Outer-sphere reduction of hexacyanoferrate(III) by enolizable and nonenolizable aldehydes in alkaline medium

Article abstract of DOI:10.1002/kin.20616

Outer-sphere reduction of hexacyanoferrate(III) by some enolizable/nonenolizable aldehydes (viz., aliphatic, heterocyclic, and aromatic aldehydes) in alkaline medium has been studied spectrophotometrically at λ_max = 420 nm. The reactions are first order each in [aldehyde] and [Fe(CN)₆^3-]. The rate increases with an increase in [OH^-] in the oxidation of aliphatic and heterocyclic aldehydes, whereas it is independent of [OH^-] in the reaction with aromatic aldehydes. The intervention of free radicals in the reaction mixture was carried out using both acrylonitrile and acrylamide scavenger in two different experiments. The kinetic results indicate that the oxidation of benzaldehyde in aqueous medium proceeds at a slower rate than the aliphatic aldehydes (other than formaldehyde) and furfural. The values of third-order rate constant (k₃) at 308 K in the oxidations of some aliphatic aldehydes and furfural follow the order (CH₃)₂CH- > CH ₃CH₂- > CH₃- > C₄H ₃O- > H-. The rate constants correlate with Taft's σ* value, the reaction constant being negative (-9.8). The pseudo-first-order rate constants in the oxidations of benzaldehyde and substituted benzaldehydes follow the order -NO₂ > -H > -Cl > -OCH₃. The Hammett plot is also linear with a ρ value (0.6488) for meta- and para-substituted benzaldehydes. The kinetic isotope effect for benzaldehyde (k_H/k _D = 1.93 at 303 K) was obtained. The rate-determining step is the outer-sphere formation of Fe(CN)₆^4- and free radicals, which is followed by the rapid oxidation of free radicals by Fe(CN) ₆^3- to give products. The kinetic data and hence thermodynamic parameters have been used to distinguish enolizable and nonenolizable aldehydes. An attempt has also been made to correlate kinetic data with hydration equilibrium constants of some aliphatic aldehydes. Copyright

Full text of DOI:10.1002/kin.20616

Outer-Sphere Reduction of
Hexacyanoferrate(III) by
Enolizable and
Nonenolizable Aldehydes
in Alkaline Medium
ASHOK K. BERA,1 BISWAJIT PAL,2 KALYAN K. SEN GUPTA3
1R & D Division, Dey’s Medical Stores (Mfg) Ltd., Kolkata 700 019, India
2Department of Chemistry, St. Paul’s C. M. College, Kolkata 700 009, India
3Department of Chemistry, Jadavpur University, Kolkata 700 032, India
Received 4 November 2011; revised 29 April 2011, 1 July 2011; accepted 26 August 2011
DOI 10.1002/kin.20616
Published online 23 April 2012 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: Outer-sphere reduction of hexacyanoferrate(III) by some enolizable/nonenolizable
aldehydes (viz., aliphatic, heterocyclic, and aromatic aldehydes) in alkaline medium has been
studied spectrophotometrically at λmax = 420 nm. The reactions are first order each in [alde-
hyde] and [Fe(CN)63−]. The rate increases with an increase in [OH−] in the oxidation of aliphatic
and heterocyclic aldehydes, whereas it is independent of [OH−] in the reaction with aromatic
aldehydes. The intervention of free radicals in the reaction mixture was carried out using both
acrylonitrile and acrylamide scavenger in two different experiments. The kinetic results indi-
cate that the oxidation of benzaldehyde in aqueous medium proceeds at a slower rate than the
aliphatic aldehydes (other than formaldehyde) and furfural. The values of third-order rate con-
stant (k3) at 308 K in the oxidations of some aliphatic aldehydes and furfural follow the order
(CH3)2CH > CH3CH2 > CH3 > C4H3O > H . The rate constants correlate with Taft’s
σ∗ value, the reaction constant being negative (–9.8). The pseudo–first-order rate constants
in the oxidations of benzaldehyde and substituted benzaldehydes follow the order NO2 >
H > Cl > OCH3. The Hammett plot is also linear with a ρ value (0.6488) for meta- and
para-substituted benzaldehydes. The kinetic isotope effect for benzaldehyde (kH /kD = 1.93
at 303 K) was obtained. The rate-determining step is the outer-sphere formation of Fe(CN)64−
and free radicals, which is followed by the rapid oxidation of free radicals by Fe(CN)36− to give
products. The kinetic data and hence thermodynamic parameters have been used to distin-
guish enolizable and nonenolizable aldehydes. An attempt has also been made to correlate
kinetic data with hydration equilibrium constants of some aliphatic aldehydes. ꢀ 2012 Wiley
C
Periodicals, Inc. Int J Chem Kinet 44: 494–505, 2012
INTRODUCTION
Correspondence to: Biswajit Pal; e-mail: palbiswajit@
Oxidation of aliphatic aldehydes can occur, in gen-
yahoo.com.
c
ꢀ
eral, by two routes [1], i.e., by terminal oxidation
2012 Wiley Periodicals, Inc.

OUTER-SPHERE REDUCTION OF HEXACYANOFERRATE(III)
495
(RCHO → RCOOH) or by attack at the α-position
(RCH2CHO → RCHOHCHO). The kinetics and
mechanism of the oxidation of aliphatic aldehydes by
Co(III) [1], Mn(III) [2], V(V) [3], Cr(VI) [4], perox-
omonosulfate [5], tetrabutylammonium tribromide [6],
morpholinium chlorochromate [7], and benzyltriethyl-
ammonium chlorochromate [8] have been reported in
acidic media. The corresponding carboxylic acids are
obtained as the products of oxidation in most of the
reactions. A number of kinetic studies have also been
reported on the oxidation of some aromatic aldehy-
des by different oxidants such as chromium(VI) [9],
manganese(VII) [10], iridium(IV) [11], vanadium(V)
[12], and bromate [13] in acid medium. There are also
reports on the kinetics and mechanism of the oxida-
tion of aromatic aldehydes by tetrabutylammonium
fluoride [14], pyridinium fluorochromate [15], H2O2
in the presence of N-methylpyrrolidin-2-one hydrotri-
bromide as catalyst [16], N-chlorosuccinimide [17],
tert-butyl hydroperoxide in the presence of ebselen (2-
phenyl benzisoselenazol-3(2H)-one) as catalyst [18],
oxone [19], and quinolinium fluorochromate [20] in
aqueous acid medium. The oxidation of different alde-
hydes by copper(III)tellurate and silver(III)tellurate in
alkaline medium [21] has also been studied.
Hexacyanoferrate(III) is known to be one of the
most useful oxidant in alkaline medium. Different val-
ues of redox potentials (E0) have been reported. E0 of
Fe(CN)36− − Fe(CN)46− has been reported to be 0.45 V
[22a]. Latimer [22b], however, quoted the value to be
0.36 V. Since hydrogen is not included either in the ox-
idized or reduced form, the reduction potential is not
pH dependent; consequently, the value remains con-
stant at 0.41 V in the pH range 4–13, whereas 0.56 V
[22c] in 0.1 mol dm−3 HCl. It has been shown [22d]
that electrode potentials of Fe(CN)36− − Fe(CN)64− in-
creases from 0.688 to 0.929 V [22d] at acidities of
1–8 mol dm−3 HCl. Since we have studied the reac-
tions in alkaline medium, E0 value will be much lower
than those reported by Leal et al. [22d] in acid medium.
S2O23− [23], tyrosine [24], and dihydroxy fumaric
acid [25] are oxidized by Fe(CN)36− in acid medium,
whereas oxidation of cyclic ketones [26], alcohols [27],
and diols using Ru(III) or Ru(VI) catalyst [28] and
α,β-unsaturated [29] compounds by the same oxidant
has been studied in alkaline medium. Speakman and
Waters [30] studied the kinetics and mechanism of
propanal, n-butanal, and isobutanal by this oxidant po-
tentiometrically in the alkaline pH, but no attempt has
been made to study systematic investigations of the
oxidation of other aliphatic aldehydes. Again, it has
been shown [31] that the reaction of aromatic alde-
hyde with this oxidant is not facile and takes place
only in the presence of OsO4. Systematic kinetic in-
vestigations on the oxidation of aliphatic, heterocyclic,
and aromatic aldehydes by hexacyanoferrate(III) have
been carried out in alkaline medium, and the results
are incorporated in this communication.
EXPERIMENTAL
Reagents
All inorganic materials used were of the highest pu-
rity available. A standard solution of potassium hex-
acyanoferrate(III) (BDH, Kandivil, Mumbai, India)
was prepared by dissolving the requisite amount of
the salt in doubly distilled water, and the concentra-
tion of the solution was ascertained by the iodometric
method [32]. The aldehydes were bought from BDH,
E. Merck (Darmstadt, Germany), or Sigma (St. Louis,
MO) and were either redistilled or recrystallized be-
fore use. Benzaldehyde-d1 was prepared following the
procedure of Wiberg [33] by the reduction of benzil
(Merck, Worli, Mumbai, India) with lithium aluminum
deuteride (Fluka, Castle Hill, NSW, Australia) to give
a diol. The diol was then oxidized by lead tetraacetate
to produce the reaction product: IR νmax (film), 2100
and 2050 cm−1 (lit. [33] 4.76 and 4.83 μm); δ (CCl4)
7.2–7.9 (m, aromatic H) and no signal for the alde-
hyde proton. All solutions were made in doubly dis-
tilled water. The experiments involving the oxidation
of aliphatic aldehydes and 2-furaldehyde were carried
out in aqueous medium, whereas those involving aro-
matic aldehydes were studied in t-butanol (15%, v/v)
unless otherwise stated.
Kinetic Measurements
The progress of the reaction was monitored spec-
trophotometrically by measuring the absorbance (A)
decay of hexacyanoferrate(III) at 420 nm (ε = 1060
10 dm3 mol−1 cm−1). No other reactant or product had
any significant A at this wavelength. The kinetic inves-
tigations were carried out in a Systronics (Ahmedabad,
India) spectrophotometer (model 106) with a ther-
mostated cell compartment under pseudo–first-order
conditions, where [aldehyde] >> [Fe(CN)36−]. The plots
of log A vs. time were linear at least up to two half-
lives, and the pseudo–first-order rate constants (kobs
)
are evaluated from such plots. Duplicate kinetic runs
showed that the rate constants were reproducible to
within 5%.
Product Analysis
After the kinetic experiments, the reaction mixtures in-
volving formaldehyde and acetaldehyde were set aside
for about 24 h at room temperature to ensure the
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

496
BERA, PAL, AND SEN GUPTA
Table I Identification of Products of the Reactions
completion of the reaction. The reaction mixture was
then acidified with dilute HCl and distilled under
reduced pressure. The distillate was subjected to the
following tests: The distillate in the oxidation of
formaldehyde was treated with HgCl2 when white pre-
cipitate of Hg2Cl2 was obtained. The precipitate turned
black in the presence of ammonia due to the forma-
tion of Hg0, indicating that a formate ion was formed
[34a]. The distillate in the oxidation of acetaldehyde
was treated with lanthanum nitrate mixed with iodine
and ammonia [34b] when dark blue precipitate was
obtained, indicating the presence of acetate ion. The
stoichiometry of the reaction involving acetaldehyde
and oxidant was studied under the condition in which
acetaldehyde was in excess to that of the oxidant in
[OH−] and at a temperature of 0.1 mol dm−3 and 298 K,
respectively. The mixture was allowed to stand until
all the oxidant had reacted and then acidified. The ex-
cess acetaldehyde was then determined iodometrically
[34c]. The results indicate that 1 mol of acetaldehyde
reacted with 1.9 mol of the oxidant. If 2 mol of ac-
etaldehyde were to give aldol in alkaline medium and
then oxidized, the stoichiometry would have been dif-
ferent. It may be mentioned that the aldol condensation
reaction takes place when acetaldehyde is heated with a
fairly strong sodium hydroxide solution. The absence
of yellow color and also the formation of resin after
the reaction indicate that aldol is not formed [35a].
Moreover, any other side reaction leading to the for-
mation of a compound containing carbon–carbon bond
by the Michael condensation [35b] has been ignored.
The product in the oxidation of propionaldehyde by
hexacyanoferrate(III) was analyzed as follows: The re-
action mixture was allowed to stand for 24 h at room
temperature, and the mixture was then evaporated to
dryness using a lyophilizer. The residue was acidified
with dilute HCl, and the solution was extracted with
ether. The ethereal solution was dried over anhydrous
Na2SO4 and filtered. The filtrate was evaporated on a
water bath to remove ether. On removal of the solvent, a
colorless liquid was obtained (boiling point = 141◦C;
lit. 140◦C [36a]). The ammonium derivative of this
product was then prepared and the melting point (m.p.)
was recorded in an argon atmosphere (m.p. 54◦C; lit.
54◦C [36a]).
Melting Melting Point
Yield
(%)
Point
(in lit.; ◦C)
[36b]
XC6H4CHO
(◦C)
Benzaldehyde
71
82
78
84
76
79
73
85
81
78
120
146
140
237
141
158
242
100
108
182
121
147
141
239
141
158
243
101
110
184
o-Nitrobenzaldehyde
m-Nitrobenzaldehyde
p- Nitrobenzaldehyde
o-Chlorobenzaldehyde
m-Chlorobenzaldehyde
p-Chlorobenzaldehyde
o-Methoxybenzaldehyde
m-Methoxybenzaldehyde
p-Methoxybenzaldehyde
Yields and melting points of the oxidation products of aromatic
aldehydes in 15% t-butanol.
ter and dried in anhydrous Na2SO4. On the removal
of the solvent, the residual solid organic acids were
obtained and determined through m.p. and mixed m.p.
[36b] with authentic samples (Table I). The residue
was confirmed as benzoic acid, the oxidation product
of benzaldehyde, by 1H and 13C NMR analysis. Spec-
tral data (in ppm) of benzoic acid are as follows:
1H NMR (300 MHz, Bruker DPX, CDCl3): δ 7.42
(2H, m, H-3 and H-5), δ 7.45 (1H, m, H-4), δ 7.90 (2H,
m, H-2 and H-6), δ 11.5 (1H, br s, COOH).
13C NMR (75 MHz, Bruker DPX, CDCl3): δ 128.9
(C-3 and C-5), δ 130.4 (C-2 and C-6), δ 130.5 (C-1), δ
134.4 (C-4), δ 169.0 ( COOH).
The aldehydes are oxidized as
RCHO + 2Fe(CN)36− + OH− → RCO2
−
+ 2Fe(CN)46− + 2H2O
(1)
where R is aliphatic, heterocyclic, or aromatic groups.
Test for Free Radicals
The polymerization test for the formation of free rad-
icals in the oxidation reaction of acetaldehyde was
carried out at 303 K in alkaline medium ([OH−] =
0.05 mol dm−3) by the addition of 3 cm3 of 50%
(v/v) acrylonitrile. Acetaldehyde solution (3 cm3) of
the concentration 5 × 10−2 mol dm−3 was added to
2 mL of 5 × 10−3 mol dm−3 Fe(CN)36−. The total vol-
ume was adjusted to 10 cm3. The appearance of white
precipitate of polyacrylonitrile showed the presence of
a free-radical intermediate in the oxidation process.
This is further supported by the fact that the rate of the
reaction was retarded by the addition of acrylamide.
The reaction was studied at different [acrylamide],
but at [CH3CHO], [Fe(CN)36−], [OH−], and tempera-
The reaction mixtures involving aromatic aldehy-
des were left at room temperature for ∼24 h and then
acidified with concentrated HCl. The precipitated crys-
talline materials were extracted with chloroform. The
combined organic layer was washed with water and
extracted with saturated aqueous solution of NaHCO3.
The alkaline solution was acidified with ice cold HCl
and the precipitated organic acids were extracted again
with CHCl3. The organic layers were washed with wa-
ture of 10 × 10−3mol dm−3, 1.0 ×10−3 mol dm−3
,
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

OUTER-SPHERE REDUCTION OF HEXACYANOFERRATE(III)
497
Table II Effect of [Fe(CN)36−] on the Rate of Oxidation of Aldehydes at 303 K
[Aldehyde]
(102 mol dm−3
[OH−]
(102 mol dm−3
kobs
(104 s−1
)
Aldehyde
)
)
HCHO
CH3CHO
CH3CH2CHO
(CH3)2CHCHO
C4H3OCHO
C6H5CHO
50
50.2
5.0
0.3
0.1
50.2
50.2
(0.185 0.004)
(6.79 0.2)
(15.3 0.4)
(17.9 0.5)
(3.44 0.1)
(0.10 0.003)
0.5
1.5
0.4
0.5
1.5
[Fe(CN)36−] = (5.0–12.5) × 10−4 mol dm−3
.
5 × 10−2 mol dm−3, and 303 K, respectively.
RESULTS AND DISCUSSION
The observed pseudo–first-order rate constants were
found to be 1.12 × 10−3, 0.96 × 10−3, 0.78 × 10−3
,
The reactions were carried out at various concentra-
tions of hexacyanoferrate(III) (5.0–12.5) × 10−4 mol
dm−3 at 303 K, keeping [RCHO] and [OH−] con-
stant. kobs was found to be independent of the ini-
tial [Fe(CN)36−] in each case (Table II). The reactions
were also studied with variations of [RCHO] (0.2–
70) × 10−2 mol dm−3 at constant [Fe(CN)36−], [OH−],
and temperature. The results indicate that the rate
of each reaction increases with increasing [aldehyde]
(Table III). The plots of kobs against [aldehyde] are lin-
ear passing through the origin, indicating that the order
with respect to [aldehyde] is unity (Fig. 1).
0.63 × 10−3, 0.44 × 10−3, and 0.31 × 10−3 s−1 at
[acrylamide] 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 mol dm−3
,
respectively. The decrease of the reaction rate with
an increase in [acrylamide] was expected since the
polymer, when formed, preferentially adsorbs one of
the reactants and reduces its bulk concentration in the
aqueous phase abnormally [37]. It may be mentioned
that the addition of acrylamide to the reaction mix-
ture gave a cloudy suspension only upon standing for
nearly an hour. No polymerization was observed when
the oxidant or reductant was treated separately with
acrylamide. All these indicate that reducing intermedi-
ates like free radicals are formed.
The effect of ionic strength on the reaction rate
was studied by varying salt-like KCl concentrations at
Figure 1 Variation of kobs with aldehyde concentrations in aqueous medium for different aldehydes. Plots of kobs against
[aldehyde] at 303 K. [Fe(CN)36−] = 0.001 mol dm−3, [OH−] are 0.502, 0.05, 0.003, 0.001, 0.502, and 0.502 mol dm−3 for a, b,
c, d, e, and f, respectively. Plot a, HCHO; b, CH3CHO; c, CH3CH2CHO; d, (CH3)2CHCHO; e, C4H3OCHO; and f, C6H5CHO.
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

498
BERA, PAL, AND SEN GUPTA
with OH− to give H2O; in the reaction product acid an-
ions RCO−2 , and not undissociated acids RCO2H, are
formed. But with benzaldehyde, the kobs values remain
unaffected at different [OH−], indicating that pseudo–
first-order rate constant is independent of the initial
Table III Variation of Pseudo–First-Order Rate
Constant with Substrate Concentration at 303 K
[OH−]
(102 mol dm−3) (102 mol dm−3) (104 s−1
[Aldehyde]
kobs
Aldehyde
HCHO
)
50.2
10
20
30
40
50
60
70
0.0413
[OH−] in the region of 0.001–0.1 mol dm−3
.
0.075
0.115
0.148
0.185
0.220
0.249
2.53
The influence of substituents on the rate of oxi-
dation of aliphatic and aromatic aldehydes has been
studied. Because the pseudo–first-order rate constants
in the oxidations of aliphatic aldehydes and furfural
could not be determined under comparable condi-
tions, the values of third-order rate constant, k3 (k3
= kobs/[RCHO] [OH−]) at 308 K was used to deter-
mine the order of reactivity, which was (CH3)2CH
> CH3CH2 > CH3 > C4H3O > H . The plot
of log k3 vs. the polar substitute constant [38a] (σ∗)
gives a linear relationship (Fig. 3). The value of ρ∗,
which measures the susceptibility of the reaction to
polar effect, has been calculated to be –9.8 from the
least-square plot. The oxidation of benzaldehyde was
carried out both in aqueous and in 15% t-butanol. Ki-
netic results indicate that the oxidation of benzalde-
hyde in the aqueous medium proceeds at a slower rate
than aliphatic aldehydes (other than formaldehyde) and
furfural under comparable conditions of experiments.
Since some of the substituted benzaldehydes are in-
soluble in water, the experiments involving the oxi-
dation of aromatic aldehydes under comparable con-
dition of experiments were carried out in t-butanol
(15%, v/v). It is to be mentioned that t-butanol re-
sists oxidation in neutral or fairly acid solutions [38b].
It is only oxidized in a strongly acidic medium by
K2Cr2O7 or KMnO4 [38c]. t-Butanol is also unreactive
toward hexacyanoferrate(III) in the alkaline medium.
The values of pseudo–first-order rate constant of the
oxidation of aromatic aldehydes are presented in Ta-
ble V. The kinetic results suggest that among the differ-
ent nuclear-substituted benzaldehydes, the NO2 com-
pounds react at a much faster rate than the corre-
sponding Cl- and CH3O-substituted derivatives. The
pseudo–first-order rate constant obtained in the ox-
idation of Cl-substituted benzaldehyde lies between
those obtained for NO2- and CH3O-substituted ben-
zaldehydes. Wiberg and Stewart [39] studied the influ-
ence of substituents on the oxidation of benzaldehyde
by KMnO4 over a wide range of pH 5–13. In the pH
range <8, the CH3O-substituted benzaldehydes react
at faster rates than NO2-substituted compounds and
the linear plot of log k against Hammett substituent
constants (σ) gave a ρ value of –0.248. On the other
hand, at pH > 9, the oxidation in alkaline solution was
strongly accelerated by electron-withdrawing groups,
as revealed by the Hammett ρ value of +1.83 for the
CH3CHO
5.0
0.2
0.4
0.5
0.8
1.0
1.5
0.5
1.0
1.5
2.0
2.5
0.2
0.3
0.4
0.5
0.6
0.25
0.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
2.5
5.25
6.79
10.36
13.43
19.38
4.80
10.2
15.3
CH3CH2CHO
(CH3)2CHCHO
C4H3OCHO
C6H5CHO
0.3
0.1
20.6
25.9
8.62
13.6
17.9
22.3
26.5
50.2
50.2
1.85
3.44
6.80
10.2
13.6
0.038
0.063
0.102
0.123
0.160
[Fe(CN)36−] = 1.0 × 10−3 mol dm−3
.
constant [Fe(CN)36−], [aldehyde], [OH−], and temper-
ature of 1 × 10−3, 1 × 10−2, and 5 × 10−2 mol dm−3
,
and 303 K, respectively. The addition of salt did not
seem to have any influence on kobs when [salt] was in
the range of 0.16–0.96 mol dm−3
.
The influence of the hydroxide ion on the reaction
rate was investigated by varying the addition of KOH
in the region of [OH−] 0.005–1.0 mol dm−3, but at
constant [RCHO], [Fe(CN)36−], and temperature. The
kobs values at various [OH−] are recorded in Table IV.
Again, the plots of kobs against [OH−] are linear pass-
ing through the origin (Fig. 2). The results indicate
that the reaction was directly proportional to the initial
[OH−] for aliphatic and heterocyclic aldehydes. How-
ever, during the reaction the H+ that is formed reacts
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

OUTER-SPHERE REDUCTION OF HEXACYANOFERRATE(III)
499
Table IV Effect of Hydroxyl Ion Concentration on the Rate of Reaction
Aldehyde
HCHO
[Aldehyde] (102 mol dm−3
)
Temperature (K)
313
[OH−] (102 mol dm−3
)
kobs (104 s−1
)
30
16.75
33.5
50.25
67.0
83.75
100.5
2.5
0.070
0.153
0.219
0.30
0.364
0.432
0.034
0.064
0.131
0.205
0.260
1.6
CH3CHO
0.5
1.0
0.3
1.0
303
303
298
308
5.0
10.0
15.0
20.0
0.05
0.1
0.2
0.3
0.4
0.05
0.1
0.2
0.3
0.4
8.37
16.75
33.5
50.25
67.0
CH3CH2CHO
(CH3)2CHCHO
C4H3OCHO
3.32
6.91
10.2
13.8
4.26
7.67
15.7
23.0
30.7
1.53
3.84
7.67
12.3
16.1
[Fe(CN)36−] = 1.0 × 10−3 mol dm−3
.
Figure 2 Influence of [OH−] on the rate of reaction of different aldehydes by hexacyanoferrate(III). [Fe(CN)63−] = 0.001 mol
dm−3. Plot a, [HCHO] = 0.3 mol dm−3, T = 313 K; b, [CH3CHO] = 0.005 mol dm−3, T = 303 K; c, [CH3CH2CHO] =
0.01 mol dm−3, T = 303 K; d, [(CH3)2CHCHO] = 0.003 mol dm−3, T = 298 K; and e, [C4H3OCHO] = 0.01 mol dm−3
T = 308 K.
,
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

500
BERA, PAL, AND SEN GUPTA
Table V Values of Pseudo–First-Order Rate Constants
of the Oxidation of Aromatic Aldehydes in 15%
t-Butanol
iso
XC6H4CHO
kobs (104s−1
)
Benzaldehyde
1.85
9.72
2.82
7.94
1.65
1.77
1.412
0.91
1.25
0.708
o-Nitrobenzaldehyde
m-Nitrobenzaldehyde
p- Nitrobenzaldehyde
o-Chlorobenzaldehyde
m-Chlorobenzaldehyde
p-Chlorobenzaldehyde
o-Methoxybenzaldehyde
m-Methoxybenzaldehyde
p-Methoxybenzaldehyde
σ
[Fe(CN)36−] = 1 × 10−3 mol dm−3, [XC6H4CHO] = 1.5 × 10−3
mol dm−3, [OH−] = 5.02 × 10−1 mol dm−3, and temperature =
313 K.
Figure 3 Variation of k3 with σ∗ for the aliphatic aldehydes
at 308 K.
reaction. The present order of kobs, which followed
NO2 > H > Cl > OCH3, was not unexpected
in view of the fact that the reactions have been studied
at pH =13.7. The plots of log (k/k0) against σ give a
linear relationship (Fig. 4). The value of ρ has been
calculated to be 0.6488 from the least-square plot of
meta- and para-substituted compounds. The values of
σ are taken from the work of Hammett [40]. For ortho-
substituted benzaldehyde, a similar correlation could
not be performed, as there are not reliable σ values
that are available in the literature for ortho-substituted
compounds [41].
respectively. The pseudo–first-order rate constant val-
ues for the oxidation of benzaldehyde in aqueous
medium and benzaldehyde-d1 in D2O medium are
1.02 × 10−3 and 0.528 × 10−3
s
−1, respectively. The
kH /kD value has been found to be 1.93. Similar kH /kD
of 1.9 has also been observed in the oxidation of
p-chlorobenzaldehyde by MnO−4 in alkaline medium
[39]. The lower values of kH /kD < 2.0 have also been
observed earlier by other workers in different reactions
[42]. The result indicates that the C H bond cleavage
in the rate-determining step in the oxidation of ben-
zaldehyde cannot be ruled out.
The kinetic isotope effect using benzaldehyde
and benzaldehyde-d1 was carried out at [substrate],
The oxidation of aldehydes by Fe(CN)36− was stud-
ied over a temperature range of 293–318 K. k3 were
determined at different temperatures and are presented
in Table VI. The values of log k3/T are plotted against
1/T (Fig. 5) for all aliphatic and heterocyclic alde-
hydes followed by the estimation of enthalpy of acti-
vation ( H=) and entropy of activation ( S=). The
values of H= gradually increase from HCHO to
(CH3)2CHCHO. Moreover, the plots of S= against
[Fe(CN)36−], [OH−], and temperature of 1.5 × 10−3
,
1.0 × 10−3, and 5 × 10−1 mol dm−3, and 303 K,
p
H
= give two different lines (Fig. 6), one for the alde-
hydes, which lack enolizable hydrogen, and the other
for the aldehydes having enolizable hydrogen. This
indicates that two different mechanisms may be oper-
ative in these reactions. Since the rate is independent
of [OH−] in the oxidation of benzaldehyde in aqueous
medium, the value of H= was calculated from the
plot of log k2/T vs. 1/T (the second-order rate con-
stant, k2 = kobs/[sub]) (Fig. 5) followed by S=.
m
m
p
m
p
Hexacyanoferrate(III) behaves as a one-electron
transfer reagent [30]. However, the addition of
hexacyanoferrate(II) to the reaction mixture had no
influence on the rate, indicating that the slowest step
σ
Figure 4 Variation of log (k/k0) of the meta- and para-
substituted benzaldehyde against σ at 313 K.
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

OUTER-SPHERE REDUCTION OF HEXACYANOFERRATE(III)
501
Table VI Influence of Temperatures on the Oxidations of Aliphatic Aldehydes, Furfural, and Benzaldehyde in
Aqueous Medium
Temperature
(K)
k3a (104mol−2
k3b (mol−2
k3c (mol−2
k3d (mol−2
k3e (101 mol−2
k2f (103 mol−1
dm6 s−1
)
dm6 s−1
)
dm6 s−1
)
dm6 s−1
)
dm6 s−1
)
dm3 s−1
)
293
298
303
308
313
318
–
–
1.076
1.707
2.688
3.995
–
13.4
23.7
34.1
64.6
–
122.4
262.5
453.3
644.9
–
–
–
–
0.68
1.02
1.36
1.86
0.783
1.35
2.45
4.28
–
0.761
1.07
1.45
2.04
–
–
–
aHCHO.
bCH3CHO.
cCH3CH2CHO.
d (CH3)2CHCHO.
eC4H3OCHO.
f C6H5CHO.
ΔH
T
K
Figure 6 Variation of S= with H= of the oxidation
of enolizable and nonenolizable aldehydes. Plots of S=
Figure 5 Dependence of temperature on k3 for the oxida-
tion of aliphatic aldehydes and furfural and k2 for the oxida-
tion of benzaldehyde by hexacyanoferrate(III). Plots of log
(k3/T ) or log (k2/T ) against 1/T . Plot a, HCHO; b, CH3CHO;
c, CH3CH2CHO; d, (CH3)2CHCHO; e, C4H3OCHO; and f,
C6H5CHO.
vs.
H
=. Plot 1, enolizable aldehydes: b, CH3CHO; c,
CH3CH2CHO; and d, (CH3)2CHCHO. Plot 2, nonenolizable
aldehydes: a, HCHO; e, C4H3OCHO; and f, C6H5CHO.
in this study that the reaction rates remain unaffected
in the presence of different concentrations of KCl.
Aliphatic, furfural, and aromatic aldehydes occur
according to the respective rate expressions (2) and (3):
is not reversible in the oxidation of the aldehydes.
Since Fe(CN)36− is a one-electron transfer oxidant, it
is likely that the reaction would take place through the
intermediate formation of the free radicals. This ob-
servation is in keeping with those made in connec-
tion with the hexacyanoferrate(III) oxidation of some
other organic substrates [30]. The oxidation of m-
and p-substituted anilines provides evidence [43a] for
specific catalytic effect by binding alkali metal ions
to Fe(CN)36− through ion pair formation. KCl and
NaClO4 also increased the rate of Fe(CN)36− oxida-
tion of H2PO−2 , but spectrophotometric measurements
did not substantiate the ion pair even in the presence of
high [NaClO4] and [KCl] [43b]. We have also noticed
ꢀ
ꢁ
−d Fe (CN)36−
dt
ꢀ
ꢁ
= k3 Fe (CN)36− [RCHO] [OH−]
(2)
where RCHO is aliphatic and furfural aldehyde and
ꢀ
ꢁ
−d Fe (CN)36−
ꢀ
ꢁ
= k2 Fe (CN)36− RCHO (3)
[
]
dt
where RCHO is aromatic aldehyde.
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

502
BERA, PAL, AND SEN GUPTA
H
slow
fast
.
3−
3−
R- C=O + Fe(CN)6 + H+
4−
R- C=O + Fe(CN)6
(4)
(5)
.
+
4−
R- C=O + Fe(CN)6
R- C=O + Fe(CN)6
fast
+
R- C=O + 2OH−
−
(6)
(7)
RCO2 + H2O
fast
H+ + OH−
H2O
Scheme 1
The oxidation of aldehydes may take place through
the intermediate formation of free radicals R C O
ions of like charge were involved in the slow step (9),
although no effect of ionic strength was noticed. We
have studied the reactions using K3Fe(CN)6, KCl, and
KOH in K+ environment. Consequently, we have not
used salts containing other cations to study the effect
of ionic strength. It may be that salts containing other
cations have ionic strength effect. However, the results
obtained in this study are not in conformity with what
might be predicted from the Brønsted–Bjerrum rela-
tion based on Debye–Hu¨ckel theory. Numerous appar-
ent anomalies are also known in the literature [46,47].
The mechanism involving aldehydes having enolizable
hydrogen may be suggested according to steps (12)–
(14), as shown in Scheme 3. The oxidation of eno-
lizable aldehydes occurs through the initial removal
of α-proton. The enolate anion that is formed is then
oxidized by Fe(CN)36− via an electron transfer process.
The rate of the hexacyanoferrate(III) oxidation of
aliphatic aldehydes depends on the first power of
[Fe(CN)36−], [RCHO], and [OH−], whereas the ox-
idation of benzaldehyde by this oxidant in aqueous
medium proceeds at a rate which is proportional to
[PhCHO] and [Fe(CN)63−] but independent of [OH−].
Since the oxidation of benzaldehyde and all the substi-
tuted aromatic aldehydes has been studied in t-butanol
medium, their rate constants cannot be compared with
those obtained with aliphatic aldehydes and furfural.
However, from the results it appears that hexacyano-
ferrate(III) oxidation of benzaldehyde proceeds at a
slower rate than that of aliphatic aldehydes (other than
formaldehyde) and furfural. It was previously believed
[22a] that enol form of the aldehydes is only oxidized
by Fe(CN)36−, but not benzaldehyde, which is not sus-
ceptible to keto–enol tautomerism. Likewise, furfural
is hardly oxidizable. Later, it was established that both
benzaldehyde and furfural are oxidized [21] by both
bis(dihydrogentellurato) cuprate(III) and argentate(III)
˙
(Eq. (4)) followed by the formation of carbonium ion
RC+=O (Eq. (5)) to give carboxylate ion (Eq. (6)) as
the oxidation product (Scheme 1). Since the rate of the
oxidation of the aliphatic aldehydes is directly propor-
tional to the hydroxide ion concentration, the oxida-
tion of aldehydes via Scheme 1 may be discounted.
On the other hand, in the oxidation of benzaldehyde
by this oxidant, the rate is independent of hydrox-
ide ion concentrations. Consequently, the oxidation of
benzaldehyde using Eqs. (4)–(7) of Scheme 1 seems
plausible. Since the reactions involving aromatic alde-
hydes were carried out in alkaline medium, the pos-
sibility of the Cannizzaro-type reaction may occur.
However, the reagent for bringing about the Canniz-
zaro reaction is 50% aqueous alkali or ethanolic al-
kali [44]. Consequently, higher concentrations of al-
kali have been avoided to eliminate such a possibility.
Since the rate of the oxidation of aliphatic aldehydes
and furfural is directly proportional to hydroxide ion
concentrations, these substrates may react with OH−
to give RCH(OH)O− in a fast step (Eq. (8)). The lat-
ter then reacts with hexacyanoferrate(III) in the−slow
˙
rate-determining step (Eq. (9)) to give RC(OH)O and
hexacyanoferrate(II). There is literature [45] evidence
−
˙
of the involvement of the radical ion RC(OH)O in
alkaline medium. The radical ion may bind with K+ to
give RCHOHO−K+ and then be oxidized by Fe(CN)36−
to give RCO2K. It is, however, unlikely that such an ion
pair will participate in the oxidation reaction in view
of its unstable character. Alternatively, the radical ion
that is formed in step (9) reacts with the oxidant to give
RC+(OH)O− and hexacyanoferrate(II) (Eq. (10)). The
former gets converted in the presence of OH− to give
a carboxylate ion (Eq. (11)), as shown in Scheme 2.
In explaining the reaction steps, it has been shown that
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

OUTER-SPHERE REDUCTION OF HEXACYANOFERRATE(III)
503
H
H
OH−
fast
R- C - O −
OH
(8)
R- C=O
H
slow
.
3−
R- C - O − + Fe(CN)6
OH
(9)
4−
R- C - O − + Fe(CN)6 + H+
OH
.
fast
+
3−
R- C - O − + Fe(CN)6
4−
(10)
R- C - O − + Fe(CN)6
OH
OH
O
fast
+
R- C - O − + OH−
R- C - O − + H2O
(11)
OH
followed by step (7)
Scheme 2
K
R1R2CHCHO + OH−
R1R2 C = CH ] + H2O
[ R1R2CCH
O
(12)
fast
−
O
(R1= R2 = H for acetaldehyde; R1 = H, R2 = CH3 for propionaldehyde; R1 = R2 = CH3 for
isobutyraldehyde)
.
slow
3−
4−
[ R1R2CCH
O
[ R1R2CCH
O
R1R2 C = CH ] + Fe(CN)6
R1R2 C = CH ] + Fe(CN)6
(13)
(14)
.
O
−
O
2OH−
fast
.
3−
−
4−
[ R1R2CCH
R1R2 C = CH ] + Fe(CN)6
R1R2 CHCO2
+
Fe(CN)6 + H2O
.
O
O
Scheme 3
in alkaline medium and a considerable amount of in-
formation is available on the oxidation of these two
aldehydes by these two oxidants. Consequently, the
observations made in this study on the oxidation of
benzaldehyde and furfural by Fe(CN)36− are in agree-
ment with those reported earlier [21] with tellurato
complexes of both copper(III) and silver(III) in alka-
line medium. Many carbonyl compounds are known to
undergo reversible hydration in the aqueous solution
[48a,48b]. The formation of gem-diols by reversible
hydration of the carbonyl group of ketones and aldehy-
des is well known. There is also literature evidence [49]
that spontaneous cyclotrimerization of aldehydes oc-
curs in the aqueous solution. 1,3,5-Trioxane is formed
by cyclotrimerization of aliphatic aldehydes such
as acetaldehyde, propionaldehyde, and isobutyralde-
hyde. The equilibrium between propionaldehyde,
propane-1,1-diol, and 2,4,6-triethyl-1,3,5-trioxane has
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

504
BERA, PAL, AND SEN GUPTA
been characterized by using the NMR technique. The
mol% at different temperatures (5–55◦C) has also been
reported [49].
its ligands at rates fast enough to compete with rapid
electron transfer. The absorption spectrum of hex-
acyanoferrate(III) was recorded in the region 300–
500 nm using a quartz cell of path length 1 cm in the
alkaline medium 0.005–1.0 mol dm−3. The absorption
maximum as well as extinction coefficient remains un-
altered indicating that CN− is not replaced by OH−.
Thus, irrespective of whether the substrate is enoliz-
able or nonenolizable, oxidation by Fe(CN)36− occurs
by means of nonbonded electron transfer of the outer-
sphere process, whereby an electron is transformed
from the substrate to the metal ion through the cyano
ligand to give products of reaction.
O
3
O
O
O
HO
3
OH
As temperature increases, the relative concentra-
tion of diol decreases. The concentration of 2,4,6-
triethyl-1,3,5-trioxane is small and practically constant
(∼10%) at the temperature range 5–55◦C using the pro-
pionaldehyde concentration of 0.5 mol dm−3. We have
carried out experiments at much lower concentrations
of aliphatic aldehydes except formaldehyde. Despite
all these findings, one point of information that has
been obtained with certainty is that the rate of the reac-
tion is slowest in formaldehyde, which is substantially
hydrated in aqueous solution (hydration equilibrium
constant, K = 2.28 × 103). On the other hand, the rate
of the reaction is increased with the decrease in hy-
dration of aldehydes. The plot of log k3 against log K
[48a,48b] follows a linear relationship in the oxidation
of enolizable aldehydes (Fig. 7) and is in keeping with
the above contention.
BIBLIOGRAPHY
1. Wiberg, K. B. Oxidation in Organic Chemistry, Part A;
Academic Press: New York, 1965; p 220.
2. Drummond, A. Y.; Waters, W. A. J Chem Soc 1953,
440.
3. Jones, J. R.; Waters, W. A. J Chem Soc 1963, 352.
4. Sen Gupta, K. K.; Adhikary, M.; Mandal, S. K.; Sen
Gupta, S. Transition Met Chem 1987, 12, 152.
5. Ranganathan, R.; Maruthamuthu, P. Int J Chem Kinet
1986, 18, 49.
6. Baghmar, M.; Sharma, P. K. Int J Chem Kinet 2001, 33,
390.
7. Soni, N.; Tewari, V.; Kumbhani, S.; Shastri, I.; Sharma,
V. J Indian Chem Soc 2008, 85, 657.
8. Chouha, K.; Prasad, R. P.; Sharma, P. K. J Indian Chem
Soc 2006, 83, 191.
Potassium hexacyanoferrate(III) is essentially a
substitution inert metal complex. It does not exchange
9. Sen Gupta, K. K.; Dey, S.; Sen Gupta, S.; Adhikary, M.;
Banerjee, A. Tetrahedron 1990, 46, 2431.
10. (a) Wiberg, K. B.; Stewart, R. J Am Chem Soc 1956, 78,
1214; (b) Freeman, F.; Lin, D. K.; Moore, G. R. J Org
Chem 1982, 47, 56.
11. Sen Gupta, K. K.; Dey, S.; Sen Gupta, S.; Banerjee, A.
J Org Chem 1984, 49, 5054.
12. Sen Gupta, K. K.; Dey, S.; Sen Gupta, S.; Banerjee, A.
J Chem Soc, Perkin Trans II 1985, 1503.
13. Sen Gupta, K. K.; Samaddar, H.; Sen, P. K.; Banerjee,
A. J Org Chem 1982, 47, 4511.
14. Chung, K. H.; Moon, B. C.; Lim, C. H.; Kim, J. P.;
Lee, J. H.; Chi, D. Y. Bull Korean Chem Soc 2006, 27,
1203.
15. Agarwal, S.; Chowdhury, K.; Banerji, K. K. J Org Chem
1991, 56, 5111.
16. Joseph, J. K.; Jain, S. L.; Sain, B. Catal Commun 2007,
8, 83.
17. Mathiyalagan, N.; Sridharan, R. Indian J Chem 2005,
44, 2044.
18. Wojtowicz, H.; Brzaszcz, M.; Kloc, K.; Mochowski,
J. Tetrahedron 2001, 57, 9743.
19. Gandhari, R.; Maddukuri, P. P.; Thottumkara, V. K.
J Chem Educ 2007, 84, 852.
Figure 7 Plot of log k3 vs. log K for the reaction be-
tween enolizable aldehydes and hexacyanoferrate(III). K =
[hydrate]/[carbonyl]. Plot a, CH3CHO; b, CH3CH2CHO; c,
(CH3)2CHCHO.
International Journal of Chemical Kinetics DOI 10.1002/kin.20616

OUTER-SPHERE REDUCTION OF HEXACYANOFERRATE(III)
505
20. Pandurangan, A.; Murugesan, V. React Kinet Catal Lett
1995, 54, 173.
P. Mechanism in Organic Chemistry; Orient Longman:
New Delhi, India, 1989; p. 200.
21. Sen Gupta, K. K.; Nandy, B. K.; Bera, A. K.; Sen Gupta,
S. Indian J Chem A 1997, 36, 190.
36. (a) Clarke, H. T. Handbook of Organic Analysis; Ed-
ward Arnold: London, 1956; p.136; (b) Vogel, A. I. Text
Book of Practical Organic Chemistry, 4th ed.; ELBS,
Longman: London, 1980; pp. 824 and 1204–1206.
37. Sen Gupta, K. K.; Sen, P. K.; Sen Gupta, S. Inorg Chem
1977, 16, 39.
38. (a) Panchenkov, G. M.; Lebdev, V. P. Chemical Kinetics
and Catalysis; Mir Publishers: Moscow, Russia, 1976;
p. 249; (b) Morrison, R. T.; Boyd, R. N. Organic Chem-
istry, Prentice-Hall: New Delhi, India, 1981; p. 521;
(c) Brewster, R. Q.; McEwen, W. E. Organic Chemistry;
Prentice-Hall: New Delhi, India, 1976; p. 159, 160.
39. Wiberg, K. B.; Stewart, R. J. J Am Chem Soc 1955, 77,
1786.
40. Sykes, P. Mechanism in Organic Chemistry; Orient
Longman: New Delhi, India, 1989; p. 363.
41. Shorter, J. Advances in Free Energy Relationships;
Plenum Press: London, 1972; p. 72.
42. Wiberg, K. B. Oxidation in Organic Chemistry, Part A;
Academic Press: New York, 1965; p. 208, 209.
43. (a) Leal, J. M.; Domingo, P. L.; Garcia, B.; Ibeas, S.
New J Chem 1994, 18, 1233; (b) Mohan, D.; Chabra,
V. K.; Gupta, Y. K. J Chem Soc, Dalton Trans 1975,
1737.
22. (a) Leal, J. M.; Garcia, B.; Domingo, P. L. Coord Chem
Rev 1998, 173, 79; (b) Latimer, W. H. The Oxidation
States of Elements and Their Potentials in Aqueous So-
lution; Prentice-Hall; New York, 1952; (c) Charlot, G.
In Les Reactions Chimiques en Solution. L’ Analyse
Quantitative Minerale; Mason, T., Ed.; Lewis Publish-
ers: Paris, France, 1969; (d) Leal, J. M.; Domingo, P. L.;
Garcia, B.; Ibeas, S. J Chem Soc, Faraday Trans 1993,
89, 3571.
23. Patil, R. K.; Chimatadar, S. A.; Nandibewoor, S. T.
Indian J Chem A 2009, 48, 357.
24. Thabaj, K. A.; Chimatadar, S. A.; Nandibewoor, S. T.
Prog React KinetMech 2008, 33, 331.
25. Garcia, B.; Ruiz, R.; Leal, J. M. J Phys Chem A 2008,
112, 4921.
26. Tandon, P. K.; Dhusia, M.; Sahgal, S. J Mol Catal A:
Chem 2009, 301, 146.
27. Mucientes, A. E.; de la Pena, M. A. J Chem Edu 2006,
83, 1643.
28. Poblete, F. G.; Mucientes, A. E.; Villarreal, S.; Santiago,
F.; Cabanas, B.; Gabaldon, R. E. J Phys Org Chem 2006,
19, 597.
29. Sen Gupta, K. K.; Bera, A. K.; Sen Gupta, S. Indian J
Chem A 1997, 36, 797.
30. Speakman, P. T.; Waters, W. A. J Chem Soc 1955, 40.
31. Radhakrishnamurti, P. S.; Sahu, B. Indian J Chem A
1979, 17, 93.
44. Finar, I. L. Organic Chemistry Volume 1: The Funda-
mental Principles, 6th ed.; ELBS: Singapore, 1986; p.
221.
45. Richardson, W. H. Oxidation in Organic Chemistry, Part
A; Academic Press: New York, 1975; p.49.
32. Vogel, A. I. Text Book of Quantitative Chemical Anal-
ysis, 5th ed.; Longman: Essex, England, 1994; p.399.
33. Wiberg, K. B. J Am Chem Soc 1954, 76, 5371.
34. (a) Feigel, F. Spot Tests in Organic Analysis; Elsevier:
Amsterdam, The Netherlands, 1966; p. 452; (b) Feigel,
F. Spot Tests in Organic Analysis; Elsevier: Amster-
dam, The Netherlands, 1966; p. 454; (c) Kolthoff, I. M.;
Belcher, R. Volumetric Analysis; Inter Science: New
York, 1957; Vol. 3, p. 383.
46. (a) Olson, A. R.; Simonson, T. R. J Chem Phys 1949,
17, 1167; (b) Hoope, J. I.; Prue, J. E. J Chem Soc 1957,
1775; (c) Davies, C. W.; Williams, I. W. Trans Faraday
Soc 1958, 54, 1547.
47. Sen Gupta, K. K.; Sen, P. K. Inorg Chem 1979, 18, 979.
48. (a) Sykes, P. Mechanism in Organic Chemistry; Orient
Longman: New Delhi, India, 1989; p. 207; (b) Borish,
E. T.; Kirschenbaum, L. J. J Chem Soc Dalton Trans
1983, 749.
35. (a) Brewster, R. Q.; McEwen, W. E. Organic Chemistry;
Prentice-Hall: New Delhi, India, 1976; p. 190; (b) Sykes,
49. Corrochanno, P.; Garica-Rio, L.; Poblete, F. J.;
Rodriguez-Dafonte, P. Tetrahedron Lett 2010, 51, 1761.
International Journal of Chemical Kinetics DOI 10.1002/kin.20616