J . Phys. Chem. 1989,93, 2781-2783
2781
Gas-Exchange Rates In the Belousov-Zhabotinskii Reaction Determined with Membrane Inlet Mass Spectrometry H. Degn* and F. R. Lauritsen Institute of Biochemistry, Odense University, Odense, Denmark (Received: August I , 1988) Membrane inlet mass spectrometry in a system open to gases was used to measure the rates of carbon dioxide formation and oxygen consumption in the Belousov-Zhabotinskii reaction. High rates of carbon dioxide evolution determined by others were confirmed. When the head space gas contained oxygen, rates of oxygen uptake were found to be of the same order of magnitude as the rate of carbon dioxide evolution. Without oxygen the reaction was simply periodic. With oxygen period doubling and chaos developed after some time.
Introduction Although carbon dioxide is assumed to be the final product of the Belousov-Zhabotinskii (BZ) reaction, the rich literature on this reaction contains few studies of the rate of carbon dioxide evolution.'" Carbon dioxide has been monitored in the BZ reaction by volume try,'^^ titration: flame ionization after catalytic reduction to m e t h a r ~ e ,and ~ . ~ p~tentiometry.~Recently, it was pointed out6 that there is a serious discrepancy between the experimentally determined rate of carbon dioxide production and the rate calculated from the currently accepted model' (FKN) of the reaction. Oxygen is known to have a profound effect on the BelousovZhabotinskii reaction.*-" However, the published studies of the interaction of oxygen with the BZ reaction have not aimed at determining rates of oxygen consumption. Most measuring systems that have been used to study the BZ reaction were more or less open to oxygen from the atmosphere, but the access of oxygen was incidental and the rate was not quantified (e.g., ref 5). In the present work we have measured the rates of formation of carbon dioxide and consumption of oxygen in the BZ reaction in a system open to exchange of gases but otherwise closed. In our measuring cell the liquid sample is stirred at a constant rate, resulting in a paraboloid surface of constant area. The head space is flushed with a gas mixture of known composition. Provided the absence of bubbles, the rate of transport of a gas across the boundary between the liquid and the gas phase is proportional to the difference between the partial pressures of the gas in the two phases. Therefore, measurements of steady-state concentrations of gases in the liquid under head space gases of known composition can be used to calculate steady-state reaction rates.'* We have used membrane inlet mass ~pectrometry'~ (MIMS) to record simultaneously the concentrations of oxygen and carbon dioxide in the BZ reaction in a system open to gases. The mass spectrometric technique is superior with regard to response time and reproducibility to other techniques for measuring dissolved gases. The technique has been used extensively in studies of gas-exchange rates in biochemical systems. We find that in the stirred BZ reaction mixture in contact with the atmosphere the rate of oxygen consumption may be of the Degn, H. Nature 1967, 213, 589. Bornmann, L.; Busse, H.; Hess, B. 2.Nururforsch. 1973, 28C, 514. Noszticzius, Z . J . Phys. Chem. 1977, 81, 185. Bar-Eli, K.; Haddad, S. J . Phys. Chem. 1979,83, 2944. (51 Vidal. C.: Roux. J. C.: Rossi. A. J . Am. Chem. SOC.1980. 102. 1241. (6) Forsterling, H. D.; Idstein, H.: Pachl, R.; Schreiber, H. 2. Naturjorsch. 1984. 39A. 993. (7) Fielh, R. J.; Koros, E.; Noyes, R. M. J. Am. Chem. SOC.1972, 94, (1) (2) (3) (4)
8648. (8) Barkin, S.; Bixon, M.; Noyes, R. M.; Bar-Eli, K. Int. J . Chem. Kinet. 1978, 10, 619. (9) Roux, J. C.; Rossi, A. C. R. Seances Acad. Sci. 1978, 287, 151. (10) Bar-Eli, K.; Haddad, S. J. Phys. Chem. 1979, 83, 2952. (11) Ruoff, P. Chem. Phys. Lett. 1982, 92, 239. (12) Degn, H.; Lundsgaard, J. S.; Petersen, L. C.; Ormicki, A. Methods Biochem. Anal. 1980, 23, 41. (13) Degn, H.; Cox, R. P.; Lloyd, D. Methods Biochem. Anal. 1985, 31, 165.
0022-3654/89/2093-2781$01.50/0
same order of magnitude as the rate of carbon dioxide evolution. Period doubling and chaos have been reported to exist in the BZ reaction in an open reaction system (continuous stirred tank reactor) where reagents are pumped in at constant rates and excess liquid is removed by overflow.14J5 In our partially open reaction system we observed period doubling and chaos when the oxygen partial pressure of the head space gas was within certain limits. With pure argon in the head space the oscillation was always simply periodic except for an initial transient.
Experimental Section The measurements were done with a Balzers Q M S 420 quadrupole mass spectrometer with a membrane inlet of our own design. The inlet was fitted into a measuring cell where the stirred liquid sample was open to transport of gas across the phase boundary between the liquid and the head space gas. The inlet and measuring cell were designed as described pre~iously'~ except that the cell was made of high-density polyethylene instead of stainless steel. The membrane was 25-rm polypropylene from Radiometer, Copenhagen, Denmark. The head space above the 4.5 mL of liquid sample was flushed with argon or a mixture of oxygen and nitrogen produced by a calibrated digital gas mixeri6 at a rate of 75 mL/min. Data were transmitted serially from the mass spectrometer and collected by an Olivetti PC M 28 and stored on disk. The concentration of a dissolved gas in the liquid sample is a steady-state concentration determined by the rates of chemical production and consumption of the gas and the rate of transport of the gas across the phase boundary. Under the conditions used in the present experiments the carbon dioxide left the solution solely by diffusion. Under such conditions the rate, V,, of transport of a gas across the phase boundary can be described by the equation where K is a constant, TLis the molar concentration of the gas in the liquid, and TG is the molar concentration of the gas when the liquid is equilibrated with the gas phase. At a steady state the rate of chemical production or consumption of a gas is equal to the rate of transport, and so the rate can be calculated from eq 1. The constant, K , which depends on the geometry of the sample cell and the rate of stirring, is determined by measuring the transient in the gas concentration in the medium without reactants after a change of the composition of the gas phase. The equilibration process is of first order as seen from eq 1. With 4.5 mL of liquid in the sample cell we found K as 0.0077 s-l for oxygen and carbon dioxide, corresponding to a half-time of about 2 min. The molar concentration of oxygen in a medium of the same sulfuric acid concentration and approximately the same ionic strength as our reaction mixture in equilibrium with the atmosphere was determined as 260 pM. The reagents used were (14) Schmitz, R. A.; Graziani, K. R.; Hudson, J. L. J . Chem. Phys. 1977, 67, 3040. (15) Roux, J. C.; Rossi, A,; Bachelart, S.; Vidal, C. Physica 1981, 2D, 395. (16) Degn, H.; Lundsgaard, J. S. J . Biochem. Biophys. Methods 1980, 3, 233.
0 1989 American Chemical Society
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Degn and Lauritsen
The Journal of Physical Chemistry, Vol. 93, No. 7, 1989 240
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Figure 1. Mass spectrometric recording of the carbon dioxide concentration in the BZ reaction in a system open to gas exchange. The head space gas was Ar. [BrOp-] = 0.044 M, [malonic acid] = 0.44 M, [Ce4+] = 0.0033 M, and [H2S04]= 0.55 M. The sample volume was 4.5 mL, and the temperature was 30 OC. Time zero in the graph is 120 min after the start of the reaction.
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Figure 3. Phase plot of carbon dioxide concentration versus oxygen concentration in the BZ reaction in a system open to gas exchange (dockwise rotation). Data are from the experiment in Figure 2.
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Figure 2. Mass spectrometric recording of carbon dioxide and oxygen concentrations in the BZ reaction with 2% oxygen in nitrogen as the head space gas. The gas was switched to argon and back to the 2% oxygen mixture at the arrows. Same concentrationsof reactants as in Figure 1 were used. Time zero is 70 min after the start of the reaction.
analytical grade ceric sulfate, potassium bromate, and sulfuric acid from Merck, and malonic acid was Merck‘s quality for synthesis. The argon used was virtually oxygen free. Stock solutions of reagents were renewed every second day. Appropriate amounts of all reagent solutions except the cerium sulfate were pipetted into the sample cell, and the mixture was equilibrated for 20 min with the head space gas. The reaction was then started by the addition of the cerium solution. The temperature was 30 “C.
Results Figure 1 shows a recording of the concentration of carbon dioxide in a stirred reaction mixture with a stream of argon through the head space. The period of the oscillation is about 100 s, and the evolution of carbon dioxide occurs in a burst of about 10-s duration. During the remainder of the period the carbon dioxide concentration declines approximately exponentially with a half-time of about 2 min, indicating that the production of carbon dioxide during this phase is insignificant. The oscillation was observed to continue with a slowly decreasing rate of carbon dioxide evolution and slowly increasing period until the experiment was interrupted after 10 h. Except at the beginning of the experiment the oscillation was always simply periodic. At 120 min after the start of the reaction the rate of carbon dioxide formation was 1.6 X 10” mol/(L s). Since carbon dioxide formation took place only 10% of the time, the average rate of carbon dioxide formation during the burst was 16 X 10“ mol/(L s) or 5.2 X mol of C02/(mol of Ce s). Figure 2 shows a recording of the carbon dioxide and oxygen concentrations in a reaction mixture that had 2% oxygen in nitrogen as the head space gas from the beginning. The shape of the carbon dioxide trace is similar to the one in Figure 1 where
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Figure 4. Mass spectrometric recording of carbon dioxide and oxygen concentration in BZ reaction with 4.5% oxygen in nitrogen as the head space gas. Same concentrations of reactants as in Figure 1 were used. Time zero in the graph is 70 min after the start of the reaction.
no oxygen was present, and the rate of carbon dioxide formation is also nearly the same. The oxygen trace has an increasing phase due to transport of oxygen into the liquid from the gas phase and a decreasing phase, where the consumption of oxygen by the reaction is much faster than the rate of supply from the gas. The average rates of carbon dioxide evolution and oxygen consumption were 1.8 X 10” and 0.20 X 10” mol/(L s), respectively. When the head space gas was changed to argon, the oscillation stopped and the rate of carbon dioxide formation fell to about one-fourth of its average value during the oscillation. When the head space gas was changed back to 2%oxygen in nitrogen, the carbon dioxide formation and the oscillations resumed. In several similar experiments we always found that once the reaction mixture had been exposed to oxygen, it would not oscillate without oxygen. However, if the reaction mixture was never exposed to oxygen, it would oscillate for a longer time than with oxygen. Figure 3 shows a phase plot from the data in Figure 2. It is seen that the consumption of oxygen precedes the production of carbon dioxide. When the oxygen content of the head space gas was further increased, period doublings and erratic fluctuations occurred. Figure 4 shows an experiment with 4.5% oxygen in nitrogen as the head space gas from the start of the reaction. With this setting of the oxygen in the gas phase the reaction initially exhibited simple oscillations as in Figure 3. After a short time these oscillations went through irregular period doublings and became seemingly chaotic. After 130 min the fluctuations in the carbon dioxide and oxygen concentrations vanished into noisy steady states as shown in Figure 5. After the fluctuations had vanished the head space gas was switched to argon. The concentration of carbon dioxide was then observed to fall to about one-fourth of its previous steady-state value, indicating that the rate of carbon dioxide formation had been reduced to one-fourth of its previous value. The rate of oxygen consumption 70 min after the start of the reaction with 4.5% oxygen in the head space gas was 0.45 X
J. Phys. Chem. 1989, 93, 2783-2791
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