Steps consecutive

Fig. 10. In the first step few small metallic particles are dispersed in an insulating host. This modifies the medium which now has a dielectric function e,jy(0)) instead of e,(M). We repeat iteratively this process (in n consecutive steps) of adding metallic particles until we reach a filling/.

The result can be derived by assuming a harmonic interaction between consecutive steps, with the strength of interaction A gff = 7r 7/Lcou. 

In this case, however, if the step separation i is small, the consecutive steps are coupled via the terrace diffusion held, and the width cannot increase as fast as but increases slowly, like the edge-diffusion-limited growth, as [68]... 

Some air treatment processes cannot he made in a single operation, and the air must pass through two or more consecutive steps to obtain the required leaving condition. 

In a consecutive step, a first-order process, the hydroxycyclohexadienyl radicals decompose to give the sulfinic acids as is given in reaction 30. The rate constants /c, and k2 are also given in Table 1. In this case kt was calculated from the build-up of the hydroxycyclohexadienyl radicals. 

Humic acid precipitates at salt concentrations >0.05 M and pH <4, while the fulvic acids are still soluble. Thus, humic acid is hardly ever found in salt water ( O.S M). Titration experiments with alkali indicate that there are consecutive steps of deprotoni-zation. A typical average pka-value would be 7 (26), and for a selected humic acid values of 4 and 9 are given for pk and pk, (27, 28). 31 aZ... 

Dilution, separation, and neutralization can take place in the same reactor or several batch units may be used for the consecutive steps (see also Sec. XX.X). Sulfuric acid sulfonation in a continuous loop reactor system is feasible when an H2S04/AB ratio of at least 1.80 is applied. In this case, as well as when 20% oleum is used, reasonably short reaction times are sufficient to complete the reaction. With increasing H2S04/AB ratio, the amount of dark 80% sulfuric acid (spent acid) will increase proportionally. 

ATP is hydrolyzed in at least two consecutive steps on F-actin, viz. cleavage of the y-phosphoester bond, followed by Pj release, according to the following scheme ... 

We finish this section with an example of a dehydrogenation reaction on a metal, which is instructive as it does not rely on equilibrium adsorption, unlike most other examples given in this book. The dehydrogenation of methylcydohexane, CfiHiiCHs, to toluene, QH5CH3, on platinum is well described by a reaction mechanism consisting of consecutive steps in the forward direction only ... 

The reaction between Np(Vl) and V(III) in perchlorate media proceeds via consecutive steps of comparable rate, viz. 

Thus, Ip (inductor peroxide, primary oxide) derived from I d is converted by Ac d into the end-product, I(,x, which is inactive regarding the induction, i.e. coupling cannot turn into catalysis. Moreover, since there are several consecutive steps, and since the direct reaction between actor and acceptor is very slow, it follows that the value of Fj will not be changed by altering the ratio, ([Ac]/[I])o. However, in most cases studied the function Fj = /(Ac/I)q attains a limiting value, or at least varies therefore it has to be concluded that Manchot s concept cannot be maintained in its original form. 

Then, in fast consecutive steps, chlorine dioxide is reduced to chloride. The induced reduction of chlorate is quantitative within a few minutes. At the beginning of the titration not only the special smell but also the faint-yellowish colour of chlorine dioxide can be observed after the complete disappearance of the cerium(IV) reagent. 

Of perhaps greater importance is the fact that the same rate constant is applicable to each of the consecutive steps in the conversion of the dibasic acid to a diester ... 

The electron transfer step is the only reaction step, which means that other parallel or consecutive steps are absent. 

This great variety of pathways makes it difficult to decide which of the steps is the rate-determining step. It is most likely that at intermediate current densities the overall reaction rate is determined by the special kinetic features of step (15.24) producing the oxygen-containing species. The slopes of = 0.12 V observed experimentally are readily explained with the aid of this concept. Under different conditions, one of the steps in which these species react further may be the slow step, or several of the consecutive steps may occur with similar kinetic parameters. 

The reaction goes through several consecutive steps. In a first step, the methanol molecule becomes dehydrogenated while adsorbing on platinum ... 

The high catalytic activity of enzymes has a number of sources. Every enzyme has a particular active site configured so as to secure intimate contact with the substrate molecule (a strictly defined mutual orientation in space, a coordination of the electronic states, etc.). This results in the formation of highly reactive substrate-enzyme complexes. The influence of tfie individual enzymes also rests on the fact that they act as electron shuttles between adjacent redox systems. In biological systems one often sees multienzyme systems for chains of consecutive steps. These systems are usually built into the membranes, which secures geometric proximity of any two neighboring active sites and transfer of the product of one step to the enzyme catalyzing the next step. 

Today it has become clear that the effect of trace elements in living systems, in food, and in the environment depends on the chemical form in which the element enters the system and the final form in which it is present. The form, or species, clearly governs its biochemical and geochemical behaviour. lUPAC (the International Union for Pure and Applied Chemistry) has recently set guidelines for terms related to chemical speciation of trace elements (Templeton et al. 2000). Speciation, or the analytical activity of measuring the chemical species, is a relatively new scientific field. The procedures usually consist of two consecutive steps (i) the separation of the species, and (2) their measurement An evident handicap in speciation analysis is that the concentration of the individual species is far lower than the total elemental concentration so that an enrichment step is indispensable in many cases. Such a proliferation of steps in analytical procedure not only increases the danger of losses due to incomplete recovery, chemical instability of the species and adsorption to laboratory ware, but may also enhance the risk of contamination from reagents and equipment. 

It is evident that huge errors may occur during aU these consecutive steps. The only way to validate the methodology is to have at hand suitable RMs certified for the trace element species content in the relevant matrix, together with suitable cali-brants. Few of these are yet commercially available. 

The process involved consists of 5 consecutive steps. The first step involves a reaction which forms an arsenate salt. This reaction requires two raw materials, raw 3 and raw 4, and can be conducted in either reactor R1 or R2. The arsenate salt from the first step is then transferred to either reactor R3 or R4 wherein two reactions take place. The first of these reactions is aimed at converting the arsenate salt to a disodium salt using raw material 1 (raw 1). The disodium salt is then reacted further to form the monosodium salt using raw material 2 (raw 2). The monosodium salt solution is then transferred to the settling step in order to remove the solid byproduct. Settling can be conducted in any of the three settlers, i.e. SE1, SE2 or SE3. The solid byproduct is dispensed with as waste and the remaining monosodium salt solution is transferred to the final step. This step consists of two evaporators, EV1 and EV2, which remove the excess amount of water from the monosodium solution. Evaporated water is removed as effluent and the monosodium salt (product) is taken to storage. States si and. S 9 in the SSN represent raw 3 and raw 4, respectively. States... 

Ans. (a) We simplify this process by imagining that it takes place in two consecutive steps. The first step is the chemical reaction, which liberates heat. (AH is negative.) This heat is the cause of the temperature rise. (b) The second step is the addition of that heat to the solution, causing the temperature rise. The solution takes in the heat. AH is positive for this step. If no heat escapes to the surroundings, the overall A H is 0. 

One may consider the above equation as a generalization of Born-Oppenheimer dynamics in which electrons always stay on the Born-Oppenheimer surface. For a given conformation of nuclei, the numerical value of the fictitious mass associated with electronic degrees of freedom determines how far the electron density is allowed to deviate from the Born-Oppenheimer one. Each consecutive step along the trajectory, which involves electronic and nuclear degrees of freedom, can be obtained without determining the exact Born-Oppenheimer electron density. 

Figure 4.5. Cumulative sums of extractable elements in soil J3 (CaC03 33.3%) in consecutive steps of the selective sequential dissolution procedure as a function of the cumulative steps. 1 CARB (carbonate) 2 CARB (carbonate) + ERO (easily reducible oxide) 3 CARB + ERO + OM (organic matter) 4 CARB + ERO + OM + RO (reducible oxide) (after Han and Banin, 1995. Reprinted from Cornmun Soil Sci Plant Anal, 26, Han and Banin A., Selective sequential dissolution techniques for trace metals in arid-zone soils The carbonate dissolution step, p 573, Copyright (1995), with permission from Taylor Francis US)...

Figure 4.6. Cumulative sums of extractable Ca, Mg, and Mn in arid soil J3, BIO, and SI in consecutive steps of two sequential dissolution procedures.

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