Numerical investigation of the uncertainty of Arrhenius parameters

The temperature dependence of rate coefficient k is usually described by the Arrhenius expression ln k = ln A − (E/R)T ⁻¹. Chemical kinetics databases contain the recommended values of Arrhenius parameters A and E, the uncertainty parameter f (T) of the rate coefficient and temperature range of validity of this information. Taking ln k as a random variable with known normal distribution at two temperatures, the corresponding uncertainty of ln k at other temperatures was calculated. An algorithm is provided for the generation of the histogram of the transformed Arrhenius parameters ln A and E/R, which is in accordance with their 2D normal probability density function (pdf). The upper and the lower edges of the 1D normal distribution of ln k correspond to the two opposite edge regions of the 2D pdf of the transformed Arrhenius parameters. Changing the temperature, these edge regions move around the 2D cone. The rate parameters and uncertainty data belonging to reactions H + H₂O₂ = HO₂ + H₂ and O + HO₂ = OH + O₂ were used as examples.     

Arrhenius parameters for reactions of oxygen atoms with the fluorinated ethylenes

Competitive studies of the reactions of ground-state oxygen atoms, generated by mercury-photosensitized decomposition of nitrous oxide, have been carried out with ethylene and all the fluoroethylenes using 2-(trifluoromethyl)-propene as reference compound. From measurements at 25°C and 150°C relative rate constants have been determined and used to calculate the Arrhenius parameters shown in the following table:

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.     

Sensitivity of viscosity Arrhenius parameters to polarity of liquids

Several empirical and semi-empirical equations have been proposed in the literature to estimate the liquid viscosity upon temperature. In this context, this paper aims to study the effect of polarity of liquids on the modeling of the viscosity–temperature dependence, considering particularly the Arrhenius type equations. To achieve this purpose, the solvents are classified into three groups: nonpolar, borderline polar and polar solvents. Based on adequate statistical tests, we found that there is strong evidence that the polarity of solvents affects significantly the distribution of the Arrhenius-type equation parameters and consequently the modeling of the viscosity–temperature dependence. Thus, specific estimated values of parameters for each group of liquids are proposed in this paper. In addition, the comparison of the accuracy of approximation with and without classification of liquids, using the Wilcoxon signed-rank test, shows a significant discrepancy of the borderline polar solvents. For that, we suggested in this paper new specific coefficient values of the simplified Arrhenius-type equation for better estimation accuracy. This result is important given that the accuracy in the estimation of the viscosity–temperature dependence may affect considerably the design and the optimization of several industrial processes.     

Arrhenius parameters and compensation behaviour in solid-state decompositions

Many instances of compensation behaviour (i.e. conformity of the Arrhenius parameters to a relationship of the form: ln A = bE_a + c, where b and c are constants) reported for solid-state decompositions, refer to reactions that are at least partially reversible under reaction conditions used in the kinetic studies. Arrhenius parameters calculated for such processes are sensitive to the prevailing pressure of volatile product and heat transfer controls that may vary appreciably between successive experiments. Thus, compensation effects have been reported for various single reactions (e.g. the decomposition of CaCO₃, the dehydroxylation of Ca(OH)₂ and the dehydration of Li₂SO₄·H₂O) where, for each solid, the reactivity of the starting material can be regarded as constant.

Compensation has also been reported for sets of chemically comparable reactants that (are expected to) decompose in the same temperature interval. Compensation may then arise either from the aforementioned variation of reaction conditions, or from differences in the reactants, such as particle sizes, packing, etc.

Because of the variety of compensation effects reported, the phenomenon is often regarded as an experimental artefact. It is of interest to examine the reasons for the concurrent changes of Arrhenius frequency factors and activation energies. The significance of activation energies in solid-state decompositions is discussed briefly and three classes can be distinguished. The accuracy of measurement of activation energies needs to be increased so that their sensitivity to prevailing reaction conditions can be established, investigated and understood.     

On the errors of Arrhenius parameters and estimated rate constant values

A detailed statistical study is presented, based on simulated experimental data, on the estimation of activation parameters using the Arrhenius equation: k = A exp(B/T). The close correlation of the two parameters is shown, which requires the computation of the covariance matrix for the representation of uncertainties. This matrix facilitates the correct estimation of the confidence interval for interpolated (or extrapolated) values of rate coefficients. It is proposed that the full correlation matrix should be published in any article dealing with the determination of Arrhenius parameters. The importance of correct weighting is emphasized. Nonlinear fitting to the Arrhenius equation can be carried out without weighting only in case the (absolute) error of rate coefficient is independent of the temperature. Simulated experiments show that noncorrect weighting shifts the average values of fitted parameters and increases the variance of the parameters as well. With respect to the modified Arrhenius equation: k = A · Tⁿ exp(B/T), statistical analysis shows that the physically meaningful estimation of all three parameters is impossible. Nonlinear fitting of three parameters is suggested for interpolation (and extrapolation) of rate coefficients, whereas in case of activation parameter estimation, the fixing of “n” on the basis of theoretical considerations is advised followed by the estimation of the remaining two parameters.     

Reaction of t-butoxy radicals with norbornadiene

95 percent of the reaction of t-butoxy radical with norbornadiene occurs by radical addition followed by rearrangement to nortricyclyl and 7-t-butoxynorbornenyl products; the remainder includes a novel radical rearrangement involving a 1,3-H shift and some radical abstraction observed for the first time.     

Arrhenius parameters determination in non-isothermal conditions for the uncatalyzed gasification of carbon by carbon dioxide

Non-isothermal thermogravimetric data were used to evaluate the Arrhenius parameters (activation energy, E, and pre-exponential factor, A) for the uncatalyzed gasification by carbon dioxide of two carbons, select as steam activated carbon (BPL) and SP-1 spectroscopically pure graphite. The paper reports on the application of the model-free isoconversional method (KAS/Vyazovkin linear method) for evaluating the activation energy of the gasification process. Activation energies have been calculated by this method were in good agreement with literature data for similar carbons. On the other hand, by means of the kinetic compensation relation between E and ln A, which was established by the model-dependent Coats–Redfern method, the value of the pre-exponential factor was estimated from the known value of the model-independent activation energy.     

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:      

Rate parameters for the reactions of the bromomethyne radical

Absolute rate parameters were measured for the gas phase reactions of CBr($\text{～}\text{X}$²Π) produced in the flash photolysis of CHBr₃ with a variety of paraffins, olefins, O₂ and NO. The rate of cycloaddition to unsaturated bond increases with alkyl substitution, pointing to the electrophilic nature of CBr. In comparison with published data on CCI and CH the reactivity follows the trend CBr ≈ CCl < CH.     

Kinetic parameters for thermal decomposition of hydrazine

The propulsion of most of the operating satellites comprises monopropellant (hydrazine––N₂H₄) or bipropellant (monometilydrazine—MMH and nitrogen tetroxide) chemical systems. When some sample of the propellant tested fails, the entire sample lot shall be rejected, and this action has turned into a health problem due to the high toxicity of N₂H₄. Thus, it is interesting to know hydrazine thermal behavior in several storage conditions. The kinetic parameters for thermal decomposition of hydrazine in oxygen and nitrogen atmospheres were determined by Capela–Ribeiro nonlinear isoconversional method. From TG data at heating rates of 5, 10, and 20 °C min^?1, kinetic parameters could be determined in nitrogen (E = 47.3 ± 3.1 kJ mol^?1, lnA = 14.2 ± 0.9 and T _b = 69 °C) and oxygen (E = 64.9 ± 8.6 kJ mol^?1, lnA = 20.7 ± 3.1 and T _b = 75 °C) atmospheres. It was not possible to identify a specific kinetic model for hydrazine thermal decomposition due to high heterogeneity in reaction; however, experimental f(α)g(α) master-plot curves were closed to F _1/3 model.     

Comparison of methods of determining Arrhenius equation parameters by the least squares method

The parameters of the Arrhenius equation determined by the linear, weighted linear and non-linear least squares methods and by the simplex method are compared. Since the non-linear least squares method permits the consideration of statistical weights of both the dependent (k) and independent (T) variables and does not involve logarithmic transformation, it is advisable to calculate the parameters of the Arrhenius equation by means of the non-linear least squares method.

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Zusammenfassung Arrhenius-Parameter bestimmt nach der linearen, mit Gewichten operierenden linearen und nicht-linearen Methode der kleinsten Fehlerquadrate oder nach der Simplex-Methode werden miteinander verglichen. Da bei der nicht-linearen Methode der kleinsten Fehlerquadrate sowohl die abhÄngige (K) als auch die unabhÄngige (T) Variable mit statistischen Gewichten versehen werden kann und keine logarithmische Transformation vorgenommen wird, ist es zweckmÄ\ig, die Berechnung der Parameter der Arrhenius-Gleichung nach der nicht-linearen Methode der kleinsten Fehlerquadrate auszuführen.

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, , . , k, T, , .

     

Arrhenius activation parameters for the loss of neutral nucleobases from deprotonated oligonucleotide anions in the gas phase

Arrhenius activation parameters (E(a) and A) for the loss of neutral nucleobase from a series of doubly deprotonated oligodexoynucleotide 10-mers of the type XT(9), T(9)X, and T(5)XT(4), where X = A, C, and G, have been determined using the blackbody infrared radiative dissociation technique. At temperatures of 120 to 190 degrees C, the anions dissociate exclusively by the loss of a neutral nucleobase (XH), followed by cleavage of the sugar 3' C-O bond leading to (a-XH) and w type ions or, in the case of the T(9)X(2-) ions, the loss of H(2)O. The dissociation kinetics and energetics are sensitive to the nature and position of X. Over the temperature range investigated, the kinetics for the loss of AH and GH were similar, but approximately 100 times faster than for the loss of CH. For the loss of AH and GH, the values of E(a) are sensitive to the position of the base. The order of the E(a)s for the loss of XH from the 5' and 3' termini is: C > G > A; while for T(5)XT(4) the order is: C > A > G. The trends in the values of E(a) do not parallel the trend in deprotonation enthalpies or proton affinities of the nucleobases in the gas phase, indicating that the energetic differences do not simply reflect differences in their gas phase acidity or basicity. The pre-exponential factors (A) vary from 10(10) to 10(15) s(-1), depending on the nature and position of X. These results suggest that the reactivity of individual nucleobases is influenced by stabilizing intramolecular interactions.     

Decomposition of the t-butoxy radical — I. Studies over the temperature range 402–443 K

By allowing the t-butoxy radical to decompose in the presence of nitric oxide, it has been possible to determine rate constants for decomposition by the measurements of the relative rates (2) and (3) Process (3) is clearly pressure dependent. The value of k₃(∞) has been determined in the presence of several inert gases (CF₄, SF₆, N₂, and Ar) and a value of k₃ interpolated for atmospheric conditions. The results may be compared with those for other relevant alkoxy radicals at room temperature. Extrapolated values for k₃ in the presence of CF₄ lead to the result      

Kinetics of the reaction of methyl radical with hydroxyl radical and methanol decomposition

The CH3 + OH bimolecular reaction and the dissociation of methanol are studied theoretically at conditions relevant to combustion chemistry. Kinetics for the CH3 + OH barrierless association reaction and for the H + CH2OH and H + CH3O product channels are determined in the high-pressure limit using variable reaction coordinate transition state theory and multireference electronic structure calculations to evaluate the fragment interaction energies. The CH3 + OH --> 3CH2 + H2O abstraction reaction and the H2 + HCOH and H2 + H2CO product channels feature localized dynamical bottlenecks and are treated using variational transition state theory and QCISD(T) energies extrapolated to the complete basis set limit. The 1CH2 + H2O product channel has two dynamical regimes, featuring both an inner saddle point and an outer barrierless region, and it is shown that a microcanonical two-state model is necessary to properly describe the association rate for this reaction over a broad temperature range. Experimental channel energies for the methanol system are reevaluated using the Active Thermochemical Tables (ATcT) approach. Pressure dependent, phenomenological rate coefficients for the CH3 + OH bimolecular reaction and for methanol decomposition are determined via master equation simulations. The predicted results agree well with experimental results, including those from a companion high-temperature shock tube determination for the decomposition of methanol.