J . Phys. Chem. 1987, 91, 6034-6040
6034
temperatures (down to 200 K), in the same pressure range as used in this work, and in bath gases of high collisional efficiency, which should help to resolve any remaining ambiguity in the magnitude of kl" and the structure of the activated complex.
Acknowledgment. W e thank the S E R C and Shell Research for a research studentship to M.K., Dr. C. Morley of Shell Research for his continuing interest, and Drs, R. G . Gilbert and D. M. Golden for helpful discussion.
Appendix 1 Calculation of STfrom n,. The parameter STis given by19
ST = 1 + T(d In q,,+/dT)
(All
where qvt is the vibrational partition function of the activated complex. The experimental temperature dependence of the rate constant for an association reaction is usually expressed in the form
k , = A , ( T / 3 0 0 K)"- exp(-t,/kT)
(A2)
while the transition-state theory expression is
km = (kT/h)[q'/[q(CH,)q(O,)lI exp(-t.,/kT) For completeness, an energy barrier to association,
e,,
643)
is included,
and the parameters q are the total partition functions for the complex, for CH3, and for 02. d In k"/dT is evaluated from both equations A2 and A3, and the two expressions are then equated. If it is assumed that all three species involved have classical translational and rotational partition functions and that there is no significant temperature dependence in the electronic partition functions and in the geometry of the complex, substitution in ( A l ) gives ST =
n,
+s/z + T[d In qV(CH,)/dT + d In qv(02)/dT]
The bracketed term can be identified with the vibrational energy of the fragment molecules, CH3 and 0,; ST is then given by ST =
n,
+ '/2 + Uv(CH,)/kT + U v ( 0 2 ) / k T
Appendix 2 Parameters Used in the Analysis of the Falloff Curves. Eo = 10 734 cm-'.I6 Molecular frequencies/cm-': for CH302,2968, 2968,2844,1453,1440,1414,1183,1118, 1112,902,492, 2o0,30*3' 1580.33 for CH,, 3162, 3162, 3044, 1396, 1396, 606;32for 02, (AE)do, = 285 cm-I, obtained by assuming that p, = 0.3 at 300 K." ( AE)downwas assumed to be independent of temperature over the experimental range covered. Registry No. (CH,)$O, 67-64-1; CH,,2229-07-4; 01, 7782-44-7; Ar, 7440-37-1.
Dynamical Behavior in the Chlorite-Iodide Reaction: A Simplified Mechanlsm' Ofra Citri and Irving R. Epstein* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: April 7, 1987)
A mechanism is proposed for the reaction of chlorite and iodide ions. This scheme, which involves eight elementary steps and six principal species, is considerably simpler and yields better agreement with experiment than the mechanism proposed earlier by Epstein and Kustin. Our new mechanism successfully simulates the observed clock reaction behavior and recovery of [I2] under batch conditions and the bistability and oscillation found in a CSTR. It also sheds light on some of the effects observed in this reaction on varying the extent of mixing. Because of the relative simplicity of the mechanism, it should be possible to combine it with models of other reactions such as bromate-iodide, or of other processes such as stirring, to yield insights into more complex dynamical phenomena.
Introduction The chlorite-iodide reaction is the "minimal oscillator"* of the chlorite-iodine group, the first systematically designed family of chemical oscillator^.^ Because of its relative simplicity, the reaction has been used as a model system for experimental studies of a variety of nonlinear phenomena. These include investigations of propagating waves in excitable media," of stirring and mixing effects on bistable and oscillatory behavior in a stirred tank reactor (CSTR),5-7 and of critical slowing down.* The chlorite-iodide (1) part 42 in the -Systematic of Chemical Part 41: Edblom, E. C.; Gyargyi, L.;Orban, M.; Eptein, I. R. J. Am. Chem. SOC. 1987, 109, 4876. (2).Epstein, I. R.; Orbin, M. In Oscillations and Travelling Waves in Chemrcal Systems; Field, R. J., Burger, M., Eds.; W h y : New York, 1985; p 257. (3) Orbin. M.; Dateo, C. E.; De Kepper, P.; Epstein, I. R. J . Am. Chem. SOC.1982, 104, 5911. (4) Weitz, D. M.; Epstein, I. R. J. Phys. Chem. 1984, 88, 5300. ( 5 ) Roux, J. C.; De Kepper, P.; Boissonade, J. Phys. Lett. 1983,97A, 168. ( 6 ) Menzinger, M.; Boukalouch, M.; De Kepper, P.; Boissonade, J.; Roux, J. C.; Saadaoui, H. J . Phys. Chem. 1986, 90, 313. (7) Luo, Y.;Epstein, I. R. J . Chem. Phys. 1986, 85, 5733.
0022-3654/87/2091-6034$01.50/0
reaction is also one of the oscillators in the couoled bromatechlorite-iodide system, which shows an extraordinarily rich variety of dynamical Our ability to understand the considerable body of experimental data about the chlorite-iodide system depends heavily upon the availability of a mechanism for the reaction. Such a mechanism, involving 13 elementary steps and 9 independent chemical species, was recently proposed by Epstein and Kustin.'* Beck and Rgbai', have pointed out that the Epstein-Kustin mechanism fails to account for the partial regeneration of iodine that occurs in the batch chlorite-ibdide reaction. They propose inclusion of an additional species, ICl, to remedy this discrepancy. We present here an alternative mechanism that, like the earlier scheme,I2 invokes no radical species. It differs primarily in the (8) Laplante, J. P.; Borkmans, P.; Dewel, G.; Gimenez, M.; Micheau, J. C. J . Phys. Chem. 1987, 91, 3401. (9) Alamgir, M.; Epstein, I. R. J . Am. Chem. SOC.1983, 105, 2500. (10) Alamgir, M.; Epstein, I. R. J . Phys. Chem. 1984, 88, 2848. (11) Maselko, J.; Alamgir, M.; Epstein, I. R. Physica D (Amsterdam) 1986, 19D, 153. (12) Epstein, I. R.; Kustin, K. J . Phys. Chem. 1985, 89, 2275. (13) Beck, M. T.; RBbai, G. J. Phys. Chem. 1986, 90, 2204.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 6035
Dynamical Behavior in the Chlorite-Iodide Reaction
r
I
I
1 ' " " "10 . '
1
I
c
2-
0
@v
20
IO
time (min)
IO 9
,
I
1
I
:
-lot! 0
,
,
,
,
!
,
,
10
,
,
!
,
,
1
20
TIME (min)
Figure 1. [I-] and [I2] as functions of time for a batch reaction at pH 3.3 with initial conditions [I-] = 4 X lo4 M,[C102-] = 2.5 X lo4 M: (a) experimental, [I2] shown as absorbance at 460 nm, [I-] calculated from potential of iodide selective electrode; (b) calculated.
set of reactions proposed to describe the oxidation of iodine by chlorite and in the elimination of the intermediate IC102, whose existence has been called into question e1~ewhere.l~The present mechanism is somewhat simpler, consisting of eight elementary steps and only six independently variable concentrations. It gives excellent qualitative and quite good quantitative agreement with both the flow results (oscillation, bistability) and with the batch data of Beck and R~5bai.l~ The relatively small number of variables offers promise for incorporating the mechanism into simulations of some of the more complex experimental data referred to above. We report elsewhere on our success in combining this mechanism with a modelI5 for the bromate-iodide oscillator to simulate birhythmicity and compound oscillations in the bromate-chloriteiodate system. (14) Ribai, G.; Beck, M. T., submitted for publication. (15) Citri, 0.;Epstein, I. R. J . Am. Chem. SOC.1986, 108, 357.
I
/
,
I
1
zxio-'
4xio-' LI-10
Figure 2. Bistability and hysteresis in a CSTR as [I-I0 is varied with [CIOJo = 2.5 X lo4 M, pH 3.3, ko = 5.4X lO-'s-': (a) experimental, (b) calculated.
Experimental Background The behavior of the chlorite-iodide system under both batch and flow conditions has been summarized by Epstein and Kustin.I2 Typical experimental traces showing the clock reaction in batch and bistability and sustained oscillation in a CSTR appear in Figures l a , 2a, and 3a, respectively. The reaction takes place through two overall stoichiometric processes. The first is the oxidation of I- to I,: C10,- + 41- + 4H' 212 + C1- + 2H20 (A) The second is the further oxidation of I, to IO3-: %lo2- + 21, + 2 H 2 0 5C1- + 4103- + 4H+ (B)
-
6036 The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 TABLE I: The Reaction Mechanism no. reaction (1) Ht + Cl(II1) + IHOC1 + HOI (2) HOI + I- + Ht s I2 + H 2 0
l a u
Citri and Epstein
-
1.1-
(3) (4) (5) (6) (7) (8)
-
+ HOI HOC1 HOI + CI+ I- + Ht S 2HOI HOI + IO3- + Ht + HOI IOF + I- + 2Ht + HOC1 10,-+ CI- + 2Ht
HClOz HOC1 HI02 2HI02 HI02 HI02
+ I-
-+
- -
ki, k+" 5 x 102 ( 5 X 1O9[Ht])/
([Ht] + 2 X lo-)), (1.6 x 10-31/ ([H+] + 2 X 10-31 6 X lo7 1.4 X lo8 1 X IO6, 25 3 x 103 2.3 X lo2 1 x 103
"All concentration units in M, times in s
Time ( m i n ) 101
,
I
I
I
I
i b 10
stirring rate is lowered. Menzinger et aL6 studied the effects of premixing the reactants before allowing them to enter the reactor and found that premixing dramatically decreased the magnitude of the changes in the bistable region produced by varying the stirring rate. Luo and Epstein7 extended these studies to include the oscillatory region and found, in addition to the existence of a previously unnoticed third steady state, that the state of mixing acts as a bifurcation parameter much like the flow rate or the input concentrations. We shall not explicitly attempt to simulate these experiments here, since that would require introduction of additional models for the mixing. We shall, however, comment briefly on how our mechanism may relate to the above observations.
I 0
I
I
I
20
40
60
I
TIME (min)
Constructing the Mechanism Choice of Species. Since our aim was to construct a simplified mechanism relevant to the dynamical behavior described above, we restricted our initial consideration to the halide ions, the halogens 12,C12, and IC], and the most stable of the oxyhalogen species. The radical C102 was not included in our scheme for the following reasons. The sequence that leads to C102 formation is thought to bel6 HOCl
Figure 3. Typical oscillations in [I2] (absorbance at 460 nm) and I-
(measured with iodide-selectiveelectrode). Each division corresponds to 1 min: (a) experimental, (b) calculated for [I-lO= 1.8 X loe3 M, [CIO2-I0 = 6.0 X
M, pH 1.5, ko = 1.8 X
< [C102-] / [I-] C
Cl2
0.8
(C)
which, after the completion of process A, leaves a stoichiometric ratio 0 < [C10,-]/[1,]
c
or
S-'.
Traces like those in Figures la-3a are obtained when chlorite ion is in stoichiometric excess for reaction A, but the remaining chlorite is far from sufficient for reaction B to go to completion. Typically, we have 0.25
1.1
+ ClO; + H+
(D)
for process B. At higher ratios the I2 in batch disappears abruptly and fails to recover, while in flow (at least in the experimentally accessible flow rate range, ko < 0.1 s-l) no oscillations occur and only a single steady state can be detected at any given set of conditions. More recently, Beck and RBbaii3~l4 have studied the kinetics of (A), (B), and related reactions. For reaction B they obtain an extremely complex rate dependence on the p H and on the concentrations of the participating species that does not lend itself to expression as a single rate law. Most of their experiments, however, were performed under conditions of large chlorite excess ([CIOz-]/[Iz]) > 2.5) where the radical C102 is present in significant concentrations. Since we are primarily interested in modeling the bistable and oscillatory behavior in a CSTR where relations C and D prevail, these studies are of limited relevance to the present investigation. Roux et aL5 showed that the range of flow rates over which the chlorite-iodide system is bistable in a CSTR decreases as the
followed by
+ (2102-
-
+ c102-
-
C1202+ H 2 0
c1202 + c12c102
(E) ( F)
+ c1-
(G) The rate constants for these reactions are not well established, but all the reported values make reactions E-G significantly slower than the competing reactions with iodine species (Table I, reactions 1, 3, and 4) under the conditions of interest here. While chlorine dioxide formation is undoubtedly of significance when chlorite is in excess, it should be permissible to neglect that species under the conditions of the experiments we seek to model in this work. We have not investigated the possibility that the low concentrations of C102that will be present under our conditions may play an essential role in the reaction. Some of the oxyhalogens have more than one protonated form, and the strong and complex dependence on pH may result in part from differences in reactivity of these different protonated species. The pK,'s of HC102, HOC], HOI, and H201+are 2.0, 7.5, 10.6, and 1.3, re~pective1y.l~These data suggest that in the pH range of interest, 1.5 < pH C 5 , the dominant forms of I(1) and Cl(1) are HOI and HOCl, respectively, while Cl(II1) is present as significant amounts of both C102- and HC102. We assume that the protonation-deprotonation reaction (21202
H+ + C102-
F?
HCIOz
(HI
is rapid enough to be at equilibrium, so that (16) Gordon, G.;Kieffer, R.G.; Rosenblatt, 0. H.Prog. Inorg. Chem. 1972, 15, 201. (17) J . Phys. Chem. Ref.Dora 1982, 11, Suppl. 2.
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 6037
Dynamical Behavior in the Chlorite-Iodide Reaction
-
to give the autocatalytic net reaction (3) HC102 and
(J) All of the I(II1) was taken to be present as HI02. Recent ~ o r k , ~ *however, ,'~ suggests that H2102+may be present to a significant extent under our conditions. Rgbai and BeckI4 report that IC1 can be detected as one of the intermediates in reactions A and B. Another recent studyZoalso suggests that the first step in the reaction between I- and HOCl gives ICl, which then hydrolyzes to yield HOI and C1-. We found that including the following reactions (with step 9 replacing step 4)
+ Cl-- H+ IC1 + H 2 0 k9 = 1.4 X lo8 M-' s-I2O IC1 + H 2 0 s HOI + C1- + H+ klo = 1 X M
HOI
IC1
+ I-
-
(9)
(10)
I2 + C1-
kl, = 8
X
lo8 M-I s-l 2o (1 1)
caused very small differences in some of the calculated concentrations, but otherwise gave results identical with those obtained with eq 1-8. Apparently IC1 behaves simply as another form of I(1) and, at this level of mechanistic detail, plays a role indistinguishable from that of HOI. Invoking Occam's razor, we therefore chose to omit IC1 and steps 9-1 1 from our simplified mechanism. Similar considerations apply to I< and C12. Triiodide ion is clearly present in the reaction, as indicated by the yellow color of the high iodide steady state, and thermodynamic considerations suggest that molecular chlorine should form in significant concentration. However, including the reactions I2 + IHOCl
+ 13-
(12)
+ C1- + H+ a C12 + HzO
(13)
with their known rate constants21J2had no effect on the calculated results. We did not attempt to include reactions between C12 or 13-and other species in our mechanism. General Outlines. In developing the mechanism we were guided by the scheme proposed by Kern and Kimz3to account for both the autocatalytic term in the rate law of process A and the subsequent rapid consumption of I2 According to this scheme, there is no direct reaction between Cl(II1) and 12. Instead, iodine is in rapid equilibrium with its hydrolysis products24 HOI
+ I- + H+ + I2 + HzO
and the key reaction is HClO2
+ HOI
Reaction 3 is followed by HOCl
+ I-
-
HI02
+ HOCl
(2)
(3)
+ C1-
(4)
+ H+ + 2HOI
(5)
HOI
and
HI02 + I-
(18) Noszticzius, Z.; Noszticzius, E.; Schelly, 2.A. J. Phys. Chem. 1983, 87, 510. (19) Furrow,S., submitted for publication. (20) Kumar, K.; Day, R. W.; Margerum, D. W. Inorg. Chem. 1986, 25, 4900. (21) Myers, 0. E. J . Chem. Phys. 1958, 28, 1027. (22) Eigen, M.; Kustin, K. J. Am. Chem. SOC.1962, 84, 1355. (23) Kern, D.; Kim, C. H. J . Am. Chem. SOC.1965,87, 5309. (24) Elementary steps are numbered in the text in agreement with the numbering in Table I.
+ 21- + H+ + HOI
+ (4) + (5): C1- + 3HOI
(K)
On adding twice reaction 2 and the protonation of chlorite ion, reaction H , we obtain the stoichiometry of process A. This autocatalytic route to I2 production begins to dominate the uncatalyzed route (1) (4) 2 X (2)
+
+
H+ + C102- + I-
-
HOCl
+ HOI
(1)
as I- decreases and reaction 3 becomes faster than reaction 1. As the reaction proceeds, [I-] decreases still further, causing reaction 2 to shift to the left in order to maintain the equilibrium. I2 and I- are then oxidized to HOI and HIO? If C l o y is in excess, the oxidation continues all the way to IO3-. When relation C holds, HOI and H I 0 2 react among themselves to give IO3- and partial regeneration of 12. The choice of a set of species constrains us to a limited (though still quite large) set of plausible elementary steps that can be combined to yield the desired stoichiometry. Keeping in mind the known thermodynamic data and the available experimental rate constants, we considered a number of possible mechanisms. After extensive simulations, we found that the mechanism in Table I gives the best agreement with the experimental kinetic results over a wide range of conditions. In general, where data were available in the literature, the assignment of rate constants was made by varying the simulation parameters within the limits set by the experimental uncertainty. However, the values ultimately chosen for k5 and especially for k6 differ significantly from those reported earlier. It is difficult to separate the discussion of these rate constant assignments from that of the simulation results. We therefore defer .detailed consideration of k5 and k6 as well as k8, which is related to k5 and k6 and is the only rate constant for which experimental data were unavailable, to the next section. The other rate constants in the mechanism of Table I were chosen in accordance with the reported experimental values as follows: kl and k3. These values were taken from the experimental study of Kern and Kim.23 Step 1 is the rate-determining step of the uncatalyzed term, while step 3, which is assumed23to involve only chlorous acid, is rate-determining for the autocatalytic term in the experimental rate law for reaction A. Kern and Kim studied reaction A at pH L 4, where Cl(II1) is present in its unprotonated form as C102-. They found the rate law for the uncatalyzed term to be R1 = 5 X 102[H+][C1(III)][I-]
(L)
If only HC102is reactive as assumed by Kern and Kim, this rate law becomes 5[H+][Cl(III)] [I-] R1 = 5[HClO2][I-] =
[H']
+ 0.01
(MI
In our batch simulations kl and k3 determine the time required for [I2]to reach its maximum, while in flow they control the oscillation period. Larger values cause [I2] to peak earlier in batch and shorten the period of oscillation. Writing the rate law for step 1 as suggested by Kern and Kim23in the form of eq M results in too long an oscillation period. We therefore chose to use eq L, which implies that C102- and HC102 are equally reactive. Even with this modification, the period of the simulated oscillations is longer than found experimentally. It is likely that the uncatalyzed rate should contain a term in [H+I2 which is negligible at pH 1 4, but which becomes significant at lower pH, i.e., R1 = k,
[H+]2[C1(III)][I-] [H+l[Cl(III)I [I-] (N) + kb [H'] + 0.01 [H'] + 0.01
This suggestion is supported by kinetic studies of the analogous reaction between chlorite and b r ~ m i d e . ~ ' The , ~ ~ chlorite-bromide (25) Simoyi, R. H. J . Phys. Chem. 1985, 89, 3570.
6038 The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 TABLE II: Literature Values of Rate Constants for Oxyiodine Reactions
ref 18" k5, M-2 s-l k-5, M-I s-' k6, M-I S-I k,, M-I s-l
1 X lo6 9 x 107
5.4 130
ref 19 5
X
loPb
25 f 5 (0.3 f 0.2)/[H+], 0.036 < [H+] < 0.58M 230 f 20, 0.1 < [ H'] < 0.4M
[H'] = 0.15 M. bNot measured directly, employed in simulations.
studies were done at much higher acidities (0.01 < [H'] < 1 M) than the chlorite-iodide experiments but still gave a rate first order with respect to [H'], even though Cl(II1) was completely protonated. For simplicity we did not include the additional kb term in our model, but the above discussion may explain why we obtain good agreement with the time scale of the batch experiments (pH > 2) on the one hand and seriously overestimate the oscillation period (pH < 2) on the other. k2 and k-,. Reaction 2 is at equilibrium at all times during our simulation. Hence only the ratio K, = k2/k-2 is of significance. We chose the most recently reported value of K , = 3.2 X I O l 3 M-*.,' At the acidities considered here, the sequence of bimolecular steps resulting in eq 2 reaches the diffusion-controlled limit, and the appropriate expression is hence 5 X 109[H+] The expression for k-2 then follows from the equilibrium constant. k4. The value employed for k4 is that of the most recently reported experimental determination.20 k+ For k-5 we chose the value reported by Furrow.Ig The reverse of step 5 , Le., the disproportionation of HOI, is significant during the slow part of the I, recovery in batch. k7. The two values reported for are in reasonable agreement (see Table 11), and we did not find it necessary to depart from the measured rate constant. Reaction 7 contributes W e to the behavior of the system under most conditions and can even be omitted without causing significant change. k718319
Calculations and Results With the choice of species described above the eight-step mechanism in Table I yields a set of six rate equations for [Cl(HI)], [HOCl], [I-], [HOI], [I,], and [HI02]. Since the experiments were performed in buffered solution, [H+] was taken to be constant and the pH dependence introduced by multiplying each rate constant by the appropriate [ H+]-dependent factor. Iodate and chloride ions were considered to be inert products. [C102-] and [HC102] are related to total [Cl(III)] via eq H, I, and J. After introducing flow terms to account for the input of I- and C102- and the outflux of all species, we integrated the resulting six equations using Hindmarsh's version of the Gear algorithm.28 The batch simulations are shown in Figure lb. They are in considerably better agreement with the experimental results of Figure la29than are the simulations obtained with an earlier mechanism.I2 The present calculations reproduce almost quantitatively the time of the [I2] peak, the recovery of both [I2] and [I-] after the rapid drop, the magnitudes of the changes, and the shapes of the curves. In particular, the [I2] recovery found experimentally over a range of conditionsI3can be simulated without invoking IC1 in the mechanism. This is not to say that the latter species is not present nor that it might not be necessary for a more (26) Valdes-Aguilera, 0.;Boyd, D. W.; Epstein, I. R.; Kustin, K. J . Phys. Chem. 1986, 90, 6702. (27) Palmer, D. A.; van Eldik, R. Inorg. Chem. 1986, 25, 928. (28) Hindmarsh, A. C. G E A R Ordinary Differential Equation Solver; Technical Report No. UCM-30001, Rev. 2; Lawrence Livermore Laboratory: Livermore, CA, 1972. (29) Dateo, C. E.; OrbPn, M.; De Kepper, P.; Epstein, I. R. J . Am. Chem. SOC.1982, 104, 504.
Citri and Epstein detailed description of the system. It does appear, however, that the experimental results obtained to date can be simulated with the sort of simplified mechanism presented here. In Figure 2 we compare the experimental and calculated hysteresis behavior in a CSTR. Again, better agreement is obtained than with the Epstein-Kustin mechanism,', particularly for the difference in concentrations between the two steady states. Both mechanisms, however, underestimate the width of the bistable region. Our simulations of the oscillatory behavior are shown in Figure 3b. Again the magnitude of the calculated [I-] oscillations is in far better agreement with experiment than are the results of earlier simulations.I2 Even more impressive is the ability of the present scheme to reproduce the shape of the double peak oscillations seen in [I,]. The previous calculations gave only a very rough approximation to this feature. The present mechanism yields the following picture of how the batch behavior arises. The autocatalytic nature of the I2formation results from the autocatalytic sequence (K) that produces HOI (see previous section). As long as [HOI] is high enough, formation of HOI leads to generation of I,. As the reaction proceeds, [I-] and [HOI] increase so that reaction 3 is no longer rate-determining, and the sequence (K) ceases to be autocatalytic. The reaction then becomes autocatalytic in HIO, according to the sequence 2 X (3) + 2 X (4)+ (5) + 2 X (H), or 31-
+ 3H+ + 2ClOT + HIO,
-
2HOI
+ 2C1- + 2HI0,
(0)
Iodine is then hydrolyzed in the reverse of reaction 2 to compensate for the rapid decrease of I-. The net result is the oxidation of Iand I2 to HOI and H I 0 2 . If the concentrations of Cl0,- and HOCl are high enough at this stage, HOI and HIO, undergo further oxidation to IO3- via reactions 3 and 8. HI02
+ HOCl
-
103-
+ C1- 4- 2H+
(8)
In the case that leads to the more interesting dynamical behavior, the oxychlorine species are present in relatively low concentrations (because of relation C) and HOI and HIO, react among themselves according to steps 6 and 7 to give IO3- and partial regeneration of I,. 2HI0, HIO,
-
+ IO3- + Hf IO3- + I- + 2H+
HOI
+ HOI
-
(6) (7)
Sequence 0 is the key process in the transition from the high iodide state to the low iodide state in both the bistable and the oscillatory regions. During the oscillations this transition is followed by a brief period in which [HOCI] and [HOI] slowly decrease due to reactions 2 and 4 until the input flow of iodide exceeds the rate at which it is consumed in these reactions (k,[I-], > (k2[H+][HOI] k,[HOCl]J[I-I). At this point [I-] increases sharply, and the system switches back to the high iodide state where process K dominates until 0 takes over again. k5, k6, k8. The identification of the transition from the high iodide state to the low iodide state with process 0 accounts for the sensitivity of the system's behavior to k5, k6, and k8. At the transition point [HIO,] increases sharply, and the subsequent behavior depends strongly on the way HIOz is consumed, Le., on the ratio between the rates of the reducing (steps 5 and 6) and oxidizing (steps 7 and 8) routes. Reactions 5-7 also play important roles in other iodine-containing oscillators. For this reason, they have been investigated recently by Noszticzius et aLL8and by Furrow.Ig The results obtained are summarized in Table 11. We found that, while it is possible to reproduce the main qualitative features with values of k5 and k6 that are closer to those in the table, the agreement between the simulated and experimental results is significantly improved by decreasing k5 and increasing k6. Reaction 5 produces two molecules of HOI and thus, through the rapid equilibrium of eq 2, pushes the system toward the low iodide state. If the other rate constants are not altered to compensate for a high value of k5, then the system remains in the low iodide state, and no oscillations are observed. This compensation can be accomplished
+
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 6039
Dynamical Behavior in the Chlorite-Iodide Reaction
I
,
I
b
t
t
-\
2L m
Y
-
{ TIME(src)
0 ._
,
,
,
.
.
I
_
Figure 5. Transition from small-amplitude, high-frequency (HF) to large-amplitude,low-frequency (LF) oscillations as calculated with the mechanism of Table I at pH 1.5, [ClOz-l0= 5 X lo4 M, [I-] = 1 X lo-' M. Initially, ko = 3.24 X ~ O - ' S - ~ . At point a, ko is changed to 3.26 X lo-' s-l, and at point b it is increased to 3.28 X lo-' s-'. No hysteresis < ko < 3.28 X is observed. The HF oscillations occur for 1 X s-l, the LF oscillations for 3.28 X lo-' < k,j < 4.6 X lo-' s-].
I b
0
1000
2000
3000
4000
TIME(sec)
Figure 4. Effects of changing rate constants on calculated batch and flow behavior. Solid curve, k5 = 1 X lo7 M-'S-', k6 = 0.3 M-' s-'/[H+], k8 = 5 x 107 M-1 s-1 ,0ther rate constants as in Table I. Dashed curve, k6 = 0.3 M-2 s-I/[H+], k14 = 1 X lo4 M-l s-l, other rate constants as in Table I. (a) Batch, conditions as in Figure 1. (b) Flow, concentrations as in Figure 3b, ko = 2.1 X lo-' s-l (solid curve), 9.5 X lo4 s-l (dashed curve).
by choosing a high value of k8,but since step 8 yields only inert products, in batch this route results in equilibrium being reached too soon (no I2recovery), while in flow it reduces the amplitude of oscillation as shown in Figure 4. Iodine recovery and largeamplitude iodide oscillations apparently require a relatively low value for k8. Oscillations can also be simulated with the reported value of k6 and a low value of kg if one includes the reaction
C102- + HI02
-
HOC1
+ IO3-
(14)
In this case, the amplitude of the [I-] oscillations is reasonable, but the waveform (dashed line, Figure 4) is distorted. Reaction 14 is somewhat analogous to reaction 6 , but, because of the high concentration of chlorite ion, retards the buildup of HI02, thereby distorting the reaction profile. We therefore chose to omit reaction 14 while keeping k8 low and selecting for k5 the lower limit given by Noszticzius et a1.18 For k6 we took a pH-independent value about 2 orders of magnitude higher than that reported in Table I1 for pH 2.
Discussion The mechanism proposed in this paper gives very good agreement with a wide variety of experimental results on the chlorite-iodide reaction. It represents, we believe, a significant improvement over earlier mechanistic proposals. Perhaps the most worrisome issue that remains in the present mechanism lies in the
difference between the reported kS and k6 and the values assigned here. This discrepancy can be attributed, at least in part, to the oversimplifications of the present model, from which several reactions and species have been omitted. For example, k6 probably represents several elementary steps and/or pathways that together yield the stoichiometry of reaction 6. A second potential source of disagreement lies in the interpretation of the experimental studies. Since it is not feasible to isolate or to monitor directly the concentration of HI02, the rate constants must be inferred by a variety of indirect means. The behavior obtained in our simulations resembles most closely that found experimentally in the non-premixed mode at moderate stirring rates.' Premixing and higher stirring rates tend to favor the low iodide steady state to a greater extent than found in our calculations. The fact that the chlorite-iodide reaction is more sensitive to the stirring rate than the bromate-iodide reaction probably results from the fact that the key autocatalytic processes K and 0 involve the input species C102- and I-. In the bromate-iodide reaction neither of the input species participates in the auto~atalysis.'~ Although no attempt was made to model mixing effects explicitly, our calculations do afford some insights into results on stirring and premixing effects in the chlorite-iodide system. Luo and Epstein' found a third or medium iodide (MI) steady state in addition to the high (HI) and low (LI) iodide states described earlier. Our simulations show, first, that in the neighborhood of the stoichiometric [C102-]o/[I-]o ratio for reaction A small changes in that ratio lead to very large (several orders of magnitude) changes in the steady state [I-] and that relaxation to the new steady state can be quite slow. We did obtain evidence for the M I state, though we did not find the reported bistability between MI and LI. One particularly suggestive set of calculations involved the inclusion of reaction 14 with a rate constant of 1 X lo4 M-I s-l, fixed input concentrations [I-]0 = 1 X M, [H+], = 0.03 M, and a flow rate ko = 3 X s-l. When [C102-], was varied from 4.2 X lo4 to 6.6 X lo4 M, the following sequence of state was observed: HI L F M I H F LO, where LF and HF represent large amplitude (6 orders of magnitude in [I-]), long period (-220 s), and small amplitude (2 orders of magnitude), short period (-75 s) oscillatory states, respectively. The L F HF transition was also observed in simulations in which eq 14 was omitted and the flow rate was varied while holding all the input concentrations fixed. This behavior, shown in Figure 5, is reminiscent of that found experimentally by Menzinger and Giraudi30 using the stirring rate as a bifurcation parameter.
- - - -
-
(30) Menzinger, M.; Giraudi, A. J . Phys. Chem. 1987, 91, 4391.
6040
J . Phys. Chem. 1987, 91, 6040-6042
In view of the central importance that the chlorite-iodide reaction has come to assume in the study of nonlinear dynamical phenomena in chemical systems, the mechanism proposed here is likely to be subject to testing in a variety of contexts. While it may well prove profitable to elaborate the mechanism by including additional species like 13-or ICl, distinguishing between protonated forms like C102- and HC102or adding additional steps like reaction 14, there may be equal or greater utility in simplifying the model still further in order to facilitate its incorporation into
more sophisticated schemes to describe other aspects of the system's behavior.
Acknowledgment. We thank Kenneth Kustin and Yin Luo for illuminating discussions and M. T. Beck, S. Furrow, J. P. Laplante, and M. Menzinger for making their results available to us prior to publication. This work was supported by Grant CHE-8419949 from the National Science Foundation. Registry No. C102-, 14998-27-7; I-, 20461-54-5.
An All Sulfur Chemistry Based Oscillator Q. Ouyang and P. De Kepper* Centre de Recherche Paul Pascal (CNRS), Universite de Bordeaux I, 33405 Talence Cedex, France (Received: April 22, 1987)
A new chemical oscillator based on sulfur chemistry is reported. The system includes sulfide ion, persulfate ion, and silver(1) ion in an aqueous solution. Sustained oscillations and bistability are observed when performed in a continuous-flowstirred tank reactor (CSTR). Bistability and oscillatory regions exchange in a cross-shaped diagram. Both potential (Pt and pH electrode) and optical measurements are made. Elements of a mechanism are proposed.
Introduction The number of oscillating chemical reactions has tremendously increased since 1980. This expansion has been favored by the now widespread use of continuous stirred tank reactors (CSTR) and the discovery of a systematic method to design new chemical oscillators.'*2 Most of these reactions are based on halogen chemistry, a reminiscence of early d i s c ~ v e r i e s . ~ , ~Our new chemical oscillator is based on the silver ion catalyzed oxidation of sulfide by persulfate. Recently, several other chemical oscillators based on sulfur chemistry were reported. They include the air oxidation of sulfide ion to polysulfide catalyzed by methylene blue,5 the oxidation of sulfide ion by hydrogen peroxide,6 the copper( 11) catalyzed oxidation of thiosulfate' or thiocyanide8 by hydrogen peroxide, and the oxidation of sulfide by b r ~ m a t e . ~ The reaction reported here initially involves Na2S, Na2S208, Ag2S04, and HC104. It shows both bistability and sustained oscillations in the potential of a Pt electrode and in optical density when performed in a continuous-flow stirred tank reactor (CSTR). Bistability and oscillatory regions exchange in a cross-shaped diagram.' Experimental Section Materials and Apparatusi Analytical grade chemicals from Prolabo were used without further purification. The sulfide stock solutions were standarized by titrating an iodine solution generated by a known amount of K I 0 3 in an acidic (HC104) KI solution. The stock solutions of sodium sulfide and of sodium persulfate were kept in neutral medium and prepared frequently because of possible decomposition of SZOs2-and evolution of H2S. A known amount of HC104 was added in the Ag2S04solution to adjust the pH. The CSTR experiments were carried out in a 30-cm3 reactor thermostated at 30 f 0.1 "C. The stirring rate was maintained (1) Boissonade, J.; De Kepper, P. J . Phys. Chem. 1980, 84, 501. (2) De Kepper, P.; Epstein, I. R.; Kustin, K. J. Am. Chem. Soc. 1981, 103, 2133. (3) Bray, W. C. J. Am. Chem. SOC.1921,13, 1262. (4) Belousov, B. P. Sb. Ref. Po. Radiatis. Med. Medgiz, Moscow 1958, 145. ( 5 ) Burger, M.; Field, R. J. Nature (London) 1984, 307, 720. (6) Orbin, M.; Epstein, I. R. J . Am. Chem. SOC.1985, 107,2302. (7) Orbin, M.; Epstein, I. R. J . Am. Chem. SOC.1987, 109, 101. (8) Orban, M.J . Am. Chem. SOC.1986, 108, 6893. (9) Simoyi, R. H.; Noyes, R. M. J . Phys. Chem. 1987, 91, 2689.
at 600 rpm throughout these studies. The reactor was fed with the aid of a Gilson peristaltic pump through three tubes, each carrying a separate stream of sodium persulfate, sodium sulfide, or silver sulfate. No air gap was present between the surface of the reacting solution and the cap of the reactor. The reaction was monitored by measuring simultaneously the potential of a platinum electrode versus a Radiometer K601 Hg/Hg2S04/K2S04reference electrode, the potential of a pH electrode, and the optical density with a double beam spectrophotometer. In the batch experiments, Na2S, Na2S20s, and Ag2S04 solutions were simultaneously poured and mixed together in a beaker. In the flow experiments, the reactor was initially filled at high pump rate (komax =9X SI). Subsequently the rate was decreased or increased stepwise while the different steady states or oscillatory states values were recorded.
Results Batch Experiments. The Sz--S201--Ag+ system can be divided into several subsystems. The full system and two of its subsystems have been studied in batch. ( i ) Subsystem Ag+-S20s2-. When Ag2S04 and Na2S208solutions are mixed in a beaker, the solution turns yellow and a blackish precipitate is observed. The precipitate, after washing with distilled water and redissolution in acid medium, can oxidize manganous ions to permanganate. This means that the reaction between Ag+ and S2Oa2-produces a powerful oxidant, probably a bi- or trivalent complex of silver.'O The yellowish filtrate shows a broad band absorption spectrum with a maximum at 420 nm. ( i i ) Subsystem S2--Ag+. It is well-known that this reaction produces a precipitate of Ag2S. Although the solubility product m013/L3),the precipitation of Ag2S is extremely small (1.6 X rate is not large in our pH range (pH 3-5). At concentrations used in our experiments, the solution becomes yellow at first but remains clear to the naked eye and presents an absorption maximum a t 400 nm (perhaps the formation of AgS-).I' Then the precipitate appears slowly (after about 30 min). On addition of S2OS2-in large excess, the precipitate disappears slowly and the solution returns to colorless (after about 10 min). ( i i i ) System S2--S2082--Ag+. Without Ag', the reaction between S2-and S20," is very slow and the solution remains colorless (10) Collonges, R. In Nouueau Traite de Chimie Minerale; Paul Pascal, Ed.; Masson: Paris, 1967; Vol. 3, p 552. (11) Treadwell; Hepenstrick Helu. Chim. SOC.1949, 32, 1872.
0022-3654/87/2091-6040$01.50/0 0 1987 American Chemical Society
