Recipes for Belousov-Zhabotinsky Reagents Wolfgang Jahnkel and Arthur T. Winfree University of Arizona, Department of Ecology and Evolutionary Biology, Tucson, AZ 85721 The Belousov-Zhabotinsky (BZ) reaction has widely been used by several researchers to investigate spatial patterns in an excitable medium (1-18). Since almost every research group has developed its own favorite recipe, the number of existing recipes for BZ reagents has become fairly large. In this paper we have compiled the major recipes, and we provide easy instructions about how t o end up with the reported molarities by mixing various amounts of defined stock solutions. Before that and in order to eliminate ambieuities in the literature, we discuss the chemistry that takes place right after mixing the reagents, before anyoscillations or chemical waves occur. This is done assuming ideal solutions and neglecting activity coefficients. At the end of the paper, we sketch the changes that have to be made in order to adapt these calculations to real solutions. The BZ reaction in its original form ( I ) exhibits spontaneous bulk oscillations. Many recipes add bromide to the mixture initially to suppress these oscillations (2)while retaining excitability. In acidic solutions, bromide is oxidized by bromate to form bromine that is visible because of its yellow color:
For sulfuric acid, the first dissociation step proceeds completely H,SO,
+ H,O
-
H30t + HSO;
K,
= lo3 (completely)
(4)
whereas the dissociation of the second proton K 2 - 10-1.82 HSO; H20 HzOt + SO:-
+
-
(5)
takes place only partly. For that second dissociation step,
both initially and a t all subsequent times (i.e., for both subscripts "0" and "a"). Suppose the initial sulfuric acid concentration [H2SOdobe c molL. After the first dissociation step (eq 4), no HzSOa is left, but c m o l L H30+ and c mol/L HSO; have been produced. Suppose that out of these c m o l L HSO;, x m o l L dissociate. Then the concentrations after the second dissociation step (eq 5) are:
After a while, if malonic acid is present, the solution turns colorless again because malonic acid has been hrominated: 3Br2+ 3H,C(COOH)2
-
3BrHC(COOH), + 3B-
+ 3Ht
(2)
Equations 7,8, and 9 can be plugged into eq 6:
The net reaction then is
This reaction we will further on call "initial bromination reaction". The limiting factor herein is usually bromide; the reaction proceeds until bromide has been completely consumed. As can be seen, each mmol bromide that has initially been added results in 0.5 mmol bromate, 1.5 mmol H+, and 1.5 mmol malonic acid being consumed and 1.5 mmol monobromomalonic acid being produced (we assume that malonic acid gets only monobrominated, not dibrominated). The production of water has a negligible effect on composition. The protons were a problem. Unfortunately, their concentration is usually not reported as [H'], but as [HzSOa], after the initial bromination reaction. If each millimole of Br- in the bromination reaction consumes 1.5 mmol H+, does it consume 1.5 mmol HzSOa or 0.75 mmol HzSOa? T o answer this question, i t is necessary to know whether sulfuric acid in the pertinent concentration range of 0.2-0.5 m o l L is mono- or didissociated. In answering this, we apply some basic chemistry. Let us first consider an aqueous solution of sulfuric acid in isolation, without any other chemicals present: (we will indicate concentrations of sulfuric acid in isolation or concentrations before the initial bromination reaction with a subscript "0" and concentrations after the initial bromination reaction with a subscript "a"). 'Permanent address: lnstitut fur Physikalische und Theoretische Chemie, Universitat Tiibingen. Auf der Morgenstelle 8. 7400 Tiibingen, Germany.
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Journal of Chemical Education
This is the [H30+]0concentration in moles per liter that stems from the second dissociation step (eq 5). The total [H30+]oconcentration is the sum of [H30+Iofrom the first dissociation step (eq 4) and from the second dissociation step (eq 5): [H,Ot],,,,,
=x
+ c = %(\le2 + 6 ~ 1 0 - +' ~ ~
+c -
(12) Table 1and the figure, parts A and B, show the total proton concentration [ H 3 0 + ] 0 , ~(= ~ lx c) and the percentage of didissociated H8Od . .molecules ( = xlc), both as a function of [HzSOJo (= c). As expected, each HzS04 molecule is didissociated for the limit of highly diluted solutions (say for [H2SO& < 0.0001 mol/L) and onlv monodissociated for concentrated solutions ~ (say f i r [ H ~ S O>~1]mol/L). In the concentration range that is of interest for us, 0.2 m o l L 5 [HzSOalo 5 0.5 molL, about 2-5% of all HnSOa molecules are didissociated. That means we cannot regard sulfuric acid as purely monodissociated nor as didissociated, which makes the calculations a little awkward. However, as the following example shows, for most recipes there is only little error in regarding sulfuric acid as purely monodissociated. We will now drop the assumption of HzSOa being in isola-
+
Table 1.
Total [H,O+].
Concentratlon and Percentage of Dldlsroclated HSSO. Molecules, Both as a Functlon of the lnltlal Sulfurlc Acld Concentratlon [H,SO&
tion and will deal with real BZ reagents where chemistry takes place. We take the recipe in ref 3, which reports the molarities before the initial bromination reaction (indicated by a subscript "O"), and we calculate the molarities after the bromination reaction (indicated by a subscript "a"), by two different but equivalent approaches. Reference 3 reports the following initial concentrations:
[H,SO,],
= 0.2 M
[NaBrOJ, = 0.35 M
[NaBr], = 0.023 M [H,C(COOH)&
= 0.122 M
[ferroin], = 0.W29 M
According to Table 1,considering the dissociation of HzS04, we actually have the following initial concentrations: [H,O+],
= 0.2108 M
[HSOJ,
= 0.1892 M
[SO:-],
= 0.0108 M
[Nat], = 0.373 M [BrOJ,
= 0.35 M
[Br-1, = 0.023 M [H,C(COOH),],
= 0.122 M
[ferroin], = 0.0029 M
The bromination reaction (eq 3) Na'
+ BrO, + 2Nat + 2Br- + 3H,C(COOH), + 3Ht + 3HSO; 3BrHC(COOH), + 3H,O + 3Nat + 3HSO;
-
Pan A (lefl): Solid curve: Tdal proton wncentration [H30t]o,- (mol1L) in an aqueous solution of sulfuric acid in isolationasafunction of the initial sulfuric acid concentration [H2SO& (mol1L). The dashed line would result if H2SO+ was purely monodissociated. Pan B (below): Percentage ol didissodated HS , O, molecules as a function of the initial sulfuric acid cancenhatlon [H,SO,], (molIL1.
0.1
rsso.1. Volume 68
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April 1991
beginning with 23 mM Br-, takes away (W23 mM = 11.5 mM BrO;, (3/2)23mM = 34.5 mM H30C and (3/~)23mM = 34.5 mM H2C(COOH)2. I t produces (3/2)23mM = 34.5 mM BrHC(COOH)2, so that the final concentrations after the bromination reaction are:
Table 2. A Llsl 01 Recipes Used by Varlous Research Groups (Concenballons In mmollL before the lnltlal Bromlnatlon Reaction: MA H2C(CWH)r, BrMA BrHC(COOH)r)
Source
NaBrO,
mncenbatlons In rnmol/L H&O. NaBr MA
ferroln
[H,Ot]. = 0.1763 M [HSO;]. = 0.1892 M [SO:-], = 0.0108 M [NaC], = 0.373 M [BrOJ. = 0.3385 M [Br], = 0 M [H,C(COOH),]. = 0.0875 M [BrHC(COOH)2]a= 0.0345 M [ferroin], = 0.0029 M
Actually, this is not quite correct since we are dealing with chemical equilibria. If a chemical equilibrium is disturbed (as i t is here by consumptionof H30+ ions), it will readjust to a new and shifted equilibrium. In this case, the lowered [HaO+]concentration leads to a slightly increased dissociation of HSO; ions. With HSO; (0.1892 - y)
+ H20-
H30r (0.1763 y)
+
+
SO:(0.0108 + y)
we calculate
and saying that only 1.8 mM H3Of (about 1%) are produced additionally. This amount we regard as negligible (since the calculation is not exact anyway: we do not yet take the activity coefficients into account), although i t becomes more important for low-acid recipes (5). In the foregoing argument, we used a rather didactic approach: We first "turned the equilibrium (eq 6) off', i.e., we pretended that [H30+]was frozen to the value [H30+]0.The initial bromination reaction then consumed H30f ions, resulting in a decreased concentration of [H30C]. = [H30f]o Y2[Br-]o. Finally, we "turned the equilibrium (eq 6) on again", resulting in a slightly higher H30f concentration of [H30C]. = [H3OfI0- Y2[Br-lo y. This is the exact solution, but we showed t h a t y is small and can be set to zero with only little error. A less concrete, but mathematically more proper way that leads to the same result is as follows: Indicating concentrations before the initial bromination reaction witb a subscript "0" and concentrations after the initial bromination reaction witb a subscript "a" as above, we see from eq 3 that
+
[BrO;l, = [Broil, [Br-1. = 0
- %[Br-I,
LH,C(COOH),l. = [H2C(COOH),I0- 'i,[Brl, [BrHC(COOH)2]. = 3i,[Brl,
The constraints for the fragments from HzSOa then become [H,Otl,
+ [HSO;],
= 2[H,S0,10
- %[Brd,
(13)
and [HSO;I.
+ [SO:-].
= LH8OJo
Thus,
(14)
Agladze et al. (4 Epstein (14 Feeney et ai. (17) Field et al. ( 1 8 ) Jahnke e t al. (3) Kuhnert el al. (5) Kuhnen el al. ( 8 ) Maselk0 e t al. (15) Muller el al. (8) Nagy-Ungvarai et al. (9) Sevclkova et al. (18) Shawakr e t al. (7) Tarn et a1. (10) Vidal (10 Welsh et al. (12) Winfree (2)
~~..
Winfree 113)
-
Zaikin e t al. (1) A
~
Journal of Chemical Education
495
83'
125'
3.0
wm
MA and NaBr but deliberatelysynthesized it before and used it as a reagent. 'Feemy et al, and Sevcikwa et al, use directly HBrOs instead of NaBms . wnmesized . and H2S01. Kuhnsnetal.(@ use Ru(blpy1,CI~Inassddferroin ascatalyst: concentrationofstock soiU1Ion assumed 10 be 25 mmalIL. dMaselko etal. and Welsh e t a i orlgiwlly use KBrO, instead of NaBrO,. '~ a ~ s l k o e t aul~. e o a t i o r ~ t ) x ~ h mresin g e beads, loaded with 2 X towSmoi ferroin per gram resin. 'Nagy-uwvarai et al, use Ce(NH&(NOlh instead of iermln as oatalyst: concentration of stock soIYtion assumed to be 50 mmoilL. n ~ n additionslly d 1.3 mmdlL Cerous nitrate
and Plugging eq 15 and eq 16 into the equilibrium for sulfuric acid dissociation (eq 61,we obtain
and, after rearrangement
Equation 18 allowsto compute [SO: 1, for any desired initial composition. By taking the values from the recipe (3) ([SO:-]. = 0.0108 M 0.00184 M = 0.01264 M, [H2SO& = 0.2 M, [Br-lo = 0.023 M), one can easily see that both approaches are equivalent. We now want to point out an ambiguity that persists in the literature. Some authors report their recipes as concentrations after the initial bromination reaction. The recipe (3), e.g., could have been reported as "165.5 mM HzS04, 338.5 m M N a B r 0 3 , 87.5 m M H 2 C ( C O O H ) ~ 34.5 , mM B~HC(COOH)Z,2.9 mM ferroin". The 165.5 mM HnSOa would dissociate to give 176.3 mM H30f, 155.1 mM HSO;, and 10.6 mM SO:-. This agrees with the real concentrations (176.3 mM H30f, 189.2 mM HSO;, 10.8 mM SO:- in the foregoing approximation) only for the &0+ions, not for the other fragments of HzSOa. I t is meaningless to talk about HzSOa after acid-base reactions (such as the initial bromination reaction) have taken place, since after acid-base reactions, [H30f] Z [HSO;] 2[SO:-1. We could just guess that recipes that
+
+
322
342
I st~ai. ~8s WBI~ Z ~as za~kinand zhabotinsky did not ~ynmesizsB ~ M Ain sit"
Table 3. Slmilar to Table 2a, but wHh ConDentratlons lmmedlately afferthe InHIal Bromlnatlon Readlon, as Calculated
Table 4.
Amounts ol Stock Solutlo~In Mlllllltem that Are Needed To OMaln 8.5 mL Reagent
In thr, Tart'
Source
BrO;
Asladre e l a!. (4) Epstein ( 14) Feeney e l ai. ( 1 7 ) Field elal. ( 1 8 ) Jahnke et al. (3) Kuhnen e l al. (5) Kuhnen 61 al. ( 8 ) Mlilier elal. ( 8 ) Nagv-Ungvarai e l al. (9) Sevcikova st al. ( 1 8 ) Showalter e l al. (7) Winlree (2) Winlree (. 1 3. Zaikin e l al. (1) R~IB~B~CB i&iZand S
300
Mncenlrations in mrnol/L H 2 S 0 4 V A BrMA
370
0
12SC
NaBrO. lerroin
3.0
15 have teen ominad because there la no initial bromination
reaction withouf NaBr. %re precisely: his is the H,S04 mncemratlonthat dissociates m give the caren [H3Ot],.(But not the correst [SO: I. and [HSO;].. see sbwe.) =SeeTebk 2,l w t m e a . Table 2. lmtnote b. 'See Table 2. foolnote c. 'SBB Table 2. IOotnDte I.
ernowl of stock solution in mL H2S0, NaBr MA ferroin water
Agladm el a1. (4 Epstein ( 1 4 ) Feeney el al. (17) Field el al. (78) Jahnke el al. (3) Kuhnen e l al. (5) Kuhnert e l al. (8) Maseiko et al. ( 1 5 ) Miller et sl. (8) Nagy-Ungvaral et al. (9) Sevcikova et ai. ( I @ showaner el al. (7) Tam e l al. ( 1 0 ) Vidal ( 1 1 ) Welsh e l al. ( 1 2 ) Winfree (4 Winlree ( XiJ
.
renort sulfuric acid concentrations after the initial bromination reaction (1,4-7,9,I8) have to be interpreted as above (but were confirmed hv all the authors we could contact)there are other possibie interpretations! In order to eliminate these ambiguities in the future, we strongly suggest that all BZ recipes be reported before the initial bromination reaction. This is easier, more precise and leads toless misunderstandings. In Tables 2 and 3 we give a summary of major recipes used by different research groups, supplemented by Table 4 with the amounts of stock solutions that are needed to end up with 8.5 mL of these reagents. If more than one recipe is given in the paper, we chose one representative recipe. The concentrations of our stock solutions are (arbitrarily): N a B r O B1.420 molfi
42.86 g recrystallized N a B r O s in 200 mL solu-
tion H 2 S 0 4 3.260 moln: 17.15 mL cone. HzSOl in 100 mL solution H z C ( C O O H ) z 1.041 moln: 13 gin 120 mL solution N a B r 0.971 molfi 10 g i n 100 mL solution
ferroin 0.025 molL commercial solution
An example: In order to obtain an initial NaBrOs concentration of 328 m m o l n , as in Agladze's recipe ( 4 ) , one has to have (328f1420) 8.5 mL = 1.96 mL of 1.42 m o l n NaBrO3 in 8.5 mL solution. Correction for Real Solutions
The foregoing analysis is made under the assumption of ideal solutions. In reality, we have to take interionic attraction and thus the activity coefficients into account. The activity coefficients are mainly influenced by the ionic strength of the solution. The ionic strength, I,is defined as
where ziis the charge of the ion i, ci is the ion's concentration, and co is the standard concentration (co = 1molL), to make the ionic strength, I, a dimensionless quantity. The summation is made over each type of ion present in the solution. The ionic strength affects the dissociation constants. They can become bigger or smaller, depending on the charge of the acid molecule. The Debye-Hiickel theory of interionic attraction states that (19)
where pK = -log K, K is the dissociation constant of the acid andz is the charge of the acid molecule (e.g., z = Ofor HzSOh z = -1 for HSO;. . and z = 1for NH!). Let us take sulfuric acid as an example. Consideration of the ionicstreneth has n o i m ~ a e on t the first dissociationsten completely anyway. But it does clear& (eq 4): i t affect the second dissociation ster, (ea 5). For that second has one negative dissociation step, z = -1 since %SO; charge. Equation 20 says that, e.g., for [HzSO& = 0.1 m o l n (and therefore I 0.1)
.
-
i.e., the 'real' dissociation constant K2 (real) = 10-'.'4 is greater than the 'ideal' dissociation constant (supposing I = 0) K P (ideal) = 10-1.92. With this altered disssociation constant. wecomoutefromea 12 that lH~O+lnt,,la~ ..,.-.-.= 0.1228mol/ L: 22.8% of ~ I ~ H moldcules ~ S O ~arddibissociated, in contrast to the 9.86% stated in Table 1. For [HzSOa]o = 1 m o l L we compute pK2 (real) = 0.92 and [HsO+]o.bbl= 1.099 m o l L 9.9% of all H&Od molecules are didissociated. In BZ soluiiois, the ionic strength is even higher than in solutions of pure sulfuricacid. The recipe of ref 3, e.g., has an ionic strength I = 0.56. Assuming that eq 20 still holds, pK2 (real) = 1.06. With that altered dissociation constant and with [H2SOa]o= 0.2 mol/L, we calculate tbat [H30+]o= 0.232 m o l L before the initial bromination reaction and [H30+]. = 0.198 mol/L after the initial bromination reaction (cf. [H30f], = 0.176 m o l L as calculated above for ideal solutions). o f course, all these numhers still have a considerable error because they have been computed from empirical laws, using constants that are fairly uncertain. Our objective was to point out that even the initial bromination reaction is not quite trivial. Consequently, we want to recommend again that the concentrations of reactants before the initial bromination reaction he reported rather than the concentrations after the initial bromination reaction tbat are, as we have Volume 66
Number 4
April 1991
323
just shown, not well defined. By doing that, one can evade the ambiguities and difficulties sketched in this paper. Acknowledgment
We thank Hana Sevcikova, Milo; Marek, Richard M. Noyes, Harry Swinney, Susanna Nagy-Ungvarai, and John Tyson for helpful suggestions and discussions. WJ thanks the Studienstiftung des deutschen Volkes for a fellowship. Literature Cited 1. Zaikin, A. N.;Zhabofinsky, A. M.Nafure 1970,223,535. 2. Winfree. A. T. Seianra 1972,175,634.
3. Jshnke, W.: Henze.C.; Winfree,A.T.Nalvre 1388,336,662. 4. Agladze. K. I.: Krinsky. V. I. Nature 1982,296,425.
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Journal of Chemical Education
Kuhnert, L.:Pohlmann, L.: Krug, H d . Physica 29D 1988,416. Kuhnert,L.;Aglsd%e,K. I.: Krinsky. V. 1.Nolure 1989,331,244. Showalter, K.: Noye8.R. M.:Turner, H. JACS 1979,101,7463. a. Mirl1er.S. C.; P1eser.T.: Heaa, B.Science 1985,230,661. b. Foerater, P.:M~ller,S. C.; HO$S,B.Science 1988,241,685. Negy-Ungvsrai, 2s.; Tyson, J. J.; Hess. B. J . Phys Cham 1989.93.707. Tam. W. Y.; Honthemke, W.; Nostierius, 2.: Swinney, H.L. J . Chem.Phya. 1988.88, 3395. r. v i d a i , ~~. . s t o r . ~ h y1987.46.1017. Welsh, B.: Gomatam, J.: Burgesa, A. Nature 1983,304,611. Winfree.A. T. Pmg. Theor. Chem. 1978.4.1. Epstein I. R. Chsm. Eng. News 1987,65(13), 24. Marelko, J.; Showsiter, K. Nature 1989,339,609. Sevcikovs, H.; Msrek. M. PhyaicoSD 1983,140. Feeney, R.; Schmidt. S.: Ortoleva. P. Physico 2D 1981,536. Fie1d.R. J.: Noyer. R. M. JACS 1974,S96,2OOl. Bell. R. P. Acids and Bases: Their Quoniiiorivs Bohouiour, 2nd ed.: Chapman & Hail, 1971.
