Kinetic study of the Ce(III)-, Mn(II)- or Fe(phen)32+-catalyzed Belousov-Zhabotinsky reaction with ethyl hydrogen malonate

Article abstract of DOI:10.1002/(SICI)1097-4601(2000)32:1<52::AID-JCK6>3.0.CO;2-7

In a stirred batch reaction, Fe(phen)₃²⁺ ion behaves differently from Ce(III) or Mn(II) ion in catalyzing the bromate-driven oscillating reaction with ethyl hydrogen malonate [CH₂COOHCOOEt, ethyl hydrogen malonate (EHM)]. The effects of N₂ atmosphere, concentrations of bromate ion, EHM, metal ion catalyst, sulfuric acid, and additive (bromide ion or bromomalonic acid) on the pattern of oscillations were investigated. The kinetic study of the reaction of EHM with Ce(IV), Mn(III), or Fe(phen)₃³⁺ ion indicates that under aerobic or anaerobic conditions the order of reactivity toward reacting with EHM is Mn(III)>Ce(IV)?Fe(phen)₃³⁺, which follows the same trend as that of the malonic acid system. The presence of the ester group in EHM lowers the reactivity of the two methylene hydrogen atoms toward bromination or oxidation by Ce(IV), Mn(III), or Fe(phen)₃³⁺ ion. No good oscillations were observed for the BrO₃-CH₂(COOEt)₂ reaction catalyzed by Ce(III), Mn(II), or Fe(phen)₃²⁺ ion. A discussion of the effects of oxygen on the reactions of malonic acid and its derivatives (RCHCOOHCOOR′) with Mn(III), Fe(phen)₃³⁺ ion is also presented.

Full text of DOI:10.1002/(SICI)1097-4601(2000)32:1<52::AID-JCK6>3.0.CO;2-7

Kinetic Study of the
Ce(III)-, Mn(II)- or
2
؉
Fe(phen)3 -Catalyzed
Belousov–Zhabotinsky
Reaction with Ethyl
Hydrogen Malonate
W.-T. HSU, J.-J. JWO
Department of Chemistry, National Cheng Kung University, Tainan, Taiwan 701, Republic of China
Received 5 February 1999; accepted 15 September 1999
2ϩ
ABSTRACT: In a stirred batch reaction, Fe(phen)3 ion behaves differently from Ce(III) or Mn(II)
ion in catalyzing the bromate-driven oscillating reaction with ethyl hydrogen malonate
[CH2COOHCOOEt, ethyl hydrogen malonate (EHM)]. The effects of N2 atmosphere, concen-
trations of bromate ion, EHM, metal ion catalyst, sulfuric acid, and additive (bromide ion or
bromomalonic acid) on the pattern of oscillations were investigated. The kinetic study of the
3ϩ
reaction of EHM with Ce(IV), Mn(III), or Fe(phen)3 ion indicates that under aerobic or an-
aerobic conditions the order of reactivity toward reacting with EHM is Mn(III) Ͼ Ce(IV) ϾϾ
3
ϩ
Fe(phen)3 , which follows the same trend as that of the malonic acid system. The presence
of the ester group in EHM lowers the reactivity of the two methylene hydrogen atoms toward
3
ϩ
bromination or oxidation by Ce(IV), Mn(III), or Fe(phen)3 ion. No good oscillations were
2
ϩ
observed for the BrO3--CH2(COOEt)2 reaction catalyzed by Ce(III), Mn(II), or Fe(phen)3 ion.
A discussion of the effects of oxygen on the reactions of malonic acid and its derivatives
3
ϩ
(RCHCOOHCOOR’) with Ce(IV), Mn(III), or Fe(phen)3 ion is also presented. ᭧ 2000 John Wiley
& Sons, Inc. Int J Chem Kinet 32: 52–61, 2000
INTRODUCTION
bromination of an organic substrate by an acidic bro-
mate. Field et al. [4] have elucidated a detailed mech-
anism of the Ce(III)-catalyzed BZ reaction with ma-
lonic acid. A number of modifications of the classical
BZ reaction have been reported. Ko¨ro¨s et al. [5] iden-
tified two different kinds of metalion catalysts for the
BZ reaction, namely, the labile Ce(III)/Ce(IV) and
Mn(II)/Mn(III) complexes with reduction potentials of
The Belousov [1]–Zhabotinsky [2] (BZ) reaction has
attracted scientists for more than two decades. Ac-
cording to a classification by Noyes [3], the classical
BZ reaction is a metal-ion-catalyzed oxidation and
Correspondence to: J.-J. Jwo (jjjwo@mail.ncku.edu.tw)
Contract grant sponsor: National Science Council of the Repub-
lic of China
Contract grant number: NSC 85-2113-M-006-011, NSC 86-
2113-M-006-011).
about 1.5 V and the inert Fe(phen)3 ϩ/Fe(phen)3 ϩ and
2
3
Ru(phen)3 ϩ/Ru(phen)3 complexes with reduction
potentials of about 1.0–1.3 V.
2
3ϩ
᭧ 2000 John Wiley & Sons, Inc.
CCC 0538-8066/00/010052-10
A number of other organic substrates such as citric

CATALYZED BELOUSOV–ZHABOTINSKY REACTION WITH ETHYL HYDROGEN MALONATE
53
acid [1,6], saccharides [7], ethyl acetoacetate [8],
oxalic acid/acetone [9], and mandelic acid/ketone [10]
have been shown to exhibit oscillations during
lows: C, 35.29; H, 4.12; with C, 34.91 and H, 4.06
3
ϩ
found. Solutions of Mn(III) [7] and Fe(phen)3 [14]
were freshly prepared according to the literature meth-
ods. The solution of ethyl hydrogen malonate (EHM)
was freshly prepared by neutralizing a known amount
of KEHM salt in H2SO4 solution just before carrying
out each run.
Ce(III)ion
catalysis,
but
malonic
acids
[RCH(COOH)2, R ϭ Me, Et, Bu, Ph, and Br] [11–
17] have been studied more than any other. It is ob-
served that the substituent R affects the reactivity of
RCH(COOH)2 toward bromination and toward reac-
3
ϩ
tion with Ce(IV), Mn(III), and Fe(phen)3 ions and
modifies the pattern of oscillations. It is generally ac-
cepted that the two adjacent carboxylic groups in
RCH(COOH)2 activates the methylene hydrogen atom
and also facilitates the complex formation during the
oxidation of RCH(COOH)2 by metalion oxidation like
the Ce(IV) ion.
Procedures
The oscillating reactions were followed potentiomet-
rically with a bromide-ion-selective electrode (Orion
94-35) against an Orion 90-02 double junction elec-
trode [19]. The kinetics of the reactions of EHM with
3ϩ
Ce(IV), Mn(III), and Fe(phen)3 ions were studied
spectrophotometrically by following [Ce(IV)],
In this article, we report the study of the Ce(III)-,
Mn(II)-, or Fe(phen)3 ϩ-catalyzed BZ reaction with
2
[Mn(III)], and [Fe(phen)3 ϩ] at 320 nm (⑀ ϭ 5.52 ϫ
2
ethyl hydrogen malonate (EHM, CH2COOHCOOEt).
The kinetics of the reaction of EHM and Ce(IV),
1
1
1
103 MϪ cmϪ ), 310 nm (⑀ ϭ 1.31 ϫ 103 MϪ1 cmϪ ),
and 480 nm (⑀ ϭ 1.05 ϫ104 MϪ1 cmϪ ), respectively,
1
Mn(III), or Fe(phen)3 ϩ ion were investigated. Ration-
3
with a conventional spectrophotometer (Hitachi U-
2000).
alization of the experimental results is also given.
The organic substrate was in great excess over the
metal ion. The observed pseudo-first-order rate con-
stant (kobs) was calculated from the linear-least-squares
(LLS) fit of the plots of ln(At Ϫ Aϱ) vs. time for
EXPERIMENTAL
Materials
Ce(IV) and Mn(III) ions and ln(Atϩ Ϫ At) vs. time
d
for Fe(phen)3 ϩ ion, where the time interval d is about
2
Ammonium ferrous sulfate (99%), manganese(II) ac-
etate tetrahydrate (99%), and cerium(III) nitrate hex-
ahydrate (98.5%) (Merck); ammonium cerium(IV)
nitrate (guaranteed reagent, Hanawa); 1,10-phenan-
throline monohydrate (guaranteed, Ishizu); and diethyl
malonate (99%, Lancaster) were used in this work.
Other reagents used were of the highest grade chem-
icals commercially available. Deionized water from
reverse osmosis (Millipore Milli-RO 20) was used.
Monopotassium salt of ethyl hydrogen malonate
(KEHM, CH2COOEtCOOK) was prepared by modi-
fying the literature method [18]. Next 14 g of KOH
was dissolved in 160 ml of commercial absolute EtOH
and then the solution was filtered to remove any res-
idue. Under magnetic stirring, the KOH solution was
added dropwise throughout 1 h to a warm (ϳ45ЊC)
solution that contained 40 g of diethyl malonate in 160
ml of absolute EtOH. The mixture was kept warm for
3 h and then allowed to stand for 12 h at room tem-
perature. Bright white crystals were formed. The mix-
ture was heated to boiling and the hot solution was
filtered to remove dipotassium malonate. The KEHM
crystals gradually formed on cooling the filtrate were
filtered off and washed with small amounts of absolute
EtOH and ether. A similar procedure was carried out
to recrystallize the KEHM salt.
half of the time needed to reach the maximum absorb-
ance [14]. Product analysis by GC/MS method showed
that propanoic acid (C2H5COOH) is one of the main
products in the reaction of Ce(IV) and EHM.
RESULTS AND DISCUSSION
Characteristics of Oscillations
In a stirred batch experiment, damped oscillations
were observed in the reaction of bromate ion with
ethyl hydrogen malonate (EHM) in aqueous H2SO4
2
ϩ
catalyzed by Ce(III), Mn(II), or Fe(phen)3 ion.
Some oscillating responses of bromide-ion-selective
electrode are shown in Figure 1 [Ce(III)cata-
lyzed], Figure 2 [Mn(II)catalyzed], and Figure 3
[Fe(phen)3 ϩcatalyzed].
2
The characteristics of oscillations depend on the
concentrations of bromate ion, ethyl hydrogen malo-
nate, metalion catalyst, and sulfuric acid. Generally,
in the Ce(III)- or Mn(II)-catalyzed system a long in-
duction period is required before the onset of oscilla-
tions. Under similar conditions, the Ce(III)- or Mn(II)-
catalyzed BZ reaction with EHM exhibits
a
considerably longer induction period than that of the
corresponding BZ reaction with malonic acid (MA)
The analysis calculated for C5H7O4K was as fol-

54
HSU AND JWO
1D and 2D) and it showed an inhibition effect on the
2
ϩ
Fe(phen)3 system (Fig. 3D). The initial presence of
bromomalonic acid (BrMA) shortened the induction
period of the Ce(III) system (Fig. 1E), whereas it in-
2ϩ
hibited the reaction of the Fe(phen)3 system (Fig.
3E).
Interesting two-stage dual-frequency oscillations
were observed for the Mn(II) system with the initial
addition of BrMA (Fig. 2E). For the Ce(III) system,
Ϫ
increasing [BrO3 ] increased the induction period and
the frequency of oscillations (Figs. 1A, 1G, and 1F).
Ϫ
For the Mn(II) system, increasing [BrO3 ] increased
the induction period and the period of oscillations
2
ϩ
(Figs. 2A, 2G, and 2F). For the Fe(phen)3 system,
Ϫ
Figure 1 Potentiometric traces of log[Br ] vs. time for
Ϫ
the BrO3 -EHM-Ce(III) oscillating reaction at 25ЊC.
Ϫ
[BrO3
] ϭ (A–E; H–N) 0.0315 M; (F) 0.0630 M; (G)
o
0.0075 M; [EHM]o ϭ (A–G; J–M) 0.0500 M; (H) 0.0890
M; (I) 0.0250 M; (N) 0 M; [Ce(III)]o ϭ (A–I; L–N)
Ϫ
3
Ϫ
4
Ϫ3
1.00 ϫ10 M; (J) 5.00 ϫ 10 M; (k) 2.00 ϫ10 M;
[H2SO4]o ϭ (A–K; N) 1.00 M; (L) 1.50 M; (M) 0.500 M;
[MA]o ϭ (A–M) 0 M; (N) 0.0500 M;[NaBr]o ϭ (A–C; E–
Ϫ
3
N) 0 M; (D) 4.00 ϫ 10 M; [BrMA]o ϭ (A–D; F–N) 0
M; (E) 4.00 ϫ 10 M; aerobic: (A; C–N); anaerobic (N2):
Ϫ
3
(B); agitation rate: (A–BB; DD–N) 150 rpm; (C) 0 rpm.
(Fig. 1, A vs. N; Fig.e 2, A vs. N). Similar to the MA
system, the Fe(phen)3 ϩ-catalyzed BZ reaction with
2
EHM (Fig. 3) oscillates with an induction period con-
siderably shorter than that of the Ce(III)- or Mn(II)-
catalyzed system (Figs. 1 and 2).
Under an N2 atmosphere, both the induction period
and the period of oscillations were increased for the
Ce(III) or Mn(II) system (Figs. 1B and 2B). The os-
cillating behavior was affected significantly by the rate
of agitation, and without agitation no oscillations were
observed for the Ce(III) or Mn(II) system (Figs. 1C
and 2C). In contrast, the N2 atmosphere and the rate
of agitation showed relatively less effects on the os-
cillating pattern of the Fe(phen)3 system (Figs. 3B
and 3C). In most of this work, the rate of agitation was
kept constant at 150 rpm.
The initial presence of bromide ion decreased the
induction period of the Ce(III) or Mn(II) system (Figs.
Ϫ
Figure 2 Potentiometric traces of log[Br ] vs. time for
Ϫ
the BrO3 –EHM–Mn(II) oscillating reaction at 25 ЊC.
Ϫ
[BrO3
] ϭ (A–E; H–P) 0.0630 M; (F) 0.0940 M; (G)
o
0.0390 M; [EHM]o ϭ (A–G; J–M) 0.0300 M; (H) 0.0230
M; (I) 0.0450 M;(N–O) 0 M; (P) 0.0210 M; [Mn(II)]o ϭ
(A–I; L–P) 3.00 ϫ 10 M; (J) 5.00 ϫ 10 M; (K)
1.00 ϫ 10 3 M; [H2SO4]o ϭ (A–K; N–P) 1.00 M; (L) 1.50
M; (M) 0.500 M; [MA]o ϭ (A–M) 0 M; (N) 0.0300 M; (O–
P) 0.0090 M; [NaBr]o ϭ (A–C; E–P) 0 M; (D) 4.00 ϫ 10
M; [BrMA]o ϭ (A–D; F–P) 0 M; (E) 4.00 ϫ 10 3 M; aer-
obic: (A; C–P); anaerobic (N2): (B); agitation rate : (A–B;
D–P) 150 rpm; (C) 0 rpm.
Ϫ
3
Ϫ3
Ϫ
2
ϩ
Ϫ
3
Ϫ

CATALYZED BELOUSOV–ZHABOTINSKY REACTION WITH ETHYL HYDROGEN MALONATE
55
for [H2SO4] ϭ 0.5 M (Fig. 1M). For the Mn(II) sys-
tem, increasing [H2SO4] decreased the induction pe-
riod and the amplitude of oscillations (Figs. 2A, 2L,
2
ϩ
and 2M). For the Fe(phen)3 system, increasing
[H2SO4] decreased significantly the period and the am-
plitude of oscillations (Figs. 3A, 3L, and 3M).
The initial presence of MA caused a substantial ef-
fect on the characteristics of oscillations of the BZ
reaction with EHM. For example, traces of oscillations
of the Mn(II)–EHM–MA BZ system (Fig. 2P) exhib-
ited both the characteristics of oscillations of the
Mn(II)–EHM (Fig. 2A) and the Mn(II)–MA (Fig.
2O) BZ systems. No good oscillations were observed
for the BrO3Ϫ –CH2(COOEt)2 reaction catalyzed by
Ce(III), Mn(II), or Fe(phen)3 ϩ ion.
3
Kinetics
A conventional spectrophotometric method was used
to investigate the kinetics of reactions of EHM with
Ce(IV), Mn(III), and Fe(phen)3 ϩ ions. It was observed
3
that the presence of O2 did not show significant effect
on the rate of the Ce(IV)- or Fe(phen)3 ϩ –EHM re-
3
Ϫ
Figure 3 Potentiometric traces of log[Br ] vs. time for the
action. In contrast, the presence of O2 accelerated the
rate of the Mn(III)–EHM reaction (Fig. 4). Therefore,
the reactant solutions were deaerated with N2 before
starting the kinetic runs. The observed pseudo-first-
order rate constant (kobs) was calculated from the LLS
Ϫ
2ϩ
BrO3 –EHM–Fe(phen) 3
oscillating reaction at 25ЊC.
] ϭ (A–E; H–N) 0.0260 M; (F) 0.0470 M; (G)
o
Ϫ
[BrO3
0.0140 M; [EHM]o ϭ (A–G; J–M) 0.0212 M; (H) 0.0313
M; (I) 0.0108 M; (N) 0 M; [Fe(phen)3 ]o ϭ (A–I; L–N)
2.00 ϫ 10 M; (J) 3.00 ϫ 10 M; (K) 1.00 ϫ 10 M;
[H2SO4]o ϭ (A–K; N) 1.00 M; (L) 1.50 M; (M) 0.500 M;
[MA]o ϭ (A–M) 0 M; (N) 0.0212 M; [NaBr]o ϭ (A–C; E–
2
ϩ
Ϫ
3
Ϫ
3
Ϫ3
Ϫ
3
N) 0 M; (D) 4.00 ϫ 10 M; [BrMA]o ϭ (A–D; F–N) 0
M; (E) 4.00 ϫ 10 M; aerobic: (A; C–N); anaerobic (N2):
Ϫ
3
(B); agitation rate: (A–B; D–N) 150 rpm; (C) 0 rpm.
Ϫ
increasing [BrO3 ] increased the frequency of oscil-
lations (Figs. 3A, 3G, and 3F).
For these three systems, increasing [EHM] de-
creased the induction period and the period of oscil-
lations (Figs. 1A, 1H, and 1I; Figs. 2A, 2H, and 2I;
Figs. 3A, 2H, and 2I). For the Ce(III) system, increas-
ing [Ce(III)] decreased the induction period and the
frequency of oscillations (Figs. 1A and 1J) and no
good oscillations were observed for [Ce(III)] ϭ 2.0 ϫ
10Ϫ3 M (Fig. 1K). For the Mn(II) or Fe(phen)3 ϩ sys-
2
tem, increasing the concentration of metalion catalyst
decreased the frequency of oscillations and increased
significantly the amplitude of oscillations (Figs. 2A,
2J, and 2K; Figs. 3A, 3J, and 3K). The concentration
of Mn(II) ion showed less effect on the induction pe-
riod of the Mn(II) system (Figs. 2A, 2J, and 2K). For
the Ce(III) system, increasing [H2SO4] decreased the
induction period and the period of oscillations (Figs.
1A and 1L) and no good oscillations were observed
Figure 4 Plots of ln(At Ϫ Aϱ) vs. time for the Mn(III)–
Ϫ
4
EHM reaction. [Mn(III)]o ϭ 4.00 ϫ 10 M, [EHM]o ϭ
Ϫ
3
6.00 ϫ 10 M, [H2SO4]o ϭ 1.00 M, 25ЊC, 310 nm.
(a) aerobic; (b) deaerated with N2.

56
HSU AND JWO
Ϫ
1
Ϫ1
Figure 5 Plots of ln(At Ϫ Aϱ) (a, b) or ln(Atϩ Ϫ At) (c)
Figure 6 Plots of kobs vs. [EHM]o for the Ce(IV)–
EHM reaction at various temperatures. [Ce(IV)]o ϭ 1.50 ϫ
d
vs. time for (a) Ce(IV)–EHM, (b) Mn(III)–EHM, and (c)
3
ϩ
Ϫ
Fe(phen)3 –EHM reactions in 1.00 M H2SO4 and at 25ЊC.
10 4 M, [H2SO4]o ϭ 1.00 M, 320 nm. (a) 21.3ЊC, (b) 23.0ЊC,
(c) 25.1ЊC, (d) 27.3ЊC, (e)30.8ЊC.
Ϫ
4
(a) [Ce(IV)]o ϭ 1.50 ϫ 10 M, [EHM]o ϭ 0.0166 M, 320
Ϫ
Ϫ3
nm; (b) [Mn(III)] ϭ 4.00 ϫ 10 4 M, [EHM]o ϭ 6.00 ϫ 10
3
ϩ
M, 310 nm, deaerated with N2; (c) [Fe(phen)3 ]o ϭ 1.00 ϫ
10 M, [EHM]o ϭ 0.200 M, 480 nm.
Ϫ4
fit of the linear plot of ln(At Ϫ Aϱ) vs. time for the
Ce(IV)–EHM or Mn(III)–EHM reaction or the plot
of ln(Atϩ Ϫ At) vs. time for the Fe(phen)3 ϩ –EHM
3
d
reaction (Fig. 5). As shown in Figures 6 and 7, the
Ϫ
1
1
plots of kobs vs. [EHM]Ϫ are linear for the Ce(IV)-
and Mn(III)–EHM reactions. These results are con-
sistent with a Michaelis–Menten mechanism (M1) as
suggested by Kasperek and Bruice [6].
k1
ϩ
1)ϩ
M(n
ϩ
1)ϩ
ϩ EHM E
R
F [M(EHM)](n
kϪ
1
k2
99
ϩ
: Mn ϩ other products (M1)
The derived rate law is shown in Eq. (1), where
ϩ1)ϩ
M(n
ϭ Ce(IV) or Mn(III), and Km ϭ (k ϩ k2)/
Ϫ
1
k1.
ϩ
1)ϩ
ϩ
1)ϩ
Ϫd[M(n
]/dt ϭ k2 [EHM][M(n
]/
(Km ϩ [EHM])
ϩ
1)ϩ
ϭ kobs [M(n
]
(1)
Ϫ
1
Ϫ1
Figure 7 Plots of kobs vs. [EHM]o for the Mn(III)–
EHM reaction at various temperatures. [Mn(III)]o ϭ 4.00 ϫ
The values of k2 and Km obtained from the plots of
Ϫ
kobs 1 vs. [EHM]Ϫ1 at various temperatures are shown
Ϫ
10 4 M, [H2SO4]o ϭ 1.00 M, 310 nm. (a) 17.2ЊC, (b)19.7ЊC,
in Table I. The apparent activation energies calculated
(c) 22.0ЊC, (d) 25.6ЊC (e) 28.2ЊC.

CATALYZED BELOUSOV–ZHABOTINSKY REACTION WITH ETHYL HYDROGEN MALONATE
57
Table I The Rate Coefficients of the Reactions of Ethyl Hydrogen Malonate (EHM) with Ce(IV), Mn(III), and
3
ϩ
Fe(phen)3 Ions at Various Temperatures
T
(ЊC)
k2
Km
(10 M)
T
(ЊC)
k2
Km
(10 M)
T
(ЊC)
k2Ј
M
Ϫ
2
Ϫ
1
Ϫ
2
Ϫ
2
Ϫ
1
Ϫ
2
Ϫ2
Ϫ
1
Ϫ1
(10
s
)
(10
s
)
(10
s )
3
ϩ
Fe(phen)3 –EHM
Reaction
Ce(IV)–EHM Reaction
Mn(III)–EHM Reaction
21.3
23.0
25.1
27.3
30.8
0.491
0.528
0.589
0.723
1.05
3.71
2.63
2.68
2.59
3.41
17.2
19.7
22.0
25.6
28.2
0.460
0.691
0.709
1.07
3.54
4.06
3.09
3.81
3.24
19.0
22.1
25.2
28.3
31.6
0.477
0.552
0.688
0.968
1.39
1.29
1
from the LLS fits of the plots of ln(k2/Km) vs. TϪ1 are
the LLS fit of the plot of ln k2Ј vs. TϪ is 63.6 Ϯ 6.6
1
1
(61.7 Ϯ 13.8 and 70.1 Ϯ 5.1) kJ molϪ for Ce(IV)–
kJ molϪ .
EHM and Mn(III)–EHM reactions, respectively. The
dissociation reaction of Fe(phen)3 ϩ or Fe(phen)3 ϩ ion
is negligible because the values of the first-order rate
constants of both reactions are about twoorders of
3
2
Discussion
Basically, the characteristics of the Ce(III)-, Mn(II)-,
3
ϩ
or Fe(phen)3 ϩ-catalyzed BZ reaction with EHM are
2
magnitude smaller than that of kobs of the Fe(phen)3
–
EHM reaction. For the Fe(phen)3 ϩ –EHM reaction,
the plot of kobs vs. [EHM] is linear (Fig. 8), which
implies that this reaction follows a second-order ki-
netics. The values of the second-order rate constant
(k2Ј) calculated from the LLS fits of the plots of kobs
vs. [EHM] at various temperatures are also shown in
Table I. The apparent activation energy obtained from
3
similar to those of the corresponding classical BZ re-
action with MA. The FKN (Field, Ko¨ro¨s, and Noyes)
mechanism [4] and the more detailed GTF (Gyo¨rgyi,
Tura´nyi, and Field) mechanism [20] are applicable to
rationalize the main features of these systems. It may
be considered that the FKN mechanism contains an
inorganic subset mainly involving reactions of oxy-
bromine species among themselves and with the me-
talion catalyst, and an organic subset involving the re-
actions of organic substrate like malonic acid and its
derivatives with oxybromine species and the oxidized
form of the metalion catalyst like Ce(IV).
Based on the results of the Ce(IV)–MA reaction
[20–23], mechanistic steps (s1–s10) are proposed to
ϩ1)ϩ
rationalize the reaction of EHM with M(n
ion
ϩ
1)
3
(M(n ϩ ϭ Ce(IV), Mn(III), or Fe(phen)3 ϩ).
ϩ1)
s1: M(n ϩ ϩ CH2COOHCOOEt
!: Mnϩ ϩ CB HCOOHCOOEt ϩ Hϩ
s2: 2CB HCOOHCOOEt ϩ H2O
!: CH2COOHCOOEt ϩ HOCHCOOHCOOEt
s3: M(n ϩ ϩ HOCHCOOHCOOEt
!: Mnϩ ϩ HOCB COOHCOOEt ϩ Hϩ
ϩ1)
s4: 2HOCB COOHCOOEt
!: HOCHCOOHCOOEt ϩ O"CCOOHCOOEt
3
ϩ
Figure 8 Plots of kobs vs. [EHM]o for the Fe(phen)3
–
3ϩ
EHM reaction at various temperatures. [Fe(phen)3 ]o ϭ
1.00 ϫ 10 M, [H2SO4]o ϭ 1.00 M, 480 nm. (a) 19.0ЊC,
(b) 22.1ЊC, (c): 25.2ЊC, (d) 28.3ЊC (e): 31.6ЊC.
ϩ1)
s5: M(n ϩ ϩ O"CCOOHCOOEt
Ϫ
4
!: Mnϩ ϩ O"CB COOEt ϩ CO2 ϩ Hϩ

58
HSU AND JWO
s6: O"CB COOEt EF O"CEtCOOD
reactivity toward reacting with EHM is Mn(III) Ͼ
Ce(IV) ϾϾ Fe(phen)3 ϩ, which follows exactly the
3
ϩ1)
s7: M(n ϩ ϩ O"CEtCOOD ϩ H2O
same trend as that of the malonic acid system. For MA,
methylmalonic acid (MeMA), ethylmalonic acid
(EtMA), n-butylmalonic acid (BuMA), phenylmalonic
acid (PhMA), and EHM, the order of reactivity under
aerobic or anaerobic conditions is (PhMA, MA) Ͼ
EHM Ͼ MeMA Ͼ EtMA Ͼ BuMA toward reacting
with Ce(IV) ion [16,17] and is MA Ͼ PhMA Ͼ
MeMA Ͼ (EtMA, BuMA) Ͼ EHM toward reacting
with Mn(III) ion [15,16]. Under aerobic conditions,
the order of reactivity toward reacting with
!: Mnϩ ϩ EtCOOH ϩ CO2 ϩ Hϩ
s8: 2O"CEtCOOD ϩ H2O
!: O"CEtCOOH ϩ EtCOOH ϩ CO2
s9: M(n ϩ ϩ O"CEtCOOH
ϩ1)
!: Mnϩ ϩ O"CB Et ϩ CO2 ϩ Hϩ
3
ϩ
s10: M(n ϩ ϩ O"CB Et ϩ H2O
!: Mnϩ ϩ EtCOOH ϩ Hϩ
ϩ1)
Fe(phen)3 ion is PhMA Ͼ MeMA Ͼ (BuMA,
EtMA) Ͼ MA Ͼ EHM [14,16,17].
In the classical BZ reaction with MA, the bromi-
nation of MA to produce bromomalonic acid (BrMA)
is one of the paths to generate bromide ion. Decreasing
the rate of bromination of organic substrate is expected
to increase the length of the induction period. The rate
of the isotope exchange reaction of EHM in D2O mea-
When the amount of EHM is in excess over that of
ϩ1)ϩ
M(n
ion, the EHMD radical (DCHCOOHCOOEt)
produced in reaction (s1) undergoes the disproportion-
ation reaction (s2) to yield HOCHCOOHCOOEt.
ϩ1)ϩ
When a sufficient amount of M(n
ion is present,
1
sured by using H NMR spectroscopy is about one
HOCHCOOHCOOEt can be oxidized further via re-
action (s3) to produce HOCB COOHCOOEt radical,
which undergoes the disproportionation reaction (s4)
to yield ethyl hydrogen mesoxalate (O"CCOOH-
COOEt). The oxidative decarboxylation reaction of
order of magnitude slower than that of MA. As ex-
pected, the induction period of the Ce(III)- or Mn(II)-
catalyzed BZ reaction with EHM is considerably
longer than that of the corresponding MA system (Fig.
1, A vs. N; Fig. 2, A vs. N). As suggested by Gyo¨rgyi
et al. [20], the ethyl hydrogen bromomalonate
(BrEHM, BrCHCOOHCOOEt) can be produced by
reactions (R2–R4). An attempt to synthesize BrEHM
was unsuccessful. However, the initial presence of
BrMA shows different effects on the Ce(III)-,
ϩ
1)
O"CCOOHCOOEt by M(n ϩ ion (s5) generates the
ethyl glyoxylate radical (O"CB COOEt). Subsequent
reactions (s6–s10) of O"CB COOEtradical rationalize
the production of propanoic acid (EtCOOH). The gen-
eration of carboxylate radical (O"CEtCOOD) via a
rearrangement reaction (s6) of O"CB OOEt radical is
similar to the hypothesis of the carboxylate malonyl
radical (CH2COOHCOOD) in the Ce(IV)–MA reac-
tion [23].
Mn(II)-, and Fe(phen)3 ϩ-catalyzed EHM–BZ sys-
2
tems (Figs. 1E, 2E, and 3E).
(R2): CH2COOHCOOEt ϩ Br2
The characterization of the preceding mechanistic
steps was carried out according to the method devel-
oped by Happel et al. [24–26]. The eight intermediate
!: BrCHCOOHCOOEt ϩ BrϪ ϩ Hϩ
(R3): CH2COOHCOOEt ϩ HOBr
!: BrCHCOOHCOOEt ϩ H2O
species are CB HCOOHCOOEt, HOCHCOOHCOOEt,
HOCB COOHCOOEt, O"CCOOHCOOEt, O"
CB COOEt, O"CEtCOOD, O"CEtCOOH, and O"
ϩ
1)
ϩ
CB Et. The seven terminal species are M(n ϩ, Mn ,
CH2COOHCOOEt, EtCOOH, H2O, Hϩ, and CO2.
The diagonalization of the step-by-species matrix of
(s1–s10) generates one direct overall reaction (R1)
(2s1 ϩ s2 ϩ 2s3 ϩ s4 ϩ s5 ϩ s6 ϩ s7) and one cycle
(2s7 Ϫ s8 Ϫ s9 Ϫ s10). Reaction (R1) was supported
by the spectrophotometric study of the stoichiometry
of the Ce(IV)–EHM reaction.
(R4): CB HCOOHCOOEt ϩ Br2
!: BrCHCOOHCOOEt ϩ BrD
Oxygen effects on the BZ reaction and the oxida-
tion of the organic substrate by the oxidized form of
the metalion catalyst have been studied extensively
[11,14–17,21,23,27–33]. The presence of O 2 may
shorten or lengthen the induction period or the fre-
quency of oscillations. Barkin et al. [21] and Gana-
pathisubramanian and Noyes [29] reported the accel-
eration effects of O2 on the rate of the Ce(IV)–MA
reaction and the rate of generating BrϪ ion in the
Ce(IV)–MA–BrMA reaction. Tkac and Treindl [31]
ϩ1)
(R1): 6M(n ϩ ϩ CH2COOHCOOEt ϩ 2H2O
!: 6Mnϩ ϩ EtCOOH ϩ 2CO2 ϩ 6Hϩ
Under aerobic or anaerobic conditions, the order of

CATALYZED BELOUSOV–ZHABOTINSKY REACTION WITH ETHYL HYDROGEN MALONATE
59
3
ϩ
Table II The Effect of Oxygen on the Reaction of RCHCOOHCOORЈ and Ce(IV), Mn(III), or Fe(phen)3 Ion
3ϩ
RCHCOOHCOORЈ
Ce(IV)
Ref.
Mn(III)
Ref.
Fe(phen)3
Ref.
CH2(COOH)2
A
NS
I
NS
NS
I
21
*
17
17
17
A
A
I
I
I
31
*
A
NS
A
A
A
14
*
CH2COOHCOOEt
MeCH(COOH)2
EtCH(COOH)2
BuCH(COOH)2
PhCH(COOH)2
BrCH(COOH)2
15
15
15
16
15
14
17
17
16
14
16
29,34
I
I
NS
NS
I
A, acceleration; I, inhibition; NS, not significant; *, this work.
ϩ
1)
also found that O2 accelerated the release of BrϪ
ion in the Mn(III)–MA–BrMA reaction. The
RCH(COOH)2-assisted liberation of BrϪ ion from the
(R5): M(n ϩ ϩ RCHCOOHCOORЈ
!: Mnϩ ϩ CB RCOOHCOORЈ ϩ Hϩ
3
ϩ
reactions of Ce(IV), Mn(III), or Fe(phen)3 ion and
BrCR(COOH)2 (R ϭ Me, Et, Bu, or Ph) under aerobic
conditions was also observed by Sun et al. [15], Lin
and Jwo [16], and Chen et al.[17]. Treindll et al. [33]
reported the detailed study of the influence of O2 and
RCH(COOH)2 (R ϭ H, Me, Et, Bu, Ph, and Bz) on
oscillations and the autocatalytic oxidation of the me-
talion catalyst by bromate in the BZ reaction. Their
results indicate that in both the presence and absence
of RCH(COOH)2, oxygen always increases the inflec-
tion time of the autocatalysis when compared with
anaerobic conditions and that the scavenging of
BB rO2 radicals, probably by CB R(COOH)2 and
DOOCR(COOH)2 radicals, affects the inflection time.
It is expected that reactions involving DCHCOOH-
COOEt and DOOCHCOOHCOOEt radicals are similar
to those of CB R(COOH)2 and DOOCR(COOH)2 radi-
cals.
(R6): CB RCOOHCOORЈ ϩ O2
!: OB OCRCOOHCOORЈ
(R7): RCHCOOHCOORЈ ϩ OB OCRCOOHCOORЈ
!: HOOCRCOOHCOORЈ ϩ CB RCOOHCOORЈ
ϩ1)
(R8): M(n ϩ ϩ HOOCRCOOHCOORЈ
!: Mnϩ ϩ OB OCRCOOHCOORЈ ϩ Hϩ
(R9): Mnϩ ϩ OB OCRCOOHCOORЈ ϩ Hϩ
ϩ1)
!: M(n ϩ ϩ HOOCRCOOHCOORЈ
(R10): 2CB RCOOHCOORЈ ϩ H2O
!: RCHCOOHCOORЈ ϩ HOCRCOOHCOORЈ
(R11): 2 CB RCOOHCOORЈ !: (CRCOOHCOORЈ)2
The effects of oxygen on the kinetics of the reac-
ϩ
1)
tions of M(n ϩ ion and MA derivatives (RCHCOOH-
COORЈ) are summarized in Table II. The following
conclusions can be deduced:
(R12): HOOCRCOOHCOORЈ
!: O"CRCOORЈ ϩ CO2 ϩ H2O
Reactions (R6–R8) explain the acceleration effect
ϩ
1)
1. An oxygen-acceleration effect is generally ob-
served in the reactions of CH2(COOH)2 or
CH2COOHCOOEt and Ce(IV), Mn(III), or
of oxygen on the rate of disappearance of M(n ϩ ion.
The inhibition effect of oxygen can be rationalized by
invoking reactions R6 and R9 as suggested by Drum-
mond and Waters [35]. The participation of reactions
R10 and R11 leads to the production of HOCRCOOH-
COORЈ, although Gao et al. [36] have shown that there
is no tartronic acid (HOCH(COOH)2) among the first
molecular intermediates of the Ce(IV)–MA reaction.
As shown in Table II, the presence of oxygen ex-
hibits opposite effects on the reactions of Ce(IV) or
Mn(III) and CH2(COOH)2 and RCH(COOH)2 (R ꢀ
H), probably due to the presence of two reactive meth-
ylene hydrogen atoms in CH2(COOH)2. These obser-
vations may be explained by invoking reactions
(R10–R12). The presence of the substituent R in
Fe(phen)3 ϩ ion.
3
2. An oxygen-inhibition effect is generally ob-
served in the reaction of monosubstituted ma-
lonic acid (RCH(COOH)2) and Ce(IV) or
Mn(III) ion.
3
ϩ
3. The reaction of Fe(phen)3
ion and
RCHCOOHCOORЈ generally requires the as-
sistance of oxygen.
In the presence of oxygen, the following reactions
(R5–R9) are assumed to occur for the reaction of
ϩ
1)
M(n ϩ ion and RCHCOOHCOORЈ.

60
HSU AND JWO
2
RCH(COOH)2 affects the reactivity of CB RCOOH-
COORЈ radicals in the disproportionation and recom-
bination reactions (R10 and R11) and the reactivity of
HOOCRCOOHCOORЈ in its decarboxylation reaction
(R12). It is expected that the presence of the substit-
uent R decreases the reactivities of HOCRCOOH-
COORЈ, (CRCOOHCOORЈ)2, and O"CRCOORЈ
toward further reaction with Ce(IV) or Mn(III) ion,
due to the absence of reactive methylene hydrogen
atom.
Similar to the MA system, the Fe(phen)3 ϩ-cata-
lyzed BZ reaction with EHM oscillates with an induc-
tion period considerably shorter than that of the
Ce(III)- or Mn(II)-catalyzed system. Under aerobic or
anaerobic conditions, the order of reactivity toward
reacting with EHM is Mn(III) Ͼ Ce(IV) ϾϾ
Fe(phen)3 ϩ, which follows the same trend as that of
the MA system. The presence of the ester group in
EHM lowers the reactivity of the two methylene hy-
drogen atoms toward bromination or oxidation by
3
3
The results of this work also strongly support the
observations by Ruoff et al. [33] that the period
lengths of the RCH(COOH)2 –BZ systems in aerobic
conditions show the same trend when the substituent
R of RCH(COOH)2 is varied as in anaerobic condi-
tions. However, the exception is with CH2(COOH)2.
Both Ko¨ro¨s et al. [5] and Smoes [37] have reported
that the BZ reaction with MA catalyzed by
Ce(IV), Mn(III), or Fe(phen)3 ϩ ion.
An oxygen-acceleration effect is generally ob-
served in the reactions of CH2(COOH)2 or
CH2COOHCOOEt and Ce(IV), Mn(III), or
Fe(phen)3 ion. An oxygen-inhibition effect is gen-
erally observed in the reaction of monosubstituted ma-
lonic acid (RCH(COOH)2) and Ce(IV) or Mn(III) ion.
The reaction of Fe(phen)3 ion and RCHCOOH-
COORЈ generally requires the assistance of oxygen.
No good oscillations were observed for the bormate-
diethyl malonate (CH2(COOEt)2) reaction catalyzed
3
ϩ
3ϩ
Fe(phen)3 ϩ ion oscillates without an induction period
2
in contrast to its Ce(III)-catalyzed system. Noyes [3]
has first pointed out that both thermodynamic and ki-
3
ϩ
2
netic arguments indicate that Fe(phen)3 ion should
not oxidize MA by the same mechanism appropriate
for the Ce(IV) ion. This argument is strongly sup-
ported by the results of the kinetic study of the
by Ce(III), Mn(II), or Fe(phen)3 ϩ ion.
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