Instantaneous fractional

Unidirectional, first-order transfer rates (day1) between compartments were developed for 6 age groups, and intermediate age-specific values are obtained by linear interpolation. The range of age-specific transfer rate values are given in Table 2-8. The total transfer rate from diffusible plasma to all destinations combined is assumed to be 2,000 day"1, based on isotope tracer studies in humans receiving lead via injection or inhalation. Values for transfer rates in various tissues and tissue compartments are based on measured deposition fractions, or instantaneous fractional outflows of lead between tissue compartments (Leggett 1993). 

In order to determine the product distribution quantitatively, it is necessary to combine material balance and reaction rate expressions for a given reactor type and contacting pattern. On the other hand, if the reactor size is desired, alternative design equations reflecting the material balances must be employed. For these purposes it is appropriate to work in terms of the fractional yield. This is the ratio of the amount of a product formed to the amount of reactant consumed. The instantaneous fractional yield of a product V (denoted by the symbol y) is defined... 

The fractional yield of a product is a measure of how selective a particular reactant is in forming a particular product, and hence is sometimes referred to as selectivity.1 Two ways of representing selectivity are (1) the overall fractional yield (from inlet to a particular point such as the outlet) and (2) the instantaneous fractional yield (at a... 

Example 18-2 illustrates the effect of two process variables (concentration and temperature) on the instantaneous fractional yield for two parallel reactions. 

The ratio under consideration is the ratio of instantaneous fractional yields of D and U. Thus, from equations 5.2-8, and (A) and (B),... 

Laplace parameter, stoichiometric number, surface site solid (phase) slope instantaneous fractional yield of P with respect to A, equation 5.2-8 substrate split point (of streams) entropy, J K-1... 

A definition of instantaneous fractional yield is based on the ratio of reaction rates... 

Quantitative Treatment of Product Distribution and of Reactor Size. If rate equations are known for the individual reactions, we can quantitatively determine product distribution and reactor-size requirements. For convenience in evaluating product distribution we introduce two terms, cp and 4>. First, consider the decomposition of reactant A, and let cp be the fraction of A disappearing at any instant which is transformed into desired product R. We call this the instantaneous fractional yield of R. Thus at any... 

For any particular set of reactions and rate equations is a function of Ca, and since in general varies through the reactor, cp will also change with position in the reactor. So let us define O as the fraction of all the reacted A that has been converted into R, and let us call this the overall fractional yield o/R. The overall fractional yield is then the mean of the instantaneous fractional yields at all points within the reactor thus we may write... 

So far, the fractional yield of R has been taken as a function of alone and has been defined on the basis of the amount of this component consumed. More generally, when there are two or more reactants involved, the fractional yield can be based on one of the reactants consumed, on all reactants consumed, or on products formed. It is simply a matter of convenience which definition is used. Thus, in general, we define (M/N) as the instantaneous fractional yield of M, based on the disappearance or formation of N. 

As a warning, be careful to get the concentrations right when you mix streams. We show this in the three sketches for this problem. Also, the instantaneous fractional yield of the desired compound is... 

For reactions in series we calculate the maximum production rate of R directly, as shown in Chapter 8. However, for reactions in parallel we find it useful to first evaluate the instantaneous fractional yield of R, or... 

Here we examine how strong pore diffusion modifies the true instantaneous fractional yield for various types of reactions however, we leave to Chapter 7... 

Here the instantaneous fractional yield at any element of catalyst surface is given by... 

Fig. 2.1 The trace element behaviors of an incompatible element in the instantaneous fractional melt and extracted fractional melt.

The cumulative effect of the instantaneous fractionations given by Equations (6)-(9) is easily calculated if it is further assumed that mass transport processes (e.g., chemical diffusion) are sufficiently fast to maintain chemical and isotopic homogeneity in both the gas and in the condensed phase. There are cases where diffusion in the residue or gas limits mass transport and these effects on isotopic and chemical fractionation have been explored by Richter et al. (2002). Let us consider first the isotopic fractionations associated with condensation in a supersaturated closed system. The change in the moles of isotope 1 of element k in the gas can be written as... 

On the basis of current knowledge, one might conclude that instantaneous fractionation factors less than 1.012 or greater than 1.022 are due mainly to bacterial sulfate reduction. Values between 1.012 and 1.022 could represent either biological or chemical sulfate reduction. 

If the distribution constant is independent of the sample amount then the retention factor is also equal to the ratio of the amounts of substance in the stationary and mobile phases. At equilibrium the instantaneous fraction of a substance contained in the mobile phase is 1 / (1 + k) and in the stationary phase k / (1 + k). The retention time and the retention factor are also related through Eq. (1.3)... 

The ratio of the instantaneous fractional change in the partial pressure of C02 (pC02) exerted by seawater to the fractional change in total C02 dissolved in the ocean waters. The buffer factor relates the partial pressure of C02 in the ocean to the total ocean C02 concentration at constant temperature, alkalinity and salinity. The Revelle factor is a useful parameter for examining the distribution of C02 between the atmosphere and the ocean, and measures in part the amount of C02 that can be dissolved in the mixed surface layer, rocketsonde... 

Appropriate stoichiometric coefficients are employed to ensure that y and Y lie between zero and 1. The overall fractional yield is the average of the instantaneous fractional yield integrated over the reactor. The proper averaging technique depends on the type of reactor employed. Because the fluid composition is constant throughout the volume of a single CSTR, this type of... 

The reactions of B and R in the film are thereby determined directly, so that the instantaneous fractional yield of intermediate R with respect to the liquid phase reagent B is given by... 

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