Initial rate assumption CHEMICAL KINETICS

Figure 1. Plot of the change in product concentration as a function of time of reaction. The initial rate phase corresponds to the early linear region, and a tangent to this early region has a slope corresponding to the initial reaction velocity. (For a detailed description of how one obtains rate constants using the initial rate assumption. See Chemical Kinetics.)...

A mathematical simplification of rate behavior of a multistep chemical process assuming that over a period of time a system displays little or no change in the con-centration(s) of intermediate species (i.e., d[intermedi-ate]/df 0). In enzyme kinetics, the steady-state assumption allows one to write and solve the differential equations defining fhe rafes of inferconversion of various enzyme species. This is especially useful in initial rate studies. 

In the first chapter, we consider the fundamental nature of the thermally-induced CVD. Initially, we consider the behavior of CVD reactions under the assumption of chemical equilibrium. Much useful information can be derived by this technique, especially for very complex chemical systems where several different solid phases can be deposited. In order to extend our understanding of CVD, it is necessary to consider reacting gas flows where the rates of chemical reactions are finite. Therefore, the next subject considered is the modeling of CVD flows, including chemical kinetics. Depending on processing conditions, the film being deposited may be amorphous, polycrystalline, or epitaxial. 

The classical chemical kinetics is based on the assumption that the closed expressions for the rates of the concentration changes with time for aU the chemical species present in the system may be written through the concentrations. This rather stringent assumption is however valid only if energy transfer processes are fast enough to maintain the thermal equilibrium during the reaction. A complete set of these expressions forms the system of kinetic equations which determines time variations of all the concentrations, provided their initial values are given. 

In this section, we will present results of microldnetics simulations based on elementary reaction energy schemes deduced from quantum chemical studies. We use an adapted scheme to enable analysis of the results in terms of the values of elementary rate constants selected. For the same reason, we ignore surface concentration dependence of adsorption energies, whereas this can be readily implemented in the simulations. We are interested in general trends and especially the temperature dependence of overall reaction rates. The simulations will also provide us with information on surface concentrations. In the simulations to be presented here, we exclude product readsorption effects. Microldnetics simulations are attractive since they do not require an assumption of rate-controlling steps or equilibration. Solutions for overall rates are found by solving the complete set of PDFs with proper initial conditions. While in kinetic Monte Carlo simulations these expressions are solved using stochastic techniques, which enable formation... 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

The rate constants calculated by EF profiles (Equation (4.6)) are necessarily crude as several assumptions must hold the initial enantiomer composition is known, only a single stereoselective reaction is active, and the amount of time over which transformation takes place is known. These assumptions may not necessarily hold. For example, for reductive dechlorination of PCBs in sediments, it is possible for degradation to take place upstream followed by resuspension and redeposition elsewhere [156, 194]. The calculated k is an aggregate of all reactions, enantioselective or otherwise, involving the chemical in question. This includes degradation and formation reactions, so more than one reaction will confound results. Biotransformation may not follow first-order kinetics (e.g. no lag phase is modeled). The time period may be difficult to estimate for example, in the Lake Superior chiral PCB study, the organism s lifespan was used [198]. Likewise, in the Lake Hartwell sediment core PCB dechlorination study, it is likely that microbial activity stopped before the time periods selected [156]. However, it should be noted that currently all methods to estimate biotransformation rate constants in field studies are equally crude [156]. 

This character of specimens o-p dependence on time can be connected with prolonged chemical or physical structuring or with the purely physical process of moisture loss by the specimens. The kinetics of moisture loss by the specimens under hold-up in air in normal conditions was investigated to test the last assumption. Moisture loss was assessed by the change over time in specimen mass relative to initial specimen mass. It was established that the rate of moisture loss during hold-up in the air gradually reduces, but even at 30 days it remains important and the maximum moisture loss by specimens was 11.9%. 

This is a method for determining the concentration dependence of a rate law that avoids the need for an integrated rate law or pseudo-first-order conditions. It is based on the assumption that the reactant concentrations are essentially constant during the initial 10% of reaction. The use of this method requires that observation can begin very soon after mixing the reactants and that the detection method is sensitive enough to provide precise data over the small extent of reaction. The latter condition usually means that the reaction half-time is about ten seconds or longer, so that this method is convenient and efficient for slow reactions. Observation over a short initial period may avoid, but also may hide, kinetic and chemical complications that only are clearly apparent later in the reaction. 

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