Reaction timescale

The lack of precise measurements of environmentally relevant chemical rate constants limits the number of quantitative evaluations of the importance of complex dynamics on uptake fluxes. Nonetheless, examples involving bicarbon-ate-CC>2 conversion [69,88] and trace metal complexation [8,46,325] have been examined theoretically in the literature. For example, comparison of the diffu-sional and reactional timescale allowed Riebesell and collaborators [69,88] to show that bicarbonate conversion to CO2 did not generally enhance the... 

Additional developmental milestones for FPOP include the demonstration of fCd determination and development of dose-dependent radical foot printing by using different scavengers and concentrations to vary and then quantify the loss of unmodified peptide signal and the increase of modified peptide. Further advances can be made by determining with certainty the reaction timescale. At the... 

For the kinetics of a reaction, it is critical to know the rough time to reach equilibrium. Often the term "mean reaction time," or "reaction timescale," or "relaxation timescale" is used. These terms all mean the same, the time it takes for the reactant concentration to change from the initial value to 1/e toward the final (equilibrium) value. For unidirectional reactions, half-life is often used to characterize the time to reach the final state, and it means the time for the reactant concentration to decrease to half of the initial value. For some reactions or processes, these times are short, meaning that the equilibrium state is easy to reach. Examples of rapid reactions include H2O + OH (timescale < 67 /is at... 

The mean reaction time or reaction timescale (also called relaxation timescale relaxation denotes the return of a system to equilibrium) is another characteristic time for a reaction. Roughly, the mean reaction time is the time it takes for the concentration to change from the initial value to 1/e toward the final (equilibrium) value. The mean reaction time is often denoted as x (or Xr where subscript "r" stands for reaction). The rigorous definition of x is through the following equation (Scherer, 1986 Zhang, 1994) ... 

The similarity between the apparent equilibrium temperature equation and the closure temperature equation can be seen by comparing Equation 5-125 and Equation 5-77b by letting Tae and Tc be equivalent, Xr (reaction timescale) and x (diffusion timescale) be equivalent, and G = 2, the two equations become the same. 

Solution From Table 2-1, the reaction timescale for reversible first-order reaction is Xr= l/(kf+kb). Hence, knowing Tae = 857.93 K, we find the mean reaction time Xr at Tae as follows ... 

The characteristic times Ta and Tde cannot be used anymore and we introduce the new characteristic time Tq — K r/sQ, which has a meaning of the superficial chemical reaction timescale. As before, we set s — H/Lr and choose Tr — Tr. 

The other dimensionless terms, like those in eqns (11.8)—(11.10) are based on the cubic reaction timescale tch = /klal the limit q ->0 corresponds to the cubic contribution becoming dominant, q -> oo to a quadratic regime. 

The ratio of reactor and reaction timescale is the (dimensionless, of course) Damkohler number of the first kind Da] = k-t (for a first-order reaction). In a... 

Although this system was useful for preparation of optically enriched secondary alcohols, prolonged reaction times limited the practicality of the process. Stoltz found that addition of Cs2C03 and t-BuOH dramatically increased the reaction rate, leading to more practical reaction timescales while maintaining selectivity (Scheme 2) [6],... 

However, not everyone was convinced by the existence of the non-classical carbocation. H. C. Brown 1977 pointed out that the norbornyl compounds are compared with cyclopentyl rather than with cyclohexyl analogues, 2.21 (eclipsing strain), and in such a comparison the endo-isomev is abnormally slow, the exo-isomer being only 14 times faster than cyclopentyl analogues. He also pointed out that the formation of racemic product is due to two rapidly equilibrating classical carbocation species (Scheme 2.17). The interconversion of enantiomeric classical carbocation species must be very rapid on the reaction timescale. 

Enantiocontrol in intramolecular cyclopropanation reactions of diazoacetamides has been developed to levels comparable with those now accessible with diazoesters. Several substituent variations in Eq. (20) are summarized in Table 3, which reveals examples where ee s exceed 90%. In general diazoamides have a conformational feature which differs from their diazoester counterparts, namely, the relatively slow syn-anti isomerization by rotation about the N-CO bond. If the interconversion of (18) and (19) or their respective metal carbenes is slow relative to the reaction timescale [50], only isomer (18) can lead to intramolecular cyclopropanation. However, an alternative process to which (18) is prone un-... 

The principal reason for the adoption of structure 20 as an irreversibly formed intermediate in the reaction under consideration comes from fascinating intramolecular deuterium isotope effects observed by Stephenson and coworkers [123, 125, 131]. The key finding was that the deuteriated derivatives, 21 and 22, of 2,3-dimethyl-2-butene exhibited the intramolecular isotope effects shown. It was therefore concluded that C-H and C-D bonds had to be cis to one another to compete, demanding an intermediate with a geometry operationally equivalent to a perepoxide. In addition, that intermediate had to be formed irreversibly and inversion of the oxonium oxygen had to be slow on the reaction timescale. 

FIGURE 19.6 Relationship between characteristic times of vertical turbulent diffusion tj) and a number of atmospheric reactions tc) for a layer of thickness Az = 10 m and different thermal stability classes (Kramm et al., 1993). For example, the HNO3—NH3—NH4NO3 equilibrium (reaction 2) has a reaction timescale comparable to that of turbulent diffusion under unstable and neutral conditions. 

For those carbon acids having pKa values in the upper 30s, imfavourable equilibria in the deprotonation imply that if reaction is to proceed satisfactorily in the forward direction, the resultant organolithiiun must either undergo a rearrangement, or be trapped out by an external electrophile present in situ (the electrophile therefore requiring compatibiHty with the lithium amide on the reaction timescale). 

The ligand substitution reactions of the bivalent first-row transition metal ions are the most studied of those of the labile metal ions, probably because the visible d-d spectra of the transition metal ions make them particularly amenable to spectrophotometric study, and also because their reaction timescale is usually well within those of the SF and NMR techniques. Thus it has been shown that the mechanism of dimethylformamide (dmf) exchange on [M(dmf)6] (M = Mn—Ni) varies systematically from L to D, in contrast to the analogous [M(solvent)6] in water, methanol, and acetonitrile where the mechanism varies from L h the number of d electrons increases. This has occasioned a spectrophotometric SF study of the closely related substitution of the bidentate ligands trans-pyndine-2-azo(p-dimethylaniline) (Pada) and diethyldithiocarbamate (Et2DTC) on [M(dmf)6] shown in Eq. (13) (where L-L represents a bidentate ligand) which... 

Note that the scaling analysis hasn t involved the reaction timescale so far. This will be required to obtain a consistent balance at 0(1) from the steady state solid mass balance. Equation 3.32 can be written as... 

Reaction timescale, tn. Since mixing does not influence the behavior of a first-order reaction, we will define the reaction timescale for a second-order reaction as the time required to decrease the reagent concentration to half its initial value. For a batch reactor, this is given by... 

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