R. J. Field University o f Oregon Eugene, 97403
A Reaction Periodic in Time and Space A lecture demonstration
In any homogeneous closed system a t constant temperature and pressure, all spontaneous chemical changes must be accompanied by a decrease in the Gibbs free energy of the system. The foregoing statement is a direct result of the second law of thermodynamics and is universally accepted. Equally as well accepted is the corollary of this statement which tells us that a chemical system a t constant temperature and pressure will approach equilibrium monotonically, i.e., it will not overshoot and come back. This means that the oscillations about a final equilibrium state that are often observed in physical systems (a pendulum for example) will not be observed in such chemical systems. As a result of the rule of monotonically decreasing Gihbs free energy in spontaneous chemical systems, the general observation is that the overall rate of the reaction decreases monotonically with time, and if there are any intermediate species produced in the course of the reaction, then their concentrations will either rapidly reach a steady state value or pass through a single maximum or minimum. However, this behavior is not required by the second law of thermodynamics. Indeed, where the presence of auto catalytic reactions in a complex mechanism leads to a peculiar sort of non-linear kinetics, repeated barely damped oscillations in both the overall reaction rate and in the concentrations of some reaction intermediates are quite possible, even in a homogeneous system. In 1959 Belousov (1) reported such a reaction. He observed that during the cerium ion catalyzed oxidation of malonic acid by bromate in a well-stirred 1 M sulfuric acid medium (Belousov Reaction), repeated undamped oscillations in (Cel")/(Ce"') occur. These oscillations can be made easily visible by use of a redox indicator such as Ferroin.' Field, Koros and Noyes (2) have recently reported that in this system bromide ion also shows repeated undamped oscillations of a most striking shape. These authors also rationalize the peculiar behavior of this reaction using a mechanism based on coupled auto catalytic reactions. Degn (3) has shown that the overall reaction rate also shows temporal oscillations. When Ferroin indicator is used to make the (CeIV)/ (Ce"') oscillations in a stirred solution clearly visible, this reaction provides a fascinating and easily staged lecture demonstration that is suitable for use in conjunction with discussions of free energy and spontaneThis work was supported in part by the US.Atomic Energy Commission. ' Ferroin is a 0.01 M solution of 1,10 (ortho)-phenanthroline ferrous sulfate, and is blue in an oxidizing solution and red in a reducing solution.
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ity, complex reaction kinetics, or whenever an attention getter is required. Busse (4) recently reported that if the Belousov reaction is not stirred, and if the initial conditions are properly adjusted, then an even more remarkable phenomenon can be observed in this system in that alternate horizontal stripes of the oxidized and reduced forms of the indicator appear and propagate themselves through the solution. I t is apparent from watching the stripes move about that this is not a supersaturation phenomenon like the Liesegang Rings (5),but that this spatial organization is being supported by the exothermicity of the oxidation of malonic acid by bromate. This phenomenon is of considerable theoretical interest (6), and its demonstration is suitable as part of a statistical mechanical discussion of fluctuat,ions. H o w T o Do It
Temporal Periodicity. Producing the temporal oscillations in (Cel")/(Cel") is an exceedingly easy task as they will occur over a wide range of concentrations and conditions. An ungraduated cylinder is a good vessel to run the demonstration in, and a magnetic stirrer is used to vigorously stir the reaction mixture throughout the demonstration. A white background for the cylinder makes it easier to see the Ferroin color changes as (Cel")/(Ce"') oscillates. The table gives the reactants used and concentration ranges which will produce oscillations. Also listed is a set of convenient concentrations which will give a system that will oscillate with a period of about 30 sec after an induction period of about 90 sec. The oscillations will continue for a t least the 50 min of an ordinary lecture period. The reactants can be mixed in any order. Some substitution of reactants is possible. Zhabotinskii (7) has found that the Mn"'/Mnl' and Feu'/ Fe" couples can be substituted for the Cel"/Ce"' one, and (8) that citric and maleic acids can be substituted for the malonic acid. Kasperek and Bruice (9) found that malic, bromomalonic, and dibromomalonic acids can also be substituted for malonic acid. Chloride ion, however, must be rigorously excluded, and no substitutions seem to be possible for the sulfuric acid and bromate ion. While the color changes that the Ferroin indicator undergoes reflect the gross oscillations in (CeIV)/ (Ce"'), the recent potentiometric investigations of FKN ( 2 ) show more clearly the specific nature of the oscillations. The figure shows the results they obtained using a tungsten electrode to follow (CeIV)/ (Ce"') and a bromide ion specific electrode to follow bromide ion concentration. This figure clearly shows the existence of an induction period before the onset
Reactant concentrations Used to Produce Oscillations in (Ce'y)/(Cell') During the Cerium Ion Catalyzed Oxidation of Malonic Acid bv Brornate
Reactant Ce(NH,IdNOah . . CHz(COOH)a KBrOa HAO! Ferrom
Concentration range (M)
Convenient concentration ( M )
0.0001-0.01 catalytic amount 0.012E-0.50 0.03-0.062.5 0.g2.5 0.0006
0.002 0.275 0.0625 1.5 0.0006
of oscillation and how the (Br-) and (Ce'v)/(Ce"') oscillations arc related to each other. Spatial Periodicity. Producing the horizontal stripes requires a little more technique, but it also is easily accomplished. The convenient concentrations listed in the table are suitable for this demonstration. The single difference in conditions that leads to spatial periodicity rather than temporal periodicity is the suppression of convective transport in the former case. To produce the temporal oscillations the solution is vigorously stirred, but to produce the spatial periodicity the reaction mixture is unstirred and started out with an initial spatial inhomogeneity in one of the reactants. A procedure that seems to work well is to mix three of the reactants with the Ferroin indicator in an ungraduated cylinder. The system is then stirred and allowed to settle. When there is no further evidence of convective movement the fourth reactant is carefully run from a pipet down the side of the cylinder into the reaction mixture. The goal of this operation is to mix the final reactant into the system, but not so well that the whole solution is homogeneous. Good results have been obtained by adding the cerium solution last. Since the sulfuric acid solution is considerably denser than the cerium solution, there is a tendency for the cerium solution to form a layer on top of the other reactants. If this happens stripes will form only a t the interface. If the cerium is added rapidly enough so that two layers do not form, but the system is not homogeneous in cerium, then stripes will form all through the solution. If mixing is complete, temporal oscillations will commence, but they may not be well synchronized throughout the solution. Under these conditions waves of blue (oxidation) will propagate through the cylinder in a manner somewhat reminiscent of the movement of an amoeba. Zhabotinskii (10) has studied this phenomenon in two dimensions. Stripes frequently can be induced in such a system by adding a few drops of one of the reactants on the surface of the reaction mixture. Temporal oscillations can be started in a solution showing spatial periodicity simply by stirring to make the solution homogeneous. Thermodynamic Implications
If there is to be no violation of the second law of thermodynamics in this reaction the oscillations in (Cel")/(Ce"') and (Br-) must be driven by another reaction that is monotonically lowering the free energy of the whole system as it approaches equilibrium. As has been pointed out previously, the cerium ion is present only as a catalyst. The maximum bromide ion concentration is much lower than that of any of the principal reactants, including cerium ion. Thus neither hro-
mide ion nor either of the cerium species need to appear in the stoichiometry of the overall reaction. The net chemical reaction taking place in the oscillating reaction is then just the cerium ion catalyzed oxidation of malonic acid by hromate cerium ion
3H+
+ 3BrOa- + SCHn(C0OH)z catalyzed 3BrCH(COOH)a
+ 2HCOOH + 4C0s + 5HaO
(1)
and the Gibhs free energy needed to drive the oscillations in (Celv)/(Cell') and (Br-) is derived from this reaction. Hence the thermodynamic requirement of constantly decreasing Gibhs free energy in a spontaneous process is met even while the overall reaction rate, and the concentrations of various intermediate species, are oscillating. Auto-Catalytic Reaciions a n d Oscillatory Systems
The detailed mechanism proposed by FKN (2) for the Belousov reaction is, as expected, exceedingly complex. Discussion of it is probably not suitable for the circumstances under which this demonstration will be used. Their mechanism does, however, closely resemble a fairly simple kinetic scheme for oscillating systems proposed by Lotka ( 1 0 , and elegantly developed by Prigogine, et al. (18). According to these authors there are four requirements for a mechanism to lead to undamped oscillatory behavior. These are: (1) The mechanism must be complex and contain a t least one autocatalytic reaction, (2) the auto-catalytic reaction(s) must be coupled to the other reactions in the mechanism in some manner, (3) the system must be far from chemical equilibrium and open in the sense that the reactants are taken from very large reservoirs and the products are rejected into a sink, and (4) the values of the rate constants of the component reactions in the mechanism must fall into certain quite large ranges.$ In order to discuss the oscillatory behavior of the Belousov reaction, it is convenient to write the four overall reactions below to describe the processes taking place, even though there is little doubt that these complex reactions do not operate independently, but are coupled through their intermediates. BrOa-
+ 2Br- + 3CHdCOOH)z + 3H+
-+
3BrCH(COOH)z
+ 3H.O
(2)
auto-catalytic
+ BrOa- + 5H+ + CHz(COOH)2B r inhibited 4Ce'V + 3H10 + BrCH(C0OH)z BrCH(CO0H)r + CeIV Br- + ? 6CelY + CH2(COOH)x+ 2H20 6Ce"' + HCOOH + 2C01 + 6Ht
4Ce1I1
A
-
(3) (4)
(5)
All of these reactions proceed in the direction written with a decrease in Gibbs free energy. Since CeIV is produced (Ce"' destroyed) in reaction (3) and dcstrayed (Cel'' produced) in reaction ( 5 ) , oscillations in (CC'~)/(C~"')can occur in this system if a suitable mechanism exists for turning reactions (3) and ( 5 )
' Lotka's mechanism and other theoretical considerations of oscillating reactions in general are discussed in the companion article by Degn (18). Volume 49, Number 5, M a y 1972
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on and off a t the proper times. The same is true for bromide ion as it is produced by reaction (4) and destroyed by reaction (2). Vavilin and Zhabotinskii (1.9) have studied reaction (3) alone and found it to be auto-catalytic and completely inhibited by bromide ion. FKN (3) found that the minimum amount of bromide ion required to inhibit reaction (3) is about lo-$ M. Their results further indicate that reaction (3) is a chain process involving ss intermediates the oxybromine compounds with bromine oxidation states from +5 to +l. The auto-catalysis arises from attack of one of these intermediates (HBr02) on bromic acid (HBi-08) to give chain branching, and the bromide ion inhibition occurs by a competitive chain terminating reaction of bromide ion with HBr02. Reaction (4) was not well understood by FKN (3), and so it is written here only as an interaction of CeIV and bromomalonic acid that produces bromide ion. The bromomalonic acid required for reaction (4) is produced by reaction (3) during the induction period (Section CD of the figure), and the necessity that bromomalonic acid be present for oscillation to take place rationalizes the presence of the induction period. Degn (3) has demonstrated that if bromomalonic acid is initially present, oscillations start without an induction period. The reaction of bromide ion and bromate ion to produce bromine and water has been studied by Bray and Liebhafsky (14), and the reaction of bromine with malonic acid was studied by West (16). Reaotion (2) is the sum of these two reactions. Sengupta and Aditya (16) have investigated reaction (5). It is of importance to point out that the Belousov reaction itself, as well as the four component reactions in its simplified mechanism, do indeed fulfill the requirements for undamped oscillations to occur. Reaction (3) is the required auto-catalytic step and as demanded by the second requirement for oscillatory behavior it is coupled to the other reactions in the mechanism. The coupling is done by bromide ion and ceric ion. Bromide ion, a product of reaction (4), inhibits reaction (3), and ceric ion, a product of reaction (3), is a reactant for reaction (4). The third requirement for oscillatory behavior is that the overall system be open. The Belousov reaction approximates an open system in that the cerium ion is present only in catalytic amounts so that each pulse in (CeIV)/ (Ce"') consumes only avery small fractionof the driving reactants, bromate ion and malonic acid. Eventually, however, after a great number of oscillations, the re-
actant concentrations do diminish and the oscillations damp out. Reaotion ( 5 ) , which leads to the final oxidation products, is essentially irreversible under the conditions of the Belousov reaction so that the products of the reaction are rejected into a free energy sink. Using reactions (2) through (5) it is possible to produce a qualitative rationalization of the oscillations in the Belousov reaction that, while not rigorous, does illustrate how the coupling of an auto-catalytic reaction(s) to the other reactions in a complex mechanism can lead to oscillatory behavior. Reference to FKN (3) will show that the rationalization is an oversimplification of the true situation, but it does form the basis of a discussion suitable to accompany the lecture demonstration. Looking at the figure we see that this particular reaction was started out a t point A with the cerium ion present entirely as Ce"', and with about M bromide ion present. Initially the only process that t a k e place is the removal of bromide ion by reaction (2). No Ce"' is oxidized until the bromide ion conM ) as centration reaches point B ((Br-)B until this time there is enough bromide ion to completely inhibit reaction (3). At point B, however, the bromide ion concentration has decreased to a point where reaction (3) is no longer inhibited and can oxidize Ce"' to CeIV. Simultaneously, the remaining bromide ion is removed, presumably by the same elementary reaction that allows bromide ion to inhibit reaction (3) during its nonauto-catalytic stage., At point C the reaction enters the induction perlod (Section CD). During the induction period reactions (3) and (5) are essentially operating under steady state conditions so that (Cel")/(Ce"') remains at a relatively constant high value while the oxidation of malonic acid by bromate ion is proceeding quite rapidly. Also during this period, reaction (3) is producing bromomalonic acid which accumulates in the system, and from which reaction (4) starts to produce bromide ion. The bromide ion produced during the induction period does not immediately accumulate but instead reacts with HBrOz andHOBr generated by reaction (3) to produce bromine. This bromine reacts with malonic acid (15) to regenerate bromomalonic acid and bromide ion. Thus steady state bromine and bromide ion concentrations develop. These steady state concentrations constantly grow as the bromomalonic acid concentration increases and reaction (3) slows down. Finally, a t point D the steady state concentration of bromide ion becomes
Pdenfiometric traces a t 25'C of log [Br-1 and log [CeIY]/[CeII'] verru. time during the Belourov reodion. 0.063 M, [Cc(Nllrll(NOa)s]o = 0.001 M, [HzSO,] = 0.8 M and [KBr]o = 1.5 X TO-' M.
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=
[MaIonic Acid] = 0.032 M, [KBrOJ =
sufficiently great to stop reaction (3). With reaction (3) no longer producing HBrOz and HOBr the bromide ion produced by the reaction of the steady state concentration of bromine with malonic acid can accumulate. This is the source of the pulse of bromide ion production seen in Section DE of the figure. At point E all of the bromine present at the end of the induction period has been converted to bromide ion and bromide ion production thus ceases, but there is now enough bromide ion present to completely inhibit reaction (3). With reaction (3) stopped CeIV starts to disappear by reaction ( 5 ) and bromide ion to disappear by reaction (2). Reaction (2) is now complicated by the presence of bromomalonic acid leading to the slower rate of bromide ion removal in E F as compared to AB. Thus during section EF both CeIV and bromide ion concentrations are decreasing. When the bromide ion concentration has decreased to point F, however, it is no longer sufficient to inhibit reaction (3), which then rapidly and auto-catalytically reoxidizes a portion of the Ce"' back to CelVand simultaneously removes most of the remaining bromide ion. It turns out that auto-catalysis in reaction (3) is also inhibited by CeIVso that after the initial burst of oxidation (Ce'v)/(Celll) slowly approaches, in a nonautocatalytic manner, the steady state defined by reactions (3) and (.5). Thc auto-catalytic formation of CeIV occurs during section FG while the nonauto-catalytic formation occurs during section GH. At point G, when the auto-catalytic phase of reaction (3) is concluded, bromide ion starts to accumulate as the Ccl" produced in the pulse gets involved in reaction (4). This leads to the slow increase in bromide ion concentration reflected in Section GH. During Section GH the steady statc involving bromine and bromide ion seen during the induction period again establishes itsclf. Because of the larger concentration of bromomalonic acid present a t this point, however, much less time is required to reach the critical bromide ion concentration necessary to shut off reaction (3). Indeed, under some circumstances (high malonic acid concentration) Section GH does not appear a t all, and the bromide ion pulse occurs immediately following the CeIV pulse. In either case the appearance of the bromide ion pulse indicates that reaction (3) has been stopped. At the end of the bromide ion pulse we have again reached point E, and the whole cycle begins again. The behavior of this mechanism is made possible by the coupling of the auto-catalytic reaction (3) to the other processes taking place. The sudden exponential bursts of reaction that these processes can produce, while the concentrations of the principal reactants remain essentially unchanged, allow the intermediate concentrations to be removcd far from their steady state values. If reaction (3) were not auto-catalytic, then an ordinary nonoscillatory steady state would be
maintained. In its overall operation this mechanism is formally analogous to the well known astable multivibrator (flip-flop) of electronics. The initial operation of process or leads to the start of process 0 which then stops process or. In the present case the system is re-initialized by the reactions of Section EF, and process or again E tarts to repeat the cycle. A qualitative rationalization of the spatial periodicity is not presently possible. Prigogine and Nicolis (6) have developed a quantitative model of a system capable of leading to spatial periodicity. The model is based upon the interaction of coupled auto-catalytic reactions with diffusion processes, and to a zeroeth order approximation the spatial structure in this model develops because of local depletion of reactants. Prigogine's model requires that there be an initial concentration inhomogeneity to produce the spatial structure, just as is experimentally required in the Belousov reaction. Franck and Geiseler (17) have recently reported temperature oscillations of the order of 1°C in the Belousov reaction, however, and it now seems likely that temperature effects on the relative rates of diffusion and chemical reaction processes may be involved in the formation of the spatial structure. Conclusion
The cerium ion catalyzed oxidation of malonic acid by bromate (Belousov reaction) proceeds with both temporal and spatial periodicities in the concentrations of some intermediates and in the overall reaction rate. This reaction provides a fascinating lecture demonstration, and discussion of it can lead to insights into the relationship between Gibbs free energy and spontaneity in chemical reactions, and into the relationship between auto-catalytic reactions and oscillatory kinetics. Acknowledgment
The author wishes to thank Professor Richard M. Noyes for the interest and discussions that lead to this article. Literature Cited (1) BELODBOV. B. P., Sh. Ref. Radiata. M c ~ Za . 1958, Medgir;, Moscow. (2) F I E ~ ~R. D J.. , K 6 ~ 6 8 ,E.. A N D NOTES,R. M., mbmitted t o J . Amsr. Chcm.Soe. (3) Deoli, H . , Noture,213,589 (1967). (4) Bass.. H. G . , J . Phya. Chcm., 73, 750 (1909). (5) LIEBEOANG, R., 2. Anorp. Chcm., 48, 364 (1900). (6) P m c o a r ~ I.. ~ , *no Nrcolls. 0.. J . Chem. Phys., 46,3542 (1907). (7) Z ~ ~ ~ o ~ mA.s M., x n Dokl. , Akod. Novk SSR. 157,392 (1964). (8) Z H A n o ~ I w s a ~ rA. , M.. Biofi#iko, 9 , 306 (1904). (9) K * s ~ e n ~ G. s , J., AND Bsnrce. T. C.. Inore. Chem., l o , 382 (1971). (10) ZAIKLN,A. N.. AND ZIABOTINSYII, A. M.. N O ~ U T225, C . 535 (1970). (11) LOTH*.A. J.. J . Amcr. Chem. Soe.. 42, 1595 (1920). (12) PRIOOOINE. I., LEFEVER,R.. GOLDBETER.A,. AND H E R B A ~ I Y I T Z K ~ u r a a * ~M., , Nature, 223, 913 (1968). (13) V ~ v r r n r V , . A,. AND Z n ~ s o m ~ s a rA. r , M., Kinel. Katol., 10.83 (1909). (14) BnAu, W. C., A N D LIEBXAFBKI, H. A,. J . Amer. Chem. SDC..57, 51
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