Rate constant, significance

For the reaction carried out in the presence of pyridine, a-deuteration did not affect the second-order rate constant significantly. However, small isotope effects of 1.19 and 1.21 were observed for the lead tetraacetate oxidation of PhCH(OD)COOD and... 

For a simplified case in which the entire polymerization reaction is assumed to occur at a constant temperature under conditions that eliminate the reverse reaction (see Reaction 32), the time needed to polymerize nylon 66 to 99% conversion is given by Equation 41. This equation yields a reaction time of 17 min for polymerization at 280 °C of nylon 66 to 99% conversion (DP = 100). This calculation emphasizes the need for condensation reactions with a fast reaction rate in view of the high reaction yield needed. Reactions with rate constants significantly smaller than the constants for aliphatic amidation will require long reaction times and, therefore, will be impractical for polymer formation, particularly if monomer side reactions or polymer degradation can occur under conditions of the polymerization. 

In contrast to the dissociation rate constant, significantly less work has been devoted to the recombination rate constant k - The latter depends, similarly to kj, on dilferent effects. Detailed discussions can be found in the articles of Marque et Gigmes and Marque and especially the very recent and... 

As is inversely proportional to solvent viscosity, in sufficiently viscous solvents the rate constant k becomes equal to k y. This concerns, for example, reactions such as isomerizations involving significant rotation around single or double bonds, or dissociations requiring separation of fragments, altiiough it may be difficult to experimentally distinguish between effects due to local solvent structure and solvent friction. 

Multidimensionality may also manifest itself in the rate coefficient as a consequence of anisotropy of the friction coefficient [M]- Weak friction transverse to the minimum energy reaction path causes a significant reduction of the effective friction and leads to a much weaker dependence of the rate constant on solvent viscosity. These conclusions based on two-dimensional models also have been shown to hold for the general multidimensional case [M, 59, and 61]. 

VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

Studies by the group directed by Mayoral have been limited to Diels-Alder reactions of type A. When water was not included, the rate constants correlate with the solvent hydrogen-bond-donating capacity Upon inclusion of water the solvophobidty parameter, Sp, contributed significantly in... 

Interestingly, the rate constants for Diels-Alder reaction of the ternary complexes with 3.9 are remarkably similar. Only with 2,2 -bipyridine and 1,10-phenanthroline as ligands, a significant change in reactivity is observed. It might well be that the inability of these complexes to adopt a planar geometry hampers the interaction between the copper ion and the dienophile, resulting in a decrease of the rate of the catalysed Diels-Alder reaction. 

Since the first-order rate constant for nitration is proportional to y, the equilibrium concentration of nitronium ion, the above equations show the way in which the rate constant will vary with x, the stoichiometric concentration of dinitrogen tetroxide, in the two media. An adequate fit between theory and experiment was thus obtained. A significant feature of this analysis is that the weak anticatalysis in pure nitric acid, and the substantially stronger anticatalysis in partly aqueous nitric acid, do not require separate interpretations, as have been given for the similar observations concerning nitration in organic solvents. 

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

The power law developed above uses the ratio of the two different shear rates as the variable in terms of which changes in 17 are expressed. Suppose that instead of some reference shear rate, values of 7 were expressed relative to some other rate, something characteristic of the flow process itself. In that case Eq. (2.14) or its equivalent would take on a more fundamental significance. In the model we shall examine, the rate of flow is compared to the rate of a chemical reaction. The latter is characterized by a specific rate constant we shall see that such a constant can also be visualized for the flow process. Accordingly, we anticipate that the molecular theory we develop will replace the variable 7/7. by a similar variable 7/kj, where kj is the rate constant for the flow process. 

Note that Eqs. (6.5) and (6.12) are both first-order rate laws, although the physical significance of the proportionality factors is quite different in the two cases. The rate constants shown in Eqs. (6.5) and (6.6) show a temperature dependence described by the Arrhenius equation ... 

What is significant about these reactions is that only two possibilities exist addition with the same configuration (D -> DD or L LL) or addition with th< opposite configuration (D DL or L LD). We shall designate these isotactic (subscript i) or syndiotactic (subscript s) additions, respectively, and shal define the rate constants for the two steps kj and k. Therefore the rates o isotactic and syndiotactic propagation become... 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

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