Analytical resolution of a parallel second‐order reaction mechanism

The competition among the three different elementary second‐order processes involving the radicals A and B, (1) (2) (3) is frequently established in many combustion and atmospheric chemistry systems. The analytical resolution of the above mechanism for k_AB = 2k_AA and k_AB = 2k_BB, that is, for a cross‐combination ratio ? = k_AB/(k_AAk_BB)^1/2 = 2, is well‐known, but it has been claimed not to exist for ? ≠ 2. In the present paper an analytical resolution of the system (1)–(3), performed under the condition k_AB ≠ 2k_AA and k_AB ≠ 2k_BB, leads to The mathematical procedure leading to this equation and the equation itself are valid independently of the nature of the products of the reactions ( 1 ), ( 2 ) and ( 3 ), that is, recombination or disproportionation products, provided that the reactants and the order of the reactions remain the same. The comparison with numerical integration for exemplary cases is performed. The solutions for the particular cases k_AB ≠ 2k_BB or k_AB ≠ 2k_AA are also presented. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 246–251, 2003     

H2S-promoted thermal isomerization of butene-2 CIS to butene-1 or butene-2 trans around 500°C

H₂S increases the thermal isomerization of butene-2 cis (B_c) to butene-1 (B₁) and butene-2 trans (B_t) around 500°C. This effect is interpreted on the basis of a free radical mechanism in which buten-2-yl and thiyl free radicals are the main chain carriers. B₁ formation is essentially explainedby the metathetical steps: whereas the free radical part of B_t formation results from the addition–elimination processes: . It is shown that the initiation step of pure B_c thermal reaction is essentially unimolecular: and that a new initiation step occurs in the presence of H₂S: . The rate constant ratio has been evaluated: and the best values of k₁ and k_1', consistent with this work and with thermochemical data, are . From thermochemical data of the literature and an “intrinsic value” of E_?3 ? 2 kcal/mol given by Benson, further values of rate constants may be proposed: is shown to be E₄ ? 3.5 ± 2 kcal/mol, of the same order as the activation energy of the corresponding metathetical step.     

Kinetics of the reaction: 2C2H4 → C2H5 + C2H3· heat of formation of the vinyl radical

The initial rates of formation of the major products in the thermal reactions of ethylene at temperatures in the neighborhood of 800 K have been measured in the presence and absence of the additives neopentane and ethane. It has been shown that in the absence of the additive the main initiation process is (1) while in the presence of neopentane and ethane the following additional initiation processes occur: (2) From the ratios of the rates of formation of the major products in the presence and absence of the additive the ratios k_N/k₁ and k_E/k₁ were measured over the temperature range of 750–820 K. Taking values from the literature for k_N and k_E, the following value was obtained for k₁: Previous results using butene-1 as additive were rexamined and shown to be consistent with this measurement. From this measurement the following values were derived: ΔH_f(C₂H₃) = 63.4 ± 2 kcal/mol and D(C₂H₃? H) = 103 kcal/mol.     

Thermal reaction of CH2O with NO2 in the temperature range of 393–476 K: FTIR product measurement and kinetic modeling

The thermal reaction of CH₂O with NO₂ has been investigated in the temperature range of 393–476 K by means of FTIR product analysis. Kinetic modeling of the measured CH₂O, NO, CO, and CO₂ concentration time profiles under varying reaction conditions gave rise to the rate constants for the following key reactions: (1) and (2) The error limits shown represent only the scatter (±1 σ) of the modeled values. In the modeling, the total rate constant for the CHO + NO₂ reaction, k₂ + k₃, was not varied and the value reported by Gutman and co-workers (ref. [8]) was used for the whole temperature range investigated here. The proposed reaction mechanism, employing these newly established rate constants, can quantitively account for nearly all measured product yields, including the [CO]/([CO] + [CO₂]) ratios reported by earlier workers.     

Kinetics of the reactions Br2 + HCN,BrCN + I−, S(CN)2 + I− in aqueous acid solution

Spectrophotometric methods have been used to obtain rate laws and rate parameters for the following reactions: with k_a, k_b, E_a, E_b having the values 85±5 l./mole · s, 5.7±0.2 s^?1 (both at 298.2°K), and 56±4 and 66±2 kJ/mole, respectively. with k_c=0.106±0.004 l./mole ·s at 298.2°K and E_c=67±2 kJ/mole. with k_d=(3.06 ±; 0.15) × 10^?3 l./mole ·s at 298.2°K and E_d=66±2 kJ/mole. Mechanisms for these reactions are discussed and compared with previous work.     

The kinetics of the thermal bromination of CF3I. Determination of the bond dissociation energy D(CF3−I)

The kinetics of the thermal bromination reaction have been studied in the range of 173–321°C. For the step we obtain where θ=2.303RT cal/mole. From the activation energy for reaction (11), we calculate that This is compared with previously published values of D(CF₃?I). The relevance of the result to published work on k_c for a combination of CF₃ radicals is discussed.     

The kinetics of the gas phase decomposition reactions of the hexafluoro-t-butoxy radical

Hexafluoro-t-butoxy radicals have been generated by reacting fluorine with hexafluoro-2-methyl isopropanol: Over the temperature range of 406–600 K the hexafluoro-t-butoxy radical decomposes exclusively by loss of a CF₃ radical [reaction (-2)] rather than by loss of a CH₃ radical [reaction (-1)]: (1) The limits of detectability of the product CF₃COCF₃, by gas-chromatographic analysis, place a lower limit on the ratio k_?2/k_-1 of ～80. The implications of this finding in relation to the reverse radical addition reactions to the carbonyl group are briefly discussed. A thermochemical kinetic calculation reveals a discrepancy in the kinetics and thermodynamics of the decomposition and formation reactions of the related t-butoxy radical:      

Addition of trichloromethyl radicals to tetrachloroethylene

The gamma-radiation-induced free-radical chain reactions in liquid CCl₄? C₂Cl₄? c? C₆H₁₂ mixtures were studied in the temperature range of 363–448°K. The main products in this system are chloroform, hexachloropropene and chlorocyclohexane. These products are formed via reactions (1)–(5): with G values (molec/100 eV) of the order of magnitude of 10² and 10³ at the lowest and highest temperatures, respectively. Values of k₂/k₁ were determined from the product distribution. In turn, these values gave the following Arrhenius expression for k₂/k₁ (θ = 2.303RT, in kcal/mol): From this result and the previously determined Arrhenius parameters of reaction (1), k₂ is found to be given by .     

Rate constants and kinetic isotope effects for hydrogen/deuterium abstraction by chlorine atoms from the chloromethyl group in CH2ClCH2Cl,CD2ClCD2Cl,CH2ClCHCl2, and CH2ClCDCl2

The abstraction of hydrogen and deuterium from 1,2-dichloroethane, 1,1,2-trichloroethane, and two of their deuterated analogs by photochemically generated ground state chlorine atoms has been investigatedin the temperature range 0–95°C using methane as a competitor. Rate constants and their temperature coefficients are reported for the following reactions Over the temperature range of this investigation an Arrhenius law temperature dependence was observed in all cases. Based on the adopted rate coefficient for the chlorination of methane [L.F. Keyser, J. Chem. Phys., 69 , 214 (1978)] which is commensurate with the present temperature range, the following rate constant values (cm³ s^?1) are obtained: The observed pure primary, and mixed primary plus α- and β3-secondary kinetic isotope effects at 298 K are k₃/k₆ = 2.73 ± 0.08, and k₁/k₂ = 4.26 ± 0.12, respectively. Both show a normal temperature dependence decreasing to k₃/k₆ = 2.39 ± 0.06 and k₁/k₂ = 3.56 ± 0.09 at 370 K. Contrary to some simple theoretical expectations, the kinetic isotope effect for H/D abstraction decreases with increasing number of chlorine substituents in the geminal group in a parallel manner to the trend established previously for C1-substitution in the adjacent group. The occurrence of a β-secondary isotope effect, k₄/k₅, is established; this effect suggests a slight inverse temperature dependence.     

Effect of olefins on the thermal decomposition of propane part I. The model reaction

Study of the thermal decomposition of propane at very low conversions in the temperature range 760–830 K led to refinement of the mechanism of the reaction. The quotient V/V characterizing the two decomposition routes connected with the 1- and 2-propyl radicals proved to depend linearly on the initial propane concentration. This suggested the occurrence of intermolecular radical isomerization: in competition with decomposition of the 2-propyl radical: The linearity led to the conclusion that the selectivity of H-abstraction from the methyl and methylene groups by the methyl radical is practically the same as that by the H atom. The temperature-dependence of this selectivity ( μ = kCH₃/kCH₂) was given by Further evaluation of the dependence gave the Arrhenius representation for the ratio of the rate coefficients of the above isomerization and decomposition reactions. Steady-state treatment resulted in the rate equation of the process, comparison of which with measurements gave further Arrhenius dependences.     

One‐step,two‐electron oxidation of cis‐diaquabis(1,10‐phenanthroline)chromium(III) to cis‐dioxobis(1,10‐phenanthroline)chromium(V) by periodate in aqueous acidic solutions

The kinetics of oxidation of cis‐[Cr^III(phen)₂(H₂O)₂]³⁺ (phen = 1,10‐phenanthro‐ line) by IO₄^? has been studied in aqueous acidic solutions. In the presence of a vast excess of [IO₄^?], the reaction is first order in the chromium(III) complex concentration. The pseudo‐first‐order rate constant, k_obs, showed a very small change with increasing [IO₄^?]. The dependence of k_obs on [IO₄^?] is consistent with Eq. (i). (i) The pseudo‐first‐order rate constant, k_obs, increased with increasing pH, indicating that the hydroxo form of the chromium(III) complex is the reactive species. An inner‐sphere mechanism has been proposed for the oxidation process. The thermodynamic activation parameters of the processes involved are also reported. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 563–568, 2011     

Time-resolved vibrational chemiluminescence: Rate constants for the reactions of F atoms with H2O and HCN,and for the relaxation of HF (v = 1) by H2O and HCN

Rate constants have been determined at (298 ± 4) K for the reactions: and the relaxation processes: Time-resolved HF(1,0) emission was observed following the photolysis of F₂ with pulses from an excimer laser operating on XeCl (λ = 308 nm). Analysis of the emission traces gave first-order constants for reaction and relaxation, and their dependence on [H₂O] and [HCN] yielded:      

Radiation-induced dehalogenation of 1,1,1,2 tetrachloroethane and 1,1,2 trichloro-1 bromoethane reactions of 1,1,2 trichloroethyl radicals

The kinetics of the radiation-induced free radical chain reactions in solutions of CCl₃CClH₂ and CCl₂BrCH₂Cl in cyclohexane (RH) were studied in the temperature range of 90–225°C. 1,1,2 trichloroethyl and 1,1,1,2 tetrachloroethyl radicals were produced by the reaction of radiolytically generated cyclohexyl (R) radicals with solutes. The reactions studied were The following rate expressins were obtained: where θ = 2.303RT in kcal/mole. From the activation parameters of the k₄/k₅ rate constant ratio and the assumption that E₄ = E, E₅ was calculated to be 20.2 ± 0.2 kcal/mole. The Arrhenius parameters for the Cl atom elimination reaction from chloroethyl radicals derived from liquid and gas-phase studies are compared.     

Kinetic isotope effect in the protonation of anthracenide salts by MeOH and MeOD role of counterions and solvents

Kinetics of protonation of Li⁺, Na⁺, K⁺, and Cs⁺ salts of anthracene radical anions (A^?_·,Cat⁺) and dianions (A^2?, 2Cat⁺) by MeOH and MeOD in tetrahydrofuran (THF) and dimethoxyethane (DME) led to the determination of the isotope effect (k_H/k_D) in the following reactions: Studies of cation and solvent influence on the rate constants of these reactions and on the magnitude of the isotope effect permitted us to draw some conclusions about the structure of the pertinent transition states. It seems that only the tight A^?·,Na⁺ pairs participate in the protonation, and on this basis the fraction of tight ion paris of A^?·,Na⁺ in DME was estimated. Our results have been compared with data reported in the literature.     

Reaction of methoxy radicals with oxygen. I. Using dimethyl peroxide as a thermal source of methoxy radicals

Using dimethyl peroxide as a thermal source of methoxy radicals overthe temperature range of 110–160°C, and the combination of methoxy radicals and nitrogen dioxide as a reference reaction: a value was determined of the rate constant for the reaction of methoxy radicals with oxygen: is independent of nitrogen dioxide or oxygen concentration and added inert gas (carbon tetrafluoride). No heterogeneous effects were detected. The value of k₄ is given by the expression In terms of atmospheric chemistry, this corresponds to a value of 10^5.6 M^?1·sec^?1 at 298 K. Extrapolation to temperatures where the combustion of organic compounds has been studied (813 K) produces a value of 10^7.7 M^?1·sec^?1 for k₄. Under these conditions, reaction (4) competes with hydrogen abstraction or disproportionation reactions of the methoxy radical and its decomposition (3): In particular k₃ is in the falloff region under these conditions. It is concluded that reaction (4) takes place as the result of a bimolecular collision process rather than via the formation of a cyclic complex.     

Influence of butadiene-1,3 on ethanal pyrolysis at 495°C

At 495°C and a low extent of reaction, ethanal pyrolysis is slightly inhibited by the addition of small quantities of butadiene-1,3, whereas it is accelerated by more important quantities. The inhibiting effect is interpreted in terms of a free-radical chain mechanism in which the main chain carriers of ethanal pyrolysis (CH₃.free radicals) reversibly add to butadiene-1,3 and yield penten-2-yl (R.) free radicals. These free radicals either react in a metathetical step: or in terminating steps. But butadiene-1,3 also gives rise to new initiation steps: which account for the accelerating effect. Process (i₃) seems to be more important than process (i₂) in the experimental conditions, but its nature could not be identified. The results are consistent with literature data and the following value of k₆: (4.57T in cal/mol).     

Rate constants for abstraction of hydrogen from ethylene by methyl and ethyl radicals relative to abstraction from propane and isobutane

A method is described for the measurement of relative rate constants for abstraction of hydrogen from ethylene at temperatures in the region of 750 K. The method is based on the effect of the addition of small quantities of propane and isobutane on the rates of formation of products in the thermal chain reactions of ethylene. On the assumption that methane and ethane are formed by the following reactions, (1) measurements of the ratio of the rates of formation of methane and ethane in the presence and absence of the additive gave the following results: Values for k₂ and k₃ obtained from these ratios are compared with previous measurements.     

Determination of the mechanism of the oxidation of the trichloromethyl radical by the photolysis of chloral in the presence of oxygen

The photooxidation of chloral was studied by infrared spectroscopy under steady-state conditions with irradiation of a blackblue fluorescent lamp (300 nm < λ < 400 nm, λ_max = 360 nm) at 296 ± 2 K. The products were hydrogen chloride, carbon monoxide, carbon dioxide, and phosgen. The kinetic results reveal that the reaction proceeds via chain reaction of the Cl atom: The results lead to the conclusion that mechanism (B) is confirmed to be more likely than mechanism (A), which was favored at one time by Heicklen for the mechanism of the oxidation of trichloromethyl radicals by oxygen molecules: The ratio of the initial rates of CO and CO₂ formation gave k₇/k₆ = 4.23M^?1, and the lower limit of reaction (5) was found to be 3.7 × 10⁸M^?1 sec^?1.     

On the gas-phase free radical displacement reaction CH3 + CD3COCD3 → CD3 + CH3COCD3

The gas-phase free radical displacement reaction has been studied in the temperature range of 240–290°C and at 140°C with the thermal decomposition of azomethane (AM) and di-tert-butylperoxide (DTBP), respectively, as methyl radical sources. The reaction products of the CD₃ radicals were analyzed by mass spectrometry. Assuming negligible isotope effects, Arrhenius parameters for the elementary radical addition reaction were derived: The data are discussed with respect to the back reaction and general features of elementary addition reactions.     

The kinetics of the Diels–Alder addition of cyclopentadiene to acetylene and the decomposition of norbornadiene

The title reactions have been investigated in a static system. The addition of acetylene to cyclopentadiene (CPD) results in formation of norbornadiene (BCH), cycloheptatriene (CHT), and toluene (T), while BCH decomposition produces CPD, C₂H₂, CHT, and T. Kinetic studies, comprising both product–time evolution and initial pressure variation, support a mechanism These reactions are almost certainly homogeneous and molecular in nature. Least mean square analysis of the data yield for temperatures of 525–656°K, log k_?1 (1./mole·s)=7.51±0.05? (24.19±0.15 kcal/mole)/RT ln 10, and for temperatures of 584–630°K,