Chemical reactions diffusion-controlled

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. 

Time. Figures 25.9 and 25.10 show the progressive conversion of spherical solids when chemical reaction, film diffusion, and ash diffusion in turn control. Results of kinetic runs compared with these predicted curves should indicate the ratecontrolling step. Unfortunately, the difference between ash diffusion and chemical reaction as controlling steps is not great and may be masked by the scatter in experimental data. 

Under conditions leading to a porous shell of magnetite, the kinetic curve displayed an induction period corresponding to formation of nuclei and the subsequent reaction followed the cube root law. Diffusion of the reducing gas to the reactant/ product interface took place readily with a porous product. Whether chemical or diffusion control predominated depended on reaction conditions. With small crystals... 

This problem was addressed by Van Deemter [1], who assumed a constant burning rate to obtain a solution in closed form. Later, Johnson et. al. [2] and Olson et al. [3] treated high-temperature, diffusion controlled burning, where the reaction rate depends only weakly on temperature. Both predicted the propagation of a sharply defined burn front, but neither gave any indication of what might happen at lower temperatures, where chemical reaction rate controls. This case was discussed by Ozawa [4], who showed that oxidation is slow and there is no clear burn front. 

The calculations set out above were based on the assumption that the catalyst surface was always at a temperature of 900°K, however, practical experience during the investigation set out in Part 1, revealed that the catalyst temperature always increased with increase in gas flow-rate. The dotted curves in Figure 4 illustrate the effect of such a variation from 900°K to 1200°K at the highest velocity, for the different values of n. When diffusion controls, the surface temperature has no effect, but when the chemical reaction rate controls (n= 7) the overall rate increases... 

At early ages, da/d/ increases markedly with w/s ratio above 0.7 (B56). Moderate variations in specific surface area have little effect on the length of the induction period, but with finer grinding, da/d/ during the acceleratory period increases (K20,O12,B56). The rate of reaction increases with temperature up to the end of the acceleratory period, but is much less affected thereafter (K21), suggesting a change from chemical to diffusion control. Introduction of defects into the CjS shortens the induction period (M53,F20,O12). 

The overall mass-transfer rate of solute can be controlled by any of the chemical reaction-diffusion resistances in the three-liquid phases. 

Transport and diffusion. With the exception of N2, O2, Ar, and numerous other long-lived species that are well-mixed in the bulk of the atmosphere, horizontal and vertical transport are closely coupled with chemical reactions in controlling atmospheric trace-substance concentrations. 

Simulations are presented below in tabular and graphical forms when the temperature at the external surface of the pellet is constant at 350 K. The effective thermal conductivity of alumina catalysts is 1.6 x 10 J/cm s K. The chemical reaction is first-order and irreversible and the catalysts exhibit rectangular symmetry. Most important in Tables 27-5 to 27-8 and Figures 27-1 to 27-3, the diffusivity ratio a(0) varies with temperature in the mass transfer equation. This effect was neglected in Tables 27-1 to 27-4. Notice that in all of these tables (i.e., 27-1 to 27-8), numerical simulations reveal that the actual max exceeds I + fi, except when the intrapellet Damkohler number is small enough and 4 a( = 0) > 0 because the center of the catalyst is not reactant starved in the chemical-reaction-rate-controlled regime. 

A common example is the Belousov - Zhabotinsky reaction [24], Beautiful patterns of chemical wave propagation can be created in a chemical reaction - diffusion system with a spatiotemporal feedback. The wave behavior can be controlled by feedback-regulated excitability gradients that guide propagation in the specified directions [25, 26]. 

Let us note that no restriction has been imposed on the extent of irreversibility in chemical conversions at finite rate and also the complexities of reactions. In other words, far away from equilibrium, chemical conversions and complex reactions such as chemical oscillations, chemical chaos, diffusion-controlled reactions having multi-steps etc. are governed by the above equation provided the system is spatially uniform. 

A quantification of DF to describe the transition from chemically-controlled to diffusion-controlled kinetics is based on the Rabinowitch equation, which is derived fi-om the activated complex theory [39,105-107], Whether a chemical reaction is controlled by diffusion depends on the relative time to diffuse and the time needed for the intrinsic chemical reaction resulting in bond formation ... 

It may be noted from this plot that the fractional conversion of solid Xg is the least when the gas film resistance controls the overall rate. This is because the gas film resistance limits the amount of A that would be available at the reaction site in the solid particle for conversion of B. The plots of Xg versus 0/x for the ash layer diffusion controlling mechanism and the chemical reaction rate-controlling mechanism intersect with each other at (9/x = 0.5) and Xg = (7/8). Conversion is higher when the ash layer diffusion controls the... 

The third limiting case of chemical reaction rate controlling is not consistent with the concept of a shrinking core model with a single diffusivity throughout the particle the existence of a sharp boundary implies transport by effective diffusion that is potentially slow with respect to the reaction. 

Of special importance for realization of the controlled gradient formation is an understanding of the reaction mechanism (polymer-analogous transformation /diffusion copolymerization) so that the dmation of the process can be determined in order to control the reaction product. Specifically, the refractive index change with time is investigated, i.e. the function n =J[t) is determined, where n is the refractive index, r is the duration of chemical reaction/diffusion. 

There are many potential advantages to kinetic methods of analysis, perhaps the most important of which is the ability to use chemical reactions that are slow to reach equilibrium. In this chapter we examine three techniques that rely on measurements made while the analytical system is under kinetic rather than thermodynamic control chemical kinetic techniques, in which the rate of a chemical reaction is measured radiochemical techniques, in which a radioactive element s rate of nuclear decay is measured and flow injection analysis, in which the analyte is injected into a continuously flowing carrier stream, where its mixing and reaction with reagents in the stream are controlled by the kinetic processes of convection and diffusion. 

Ceramic—metal interfaces are generally formed at high temperatures. Diffusion and chemical reaction kinetics are faster at elevated temperatures. Knowledge of the chemical reaction products and, if possible, their properties are needed. It is therefore imperative to understand the thermodynamics and kinetics of reactions such that processing can be controlled and optimum properties obtained. 

If the gas has the correct composition, the carbon content at the surface increases to the saturation value, ie, the solubiUty limit of carbon in austenite (Fig. 2), which is a function of temperature. Continued addition of carbon to the surface increases the carbon content curve. The surface content is maintained at this saturation value (9) (Fig. 5). The gas carburizing process is controlled by three factors (/) the thermodynamics of the gas reactions which determine the equiUbrium carbon content at the surface (2) the kinetics of the chemical reactions which deposit the carbon and (J) the diffusion of carbon into the austenite. 

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