Reaction rates, gross

By gross reaction rate one understands either a product formation rate c/[prod-uct]/df or a starting material consumption rate — [starting materialj/c/f. The following applies unless the stoichiometry requires an additional multiplier ... 

These data show that EPl does not leave the glassy state when RTC samples are post-cured at 40°C for 1 h (PC40), either in the bulk or in the layers. Therefore, PC40 proceeds under diffusion control and is only little accelerated. As for RTC, the gross reaction rate slows down due to the decreasing mobility and only some additional oxirane conversion is obtained, but not full consumption (Pig. 30.3). Hence, the glass transition rises to only = 66.6 0.3 °C in the bulk... 

The easiest approach to developing a gross reaction rate law for the polymerization process in total is to make use of the monomer consumption. 

From this it follows for the gross reaction rate law ... 

In general the monomer concentration cm by far exceeds die initiator concentration ci and the rate constant of the termination reaction kr is much higher than the rate constant of the decomposition kn. This allows the formulation of the gross reaction rate with the help of the following approximation, which is still of satisfying accuracy ... 

Finally a fourth boundary condition shall be valid to support the worst case character of the procedure. The reaction order necessary for the formal kinetic description of a process has a severe influence on the pressure/time and respectively the tempera-ture/time-profiles to be expected. Industrial experience has shown that approximately 90% of all processes conducted in either batch or semibatch reactors can be described with a second order formal kinetic rate law. But it remains uncertain whether this statement, which is related to isothermal or isoperibolic operation with a rather limited overheating, remains valid if the reaction proceeds adiabatically and if side reactions contribute to the gross reaction rate at a much higher degree. In consequence, it shall be assumed for a credible worst case evaluation that the disturbed process follows a first order kinetics. Any reactions occurring in reality will almost certainly proceed at a much lower rate. 

There are additional kinetic effects in the high-temperature chain reaction regime, besides the much higher and nonsteady gross reaction rate, which arise from the Arrhenius temperature dependence of the rate coefficients of most of the initiation and propagation (including... 

The decades of SO2 research have given almost only gross reaction rates such as those first studied by Mader (1958) and later recognized as being atmospherically important by Hoffmann and Edwards (1975) and Penkett et al. (1979) ki.292 — (5.3 2.7) 10 L moF s recommended by Moller and Mauersberger (1995), see Table 5.20. 

Control of the core is affected by movable control rods which contain neutron absorbers soluble neutron absorbers ia the coolant, called chemical shim fixed burnable neutron absorbers and the intrinsic feature of negative reactivity coefficients. Gross changes ia fission reaction rates, as well as start-up and shutdown of the fission reactions, are effected by the control rods. In a typical PWR, ca 90 control rods are used. These, iaserted from the top of the core, contain strong neutron absorbers such as boron, cadmium, or hafnium, and are made up of a cadmium—iadium—silver alloy, clad ia stainless steel. The movement of the control rods is governed remotely by an operator ia the control room. Safety circuitry automatically iaserts the rods ia the event of an abnormal power or reactivity transient. 

Equation 1 has as its basis the concept that diffusion, either through pores or to the gross surface of the catalyst particle, controls the reaction rate. When the control is strictly by the gas film surrounding the catalyst, one would have to convert Equation 1 to... 

For the first assumption, the value of Kw for the shift appears to be too high. It must be this high because it is necessary to make C02 appear while both C02 and CO are being consumed rapidly by methanation. The data may be tested to see if the indicated rate appears unreasonable from the standpoint of mass transfer to the gross catalyst surface. Regardless of the rate of diffusion in catalyst pores or the surface reaction rate, it is unlikely that the reaction can proceed more rapidly than material can reach the gross pill surface unless the reaction is a homogeneous one that is catalyzed by free radicals strewn from the catalyst into the gas stream. 

If the reaction proceeds by more than one pathway, when it attains equilibrium the rates along each pathway (separately) are equal, not merely the total rates. Not only must the gross opposing rates be equal as a condition of thermodynamic equilibrium, but the opposing rates along each pathway must be equal as well. This relation can be applied to the kinetic data for the reaction between thiocyanate and hexaaquairon(3+) ions. The net reaction is... 

The complete chemical modelling of a cloud in the ISM looks tractable, if complicated, although there will always be assumptions, some of which will be rather gross, such as surface reaction rates, but they can all be refined in time. Molecular cloud modelling is at the frontier of astrochemistry and it would be hard to consider all of the results. The basic process of generating a kinetic model for a molecular cloud must follow the pathway ... 

Uq c Ty T0) FI ctj a0 When only the gross reaction is present, the ratio of the rate of heat release to the rate of change of the concentration is the same as that of total amount of released heat, c(T1 — T0), to the total change in concentration, (ax — a0), when the reaction runs completely. But then, assuming D = k, the differential equations as well as the boundary conditions for 0 and a coincide ... 

With spectral properties as complex as these, one can anticipate at the outset that kinetic studies will yield complex results. This prediction is in fact borne out. The gross features permit easy evaluation of, for example, the reaction rate of solvated electrons with water but working out the kinetics in detail is quite another matter. This paper reports our experiments and results to date using these methods. 

The unidirectional fluxes involved in the simplified sequence above are proportional to the gross CO2 concentration gradient times the conductance, g, or the reaction rate constant, k, for each step, such that we can define Fy = gc, F3 = gCc and F2 = febCc g(Ca - c ), where c and Cc are respectively the ambient and chlor-oplast concentrations of CO2. As noted above it is common to use discriminations, a—1, represented by a, b, and A for the diffusion step, the enzymatic step, and the overall sequence, respectively. These terms can be substituted into Equation (23) that rearranges to... 

The first results of degradation of polyamides shown above are based on fast melt modification reactions. The determination of the gross kinetical reaction rate was impossible. Only a very vague estimation could be made during reactive extrusion processes. 

The first fundamental examinations with polycondensates like polyanoides and polycarbonates were carried out in an interdisciplinary cooperation between chemists and engineers as published in [33-35] by use of fast in situ chemical reactions at high melt temperature. It is well known that the gross kinetical reaction rate decreases very fast with decreasing temperature. 

The first requirement is mainly important for the assessment of chemical reactions. In the overwhelming majority of chemical processes, not only the chemical conversion into the single desired product takes place. Instead, the desired reaction is accompanied by numerous parallel and consecutive reactions. Under the defined operating conditions resulting from the optimization work, the effect of these simultaneous reactions on yield and selectivity has been minimized by the choice of mode of operation (continuous, batch or semibatch) and of process parameters, such as pressure, temperature, concentration, pH-value, mass flow rates etc. A performance of the safety tests under conditions deviating fi-om those chosen for the plant process would inadvertently favour those secondary reactions in a different manner. Values for the gross value of heat output and reaction rate obtained this way would not be suitable for any process safety evaluation. Modem reaction calorimeters, like those commercially available today, enable the conduction of experiments with sufficient similarity to actual plant conditions. 

In the introduction to this section a wording was used which is of some importance to chemical process safety knowledge of a reaction rate law which describes the investigated process with sufficient accuracy. Nature is complex, so that the desired process is very rarely the only one to proceed under the conditions chosen for the manufacture of a desired plant product. Normally, numerous reactions take place simultaneously. Based on experience and know-how the development chemist was able only to optimize the process with respect to operational conditions up to an extent that the desired process is favoured. But it remains part of reality that the heat production rate measured and the reaction enthalpy obtained by its integration represent gross values which are formed as the sum of all simultaneously contributing reactions. 

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