Timescale chemical

We must note that kl is effectively a third-order rate constant, with units of (concentration)-2 (time)-1. Thus multiplying by al and then taking the inverse gives a chemical timescale... 

The reaction rate curve R is zero at complete conversion and also has low (but non-zero) values close to 1 — a = 0, with a maximum close to two-thirds conversion (actually at 1 — a = — / 0). Importantly, R does not depend on the residence time rres, although it does vary if / 0 is changed. The flow line L is zero when 1 — a = 0 since the inflow and outflow have the same composition (no conversion of A to B). The gradient of the flow line (Fig. 6.7(b)) is given by 1 /Tres, so it is steep for short residence times (fast flow rates) and relatively flat for long rres. (Note how tres actually compares fres and lch, so short residence times are those that are much less than the chemical timescale etc.) The flow line is, however, unaffected by the inflow concentration of the autocatalyst f 0. 

We can identify a chemical timescale tch from the value of the first-order rate constant k evaluated at our reference temperature T0 ... 

The quadratic Fisher result of the previous section is based on the quadratic chemical timescale tch = 1 /kqa0 if we represent the wave velocity measured in these terms as k, defined by... 

Table II summarizes the pertinent time and space scales in this problem. Assuming the speed of sound is 105cm/sec, a time-step of about 10-3 sec would be required to resolve the motion of sound waves bouncing across the chamber. Chemical timescales, as mentioned above, are about 10-6 sec. This number may be reduced drastically if the reaction rates or density changes are very fast. It takes a sound wave about 10 3 seconds to cross the 1 meter system and it takes the flame front about one second to cross. We further assume that the flame zone is about 10-2 cm wide and that it takes grid spacings of 10 3 cm to resolve the steep gradients in density and temperature in this flame zone.

Above the intermediate layer a hot, rarefied, and heavily irradiated disk atmosphere exists (T > 100 K). This is a molecule-deficient region (apart from H2) where only simple light hydrocarbons, their ions, and other radicals, such as CCH and CN, are able to survive ( zone of radicals ). Chemical timescales are short ( lOOyr) and defined by ionization and irradiation. 

In solution the C R ring usually rotates very rapidly on the NMR and chemical timescales. Introduction of excess steric bulk into the ring substituents and/or low temperatures may slow this process. 

In the examples given above we have tried to describe some of the phenomena which arise as a result of chemical kinetic-fluid dynamic coupling. First, we described studies of the isolated effects of chemical-acoustic coupling, emphasizing the effects on the chemical kinetics. The major conclusion is that sound waves and entropy perturbations can alter chemical timescales, and that this effect can be quantified. We then described a system in which sound waves and entropy perturbations behind a shock wave caused early ignition at unpredictable locations and at reduced ignition times. A series of reaction centers formed and one of these close to the shock front eventually ignited. 

The photodissociation rates for a number of important astrophysical molecules are summarized in Table 1 for the unattenuated interstellar radiation field given by Draine (1978 Eq. (3)). In order to calibrate the significance of a rate of 3 x 10 s , say, it is useful to note that this rate corresponds to a lifetime of a molecule of 10 years, which is short in comparison with dynamical lifetimes of interstellar clouds (often estimated to be 10 - 10 years), and with most other chemical timescales. In particular, destruction of a molecule by reaction with an ion in a cloud of density 10 cm with a fractional ionization less than 10 will occur with a characteristic lifetime of 300 years or more. 

In a reactive flow system, the chemical timescales should not be treated in isolation from the relevant timescales of the flow processes which may include diffusion, convection/advection or turbulent mixing (Goussis et al. 2005b). The simple initial value problem expressed in Eq. (2.9) must therefore be extended to a system of partial differential equations. Using the notation of Bykov and Maas (2007), the evolution equation for the scalar field of a reacting flow can be described by... 

In the second approach, the spatially homogeneous chemical slow manifold is used, and the method must somehow accoxmt for reaction-transport coupling. For a chemical timescale to be defined as fast in a reactive flow system, the Damkohler number, which is defined as the ratio of the flow timescale tf and the chemical timescale Tc, must be large ... 

The timescale is just one sub-classification of chemical exchange. It can be further divided into coupled versus uncoupled systems, mutual or non-mutual exchange, inter- or intra-molecular processes and solids versus liquids. However, all of these can be treated in a consistent and clear fashion. 

The approach is ideally suited to the study of IVR on fast timescales, which is the most important primary process in imimolecular reactions. The application of high-resolution rovibrational overtone spectroscopy to this problem has been extensively demonstrated. Effective Hamiltonian analyses alone are insufficient, as has been demonstrated by explicit quantum dynamical models based on ab initio theory [95]. The fast IVR characteristic of the CH cliromophore in various molecular environments is probably the most comprehensively studied example of the kind [96] (see chapter A3.13). The importance of this question to chemical kinetics can perhaps best be illustrated with the following examples. The atom recombination reaction... 

A reasonable approach for achieving long timesteps is to use implicit schemes [38]. These methods are designed specifically for problems with disparate timescales where explicit methods do not usually perform well, such as chemical reactions [39]. The integration formulas of implicit methods are designed to increase the range of stability for the difference equation. The experience with implicit methods in the context of biomolecular dynamics has not been extensive and rather disappointing (e.g., [40, 41]), for reasons discussed below. 

For the NH azoles (Table 3), the two tautomeric forms are usually rapidly equilibrating on the NMR timescale (except for triazole in HMPT). The iV-methyl azoles (Table 4) are fixed chemical shifts are shifted downfield by adjacent nitrogen atoms, but more by a pyridine-like nitrogen than by a pyrrole-like iV-methyl group. 

For a radionuclide to be an effective oceanic tracer, various criteria that link the tracer to a specihc process or element must be met. Foremost, the environmental behavior of the tracer must closely match that of the target constituent. Particle affinity, or the scavenging capability of a radionuclide to an organic or inorganic surface site i.e. distribution coefficient, Kf, is one such vital characteristic. The half-life of a tracer is another characteristic that must also coincide well with the timescale of interest. This section provides a brief review of the role of various surface sites in relation to chemical scavenging and tracer applications. 

Before considering the role of the electrode material in detail, there is one further factor which should be pointed out. The product of an electrode process may be dependent on the timescale of the contact between the electroactive species and the electrode surface, particularly when a chemical reaction is sandwiched between two electron transfers in the overall process. This was first realized when it was found that ir E curves and reaction products at a dropping mercury electrode were not always the same as those at a mercury pool electrode (Zuman, 1967a). For example, the reduction of p-diacetylbenzene at a mercury pool was found to be a four-electron process, giving rise to the dialcohol, while at a dropping mercury electrode the product was formed by a two-electron process where only one keto group was reduced (Kargin et al., 1966). These facts were interpreted in terms of the mechanism... 

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

Whilst, in general terms, industry is in agreement with the objectives of the White Paper there is disagreement over implementation. The main concerns of industry centre on the cost, timescale and increased use of animals for the testing of existing substances, many of which have been used for 30 years or more without any obvious problems. Satisfactory resolution of the issues could have a significant impact on the future direction of the European chemical industry. 

Approaches to the fundamental need to shift from fossil to renewable feedstocks for chemicals production wiU range from modifications to, and developments of, traditional chemical, engineering and biotechnological methods (that maybe implemented on a relatively short timescale, say, 10-15 years) to much more radical processes (such as direct capture of solar energy, through artificial photosynthesis), requiring longer time to implement (say 15-30 years). 

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