Kinetic , generally coefficient

For both eqs. (13-25) and (13-26), the chemical reactions are for stoichiometric coefficients and kinetic rate exponents of one for both components. Middleton and Levenspiel give eqnations for general coefficients, but such cases are not common for fast reactions, since more than one reaction is usually involved in... 

More generally, the relaxation follows generalized first-order kinetics with several relaxation times i., as depicted schematically in figure B2.5.2 for the case of tliree well-separated time scales. The various relaxation times detemime the tiimmg points of the product concentration on a logaritlnnic time scale. These relaxation times are obtained from the eigenvalues of the appropriate rate coefficient matrix (chapter A3.41. The time resolution of J-jump relaxation teclmiques is often limited by the rate at which the system can be heated. With typical J-jumps of several Kelvin, the time resolution lies in the microsecond range. 

This matrix represents an effective operator that still has to act on the bending functions/ (p),/ (p). A generalization of (24) to the case when the kinetic energy operator (i.e., the coefficients 7 and A) has a different form in the... 

In the kinetics of formation of carbides by reaction of the metal widr CH4, the diffusion equation is solved for the general case where carbon is dissolved into tire metal forming a solid solution, until the concentration at the surface reaches saturation, when a solid carbide phase begins to develop on the free surface. If tire carbide has a tirickness at a given instant and the diffusion coefficient of carbon is D in the metal and D in the carbide. Pick s 2nd law may be written in the form (Figure 8.1)... 

With the chosen coefficient the general character of the simulation agreed with the experimental data. For better agreement, a more detailed kinetic model would be needed. 

Peroxides are used most commonly either as thermal initiators or as a component in a redox system. While peroxides are photochemically labile, they seldom find use as photoinitiators other than in laboratory studies because of their poor light absorption characteristics. They generally have low extinction coefficients and absorb in the same region as monomer. Kinetic parameters for decomposition of some important peroxides are given in Table 3.5,... 

If both addition and fragmentation arc irreversible the kinetics differ little from conventional chain transfer. In the more general case, the rate constant for chain transfer is defined in terms of the rate constant for addition and a partition coefficient which defines how the adduct is partitioned between products and starting materials (eq. 19). 

The greater dependence of rate coefficient upon acidity for detritiation compared to dedeuteration is apparent for benzene as it was for toluene and is more marked, but in view of the errors in the benzene work (which appear to arise only from measuring the acid concentration but could possibly arise from some feature of the kinetic method) and element of doubt must remain here. Nevertheless, this phenomenon (which is understandable on the basis that when the reactions are infinitely fast they will then both take place at the same rate, and the more reactive the compound and the stronger the acid, the more closely this situation is approached) seems to be general, for Gold et a/.460 found that the log rate coefficient... 

A shift in the velocity constant such as is observed in bulk esterification is the exception rather than the rule. A source of more general concern is the enormous increase in viscosity which accompanies polymerization. Both theory and experimental results indicate that this factor usually is of no importance except under the extreme conditions previously mentioned. Consequently, the velocity coefficient usually remains constant throughout the polymerization (or degradation) process. Barring certain abnormalities which enter when the velocity coefficient is sensitive to the environmental changes accompanying the polymerization process, application of the ordinary methods of chemical kinetics to polymerizations and other processes involving polymer molecules usually is permissible. 

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