Electrochemical reduction of bisulfite in mildly acidic buffers: Kinetics of sulfur dioxide - Bisulfite interconversion

Article abstract of DOI:10.1021/jp983752c

The reduction of bisulfite on a bismuth rotating disk electrode (RDE) was studied in aqueous buffered electrolytes over the pH range 3-6. Clearly defined limiting currents were observed in all solutions examined; however, their magnitudes were not only smaller than those expected for a process limited by the diffusion of bisulfite from the bulk solution, but were also found to decrease as the media became less acidic. This behavior was attributed to a preceding homogeneous process that generates sulfur dioxide, the actual electroactive species. UV - visible absorption - reflection spectroscopy measurements at a RDE showed that in the potential region in which such limiting currents are observed, dithionite is produced with 100% faradaic efficiency, Results of rotation rate staircase scan amperometric RDE experiments were found to be consistent with the conversion of bisulfite into SO₂ proceeding via a general acid catalysis mechanism, and allowed values for the rate constants for the following reactions to be determined: SO₂ + H₂O → HSO₃^- + H₃O⁺, k_b = (1.6 ± 0.2) 10⁷ s^-1; HSO₃^- + H₃O → SO₂ + H₂O, k_f^H = (1.2 ± 0.15) 10⁹ M^-1 s^-1; HSO₃^- + CH₃COOH → SO₂ + H₂O + CH₃COO^-, k_f^HA = (1.7 ± 0.5) 10⁴ M^-1 s^-1. On this basis, and assuming diffusion-controlled rates for proton transfer from strong acids to oxygen bases, a more detailed mechanism involving formation of sulfurous acid as an intermediate is discussed and some thermodynamic and kinetic properties of the latter are estimated.

Full text of DOI:10.1021/jp983752c

1572
J. Phys. Chem. A 1999, 103, 1572-1578
Electrochemical Reduction of Bisulfite in Mildly Acidic Buffers: Kinetics of Sulfur
Dioxide-Bisulfite Interconversion
Yuriy V. Tolmachev and Daniel A. Scherson*
Department of Chemistry and Ernest B. Yeager Center for Electrochemical Sciences, Case Western ReserVe
UniVersity, CleVeland, Ohio 44106-7078
ReceiVed: September 17, 1998; In Final Form: December 30, 1998
The reduction of bisulfite on a bismuth rotating disk electrode (RDE) was studied in aqueous buffered
electrolytes over the pH range 3-6. Clearly defined limiting currents were observed in all solutions examined;
however, their magnitudes were not only smaller than those expected for a process limited by the diffusion
of bisulfite from the bulk solution, but were also found to decrease as the media became less acidic. This
behavior was attributed to a preceding homogeneous process that generates sulfur dioxide, the actual
electroactive species. UV-visible absorption-reflection spectroscopy measurements at a RDE showed that
in the potential region in which such limiting currents are observed, dithionite is produced with 100% faradaic
efficiency. Results of rotation rate staircase scan amperometric RDE experiments were found to be consistent
with the conversion of bisulfite into SO
2
proceeding via a general acid catalysis mechanism, and allowed
-
+
values for the rate constants for the following reactions to be determined: SO
2
+ H
2
O f HSO
3
3
+ H O ,
7
-1
-
+
H
9
-1 -1
-
k
b
) (1.6 ( 0.2) 10 s ; HSO
3
+ H
3 f
3
O
f SO
2
+ H
2
O, k
f
) (1.2 ( 0.15) 10 M s ; HSO
3
+
-
HA
4
-1 -1
CH COOH f SO + H O + CH COO , k
3
2
2
) (1.7 ( 0.5) 10 M s . On this basis, and assuming
diffusion-controlled rates for proton transfer from strong acids to oxygen bases, a more detailed mechanism
involving formation of sulfurous acid as an intermediate is discussed and some thermodynamic and kinetic
properties of the latter are estimated.
Introduction
support their view. In particular, the existence of H2SO3 in any
of its tautomeric forms has never been established even in a
cryogenic matrix; hence, if any of such species exist, their
The electrochemical reduction of bisulfite in aqueous elec-
trolytes has received renewed attention in recent years prompted
by the advantages this process offers over chemical methods
for the industrial synthesis of dithionite, which include higher
yields and purity, reduced cost, and fewer environmental and
safety concerns.1-4 This paper examines the nature of the
cathodic limiting currents in buffered bisulfite solutions over a
pH range of relevance to practical applications using rotating
disk electrode (RDE) techniques. The results of these studies
9
lifetime would be too short to account for the observed currents
(see eqs 6 and 7 below). Also to be considered is the possibility
of one of the two tautomers of bisulfite as the electroactive
species; however, these species are found to be present in
comparable concentrations in the pH range 2-6 and their
equilibrium quotient does not show a significant pH depen-
10,11
dence.
This behavior is not compatible with the experimen-
tally observed decrease in the rate of the preceding chemical
reaction with increasing pH, and with the eventual disappearance
of the wave at pH 6, a value at which the concentration of
bisulfite (pK2 ca. 6.96) is still high.
-
made it possible to determine the kinetics of the SO2-HSO3
interconversion and to elucidate certain mechanistic aspects of
this process.
Sulfur dioxide is known to undergo reversible reduction in
Brief Background
strongly acidic media on a variety of electrode materials at
The pH-dependent limiting currents on a dropping mercury
electrode in acidified sodium sulfite solutions were described
as early as 1930 by Gosman, who attributed the most positive
cathodic wave to the formation of dithionous acid with the
current being limited by the slow protonation of bisulfite to yield
H2SO3, regarded as the most likely electroactive species.
6-8,12,13
around -0.4 V vs SCE;
it seems, thus, conceivable that
at pH > 3, SO2 is also the electroactive species in this potential
region, as was recently proposed in this laboratory. In this
5
14
pH range, however, the amount of free SO2 in the solution is
low and the current would become limited by the rate of its
formation from bisulfite (eq 1, Scheme 1). Sulfur dioxide
6
Kolthoff and Miller found similar waves in mildly acidic
buffered solutions, but explained the limiting current behavior
in terms of the slow tautomerization of sulfurous acid (H2SO3)
prior to the electron transfer step. The importance of preceding
SCHEME 1
HSO3- + H T SO + H O
+
(1)
(2)
2
2
7
protonation was later emphasized by Cermak, although both
-
•-
2
SO + e T SO
the nature and the kinetics of the reaction were not clearly
identified.
2
2SO2•- f S O
2-
4
(3a)
8
More recently, Reynolds and Yuan reexamined this problem
2
and concluded that the electroactive species in the range 1.3 <
pH < 3 is sulfur dioxide (SO2). Several arguments appear to
-
e
9
SO2•- + SO T S O
•-
4
8 S O
2-
4
(3b)
or
2
2
2
1
0.1021/jp983752c CCC: $18.00 © 1999 American Chemical Society
Published on Web 03/03/1999

Electrochemical Reduction of Bisulfite in Mildly Acidic Buffers
undergoes rapid one-electron reduction, to yield a radical, eq
J. Phys. Chem. A, Vol. 103, No. 11, 1999 1573
to its definition, eq 6, u is independent of DX and ν, but depends
0
2, which generates dithionite as the final product, either via fast
on C . An alternate means of analyzing these data involves a
1
9
dimerization, eq 3a, or SO2 addition followed by a subsequent
rearrangement of eq 6 suggested by Vielstich, i.e.
electron transfer, eq 3b. The latter two processes are analogous
to those found in aprotic solvents15 and will not be pursued in
1/2
i /ω ) a - bilim
(7)
lim
this work; rather, the purpose of the present investigation is to
get further insight into the mechanism and kinetics of SO2
formation from bisulfite, i.e., eq 1 in Scheme 1.
where a is the same as in eq 6 and b ) a/u )DX2/3DY-1/2(Kkb)-1/2
.61ν . In this case, a plot of ilim/ω vs ilim would give a
straight line with a slope b, independent of C . Although this
latter approach allows a clearer and more compact presentation
of results, the Koutecky-Levich coordinates (eq 6) would be
preferable for situations in which the solution viscosity varies
within the set of measurements.
/
1
/6
1/2
1
0
Theory
The reaction mechanism of relevance to this work, known
as chemical-electrochemical (CE), involves the reduction (or
oxidation) on the electrode, of a species produced by a preceding
chemical reaction in the bulk solution, and may be represented
as follows:
Experimental Section
Both the optical and electrochemical instrumentation have
been described in detail in ref 14. A Ag/AgCl in 3 M NaCl
SCHEME 2
kf
(BAS) separated by a closed (wet) glass stopcock and connected
X {
\kb} Y in the solution
(4)
(5)
to the working electrode compartment through a Luggin
capillary was used as the reference electrode. A large area (4
Y f Z on the electrode
2
cm ) gold foil separated by a glass frit served as the auxiliary
In this scheme, X is the solution-phase, electrochemically
inactive species in the potential range of interest that generates
the actual redox active species Y, and kf and kb are the forward
and backward rate constants for the corresponding reactions in
eq 4. This model would be applicable to Scheme 1, eqs 1-3,
for X ≡ HSO3 ; Y ≡ SO2, and Z ≡ S2O4 , provided the media
are well buffered, so that the reaction in eq 1 may be regarded
as pseudo first order.
electrode. A bismuth electrode was selected for these studies
to take advantage of its wide potential window and the relative
2
0
ease by which clean surfaces can be prepared. The bismuth
2
RDE (0.295 cm ) was fabricated by casting a Bi rod (99.999%,
Alfa Aesar) into an epoxy matrix which was later machined to
shape. Immersion of the Bi electrode into solution was done
under potentiostatic control as described in ref 21. The citrate
and acetate buffers were prepared using citric acid (ACS reagent,
Aldrich), and trisodium citrate dihydrate (certified, Fisher) or
sodium hydroxide (semiconductor grade, Aldrich), and glacial
acetic acid (certified ACS+, Fisher), and sodium hydroxide or
sodium carbonate (ACS certified), respectively. Sodium per-
chlorate hydrate (99.99%, Aldrich) was used as the background
electrolyte. Water was obtained from an EASYpure UV
purification system (Barnstead). In order to reduce the loss of
-
2-
Reactions that proceed via a CE mechanism, for which the
rates of the forward and/or backward reactions in eq 4 are fast
compared to the rate of diffusion (see details in refs 16 and 17
and also in the Appendix), will elicit limiting currents at a RDE
controlled by the kinetics of the homogeneous process, as
opposed to pure convective diffusion. An analytical solution to
this problem, within Levich’s mass transport model, was first
16
reported by Koutecky and Levich, and shortly thereafter,
generalized by Dogonadze17 to include the case of unequal
diffusion coefficients for X and Y. A further extension of this
formalism to account for currents below limiting values is given
in the Appendix. Compton and Harland18 calculated limiting
currents of CE processes using numerical techniques and found
good agreement with the previously reported analytical solutions
for fast reactions.
volatile components from the solutions examined (SO and
2
acetic acid), the Ar gas used for deaeration was saturated with
the vapor of the same solution in a bubbler. Measurements of
pH were made using a glass electrode (Fisher) with a high-
impedance pH meter (Chemcadet). Calibration was achieved
using commercial standards with pH ) 4.00 and 7.00. The cell
used in this work was not thermostated; however, the room in
which experiments were performed was equipped with micro-
climate control affording temperatures of 23.3 ( 0.3 °C.
In the course of our work it was found that the reduction of
bisulfite on Bi, and other electrode materials as well, was
sensitive to the presence of trace impurities, most likely organic
surfactants in the solution, yielding in many instances tilted
limiting currents of the type shown in ref 1. Larger and potential
independent ilim values could be restored momentarily, however,
by repolishing the electrode with 0.05 µm alumina.
More detailed studies were performed in 10 mM solutions
of sodium sulfite in citrate buffer (see below) at pH 4.20 to
examine the effects of electrode potential and convection on
the kinetics of inhibition of bisulfite reduction. To monitor
changes in the polarization curves as a function of the total
holding time, th, the electrode potential was held at a selected
value Eh, either with or without rotation to allow impurities to
adsorb, and scanned every 5 min at 20 mV/s, down to -1.1 V
and then up to Eh, while rotating at 3600 rpm. No noticeable
hysteresis nor tilted limiting currents could be found in the
polarization curves between the scans in the positive and
negative directions, indicating that, within the time scale and
Based on Dogonadze’s derivation17 (see also eq A19 in the
Appendix), the dependence of the limiting current, ilim, on the
rotation rate ω of the RDE for a CE mechanism can be written
as follows:
1/2
1
/ilim ) 1/u + 1/(aω )
(6)
-
Since K ) [SO2]/[HSO3 ] ) [Y]/[X] ) kf /kb , 1 in the pH
range examined in this work, the parameters u and a reduce to
0
1/2
u ) nFC k (D /k )
(6a)
(6b)
f
Y
b
0
1/3 1/6
X
a ) (nFD C )/(1.61D ν )
X
0
where C represents the sum of the bulk concentrations of X
and Y. Note that a may be regarded as the Levich slope for a
redox process involving the same number of electrons as for Y
(
n ) 1 for eq 2), but for a species with the diffusion coefficient
1/2
of X. Hence, plots of 1/ilim vs 1/ω are linear with intercepts
/u, the parameter that carries kinetic information. According
1

1574 J. Phys. Chem. A, Vol. 103, No. 11, 1999
Tolmachev and Scherson
potential range of the scan, the coverage of the surfactant
remains essentially constant. The values of the current at -0.9
V vs th were fitted to single-exponential decay functions. For
example, for Eh ) -0.6 V vs Ag/AgCl, i.e., the reported point
of zero charge (pzc) of polycrystalline Bi,2 the decay time
constant, τ, for ω ) 0 and 3600 rpm, was 35 and 13 min,
respectively. At more negative Eh values, τ increased, e.g. at
0
-0.8 V and 0 rpm, τ ) 73 min. The enhanced inhibition
observed under rotation and at potentials close to the pzc
corroborates our suggestion that solution phase surfactants are
responsible for this effect. Unfortunately, neither the concentra-
tion of the surfactant nor its coverage at a specific time is known.
It is, nevertheless, instructive to estimate the first of these
quantities assuming that adsorption occurs under diffusion-
limited conditions with a sticking coefficient of unity and that
a significant fraction of the surface is covered by the surfactant
Figure 1. Polarization curves for bisulfite reduction obtained with a
2
(
1 nmol/cm ) at t ) τ, e.g., 13 min at ω ) 3600 rpm. Based on
Bi RDE in 0.10 M citric acid + xM NaOH + (0.50 - x)M NaClO
0 mM Na SO solutions, at the specified pH values (0.1 < x < 0.4).
Rotation rate ω ) 900 rpm. Scan rate: 10 mV/s.
4
+
1
2
3
this model and a diffusion coefficient for the surfactant of ca.
-
6
2
1
0
cm /s, its concentration in solution would be on the order
of tens of pM. Very similar inhibitory effects were observed
using a Bi rod in the hanging meniscus configuration RDE, i.e.,
without the epoxy shroud, suggesting that the soluble fractions
of the resin are not the major source of contamination. We also
found similar inhibition phenomena in other buffers (acetate,
phosphate) and that the kinetics of the poisoning became slower
at lower pH.
Complications derived from these contaminants could be
avoided by polarizing electrodes at potentials at least 0.5 V
negative to the pzc of Bi just prior to data collection to allow
impurities to desorb. As judged by the results obtained in
independent runs, the reproducibility of ilim employing this
pretreatment was better than (3%.
Limiting currents as a function of ω, required for the kinetic
analysis (see eqs 6 and 7), were recorded at fixed potentials by
stepping ω in fixed increments (50-200 rmp), i.e., staircase
scan method, in the range 200-8000 rpm toward both faster
and slower rates, using computer-generated voltages as inputs
to the Pine MSRX speed control and rotator. Five to 10 rotations,
or 0.1 s, whichever was longer, were allowed for the disk
currents to achieve steady state before data were acquired. This
ω vs time program allows the most expedient means of
collecting steady-state data over a given ω range (for a fixed ω
increment), as shown by Miller and co-workers22 for a similar
technique, in which ω was ramped exponentially using an
analogue signal generator.
Figure 2. Representative ilimω1/2 vs ilim plots obtained from data
recorded in the same solutions specified in caption Figure 1 at the pH
values indicated.
Results
Figure 1 shows polarization curves obtained with a Bi RDE
in 10 mM Na2SO3 in citrate buffer solutions of different pH in
the range 3.09-5.36 at a scan rate of 10 mV/s and ω ) 900
rpm. As indicated, the values of ilim for the electroreduction
dropped significantly as the pH increased. The faradaic ef-
ficiency for dithionite production, as determined by in situ UV-
Figure 3. Logarithm of the kinetic parameter b obtained from the
slopes of the lines in Figure 2 as a function of pH.
solution becomes less acidic. In agreement with theoretical
predictions (see eq 7), the intercepts, a, at fixed pH, were found
to vary linearly with the concentration of bisulfite in the range
1
4
visible reflection-absorption spectroscopy at a RDE, was
00% down to the onset of hydrogen evolution, indicating that
2
-50 mM (not shown in this work), whereas the slopes remain
1
unaffected.
no further reduction or decomposition of this product occurs
under these conditions.
The pH dependence of the kinetic parameter b was found to
be linear in log coordinates (see Figure 3); the slope of the line,
1/2
2
3
Plots of ilimω vs ilim obtained in the same solutions specified
however, was closer to / rather than 1, as would be expected
in the caption Figure 1 (see Figure 2) yielded straight lines with
for the mechanism shown in eq 1, Scheme 1, suggested in the
Introduction. Not considered in that reaction sequence was the
possibility that undissociated acid may also serve as a proton
donor, i.e., a general acid catalysis route. In such a case,
an intercept of -0.193 ( 0.005 mA cm- rpm , which is
equal to one-half of the Levich slope for the oxidation of
bisulfite on gold measured in the same solution. The slopes of
these lines, b (see eq 7), increased with pH, supporting the view
that the rates of the preceding reaction, kf, decrease as the
2
-1/2
H
f
+
HA
f
k ) k [H O ] + k [HA]
(8)
f
3

Electrochemical Reduction of Bisulfite in Mildly Acidic Buffers
J. Phys. Chem. A, Vol. 103, No. 11, 1999 1575
Discussion
The values of the rate constants obtained in this work were
found to be comparable to those reported by other groups using
different experimental techniques, as summarized in Table 1.
H
8
-1 -1
Not listed in this table is the value of kf ) 3.7 × 10 M s
8
obtained from polarographic measurements closely related to
our technique.
Also of interest is to compare various aspects of the SO2/
-
HSO3 reaction with a chemically similar, albeit much slower
transformation, namely the hydration of carbon dioxide to
-
bicarbonate ion, CO2/HCO3 , for which the intermediate, H2-
CO3, can be easily identified. If the SO2/HSO3- reaction is
30
Figure 4. Rate constant of conversion of HSO -
as a function of the concentration of free acetic acid [AcOH] in solutions
of (0.288x)M AcOH + x M AcONa + + (0.5 - x) M NaClO + 10mM
Na SO at constant pH 5.30. For x > 0.5 M no perchlorate was added.
assumed to proceed via Scheme 3
3
2
into SO (see eq 9)
4
2
3
The error bars show standard deviations observed with 20 consecutive
rotation rate scans in the same solution. Solid line: linear fit; dashed
line: non linear fit. See text for discussion.
-
which combined with eq 6a would yield,
(see below, where SO ≡ Y and HSO ≡ X), a mechanism
2
3
that involves the same corresponding intermediate, i.e., H2SO3
HX), the data presented in this work enables some of its kinetic
1
/2
1/2
+
HA
1/2
(
u ) nFCDY {(kb /K )[H O ] + (k /kb )[HA]} )
1
3
f
and thermodynamic properties to be estimated. Although this
scheme ignores the existence of tautomeric forms of both
bisulfite and sulfurous acid, it can be used as a working model
+
p[H O ] + q[HA] (9)
3
where K ) kb/kfH is the equilibrium constant [H3O ][HSO ]/
+
-
as illustrated by Eigen and co-wokers.
28
[SO2]. This type of catalysis has been found, for example, for
For carbonic acid, the rate of dissociation kXH is higher than
+
30
the protonation of pyruvate with imidazolinium cation yielding
the electroactive pyruvic acid, as shown by Becker and Strehlow
using polarography.23
the rate of dehydration k ; hence, one can expect a similar
behavior for sulfurous acid, since in both cases dissociation
involves fewer structural changes than dehydration. The con-
sistency of this assumption will be verified below. This approach
allows one to consider the formation of HX as a preequilibrium
step yielding the following relationships:
Further insight into this issue was gained by performing
experiments of the same type described above at fixed pH, 5.30,
and fixed ionic strength, 0.50 M,24 in acetate buffer solutions
of varying buffer capacities. The results obtained showed a
-
kb ) k
(11)
gradual decrease in the magnitude of a from -0.21 to -0.17
1/2
2
mA rpm /cm as the concentration of acetate buffer increased
from 0.06 to 1.21 M, owed most likely to a gain in solution
viscosity, whereas b decreased more markedly, from 0.030 to
kHX
kAX
+
[
H O ] +
[HA]
3
k
k
XH
+
XH
-
1/2
kf ) k
(12)
0
.015 rpm . The ratio a/b ) u as a function of concentration
kXA
1 + kXH[A ]
-
of free acetic acid [AcOH] is shown in Figure 4. Despite some
scatter, the quality of the data obtained with the staircase rotation
rate scan method appears superior to all previous studies of
It is evident from these equations that the linear dependence of
u on [AcOH] proposed in the Results section, eq 8, is equivalent,
in this microscopic model (Scheme 3), to the condition kXA-
A ]/kXH , 1; then, from eqs 8 and 12
25
protonation reactions involving voltammetric methods, indicat-
ing beyond a doubt that the rate of protonation increases with
[
AcOH]. A linear regression of the data, shown in Figure 4,
-
[
5
-2
-1
yielded p ) (12.3 ( 0.9) × 10 mA cm
M
and q ) 17.7
-
2
-1
1.86
(
2.3 mA cm M . From these values, and using literature
H
+
kf ) k kHX/k
XH
(13)
(14)
-
26
-5
2
27
data for K1 ) 10
M and DY ) 1.8 10 cm /s, obtained
at the same ionic strength, the values of all the relevant rate
HA
+
kf ) k kAX/k
7
XH
constants can be estimated, namely, kb ) (1.6 ( 0.2) × 10
-
1
H
9
-1 -1
HA
s , kf ) (1.2 ( 0.15) × 10 M
s
and kf ) (1.7 ( 0.5)
It will be assumed in what follows that this is the case, since it
agrees with the experimental data, and the issue of consistency
will be discussed later in this section.
4
-1 -1
×
10 M s .
Two-dimensional linear regression of u as a function of both
+
[
0
H3O ] and [AcOH] in the pH range 4.5-5.5 and [AcOH]
Based on our experimental results and eqs 13 and 14
.05-0.6 M, comprising a total of 20 points, including those
5
-2
-1
H
f
HA
4
in Figure 4, yielded p ) (12 ( 7) × 10 mA cm M , q )
kHX/kAX ) k /k ≈ 7 × 10
(15)
f
-
2
-1
-2
2
5 ( 6 mA cm M , and an intercept of -0.6 ( 4 mA cm .
Larger standard deviations in this case are caused by a weaker
dependence of u on [AcOH] relative to [H3O ] at lower pH, as
well as a possible dependence of these values on [A ] to be
A further analysis of these results is possible only if additional
assumptions concerning the rate constants are introduced. In
particular, some of the reactions in Scheme 3 are likely to be
diffusion controlled, and, therefore, their rate constants, as
discussed by Crooks, can be estimated. For example, the rates
of protonation of oxoanions by hydronium cation have rate
+
-
considered further in the Discussion section. The small value
of the intercept suggests that water does not contribute
significantly to the total rate of bisulfite protonation.
31

1
576 J. Phys. Chem. A, Vol. 103, No. 11, 1999
Tolmachev and Scherson
this work
b f
TABLE 1: Comparison of k Obtained in This Work with Those Reported in the Literature
and k H
reaction
rate const
(s-1
Eigen et al.28 a
Betts and Voss29 b
-
+ H+
6
8
7
SO
HSO
2
+ H
3
2
O f HSO
3
k
k
b
)
3.4 × 10
1.1 × 10
1.6 × 10
-
+
H
(M s-1
-1
8
9
9
+ H f SO
2
+ H
2
O
f
)
2 × 10
2.5 × 10
1.2 × 10
a
From ultrasound absorption in acidic solutions. b From oxygen isotope exchange rates in alkaline solutions.
constants of ca. 2 × 10 M-1 s , which can then be regarded
1
0
-1 24
ref 34. Also kXH ) 1 × 10 s-1 . 7 × 10 s ) k , justi-
fying, therefore, the assumption of preequilibrium formation of
H2SO3.
10
8
-1
+
as a good approximation for kHX, and, therefore, yield from eq
5
-1 -1
1
5 kAX ≈ 3 × 10 M s .
The magnitude of kAX is far below the diffusion-controlled
The other assumption used in the foregoing kinetic analysis,
i.e., negligible rate of deprotonation of sulfurous acid by acetate
compared to the rate of dissociation, may not seem consistent
with the results of the analysis (Scheme 3), since under the
limit, indicating that sulfurous acid is stronger than acetic acid
and, as also discussed by Crooks, that the reverse reaction, i.e.,
proton abstraction by acetate anion from neutral sulfurous acid,
should be diffusion controlled. Typical rate constants for
-
conditions shown in Figure 4, kXA[A ]/kXH e 0.7 and, thus,
1
0
protonation of oxoanions by stronger acids are about 1 × 10
not much smaller than 1. However, a nonlinear fit to the data
shown in Figure 4 (dashed line) based on eq 6a, 11, and 12
yielded values for the microscopic rate constants, which, within
their uncertainty, are not different than those obtained from the
linear fit. Although the statistical analysis does not favor one
model over the other, the experimental results clearly support
a general acid catalysis mechanism.
-1
-1 31
M
s . Assigning this latter value to kXA, the ratio of
dissociation constants of the two acids can now be calculated:
kXA/kAX ) KHX/KHA
)
-
3
-
4
[
HSO ][AcOH]/[H SO ][AcO ] ) 3 × 10
2
3
Using KHA ) 10-
4.75
M,32 one obtains KHX ) 0.6 M and,
Conclusions
10
-1
hence, kXH ) KHXkHX ) 1 × 10 s .
32
Sillen’s compilation lists two values for KHX: 0.35 M,
attributed to Kolthoff,33 and 0.040 M, claimed by Flis et al.;
however, both these entries appear unreliable. In particular,
Kolthoff used the notation H2SO3 to refer to what is currently
regarded as the sum of free dissolved SO2 and the acid, and,
therefore, did not introduce pKHX. Rather, he used the pK
Analysis of the limiting currents observed using a bismuth
rotating disk electrode for the reduction of bisulfite to dithionite
in mildly acidic buffered solutions is consistent with the reaction
proceeding by a chemical electrochemical (CE)-type mechanism
with sulfur dioxide being the reactive species. The kinetics of
34
-
+
the preceding reaction, HSO3 + H a SO2 + H2O, was found
to be dependent on pH and concentration of the buffer as
prescribed by a general acid catalysis mechanism, i.e., both
hydronium and undissociated acid serve as proton donors. On
the basis of the values of the rates constants obtained in this
work, H2SO3 may be characterized as a strong acid (KHX ) 0.6
M) which undergoes dehydration within a few nanoseconds,
and, thus, explain its highly elusive character.
-
2
reported in an earlier publication (1.74 × 10 M), which
+
-
26
matches that currently accepted for K1 ) [H ][HSO3 ]/[SO2].
On this basis, the entry in Sillen’s monograph is difficult to
justify. In fact, the actual value listed in those tables does not
appear explicitly in Kolthoff’s publication. Later, Flis et al.
3
4
examined solutions obtained by dissolving SO2 in water using
iodometry to determine the total concentration of S(IV). In such
unbuffered media, the net reaction would yield equal concentra-
tions of hydronium ions and bisulfite; hence, the equilibrium
concentration of bisulfite can be determined from pH measure-
ments using appropriate corrections for activity coefficients. The
difference between the total S(IV) concentration and bisulfite
would then equal the sum of SO2 and H2SO3. By assuming that
the UV absorption band centered at 277 nm is due solely to
Acknowledgment. This work was supported in part by the
Advanced Research Projects Agency, ONR Contract No.
N00015-92-J-1848. The authors wish to express their apprecia-
tion to Prof. John Stuehr for interesting discussions.
Appendix
-
SO2 (and not to HSO3 or H2SO3), its concentration could be
Current on the RDE in the Case of CE Process. The
equations of mass balance at a RDE for an electrochemical
process involving a preceding (pseudo)first-order homogeneous
reactions 4 and 5 may be written as follows:
measured by spectrophotometric techniques and, thus, by
subtraction, that of H2SO3. According to these authors a
significant amount of H2SO3 should be present in equilibrium
with SO2 at pH lower than 2. This observation, however, was
not confirmed by Raman spectroscopy.11,35 A likely source of
2
d Y
dY
dz
-
error in that publication lies in the calculation of [HSO3 ] from
DY
DX
- V(z) + k X - k Y ) 0
(A1)
(A2)
f
b
2
dz
pH measurements. A more rigorous approach to estimate activity
coefficients was used by Huss and Eckert36 to study equilibria
in aqueous SO2 solutions by very similar iodometric, UV
absorbance, and conductance measurement techniques who
found no evidence for the presence of H2SO3.
2
d X
dX
dz
- V(z) + k X - k Y ) 0
f
b
2
dz
On the basis of empirical thermodynamic correlations analysis
and simple molecular calculations, Guthrie obtained kHX )
.005 M for SO(OH)2 and 400 M for HSO2(OH). These data
The appropriate boundary conditions in the bulk represent
chemical equilibrium between X and Y
37
0
0
indeed show, in agreement with our conclusions, that sulfurous
acid is stronger than acetic acid.
z f ∞
z f ∞
X + Y ) C
(A3)
(A4)
+
k X - k Y ) 0
f b
The last undetermined constant, k , can be determined from
8
-1
eq 13 yielding a value of 7 × 10 s . The equilibrium constant
H2SO3]/[SO2] ) k /k ) 2 × 10 is close to 5 × 10 ,
attributed by Sillen to ref 31, but lower than 0.33 claimed in
-
+
-2
-2
[
The boundary conditions on the electrode will be referred to
the case of constant surface concentration of Y and nonelec-

Electrochemical Reduction of Bisulfite in Mildly Acidic Buffers
troactive X:
J. Phys. Chem. A, Vol. 103, No. 11, 1999 1577
0
B(êf∞) ) (D/D )C
(A12)
Y
z ) 0
z)0
Y ) YS
(A5)
(A6)
A(0) ) Y (k + k (D /D )) - B(0)k (D /D ) (A13)
S
b
f
Y
X
f
Y
X
dX/dz ) 0
A′(0) ) k B′(0)
(A14)
b
For high Schmidt number Sc ) V/DY >1000, the normal
component of the fluid velocity in the vicinity of the electrode
The solution of eq A9 satisfying these boundary conditions is
A(ø) ) A(0)e ; hence, eq A14 can be written as
-
1/2 3/2 2 37
can be approximated by V(z) ) - 0.51V
ω
z . On this
-ê/ꢀ
basis, and introducing a dimensionless coordinate normal to the
electrode surface ê ) z/δY, where δY ) 1.61DY1 V ω , eqs
/3 1/6 -1/2
A(0) ) -k ꢀB′(0)
(A14a)
b
A1 and A2 can be rewritten as
2
2
The solution of eq A10 satisfying boundary conditions at ê
) 0, eqs A13 and A14 is given by
δ
Y
d Y
2
dY
dê
+
Fê
+
(k X - k Y) ) 0
(A1a)
(A2a)
f
b
2
dê
DY
2
F
ꢀκ
ê
t
ꢀ
2
2dY
δ
B(ê) ) B′(0)I(ê) - A(0) exp -
×
d X
dX
Y
∫
(
)
0
+
Fê
-
(k X - k Y) ) 0
f
b
2
dê
dX dê
DX
DY
1
3
2
exp(
Ft t [I(ê) - I(t)] dt + B(0) (A15)
)
3
3 D
where F ) 1.61 × 0.51 ) 2.13.
Let us multiply (A1a) by kb and (A2a) by kf and subtract one
where in the latter formula
from the other
2
ꢀ2
d
(k Y - k X) + ꢀ Fê
2
2
d
kbY - kf X - (k Y - k X) )
DY
ê
F
D
Y 3
b
f
b
f
I(ê) )
∫
exp -
(
t
) dt
2
dê(
)
DX
0
3 D
dê
0
(A7)
In order to analyze the boundary condition at ê f ∞ (A12), the
integral in eq A15 should be expanded for small ꢀ:
where ꢀ ) µ/δY, µ- ) [(kf/DX) + (kb/DY)] . Stretching of the
independent variable ê ) øꢀ gives the “distinguished limit”
form39 for eq A7:
1
1/2
38
∞
t
2
3
∫
exp - f(t)dt ) ꢀf(0) + ꢀ f′(0) + ꢀ f′′(0) + ...
0
(
)
ꢀ
2
d
3
2
d
DY
(k Y - k X) + ꢀ Fø
kbY - kf X - (k Y - k X) ) 0
b
f
b
f
2
dø(
)
dø
DX
Using this result, eq A15 can be expressed as
(A8)
1
6,17
2
The parameter µ, known as the “reaction layer thickness”,
B(∞) ) B′(0) I(∞) + B(0) - 2I(∞)(F/κ)A(0)ꢀ + ... (A16)
has dimension of length and, as indicated above, depends on
the rate constants of the preceding chemical reaction. If µ ,
δY, i.e., the preceding chemical reaction is fast, ꢀ , 1, and can,
therefore, be treated as a perturbation parameter and the term
1
/3
where I(∞) ) (D/D ) . Within the framework of the first-order
Y
2
solution discussed here, the ꢀ term in eq A16 should be
dropped.
3
in ꢀ in eq A8 can be dropped as the first-order approximation.
Expressions for A(0), B(0), and B′(0) in terms of known
parameters can be obtained by solving the system comprised
of eqs A13, A14a, and A16. In particular, for A(0) one obtains
2
2
d A/dø - A ) 0
(A9)
where A ) kbY - kfX. Note that a solution for nonequal diffusion
coefficients can be obtained only within this approximation.
The other equation can be obtained by multiplying eq A2a
by DX/DY and adding eq A1a.
D
DY
DX
YS
K
0
-
+ K
(
)C
0
DY
A(0) ) -k
C
(A17)
b
DX
1/3
K D
+
2
( )
DY
d
dê
F
d
DY
ꢀ D
Y
d
2
2
2B + F
ê
B ) ê
κ dê
A
(A10)
D
dê
where K) kf/kb as defined in eq 6a.
The final expression for the current can now be obtained,
namely
where
B ) Y + (D /D )X
X
Y
dY
i ) nFDY (0) )
dz
nFDY
dA
(0) ) -
nFDY
k D + k D
b
X
f
Y
A(0) )
D )
κ )
k δ dê
k δ ꢀ
b
Y
b Y
kb + kf
1
+ K YS
1
-
+
k D + k D
0
0
b
X
f
Y
DC
K
C
nF
(A18)
Y
D - DX
δ
1
DX
µ
1
+
K D δ
Y
The boundary conditions eqs A3-A6 then become
A(êf∞) ) 0
1/3
(A11)
where δ ) δY(D/DY) . In the case of limiting current conditions

1578 J. Phys. Chem. A, Vol. 103, No. 11, 1999
Tolmachev and Scherson
(
YS ) 0), eq A18 reduces to the Dogonadze’s expression:17
(10) Horner, D. A.; Connick, R. E. Inorg. Chem. 1986, 25, 2414.
(11) Littlejohn, D.; Walton, S. A.; Chang, S. G. Appl. Spectrosc. 1992,
4
0
DC
nF
δ
DX
(13) Benayada, A.; Bessiere, J. Electrochim. Acta 1985, 30, 593.
i )
(A19)
(14) Tolmachev, Y. V.; Wang, Z.; Hu, Y.; Bae, I. T.; Scherson, D. A.
1
µ
Anal. Chem. 1998, 70, 1149.
1
+
(15) Kim, B. S.; Park, S. M. J. Electrochem. Soc. 1995, 142, 26.
(16) Koutecky, J.; Levich, V. G. Zh. Fiz. Khim. 1958, 32, 1965.
(17) Dogonadze, R. R. Zh. Fiz. Khim. 1958, 32, 2437.
K D δ
Y
It is worth checking the range of ꢀ for which eq A19 is valid
by comparison with the results of numerical simulations. In
the case of equal diffusion coefficients Compton and Harland
(18) Compton, R. G.; Harland, R. G. J. Chem. Soc., Faraday Trans. 1
1989, 85, 761.
1
8
(
19) Vielstich, W. Z. Anal.Chem. 1960, 173, 84.
(20) (a) Palm, U.; Tenno, T. J. Electroanal. Chem. 1973, 42, 457. (b)
-
2
used a parameter kA which is equal in our notation to ꢀ (1/
Salve, M.; Palm, U. Trans. Tartu UniVersity 1974, 332, 71 and references
therein.
2
2/3
1
.61 × 0.51 )K/(1 + K). Based on Figure 1 in ref 18, one
(
21) Tolmachev, Y. V.; Fedorovich, N. V. Russ. J. Electrochem. 1994,
0, 1368.
22) Miller, B.; Bellavance, M. I.; Bruckenstein, S. Anal. Chem. 1972,
may conclude that the agreement between numerical solution
and eq A19 is good for log kA > -0.5 that is ꢀ < 0.4. For the
case of unequal diffusion coefficients illustrated in Figure 2 of
ref 18 one finds good agreement for the variable defined in ref
3
(
44, 1983-1992.
(23) Becker, M.; Strehlow, H. Z. Electrochem. 1969, 64, 42.
(24) For these studies the following solutions were used: (0.288x) M
1
8, if
AcOH + x M AcONa + (0.5 - x) M NaClO4 + 10 mM Na2SO3 at constant
pH 5.30. For x > 0.5 M, for which the ionic strength was higher than 0.5
M no perchlorate was added.
1
/3
1/3
k V
DY
1
K
-2
0.66
)
ꢀ
> 10
(25) Strehlow, H. In Techniques of Organic Chemistry; Wessberger, A.,
Ed.; J. Wiley & Sons: New York, 1963; Vol. VIII, Part II, pp 799-844.
2
ω
DY
1
.61
1
+ K
(26) Yakovlev, V. A.; Makarenko, V. A.; Poltoratskii, G. M. J. Appl.
DX
Chem. USSR 1989, 62, 1273.
27) Samec, Z.; Weber, J. Electrochim. Acta 1975, 20, 413.
(28) Eigen, M.; Kustin, K.; Maass, G. Z. Phys. Chem. NF 1961, 30,
30.
29) Betts, R. H.; Voss, R. H. Can. J. Chem. 1970, 48, 2035.
30) Falcke, H.; Eberle, S. H. Wat. Res. 1990, 24, 685.
(31) Crooks, J. In ComprehensiVe Chemical Kinetics; Bamford, C. H.,
Tipper, C. F. H., Eds.; Elsevier: Amsterdam, 1977; Vol. 8.
32) Bjerrum, J.; Schwarzenbach, G.; Sillen, L. G. Stability Constants,
(
or, equivalently, ꢀ < 0.009.
1
For the system examined in this work ꢀ was found to be
smaller than 0.01 and, therefore, within the range of validity of
this model.
(
(
(
References and Notes
Part I; Chemical Society: London, 1957.
(
1) Scott, L. L.; Ding, Y.; Stadler, S. M.; Kohl, P. A.; Winnick, J.;
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Bottomley, L. A. J. Electrochem. Soc. 1998, 145, 4057.
(
(
(
(
(
(
(
(
2) Oloman, C. J. Electrochem. Soc. 1970, 117, 1604.
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