Rate of disappearance

The quantity dnjdt is essentially the rate of disappearance of primary particles and hence the rate of decrease in the total number of particles. Integration gives... 

Normally, when a material reacts, its initial rate of disappearance is high and the rate decreases continuously as the reactant is consumed. However, in autocatalytic reaction, the initial rate is relatively slow... 

Assuming that the rate equations are second order, the rate of disappearance of component A is ... 

If kj and kj denote tlie forward and reverse rate constants respectively, die general rate of disappearance (-r ) for any type of reaction is defined as ... 

Assuming this reaction is an elementary reaction, its molecularity is 2 that is, it is a bimolecular reaction. The velocity of this reaction can be determined from the rate of disappearance of either A or B, or the rate of appearance of P or Q ... 

Reaction rate = Rate of disappearance of alkyl halide = k X RX]... 

A solution of the 2-azido ester or amide (ca. 2 g) in a mixture of MeOII (95 mL) and sodium-dried THF (95 mL) was photolyzed under N2 in a Hanovia photochemical reactor (110-W medium-pressure Hg lamp with a Pyrex filter). The reaction was monitored by observing the rate of disappearance of the absorption band (Nf) at 2140 cm 1 (irradiation times of 3-5 h were generally required). When the reaction was complete the solvent was removed in vacuo and the brown residual oil chromatographed on alumina [petroleum ether (bp 60-803C)/benzene 7 3]. Further elution with benzene followed by removal of the solvent gave the product (the esters as pale yellow oils, the amides as crystalline solids), which were further purified by vacuum distillation or by recrysiallization. 

The plot of the rate of disappearance of CO per volume of liquid in the serum bottles versus partial pressure of CO in the gas phase based on (3.14.4.14) could give the constant slope value of KLa/H. Henry s constant is independent of the acetate concentration but it is only dependent on temperature. The overall volumetric mass transfer coefficient can be calculated based on the above assumption. The data for various acetate concentrations and different parameters were plotted to calculate the mass transfer coefficient. 

Observed rates of disappearance for diacyl peroxides show marked dependence on solvent and concentration.146 In part, this is a reflection of their susceptibility to induced decomposition (see 3.3.2.1.4 and 3.3.2.1.5). However, the rate of disappearance is also a function of the viscosity of the reaction medium. This is evidence for cage return (see 3.3.2.1.3).143 The observation144 of slow scrambling of the label in be.x LQy -carbonyl- %0 peroxide between the carbonyl and the peroxidic linkage provides more direct evidence for this process. 

For this reaction, the net rate of disappearance of A is given by the equation... 

The former investigation was motivated, in part by the fact that in a previous study (7) there had been a marked difference on the rates of reactions of e (aq) and U(VI) between homogeneous solutions and those containing micellar material. When the rate of disappearance of the hydrated electron is measured over a range of concentrations from 2 x 10-5 M to 8 x 10-lt M at pH = 9.7 in solutions formally 0.003 M Si02, the calculated second order rate parameter is 1.4 x 109 M-1s-1. This is a marked decrease from any of the previous measurements and emphasizes the point that the prediction of Pu chemistry in a natural water system must take cognizence of factors that are not usually deemed significant. 

FIGURE 13.8 (a) When the rates of disappearance of NO, are plotted against its concentration, a straight line is not obtained, (hi However, a straight line is obtained when the rates are plotted against the square of the concentration, indicating that the rate is directly proportional to the square of the concentration. 

Because ATP hydrolysis on F-actin takes place with a delay following the incorporation of ATP-subunits, and because in the transient F-ATP state filaments are more stable than in the final F-ADP state, polymerization under conditions of sonication can be complete, within a time short enough for practically all subunits of the filaments to be F-ATP. At a later stage, as Pj is liberated, the F-ADP filament becomes less stable and loses ADP-subunits steadily. The G-ADP-actin liberated in solution is not immediately converted into easily polymerizable G-ATP-actin, because nucleotide exchange on G-actin is relatively slow, and is not able to polymerize by itself unless a high concentration (the critical concentration of ADP-actin) is reached. Therefore, G-ADP-actin accumulates in solution. A steady-state concentration of G-ADP-actin is established when the rate of depolymerization of ADP-actin (k [F]) is equal to the sum of the rates of disappearance of G-ADP-actin via nucleotide exchange and association to filament ends. [G-ADP]ss in this scheme is described by the following equation (Pantaloni et al., 1984) ... 

The effect of added [Br ] on the bromination reaction is such as to retard the rate. This phenomenon is attributable to a competing equilibrium,Br" + Br2 Br3 that decreases the available free [Br2]. In HOAc, the accepted value for the tribromide equilibrium constant is Kgq = 92 M-1 (ref. 11). Both Br2 and Br3 are brominating agents so that the rate of disappearance of total bromine, or [Br2]j, is... 

The rate of a homogeneous reaction is the rate of disappearance of a reactant or appearance of a product. The rate nearly always changes with time, since it is usually proportional to concentration and the concentration of reactants decreases with time. However, the rate is not always proportional to the concentration of all reactants. In some cases, a change in the concentration of a reactant produces no change at all in the rate, while in other cases, the rate may be proportional to the concentration of a substance (a catalyst) that does not even appear in the stoichiometric equation. A study of which reactants affect the rate often tells a good deal about the mechanism. 

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