Large amplitude pH oscillations in the hydrogen peroxide-dithionite reaction in a flow reactor

Article abstract of DOI:10.1021/jp012007o

The kinetics of the reaction between S₂O₄^2- and H₂O₂ is found to be very complex both in a closed reactor and in a continuous-flow stirred tank reactor (CSTR) in an unbuffered aqueous solution. The ma

Full text of DOI:10.1021/jp012007o

J. Phys. Chem. A 2001, 105, 9183-9187
9183
Large Amplitude pH Oscillations in the Hydrogen Peroxide-Dithionite Reaction in a Flow
Reactor
Kl a´ ra M. Kov a´ cs and Gyula R a´ bai*
Institute of Physical Chemistry, UniVersity of Debrecen, P.O. Box 7, H-4010 Debrecen, Hungary
ReceiVed: May 24, 2001; In Final Form: July 9, 2001
2
-
The kinetics of the reaction between S
O
2 4
2 2
and H O is found to be very complex both in a closed reactor
and in a continuous-flow stirred tank reactor (CSTR) in an unbuffered aqueous solution. The main products
2-
2-
of the oxidation are SO
4
and S O
2 6
2 2
in excess H O . The reaction is accompanied by acidification of the
initially alkaline mixture. The measured pH-time traces show multiple inflection points in a closed reactor,
2
-
-
suggesting that the reaction takes place in several distinct steps. Transient formation of SO
3
3
/HSO buffer
system is observed in the early stage of the reaction. Next, the sulfite ions are oxidized further to sulfate ions
in an autocatalytic reaction. Simultaneously a small amount of dithionate ions is also formed. The pH exhibits
very large amplitude relaxation oscillations in a CSTR in a narrow range of input concentrations, flow rate,
and temperature. A simple empirical rate law model consisting of three redox reactions and three protonation
equilibria is proposed. Numerical simulations based on this model agree well with the experimental results.
+
The key to the pH-regulated oscillation is the H -autocatalysis that results from the more rapid oxidation of
the protonated than of the unprotonated sulfite intermediate.
Introduction
dithionite ion is thought to be an old example of the oscillatory
chemical reactions. This view found its way into many review
Sodium dithionite (Na2S2O4) is a powerful reducing agent.
The average oxidation number of its sulfur atoms is +3, which
is very easily oxidized. Understanding the stoichiometry,
kinetics, and mechanism of its redox reactions is of importance
because this compound is widely used in dyeing and bleaching
processes. But its redox reactions are very difficult to study for
at least two reasons: (i) S2O42 is very sensitive to air oxygen,
articles and books devoted to the oscillatory reactions. How-
ever, we point out that other laboratories have never confirmed
6
,7
these oscillations. Our own efforts repeatedly failed to
reproduce pH oscillations of any kind in a closed reactor when
2
-
we studied the disproportionation of S2O4 in a concentra-
tion range 0.001-0.05 M and in a temperature interval 25-70
-
°
C excluding the air oxygen. Only a minimum, followed by
(ii) it undergoes rather rapid disproportionation in aqueous
a single maximum, appeared on the experimental pH-time
curves. We believe that the thermal decomposition of aqueous
dithionite is not an oscillatory reaction, at least in a closed
reactor.
solution to form more stable sulfur compounds in different
-
2-
oxidation states ranging from HS to SO4 . The main products
of the decomposition are hydrogen sulfite ions and thiosulfate
ions, which are formed according to the generally accepted eq
On the other hand, oxidation of a compound-containing sulfur
atom in a low oxidation state usually shows oscillations if it is
1
:
9
run in a continuous-flow stirred tank reactor (CSTR). For
2
-
+ H O f 2HSO3- + S O3
2-
2
S2O
(1)
4
2
2
example, hydrogen peroxide oxidation of a mixture of hydrogen
sulfite and thiosulfate exhibits chaotic and periodic pH oscil-
lations if a continuous inflow of the reactants and an outflow
of the reaction mixture are maintained in a CSTR.10 Since the
decomposition of dithionite ions is supposed to lead to the
formation of both sulfite and thiosulfate ions,7 a logical
expectation is that an oscillatory reaction may take place in a
mixture of hydrogen peroxide and sodium dithionite. Namely,
Colloidal sulfur has also been identified as a product or
intermediate that forms in small amounts. The rate of reaction
1
is greatly affected by the pH, being slow in alkaline medium
and very rapid at low pH values. Furthermore, the hypothesis
of an autocatalytic kinetics was put forward by Meyer who
1
found an S-shaped curve: An early induction period is fol-
lowed by a rapid autocatalytic stage to completion. This
observation was confirmed by others.2 Moreover, with an
excess of sulfite ion, so as to minimize the effect of decomposi-
tion products, neither the induction period nor the fast reaction
are detectable.
It has been reported that during the decomposition, at elevated
temperatures, the concentration of dithionite ions and the pH
show several small peaks in time, even in a system closed with
2
-
one may expect that the decomposition of S2O4 in aqueous
-7
2-
2-
solution continuously supplies S2O3 and SO3 at a more-or-
less constant rate according to eq 1. These intermediates are
expected to be used up by H2O2 periodically in an autocatalytic
oxidation process. In such a way, periodic concentration changes
would be expected to develop in the reaction system. To test
this hypothesis we carried out experiments both in a closed
reactor and in a CSTR. These experiments have revealed that
the oxidation of dithionite ions by hydrogen peroxide in aqueous
solution is, indeed, oscillatory in a CSTR under a certain range
of experimental conditions.
8
respect to mass. Based on this report, the decomposition of
*
To whom correspondence should be addressed.
1
0.1021/jp012007o CCC: $20.00 © 2001 American Chemical Society
Published on Web 09/13/2001

9184 J. Phys. Chem. A, Vol. 105, No. 40, 2001
Kov a´ cs and R a´ bai
We think that discovery of a new pH oscillatory system is
still of importance, because of the possible application of the
pH oscillations in periodic control of pH-sensitive processes.
For example, pH oscillators might be of importance in the
1
1-13
temporally controlled periodic drug-delivery systems.
Furthermore, understanding the mechanism of the oscillations
in this particular reaction would provide valuable information
for the mechanism of the oxidation of dithionite ions in general.
Here we report on the experimental study and simulation
calculations of the large amplitude pH oscillations exhibited by
the oxidation of dithionite ion with hydrogen peroxide in a
CSTR.
Experimental Section
Materials. Reagent grade NaOH, H2O2 solution, and crystal-
line Na2S2O4 of 85% purity (Fluka) were used without further
purification. The contamination of sodium dithionite is mostly
Na2SO4, which did not disturb our experiments. Some Na2SO3
Figure 1. Measured pH-time traces in a closed reactor. [Na
0.00375; [H ) 0.020 (a), 0.0105 (b) M; The initial pH ) 11.5
was adjusted by adding NaOH to the dithionite solution before the
addition of H . T ) 21.0 °C.
2 2 4 0
S O ]
)
2 2 0
O ]
2-
is also found in the commercial sodium dithionite. Since SO3
2 2
O
-
(
or HSO3 ) appears to be an intermediate in the oxidation
ions are assumed to form in the oxidation according to eqs 2
and 3, respectively. Contribution of reaction 2 to the overall
stoichiometry is always high, but reaction 3 cannot be neglected
under the conditions of our experiments.
process, the sulfite-content might affect the kinetics. We studied
the effect of a small amount of added Na2SO3 on the system’s
behavior. Apart from some small increases in the period length
of oscillations, there was no noticeable effect of the added Na2-
SO3 on the observed kinetics. Doubly-distilled water used in
preparing solutions was first purged with N2 for elimination of
O2 and CO2 impurities. Two input solutions were prepared
daily: one contained H2O2, which was standardized with
permanganate, and the other contained Na2S2O4 and NaOH.
NaOH prevented S2O42 from fast autocatalytic decomposition
in the aqueous stock solution. Throughout the experiments in
CSTR, the solution of S2O42 in its reservoir was bubbled with
nitrogen gas to avoid autoxidation. In such a way we were able
to stabilize the stock solution of sodium dithionite for at least
2
-
2-
+
S2O4 + 3H O f 2SO + 2H + 2H O
(2)
(3)
2
2
4
2
2
-
+
-
S2O4 + 2H O + H f HS O + 2H O
2
2
2
6
2
-
Equation 2 predicts that the reaction is accompanied by a
significant decrease in the pH in an unbuffered reaction mixture.
-
+
On the contrary, reaction 3 consumes H as the protonation of
dithionate ions takes place in acidic medium. In our experiments,
2
-
the initial pH of the S2O4 solution was adjusted at pH 11-12
with NaOH. Most of the kinetic runs were carried out without
a buffer. After starting the reaction by adding excess amount
1
2 h. During storage for a longer time, the pH of the stock
solution decreased, and colloidal sulfur precipitated in an
autocatalytic decomposition process.
2
-
of neutral H2O2 solution to the alkaline S2O4 solution, we
measured a significant decrease in the pH of the reaction mixture
as a function of time, as expected. Shown in Figure 1 are typical
pH-time curves. The pH traces exhibit multiple inflection
points, strongly suggesting that the reaction takes place in several
distinct steps. An induction period and an increasing slope can
be observed during the early phase of the reaction. Then a
plateau appears between pH 7 and 8 indicating a transient
Reactor. The continuous flow experiments were carried out
in a water-jacketed cylindrical-shaped glass reactor with a liquid
volume of 19.5 mL. The reactor was closed with a silicon cap.
A combination glass electrode, a thermometer, two input tubes,
and three output tubes were led through the cap. The batch
experiments were performed in a similar thermostated glass
vessel but with a liquid volume of 50 mL.
Procedures. Reactant solutions were pumped into the reactor
through the inlet tubes by means of a peristaltic pump
2
-
-
buildup of SO3 /HSO3 buffer system in the first stage of the
reaction. This buffer keeps the pH at approximately 7, tempo-
rarily (pK ) 7). Then, a final very rapid pH drop occurs, which
(DESAGA). The excess reaction mixture was removed with the
same pump through three outlet tubes. A magnetic stirrer was
used to ensure uniform mixing. The maximum pumping rate
was used to fill the reactor, and then the rate was gradually
lowered to the desired value. The reactions in the batch system
were initiated by the addition of the H2O2 solution. Constant
temperature during the experiments was established. The pH
and the temperature inside the reactor were continuously
measured and the pH-time data were collected by a computer.
+
-
is due to the autocatalytic H producing oxidation of HSO3
2
-
to SO4 . All portions of the pH traces slow with decreasing
initial [H2O2]0.
If the ratio [H2O2]0/[S2O42-]0 is chosen to be below 2.5, the
final pH drop does not occur at all on the pH-time curve, and
some white sulfur precipitate appears in the reaction mixture.
H2S evolution is also observed when the excess of H2O2 is not
high enough. Formation of S and H2S clearly indicates that the
2-
disproportionation of S2O4 takes place in the reaction mixture
when the excess of H2O2 is not high enough to oxidize all the
intermediates. The reproducibility of the kinetics experiments
is about 10% because the side reactions such as disproportion-
ation and oxidation by air oxygen are difficult to avoid. We
found no pH oscillations in a closed reactor.
Results
Batch Experiments. Formation of colloidal sulfur was not
observed in the reaction mixture when H2O2 was applied in high
excess. This observation is significant because elementary sulfur
usually appears as one of the products of the decomposition
and oxidation of dithionite ions in aqueous solution. Based on
CSTR Experiments. We performed a series of experiments
2
-
the measured pH-change and the mole consumption ratio
in a CSTR, in which both the H2O2 and S2O4 concentrations
and other experimental constraint parameters were varied. In
-
[
∆H2O2]/∆[S2O42 ], a mixture of the sulfate ions and dithionate

Hydrogen Peroxide-Dithionite Reaction
J. Phys. Chem. A, Vol. 105, No. 40, 2001 9185
Figure 2. Measured pH oscillations in a CSTR at different flow rates
Figure 4. pH-time series measured in a CSTR at different temper-
-
3
(
2
k
0
). [Na
2
-
S
2
O
4
]
0
) 0.00375; [H
2
O
2
]
0
) 0.0115 M; T ) 19.1 °C; k
0
)
atures. [Na
2
S
2
O
4
]
0
) 0.00375; [H
; pH of the input solution of Na
(b), 25.9 °C (c).
2
O
2
]
0
) 0.011 M; k
0
) 2.7 × 10
3
-3
-3 -1
-1
.0 × 10 (a), 2.7 × 10 (b), 3.1 × 10
s
(c). The pH of the input
s
2 2 4
S O was 11.5; T ) 20.4 (a), 22.4
Na solution was 11.5.
2 2 4
S O
The effect of temperature on the parameters of chemical
oscillations is of interest because of the theoretical possibility
1
5
of a temperature-independent period length. A phase diagram
is shown in Figure 3 in the temperature-[H2O2]0-plane observed
in a CSTR. The flow system exhibits two stationary steady
states, one with low pH (SSL) and the other with high pH (SSH).
At low temperatures SSL is stable, while high pH steady state
develops at high temperatures. Between the two stationary steady
states an oscillatory state exists. Bistability between the oscil-
latory and steady states can be observed. Oscillations occur in
a very narrow range of the temperature, hardly exceeding 5
degrees.
We examined the effect of temperature on the amplitude and
on the period length of the oscillations. Shown in Figure 4 are
pH-time series obtained at different temperatures when the flow
rate was fixed. The amplitude increases with decreasing
temperature. The length of the high pH stage of an oscillatory
period increases, while the length of the low pH stage decreases
with decreasing temperature. Although such an opposing effect
of the temperature is a necessary precondition of the temper-
ature-independent period length, such behavior could not be
observed in the present reaction. On the contrary, we found that
the overall period length increased with decreasing tempera-
ture.
Figure 3. State diagram in the temperature-[H
2
O
2
]
0
plane. Fixed
was 11.5; k
s ; ] low pH steady state, 4 high pH steady state, b
2
-
0
parameters: [S
2
-1
O
4
]
) 0.00375 M; pH of Na
2
S
2
O
4
0
)
-
3
2
.7 × 10
oscillatory state. Two symbols one on the other indicate bistability.
this way, the conditions for stable pH oscillations were
systematically searched for with success. We found that
hydrogen peroxide concentration should be applied in excess
over dithionite concentration for the oscillations to be sustained.
NaOH should be added to the input solution of S2O42- in order
to avoid spontaneous decomposition in the reservoir. On the
other hand, NaOH is also needed to adjust the initial pH. The
ratio [NaOH]0/[S2O42 ]0 should be kept between 1.6 and 1.9
for the oscillations to occur in the CSTR.
Modeling. We attempted to use an empirical rate law
approach to describe the dynamics of the H2O2-S2O42 reaction
using overall stoichiometric processes rather than elementary
steps. We propose a simple model derived from the stoichio-
metric eqs 2 and 3. The model contains three redox reactions
(M1-M3) and three protonation equilibria (M4-M6). The
composite reactions, their rate laws, and rate constant values
are shown in Table 1. Formation of sulfate (eq 2) is assumed
to take place in two stages (M1 and M2). Reaction M1 leads to
the transient accumulation of sulfite/hydrogen sulfite ions in
slightly alkaline medium. v1 is a hypothetical rate law for M1
with an estimated rate constant value. Further oxidation of
hydrogen sulfite ions in reaction M2 is known to be autocatalytic
-
-
Typical oscillatory time series obtained with different flow
rates at fixed temperature are presented in Figure 2. We
emphasize that the most striking feature of these oscillations is
that the amplitude is extremely high, exceeding 6 pH units
between pH 3.5 and 10 in certain cases. Such a high amplitude
seems to be the largest one on record in the pH oscillator family
reported so far. High amplitude pH oscillations are expected to
be important for the possible control of pH-sensitive processes.
The oscillatory waveform indicates that durations of both the
high pH stage and the low pH stage within an oscillatory period
are rather long, while transitions between the stages are rapid,
which are characteristic for the relaxation oscillations. Fast
transitions between the two stages are also advantageous for
the periodic control of pH-sensitive processes.
+
in H . Reaction M2 is a composite reaction of several other
known pH oscillators. v2 is an empirical rate law, which was
-
14
used in describing the kinetics of the H2O2-HSO3 reaction
1
6
and other pH oscillators. The other channel for the oxidation
of dithionite is reaction M3 that leads to the formation of
dithionate. Reaction M3 is a H consuming composite reaction
+
with an estimated rate law v3. Three known protonation
equilibria are also taken into account (M4-M6). The ratios of

9186 J. Phys. Chem. A, Vol. 105, No. 40, 2001
Kov a´ cs and R a´ bai
Figure 6. Calculated pH oscillations under flow conditions. Input
Figure 5. Simulated traces in a closed reactor. Conditions are the same
as in Figure 1.
concentrations: [NaOH]
0.0115 M; k
) 2.0 × 10 (a) 2.7 × 10 (b), 3.1 × 10
Measured oscillations are shown in Figure 2.
0
) 0.00313; [Na
2
S
2
-3
O
]
4 0
2 2 0
) 0.00375; [H O ]
-
3
-3 -1
)
0
s
(c).
TABLE 1: Composite Reactions, Rate Laws, and Rate
2-
Constants of the H
2
O
2 2
-S O
4
Reaction
very similar. The shape, the period length, and the amplitude
all agree well with their calculated counterparts.
reactions
2
-
-
-
3
H
H
2
O
O
2
+ S
2
O
4
f 2HSO
(M1)
(M2)
(M3)
(M4)
(M5)
(M6)
2-
+
2
2
+ HSO
3
f SO
4
+
2
+ H + H O
2
-
-
Conclusion
2
H
2
O
2
+ S
2
2-
O
4
+ H f HS
2
O
6
2
+ 2H O
+
-
H + SO
H + S
3
h HSO
3
A new sulfur-based oscillator is reported in this paper. The
mechanism of the sulfur-based oscillators is very complex
because of the large number of possible reactive intermediates.
An experimentalist should face considerable difficulties in
monitoring these species spectrophotometrically or potentio-
metrically. Here we applied a pH measurement for collecting
information about the kinetics of such a reaction system.
Because of the complexity and the experimental difficulties,
the sulfur-based oscillators have been among the last to yield
+
2-
-
6
2
O
6
h HS
2
O
+
-
H + OH h H
2
O
rate law
rate constants (at 25 °C)
2
-
-1 -1
V
V
1
) k
) (k
1
[S
O
2 4
][H
2
O
2
]
k
k
k
k
k
k
k
k
k
k
1
2
) 0.60 M
s
+
-]
-1 -1
2
2
+ k2′[H ])[H
2
O
2
2
][HSO
3
) 4.0 M
s
2′ ) 1.0 × 10 M s-1
7
-2
+
2-]
-1 -1
V
3
) (k
3
+ k3′[H ])[H
2
O
][S
2
O
4
3
) 0.050 M
s
4
-2 -1
3′ ) 1.24 × 10 M
s
2
-
+
10
-1 -1
V
V
V
V
V
V
4
) k
4
[SO
3
][H ]
4
) 5.0 × 10
M
s
9
to mechanistic analysis. Rushing et al. have just proposed a
-
3 -1
-4 ) k-4[HSO
3
]
-4 ) 3.0 × 10 s
2
-
+
10
-1
-1
s-1
general model for the oscillatory oxidation of sulfur(-II)
species. Their model is capable of simulating very large
amplitude pH oscillations both in a CSTR and in a closed
reactor, assuming both hydrogen-ion producing and consuming
composite reactions. A significant portion of their model is the
transient formation and further oxidation of hydrogen sulfite
ions by the oxidant. Such a formation of hydrogen sulfite ion
is an important part in the dithionite-hydrogen peroxide system.
We think that the general model may be valid, with some
modification, for the oscillatory systems containing not only
sulfur(-II) species, but also sulfur species of higher oxidation
state.
5
) k
5
[S
O
2 6
][H ]
5
) 1.0 × 10
M
-
6
-5 ) k-5[HS
2
O
6
+
]
-5 ) 3.98 × 10 s
-
11
-1
s-1
6
) k
6
[OH ][H ]
6
) 1.0 × 10
M
-6 ) 1.0 × 10 M s-1
-3
rate constants for the forward and reverse reactions of the
equilibria are chosen to be consistent with the known values of
the equilibrium constants.
Simulations of the Closed System Kinetics. The model
proposed here served as the basis for numerical simulations.
The system of differential equations based on the rate laws of
the component reactions in Table 1 was solved numerically by
17
a semiimplicit Runge-Kutta method with an error parameter
-
5
of 10 . Calculated time points for making the pH-time curves
Acknowledgment. Financial support was obtained from the
Hungarian Science Foundation (OTKA 25076).
were collected in every tenth of a second. For the calculations
-
the initial concentration of OH was derived from the measured
initial pH.
References and Notes
As a comparison of calculated pH-time curves (Figure 5)
with the measured ones (Figure 1) demonstrates that our
simulations are able to reproduce well the shape of the
experimental curves obtained in a closed vessel. But, the pH
change appears to be more rapid in the experiments than in the
calculations.
(
(
(
(
(
1) Meyer, J. Z. Anorg. Chem. 1903, 34, 45.
2) Jellinek, K. Z. Anorg. Chem. 1911, 70, 93.
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65 (554), Part 2, 496.
Simulations of the pH Oscillations in a CSTR. To simulate
the kinetic behavior in a CSTR, we added appropriate flow terms
(6) Lem, W. J.; Wayman, M. Can. J. Chem. 1970, 48, 776.
(7) Lem, W. J.; Wayman, M. Can. J. Chem. 1970, 48, 2778.
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to the model including input flows for H2O2, S2O42 , and OH
-
-
and output flows for all the variable species. Figure 6 shows
calculated pH oscillations in a CSTR. The agreement between
the experimental and simulated oscillations is quite good. The
calculated and measured concentration range of oscillations are
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104, 11561.
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Hydrogen Peroxide-Dithionite Reaction
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(
11) US Patent 6,068,853, 2000.
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39.
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