Kinetics of Free-Radical Nonbranched-Chain Addition of Hydrogen Atom to Oxygen Molecule

Silaev MM, J Mod Chem Sci 2018, 1: 003 HSOA Journal of Modern Chemical Sciences Review Article

gen concentration has a maximum. From the energetic standpoint Hydrogen Oxidation: possible nonchain pathways of the free-radical oxidation of hydrogen and the routes of ozone decay via the reaction with the hydroxyl Kinetics of Free-Radical free radical (including the addition yielding the hydrotetraoxyl free radical) in the Earth’s upper atmosphere were considered. Nonbranched-Chain Addition Keywords: Competition; Energy; Hydrogen; Low-reactive hydro- of Hydrogen Atom to Oxygen tetraoxyl free radical; Thermochemical data Molecule Introduction Michael M Silaev* The kinetics of inhibition for nonbranched-chain processes of Chemistry Faculty, Lomonosov Moscow State University, Moscow, Russia 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 Abstract two reactions at the chain evolution stage is the addition of the per- New reaction scheme is suggested for the initiated non- oxyl radical to the oxygen molecule (provided that the oxygen con- branched-chain addition of hydrogen atoms to the multiple bond of centration is sufficiently high). This reaction yields the secondary hy- the molecular oxygen. The scheme includes the addition reaction drotetraoxyl 1:2 adduct radical, which is the heaviest and the largest of the hydroperoxyl free radical to the oxygen molecule to form the among the reactants. It is less reactive than the primary peroxyl 1:1 hydrotetraoxyl free radical which is relatively low-reactive and in- adduct radical and, as a consequence, does not participate in further hibits the chain process by shortening of the kinetic chain length. chain propagation. At moderate temperatures, the reaction proceeds This reaction competes with chain propagation reactions through a hydrogen atom. Based on the proposed scheme rate equations via a nonbranched-chain mechanism. (containing one to three parameters to be determined directly) are The aim of this study was the mathematical simulation of oxida- deduced using quasi-steady-state treatment. The kinetic description with use the obtained rate equations is applied to the γ-induced tion process autoinhibited by oxygen, when the dependence of the nonbranched-chain process of the free-radical oxidation of hydrogen peroxide formation rate on the dissolved oxygen concentration has a dissolved in water containing different amounts of oxygen at 296 K. maximum. The simulation was based on experimental data obtained The ratio of rate constants of competing reactions and the rate con- for γ-radiation-induced addition reaction of hydrogen atom to the mo- stant of the addition reaction to the molecular oxygen are defined. In lecular oxygen for which the initiation rate V1 is known (taking into this process the oxygen with the increase of its concentration begins • to act as an oxidation auto inhibitor (or an antioxidant), and the rate account that V = GP and V1 = G(H )P, where P is the dose rate, and • • of hydrogen peroxide formation as a function of the dissolved oxy- G(H ) is the initial yield of the chain-carrier hydrogen atom H - initiation yield [2,3]). *Corresponding authors: Michael M Silaev, Chemistry Faculty, Lomonosov Moscow State University, Moscow, Russia, Tel: +7 495939 4870; E-mail: Based on the reaction scheme suggested for the kinetic description [email protected] of the addition process to oxygen, the kinetic equations with one to three parameters to be determined directly were derived. Reducing Citation: Silaev MM (2018) Hydrogen Oxidation: Kinetics of Free-Radical Non- branched-Chain Addition of Hydrogen Atom to Oxygen Molecule. J Mod Chem the number of unknown parameters in a kinetic equation will allow Sci 1: 003. one to decrease the narrowness of the correlation of these parameters and to avoid a sharp buildup of the statistical error in the nonlinear Received: September 05, 2018; Accepted: October 29, 2018; Published: November 13, 2018 estimation of these parameters in the case of a limited number of experimental data points. The rate constant of the addition to oxygen, Copyright: © 2018 Silaev MM. This is an open-access article distributed estimated as a kinetic parameter, can be compared to its reference under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the value if the latter is known. This provides a clear criterion to validate original author and source are credited. the mathematical description against experimental data. Citation: Silaev MM (2018) Hydrogen Oxidation: Kinetics of Free-Radical Nonbranched-Chain Addition of Hydrogen Atom to Oxygen Molecule. J Mod Chem Sci 1: 003.

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Kinetics of Hydrogen Atom Addition 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] (Figure 1) and in the liquid phase [7] (Figure 2, 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 figure 1 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 Figure 2: (1, ) Reconstruction of the functional dependence of the total hydrogen peroxide formation rate V3, 7(Н2О2) on the dissolved oxygen concentration x from em- at atmospheric pressure, the number of triple collisions is roughly es- pirical data (symbols) using equations (1a) and (4a) (model optimization with respect 3 timated to be 10 times smaller than the number of binary collisions to the parameter α) for the γ-radiolysis of water saturated with hydrogen and contain- -8 (and the probability of a reaction taking place depends on the speci- ing different amounts of oxygen at 296 K [7] (SY = 1.13 × 10 ). (2) The dashed curve described V (H O ) as a function of the oxygen concentration x based on equation ficity of the action of the third particle) [14]. Note that in the case of 3 2 2 (1a) (model optimization with respect to α) and the experimental data of curve 2 (S a gas-phase oxidation of hydrogen at low pressures of 25-77 Pа and Y = 1.73 × 10-8). 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 Scheme tube) also has a pronounced maximum (see curves 3 and 4 in Figure 2) that indicates a chemical mechanism providing the appearance of a Nonbranched-chain oxidation of hydrogen and changes in enthal- -1 1 maximum (see reaction 4 of Scheme). py ( , kJ mol ) for elementary reactions Chain initiation

Chain propagation

Inhibition

1. According 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 Figure 1: (1, 2) Quantum yields of (1, ●) hydrogen peroxide and (2, ○) water resulting -1 • mol , respectively. Calculations for the HO4 radical with a helical structure were car- from the photochemical oxidation of hydrogen in the hydrogen-oxygen system as a • • ried out using the G2(MP2) method [16]. The stabilization energies of HO2 , HO4 and • function of the oxygen concentration x (light wavelength of 171.9-172.5 nm, total HO3 were calculated in the same work to be 64.5 ± 0.1, 69.5 ± 0.8, and 88.5 ± 0.8 kJ 5 -1 pressure of 10 Pa, room temperature [4]). (3,4) Hydrogen peroxide formation rate mol , 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 hypo- V(Н2О2) (dashed curves) as a function of the rate V(О2) at which molecular oxygen is passed through a gas-discharge tube filled with 3( , Δ) atomic and (4, □) molecular hy- thetical cyclotetraoxygen molecule O4, a species with a high energy density, were cal- drogen. Atomic hydrogen was obtained from molecular hydrogen in the gas-discharge culated by the CCSD method, and its enthalpy of formation was estimated [19]. The photochemical properties of O and the van der Waals nature of the О -О bond were tube before the measurements (total pressure of 25-77 Pa, temperature of 77 K [5]). 4 2 2 investigated [20,21]. The most stable geometry of the dimer is two O molecules par- The symbols represent experimental data. 2 allel to one another. The O4 molecule was identified by NR Mass Spectrometry [22].

Volume 1 • Issue 1 • 100003 J Mod Chem Sci ISSN: HMCS, Open Access Journal

Citation: Silaev MM (2018) Hydrogen Oxidation: Kinetics of Free-Radical Nonbranched-Chain Addition of Hydrogen Atom to Oxygen Molecule. J Mod Chem Sci 1: 003.

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(87%, Keq = 6.5) [34]. Chain termination Reaction 4 and, to a much lesser degree, reaction 6 inhibit the chain process, because they lead to inefficient consumption of its main participants- 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 [36]. To simplify the form of the kinetic equations, it was assumed The chain evolution (propagation and inhibition) stage of the that the rate of the bimolecular deactivation of the molecule substan- Scheme includes consecutive reaction pairs 2-3 and 3-3′; the parallel tially exceeds the rate of its monomolecular decomposition, which is (competing) reaction pair 3-4; and consecutive-parallel reactions 2 the reverse of reaction 5 [37]. and 4. Reactions3 6 and 7 regenerate hydrogen and oxygen (in the form The hydroperoxyl free radical [23-25] resulting from reac- of О ( ) molecules, including the singlet states with (О , tion 2 possesses an increased energy due to the energy released the 2 2 1 1 + • ∆ -1 [ ] Σ -1 conversion of the О=О multiple bond into the НО–О ordinary bond. a g ) = 94.3 kJ mol 15,18 and (О2, b g ) = 161.4 kJ mol [ ] Therefore, before its possible decomposition, it can interact with a hy- 18 , which are deactivated by collisions, and in the form of O3) and drogen or oxygen molecule as the third body via parallel (competing) yield hydrogen peroxide or water via a nonchain mechanism, pre- reactions 3 and 4, respectively. The hydroxyl radical НО• that appears sumably through the intermediate formation of the unstable hydro- 4 and disappears in consecutive parallel reactions 3 (first variant) and gen tetraoxide molecule H2O4 [38,39]. Ozone does not interact with 3′ possesses additional energy owing to the exothermicity of the first molecular hydrogen. At moderate temperatures, it decomposes fairly [ ] variant of reaction 3, whose heat is distributed between the two prod- slowly, particularly in the presence of О2 ( ) 18 . The reaction of ucts. As a consequence, this radical has a sufficiently high reactivity ozone with Н• atoms, which is not impossible, results in their replace- not to accumulate in the system during these reactions, whose rates ment with НО• radicals. The relative contributions from reactions 6 and 7 to the process kinetics can be roughly estimated from the corre- are equal (V3 = V3′) under quasi-steady-state conditions, according to the above scheme. Parallel reactions 3 (second, parenthesized variant) sponding enthalpy increments (Scheme). and 3′ regenerate hydrogen atoms. It is assumed [9,10] that the hydrotetraoxyl radical (first reported in [26-28]) resulting from en- When there is no excess hydrogen in the hydrogen-oxygen sys- dothermic reaction 4, which is responsible for the peak in the experi- tem, the homomolecular dimer O4 [19-22,40,41], which exists at low mental rate curve (Figure 1, curve 3), is closed into a five-membered concentrations (depending on the pressure and temperature) in equi- • • [ОО─Н···ОО] cycle due to weak intramolecular hydrogen bonding librium with O2 [18], can directly capture the Н atom to yield the 5 [29,30]. This structure imparts additional stability to this radical and heteronuclear cluster . This cluster is more stable than O4 [18] makes it least reactive. and cannot abstract a hydrogen atom from the hydrogen molecule. The radical was discovered by Staehelin et al., in a pulsed Therefore, in this case, nonchain hydrogen oxidation will occur to radiolysis study of ozone degradation in water; its UV spectrum with give molecular oxidation products via the disproportionation of free 2 -1 an absorption maximum at 260 nm ( = 320 ±15 m mol ) radicals. was reported [31]. The spectrum of the radical is similar to that of ozone, but the molar absorption coefficient of the former is The low-reactive hydrotetraoxyl radical [31], which presum- almost two times larger [31]. The assumption about the cyclic struc- ably has a high energy density [19], may be an intermediate in the ture of the radical can stem from the fact that its mean lifetime in efficient absorption and conversion of biologically hazardous UV -5 water at 294 K, which is (3.6 ± 0.4) × 10 s (as estimated [11] from radiation energy the Earth upper atmosphere. The potential energy k the value of 1/k for the monomolecular decay reaction → surface for the atmospheric reaction HO• + О , in which the adduct + O [31]), is 3.9 times longer than that of the linear radical 3 2 (2А) was considered as an intermediate, was calculated by the [16,32] estimated in the same way [11] for the same conditions [33], DMBE method [42]. From this standpoint, the following reactions are (9.1 ± 0.9) × 10-6 s. possible in the upper troposphere, as well as in the lower and middle MP2/6-311++G** calculations using the Gaussian-98 program stratosphere, where most of the ozone layer is situated (altitude of confirmed that the cyclic structure of [34] is energetically more 16-30 km, temperature of 217-227 K, pressure of 1.0 × 104-1.2 × 103 favorable than the helical structure [16] (the difference in energy is Pa [43]; the corresponding reaction values are given in kJ mol-1 -1 4.8-7.3 kJ mol , depending on the computational method and the [15]): 2 basis set). For example, with the MP2(full)/6-31G(d) method, the difference between the full energies of the cyclic and acyclic conformers with their Zero-point Energies (ZPE) values taken into 3. Taking into account the principle of detailed balance for the various pathways of -1 formation of products, whose numbers in the elementary reaction should not exceed account (which reduces the energy difference by 1.1 kJ mol ) is -5.1 three for possible involvement in the triple collisions in the case of the reverse reac- -1 kJ mol and the entropy of the acyclic-to-cyclic transition is tion, since the probability of simultaneous interaction of four particles is negligible.  -1 -1 ∆S298 = −1.6 kJ mol K . Therefore, under standard conditions, can exist in both forms, but the cyclic structure is obviously dominant 4. The planar, six-atom, cyclic, hydrogen-bonded dimer was calculated using quantum chemical methods (B3LYP density functional theory) [39]. The hydrogen 2. There were calculations for the two conformers (cis and trans) of the rad- bond energy is 47.7 and 49.4 kJ mol-1 at 298 K for the triplet and singlet states of the ical [35] using large scale ab initio methods and density functional techniques dimer, respectively. 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. 5. It is impossible to make a sharp distinction between the two-step bimolecular The most stable conformer of radical is the cis one, which is computed to interaction of three species via the equilibrium formation of the labile intermediate • be endothermic with respect to O4 and the elementary trimolecular reaction О2 + О2 + Н → Volume 1 • Issue 1 • 100003 J Mod Chem Sci ISSN: HMCS, Open Access Journal

Citation: Silaev MM (2018) Hydrogen Oxidation: Kinetics of Free-Radical Nonbranched-Chain Addition of Hydrogen Atom to Oxygen Molecule. J Mod Chem Sci 1: 003.

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8. the condition of the extremum of the rate function ∂V3/∂x = 0; lm and

xm are the concentrations of the components l and x, respectively, at 9. the maximum of the function; f = k x2 + (αl + x) 2k V f = 2 5 1 and m 22 x++()αα l xx l and 2k is the rate constant of hydrogen 10. mm; 5 atom recombination reaction 5 considered to be bimolecular in this approximation.

The rate constant 2k5 in the case of the pulsed radiolysis of ammo- The radical can disappear via disproportionation with a mole- nia-oxygen (+ argon) gaseous mixtures at a total pressure of 105 Pa cule, free radical, or atom in addition to dissociation. Note that emis- and a temperature of 349 K was calculated to be 1.6 × 108 dm3 mol-1 sion from О ( a1∆ ) and О ( 1Σ+ ) is observed at altitudes of 30-80 2 g 2 b g s-1 [6] (a similar value of this constant for the gas phase was report- and 40-130 km, respectively [44]. ed in an earlier publication [47]). Pagsberg et al., [6] found that the Staehelin et al., [31] pointed out that, in natural systems in which dependence of the yield of the intermediate НО• on the oxygen con- the concentrations of intermediates are often very low, kinetic chains centration has a maximum close to 5 × 10-4 mol dm-3. In the computer in chain reactions can be very long in the absence of scavengers since simulation of the process, they considered the strongly exothermic the rates of the chain termination reactions decrease with decreas- → • reaction + NН3 Н2О + NНОН, which is similar to reaction ing concentrations of the intermediates according to a quadratic law, 3 in Scheme, whereas the competing reaction 4 was not taken into whereas the rates of the chain propagation reactions decrease accord- account. ing to a linear law. The ratio of the rates of the competing reactions is V /V = αl/x and The kinetic description of the noncatalytic oxidation of hydrogen, 3 4 the chain length is ν = V /V . Equation (1a) was obtained by substitu- including in an inert medium [37], in terms of the simplified scheme 3 1 tion of the rate constant k into Equation (1) with its analytical expres- of free-radical nonbranched-chain reactions (Scheme), which con- 2 siders only quadratic-law chain termination and ignores the surface sion (in order to reduce the number of unknown parameters that are effects [5], at moderate temperatures and pressures, in the absence to be measured directly). The optimum concentration xm of oxygen, of transitions to unsteady-state critical regimes, and at a substantial at which the rate of oxidation is maximum, can be calculated from excess of the hydrogen concentration over the oxygen concentration Equation (1a) or the analytical expression for k2 if other parameters was obtained by means of quasi-steady-state treatment, as in the pre- that appear in these expressions are known. vious studies on the kinetics of the branched-chain free-radical oxi- The rates of nonchain formation of molecular hydrogen, hydrogen dation of hydrogen [45], even though the applicability of this method in the latter case under unsteady states conditions was insufficiently peroxide, and water in reactions 5, 6, and 7 of quadratic chain termi- 6 nation are as follows: substantiated. The method was used with the followingcondition for 2 22α + the first stages of the process: k = [46] and, hence, V = V V5 = Vk152 ( lx) f, (2) 6 2k5 2k7 1 5 22 + 2V + V = ( [Н•] + [ ])2 which allow the exponent of 2V = 22V kV(αβ l++ x) k x f , (3) 6 7 2k5 2k7 6 1 51 2 • 2 • the 2k5[Н ] term in the d[Н ]/dt = 0 equation to be reduced to 1 [1,46]. 222 -3 -1 The kinetic equations were derived for the rates (mol dm s ) of the V7 = V1 (kx2 ) f . (4) elementary reactions for the formation of molecular products of hy- The designations of the parameters in this equation are the same as drogen oxidation. in Equation (1). The kinetic equations were derived for the rates (mol dm-3 s-1) of the elementary reactions for the formation of molecular products of The rate of the nonbranched-chain free-radical oxidation of hydro- hydrogen oxidation. gen is a complex function of the rates of formation and disappearance • of Н atoms and radicals: V1 + V3, 3’ - V4 - V5 + V7. Unlike the The rate of the chain formation of hydrogen peroxide in propaga- ≤ dependences of the rates V4 (V4 V1), V5 and V7, the dependences tion reaction 3 and of water in reactions 3 and 3’ with V3, 3’(H2O) = 2V3 of the rates V2, V3, 3’, and 2V6 on the oxygen concentration x show a is maximum. α V3(H2O2; H2O) = V3’(H2O) = V12 lk x f (1) Equation (1) under the conditions (a) k x2 << (αl + x) 2k V , αl = α (1a) 2 5 1 V1 lx fm 2 2k V >> x and (b) k2x >> (αl + x) 5 1 corresponding to the ascending 7 , In this equation , V1 is the initiation rate, l = [H2] and x = [O2] and descending branches of the curve with a maximum, can be trans-

are the molar concentrations of the reactants with l >> x; α = k3/k4 is formed into simple equations which allow preliminary to estimate the the ratio of the rate constants of the competing (parallel) reactions; parameters α and k2 and express directly and inversely proportional 2 functions of concentration x: k2 = αlm 2k5V1 xm is the rate constant of reaction 2 of hydrogen

atom addition to the oxygen molecule, whose analytical expression V3 = V1 k2 x 2k5 , (5) is obtained by the solution to the quadratic equation derived from αϕ 6. For example, the ratio of the rate constants of the bimolecular dispropor- V3 = Vl1 x, (6) tionation and dimerization of free radicals at room temperature is k(HO• + 2 • • • 0.5 • • where φ = 2 at maximum when k2x (αl + x) and φ = 1 at the HO2 )/[2k(2HO )2k(2HO2 )] = 2.8 in the atmosphere [43] and k(H + HO )/ [2k(2H•)2k(2HO•)]0.5 = 1.5 in water [3]. These values that are fairly close to unity. decreasing part of the curve. 7. This 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, In the case of nonchain hydrogen oxidation via the above addition • kadd etc., which result in the formation of molecular 1:1 adducts in binary reaction systems reaction (Н + О4 → ), the formation rates of the molecular of saturated and unsaturated components [1,9,10]. Volume 1 • Issue 1 • 100003 J Mod Chem Sci ISSN: HMCS, Open Access Journal

Citation: Silaev MM (2018) Hydrogen Oxidation: Kinetics of Free-Radical Nonbranched-Chain Addition of Hydrogen Atom to Oxygen Molecule. J Mod Chem Sci 1: 003.

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oxidation products in reactions 6 and 7 (Scheme, k2 = k3 = k4 = 0) are of hydrogen peroxide by intermediate products of water radiolysis defined by modified equations (3) and (4) in which β = 0,αl ( + x) is ( , Н•, НО•), with the major role played by the hydrated electron [3]. replaced with 1, and k is replaced with k K (k K is the effective 2 add eq add eq Conclusions • ′ rate constant of Н addition to the О4 dimer, Кeq = k/k is the equilibri- k Thus, the addition reaction of the radical that possesses an ′ [ •] um constant of the reversible reaction 2О2 ⇔ О4 with k >> kadd Н ). k' elevated energy in statu nascendi with the oxygen molecule (at The formation rates of the stable products of nonchain oxidation (k = sufficiently high oxygen concentrations) to give the radical was 3 used for the first time in the kinetic description of the initiated hydro- 0), provided that either reactions 2 and 4 or reaction 2 alone (k4 = 0) occurs (Scheme; in the latter case, reactions 6 and 7 involve the gen oxidation at moderate temperature and pressure [9,10]. This reac- radical rather than ), are given by modified equations (3) and (4), tion is endothermic and competes with the chain propagation reaction • in which (αl + x) replaced with 1, and х2 replaced with х. In the latter via the Н atom. The radical generated in the former reaction has 8 case, the radical, rather than , takes part in reactions 6 and 7. a low reactivity and inhibits the chain reaction.

It is important to note that, if in the Scheme chain initiation via The above data concerning the competition kinetics of the non- reaction 1 is due to the interaction between molecular hydrogen and branched-chain addition of hydrogen atoms to the multiple bonds of the oxygen molecules make it possible to describe, using rate equa- molecular oxygen yielding the hydroxyl radical НО• instead of Н• tions (1a) and (4a), obtained by quasi-steady-state treatment, the atoms and if this radical reacts with an oxygen molecule (reaction peaking experimental dependences of the formation rates of molecu- 4) to form the hydrotrioxyl radical (which was obtained in the lar 1:1 adduct H2O2 on the concentration of the oxygen over the entire gas phase by Neutralization Reionization (NR) Mass Spectrometry range of its variation in binary system (Figure 2). In such reaction -6 [32] and has a lifetime of >10 s at 298 K) and chain termination systems consisting of saturated and unsaturated components [50,51], • takes place via reactions 5-7 involving the НО and , radicals the unsaturated compound (in this case the O ) is both a reactant and • 2 instead of Н and , respectively, the expressions for the water an autoinhibitor, specifically, a source of low-reactive free radicals (in chain formation rates derived in the same way will appear as a ra- this case the radicals) shortening kinetic chains. tional function of the oxygen concentration x without a maximum: The progressive inhibition of the nonbranched-chain processes, V (Н О) = V1k3'l (k4 x + 2k5V1 ) . 3′ 2 which takes place as the concentration of the unsaturated compound Curve 2 in figure 2 describes, in terms of the overall equation is raised (after the maximum process rate is reached), can be an ele- for the rates of reactions 3 and 7 (which ment of the self-regulation of the natural processes that returns them was derived from equations (1a) and (4), respectively, at that equa- to the stable steady state. = 4 2 tion (4) in the form [48] of V7 V1x fm (4a) in which k2 is re- Using mechanism of the nonbranched-chain free-radical hydro- 2 gen oxidation considered here, it has been demonstrated that, in the placed with its analytical expression αlm 2k5V1 xm derived from equation (1)), the dependence of the hydrogen peroxide formation 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 rate (minus the rate V = 5.19 × 10-8 mol dm-3 s-1 of the primary H 2O 2 ozone molecule, yielding the radical, which is capable of effi- formation of hydrogen peroxide after completion of the reactions in ciently absorbing UV radiation [31]. spurs) on the concentration of dissolved oxygen during the g-radiolysis of water saturated with hydrogen (at the initial concentration References 7 × 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 1. Silaev MM, Bugaenko LT (1992) Mathematical simulation of the kinetics versus dose curves for a 60Co g-radiation dose rate of Р = 0.67 Gy s-1 of radiation induced hydroxyalkylation of aliphatic saturated alcohols. In- @ ternational Journal of Radiation Applications and Instrumentation. Part C. and absorbed doses of D 22.5-304.0 Gy. The following values of Radiation Physics and Chemistry 40: 1-10. the primary radiation-chemical yield G (species per 100 eV of energy 2. Silaev (2002) Applied Aspects of the γ-Radiolysis of C -C Alcohols and absorbed) for water g-radiolysis products in the bulk of solution at pH 1 4 Binary Mixtures on Their Basis. High Energy Chemistry 36: 70-75. 4-9 and room temperature were used (taking into account that V = GP G 3. Pikaev AK (1986) Sovremennaya radiatsionnaya khimiya. Radioliz gazov and V1 = GHP): H2O2 = 0.75 and GH = 0.6 (initiation yield) [3]; V1 = 4.15 × 10-8 mol dm-3 s-1; 2k = 2.0 × 1010 dm3 mol-1 s-1 [3]. As can be i zhidkostei (Modern Radiation Chemistry: Radiolysis of Gases and Liq- 5 uids), Nauka, Moscow. seen from figure 2, the best description of the data with an increase in the oxygen concentration in water is attained when the rate V of 4. Smith HA, Napravnik A (1940) The Photochemical Oxidation of Hydro- 7 gen. Journal of the American Chemistry Society 62: 385-393. the formation of hydrogen peroxide via the nonchain mechanism in the chain termination reaction 7 (curve 1, α = (8.5 ± 2) × 10-2) is 5. Badin EJ (1948) The Reaction between Atomic Hydrogen and Molecular taken into account in addition to the rate V of the chain formation Oxygen at Low Pressures. Surface Effects. Journal of the American Chem- 3 istry Society 70: 3651-3655. of this product via the propagation reaction 3 (dashed curve 2, α = 0.11 ± 0.026). The rate constant of addition reaction 2 determined 6. Pagsberg PB, Eriksen J, Christensen HC (1979) Pulse radiolysis of gas- 7 10 eous ammonia-oxygen mixtures. J Phys Chem 83: 582-590. from α is substantially underestimated: k2 = 1.34 × 10 (vs. 2.0 × 10 [3]) dm3 mol-1 s-1. The difference can be due to the fact that the ra- 8. Note that in the case of similar nonbranched-chain (i.e., “slow”) oxidation of RH hydrocarbons, the corresponding reactive and low-reactive radicals participate diation-chemical specifics of the process were not considered in the in the process [49]. The only difference between the kinetic model of oxidation and kinetic description of the experimental data. These include oxygen the kinetic model of the chain addition of 1-hydroxyalkyl radicals to the free (unsol- consumption via reactions that are not involved in the hydrogen ox- vated) form of formaldehyde in nonmethanolic alcohol-formaldehyde systems [1, 9, 10] is that in the former does not include the formation of the molecular 1:1 adduct idation Scheme and reverse reactions resulting in the decomposition via reaction 4.

Volume 1 • Issue 1 • 100003 J Mod Chem Sci ISSN: HMCS, Open Access Journal

Citation: Silaev MM (2018) Hydrogen Oxidation: Kinetics of Free-Radical Nonbranched-Chain Addition of Hydrogen Atom to Oxygen Molecule. J Mod Chem Sci 1: 003.

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