Mechanism of the Oscillatory Decomposition of Hydrogen Peroxide in the Presence of Iodate Ion Iodine etc. BY ISAO MATSUZAKI NAKAJIMA AND TSUYOSHI Dept. of Synthetic Chemistry Faculty of Engineering Shinshu University Nagano Japan AND HERMAN A. LIEBHAFSKY Dept. of Chemistry Texas A & M University College Station Texas U.S.A. Received 25th July 1974 Various mechanisms are constructed with the aid of information on associated reactions and ~ tested in the light of the theory of two-variable oscillating reactions as well as by means of computer simulations. Reactions were run mainly at [HC1OJo= 0.035 to 0.080 [KIO3l0 = 0.40 and [H,O& = 0.30mol I.-' and compared with computer results for a promising mechanism. Agreement is so good with respect to the induction period the pulses of [I-] and the rate of O2evolution the abrupt decrease in [Iz]etc.for one to conclude the mechanism to be plausible. The plausible mechanism contains HI02 HIO I- H21203 and H31305 as intermediatesand the second-order back-activation step 2HI02+HIO+ H20z -f 3HIo2+H20as the key step for the oscillation which results from the sequence of HIOz+HI0 +HzIzO~,H2Iz03+HI02 + H31305 and H31305+H202-+ 3HI02+ HzO. The oscillation source of the mechanism has been found to be in conformity with the Brusselator. 1. INTRODUCTION Since Bray discovered the oscillatory decomposition of H202 by the 103-12 couple not a few investigations 2-9 have been carried out without giving any concrete mechanisms. Recently we have succeeded in finding a plausible mechanism which enables us to understand the capability of the system to oscillate.Success was attained in the following way. First information was collected on possible intermediates and elementary reactions. Second mechanisms were con- structed and examined for the capability of oscillation both theoretically and by means of a computer. Finally experimental data were compared with computer results. This paper is concerned with the process leading to the plausible mechanism its nature and experimental evidence for it. 2. THE PROCESS LEADING TO THE PLAUSIBLE MECHANISM A survey of the literature 2-9 has shown that aqueous solutions capable of oscil-latory decomposition contain IO, H+ 12,I- and H20z as stable species. In such solutions the following reactions also can take place.210; +2H+ +5H202+ I2+502 +6H20 lo (2.1) I2+5H2O2+ 210;+2H++4H20 11* l2 (2.2) 10 +51-+6H+ + 312+3H,0 13-15 (2.3) 21-+2H++H202 4 12+2H20l6 (2.4) 12+H20+ HIO+I-+H+ l7 (2.5) H202 3H2O+O.5 02. '* (2.6) 55 OSCILLATORY H202 DECOMPOSITION Here we adopt a view that if we find a mechanism which can explain all the above reactions mechanistically the mechanism has a good chance of accounting for the oscillatory decomposition. Previous investigations on the six reactions have suggested a number of inter-mediates such as HIO, HIO H,IO+,l9* 2o and H21203.12 Using such intermediates and supplementary intermediates H210 * and H31305,ta comprehensive mechanism of an oscillatory nature was constructed by the trial and error method as shown in fig.1 in which $ denotes so rapid a reversible step as to be usually in equilibrium 16 FIG. 1 .-The comprehensive mechanism of oscillatory nature for the HzOz-IO;-12 system. The numerals denote the step number. and each step is specified by an Arabic figure; HI03 a medium acid is used as a generic symbol for HI03 and 10 also in what follows ; species IO, 10- and 1; are neglected since HIO and HI0 are weak acids and no I; is formed under the oscil- lation conditions. The detail of each step is listed below. Step 1 HI03+H202+ HI02+H20+O2 (2.7) Step 2 H2IOi +HZ02 + HIOj+H++HzO (2.8) Step 3 H210; + H++HI02 (2.9) Step 4 HTOz+H202 + HIO+H,O+02 (2.10) Step 5 H210++H202-+ HT02+H++H20 (2.1 1) Step 6 HlIOf + HI0 +H+ (2.12) Step 7 HIO+H202 -+ H++I-+H,O+O (2.13) Step 8 I-+H++H,O2 -+ HIO+H20 (2.14) Step 9 I,+H20 f HIO+I-+H+ (2.15) * This species was devised by analogy to H210f but its presence is probable from the Occurrence of X0;+2H+ + H2XO (X = CI Br or t This species was devised without experimental support but its formation is probable since large molecules 24s 25 such as H2130:;and H4130:4 and those 26 such as [I03(HI03),]-(n > 1) are suggested.I. MATSUZAKI T. NAKAJIMA AND H. A. LIEBHAFSKY Step 10 HI02+H++I-+2HIO (2.16) Step 11 HZ1203+H++I-~t 3HI0 (2.17) Step 12 HI02 +HI0 +€I21203 (2.18) Step 13 HIO,+H++I-+ H21203 (2.19) Step 14 H2T203+H202-+ 2HI02+H20 (2.20) Step 15 H21203+HT02+ H31305 (2.21) Step 16 H31305+H202-+ 3HI0 +H,O.(2.22) According to the comprehensive mechanism reactions (2.1) to (2.6) take place via the sequences of steps shown in fig. 2. Reactioii @,I) Reaction (2,4) Rcaition<:,5) ;i ~ HIO -HIO -HI0 -I-A HI0 -I-HI0 1-Reaction (2,2) n HIO HIOz HI0 -I-\# \J HJO,' H,IO+ HIO -HIO -,,HI0 s I-\J HJO FIG.2.-The sequences of steps for reactions (2.1) to (2.6) according to the comprehensive mechanism. According to the theory 27 of oscillating reactions a feedback step is indispensable for oscillation so in the trial-and-error search a mechanism equal to the compre- hensive mechanism minus steps 15 and 16 was first subjected to computer simulations with 92 sets of values of rate constants for each step since it contains a feedback step HIO +HI0 +H,02 -+ 2HI02+H20 (first-order back-activation) as a consequence of the sequence of steps 12 and 14 but without giving any oscillations.Here we examined the sequence theoretically (see section 3 (ii)) HIO 7+ HI02 * HI0 (2.23) U (act)" and found that the feedback step HI0 -+ HIOz should have an order nhigher than 1. Based on this finding we chose 2 the smallest favourable integer for n,and added steps OSCILLATORY H202 DECOMPOSITION 15 and 16 so that the second-order back-activation step 2HI0,+HIO+H202 + 3HIO2+H20might participate. Of course it is possible to get a favourable sequence of steps using such intermediates as 100, HO- and HOz- but at present we would like to retain the use of radical species as a possibility.3. NATURE OF THE COMPREHENSIVE MECHANISM (i) STEPS DOMINANT IN THE OSCILLATION The failure of the associated mechanism to yield oscillation mentioned in section 2 suggests that any steps but steps 15 and 16 are not responsible for the oscillation. On this basis we picked up such steps as would be dominant under oscillation condi- tions arriving at the practical mechanism shown in fig. 3 in which step 2' is the combi- I HIQZ H102 __* HI0 7 I-2' 1 FIG.3.-The practical mechanism derived from the comprehensive mechanism as applicable for oscillation conditions. nation of steps 2 and 3 with k2t =k2/K3 where k2 is the rate constant for step 2 and K3the equilibrium constant for step 3 ;steps 11 and 13 were eliminated on an idea that' step 10 should outweigh them in the interaction with I-; steps 5 6 and 14 were also eliminated since step 16 should be the major step for supplying the key species HI02.The practical mechanism was fed into computer simulation. The simulation is based on the Euler method.28 Steps 12 and 15 were regarded as being in equilibrium while steps 9 and 10 were each decomposed into two reversible steps 9' and 9" and 10' and lo" respectively. The rate law for each step is determined according to the mass action law as exemplified by 08 = k,[I-][H,O,][H+] for step 8 and v16 =k16K12K15[H102]2[H10][H202] for step 16; that for step 1is given by the experimental one lo for reaction (2.1) ul/moll.-l min-l = 2.6 x 10-4[H103][H202]+ 129 x 10-4[H+][HI0,][H202]. (3.1) Based on previous experimental results the simplification was adopted that [HI03] [H202] and [H+] might be regarded as constant for a run as long as the switch- over of the system to oscillation is concerned leading to condensed rate constants E as exemplified by u1 =eqn (3.1) =El tlg =k8[I-][H202][H+]=E8[1-] 016 = kl6K12K15[H102]2[HIO][H202J =k,,[HI02]2[HIO].The sets of k and R values employed for the simulation are summarized in table 1 and the time courses obtained I. MATSUZAKI T. NAKAJIMA AND H. A. LIEBHAFSKY are shown in fig. 4. In the sets of ki and Ei values employed only ki was changed systematically. In choosing the sets we did not adhere to experimentally determined ki and Ki values because in this computer simulation we aimed at making the oscil- latory nature of the mechanism visualizable.It is clear from fig. 4 that the practical mechanism is so versatile as to reproduce almost all the aspects of the system such as the oscillatory decomposition initial stage of reaction catalytic decomposition and one-way I2 formation. TABLESUMMARY OF THE COMPUTER RUNS CONDUCTED BASED ON THE PRACTICAL MECHANISM runno. Ela kztb k4C Elad E7’ xgl Eq,g kg, klo klo, nitofconc.h (mol L-1) 1 2 3 3 4 5 2 2 2 10 10 10 4 4 4 5 5 5 5 5 5 2 2 2 0.05 0.05 0.05 4 4 4 4 4 4 u,/E~u,/kl VJEl 4 6 2 - 10 4 5 5 - 2 0.05 4- 4 vl/kl -Qkl = eqn (3.1). -bk2f= (kz/K3)[H+][H+l. ck4 = k4[H2021. dk16 = (k16K12K1s)[HzOzl. e k = k7[H202]. fka = k8[H+][H2O2]. kgt = kg[H+]. h For example run 1 gives results for which u1/3 corresponds to one unit of concentration where v1 is the actual rate of step 1 given by eqn (3.1) (cf.the [I2] calculation in section 4 (ii)). OSCILLATORY HZ02 DECOMPOSITION (ii) OSCILLATION SOURCE The failure of the associated mechanism mentioned in section 2 coupled with the success of the practical mechanism indicates that the first-order back-activation step consisting of steps 12 and 14 is not effective whereas the second-order one composed of steps 12 15 and 16 is the oscillation source. It is now necessary to make a theoretical check on the above indication. For this purpose the following sequence is the simplest including a nth order back-activation = step. Since this sequence is a two-variable system (because [HI03]const.under consideration) its necessary condition for oscillation can be derived along the line by Higgins 27 as follows. K1 E4 HIO HIO s HI0 E2' E (act)" The rates of increases in A and B are given by dA/dt = -(k2t+ EJA + EAnB (3.3) dB/dt = k4A-EAnB (3.4) where A and B stand for [HIO,] and [HIO] respectively. The singularity is obtained as A = E1/K2? and B = (K4/k)(k2,/E,)"-' (3.5) by setting both the above derivatives equal to zero. The self- and cross-coupling terms at the singularity are obtained as by differentiating the derivatives of eqn (3.3) and (3.4) with respect to A or B and substituting eqn (3.5). From eqn (3.6) to (3.9) we obtain under the condition of n > 1 and (n-l)E4 > k2#at singularity IAb x BaJ-IAa x Bbl = kA"(n-l)kAn-'B -EA"{(n-l)kA"-'B-E2') = JE2fEA"> 0 (3.10) and AaxBb < 0 and BaxAb < 0 (3.11) the other necessary condition being Aa+ Bb > 0 at singularity i.e.(n-1)E4-k2e-E(El/?i2#)n > 0. (3.12) From the condition for (3.10) and (3.11) or eqn (3.12) it is evident that the first-order (n = 1) back-activation step is ineffective whereas the second-order (n = 2) can confer possibility of oscillation in favow of the above-mentioned indication. I. MATSUZAKI T. NAKAJIMA AND H. A. LIEBHAFSKY It should be pointed out that the part of the comprehensive mechanism corres- ponding to sequence (3.2) with n = 2 is equivalent to the Bru~selator,~~’~~ which according to Tyson 35 is the only known two-variable chemical scheme which admits limit cycle oscillations.This equivalence can readily be understood if we apply a replacement of A E = HI03 X = HI02 B = H202 Y = HIO and D = O2on the Brusselator A-+X B+X + Y+D 2X+Y -b 3x X -+ E. On the other hand the unfavourable sequence (3.2) with n = 1 corresponds to the Brusselator with its step 2X+Y + 3X replaced by X+Y + 2X ;with respect to such a replacement Tyson 35 has stated in support of our unsuccess in getting oscillations that the steady state of such a replaced scheme is always stable for positive values of the parameters. 4. EXPERIMENTAL EVIDENCE FOR THE PRACTICAL MECHANISM (i) EXPERIMENTAL The present experiment was designed to get time courses comparable with those of fig. 4 on the basis that the change in k1 corresponds to a change in [H+] when [KIO& and [H20210are kept constant.All the chemicals used were of guaranteed grade and used without further purifica- tion. The hydrogen peroxide contained no inhibitor. Two kinds of reaction vessels open-type and closed-type both made of Pyrex were used. Both the vessels were used in previous experiments 6-9 and are to be described in detail elsewhere. The open-type was designed especially for the spectrophotometric [I,] measurement. The [I-] measurement was made by means of an Orion I-selective electrode and the d02/dt (rate of O2evolution) measurement by means of a Matheson Company LF-20 mass flowmeter. A solution containing KIOJ and HC104 was kept at 323 K and then an amount of 30 % H202was added to initiate the reaction.In table 2 are summarized the runs of reaction conducted and the time courses TABLE 2.-sUMMARY OF THE RUNS OF REACTION CONDUCTED AT 323 K initial conc./mol1.-1 volume type of quantities run no. WC104lo WOdo [HzOdo (V/ml) vessel used followed 1’ 0.035 0.40 0.30 150 closed 2‘ 0.051 6 0.40 0.30 150 closed 3’ 0.060 0.40 0.30 150 closed 4’ 0.070 0.40 0.30 150 closed 5‘ 0.080 0.40 0.30 150 closed 6‘ 0.070 0.40 0.30 140 open 7’ 0.0576 0.282 0.494 140 open 8’ 0.0576 0.282 0.494 150 closed obtained are shown in fig. 5to 7. A number of preliminary runs have concluded that the series of runs 1‘ to 5’ has shown all kinds of time courses for [I-] and d02/dt. Run 6’ is a separate run of run 4’ for the time course of [I2]. In fig.4 and 5 to 7 lower case letters are used to make clear the synchronization among [iJ [I-] and d02/dt. The initial period a-b where [I-3 [I2] and d02/dt increase will be called the OSCILLATORY H2Oz DECOMPOSlTION I I I I 1. 0 10 20 30 40 d " h time /min FIG.5.-The experimentally obtained time courses of dO,/dt and [I-] for runs 1' to 5' of table 2. Thc numerals indicated denote the run number timelmin FIG.6.-The experimentally obtained time courses of [I,] and [I-] for run 6' of table 2. induction period and during the flat part after point gthe smooth catalysis H202+ H20+0.502proceeds almost exclusively. Fig. 5 to 7 coupled with observations in preliminary experiments characterize each time course as follows (all concentrations in mol I.-') I.MATSUZAKI T. NAKAJIMA AND H. A. LIEBHAFSKY 4 Run 1’ ([HClO4Io= 0.035) ... . [I-] and [I,] increase monotonously to reach a constant where I2 begins to precipifate. d02/dt increases similarly but decreases as H202is consumed. Run 2’ ([HCIO,] = 0.051 6) . . . . The induction period is followed by pulse-like oscillations where [I-] first decreases inducing [I2] to decrease and dO,/dt to increase. Run 3’ ([HCIO,] = 0.060) and runs 7’ and 8’ ([HC10410 = 0.057 6). . . . The same as in run 2’ with oscillations appearing earlier with smaller ampli- tudes and shorter periods. Run 4‘ ([HC10410 = 0.070) . . . . The induction period is followed by smooth catalysis via a half-pulse and oscillations appear later via several wiggles.Run 5’ ([HClO,] = 0.080). . . . The induction period is followed by smooth catalysis. Runs 1’ to 5’ . . . . The changes in the position and size of [I-] and d02/dt pulses in runs 2’ and 3’ and the descents of the line for the smooth catalysis in runs 4‘ and 5’ result from the consumption of H202 ;the later oscillation in run 4’ will be absent if H202is supplied constantly. time/min FIG.7.-The experimentally obtained time courses of [I-] and [I2] for run 7’ and that of dOzldr for run 8’ of table 2. OSCILLATORY H202 DECOMPOSITION The nearly linear increases in [I2] in the induction period are in accord with the rate law (3.1) which indicates that the formation of I2 is due to reaction (2.1). One quantity of interest is the ratio (d02/d12)ina.of the amount of 0 evolved to that of I2 formed in the induction period. Values of this ratio estimated from the combined data of runs 4' and 6' and of runs 7' and 8' increase from 1 to about 15 near the end of the induction period indicating that the catalytic decomposition resulting from elementary reactions involving intermediates becomes predominant before the start of a pulse or smooth catalysis. Another quantity of interest is the ratio (d02/d12)pulse of the amount of O2evolved to that of I2 disappearing during a pulse. For the second pulse in fig. 7 the amount of I disappearing is 1.6 x moll.-' and that of O2evolved from 150 ml of reaction mixture is 25.08 ml (stp) hence the value of the ratio is as large as 46.7. (ii) COMPARISON BETWEEN THE COMPUTER AND EXPERIMENTAL RESULTS It is readily seen from a comparison between fig.4 and fig. 5 to 7 that the change in the time courses of runs 1 to 4with Elis qualitatively similar to that of runs 1' to 5' with [H+l0. For quantitative comparison with the experimental results we have to carry out computer simulations with actual kiand Ei values and with consideration paid on the effect of [H+] upon all the kiand ki values. Let us make a quantitative check on some significant quantities. The value of [I2]at point b for run 4 is obtained from fig. 4(c) as 30(2.6 x 10-4[H~02][HI'0,]+ 129 x lO-"[H+][HIO~][Hz02])/6 = 30(2.6 x x 0.30 x 0.40-t-129 x x 0.07 x 0.30 x 0.40)/6 = 7x (mol l.-l) which agrees with the experimental value of 7.6 x (run 6').The value of (d02/d12)pulse for run 3 is calculated as 0.5(55 +35) x 25/(59-27) = 37 in approxi- mate agreement with the experimental value of 46.7. 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