The correctional kinetic equation for the peak temperature in the differential thermal analysis

The peak temperature (T _p) and different temperature (ΔT) are the basic information in the differential thermal analysis (DTA). Considering the kinetic relation and the heat equilibrium in DTA, a correctional differential kinetic equation (containing T _p and ΔT parameter) is proposed. In the dehydration reaction of CaC₂O₄·H₂O, the activation energy calculated from the new equation showed some smaller than that from Kissinger equation, but some bigger than that from Piloyan equation.     

An equation for the calculation of retention indices in temperature-programmed gas chromatography with allowance for the nonlinear variation of the retention parameters ofn-alkanes

In view of the nonlinear variation of the temperature increments ofn-alkanes found previously, the accuracy of the calculations of the retention indices (I _pr) of substances in temperature-programmed capillary gas chromatography carried out in terms of six known equations was verified. A new four-parameter equation was proposed, and a general method for the calculation of its coefficients, suitable for all stationary phases, based on the adjusted retention times ofn-alkanes was suggested. The coefficients of the equation for 12 temperature variation programs were determined. Using the homologous series of methyl esters of fatty acids as an example, it was shown that the proposed equation ensures the minimum error of determination ofI _pr under various conditions. The equation also makes it possible to carry out interpolation and extrapolation calculations. The coefficients of the equation are found using the least-squares method based on data for any 4–5 referencen-alkanes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 323–327, February, 1997.     

Polymerization of vinyl chloride in the presence of precipitants. II.

The kinetics of the radiation-induced polymerization of vinyl chloride in the presence of precipitants has been successfully described by a one-parameter equation as follows, where ?₀ is initial monomer volume fraction, X is conversion, t is time, and k is reaction constant. The equation was confirmed for extensive conditions of temperatures and monomer concentrations in the case of polymerization in methanol. The degree of polymerization was related with the reaction constant k, initial monomer volume fraction ?₀, monomer chain transfer constant C_m, conversion X, and the initiation rate I as follows, The factors which determine the value of the reaction constant k were elucidated through measurements of the reaction constant k and the degree of polymerization DP _n.     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Some reactions of the isopropyl radical

The decomposition of ethane sensitized by isopropyl radicals was studied in the temperature range of 496–548°K. The rate of formation of n-butane, isopentane, and 2,3-dimethylbutane were measured. The expression k₁/k₂^½ was found to be where k₁ and k₂ are rate constants of The decomposition of propylene sensitized by isopropyl radicals was studied between 494 and 580°K by determination of the initial rates of formation of the main products. The ratio of k₁₃/k₂^1/2 was evaluated to be where k₁₃ is the rate constant for The isomerization of the isopropyl radical was investigated by studying the decomposition of azoisopropane. The decomposition of the iso-C₃H₇ radical into C₂H₄ and CH₃ was followed by measuring the rate of formation of C₂H₄. On the basis of the experimental data, obtained in the range of 538–666° K, k₁₅/k₂^½ was found: where k₁₅ is the rate constant of      

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).     

A kinetic and mechanistic study of the formation of alkyl nitrates in the photo-oxidation of n-heptane studied under atmospheric conditions

The photo-oxidation of n-heptane in synthetic air containing methyl nitrite and nitric oxide has been ivestigated in an atmospheric flow reactor. By measuring the total yields of heptyl nitrate products, relative to the depletion of the n-heptane, the rate constant ratio, k_3b/k_3a has been determined for the reactions: (1) Over the temperature range 253–325 K and at a total pressure of 730 Torr, the following relative Arrhenius equation has been obtained from the present study together with literature data: These results confirm that the formation of alkyl nitrates from the photo-oxidation of n-alkanes arise from a primary reaction between the alkylperoxy radicals and nitric oxide. Furthermore the present experiments show that the lifetime of the intermediate in this type of reaction, presumed to be an alkyl peroxynitrite, ROONO, must be less than a few seconds.     

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:      

Thermal stability of intermediate sized acetylenic compounds and the heats of formation of propargyl radicals

4-Methylhexyne-1, 5-methylhexyne-1, hexyne-1, and 6-methylheptyne-2 have been decomposed in comparative-rate single-pulse shock-tube experiments. Rate expressions for the initial decomposition reactions at 1100°K and from 2 to 6 atm pressure are In combination with previous results, rate expressions for propargyl C? C bond cleavage are related to that for the alkanes by the expression These results yield a propargyl resonance energy of D(nC₃H₇-H) – D(C₃H₃-H) = 36 ± 2 kJ, in excellent agreement with a previous shock-tube study. They also lead to D(CH₃C≡CCH₂-H) – D(C₃H₃-H) = 0.6 ± 3 kJ, D(sC₄H₉-H) – D(iC₃H₇-H) = 0 ± 3 kJ, D(iC₄H₉-H) – D(nC₃H₇-H) = 2 ± 3 kJ, and D(nC₃H₇-H) – D(iC₃H₇-H) = 13.9 ± 3 kJ (all values are for 300°K). The systematics of the molecular decomposition process are explored.     

Kinetics of the reactions of cyclopropane derivatives. III. Gas-phase unimolecular isomerization of cyclopropyl cyanide to the cyanopropenes

Cyclopropyl cyanide isomerizes in the gas phase at 660°–760°K and 2–89 torr to give mainly cis- and trans-crotonitrile and allyl cyanide, with traces of methacrylonitrile. The reactions are first order, homogeneous, and unaffected by the presence of radical-chain inhibitors. The rate constants are given by Overall: cis-Crotonitrile: trans-Crotonitrile: Allyl cyanide: where the error limits are standard deviations. On the basis of a biradical mechanism, it is deduced that the ? CH? CN radical center is resonance stabilized by ca. 30 kJ mole^?1. Approximate equilibrium data are given for interconversion of the 1- and 3-cyanopropenes.     

Carbon-13 NMR spectra and the method for their calculation for long-chain polybranched carboxylic acids and their derivatives

Carbon-13 NMR spectra of 56 long-chain polybranched carboxylic acids their esters, including chloroand acetoxy-substituted derivatives, have been studied. An empirical linear two-parameter equation, relating carbon chemical shifts in α-branched carboxylic acids and their derivatives to the chemical shifts of the corresponding carbon atoms in analogous hydrocarbons, and to the degree of branching at the α-carbon atom, is suggested for the assignment of the signals, where δ_X is the shift in the acid (ester), δ_H the shift in its hydrocarbon counterpart and n the degree of branching. The regression coefficients, A, B and C, are given for X=COOH, COOMe and COOEt. It is shown that with polysubstituted derivatives, the equation may be applied sequentially. The secondary coefficients for the α-substituent then depend on the nature of the substituent X entering the primary equation. The equation may, if necessary, be applied in combination with the additive and structural increments of halogen atoms.     

Effect of Crack Temperature on the Pyrolysis of Ethane in Shock Tubes

Accepting a previously proposed mechanism of ethane pyrolysis in shock tubes, experimental product distributions observed by Burcat et al. have been used, through computer simulation technique, to measure rate constants of following reactions in the temperature range 1206–1386°K. Obtained k₂values are substantially higher than the extrapolation from an Arrhenius equation reported for the same rate constant at low temperatures. Rate constant k₂ is found decreasing with the system temperature at 6.3 atm of argon.     

Decomposition of the t-butoxy radical: II. Studies over the temperature range 303—393 K

The near U-V photolysis of t-butyl nitrite has been studied over the temperature range 303–393 K. Under these conditions t-butyl nitrite was shown to be a very clean photochemical source of t-butoxy radicals. This allows a study of the decomposition of the t-butoxy radical to be made over this temperature range (3). (1) Extrapolation of the rate constants k₃ to high pressure and combination with our previous thermal data give the results:      

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.     

Surface tension and density of binary mixtures of monoalcohols,water and acetonitrile: equation of correlation of the surface tension

Measurements of the surface tension (σ) and density (ρ) of binary mixtures of monoalcohols, water and acetonitrile at 298.15 K and at atmospheric pressure, as a function of mole fraction (x) have been made. The experimental values of the deviation of surface tension and the excess of molar volume (Δσ, V ^E) have been correlated by the Redlich–Kister equation. An empirical correlation equation is presented for the study of the surface tension of these mixtures, and comparisons are made of the experimental values of surface tension versus those obtained with the correlation equation and with other models of correlation. Finally, with the purpose of corroborating the validity of the correlation equation, the latter is applied to other reference binary mixtures.     

The kinetics of the gas-phase thermal isomerization and decomposition of Trans- and Cis-1,2-Bis(trifluoromethyl)-1,2,3,3-tetrafluorocyclopropane

The kinetics of the gas-phase thermal isomerization between trans- and cis-1,2-bis(trifluoromethyl)-1,2,3,3-tetrafluorocyclopropane as well as their decomposition to trans- and cis-perfluoro-2-butene, respectively, and CF₂, was studied in the temperature range of 473–533°K, with an initial pressure of reactant of 1.5 to 7.0 Torr. Some runs were also made with the addition of SF₆ as an inert gas up to a total pressure of 100 Torr. The reactions are first order and homogeneous. The rate constants for the geometrical isomerization fit the following Arrhenius relations: and the corresponding equations for the decomposition of the trans and cis-cyclopropane are .     

Study of an approximate relation between the energy of an atom and the electronic potential at the nucleus

This paper provides an analysis of the reasons for the approximate validity of the relation \documentclass{article}\pagestyle{empty}\begin{document}$ E = \frac{3}{7}NV(0) $\end{document}, between the total energy E of a neutral atom, the number N of electrons, and the electronic potential at the nucleus V(0). Using the density functional formalism we find that the right-hand side of the above equation also appears (and is the leading term) in density functional approximations more sophisticated than the Thomas–Fermi (TF ) approximation (the above equation is exact in the TF approximation). Systematic improvements to the equation appear to be difficult because the main corrections come from those terms which are more difficult to handle in the density functional formalism. After this analysis we propose a kinetic energy functional for neutral atoms in the Hartree–Fock approximation. The first term of this new functional is a rescaled Thomas–Fermi term , where γ = ?0.0063 for light atoms and γ = 0.0085 for the others. The second term is the first gradient correction due to Kirzhnits . For lithium to krypton atoms, this new functional gives an average error of 0.22%.     

Direct determination of the rate constant of the reaction NO + HO2 → NO2 + OH with the LMR

The rate of the reaction was determined in an isothermal discharge flow reactor with a combined ESR–LMR detection under pseudo-first-order conditions in HO₂. The rate constant was identical in experiments with two different HO₂ sources: F + H₂O₂ and H + O₂ + M. The absolute rate constant at T = 293 K was measured as In the range 2 ≤ p mbar ≤ 17 no pressure dependence for k₁ was found.     

An Empirical Relation for the Evaluation of the Dielectric Constants of Some Miscible Aqueous-Organic Solvent Mixtures at 298.15 K

Abstract

Dielectric constants of some miscible aqueous-organic solvent mixtures at 25°C have been analyzed by an equation analogous to Tamura and Kurata equation for viscosity. The hydration numbers n_h found out from the plots of Δ? vs. x₂ are explained in terms of H-bonding both in water-rich and alcohol-rich medium.     

Relative rate constants of the gas-phase decomposition reactions of the s-butoxy radical

s-Butoxy radicals have been generated by reacting fluorine with s-butanol: Over the temperature range 398.6 to 493.3 K the s-butoxy radical decomposes by two different pathways to yield acetaldehyde and propionaldehyde, acetaldehyde being the major product: The ratio k₁/k₂ was found to be temperature dependent. An Arrhenius plot of the data (398.6 to 493.3 K) yields the relative Arrhenius parameters, E₁ - E₂ = ?11.2 ± 0.8 kJ mol^?1 and (A₁/A₂) = 0.59 ± 0.14. The ratio of rate constants k₁/k₂ was shown to be independent of total pressure (80–600 torr) and of the pressure of s-butanol (2–13 torr). The kinetic results for these s-butoxy decomposition reactions are discussed in relation to the literature data and in terms of the thermochemistry of the reactions.