J. Phys. Chem. 1992, 96, 3067-3072
(R)-(-)-l was obtained with a preparative MCT column prepared by following the reported procedurez9 under a pressure of 160 psi. A mixture of methanol and water (9633.5, v/v) was used as the mobile phase for both analytical and preparative purposes. Photolyses. All irradiations were performed with a Oriel high-pressure 1-kW Hg(Xe) lamp at room temperature unless otherwise indicated. Irradiations of (-)-2 and (-)-5 in solutions were carried out in dry THF at wavelengths above 305 nm under both aerated and deoxygenated conditions in a square quartz cell equipped with a latex septum. Solutions were magnetically stirred during irradiation to maintain homogeneity. Deoxygenation was accomplished by bubbling Nzthrough the solutions for 20 min before irradiation. Irradiations in liquid crystal phases were performed with a very thin cell at 334 nm isolated by means of a narrow band-pass filter. The phase transitions induced by irradiation were analyzed microscopically using a Micromaster polarizing microscope equipped with a Mettler FP82 hot stage. WOt~~&tion Of (R)-(-)-Ethano-BriageaBinapbthyl 1 and Attempted Photoresolutions. A 2-mL N,-saturated cyclohexane solution of enantiomerically enriched 1 was irradiated at 350 nm in a Rayonet reactor. The progress of the reaction was monitored
3067
by UV and CD spectroscopy. The A A z 5 4 value of the solution at the start of the irradiation was 1.1 X lo4. After 1 h of irradiation, AAl5, decreased to 6.6 X This decrease in the circularly dichroic absorption corresponds to 40% racemization of 1. Attempted photoresolutions both in solutions and in liquid crystal phase were carried out with a standard circularly polarized light setup.30 Control experiments" showed the quality of the circular polarization. The photoresolution in solutions was monitored by CD and polarimetric measurement. Attempted photoresolutions in liquid crystal phases were carried out in the isotropic temperature range and analyzed at a lower temperature liquid crystal phase.
Acknowledgment. This work was supported by a grants from the National Science Foundation and the Army Research Office for which we are grateful. We thank Professor W. H. Pirkle of this department, who provided valuable assistance and advice on the chromatographic separation of chiral compounds, and Professor F. Momicchioli of the University of Modena, Italy, who provided results of theoretical calculations on triplet binaphthyls. Registry No. 1, 139163-39-6;2, 129647-55-8;3, 86334-03-4;4, 86289-52-3;5, 86289-53-4;K-15,40817-08-1.
(29) Kooler, H.;Rimbock, K.; Mannschreck, A. J. Chromarogr. 1983,282, 89.
(30)Stevenson, K. L.; Verdieck, J. F. Mol. Phofochem. 1969, I , 271.
Effects of Ce4+/Suifato Complex Formation in the Belousov-Zhabotlnskli Reaction: ESR Studies of Malonyl Radical Formation Horst-Dieter Forsterling* Fachbereich Physikalische Chemie, Philipps- Universitat Marburg, 3550 Marburg, Germany
and Linda Stuk Center for Nonlinear Dynamics, Department of Physics, The University of Texas, Austin, Texas 78712 (Received: October 8, 1991; I n Final Form: December 10, 1991)
We investigated the effects of the formation of sulfato complexes from Ce4+ and H2SO4 on the oxidation of malonic acid (MA) by Ce4+in the Belousov-Zhabotinskii (BZ) reaction. We found from measuring malonyl radical concentrations in an ESR flow experiment that the rate of formation of sulfato complexes is very fast compared to the rate of the MA/Ce4+ reaction. This result is important in the theory of the BZ reaction; there is no difference in the reaction rate whether Ce4+ is freshly produced in the autocatalytic cycle or it is introduced in the sulfato-complexed form. Moreover, we did absolute calibrations of the malonyl radical concentrations by using Mn2+and 3-carbamoyl-PROXYL as calibration standards. From these concentrations we calculated malonyl radical self-decay rates of 4.2 X IO8 M-l s-' in 1 M H2S04and 1.5 X lo9 M-I s d in 2 M HCIO,.
1. Introduction Several recent experiments'+ have demonstrated the crucial role of malonyl radicals in the Belousov-Zhabotinskii (BZ) reaction. In a detailed modeling study, Gyorgyi et al.' raised some questions about the primary reactions determining the concentration of malonyl radicals in the oscillating system. These reactions are Ce4+ MA Ce3+ + MA' + H+ (1) (2) 2MA' + HzO products The abbreviations are as follows: MA = malonic acid, CH2(COOH),;MA' = malonyl radical, 'CH(COOH),. The products of reaction 2 are assumed' to be malonic acid and tartronic acid, but the identity of these products is not important for our present
+
--
To whom correspondence should be addressed.
0022-3654/92/2096-3067$03.00/0
considerations since it does not affect the concentration of malonyl radicals. The problem to be resolved for reaction 1 is whether freshly oxidized Ce4+, formed in the BZ autocatalytic reaction, reacts with MA significantly faster than sulfato-complexed Ce4+ which was used6*8,9to measure the rate constant, k l , for reaction 1 in (1) Forsterling, H. D.;Murlnyi, S. Z . Nafurforsch. 1990, 450, 1259. (2) Forsterling, H.D.;Murlnyi, S.;Noszticzius, Z . Reacf. Kinet. Cam/. Lett. 1990, 42, 217. (3) Forsterling, H.D.;Murlnyi, S.;Noszticzius, Z . J . Phys. Chem. 1990, 94, 2915. (4) Murlnyi, S.; Forsterling, H. D. Z . Nafurforsch. 1989, 45a, 135. (5) Forsterling, H.D.;Noszticzius, 2.J . Phys. Chem. 1989, 93, 2740. (6) Forsterling, H.D.;Pachl, R.; Schreiber, H. Z . Nafurforsch. 1987,420, 963. (7)Gyorgyi, L.;Turlnyi, T.; Field, R. J. J . Phys. Chem. 1990, 94, 7162.
0 1992 American Chemical Society
3068 The Journal of Physical Chemistry, Vol, 96, No. 7, 1992 1 M H2S04. It is knownI0 that Ce4+ forms complexes such as [CeSO4I2+,Ce(S04)2,and [Ce(S0,),l2-. It has also been established that kl is significantly higher for uncomplexed Ce4+. For the perchlorate salt of Ce4+in 1 M HCIO, solution,” kl = 6.0 M-I s-l at 25 OC. For Ce(S04)2in 1 M H2S04,k , = 0.23 M-I s-I at 20 OC6 and 0.30 M-l s-l at 25 OC.I2 We have found no reported rate constants for the formation of cerium/sulfato complexes, but Ganapathisubramanian and Noyesl, concluded from spectroscopic experiments that approximately 1 h is required for the equilibrium to be established for 1.72 X lo-, M Ce4+in 1.5 M H2S04. A relatively slow cerium/sulfato complexing process has been assumed to explain two other observations. The first is an experiment by Field and Boyd14 on an oscillating BZ system containing oxalic acid/acetone. These authors found that the first reduction of Ce4+occurred at a rate approximately 1000 times slower than the subsequent reductions of Ce4+ which had been produced in the autocatalytic reaction. The second is the observation of Gyorgyi et al. that their detailed BZ model cannot adequately simulate experimental results both at the beginning and at later stages of the BZ reaction. They found that the discrepancies could be decreased by assuming a higher rate constant for the reaction of freshly oxidized Ce4+with the organic species. It seems reasonable, therefore, to check this assumption directly. For reaction 2, Gyorgyi et al.’ state that the rate constant reported by Brusa et al.,I5 k2 = 3.2 X lo9 M-I s-I, seems too large compared to similar organic radical disproportionation reactions. This rate constant is important to our understanding of free radicals in the BZ reaction because it is used for the calculation5 or estimation’ of rate constants for several other radical reactions. Brusa et al. measured the concentration of malonyl radicals formed from the reaction of M A and Ce4+ (from Ce(SO,),) in 2 M HC10, solution in a flow ESR system. A calibration with Fremy’s salt was used to determine the absolute malonyl radical concentration. k2 was then calculated from d[MA’]/dt = 0 = kl[Ce4+][MA]- 2k2[MA’I2
(3)
where kl was determined spectrophotometrically from the decay of Ce4+. However, it has not been clear whether the rate constant should be the same in the usual BZ medium of 1 M H2S04.We have therefore measured the concentrations of malonyl radicals in several acidic media and calculated k2 from eq 3. 2. Experimental Section 2.1. Materiala Malonic acid (Huh), Ce(S04),4H20 (Fluka), Ce(NH4)2(N03)6 (Fluka), MnSO4.H20 (Fluka), HC104 (70% Riedel), and H2S04(95%, Riedel) were all analytical grade and were used without further purification. 3-Carbamoyl-PROXYL (3-carbamoyl-2,2,5,5-tetramethylpyrrolidhe1-oxyl) was obtained as 97% free radical from Aldrich and also used without further purification. All solutions were prepared from doubly distilled water. 2.2. ESR Experiments. 2.2.1. Calibration for Spin Concentration. Calibration of ESR signals for the measurement of absolute spin concentrations is more difficult than most analytical methods, so careful attention to experimental detail is necessary in order to obtain errors of -+lo%or less.16 The calibration is usually done by comparing the signal of the unknown with that (8) Forsterling, H. D.; Idstein, H.; Pachl, R.; Schreiber, H. Z. Naturforsch.
1984, 390, 993.
(9) Pachl, R. Ph.D. Thesis, Philipps-UniversittitMarburg, Germany, 1989. (10) Hardwick, T. J.; Robertson, E. Can. J . Chem. 1951, 29, 828. (11) Amjad, Z.; McAuley, A. J . Chem. SOC.,Dalton Trans. 1977, 304. (12) Forsterling, H. D. Unpublished data. (13) Ganapathisubramanian, N.: Noyes, R. M. J . Phys. Chem. 1982,86, 515’8.
(14) Field, R. J.; Boyd, P. M. J . Phys. Chem. 1985, 89, 3707. (15) Brusa, M. A.; Perissinotti, L. J.; Colussi, A. J. J . Phys. Chem. 1985,
89, 1572. (16) Schossler, W.; Kirsch, D.; Lassmann, G. Z . Chem. 1973.13 (10). 364.
Forsterling and Stuk
magnetic field Figure 1. ESR calibration for absolute radical concentrations. The units for the ordinates are arbitrary, but they are the same in cases A C , and in cases D-F, respectively. The starting values of the magnetic field are 3401 G (A and D), 3370 G (B and E), and 3000 G (C and F). The top row shows measured signals for the following: (A) high-field peak of MA’ in 1 M H2S04 (concentrations of reactants immediately after mixing are [Ce4’] = 0.02 M, [MA] = 0.2 M; gain 1.25 X lo4); (B) central peak of 3-carbamoyl-PROXYL, 10” M in water (gain 5 X lo4); (C) complete spectrum of Mn2’, M in water (gain 2.5 X lo4). The bottom row shows the corresponding first integrals of the measured signals.
of a primary standard, which is a substance containing a known concentration of unpaired electrons. The results may be considered more reliable when two or more primary standards are compared. We used two primary standards, Mn2+ and the stable nitroxide free radical 3-carbamoyl-PROXYL. In the rest of this paper, we will write “PROXYL radicals” or simply “PROXYL” to mean 3-carbamoyl-PROXYL. Several functionalized derivatives of PROXYL are commercially available; we used 3-carbamoylPROXYL because it is water soluble. A secondary standard, pitch in KCI (supplied by Varian) was also used for additional information on the effects of the acidic media on the ESR signal. The ESR signals for Mn2+ and PROXYL were measured in water solution and in each of the acidic media used for the MA’ radicals. The signal of a standard ESR sample of pitch was measured with the pitch sample in the second cell of a dual-cell cavity and with each solvent of interest in the primary cell. The two primary standards were measured in the same cell as the unknown MA’ samples (see section 2.2.2). The area under the curve of energy absorbed versus magnetic field strength is proportional to the number of free radicals in a sample. The measured signal is the first derivative of this curve. It is therefore necessary to numerically integrate the measured signal twice. The ESR signals were recorded with an IBM PC; the numerical double integration was performed with a program written by Dr. F. Bar, Fachbereich Chemie, Philipps-Universittit Marburg. Figure 1 shows the measured signals and their first integral curves for malonyl radicals, PROXYL radicals, and Mn2+. The first integral curves are proportional to the energy absorbed as a function of magnetic field strength, and the areas under these curves are compared in order to calculate the MA’ concentration. For signals of the same line shape, both the first integral curves and the areas under these curves are proportional to the amplitude of the measured ~ i g n a l . ~ ~Comparison -I~ of, e.g., pitch signals with different acidic solutions in the primary cell were made by measuring the signal amplitudes. The results of the calibration experiments will be described in section 3.2. 2.2.2. Malonyl Radical Study. The flow system for producing malonyl radicals has been described previouslyS and will be only summarized here. The malonyl radicals were produced by pumping separate solutions of MA and Ce4+into a flat flow ESR cell mounted in the cavity of a Varian E l 2 ESR spectrometer. The volume of the cell (Wilmad Glass Co., Bueno, NJ, type WG-804-Q, dimensions 8 X 0.25 X 60 mm) was 125 pL. The ~
~
(17) Poole, C. P. Electron Spin Resonance, 2nd ed.; Wiley: New York, 1983. (18) Ayscough, P. B. Electron Spin Resonance in Chemistry; Methuen: London, 1967. (19) Wertz, J. E.; Bolton, J. R. Efectron Spin Resonance; Chapman and Hall: New York, 1972.
The Journal of Physical Chemistry, Vol. 96, NO. 7, 1992 3069
Ce4+/Sulfato Complex Formation
2t l t
A
I
I
1 I
2 -
c a b c d e f
1-
-
-
Ok
(continuously stirred tank reactor) experiments. The figure caption includes the residence times, calculated from the flow rate and cell volume. Each experiment was begun with no flow, in order to establish a base line. The sharp rise in malonyl radical concentration indicates the time when the pump was turned on. The pump speed was increased from zero to the desired initial value manually, by adjusting a potentiometer, so the shape of the initial steep rise is somewhat different for each experiment. These differences have no significance. The fall in [MA'] indicates the time when the pump was turned off. The stopped-flow experiments were done to measure k l , as in refs 15 and 21. The calibration for the ordinates of Figure 2 are taken from the next section. This section is presented first because the flow rate dependence of the signal is necessary for our calibration, while the absolute calibration is not necessary for the interpretation of the sulfato-complexing effects. Parts A and B of Figure 2 are control experiments for the effects of cerium/sulfato complexing on the rate of formation of MA*. The effects of the sulfato ions can be summarized as follows:
c+s-cs
(4)
C+MA-MA'
(5)
CS
+ MA
+
MA'
(6)
where C = uncomplexed Ce4+,S = sulfato ion group, e.g. (SO,),+, and CS = sulfato-complexed Ce4+. The MA' radicals decay by reaction 2. Hardwick and RobertsonlO found that Ce(S04)32-is the dominant cerium species for Ce4+in high concentrations of sulfate. We assume for the moment that we can neglect intermediate reactions such as Ce4+ (uncomplexed) S042[CeSO4I2+and [CeS04]2++ MA MA'. Equation 4 considers the formation of the equilibrium cerium/sulfato complex to be an overall reaction, with a single rate constant which is the slowest of the rate constants for the addition of the first, second, and third sulfato groups. The justification for this simplification will be seen below. The concentration of malonyl radicals under steady-flow conditions is then given by
-
d[MA']/dt = 0 = (k,[C]
+
+ ks[CS])[MA] - 2k2[MA'IZ
-
(7)
where [C] + [CS] = [Ce4+],the total concentration of cerium in the oxidized state. Solving for [MA'], we find
Figure 2A illustrates the results of the flow experiments with 2 M HC1O4 as solvent and Ce(NH4)2(N0,)6as the Ce4+source. Here [CS] = 0, since there is no sulfate in the system. The maximum MA' concentration is 2.19 X lod M, reached at residence times of 23 ms or less. The flow rate dependence shows the maximum time for which Ce4+and [MA] may be adequately approximated by their values immediately after mixing, in eq 8. At longer residence times, the concentration is lower because a measurable amount of Ce4+ has been consumed. For the experiment of Figure 2B, each feed stream contained a mixture of 1 M H 2 S 0 4and 1 M HClO,. Here [C] = 0, since all the cerium is complexed before being mixed with MA. The maximum MA' concentration is only 59% of the maximum value in the experiment of Figure 2A. In the experiment of Figure 2B, the maximum [MA'] is reached at a residence time of 139 ms. Decreasing the residence time below 139 ms has no measurable effect in this case because reaction 6 is much slower than reaction 5. That is, the sulfato-complexedcerium requires more than 139 ms for a measurable amount to be consumed, while the uncomplexed cerium requires only 23 ms under the conditions of our experiment. (20) Forsterling, H. D.; Schreiber, H.; Zittlau, W. Z. Narurforsch. 1978, 33a, 1552.
(21) Forsterling, H. D.; Stuk, L. J . Phys. Chem. 1991, 95, 7320. (22) Ingold, K. U.In Free Radicals; Kochi, J. K., Ed.; Wiley: N e w York, 1973.
3070 The Journal of Physical Chemistry, Vol. 96, No. 7, 199'2 Figure 2C illustrates a flow experiment in which one feed stream contained Ce4+in 2 M HClO,; the other MA in 2 M H2S04.Thus the concentrations after mixing were identical to those in the experiment of Figure 2B. However, in this case the cerium was not complexed prior to exposure to MA. As the two feed streams were mixed, reactions 4 and 5 competed for the uncomplexed cerium. In the limiting case k,[MA] >> k4[S], [CS] should approach zero and [MA'] should approach the value observed in Figure 2A (2.19 X lod M, almost twice the maximum value for Figure 2B) for small residence times. In the limiting case k4[S] >> k,[MA], [C] should approach 0 even at small residence times, and the flow rate dependence of [MA'] should be identical for the experiments of parts C and B of Figure 2. This latter limiting case is consistent with the experimental results for all our measurements. Even at residence times down to 17 ms (part f of Figure 2C), the signal did not increase as would be expected for reaction of some uncomplexed Ce4+ with MA. Our flow system results are not consistent with earlier sugg e s t i o n ~ ~that * ~ ~uncomplexed *'~ Ce4+may play a significant role in the BZ system. Therefore we will comment on each of these earlier suggestions. 3.1.1. Ce4+Decay Results of Ganapathisubramanian and Noyes. The first report of possible effects of uncomplexed Ce4+was made by Ganapathisubramanian and Noyes.I3 Their experiment was as follows: a 0.1-mL amount of 5.16 X M Ce4+ in 1.5 M H2S04was added to 2.8 mL of 1.5 M H2S04. After a specified time elapsed, 0.1 mL of 0.6 M MA in 1.5 M H2S04was added to the solution, and the reaction was observed spectrophotometrically. When the specified time was less than 1 h, plots of light absorbance versus time consisted of two straight line segments of different slopes. Ganapathisubramanian and Noyes' explanation of these data was that Ce4+was complexed with sulfates in the original solution, and that these complexes dissociated within 1 h of the dilution of the original cerium solution by a factor of 29. So the steep sections of each line corresponded to reaction of MA with uncomplexed cerium, and the sections with smaller slope to the reaction of MA with the remaining complexed cerium, in their explanation. Hardwick and RobertsonIo have presented the following equilibrium constants for ceriumfsulfato complexes: (9)
Thus we calculate [Ce(S04)32-] = 1.4 X 107([HS04-]/[H+])3[Ce4+] (12) For 1.5 M H2S04,the factor ([HS04-]/[H+])3 = 1, regardless or 1.78 X M Ce(S04)2is added to of whether 5.16 X the H2S04solution. So at equilibrium in 1.5 M H2S04, essentially all the Ce4+ is complexed with three S042-groups. These data indicate that the dilution of the Ce(S04)2solution could have no effect on the sulfato complexation of the cerium in the experiments of ref 13. We do not understand the cause of the change in slopes observed by Ganapathisubramanian and Noyes,I3 but we believe that it is something other than a ceriumfsulfato complexing effect. 3.1.2. osCillatiom in an Oxalic Acid/Acetone System Observed by Field and Boyd. The next report of uncomplexed Ce4+effects was made by Field and Boyd.14 These authors found that the reduction of Ce4+in the first oscillation of a BZ system with oxalic acid and acetone as organic substrates was slower by a factor of approximately 1000, compared to the reduction of Ce4+ in subsequent oscillations. They concluded, on the basis of the report of Ganapathisubramanian and Noyes," that Ce4+freshly produced in the subsequent oscillations could be uncomplexed, while Ce4+
Forsterling and Stuk TABLE I: Second Integral (Area) Values for Reference Radicals and for MA' Radicals" scan radical solvent range, G gain area M Mn2+ water 1000 2.5 x 104 1.5 1 M HIS04 lo-' M Mn2+ 1000 2.5 x 104 0.94 M Mn2+ 1 M H 2 S 0 4+ 1000 2.5 x 104 0.80 1 M HCIO, 2 M HC104 lo-' M Mn2+ 1000 2.5 x 104 0.68 10-5 M PROXYL water io 1.25 x 104 1.75 10-5 M PROXYL 1 M HIS04 io 1.25 x 104 1.10 10-5 M PROXYL 2 M HC10, io 1.25 x 104 0.97 MA' 1 M H2S04 4 1.25 x 104 1 .oo 1 M HC10, MA' 4 1.25 x 104 1.10 1 M HZSO4 2 M HC104 MA' 4 1.25 x 104 1.74
+
"The areas for Mn2+ correspond to the complete signal; the areas for PROXYL and MA' correspond to one peak only (see Figure 1).
in the first oscillation was fully sulfato-complexed in the solution which was used to start the reaction. It is also possible that the observed difference was due to the formation of some other organic compounds during the first oscillation. That is, the first cerium reduction may represent an induction period before the regular oscillationsbegin. The different Ce4+decay rates may then be explained by the fact that the initial conditions for subsequent oscillations are not equivalent to those for the first oscillation. 3.1.3. Earlier Simulation Results. Finally, Gyorgyi, Turhyi, and Field7 have reported that better agreement between simulations and experiment could be achieved for their detailed BZ model if freshly oxidized Ce4+reacted faster than sulfato-complexedCe4+. The model contains a large organic subset and predicts induction periods well for several experimental systems. G ~ o r g y has i~~ suggested that Ce3+could be complexed with the malonic acid in the actual BZ system. In this case it is proposed that freshly oxidized Ce4+in the BZ system is not equivalent to Ce4+in HC104 used in our experiments. However, simulations3 of a BZ system which oscillates with no induction period (the Rgcz system) produced good agreement with experiment by using the rate constant for the Ce4+/MA reaction which was measured in H2S04solution. This system is started with Ce3+, and Ce4+is freshly produced in each cycle. If the Ce4+/MA rate constant is changed significantly, then the simulations will no longer agree with experiment in this relatively simple system. Moreover, starting the same system with sulfato-complexed Ce4+ instead of Ce3+does not change the experimentally observed Ce4+ decay kinetics in the first oscillation.12 We are not aware of any evidence for a Ce3+/MA complexing effect, but of course the possibility of such a complex can only be determined by direct experiments. 3.2. [MA'] Calibration. We calculate the concentrations of radicals fromI6-I9 [sample] = [reference]
A,G,S,(S, + 1) A,G,S,(S, + 1)(
z) u
s
(13)
where A = area under the integrated curve, G = gain setting of the instrument, S = spin quantum number of the radical, AH = scan range, and the subscripts s and r refer to the sample and reference, respectively. The spin quantum numbers are as follows: Mn2+, MA' and PROXYL, I f 2 . The areas, gain settings, and scan ranges are given in Table I. The areas are given in arbitrary units, since only the ratios are significant. Several corrections are necessary for the areas listed in Table I. First, we integrated only one peak for each spectrum of malonyl or PROXYL radicals. This method reduces error from integrating over a large segment of base line. So the areas must be multiplied by the number of (identical) peaks, two for MA' and three for PROXYL. For Mn2+, the peaks are not resolved, so it was (23) Gyorgyi, L. Private communication.
The Journal of Physical Chemistry, Vol. 96,No. 7, 1992 3071
Ce4+/Sulfato Complex Formation
TABLE 111: First-Order Rate Constants krxpfor Malonyl Radical Formation in 2 M HCIO, at 25 OC [Ce4+Io,
M
0
2
2
4 0
4 0
2
0.002 0.002 0.002 0.002
4
[MA],,
M
0.01 0.02 0.04 0.05
(mW0.5)
0.4
[Ce4+lo, M
[MA],,
k,, ,
S-p
0.1 0.18 0.32 0.40
0.002 0.002 0.002 0.02
0.10 0.15 0.20 0.20
0.65 0.80 0.85
k,, ,
M
S-p
0.77
,
I
Figure 3. ESR signal versus square root of microwave power for the M in water); (B) PROXYL radicals following: (A) Mn2+ M in water); (C) malonyl radicals (flow experiment as described in Figure I).
Y 1 c
-2
+
e,
-3
-
-4
u, v
c
A
B
2
1
3
5
4
time (s)
C
solvent Figure 4. Solvent effects on the ESR signal for Mn2+ (pluses), for PROXYL (circles), and for pitch (triangles). The relative signal is the ESR signal measured in the given solvent divided by the signal measured in water. The solvents are as follows: (A) 1 M H2S04;(B) 2 M HC10,; (C) 1 M H2SO4 + 1 M HC104. TABLE 11: Concentrations of Malonyl Radicals Formed from 0.02 M Ce4+ and 0.2 M Malonic Acid at 24 OC solvent 1 M H2S04 1 M H2S04 + 1 M HC104 2 M HClO,
0
Figure 5. Absorbance and In ( [Ce4+]/[Ce4+],)versus time for reaction at 25 OC with initial conditions [Ce4+Io= 0.02 M, [MA], = 0.2 M, and [HC104]o = 2 M.
*
signal in acidic solution is 57 6% of the signal in water. Substituting in eq 13, we find that the calibration for MA' using the Mn2+ standard is MA'] =
(
I S + 1 2(1.22(MA' area)) 2.5 x 104 2 2 ) ( L ) 2 (0.57)(1.5) 1.25 x 104 -l ( -1 1 ) 1000 2 2
[MA'], M 1.19 X 10" 1.30 X IOd 2.19 X 10"
+
necessary to integrate the entire spectrum. Second, the spectra for MA' were all taken at a residence time of 139 ms. In 1 M H2S04 and in the mixture of 1 M H2S04 1 M HC104, this residence time is short enough so that the Ce4+ concentration is essentially equal to its value immediately after mixing, as discussed in the last section. In 2 M HClO,, however, the MA' concentration at 139 ms is only 94% of its maximum value, so the area from Table I must be multiplied by 1.06. Third, the measured signals must be corrected for microwave power saturation. Figure 3 illustrates this effect. In order to compare the second integrals from different radicals, the signal from each radical should be proportional to the square root of the microwave power." This was true for the two standards in our experiments, as seen from Figure 3A,B. However, the malonyl radical signal at 15 mW falls below the line determined by the signals at lower power. The malonyl radical signal must therefore be corrected" to the extrapolated value for 15 mW. This correction is a factor of 1.22. Finally, the solvent effects must be included. Figure 4 illustrates the effects of different solvents on the observed ESR signal. The areas under the first integral curves (see Figure 1) are compared for Mn2+and for PROXYL in acidic media. The areas are all normalized by the value for the appropriate radical in water. Figure 4 also includes normalized signals for the standard ESR pitch sample which was placed in the second cell of a dual-cell sample holder, while the first cell contained the indicated acidic media. The scatter of the points is one indication of the experimental error in absolute calibration. There is no clear distinction between the different solvents, so we calculate the effect of electrolyte damping on the signal as the average value; Le., the
+
= (1.07 X lod M)(MA' area)
(14)
Jsing the PROXYL standard, the calibration is [MA'] =
+!(A A(
(2)(1.22)(MA' area) 1.25 x 104 2 2 (10-5 M) (0.57)(3)(1.75) 1.25 x 104 2 2 = (1.30 X 10" M)(MA' area)
1) +
1)
(4
(15) In each case, the areas are taken from Table I, and the value for MA' in 2 M HC104 must still be multiplied by 1.06. From eq 14 and 15, we see that the average value for the calibration with the two standards is [MA'] = (1.19 X 10" M)(MA' area), with an error of *lo%. Table I1 summarizes the results for the [MA'] calibration. 3.3. Rate Constants for MA' Formation and Self-Decay. The rate constants for MA' formation in 1 M H2S04 and in 1 M H2S04 1 M HC104were extracted from the stopped-flow ESR experiments, as in refs 15 and 21. For the system in 2 M HC104, the decay was too fast for reproducible results to be obtained in the ESR stopped-flow experiments, so the rate constant was measured spectrophotometrically, as in ref 21. Table I11 lists the first-order rate constants k,, for reaction 1 as a function of initial MA concentration. The last entry of Table I11 is identical to the concentrations used in the ESR experiment with 2 M HClO,. The logarithmic plot for this experiment is shown in Figure 5. The data of Table I11 are plotted in Figure 6. These data show a nonlinear de-
+
3072 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
Forsterling and Stuk TABLE V: Recalculation of Rate Constants for Malonyl Radical Reactions in 1 M H2SOI Investigated in Reference 5 by Changing k 2 from 3.2 X lo9 M-I s-' Is to 4.2 X lo8 M" s-, (This Work) rate constant, M-' s-I reaction ref 5 this work MA' + HOBr products 9.7 X lo6 3.6 X lo6 1.5 x 108 5.4 x 107 MA' + Br, products 8.0 X 10, MA' + Br03products 2.9 X lo2 MA' + BrO,' products 5 X lo9 5 x 109
---
0
0.2
0.1
[ M A b (MI Figure 6. First-order rate constant k for Ce4+decay versus [MA],. Initial conditions are as follows: [Ce4y0= 0.002 M; [HC10410= 2 M. The temperature is 25 f 0.1 OC.
TABLE I V Rate Constants for Malonyl Radical Production and Self-Decay at 24 OC ( k , for 2 M HCIOl Solution Calculated as ki(24 "C) = 0.95k,(25 "C), kl(25 "C)= (0.77 ~-')/(0.20M) = 3.85 M-' s-l; See Table 111) solvent k , , M-I s-I k,, M-' SKI 1 M H2S04 0.29 4.2 X lo8 1 M H2SO4 + 1 M HCIO4 0.36 4.3 x 108 2 M HC104 3.7 1.5 x 109
pendence of k on [MAIo, probably due to a pre-equilibrium of MA and Ce4+?ith a MA/Ce4+ complex, as suggested by Amjad and McAuley." Table IV summarizes the results of the experiments to obtain k2. For each solvent, the table lists the second-order MA' production rate constant kl and the MA' decay rate constant k2, also second order. k l was measured at 25 OC for the case of 2 M HClO, solvent, so from the temperature dependence of k, in 1 M H2S04,we estimate kl at 24 OC = 0.95(k1 at 25 "C) = 0.95ke,,/[MA] = 0.95[0.77/(0.2 M-' s-l)] = 3.7 M-I s-l, with kcxptaken at [MA] = 0.2 M as in the ESR experiments. k2 is then calculated as k2 =
kl [Ce4+][MA] 2[MA'] kl
= (2 x 10-3 ~ 2 ) [MA']
Since the values for the malonyl radical concentrations are uncertain to *lo%, the rate constants k2 are uncertain to &20%. Our value for k, = 1.5 X lo9 M-I S-I in 2 M HClO, is about half the value reported by Brusa et al.I5 (k, = 3.2 X lo9 M-' s-I). That means the discrepancy in the measured radical concentration is about 40% which is more than the error of the method. One crucial point in the procedure of Brusa et al. is their calibration with Fremy's salt. Fremy's salt is not stable in water or in acidic solution, so it must be used in concentrated K2C03solution. Hence we assume that the medium in the calibration experiment of Brusa et al. was not the same as that in the flow experiments. This difficulty does not arise in our calibration procedure with MnZ+ and PROXYL radicals. It is not clear why the malonyl radical self-decay rate is slower in H2S04than in HClO, solution by a factor of 3.6. However, solvent effects have been reported previously for the rate constants of organic radical self-reactions.22 These effects were attributed to (1) solvent viscosity differences, affecting the diffusion velocities of the reactants; and (2) differences in the reaction mechanism,
where disproportionation or combination may be favored in a particular solvent. It was suggested by one of our reviewers that uncomplexed Ce4+ might react with malonyl radicals in HClO, solution. However, Brusa et al.15 found that the malonyl radical concentration is proportional to the square root of [Ce4+][MA] in HC104. Reaction 2 predicts the correct square root dependence, while a decay mode of MA' Ce4+ Ce3+ (other products) would predict [MA'] independent of [Ce"] and proportional to the first power of [MA].
+
-
+
4. Conclusions
Our results support the use of the reported values of the rate constant for reaction 1 in the oscillating BZ system. The sulfato-complexing process for freshly oxidized Ce4+ is fast enough, compared to reaction 1, to be regarded as instantaneous for purposes of calculating the MA' concentration. If there is any anomaly in the rate of reaction of freshly oxidized Ce4+with MA, as suggested by Gyorgyi et then such an anomaly is not due to a slow rate of complex formation between the Ce4+ and the groups. We find that the rate constant for reaction 2, however, should be reduced from 3.2 X lo9 to 1.5 X lo9 M-' s-I in 2 M HC104 and to 0.42 X lo9 M-' SKI in 1 M H2S04. This affects the calculation of other rate constants from ref 5, primarily for the reaction
+ BrO,'
-
P (17) where P is the unspecified product. In ref 5, k17 = 8.3 X lo9 M-I S-I was calculated from the experiments, and the value 5 X lo9 was suggested as a lower limit for k17. A recalculation of k17 with k2 = 4.2 X lo8 M-I s-I a s reported in this paper for 1 M H2S04 medium gives k17 = 5.9 X lo9 M-I S-I. So we may still take k17 = 5.0 X lo9 M-' s-I as a reasonable value. Table V summarizes the reactions and rate constants affected by the results of this work. Several other radical disproportionation reactions for the BZ system in 1 M H2S04have been estimated7 on the basis of the previously reported15 value for MA' self-decay in 2 M HC104. Future refinements of the BZ mechanism should take into account the lower value measured in 1 M H2S04. Future work is planned to investigate the effects of H2S04on organic radical self-decay. MA'
Acknowledgment. We thank the Fachbereich Chemie of the Philipps Universitat Marburg for supplying the ESR equipment and Dr. F. Bar (Fachbereich Chemie, Philipps-Universitat Marburg) and S. Sorey (Chemistry Department, The University of Texas, Austin) for valuable advice on the ESR measurements. We also thank Dr.H. Schreiber, Prof. Z. Noszticzius, and Prof. W. D. McCormick for critical reading of the manuscript and Dr. L. Gyorgyi for valuable discussions about the cerium/sulfato complexing problem. This work was supported by the Stiftung Volkswagenwerk, the Fonds der Chemischen Industrie, and the Department of Energy, Office of Basic Energy Sciences. L.S. is supported by the Fannie and John Hertz Foundation.
