Compensation effect and isokinetic temperature in thermal dissociation reactions of the type Asolid ⇌ Bsolid + Cgas

It is shown that the Zawadzki — Bretsznajder rule, compensation effect, and isokinetic temperature are simple consequences of interpretation of the Arrhenius equation as a projection correlation. It is established that such an interpretation of the Arrhenius equation allows the discrimination of the deviation factors which impart a definite (although not always simple and recognized) physical sense, to the known empirical correlation. A possibility of deriving new correlation relationships by this method of reasoning is presented.     

Determination of kinetic constants of the cationic copolymerization of isobutylene with isoprene

A theoretical kinetic model has been developed for cationic isobutylene–isoprene copolymerization in methyl chloride with an AlCl₃ catalyst. Kinetic constants of this process have been derived from experimental data available on copolymerization kinetics (isobutylene conversion curve) and on molecular weight characteristics of the isobutylene–isoprene copolymer (butyl rubber). The adequacy of the theoretical kinetic model of the isobutylene–isoprene copolymerization process has been demonstrated by comparing the calculated molecular weight characteristics and degree of unsaturation of butyl rubber to the corresponding independent experimental data.     

Test of the procedure for obtaining detailed endothermic rate constants from microscopic reversibility

Experimental data concerning the effect of varying reagent vibrational, rotational and translational energy on the rates of endothermic reactions can be obtained from the application of microscopic reversibility to the corresponding exothermic processes. A 3D classical trajectory computation has been performed to test this procedure. On the basis of this study we conclude that the ‘triangle plots’ of endothermic detailed rate constants published previously can be depended on to 5–10% theoretical accuracy (expressed as a percentage of the maximum endothermic rate constant).     

Determination of kinetic rate constants in electrochemically initiated anionic polymerization of 1,3-butadiene

The rate constants for electrochemically initiated polymerization were determined by employing a pulsing technique. An electrochemical titration was conducted in which polymer chains were initiated electrochemically, propagated in the absence of current, and terminated electrochemically. The concentrations of supporting electrolyte and monomer were chosen to correspond to those employed in electropolymerization syntheses. The temperature range ?10°C to ?72°C gave k_p = 1.45 × 10² exp {2600/RT}. The Arrhenius parameters are compared to those from previous studies and are interpreted in terms of ion-pair propagation. Precise control of molecular weight distributions is implicit from an accurate knowledge of the kinetic parameters and is reported separately.     

Determination of equilibrium constants for the reaction between acetone and HO2 using infrared kinetic spectroscopy

The reaction between the hydroperoxy radical, HO(2), and acetone may play an important role in acetone removal and the budget of HO(x) radicals in the upper troposphere. We measured the equilibrium constants of this reaction over the temperature range of 215-272 K at an overall pressure of 100 Torr using a flow tube apparatus and laser flash photolysis to produce HO(2). The HO(2) concentration was monitored as a function of time by near-IR diode laser wavelength modulation spectroscopy. The resulting [HO(2)] decay curves in the presence of acetone are characterized by an immediate decrease in initial [HO(2)] followed by subsequent decay. These curves are interpreted as a rapid (<100 μs) equilibrium reaction between acetone and the HO(2) radical that occurs on time scales faster than the time resolution of the apparatus, followed by subsequent reactions. This separation of time scales between the initial equilibrium and ensuing reactions enabled the determination of the equilibrium constant with values ranging from 4.0 × 10(-16) to 7.7 × 10(-18) cm(3) molecule(-1) for T = 215-272 K. Thermodynamic parameters for the reaction determined from a second-law fit of our van't Hoff plot were Δ(r)H°(245) = -35.4 ± 2.0 kJ mol(-1) and Δ(r)S°(245) = -88.2 ± 8.5 J mol(-1) K(-1). Recent ab initio calculations predict that the reaction proceeds through a prereactive hydrogen-bonded molecular complex (HO(2)-acetone) with subsequent isomerization to a hydroxy-peroxy radical, 2-hydroxyisopropylperoxy (2-HIPP). The calculations differ greatly in the energetics of the complex and the peroxy radical, as well as the transition state for isomerization, leading to significant differences in their predictions of the extent of this reaction at tropospheric temperatures. The current results are consistent with equilibrium formation of the hydrogen-bonded molecular complex on a short time scale (100 μs). Formation of the hydrogen-bonded complex will have a negligible impact on the atmosphere. However, the complex could subsequently isomerize to form the 2-HIPP radical on longer time scales. Further experimental studies are needed to assess the ultimate impact of the reaction of HO(2) and acetone on the atmosphere.     

Usefulness of kinetic parameters in investigations of thermal decompositions of solids

The theoretical curves in the coordinates a vs. time for isothermal, and avs. temperature for non-isothermal experiments are calculated as functions of three kinetic parameters: activation energyE, pre-exponentical factorA and theg() function describing the mechanism of thermal decomposition of solids. The results show that conclusions not taking into consideration all three parameters can lead to information of little value concerning the mechanism of the decomposition and kinetic calculations. A correlation between non-isothermal and isothermal experiments, important for determination of the thermal stabilities of the compounds, is impossible without a knowledge of theg() function.

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Zusammenfassung Theoretische Umsatzkurven gegent für isotherme bzw gegen Temperatur für nichtisotherme Versuchsführung wurden berechnet in Abhängigkeit von den drei kinetischen Parametern AktivierungsenergieE, PräexponentialfaktorA und derg()-Funktion, die den Mechanismus der Zersetzung von Festkörpern beschreibt. Die Ergebnisse zeigen, dass Schlussfolgerungen, die nicht alle drei Parameter berücksichtigen, zu, Ergebnissen von geringer Aussagekraft bezüglich des Zersetzungsmechanismus und der kinetischen Interpretation führen. Eine Korrelation nicht-isothermer und isothermer Experimente, die für die Bestimmung der thermischen Stabilität der Verbindungen wichtig ist, ist ohne Kenntnis der Funktiong() unmöglich.

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- - : , - g(), . , , , . , g().

     

Remarks on the determination of kinetic constants from thermogravimetric data

The methods for determining kinetic constants may have significant effects on the estimation results. The two-variable linear correlation method leads to values of the kinetic constants for which the difference between the calculated and measured values is comparable to or greater than the measurement precision. The non-linear method for calculating kinetic constants by searching for the minimum of the error function \(S1 = \sum\limits_{i = 1}^N {(m_{it} - m_i )^2 /N}\) , wherem _i andm _i are the measured and calculated values, respectively, andN is the number of experimental data, gives very precise results. A simple calculating technique is necessary for the fitting of the minimum point and the confidence region limit at the significance level. An appropriate calculation was made for metal oxidation according to the parabolic law.     

Effect of substituents on the kinetic energy release in unimolecular decompositions of substituted anisoles

The kinetic energy relased on the loss of a CH₃ ? radical from para substituted anisoles appears to depend on the nature of the substituent. The application of the dual parameter equation of Yukawa and Tsuno yields a linear correlation with the T_0.5-values. The mesomeric effect predominates strongly over the inductive effect.     

Determination of the kinetic constants of the reversible opening of a triazolo‐1,4‐thienodiazepine in water at different pH values: A striking example of the determination of intimately intricate kinetic and equilibrium constants

Apparent kinetic constants of the reversible opening of a triazolo‐1,4‐thienodiazepine were determined by UV‐spectrophotometry and by polarography in water at several pH values assuming as a hypothesis a stationary state for the carbinolamine intermediate. Both the apparent kinetic constants, k_f and k_r, exhibited a maximum for the values H₀ = −0.25 and pH = 6.07. A possible determination of the elementary kinetic constants of the several acido‐basic species which may be involved in the opening and closing process according to the pH and pKa values was studied and is discussed. The results are consistent with the hypothesis that both the opening of the diazepine cycle and the closing of the opened form proceed through a mechanism suggesting that the protonated form of the carbinolamine function of the intermediate is involved. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 826–834, 1999     

Thermal kinetic studies on the decompositions of cefuroxime lysine in different atmospheres and heating rates

The thermal decomposition of a new antibiotic agent, cefuroxime lysine, was investigated by thermogravimetry analysis/derivative thermogravimetry and differential scanning calorimetry (DSC) methods in anoxic and oxidative environments. The influence of heating rates (including 5, 10, 15, and 20 °C/min) on the thermal behavior of cefuroxime lysine was revealed. By the methods of Kissinger and Flynn–Wall–Ozawa, the thermal kinetic parameters of activation energy and pre-exponential factor for the exothermic processes under non-isothermal conditions were calculated using the analysis of corresponding DSC curves.     

Determination of stability constants of complexes of MiKjHkL type in concentrated solutions of mixed salts

This paper suggests a non-conventional approach towards the correct determination of stability constants K_ijk of mixed complexes from the results of potentiometric titrations. The method is based on inaccurate (in principle) results of titrations made in isomolar titrand–titrant systems. The data thus obtained are validated on the basis of relationships between log K_ijk and relative error (%e) of the determination of an analyte concentration. Accurate values for K_ijk are calculated for the set (ijk) of possible complexes. The accuracy depends on the degree of linearity between the variables considered. The model obtained was thoroughly tested on the system containing malonic acid together with sodium and potassium nitrates.     

Confidence range for the determination of kinetic constants obtained from steady-state measurements

The problem of the confidence range for the determination of kinetic constants obtained from steady-state measurements is studied. The range of constants every point of which reproduces the results with equal accuracy is selected. As an illustration, the steady-state kinetic model of butadiene cyclooligomerization in the presence of low-valent Ni complexes is discussed.

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Some experimental aspects of DSC determination of kinetic parameters in thermal decompositions of solids

Some particular methods of collecting and treating DSC data for the determination of kinetic parameters in thermal decompositions of solids are suggested. These are mainly concerned with an extrapolation method to avoid the effect of the sample mass; with an approximate method to obtain the activation energy and the exponent of the decay-law for runs at constant temperature in which the total area under the thermal curve is not known with accuracy; and with a method to ascertain whether a particular decomposition takes place by a single mechanism or by a sequence of different mechanisms.

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Zusammenfassung Einige besondere Methoden der Sammlung und Verarbeitung von DSC-Daten zur Bestimmung kinetischer Parameter bei der thermischen Zersetzung von Festkörpern werden vorgeschlagen. Diese befassen sich hauptsächlich mit einer Extrapolationsmethode um die Wirkung der Einwaage zu vermeiden; mit einer Annäherungsmethode um die Aktivierungsenergie und den Exponenten des Zersetzungsgesetzes von Versuchen bei konstanter Temperatur zu erhalten, bei welchen die Gesamtoberfläche unter der thermischen Kurve nicht genau bekannt ist; und mit einer Methode zur Bestimmung ob eine bestimmte Zersetzung durch einen einzigen Mechanismus oder durch eine Reihenfolge verschiedener Mechanismen herbeigeführt wird.

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Résumé On propose quelques méthodes particulières pour rassembler et traiter les données de l'analyse calorimétrique différentielle (DSC) dans le but de déterminer les paramètres cinétiques de la décomposition des corps solides. Ces méthodes comportent surtout une extrapolation afin d'éviter l'influence de la prise d'essai, une approximation afin d'obtenir l'énergie d'activation et l'exposant de la loi de décomposition pour les expériences effectuées à température constante dans lesquelles la surface totale délimitée par la courbe n'est pas connue avec exactitude, et enfin un moyen de s'assurer si une décomposition particulière est due à un seul mécanisme ou à une succession de divers mécanismes.

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. : , ; , , , ; , , .

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Work supported by the Italian Consiglio Nazionale delle Ricerche (C. N. R.). Contrac No. 71.01589.03.     

The kinetic study of isothermal solid state decompositions. The influence of sample variables

The reactions which proceed by a contracting-interface mechanism, the intractability of the rate equation often leads researchers to assume a value for the “order”, n. The assumed value (usually either 0, $\text{1}\text{2}$, $\text{2}\text{3}$, or 1) which gives the best fit to the experimental data is then used to characterise the mechanism and to determine the rate constant, k. Since these assumed values of n correspond only to simple theoretical considerations of the geometric advance of the interface and not to any critical experimental observation, the validity of this approach is questionable. In the present study, we use the non-linear least squares method of data analysis, reported previously, to obtain (simultaneously) optimal values of both k and n. We report how these optimal values vary with the experimental conditions, e.g. sample mass, particle size, etc., for the dehydration reactions of strontium hydroxide octahydrate and of strontium formate dihydrate. The applicability of a contracting-interface mechanism to these reactions is supported by thermoanalytical/kinetic studies, and in the latter case, also by microscopic examination.     

An adiabatic type of palladium membrane reactor for coupling endothermic and exothermic reactions

Palladium can play an interesting role as a catalytic membrane, that is, a hydrogen separative and catalytically active wall. Utilizing this function, a palladium membrane reactor capable of working under an adiabatic condition was designed in this study for coupling two conjugated reactions. On one side of the membrane, dehydrogenation of cyclohexane as a model takes place in the catalyst-packed layer, and on the membrane surface of the other side hydrogen permeated reacts in-situ with oxygen. In the adiabatic membrane reactor, a heat compensation between the endothermic dehydrogenation and the exothermic oxidation is expected to be realized. As a result, it became obvious experimentally that the generated heat due to the oxidation refluxed to the dehydrogenation side, heated up the catalyst layer and therefore enhanced the dehydrogenation. A simple mathematical model derived for analyzing the reaction process could simulate the practical reactor performances well.