J. Phys. Chem. 1995,99, 10231-10236
10231
Oxyhalogen-Sulfur Chemistry: Oxidation of Hydroxymethanesulfinic Acid by Bromate in an Acidic Medium1 Sreekantha B. Jonnalagadda Department of Chemistry, University of Durban- Westville, Private Bag X54001, Durban 4000, Republic of South Africa
Cordelia R. Chinake and Reuben H. Simoyi* Center for Nonlinear Science and the Department of Chemistry, West Virginia University, Box 6045, Morgantown, West Virginia 26506-6045 Received: September 22, 1994; In Final Form: March 13, 1995@
The reaction between hydroxymethanesulfinic acid, HOCHzSOzH (HMSA), and bromate ion has been studied in the pH range 0.3-2.0. The stoichiometry of the reaction in excess HMSA was determined as Br03HOCH2S02H Br- S042- HCOOH 2H'. In excess bromate the stoichiometry is 6Br03- SHOCH2S02H 3Br2 5S042- SHCOOH 4Hf 3H20. In excess bromate, the reaction exhibits clock reaction behavior. An initial induction period in which there is no redox potential or absorbance (A = 390 nm) activity is followed by a sudden and rapid production of Br2. This is explained via the coupling of three reactions: oxidation of HMSA, production of Br2, and consumption of Br2. The consumption of Br2 is so fast that the end of the induction period is an indicator that all the HMSA has been consumed. The rapid Br2-HMSA reaction also precludes oligooscillatory behavior, which seems to be a usual feature of reactions between sulfur compounds and oxyhalogen ions.
- -+
+
+
+
+
+
Introduction Recently we embarked on a systematic series of studies aimed at elucidating the kinetics and mechanisms of oxidation of sulfur compounds.2 For this series we have concentrated on thiocarbony1 compounds, R2C=S, and the thiocyanate ion, SCN-, which are some of the most stable and well-behaved sulfur compounds. The sulfur environment in these compounds discourages uncontrolled polymerizations, thereby giving kinetics results that are more reproducible than those normally encountered in sulfur chemi~try.~ Oxyhalogen chemistry has been very important in the generation of chemical oscillatory b e h a ~ i o r . ~The first two accidentally discovered oscillators involved oxyhalogen chemi ~ t r y . ~The , ~ involvement of oxyhalogens in novel oscillatory behavior fueled the study of kinetics and mechanisms of oxyhalogen reaction^.^ A general algorithm has been derived for oxyhalogen reactions in which rapid radical processes are coupled with slow molecular processes.' Bromate-driven oscillators are by far the most thoroughly studied of all known oscillators.* Among them is the bromate-thiourea reaction: which has not been fully characterized because of the lack of understanding of the kinetics and mechanism. A recent study of this reaction suggested a mechanism which involved oxygen addition to the sulfur center giving successively the sulfenyl, sulfinic, and sulfonic acids before cleavage of the C-S bond to produce sulfate.I0 The aim of this paper is to provide more experimental data to support the postulated mechanism. Very little is known about sulfur chemistry although it is known to be heavily involved in nonlinear dynamics observed in chemistry." The involvement of sulfur-containing compounds in pH-driven oscillators has given greater importance to the mechanisms of oxidation of these compounds.I2 The fist @
Abstract published in Advance ACS Abstracts, June 1, 1995.
0022-365419512099-10231$09.00/0
+
+
+
known halogen-free chemical oscillator, the methylene bluesulfide oscillator, involved sulfur compound^.'^ The rate of discovery of various types of nonlinear dynamical behavior in chemistry based on sulfur chemistry has outgrown the basic knowledge available on sulfur compounds. The study of kinetics and mechanisms of sulfur reactions is complicated by such features as free radical mechanism^,'^ polymerization^,'^' oligooscillations,I6 and variable ~toichiometries.'~To date, all complete kinetic studies of the oxidation of sulfur compounds by oxyhalogens involve at least one of these nonlinearities. The combination of oxyhalogen anions, e.g. I03-, ClOz-, and BrO-, with sulfur compounds invariably produces nonlinear kinetics. A good example is the series of two-component oxyhalogen-sulfur oscillators mentioned earlier. The bromatethiourea reaction is a clock reaction with a variable stoichiometry.1° The sulfur center in thiourea has an oxidation state of -2, while in the final oxidation product, S o d 2 - , the oxidation state is +6. The range of oxidation states involved in such a transformation is so large that many intermediates are possible. By using a compound in which the sulfur center is at a higher oxidation state, the complexity and number of possible intermediates can be reduced. We report, in this paper, on the oxidation of hydroxymethanesulfinic acid (HMSA), HOCHZSOZH,by bromate in an acidic medium. The sulfinic acid, in which the sulfur center has an oxidation state of $2, has been postulated as a possible intermediate in the oxidation of thiourea.I0 Included in this paper is a computer simulation study of the proposed mechanism.
Experimental Section Materials. Hydroxymethanesulfinic acid (HMSA) (Aldrich) was used without further purification as were perchloric acid (70-72%), sodium bromate, and sodium bromide (all from 0 1995 American Chemical Society
Jonnalagadda et al.
10232 J. Phys. Chem., Vol. 99, No. 25, 1995 Fisher). HMSA solutions were prepared just before use and kept for less than 2 h. Reaction solutions were prepared using singly-distilled water. Perchloric acid was standardized by standard sodium hydroxide. Methods. All experiments were carried out at 25 & 0.1 "C and an ionic strength of 0.5 M (NaC104). Two kinetics systems were studied: the Br03--HMSA and the Br2-HMSA reactions. Both reactions were monitored spectrophotometrically by following the absorbance of Br2 at 390 nm. Kinetic measurements were performed on a Hi-Tech Scientific SF-61AF stopped-flow spectrophotometer with an M300 monochromator and a spectrascan control unit. The signal from the spectrophotometer was amplified and digitized via an Omega Engineering DAS-50/1 16-bit A/D board interfaced to a computer. The stoichiometric determinations were performed both in excess BrO3- and excess HMSA. In excess Br03-, the total oxidizing power (Br03HOBr Br2) was determined iodometrically, while excess HMSA was determined titrimetrically.'* Sulfate was determined gravimetrically as BaS04. Bromine formed in excess Br03- concentrations could be separately determined by its absorbance at 390 nm using the absorptivity coefficient of 142 M-' cm-'. Formic acid was qualitatively determined using mercuric chloride. l9
producthntermediate, HCHO:
Results
For a bromate oxidation, this reaction was very fast, often going to completion within 10 s or less at pH range 0.3-1.0. The reaction starts with an induction period in which no activity is observed in the absorbance at 390 nm. At the end of the induction period Br2 is formed rapidly (Figure la). The induction period is determined by initial conditions. The induction period and the initial Br03- concentrations are inversely related (Figure 1B). The x-axis intercept of Figure 1B is significant; it gives the value of [BrO3-]o when induction time is infinite (Le., no bromine is formed). This is the stoichiometric equivalent of [BrO3-]0 needed for excess HMSA conditions (stoichiometry A). Thus, this series of experiments established stoichiometry A. For a fixed initial amount of HMSA, the final Br2 formed is constant, although the rates of formation of Br2 at the end of the induction period will vary with [H+]o and [BrO3-]0. Acid concentration has a profound effect on the reaction. The reaction does not proceed at all at pH > 3.5. An increase in initial acid concentrations shortens the induction period quite considerably (Figure 2A). Acid also affects the rates of the oxyhalogen reactions which control the formation of Br2. A plot of induction time vs the square of the inverse of the acid concentration gives a straight line (Figure 2B). This acid dependence suggests that the kinetics of the precursor reaction to Br2 formation has a second-order dependence on the acid concentration. One fascinating result was the dependence of the induction period on the initial HMSA concentration in excess oxidant environment (25-50-fold excess). If a large excess of oxidant is maintained during the course of the reaction, no variation in the induction period is observed (Figure 2C, trace a). If the initial HMSA concentration is increased such that it approaches the initial BrO3- concentrations, there is no noticeable change in the induction period (Figure 2C, traces b-e). Although the initial HMSA concentration does not affect the induction period, it does affect the rate of formation of bromine at the end of the induction period (Figure 2C). Formation of Bromine. The data in Figure 2C clearly indicate that complete consumption of the substrate is the precursor reaction to the formation of Br2. In the series of experiments for determining rate of formation of bromine, the ratio of bromate to HMSA was maintained at 225. Thus, the BrO3- concentration will still be very close to initial values at
+
+
Stoichiometry. The stoichiometry of the reaction was complex and depended on the ratio of oxidant to reductant as well as on the incubation period before quantitative analyses were performed. Reaction solutions at various oxidant to reductant ratios (in an acidic medium) were mixed in volumetric flasks and tightly capped. These were left to react overnight or for at least 6 h. For solutions left overnight, the most consistent stoichiometry obtained in excess HMSA was Br03-
+ HOCH2S02HBr-
+ SO-: + HCOOH + 2H'
(A)
By assuming that bromine is formed through the purely oxyhalogen reaction20 HOBr
+ Br- + H+ t Br2 + H,O
(B)
formation of bromine implies total consumption of the reductant. Thus, any bromate in excess of what is required by stoichiometry A will produce Br2. By gradually increasing BrO3- for a fixed amount of HMSA, stoichiometry A gives the maximum amount of Br03- needed just before Br2 is produced as a product. In excess BrO3- the stoichiometry was deduced by correlating the amount of Br2 formed to the initial HMSA concentration. For solutions left overnight, the ratio was consistently 5:3, that is 5 mol of HMSA produces 3 mol of Br2. Each mole of HMSA produced a mole of S042-. The remaining Br03- as well as the Br2 formed was determined iodometrically. This led to the following stoichiometry: 6Br0,-
+ 5HOCH2S02H3Br2 + 5SO:+ SHCOOH + 4H' + 3 H 2 0 (C)
Formic acid, HCOOH, was determined qualitatively by using mercuric acid.I9 Iodometry established the 6:5 ratio for oxidant to reductant. Stoichiometries A and C were established at the extreme limits of excess HMSA and excess BrO3-, respectively. Generally, the stoichiometry was not clean. The complexity in the stoichiometry is brought about by the oxidation of the organic
HCHO
+ H,O t HCOOH + 2H' + 2e-
(D)
If stoichiometric determinations are performed soon after mixing of reagents, reaction D may not have gone to completion, thus giving a complex stoichiometry. Reactions with a slight excess of oxidant also gave mixed stoichiometries as reaction D became very slow due to low concentration of oxidant. In excess HMSA and monitoring the reaction by iodometry only, a stoichiometry different from A was obtained: 2Br03-
+ 3HOCH2S02H3SO;- + 3HCHO + 2Br- + 6H'
(E)
On varying the initial BrO3- concentration while maintaining stoichiometry E, no excess BrO3- is observed on titration. Adding more BrO3- does not give Br2 as a product. Br2 can only be formed after HCHO has been totally oxidized as in reaction D.
Reaction Kinetics
Oxidation of Hydroxymethanesulfinic Acid by Bromate
J. Phys. Chem., Vol. 99, No. 25, 1995 10233
A 0.12
A 0.16 0.14
0.10
-E
0.12
E
0.08
-
$0.10
al 0
m
6
e e
0.06
10.08
0.04
4
P
n
0.06 0.04
0.02 0.02
0.00 0
0.00 2
4
8
6
10
2
0
4
time (seconds)
€3
1.0
6
10
8
time (seconds)
,
0.8
E
P
c
8
E
0.6
. r
0.4
0.2
'
0.04
0.06
0.08
0.10
0.12 0
[ bromate] (M)
Figure 1. (A) Absorbance plots at 1 = 390 nm for the BrO3--HMSA reaction showing the effect of BrO-. Higher Br03- concentrations decrease the induction period as well as increase the rate of formation of Br2. The final Br2 absorbances for all these traces were the same at infinite time. [H+]o = 0.50 M, [HMSAIo = 0.0025 M. [BrO3-]o: (a) 0.050 M; (b) 0.060 M; (c) 0.070 M; (d) 0.080 M; (e) 0.10 M. (B) Effect of initial BrO3- concentrations on the induction time. Reaction conditions were as in part A.
the point of bromine formation, while the concentration of the substrate would have greatly diminished. With a pH around 0.3, the H+ concentration can be assumed to be buffered. Thus, the rate of formation of Br2 at the end of the induction period can be related to the initial concentrations of BrO3- and H+. The rate constants were calculated by fitting Brz formation data to a first-order rate equation. Figure 3A shows a linear relationship between the pseudo-first-order rate constant and [BrO3-]0. A log-log plot of rate constant rate vs acid concentration gives a linear plot with a slope of 2, indicating a second-order dependence on acid concentration (Figure 3B). A linear dependence also exists between initial HMSA concentrations and the initial rate of formation of Br2 (Figure 3C). Bromine-HMSA Reaction. The reaction dynamics seemed to suggest that the reactions which form bromine occur after the sulfur compound has been completely oxidized. This is possible if the reaction of bromine with the sulfur compounds is so rapid that these species cannot coexist in the same reaction solution. A series of experiments were performed in which the direct reaction of Br2 and HMSA was monitored. The data
10
5
15
20
25
30
1/(H+]2
0.3
8 60.2 8
! 2
0.1
0.0 0
2
4
6
0
10
time (seconds)
Figure 2. (A) Effect of acid concentration on absorbance at 390 nm. Rate of production of Br2 increases with acid Concentration. [Br03-]0 = 0.080 M, [HMSAIo = 0.0025 M. [H+]o: (a) 0.30 M; (b) 0.50 M; (c) 0.70 M; (d) 0.90 M. (B) Plot of induction period vs inverse of the square of acid concentration. (C) Effect of varying HMSA in conditions where [BrO3-]o >> [HMSAIo. Though induction period does not change, rate of formation of Br2 does vary. [BrO3-]0 = 0.080 M, [H+]o = 0.50 M. [HMSAIo: (a) 0.0030 M; (b) 0.0035 M; (c) 0.0040 M; (d) 0.0045 M; (e) 0.0050 M.
Jonnalagadda et al.
10234 J. Phys. Chem., Vol. 99, No. 25, 1995
A
0.035
I
0.030 -0.025
0.010
'
-0.8
1 \
0.000 I
I
-1.3
-1.2
I
I
.1.1
-1 .o
I
I
I
I
log [bromate]
B
-
-0.4
-0.8
-8
Br0,-
-1.2
-0.6
-0.8
-0.4
-0.2
0.0
log [acid]
0.09
-s
-
HBrO,
+ Ox
+ HMSA + H+ - HOCH,SO,H + HBrO,
(G)
HBr02 represents the first of the reactive oxybromine species which will be able to react faster with substrate than Br03-. HBrO2 can react further to successively give HOBr and Br-:
91
e
10.07
+ 2H+ + 2e- t HOBr + H,O HOBr + Hf + 2e- t Br- + H,O
'j
.-
HBrO, 0.06
0.05
(F)
RedP- can be any two-electron reductant. induction Period. There is no net production of Br2 in this time interval, since any Br2 produced in this period is immediately consumed by HOCHZSO~H,HOCH2S03H, and HCHO. The rate of reaction of Br2 with these compounds is faster than the corresponding BrO3- reactions23 (compare Figures 1A and 4). The dominant reaction during the induction period is the oxidation of the HMSA. Using reaction F, the first step in the oxidation of HMSA is the direct reaction of bromate and HMSA:
Br0,0.08
+ RedP- + (p + 1)H'
I
0.003
I
I
0.004
0.005
[hmsal (MI Figure 3. (A) Log-log plot of [Br03-]o vs the pseudo-first-order rate constant, k,,,, for production of Br2. Slope of the plot was 1.00. (B) Log-log plot of kappvs [H+]o. The slope of the plot is 2.00. ( C ) Relationship between [HMSAIo and the initial rate of formation of Br2 after the induction period.
obtained (see Figure 4) show that the reaction is so fast that it approaches the physical limitations of our stopped-flow instrument (3
(HI (1)
The reductants in reactions H and I can be HOCH~SOZH, HOCH2S03H, HCHO, or Br-. Reaction G serves only as an initiator. The bulk of the oxidation of HMSA is accomplished by the reactive species HBrO2 and HOBr. The production of Br- in reaction I now gives a new rate-determining step in the system:24 Br03-
+ 2H' + Br- * HBrO, + HOBr
(J)
Reaction J is analogous to reaction F. Only catalytic amounts of Br- are needed in the initial stages of the reaction HBrO,
+ Br- + 2H'
2HOBr
(K)
as subsequent production of Br- is autocatalytic (combination
Oxidation of Hydroxymethanesulfinic Acid by Bromate
J. Phys. Chem., Vol. 99, No. 25, 1995 10235
+
of 2(I) (K) shows that Br- is autocatalytically produced). With sufficient Br-, the rate-determining step now becomes a reaction similar to reactions F, G, and J: -d[HMSA] rate = = k,[Br03-][H+]2[Hh4SA] dt
(1)
TABLE 1: Mechanism of the Bromate-Hydroxymethanesulfinic Acid Reaction reaction number M1 M2
Equation 1 will determine the length of the induction period. The results of the experiments on the Br2-HMSA reaction (Figure 4) indicate that it is a very fast reaction with a bimolecular lower limit rate constant of 5 x 104 M-' s-' (based on the limit of measurement of our instrument). The low absorptivity coefficient of Br2 (142 M-I cm-I) does not support the use of lower Br2 and HMSA concentrations to slow down the reaction. Experimental data suggest that the Brz-HMSA reaction is a fast two-electron transfer process followed by hydrolysis:
Br,
+ HOCH,SO,H + H,O -
HOCH,SO,H
+ 2Br- + 2H+ (L)
Further oxidation of the sulfonic acid cleaves the C-S bond to give SCh2-: Br,
+ HOCH,SO,H + H 2 0SO:- + 2Br- + HCHO + 4Hf
M3 M4 M5 M6
M7 M8 M9 M10 M11 M12
(M)
M13
The very rapid rate of reaction L suggests that Brz and HMSA cannot coexist in the same solution. Hence, at the point where the induction period ends, there will be no HMSA left in solution. At the end of the induction period, the stoichiometry will be reaction A (as far as there being a 1:l ratio of BrO3- to HMSA). The bromine species, however, will not all go to Brbut will be in various oxidation states such as in HBr02, HOBr, and Br-. The rapid formation of Br2 is due to reaction B. Since reaction B is very fast, it is not rate-determining. The ratedetermining step is the rate of formation of HOBr (reaction J):
M14
d[HOBr] = k2[Br03-] [H'] dt
[Br-1
Rate of Formation of Brz. The rate of formation of Br2 at the end of the induction period is much faster than would be the case if excess Br03- and Br- (stoichiometry A) were mixed together. This is because not all the Br03- is reduced all the way to Br- before formation of HMSA. The quantity of reactive species is proportional to the initial HMSA concentration. Thus the rate of formation of Br2 will be proportional to the initial HMSA concentration. This is shown in Figure 2C. If it is assumed that at the end of the induction period bromate concentration is essentially unchanged, then an upper limit rate constant of the constant for the formation of Br2 can be calculated and related to initial conditions. This has been done in Figure 3. Discussion The BrO--HMSA reaction seems to have all the properties that are needed for the generation of nonlinear kinetics: (a) The reaction possesses variable stoichi~metry.~~ The final brominecontaining species product determines the reaction's stoichiometry. In the presence of Br- and acid, Br03- is unstable with respect to Br2. (b) There are at least two reactions competing for the species HOBr. Both formation of Brz and oxidation of HMSA require HOBr. (c) There are at least three reactions which couple to produce the observed reaction dynamics. These reactions are oxidation of HMSA by Br03(reaction A), the formation of Br2 (reaction B), and consumption
M15
reaction
+ + + + +
Br03- Br- 2H+ t HBr02 HOBr HBr02 H+ Br- t 2HOBr
+ H+ + Br- 2 Br2 + H20 BrO3- + HOCHZSOZH+ H+ 2 HBr02 + HOCH2S03H HOBr + HOCHzS02H HOCH2SO3H + Br- + H+ HBr02 + HOCH2S02H HOBr + HOCHzSOsH HOBr + HOCHISO~HSO:- + HCHO + Br- + 3H+ Br2 + HOCHzSOzH + H20 HOCHZSO~H+ 2Br- + 2H+ Br2 + HOCH2S03H + H20 SO:- + HCHO + 2Br- + 4H+ Br2 + HCHO + HzO HCOOH + 2Br- + 2H+ HOBr + HCHO HCOOH + Br- + Hf HBr02 + HOCH2S03H SOf + HCHO + HOBr + 2H+ HBrOz + HCHO HOBr + HCOOH Br03- + HOCH2S03H SO:- + HCHO + HBr02 + H+ BrO3- + HCHO + H+ HCOOH + HBr02 HOBr
rate constant 2.1 (M-3 s-I) 1.0 x 104 ( M - I s-I 1 2.0 x lo6 (M-? s-l 1 2.0 x 10-5 ( M - I s-I1 8.9 x lo8 (M-2 s-l 1 110 ( S K I ) 10.3 (M-2 s-I) 1.0 x (M-l s-l 1 1.05 x 104 ( ~ - 1s-1 1 2.5 x 104 (M-I s-1 1 2.05 x 10' (M-]
1
8 x lo8 (M-] s-] 1 1.5 x 103 (M-I S-1
1
6.0 x lo2 (M-I
1
s-I
4.0 x 10' (M-I s-I 1 5 x 103 (M-I s-I1 1.0 x 10' (M-I s-l 1 5.6 (M-I s-l) 2.2 (M-I s-l)
of Br2 by the sulfur-containing and other organic compounds (e.g. reactions L and M). Normally, reacting systems with these three properties display oligooscillatory behavior. That is, an intermediate displays two or more maxima before the reaction goes to completion.26 However, no oligooscillatory behavior was found in this reaction because one of the reactions in this scheme is much faster than the other two (Le. the consumption of Br2 by the sulfur compounds).
Computer Simulations These three processes can be represented by the simplified reaction mechanism scheme shown in Table 1. Only three types of reactions are shown in the table: standard oxybromine reactions, oxybrominefbromine- sulfur reactions, and oxidations of formaldehyde, HCHO. Apart from the oxybromine reactions, the rest of the reactions can be made essentially irreversible. Rate constants for reactions Ml-M3 were obtained from the l i t e r a t ~ r e . ~The . ' ~ rate constants for M4, M8, M9, M10, M14, and MI5 were estimated from this work. Rate constants for M5, M6, M11, and M13 could be fixed, since they are considered rapid enough not to be rate-determining. This left only a few rate constants that could be freely altered for an accurate simulation using a semiimplicit Runge-Kutta integration techniq~e.~' There are four possible oxidizing agents present in solution (Br03-, HBr02, HOBr, and Br2) and three possible reducing agents (HMSA, HOCH2S03H, and HCHO). Br03- oxidations are generally slow, while HOBr and Br2 oxidations are very fast. The mechanism thus contains the six reactions which involve an oxidation by HOBr and Brz. Despite the slowness of BrO3- oxidations, all three possible BrO3- oxidations are included because the concentration of Br03- is much higher than that of any of the other species in solution. Thus the final mechanism proposed contains the twelve reactions which are a
Jonnalagadda et al.
10236 J. Phys. Chem., Vol. 99, No. 25, 1995
containing intermediate is the sulfonic acid. No interactions can be possible between the sulfinic and sulfonic acids. The simulations correctly predicted the induction period of the reaction (Figure 5A). They also show that the sulfonic acid concentration rises to a maximum before falling to zero as S042is formed (Figure 5B). We feel that this is the most concise mechanism that can explain the observed reaction dynamics.
Acknowledgment. This work was supported by the West Virginia EPSCoR program. References and Notes
0
2
6
4
6
10
time (seconds)
B
0.006
,
I
~
.. -. .-..-. .-..-..-..-..
/a
0
2
4
6
8
10
time (seconds)
Figure 5. (A) Comparison between computer simulations (0)and experimental data (-) for the production of Brz. [BrO3-]o = 0.080 M, [HMSAIo = 0.0050 M, [H+]o = 0.50 M. (B) Computer simulation of other species under the experimental conditions used in part A. This shows a rapid depletion of HMSA (O), rapid formation and depletion of the sulfonic acid HOCHISO~H(-), formation of bromine (0),and quantitative formation of anism.
sod2-(. * -
-
*)
as predicted from the mech-
permutation of four oxidizing agents and the three reducing agents. The mechanism, though relatively simple, is exhaustive. Omitted from this mechanism are any sulfur-sulfur interactions. By starting with the sulfinic acid, the only possible sulfur-
(1) Part 13 in the series Nonlinear Dynamics in Chemistry Derived from Sulfur Chemistry. Part 12: Jones, J. B.; Chinake, C. R.; Simoyi, R. H. Oxyhalogen-Sulfur Chemistry: Oligooscillations in the Formamidine Sulfinic Acid-Chlorite Reaction. J . Phys. Chem. 1995, 99, 1523. (2) Mambo, E.; Simoyi, R. H. J . Phys. Chem. 1993, 97, 13662. (3) Nagypal, I.; Epstein, I. R. J . Phys. Chem. 1986, 90, 6285. (4) Noyes, R. M. Ber. Bunsen-Ges. Phys. Chem. 1980, 84, 295. (5) Belousov, B. P. Ref. Radials. Med. 1958, 145. (6) Bray, W. C. J. Am. Chem. SOC. 1921, 43, 1265. (7) Noyes, R. M. J . Am. Chem. SOC. 1980, 102, 4644. (8) Alamgir, M.; De Kepper, P.; Orban, M.; Epstein, I. R. J. Am. Chem. SOC. 1983, 105, 264. (9) Simoyi, R. H. J . Phys. Chem. 1986, 90, 2802. (10) Simoyi, R. H.; Epstein, I. R.; Kustin, K. J . Phys. Chem. 1994, 98, 551. (11) Chinake, C. R.; Simoyi, R. H. S. Afr. J . Chem., in press. (12) Rabai, G.; Orban, M.; Epstein, I. R. Acc. Chem. Res. 1990, 23, 258. (13) Burger, M.; Field, R. J. Nature (Landon) 1984, 307, 720. (14) Luo, Y.; Orban, M.; Kustin, K.; Epstein, I. R. J. Am. Chem. SOC. 1989, 111, 4541. (15) Barnard, D. J . Chem. SOC.1957, 4675. (16) Rabai, G.; Beck, M. J . Chem. Soc., Dalton Trans. 1985, 1669. (17) Alamgir, M.; Epstein, I. R. lnt. J . Chem. Kinet. 1985, 17, 429. (18) Stirling, C. J. M. Int. J . Sulfur Chem. 1971, 6, 277. (19) Feigl, F.; Anger, V.; Oesper, R. E. Spor Tests in Organic Analysis, 1st ed.; Elsevier Publishing Company: Amsterdam, 1966. (20) Eigen, M.; Kustin, K. J . Am. Chem. SOC. 1962, 84, 1355. (21) The limitation of our stopped-flow instrument is based on mixing time. Reactions that occur faster than the rate of mixing in our apparatus (about 3 ,us) cannot be followed. (22) Chinake, C. R.; Simoyi, R. H.; Jonnalagadda, S. B. J. Phys. Chem. 1994, 98, 545. (23) The reaction of Brz with CS(NH2)2,for example, is too fast to follow by stopped-flow, while the Br03--CS(NH& reaction is much slower. See: Simoyi, R. H.; Epstein, I. R. J . Phys. Chem. 1987, 91, 5124. (24) Barton, A. F. M.; Wright, F. A. J . Chem. SOC. A 1968, 1747. (25) Simoyi, R. H.; Epstein, I. R.; Kustin, K. J . Phys. Chem. 1989, 93, 2792. (26) Variable stoichiometry has been conjectured as being important in the generation of oligooscillatory behavior, but this has not been proved. See: Chinake, C. R.; Mambo, E.; Simoyi, R. H. J . Phys. Chem. 1994, 98, 2908. (27) Kaps, P.; Rentrop, P. Numer. Math. 1979, 23, 55.
JP942603 1
