2952
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979
(15) K. Showalter, R. M. Noyes, and K. Bar-Eli, J. Chem. fhys., 69, 2514 (1978). (16) R. A. Schmitz, K. R. Graziani, and J. L. Hudson, J . Chem. Phys., 67, 3040 (1977). (17) A. I. Vogel, "Quantitative Inorganic Analysis", 3rd ed, Longmans, London, 1961, p 343. (18) S. Barkin, M. Bixon, R. M. Noyes, and K. Bar-Eli, Int. J. Chem. Kinet., 10, 619 (1978). (19) J. C. Roux and A. Rossie, C.R. Acad. Sci., Ser. C, 287, 156 (1978). (20) S. Barkin, M. Bixon, R. M. Noyes, and K. Bar-Eli, Int. J. Clem. Kinet., 9, 841 (1977). (21) K. Bar-Eli and R. M. Noyes, J . fhys. Chem., 82, 1352 (1978). (22) (a) C. W. Gear, "Numerical Initial Value Problems in Ordinary Differential Equations", Prentice-Hail, EnglewoodCliffs, N.J., 1971, pp 209-229. (b) A. C. Hindmarsh, "Gear": Ordinary Differential Equation System Solver, UCID-30001 Revised Dec 3, 1974. (23) E. Koros, Nature (London),251, 703 (1974). (24) E. Koros, M. Orban, and Z. Nagy, Magy Kem. Foly., 83, 104 (1977). (25) (a) L. Bormann, H. Busse, and B. Hess Z. Naturforsch. B ,28, 93, 824 (1973); (b) Z. Naturforsch. C , 28, 514 (1973). (26) H. Degn, Nature (London), 213, 589 (1967).
K. Bar-Eli and S. Haddad (27) E. K&os, M. Burger, V. Friedriech, L. Landanyi, Z. Nag, and M. Orban, Faraday Symp., Chem. Soc., 9, 28 (1974). (28) G. J. Kasperek and T. C. Bruice, Inorg. Chem., 10, 382 (1971). (29) M. L. Smoes, paper presented at the 13th Meeting of Mawest Chapter of the American Chemical Society, 1977. (30) P. De Kepper, Ph.D. Thesis, University of Bordeaux, France. (31) K. R. Graziani, J. L. Hudson, and R. S. Schmitz, Chern. Eng. J . , 12, 9 (1976). (32) M. Marek and E. Svobodova, Biophys. Chem., 3, 263 (1975). (33) E. Koros, Faraday Symp., Chem. Soc., 9, 92 (1974). (34) K. Bar-Eli and S.Haddad, J. fhys. Chem., followlng article in thls issue. (35) The calculated time was chosen arbitrarlly as the first minimum of ceric ion concentration. Other criteria can be chosen, such as the first maximum of bromide or the first change in the slope of one of the measured specles. For each criterion, slightly different numbers are obtained but the same general trends are observed. (36) Experiments which were done without bubbling nitrogen, e.g., on the Caw spectrophotometer, gave the same qualitative results. A detailed analysis of the influence of oxygen Is the subject of a separate p~blication.~~
Effect of Oxygen on the Belousov-Zhabotinskii Oscillating Reaction K. Bar-Eli" and S. Haddad Department of Chemistry, Tel-Aviv Universlty, Tel-Avlv, Israel (Received January 25, 1979)
The BZ oscillating reaction was run while bubbling nitrogen, oxygen, or both alternately in a closed system. Under oxygen the reaction has longer induction time, the oscillations stop earlier, and the period time change faster than under nitrogen. The results of calculations based on an improved Oregonator mechanism are compared to the experimental data.
Introduction The effect of oxygen on the oscillating Belousov-Zhabotinskii (BZ)l reaction was not fully recognized until recently. De-Kepper2working in a flow system showed that the range of concentrations of reactants in which oscillations can occur changed according to the flux of oxygen. Roux and Rossi3 studied the effect of oxygen with solutions of varying amounts of malonic acid while the other reactants were kept constant, again under flow conditions. At [MA] = 0.018 M oscillations stop when oxygen is bubbled into the solutions, while at [MA] = 0.4 M oscillations start when oxygen is bubbled. Between these concentrations, the oscillations change frequency. That oxygen must have an effect on the BZ reaction was pointed out by Barkin et aL4 in their study of ceric ions reduction by malonic acid. They found that in presence of oxygen this reduction is enhanced. A mechanism involving peroxy radicals and peroxides of malonic acid and possibly other reaction products and intermediates was suggested and gave good agreement with the experimental data. Similar intermediates were suggested by Roux and Since this reduction plays a dominant role in the BZ reaction, the effect of oxygen in the reaction is obvious. In this work, we present some results on the effect of oxygen on the BZ reaction conducted in a closed system, and compare them with computations done on the basis of a previously suggested mechanism.6 Experimental Section Experiments were conducted while bubbling nitrogen, oxygen, or both alternately into the reaction mixture, while measuring the oscillations with bromide-sensitive electrodes (Orion Research Inc.) or Pt black electrodes. The gases were passed through a 1.5 M sulfuric acid trap before 0022-3654/79/2083-2952$0 1.OO/O
entering the reaction mixture. Both the trap and the reaction mixture were thermostated. Materials. All solutions were made in ultra pure Aristar(BDH) 1.5 M sulfuric acid (which contains less impurities than regular commercial acid). Malonic acid (Aldrich Chemical Go.) was recrystallized from 2-propanol. The ceric ion source was Ce(S04)2.4H20(puriss) from Merck. Bromate was the sodium or potassium salt (Merck analar). All solutions were prepared in 1.5 M sulfuric acid and were always mixed in the same order, namely, bromate, malonic, and finally the cerium solution after which the reaction time was started. The stock solutions were discarded after 1 week, and thus all experiments were conducted with solutions of roughly the same age. Calculations As indicated in the Introduction, the kinetic model used for the computations is a slightly improved Oregonator5p6 used earlier by Showalter, Noyes, and Bar-Elik to explain the results of Schmitz et a1.8 obtained in an open flow system. The authors6dused the same model to explain their own results in a closed system. Details of the above computations are given in the references. The bubbled gases probably wash out the elementary bromine (which does not appear in our mechanism). Our system is, therefore, not completely closed, and we use this term in order to contrast it with flow sy~tems.~B The model is given in reactions 1-6. The first five Br0,- Br- 2H+ s HBrOz HOBr (1) h-l = lo4 M-l s-' hl = 2.1 M-3
+
+
HBrOz + Br-
+
+ H+ F? 2HOBr
h2 = 2 x 109 M-2 0 1979 American Chemical Society
K - ~= 5 x 10-5 M-1
(2) 8-1
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979 2953
Belousov-Zhabotinskii Oscillating Reaction
Br03- + HBr02 + H+ + 2Br02. + H 2 0 k 3 = 1 x 104 M-2 s-1
Ce3+ + Br02.
k-3 = 2 x 107 M-I
k4= 2.4
2HBr02 e HOBr
k5 = 4
X
-
X
k-5 = 2
+
+ Ce3++ product
Ce4+ MA
kg = 0.53 M-l s-l
gBr-
(5)
M-2 s-l
lo7 M-I s-l
X
(4)
lo7 M-I s-l
+ BrOL + H+
I
I
I
I
I
1
1
I
- t
1.
-{
200
k
160
fp
120
u
[~;+4] = 0 5 .
.. *...
:1
(6)
M
[MA]=O.OSM
[BrO;]:O
IM
x x x x x x x
e
n
1
-I
2401
s-1
+ H+ + Ce4++ HBr02
k4 = 6.5 X lo5 M-2 s-l
280
(3)
x x x x x x x x x x
xxxxx
g = 0.4615 (var param)
reactions are part of the seven reactions used successfully by Barkin et al.5bto explain the oxidation of cerous ions. We have omitted the bromine-bromide-hypobromous acid equilibrium and the reduction of ceric ions by Br02. radicals since they were shown by Barkin et al.5bto contribute very little. The kinetic equations were solved numerically by the method of Gear.g Water was taken at unit activity, and the [H+] was 1.5 M and constant. Equation 6 is a schematic sum of the reactions that produce bromide ions via the reduction of ceric ions by malonic acid and its brominated substituents. A detailed mechanism of ceric reduction without bromine containing species is given by Barkin et al.: while details of the entire kinetics are given by Edelson, Field, and no ye^.^ The model does not show how the brominated substituents of malonic acid are formed, or how these brominated species form bromide ion at later stages. These steps are certainly changed when nitrogen is substituted for oxygen as was explained in the Introduction. We shall show later how the change of the parameters kg and g can account for most, however not all, of the observed data. It is obvious that the mechanism as it stands cannot be complete, since reaction 6 only averages out many reactions. The advantage of the mechanism is its relative simplicity. It is the purpose of the paper to examine how much this simple mechanism can predict. The agreement we can expect from this analysis is at most semiquantitative, and in many cases only qualitative, and only general trends are shown. Results In Figure 1the results of a typical experiment are shown. Each experiment was run twice, once with nitrogen and a second time with oxygen bubbled into the reaction mixture. The results of this and similar experiments are summarized in Table I. The following can be concluded from these data: (a) The oscillations time is much shorter for the oxygen reaction than for the nitrogen one. While the nitrogen reaction continued for at least 12 h (only the first 6 h are shown in Figure l),the oxygen oscillations stopped after, at most, 6 h and usually in much less time. Moreover, once the oscillations stopped they can be restarted by bubbling nitrogen. This is clearly seen in Figure 2 in which the gases are bubbled alternately. After a period of no oscillations with oxygen bubbling, they restart by changing to nitrogen. When the oscillations stop completely, the state of oxidation of the cerium will depend on whether there is an excess of oxidizing or reducing agent. (b) The induction time in most cases is larger for the oxygen reaction. This is more pronounced in the case of the lower cerium concentrations in which the oxygen induction times are about twice that of the nitrogen induction times. This is so since the induction time depends strongly on the cerium concentration, decreasing as the latter is increasing.5d Thus, the differences between oxygen and ni-
I
0
40
80
120
t 160
i I 200 240
1 280
320 360
Reaction Time lmin)
Figure 1. The period time vs. the time of the reaction when nitrogen (X) oxygen (0)are bubbled into the system. The start and end of the oscillations are marked with upward or downward arrows, respectively. The temperature is 25 'C.
trogen become more pronounced as cerium concentration decreases. (c) The period times change with reaction times much faster in the case of oxygen. In most cases the oxygen rate is about twice that of the nitrogen. There are two exceptions to these results. Line 1of Table I shows a negative slope for the oxygen case, i.e., the period time decreases as the reaction proceeds. In line 7 of Table I, all oxygen oscillations have shorter periods than the nitrogen ones, i.e., the positions of the plots of Figure 1are reversed. We do not have any explanation for these unusual experimental results. It seems there are still some experimental factors which are beyond our understanding and which influence the results. We shall disregard these exceptional results in what follows. (d) When the gases are bubbled alternately (Figure 2), each nitrogen section has a slope 2-3 times larger than the average slope, while the latter is about the same as in Table I. Each oxygen section is decreasing although, as a whole, the period increases. The greater slope of the nitrogen sections shows that the reaction intermediates which occur in the presence of oxygen, such as peroxides and peroxy radicals: remain in the solution and influence the reaction even after the oxygen is expelled. Results of Calculations It was shown by Roux and Rossi3 that oxygen is not absorbed and does not affect the reaction between cerous ions and bromate. Therefore, no effect of oxygen is expected to be found in reactions 1-5 in our mechanism. On the other hand, as stated earlier, Barkin et al.* found a profound effect of oxygen on the reduction of ceric ions by malonic acid. Roux and Rossi3also have found an effect of O2 on the complete BZ reaction, and so only reaction 6 is expected to be affected by 02,since this reaction sums up all the reactions causing the reduction of ceric ions by malonic acid and its derivatives, and all the reactions creating bromide ion from the organic bromo derivatives of malonic and the other organic acids and radicals found during the reduction. All these complicated reactions are summed up and described by rather empirical constants, namely, the rate constant, kg, and the stoichiometric factor, g. It is reasonable to assume that oxygen may change both these values (provided of course that we adhere to the same mechanism). Figure 3 shows a typical plot of ceric ion concentration vs. time, where the values of k6 and g are those given above and will be referred to as the nitrogen conditions. The
2954
K. Bar-Eli and S. Haddad
The Journal of Physical Chemistry, Vol. 83, No. 23, 1979
TABLE I
__
[MA],
_ I _ . -
___I___
M
[ C e 4 + ]x 10->M
0.05 0.1 0.1 0.05 0.05 0.1 0.15 0.05 0.1 0.05 0.1
0.1 0.1 0.1 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.5
[BrO;],
M
0.1 0.05 0.1 0.2 0.05 0.05 0.05 0.1 0.1 0.2 0.18
induction time. min '
0,
oscillations end,a min
98 136 126 104 18 36 48 22 21 14 20
41 64 76 94 18
17 13 15 15 14 14
1st period,h s
0,
0,
N2
260 230 28 2 >330 55 169 98 56 96 59 69
52 43 42 30 104 68 55 60 41 34 23
24 32 30 24 84 44 94 50 44 30 24
N2
-
slope,c s/min 0,
temp, "C
"2
-0.17 0.17
0.076 0.15 0.087 0.005 0.68 0.33 0.6 0.44 0.38 0.19 0.24
0.17 0.05 1.25 1.36 1.08 1.36 1.38 0.60 1.05
7
31 31 25 25 25 25 25 25 25 25 25
a The oscillations in the nitrogen reaction last for at least 1 2 h in all cases. In some cases the first period marked is the minimal one after a slight initial dip (see ref 5d). The slope is the best linear fit in spite of the obvious curvature; it serves only as a rough measure.
7T
02
n --I 02
N2
1
02
N2
N2
02
0
.-E
j2T 20
16
14
20
no osc
. ..
...
24
I-
60
x
x x
0os
X
x x x
40
7
x x
X
X
X
-L -L a0 IOC
1.
u -_I 20 148
- 1,
160
iao 200
I 260 280 30 l d 10 24
320 340 360
R e o c t i o n Time(min1
Figure 2. The period time vs. the reaction time when N, ( X ) and O2(0)are bubbled alternately. [MA] = 0.1 M, [BrO,-] 1X M. The temperature is 28 O C .
= 0.05 M, [Ce4+] =
rn
0.0006 term oxygen conditions will be used for calculations with k6 = 5.3 M-l s-*and g = 0.2. These values are somewhat arbitrary and the rational for using them is explained 0 0005B D below. The pattern shown in the figure appears in all calculations and experiments: a region without oscillations 0 0004 (the induction time), a region of regular oscillations with increasing period, and a region (not shown) of slow ap5 TO 0003 proach to equilibrium without oscillations. u The following description gives a detailed account of the 0 u series of events from the start of the reaction. Under the 0 0002 initial conditions [Br03-] = 0.1 M, [MA] = 0.1 M, [Ce3+] = 0.7 X lo9 M, [Br-] = 1.5 kJ04 M, and all other species 0 0001 were zero at t = 0. The effe'ct of changing the initial conditions was investigated in an earlier p ~ b l i c a t i o n . ~ ~ A When other initial conditions prevail, the qualitative ~0000' ! I IbO 2Ao 3bo 4 6 0 5bo 60i description will be the same, although the actual values TIME l s e c ) will of course differ. Many of the details given below can Figure 3. Calculated ceric ion concentrationvs. time. Initial conditions: only be obtained by a careful examination of the solutions [MA] = [BrO,-] = 0.1 M, [Br-] = 1.5 X IO-' M, [Ce3+] = 7 X of the relevant differential equations. Special attention M. is given to the differences between the two conditions, without the presence of malonic acid. These authors obnamely, those of nitrogen and those of oxygen. tained a very fast increase of ceric ions under similar initial Region A. The bromide ion is consumed in a very short conditions (see Figure 3 in ref 5b). However, the presence time (
