2472
J. Phys. Chem. 1988, 92, 2472-2419
Initial Processes In the Reaction of Sllver Ion with Bromide Ion in 1 M Sulfuric Acid: Implications for Sllver Ion Perturbation of the Belousov-Zhabotinskii Reaction Girish Kshirsagar, Richard J. Field,* and LPszl6 Gyorgyit Department of Chemistry, University of Montana, Missoula, Montana 59812 (Received: September 1 , 1987)
The rate of reaction of Ag+ with Br- in 1 M H2S04has become of interest as a result of experiments on the perturbation of the oscillatory Belousov-Zhabotinskii reaction by Ag'. The major effect of such a perturbation is expected to be removal of Br- (a most important intermediate species in the mechanism of the oscillations) from the reaction mixture, presumably with the formation of some form of AgBr. The major experimental results of Ag+ perturbation experiments have been rationalized in this way by assuming that the rate of reaction of Ag' with Br- is much less than diffusion controlled. We have investigated by a spectrophotometric method the initial processes of the reaction of Ag+ with Br- in 1 M H2S04. There is an initial, narrow, sharp absorbance centered near 220 nm that appears probably at a nearly diffusion controlled rate during mixing. The species responsible for this appears to be (AgBr)4, an oligomer of AgBr, which then decays on a time scale of ==los to a second species, presumably a larger oligomer of AgBr, which has a similar spectrum but with a shoulder near 250 nm. This time scale is that necessary to rationalize the Ag+-perturbed BZ reaction experiments, and it is likely this process that effectively removes Br- from the BZ reaction. The mechanism of conversion of the first to the second species seems to be dissociation to Ag+ and Br- followed by reattachment (perhaps as AgBr monomers) to growing (AgBr), oligomers. When [Ag+Io= [Br-lo = lo4 M, a AgBr sol forms on a time scale of 10 min. We show that it is possible to accurately simulate the results of Ag'- perturbation of the BZ reaction on the basis of this mechanism for the initial interaction of Ag' with Br-.
is the oxidation The Belousov-Zhabotinskii (BZ) of an organic material (e.g., CH2(COOH)2)by Br0Y in a strongly acidic (usually H,SO,), aqueous medium. The overall chemical change is normally catalyzed by a metal-ion redox couple such as Ce(IV)/Ce(III). During the course of the reaction, the ratio Ce(IV)/Ce(III), as well as the concentrations of various intermediate species such as Br-, HBr02, and Br,, oscillate^.^ The oscillations can be monitored spectrophotometrically, potentiometrically by using a Pt electrode to measure the overall redox potential (which is mainly due to the Ce(IV)/Ce(III) couple), or potentiometrically by using a bromide-ion-selective electrode to measure [Br-1. The detailed mechanism of the BZ reaction was elucidated by Field, Koros, and Noyes3 (FKN) in 1972. Bromide ion plays a most important role in this The oscillations occur as control of the reacting system is passed back and forth between two separate sets of reactions, one involving nonradical species and the other involving radical species. Bromide ion controls which set of reactions is dominant at a particular point in the reaction. The set of nonradical reactions is dominant when [Br-] is greater than a critical value, and the set of radical processes is dominant when [Br-] is less than this critical value. The switch from control by the set of nonradical reactions to control by the set of radical reactions (or vice versa) occurs when [Br-] passes through the critical value. The nonradical reactions consume Br- and lead inevitably to the onset of the radical reactions. However, the radical processes lead indirectly to the regeneration of Br-, which causes the nonradical reactions to eventually regain control of the system. Thus, bromide-ion-controlled oscillation occurs according to the FKN mechanism. Considering the role of Br- in the mechanism of the BZ reaction, there has been much interest in the effect of added Ag+ on the BZ oscillations. It is naively expected that sufficient Ag+ will suppress the oscillations (leaving the set of radical reactions in control) by removing Br- from the reaction with formation of insoluble AgBr. The first experiment of this type was carried out by Vavilin et al.,' who found that small amounts of added Ag+ cause a phase shift of the oscillations. Much more remarkable are the results of Noszticzius,8 who found that continuous addition of Ag' apparently suppresses the oscillations in [Br-] but that high-frequency oscillations in redox potential continue. On the
* Author to whom correspondence should be addressed. 'Permanent address: Institute of Inorganic and Analytical Chemistry, Edtvds Lorand University, P.O.Box 123, H-1443 Budapest, Hungary. 0022-3654/88/2092-2472$01.50/0
basis of this result, Noszticzius concluded that, at least in the presence of Ag', the BZ oscillations may not be bromide ion controlled. Ganapathisubramanian and Noyesg confirmed and extended Noszticzius' observations. Ruoff'O also extended the Ag+ perturbation experiments and further demonstrated that the BZ reaction shows excitability" in the presence of Ag'. There was considerable initial difficulty in fitting Ag+-perturbed BZ oscillations within the framework of the Br--controlled FKN me~hanism,~"which led to some confusion12 concerning the universal applicability6 of the FKN mechanism. Finally, Ruoffl3l6 demonstrated that all experiments on Ag+ perturbation of the BZ reaction can be semiquantitatively modeled as bromide ion controlled in terms of a simplification of the FKN mechanism based on the O r e g ~ n a t o r .Some ~ of the more remarkable effects of Ag+ perturbation noted by Noszticzius* were interpreted as artifacts of the behavior of Br--selective electrodes when [Ag+]/[Br-] > 1.
RuoffI3-l6 proceeded by adding reaction 1, the formation of AgBr(,, from Ag+(,,, and Br-(,,), to the basic model. (1) Belousov, B. P. Sbornik Referator PO Radiatsionni Meditsino, 1958; Medgiz: Moscow, 1959. See also: Belousov, B. P. In Oscillafions and Traveling Waves in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985; p 605. (2) Zhabotinskii, A. M. Dokl. Akad. Nauk SSSR 1964, 157, 392. (3) Field, R. J.; Koros, E.; Noyes, R. M. J . A m . Chem. Soc. 1972, 94, 8649. (4) Field, R. J. In Oscillations and Traueling Waves in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985; p 55. (5) Field, R. J.; Noyes, R. M. J . Chem. Phys. 1974, 60, 1877. (6) Noyes, R. M. J . Chem. Phys. 1984, 80, 6071. Noyes, R. M . J . A m . Chem. SOC.1980, 102, 4644. (7) Vavilin, V. A,; Zhabotinskii, A. M.; Zaikin, A. N. In Biological and Biochemical Oscillators; Chance, B., Ghosh, A. K., Pye, E. K., Hess, B., Eds.; Academic: New York, 1973; p 73. (8) Noszticzius, Z. J . A m . Chem. SOC.1979, 101, 3660. (9) Ganapathisubramanian, N.; Noyes, R. M. J . Phys. Chem. 1982, 86, 5 155. (10) Ruoff, P. Chem. Phys. Lett. 1982, 90,76. Ruoff, P. J . Phys. Chem. 1984, 88, 1058. Ruoff, P. J . Phys. Chem. 1984, 88, 2851. (1 1) Field, R. J.; Noyes, R.M. Faraday Symp. Chem. SOC.1974, No. 9, 21.
(12) Noszticzius, Z.; Farkas, H.; Schelly, Z . J . Chem. Phys. 1984, 80, 6062. (13) Ruoff, P. Z. Naturforsch., A : Phys., Phys. Chem., Kosmophys. 1983, 38A, 974. (14) Ruoff, P. Chem. Phys. Lett. 1982, 92, 239. (15) Ruoff, P.; Schwitters, B. J . Phys. Chem. 1984, 88, 6264. (16) Schwitters, B.; Ruoff, P. J . Phys. Chem. 1986, 90,2497.
0 1988 American Chemical Society
Reaction of Ag+ with Br- in H2S04
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2473 0.57
I
The actual kinetic form of reaction 1 used was
The necessity for reversibility of some sort in reaction 1 was noted by Ruoff and Schwitted5and seems clear from the work of Koros and VargaI7 and Varga et all8 on perturbation of the BZ reaction by Hg2+and T13+ions, which reversibly form complexes with Br-. However, in order to reproduce the experimentally observed effect of Ag+ perturbation of the BZ reaction, it was necessary for RuoffI4 as well as Ruoff and SchwittersI5 to assume that k, is far smaller than diffusion c ~ n t r o l l e d and ' ~ also much less than the rate expected20,z1for the substitution of Br- for HzO or HSO, in the coordination sphere of Ag+. They used kl = lo4 M-I s-l in their calculations. There is then some need to investigate reaction 1 more carefully. There has been considerable workZZon reaction 1, but most of it has been concerned with the appearance of precipitation nuclei and the precipitation process itself rather than the initial interaction of Ag+ with Br-, which is more important for understanding Ag+ perturbation of the BZ reaction. Much previous work also has been done with [Br-]/[Ag+] >> 1 where species such as AgBrz-, AgBr?-, etc., are importantZ3rather than under the [Br-]/[Ag+] 5 1 conditions that normally prevail in Ag+-perturbed BZ reaction experiments. However, several experimental determinations of k l in 1 M HzSO4 (the BZ medium) and with [Br-]/[Ag+] = 1 have appeared recently. Varga and KOrosZ4used a competition technique in the BZ reaction itself to infer the value kl = lo4 M-' s-l. This result may be uncertain by a factor of a few times because of problemsZ5with the precipitation of AgBrO,, but their data still imply that the net rate of effective Br-(aq)removal by Ag+(as) is much less than diffusion c ~ n t r o l l e d . ' ~RuofP6 has recently reported an essentially identical value based on a direct investigation of reaction 1 using a Br--selective electrode to monitor [Br-(,,)] after a solution of Ag+ is injected into a solution containing Br-. However, Noszticzius and McCormickZ7reported simultaneously with Ruoff that, using a Ag+-wire electrode to monitor [As+] in essentially the same experiment, reaction 1 seems to go to completion during mixing. This implies k , > lo6 M-' s-I . Unfortunately, it is very difficult to unambiguously interpret these experiments because the dynamics of mixing as well as of the electrodes themselves are uncertain. In particular, because of the matrix construction of commercial Br--selective electrodes, their response time may be longer than that of a Ag/AgBr wire electrode and may be different depending on whether Ag+ or Bris present in excess. We report here a spectrophotometric investigation of the interaction of Ag+(,,) with Br-(,,) in 1 M HzSO4. We find it to be a very complicated process involving several time scales on the route from Ag+(,,) and Br-(,,) to AgBr,,). The initial interaction of Ag+(,g)with Br-(,,) to yield simple AgBr,,,) oligomers is indeed very rapid, probably diffusion controlled, and is complete in our experiments during mixing. However, we find secondary processes, one of which occurs on the time scale suggested by Ruoff,I4,l5by which the initially formed simple species grow to crystallization (17) KGr6s, E.; Varga, M. J . Phys. Chem. 1984,88, 4166. (18) Varga, M.; Gyorgyi, L.; Karos, E. J . Phys. Chem. 1985, 89, 1019. (19) Keizer, J. Chem. Rev. 1987, 87, 167. (20) Eigen, M. Ber. Bunsen-Ges. Phys. Chem. 1963, 67, 753. (21) Basolo, F.; Pearson, R. G. Mechanisms of Inorganic Reactions, 2nd ed.; Wiley: New York, 1967; p 155. (22) Walton, A. G. The Formation and Properties of Precipitates; Interscience Publishers: New York, 1967. (23) Berne, E.; Leden, I. Z . Naturforsch., A : Astrophys., Phys. Phys. Chem. 1953, 8 A , 719. (24) Varga, M.; Koros, E. J . Phys. Chem. 1986, 90,4373. (25) Ruoff, P.; Varga, M.; KorBs, E. J . Phys. Chem. 1987, 91, 4431. (26) Ruoff, P., private communication. (27) Noszticzius, Z.; McCormick, W. D., private communication.
I
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570 nm
50
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Figure 1. Absorbances recorded at 0.2-s intervals at 212, 220, 250, 330, 410, and 570 nm after the injection of 6 fiL of 6.438 X lo-) M AglSOp M KBr in 1 M H2S04. [Agt], = 3.85 X into 2.0 mL of 1.012 X M and [Br-1, = 1.010 X lo4 M.
nuclei leading eventually to a AgBr,,, sol.
Spectral Measurements Experiments were carried out by injecting microliter (1-100 pL) quantities of Ag+ (from AgzS04)or Br- (from KBr) into 2.0 mL of solutions lo4 M respectively in either Br- or Ag'. Reactions were carried out in a thermostated, well-stirred cuvette positioned in a HP8452a diode-array spectrophotometer. All experiments were done in 1 M HZSO4, the BZ medium, but essentially identical results were obtained in 1 M HC104 with AgC104. Results were very different in pure water, presumably because of interference from species such as AgOH. Figure 1 shows time-resolved absorbances at 212, 220,250, 330, 410, and 570 nm obtained after 6 pL of a 0.0129 M solution of M Ag+ in 1 M H2S04is injected into 2.00 mL of a 1.01 X solution of KBr in 1 M H2S04. The initial [Ag'] ([Ag+l0) was 3.85 X M, and Ag+ was the limiting reactant. There are several time scales evident in Figure 1. The absorbances at 21 2 and 220 nm reach their peak essentially during the mixing time of 1-2 s, while the absorbance at 250 nm does not reach its peak until about 25 s after mixing. The absorbances at 330, 410, and 570 nm are still growing after 250 s. We conclude that a t least three distinct time scales and processes are involved. Figure 2A shows a spectrum taken 4 s after mixing. It extends from near 190 nm to about 330 nm with a sharp maximum at 204 nm. We attribute this spectrum to a species (which we will refer to as the "220-species") formed during mixing. Figure 2B shows a spectrum taken 25 s after mixing. This spectrum extends over very nearly the same wavelength range as does the spectrum seen at 4 s; however, its maximum is at about 228 nm, and a shoulder has appeared in the region 250-320 nm. The time-resolved data at 250 nm in Figure 1 show the growth of this shoulder. The initial rapid growth at 250 nm results from the 220-species. We attribute this spectrum to a species (which we will refer to as the "250-species") formed from the 220-species because the absorbance at 220 nm decreases as the absorbance at 250 nm grows (see Figure 1). The spectra of the 220-species and the 250-species are narrow and sharp. They probably result from n-u* transitions in small molecule-like species. Similar spectra have been observed by Iwasaki and TanakaZ*in stopped-flow experiments and assigned to AgBr(,, or oligomers of it. Other worker^^^^^ have also reported transient absorbances during the initial stages of the reaction of Ag+ with Br-. Figure 2C shows the spectrum obtained at 14 min. It is very broad, and the peak in the vicinity of 2OC-300 nm has disappeared. This spectrum presumably reflects a complex combination of (28) Iwasaki, M.; Tanaka, T. Nippon Kagaku Kaishi 1984, 6, 948. (29) Matsubara, T.; Tanaka, T. Nippon Shashin Gakkaishi 1982,45,342. (30) Wey, J. S.;Leubner, I. H.; Terwilliger, J. P. Photogr. Sci. Eng. 1983, 27, 4690.
Kshirsagar et al.
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988
2474
0.50i
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Figure 3. Maximum absorbances observed (see Figure 1) at 220 and 250 nm after injection of various amounts (2-35 ML) of 6.438 X M Ag,SO, into 2.0 mL of 1.012 X M KBr in 1 M H2S04. The least-squares lines are calculated from experiments for which [Ag'], < [Br-1,. The absorption coefficients (calculated on the basis of the concentration of [Ag'],) are 12910 M-' cm-' at 220 nm and 6396 M-' cm-' at 250 nm. The sharp break occurs at [Ag'], = [Br-1, indicating that the absorbances result from a single species of stoichiometry (AgBr),.
n 6n
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INITIAL [Br-] ADDED (M)
200
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Figure 2. Spectra at various times after injection of Ag' into a KBr solution in an experiment identical with that shown in Figure 1: (A) 4 s after injection, (B) 25 s after injection, and (C) I4 min after injection. Integration time for all spectra is 0.5 s.
scattering, absorbance, and possibly l~minescence.~' These results indicate that the reaction of Ag+ with Br- can be broadly represented by the scheme Ag+,as)
+ Br-faq)s (?) s (220-species) s (?) s (250-species)
F!
(?) s (AgBr,,,))
+ (AgBr,,,)
(3)
where (?) indicates the potential presence of transient intermediate species. In later sections we will suggest the identity of the 220and 250-species.
Titration Curves The stoichiometry of the 220- and 250-species may be determined by addition of increasing amounts of Ag' to solutions of constant [Br-1, or vice versa. Figure 3 shows the maximum absorbances observed at 220 and 250 nm when increasing amounts of Ag+ ion are added to a 0.000 101 M solution of KBr. Figure 4 shows the maximum absorbances observed at 220 and 250 nm when increasing amounts of Br- are added to a 0.000 100 M (31) Yu,P.Y . Comments Solid State Phys. 1985, 12, 33.
Figure 4. Maximum absorbances observed (see Figure 1) at 220 and 250 nm after injection of various amounts (2-35 pL) of 1.012 X M KBr M Ag2S04in 1 M H2S04. The least-squares into 2.0 mL of 5.151 X lines are calculated from experiments for which [Br-1, < [Ag'l0. The absorption coefficients (calculated on the basis of [Br-I,) are 13 379 M-I cm-' at 220 nm and 6467 M-' cm-' at 250 nm. These are the same within experimental error as obtained from Figure 3. The sharp break occurs at [Ag'], = [Br-1, indicating that the absorbances result from a single species of stoichiometry (AgBr),.
solution of Ag'. All absorbances in Figures 3 and 4 have been corrected for excesses of Ag+ or Br- so that they can be ascribed to reaction products of Ag+ with Br-. The necessary corrections are small because the observed absorbances are quite large compared to the absorbances of equivalent amounts of Ag+ or Br-. The absorption coefficient of Ag+ at 220 nm in 1 M H2S04is 710 M-' cm-'. There is little absorbance due to Br- at 220 nm, and neither Ag+ nor Br- absorbs significantly at 250 nm at the concentrations used here. In both cases the absorbance grows linearly at both 220 and 250 nm until the equivalence point (0.0001 M) is reached, a n d no further growth of absorbance is observed. This implies that the stoichiometry of the absorbing species at both 220 and 250 nm is (AgBr), and that essentially all of the limiting ion (Ag' or Br-) is tied up as the 220-species immediately on mixing. The solid lines in Figures 3 and 4 are least-squares fits to the data points at less than the equivalence point. The slopes yield absorption coefficients based on the concentration of the limiting ion of 13 150 M-I cm-* at 220 nm and 6430 M-I cm-' at 250 nm. That the maximum absorbances at 220 and 250 nm occur at different times implies that they result from different species. The titration curves in Figures 3 and 4, which are based on the maximum absorbances at 220 and 250 nm, imply that the maximum absorbance at each wavelength results from a single species, which we already have labeled the 220-species and the 250-species,
Reaction of Ag+ with Br- in H2S04
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2475
respectively. The 220-species is present immediately after mixing and decays on a time scale of tens of seconds to the 250-species. The 250-species then decays on a time scale of minutes to the species responsible for the spectrum in Figure 2C. The identities of the 220- and 250-species are not obvious, although they clearly have the stoichiometry (AgBr),. The simplest such species is the AgBr,,,) molecule, which should be in equilibrium with Ag+(aq)and Br-,,,) as in the reaction Ag+(aq)+ Br-(aq) + AgBr(aq)
(4)
However, it is unlikely that the 220-species is AgBr,,,,. The stability constant (K4) for the formation of AgBr(,,) from Ag+(,,) and Br-(aq)has been measured directly23and can be calculated from tabulated32 thermodynamic data. Its value is about 1.5 X lo4 M-l. For this stability constant and the initial values [Ag+Io = [Br-1, = 1 X M, the equivalence point in Figures 3 and 4, only about 50% of the initially present Ag+(,,! and Br-(,,) should be tied up as AgBr,,,). This is inconsistent with the very sharp breaks at the equivalence point seen in Figures 3 and 4,which imply values for the equilibrium constant between Ag+(,,), Br-(aqi and the 220- or 250-species of at least lo8 M-l. The measured value of the equilibrium constant between Ag+(,,), Br-,,,), and AgBr,-,,,, is 1.3 X lo7 M-2, and that33between Ag+(,,), Br-(,,), and Ag2Br+(,,) is 5 X lo9 M-2, so that these species are not expected to be stoichiometrically significant in our experiments M. with [Ag'], i= [Br-lo = We assume that the 220-species is more complex than AgBr,,,, and tentatively suggest that it is (AgBr)4(aq).The major evidence for this suggestion is the inhibiting effect of a 25% excess of Ag+ on the conversion of the 220-species to the 250-species discussed below. This suggests formation of a species of the stoichiometry (AgBr),,(Ag+), that is less reactive than (AgBr)4,. We further point out that (AgBr),,,,) is the first symmetrical, three-dimensional polymer of AgBr(,,, and that it is not unreasonable to expect it to be the first with sufficient stability to behave as an intermediate in the precipitation of AgBr(,). duch species (referred to as the unit cell) have been suggested to serve as nuclei for the growth in general of precipitates of sparingly soluble salts34as well as in the case of AgBr itself.28 Conversion of (AgBr),,,,, to the next stable polymer of AgBr,,,) is expected35to show a nucleation effect. Thus, it is not unreasonable for (AgBr),,,,) to be relatively long lived. The identity of the 250-species is even less clear, but we assume it to be the next stable AgBr,,,) oligomer, perhaps (AgBr),,,,).
Kinetics of Conversion of the 220-Species to the 250-Species The formation kinetics of the 220-species are lost in the mixing process. This means that if the 220-species is actually AgBr(,,), then k , must be at least 10, M-' s-l. If the 220-species is indeed a secondary species such as (AgBr),,,,,, then the direct reaction of Ag+(,,) and Br-,,,) must be very fast, probably diffusion controlled. The kinetics of the conversion of the 220-species to the 250species are slow enough to be observed in our experiment. Furthermore, they are clean and reproducible. The growth of the 250-species is first order in the concentration of the 220-species, i.e. d[ 250-species] = k5[220-species] dt
(5)
and if the 220-species and the 250-species are the only ones present so that ([AgBr],)x ([AgBr],)y = C (where x is the number of AgBr monomers in the 220-species, y is the number of AgBr monomers in the 250-specieq and C is the concentration of the
+
(32) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J . Phys. Chem. ReJ Data, Sppl. 1982, 11, 2-162. (33) Yatsimirskii, K. B. Dokl. Akad. Nauk SSSR 1951, 77, 8 1 9 . (34) Reference 22, p 36. (35) Reference 22, p 46.
I
&
0.0
10.0
20.0
30.0
TIME (SECONDS)
Figure 5. Plots of In [A(250),/(A(250), - A(250),)] vs time (see text for variable identification) for various values of [Ag+]o/[Br-]o: (A) 30 p L of 1.012 X M KBr injected into 2.0 mL of 5.059 X M Ag2S0, in 1 M H2S04. [Ag+Io = 9.852 X M and [Br-lo = 1.495 X l o 4 M. (B) 16 p L of 6.438 X M Ag2S04injected into 2.0 mL of 1.012 X lo-" M KBr in 1 M H2S04. [Ag+]o = 1.022 X lo-" M and [Br-Io = 1.003 X lo4 M. (C)35 p L of 6.438 X 10" M Ag2S04injected into 2.0 mL of 1.012 X l o 4 M KBr in 1 M H2S04. [Ag+Io = 2.214 X lo4 M and [Br-1, = 9.927 X M.
REGRESSION LINE rAg+l, ( [Br-I, = 0.0001 M
[Br-1,
jo0 0 0
0
0
0
0
19' 0.0
1 .OE-4
2.OE-4
INITIAL [Ag']
3.OE-4
4.OE-4
ADDED (M)
Figure 6. Plot of k5, the first-order rate constant for conversion of the 220-species to the 250-species, vs [Ag+l0. The least-squares line through the experiments with [Ag*Io < [Br-1, gives the value k5/[Ag+]o= 5.03 x 103 M-1 ~ 1 .
limiting ion, either Ag+ or Br-), then it is easy to show that plots of In [A(250),/(A(250), - A(250),)] should be linear with slope equal to k5. The quantity A(250), is the maximum absorbance at 250 nm, and A(250), is the absorbance at 250 nm at a particular time before the maximum is reached. Figure 5 shows three typical first-order plots with respectively a large excess of Br-, nearly stoichiometric amounts of Ag' and Br-, and a large excess of Ag+. All are linear up to at least 98% reaction. The initial (2-3 s), rapid portion of each plot results from the absorbance at 250 nm due to the formation of the 220-species during mixing. While the integrated rate of growth of the 250-species is clearly first order in all of our experiments, the calculated first-order rate constants depend strongly on the initial concentration of the limiting species, either Ag+ or Br-. Figure 6 shows a plot of first-order rate constant vs [Ag+l0when various amounts of Ag+ are added to O.OO0 100 M KBr. Below the equivalence point where the initial [Ag'] is limiting and Br- is in excess, the first-order rate constant rises linearly with increasing [Ag'], (decreasing excess Br-). After the equivalence point where the initial [Br-] is limiting and Ag+ is in excess, the first-order rate constant decreases rapidly until about a 25% excess of Ag+ is reached, after which the first-order rate constant decreases only very slowly as Ag+ increases to a severalfold excess. The value of k5 in the presence of more than 25% excess of Ag' is about one-half of its value at the equivalence point. Figure 7 shows the inverse experiment in which various amounts of Br- are added to 0.000 100 M Ag+. The results of this experiment are qualitatively similar to those in Figure 6, but there
2416
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 1 .o
1
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Kshirsagar et al.
0 0
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021
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0 0 0
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0 04 0 c
2 OE-4 INITIAL [Br-]
4 OE-4
1
6 OE-4
ADDED (M)
Figure 7. Plot of k5,the first-order rate constant for conversion of the 220-species to the 250-species, vs [Br-1,.
are subtle differences. Below the equivalence point where Ag' is in excess, the first-order rate constant increases but not linearly. The rate of increase instead accelerates as the equivalence point is approached and the excess of Ag+ drops below 25%. After the equivalence point, where Br- is in excess, the first-order rate constant does not show the rapid decrease seen in Figure 6 when Ag' is in excess, although a much smaller decrease is seen at a large excess of Br-. Conversion of the 220-species to the 250-species is fastest when Ag' and Br- are initially present in the stoichiometric ratio, Le., 1:1. Near the equivalence point excess Ag' inhibits conversion of the 220-species to the 250-species, but this effect saturates when the excess of Ag+ exceeds 25%. A similar inhibition effect in the precipitation of AgBr(,) has been observed by Iwasaki and Tanaka.28 Excess Br- does not seem to have as strong an inhibiting effect as does Ag'. The inhibitory effect of excess Ag+ may be particularly important in the BZ Ag' perturbation experiments in which [Ag+]/[Br-] often exceeds 1. The above kinetic observations can be best rationalized by assuming that the rate of conversion of the 220-species to the 250-species is proportional to the concentration of the 220-species as well as to [Ag+(,q)] and [Br-(,q)]. It must further be assumed that [Ag+(,,)] and [Br-,,)] do not change much as the 220-species changes to the 250-species. This implies that the 220-species and the 250-species are quite similar, e&, (AgBr)4(:q) and ( k ~ g B r ) ~ ( ~ ) , so that the amounts of Ag+(,) and Br-(aca4, in equilibrium with either species are very similar and do not change significantly as one is converted to the other. Of course, the concentrations of Ag'!,, and Br-(aq)do depend on the total concentration of AgBr pairs in the system, Le., the initial concentration of either Ag' or Br-, depending on which is limiting. The rate expression for the conversion of the 220-species to the 250-species then becomes -d[ 220-species] = k6[220-species] [Ag'] [Br-] (6) dt By assuming that Ag+(,q)and Br-(aq)are in equilibrium with the total [(AgBr),(,,)], we write [As+][Br-I = ([Ag+loor [Br-lo)/K,, depending on whether Ag+ or Br- is limiting and thus which determines total [(AgBr),(,,)]. The value of [Ag'] [Br-] and thus the rate of conversion of the 220-species to the 250-species increase as the concentration of the limiting ion increases toward the equivalence point. No further increase in rate is seen after the equivalence point because total (AgBr), remains constant, and an increase in the concentration of the ion present in excess is balanced by an accompanying decrease in the concentration of the other ion; Le., [Ag'][Br-] is constant if total [(AgBr),(,,,] is. The relationship between k6 and the experimental first-order rate constant (k,) is given by k6
= k5Kq/([Ag'10
or [Br-lO)
(7)
The data in Figure 5 yield k5/([Ag+Io or [Br-lo) = 5 X lo3 M-I s-'. The titration curves in Figures 3 and 4 indicate K,, IIOs M-' and so k6 I5 X 10" W2s-l.
(36) Moore, W. J. Physical Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1972; p 888. (37) Reference 22, p 105. (38) Chateau, H.; Pouradier, J. C. R. Hebd. Seances Acad. Sci. 1955, 240, 1882.
The Journal ofphysical Chemistry, Vol. 92, No. 9, 1988 2411
Reaction of Ag+ with Br- in HzS04
-
I
7-
0
0.04
15.0
0
20.0
25.0
'
0.00 0.0
30.0
TIME (SECONDS)
X lo4 M-'. If indeed the 220-species and the 250-species are in rapid equilibrium with Ag'!,,) and Br-(aq),then they should be removed from the system with formation of AgS203-(,,) by the addition of sufficient Sz032-(aq).Figure 8 shows absorbances at 220, 250, and 300 nm in such an experiment. Initially, 10 HL M) is injected into 2.0 mL of of Ag+ ([Ag'j, = 6.21 X 0.000 100 M KBr. Rapid, mixing-controlled, growth of absorbance due to the 220-species is seen at 220 nm, and a slower growth in absorbance due to the 250-species is seen at 250 and 300 nm. A M) is then 100-pL sample of S2032- ([S203z-]o= 2.4 X injected as the absorbance at 250 nm nears its peak. The immediate large jump in absorbance at 220 nm and smaller jumps a t 250 and 300 nm are due to absorbance by S2032-. After the initial jump, the absorbance at 300 nm decreases to near zero, presumably as Ag+ is tied up as AgSZ0,- and Ag(S2O3)?-, which have little absorbance at this wavelength. We find no evidence at the low SZO3*- concentrations and rapid reaction times used here of the well-known39 decomposition in strongly acid media of S203*-to elemental sulfur. The decrease in absorbance at 300 nm can be interpreted by assuming that Ag+(,,) and Br-(aq)are always in equilibrium with the 250-species and that reaction 8 is rate determining for the formation of AgSz03-. This leads to the equation
(10)
Integration of eq 10 yields b+A-A,
1.1 b
+&-A,
2.5E-1 1 1 /(WAVELENGTH)4
Figure 9. Plot of the left-hand side of eq 11 vs time. The linearity of this plot implies that eq 10 governs the dissolution of the 220-species and the 250-species to yield AgS,03-. The least-squares slope of the line is 0.193 s-l.
-d[ 250-species] [250-species] [SZO3*-] = kg dt Keq [ Br- 1
1
(b + A - A,)(Ao - A,) j + i l n { ( A - &)(b + A0 - A , ) (11)
In eq 11, A is the absorbance at 300 nm at time t , A. is the maximum absorbance at 300, A, is the final absorbance at 300 nm, a = [Br-1, and b = [Sz03z-]o- [Ag+l0. While substantial amounts of Ag(Sz03)23-may form, this does not seem to affect the rate of removal of the 220- and 250-species. Figure 9 shows a plot of eq 11 for the data in Figure 8. It is linear to 95% reaction with a slope of 0.193 s-l. Seven experiments with [Ag+l0 and [S2032-]o varying over factors of 4 showed no trends and an average value of k8/Kcs = 0.24 s-l. Assuming as we have that Kq 1 lo8 M-l, we find k8 1 2 X lo7 M-I s-l, a quite reasonable value. We point out that Ks = 6.7 X lo7 M-' and that the 220-species disappears with [S203z-]/ [Br-] Z 1, so that Kq hardly can exceed 10' M-' by very much. Formation of AgBr Sol at Long Times Our major interest here has been the molecule-like (AgBr),,,,) oligomers in rapid equilibrium with Ag+(,,) and Br-(aq)that are (39) LaMer, V. K.; Dinegar, R. H. J . Am. Chem. Soc. 1950, 72, 4847.
5
9
5.0E- 1 1
7.5E-1 1
(nm-4)
Figure 10. Plot of absorbance vs l / ( ~ a v e l e n g t h )in~ the wavelength M Ag2S04 range 35C-820 nm 5 min after injecting 15 pL of 6.41 X into 1.011 X lo4 M KBr in 1 M H2S04. [Ag+]o = 9.54 X M and [Br-1, = 1.003 X M. This is an essentially stoichiometric mixture of Ag' and Br-. The linearity of this plot indicates that the absorbance results from a turbidity caused by light scattering from a AgBr sol.
I
1.5,
0.0 0
50
100 150 TIME (SECONDS)
200
250
Figure 11. First-order plot of the decay of absorbance at 250 nm as the 250-species grows to the AgBr sol responsible for the turbidity shown in Figure 10. The least-squares first-order rate constant is 6.35 X s-'. Experimental conditions are the same as in Figure 10. A. is the absorbance at 30 s where the maximum absorbance at 250 nm occurs, and A , is the final absorbance when the sol is completely formed.
likely to be important to Ag+-perturbed BZ reaction experiments. We assume that Ag+ and Br- tied up in larger particles of AgBr are effectively removed from the BZ reaction. However, when [Ag+Io= [Br-lo = M, we do see the formation of a AgBr sol4O after 5-10 min. Sols do not form on this time scale in our experiments if [Ag+]o/[Br-]o is not near 1. Spectra of such sols look much like that displayed in Figure 2C. Figure 10 shows that such spectra show the 1/ ( ~ a v e l e n g t h )dependence ~ expected of a turbidity41resulting from a AgBr sol. The kinetics of sol growth from the 250-species seem similar to the kinetics of the conversion of the 220-species to the 250-species. The decay of absorbance at 250 nm (and the growth of absorbance at wavelengths longer than 350 nm) is first order in A(250) as shown by the plot of In [(A(250), - A(250),)/(A(250), - A(250),)] in Figure 11. A similar result has been obtained by Reza et al.42using Guggenheim plots. They concluded that the turbidity is a daughter of the previous absorbing species and results from increase in the size of AgBr particles rather than from growth in their number. The rate of disappearance of absorbance at 250 nm is a maximum when [Ag'] = [Br-] and is inhibited more by excess [Ag'] than by excess [Br-1. These results indicate that the mechanism of growth of the 250-species t o a AgBr sol is similar to the mechanism by which the 220-species is converted to the 250-species. (40) Meacham, E. J.; Beattie, W. H. J . Phys. Chem. 1960, 64, 1006. (41) Johnston, F. A. Rndiat. Res. 1978, 75, 286. (42) Reza, M. A,; Ferdusi, T.; Nawab, M. A. Dnccn Uniu. Stud. 1971, 29, 1.
2478
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988
Kshirsagar et al.
Implications for BZ Ag' Perturbation Experiments There are two basic resultsX-l0of BZ Ag' perturbation experiments which must be understood. The first is a distinct shortening of the oscillatory period as reflected by measured redox potential oscillations, and the second is disappearance of oscillations as measured by a Br--selective electrode and their replacement by a nonoscillatory potential corresponding to a very low [Br-] . We will consider the period shortening first. The period of the BZ reaction is mainly determined by the length of the slow bromide consumption (SBC) period43i44during which Br- is consumed by the reaction Br-
+ Br03- + 2H'
st HOBr
+ HBr02
(1 2)
When [Br-] is driven below the critical value by reaction 12, the BZ reaction makes a short excursion which oxidizes Ce(II1) to Ce(IV), the latter of which indirectly regenerates Br-, so that the system reenters the SBC period, where it spends most of its time. The period of the BZ reaction may then be shortened by any reaction which removes Br- simultaneously and on the same time scale with reaction 12. This is the approach taken by RuoffI3-l5 and by Varga et a1.,18 who assumed that Ag+ or T13+,respectively, removes Br- on a time scale comparable to the length of the SBC period. This corresponds to a second-order rate constant for reaction 1 and the corresponding reaction with T13+of about lo4 M-I s-l. However, we have now demonstrated that the initial interaction of Ag+ with Br- is much faster than this. The above procedure reproduces in numerical simulations the period-shortening effect of added Ag' but does not change the basic dynamic behavior of [Br-1. It still oscillates in a concentration range and with an amplitude that should be easily detectable by a Br--selective electrode. This is in contradiction with the experimental observation that, on addition of sufficient Ag', the potential measured by a Br--selective electrode falls to a value corresponding to a very low [Br-] and does not oscillate. To solve this problem, Schwitters and Ruoff16 made the most reasonable suggestion that Br--selective electrodes do not measure [ Br-] in the presence of excess Ag' but that the normal BZ reaction [Br-] oscillations still occur. They supported their argument with a theoretical treatment of the behavior of a Br--selective electrode under such conditions. However, it is also possible to rationalize this experimental result, as well as the period-shortening effect discussed above, on the basis of the mechanism for the reaction of Ag+(as)with Br-(aq)developed here. We demonstrate our suggestion using simulations based on the Oregonator5 model shown in eq 01-05. Variable identifications A+Y-X+P
(01)
X+Y-P+P
(02)
A+X+C-X+X+Z
(03)
X+X+A+P
(04)
z-+"fY+c
I
I
(05)
are A Br03-, X HBr02, Y = Br-, Z Ce(IV), C Ce(III), and P HOBr. A batch reactor is simulated by treating A as well as X, Y , Z , and C as dynamic variables. It is necessary to enforce metal-ion catalyst conservation to get good agreement with experimental absolute species concentration^.^^ Rate parameters used are kol = 2.1 M-] s-l, ko2 = 1 X lo6 M-I s-l , k 0 3 = 4 2 1 ~ M-2 s-l (C, = [Ce(III)] + [Ce(IV)]), ko4 = 2 X IO3 M-l s-l * k os = 0.2 s&, and f = 1. These are the parameters defined by Field and F o r ~ t e r l i n g . ~Figure ~ 12 shows oscillations in log ([Ce(IV)]/[Ce(III)] and log [Br-] calculated by using this model and
i
I
-'4
-8
C
I 100
200
a;C
503
Figure 12. Simulation based on the unperturbed Oregonator (eq 010 5 ) . [BrOC], = 5 X lo-* M, [HBr0210= lo-* M, [Br-], = M, [Ce(IV)],, = 1 X M, and [Ce(III)lo = 9 X M. Initial period = 45 s.
parameters with major reactant concentrations in the range used in Ag' perturbation experiments. The initial calculated oscillatory period is =45 s, and the period lengthens as Br0,- is consumed. The effect of added Ag+ is modeled by assuming that Agf(aqj and Br;ap, react rapidly in reaction PI to yield an oligomeric AgBr &+(a,)
+ Br-(aqj
(A@r)(aq)
(PI)
species (perhaps the 220-species) represented by (AgBr)(a,,). We assume that reaction P1 is nearly diffusion controlled in the forward direction, Le., kP1= lo9 M-' s-], and that KpI = lo8 M-l, in keeping with the equilibrium constants determined here for the 220-species and the 250-species. This leads to Lp1= 10 SKI.Thus in the presence of Ag', [ B T - ( ~ ~is)driven ] very rapidly to a very low level. We further assume that (AgBr),,,, reacts with Br03and HBrO, at about the same rates ( k p 2= k,, and k p , = kp2) as Br-(aq)itself, as shown in reactions P2 and P3. Forsterling (AgBr),,,)
+ Br03- + 2H'
(AgBr)(,,)
+ HBrO, + Hf
-
-
HBrO, HOBr
+ HOBr + Ag' + HOBr + Ag'
(P2) (P3)
and S ~ h r e i b e have r ~ ~ demonstrated that reaction P3 proceeds in the direction written and directly investigated the competition of reactions 1 and P3. They also infer the presence of several (AgBr), species of different reactivity toward HBr02 and find that effective removal of Br- by Ag' proceeds at the same rate determined here. Reactions P2 and P3 essentially make the BZ oscillations "AgBr controlled" rather than "Br- controlled", although this distinction is minor as all that has happened is that Br- has become complexed by Ag' but is still available for its usual control function in the BZ reaction. However, [Br-(,,] is driven to a very low value, and the Br--selective electrode will respond instead to the much larger and relatively constant [Ag']. The period shortening is introduced by assuming that (AgBr),,,, decays by a first-order reaction to another species, say (AgBr),,, (perhaps the 250-species), which is much less reactive in reactions P2 and P3 than is (AgBr)(aql. This process is presumed to be similar to the transition from the 220-species to the 250-species, and we use the rate constant for that process in excess Ag+ (see Figure 6) determined here, 0.40 s-I, for reaction P4. With [Ag'] (AgBr)(aq)
(43) Edeison, D.; Thomas, V. J . Phys. Chem. 1981, 85, 1555. (44) Gyorgyi, L.; Deutsch, T.; Koros, E. In?. J . Chem. Kine?. 1987, 19, 35. (45) Tyson, J. J. In Oscillations and Traveling Waoes in Chemical Systems, Field, R. J . , Burger, M., Eds.; Wiley-Interscience: New York, 1985; p 93. (46) Field, R. J.; Forsterling, H.-D. J . Phys. Chem. 1986, 90, 5400. See also: Ariese, F.; Nagy-Ungvlrai, Z s . J . Phys. Chem. 1986, 90, 1 and 1496.
300
TIME (SECONDS)
-
(AgBr)(s)
(P4)
= low3M, this procedure removes (AgBr)(,,) about as fast as reaction 1 with k , = lo4 M-I s-l , a s suggested by R ~ o f f , ' ~ and -'~ has about the same period-shortening effect. (47) Forsterling, H.-D.; Schreiber, H. J . Phys. Chem., in press.
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2419
Reaction of Ag+ with Br- in H2S04
when the added Ag+ has been consumed, again in agreement with experiment. It is apparent that Ag' perturbations of the BZ reaction can be explained as only a very minor variation of Br- control within the context of the FKN mechanism by using the information on the initial interaction of Ag+(,,, and Br-(aq)developed here.
I
-124
0
100
200
300
400
500
TIME (SECONDS)
Figure 13. Simulation of Ag+-perturbedexperiments based on reactions 01-05 and Pl-P4. Initial conditions of X, Y, C, and Z correspond to time = 500 s in Figure 12 with [BrO
