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Reaction Kinetics, Mechanisms and Catalysis
Authors: Andrés Pena, Santiago Veiga, Mariángeles Sapelli, Natalia Martínez, Victoria Márquez, Eduardo Dellacassa, and Juan Bussi

presence of pure oxygen. In contrast, the reaction of limonene takes place when a NiAl-HT catalyst is present, with increasing reaction rates up to 90 °C as shown in Fig. 3 . Conversions at 6 h of reaction time were 16.7 % at 70 °C, 43.9 % at 80 °C and 51

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On the basis of the theory of thermokinetics proposed in the literature, a novel thermokinetic method for determination of the reaction rate, the characteristic parameter method, is proposed in this paper. Mathematical models were established to determine the kinetic parameters and rate constants. In order to test the validity of this method, the saponifications of ethyl benzoate, ethyl acetate and ethyl propionate, and the formation of hexamethylenetetramine were studied with this method. The rate constants calculated with this method are in agreement with those in the literature, and the characteristic parameter method is therefore believed to be correct.In the light of the characteristic parameter method, we have developed further two thermo-kinetic methods, the thermoanalytical single and multi-curve methods, which are convenient for simultaneous determination of the reaction order and the rate constant. The reaction orders and rate constants of the saponifications of ethyl acetate and ethyl butyrate and the ring-opening reaction of epichlorohydrin with hydrobromic acid were determined with these methods, and their validity was verified by the experimental results.

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Hydrogen isotope exchange reaction rate in tritium and methane mixed gas, as induced by tritium decay and beta radiation, has been experimentally measured. Initially T2 gas was filled to 40 kPa and 20 kPa of CH4 gas was added. The mixed gas spectrum was analyzed periodically by laser Raman spectrometry. The first order HT and H2 formation rates and T2 and CH4 decay rates by hydrogen isotope exchange reaction were observed between 2.9·10–3 h–1 and 4.8·10–3 h–1. Although the estimated hydrogen isotope exchange reaction rate was 1/20–1/10 slower than the rate of H2+T2 mixed gases, it was nearly equivalent to the ion formation rate by tritium beta radiation. This suggested that isotopic hydrogen radicals formed via ionization would disappear in the presence of methane.

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The authors present some theoretical considerations concerning the influence of the form of the conversion functionf(α) on the values of the degree of conversion corresponding to the maximum value of the reaction rate (αmax) as well as on the inflexion points (αinf) of the DTG curve. The obtained equations are characterized by a general validity no matter the form off(α).

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A simple operation mode to determine the apparent activation energy E a is introduced. E a can be determined with a double-curve method by using a constant reaction rate (CRR) approach of Hi-Res TG. The most appropriate mechanism function f(α) and frequency factor A are determined by a single-curve method when the activation energies provided by the two methods are in good agreement with each other. The deacetylation of EVA copolymer has been used for illustration. Advantages of the CRR are discussed.

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An alternative convention for use in the k0-method describing the (n, )-reaction rate upon reactor neutron irradiation has been derived by dividing the cross-section in a (v)= 0v0/v part and a pure resonance integral, instead of splitting up the neutron spectrum. It describes the (n, )-reactions with the Westcott factor g(T)1 but without resonances below 0.35 eV, and should yield better results for those with resonances below this limit. The resulting formulas are simpler than the ones currently used. An important practical aspect of this new convention is that no irradiations under Cd-cover are needed to determine the parameters to be used in the k0-method. The parameters determined previously for (n, )-reactions with g(T)=1 can still be used.

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The present study deals with the immobilization of Aspergillus nidulans SU04 cellulase onto modified activated carbon (MAC). The effect of contact time, cellulase concentration, MAC dosage, and temperature for maximum immobilization percentage and immobilization capacity is investigated. The equilibrium nature of immobilization is described by Langmuir and Freundlich isotherms. The kinetic data were tested using the pseudo first order. The activation energy of immobilization was evaluated to be 11.78 J mol−1. Results of the thermodynamic investigation indicate the spontaneity (ΔG <0), slightly endothermic (ΔH >0), and irreversible (ΔS >0) nature of the sorption process. Entropy and enthalpy were found to be 41.32 J mol−1 mg−1 and 10.99 kJ mol−1, respectively. The Gibbs free energy was found to be −22.79 kJ mol−1. At 80 rpm, 323 K, 2 h, 5 mg of MAC, immobilization capacity was 4.935 mg cellulase per mg of MAC from an initial cellulase concentration of 16 mg ml−1 with retention of 70% of native cellulase activity up to 10 cycles of batch hydrolysis experiments. The diffusion studies that were carried out revealed the reaction rate as μmol min−1. At optimized conditions, immobilized cellulase had a higher Michaelis–Menten constant, K m of 1.52 mmol and a lower reaction rate, V max of 42.2 μmol min−1, compared with the free cellulase, the K m and V max values of which were 0.52 mmol and 18.9 μmol min−1, respectively, indicating the affinity of cellulase for MAC matrix.

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By using the LKB 2277 thermal activity monitor, it is demonstrated that both ampoule and flow-through modes can be used to monitor the reaction parameters for chemical reactions. Theoretical relationships applicable to first-order reactions are proposed and compared with those reported in the literature. Mathematical relationships applicable to second-order reactions are also proposed. The experimental results confirmed the validity of the theoretical relationships and showed that flow microcalorimetry is a rapid technique in kinetic studies.

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Light emission during the dissolving of irradiated sugars (lyoluminescence, LL) allows the estimation of absorbed dose. The use of 1-mannose as LL substance and the correlation between the concentration of paramagnetic centres and LL yield in the presence of [Fe(CN)6]4− and CNS anions demonstrated the possibility to measure relative rate constants of the reaction of mannose peroxy-radicals with different substances soluble in water.

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A novel method for the determination of rate constants of reactions, the time-variable method, is proposed in this paper. The method needs only three time points (t), peak heights () and pre-peak areas (), obtained from the measured thermoanalytical curve. It does not require the thermokinetic reaction to be completed. It utilizes data-processing on a computer to give the rate constants. Four reaction systems, including a first-order reaction, second-order reactions (with equal concentrations and with unequal concentrations) and a third-order reaction, were studied with this method. The method was validated and its theoretical basis was verified by the experimental results.

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