Stationary concentration

In general, the assumption of quasi-stationarity is difficult to justify a priori. There may be several possible choices of intemiediates for which the assumption of quasi-stationary concentrations appears justified. It is possible to check for consistency, for example [A ]qj, [Pg.792]

In first-order nitration the anticatalysis is of the same form because the deprotonation of nitric acidium ion diminishes the stationary concentration of nitronium ion and therefore diminishes the rate of nitration. 

Properties of T2O. Some important physical properties of T2O are Hsted in Table 2. Tritium oxide [14940-65-9] can be prepared by catalytic oxidation of T2 or by reduction of copper oxide using tritium gas. T2O, even of low (2—19% T) isotopic abundance, undergoes radiation decomposition to form HT and O2. Decomposition continues, even at 77 K, when the water is fro2en. Pure tritiated water irradiates itself at the rate of 10 MGy/d (10 rad/d). A stationary concentration of tritium peroxide, T2O2, is always present (9). AH of these factors must be taken into account in evaluating the physical constants of a particular sample of T2O. 

Finally, stereoregularity of the initial PAN also affects the disposition of a CTC obtained from this polymer to the formation of photoinduced states with complete charge transfer. Both the values of the stationary concentration of these states and the rate of growth to this level, are considerably higher for a PCS obtained from the polymer with elevated stereoregularity. All this characterizes the effect of PCS stereoregularity on their reactivity in the formation of a CTC. The semi-conductive properties of PCS complexes of various classes with electron donors have been studied267, 268 ... 

The stationary concentration of the propagation centers reached a maximum value of about 1.5 X 10 4 mole per mole of TiCl2 in this way less than 0.5% of the number of titanium ions adjacent to the surface take part in the formation of the propagation centers (for a sample of TiCl2... 

J. G. Tolpin, G. S. John, and E. Field The Elucidation of Reaction Mechanisms by the Method of Intermediates in Quasi-Stationary Concentrations J. A. Christiansen... 

Apparently, all DHAP aldolases are highly specific for (25) as the donor component for mechanistic reason [30-33], a fact which requires an economical access to this compound for synthetic applications. Owing to the limited stability of (25) in solution, particularly at alkaline pH, it is preferentially generated in situ to avoid high stationary concentrations. 

Simple analysis of the motion of mapping point through the phase trajectory (Fig. 2.13) indicates that X represents the stationary concentration of chemisorbed radicals corresponding to a given external conditions. 

In two limiting cases differing in the values of stationary concentration of chemisorbed radicals and initial electric conductivity of adsorbent the expression (2.94) acquires the following shape ... 

The relationship between the stationary concentrations of free H-atoms in the volume and chemisorbed H -atoms would be determined by what reaction (III, IV or inverse one I) is a dominant one under given conditions of experiment. 

It was first shown in study [37] that adsorption of N-atoms on films of zinc oxide reduces its conductivity to a certain stationary value which depends, as with oxygen atoms, both on the stationary concentration of particles in the volume adjacent to the sensor s film and on the temperature. 

Stationary concentration of adsorbed acceptor particles of O- and N-atoms on a film of zinc oxide is attained for the most part due to the competition between the chemisorbtion of particles and their interaction, i. e. mutual recombination on the adsorbent surface, and with free atoms attacking the adsorbed layer of the adsorbent from outside. 

The study [39] shows that similar equation is valid for adsorption of NH- and NH2-radicaIs, too. There are a lot of experimental data lending support to the validity of the proposed two-phase scheme of free radical chemisorbtion on semiconductor oxides. It is worth noting that the stationary concentration of free radicals during the experiments conducted was around 10 to 10 particles per 1 cm of gas volume, i.e. the number of particle incident on 1 cm of adsorbent surface was only 10 per second. Regarding the number of collisions of molecules of initial substance, it was around 10 for experiments with acetone photolysis or pyrolysis provided that acetone vapour pressure was 0,1 to 0,01 Torr. Thus, adsorbed radicals easily interact at moderate temperatures not only with each other but also with molecules which reduces the stationary concentration of adsorbed radicals to an even greater extent. As we know now [45] this concentration is established due to the competition between the adsorption of radicals and their interaction with each other as well as with molecules of initial substance in the adsorbed layer (ketones, hydrazines, etc.). 

Taking into consideration the above, it is easy to assume that the stationary value of coverage of chemisorbed radicals on the surface of a film under these conditions is insignificant and is subject to change in direct proportion to the stationary concentration of free radicals in the vessel volume, i.e. may be expressed in this particular case by the following universal relationship ... 

Due to the competition of the phases shown in the diagram, there appears a stationary concentration of adsorbed particles J/ljJ and [A ]... 

To detect radicals by means of semiconductor films there may be used both kinetic and stationary methods. The latter is based on relationship between the stationary conductivity of semiconductor film (e. g., ZnO, CdO, etc.) and stationary concentrations of active particles being detected. 

Calculation yields that in these experiments the stationary concentration of radicals [ 4] for the maximum intensity of light of a mercury lamp SVDSh-500 was no more than 10 radicals/cm, the stationary conductivity of a ZnO film at 300 C changing by 300 to 400% compared to its initial pre-adsorption value. Thus, in accordance with the above formula (3.21), concentrations of radicals equal to 10 -10 radicals/cm may be detected by means of semiconductor sensors which is 7 magnitudes lower than existing methods would allow. 

In order to find the relationship between the stationary concentration of current carriers in semiconductor film and concentration of dissolved oxygen in polar liquid, it is essential to examine the expression for rate of chemisorbtion of dissolved oxygen molecules on ZnO film and its chemical desorbtion from the surface under effect of solvent... 

Therefore, the kinetics of generation of defects in surface-adjacent layers is similar to kinetics of emission of O-atoms. (The estimates indicate that the maximum concentration of vacancies in this case may attain the value of 10 for a sample with area 1 cm ). If one assumes that the emission of oxygen atoms is caused by processes of annihilation of vacancies in the sample, then the coincidence in time dependence of stationary concentration of defects can be indicative that these processes are limited by generation of defects, which, in its turn, is controlled by processes of formation of oxide phase in surface-adjacent silver layers. Oxidation, especially at initial stage, is characterized by intensive formation of defects [54]. 

Thus the time during which the transport process attains the steady state depends strongly on the radius of the sphere r0. The steady state is connected with the dimensions of the surface to which diffusion transport takes place and does, in fact, not depend much on its shape. Diffusion to a semispherical surface located on an impermeable planar surface occurs in the same way as to a spherical surface in infinite space. The properties of diffusion to a disk-shaped surface located in an impermeable plane are not very different. The material flux is inversely proportional to the radius of the surface and the time during which stationary concentration distribution is attained decreases with the square of the disk radius. This is especially important for application of microelectrodes (see page 292). 

When the rate of initiation is very low the important moment of chain reaction becomes the kinetics of the establishment of the stationary concentration of free radicals. This time is comparable with the lifetime of the radical that reaction limits the chain propagation. The... 

In the presence of specially added hydrogen peroxide, the stationary concentration of hydroperoxyl radicals increases due to the exchange reaction. 

If we solve the kinetic problem assuming stationary concentration of [QIC], one gets the following equations for k+ and k- in terms of the kinetic coefficients appearing in eq(73) ... 

Although an initiator may have reacted completely with monomer to yield P+n, the end of the growing chain may be involved in a BIE, so that the stationary concentration [P+J is then less than the original concentration, [Int+]0 = cQ, of the initiator ... 

According to Lindemann s hypothesis, the activation by collision can still give rise to first order kinetics if the activated molecules decompose only slowly compared to the rate at which they are deactivated. There is a time-log between the moment of activation and the moment of decomposition and in such a case, a stationary concentration of the activated molecules gets built up. Since the activated molecules will be in equilibrium with the normal molecules, their concentration will be proportional to that of normal molecules. The activated molecules disappear through two parallel processes, i.e. through deactivation and decomposition, represented as follows ... 

In an attempt to obtain the benefits of repeated spray formations, a centrifugal type absorber has been developed from the ideas of Piazza for a still head. The principle of the unit is shown in Figure 12.31. A set of stationary concentric rings intermeshes with a second set of rings attached to a rotating plate. Liquid fed to the centre of the plate... 

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