Formation of Hydrogen Polyoxides As Constituents of Peroxy Radical

Article pubs.acs.org/JPCA

Formation of Hydrogen Polyoxides As Constituents of Peroxy Radical Condensate upon Low-Temperature Interaction of Hydrogen Atoms with Liquid Ozone Alexander V. Levanov,*,† Oksana Ya. Isaykina,‡ Ewald E. Antipenko,† and Valerii V. Lunin†,‡ †

Department of Chemistry, M.V. Lomonosov Moscow State University, Leninskiye Gory 1, building 3, 119991 Moscow, Russia A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky prospect 29, 119991 Moscow, Russia

‡

ABSTRACT: The composition of low-temperature condensates obtained by the reaction of hydrogen atoms with liquid ozone has been determined from the Raman spectra and data on the molar ratio of O2 to H2O2 in the decomposition products. The main constituents are hydrogen tetroxide H2O4, trioxide H2O3, and peroxide H2O2 in comparable amounts and also water H2O. The mechanism and quantitative kinetic model of their formation have been proposed. H2O4, H2O3, and H2O2 are formed in the diffusion-controlled reactions between OH and HO2 in the liquid ozone layer and stabilized by transfer to the solid phase. OH and HO2 radicals are generated via a sequence of the reactions initiated by the interaction H + O3(liq). The model adequately reproduces the properties of the real condensates.

■

INTRODUCTION

measuring its pressure in a known volume. An essential PRC property is the molar ratio NO2/NH2O2 of oxygen evolved to hydrogen peroxide formed during the decomposition at elevated temperatures. It is connected with the quantities of freshly prepared condensate components by the expression

When liquid ozone kept at 77 K on a cold surface is treated with a stream of hydrogen atoms, a transparent glassy substance is obtained. Similar substances are prepared by condensation on the cold surface of water or hydrogen peroxide vapor or H2 + O2 mixtures dissociated in a low-pressure electrical discharge and also by low-temperature interaction of hydrogen atoms with gaseous O2 or O3. These substances can be termed peroxy radical condensates (PRCs)1 (for a review, see ref 2 and also refs 3 and 4). The main components of the PRC prepared from H2 + O2 mixtures are water H2O, hydrogen peroxide H2O2, hydrogen trioxide H2O3 (H−O−O−O−H), and hydrogen tetroxide H2O4 (H−O−O−O−O−H) in varying ratios.4 A characteristic property of the condensates is that they decompose vigorously upon heating above 150 K and yield large amounts of gaseous oxygen and concentrated hydrogen peroxide aqueous solution. This is due to the decomposition of active components according to the reactions H 2O3 → H 2O + O2

and

n(H 2O3) + n(H 2O4 ) NO2 = NH2O2 n(H 2O2 ) + n(H 2O4 )

In the strict sense, eq 1 is approximate as PRCs contain also small amounts of HO2 radicals5,6 and occluded molecular oxygen,4 besides the main components H2O, H2O2, H2O3, and H2O4. The PRC obtained by the reaction H(gas) + O3(liq.) contains the admixture of unreacted ozone. As a rule, the quantity of HO2/O2/O3 is small, and therefore, eq 1 holds well. The significance of the ratio NO2/NH2O2 lies in the fact that it can be assessed only from the results of a simple chemical analysis and it is a good index of the condensate quality; the more the content of hydrogen tetraoxide and trioxide compared to hydrogen peroxide, the greater its value. The subject of the present investigation is the lowtemperature condensate obtained by the reaction of atomic hydrogen with liquid ozone. For the first time, it was prepared by a group of investigators led by N. I. Kobozev.7,8 As contrasted to the condensates obtained by any other methods, this one possesses a unique feature: under certain reproducible conditions, the molar ratio NO2/NH2O2 is nearly unity and does not depend on the experimental factors, such as time of

H 2O4 → H 2O2 + O2

An investigation of the condensates is of interest because of the high content of hydrogen polyoxides. At present, the only feasible method to produce macroscopic amounts of these substances is to prepare them as constituents of the PRC. However, the mechanism of H2O3 and H2O4 formation during the PRC synthesis has not been elucidated yet. A chemical analysis of PRC decomposition products is an important method of its characterization.4 The total quantity of hydrogen peroxide−water solution is determined by weighing, the content of H2O2 by titration with permanganate, and the amount of molecular oxygen evolved is deteremined by © XXXX American Chemical Society

(1)

Received: November 6, 2013 Revised: December 8, 2013

A

dx.doi.org/10.1021/jp410938b | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

Article

discharge (nominal power 12 W) at low pressure (∼0.2 Torr). The distance from the discharge zone top to the cold finger bottom end measured ∼9 cm. The hydrogen gas flow rate and the duration of treatment were, respectively, 0.1 L/h (STP) and 22 min in reactor A and 0.45 L/h (STP) and 13 min in reactor B. The Raman spectra were recorded by means of a Horiba Jobin Yvon LabRam HR 800 UV spectrometer with a remote sensing unit (“superhead”). An ion argon laser was employed for spectra excitation, the power at a sample being ∼15 mW and the exposition time being 100 s. When developing the kinetic model, analysis and numerical solution of the system of algebraic equations, corresponding to kinetic equations in the steady state, were performed with Maple computer algebra package.16 The calculations have been carried out for two characteristic compositions of the liquid phase, 100 mol % O3 and 80 mol % O3 + 20 mol % O2. The rate constants of diffusion-controlled reactions were evaluated by the Smoluchowski equation17,18

treatment and concentration of hydrogen atoms in the gas phase.7−10 The freshly prepared condensate does not virtually incorporate occluded molecular oxygen, as shown by means of magnetic susceptibility measurements.11 It was claimed on the basis of these results that the condensate obtained by the H(gas) + O3(liq) reaction contained only hydrogen tetroxide H2O4 and water H2O8,11 (and does not contain H2O3 and H2O2). Indeed, the equality NO2/NH2O2 ≡ 1 follows from eq 1 in this instance. However, the exact composition of the condensate is still unknown. The investigation of this substance by the method of IR spectroscopy led to contradictory results.10,12−14 The application of the method involves difficulties because of the abundance of water H2O in the sample. This substance exhibits very strong and broad bands in the IR spectrum, which virtually cover up relatively weak signals of hydrogen polyoxides H2O3 and H2O4. In our investigations, the method of Raman spectroscopy is employed. It has the advantage compared to infrared that water does not interfere, and hydrogen polyoxide oxygen frame characteristic bands can be easily observed. The aim of this work is, first, to determine the chemical composition of the PRC obtained by the reaction of hydrogen atoms with liquid ozone and, second, to elucidate the mechanism (a set of chemical reactions with rate constants) and develop the quantitative kinetic model of hydrogen polyoxides formation during the PRC synthesis.

kD(L· mole−1·s−1) =

2 4 × 103 × RT (rA + rB) 6×η rA × rB

(2)

where η (Pa·s) is the dynamic viscosity of a liquid medium, T (K) is the liquid phase temperature, R = 8.3145 J·mol−1·K−1 is the universal gas constant, and rA and rB are the relative radii of reacting particles. The parameters of the Smoluchowski equation and other medium properties are given in Tables 1 and 2. The viscosity and density of liquid ozone and ozone− oxygen mixtures were estimated on the basis of data.19−21

■

EXPERIMENTAL AND CALCULATIONAL METHODS The experiments were performed on a conventional dischargeflow setup with a low-temperature reactor cryostat, described in detail in our previous work.4 On the whole, the techniques of PRC synthesis and investigation were similar to those employed in ref 4. The synthesis of liquid ozone was carried out in an auxiliary reactor by cooling the plasma of glow discharge in pure molecular oxygen with liquid nitrogen. Then, the liquid ozone was recondensed on the finger of the main reactor and treated with a stream of hydrogen atoms. The condensate obtained was investigated by the method of Raman spectroscopy. Thereafter, the condensate was decomposed by heating. The quantities of O2 and H2O2 in the decomposition products were determined as described in the paper.4 The construction of the auxiliary reactor for liquid ozone synthesis is shown in our work15 in Figure 2. In the present work, the distance between electrodes was somewhat greater, which resulted only in the alteration of discharge voltage. The discharge burned in the flow of pure O2 at a flow rate of 1.2 L/h (STP), pressure of ∼0.2 Torr, current strength of 20−40 mA, and voltage of 2.4 kV. The time of synthesis was 7 min. The liquid solution O3−O2, of dark blue color, was formed at the reactor bottom. After the synthesis, it was evaporated and then condensed in a trap. In doing so, the major part of molecular oxygen remained in the gas phase and was subsequently removed by pumping. Then, the purified ozone preparation was recondensed on the main reactor finger and kept at liquid nitrogen temperature. The quantity of ozone obtained by this procedure was 2.1−2.6 mmol. CAUTION: Liquid ozone and its concentrated solutions in oxygen are highly explosive materials. Two reactors (A and B) were employed for the experiments of treatment of liquid ozone with hydrogen atoms. Their schemes are depicted in Figure 1 of ref 15 (reactor A) and in Figure 6 of ref 4 (reactor B). Hydrogen atoms were produced by passing pure molecular hydrogen through a microwave

Table 1. Physical Properties of Liquid Ozone, Molecular Oxygen, and an Ozone−Oxygen Mixture at 80 K (according to refs 19−21) substance

viscosity, Pa·s

density, g/cm3

concentration, mol/L

O3(liq.) O2(liq.) liquid solution 80 mol % O3 + 20 mol % O2

3.23 × 10−3 2.62 × 10−4 2.00 × 10−3

1.61 1.19 1.53

33.5 37.2 O3 27.4, O2 6.8

Table 2. Assumed Radii of Particles (au) H

O2

O3

OH

HO2

H2O2

H2O3

H2O4

1

2

2.8

1.5

2.5

3

4

5

Hydrogen atoms arrive at the liquid ozone layer from the gas phase. The rate of this process is evaluated by the relation wH(mole ·L−1·s−1) =

CH 4

8RT S 105 πMH V NA

(3)

3

where CH (atoms/cm ) is the concentration of hydrogen atoms in the gas phase, T = 300 K is the (assumed) temperature of the gas phase, R = 8.3145 J·mole−1·K−1 is the universal gas constant, MH = 1.01 × 10−3 kg/mol is hydrogen atomic mass, NA = 6.022 × 1023 is Avogadro’s number, S (cm2) is the surface area of the liquid ozone layer, and V (cm3) is its volume. Equation 3 represents the well-known Hertz−Knudsen equation for a flux of molecules from the gas phase onto a surface of the liquid phase, the flux (molecules·cm−2·s−1) being recalculated into the rate of molecule absorption (mole·L−1· s−1) in the volume of the liquid phase. The exact values of the parameters CH, S, and V are not known, but the variation range of the CH·S/V parameter B



Article

H2O4 but also H2O3 and/or H2O2. Recalling the result NO2/ NH2O2 ≈ 1 leads to the conclusion that the amounts of H2O2 and H2O3 are approximately equal, n(H2O2) ≈ n(H2O3). Thus, the low-temperature condensate prepared by the reaction of atomic hydrogen with liquid ozone consists not only of hydrogen tetroxide H2O4 and water H2O, as was considered in refs 8 and 11, but also of hydrogen trioxide H2O3 and hydrogen peroxide H2O2, the quantities of H2O4, H2O3, and H2O2 being of the same order of magnitude. Also present in the condensate Raman spectrum are lines of ozone (705, 1038, 1106 cm−1) and molecular oxygen (1552 cm−1).4 Besides, the spectrum has two peaks of unknown origin with wavenumbers ∼1275 and ∼1381 cm−1. Signals such as these are frequently observed in our experiments in the Raman spectra of substrates containing condensed ozone and likely are connected with the action of laser radiation on ozone. The succeeding section of this work is devoted to the development of the chemical mechanism and the quantitative kinetic model of hydrogen polyoxides formation during the PRC synthesis. As is known, the PRC is a solid glassy substance, and hydrogen polyoxides are stabilized in its matrix. On the other hand, synthesis of hydrogen polyoxides by the reaction H + O3 takes place only if a layer of liquid ozone is present on the lowtemperature surface; on the action of hydrogen atoms on solid ozone, neither H2O4 nor H2O3 is generated22 (cf. refs 7−10 and refs 23 and 24). Therefore, the process of PRC synthesis can be conceived as follows (Figure 2). The layer of liquid

complex can be evaluated. In all of the experiments, the relationship CH = 1014−1016 atoms/cm3 is always valid. Besides, we estimate that the magnitude of V/S changes from 0.1 to 10−3 cm. Therefore, at the calculations, we vary the value of CH· S/V in the range from 1015 to 1019 particles/cm4.

■

RESULTS AND DISCUSSION For the condensates prepared in the course of the present work, the values of the NO2/NH2O2 ratio lie in the range of 0.95−1.1. This agrees with the conclusion of the preceding studies7−10 that for the PRC obtained by the H(gas) + O3(liq.) reaction, the equality NO2/NH2O2 ≈ 1 holds true. The nature of hydrogen polyoxides can be revealed from the Raman spectra of their oxygen frame oscillations observed in the range of 400−900 cm−1. The condensate spectra are shown in Figure 1. The amount of substance in the samples is small,

Figure 1. Raman spectra of PRCs synthesized by the reaction H(gas) + O3(liq.) (A,B) and a spectrum of fused glassy quartz (C): (A) diffraction grating, 1800 l/mm; laser wavelength 488 nm; (B) diffraction grating, 300 l/mm; laser wavelength 514.5 nm; (C) diffraction grating, 1800 l/mm; laser wavelength, 514.5 nm.

and that is why the spectra are appreciably distorted by the superimposition of the spectrum of quartz (material of the reactors). Also, the presence of residual ozone brings about reduction in the spectral line intensities because it is a colored material absorbing scattered light. As a result, the only signal of the condensate active components that is observed without interferences is the intense peak in the neighborhood of 880 cm−1. This peak represents superposition of three lines with maxima at 865, 878, and 881 cm−1, which belong to symmetrical OO stretch vibrations of H2O4, H2O3, and H2O2, respectively.4 The lines at 878 and 881 cm−1 are always merged together, while the line at 865 cm−1 is partially separated and can be explicitly observed as a shoulder in spectra with higher resolution.4 These features of the peak make it possible to draw some conclusions about the condensate composition and, in particular, to test the assertion8,11 that the condensate contains only hydrogen tetroxide H2O4 and water H2O. Should the latter statement be true, then the peak would consist of the sole line with the maximum at 865 cm−1. Obviously, this is not the case; in the experimental spectra, the maximum is positioned at 879−880 cm−1. The line at 865 cm−1 is a shoulder, and its height is about half as large as that of the main signal. Therefore, the condensate active components are not only

Figure 2. Scheme of PRC synthesis by the reaction of hydrogen atoms with liquid ozone.

ozone placed on a low-temperature surface (T = 77 K) is bombarded by hydrogen atoms coming from the gas phase. In the liquid phase, the chemical reactions proceed, causing the formation of H2O, H2O2, H2O3, and H2O4. These substances diffuse to the low-temperature surface and form on it a layer of solid phase. The molecules in the solid phase are no longer available for chemical transformations. In the liquid phase, the primary reaction is the interaction of the hydrogen atom with an ozone molecule. Its products are hydroxyl radical OH and molecular oxygen O2, and the mechanism involves formation of HO3 intermediate, H + O3 → HO3 → OH + O2.25−28 The HO3 radical is labile and dissociates easily into OH and O2.29 Because of this, the HO3 radical is not incorporated in our model, and the reaction between H and O3 is written as H + O3 → OH + O2

(R1)

Reaction R1 is quite fast, and according to quantum chemical calculations, its velocity is rather high even at 77 K.25 Further C



Article

components only and described by the quasi-chemical equations

chemical reactions consist of interaction of OH and HO2 radicals with ozone. OH + O3 → HO2 + O2

(R2)

HO2 + O3 → OH + 2O2

(R3)

The question about their velocity at low temperature is discussed below. Reactions R1−R3 cause the formation of free radicals OH and HO2 in the liquid ozone layer. The following combination reactions can proceed involving these radicals, H atoms, and also O2 molecules: H + O2 → HO2

(R4)

H + OH → H 2O

(R5)

H + HO2 → H 2O2

(R6)

OH + OH → H 2O2

(R7)

OH + HO2 → H 2O3

(R8)

HO2 + HO2 → H 2O4

(R9)

(R10)

rises as the temperature decreases (in the experimental range of 96−296 K); at 96 K, its value is very high and equal to 1.2 × 10−11 cm3·molecule−1·s−1 (7.2 × 109 L·mole−1·s−1).34 The negative temperature dependence is due to the formation of the OH···H2O2 complex, whose stability increases as the temperature falls.35,36 The products are formed by a mechanism of hydrogen atom transfer via quantum-mechanical tunneling. The reactions of OH with H2O3 and H2O4 have not been investigated. We consider that they are analogous to reaction R10, described by the equations OH + H 2O3 → H 2O + OH + O2

(R11)

OH + H 2O4 → H 2O + HO2 + O2

(R12)

(R13)

H 2O2 → H 2O2 (s)

(R14)

H 2O3 → H 2O3(s)

(R15)

H 2O4 → H 2O4 (s)

(R16)

The specific rates of processes R13−R16 are assumed to be equal; they are designated as kLS. The value of the kLS coefficient is not known. It is an undetermined parameter of the model and is varied though a large range during the calculations. Let us estimate the rate constants of reactions R1−R12. The temperature of the liquid phase is assumed to be 80 K. Published data on the constants at this temperature are unavailable. Reactions R4 − R9 are diffusion-controlled. Their rate constants are determined by the Smoluchowski eq 2.17,18 It can be inferred from the data published that the rate constants of reactions R125,28 and R1034 in the gas phase at the temperature of 80 K are great and significantly more than the value of the diffusion limit in the liquid phase. Because of this, the rate constants of the reactions in the liquid phase R1, R10, as well as R11 and R12, which are similar to R10, are also calculated by the Smoluchowski eq 2. Reactions R2 and R3 are slower than reactions R1 and R4−R12. The rate constant of the gas-phase reaction R3 possesses anomalous temperature dependence. As the temperature lowers, its value decreases but approaches to a limit of 10−15 cm3·molecule−1·s−1 (6.02 × 105 L·mole−1·s−1).37,38 This value is taken as an estimate of the reaction R3 rate constant in the liquid phase at 80 K. The experimental and calculated data on the rate constant of reaction R2 do not allow unambiguous determination of its value at low temperature. Extrapolation of temperature dependencies given in refs 39 and 40 leads respectively to the estimates of k2 of ∼10−15 or ∼10−17 cm3·molecule−1·s−1 at 80 K. In this study, the calculations are performed at different values of k2, varied from 10−17 to 10−15 cm3·molecule−1·s−1 (6.02 × 103 − 6.02 × 105 L·mole−1·s−1). The values of rate constants of reactions R1−R12 used in the calculations are summarized in Table 3. According to the scheme adopted for PRC formation, the liquid phase is an open system. It is bombarded by a stationary flux of hydrogen atoms. H2O4, H2O3, H2O2, and H2O molecules formed in reactions R1−R12 transfer into the solid phase with a constant specific rate. In the course of the synthesis, the concentrations of ozone (and molecular oxygen, if the azeotropic solution O3 − O2 is used) in the liquid phase remains unchanged, but its volume decreases. Under these conditions, a steady state is established wherein intermediate formation and consumption rates in the liquid phase are equal, and its concentration does not depend on time. The intermediates are H, OH, HO2, H2O, H2O2, H2O3, and H2O4. The steady-state conditions (equality of the rates) are written as algebraic equations, which are the consequences of differential equations of chemical kinetics for the intermediates.

These reactions are characterized by nearly zero height of the activation barrier. In the gas phase their product formation rate is mainly limited by the dynamics of dissipation of excess energy of initial particles. In the liquid phase, processes such as these are diffusion-controlled; at low temperature, this was confirmed experimentally by the example of the reaction O + O2 → O3.30 H atoms and OH radicals present in the liquid phase are highly reactive and, in principle, may interact with H2O2, H2O3, and H2O4 molecules. The extrapolation of experimental and calculated data31−33 on the rate constants of the gas-phase reactions H + H2O2 → H2 + HO2 and H + H2O2 → OH + H2O to the temperature of 77 K suggests that the reactions between the hydrogen atom and H2O2 as well as compounds of analogous structure H2O3 and H2O4 can be neglected. Meanwhile, the reactions between OH radical and H2O2, H2O3, and H2O4 molecules have to be incorporated into the model. The point is that the rate constant of the gas-phase reaction OH + H 2O2 → H 2O + HO2

H 2O → H 2O(s)

and their rate constants are approximately equal to that of reaction R10. In the context of the above-stated scheme, reactions R1−R12 represent all feasible chemical transformations in the liquid phase in the course of PRC synthesis. The processes of transfer from the liquid to the solid phase are considered for main PRC D



Article

ozone and ozone−oxygen solutions19,20 (see Table 1). The generation of O2 in reactions R1, R2, R3, R11, and R12 was neglected. The undetermined parameters of the model are k2, kLS, and the parameter complex CH·S/V. They have been varied within the following ranges: k2 = 6.02 × 103−6.02 × 105 L·mole−1·−1 (see above) and kLS = 103−108 s−1 (tentatively chosen wide range), CH·S/V = 1015−1019 particles/cm4 (see the Experimental and Calculational Methods section). Analysis of the system (eqs 4−9) has shown that in all cases, it possesses only one positive solution. The concentrations of H, OH, HO2, H2O2, H2O3, and H2O4 in the liquid phase were obtained by numerical solution of this system. The concentration of H2O was calculated by eq 10. According to eqs R13−R16, the formation rates of the solid phase components are given by the expressions

Table 3. Estimated Values of Rate Constants of Liquid-Phase Chemical Reactions at 80 K (L·mole−1·s−1) composition of the liquid phase reaction R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12

pure O3

80 mol % O3 + 20 mol % O2

6.89 × 108 1.14 × 109 5 4 6.02 × 10 ; 6.02 × 10 ; 6.02 × 103 6.02 × 105 6.02 × 105 6.01 × 108 9.99 × 108 5.57 × 108 9.25 × 108 8 6.54 × 10 1.09 × 109 8 5.34 × 10 8.88 × 108 5.70 × 108 9.47 × 108 5.34 × 108 8.88 × 108 8 6.01 × 10 9.99 × 108 8 6.73 × 10 1.12 × 109 7.52 × 108 1.25 × 109

d[H 2O(s)]/dt = kLS[H 2O] d[H 2O2 (s)]/dt = kLS[H 2O2 ] d[H 2O3(s)]/dt = kLS[H 2O3] d[H 2O4 (s)]/dt = kLS[H 2O4 ]

d[H]/dt = 0:

where [H2O(s)], [H2O2(s)], [H2O3(s)], [H2O4(s)] and [H2O], [H2O2], [H2O3], [H2O4] are the concentrations in the solid and liquid phases, respectively. Therefore, the mole fractions of solid-phase components are directly proportional to the corresponding liquid-phase concentrations, and the calculated value of the ratio NO2/NH2O2 can be computed by the formula

wH = k1[H][O3] + k4[H][O2 ] + k5[H][OH] + k6[H][HO2 ]

(4)

d[OH]/dt = 0: k1[H][O3] + k 3[HO2 ][O3] = k 2[OH][O3] + k5[H][OH] + 2k 7[OH]2 + k 8[OH][HO2 ] + k10[OH][H 2O2 ] + k12[OH][H 2O4 ]

[H 2O3] + [H 2O4 ] NO2 = NH2O2 [H 2O2 ] + [H 2O4 ]

(5)

The most important property of the PRC obtained by the H(gas) + O3(liq) reaction is the almost sure equality of the molar ratio NO2/NH2O2 to unity.7−10 It can be reproduced by the calculations only if the rate constant of reaction R2 satisfies the condition

d[HO2 ]/dt = 0: k 2[OH][O3] + k4[H][O2 ] + k10[OH][H 2O2 ] + k12[OH][H 2O4 ] = k 3[HO2 ][O3] + k6[H][HO2 ] + k 8[OH][HO2 ] + 2k 9[HO2 ]2

(6)

k 2 ≥ k3

(7)

d[H 2O3]/dt = 0: (8)

d[H 2O4 ]/dt = 0: k 9[HO2 ]2 = k12[OH][H 2O4 ] + kLS[H 2O4 ]

(9)

d[H 2O]/dt = 0: k5[H][OH] + k10[OH][H 2O2 ] + k11[OH][H 2O3] + k12[OH][H 2O4 ] = kLS[H 2O]

−1 −1

that is, k2 ≥ 6.02 × 10 L·mole ·s . The true value of the constant k2 is unknown at low temperature. The reference values are given only at temperatures above 220 K, and the equality k2/k3 = 30−4041 holds good in the interval of 250−340 K. The theoretical results39,40 predict that the constant k2 decreases more rapidly than k3 as the temperature falls. On these grounds, we assume that k2 ≈ k3 = 6.02 × 105 L·mole−1· s−1 under the conditions of PRC synthesis by the reaction H(gas) + O3(liq). The subsequent calculations have been performed with regard to this assumption. The calculated values of the molar ratio NO2/NH2O2 are presented in Figure 3. They depend almost not at all on the parameters kLS and CH·S/V and lie in the range of 0.97−1.03, the average value of all of the points in Figure 3 being equal to 1.01. The agreement with the experimental results7−10 (and the present work) is excellent. The calculated values of mole fractions of the condensate components are subject to the relationships x(H2O3) = 1.05·x(H2O2) and x(H2O4) = 0.97· x(H2O2). This agrees with the above-made conclusions of the present work that the amounts of H2O2 and H2O3 in the condensate are approximately equal, and the quantities of H2O4, H2O3, and H2O2 are of the same order of magnitude. The model allows us to gain insight into the mechanism of PRC synthesis. According to the calculations, OH and HO2 free radicals are predominantly formed in reactions R1−R3, and hydrogen atoms are mainly consumed in reaction R1. If O3−O2

k6[H][HO2 ] + k 7[OH]2 = k10[OH][H 2O2 ]

k 8[OH][HO2 ] = k11[OH][H 2O3] + kLS[H 2O3]

(12) 5

d[H 2O2 ]/dt = 0: + kLS[H 2O2 ]

(11)

(10)

In these equations, in square brackets are given the concentrations of substances in the liquid phase; k1−k12 are the rate constants of chemical reactions R1−R12, kLS is the specific rate of processes R13−R16 of transfer from the liquid to the solid phase, and wH is the rate of the hydrogen atoms’ entry into the liquid phase from the gas according to eq 3. The concentrations of ozone and molecular oxygen in the liquid phase have been estimated on the basis of densities of liquid E



Article

Figure 4. The dependency of the molar ratio NO2/NH2O2 on the decimal logarithm of the k2/k3 quotient according to eq 14.

formed,23,24 and polyoxides H2O3 and H2O4 cannot be obtained. The model supposes that upon bombardment of solid ozone with hydrogen atoms, OH and HO2 radicals are generated according to reactions R1−R3. Diffusion in the solid phase is characterized by a low velocity, and therefore, the OH and HO2 radicals are immobile compared with the liquid phase. As a consequence, they can only interact by reactions R5 and R6 with hydrogen atoms coming from the gas phase. The products of these reactions are H2O and H2O2 only. Reactions R8 and R9 producing H2O3 and H2O4 are unfeasible.

Figure 3. The calculated dependencies of the molar ratio NO2/NH2O2 on the parameter CH·S/V at the compositions of the liquid-phase 100 mol % O3 and 80 mol % O3 + 20 mol % O2 and the values of kLS (s−1) 1 × 103 (◊), 1 × 104 (□), 1 × 105 (△), 1 × 106 (×), 1 × 107 (+), and 1 × 108 (○).

■

CONCLUSIONS In the present work, for the first time, the qualitative composition of the peroxide radical condensate synthesized by the H(gas) + O3(liq) reaction has been determined on the basis of its experimental Raman spectra and data on the molar ratio of molecular oxygen to hydrogen peroxide in the decomposition products. Hydrogen tetroxide H2O4, trioxide H2O3, and peroxide H2O2 are the main active components of the condensate, and their quantities are comparable. The mechanism and kinetic model of the condensate synthesis in the system H(gas) + O3(liq) have been proposed. The condensate constituents H2O4, H2O3, and H2O2 are formed via barrierless diffusion-controlled reactions between OH and HO2 free radicals in the liquid ozone layer and stabilized by transfer to the solid phase. The initial step is the interaction between the hydrogen atom and liquid ozone; OH and HO2 radicals are generated in the subsequent reactions with liquid ozone. Water is formed in the liquid-phase reactions between OH and H2O4, H2O3, and H2O2. According to the information available in the literature, this model is the firstever quantitative model of PRC synthesis, which explains and predicts its composition. The model adequately reproduces the characteristic properties of the real condensate H(gas) + O3(liq), the equality of the molar ratio NO2/NH2O2 to unity and its independence on experimental factors, and confirms the experimental conclusion that the molar amounts of H2O4, H2O3, and H2O2 in the condensate are in the same order.

solution is used instead of pure O3, then the role of reaction R4 in HO2 generation and H consumption is noticeable. Reactions R5 and R6 can be neglected. H2O2, H2O3, and H2O4 are formed in the liquid phase by the combination reactions of OH and HO2 (reactions R7−R9). Water H2O is obtained from reactions R10−R12 between OH and H2O2 and H2O3 and H2O4. An approximate analytical expression of the molar ratio NO2/ NH2O2 can be derived. If it is taken into account that the diffusion-controlled rate constants are roughly equal in the same medium, then from eqs 7−9 and eq 11, it follows an auxiliary relation NO2 1 + [OH]/[HO2 ] ≈ NH2O2 1 + ([OH]/[HO2 ])2

(13)

The calculations show that an approximate equality k3[HO2] ≈ k2[OH] holds well. In this instance, the desired expression can be easily derived from eq 13 k /k + (k 2/k 3)2 NO2 ≈ 2 3 NH2O2 1 + (k 2/k 3)2

(14)

The plot of eq 14 (Figure 4) validates the above conclusion that the concordance between calculated and experimental values of the molar ratio NO2/NH2O2 can be attained only when the condition in eq 12, k2 ≥ k3, occurs. Equation 14 is of importance to confirm that the molar ratio NO2/NH2O2 is virtually independent of experimental conditions and model parameters with the exception of the k2/k3 quotient. The proposed model is consistent with the experimental observation that upon interaction of hydrogen atoms with solid ozone, only water H2O and hydrogen peroxide H2O2 are

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. F



■ ■ ■

Article

Discharge. Russ. Chem. Bull. 2000, 49 (4), 642−648; Izv. RAN, Ser. Khim. 2000, 4, 638−644. (16) Maple, version 14, computer algebra system; Maplesoft, a division of Waterloo Maple Inc.: Waterloo, ON, Canada, 2010. (17) Von Smoluchowski, M. Versuch einer Mathematischen Theorie der Koagulationskinetik Kolloider Lösungen. Z. Phys. Chem 1917, 92 (9), 129−168. (18) Caldin, E. F. The Mechanisms of Fast Reactions in Solution; IOS Press: Amsterdam, The Netherlands, 2001. (19) Jenkins, A. C.; Dipaolo, F. S. Some Physical Properties of Pure Liquid Ozone and Ozone−Oxygen Mixtures. J. Chem. Phys. 1956, 25 (2), 296−301. (20) Gaynor, A. J.; Hersh, C. K. Physical Properties of the Liquid Ozone−Fluorine System. In Advanced Propellant Chemistry; American Chemical Society: Washington, DC, 1966; p 279−286. (21) Hilton, D. K.; Van Sciver, S. W. Absolute Dynamic Viscosity Measurements of Subcooled Liquid Oxygen from 0.15 to 1.0 MPa. Cryogenics 2008, 48 (1−2), 56−60. (22) Nekrasov, L. I.; Skorokhodov, I. I.; Kobozev, N. I. The Nature of Peroxide-Radical Condensates (A reply to P. A. Giguere and D. Chin). Russ. J. Phys. Chem. 1961, 35 (3), 337−339; Zh. Fiz. Khim. 1961, 35 (3), 691−693. (23) Giguere, P. A.; Chin, D. Reaction Products of Atomic Hydrogen with Solid Ozone. J. Chem. Phys. 1959, 31 (6), 1685−1686. (24) Romanzin, C.; Ioppolo, S.; Cuppen, H. M.; Van Dishoeck, E. F.; Linnartz, H. Water Formation by Surface O3 Hydrogenation. J. Chem. Phys. 2011, 134 (8), 084504. (25) Szichman, H.; Baer, M.; Varandas, A. J. C. Quantum Dynamical Rate Constant for the H + O3 Reaction Using a Six-Dimensional Double Many-Body Expansion Potential Energy Surface. J. Phys. Chem. A 1997, 101 (47), 8817−8821. (26) Yu, H. G.; Varandas, A. J. C. Dynamics of H(D) + O3 Reactions on a Double Many-Body Expansion Potential-Energy Surface for Ground State HO3. J. Chem. Soc., Faraday Trans. 1997, 93 (16), 2651− 2656. (27) Varandas, A. J. C.; Caridade, P. J. S. B. The OH(v′)+O2(v″) Reaction: A New Source of Stratospheric Ozone? Chem. Phys. Lett. 2001, 339 (1−2), 1−8. (28) Fernández-Ramos, A.; Varandas, A. J. C. A VTST Study of the H + O3 and O + HO2 Reactions Using a Six-Dimensional DMBE Potential Energy Surface for Ground State HO3. J. Phys. Chem. A 2002, 106 (16), 4077−4083. (29) Le Picard, S. D.; Tizniti, M.; Canosa, A.; Sims, I. R.; Smith, I. W. M. The Thermodynamics of the Elusive HO3 Radical. Science 2010, 328 (5983), 1258−1262. (30) Hippler, H.; Rahn, R.; Troe, J. Temperature and Pressure Dependence of Ozone Formation Rates in the Range 1−1000 bar and 90−370 K. J. Chem. Phys. 1990, 93 (9), 6560−6569. (31) Tarchouna, Y.; Bahri, M.; Jaïdane, N.; Ben Lakhdar, Z. Kinetic Study of the Hydrogen Abstraction Reaction H2O2+H→H2+HO2 by Ab Initio and Density Functional Theory Calculations. J. Mol. Struct.: THEOCHEM 2006, 758 (1), 53−60. (32) Koussa, H.; Bahri, M.; Jaïdane, N.; Ben Lakhdar, Z. Kinetic Study of the Reaction H2O2 + H → H2O + OH by Ab Initio and Density Functional Theory Calculations. J. Mol. Struct.: THEOCHEM 2006, 770 (1−3), 149−156. (33) Tarchouna, Y.; Bahri, M.; Jaidane, N.; Ben Lakhdar, Z.; Flament, J. P. Ab Initio Transition State Theory Calculation of the Rate Constant for the Hydrogen Abstraction Reaction H2O2 + H → H2 + HO2. J. Chem. Phys. 2003, 118 (3), 1189−1195. (34) Vakhtin, A. B.; Mccabe, D. C.; Ravishankara, A. R.; Leone, S. R. Low-Temperature Kinetics of the Reaction of the OH Radical with Hydrogen Peroxide. J. Phys. Chem. A 2003, 107 (49), 10642−10647. (35) Ginovska, B.; Camaioni, D. M.; Dupuis, M. Reaction Pathways and Excited States in H2O2 + OH → HO2 + H2O: A New Ab Initio Investigation. J. Chem. Phys. 2007, 127 (8), 084309. (36) Buszek, R. J.; Torrent-Sucarrat, M.; Anglada, J. M.; Francisco, J. S. Effects of a Single Water Molecule on the OH + H2O2 Reaction. J. Phys. Chem. A 2012, 116 (24), 5821−5829.

ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, Grant # 13-03-00319-a. ABBREVIATIONS PRC, peroxy radical condensate REFERENCES

(1) Skorokhodov, I. I.; Nekrasov, L. I.; Kobozev, N. I.; Makarova, E. I. The Higher Peroxide of Hydrogen and Frozen Radicals. 3. Kinetics of Decomposition of the Peroxide-Radical Condensate Formed from Dissociated Water Vapor. Russ. J. Phys. Chem. 1961, 35 (4), 443−446; Zh. Fiz. Khim. 1961, 35 (4), 905−910. (2) Venugopalan, M.; Jones, R. A. Chemistry of Dissociated Water Vapor and Related Systems. Chem. Rev. 1966, 66 (2), 133−160. (3) Yagodovskaya, T. V.; Nekrasov, L. I. Application of IR Spectroscopy Method for Study of Frozen Hydrogen−Oxygen Systems, Having Hydrogen Polyoxides. Zh. Fiz. Khim. 1977, 51 (10), 2434−2445. (4) Levanov, A. V.; Sakharov, D. V.; Dashkova, A. V.; Antipenko, E. E.; Lunin, V. V. Synthesis of Hydrogen Polyoxides H2O4 and H2O3 and Their Characterization by Raman Spectroscopy. Eur. J. Inorg. Chem. 2011, 2011 (33), 5144−5150. (5) Antipin, M. Y.; Antipenko, E. E.; Strakhov, B. V.; Lunina, E. V.; Nekrasov, L. I. The Higher Hydrogen Peroxide and Frozen Radicals. XX. An ESR Study of the Kinetics of the Decomposition of the Peroxy Radical Condensate. Russ. J. Phys. Chem. 1977, 51 (12), 1790; Zh. Fiz. Khim. 1977, 51 (12), 3064−3077. (6) Skorokhodov, I. I.; Golubev, V. B.; Nekrasov, L. I.; Evdokimov, V. B.; Kobozev, N. I. The Higher Peroxide of Hydrogen and Frozen Radicals. 5. Electron Paramagnetic Resonance Study of PeroxideRadical Condensates. Russ. J. Phys. Chem. 1962, 36 (1), 47−49; Zh. Fiz. Khim. 1962, 36 (1), 93−97. (7) Kobozev, N. I.; Nekrasov, L. I.; Eremin, E. N. The Physical Chemistry of Concentrated Ozone. I. The Synthesis of the Higher Peroxide H2O4 by Means of Concentrated Ozone. Zh. Fiz. Khim. 1956, 30 (11), 2580−2581. (8) Kobozev, N. I.; Skorokhodov, I. I.; Nekrasov, L. I.; Makarova, E. I. The Physical Chemistry of Concentrated Ozone. II. A Study of the Synthesis of the H2O4 Higher Peroxide of Hydrogen by the Reaction between Concentrated Ozone and Atomic Hydrogen. Zh. Fiz. Khim. 1957, 31 (8), 1843−1850. (9) Tsentsiper, A. B.; Danilova, M. S.; Kanishcheva, A. S.; Gorbanev, A. I. New Data on the Existence of a Superoxide of Hydrogen. Russ. J. Inorg. Chem. 1959, 4 (9), 886−889; Zh. Neorg. Khim. 1959, 4 (9), 1952−1957. (10) Wojtowicz, J. A.; Martinez, F.; Zaslowsky, J. A. The Reaction of Hydrogen Atoms with Liquid Ozone. J. Phys. Chem. 1963, 67 (4), 849−852. (11) Skorokhodov, I. I.; Nekrasov, L. I.; Kobozev, N. I.; Evdokimov, V. B. Frozen Radicals and a Higher Peroxide of Hydrogen. VI. Magnetic Properties of Peroxide-Radical Condensates. Russ. J. Phys. Chem. 1962, 36 (2), 136−140; Zh. Fiz. Khim. 1962, 36 (2), 274−281. (12) Yagodovskaya, T. V.; Nekrasov, L. I. Frozen Radicals and a Higher Peroxide of Hydrogen. X. Infrared Absorption Spectrum of a Peroxy-Radical Condensate Obtained in Reaction between Liquid Ozone and Atomic Hydrogen. Russ. J. Phys. Chem. 1966, 40 (6), 698− 702; Zh. Fiz. Khim. 1966, 40 (6), 1304−1312. (13) Herman, K.; Giguère, P. A. Studies on Hydrogen−Oxygen Systems in the Electrical Discharge. II. The Reactions of Hydrogen Atoms with Liquid Ozone. Can. J. Chem. 1968, 46 (16), 2649−2653. (14) Nekrasov, L. I.; Yagodovskaya, T. V. Further Comment on Infrared Spectra of Products of Low-Temperature Reaction of Liquid Ozone with Atomic Hydrogen. Russ. J. Phys. Chem. 1970, 44 (7), 1056; Zh. Fiz. Khim. 1970, 44 (7), 1861−1863. (15) Levanov, A. V.; Gromov, A. R.; Antipenko, E. E.; Lunin, V. V. The Formation of Formic Acid upon Low-Temperature Condensation of CO2−H2 and CO−H2O Gas Mixtures Dissociated in Electric G



Article

(37) Herndon, S. C.; Villalta, P. W.; Nelson, D. D.; Jayne, J. T.; Zahniser, M. S. Rate Constant Measurements for the Reaction of HO2 with O3 from 200 to 300 K Using a Turbulent Flow Reactor. J. Phys. Chem. A 2000, 105 (9), 1583−1591. (38) Xu, Z. F.; Lin, M. C. Ab Initio Study on the Kinetics and Mechanisms for O3 Reactions with HO2 and HNO. Chem. Phys. Lett. 2007, 440 (1−3), 12−18. (39) Mansergas, A.; Anglada, J. M. The Gas-Phase Reaction between O3 and HO Radical: A Theoretical Study. ChemPhysChem 2007, 8 (10), 1534−1539. (40) Ju, L.-P.; Han, K.-L.; Varandas, A. J. C. Variational TransitionState Theory Study of the Atmospheric Reaction OH + O3 → HO2 + O2. Int. J. Chem. Kinet. 2007, 39 (3), 148−153. (41) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.; Hampson, R. F.; Hynes, R. G.; Jenkin, M. E.; Rossi, M. J.; Troe, J. Evaluated Kinetic and Photochemical Data for Atmospheric Chemistry: Volume I - Gas Phase Reactions of Ox, HOx, NOx and SOx Species. Atmos. Chem. Phys. 2004, 4 (6), 1461−1738.

H


Formation of Hydrogen Polyoxides As Constituents of Peroxy Radical

Recommend Documents