J . Phys. Chem. 1989, 93, 2740-2748 depth is more consistent with buoyancy-driven convection. To sum up, convection takes place in a liquid layer of an oscillatory BZ reagent, even in the absence of a gas-liquid interface, provided the depth of the layer is at least 1.5 mm at room temperature. This phenomenon is attributed to the spontaneous
development of inhomogeneities associated with the chemical reaction. Registry No. Malonic acid, 141-82-2; bromate, 15541-45-4; ferroin, 14708-99-7.
An Additional Negatlve Feedback Loop tn the Classical Belousov-Zhabotinsky Reaction: Malonyl Radical as a Second Control Intermediate Horst-Dieter Forsterling* and Zoltan Noszticziust Fachbereich Physikalische Chemie, Philipps- Universitat Marburg, 0-3550 Marburg, Federal Republic of Germany (Received: July 12, 1988)
Reactions of malonyl radicals with inorganic bromine species (oxidation numbers -1 to + 5 ) of the Belousov-Zhabotinsky (BZ) reaction are investigated in 1 M sulfuric acid medium by electron spin resonance spectroscopy in continuous-flow experiments. A very high reaction rate is found for Br02' (k7 5 X lo9 M-' s-l), followed by Br2 and HOBr ( k , C 1.5 X lo8 M-I s-l and k8 < 1 X lo7 M-' s-l, respectively). At high concentrations acidic bromate and bromide have some effect too, but this is probably due to indirect reactions. The results indicate that malonyl radical plays an important role as a second control intermediate besides bromide ion in the oscillatory mechanism of the BZ reaction.
-
Introduction The oscillatory Belousov-Zhabotinsky (BZ) reaction is a prime example for nonlinear dynamics in chemical kinetics, and its mechanism was extensively studied in the past 2 decades.'S2 In its classical variant malonic acid is oxidized by acidic bromate in the presence of cerium catalyst. A qualitative explanation for the observed oscillations was already given by Vavilin and Zhab o t i n ~ k y . ~A. ~characteristic feature of their mechanism is the interaction of an instantaneous positive feedback loop with a delayed negative one. In the positive feedback loop the autocatalytic oxidation of Ce3+ takes place. In the negative feedback loop a delayed Br- ion production occurs via a reaction of Ce4+ with bromomalonic acid (the delay is between the autocatalytic process and the bromide production). As bromide ions react with the autocatalytic intermediates of the positive loop, they stop the autocatalytic process. After a recovery period, during which the inhibitory bromide is removed, the whole cycle is repeated. A more quantitative understanding of the mechanism is due to Field, Koros, and Noyes (FKN), who worked out a detailed theory in their landmark paper.I They also followed the oscillations of the control intermediate with a bromide-selective electrode, and in their work with Thompson5 they proposed that the autocatalytic intermediates are bromous acid (HBr02) and Br02' radicals. In fact, Br02' was identified as an intermediate in the complete BZ system as well as in the reactions during the positive feedback loop by Forsterling et a1.6-8 On the basis of the FKN theory, Field and Noyes, skeletonized their famous Oregonator model. While the Oregonator and the more complete FKN theory were highly successful in explaining many experimental observations on different BZ systems, there were more and more signs that the understanding of the mechanism was not yet complete. The oxybromine chemistry of the positive feedback loop was well established, and its rate constants were recently clarified by Field and Forsterling.Io There are additional problems with the negative loop, however. First, oscillations were observed in the presence of silver ions," when bromide cannot play a control role. Second, Koros and coworkersi2 pointed out recently that the main source of the inhibitory bromide in the classical BZ reaction is not the bromomalonic acid as was assumed originally. Regarding the first problem, there 'Permanent address: Institute of Physics, Technical University of Budapest, H-1521 Budapest, Hungary.
0022-3654/89/2093-2740$01.50/0
were opinion^^^^^^ that the silver perturbed BZ systems are in fact bromide controlled too. This would be possible if the primary step of the Ag' Br- AgBr reaction were a relatively slow reaction. Experiments and theoretical considerations do not support that hypothesis, h o w e ~ e r . l ~ - ~ ' Thus there were different suggestions for an additional control intermediate. Namely, bromine atoms (Br*),I8elementary bromine (Br2),I9malonyl radicals,i~i5~i8~20~21 bromomalonyl radicals,I5 and recently Ag4Brt2controls were proposed. Later on, some control candidates were ruled out. For example, Noszticzius, Gaspar, and F o r ~ t e r l i n gcould ~ ~ prove that Br2 does not react directly with
+
-
( I ) Field, R. J.; Koros, E.; Noyes, R. M. J . Am. Chem. SOC.1972, 94, 8649. (2) Field, R. J. In Oscillations and Travelling Waues in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985; p 55. (3) Vavilin, V. A.; Zhabotinsky, A. M. Kinet. Katal. 1969, 10, 83. (4) Vavilin, V. A,; Zhabotinsky, A. M. Kinet. Katal. 1969, IO, 657. (5) Noyes, R. M.; Field, R. J.; Thompson, R. C. J . Am. Chem. SOC.1971, 93, 7315. (6) Forsterling, H. D.; Schreiber, H.; Zittlau, W. Z . Naturforsch. 1978, 33a, 1552. (7) Forsterling, H. D.; Lamberz, H.; Schreiber, H. Z . Naturforsch. 1980, 35a, 329. ( 8 ) Forsterling, H. D.; Lamberz, H.; Schreiber, H. Z . Naturforsch. 1980, 35a, 1354. (9) Field, R. J.; Noyes, R. M. J . Chem. Phys. 1974, 60, 1877. (IO) Field, R. J.; Ftirsterling, H. D. J . Chem. Phys. 1986, 90, 5400. (11) Noszticzius, Z. J . Am. Chem. SOC.1979, 101, 3660. (12) Varga, M.; Gyorgyi, L.; Koriis, E. J . Am. Chem. Soc. 1985,107,4780. (13) Ruoff, P.; Schwitters, B. J . Phys. Chem. 1984, 88, 6424. (14) Schwitters, B.; Ruoff, P. J . Phys. Chem. 1986, 90, 2497. (15) Noszticzius, Z.; McCormick, W. D.; Swinney, H. L.; Schelly, Z. A. Acta Polytech. Scand., Chem. Incl. Metall. Ser. 1987, 178, 57. (16) Noszticzius, Z.; McCormick, W. D. J . Phys. Chem. 1987, 91, 4430. (17) Noszticzius, Z.; McCormick, W. D. J . Phys. Chem. 1988, 92, 374. ( 1 8 ) Ganapathisubramanian, N.; Noyes, R. M. J . Phys. Chem. 1982,86, 5155. (19) Noszticzius, Z.; Farkas, H.; Schelly, Z. A. J . Chem. Phys. 1984, 80, 6062. (20) Brusa, M. A,; Perissinotti, L. J.; Colussi, A. J. J . Phys. Chem. 1985, 89, 1572. (21) Forsterling, H. D.; Pachl, R.; Schreiber, H. 2.Naturforsch. 1987, 42a, 963. (22) Khirsagar, G.; Field, R. J.; Gyorgyi, L. J . Phys. Chem. 1988, 92, 2412. (23) Noszticzius, 2.;Gaspar, V.; Forsterling, H. D. J . Am. Chem. SOC. 1985, 107, 2314.
0 1989 American Chemical Society
Negative Feedback Loop in the BZ Reaction the autocatalytic intermediates HBr02 and BrO,'; thus Brz is not a control intermediate. Malonyl and bromomalonyl radicals are still suspects, however, for the role of additional control intermediates. Such suggestions were made recently by Noszticzius et al,Is and by Forsterling et aLzl Especially the results of Forsterling and co-workers indicate that malonyl radicals can react with the autocatalytic intermediates. To test these hypotheses, we devised experiments to obtain direct evidence about the reaction of malonyl radicals with H B r 0 2 and Br02'. Moreover, we also wanted to study the reaction of malonyl radicals with other bromine species such as Br03-, HOBr, Br2, and Br-. The results of these experiments are reported here.
Experimental Section Materials. NaBr02 stock solutions in 0.1 M NaOH were prepared following the method of Noszticzius et al.24 The starting material Ba(Br02)2was also synthesized according to their prescription, except the disproportionation time of Ba(BrO)2 was increased from 2 to 6 h to obtain a higher yield of Ba(Br02)2. HOBr solution in 1 M sulfuric acid was produced by a method of Noszticius et al.>s except the bromine was removed by a stream of nitrogen gas instead of extracting it with CC1+ Separate experiments that followed the removal of bromine spectrophotometrically confirmed that no measurable loss of HOBr occurs during half an hour even when a rather intense N2 gas stream is applied (2-3 mL/min into 1 mL of solution). With that intensive scrubbing the removal of bromine was complete after 10 min. NaBr03 (Fluka, puriss) was recrystallized twice from hot water to remove any traces of bromide. Malonic acid (Fluka, puriss) was used without further purification as trace contaminants of malonic acid26had no effect on the present experiments. Sulfuric acid solutions were prepared from 96% HzSO4 (Merck, pa.). Ce(S04)2,Ce(NH4)2(N03)6, Ce2(S04)3, Ce(NO3)3, NaBr, and Br2 (Fluka puriss) were used without further purification. Apparatus and Methods. The experiments were carried out in the cavity of a Varian El2 ESR spectrometer. 'Malonyl radicals were produced following the method of Brusa, Perissinotti and Colussi20 except 1 M sulfuric acid was used instead of 2 M perchloric acid. Thus 0.2 M malonic acid in 1 M sulfuric acid was mixed rapidly with 0.002 M Ce(S04)2in 1 M sulfuric acid in a mixer mounted together with a flat quartz ESR cell (Wilmad Glass Co., New Jersey, type WG-804-Q, dimensions 8 X 0.25 X 60 mm, mixing time 1 ms at a flow rate of 4 mL/s). The total volume of the cell was 125 ML. The region active for radical detection was a 5-mm zone around the center of the cell. Additional reagents were dissolved in the ceric solution in the case of bromate, hypobromous acid, bromine, and Ce( 111). Bromide was added to the malonic acid solution. When the effect of H B r 0 2 was studied, NaBr02 was added to a 0.2 M sodium malonate solution in 0.1 M NaOH; in this particular case the ceric solution was prepared in 2 M sulfuric acid. The liquids were transported to the ESR cell by a homemade electronically controlled peristaltic pump using Tygon Masterflex tubings (3.2 mm i.d., 6.3 mm 0.d.). The flow rate was found to be stable within 2%. Fluctuations in the flow due to the peristaltic action were damped by a system of capillaries and small bubble traps containing N 2 (99.999%purity) bubbles. The glass capillaries and the bubble traps were connected alternately in series in both feed lines between the pump and the mixer. Most of the tubings of the apparatus were made of glass, and the short flexible connections were made with thick-walled (2.4 mm) Tygon tubings. Changing the atmosphere around the plastic tubings (including the peristaltic pump) from air to ultrapure nitrogen had no effect on the experimental results (in sharp contrast, when Teflon tubings were applied in a preliminary experiment, oxygen diffusion through ~~~~
~
(24) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Phys. Chem. 1983, 87, 510. (25) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J . Am. Chem. SOC. 1982, 104, 6194. (26) Noszticzius, 2.; McCormick, W. D.; Swinney, H. L J . Phys. Chem. 1987, 91, 5129.
The Journal of Physical Chemistry, Vol. 93, No. 7, 1989 2741
t-=!5
low field signal
I
high field signal
Figure 1. ESR spectrum of malonyl radicals. During the measurement a total flow rate of 16 mL/min was maintained combining 8 mL/min of solution A and 8 mL/min of solution B. Composition of solution A: 2 X lo-) M Ce(S04)2in 1 M sulfuric acid. Composition of solution B: 0.2 M malonic acid (MA) also in 1 M sulfuric acid. Concentrations after mixing: [Ce4+]= 0.001 M, [MA] = 0.1 M, [HzSOd] = 1 M. Note the wide peak due to the larger than usual modulation amplitude (2 G ) . The peak-to-peakdistance of 85.2 units was equivalent to a malonyl radical concentration of 6 X lo-* M ([MA'] = 60 nM). See text for other instrumental parameters. tubing walls caused a significant effect). Before each series of experiments the apparatus was flushed with ultrapure N2 (-200 mL/min), and simultaneously the liquid containers (2 L bottles) were also bubbled through with ultrapure N2 (-0.5 L/min into 1 L of solution) for 30 min. The bubbling with a reduced rate was continued during the experiments as well, except when elementary bromine was added to the ceric solution. In that case, to avoid any loss in the dissolved bromine, after the addition of bromine the nitrogen stream was applied only above the solution. Instrumental Parameters and Measurement of the Maionyl Radical Concentration. The spectrum of the malonyl radicals and their magnetic parameters were the same as already reported by Brusa et aLzo To measure the radical concentration in our continuous-flow experiments, the first peak (low-field signal) was recorded. The following instrumental settings were applied: frequency 9.478 GHz, microwave power 15 mW (1 2 dB), scan range 100 G, scan time 1 h, gain 2.5 X IO5,phase 4 5 O , modulation 2 G, time constant 4 s. With these instrumental parameters the peak was broader than usual, but on the other hand the reproducibility of the peak height (the peak-to-peak distance) was considerably improved (Figure 1). A 2% relative standard deviation was typical. One peak height measurement required about 3 min with the above parameters. Two or three parallel measurements were always made, except for some cases in the high-flow region (total flow rates of 64 mL/min and above) where sometimes a limited amount of the available liquid prevented the repetition. The malonyl radical concentration was determined from the peak height in the following way. First peak height measurements were made in experiments where only malonic acid ([MA], = 0.1 M) and Ce4+ ([Ce4+], = 0.001 M) were reacting in 1 M sulfuric acid (concentrations after the mixing process). These results were regarded as calibration standards. The radical concentration for these experiments can be calculated according to the formula [ MA'] = [ k ,[ MA],[Ce4+],/ ( 2k2)]
(1)
(eq 3 in ref 21) where [MA'] is the malonyl radical concentration, k,[MA], = 0.023 s-l determined by Forsterling et al.21(in the case of [MA], = 0.1 M), and k2 = 3.2 X lo9 M-I S-I reported by Brusa et aLzo Thus the calibration experiment produced a malonyl radical concentration of about 60 X M in the case of [Ce4+Io= 0.001 M. When other reagents (such as BrO,-, HBr02, HOBr, etc.) were added, the peak height decreased compared to the standard. Radical concentrations for these experiments were calculated by
2742
Forsterling and Noszticzius
The Journal of Physical Chemistry, Vol. 93, No. 7, 1989
these experimental results, we shall regard the following set of reactions:
[MA.)~M
6o
I
Ce4+ + MA
-
Ce3+ + H+ + MA'
2MA' 4 0.
30.
[SrO;]= 0 5 M [MA.
MA'
1- 3 6 ZnM
-+
P2
+ Br03- + H+
-
(R1) (R2)
P,
(R3)
where P2 and P3 are the products of reaction R2 and R3, respectively. In our derivation of the rate equations we shall assume at first that these products do not react with malonyl radicals significantly. Thus, applying a steady-state approximation for the malonyl radical concentration, we obtain
10
time/s
Figure 2. Malonyl radical concentration as a function of the residence
time in the presence of acidic bromate. Initial reactant concentrations (after mixing): [Ce4+]= 0.001 M, [MA] = 0.1 M, [NaBrO,] = 0.5 M, [H2S04]= 1 M. The residence time is calculated from the flow rate r and the half-cell volume VI,,: residence time = ( V 1 , , ) / r . For example, with r = 16 mL/min and V I , , = 125/2 p L = 62.5 pL, we obtain residence time = 0.234 s. V I , , was used instead of V because the narrow zone active for radical detection was about halfway between the inlet and the outlet of the ESR cell. The residence time calculated this way is an average reaction time; a time the reactants have spent together when they reach the detection zone after they were mixed at the inlet of the ESR cell. This is an approximation only because the parabolic velocity profile of the liquid flow and the resulting Taylor diffusion39makes the real situation more complex. using the standard value and assuming that the peak height was proportional to the radical concentration. Calibration experiments were carried out with different flow rates. The peak height was independent of the flow rate between 16 and 128 mL/min (total flow rates through the cell) and was somewhat decreased (by 10%) at 8 mL/min. At 4 mL/min the peak height was considerably smaller, showing that the mixing was not complete. Thus no measurements were made below 8 mL/min. The temperature of the laboratory where all experiments were performed was kept between 19 and 21 "C.
-
Results and Discussion We studied the reaction of malonyl radicals with inorganic bromine species of different oxidation levels starting with bromate (oxidation number + 5 ) and ending with bromide (oxidation number -1) as reagents. To measure the rate of the malonyl radical-reagent reaction, the peak-to-peak height of the low-field ESR signal was recorded in the absence and in the presence of the reagents at different flow rates in continuous-flow experiments. If the reagent concentration was high enough, the peak height in the presence of the reagent was considerably smaller, indicating a proportionally smaller malonyl radical concentration. The smaller malonyl radical concentration shows that in the presence of a reagent the malonyl radicals can disappear via reaction pathways other than self-recombination. Assuming a steady-state, the rate of these other reactions can be calculated from the difference of the (unchanged) production rate and the (decreased) self-recombination rate of the malonyl radicals. Experiments with Acidic Bromate. Brusa et a1.20have already studied the malonyl radical-bromate reaction. Their medium, however, was perchloric acid solution instead of sulfuric acid, which is necessary for the BZ reaction. Moreover, the applied technique was somewhat different: they combined stopped-flow ESR and spectrophotometric measurements. We performed continuous-flow ESR experiments in 1 M sulfuric acid medium with sodium bromate added in 1 M concentration to the ceric solution (thus a 0.5 M bromate concentration was established in the reaction mixture). The results of our experiments are depicted in Figure 2. As can be seen, the malonyl radical concentration is smaller (- 36.2 nM) in the presence of 0.5 M bromate compared to the malonyl radical concentration (-60 nM) measured in a bromate-free experiment. Also, it can be observed that the decreased malonyl radical level does not depend on the flow rate. To evaluate
kl[Ce4+][MA]- 2k2[MA'I2 - k,[MA'][BrO3-] = 0 (2) The first term in (2) is the production rate of the malonyl radicals, while the second and third terms are consumption rates due to self-recombination and to a reaction with bromate, respectively. If [MA'], is the steady-state concentration of MA' in the absence of bromate ([Br03-] = 0 in (2)) and [MA'], is the steady-state concentration in the presence of the reagent bromate, we derive from (2)
(3) With [MA'], = 60 nM and [MA'], = 36.2 nM as measured in our experiment described above, the value k3/(2k2) = 1.27 X lob7 is calculated. As k2 = 3.2 X lo9 M-' s-I (ref 20), we obtain k3 = 0.8 X lo3 M-' s-l. This value is smaller than the value k3 = 6.7 X lo3 M-I s-l measured by Brusa et al.m in 2 M HClO,. Also, we have to emphasize that our result is an upper limit only for a direct reaction between the malonyl radicals and bromate. This is because of the following: (i) There is spectroscopic evidence27 that in acidic bromate solutions a minute level of Br02' is always present. Consequently, we cannot rule out the possibility that it is the Br02' supplied continuously by acidic bromate that reacts directly with the malonyl radicals (Br02' radicals react very fast with malonyl radicals; see later). The low level of BrO; should be established by a "fast" equilibrium. Slow accumulation of Br02' cannot explain our observations. In that case the signal would have depended on the time and also on the flow rate. (ii) Moreover, Br0; radicals may emerge from another possible source too. A slow direct reaction between acidic bromate and malonic acid could produce HBr02, which would combine with bromate to give BrO; radicals. A similar direct reaction between aliphatic alcohols and bromate is ~ e l l - k n o w n . ~ *If~such ~~ a reaction between acidic bromate and malonic acid3, plays a role in our system, then the presence of bromate would reduce the malonyl radical concentration without any direct malonyl radical-bromate reaction. (iii) Finally, even if malonyl radicals and acidic bromate can react directly with a measurable rate, there is a further problem. Namely, the products of reaction R3 are not necessarily inert toward malonyl radicals. For example, Brusa et aL20propose the following products: P, = MAO'
+ HBr02
where MAO' is the alkoxy radical (HOOC)2CHO'. There is no guarantee that these alkoxy radicals will disappear in self-recombination exclusively, and probably most of them will combine (27) Forsterling, H. D., unpublished results. (28) Forsterling, H . D.; Lamberz, H. J.; Schreiber, H. Z . Naturforsch. 1983, 38a, 483. (29) Forsterling, H. D.; Lamberz, H. J.; Schreiber, H. 2. Naturforsch. 1985, 40a, 368. ( 3 0 ) Koros, E.; Orban, M.; Nagy, 2.Acta Chim. Hung. 1979, 100, 449. ( 3 1) Pachl, R. Theses, Philipps-Universitat Marburg, 1989. (32) Robertson, E.B.; Dunford, H. B. J . Am. Chem. SOC.1964,86, 5080.
The Journal of Physical Chemistry, Vol. 93, No. 7, 1989 2743
Negative Feedback Loop in the BZ Reaction with malonyl radicals, which are present in a higher concentration compared to the alkoxy radicals. Furthermore, regarding the high concentration of bromate, any HBr0, will react very fast (estimated time constant -5 X lo-, s using data from ref 10) to form two Br0; radicals. This way reaction R3 can produce three active radicals which can react with three more malonyl radicals. Thus the rate constant for the primary reaction (R3) can be as many as 4 times smaller than the value calculated from (3) if the products of (R3) are really MAO' and HBr0,. Experiments with Bromous Acid and BrO,'. Different initial levels of HBrO, were established in the reactor by adding small amounts of NaBrO, stock solutions in 0.1 M N a O H to sodium malonate (0.2 M) solutions also in 0.1 M NaOH. The latter mixture was prepared in 1-L volumetric flasks by adding 200 mL of 1 M malonic acid solution to 500 mL of 1 M N a O H and diluting it with distilled water. We had to apply an alkaline medium because NaBrO, is stable in 0.1 M NaOH, but HBrO, in 1 M H2S04 disproportionates rather quickly. Thus we generated HBr0, instantaneously in the reactor and in low concenM) to avoid any measurable loss of trations (less than 5 X HBrO, due to its disproportionation during the short (less than 0.5 s) residence times applied in our experiments. The alkaline sodium malonate solution was mixed in the ESR cell in a 1:l ratio M Ce(S04), solution in 2 M H,SO,. The resulting with a 2 X concentrations, without adding bromite to the system, were the following: [MA] = 0.1 M, [Ce4+] = 1 X M, [H2S04]= 0.75 M, [NaHS04] = 0.25 M. If no bromite was present, the peak height of the ESR signal was the same within the experimental error as in the experiments where the medium was 1 M sulfuric acid. That is, changing one-quarter of sulfuric acid to sodium hydrogen sulfate had no measurable impact on the radical concentration. Qualitative Evaluation of the Experiments. The results of our first experiments with different initial bromous acid concentrations are depicted in Figure 3a. Those diagrams provide two important pieces of information immediately: (i) Even very low initial bromous acid concentrations (e.g., [HBrO,] = 3.5 X lod M) can be very effective in decreasing the malonyl radical concentration. (ii) The signal depends strongly on the residence time. Beyond this valuable information we have to face two problems if we want to evaluate those diagrams quantitatively: (i) It would be necessary to know the peak height at zero residence time. The flow dependence of the signal shows that the reagent is consumed rather quickly. To calculate rate constants, we should use initial rates because we have reliable data on the initial concentrations only. However, extrapolating the curves in Figure 3a back to zero residence time is problematic. Most points of interception are in the neighborhood of the origin and their exact position is uncertain. The only exception is the first curve with the lowest HBrO, concentration ([HBrO,lo = 3.5 pM), 8 nM can be roughly for which an interception of [MA'], estimated. The interception points of the other curves, however, practically coalesce with the origin. (ii) It is not clear what is the active reagent that reacts directly with malonyl radicals. This is a problem because the initial bromous acid amount is transformed rapidly to BrO,' radicals via
-
HBrO,
+ Ce4+
-
BrO,'
+ Ce3+ + H+
(R4)
where
k4 = 8.4
X
lo3 M-' s-'
k4 = 8
X
lo4 M-,
s-l
(r ef 10)
There are two possib es: malonyl radicals are removed by HBrOz directly or, in fact, they react with BrO; radicals produced from HBrO, in (R4). Of course, there is always the third possibility that both BrO,' and HBrO, can react with MA'. To decide the above dilemma we carried out a series of experiments similar to the one displayed in Figure 3a, but an increasing amount of Ce3+was added to the system in the form of cerous sulfate. The results of these experiments with 0.002, 0.01, and 0.02 M Ce3+are shown in Figure 3b-d. Ce3+was added to
rMAJ/nM
-
7 LuM 120uM
17 8uM
10
'
60 50 ZLUM
20
10
I
60 [Ce3*],
=
M
501
time/s
[MAj/nM
1
I
12 OpM
20
33 7uM
0 1 02 0 3 04 0 5
residence time/s
Figure 3. Concentration of MA' radicals as a function of the residence time in the ESR cell at different HBr02 initial concentrationswith and without added Ce'+. Initial reactant concentration (after mixing): [Ce4+]= 0.001 M, [MA] = 0.1 M, [H2S04]= 0.75 M, [NaHS04] = 0.25 M. Ce3+and HBr02 are applied in the following concentrations: (a) [Ce3+Io= 0, [HBrO&,= 3.5, 7.4, 12.0, and 17.8 pM; (b) [Ce3*Io = 0.002 M, [HBr0210= 5.6, 11.3, and 24 pM; (c) [Ce'+lo = 0.01 M, [HBr0210= 9.8 KM;(d) [Ce3+lO = 0.02 M, [HBr02jo= 11.2, 12.0, 33.7, and 49.0 pM.
the system to promote (R-4), the back reaction of (R4). to establish a lower BrO,' level this way. Our expectation was that the reagent-malonyl reaction would slow down in the presence
2144
The Journal of Physical Chemistry, Vol. 93, No. 7, 1989
Forsterling and Noszticzius
TABLE I: Reactions Used in Model Calculations for Figure 4d
- + + -++ -- ++ ++ + -+ + + - + + + + + - + + + + - + +
( R l ) Ce4+ M A (R2) 2 M A ' + P 2
(R4) (R5) (R6) (R7) (R8) (Cl) (C2) (C3) (C4) (C5)
reaction Ce3* Ht
ref 21 20 10
MA'
HBr02 Ce4+ BrOi Ce3+ Ht 2Br02' Br204 Br204 H 2 0 HBr02 Ht Br03MA' Br02' P7 MA' HOBr P8 Br- HOBr Ht Br2 H 2 0 Br- HBr02 Ht 2HOBr Br- BrOy 2 Ht HOBr HBr02 2HBr02 HOBr Ht BrO< MA HOBr BrMA H 2 0
10 10 this work
this work 10 10 10 10 31
k+/(M-' s-l) 0.23 3.2 x 109 8.4 x 103 1.4 x 109 2.2 x 1 0 3 b 5.0 x 109 1 x 107 8.0 x 109" 3.0 X lo6" 2.w
3.0 X 10' 8.2
k-/(M-' s-I) 2.2 x 104a4 0 8.0 x
1040
7.4 x 104* 42.0' 0 0 110 2.0 x 10-5
0.32 1 x 10-8" 0
" Ht ion concentration is merged into a second-order rate constant. Examples: kTl = (kJ[Ht]
or kc3 = (kc3)'[H'I2, where (k-])' and (kc3)' are third- and fourth-order rate constants, respectively. As [H2S04]= 1 M in our experiments, [H'] = 1.29 M.32 bFirst-order rate constant, unit s-l. CThisvalue of k-l derived from the experiments in ref 21 depends on the value of k2. In ref 21, k2 = 1 X lo9 M-' s-I is used, leading to k-, = 1.2 X lo4 M-I s-I. As k2 = 3.2 X lo9 M-Is-I is used in this work, k-l was recalculated, and k-, = 2.2 X lo4 M-I s-l is obtained. dReactions used in model calculations for Figure 4. Reactions Rl-RS are discussed elsewhere in this work. Reactions Cl-C5 are applied only in these model calculations. k- and k, denote the forward and reverse rate constants, respectively.
of Ce3+ if the active reagent were Br02'. Indeed, Figure 3b,c and especially 3d show that the higher the Ce3+ concentration, the less the effect of added HBr02, although the level of H B r 0 2 is even higher in the presence of Ce3+due to (R-4). Without Ce3+, as Figure 3a shows, 3.5 pM H B r 0 2 added to the system reduces the malonyl radical concentration by 87% (from 60 to 8 nM, which latter value is extrapolated to t = 0). In the presence of 0.002 M Ce3+ (Figure 3b) even a higher bromous acid concentration has less effect: 5.6 p M H B r 0 2 can reduce the malonyl radical level by 70% only (from 57 to 17.5 nM). If the Ce3+concentration is raised to 0.02 M (Figure 3d), then the effect of added H B r 0 2 decreases even further. In this case 11.2 p M H B r 0 2 can reduce the malonyl radical concentration from 35 to 25 nM, which is a mere 28% reduction. Also the relatively high Ce3' level helps to eliminate most of the flow dependency of the signal, and the extrapolation to zero residence time is more accurate now. From these experimental results we conclude that the real active reagent in the malonyl radical-bromous acid reaction is the Br0; radical produced in the Ce4+-HBr02 reaction and any direct reaction between H B r 0 2 and malonyl radicals is relatively unimportant. It is important to remark that in the presence of Ce3+the ESR signal is smaller even without any added HBr02. This is because malonyl radicals can react with Ce3+ in the back reaction (R-I) as was shown by Forsterling et aL2' On the basis of a steady-state assumption for MA' we obtain from ( R l ) and (R2) (eq (15) in ref 21) [MA'],, = A
+ ( A 2 + B)'I2
(4)
where A = -(k-l[Ce3+])/(4k2)
B = ( ~ , [ M A[ce4+I)/(2k2) I
With the rate constants k l , Ll,and k2 in Table I the calculated radical concentrations are found to be in fair agreement with our experiments (Table 11). Quantitative Evaluation of the Results. As there are many reactions taking place simultaneously in our system, it seemed reasonable to perform model calculations before evaluating the experimental curves. Figure 4a-d shows computed curves (malonyl radical concentration dependence on time) for the same experimental conditions as in Figure 3a-d. For comparison, the computed concentrations of H B r 0 2 and of Br02' are depicted in Figure 5a,b in the case of [HBr0210= 12 pM. The complete set of reactions and their rate constants used in the model calculations are displayed in Table I. The most important reactions in these experiments are ( R l ) , (R2), (R4), and the following:
- -+ 2Br02'
Br204
Br204
HBrO,
MA'
+ Br02'
Br03- + H+
-
P,
(R5)
(W (R7)
TABLE II: Concentration of MA' Radicals in the Absence aad in the Presence of Ce3+ during the Reaction of Ce4+ with MA in Sulfuric Acid Solution" ESR signal/ [MA']/nM ~ 3 + 1 / M arb units exDtl calcd 0.000 83.3 60 60 0.002 79.3 57 57 0.010 56.1 40 45 0.020 42.2 31 35
" [Ce4'Io = 0.001 M and [MA], = 0.1 M in all experiments;calculated values are based on (4) by using the rate constants in Table I. It should be mentioned that no dependency of the radical concentration on added Ce3' is observed in 1 M perchloric acid solution. Rate constants for reactions ( R l ) , (R2), and (R4)-(R6) were taken directly from the work of Field and FBrsterling.'O For the radical-radical reaction (R7) it is reasonable to assume that it is diffusion-~ontrolled~~ with a rate constant somewhere between 1 X lo9 and 1 X IOio M-l s-l. Thus, as a first approximation, we used the value k7 = 5 X lo9 M-' s-l. Reaction products P2 and P7 were assumed to be inactive. Comparing the measured and calculated curves, we can make two important observations: (i) While the qualitative courses of the measured and calculated curves are roughly similar, there are quantitative differences especially when no Ce3+is present initially. For that case theoretical calculations predict "titration"-like curves (Figure 4a). That is, calculated curves stay near the time axis for short residence times and then rise steeply to a higher malonyl radical level. This occurs when, according to the calculations, nearly all HBr02 and BrO; has been eliminated by the continuously generated malonyl radicals. Experimental curves show a different pattern. These curves start at the very beginning with a sharp rise followed by a slow drift toward the final value. The sharp initial rise indicates that Br02' radicals are eliminated faster than expected; they are consumed by some other reactions besides the BrO
