A method for computer analysis of kinetics of competing first- and second-order reactions

Competing first- and second-order reactions of transient molecular species (e.g., triplet states and free radicals) are a common occurrence in kinetic studies such as flash photolysis and pulse radiolysis. We have developed a method for analyzing the decay kinetics of any species (Y) whose disappearance is described by ?dY/dt = k₁Y + k₂Y². The computer program (written in time-sharing BASIC) employs an iterative technique to obtain the least-squares estimates of the three parameters in the integrated rate equation.     

Kinetics of the thermal gas phase isomerization of bicyclo[4.1.0]heptane

The kinetics of the gas-phase decomposition of bicyclo[4.1.0]heptane has been studied over the temperature range of 708–769 K at pressures between 1 and 17 torr. Isomerization to 1-methylcyclohex-1-ene, methylenecyclohexane, and cycloheptene accounts for 96–98% of the primary reaction products and occurs by first-order, homogeneous, nonradical processes.      

Eyringpy: A program for computing rate constants in the gas phase and in solution

Eyringpy is a modular program for calculating thermochemical properties and rate constants for reactions in the gas phase and in solution. The code is written in Python and it has a user-friendly interface and a simple input format. Unimolecular and bimolecular reactions with one and two products are supported. Thermochemical properties are estimated through canonical ensemble and rate constants are computed according to the transition state theory. One-dimensional Wigner and Eckart tunneling corrections are also available. Rate constants of bimolecular reactions involving the formation of pre-reactive complexes are also estimated. To compute rate constants in solution, Eyringpy uses the Collins–Kimball theory to include the diffusion-limit, the Marcus theory for electron transfer processes, and the molar fractions to account for the solvent pH effect.     

Ozone–olefin reactions in the gas phase 1. Rate constants and activation energies

Reactions of ozone with simple olefins have been studied between 6 and 800 mtorr total pressure in a 220-m³ reactor. Rate constants for the removal of ozone by an excess of olefin in the presence of 150 mtorr oxygen were determined over the temperature range 280 to 360° K by continuous optical absorption measurements at 2537 Å. The technique was tested by measuring the rate constants k₁ and k₂ of the reactions (1) NO + O₃ → NO₂ + O₂ and (2) NO₂ + O₃ rarr; NO₃ + O₂ which are known from the literature. The results for NO, NO₂, C₂H₄, C₃H₆, 2-butene (mixture of the isomers), 1,3→butadiene, isobutene, and 1,1 -difluoro-ethylene are 1.7 × 10^{?1 4} (290°K), 3.24 × 10^?17 (289°K), 1.2 × 10^{?1 4} exp (–4.95 ± 0.20/RT), 1.1 × 10^{?1 4} exp (–3.91 ± 0.20/RT), 0.94 × 10^{?1 4} exp ( –2.28 ± 0.15/RT), 5.45 ± 10^{?1 4} exp ( –5.33 ± 0.20/RT), 1.8 ×10^?17 (283°K), and 8 × 10^?20 cm³/molecule ·s(290°K). Productformation from the ozone–propylene reaction was studied by a mass spectrometric technique. The stoichiometry of the reaction is near unity in the presence of molecular oxygen.     

A differential modification of the thermal maximum method for evaluating the enthalpies and rate constants of homogeneous reactions

Both the change of enthalpy associated with a reaction and the rate constant of the reaction can be found from the dependence on time of the difference between the temperatures of a reaction mixture and a reference solution contained in identical non-insulated vessels submerged in a thermostat. Heats of dilution and fluctuations of the temperature of the thermostat are cancelled by the differential arrangement, and the heat-transfer constant for the reaction vessel need not be known or measured separately, which is an important advantage over the classical thermal maximum method. For half-times between about 9 and 30 s and overall changes of temperature between 25 and 90 mK, relative standard deviations of a few per cent in both ΔH and k are easily attainable.     

Kinetics of the iodine atom catalyzed gas phase geometrical isomerization of diiodoethylene. Rotation about a single bond

The spectrophotometric determination of the rate of iodine atom catalyzed geometrical isomerization of diiodoethylene in the gas phase from 502.8 to 609.1°K leads to a rate constant for the bimolecular reaction between I and trans-diiodoethylene of log k_t?c(M^?1 sec^?1) = 8.85 ± 0.12 ? (11.01 ± 0.30)/θ. Estimates of the entropy and enthalpy change for the addition of I atoms to trans-diiodoethylene (process a.b) lead to log K_a.b(M^?1) = ?2.99 ? 4.0/θ, and thus to log k_c (sec^?1) = log k_t?c – log K_ab = 11.8 ?7.0/θ for the rate constant for rotation about the single bond in the adduct radical. The theory for calculation of the rotation rate constant is presented and it is shown that while the exact value depends on the barrier height, a value of 6.8 kcal/mole for this quantity leads to log k (sec^?1) = 11.8 ?6.7/θ. The activation energy points to a better value of the group contribution to heat of formation of the group C -(I)₂(H)(C) than one based on bond additivity.     

Kinetics and mechanism of the thermal chlorination of chloroform in the gas phase

The gas‐phase thermal chlorination of CHCl₃ has been studied up to high conversions by photometry and gas chromatography in a conditioned static quartz reaction vessel between 573 and 635 K. The initial pressures of both CHCl₃ and Cl₂ ranged from about 10–100 Torr, and the initial total pressure was varied between about 30–190 Torr. The reaction is rather complex because the produced CCl₄ is not stable. The rate of consumption of Cl₂ therefore increases in the course of time. This acceleration is explained quantitatively in terms of a radical mechanism and its kinetic and thermodynamic parameters. This reaction model is based on a known model for the pyrolysis of CCl₄ to which only one reaction couple involving CHCl₃ has been added. Analyses of the rates of the homogeneous elementary steps show that the primary source of Cl atoms is the second‐order dissociation of Cl₂, which is rapidly superseded by a secondary source, the first‐order dissociation of the CCl₄ primary product. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 466–472, 2000     

Kinetics of some reactions of vinyl and isopropyl radicals in the gas phase

Vinyl and isopropyl radicals were generated by the pyrolysis of azoisopropane in the presence of acrolein at 473–563 K. Reaction products were analyzed by gas chromatography. Rate constant ratios k₂/k₁ = 0.02 ± 0.01 and k₄/k₃ = 0.01 ± 0.005 are suggested for the following reactions: The rate constant ratio of reactions (7) and (c) obeys the Arrhenius equation The Arrhenius equation was derived for (k₈ + k₉).     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 2. Accurate thermal rate constants

Multistructural canonical variational-transition-state theory with multidimensional tunneling (MS-CVT/MT) is employed to calculate thermal rate constants for the abstraction of hydrogen atoms from both positions of methanol by the hydroperoxyl and methyl radicals over the temperature range 100-3000 K. The M08-HX hybrid meta-generalized gradient approximation density functional and M08-HX with specific reaction parameters, both with the maug-cc-pVTZ basis set, were validated in part 1 of this study (Alecu, I. M.; Truhlar, D. G. J. Phys. Chem. A2011, 115, 2811) against highly accurate CCSDT(2)(Q)/CBS calculations for the energetics of these reactions, and they are used here to compute the properties of all stationary points and the energies, gradients, and Hessians of nonstationary points along each considered reaction path. The internal rotations in some of the transition states are found to be highly anharmonic and strongly coupled to each other, and they generate multiple structures (conformations) whose contributions are included in the partition function. It is shown that the previous estimates for these rate constants used to build kinetic models for the combustion of methanol, some of which were based on transition state theory calculations with one-dimensional tunneling corrections and harmonic-oscillator approximations or separable one-dimensional hindered rotor treatments of torsions, are appreciably different than the ones presently calculated using MS-CVT/MT. The rate constants obtained from the best MS-CVT/MT calculations carried out in this study, in which the important effects of corner cutting due to small and large reaction path curvature are captured via a microcanonical optimized multidimensional tunneling (μOMT) treatment, are recommended for future refinement of the kinetic model for methanol combustion.     

The thermal decomposition of diimide in the gas phase: Kinetics and stoichiometry

The kinetics and stoiehiometry of the decomposition of N₂H₂ and N₂D₂ have been studied as a function of sample size, pressure, and temperature. The reaction follows a single first order kinetic expression over most of its time course. It is suggested that the rate-determining step in the mechanism is a first-order homogeneous gas-phase isomerization of trans-diimide with rate constants:k = 1.8 exp (-4.2 kcal/mol/RT) sec^?1 and k = 1 exp (-4.4 kcal/mol/RT) sec^?1. The detailed mechanism of this isomerization, however, is not evident. At temperatures above room temperature, self-heating has been observed which leads to an initial fast decay. At room temperature the reaction exhibits autocatalysis with the rate increasing as the reaction proceeds. This has been attributed to enhancement by a surface decay process involving adsorbed hydrazine. The only significant products from the decomposition of N₂H₂ are N₂, H₂, and N₂H₄, and the results are interpreted in terms of two parallel reactions: The decomposition of N₂D₂ occurs almost completely by the single reaction giving N₂ + N₂D₄. No azide formation has been detected from either N₂D₂, or N₂D₂, and limits have been put on the yield of ammonia. Extinction coefficients at 365 nm of 3.9 ± 0.2 for N₂H₂ and 3.3 ± 0.1 for N₂D₂ have been measured. Both the rate of decay and the stoichiometry of products show pressure dependence below 150 torr, and this is suggested to be due to direct decomposition of cis-N₂H₂ on the surface.     

Flash photolysis of biacetyl in gas phase. Rate constants of reactions between methyl and acetyl radicals

The flash photolysis of biacetyl produces CO, C₂H₆, and CH₃COCH₃ as main products, and in small amounts CO₂, C₂H₄, and CH₃CHO. The rate constants of reactions (2) and (3) of thermally equilibrated radicals were calculated from the amounts of products: .     

Digital simulation of electrochemical processes involving very fast chemical reactions : Part 2. A new criterion for determining rate constants of consecutive second-order irreversible chemical reactions

Electrode reactions followed by very fast chemical reactions are considered. A simple approach, in which steady state and linear concentration profiles in the reaction layer are assumed, is proposed for the simulation of these processes when the substrate is not present in large excess. When the substrate/depolarizer mole ratio is less than one, two well-separated peaks are detected; under such conditions, working curves that enable the corresponding second-order homogeneous rate constant to be evaluated can be derived by the finite-difference simulation technique. The method is applied to elucidation of the reduction of the tetrakis(triphenylphosphine)nickel(I) complex in the presence of hydrogen ions in acetonitrile at ?30°C.     

Structure and isomerization of arenonium ions of dichlorobenzenes in the gas phase. A theoretical study

Ab initio MP2 calculations of all isomeric arenoium ions (AI) ofortho-, meta-, andpara-dichlorobenzenes in the gas phase were carried out with full optimization of geometry with the 6–31 G^* basis set. The calculated proton affinities depend substantially on the position of geminal center in the corresponding dichlorobenzenonium ion and decrease in the series 1,2-dichloro-4H-benzenonium>1,2-dichloro-3H-benzenonium>1,2-dichloro-2H-benzenonium; 1,3-dichloro-4H-benzenonium>1,2-dichloro-3H-benzenonium >1,3-dichloro-5H-benzenonium>1,3-dichloro-3H-benzenonium; 1,4-dichloro-2H-benzenonium >1,4-dichloro-4H-benzenonium. The structures of transition states and activation energies (E _a) of almost all 1,2-shifts of H and Cl atoms in Al were determined. The activation energies of migrations of H atoms are about 6 kcal mol⁻¹ less than those of migrations of Cl atoms in similar structures. The isomerization routes and relations between the rate constants for isomerization of dichlorobenzenes through Al were established. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1726–1731, September, 1998.     

Kinetics of partly diffusion-controlled reaction XXI: A simple algorithm for computing the apparent rate of reaction

Starting from Smoluchowski's hypothesis, a simple algorithm is developed in order to obtain the apparent rate constant at large values of time, t, with some physical and chemical processes, as in the case of diffusion controlled reactions. Some practical examples are illustrated, assuming nonuniform distribution function, space-dependent diffusion coefficient or short-range interaction leading to an asymptotic analytical expression of the form α + β/√t, where α and β are constants function of the system of interest.     

Kinetics and mechanism of the thermal decomposition reaction of acetone cyclic diperoxide in the gas phase

The kinetics of the thermal decomposition reaction of gaseous 3,3,6,6-tetramethyl-1,2,4,5-tetroxane (ACDP) in the presence of n-octane was studied in the 403.2–523.2 K temperature range. This reaction yields acetone as the organic product. Under optimum conditions, first-order kinetics were observed, included when the S/V ratio of the Pyrex reaction vessel was increased by a nearly six-fold factor. In the range 443.2–488.2 K the temperature dependence of the rate constants for the unimolecular reaction in conditioned vessels is given by In k₁/(s^?1) = (31.8 ± 2.5) ? [(39.0 ± 2.5)/RT]. The value of the energy of activation in kcal/mol correspond to one O? O bond homolysis of the ACDP molecule in a stepwise biradical initiated decomposition mechanism. At the lower reaction temperatures as well in preliminary experiments participation of a surface catalyzed ACDP decomposition process could be detected. © 1994 John Wiley & Sons, Inc.     

Kinetics and mechanism of the thermal reactions of endo- and exo-5-cyanobicyclo[2.2.2]oct-2-ene and methyl-substituted derivatives in the gas phase

The thermal reactions of endo- and exo-5-cyanobicyclo-[2.2.2]oct-2-ene and their trans- and cis-6-methyl-substituted derivatives have been investigated in the gas phase between 518 and 630 K. Each product decomposes by two parallel first-order retro-Diels-Alder reactions, a main one with formation of cyclohexa-1,3-diene and a minor one with elimination of ethene. Slight isomerizations are also observed. The kinetic results can be explained in terms of a biradical mechanism. The rate-determining step is shown to depend on the amount of resonance energy in the biradical. Heats of formation and entropies of the bicyclo[2.2.2]oct-2-enes studied are estimated.