Isotopic Effect on the Kinetics of the Belousov-Zhabotinsky Reaction

In this work we present results about the deuterium isotope effect on the global kinetics of a Belousov-Zhabotinsky reaction in batch conditions. A nonlinear dependence of the Induction Period upon the percentage of deuterated reactants was found. The isotopic effect on the bromination reaction of malonic acid was evaluated.


Introduction
The Belousov-Zhabotinsky (BZ) reaction represents the most famous example of chemical oscillator [1]. Briefly it consists of a catalytic oxidation of an organic substrate with active methylenic groups, by bromate ions in acidic aqueous solution. The most used substrate is malonic acid (MA), catalysts are generally metal redox couples (Ce(IV)/Ce(III), Mn(III)/Mn(II)) or metallo-complexes (ferroin, Ru(bpy) 3 2+ ).
From 1972 various detailed kinetic models have been proposed to explain the oscillatory behavior of the BZ reaction. The first and simplest is known as the FKN [2], which involves 18 elementary steps and 21 chemical species but can be simplified considering the role of three key species: HBrO 2 as exchange intermediate, Bras control intermediate and M ox , i.e. the oxidized form of the catalyst, as regeneration intermediate. Successively other models have been proposed to improve or fix some aspects of the FKN mechanism: the radicalator model [3], the GTF model [4] and the MBM model [5].
Isotopic effect due to the Hydrogen substitution by Deuterium is a subject of widespread interest among the chemical kinetics discipline. Several organic and inorganic reactions (enolization, substitution, exchange) have been studied in the past for a large class of compounds. The implications of the H-D substitution are also important for the kinetics and the rate of more complex reaction mechanisms. As an example, in the past, the kinetics of the isotope exchange reactions of RCH(COOH) 2 (R=H, D, Me, Et, Bu, and Ph) in D 2 O solutions were studied by using 1 H NMR spectroscopy, and the implications for the BZ reaction have been discussed [6].
The influence of deuterated compounds on the global kinetics of BZ reaction was discussed by Karavaev et al. for Ru-catalyzed systems [7]. It was found that the substitution of H 2 O by D 2 O as solvent caused a complete suppression of the oscillating regime.
In our study we found a nonlinear increment of the Induction Period (IP) upon the addiction of deuterium substituted reactants for a Ce-catalyzed BZ system.
The Induction Period is the preoscillatory stage in which [Br -] is increased and brominated organic species are accumulated. According to the GTF model [4] the length of IP is determined by the concentration of bromomalonic acid (BrMA). The crucial amount of BrMA necessary for the onset of oscillations is produced through two main pathways: (a) the bromination of the enol form of malonic acid by Br 2 and (b) the reaction between Br 2 and the malonyl radical formed in the Ce-MA subsystem [8]. Previous works showed a direct relationship between the enolization constant of different organic substrates in BZ-like oscillating systems and the length of the IP [9][10][11].
In this paper we evaluate the effect of hydrogen-deuterium substitution for reaction pathway (a).

Experimental Section
Isotopic effect on bromination reaction was evaluated following changes in the bromine concentration with a double beam spectrophotometer (ULTROSPEC 2000 UV-VIS, Pharmacia Biotech) at λ = 500 nm, where Br 2 has an absorption shoulder and its molar extinction coefficient ε is 37.5 M -1 cm -1 . Measures were performed in thermostated quartz cuvettes (1 x 1 x 4.5 cm) at 20 °C. The spectrophotometer was connected to a PC for data storage and treatment. All reagents were of analytical grade (SIGMA) and they were used without further purifications.  Figure 1 shows the comparison between a BZ reaction with fully deuterated reagents ( Figure 1a) and a BZ reaction in H 2 O (Figure 1b). The effect of deuterium substitution is not as dramatic as in the Ruthenium catalyzed BZ systems, where oscillations are completely damped [7], nevertheless the global kinetics of the reaction results slower. Addition of deuterated reactants does not alter the qualitative profile of the absorbance as a function of time but influences the oscillatory parameters. This fact is particularly evident from a markedly longer Induction Period, from 150 seconds in H 2 O to 390 seconds in D 2 O. Kreuels et al. [12] found a linear D 2 O dosage dependence of the oscillation frequency (OF) both at low (increased OF) and high (decreased OF) catalyst concentration. In our experimental condition the oscillation frequency was found substantially independent from D 2 O dosage, in fact it changes from 0.023 Hz in H 2 O to 0.021 Hz for fully deuterated reagents.

Results and Discussion
On the contrary, respect to data on the oscillation frequency, a nonlinear response of IP to D 2 O content was found. The dependence of IP upon the percentage of deuterated reactants present in solution is shown in Figure 2. The monotonic increase of IP is in line with an expected isotopic effect, which generally slows down rates of elementary reactions with proton involvement [13].
As stated before, to understand the IP behavior we investigated the bromination reaction of malonic acid through its enolic form. For practical purposes this study reduces to the investigation of the ketoenolic equilibrium, which is the rate determinant step [14,15]. According to the GTF model, the bromination proceeds as follows: Where CH 2 (COOH) 2 is the keto form (MA) and (COOH)CHC(OH) 2 is the enolic form (ENOL).
It has been shown [15] that HOBr in reaction (4) does not compete with Br 2 , hence the kinetics of bromination is well described by steps (2), (3) and (5). In particular we were interested in the first two steps. The global reaction rate can be written in terms of Br 2 disappearance [14]: From equations (2) and (3) [16], the variation of enol concentration with time is close to 0 (steady state approximation) [14]: It follows that: Substituting in (6): Finally, in our experimental condition we know that k 2 [Br 2 ] >> k -1 , so at the end we get the operative equation to calculate enolization rate constant: Equation (11) describes a pseudo zero order kinetics. Using calibration curves and equation (11) we finally could calculate enolization constants from spectrophotometric data for H 2 O system (k 1 h = 2.025 x 10 -3 s -1 , slightly lower than that reported in literature at 25 °C, 3 x 10 -3 s -1 ) and D 2 O system (k 1 d = 2.666 x 10 -4 s -1 ). The value of the ratio k 1 h /k 1 d = 7.6 suggests a primary isotopic effect [13] due to the D-H substitution of the methylenic hydrogens of malonic acid. In conclusion, we showed how the progressive substitution of deuterated reactants in a Cerium catalyzed BZ reaction caused an increase in the Induction Period length. Data on the bromination reaction revealed a primary isotopic effect on the enolization kinetic constant of malonic acid, which in turn determined a slower production of bromomalonic acid contributing to a delayed onset of oscillations. In order to fully understand modifications induced by deuterated reagents to the BZ system, also the BrMA production occurring through the reaction between Br 2 and the malonyl radical should be investigated. A deeper investigation can result in a better understanding of experimental data reported in Figure 2.