A new explanation of the oscillations in the Bray ... - ACS Publications

Apr 21, 1993 - Henry Taube, now at Stanford, has confided that in the 1930s .... Figure 1. Spectrophotometric recording at 50 0 C of iodine concentrat...
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11354

J. Phys. Chem. 1993,97, 11354-1 1362

A New Explanation of the Oscillations in the Bray-Liebbafsky Reaction Ludovit Treindlt and Richard M. Noyes' Department of Chemistry, University of Oregon, Eugene, Oregon 97403 Received: April 21, 1993; In Final Form: August 5, 1993"

Over 70 years ago, Bray discovered oscillations in iodine concentration during the iodate-catalyzed disproportionation of aqueous hydrogen peroxide. Although a t least 50 papers have been published about this reaction, the mechanism has not been definitively established. We have now observed, apparently for the first time, that oscillations can be inhibited by very rapid stirring. The frequency can also be slowed greatly by sonication. We believe that transport of oxygen from supersaturated solution to surrounding atmosphere must be included in any detailed mechanistic explanation of the oscillations. We propose a skeleton mechanism which appears to explain a t least most of the observed behaviors. Additional experiments are proposed which should either support or discredit the proposed new mechanism.

I. Introduction In 1921, Bray' reported that formation and consumption of elementary iodine could alternate during the catalysis by iodate of the disproportionation of aqueous hydrogen peroxide. At that time, oscillations in a truly chemical reaction were unprecedented. Henry Taube, now at Stanford, has confided that in the 1930s Professor Bray used to talk about his oscillating reaction to graduate students-who listened indulgently. However, Herman Liebhafsky was a student who became associated with nine papers which are cited as numbers 4-1 1 in ref 2. After a scientific career which did not involve chemical kinetics, Liebhafsky became a faculty member at Texas A&M and was responsible for another 16 papers, 11 of which are cited as numbers 12-22 in ref 2, while the others are cited here in ref 3. Finally, we possess two submitted but unpublished manuscripts dated 1972 and 1981 which Prof. Liebhafsky made available to us before his death July 24, 1982. The research group of Richard Noyes in Eugene, OR, has looked at this reaction intermittently since 1975 and in addition to ref 2 has published three other papers4 and has discussed the mechanism in a re vie^.^ Two European research groups have also devoted serious attention to the mechanism of this reaction. Guy Schmitz in Brussels has published at least five papers? and the laboratory of Slobodan Ani6 and Ljiljana Kolar-Ani6 in Belgrade has been associated with 13 papers' of which we are aware. Furthermore, a recent joint publication from these two laboratories8 presents detailed computations which are asserted to explain the mechanism. Reference 2 also cites four other laboratories which have each publishedoneor two papers on this system. Therefore,the reaction discussed in the present paper was discovered over 70 years ago and has been the subject of at least 50 papers! Furthermore, there is surprisingly good agreement about the experimental behavior of this complex system. Reference 2 asserts 46 different types of behavior with which any mechanistic explanation should comply, and other papers report many further observations. However, all of our reading indicates that whenever studies in different laboratories overlapped the observations were in semiquantitative or at least qualitative agreement. Nevertheless, different groups disagree seriously about the mechanistic explanationsfor those agreed experimentalbehaviors, although virtually all of those explanations to date assume the oscillations could be modeled by means of homogeneous chemical t Permanent address: Department of Physical Chemistry, Comenius University, 842 15 Bratislava, Slovak Republic. e Abstract published in Aduonce ACS Absrracrs, October 1, 1993.

processes in a single uniform medium. We were sufficiently disturbed by the implications of ref 8 that we undertook further experimental studies. As a result of those studies, we have become convinced that a satisfactory explanation of these oscillations must also invoke interphase transport between gas and solution. Furthermore, we have developed a qualitative mechanistic explanation which differs significantly from all previous explanations (including our own) but which seems to be consistent with at least most of what is known about this venerable system. In section I1 below, we summarize major features of what has previously been observed in many laboratories. In section 111,we analyze the chemical species which must be present, the processes which they may undergo, and the steady states which those processes may generate; the stabilities of steady states are crucial to the understanding of chemical oscillators. In section IV, we present our own new experimental observations, and in section V, we summarize the constraints which any mechanistic explanation must satisfy and present our new skeleton mechanism which seems to be consistent with what is known.

11. Summary of Known Experimental Behavior Experiments have typically been conducted at 50-60 OC. on aqueous solutions prepared from the three components hydrogen peroxide(H202),iodate(asKI03),andacid (asH2SO4or HClOd). Behavior in a typical moderately-stirred system is strongly dependent upon acidity, and if [H+] is below about 0.04 M or is above about 0.06 M while [IO3-] is about 0.1 M or less, properties either vary monotonically or exhibit single extrema. Figures 1-5 from refs 2 and 6d show selected behaviors in the window of acidity for oscillatory behavior. Figures 1 and 2 show that the concentration of elementary iodine (as measured by spectrophotometry) increases with mild autocatalysistoa maximumatwhichit suddenlystarts todecrease. At the lower acidity (Figure l ) , absorbance of light changes discontinuously from monotonic increase to oscillations at full amplitude. At the higher acidity (Figure 2), absorbance discontinuously reverses direction of change but then decreases monotonically for a considerabletime until oscillations commence with amplitudes which are first infinitesimal but then increase to full blown. Figures 3 and 4 show the negative of the potential of an electrode specificto iodide ion in solutionsconsiderably more concentrated in iodate than Figures 1 and 2. At the lower acidity (Figure 3), thesystemspends most of the timeat relatively high concentrations of I- which undergo occasional pulses of decrease by about an order of magnitude. At the higher acidity (Figure 4), [I-] exhibits a rounded maximum at the time when the maximum in [I21 in

0022-365419312097-11354$04.00/0 0 1993 American Chemical Society

The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11355

Bray-Liebhafsky Reaction Oscillations

I

Y

w

0

.*#

X

3

u

0 pi

~

u

0

10

~

20

l

30

~

50

40 t (mid

t(mirJ

Figure 1. Spectrophotometric recording at 50 OCof iodine concentration in solution initially containing 0.104M KI03,0.490M H202, and 0.047 M HClO4. Reproduced from ref 2.

l

60

70

Figure 4. Potentiometric recording (presented as -PI) at 50 OC with an iodide-ionspecificelectrodein solution initiallycontaining 0.432M KIOo, 0.490 M H202, and 0.071 M HClO4. Reproduced from ref 2.

QO 6 15

F l p e 2. Spectrophotometric recording at 50 'C of iodine concentration in solution initially containing 0.104M KIO3,0.490M H202, and 0.059 M HC104. Reproduced from ref 2.

30

45

Figure 5. Variation at 60 OC of concentrationof H202 in M against time in minutes in a solution initially containing 0.095 M NaIO3, 0.100M H202, and 0.065 M HC104. Reproduced from ref 6d with the permission of the author. increases as [I21 decreases. This behavior is exactly what would be expected from the stoichiometries of processes I and I1 below. Studies by Sharma and Noyes294a and by Schmitza show that the concentration of dissolved 0 2 also oscillates in synchronization, and this gas seems to promote consumption of 12. Finally, light behaves somewhat as 02 and promotes conversion of 1 2 to IO3-. This brief summary has been only qualitative, but it lists a number of different features which any mechanistic analysis should explain.

111. Analysis of Selected Characteristics

0

IO

20

30,(mlJ0

50

60

FIgure 3. Potentiometricrecording (presented as -PI) at 50 O C with an iodide-ion specificelectrodein solution initially containing 0.432M KIO3, 0.490 M H202, and 0.055 M HClO4. Reproduced from ref 2. Figure 2 is sharp; it then decreases monotonically until oscillations commence starting with infinitesimal amplitude, just as happens with absorbance in Figure 2. Of course, the concentration of hydrogen peroxide decreases monotonically. However, Figure 5 from ref 6d shows that during oscillations the decrease takes place in steps. Periods when decrease in [HzOz] is slow correspond to times when [I21 is low and increasing, while periods when [H202] decreases rapidly correspond to times when [I21 has just passed its maximum and is also decreasing. As is discussed below, these rate correlations are directly opposite to those anticipated from the stoichiometries of net change happening at different stages in the reaction. Matsuzaki et al.9 observed that the concentration of H+ also oscillates in synchronization with other species so that [H+]

A. Chemical Species Which May Be hesent. The solution contains a few inert ions like Na+ or K+ and C104- or S042which must be present to preserve electroneutrality. Otherwise, every molecule or ion in the oscillating system contains atoms of the three elements hydrogen, oxygen, and iodine only. A convenient further classification is to distinguish species which do not or do contain iodine. Because decomposition of hydrogen peroxide produces oxygen irreversibly, the total system must contain the two phases: gas and aqueous solution. In most of the experiments reported in the literature, the system was open so the gas above the solution could mingle with the atmosphere, but such a situation is not essential. The gas in contact with the atmosphere will contain O2molecules and a t these elevated temperatures will also contain some I2 molecules, although escape of this species to gas phase usually will not significantly deplete the total iodine in thesolution. In a typical solution, species containing hydrogen and oxygen only and present in concentrations of over 0.01 M are H20, H202, and H+. Elementary oxygen, 02, will be present a t least a t its saturation concentration of slightly over 0.001 M and may supersaturate the solution at times.2~4a.M Negative ions and radicals such as OH-, OOH-, H', HO', and HOO' will be present at very much lower concentrations. Any other conceivable hydrogen-oxygen species will be present a t still more trivial concentrations.

l

Treindl and Noyes

11356 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993

Of the species containing iodine, IO3- will account for over 90% of all of the iodine present in a typical system. Elementary iodine, I2 (perhaps including 13-), will be between 1W and 10-3 M in a typical oscillator. N o other species contributes more than 1% to the total iodine present. The composition of the solution can therefore be described almost quantitatively in terms of the amounts of I2 and of IO3- only; however, some other composition variable must be specified to explain why sometimes one and sometimes the other of those two species is increasing. It is also convenient to classify iodine-containing species as oxidized or reduced. In addition to IO3-, hypothetical oxidized species might include HI02 and 102'. Liebhafsky et al.3a also postulate a species H21203but do not offer experimental evidence for its existence. In addition to 1 2 (and 13-),the most important reduced species is obviously I-, even though its concentration never seems to be more than of the order of 106 M in an oscillating system. Free iodine atoms, I*, must be invoked to explain the photochemical sensitivity of the reaction.2v4a The pivot between oxidized and reduced species is hypoiodous acid, HOI. In much of what follows, the ratio of concentrations of I- and HOI will be a measure of whether the solution is oxidizing or reducing. Schmitz6dS6c also invokes the species I20 as the anhydride of HOI. He does not cite any experimental evidence for its existence, and we would expect such a species to be rapidly hydrolyzed. The above analysis puts severe constraints on the possibility of explaining oscillations. Over 99% of the iodine in the solution exists as one of the two species I2 and IO3-. However, sometimes [I21 increases and sometimes it decreases at different times in the same solution. The key to explaining the oscillatory behavior of [I21 will be associated with the differences in composition associated with these different behaviors. B. Chemical Processes Which May Occur. The overall chemical change in the system is described by process T.

This process may be accompanied by a lot of complicated oxyiodinechemistry. However, by the time thesystem has reached equilibrium, all of the hydrogen peroxide will have been irreversibly destroyed, and the composition of the remaining system will be determined solely by the amounts of iodate and acid which were added initially. Process T does not take place in a single step. It can be described as the sum of two processes involving species containing hydrogen and oxygen only.

Ever since the original paper by Bray,l investigators have treated reactions I and I1 (given below) as important component processes. Each is irreversible under the conditions considered, and the sum of I + I1 is precisely 5 times the stoichiometry of irreversible process A. It is process A (perhaps in association with B) which generates the change in Gibbs free energy which drives the oscillating reaction. Furthermore, processes I and I1 must go a t equal rates in the steady state associated with oscillations in [I21 and [IO3-]. As commented in section I1 above, evolution of 0 2 is fastest when process I1 (which produces no 02)is dominant and is much slower when process I (which does produce 02)is dominant!

210;

+ 5H,O, + 2H+ I,

-

+ 5H202

-+

210;

I,

50,(aq)

+ 6H,O

+ 2H+ + 4H,O

(I)

Irreversible processes I11 and IV are also important. Liebhafskylo recognized their significance 60 years ago, and he studied their kinetics.lI-l3

HOI + H,O, H+ + I-

-

H+ + I- + O,(aq)

+ H,O,

-

+ H20

HOI + H,O

(111) (IV)

Processes I11 + IV also generate the precise stoichiometry of process A and may or may not be elementary. If processes I11 and IV went at equal rates, they also would generate a steady state in which net chemical change is described by process A. Finally, we should recognize the forward and reverse processes associated with the hydrolysis of elementary iodine, V.

I,

+ H,O

H+ + I-+ HOI

C. Characteristics of Selected Steady States. Sustained oscillations in chemical behavior can only take place in a system far from equilibrium. Furthermore, oscillations involve two or more opposing processes whose relative importance reverses during the oscillations. These opposing processes in concert can sometimes generate a single steady state which is unstable to infinitesimal perturbations. Alternatively, two steady states which would each be stable in the absence of the other processes may have comparable relaxation times and may couple to generate an oscillatory instability. The processes presented in subsection B can be combined to create four different steady states, at least some of which should individually or collectively be responsible for the oscillations in the Bray-Liebhafsky system. We shall here examine each of these steady states and its stability to perturbation. ( i ) Concentration of Dissolved Elementary Oxygen. Overall process T is the consequence of process A, which creates dissolved oxygen, and process B, which discharges it to the atmosphere. When A and B are going at equal rates, [ 0 2 ] will be in a steady state. Such a steady state may be unstable to perturbation if the system is a gas-evolution oscillator.5J4 However, the Bray-Liebhafsky oscillations take place in a stirred solution a t well above ambient temperature. Our experiencel4makes us doubt that the experimental conditions employed would generate a steady state which would be unstable solely because of the nucleation and escape of bubbles. If the rate of chemical production of dissolved 0 2 were constant, and if the system were stirred at least moderately, we would anticipate a stable steady state in which the concentration of dissolved gas was uniform. However, the concentration of that uniform solution would depend upon the rate of stirring and would be smaller the greater the rate of stirring. This kind of situation has been treated recently by Noyes, Rubin, and Bowers.15 Even though we anticipate that the steady state for transport of oxygen to the atmosphere should be stable for a constant chemical rate of production, we shall see below that steady-state processes for chemical production and for transport might couple tocreate an instability even when no steady state would beunstable in isolation. (ii) Hydrolysis of Zodine. The forward and reverse steps of process V behave like any chemical equilibrium. When they go at equal rates, they contribute no net chemical change to the state of the system. Furthermore, they are fast. Eigen and Kustin16 showed that the equilibrium of process V will be established in a period of the order of a second or less. Therefore, process V generates a stable equilibrium on a time scale fast compared to the other processes in the system. That equilibrium steady state is necessarily stable to perturbation and will be established too rapidly to couple with any other steady state in the system. In what follows, we shall assume that we can always write eq 1 where Kh is the equilibrium constant for hydrolysis process V.

The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11357

Bray-Liebhafsky Reaction Oscillations This equilibrium was studied by Burger and Liebhafsky," who concluded that a t 50 OC Kh = 4.12 X 10-12 M2.

(iii) Steady States Generated by Processes III and IV. A steady state will be attained when processes I11 and IV are going at equal rates. Such equality of rates will not represent a true chemical equilibrium, as discussed in (ii). Even if the rates of I11 and IV are equal, irreversible process A is simultaneously taking place. A system in such a steady state is far from equilibrium, just as it must be if oscillations are possible. If the kinetics of processes I11 and IV were the same as their stoichiometries with rate constants k111and k ~ vrespectively, , we could write eqs 2 and 3 in a steady state.

(3) LiebhafskyIO made precisely this sort of analysis. However, he also showedI3 that the situation is more complicated and that the k~v[H+]term should be combined with one which is zero order in [H+]. The species in such a steady state need not be in the same ratios as in an equilibrium expression. Therefore, at least k ~ in v eq 3 may be a function of pH even though the steady state will necessarily contain the three species I-, 12, and HOI in concentrations which satisfy eq 1 and which also produce equal rates for processes I11 and IV. If a system does not contain a significant amount of IO3- or of other oxidized iodine species, and if there are no reduced species except those in processes I11 and IV, there can be only one composition which satisfies eqs 1 and 2 simultaneously for a specific total concentration of reduced iodine. That composition will describe a steady state which we believe should necessarily be stable to perturbation. (iu)Steady States Generated by Processes I and II. As pointed out in subsection B, a steady state is produced when processes I and I1 are going at equal rates. Of course, irreversible process A is also proceeding. The system will have I2 and IO3- in the proper relative amounts to maintain the equality of rates and will also contain I-, 12, and HOI in amounts which satisfy eq 1. One could equate kinetics to stoichiometry to derive equations for such a steady state which resemble eqs 2 and 3 above. However, work at Berkeley over 60years agolB-20showsthat such an exercise would be pointless. Thus a t 25 'C, process I1 exhibits an induction period of hours unless acidity is much greater than that appropriate for oscillations. The processes which establish such steady states are obviously complicated. The experimental oscillations in the Bray-Liebhafsky system involve the species I2 and IO3-. The argument in (iii) concluded that a steady state involving only reduced species is probably stable to perturbation. If we add the single variable [Io3-] and also impose the constraint that rates of processes I and I1 are equal, we believe that the resulting steady state will still be stable. Unless some of the kinetics are unanticipatedly complex, processes I-V are insufficient to generate an oscillatory instability unless that instability arises because the rates of those processes are affected by still unspecified intermediate species. D. Conclusions about Steady States. Subsection C above discussed four different coupled pairs of processes such that each pair can generate a steady state. The equilibrium hydrolysis of I2 (ii) is too rapid to combine with any of the other steady states in a way to generate oscillations. The steady-state transport of 0 2 to gas phase (i) will almost certainly generate a stable steady state if chemical production of O2 is taking place at a constant rate. The coupling of processes I11 and IV (iii) will probably generate a stable steady state if only the reduced species 12, I-, and HOI are present. The coupling of processes I and I1 (iv)

involves the species I2 and 103-, which are observed experimentally to oscillate and must therefore be associated with an unstable steady state. Either this steady state is unstable because of the unusual kinetic features of processes I and I1 or else the steady state in (iv) is coupled to the gas-transport steady state in (i). IV. Experimental Section

A. Materials. The species NaI, KIO,, 12, HC104,and NaC104 were reagent grade chemicals used without further purification. Solutions of hydrogen peroxide were made from 30% aqueous material without stabilizer obtained from the Eastman Chemical Co. We usually obtained similar results from reagent grade material which contained stabilizer but felt it was best to use stabilizer-free material for the results we reported. B. General Procedures. All measurements were made at 50 O C . Because these studies did not include quantitative kinetic measurements, we did not impose severe thermostatic constraints but probably controlled temperature to about a tenth of a degree. In order to make sure that our light beam or electrode was sampling a uniform medium, solutions were lightly stirred. Effects of more severe stirring are discussed in subsection H. The steady-state compositions which we report were not obviously perturbed by evolution of oxygen bubbles. C. SpectrophotometricProcedures. Measurements were made with quartz cells in a Hewlett Packard 8452A diode array spectrophotometer. Cells were thermostated and stirred magnetically with Hewlett Packard accessories to prevent development of gradients in composition. We made our measurements at 440 nm, where we found an extinctioncoefficient of 596.1. Wemade this choiceof wavelength because our absorbance was not affected by addition of I-. Stanley Furrow of the Berks Campus of Pennsylvania State University has since told us that the isosbestic point which he finds for 1 2 Is- is 470 nm. We have not resolved the discrepancy between our laboratories, but the measurements we report in this paper were on solutions which did not contain significant amounts of I- or Is-. D. Potentiometric Procedures. Concentrations of iodide ion were measured with an Orion iodide-ion-specific electrode against a mercury sulfate reference electrode. We used an Orion pH/ ISE meter Model 720A and a Linear Scientific Inc. Deluxe Laboratory Chart Recorder Model 500. These solutions also were lightly stirred. The electrode was first calibrated by measuring potentials, E , of solutions of I- and of Ag+ between lc3 and 1V M,and [I-] in any other solution was calculated by use of eq 4 obtained in the same way as the equation for bromide concentrations derived by Ganapathisubramanian.21

+

E/mv = -385.4 - 0.06412 log [I-]

(4) In eq 4,0.064 12 is the theoretical slope of potential against logarithm of concentration a t 50 OC. The number -385.4 mv is the potential such that the extrapolated curves for log [I-] and log [Ag+] coincide; it leads to -14.5 for the logarithm of the solubility product of AgI at 50 'C and ionic strength of 0.1 M compared to textbook values of about -16 at 25 OC and infinite dilution. The difference is in the direction to be expected. E. Studies in Systems without Initial Iodate. We tried to prepare a few solutions in steady states generated by processes I11 and IV only. The solutions had initial compositions [I-], = 0.01 M,[H202],= 0.025 M,and [HClO4], + [NaC104], = 0.1 M. We varied [H+], between 0.01 and 0.1 M. Therefore, the concentration of hydrogen peroxide was rather small, and the ionic strength was approximately constant. Absorbance at 440 nm rose to a maximum due to combined processes IV and V and then began to decrease because of the onset of process 11. At that maximum, stoichiometry requires that [121max 5 0.005 M. For the systems reported in Table I, the

11358 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993

Treindl and Noyes

TABLE I: Compositions (in M) of Steady-State Systems at 50 'C [H+l0 0.01

[IO3-lo 0.05 0.1

0.04

0.05 0.1

0.045

0.05 0.1 0.2

0.05

0.05 0.1 0.2

0.055

0.05 0.1

0.06

0.05 0.1

0.1

0.05 0.1

[H202], 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3

l@[Iz] 1.42 1.54 2.16 1.55 3.97 6.27 1.21 2.78 3.86 1.69 2.40 3.64 1.66 2.61 3.26 1.71 2.61 2.74 1.71 1.09 1.97 0.72 0.92 0.94 1.09 1.58 1.84 0.30 0.63 0.65 0.61 0.79 1.14 0.63 1.1 2.04 0.28 0.87 1.34 0.45 0.63 0.81 0.21 0.72 0.87 0.29 0.42 0.72

108[1-] 53.5 114.6 166.6 72.7 152.8 239.4 5.4 11.0 12.2 6.1 10.2 15.4 1.5 4.0 8.9 2.2 4.4 9.2 2.7 0.8 3.6 3.2 2.5 1.7 1.o 1.3 1.9 0.7 1.3 1.2 1.1 1.3 1.6 0.9 0.9 1.4 1.2 1.1 1.4 0.9 0.8 1.1

0.5 0.5 0.6 0.4 0.4 0.6

[I-]/[HOI]

10*[HOI][HzOz]

101z[H+]2[I-][I03-]

4.9 20.7 31.2 8.2 14.3 22.2 0.23 0.42 0.37 0.22 0.42 0.63 0.015 0.068 0.267 0.031 0.079 0.339 0.046 0.006 0.070 0.169 0.083 0.038 0.012 0.013 0.025 0.017 0.033 0.027 0.028 0.029 0.030 0.015 0.01 1 0.012 0.07 1 0.021 0.021 0.024 0.015 0.023 0.029 0.009 0.009 0.014 0.01 1 0.012

1.1 1.1 1.6 0.9 2.1 3.2 2.3 5.2 9.8 2.8 4.8 7.3 10.1 11.9 10.0 7.1 11.0 8.2 5.8 25.1 15.2 1.9 6.1 13.5 8.8 19.9 23.4 3.8 7.9 13.5 4.0 9.1 16.2 5.5 17.8 33.8 1.7 10.7 20.0 3.6 10.8 14.6 1.7 11.4 18.6 3.0 8.1 15.0

2.7 5.7 8.3 7.3 15.3 23.9 4.3 8.8 9.7 9.8 16.4 24.6 1.5 4.1 9.0 4.5 8.8 18.7 10.9 3.2 14.4 4.0 3.1 2.1 2.5 3.3 4.9 3.3 6.6 6.0 1.7 2.0 2.4 2.6 2.8 4.1 2.1 2.1 2.5 3.1 2.1 4.1 2.5 2.6 2.9 4.0 4.3 6.0

maxima were reached within 5 min, and measured values of [I z ] ~ ranged from 0.004 81 to 0.005 12 M, agreeing with the stoichiometric constraint if we accept an error of the order of 2%. At those maximum values of [Iz], no significant amounts of iodate had yet been produced. The maxima in absorbance due to [Iz] did not correspond to true steady states because [I-] continued to decrease as measured potentiometrically. However, for all runs where [H+],, was between 0.05 and 0.1 M, we found [H+][I-]/[HOI] = 8 X 104 within about 10% at the time of maximum absorbance. At low acidities, that value decreased by a factor of up to 4. Equation 3 predicts that this quantity should have been constant for a steady state in the absence of iodate. Even these deviations from constancy are consistent with the observations of Liebhafsky and Mohammad13 on the kinetics of process IV. Their work indicates that the k~v[H+]in eq 3 should be replaced by k, + k,[H+] with the two terms of comparable magnitude near the middle of the range of acidities we used. Once again, observations of this system in different laboratories are internallyconsistent even when different studies were separated by several decades! Our crude data did not indicate any kinetic anomalies in systems containing only insignificant amounts of iodate. Although our observations certainly do not preclude the existence of the 120

behavior

osc osc osc osc osc

osc osc osc osc sc-osc osc osc sc-osc osc osc osc

anhydride invoked by Kolar-Anic and Schmitz,8they also do not suggest its significance. As long as the reduced iodine species I-, 12, and HOI are the only iodine species reacting with acidic hydrogen peroxide, the system appears to behave as proposed above with no behaviors which anticipate oscillatory behavior. F. Compositiwsof Combined Steady States. We also prepared a number of systems which resembled those in subsection E except that K I 0 3 was added initially at 0.1 M and NaI was omitted. Each solution was stirred moderately at the same setting of the stirrer motor intended to create reproducible uniformity. Each system was followed both spectrophotometrically and potentiometrically in different cells. Some systems exhibited oscillations soon after they had been prepared, but all eventually attained steady states which obviously required equal rates of processes I and 11. The properties of these systems at 50 OC are presented in Table I. The first three columns define the initial compositions immediately after mixing. Although [H202] then decreased monotonically, we made no effort to estimate this effect. The fourth and fifth columns provide concentrations of IZ and of Iin the steady states from our spectrophotometric and potentiometric measurements, respectively. The ratio [I-]/ [HOI] in the sixth column is an inverse measure of the oxidizing nature of the

Bray-Liebhafsky Reaction Oscillations

The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11359

TABLE II: Behaviors of Indicated Compositions at 50 O C When [HCIO& = 0.045 M and [NaC1041, = 0.055 M (B)

(h)

(9

ci) (k)

(1)

(m)

[H202], = 0.1 M [IO3lO= 0.1 M goes to steady state with [I21 = 1.7 X lo-' M (Table I) [H202], = 0.1 M [ I ~ I=, 5 x 10-5 M [I03-], = 0 no detectable change in absorbance in 1 h consistent with Liebhafsky observation quoted in (a) [ I ~ I= , 5 x 10-5 M [I03-], = 0.1 M [ H ~ o ~ l o0 absorbance decreases but less than 10%in 1 h [I-], = lo-'M [103-], 0.1 M [H20210 = 0 essentially instantaneous formation of 12 followed by behavior identical with that in (i) [H202], = 0.1 M [Iz], = 5 X lesM [I03-], = 0.1 M absorbance exhibited saw-tooth oscillations commencing by the time measurements could be initiated. Amplitude was about 15% and period was about 6 min. Oscillations were scarcely changed for over 2 h, but total absorbance drifted down about 15% per hour [I-], = lo-'M [IO3-], 0.1 M [HzOz], 0.1 M absorbance rose slightly autocatalytically for about 15 min until oscillations commenced at full amplitude. Subsequent behavior was identical with that in (k) [I-], = 3.4 X lo-' M [I03-], 0.1 M [Hz02], = 0.1 M absorbance behaved much as in (k) but no oscillations in potentiometric trace [I210 = [I-lo = 0

medium and varies from over 20 in less acidic reducing media to 0.01 in the most acid oxidizing media. The seventh and eighth columns in Table I are derived from assumptions about the kinetics of processes I and 11. Those two processes involve oxidation and reduction of H202, but that species does not react rapidly directly with either 1 2 or IO3-. The [HOII[H202] product in the seventh column is proportional to the rate at which elementary 02 is being produced by process 111; it is this species which we believe is responsible for initiating process 11. The ion product in the eighth column is proportional to the determination by Furuichi et al.22 of the rate of the D ~ s h m a n ~ ~ reaction in which IO3- is reduced by I-. The final column in Table I uses OSC to indicate a system which exhibited oscillations before decay to the study state and uses SC-OSC to indicate that those oscillations were preceded by a smooth catalysis of H202 decomposition. Table I illustrates the comments in section I1 that oscillations occur only in avery limited range of acidities. All of theoscillating systems in Table I have [H+l0between 0.045 m and 0.055 M, although that rangecould be extended by changing concentrations of iodate and peroxide. We have not been able to develop quantitative criteria which use the entries in Table I to determine which steady states are stable and which are unstable and bscillatory. However, all of the oscillatory steady states have [HOI][H202] greater than about 4 X 10-8 MZ.Most steady states which were previously oscillatory also have ratios [I-] / [HOI] below about 0.08. The reasons for these effects will become apparent in the discussion in section V. G. PreviousStudieaofProcessesWhichGenerateSteadyStates. Table I lists properties of a number of systems in steady states where processes I and I1 were going at equal rates. The experimental fact that some of those steady states were unstable to oscillations requires that the kinetics of processes I and I1 are at least sometimes quite different from their stoichiometries. Those processes were studied extensively at Berkeley in 1931 and reported in refs 18-20. We have selected a few of the observations from then which seem particularly relevant to the mechanisms of these complicated processes. Page numbers in these citations refer to Volume 53 of the 1931 Journal of the American Chemical Society: (a) 'When hydrogen peroxide and iodine solutions are mixed with peroxide in moderate excess, no great change in the concentration of iodine occurs even after several weeks, but the hydrogen peroxide gradually disappears. ... If the mixture is made acid, this induction period may be greatly shortened; if iodate ion is added also, ...the initial delay may be eliminated entirely and iodate is formed. The time then required, at room temperature, for half the iodine to be oxidized is approximately one minute" (p 2075). (b) The rate of oxidation of I2 by H2Oz (process I1 in presence of air) is first order in [I21 except at very low concentrations,

when the order approaches zero, but the rate is independent of [HzOzl (PP 47,2078). (c) With moderate [HzOz], the ability of IO3- to accelerate process I1 (which produces IO3-) saturates above about [I03-] = 0.1 M (Figure 3, p 2080). (d) The rate of catalytic decomposition of H202 decreases as [I2] decreases (p 2083). (e) H202 cannot oxidize HOI fast enough to explain oxidation of 1 2 to IO3- in the Bray reaction (p 2083). ( f ) The induction period for reduction of IO3-by H202 (process I) is inversely proportional to [HzOz] (p 905). These unusual kinetic behaviors should be accommodated to any mechanistic model which is finally developed for processes I and 11. We also made a few measurements far from steady-state conditions of processes I and 11. The results are presented in Table I1 with individual experiments designated (g) to (m) for easy reference. Experiments (8) to (i) confirm the Liebhafsky observations in 1931 that H202 does not react with 1 2 at a detectable rate, that IO3- reacts with it only very slowly, but that the two oxidants together react with it fairly rapidly. Experiments (i) and (j)demonstrate that I- reacts very rapidly with excess IO3- to form 12, which then reacts very slowly in the absence of H202. Experiments (k) and (1) show that a solution with I2 and excess IO3- reacts much the same with H202 whether I2 was present initially or whether it was created by reaction of I- with IO3--. Experiments (g) and (k) to (m) raise somedisturbing questions about reproducibility for these experiments near the minimum acidity at which oscillations are observable. Experiment (8) generated an entry in Table I. The potentiometric cell generated two oscillations of small amplitude which were responsible for the OSC entry in the table; the spectrophotometric cell was not followedcloselybut went to an unequivocal steady state as reported in the table. After experiment (k) exhibited unanticipated oscillations, experiment (1) was performed with both cells; the spectrophotometric cell behaved much like (k), just as anticipated, while the potentiometric cell underwent somewhat damped oscillations for an hour before attaining a steady state. Experiment (m) was designed to create instantaneously a solution like the steady state in (g). The spectrophotometric cell exhibited persistent oscillations, while the potentiometric cell exhibited only five oscillations before attaining a steady state. We finally attempted to reproduce experiment (8) exactly as had been done a few weeks earlier. The spectrophotometric cell exhibited persistent oscillations where it had generated a steady state a few weeks before, and the potentiometric cell exhibited no oscillations whatsoever where it had oscillated twice in experiment (g )!

11360 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993

r

Treindl and Noyes

-

t

M p e 6. Potentiometric rccording at 50 "C for a solution initially containing [H+l0 0.045 M, [IOS-]~ = 0.2 M, [HzOzlo = 0.1 M, [HC104] + [NaClO,] = 0.1 M. At the time of the first vertical arrow, the rate of stirring was increased from moderate to very fast; at the time of the sccond vertical arrow, it was reduced to the same moderate rate.

t

t

t

-

t

t

Figure 7. Potentiometric recording at 50 "C for a solution initially containing [H+l0 0.055 M, [ I o r l o = 0.05 M, [HzO~],= 0.2 M,[HCIO,] + [NaCIOd] = 0.1 M. At the times of the first and third vertical arrows, the rate of stirring was increased from moderate to very fast; at the times of the sccond and fourth arrows, it was reduced again to the same moderate rate.

We conclude that this combination of concentrations is very close to the bifurcation between oscillations and stability and that these systems arevery sensitiveto environmental factors like stirring and temperature which are very difficult to control precisely. H. Effects of Stirring and of Sonication on Behavior. The comment in the preceding paragraph introduces the effect which we believe is the most important observation reported in this paper. During some correspondence with Dr. Guy Schmitz of the UniversitC Libre de Bruxelles, he reminded us that theoriginal paper by Bray' reported oscillations with periods of days and continuing for weeks. As we pondered ways to explain that observation, we began to wonder whether transport of oxygen to the atmosphere (process B in this paper) might be associated with the oscillations. We therefore performed the experiments illustrated in Figures 6 and 7. In each experiment, the potentiometric cell was stirred at a reproducible motor setting which gave good mixing but not extreme disruption. Both spectrophotometricand potentiometric systems were oscillatory. Figure 6 for the potentiometric cell at the lower acidity exhibited pulsed relaxation oscillations, and Figure 7 at the higher acidity exhibited moresinusoidaloscillations just as expected. At the times indicated by arrows, stirring was suddenly increased to the maximum possible for the motor employed. Oscillations were immediately suppressed in both experiments but could be restored if the rate of stirring was reduced to the previous value. Sonication very much extended the period of the oscillations but did not suppress them entirely. We regard these observations as unequivocal evidence that rapid removal of oxygen can suppress oscillations, and we have not thought of any plausible explanation unless the transport of oxygen from the supersaturated solution is a significant component of the overall mechanism of the oscillations.

iodine in the system, the optical absorption (measure of [Iz]),the potential of an ion-specific electrode (measure of [I-]), and the value of Kh in eq 1. Those constraints will be sufficient to uniquely define the state of the system in terms of the four composition variables unless kinetic behavior near a steady state is even more bizarre than we think it is or unless there is another compositionalvariable which is comparable in magnitude to [I,] and which relaxes on a time scale comparable to that for establishing a steady state between [Iz] and [103-]. Two iodine-containings p i e s have been postulated previously to perform as such a compositional variable. Liebhafsky et al.3. have invoked HzIzOp. Kolar-Ani6 and Schmit-8 have invoked 1 2 0 . Edelson and no ye^'^ invoked [Oz(aq)] along with other iodine-containing species. None of the previous groups developed experimental evidence for their proposals, although Sharma and Noyesk did demonstrate that the solution was supersaturated with 02,at least at some times during an oscillatory period. A final decision among these mechanistic proposals must await quantitative comparison with experiment. However, we believe that effects of stirring we report here make a strong case that [Oz(aq)] deserves to be considered as a species which should be invoked in the mechanistic explanation. B. Our New Skeleton Mechnlsm. After considering various possibilities, we have selected elementary processes S1 to S9 as a mechanistic sequence which we believe can be combined with process B to explain at least a very large portion of the observations which have been made on this complex system.

IO;

HIO,

V. Development of the New Explanation A. SpeciesNecessary To Develop a Mechanism. The material in section I11 invokes only four iodine-containing species-I-, 12, HOI, and IOp-. As was pointed in section III(A), over 99% of the composition of any system of interest can be described by specifying concentrations of I2 and IO3- only. For any system, we can also determine four independent experimental constraints. They are the total concentration of

+ I- + 2H+

-

HIO,

+ I- + H+

-

+ HOI

2HOI

(sa

HOI+I-+H+~,+H,O HOI + H,O, I-

-+ I-

+ H+ + H,O,

H+ + O,(aq)

-

HOI

(SI)

+ H,O

+ H,O

(S3) (S4) (S5)

Bray-Liebhafsky Reaction Oscillations

I'

210,'

The Journal of Physical Chemistry, Vol. 97, No. 43, 1993

+ 02(aq) e 100'

+ H20

-

(S7)

+ H+ + HIO,

IO;

(S9)

The stoichiometry of process I is generated by the sequence of eq 5. (I)

2(S1)

+ 2(S2) + (S3) + 5(S4)

(5)

Equation 5 is dictated by the requirement that IO3- reacts readily with I- but not at a significant rate with H202 or with I2 directly (see refs 18-20 and experiments (g) to (j)in Table 11). We have no evidence whether HI02 does or does not react with H202 in a direct step, but we prefer to leave HOI as the only oxidant which can attack H202. This sequence also supports the proposal of Furuichi et a1.21 about the importance of the Dushman22 reaction for the mechanism of the Bray reaction. The explanation of process I1 is somewhat more involved. This process as written does not contain 0 2 either as a reactant or as a product, yet process I is fastest when process I1 is producing 0 2 as illustrated by Figure 5 . The oxidation of reduced iodine by 0 2 is then initiated by step (S7), which first forms the peroxy radical 100'. That peroxy radical then rearranges by step S8 to the symmetric 010' radical written as 102'. The sequence does not pass through HI02 as an intermediate, and the net stoichiometry is that reduced iodine is oxidized by H202 even though the mechanism is that it is oxidized by 0 2 ! The stoichiometry of process I1 is then generated by decomposing it to processes a,8, and A and developing the sequences of eqs 6-9.

I,

+ 202(aq) + H 2 0 2HI02

-

IO;

+ + H+ + HIO,

+ 3H20,

-+ I,

302(aq)

2H,02

2H,O

+ 02(aq)

-

+ 4H20

+ 2(S7) + 2(S8) + (s9) (0)= 2(S2) + (S3) + 3(S4)

(a)E (S6)

(A)

= (S4)

+ (S5)

(a)

(P) (A) (6) (7) (8)

Of course, the stoichiometries of processes I11 and IV are identical with those of steps S5 and S4, respectively. This mechanistic explanation accounts for some things which have been frustrating the senior author of ref 2 ever since he wrote the manuscript for that paper. Thus, process I1 does not involve 0 2 in its stoichiometry even though the effects of other gases and the sensitivity of photochemical effects seem to invoke 0 2 in the mechanism. H e also reached the conclusion then that H202 was not a strong enough oxidant to oxidize HOI to HI02. Finally, we felt even then that if HI02 were an intermediate in both processes I and 11, then it was hard to explain why it was

11361

sometimes oxidized and sometimes reduced in a medium which seemed almost invariant. Those concerns have suddenly disappeared! The stoichiometric sequences of eq 6-8 produce and consume 0 2 in precisely equal amounts. Furthermore, HI02 is not an intermediate in the sequence which leads to IO3-, and HI02 in this skeleton mechanism functions only as an oxidant (in process I or 8) and never as a reductant. Since the first draft of this manuscript was submitted, Henry Taube has called our attention to a paper by Rice and Reiff,24 who also reported significant effects of stirring on the Bray reaction. They interpreted their observations as indicating heterogeneous catalysis of oscillations by dust particles. Although wedisagree with that interpretation, we are interested that effects of stirring have previously been reported. Although the paper by Rice and Reiff was cited in ref 2, the reported stirring effects have been overlooked. C. Summary of Our Mechanism. As Bray' and everybody since have recognized, oscillations result from alternating dominance of processes I and I1 coupled with the necessity for 0 2 to escape to the atmosphere by process B. Process I is the oxidation of H202 to 0 2 by IO3- while the oxidant is reduced to 12. We propose that H202 is oxidized only by HOI in step S4. Because HOI is produced late in the sequence, the overall production of 1 2 is aucatalytic, as is evident in Figures 1 and 2. Process I1 is the oxidation of I2 by H202 while the reductant is oxidized to IO3-. However, we propose that the real oxidant is O2and that H202 itself can oxidize no iodine-containing species except iodide ion, I-, even though H202 is the only oxidant in the overall stoichiometry for process II! The rapid hydrolysis and dissociation equilibria of elementary 12 provide the species which are actually being oxidized. Everybody agrees that processes I and I1 going at equal rates generate a steady state whose net chemical change is process A. Processes I11 and IV going at equal rates also generate a steady state whose net chemical change is process A. Steps in this latter steady state are even faster than those in the one involving only processes I and 11, so production of 0 2 will be faster when more of the iodine is present as 1 2 than when it is almost entirely IO3--just as is observed experimentally. However, the argument developed in section IV(E) concludes that the steady state generated by chemical processes I-V alone should be stable instead of the oscillatory instability observed experimentally. We propose that transport process B proceeding at the proper rate can couple with the purely chemical steady states to generate the observed instability. If I2 is present in sufficient amount, the 02 being produced will drive the system to convert I2to IO3- by process I1 and thereby to move away from the steady state generated by chemical processes only. Production of O2will then slow down until process I becomes dominant, and the system again approaches the chemical steady state. We do not claim that the relatively small number of observations reported in this paper is sufficient to demonstrate a mechanism of oscillations radically different from any proposed during decades of study of this reaction. We do believe that our alternative mechanism deserves serious consideration. We are initiating an effort to perform model calculations with this chemical mechanism. We also think additional experiments could determine further how transport of 0 2 to the atmosphere can couple with the chemical steady state of processes I and 11. For instance, it occurs to us that a sufficient stream of argon should inhibit oscillations at least under some conditions. The observations of Noyes, Rubin, and Bowed5 also suggest that oscillatory behavior should depend in other ways on the rate of stirring. Thus, minimal or even no stirring should greatly reduce the frequency of oscillations, just as Bray' observed. Presumably, most of the previously reported studies were a t stirring rates which

11362 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993

fell on the “plateau” of transport rates observed by Noyes et al.;ls behavior should then be independent of stirring rate. Finally, very rapid stirring should greatly increase the rate of transport and strongly inhibit oscillations, just as we report in the present paper. Systematic study of effects of argon stream and stirring rate deserves to be made. Wealso wonder whether thecoupling of transport andchemistry might be involved in other oscillatory systems where elementary oxygen is produced or absorbed by autocatalytic processes. A prime candidate might be the cobalt-salt catalyzed oxidation of benzaldehyde known as the Jensen oscillator.25 It may be significant that JensenZSareportedin the first paper that oscillatory behavior was strongly impacted by the rate of flow of 0 2 to the solution.

Acknowledgment. This research was supported by Grant No. CHE-9113897 by the National Science Foundation. This paper is No. 98 in the series ”Chemical Oscillations and Instabilities.” No. 97 is as follows: Bar-Eli, K., Noyes, R. M. J. Phys. Chem. 1992, 96, 7665-7670. We are indebted to Dr. Guy Schmitz of the Universite Libre de Bruxelles for giving us permission to use Figure 5 and for reminding us of oscillations with very long period which Bray observed in his original paper. His comments led us to examine the effects of stirring which constitute the most important experimental contribution of this manuscript. Dr. Henry Taube of Stanford University alerted us to references and comments over half a century ago. References and Notes (1) Bray, W.C. J . Am. Chem. SOC.1921,43,1262-1267. (2) Sharma, K. R.; Noyes, R. M. J. Am. Chem. SOC.1976,98,43454361. (3) (a) Matsuzaki, I.; Nakajima, T.; Liebhafsky, H. A. Faraday Symp. Chem. Lett. 1974,1463-1466. (b) Liebhafsky, Chem. SOC.1974,9,55-65; H.A.; McGavock, W. C.; Reyes, R. J.; Roe, G. M.; Wu, L. S. J. Am. Chem. SOC.1978,ZOO, 87-91. (c) Liebhafsky, H.A.; Roe, G. M. In!. J. Chem.Kinet. 1979,1 1 , 693-703. (d) Liebhafsky, H.A.; Furuichi, R.; Roe, G. M. J . Am. Chem. SOC.1981,103,51-56. (4) (a) Sharma, K. R.; Noyes, R. M. J. Am. Chem. SOC.1975,97,202204. (b) Edelson, D.;Noyes, R. M. J. Phys. Chem. 1979,83,212-220.(c) Odutola, J. A.; Bohlander, C. A.; Noyes, R. M. J . Phys. Chem. 1982,86, 818-824. (5) Noyes, R. M. J . Phys. Chem. 1990,94,44044412.

Treindl and Noyes (6) (a) Schmitz, G. J . Chim. Phys. 1974,71,689-692.(b) Schmitz, G.; Rooze, H. In Synergetics, Farfrom Equilibrium; Pacault, A,, Vidal, C. Eds.; Springer-Verlag: Berlin, 1979;pp51-56. (c) Schmitz,G. InNon-Equilibrium Dynamics in Chemical Systems; Vidal, C., Pacault, A., Eds.; SpringerVerlag: Berlin, 1984;p 237. (d) Schmitz, G.J. Chim. Phys. 1987,84,957965. (e) Schmitz, G. J . Chim. Phys. 1991,88,15-25. (7) (a) VeljkoviC, S.R. Bull. SOC.Chim.Beograd 1981,46,711-714.(b) AniC, S.;MitiC, D.; Kolar-AniC, L. J. Serb. Chem. SOC.1985, 50, 53. (c) AniC, S.;MitiC, D.; VeselinoviC,D.; Kolar-Ani6 J. Serb. Chem. SOC.1985,50, 529. (d) Ani& S.;Kolar-AniC, L. Ber. Bunsenges. Phys. Chem. 1986,90, 539-542,10861086.sen: (e) AniC, S.;MitiC, M.; Curcija, M. J. Serb. Chem. Soc. 1987,52, 575-579. (0 AniE, S.;Kolar-AniC, L. Ber. Bunsenges. Phys. Chem. 1987,91, 1010-1013. (8) AniC, S.;MitiC, D. J . Serb. Chem. SOC. 1988,53, 371-376. (h) AniC, S.;Kolar-AniC, L. J Chem. Soc., Faraday Trans. 1 1988,84, 3413-3421. (i) AniC, S.;Stanisavljev, D.; Kmajski, G.; Belovljev, Kolar-AniC, L. Ber. Bunsenges. Phys. Chem. 1989, 93,488491. (j) AniC, S.;VukojeviC, V.; RadenkoviC, M.; Kolar-AniC, L. J . Serb. Chem. Soc. 1989,54,521-526.(k) Kolar-Anit, L.; MisljenoviC, D. R.; Stanisavljev, D. R.; AniC, S.R. J. Phys. Chem. 1990,94,8144-8146. (1) AniC, S.;KolarAniC, L.; Stanisavljev, D.; BegoviC, N.; MitiC, D. React. Kinet. Catal. Lett. 1991, 43, 155-162. (8) Kolar-AniC, L.; Schmitz, G. J. Chem. Soc., Faraday Trans. 1992, 88,2343-2349. (9) Matsuzaki, I . ; Woodson, J. H.; Liebhafsky, H. A. Bull. Chem. SOC. Japan 1970,43,3317. (10) Liebhafsky, H.A. J. Am. Chem. SOC.1932,54, 1792-1806. (1 1) Liebhafsky, H. A. J . Am. Chem. SOC.1932,54,3499-3503. (12) Liebhafsky, H.A. J. Am. Chem. Soc. 1932,54,35043508. (13) Liebhafsky, H.A.; Mohammad, A. J. Am. Chem. SOC.1933,55, 3977-3986. (14) Rubin, M. B.; Noyes, R. M.; Smith, K. W. J . Phys. Chem. 1987,91, 1618-1 622. (15) Noyes, R. M.; Rubin, M. B.; Bowers, P. G. J.Phys. Chem. 1992,96, 1000-1005. (16) Eigen, M.; Kustin, K. J . Am. Chem. Soc. 1962,84,1355-1361. (17) Burger, J. D.;Liebhafsky, H. A. Anal. Chem. 1973,45,600-602. (18) Bray, W. C.;Liebhafsky, H. A. J. Am. Chem. SOC.1931,53,3844. (19) Bray, W. C.; Caulkins, A. L. J . Am. Chem. Soc. 1931,53,44-48. (20) Liebhafsky, H.A. J . Am. Chem. SOC.1931,53, 896-911, 20742090. (21) Ganapathisubramanian, N.; Noyes, R. M. J . Phys. Chem. 1982,86, 3217-3222. (22) Furuichi, R.; Matsuzaki, I.;Simic,R.; Liebhafsky,H. A. Inorg. Chem. 1972, 11, 952-955. (23) Dushman, S.J. Phys. Chem. 1904,8,453. (24) Rice, F. 0.; Reiff, 0. M. J . Phys. Chem. 1927,31,1352-1356. (25) (a) Jensen, J. H. J . Am. Chem.SOC.1983,105,2639-41.(b) Roelofs, M. G.; Wasserman, E.; Jensen, J. H. J. Am. Chem. SOC.1983,105, 63296330;1987,109,4207-4217. (c) Reimus, A. M.; Massie, J. M.; Hudson, J. H. Ind. Eng. Chem. Res. 1989,28,590-599. (d) Colussi, A. J.; Ghibaudi, E.; Yuan, Z.; Noyes, R. M. J. Am. Chem. SOC.1990,112,8660-8670. (e) Guslander, J.; Noyes, R. M.; Colussi, A. J. J. Phys. Chem. 1991, 95,43874393.

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As a result of an error by the printer, an incorrect version of the masthead omitting Senior Editor Arthur J. Nozik appeared in the September 16, 23, and 30 issues.