal),8d see
Fig. 1.
1 The literature on this topic is voluminous. See as an example: M. S. Blois,
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C. Berset, Lebensm.-Wiss. Technol., 1995, 28, 25.
2 G. W. Burton and K. U. Ingold, J. Am. Chem. Soc., 1981, 103, 6472
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3 M. C. Foti, E. R. Johnson, M. R. Vinqvist, J. S. Wright, L. R. C.
Barclay and K. U. Ingold, J. Org. Chem., 2002, 67, 5190.
4 (a) M. Foti, K. U. Ingold and J. Lusztyk, J. Am. Chem. Soc., 1994, 116,
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CRC Press, Boca Raton, FL, 2nd edn, 2000.
5 G. Litwinienko and K. U. Ingold, J. Org. Chem., 2004, 69, 5888 and
cited references.
6 D. W. Snelgrove, J. Lusztyk, J. T. Banks, P. Mulder and K. U. Ingold,
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7 E. T. Denisov and I. V. Khudyakov, Chem. Rev., 1987, 87, 1313.
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G. F. Pedulli and K. U. Ingold, J. Phys. Chem. A, 2005, 109, 2647; (b)
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J. Agric. Food Chem., 2006, 54, 2932.
10 M. Lucarini, G. F. Pedulli and M. Cipollone, J. Org. Chem., 1994, 59,
5063.
11 L. R. Mahoney, G. D. Mendenhall and K. U. Ingold, J. Am. Chem.
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13 For an exception see: K. E. Russell, J. Phys. Chem., 1954, 58, 437. See
also: A. H. Ewald, Trans. Faraday Soc., 1959, 55, 792.
14 S. W. Benson, Thermochemical kinetics, Wiley, New York, 2nd edn,
1976.
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The temperature-dependence of k2 in cyclohexane in the range
280–348 K yielded the Arrhenius parameters given in Table 2. The
pre-exponential factors show that reaction 2 is strongly affected by
the steric effects of the substituents ortho to the reactive OH. The
A-factors span, in fact, a comparatively large range, log(A/
M
21s21) = 3.65–6.32, with 13 and phenols 1 and 4 located,
respectively, at the lower and higher limit of this range. However,
no detectable difference seems to emerge from the A-factors of
mono- and disubstituted phenols with methyl/methoxy groups at
the ortho-positions.
The H-atom abstraction from 1–13 by the dpph? radical appears
to be characterized by unusually low A-factors13 when compared
with the ‘‘normal’’ value for an H-atom transfer reaction of ca.14 3
6 108 M21 21
or even when compared with the available data for
s
the RO?2 radicals,15 see Table 2. This dramatic decrease of the
A-factors with dpph? may have various origins. Steric shielding of
the divalent N in dpph? by the o-NO2 of the picryl ring is likely the
most important of them. In fact, the stability of this radical had
been suggested to be closely connected to the shielding effects more
than the electronic effects of the nitro groups since removal of
p-NO2 had little effect while removal of one o-NO2 group greatly
increased its reactivity.16 Another possible and generally accepted
explanation for low A-factors in H-atom transfer reactions
?
between two heteroatoms X–H and Y (X, Y = N, O) is that
such transfer reactions occur after a prior-equilibrium between a
3254 | Chem. Commun., 2006, 3252–3254
This journal is ß The Royal Society of Chemistry 2006