Fraction reacted

If this reaction is implemented at temperatures where the iron yielded is a solid, a sectioned, fractionally reacted iron oxide might appear as shown in Figure 3.26. As shown, for the hydrogen to reach the iron oxide with which it reacts, it has to diffuse through a layer of iron (mostly porous). In addition, the water vapour produced as a consequence of the reaction must be transported away from the iron-iron oxide interface by diffusion. Failing this, there will be accumulation of water vapour at the interface which will permit equilibrium point to be attained and the reaction ceases from further occurring. 

If the fraction reacted is a, then (1 - a) is the amount of sample unreacted, and we see that a plot of —ln(l - a) versus time would be linear with a slope of k. It should come as no surprise that reactions... 

When y is the percent reacted, y/100 is the fraction reacted, which is equal to a, and the equation can be written as... 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

E, progress variable for extent of reaction fraction reacted... 

The distribution of pressure, temperature, and density behind the shock depends upon the fraction of material reacted. If the reaction rate is exponentially accelerating (i.e., follows an Arrhenius law and has a relatively large overall activation energy like that normally associated with hydrocarbon oxidation), the fraction reacted changes very little initially the pressure, density, and temperature profiles are very flat for a distance behind the shock front and then change sharply as the reaction goes to completion at a high rate. 

Since we planned to collect on a receiving surface the material passing straight through the molecular stream, and to ascertain from analysis of this portion the fraction reacting, it seemed inexpedient to employ nitrogen pentoxide or any other sul tance which dissociates into two or... 

Explosive Arrhenius Parameters r (nanosec) la (°K) Fraction Reacted (0... 

Invertase from a Saccharomyces cerevisiae mutant could be separated into two fractions on the basis of solubility in ammonium sulfate.382 The soluble fraction reacted with endo-(l - 6)-a-mannanase, when it became insoluble. The results suggested that the insoluble fraction contained only the highly branched, core section, but the soluble fraction also had the (l->6)-a-D-mannan chain attached. 

The multireaction approach, often referred to as the multisite model, acknowledges that the soil solid phase is made up of different constituents (clay minerals, organic matter, iron, and aluminum oxides). Moreover, a heavy metal species is likely to react with various constituents (sites) via different mechanisms (Amacher et al 1988). As reported by Hinz et al. (1994), heavy metals are assumed to react at different rates with different sites on matrix surfaces. Therefore, a multireaction kinetic approach is used to describe heavy metal retention kinetics in soils. The multireaction model used here considers several interactions of one reactive solute species with soil matrix surfaces. Specifically, the model assumes that a fraction of the total sites reacts rapidly or instantaneously with solute in the soil solution, whereas the remaining fraction reacts more slowly with the solute. As shown in Figure 12.1, the model includes reversible as well as irreversible retention reactions that occur concurrently and consecutively. We assumed that a heavy metal species is present in the soil solution phase, C (mg/L), and in several phases representing metal species retained by the soil matrix designated as Se, S, S2, Ss, and Sirr (mg/kg of soil). We further considered that the sorbed phases Se, S, and S2 are in direct contact with the solution phase (C) and are governed by concurrent reactions. Specifically, C is assumed to react rapidly and reversibly with the equilibrium phase (Se) such that... 

The solid state reaction was discussed in detail in Chapter 5. The volume fraction reacted is given by... 

As in the case of alum, the most general notion is that Mpj.in] gj.q is reacted by all the alkalinities. Let /Feinca(Hco3)3 be the fraction of Mpj.ni] gj.q reacted by calcium bicarbonate and /Femcao. the fraction reacted by lime. If calcium bicarbonate and lime are the only alkalinities reacting with the ferric salt, /Feiiica(eco3)2 +/Feiiicao = 1-We now have... 

Explosive Arrhenius Parameters r (nano sec) Tcj <°K) Fraction Reacted (f)... 

The major differentiation of the cystine suggested by Middlebrook and Phillips was into fractions designated as A - - B and C - - D. The A + B cystine reacted with bisulfite solution and could be reduced by thioglycolate at pH 5, whereas the C -f- D fraction was supposedly completely inert under the conditions. If made to react under more drastic conditions (e.g., boiling bisulfite) the C - - D fraction reacted in a different and less well-understood fashion involving sulfur loss from the protein. 

FIGURE 6.3 Plots of fraction reacted against time at various temperatures (isothermal reactions), calculated from the weight loss for (a) aspartame and (b) asphartylphenylamine. (Reproduced from Leung, S. and Grant, D.J., J. Pharm. Sci., 86, 64-71, 1997. With permission.)... 

Where Raf — (A/A ) after the fraction / of the substrate of chemical species A has reacted, and is the initial ratio (A/A )0. Since the fraction reacted, /, is given by the stoichiometric relationship... 

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