The iodate-arsenite reaction

The simple autocatalytic model system described in the previous seaion can be directly correlated with an ocperimental system known to exhibit bistability, the iodate-arsenite reaction. This system can be described in terms of only one dynamic variable it is thus a uniquely simple experimental sys-tem.13.14 It is, in fact, accurately described by reactions [1] and [2] when carried out in buffered solutions and with iodate the stoichiometrically limiting reagent. This can be seen by considering the net reaction 

Between the two discontinuous transitions, the system may exist in either a high-iodide steady state or a low-iodide steady state. Of course the concentrations of all the other species in the system reflect the differences in iodide concentration in particular, the iodate concentration is given by the conservation relation above. Which state the system ochibits depends on its past history—whether it has been approached from hi or low flow rates. Thus, for any particular flow rate in the bistability range, the extent of reaction may be very high or very low, even though the reactant concentrations, residence time, and so forth are identical. 

Many studies ctf the dynamics of bistable systems have been carried out, with particular attention paid to the relaxation kinetics near the transition 

F nie 5 Computed steady state iodide concentration, b in Eq. [4] or [1 ] in Eq. [6], as a (unction of tedptocal residence time showing mushroom behavior. (Reprinted from Ref. 14 with permission of the American Institute of Physics.) 

We have restricted our discussion in this section to bistability in well-stirred, homogeneous systems. Multiple steady states may also occur in unstirred systems, where domains of the system in one steady state coexist with domains in the other steady state. In addition to the obvious application to nondhemical systems, chemical systems (in fact the iodate-arsenite system considered here) sometimes exhibit domains that are connected by propagating reaction-diffusion fronts. We will return to this system in our discussion of chemical waves, which will include a description of these fronts. 

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The induction period, followed by a sharp increase in rate is, however, the most characteristic feature of autocatalysis in closed vessels. One manifestation of this behaviour is the clock reaction . An experimental system which is a typical chemical clock and which also exhibits cubic autocataiysis is the iodate-arsenite reaction. In the presence of excess iodate, the system which is initially colourless eventually undergoes a sudden colour change to brown (or blue in the presence of starch). The potential of an iodide-sensitive electrode shows a barely perceptible change during most of the induction period, but then rises rapidly, reaching a peak at the point of colour change. 

A typical experimental study of bistability requires monitoring the steady state concentration of a particular species as a function of a bifurcation parameter such as reactant flow rate. (Bihircation parameters are described in more detail in a following section.) A convenient species to monitor in the iodate-arsenite reaction is iodide, the autocatalyst. Figure 4 shows the steady state iodide concentration as a function of the reciprocal residence time, kQ. As the flow rate is increased, displacing the system from equilibrium (where the extent of reaction, and iodide concentration, is high), the iodide concentration gradu-... 

Again if reaction (1.21) is held in a pre-equilibrium state, the overall rate of conversion of A to B can show a cubic form. This realization of cubic autocatalysis seems to be of importance for the iodate-arsenite and iod-ate-hydrogen sulphite reactions. There the corresponding elementary steps include... 

The fact that bistability is found in such disparate systems as autocataly-tic chemical reaction kinetics and predator-prey dynamics such as that associated with the spruce budworm has led to the concept of normal forms, dynamical models that illustrate the phenomenon in question and are the simplest possible expression of this phenomenon. Physically meaningful equations, such as the reaction rate law for the iodate-arsenite system described above, can, in principle, always be reduced to the associated normal form. Adopting the usual notation of an overhead dot for time differentiation, the normal form for bistability is the following... 

The two systems we combined are the arsenite-iodate and the chlorite-iodide reactions. We first describe the arsenite subsystem. 

The development of an adequate mechanism for the BZ reaction required nearly 15 years from the discovery of oscillations in that system, and refinement of that mechanism is still under way56. It is a measure of the progress in the field of oscillating reactions that only 15 months after the design of the first chlorite oscillator, a mechanism for that system seems well within reach. Without setting forth a full mechanistic treatment, which is not yet available, we sketch here what we believe to be the key elements in the oscillation of the chlorite-iodate-arsenite oscillator and, by extension, several of the related systems to be discussed below. A partial mechanism for the prototype chlorite-iodide system will be presented in the following section. 

The chlorite-iodate-arsenite oscillator was the first oscillating reaction discovered which is based upon chlorite chemistry. The BZ reaction and its relatives are bromate oscillators, while the BL and Briggs-Rauscher oscillators are iodate systems. The initial chlorite oscillator was rapidly followed by a large family of related systems58"60, which are summarized in Table 8. We note that while most of these systems contain an iodine species (I-, I2, IOf) as well as the chlorite, at least two iodine-free chlorite oscillators exist. 

Some of these chlorite oscillators exhibit particularly interesting or exotic phenomena. Batch oscillations in the absence of flow may be obtained in the systems numbered 3, 10 a and 13, while the chlorite-iodide-malonic acid reaction gives rise to spatial wave patterns as well. These latter, which are strikingly similar to those observed in the BZ reaction61 are shown in Fig. 12. Addition of iodide to the original chlorite-iodate-arsenite oscillator produces a system with an extremely complex phase diagram58, shown in Fig. 13, which even contains a region of tristability, three possible stable steady-states for the same values of the constraints. 

In the classical case, R is sulphite and Ox sulphate. Three classes of related reactions have been recognised. To the first belong the sulphite, thiosulphate and stannous ion reactions, and with these (4) is always faster than (3) so that the starch-iodine colour emerges very suddenly when all the reductant is exhausted (by excess iodate). The second type can attain equal rates of iodine production, through (2) and (3), and decomposition (4). Starch-iodine colour is seen at about that point, with partial removal of the reductant e.g. arsenite, ferrocyanide, Fe(II) complexed with oxalate or EDTA). In the third type, reaction (3) is so much faster than (4) that the necessary iodide concentration to give starch-iodine colour is only attained late in reaction. Iodine is then present early but the blue colouration only develops later. A number of organic reductants fall into this class. The rates of colour development in the normal reaction system have been treated in semiquantitative fashion . ... 

De Kepper, et al. (1981-1) designed a homogeneous oscillating reaction by coupling the autocatalytic oxidation of arsenite by I03 to the autocatalytic C102 -I03- reaction in a CSTR. Both I2 and I concentrations oscillate with the concentration of the latter changing by a factor of > 105 during each cycle. This arsenite-iodate-chlorite system was obtained in two separate reactions. The oxidation of arsenite by iodate, a reaction autocatalytic in iodide is ... 

The first systematic design of a chemical oscillator had been achieved There remained some ambiguity, however. Since two autocatalytic reactions had been employed, it was not immediately clear which constituted the fundamental autocatalytic reaction and which provided the feedback in the model scheme. Historically, the arsenite-iodate system had been chosen for the former role, since its bistable behavior had been established first. More careful investigation revealed that, in fact, it was the chlorite-iodide reaction that provides the essential dynamical features of this system. The evidence comes in two forms. First, the chlorite-iodide reaction is also bistable in a CSTR (Dateo et al., 1982) and the relaxation to its steady states is more rapid than the relaxation behavior of the arsenite iodate system. According to our theory,... 

Another noteworthy achievement is the report of a systematically designed oscillating system, in which two autocatalytic subsystems, arsenite-iodate and chlorite-iodide, were linked in a continuous flow stirred-tank reactor. These two subsystems have been studied independently of each other. The arsenite-iodate subsystem has been thoroughly examined in a CSTR and shown to exhibit bistability under a range of conditions. The oscillations of iodide concentration involved a variation by a factor of more than 10 during each oscillation In an unstirred system, well-defined waves were observed. The chlorite-iodide reaction has also been studied. ... 

While no confirmed reports of new iodate oscillators have yet appeared, it seems inevitable that systems based on the bistable arsenite-iodate [30,31] or related Landolt-type [32] reactions will soon be made to oscillate. The iodide-peroxydisulfate-oxalate reaction discussed by Chopin-Dumas elsewhere in this volume may be the first of the new iodate oscillators. 

The first system on which this approach was tried (De Kepper, Epstein and Kustin, [ 18]) employed two coupled autocatalytic reactions, chlorite plus iodide, and arsenite plus iodate, which have key intermediates in common. As Figure h shows, the chlorite-iodate-arsenite system did indeed prove to oscillate, constituting the first systematically designed chemical oscillator. More recently, by starting from the fundamental or minimal chlorite-iodide bistable system and adding different feedback species, it has been possible to generate a family of nearly 20 different chlorite-iodine species oscillators (Orb n et al., [19]). In addition, two iodine free chlorite oscillators involving thiosulfate (Orban, De Kepper and Epstein, [ 20] ) and bromate (Orban and Epstein, [21]) have been found. 

The species HOI is then rapidly converted to iodide, by reaction first with I" to produce I2 which is then reduced by the arsenite of hydrogen sulphite. Thus, identifying A with the reactant iodate and B with iodide, the system shows a cubic autocatalysis with rate proportional to [IOJ][I-]2 at constant pH. 

The reaction between iodate and arsenite ions appears to have contributions from both cubic and quadratic autocatalysis (the autocatalyst is the product, iodide ion). In the previous sections we have treated these two rate laws separately and by different methods. Both methods can be applied to the system in which these processes occur simultaneously, yielding results which, despite not being consistent at first sight, can be resolved by the idea of stability. 

The induction period of the reaction may be curtailed 2 by (1) the presence of an excess of iodic acid, (2) an increase in the concentrations of the reactants, (3) the addition of a trace of arsenic acid, (4) the addition of a mineral acid and (5) exposure to sunlight. On the other hand, the period may be prolonged by the addition of mercuric chloride or by violent shaking. The proportion of the iodine liberated increases with the arsenious acid concentration and passes through a maximum. The iodine appears on the surface of the solution even though the latter may be covered with benzene (or occasionally it appears at a nucleus on the glass). The reduction of periodate to iodate by means of arsenite is a bimolecular reaction and is of the first order with respect to both components.3 At 25° C. it proceeds according to the velocity equation... 

Solutions of periodic add and of sodium metaperiodate in water are quite stable at room temperature. The periodate content is readily determined by titrating, with standard sodium arsenite solution, the iodine liberated from iodide in neutral solution.49 103-197 Periodate also may be determined accurately in the presence of iodate, since in neutral solution periodate is reduced by iodide to iodate. The reaction in the presence of a boric add-borax buffer is shown by the following equation. 

A solution of 12.6 g. of pure a-methyl-D-glucopyranoside (XXVII) in distilled water is added to 260 cc. of 0.54 M aqueous periodic acid solution (2.1 molecular equivalents). The solution, after being diluted with water to 500 cc., is kept at 20-25° for about twenty-four hours. If desired, the excess periodic acid can be determined by the arsenite method. The rotation of the reaction solution should correspond to [a]i> = +121° calculated for the dialdehyde XXVIII. The solution is neutralized to phenolphthalein with hot strontium hydroxide solution with care to avoid any excess. The precipitate of strontium iodate and strontium periodate is filtered and washed with cold water. After the addition of 1 g. <5f strontium carbonate, the solution is concentrated in vacuum with the water bath at 50° to a volume of about 50 cc., filtered to Temove strontium carbonate, and the concentration (bath, 40°) continued to dryness. The residue is extracted six times with 25-cc. portions of cold absolute ethanol, which separates the dialdehyde completely from slightly soluble strontium salts, as shown by the lack of optical activity of an aqueous solution of these salts. The dialdehyde XXVIII is recovered from the ethanol solution as a colorless syrup in quantitative yield by distillation of the solvent in vacuum with the bath at 40-45°. 

Before considering the chlorite reaction, we mention one further aspect of the arsenite-iodate reaction, its spatial inhomogeneity. Epik and Shub first reported chemi-... 

Table 6. Some mechanistic steps in the arsenite-iodate reaction...

Like the arsenite-iodate reaction, chlorite-iodide is a clock reaction50,51 however, it is more complex. This reaction shows a dramatic rise in the intensity of the brown color of iodine, followed by an even more abrupt fade-out. This behavior resembles that of the ferrous-nitrate clock, where the color is due to formation of the FeNOz+ complex52. ... 

It will be appreciated that iodate is incompatible with both iodide (cf. Section IV.21, reaction 6) and with thiocyanate (Section IV.21, reaction 9) since iodine is liberated in acid solution. Also sulphide is incompatible with both bromate and iodate (oxidation to sulphate occurs), and an arsenite is oxidized by iodate in acid solution. These facts should therefore be borne in mind when interpreting Table V.30. An independent test for iodate (test 11) is provided below this can be performed before the silver nitrate tests. 

Reactions of the three halide ions with iodate are reported as obeying different kinetic laws (Table 28). For the chloride and bromide reactions, the evidence is not extensive, and even the great attention given to the iodide reaction has not produced complete agreement about the reaction orders. Earlier papers refer to this last as the Dushman reaction, on account of a kinetic study which established the reaction as close to fifth order overall (rate = k[H ] [IOJ][I ] ). Kubina examined the same reaction in the presence of arsenite (which did not affect the rates) and claimed that the rate expression was different, viz. 

Not only iodide ion and iodine but also iodate and even periodate can be determined using this reaction by simply converting the analyte into the catalytically active species (i.e., iodide). The reduction is effected by arsenite ion itself on heating for 30 min. This treatment allows the resolution of iodate/iodide mixtures. The reaction can also be used for the determination of iodine-containing biological substances such as iodoproteins (thyroid hormones) by simply pretreating the samples in order to release iodine. 

Kepper, P.D., Kustin, K., Epstein, I.R. A systematically designed homogeneous oscillating reaction the arsenite-iodate-chlorite system. J. Am. Chem. Soc. 103, 2133 (1981)... 

The most natural, and most common, method to look at and present one s data is the way in which those data are taken. In a typical experiment, we measure some function of concentration (e.g., electrode potential or absorbance) as a function of time at one set of constraints. A plot of signal vs. time is known as a time series. Time series can be exceedingly dull, for example, in the case of a steady state, or they can be quite difficult to interpret, as in the case of a system that may or may not be chaotic. Nevertheless, they can yield valuable information, and they are certainly the first thing one should look at before proceeding further. Figure 2.12 shows a time series that establishes the occurrence of bistability in the arsenite-iodate reaction. 

Figure 2.12 Time series showing the iodide concentration in the arsenite-iodate reaction in a CSTR. The system is initially in an oxidized steady state (the potential shows a slight downward drift because of an experimental artifact). At the time s indicated by the arrows, a measured amount of acid is injected. With a small injection, the system returns to the steady state, demonstrating the stability of that state. With a larger injection, there is a transition to a second, reduced, steady state. (Adapted from De Kepper et al., 1981a.)...

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