Effect of Ionic Strength on the Kinetics of the Oxidation of Ascorbic Acid by Hexacyanoferrate(III): Comparison between Specific Interaction Theories and the Mean Spherical Approximation

Article abstract of DOI:10.1039/a801853g

The influence of ionic strength on the rate constant of the oxidation reaction of ascorbic acid by hexacyanoferrate(III) in acidic medium is investigated. The dependence of the rate constant on ionic strength is discussed according to different specific i

Full text of DOI:10.1039/a801853g

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558 J. CHEM. RESEARCH (S), 1998
J. Chem. Research (S),
1998, 558±559$
Effect of Ionic Strength on the Kinetics of the
Oxidation of Ascorbic Acid by Hexacyanoferrate(III):
Comparison between Specific Interaction Theories
and the Mean Spherical Approximation$
T. Vilarino, P. Alonso, X. L. Armesto, P. Rodrõguez and
M. E. Sastre de Vicente*
Dpto de Quõmica Fundamental e Industrial, Facultad de Ciencias, Universidade da Coruna,
15071-A Coruna, Spain
The influence of ionic strength on the rate constant of the oxidation reaction of ascorbic acid by hexacyanoferrate(III) in
acidic medium is investigated. The dependence of the rate constant on ionic strength is discussed according to different
specific interaction theories and the mean spherical approximation.
The reactivity of ascorbic acid is of great importance,
mainly due to the biochemical signi®cance of this species;
numerous studies of the mechanisms of its oxidation by
metal complexes have been undertaken.1±3 On the other
hand, this reaction has often been used in physical chemistry
from an educational point of view.4±7 In the present work
the in¯uence of ionic strength, in the range 0.05±2.0 M
on the rate constant of oxidation of ascorbic acid by
hexacyanoferrate(III) in acidic medium is investigated.
Some speci®c interaction models (SIT)8,9 and also the
mean spherical approximation (MSA), an integral equation
based method,10±13 have been employed in order to explain
the variation of the logarithm of the rate constant (log k)
with ionic strength.
on pH since the latter controls the actual ascorbic acid/
ascorbate species that participate in the rate-determining
step. On the other hand, as the rate-determining step, for
one of the reaction pathways, involves the collision between
two anionic species, the rate constant is also in¯uenced by
the ionic strength of the medium which causes an alteration
of the anionic atmosphere and changes the charge density
around the anions.
From the above mechanism the rate of disappearance of
hexacyanoferrate(III) is given by
‡
3
d‰FeꢁCN†
dt
Š
2ka‰H Š ‡ 2kbK1
6
3
ˆ
‰H2AŠ ‰FeꢁCN†
Š
ꢁ7†
6
T
‡
‰H Š ‡ K1
then
‡
2ka‰H Š ‡ 2kbK1
Results and Discussion
kobs
ˆ
‰H2AŠ
ꢁ8†
T
‡
‰H Š ‡ K1
In order to make a quantitative study of the ionic strength
The reaction was followed using a spectrophotometric
method and pseudo-®rst-order conditions, i.e. at least a 10-
fold excess of ascorbic acid. The corresponding ®rst order
plots were linear for at least three half lives of the reaction.
For the reduction of hexacyanoferrate(III) by ascorbic
acid in acidic medium, a mechanism has been proposed
which involves the attack of hexacyanoferrate(III) on the
neutral ascorbic acid or the ascorbate anion (H2A, HA )
in a slow and rate determining step; this is followed by
a fast step in which ascꢀorbate radical-ion or ascorbate
on the reaction rate, data obtained at pH12 were used,
‡
which, since K1W [H ], simpli®es the denominator of
eqn. (8). On the other hand, the pronounced dependence of
rate constant on ionic strength, as well as the approximate
reactivity ratio ka/kb of 10 suggested in the literature,14
4
allow us to consider the ®rst term in the numerator negli-
gible and the expression for the observed rate constant
becomes
free radical, (H2Aꢀ , HA ) respectively, is attacked by a
‡
2kbK1‰H2AŠ
T
fresh hexacyanoferrate(III) ion to give the end product,
dehydroascorbic acid:
kobs
ˆ
ꢁ9†
‡
‰H Š
According to the proposed mechanism, the expression for
log kobs will be given by
K41
‡
H2A ‡ H2O
HA ‡ H3O
ꢁ1†
3
K24
‡
log kobs ˆ log 2kb ‡ log KÃ1 log‰H Š ‡ log gAH
2
‡
HA ‡ H2O
A
‡ H3O
ꢁ2†
ꢁ3†
3
‡ log gFeꢁCN†
log gACz
3
6
ka
3
4
H2A ‡ FeꢁCN†
4 FeꢁCN†
‡ H2Aꢀ ‡
‡ HAꢀ
ˆ log 2kb ‡ log KT1 2 log g2 log 10pH ‡ log gH
6
6
‡
kb
3
4
‡ log gAH ‡ log gFeꢁCN†
log gACz
3
6
HA ‡ FeꢁCN†
4 FeꢁCN†
ꢁ4†
ꢁ5†
6
6
The e€ect of ionic strength on the rate constant has
been studied by modelling the activity coecients by use
of some speci®c interaction models,8,9 all based on the
Debye±Huckel equation, and also a statistical mechanics
treatment, the mean spherical approximation.4,5,15 General
equations for the calculation of activity coecients by use
of MSA appear in Table 1.
Substituting the activity coecient expressions obtained
from the di€erent models the equations for the dependence
of log kobs on ionic strength (I) are shown in Table 2. As
can be seen, MSA, contrary to SIT (Debye±Huckel, Pitzer,
. . . ), does not lead to analytical functions on ionic strength,
but it is possible to take into account the size of the ions
fast
‡
H2Aꢀ ‡
3
4
‡ FeꢁCN†
4 FeꢁCN†
‡ A ‡ 2H3O
6
6
fast
‡
3
4
HAꢀ ‡ FeꢁCN†
4 FeꢁCN†
‡ A ‡ H3O
ꢁ6†
6
6
In order to study the e€ect of ionic strength on the
reaction rate, kinetic runs were performed with increasing
concentrations of sodium perchlorate at di€erent pH values.
It was noted that the rate of the reaction strongly depends
*To receive any correspondence.
$This is a Short Paper as de®ned in the Instructions for Authors,
Section 5.0 [see J. Chem. Research (S), 1998, Issue 1]; there is there-
fore no corresponding material in J. Chem. Research (M).

View Article Online
J. CHEM. RESEARCH (S), 1998 559
Table 1 General equations and parameters for calculation of activity coefficients by use of mean spherical approximation
General equations4,5,15
zi2
2zi
(1+
π
2
4
2
Pn Pn
i
i
i
ln el = –
–
–
Electrostatic contribution: Debye–Hückel type
Σ
i
(1+
)
)
(1+
)
i
4πΣ
4
24
i
i
i
i
i
3 X0 + 3 2X1 + 3 i X
3
3X1 X2 + 9/2 2X22
+ 3 3X2
i
3
i
i
i
i
2
Hard-sphere contribution: Percus–Yevick equation
ln hs = – ln
i
+
+
+
2
3
Common parameters for all systems
Specific parameters for the studied system
Electric charges (zi) defined by the model
1/2
i zi2
n
4πe 2
kT
2 Σ
2
=
2
=
2
i=1
(1+
)
i
Numerical densities (
)
experimental conditions: constant ionic medium
i zi
i
π
6
1
Ω
i
k
=
=
= 6.0225 x 10–4 (2 CNaClO
)
Xk
Pn
Σ
Σ (1+
i
=
+
ClO–
4
i
)
Σ
i
Na+
i
i
i
4
i
(k = 0,1,2,3)
3
–
(ClO4)=4.79 Å (Pauling diameter)
+
π
6
π
2
i
i
3
Ionic diameters (
)
electrolyte ions16
reactive ions17
= 1–
Ω = 1 +
Σ
Σ
i
i
i
(Na )=2.18–0.728CNaCl +0.0919C2NaClO
i
(1+
)
i
i
4
4
([Fe(CN6)]3–)=8.8 Å
(C6H7O6)=7.0 Å
e: electron charge
k: Boltzman constant
T: temperature (K)
constants
(AC‡)=11.1 Å (optimized)
ε
: dielectric constant
Table 2 Dependence of log k on ionic strength according
to several specific interactions models and the mean
spherical approximationa
Figure 1 shows the experimental data and the correspond-
ing plots for the di€erent ®tting equations of Table 2. As
can be seen, a highly satisfactory ®t is obtained when MSA
is applied taking the diameters given in Table 1. All these
diameters were taken from the literature16,17 except that of
the activate complex (AC%), which was optimized. All
approaches, except the Debye±Huckel approach, seem to ®t
the experimental results satisfactorily.
Equation type
log k
obs
A
I
C1 + 7
C2 + 7
Debye–Hückel
1 + 2.5
I
A
I
+ BI
Debye–Hückel +
linear term
1 + 2.17
I
MESV thanks Xunta de Galicia for ®nancial support
received through Project XUGA 10310B97.
I
2
γ
+
C3 + A'
In(1 + 1.2
I) + B'I
f
(Pitzer) + linear
1.2
(
(
1 + 1.2
I
term
Received, 6th March 1998; Accepted, 27th May 1998
Paper E/8/01853G
el
C4 + logγ AHhs + (log γ Fe(CN)63–
2
References
hs
+ log γ Fe(CN)63–
)
Mean spherical
approxim ation
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Fig. 1 Ionic strength dependence of log kobs for the oxidation
of L-ascorbic acid by hexacyanoferrate(III) according to
equations given in Table 2: (ÐÐ) MSA; (±±±) Debye±Huckel;
(- - - - - -) Debye±Huckel ‡ linear term; (....) f g(Pitzer) ‡ linear
3
4
term. Experimental conditions: [Fe(CN)6 ] ˆ 2.49 10 M,
3
[H2A]t ˆ 4.97 10 M, pH<2 and T ˆ 25 8C
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application of the method to studies of acid±base equilibria
can be found in refs. 10±13.