Fast reactions, defined

The size of the cataly.st particle influences the observed rate of reaction the smaller the particle, the less time required for the reactants to move to the active catalyst sites and for the products to diffuse out of the particle. Furthermore, with relatively fast reactions in large particles the reactants may never reach the interior of the particle, thus decreasing the catalyst utilization. Catalyst utilization is expressed as the internal effectiveness factor //,. This factor is defined as follows ... 

The photopontential also approaches to zero when the semiconductor photoelectrode is short-circuited to a metal counterelectrode at which a fast reaction (injection of the majority carriers into the electrolyte) takes place. The corresponding photocurrent density is defined as a difference between the current densities under illumination, /light and in the dark, jDARK ... 

The chemical time scales ra and the mixing time scale can be used to define the Damkohler number(s) Da, = /x . Note that fast reactions correspond to large Da, and... 

The catalytic cycle for the thiolperoxidase and haloperoxidase-like activity of diorganoselenides and tellurides is summarized in Fig. 25. Stopped-flow spectroscopy has been used to elicit mechanistic details of the cycle. " " Following oxidation to the selenoxide or telluroxide, the catalytic cycle for thiolperoxidase-like activity is shown in Fig. 21. The details of the haloperoxidase-like cycle are not as well defined. Using dihydroxytellurane 52 as a substrate, the addition of 0.5 M sodium iodide in pH 6.8 buffer gave a fast reaction with a second-... 

A mathematical function used in fast-reaction kinetics to describe how a perturbation of definable strength and duration leads to a change in the kinetic parameters from an initial condition or state to a final state preceding or overlapping with the ensuing chemical relaxation process under investigation. 

Electron transfer is a fast reaction ( 10-12s) and obeys the Franck-Condon Principle of energy conservation. To describe the transfer of electron between an electrolyte in solution and a semiconductor electrode, the energy levels of both the systems at electrode-electrolyte interface must be described in terms of a common energy scale. The absolute scale of redox potential is defined with reference to free electron in vacuum where E=0. The energy levels of an electron donor and an electron acceptor are directly related to the gas phase electronic work function of the donor and to the electron affinity of the acceptor respectively. In solution, the energetics of donor-acceptor property can be described as in Figure 9.6. 

Regime 4 - fast reactions in the film In region 4 ozone is entirely consumed inside the liquid film, so that no ozone can escape to the bulk liquid, i. e. cL = 0. Here, the enhancement factor is defined as ... 

This non-converted reactant B is called the reactant accumulation. It results from the mass balance, that is, the feed rate as input and the reaction rate as consumption. In other words, a low accumulation is obtained when the feed rate of B is slower than the reaction rate. Since, as defined in Equation 7.4, the reaction rate depends on both concentrations CA and CB, this means that both reactants must be present in the reaction mixture in a sufficiently high concentration. For fast reactions, such as those with a high rate constant, even for low concentrations of the reactant B, the reaction will be fast enough to avoid the accumulation of unconverted B in the reactor. For slow reactions, a significant concentration of B is required to achieve an economic reaction rate. Thus, two cases have to be considered fast reactions and slow reactions. 

A simple qualitative description of how fast reaction occurs can be taken from a direct observation of how long it takes for a certain percentage reaction to occur. But in a quantitative analysis rate must be precisely defined, and once this has been done it becomes apparent how inadequate the loose definition of rate in terms of percentage reaction actually is. 

The more precise meaning of the term rate of reaction, defined as how fast the [reactant] changes with time, can be illustrated on graphs of concentration versus time (see Figures 3.3(a), (b) and (c)). 

The value of Ha determines the rate of the ozone reaction. Thus, for Ha < 0.3 ozone reactions are slow reactions, whereas for Ha > 3 they are fast reactions. There is also an intermediate kinetic regime defined as moderate, which is rather difficult to treat kinetically [53]. However, for most common situations, reactions of ozone in drinking water are considered as slow reactions. This does not mean that the time needed to carry out the ozonation is high (time needed to have high destruction of pollutants), but that the mass transfer rate is faster than the chemical reaction rate. For instance, in most cases, ozonation of micropollutants, which are found in very low concentrations (mg L-1 or pg L ), lies in this kinetic regime. In other cases, where the concentration of pollutants is higher (i.e., wastewaters... 

Volatilization processes, combined with gas adsorption chromatographic investigations, are well established methods in nuclear chemistry. Fast reactions and high transport and separation velocities are crucial advantages of these methods. In addition, the fast sample preparation for a-spectroscopy and spontaneous fission measurements directly after the gas-phase separation is a very advantageous feature. Formation probabilities of defined chemical compounds and their volatility can be investigated on the basis of experimentally determined and of predicted thermochemical data, the latter are discussed in Part II of this chapter. 

Thus, using REACTION 1, 2, 3, 4, 5, 6, and 6.5 mg/L 02 (converted into mol/L) are added. For C02, equilibrium with the atmospheric partial pressure can be defined simply by using the key word EQUILIBRIUMPHASES, since all the subsequent reactions depend only on the diffusion of the C02 and its dissociation in water. Contrary to redox reactions with oxygen both processes are fast reactions, hence can be described by equilibrium reactions, neglecting kinetics. 

The experiments with the inert tracer may only show that the time, necessary for the fluid in the reactor to be well mixed, is much smaller than the average residence time. When a chemical reaction takes place, an additional time-scale, the time constant of the chemical reaction, appears. This time characterizes the reaction rate and can be defined as the time in which the reaction proceeds to a certain conversion, say 50%. For many practical heterogeneous catalytic reactions, the reaction time is so short that reactants entering the reactor may be converted without being mixed, for example, during the first cycle. For such fast reactions, of course, the reactor cannot be considered as gradient-free, whatever the recirculation ratio is. 

Qi is defined in the same manner as in the fast reaction. Dc is the diflusivity of species C in the liquid phase. All other nomenclature is the same as that described earlier. The perturbation and the Galerkin solutions to the resulting equations for the cocurrent-flow case are given by Szeri et al.5fi... 

For a reaction to be applicable in kinetic analysis, its rate must be neither too high nor too low. We may define fast reactions as those that approach equilibrium (several half-lives) during the time of mixing. For analytical measurements, reaction... 

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