Rate of chemical production

The rate of the chemical reaction is crucial. An extremely slow reaction would show up as a slowly rising conventional diffusion-controlled wave. However if the rate of chemical production is faster than the rate of diffusion, the limiting current will be diffusion controlled. For a kinetic wave to form, the rate of the chemical reaction must be relatively rapid but significantly slower than the rate of diff-ision. 

Write the rates of chemical production which correspond to the reaction scheme shown in Example 10. 

The net rates of chemical production of each of the constituents are deduced from the kinetic laws (131) and (132) ... 

The fact that a homogeneous element of volume is considered results in the fact that the rate of reaction, which is a function of the concentrations, of the temperature and of the pressure, is the same at each point within the volume element which causes the rate of chemical production to be proportional to the volume of the element. 

Calculate the rate of chemical production of the product B under these conditions, as... 

As the concentrations are constantly changing along the reactor, the same is true of the rate of chemical production Rj of the constituent Cj. A mass balance on a differential element of volume dV must therefore be carried out, in which the rates Rj can be considered to have well-defined values. 

The rates of chemical production Wj are obtained from the laws of chemical kinetics. The adsorption desorption and chemisorption laws lead us to similar consequences. 

Enzymes increase the rate of chemical reactions by decreasing the activation energy of the reactions. This is achieved primarily by the enzyme preferentially binding to the transition state of the substrate. Catalytic groups of the enzyme are required to achieve a specific reaction path for the conversion of substrate to product. 

Because the rates of chemical reactions are controlled by the free energy of the transition state, information about the stmcture of transition states is crucial to understanding reaction mechanism. However, because transition states have only transitory existence, it is not possible to make experimental measurements that provide direct information about their structure.. Hammond has discussed the circumstances under which it is valid to relate transition-state stmcture to the stmcture of reactants, intermediates, and products. His statements concerning transition-state stmcture are known as Hammond s postulate. Discussing individual steps in a reaction mechanism, Hammond s postulate states if two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have neariy the same energy content, their interconversion will involve only a small reorganization of molecular stmcture. ... 

Thermal runaway reactions are the results of chemical reactions in batch or semi-batch reactors. A thermal runaway commences when the heat generated by a chemical reaction exceeds the heat that can be removed to the surroundings as shown in Figure 12-5. The surplus heat increases the temperature of the reaction mass, which causes the reaction rate to increase, and subsequently accelerates the rate of heat production. Thermal runaway occurs as follows as the temperature rises, the rate of heat loss to the surroundings increases approximately linearly with temperature. However, the rate of reaction, and thus the... 

An accident sequence source term requires calculating temperatures, pressures, and fluid flow rates in the reactor coolant system and the containment to determine the chemical environment to which fission products are exposed to determine the rates of fission product release and deposition and to assess the performance of the containment. All of these features are addressed in the... 

From the study of the influencing of single reactions by products and by other added substances and from the analysis of mutual influencing of reactions in coupled systems, the following conclusions can be drawn concerning adsorption of the reaction components. (1) With the exception of crotyl alcohol on the platinum-iron-silica gel catalyst, all the substances present in the coupled system, i.e. reactants, intermediate products, and final products, always adsorbed on the same sites of the catalytic surface (competitive adsorption). This nonspecificity was established also in our other studies (see Section IV.F.2) and was stated also by, for example, Smith and Prater (32), (2) The adsorption of starting reactants and the desorption of the intermediate and final products appeared in our studies always as faster, relative to the rate of chemical transformations of adsorbed substances on the surface of the catalyst. 

Pavich, M. J. (1986). Processes and rates of saprolite production and erosion on a foliated granitic rock of the Virginia Piedmont. In "Rates of Chemical Weathering of Rocks and Minerals" (S. M. Coleman and D. P. Dethier, eds), pp. 551-590. Academic Press, New York. 

Fig. 9-3 Conceptual model to describe the interaction between chemical weathering of bedrock and down-slope transport of solid erosion products. It is assumed that chemical weathering is required to generate loose solid erosion products of the bedrock. Solid curve portrays a hypothetical relationship between soil thickness and rate of chemical weathering of bedrock. Dotted lines correspond to different potential transport capacities. Low potential transport capacity is expected on a flat terrain, whereas high transport is expected on steep terrain. For moderate capacity, C and F are equilibrium points. (Modified with permission from R. F. Stallard, River chemistry, geology, geomorphology, and soils in the Amazon and Orinoco basins. In J. I. Drever, ed. (1985), "The Chemistry of Weathering," D. Reidel Publishing Co., Dordrecht, The Netherlands.)...

This is the first example where we have tested to see if the concentration of a product affects the rate of a reaction. It may seem intuitive that products should not be involved in rate laws, but as we show in Section 15-1. a product may influence the rate of a reaction. In careful rate studies, this possibility must be considered. It is common for some reagents in a chemical system to have no effect on the rate of chemical reaction. Although it is unusual for none of the reagents to affect the rate, there are some reactions that are zero order overall. Such reactions have a particularly simple rate law Rate = t. 

A reaction at steady state is not in equilibrium. Nor is it a closed system, as it is continuously fed by fresh reactants, which keep the entropy lower than it would be at equilibrium. In this case the deviation from equilibrium is described by the rate of entropy increase, dS/dt, also referred to as entropy production. It can be shown that a reaction at steady state possesses a minimum rate of entropy production, and, when perturbed, it will return to this state, which is dictated by the rate at which reactants are fed to the system [R.A. van Santen and J.W. Niemantsverdriet, Chemical Kinetics and Catalysis (1995), Plenum, New York]. Hence, steady states settle for the smallest deviation from equilibrium possible under the given conditions. Steady state reactions in industry satisfy these conditions and are operated in a regime where linear non-equilibrium thermodynamics holds. Nonlinear non-equilibrium thermodynamics, however, represents a regime where explosions and uncontrolled oscillations may arise. Obviously, industry wants to avoid such situations ... 

From the coverage made thus far, it may be of interest to record in one place the different factors which influence the rate of chemical reactions. The rate of chemical reaction depends essentially on four factors. The nature of reactants and products is one. For example, certain physical properties of the reactants and products govern the rate. As a specific example in this context mention may be of oxidation of metals. The volume ratio of metallic oxide to metal may indicate that a given oxidation reaction will be fast when the oxide is porous, or slow when the oxide is nonporous, thus presenting a diffusion barrier to the metal or to oxygen. The other two factors are concentration and temperature effects, which are detailed in Sections. The fourth factor is the presence of catalysts. 

First, the rate of heat production is again related to the sum of the rates of depositional and burning processes, and if the predominant factor affecting the overall rate is temperature, then it does not seem likely that the specific effect of water vapor on the oxidation reported here is chemical catalysis, since a lowering of activation energy for either process would result in an increase in the overall rate relative to dry oxidation. 

Both of the above chemical studies point towards the increased importance of the burning process at 285°C in determining the initial rate of heat production. The role of water as yet remains undefined other than at the higher temperature of 285°C it appears to have the opposite effect on the bitumen sample compared to the process at 225°C i.e., it appears that water vapor encourages pathways by which the various components of bitumen react with oxygen. Preliminary calculations of the total heats evolved during the wet oxidation of bitumen sands indicate that they are independent of the partial pressure of oxygen in the system at... 

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