Periodicity in Chemically Reacting Systems A Model for the Kinetics of the Decomposition of Na2S204 BY PHIL E. DEPOYAND DAVID M. MASON Stanford University Stanford California U.S.A. Received 23rd July 1974 Sodium dithionite undergoes thermal decomposition in aqueous solution to form sodium bi- sulphite and sodium thiosulphate. It has been observed previously that in the decomposition under some conditions the concentration of the reactant oscillates in time. Although various theoretical mechanisms such as the Lotka system have been proposed which would produce oscillations in the rate of reaction and in the concentrations of intermediate species in a reacting system none of the theoretical mechanisms can explain the oscillations including periodic increases of the reactant concentration observed in the dithionite system.In this paper the observed behaviour of the dithionite system is described. Three mechanisms are discussed which have been proposed by others to explain various characteristics other than the oscillations of the decomposition. It is then shown how these mechanisms could with certain modifications produce oscillations such as are observed with the dithionite system. Sodium dithionite (Na2S20,) is a powerful reducing agent used in the manu- facture of various organic chemicals and in dyeing and bleaching processes. It under-goes thermal decomposition in aqueous solution to form sodium bisulphite (NaHS03) and sodium thiosulphate (Na2S,03) according to the stoichiometry 2Na2S204+H20-+2NaHS03 +Na2S203.(1.1) Although relatively little has been published regarding the kinetics of the decomposi- tion those findings available are contradictory. The reaction has two distinct regimes as shown by the data in fig. 1 taken from the work of Lem and Wayman.' There is an induction period in which the dithionite concentration decreases slowly with time followed by a rapid autocatalytic reaction. Most of the published work I I I I 1 2 3 4 5 6 tirne/s x lo-* FIG.1.-Sodium dithionite concentration against time. 47 DECOMPOSITION OF SODIUM DITHIONITE deals with behaviour during the initial induction period. Different investigators have reported the order of the reaction in this initial period to be first three-halves and second with respect to the dithionite concentration and one-half and first with respect to the hydrogen ion concentration.Rinker Lynn Mason and Corcoran first reported that at some temperatures marked oscillations in the dithionite concentration were observable even in a system closed with respect to mass. Fig. 2 shows some of their results obtained at 60°C where reproducible oscillations including periodic increases in the dithionite con- centration as high as j 15 % are evident. At 70°C the magnitudes of the oscillations were reported to be considerably less and at 80°C practically no oscillations were observed. time/s x lo-* FIG.2.-OscilIations with time in sodium dithionite concentration.2 Rinker and associates reported as have other investigators that the addition of the products of the reaction to fresh dithionite greatly increased the initial rate of decomposition.If products were added in sufficient concentration the induction period was completely eliminated. It was also observed that the dithionite solution is turbid probably due to the presence of colloidal sulphur. It was reported that in an unbuffered solution the concentration of the hydrogen ion is oscillatory. Fig. 3 shows the time-dependence of the concentration of dithionite and hydrogen ion measured in situ with a glass electrode. As can be seen the hydrogen ion behaviour appears to be nearly a mirror image of the dithionite concentration. PROPOSED MECHANISMS Rinker et aL2 proposed a mechanism which is consistent with the observed rate for the induction period except that it does not account for the oscillatory behaviour.The mechanism that was suggested is as follows S20; +H+fztHS20; HS2Oq +H++2HSO,* fast HSO2*+HS2O,-+HSO,*+HS20 controlling HSO,*+HSO2*+H,O+2HSO3 +2H+. fast P. E. DEPOY AND D. M. MASON This reaction scheme leads to a rate expression of the form r = k[H+]f[HS,Oi]*. To be in accord with their observed kinetics i.e. a rate first-order with respect to [HSOJ variable fractional order in [H+] and zero order in [SO$-],Spencer and Burlamacchi Guarini and Tiezzi have concluded that the rate-determining step must be HSO,.+ SO; +HSO; +intermediate products. (2.6) Wayman and Lem proposed the following sequence of reactions S20 +H++HS,O fast S2O,'+H++HSO +SO (2.8) HS204 +H,O+HSO +HSO; +H+ (2.9) HSO +HS,O,-+HSO +S205 +H+.(2.10) They assumed that the reaction step eqn (2.10) is slow in the absence of a catalyst such as H2S or colloidal sulphur. They have proposed three reactions of sulphoxy-late (HSO;) which might produce H2S or S H++3HSOj -+H$ +2HSO, H++2HSO; +S +HSO3 +H20 (2.1 1) (2.12) and H++HSO +H2S-+2S +2H20. (2.13) They suggest that the catalytic action of hydrogen sulphide may be due to its ability to accept electrons and that its presence may improve the ability of the dithionite and sulphoxylate to react by facilitating the formation of the sulphoxylate free radical to produce a more rapid reaction (2.14) The free radical product becomes the ion by reacquiring an electron from the H2S HSO,-+e-+HSO,.(2.15) Polysulphides formed by the reaction of hydrogen sulphide and sulphur would be even more effective radical stabilizers and explain the observed catalytic effect of colloidal sulphur. Assuming that reaction (2.9) (the reaction of hydrogen dithionite with water) is rate-limiting during the induction period and that reaction (2.10) (the reaction of hydrogen dithionite ion with sulphoxylate) is limiting during the rapid decomposition the overall rate equation is r = kl [H+][S,OT] +k,[H+][S20 T][HSO,]. (2.16) Assuming that the catalytic effect of products of the reaction controls the rate during the fast decomposition Wayman and Lem obtain an overall rate expression of the form where C represents the concentration of dithionite.The Wayman-Lem expression (eqn (2.17)) does appear to give reasonably good agreement with the observed behaviour as shown in fig.4 and 5. Fig. 4 compares their best fit of the rate equation with data obtained by them for a solution of 10 mM DECOMPOSITION OF SODIUM DLTHIONITE dithionite buffered at a pH of 4 and at a temperature of23"C. Fig. 5 is their com- parison of the best fit of the rate equation to data obtained by Rinker et aL2 for a solution of 11.5 mM dithionite at a pH of 6 and a temperature of 60°C. 4-2-0 A R 12 16 20 24 time/s x FIG.3.-Concentration of dithionite and hydrogen ion against time ';0,dithionite ;A,hydrogen ion. -0 I 2 3 4 5 6 timels x FIG.4.-Comparison of Wayman-Len1 data with mechanism of eqn (2.16); -experimental --best fit of eqn (2.16).3. DISCUSSION It can be easily shown that no oscillations can occur with the Wayman-Lem mechanism or the Rinker mechanism since the rate-controlling steps are not auto- catalytic. It has been demonstrated theoretically by several investigators e.g. Higgins,6 that at least one autocatalytic step is required to produce damped oscilla- tions of intermediates and two or more autocatalytic steps are required to give undamped oscillations in open systems. It has also been shown that damped oscil- lations can be produced by autocatalytic reactions in systems which are closed with P. E. DEPOY~ANDD. M. MASON respect to mass.7 The rate-controlling step proposed by Spencer and by Burla- macchi Guarini and Tiezzi is autocatalytic but with respect to one of the products and this also would not produce oscillations.I time/s x FIG.5.-Comparison of the Rinker et af.’ data with mechanism of eqn (2.16). As mentioned earlier the most unusual characteristic of the dithionite system is the periodic increases which are observed in the dithionite concentration itself (fig. 2). Although closed-loop “ feedback ” mechanisms i.e. mechanisms in which one or more of the intermediates or products react to form the reactant can be postulated which could produce such increases it can be shown that these require that the con- centrations oscillate through an equilibrium point and this has been demonstrated in accordance with the Wegscheider constraint * to be thermodynamically unfeasible.Thus no closed-loop system can produce such oscillations. The most appealing explanation of the periodic increases in the dithionite con- centration is that the dithionite does in fact behave as an intermediate during the decomposition process. This behaviour can be accomplished if the dithionite reacts to form some side-products (other than the products or intermediates of the principal decomposition reaction) and reaches equilibrium with them possibly at a low temp- erature at which the concentrated dithionite solution is initially prepared. As the dithionite is consumed by the decomposition the equilibrium with these side-products would be shifted and they would react to form more dithionite thus producing a singular or quasi-singular point in the dithionite concentration.Inview of the observed appearance of what is believed to be colloidal sulphur in the solution the formation of various complexes such as polythionic acids (H,S,06) observed in the decomposi- tion of sodium thiosulphate in acid is a suspected side-reaction. Several mechanisms for the decomposition can be postulated which produce oscillations. One which appears to satisfy nearly all the observed characteristics of the reaction is as follows. As postulated the dithionite reaches equilibrium in a side reaction with various sulphur-compound complexes and possibly with colloidal sulphur S,OT+complexes+[S]+ . . . .. (3.1) As proposed in the other mechanisms the dithionite is in rapid equilibrium with DECOMPOSITION OF SODIUM DITHIONITE HS204 in a manner such as proposed by Rinker et aL2 and the HS204 is in equi-librium with sulphoxylate ions and SO similar to the stoichiometry of eqn (2.8) H++S2O%+HS2O fast HS204%HSO; + SO2 (3.3) fast Sulphur dioxide forms sulphurous acid SO +H20+H+ +HSO;.(3.4) Some sulphoxylate ions give up electrons to become the radical HSO,.. As assumed by Rinker et al. the sulphoxylate radical reacts slowly with HS,O, as follows HSO2*+HS2O,+HSO,*+HS20,. (3.5) Modifying their assumption about the reaction between sulphoxylate and bisulphite radicals eqn (2.4) we postulate that the radicals might react to form disulphurous acid which reacts rapidly with HS20i HSO2*+ HS03*+H2Sz05 (3.6) H2S205 + HS204 +2HS03*+ HS203.(3.7) As assumed in the Weyman-Lem mechanism the bisulphite radical absorbs an electron to give the ion HSO,-+e-+HSO;. (3.8) Overall this reaction is very similar to the theoretical oscillating mechanism first proposed by Lotka in 1910 i.e. XcI4Xl XI +xp2xz (3.9) (3.10) X +products (3.1 1) where the precursor Xo corresponds to various sulphur-compound complexes the first intermediate XI corresponds to the dithionite ion in equilibrium with the sulphoxylate radical and the second intermediate Xz corresponds to the bisulphite radical. time/s x FIG.6.-Behaviour of proposed mechanism. P. E. DEPOY AND I>. M. MASON Assuming a first-ordtr decay of the precursor the rate equations for our mech-anism are io = -klxo (3.12) 11 = klxo-2k2xl/e-2k3xlx2/e (3.13) i2= k2x2/e+k3xlx2/e-k4ex2 (3.14) and i3= k2x1/e+k3x1x2/e+k,ex2 (3.15) where xo is the concentration of the precursor x1 is the concentration of dithionite x2 is the Concentration of the bisulphite radical x3 is the concentration of the bi- sulphite ion and e is an electron availability factor.If the electron availability factor is constant based on the results derived for the closed Lotka system,' it would be expected that this system would exhibit multiple damped oscillations when the factor (k3x;/kle)*is of the order of 5 or greater. If the electron availability factor is related to the precursor and product concentrations by e = xo/(xo+cx3) (3.16) (which can be explained by assuming that the precursor or a substance in equilibrium with it is an electron donor and that the bisulphite and another substance in equi- librium with the precursor are electron sinks) the autocatalytic behaviour of the dithionite is produced.This relationship was selected because it produces the observed autocatalytic-type behaviour (since the precursor concentration xo falls off ex-ponentially with time) and it does not dampen the oscillations as is the case if the electron availability is a strong function of the dithionite concentration xl. As an example of the behaviour of this system of reactions fig. 6 shows the di- thionite concentration when parameters are chosen to approximate the observed behaviour shown in fig. 2 i.e. a period of the oscillations of approximately 150-200 s and an induction period of about 600 s.Parameters on which the figure is based are kl = 2 x k2 = k3 = 290 k4 = 1.6 c = 0.07and x6 =4 x (all based on concentrations in mol/l-l and time in seconds). As can be seen the mechanism compares reasonably well with the observed behaviour. This new mechanism is similar enought to the other three mechanisms presented by others that nearly all the observed characteristics of these mechanisms are preserved ; 1. the reaction appears autocatalytic i.e. the decrease in dithionite concentration is slow at first then rapidly accelerates 2. the reaction appears to be catalyzed by the addition of products (in the new mechanism the addition of bisulphite ion would produce more of an electron sink thereby more rapidly reducing the dithionite concentration) and 3.the reaction is catalyzed by the addition of sulphur (in the new mechanism sulphur would also act as an electron sink). In addition other results observed by Rinker et aZ.,2 e.g. the oscillation of the hydrogen ion concentration are also consistent with our mechanism. 4. SUMMARY In summary we have briefly discussed the behaviour of an oscillating chemical system the thermal decomposition of sodium dithionite. We have discussed three mechanisms which have been proposed by others to explain the general behaviour not including oscillations of the dithionite system. Finally we have suggested modi- fications to those mechanisms which could produce the type of oscillations which have been observed.DECOMPOSITION OF SODIUM DITHIONITE Obviously the mechanism of the dithionite decomposition is complex and a great deal more work would be required to gain a thorough understanding of it. Because of its uniqueness in the domain of oscillating chemical systems further investigation is warranted. W. J. Lern and M. Wayman Canad. J. Chem. 1970,48,776. R. G. Rinker S. LYM,D. M. Mason and W. H. Corcoran Ind. and Eng. Chem. Fund. 1965 4 282 ;S. Lynn Ph.D. Thesis (California Institute of Technology 1952). M. S. Spencer Trans. Faraday Suc. 1967 63,2510. L. Burlamacchi G. Guarini and E. Tiezzi Trans. Faraday Suc. 1969 65,496. M. Wayman and W. J. Lem Canad. J. Chem. 1970,48,782. J. Higgins Ind. and Eng. Chem. 1967 59 19. 'P. E. DePoy and D. M. Mason Combustion and Flame 1973,20,127. R. Wegscheider 2.phys. Chem. 1902 39,257. A. J. Lotka J. Phys. Chem. 1910,14,271.