Introduction

Imidazoles have potent biological activities in humans like anti-inflammatory, antimycotic, antitumor, antiviral, antituberculotic, antimicrobial properties, etc. [1]. Metronidazole (MTZ) is a very prominent antiprotozoal drug to treat amoebiasis caused by a protozoan Entamoeba histolytica [2]. Structurally MTZ contains an electronegative nitro group attached in the imidazole moiety, which is the reducible center of the molecule [3].

Bromate, Br (V), is known to be a powerful oxidizing agent with redox potentials of 1.44V in acidic medium and 0.61V in alkaline medium. The potentials show that bromine in basic solutions can be disproportionate simultaneously [4].

In recent times, the N-halosuccinimide have shown promising results in the system where it is exploited as positive halogen source. Although various reactions involving Br (V) as an oxidizing agent are known, still mechanistic and kinetic aspects of these reactions have yet received very little attention [4, 5]. To study these types in reaction detail, catalysis also plays an important role [6]. For this, Ruthenium (III) has been chosen as it shows a significant role in explaining redox reactions in detail [7].

Although oxidation–reduction reactions incorporating such catalyst and oxidant combinations reactions have been studied in detail, scant attention has been paid in using Potassium bromate as an oxidant in various metal-catalyzed reactions [6,7,8,9,10,11].

Molecular orbital calculations are widely used in the material, chemical and biological applications. These calculations elaborate the properties such as- (i) electronic coupling between the donor and acceptor species, (ii) structure and geometry, and (iii) nonlinear optical properties by hyper-polarizability calculations. The DFT calculations incorporate MESP, NLO, electronic absorption spectra, Global reactivity descriptors and thermodynamic properties were investigated using the DFT method with B3LYP function using 6-31G (d,p) basis atomic set. Global reactivity descriptors like electron affinity, electronegativity, ionization potential, electrophilicity index and chemical potential have been computed to anticipate the molecule’s reactivity. These calculations also help to explain experimental data.

Literature Review reveals, it was found that no satisfactory information is available on the catalyzed oxidation kinetics of MTZ with any oxidant. There was a need to understand the oxidation mechanism of this drug in acidic and alkaline media that corresponds to the computational data as well. Santana et al. [12] reported that MTZ is a potential human carcinogen, as listed by International Agency for Research on Cancer, due to its genotoxic nature, mutagenicity and adverse influence on human DNA along with high solubility and low biodegrability. The study in this particular article was carried out to pave the way for future scope of MTZ and its oxidative product that can minimize aforesaid adverse effects of parent compound.

This compelled us to perform the present investigation, which includes Ru (III) catalyzed oxidation of MTZ by potassium bromate in an acidic medium so that its study could shed light on the drug's fate in the biological systems [13].

Experimental

Material and kinetic measurements

All the chemicals were A.R. grade and their respective solutions were prepared in the double distilled water [5]. A solution of MTZ (CDH Ltd, New Delhi) of required strength was prepared freshly [3]. The Stock solution of potassium bromate was prepared in double distilled water and its concentration was regularly checked iodometrically [14]. The stock solution of Ruthenium Chloride was prepared by dissolving the known amount in HCl of known strength in a darkened flask to avoid photochemical effects [15]. KCl, HClO4, Hg (OAc)2 of known strength were also used without further purification. Solutions used were freshly prepared for each kinetic run [5]. All the vessels used in the reaction were also coated black to dodge any photochemical reaction [16]. Aliquots of the reaction mixture were placed in the thermostat-controlled water bath, which was equilibrated at 313 K. Requisite volume of thermostatic MTZ solution was quickly pipetted out and then spewed into the reaction vessel. The total volume of the reaction mixture was 50 ml. 5 ml from the reaction mixture was sucked out at different intervals of time which was quenched with acidified potassium iodide solution. The advancement of the reaction was surveilled by iodometric estimation of oxidant unreacted in measured aliquots of the reaction mixture withdrawn at regular intervals. The kinetic runs were carried out at four different temperatures.

Computational details

Molecular orbital calculations of reactants and products for theoretical and experimental corroboration were done by density functional theory (DFT) with B3LYP [17] with 6-31G(d,p) as basis set with the Gaussian 09 package [18]. The graphical presentations of calculated IR and UV spectra were done by GaussView 06 program. At DFT/B3LYP level the NBO calculations [18] for complete geometrical optimization were carried out so as to interpret assorted second-order interactions. The time dependent density functional theory (TD-DFT) at B3LYP/6–31-G(d,p) level in solvent (Water) by using IEFPCM model was interpreted the frontier orbital analysis.

Results and discussion

Product identification and stoichiometry -

Varying ratios of KBrO3 and MTZ reaction mixtures containing in the presence of HClO4 at 303 K were kept aside for 48 h, so that the substrates can wholly convert into products [1]. Estimation of the unreacted KBrO3 showed that one mole of substrate depleted one mole of oxidant in both cases [19]. The observed stoichiometry (1:1) for MTZ can be embodied by Scheme. The reaction product was of MTZ was found to be 2-(2-methyl-5-nitro-1H-imidazol-1-yl) acetaldehyde and extracted with ether and recrystallized from aqueous alcohol. The obtained product was detected by the 2,4-DNP derivative and conventional spot tests [20]. Further, the presence of aldehyde was confirmed by its IR absorption bands at 1700–1720 cm−1 for C = O stretching and at 2852 cm−1 for aldehydic C-H stretching modes (Fig. 1). The FT-IR spectra were recorded on JASCO FT-IR spectrometer using KBr pellets. UV–Vis spectra (Fig. 2) of above reaction were also documented which exhibited the outcomes in accordance with spectra.

scheme a

Scheme showing chemical reaction and stoichiometry of oxidation of MTZ by acidic potassium bromate

Fig. 1
figure 1

FT-IR Spectra of reaction product

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Fig. 2
figure 2

UV–Vis Spectra of reaction product

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Kinetic study of reaction orders

The order of reaction was calculated from the slope of log [conc.] vs. log dc/dt plots by varying the concentrations of MTZ, HClO4, KBrO3, Ru (III), and Hg (OAc)2 in order such that rest of the concentrations and conditions were kept constant. The reaction was found to have the first-order dependence with respect to KBrO3 between the concentration range of 1.0 × 10–3 to 2.25 × 10–3 mol dm–3 at fixed concentrations of MTZ, RuIII, HClO4, Hg (OAc)2 (Figs. 3, 4, 5).

Fig. 3
figure 3

Plot between rate of reaction (-dc/dt) × 107 vs [KBrO3 × 10–3] for the oxidation of MTZ at 35℃

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At a fixed Ru(III), HClO4, Hg(OAc)2 and KBrO3, the apparent order in MTZ in the range 0.5 × 10–3 to 1.75 × 10–3 mol dm–3was zero (Fig. 4). The effect of acid in the range of 0.1 × 10–3 to 3.0 × 10–3 mol dm–3 at fixed concentrations of Ru(III), MTZ, KBrO3 and Hg(OAc)2 at consistent ionic strength 0.005 mol dm–3 depicts that the rate constants dwindled with increase in alkali, i.e., negative order dependence on reaction rate. This was also confirmed by the linearity of the plots of log [H+] vs. log(dc/dt) (r ≥ –0.97839, S ≤ 0.01639) for different [HClO4] (Fig. 5). Addition of mercuric acetate at regular intervals shows that bromide ion had an inconsequential mark on the reaction rate [21]. This further corroborates that Hg (OAc)2 merely does sequestration for bromide ion formed during the reaction [22] (Table 1).

Fig. 4
figure 4

Plot between rate of reaction (-dc/dt) × 107 vs [MTZ] × 10–3 on the reaction rate at 35℃

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Fig. 5
figure 5

Plot between rate of reaction (-dc/dt) × 107 vs [HClO4] × 10-3 on the reaction rate at 35℃

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Table 1 Effect of variation of [KBrO3], [MTZ], [HClO4], and [Ru(III)] on the Ruthenium (III) catalyzed oxidation of MTZ by KBrO3in aqueous acidic medium at 298 K
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Dielectric constant and ionic strength variation

KClO3 was used to study the ionic strength at concentrations between 0.1 and 0.9 mol dm–3, keeping concentrations of other reactants constant at 30 °C. Likewise, the dielectric constant varied using acetic acid and water in different ratios [23]. Conclusively, both showed no appreciable effects on reaction rate [22, 24].

Effect of change of temperature-

The influence of the temperature on Ruthenium (III) catalyzed oxidation was studied at a temperature range between 30℃-45℃. Rate constants of the slowest step of the aforesaid Scheme were calculated through the intercepts and slopes of [Ru (III)]/k1 vs. 1/[MTZ] at least four varying temperatures. Apparently, observations showed that the oxidation of MTZ was accelerated by augmenting the temperature.

Effect of change in concentration of catalyst –

The above reaction rate showed first-order dependence on [catalyst] in the 8.0 × 10–5–8.0 × 10–4 mol dm−3 range. Reaction rate in the devoid of catalyst, under the given concentration conditions, was very incremental (Fig. 6). Order in Ru(III) was unity as confirmed by least square method and linearity of plots of log kc versus log[Ru(III)] (r ≥ 0.9772, S ≤ 0.04544).

Fig. 6
figure 6

Plot between rate of reaction (-dc/dt) × 107 vs [Ru(III)] × 10–3 on the reaction rate at 35℃

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The electronic spectrum of the Ruthenium(III) solution employed is similar to that reported [25, 26] for the [Ru(H2O)6]3+ spectrum [27]. Therefore, [Ru(H2O)6]3+ is considered to be the most active species of Ru(III) under our experimental conditions [25, 26, 28].

Utility of scavenger

It is to be noted that reaction is assumed to be disencumbered by any free radical. This can be inferred by the negligible effect of mercuric acetate (Fig. 7).

Fig. 7
figure 7

Plot between rate of reaction (-dc/dt) × 107 vs [Hg(OAc)2] × 10–4 on the reaction rate at 35℃

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Fig. 8
figure 8

Optimized Structure of reactant and products

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It averts any parallel oxidation of bromine that the bromate and bromide ion interaction could have devised. The reported empirical rate constants, therefore, stand for pure bromate oxidation as Hg (OAc)2 acts as a scavenger for any bromide ion formed (Fig. 7).

The presence of mercuric acetate (in excess of bromate concentration) clearly indicates that Br2 oxidation has been completely subdued [29, 30]. Br2 otherwise could have been formed by the interaction of Bromide ion and bromate as follows:

$${\text{BrO}}_{3}^{ - } + {\text{Br}}^{ - } + {\text{6H}}^{ - } \to {\text{Br}}_{2} + 3{\text{H}}_{2} {\text{O}}$$

Computational details of Ru (III) catalyzed oxidation of MTZ by Potassium Bromate in acidic medium-

Crystal structure and molecular geometry

The computational calculated longest distance of MTZ lies between C6–C7 is established to be 1.5295 Å, analogous to the experimental value (1.54 Å) which was a pure single bond character. Due to electron withdrawing group NO2, the bond length between C2-H5 becomes shortest one. All C = C and C–H bond distances of rings are in the range 1.37– 1.52 and 1.07–1.09 Å, respectively. The symmetry of the ring, with an electron withdrawing nitro group, is distorted in ring angles at the point of substitution. In substituted imidazole ring there is a deviation in bond angle C1-N4-C3 since it decrease from 105.274° to 105.192° which may be attributed to the oxidation of alcoholic group to aldehydic carbonyl group at C7 (Fig. 8).

Product was obtained as needle shaped crystal by slow evaporation of solvent at room temperature and crystallized in triclinic system with space group C1.In 2- (2-methyl-5-nitroimidazol-1-yl) acetaldehyde the computational calculated longest distance between C–C is 1.52 Å, analogous to the experimental value (1.54 Å) and this was exactly similar for all C–C bonds and the smallest bond lengths are in between C–H i.e., 1.08 almost similar to experimental value (1.09).

Electronic absorption spectra

Formation of 2- (2-methyl-5-nitroimidazol-1-yl) ethanol as oxidation product of of metronidazole was ascertained by peak around 290 nm in UV–Vis Double-Beam Spectrophotometer (systronic-2203) instrument with water as a solvent (Fig. 2). The UV–Vis spectrum of reactant and compound have been studied by TD-DFT method using B3LYP an 6–31- (,p) basis sets. The solvent effect has been calculated using integral equation formalism polarizable continuum model (IEFPCM) [31, 32]. The UV data with oscillator strength (f), excitation energies, percentage contribution of anticipated transitions and resultant absorption wavelengths have been probed with experimental results. The theoretical UV spectrum of MTZ (ƒ = 0.2359) in water has a broad and intense electronic transition at 299 nm and product (ƒ = 0.0042) has electronic transition at 292 nm and, which complies with the measured experimental data of MTZ (303 nm in water) and Product (300 nm in water) (Fig. 2). The HOMO–LUMO of any molecule helps to explain the reactivity and kinetic sustainability of its interaction. If energy gap is less, then the compound is less stable since it favors the promotion of e– to less energy LUMO. The molecular orbital diagram shows that product has lowest HOMO–LUMO gap so it is more reactive than reactant (Fig. 9). The Vibrational theoretical spectra of the reactant and product show intense troughs at 1562 cm−1 and 1813 cm−1 which very well correlates with the experimental values at 1550 cm−1 and 1809 cm−1 (Fig. 1).

Fig. 9
figure 9

HOMO–LUMO transitions for MTZ and main product

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Molecular electrostatic potential

The molecular electrostatic potential (MESP) renders the electronic density and gives content about electrophilic, nucleophilic attack as well as hydrogen– bonding interactions [33]. Molecular electrostatic potential counter map are prepared by B3LYP/6- 31G(d,p) method using Gauss view 9.0 program. The molecular electrostatic potential contour surface of product and reactant is generated. The 3D surface MESP shows the negative regions are electrophilic regions, these are mainly over the oxygen and nitrogen atoms in reactant and in product, the positive regions are the nucleophilic regions and these are over the carbon atoms connected with oxygen and nitrogen atom and over the hydrogen atoms of the title molecule (Fig. 10). The MEP value of MTZ around O19 is + 7.443 and MEP values of Product around O19 are –9.49 and + 9.498, respectively. The red regions on oxygen atom assayed nucleophilic nature so it participate further in reaction with electrophilic while blue regions on hydrogen implies its electrophilic nature which can easily be abstracted by nucleophile [34].

Fig. 10
figure 10

3D plots of the molecular electrostatic potential of metronidazole and oxidation product

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Non-linear optical analysis

The utilization of NLO in telecommunication, broadcasting and optical interconnection is the current prevalent area for researchers. The dipole moment of product is 4.69 D which is much higher than MTZ while the calculated polarizability and hyper polarizability of product are 11.24 × 10–24 and 311.52 × 10–30 esu, respectively, that are higher than that of MTZ. Thus, product has more optical properties than reactant. The values for both reactant and product were found to be greater than those of urea (βurea = 0.3728 × 10.–30 esu). Thus, both are good NLO material (Table 2).

$$\begin{gathered} \mu_{total} = \left( {\mu_{x}^{2} + \mu_{y}^{2} + \mu_{z}^{2} } \right)^{1/2} , \hfill \\ \alpha_{total} = \frac{1}{3}\left( {\alpha_{xx} + \alpha_{yy} + \alpha_{zz} } \right), \hfill \\ \beta_{total} = \left[ {\left( {\beta_{xxx} + \beta_{xyy} + \beta_{xzz} } \right)^{2} + \left( {\beta_{yyy} + \beta_{xzz} + \beta_{yxx} } \right)^{2} + \left( {\beta_{zzz} + \beta_{zxx} + \beta_{zyy} } \right)^{2} } \right]^{1/2} \hfill \\ \end{gathered}$$
Table 2 NLO ANALYSIS
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Global reactivity descriptors-

The DFT based Global reactivity descriptors are utilized for various aspects of chemical bonding, mechanism and reactive centers. Ionization potential (IP), electron affinity (EA), electronegativity (χ), chemical potential (μ), global hardness (η), global softness (S), and electrophilicity index (ω) [34] were calculated (Table 3).

$$\begin{gathered} IP = - \varepsilon_{HOMO} , \, EA = - \varepsilon_{LUMO} , \hfill \\ \chi = - \frac{1}{2}\left( {\varepsilon_{HOMO} + \varepsilon_{LUMO} } \right), \, \eta = - \frac{1}{2}\left( {I - A} \right) \hfill \\ \mu = - \frac{1}{2}\left( {I + A} \right), \, \omega = \frac{{\mu^{2} }}{2\eta }, \hfill \\ S = \frac{1}{2\eta }, \, \Delta N_{\max } = - \frac{\mu }{\eta } \hfill \\ \end{gathered}$$
Table 3 Global Reactivity Descriptors and Thermodynamic Analysis of the product
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As the HOMO–LUMO energy gap increases, the molecule becomes harder, which resist deformation of electron cloud. Higher the value of the electrophilicity index (ω) better is electrophilic character. Hence, reactant is less electrophilic than product which has electrophilicity index (ω) of 6.400.

Thermodynamic analysis

Due to various chemical and physical phenomena thermodynamic analysis play consequential role. In present analysis, we have calculated various thermodynamic parameters such as chemical potential, electronegativity, ionization potential, etc. using DFT B3LYP/6-31G (d,p) method (Table 3). All the thermodynamic calculations are conducted in gas phase and not in solution (Scheme).

Discussion

Scheme

figure 1

In the absence of catalyst oxidation of MTZ is very sluggish but it becomes facile in presence of Ru (III) catalyst. The observed modest enthalpy of activation and a higher rate constant for slow step indicates that oxidation presumably occurs via an inner-sphere mechanism. Reactive species of oxidant-catalyst, product and activation parameters have been identified. The observed results have been explained by mechanism and related law has been deduced.

The reaction follows 1:1 stoichiometry between bromate and MTZ in the presence of a ruthenium (III) as a catalyst. Orders were found to be unity in bromate and ruthenium (III) each, but zeroth order in substrate and negative fractional order in [H+].

Based on the above discussions and observed kinetic data, a potential mechanism is offered for the oxidation of MTZ (Scheme).

Rate law

$$\begin{array}{*{20}l} {\frac{{ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right]}}{{{\text{dt}}}} = {\text{ k}}_{2} \, \left[ {{\text{C}}_{2} } \right]\left[ {{\text{H}}^{ + } } \right] \, } \hfill & {(1)} \hfill \\ {\frac{{{\text{d}}\left[ {C_{2} } \right]}}{{{\text{dt}}}} \, = {\text{ k}}_{1} \, \left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right] - {\text{ k}}_{ - 1} \left[ {{\text{C}}_{2} } \right]\left[ {{\text{H}}^{ + } } \right] - {\text{k}}_{2} \, \left[ {{\text{C}}_{2} } \right]\left[ {{\text{H}}^{ + } } \right]} \hfill & {(2)} \hfill \\ {{\text{at steady state, }}\frac{{{\text{d}}\left[ {C_{2} } \right]}}{{{\text{dt}}}} = 0} \hfill & {(3)} \hfill \\ \end{array}$$

From (2) and (3) we have;

$$\begin{array}{*{20}l} {{\text{k}}_{1} {\text{ }}\left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right] = \left[ {{\text{C}}_{2} } \right]\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}} \hfill \\ {{\text{or}}} \hfill \\ {\left[ {{\text{C}}_{2} } \right] = \frac{{{\text{k}}_{1} {\text{ }}\left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}} \hfill \\ \end{array}$$
(4)
$$\begin{array}{*{20}l} {{\text{k}}_{1} {\text{ }}\left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right] = \left[ {{\text{C}}_{2} } \right]\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}} \hfill \\ {{\text{or}}} \hfill \\ {\left[ {{\text{C}}_{2} } \right] = \frac{{{\text{k}}_{1} {\text{ }}\left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}} \hfill \\ \end{array}$$
(5)

From (1),

$$\begin{array}{*{20}l} {\frac{{ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right]}}{{{\text{dt}}}} = {\text{ }}\frac{{{\text{k}}_{2} {\text{k}}_{1} \left[ {{\text{H}}^{ + } } \right]{\text{ }}\left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}} \hfill \\ {{\text{or,}}} \hfill \\ \begin{gathered} \frac{\begin{gathered} \hfill \\ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right] \hfill \\ \end{gathered} }{{{\text{dt}}}} = {\text{k}}_{2} {\text{ }}\frac{{{\text{k}}_{1} \left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}{\text{ }} \hfill \\ \left[ {{\text{Ru}}^{{{\text{III}}}} } \right] = \left[ {{\text{C}}_{1} } \right] + \left[ {{\text{C}}_{2} } \right]{\text{ }} \hfill \\ \end{gathered} \hfill \\ \end{array}$$
(6)

By (4) and (6);

$$\begin{array}{*{20}l} {\left[ {{\text{Ru}}^{{{\text{III}}}} } \right] = \left[ {{\text{C}}_{1} } \right] + \frac{{{\text{k}}_{1} {\text{ }}\left[ {{\text{C}}_{1} } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}} \hfill \\ {\left[ {{\text{Ru}}^{{{\text{III}}}} } \right]{\text{ = }}\left[ {{\text{C}}_{1} } \right]\left\{ {1 + \frac{{{\text{k}}_{1} {\text{ }}\left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}} \right\}} \hfill \\ {\left[ {{\text{Ru}}^{{{\text{III}}}} } \right]{\text{ = }}\left[ {{\text{C}}_{1} } \right]\left\{ {1 + \frac{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right) + {\text{k}}_{1} \left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right)}}} \right\}} \hfill \\ {\left[ {{\text{C}}_{1} } \right]{\text{ = }}\frac{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right)\left[ {{\text{Ru}}^{{{\text{III}}}} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right) + {\text{k}}_{1} {\text{ }}\left[ {{\text{HBrO}}_{3} } \right]}}} \hfill \\ \end{array}$$
(7)

From (5);

$$\begin{array}{*{20}l} {\frac{\begin{gathered} \hfill \\ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right] \hfill \\ \end{gathered} }{{{\text{dt}}}} = {\text{ }}\frac{{{\text{k}}_{1} {\text{k}}_{2} \left[ {{\text{HBrO}}_{3} } \right]}}{{\left\{ {{\text{k}}_{{ - 1}} + {\text{k}}_{2} {\text{ }}} \right\}}}\frac{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right)\left[ {{\text{Ru}}^{{{\text{III}}}} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right) + {\text{k}}_{1} {\text{ }}\left[ {{\text{HBrO}}_{3} } \right]}}} \hfill \\ {or,} \hfill \\ {\frac{\begin{gathered} \hfill \\ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right] \hfill \\ \end{gathered} }{{{\text{dt}}}} = \frac{{{\text{k}}_{1} {\text{k}}_{2} \left[ {{\text{Ru}}^{{{\text{III}}}} } \right]\left[ {{\text{H}}^{ + } } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{\left[ {{\text{H}}^{ + } } \right]\left( {{\text{k}}_{{ - 1}} + {\text{k}}_{2} } \right) + {\text{k}}_{1} \left[ {{\text{HBrO}}_{3} } \right]}}{\text{ }}} \hfill \\ \end{array}$$
(8)

If k1 k2 and k2 can be neglected;

$$\begin{array}{*{20}l} {\frac{{ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right]}}{{{\text{dt}}}} = \frac{{{\text{k}}_{1} {\text{k}}_{2} \left[ {{\text{Ru}}^{{{\text{III}}}} } \right]\left[ {{\text{H}}^{ + } } \right]\left[ {{\text{HBrO}}_{3} } \right]}}{{{\text{k}}_{{ - 1}} \left[ {{\text{H}}^{ + } } \right] + {\text{k}}_{1} \left[ {{\text{HBrO}}_{3} } \right]}}} \hfill \\ \end{array}$$
(9)

Also k-1 [H +] k1 [HBRO3]

$$\begin{array}{*{20}l} {{\text{and }}\left[ {{\text{HBrO}}_{3} } \right] = \left[ {{\text{BrO}}_{3}^{ - } } \right]{\text{ at constant }}\left[ {{\text{H}}^{ + } } \right]} \hfill \\ \end{array}$$
(10)

Therefore Eq. (9) becomes,

$$\begin{array}{*{20}l} {\frac{{ - {\text{d}}\left[ {{\text{BrO}}_{3}^{ - } } \right]}}{{{\text{dt}}}} = {\text{k}}_{1} {\text{k}}_{2} \left[ {{\text{Ru}}^{{{\text{III}}}} } \right]\left[ {{\text{BrO}}_{3}^{ - } } \right]{\text{ }}} \hfill \\ \end{array}$$
(11)

Therefore, the rate law (11) conforms well to the experimental observations.

Conclusions

The kinetics of oxidation of Metronidazole by Potassium Bromate with Ru(III)[35] as catalyst in acidic medium follows first-order kinetics with respect to oxidant and catalyst and zero order with respect to substrate. The above reaction rates are obtained experimentally and corroborates well with that of available theoretical. The rate law is in adherence with all kinetic observations and propound mechanistic steps are supported by the trifling effect of ionic strength. Uniform effect of acetic acid addition signifies a footling dielectric effect. From these investigations, it is concluded that \({\text{BrO}}_{{3}}^{ - }\) [13] and [Ru(H2O)6]3+ are the reactive species of KBrO3 and RuCl3, respectively, in acidic medium. The observed results were explained by plausible mechanisms and the related rate laws were deduced which were further justified by the application of computational approach. Since the HOMO–LUMO energy gap of product is lower than MTZ so oxidation product is more stable. On basis of NLO calculations value of βo for both reactant and product were higher than urea so both have good optical property. There is, thus, urgent need to find alternative ways by which the biological toxicity of this particular drug can be dealt in a productive manner. Such oxidative study of MTZ interpret the mechanism of transfiguration of such compounds in biological systems which is of utmost biological and industrial significance. [36].