Kinetics isothermal

Theoretical formulation of kinetic expressions from specified geometry and/or mechanisms of reaction have often assumed particles to be of a regular, perhaps defined, shape and of uniform size. Equations developed in this way have frequently been found to give a satisfactory representation of observed isothermal kinetic characteristics in many reactions of interest. Other authors have, however, introduced an allowance for particle size distribution [480—482] into kinetic analyses. 

Tests of obedience of isothermal kinetic data to theoretical kinetic equations... 

Many non-isothermal kinetic studies use a linear rate of temperature increase from an initial value, T0, so that the three equations involved can be written... 

Thermal analyses of the sodium salts of several sulphuroxyacids, including some non-isothermal kinetic data, have been reported [813], Evidence for the formation of SOi radicals during such reactions has been obtained [348] by electron spin resonance measurements. 

References to a number of other kinetic studies of the decomposition of Ni(HC02)2 have been given [375]. Erofe evet al. [1026] observed that doping altered the rate of reaction of this solid and, from conductivity data, concluded that the initial step involves electron transfer (HCOO- - HCOO +e-). Fox et al. [118], using particles of homogeneous size, showed that both the reaction rate and the shape of a time curves were sensitive to the mean particle diameter. However, since the reported measurements refer to reactions at different temperatures, it is at least possible that some part of the effects described could be temperature effects. Decomposition of nickel formate in oxygen [60] yielded NiO and C02 only the shapes of the a—time curves were comparable in some respects with those for reaction in vacuum and E = 160 15 kJ mole-1. Criado et al. [1031] used the Prout—Tompkins equation [eqn. (9)] in a non-isothermal kinetic analysis of nickel formate decomposition and obtained E = 100 4 kJ mole-1. 

There is an extensive literature devoted to the preparation and structure determination of coordination compounds. Thermal analysis (Chap. 2, Sect. 4) has been widely and successfully applied in determinations [1113, 1114] of the stoichiometry and thermochemistry of the rate processes which contribute to the decompositions of these compounds. These stages may overlap and may be reversible, making non-isothermal kinetic data of dubious value (Chap. 3, Sect. 6). There is, however, a comparatively small number of detailed isothermal kinetic investigations, together with supporting microscopic and other studies, of the decomposition of coordination compounds which yields valuable mechanistic information. 

Although TPD is a versatile and useful technique widely available within the surface-science community, it does have some limitations. For one, because the experiments are carried out under vacuum, they can only probe irreversible reactions no readsorption of the desorbing products is possible. In addition, as the temperature is ramped during detection, the surface temperature and the reaction rates become coupled in a way difficult to separate or control. Of particular importance here is the fact that as the reactions proceed and the products desorb, the surface coverages decrease, so the rates at higher temperatures correspond to the new lower surface concentrations. In order to overcome this problem, isothermal kinetic experiments have been carried out using molecular beams [22,23],... 

Aryafar, M. and Zaera, F. (1998) Isothermal kinetic study of the decomposition of nitric oxide over Rh(lll) surfaces , J. Catal., 175, 316. 

Thirunavukkarasu, K., Thirumoorthy, K., Libuda, J. et al. (2005) Isothermal kinetic study of nitric oxide adsorption and decomposition on Pd(lll) surfaces Molecular beam experiments , J. Phys. Chem. B, 109, 13283. 

Isothermal Kinetics of Polymers Oxidation and Its Relation to the Concentration of Oxygen in Surrounding Atmosphere 487... 

ISOTHERMAL KINETICS OF POLYMERS OXIDATION AND ITS RELATION TO THE CONCENTRATION OF OXYGEN IN SURROUNDING ATMOSPHERE... 

Keywords non-isothermal kinetics, open-framework, TG analysis, SBA-3, cetyltrimethylammonium bromide (CTMAB), liquid-crystal templating. 

Keywords Activated carbon, isotherm, kinetics, metobromuron, pesticide... 

The solvent system extractant, diluent, and, if necessary, modifier Equilibrium data extraction and stripping isotherms Kinetic data, as these will govern, to a large extent, the type of contactor required... 

Because the catalytic reaction A R is highly exothermic with rate highly temperature-dependent, a long tubular flow reactor immersed in a trough of water, as shown in Fig. P18.39, is used to obtain essentially isothermal kinetic data. Pure A at 0°C and 1 atm flows through this tube at 10 cm / sec, and the stream composition is analyzed at various locations. 

The time course of the emission intensity is proportional to the concentration of the HEI and, in the case of isolated HEIs, the rate constant for its decomposition is obtained from the CL emission curves. Isothermal kinetic measurements give rise to the activation parameters for the whole transformation and can be used for mechanistic discussion in the case of isolated HEI ° . Specific CL methods have also been used to determine... 

It has been suggested that the experimental isothermal kinetic rate constants of some reactions at near and supercritical conditions could not be explained solely by the thermodynamic pressure effect, but from the combination of local composition enhancement and density augmentation around reactants. 

Besides having the capital property of being able to imitate any kinetics—see Eq. 61—Astarita s uniform kinetics are often patient of a mechanistic derivation. Thus, for what Astarita and Ocone call uniform generalized Langmuir isotherm kinetic mechanism (UGLIKM), we might take 6(x) dx to be the fraction of catalytic surface occupied by the species A(x) with index in... 

Thus, for the temperature-dependent electron tunneling reactions, the mismatch of the decay curves for the samples kept at different temperatures all the time can be observed only with large observation time intervals. In contrast to this, the presence or absence of the acceleration of the reaction with the rapid increase in temperature at a certain instant t0 can be easily noticed even with a very short observation time interval. Consequently, the method based on registering the change in kinetics with a jumpwise variation in temperature, is a more sensitive test for the presence or absence of the activation energy for the electron tunneling reaction than the method based on comparing the isothermic kinetic curves. 

Isothermal kinetic runs for the same system were also analyzed by Mauri et al. (1997) and Galante et al. (1999). An excellent fit of a first-order kinetics after an induction period was reported, with E lying in the range of 70-75 kJ mol-1. Obviously, the overall behavior, including the induction period, is autocatalytic. However, for conversions higher than about 0.15, a first-order kinetics provided an excellent agreement, particularly at low cure temperatures and up to vitrification. This behavior is partially explained by Eq. (5.29) the function f(x) exhibits a behavior close to (1 — x) in the 0.4—0.8 conversion range. 

Considerable variation in K(k values appear in the literature. For example, Mackay et al. (1992) provided 24 values of K(k for benzene, ranging from 0.11 to 2.08 L/kg. Variation is likely the result of differences in the sorption characteristics of SOM, variation in the methods used to determine K(k (separation of phases, mass balance, single point, or isotherm, kinetics), impact of other soil properties, and the properties of chemicals being sorbed. The variability in Koc values is generally greater for the more polar compounds. 

Maeder, M., Molloy, K.J., and Schumacher, M.M., Analysis of non-isothermal kinetic measurements, Anal. Chim. Acta, 1997, 337, 73-81. 

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