Rate-controlled processes, dependence

We use two examples to illustrate (1) the dependence of /B on t and the sensitivity to the type of rate-controlling process, and (2) the situation in which more than one rate process contributes resistance. We use particles of the same size in BMF in both examples, but PF could be considered, as could a particle-size distribution. 

Dependence offB ont and Sensitivity to Rate-Controlling Process... 

Extend Example 22-3 to examine the dependence of fB on t and the sensitivity to the type of rate-controlling process. For this purpose, using the data of Example 22-3, calculate and plot /B as a function of t over the range 0 to 25 min for each of the three cases in Example 22-3(a), (b), and (c). 

Chemical Reaction Rate Controlled Process If the diffusion is very rapid compared to the rate of chemical reaction, then the concentration of water and EG can be considered to be nearly zero throughout the pellet and the rate of the reverse reaction can be neglected [21], This represents the maximum possible reaction rate. It is characterized by a linear molecular weight increase with respect to time and is also dependent on the starting molecular weight and the reaction rate constants ki and k2. 

Diffusion Rate Controlled Process If the rate of chemical reaction is much faster than the diffusion of water and EG through the solid amorphous phase, then the reaction can be considered to be at equilibrium throughout the pellet [21], The reaction rate is dependent upon the pellet size, the diffusivity of both water and EG, the starting molecular weight, and the equilibrium constants Ki and K5. In addition, the pellet can be expected to have a radial viscosity profile due to a by-product concentration profile through the pellet with the molecular weight increasing as the by-product concentrations decreases in the direction of the pellet surface [22-24],... 

Temperature dependence and activation energy. The importance of the evaluation of the temperature coefficient of the reaction rate has been previously discussed (27). Since the oxidation rate follows a parabolic equation, it is possible to evaluate the rate constants and, using these constants, the energy and entropy of activation of the rate-controlling processes. 

Quantification of rate constants for this multistep process hinges on the assumed rate-controlling step. Depending on the steps that are assumed to dictate the rate, reaction rates or diffusion constants are calculated from the net kinetics of reaction or sorption. Various studies have assumed that either of two steps are rate controlling either the surface diffusion or the actual spillover from the source. All analyses have assumed a first-order dependence of the concentrations of atomic hydrogen for each step in the sequence. 

Item d implies that in terms of the Hansch model of Equation 1, partitioning STEP 1 is the primary rate-controlling process characterizing the herbicidal action of the 3-TFMS compounds on Wild Mustard in the presence of Tween 80. Since all the other Hansch relationships in Table XI include fairly significant pa contributions, partitioning as well as other rate processes (possibly more intimately connected with the receptor site within the plant or seed) must be involved in determining overall herbicidal activity in these latter cases. One may speculate that the anomalous observations (a-c) above are the direct consequence of (d)—the lack of Hammett a dependence. If the pa term in the Hansch equation does indeed reflect rate or equilibrium events occurring at or near the herbicidal site of action within the plant or seed (as is often assumed but not... 

Depending on the mutual solubilities of reactants and products, chemical and physical reactions in (or between) solids may involve phase changes. In most reactions of solids, the process of diffusion is sufficiently slow that it becomes a rate-controlling process and nucleation is relatively unimportant. This has been found to be the case in the reaction of... 

MgO single crystals and powder samples with regard to H and Mg concentrations. Several pH-dependent rate-controlling processes were found to be present at room temperature. 

Crack growth response reflects the dependence of the rate controlling process on the environmental, microstructural and loading variables. ... 

At high pressures, where n = 0 and 0 = 1, the solid surface is saturated by and the hydriding kinetics are unaltered by changes in pressure. The rate is then controlled by a process occurring within the solid and depends only on temperature, as defined by the Arrhenius term. As fixed by the pressure-independent isotherms beyond the saturation boundary indicated by P, in fig. 14, for the rate-controlling process in the solid phase is 29kJ/mol as determined by Bloch and Mintz (1981). 

Above 700 °C for Mo and approximately 900 °C for W, evaporation of the volatile oxides M0O3 and WO3 is the rate-controlling process and the oxidation follows a linear time dependence. Above 2000 °C for Mo and 2400 °C for W, the metal loss increases because of the increasing vapor pressure of the pure metals. The time... 

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