Free-Radical Nonbranched-Chain Hydrogen Oxidation

Free-Radical Nonbranched-Chain Hydrogen Oxidation

Article Type: Article

Authors:

Michael M . Silaev

Abstract:

New reaction scheme is suggested for the initiated nonbranched-chain addition of hydrogen atoms to the multiple bond of the molecular oxygen. The scheme includes the addition reaction of the hydroperoxyl free radical to the oxygen molecule to form the hydrotetraoxyl free radical which is relatively low-reactive and inhibits the chain process by shortening of the kinetic chain length. This reaction competes with chain propagation reactions through a hydrogen atom. Based on the proposed scheme rate equations (containing one to three parameters to be determined directly) are deduced using quasi-steady-state treatment. The kinetic description with use the obtained rate equations is applied to the γ-induced nonbranched-chain process of the free-radical oxidation of hydrogen dissolved in water containing different amounts of oxygen at 296 K. The ratio of rate constants of competing reactions and the rate constant of the addition reaction to the molecular oxygen are defined. In this process the oxygen with the increase of its concentration begins to act as an oxidation autoinhibitor (or an antioxidant), and the rate of hydrogen peroxide formation as a function of the dissolved oxygen concentration has a maximum. From the energetic standpoint possible nonchain pathways of the free-radical oxidation of hydrogen and the routes of ozone decay via the reaction with the hydroxyl free radical (including the addition yielding the hydrotetraoxyl free radical) in the Earth’s upper atmosphere were considered.

Address:

Chemistry Faculty, Lomonosov Moscow State University, Vorobievy Gory, Moscow, 119991, Russia Corresponding author Email: mmsilaev@rc.chem.msu.ru

Keywords:

Competition; Hydrogen; Low-reactive hydrotetraoxyl free radical; Thermochemical data; Energy.

Introduction

The kinetics of inhibition for nonbranched-chain processes of saturated free-radical addition to the C=C and C=O double bonds of alkene and formaldehyde molecules, respectively, by low-reactive free radicals that can experience delocalization of the unpaired p-electron was first considered in [1]. In these processes a low- reactive free radical is formed in the reaction competing with chain propagation reactions through a reactive free radical. In the present work the kinetics of inhibition by low-reactive hydrotetraoxyl free radical is considered for the nonbranched-chain process of the addition of a hydrogen atom to one of the two multiply bonded atoms of the oxygen molecule yielding a hydroperoxyl free radical. The hydroperoxyl free radical then abstracts the most labile atom from a molecule of the compound being oxidized or decomposes to turn into a molecule of an oxidation product. The only reaction that can compete with these two reactions at the chain evolution stage is the addition of the peroxyl radical to the oxygen molecule (provided that the oxygen concentration is sufficiently high). This reaction yields the secondary hydrotetraoxyl 1:2 adduct radical, which is the heaviest and the largest among the reactants. It is less reactive than the primary peroxyl 1:1 adduct radical and, as a consequence, does not participate in further chain propagation. At moderate temperatures, the reaction proceeds via a nonbranched- chain mechanism.

The aim of this study was the mathematical simulation of oxidation process autoinhibited by oxygen, when the dependence of the peroxide formation rate on the dissolved oxygen concentration has a maximum. The simulation was based on experimental data obtained for γ-radiation-induced addition reaction of hydrogen atom to the molecular oxygen for which the initiation rate V1 is known (taking into account that V = GP and V1 = G(H•)P, where P is the dose rate, and G(H•) is the initial yield of  the chain-carrier hydrogen atom H• – initiation yield [2, 3]).

Based on the reaction scheme suggested for the kinetic description of the addition process to oxygen, the kinetic equations with one to three parameters to be determined directly were derived. Reducing the number of unknown parameters in a kinetic equation will allow one to decrease the narrowness of the correlation of these parameters and to avoid a sharp buildup of the statistical error in the nonlinear estimation of these parameters in the case of a limited number of experimental data points. The rate constant of the addition to oxygen, estimated as a kinetic parameter, can be compared to its reference value if the latter is known. This provides a clear criterion to validate the mathematical description against experimental data.

KiNetiCs of Hydrogen Atom Addi Tion to the Oxygen MOlecule

A number of experimental findings concerning the autoinhibiting effect of an increasing oxygen concentration at modest temperatures on hydrogen oxidation both in the gas phase [4–6] (Fig. 2) and in the liquid phase [7] (Fig. 1, curve 2), considered in my earlier works [8–11], can also be explained in terms of the competition kinetics of free radical addition [12, 13]. From Fig. 2 shows that the quantum yields of hydrogen peroxide and water (of products of photochemical oxidation of hydrogen at atmospheric pressure and room temperature) are maximum in the region of small concentrations of oxygen in the hydrogen–oxygen system (curves 1 and 2, respectively) [4].

In the familiar monograph “Chain Reactions” by Semenov [14], it is noted that raising the oxygen concentration when it is already sufficient usually slows down the oxidation process by shortening the chains. The existence of the upper (second) ignition limit in oxidation is  due  to  chain  termination  in  the  bulk  through  triple collisions between an active species of the chain reaction and two oxygen molecules (at sufficiently high oxygen partial pressures). In the gas phase at atmospheric pressure, the number of triple collisions is roughly estimated to be 103 times smaller than  the number  of binary collisions (and the probability of a reaction taking place depends on the specificity of the action of the third particle) [14]. Note that in the case of a gas-phase oxidation of hydrogen at low pressures of 25-77 Pа and a temperature of 77 К [5] when triple collisions are unlikely, the dependence of the rate of hydrogen peroxide formation on oxygen concentration (the rate of passing of molecular oxygen via the reaction tube) also has a pronounced maximum (see curves 3 and 4 in Fig. 2) that indicates a chemical mechanism providing the appearance of a maximum (see reaction 4 of Scheme).

Figure 1  

Figure 1

 

Figure 2  

Figure 2

 

1According to Francisco and Williams [15], the enthalpy of formation (ΔНf˚298 ) in the gas phase of Н•, НО•, HO2, HO4   (the latter without the possible intramolecular hydrogen bond taken into account), О3, Н2О 6, Н2О2, and Н2О4  is 218.0  0.0, 39.0  1.2, 12.6  1.7,  122.6  13.7, 143.1   1.7,  –241.8   0.0,  –136.0   0,  and  –26.0   9  kJ  mol–1, respectively. Calculations for the  HO4  radical with a helical structure were carried out using the G2(MP2) method [16]. The stabilization nergies of HO2, HO4 , and HO3  were calculated in the same work to be 64.5  0.1, 69.5  0.8, and 88.5  0.8 kJ mol–1, respectively.  The types of the O4 molecular dimers, their IR spectra, and higher oxygen oligomers were reported [ 17, 18]. The structure and IR spectrum of the hypothetical cyclotetraoxygen molecule O4, a species with a high energy density, were  calculated by the CCSD  method,  and its enthalpy of formation was estimated [19]. The photochemical properties of O4 and the van der Waals nature of the О2–О2 bond were investigated [20, 21]. The most stable geometry of the dimer is two O2  molecules parallel to one another. The O4 molecule was identified by NR mass spectrometry [22].

formula1

The chain evolution (propagation and inhibition) stage of the Scheme includes consecutive reaction pairs 2–3 and 3–3;  the  parallel  (competing)  reaction  pair  3–4;  and consecutive–parallel reactions 2 and 4

The hydroperoxyl free radical HO•2 [23–26] resulting energy released the conversion of the О=О multiple bond into the НО–О• ordinary bond. Therefore, before its possible decomposition, it can interact with a hydrogen or oxygen molecule as the third body via parallel (competing) reactions 3 and 4, respectively. The hydroxyl radical НО•  that appears and disappears in consecutivefrom reaction 2 possesses an increased energy due to the

parallel  reactions  3  (first  variant)  and  3   possesses additional energy owing to the exothermicity of the first variant of reaction 3, whose heat is  distributed between the two products. As a  consequence, this radical has a sufficiently  high  reactivity  not  to  accumulate  in  the system during these reactions, whose rates are equal (V3 =V3) under quasi-steady-state conditions, according to the above scheme. Parallel reactions 3 (second, parenthesized variant) and 3regenerate hydrogen atoms. It is assumed  [9, 10] that the hydrotetraoxyl radical HO •4(first reported in [27–29]) resulting from endothermic reaction 4, which is responsible for the peak in the experimental rate curve (Fig. 2, curve  3), is closed into a five-membered [ОО─Н···ОО]• cycle due to weak intramolecular hydrogen bonding [30, 31]. This structure imparts additional stability to this radical and makes it least can stem from the fact that its mean lifetime in water at 294 K, which is (3.6 ± 0.4) × 10–5  s (as estimated [11] from  the  value  of  1/k  for  the  monomolecular  decay

reaction HO •⎯⎯k →HO •+O2  [32]), is 3.9 times longer  than that of the linear HO3 radical [16, 33] estimated

the same way [11] for the same conditions [34], (9.1 ± 0.9) × 10–6 s.in MP2/6-311++G** calculations using the Gaussian-98

program confirmed that the cyclic structure of HO •4[35] is energetically more favorable than the helical structure [16]  (the  difference  in  energy  is  4.8–7.3  kJ  mol–1 depending on the computational method and the basis set).2  For example, with the MP2(full)/6-31G(d) method, the difference between the full energies of the cyclic and acyclic HO•4 conformers with their zero-point energie (ZPE)  values  taken  into  account  (which  reduces  the energy difference by 1.1 kJ mol –1) is –5.1 kJ mol–1 and  the  entropy  of  the  acyclic-to-cyclico HO •4 transition  is  S298 = −1.6 kJ  mol–1 K–1.  Therefore,  under  standard  conditions,HO •4 can exist in both forms, but the cyclic  structure is obviously dominant (87%, Keq = 6.5) [35]. Reaction 4 and, to a much lesser degree, reaction 6 inhibit the  chain  process,  because  they  lead  to  inefficient consumption of its main participants – HO •  and Н•.

The hydrogen molecule that results from reaction 5 in the gas bulk possesses an excess energy, and, to acquire stability within the approximation used in this work, it should have time for deactivation via collision with a particle M capable of accepting the excess energy [37]. To simplify the form of the kinetic equations, it was assumed that the rate of the bimolecular deactivation of the molecule substantially exceeds the rate of its monomolecular decomposition, which is the reverse of reaction 5 [38].

are deactivated by collisions, and in the form of O3) and yield hydrogen peroxide or water via a nonchain reactive.

mechanism,presumably through the intermediate formation of the unstable hydrogen tetraoxide molecule

2There were calculations for the two conformers (cis and trans) of the  HO 4 radical  [36]  using  large  scale  ab initio methods  and  density functional techniques with extended basis sets. Both conformers have a nearly planar geometry with respect to the four oxygen atoms and present an unusually long central O–O bond. The most stable conformer of HO4  radical is the cis one, which is computed to be endothermic with

Taking into account the principle of detailed balance for the various

pathways of formation of products, whose numbers in the elementary reaction should not exceed three for possible involvement in the triple collisions in the case of the reverse reaction, since the probability of simultaneous interaction of four particles is negligible.

The reaction of ozone with Н• atoms, which is not impossible, results in their replacement with НО• radicals. The relative contributions from reactions 6 and 7 to the process kinetics can be roughly estimated from the corresponding enthalpy increments (Scheme).H2O4 [39, 40].4 Ozone does not interact with molecular hydrogen. At moderate temperatures, it decomposes fairly slowly, particularly in the presence of О2( Χ 3− )  18.

When there is no excess hydrogen in the hydrogen– oxygen system, the homomolecular dimer O4 [19–22, 41, 42], which exists at low concentrations (depending on the pressure and temperature) in equilibrium with O2 [18], can directly capture the Н• atom to yield the heteronuclear  cluster5 HO • . This HO • cluster is more stable than O4 [18]  and  cannot  abstract  a  hydrogen  atom  from  the hydrogen molecule. Therefore, in this case, nonchain hydrogen oxidation will occur to give molecular oxidation products via the disproportionation  of  free radicals.

The  low-reactive  hydrotetraoxyl  radicalHO •4 [32], which presumably has a high energy density [19], may be an intermediate in the efficient absorption and conversion of biologically hazardous UV radiation energy the Earth  upper atmosphere. The potential energy surface for the atmospheric  reaction  HO•   +  О3,  in  which  the  adduct HO4 (2А) was considered as an intermediate, was calculated by the DMBE method [43]. From this standpoint, the following reactions are possible in the upper troposphere, as well as in the lower and middle stratosphere, where most of the ozone layer is situated (altitude of 16–30 km, temperature of 217–227 K, pressure  of 1.0  104 – 1.2  103 Pa [44]; the corresponding kJ mol–1 [15]): 298 reaction values are given in

Staehelin et al. [32] pointed out that, in natural systems in which the concentrations of intermediates are often very low, kinetic chains in chain reactions can be very long in the absence of scavengers since the rates of the chain termination reactions decrease with decreasing concentrations of the intermediates according to a quadratic law, whereas the rates of the chain propagation reactions decrease according to a linear law.

The kinetic description of the noncatalytic oxidation of hydrogen, including in an inert medium [37], in terms of the simplified scheme of free-radical nonbranched-chain reactions (Scheme), which considers only quadratic-law chain termination and ignores the surface effects [5], at moderate temperatures and pressures, in the absence of transitions  to  unsteady-state  critical  regimes,  and  at  a substantial excess of the hydrogen concentration over the oxygen concentration was obtained by means of quasi-steady-state treatment, as in the previous studies on the kinetics of the branched-chain free-radical oxidation of hydrogen [46], even though the applicability of this method in the latter case under unsteady states conditions was insufficiently substantiated.  The method was used with the following condition6  for the first stages of the 

The kinetic equations were derived for the rates (mol dm–3 s–1) of the elementary reactions for the formation of molecular products of hydrogen oxidation.

The rate of the chain formation of hydrogen peroxide in propagation reaction 3 and of water in reactions 3 and 3′ with V3, 3′(H2O) = 2V3 is

calculated using quantum chemical methods (B3LYP density functional theory) [40]. The hydrogen bond energy is 47.7 and 49.4 kJ mol–1 at 298 K for the triplet and singlet states of the dimer, respectively.

5It is impossible to make a sharp distinction between the two-step bimolecular interaction of three species via the equilibrium formation of the labile intermediate O4 and the elementary trimolecular reaction О2 +H→HO4.

6For  example,  the  ratio  of  the  rate  constants  of  the  bimolecular disproportionation and dimerization of free radicals at room temperature is k(HO• + HO2•)/2k(2HO•)2k(2HO2•)0.5 = 2.8 in the atmosphere  [44] and k(H•  + HO•)/2k(2H•)2k(2HO•)0.5  = 1.5 in water [3]. These values that are fairly close to unity.

7This equation can be used to describe a wide range of nonbranched- chain reactions of addition of any free radicals to the C=C bonds of unsaturated hydrocarbons, alcohols, etc., which result in the formation of molecular 1:1 adducts in binary reaction systems of saturated and unsaturated components [1, 9, 10]. x2  + (l + x)x2    l ; and 2k is the rate constant of

hydrogen atom recombination reaction 5 considered to be bimolecular in this approximation. The rate constant 2k5 in the case of the pulsed radiolysis of ammonia–oxygen (+ argon) gaseous mixtures at a total pressure of 105 Pa and a temperature of 349 K was calculated to be 1.6 × 108 dm3 mol–1 s–1 [6] (a similar value of this constant for the gas phase was reported in an earlier publication [48]). Pagsberg et al. [6] found that the dependence of the yield of the intermediate НО• on the oxygen concentration has a maximum close to 5 × 10–4 mol dm–3. In the computer simulation of the process, they

considered the strongly exothermic reaction HO •+ NН3→ Н2О  +  •NНОН,  which  is  similar  to  reaction  3 in Scheme, whereas the competing reaction 4 was not taken modified Eqs. (3) and (4), in witch (αl + x) replaced with into account.The ratio of the rates of the competing reactions is V3/V4 = αl/x and the chain length is ν = V3/V1. Equation (1a) was  obtained by substitution of the rate constant k2  into Eq. (1) with its analytical expression (in order to reduce the number of unknown parameters that are to be measured directly). The optimum concentration xm  of oxygen, at which the rate of oxidation is maximum, can be calculated from Eq. (1a) or the analytical expression for  k2 if other parameters that appear in these expressions are known.

The rates of nonchain formation of molecular hydrogen, hydrogen peroxide, and water in reactions 5, 6, and 7 of quadratic chain termination are as follows:

radical, rather than HO 4 , takes part in reactions 6 and 7. It is important to note that, if in the Scheme chain initiation via reaction 1 is due to the interaction between molecular hydrogen and molecular oxygen yielding the  hydroxyl  radical  НО• instead  of  Н• atoms  and  if  this radical reacts with an oxygen molecule (reaction 4) to form the hydrotrioxyl radical  HO 3(which was obtained in the gas phase by neutralization reionization (NR) mass spectrometry [33] and has a lifetime of >10–6 s at 298 K) and chain termination takes place via reactions 5–7 involving the НО•  and  HO•  , radicals instead of Н•  and HO •  , respectively, the expressions for the water chain formation rates derived in the same way will appear as a rational function of the oxygen concentration x without a

10–4  mol dm–3) at 296 K [7]. These data were calculated in the present work from the initial slopes of hydrogen peroxide buildup versus dose curves for a 60Co -radiation dose rate of Р = 0.67 Gy s–1 and absorbed doses of D 22.5–304.0  Gy.  The  following  values  of the primary radiation-chemical yield G (species per 100 eV of energy absorbed) for water -radiolysis  products in the bulk of solution  at  pH  4–9  and  room  temperature  were  used

at the decreasing part of the curve. In  the  case  of  nonchain  hydrogen  oxidation  via the GP and V1 = GHP): G 0.75 and GH = 0.6 (initiation yield) [3]; V1 = 4.15  10–8 mol dm–3 s–1 ; 2k5  = 2.0 × 1010 dm3 mol–1 s–1  3. As  be seen from Fig. 1, the best description of the data with an  increase  in  the  oxygen  concentration  in  water  is attained when the rate V7  of the formation of hydrogen peroxide  via  the  nonchain  mechanism  in  the  chain termination reaction 7 (curve 1, α = (8.5  2)  10–2) is  taken into account in addition to the rate V3  of the chain formation of this product via the propagation reaction 3 (dashed curve 2, α = 0.11  0.026). The rate constant of addition reaction 2  determined  from  α is  substantially underestimated: k2  = 1.34  107  (vs. 2.0  1010 [3]) dm3 mol–1 s–1. The difference can be due to  the fact that the radiation-chemical specifics of the   process  were  not considered in the kinetic description of the experimental data. These include oxygen  consumption via reactions that are not involved in the  hydrogen oxidation Scheme and reverse reactions  resulting in the decomposition of hydrogen  peroxide  by  intermediate  products  of  water radiolysis ( e−, Н•, НО•), with the major role played by the hydrated electron [3].

Conclusion

Thus,  the  addition  reaction  of  the HO • radical  that possesses an elevated energy in statu nascendi with the oxygen molecule (at sufficiently high oxygen concentrations) to give the HO •radical was used for the 

first  time  in  the  kinetic  description  of  the  initiated

hydrogen oxidation at moderate temperature and pressure [9, 10]. This reaction is endothermic and competes with radical generated in the former reaction has a low reactivity and inhibits the chain reaction.8the chain propagation reaction via the Н• atom. The HO • The above data concerning the competition kinetics of the nonbranched-chain addition of hydrogen atoms to the multiple bonds of the oxygen molecules make it possible to describe, using rate equations (1a) and (4a), obtained by quasi-steady-state treatment, the peaking experimental dependences of the formation rates of molecular 1:1 adduct H2O2 on the concentration of the oxygen over the entire range of its variation in binary system (Fig. 1). In such reaction systems consisting of saturated and unsaturated components [51, 52], the unsaturated compound (in this case the O2) is both a reactant and an autoinhibitor, specifically, a source of low-reactive free chains.radicals (in this case the HO • radicals) shortening kinetic  The progressive inhibition of the nonbranched-chain processes, which takes place as the concentration of the unsaturated compound is raised (after the maximum process rate is reached), can be an element of the self- regulation of the natural processes that returns them to the stable steady state.

Using mechanism of the nonbranched-chain free-radical hydrogen oxidation considered here, it has been demonstrated that, in the Earth’s upper atmosphere, the decomposition of O3 in its reaction with the НО• radical can  occur  via the  addition  of  the  latter  to  the  ozone molecule, yielding the HO 4 radical, which is capable of efficiently absorbing UV radiation [32].

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