Half-time, of reaction

Assuming first order reaction kinetics, the sorption rate that was determined for adsorption and desorption was 0.187 sec . A reaction rate of 0.187 sec implies a half time of reaction of 3.7 seconds. 

Factor Observation Temperature °C Medium Half time of reaction (minutes) Reference... 

Let us now assume that the residence time of a system is equivalent to the period of time that the system behaves as a closed system thermodynamically. With this assumption it is useful to qualitatively compare the residence times of different aqueous systems in the hydrosphere to the halftimes of some example reactions and reaction types. This has been done schematically in Fig. 2.2. In essence, as we examine the diagram, we can assume reactions are at equilibrium in waters whose residence times significantly exceed the half-times of reactions of interest. Note that the half-times of some solute-solute and solute-water reactions (these include some complexation and acid-base reactions [see Chaps. 3 and 5]) are shorter than the residence times of raindrops and so can be assumed to be at equilibrium in rain. These are homogeneous reactions. However, the other types of reactions shown, including atmospheric gas exchange, which is heterogeneous, are too slow to have... 

Understand the definitions of system (or substance) residence time and the half-time of reactions in a system and how these concepts can be used to decide the applicability of equilibrium and kinetic concepts. 

Evidence for this type of superoxide elimination exists in similar non-a-hydroxyl systems [70], with rates apparently varying across a wide range. Thus, the half-time of reaction (43) is 30 xs [71] whereas that of reaction (44) is at least three orders of magnitude longer [72]. 

The effect of the addition of hydrogen or nitrogen on the rate is only small and may be neglected. At 1100 °C, Kunsman (J. Amer. Chem. Soc. 1928, 50, 2100) obtained values of the half-time of reaction r, as a function of the initial ammonia pressure, given in table 2. 

Thus the half-time of reaction is, except at the lowest pressure, strictly proportional to the pressure confirming that the reaction is zero order as long as the pressure is sufficient for the surface to be saturated. 

Ligand Average affinity (1/mole) Heterogeneity index Percent of sites label ed Half-time of reaction (hr) ... 

Time Constants. If the transport equation were a bit simpler, one could treat reaction with mass transfer as a process of rates in series, such as heat or mass transfer. One could compare half-times of reaction with inverse mass transfer coefficients and even include mixing times as a rate constant. Although an interesting thought, it is hardly ever done. 

In relaxation studies, the perturbation applied to the system is always of very small amplitude, in such a way that the system remains close to equilibrium during the entire cormse of its evolution. Nevertheless, the perturbation must be sufficient for generating a relaxation signal large enough with respect to noise. Chemical relaxation methods permit the study of chemical processes, with half-time of reaction ranging from minutes to nanoseconds. Several books and review papers on chemical relaxation methods have been published. Only the main featmes of chemical relaxation methods are presented in this section. 

In some apparatuses, very similar to stopped-flow the flow of reactants is continuous (continuous flow methods). The observation of the reaction is integrated. An apparatus based on this principle has been described that allows the study of systems with half-time of reaction as short as 5 )xs. ... 

PR] = 10 mol r the pseudo first order rate constant is equal to 10 s and the corresponding lifetime is 10" s. The lifetime of inactive species is 10 s and the number of periods during the required lO s is 10. The lifetime of an average maaoradical is 10 s. In one period, 1 monomer molecule is added thus, in 10 periods there are 10 monomer molecules added, providing the required Pn=100. Therefore, the lifetimes (the kinetic meaning of lifetimes and half-times of reactions are given in the Appendix) of active and inactive species are... 

On heating a solution of the complex in slightly acidified aqueous solution, one coordinated chloride is replaced by a water molecule to produce the pink ion [Coen2Cl(H20)]. The half time of reaction, to.5, is indicated by the appearance of a grey colour. The first order kinetics and the activation parameters can be studied in a similar way to the acid hydrolysis of the trisoxalatocobaltate (Sec. 14.5.2), replacing dilute sulphuric acid by 0.1 M nitric acid and carrying out runs at temperatures between 50°-75 C. 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

Hydroxy-8-azapurine was shown by rapid-reaction techniques (see Section II, E) to be anhydrous in the anion and hydrated in the neutral species. The hydration reaction has a half-time of about 0.5 second, which is too rapid for exact measurements with existing apparatus. The cation of 2-amino-8-azapurine was shown to have an anomalous value and ultraviolet spectrum, although its 6-methyl derivative is quite normal. Hydration in this case proved to be too fast to register in the rapid-reaction apparatus. 

A further factor which must also be taken into consideration from the point of view of the analytical applications of complexes and of complex-formation reactions is the rate of reaction to be analytically useful it is usually required that the reaction be rapid. An important classification of complexes is based upon the rate at which they undergo substitution reactions, and leads to the two groups of labile and inert complexes. The term labile complex is applied to those cases where nucleophilic substitution is complete within the time required for mixing the reagents. Thus, for example, when excess of aqueous ammonia is added to an aqueous solution of copper(II) sulphate, the change in colour from pale to deep blue is instantaneous the rapid replacement of water molecules by ammonia indicates that the Cu(II) ion forms kinetically labile complexes. The term inert is applied to those complexes which undergo slow substitution reactions, i.e. reactions with half-times of the order of hours or even days at room temperature. Thus the Cr(III) ion forms kinetically inert complexes, so that the replacement of water molecules coordinated to Cr(III) by other ligands is a very slow process at room temperature. 

Under conditions where the dismutation reaction is slow the exchange between Au(III) and Au(I) has been shown to proceed at a measurable rate at 0 °C in 0.09 M HCl, an exchange half-time of about 2 min was observed. The isotopic method ( Au) and a separation method based on the precipitation of dipyridine -chloroaurate(III) was used to obtain data. An acceleration in the exchange rate was observed as the HCl concentration was increased. ... 

In perchlorate media the latter reaction was found to be rapid (100 % exchange in < 60 sec) and the former reaction slow (half times of > 200 hours at 100 °C). The isotopic method was used ( Am). 

When the half-life time of reaction and the half-life time of micromixing in the absence of chemical reaction are of the same order or the former is less than the latter, the role of micromixing may become crucial. For instance, nitration or bromination of resorcinol, even when the ratio of moles of resorcinol to moles of bromine is high, can lead to predominantly disubstituted product contrary to the general belief. In such cases, in many respects, the theory of coupling between reaction and micromixing has parallels with the formalism of theory of mass transfer with chemical reaction (Bourne, 1983). 

Over zinc oxide it is clear that only a limited number of sites are capable of type I hydrogen adsorption. This adsorption on a Zn—O pair site is rapid with a half-time of less than 1 min hence, it is fast enough so that H2-D2 equilibration (half-time 8 min) can readily occur via type I adsorption. If the active sites were clustered, one might expect the reaction of ethylene with H2-D2 mixtures to yield results similar to those obtained for the corresponding reaction with butyne-2 over palladium That is, despite the clean dideutero addition of deuterium to ethylene, the eth-... 

The filtration conditions (i.e., the rate and time of filtration) should be established in preliminary experiments. The two major considerations are (1) filter washing must be sufficient to minimise the nonspecific retention of radiologand by the filter and (2) the time course of filtration should be sufficiently short that dissociation of the radioligand from its receptor is avoided. In these studies, it is important to have a preliminary estimate of the dissociation rate, i.e., k i in equation23. For a simple exponential reaction, the half-time of dissociation (t./,) is related to the dissociation rate constant by t./, = 0.693/k i... 

Most redox reactions in vitro reach equilibrium only extremely slowly with half times of the order of months or years, even though they may be highly favoured thermodynamically. This is illustrated by the persistence of N2 in oxic systems even though its oxidation to NOs is strongly favoured (Table 4.1). However, microbes in soil and water are capable of catalysing particular reactions from which they obtain energy for metabolism. The half times of such microbially catalysed reactions are of the order of hours or days. 

The depolymerization of the plutonium polymers is a very slow reaction at room temperatures and moderate acid concentrations. It is only upon heating or by the use of very concentrated acid that the depolymerization rate can be made appreciable. Kraus (16) has compared, in two nitric acid media, 6M and 10M, the depolymerization of already formed polymers—one at room temperature and the other at 95 °C. for one hour. The values for the half time of the reactions ranged from 29 minutes for the non-heated, 10M HN03 solution to 730 minutes for the heated, 6M HN03 solution. Lindenbaum and Westfall (22) found that at pH 7.8, a region of environmental interest, the rate of depolymerization was only about 0.04% per hour and at pH 4.0 increased to only 0.18% per hour. 

The fastest steps in an enzymatic process cannot be observed by conventional steady-state kinetic methods because the latter cannot be applied to reactions with half-times of less than about 10 s. Consequently, a variety of methods have been developed18 56-593 to measure rates in the range of 1 to 1013 s... 

These results indicate that Cr(VI) is reduced only in the presence of Fe(II) or sulfide as reductants. Reduction by organic compounds probably does not occur fast enough under the conditions of the lake. However, calculations indicate that a slow removal process, with a half-time of 100-230 days, removes Cr(VI) from the water column in both oxic and suboxic waters (83). It is not known whether this process is reduction, possibly by organic material, or a weak sorptive reaction. 

Peroxy radicals are intermediates in the atmospheric oxidation of air pollutants and in oxidation reactions at moderate temperatures. They are rapidly formed from free radicals by addition of 02. Free radicals in the atmosphere are quantitatively converted to R02 with a half-time of about 1 fis. The peroxy radicals are then removed by reaction with other trace species. The dominant pathways are reactions with NO and NOz. Only a few peroxy radicals have been detected with a mass spectrometer, and extensive research on these reactions has been done by UV absorption spectroscopy with the well-known and conveniently accessed band in the 200- to 300-nm region. Nevertheless, FPTRMS has been used for some peroxy radical kinetics investigations. These have usually made use of the mass spectrometer to observe more than one species, and have given information on product channels. The FPTRMS work has been exclusively on atmospheric reactions of chlorofluoromethanes and replacements for the chlorofluoromethanes. 

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