Effect of solvent viscosity on the kinetics of reversible dimerization of phenoxy radicals

Flash photolysis technique has been used to obtain the rate and thermodynamic parameters of the reversible dimerization reactions of a range of ten phenoxy radicals (I–X) in a toluene–dibutylphthalate mixture (0.6 cP ≤η≤18.4 cP): The main reason for the difference in the k₁ values are the different steric hindrances in radicals. It has been found that the values of k₁ for 2,6-diphenyl-4-methoxy- (I), 2-phenyl-(III), and 2-methoxyphenoxy (IV) radicals are 3–5 times smaller than the respective diffusion constants calculated according to the Debye formula with regard to the spin-statistical factor: The resultant ΔH₁^≠values for these radicals in toluene and dibutylphthalate are close to the activation energies of the viscous flow of the solvents B. Linear relationships with a slope equal to unity are observed between log k₁ and log(T/η). The recombination of radicals I, III, and IV is limited by translational diffusion. The k₁ values for 2,6-diphenyl- (VII), 2,6-di-tert-butyl- (IX), and 2,6-di-tert-butyl-4-methylphenoxy (X) radicals are 10–60 times smaller than k_diff and Δ H^≠ B. In the case of radical X in toluene ΔH₁^≠ 0. The recombination of these three radicals includes an intermediate step of complex formation: For 4-phenyl- (II), 2,6- dimethoxy- (V), 2,4-diphenyl- (VI), and radicals VII, IX, and X the linear relationships between log k₁ and log (T/η) have a slope of from 0.5 ± 0.05 to 0.8 ± 0.05. The k₁^-1 versus η relationships for these radicals are not straight lines. The recombination of these six radicals is limited by translational and rotational diffusion. With the aid of theoretical models, the k₁ versus η relationships have been used to derive the steric factor f in radical recombination and the angle θ between the axis and the solid angle generatrix. The solid angle defines the reaction spot on the radical-sphere surface. The recombination of the 2,6-diphenyl-4-diphenylmethylphenoxy radical (VIII) takes place in the region intermediate between the diffusion and the kinetic ones, and the relationship between log k₁ and log (T/η) for this radical has a plateau portion. The log k_-1 versus log (T/η) relationships have precisely the same form as the corresponding k₁ relationships, which is quite in line with the theory of diffusion-controlled reversible recombination reactions.     

Bimolecular self-reactions of 2-arylindandione- 1,3-yl radicals studied by flash photolysis

Kinetic and thermodynamic data for reaction (1) of certain C-centered aromatic radicals (referred to in this paper by the numbers I to X) in chlorobenzene: have been obtained. The k₁ values of radicals varied between (1.1 ± 0.2) × 10⁶M^?1·sec^?1 (radical VIII) and (3.6 ± 0.7) × 10⁹M^?1 sec^?1 (radical VI) at 20°C. An investigation of the relationship between the recombination rates of radicals I–VIII and X and the solvent viscosity (mixture of toluene and dibutylphthalate, 0.6 < η < 18.4 cP) has shown that the recombination reactions involving radicals I–IV are limited by diffusion in solvents having a viscosity η> 10 cP and are activation reactions in solvents having a viscosity η < 10 cP. The recombination of radicals VIII and IX is an activation reaction, while that of radicals V–VII is diffusion-controlled in the entire viscosity range. The recombination of radical X is limited, in the viscosity range of 18.4 to 2 cP, by intrusion into the first coordination sphere of the partner, the effect of viscosity on the radical X recombination rate in the specified range being the same as its effect on diffusion-controlled reactions. The possible reasons of the discrepancies between the experimental fast recombination rate constants and the theoretical values calculated by the Debye–Smoluchowski theory are discussed. The equilibrium constant depends strongly on the nature of the substituent in the phenyl fragment: the substituents which increase unpaired electron delocalization in the radical intensify the dissociation of the respective dimer. Long-wave absorption bands have been recorded for radicals I–X and their extinction coefficients obtained. Dimers I–V are thermo- and photochromic compounds.     

Rate constants for the reaction of tert-butyl radicals with chloroform in solution

The decay of photochemically generated tert-butyl radicals in methylcyclopentane solutions containing chloroform is studied by time-resolved ESR spectroscopy. In the pure solvent it perfectly follows the second-order rate law for radical self-termination. Increasing chloroform concentrations cause increasing admixture of a pseudo-first-order decay from which the rate constant of the title reaction is obtained. For 273 K ≦ T ≦ 323 K, where θ = 2.303RT kcal/mol. CIDNP studies of the reaction mechanism and NMR product yields show H and Cl abstractions to occur with the temperature-independent ratio k_H/k_Cl = 1.4 ± 0.1. The results point to polar effects in the transfer reactions of tert-butyl. The potential of time-resolved ESR spectroscopy in studies of first- and pseudo-first-order reaction rates is discussed.     

Reaction of CF3 radicals with H2S

Hydrogen abstration from H₂S by CF₃ radicals, generated by the photolysis of both CF₃COCF₃ and CF₃I, has been studied in the temperature range 314–434 K. The rate constant, based on the value of 10^13.36 cm³/mol · s for the recombination of CF₃ radicals, is given by with CF₃COCF₃ as the radical source, and with CF₃I as the radical source, where k₂ is in cm³/mol · s and E is in J/mol. These results resolve a previously existing controversy concerning the values of the rate constants for this reaction. They show that CF₃ radicals are less reactive than CH₃ radicals in attacking H₂S, and this behavior indicates that polar effects play a significant role in the hydrogen transfer reactions of CF₃ radicals.     

Arrhenius parameters for the hydrogen abstraction from ammonia by CF3 radicals

The reaction of CF₃ radicals with NH₃ has been studied over a wide temperature range 298–673 K, using the photolysis and the thermal decomposition of CF₃I as the free radical source. It was found that the reaction could not be explained in terms of a simple mechanism in the whole temperature range because a marked pressure dependence on the rate of products formation and the presence of a dark reaction complicate the system at low temperatures. Thus, Arrhenius parameters for reaction (1) have been calculated relative to the CF₃ recombination from data in the range 523–673 K where pure hydrogen transfer occurs. The rate constant expression is given by where k_H/k is in units of cm^3/2/mol^1/2 s^1/2 and θ = 2.303 RT/kJ/mol.     

Reaction Rates of t-Butyl and Pivaloyl Radicals in Solution

The rate constants of the unimolecular decomposition of the pivaloyl radical (k_D) and of the bimolecular self terminations of pivaloyl (k₁) and t-butyl radicals (k₂) in liquid methylcyclopentane are determined by ESR.-spectroscopy: The viscosity dependence of (k₂) is analysed with respect to diffusion control of the reaction. Comparison of (k_D) values of different acyl radicals reveals a strong dependence of the activation energies on radical structure.     

Effect of solvation on the reactivity of peroxide radicals in oxidation reactions

The reactivity of RO ₂ ^. peroxide radicals in oxidation reactions depends greatly on specific and nonspecific solvation by the solvent. With increasing dielectric constant () of the medium, the rate constant for the interaction of RO ₂ ^. radicals with methyl ethyl ketone (k₂) and the rate constant of the recombination of RO ₂ ^. radicals (k₆) increase. The specific solvation of RO ₂ ^. radicals due to hydrogen bonds of water diminishes their reactivity. Equilibrium constants for the solvation of peroxide radicals and all rate constants of chain propagation and termination reactions involving solvated and unsolvated RO ₂ ^. radicals were measured. The change in composition of the oxidation products when methyl ethyl ketone was diluted with benzene or water is caused by nonspecific and specific solvation by the solvent affecting the chain propagation reaction.     

Fourier transform infrared study of the self reaction of C2H5O2 radicals in air at 295 K

Fourier transform infrared spectroscopy was used to identify and quantify products of the self reaction of ethylperoxy radicals, C₂H₅O₂, formed in the photolysis of Cl₂/C₂H₆ mixtures in 700 torr total pressure of synthetic air at 295 K. From these measurements, branching ratios for the reaction channels (1) of k_1a/(k_1a + k_1b) = 0.68 and k_1c/(k_1a + k_1b + k_1c) ? 0.06 were established. Additionally, using the relative rate technique, the rate constant for the reaction of Cl atoms with C₂H₅OOH was determined to be (1.07 ± 0.07) × 10^?10 × cm³ molecule^?1 s^?1. Results are discussed with respect to the previous kinetic and mechanistic studies of C₂H₅O₂ radicals.     

High‐temperature reaction of C2 with NO including product channel measurements

The reaction of C₂ radicals with NO was studied behind reflected shock waves in the temperature range 3150 K≤T≤3950 K. The shock‐induced pyrolysis of acetylene, highly diluted in argon, was used as a well defined source for C₂ radicals, which were detected by ring‐dye‐laser absorption spectroscopy (RDLAS) at 516.646 nm. The perturbation of the C₂ by the addition of NO to the initial mixtures results in a fast removal of the C₂ radicals, which is mainly caused by the reaction: ((R5)) for which the overall rate coefficient was obtained. The product channels of this reaction were studied by additional measurements of O‐atoms, N‐atoms, and CN radicals. O and N were detected using atomic resonance absorption spectroscopy (ARAS) and the CN radicals were followed by their emission using a spectrograph and an intensified CCD‐camera. The reactions leading to the product channels C₂N+O (R5a) and to C₂O+N (R5b) were identified as the main channels with a branching ratio of k_5a/k₅=70% and k_5b/k₅=30%, while the channel leading to CN+CO (R5c) was found to be neglectable. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 11–21, 1999     

Pulse radiolysis and fourier transform infrared study of neopentyl peroxy radicals in the gas phase at 297 K

The ultraviolet absorption spectrum of the neopentyl peroxy radical (CH₃)₃CCH₂O₂, and the kinetics and products of its self reaction have been studied in the gas phase at 298 K. Absorption cross sections were quantified over the wavelength range 230–290 nm. The measured cross section at 250 nm was; Errors represent statistical (2σ) together with our estimate of potential systematic errors(15%). The kinetics of the decay of the UV absorption following the generation of the neopentyl peroxy radicals was complicated by the rapid decomposition of the (CH₃)₃CCH₂O radicals formed in channel (4a). By measuring the yield of t-butyl peroxy radicals, the branching ratio k_4a/(k_4a + k_4b) was determined to be 0.39 ± 0.03. The rate constant for the self reaction of neopentyl peroxy radicals was k₄ = (1.07 ± 0.22) × 10^?12 cm³ molecule^?1 s^?1. Quoted errors represent 2σ. These results are discussed with respect to the available literature data. © John Wiley & Sons, Inc.     

Kinetics and mechanism of the acid-catalysed decarboxylation of thecis-α- andcis-β-carbonato(3,6-dimethyl-1,8-diamino-3,6-diazaoctane)-cobalt(III) ions

Summary The acid-catalysed decarboxylation of thecis-- andcis--[CoL(CO₃)]⁺ complexes (L = 3,6-dimethyl-1,8-diamino-3,6-diazaoctane) have been studied over a range of HClO₄ concentrations and the temperatures 25, 35 and 45° at I = 1.0 mol dm^–3 (NaClO₄). The rate expression takes the form k_obs = k₀ + k₁[H⁺] where k_obs is the observed first order rate constant at constant hydrogen ion concentration. The k₀ term makes only a minor contribution to the overall reaction. Both complexes display solvent deuterium isotope effects ofca. 2.6 for the acid-catalysed decarboxylation, consistent with a rapid proton pre-equilibrium mechanism. Activation parameters have been determined and the mechanism of the reaction discussed. The magnitude of the solvent isotope effect is consistent with an A-1 type mechanism involving formation of a 5-coordinate intermediate.     

Recombination of 1,1-dimethylpropyl peroxy radicals in polar solvents

The kinetics of 1,1-dimethylpropyl peroxy radicals recombination in polar solvents—water, methanol, and their mixtures—was studied by EPR spectroscopy in combination with the stopped-flow method, and the rate constants of this reaction were determined. Peroxyl radicals were generated by mixing solutions of Ce⁴⁺ sulfate and 1,1-dimethylpropyl hydroperoxide. The observed EPR signal of the peroxyl radical is a singlet with a g-factor of 2.015 ± 0.001, and a line width of ΔH = (1.36 ± 0.02) × 10^?3 T for methanol and ΔH = (9.7 ± 0.2) × 10^?4 T for water. The measured rate constants of (CH₃)₂C(O₂^·)CH₂CH₃ radical recombination at 298 K are 2k_t = (3.9 ± 0.4) × 10⁴ L mol^?1 s^?1 for water and 2k_t = (5.2 ± 0.5) × 10³ L mol^?1 s^?1 for methanol. A linear relationship between ln(2k_t) and the Kirkwood function (ε?1)/(2ε + 1), where e is the dielectric constant of the medium, has been established, indicating an important role of nonspecific solvation in the recombination of tertiary peroxyl radicals.     

FTIR study of the reaction of ethyl radicals with O2 and Cl2 in air at 295 K

Using Fourier transform infrared spectroscopy, the ethene yield from the reaction of C₂H₅ radicals with O₂ has been determined to be 1.50 ± 0.09%, 0.85 ± 0.11%, and <0.1% at total pressures of 25, 50, and 700 torr, respectively. Additionally, the rate constant of the reaction of C₂H₅ radicals with molecular chlorine was measured relative to that with molecular oxygen. (1) A ratio k₆/k₇ = 1.99 ± 0.14 was measured at 700 torr total pressure which, together with the literature value of k₇ = 4.4 × 10^?12 cm³ molecule^?1s^?1, yields k₆ = (8.8 ± 0.6) × 10^?12 cm³ molecule^?1s^?1. Quoted errors represent 2σ. These results are discussed with respect to previous kinetic and mechanistic studies of C₂H₅ radicals.     

Kinetics and mechanism of the reaction H + CH3ONO

The reaction of hydrogen atoms with methyl nitrite was studied in a fast-flow system using photoionization mass spectrometry and excess atomic hydrogen. The associated bimolecular rate coefficient can be expressed by in the temperature range of 223-398°K. NO, CH₃OH, CH₄, C₂H₆, CH₂O, and H₂O are the main products; OH and CH₃ radicals were detectable intermediates. The mechanism was deduced from the observed product yields using normal and deuterated reactants. The primary reaction steps were identified as followed by a rapid unimolecular decomposition of CH₂ONO into CH₂O and NO. Since the extent of reaction channel (1b) could not be determined independently, only extreme limits could be obtained for the individual contributions of the two channels of reaction (3) which follows the generation of CH₃O radicals: The most probable values, k_3a/k₃ = 0.31 ± 0.30 and k_3b/k₃ = 0.69 ± 0.30, support the previous results on this reaction, although the range of uncertainties is much greater here.     

Kinetic Study of the CCl2 Radical Recombination Reaction by Laser‐Induced Fluorescence Technique

An experimental setup that coupled IR multiple‐photon dissociation (IRMPD) and laser‐induced fluorescence (LIF) techniques was implemented to study the kinetics of the recombination reaction of dichlorocarbene radicals, CCl₂, in an Ar bath. The CCl₂ radicals were generated by IRMPD of CDCl₃. The time dependence of the CCl₂ radicals’ concentration in the presence of Ar was determined by LIF. The experimental conditions achieved allowed us to associate the decrease in the concentration of radicals to the self‐recombination reaction to form C₂Cl₄. The rate constant for this reaction was determined in both the falloff and the high‐pressure regimes at room temperature. The values obtained were k₀ = (2.23 ± 0.89) × 10^?29 cm⁶ molecules^?2 s^?1 and k_∞ = (6.73 ± 0.23) × 10^?13 cm³ molecules^?1 s^?1, respectively.     

Effects of solvents on the reactions of coordination complexes: Part 20. Kinetics and mechanism of base hydrolysis of (αβS) (Salicylato) (Tetraethylenepentamine) Cobalt(III) in aquo-organic solvent media

The kinetics of base hydrolysis of (αβS) (salicylato) (tetraethylenepentamine) cobalt(III) have been investigated in aquo-organic solvent media at 15.0 < t, °C < 40.0, and I = 0.10 mol dm (ClO₄^?) using propane-2-ol (?70% v/v), t-butanol (?60% v/v), acetone (?70% v/v), acetonitrile (?50% v/v), and ethylene glycol (?70% v/v) as cosolvents. Both the spontaneous and base-catalyzed hydrolysis of the phenoxide species [(tetren)CoO₂CC₆H₄O]⁺ were appreciably accelerated by the cosolvents PrⁱOH, Bu^tOH, Me₂CO, and MeCN. On the contrary the base hydroylsis (k₂) was retarded while spontaneous aquation (k₁) was accelerated to a small extent with increased EG content. Variation of log k₁ and log k (k = k₂ at I = 0) with mole fraction (_X0.S) or reciprocal of the relative permitivity (D_s^?1) of the media were nonlinear. The transfer free energy of the transition state relative to that of the initial state of the substrate for transfer of species from water to mixed solvents also varied nonlinearly with _X0.S, or D_s^?1 indicating solvent specificity. The activation parameters, ΔH^≠ and ΔS^≠ varied nonlinearly with solvent composition exhibiting extrema. The preferential solvation and solvent structural effects mediated the kinetics and energetics of the reaction. © 1995 John Wiley & Sons, Inc.     

The reaction of C2F5 radicals with H2S

The reaction of C₂F₅ radicals with H₂S was studied over the range 1°?123°C using C₂F₅ radicals generated by photolysis of perfluoropropionic anhydride. The rate constant k_H for reaction (2) is given by where θ = 2.303RT/cal mole^?1. The relevance of this result to conflicting published data on the analogous reaction between CF₃ radicals and H₂S is discussed. It is concluded that there is little difference in the Arrhenius parameters for reaction of CF₃ and C₂F₅ radicals with H₂S.     

Reactions of primary and secondary butoxy radicals in oxygen at atmospheric pressure

The reaction pathways of n-butoxy and s-butoxy radicals have been investigated by TLC and HPLC analysis of end products, particularly peroxides and carbonyl compounds. The butoxy radicals were produced by the pyrolysis of very low concentrations of the corresponding dibutylperoxide in an atmosphere of oxygen and nitrogen, at atmospheric pressure. The decomposition reaction (3) s-BuO → C₂H₅ + CH₃CHO and the reaction (2) s-BuO + O₂ → HO₂ + CH₃COC₂H₅ have been studied, and the ratio k₃/k₂ has been determined in the temperature range 363–503 K by kinetic modeling of the formation of the observed acetaldehyde and methylethylketone. The rate constant k₃ obtained was: A good agreement was observed between experimental data and RRKM theory. The implications of the results for atmospheric chemistry and combustion are discussed. At room temperature, the reaction with O₂, yielding HO₂ radicals and methylethylketone is, by far, the main channel for s-BuO radicals. In the field of low temperature combustion, the decomposition of s-BuO radicals producing C₂H₅ and CH₃CHO is the main pathway; the route s-BuO + O₂ decreases tremendously in importance as the temperature is raised above 393 K.     

Shock-initiated decomposition of tetramethylgermane and the reaction of methyl radicals with toluene

The shock-initiated decomposition of tetramethylgermane (1078–1242 K) has been found to involve successive elimination of methyl radicals with the rate constant k₁ for the first step given by In the presence of excess toluene the products were CH₄ (major), C₂H₄, and C₂H₆. Results relevant to the reaction of methyl radicals with toluene compared to methyl radical recombination are discussed.     

Kinetics of reversible recombination of aromatic C-centered radicals

The kinetics of the reversible recombination of the 2-phenyl- (I), 2-p-methoxyphenyl-(II), and 2-p-nitrophenyl-3-oxo-2,3-dihydrobenzothiophene-2-yl (III) radicals have been investigated. Recombination rate constants of R(I–III) have been determined in different solvents (2k₁ ～ 10⁹ M^?1 s^?1). The rate of reaction (I) with R(I–III) decreases with increasing solvent viscosity η. In the toluene-vaseline oil mixture (2 ? η ? 120 cP) the recombination of R(I–III) is molecular mobility limited. The thermodynamic parameters of reaction (I) have been determined: ΔH⁰ = 20–30 kcal/mol. Activation volumes ΔV for recombination of R(II) have been measured. In n-propanol ΔV is equal to the viscous flow activation volume of the solvent ΔV. In toluene and chloroform ΔV < ΔV. For the last two solvents the activation volumes of the cage reaction have been estimated ΔV = ?(2–3) cm³/mol. Visible-range absorption spectra and ESR spectra have been recorded for R(I–III). The role of cage effect in the reactivity anisotropy averaging of R(I–III) is discussed. The potential of the high-pressure tests for deriving information about the elementary act of a fast bimolecular reaction is considered.