7740
J . Phys. Chem. 1991, 95, 7740-7742
A Mechanistic Study of Some Oscillatory Reactions John Happel* Department of Chemical Engineering and Applied Chemistry, Columbia University, New York, New York 10027
and Peter H. Sellers The Rockefeller University, 1230 York Avenue, New York. New York 10021 (Received: February 26, 1991; In Final Form: May 6, 1991)
Since the discovery of the Belousov-Zhabotinski (BZ) reaction there has been increasing interest in understanding such systems of oscillatory reactions. Aside from the detailed kinetics of these networks, they must necessarily be characterized by more than a single steady-state mechanistic sequence leading to the observed overall chemical reaction. Therefore, the enumeration of all possible sequences corresponding to a given set of elementary reaction steps is of basic interest. In this paper we analyze several oscillatory reactions by a method that we have developed and applied to a variety of chemical systems during recent years.
Introduction This paper is concerned with a fundamental approach to chemical systems that oscillate, undergoing periodic changes in concentrations of intermediates. In recent years, as noted by Borman,' there has been an explosion of interest in such systems, which often exhibit chaotic features. NoyesZobserves in a comprehensive account of research on chemical oscillators that most chemists twenty years ago either had never heard of oscillatory reactions or else believed that the few alleged examples were artifactual. This situation has now completely changed with many different groups actively engaged in various aspects of the subject. By far the most studied and best example of a chemical oscillator was discovered by the Russian scientist Belousov who observed periodic color changes in the oxidation of an organic substrate such as malonic acid by acidic bromate catalyzed by a cerium ion redox couple. Belousov had difficulty in publishing his findings but they were finally brought to the attention of western chemists by Zhabotinsky in 1970, who showed that oscillations in the concentrations of intermediates were the cause of the color changes that Belousov had observed. Noyes and co-workers have thoroughly investigated the mechanism of this system, now called the Belousov-Zhabotinsky (BZ) reaction. The main features of the mechanism were studied by Field, Koros, and Noyes.' Other homogeneous redox relaxation oscillators considered by Noyes2 and co-workers included the Bray-Liebhavsky (BL), and Briggs-Rauscher (BR) reactions. Independent reaction routes developed by Noyes have been studied by Masuda and Nakamura4 who found that the generalized stoichiometric number theory originally developed by Horiuti and Nakamuras could be advantageously applied to the study of these systems. In a further study of the BelousovZhabotinsky (BZ) reaction Masuda6 applied this interesting theory to confirm the two overall sets of mechanistic steps found by Noyes et ale3 Masuda also found an additional route necessary for more complete description of this reaction that Noyes had not found and presented further analysis of a reduced mechanism that Noyes had developed. We have previously presented a method for characterizing complex chemical systems' and applied it to studies of homogeneous, heterogeneous, catalytic, and enzyme reactions. Our method, in addition to finding the linearly independent mechanisms
as shown by the Horiuti-Nakamura method, uses a combinatorial approach to develop additional cycle-free mechanisms. In the present paper, we further investigate the possible conditions for occurrence of the BZ, BL, and BR reactions as described by Noyes. We show that a more complete listing of possible mechanisms exists than was obtained by either Noyes or Masuda. Methodology In the study of a chemical reaction, the first step is often the proposal of appropriate mechanisms showing how elementary steps may be combined to produce observed overall reactions. We have shown' how to determine a unique set of possible mechanisms corresponding to an initial choice of elementary reactions. These mechanisms, which we have termed direct, demonstrate the various ways that an overall reaction can be broken down into elementary reactions. Each such direct mechanism is irreducible in the sense that it cannot be separated into submechanisms, each of which produces the same overall reaction. What we have called a direct mechanism is a formalization of what is usually called simply a mechanism in the chemical literature without an explicit definition being given. We have treated a number of complex reaction systems in heterogeneous catalysis8 using this procedure. More recently it has been discussed by Ostrovski et aL9 as applied to computer programs in kinetics, and by de Bokx et all0 in the context of a mechanism for methanol decomposition. To understand and confirm the results we obtain it is not necessary for the reader to follow the mathematical details involved, which are given in the reference^.^.^ In the following sections we will illustrate its applicability in a readily demonstrable manner to the oscillatory reactions considered. The Belousov-Zhabotinsky (BZ) Reaction The reaction network for the BZ reaction considered by Masuda6 consists of l l stages detailed by Ruoff and Noyes," expressed as follows SI:
s2:
S,: Sq:
( I ) Borman, S. Chem. Eng. News 1991, Jan 21. Noyes, R . M. J. Phys. Chem. 1990, 94, 4404. Field, R . J.; Koros, E.; Noyes, R. M. J . Am. Chem. SOC.1972, 94,
(2) (3) 8649. (4) (5) (6) (7) 1057.
Masuda, M.; Nakamura. T. Chem. Eng. Commun. 1989, 82, 245. Horiuti, J.; Nakamura, T. Z.Phys. Chem., N . F. 1957, I / , 358. Masuda, M. J. Chem. Phys. 1990, 92, 6030. Happel, J.; Sellers, P. H.; Otarod, M. Ind. Eng. Chem. Res. 1990, 29,
0022-3654/91/2095-7740$02.50/0
S5:
-
+ Br- + 2H+ HBr02 + HOBr HBr02 + Br- + H+ - 2HOBr Br03- + HBr02 + H+ - 2Br02 + H 2 0 Br02 + M"+ + H+ - HBr02 + M("+I)+ BrOy
2HBr02
- Br0,- + HOBr + H+
(8) Happel, J.; Sellers, P. H.Adu. Cmal. 1983, 32, 273. (9) Ostrovski, G . M.;Syskin, A. G . ; Snagovski, Yu S.I n f . Chem. Eng. 1989. 29. 435. (IO) de Bokx, P. K.; Balenende, A. R.; Geus, J. W. J. Carol. 1989, 117: 467. ( 1 1 ) Ruoff, P.; Noyes, R. M. J. Chem. Phys. 1986, 84, 1413.
0 1991 American Chemical Society
Mechanistic Study of Oscillatory Reactions
The Journal of Physical Chemistry, Vol. 95, No. 20, 1991 7741
+ Br- + H+ - Br2 + H 2 0 R H + Br2 - RBr + Br- + H+ HOBr + R' - ROH + Br' R H + Br' - Br- + H+ + R'
HOBr
s6: s7: Sa: s9:
SIO:
RH
+
+
-
+
+
The Bray-Liebhafsky (BL) Reaction The BL reaction constitutes another system studied by Noyes2 and co-workers. Its mechanism is not as well understood as is the BZ reaction, and its elementary reactions have not as yet been elucidated. Some proposed reaction steps have been listed by Noyes as follows:
s3:
+ 5 H 2 0 2+ 2H+ - I2 + 5 0 2 + 6 H 2 0 I2 + 5 H 2 0 2- 2103- + 4 H 2 0 + 2H+ I- + H202 + H+ HOI + H2O HOI + H202 I- + 02 + H2O + H+
2103-
(3) This series of pseudoelementary steps is consistent with the overall stoichiometric equation 2H20 2H20 02 (4) s4:
D E F
+
Br0< 3RH H+ 2ROH RBr H 2 0 (2) We have employed single arrows to designate the directions of reactions, including not only irreversible steps but those with the indicated net directions. In results reported here it is not necessary to make such a distinction. There is a total of 15 species in eq 1. If the 6 species in eq 2 are considered to be terminal species, the remaining 9 species may be regarded as intermediates. Using our methodology, we find that there are six mechanisms whereby steps may be combined to result in eq 2. These mechanisms are listed in Table I. In Table I each of the six mechanisms A-F can be verified by adding the species corresponding to the number of occurrences of the steps sI-sIIas listed in eq 1. Such an addition corresponding to each of the rows will result in a mechanism that produces the overall reaction, eq 2. The designations A, B, and C agree exactly with reactions listed in eq 13a-I 3c by Masuda.6 Mechanisms B and C, as noted by her, correspond to the two mechanisms of Ruoff and Noyes." Mechanism A was not found by them but was reported by Masuda. Table I lists three additional mechanisms based on the assumption that the separate steps s l s l lcould occur in both directions. As listed by Ruoff and Noyes, all steps are taken to occur in one direction. On this basis, mechanism E would be ruled out because ss must occur in the negative direction for that mechanism. Similarly F would be ruled out because sl must occur in the negative direction. However, D requires all steps to occur in the positive direction and thus represents another possibility to consider in addition to those mentioned by Noyes and Masuda.
-
+
There is a total of eight species listed in eq 3. Considering the three species in eq 4 as terminal, there remain five intermediates. Following the same method as used for the BZ reaction, there are only two mechanisms, as shown in Table 11. The Briggs-Rauscher (BR) Reaction The BR reaction was also studied by Noyes2 and others.I2-l3 I n the case of this system, characterized by dramatic color sequences, mechanistic studies are more complete. As in the case of the BZ reaction, our methodology indicates that there may be (12) Noyes, R. M.: Furrow, S. D. J . Am. Chem. Soc. 1982, 104, 45. (13) De Kepper, P.: Epstein. I . R. J . Am. Chem. Soc. 1982, 104, 49.
2 1 0 0 0 -1
B C
- Mn+ + H+ + R*
2R' + H2O R H ROH (1) Here R H is an organic substrate, R' its radical, and Mn+ and M('"+l)+are metal ion catalysts. The 11 steps in eq 1 are consistent with a single overall stoichiometric reaction:
s2:
A
+ M(n+I)+
SII:
SI:
TABLE I: Mechanisms for the BZ Reaction step numbers mechanisms sI s2 s3 s4 s5 s6 s7 s8 0 1 0 1 2 1
0 0 1 0 0 0 2 4 1 1 2 0 0 0 -1 2 4 0
I 1 1 1 1
1 1 1 1 1
1
1
s9 sl0 2 2 0 2 2 0 0 0 4 1 1 2 2 2 0 0 0 4
TABLE 11: Mechanisms for the BL Reaction step numbers mechanisms SI s2 s3
sII 0 0 2 1 0 2
S4
A
1
1
0
0
B
0
0
1
1
TABLE 111: Mechanisms for the BR Reaction step numbers mechanisms A
B C
D E F
sI s2 s3 s, s5 1 1 2 0 0 0 0 0 2 4 0 1 1 1 2 2 0 2 0 0 0 2 2 0 0 0 - 1 1 0 2 4
s7 s8 s9 0 0 1 2 1 1 1 0 1 0 1 1 0 - 1 1 4 2 0 1
s6
0 4 2 0
sIo s l I 1 1 1 1 1 1 1
1
1
1
1
1
additional possibilities worth examining. There are 11 pseudoelementary process steps proposed to describe the system.
s2:
s3: s4:
.
S5:
s6:
s7: Sg:
s9:
SIO: SI 1:
+ 2H+ - H I 0 2 + HOI H I 0 2 + I- + H+ - 2HOI HOI + H202 I- + 0 2 + H+ + H 2 0 103- + HI02 + H 2102' + H20 IO2'+ Mn2+ + H 2 0 - H I 0 2 + Mn(OH)2+ Mn(OH)2+ + H 2 0 2 - Mn2+ + H 2 0 + HOO' IO3-+ I-
SI:
F=
+ 02 2 H I 0 2 - IO3-+ H 0 1 + HS HOI + I- + H+ I2 + H 2 0 2H00'
H202
RH I2 + enol
enol
- RI + I- + H+
(5)
The 1 1 steps in eq 5 correspond to the overall reaction
IO3-+ 2H202+ RH
+ H+ - RI + 20, + 3 H 2 0
(6)
There is a total of 16 species in the system. If the 7 species in eq 6 are taken to be terminal, the remaining 9 species may be regarded as intermediates. With these assumptions, we find that there are 6 mechanisms whereby steps may be combined to result in eq 6. These are listed in Table 111. All six of the mechanisms listed in Table 111 will produce the overall reaction, eq 6. Steps sgs,I, corresponding to steps P( 13)-P( 15) in the article by Noyes? are required in each of the six mechanisms so that they will not change for a mechanism corresponding to eq 6. What we have designated as mechanisms A and B agrees exactly with the sequences listed by Noyes's* eqs 19, 20, and 21. Thus our mechanism A is equal to J, + K of Noyes and our mechanism B is equal to J, + K of Noyes. Mechanisms E and F may be ruled out, if we adopt the restriction given by Noyes that steps sI and s8 can only occur in the positive direction. Discussion In study of oscillatory chemical reaction systems, it is of interest to enumerate all possible steady-state mechanisms that are consistent with a given choice of elementary steps. The procedure
J. Phys. Chem. 1991, 95,7742-7746
7142
discussed in this paper accomplishes this. We have applied our procedure to the three homogeneous oscillators treated by Noyes2 and have shown that there are possible mechanisms in addition to those which he reported. Noyes showed that for the BZ, BL, and BR reactions two mechanisms could be identified for each that together would involve all assumed elementary steps. These are B and C in Table I, A and B in Table 11, A and B in Table 111, respectively. Examination of these tables shows that for the BZ reaction A and D could be combined and for the BR reaction C and D could also be combined in a similar manner. Aside from detailed kinetic considerations there is considerable room for additional speculations as to how mechanisms might be combined. For example, one of the reviewers of this paper ob-
served that paths B and C proposed by Noyes for the BZ reaction system would each employ entirely different steps, if steps s6 and s7 (which occur in all mechanisms listed in Table I) were combined to give a separate additional overall reaction. The stoichiometry of s6 s7 is R H + HOBr RBr HzO (7)
+
-
+
so, if this reaction could occur separately, an additional terminal species, HOBr, would be required. The kinetics of two overall reactions occurring simultaneously would then be involved. We suggest that a procedure such as that presented here could be advantageously employed in the course of study of oscillatory systems in order to ensure that no viable combination of steps is omitted from consideration.
Reactlon of Ketene Ions with Ammonla M. Iraqi, C. Lifshitz,*lt Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904. Israel
and B. C.Reuben* Department of Chemical Engineering, South Bank Polytechnic, London SE1 OAA, England (Received: February 26, 1991; In Final Form: May 24, 1991)
Reactions of ketene ions with NH3, ND,,H20, and CHI were investigated in a selected ion flow tube (SIFT).There were no observable products for H 2 0 and CH, and no ion/neutral complex stabilization in any of the systems investigated. The ammonia system demonstrated two reaction channels, in agreement with previous FTICR data (i) distonic ion CH2NH3'+ formation, with a branching ratio of 0.2 and (ii) proton transfer, with a branching ratio of 0.8. The overall second-order rate constant for NH, is (2.2 h 0.15 ) X IO4 cm3 molecule-' s-l, in agreement with the gas kinetic iondipole collision rate. Isotope scrambling was studied for primary (CH2CO+)and for secondary (CH2NX3'+and NX4+,X = H or D) proton-transfer reactions with ND,; CH2NH3'+ appears to transfer an X+ ion to ND, without any scrambling. CH2CO'+ undergoes reaction with partial scrambling and NX4+seems to react with almost complete scrambling. The results are compared with those of Adams, Smith, and Henchman on the NH4+/ND, system.
Introduction Considerable amount of work has been done on the structure of gas-phase ions to identify isomeric ions and to investigate their possible interconversion by movement over barriers on potential energy surfaces.' Of particular interest is the role of ion/neutral complexes in unimolecular decompositions,2 such as ion/dipole complexes, e.g., the ketene ion/water complex? [CHzCO'+/H20] and ion-indud dipole complexes, e.g., the ketene ion/methane complex? [CH2CO'+/CH4]. The possibility arises of approaching these isomeric ions not only by fragmentation of larger molecules but also by bimolecular collision processes. Noteworthy is the paper by Drewello et aLs on the distonic ionbs CH2NH3'+ generated both from ionized acetamide and from the isomeric complex of a ketene ion plus ammonia [CH2CO'+/NH,]. It was noted' that there had been suggestions that nucleophilic substitutions involving radical cations were 'forbidden" processes and the reactions should therefore be slow. The substitution reaction
-
CH2=C=O'+ + N H 3 CH2NH,'+ + C O (la) was observed in contrast to be f a ~ i l ebut , ~ its rate has not been reported. The aim of this work was to search for other bimolecular processes analogous to the above, to try to collisionally stabilize the short-lived complexes from bimolecular collisions such as 'Archie and Marjorie Sherman Professor of Chemistry.
[CH2CO'+/NH3], and to investigate the ketene ion-ammonia system in more detail with particular attention to rates and isotope effects. Experimental Section The experiments were performed on a selected-ion flow tube (SIFT) described r e ~ e n t l y . ~ -The ' ~ reactant ions are generated in a suitable ion source. They are mass selected by a quadrupole mass filter and injected into the flow tube by a helium carrier gas using a Venturi inlet. A neutral reactant is introduced into the flow tube at an appropriate distance downstream to assure laminar (1) Burgers, P. C.; Terlouw, J. K. Spec. Period. Rep. Muss Spectrom. 1989, 10, 35. (2) McAdoo, D. J . Mass Spectrom. Rea. 1988, 7, 363. (3) Heinrich, N.; Schwarz, H . Inr. J . Mass Specfrom. Ion Processes 1987, 79, 295. (4) Heinrich, N.; Louage, F.; Lifshitz. C.; Schwarz, H. J . Am. Chem. Soc. 1988, 110, 8183. ( 5 ) Drewello, T.; Heinrich, N.; Maas, W. P. M.; Nibkring. N. M . M.; Weiske, T.; Schwarz, H . J . Am. Chem. SOC.1987, 109,4810. (6) Yates, B. F.; Bouma, W. J.; Radom, L. J . Am. Chem. Soc. 1987,106, 5805. (7) Gross,M. L.; McLafferty, F. W. J . Am. Chem. Soc. 1971, 93, 1267. (8) Sack, T. M.; Cerny, R . L.; Gross,M . L. J . Am. Chem. Soc. 1985,107, 4562. (9) Iraqi, M.; Peres, M.; Petrank, A.; Lifshitz, C. Rupid Commun. Mats Specfrom. 1990, 4, 323. (IO) Iraqi, M.; Petrank, A.; Peres, M.; Lifshitz, C. Inr. J . Muss Specfrom. Ion Processes 1990, 100, 679.
0022-3654/91/2095-7742$02.50/00 1991 American Chemical Society
