Instantaneous yield ratio

The instantaneous yield ratio Tpq of the two products is defined as the ratio of the ... 

Fractional conversion of a reactant is defined as the ratio of the amount consumed to that charged. In this book, the following definitions of yield, yield ratio, and selectivity are used The yield of a product is the ratio of the amount of reactant (or reactants) converted to the product to the total amount of reactant (or reactants) charged. The cumulative yield ratio of two products is the ratios of their yields. The instantaneous yield ratio is the ratio of the momentary rates of conversion to these products. The cumulative selectivity to a product is the ratio of the amount of reactant (or reactants) converted to that product to the amount consumed. The instantaneous selectivity is the ratio of the momentary rate of reactant conversion to the product to that of reactant consumption. Not used in this book is the extent of reaction, defined as the number of moles consumed or formed, divided by the stoichiometric coefficient of the respective participant. 

Unfortunately, most combinations of steps of different orders lead to rather unwieldy mathematics as far as reactor performance is concerned [G1.G10]. However, one important general facet of such networks warrants special attention and is easily demonstrated with the simplest case, the network 5.26. Of interest are the yield ratio of the two products and the selectivity of conversion to one of them. For the network 5.26, the instantaneous yield ratio is seen to be... 

Often, the first product in a pathway of sequential steps is the desired one. In such cases, the yield ratio of the first product (K) to the subsequent ones (lumped into P) is of special interest. The instantaneous yield ratio is... 

For elucidation of networks, yield-ratio equations are much more convenient than rate equations. The (instantaneous) yield ratio PpQ is defined as the ratio of the molar conversion rates of a reactant to products P and Q ... 

For those cases where the rate expressions for all reactions taking place in the system under study are known, the use of the instantaneous yield in the above equations does not contribute significantly to understanding the system behavior. In such cases it is easier to determine the overall yield by substituting the appropriate ratio of reaction rate expressions for the instan-... 

Hence the area under the curve of y versus CA multiplied by the ratio of stoichiometric coefficients represents the overall change in valuable product concentration between the inlet and outlet streams in a plug flow reactor or in a batch reactor. For the case of a CSTR the instantaneous yield is evaluated at the effluent composition, and the corresponding equation is... 

The distinction between instantaneous and cumulative yield ratios or selectivities becomes immaterial in gradientless reactors (continuous stirred-tank at steady state or differential once-through reactors) or if the instantaneous values do not vary with conversion. 

The instantaneous yield at a point is defined as the ratio cf tiie rate of formation of a specified product D to the rate of depletion of the key reactant A ... 

Reaction yield, like the selectivity, has two definitions one based on the ratio of reaction rates and one based on the ratio of molar (low rates. In the first case, the yield at a point can be detined as the ratio of the reaction rate of a given product to the reaction rate of the key reactant A. This is sometimes referred to as the instantaneous yield, ... 

Molar flux of species A (mol/m -s) Conversion of key reactant, A Instantaneous yield of species i Overall yield of species i Pressure ratio P/Pq Mole fraction of species i Initial mole fraction of species i Compressibility factor Linear distance (cm)... 

The instantaneous yield can also be viewed as the ratio of the rate of formation of product X to the rate of consumption of substrate S ... 

Instantaneous selectivity As the reaction rates depend on the reactant concentrations, the instantaneous yield and selectivity can change with time or the location in the reactor. The instantaneous or differential selectivity is defined as the ratio between the rate of product formation and the rate of... 

Crystalline triose reductone has been shown (56) by titration with strong base and with iodine, to exist in solution, for practical purposes, entirely as the enol form. In addition, the fact that it reduces exactly three molar equivalents of periodate to give quantitative yields of formic acid and of carbon dioxide indicates that it is also oxidized entirely in this form. However, nothing is known of the rate of enolization of tartronic dialdehyde and the possibility therefore remains that part of it may be oxidized in the dialdehydo form. If this were the case, the results of periodate oxidations would be dependent on the ratio of the rate of enolization of tartronic dialdehyde to the rate of its oxidation by periodate, since the oxidation of triose reductone is, again, for practical purposes, instantaneous. 

Lewin and Cohen (1967) determined the products of dediazoniation of ben-zophenone-2-diazonium salt (10.42, Scheme 10-77) in five different aqueous systems (Table 10-7). About one-third of the yield is 2-hydroxybenzophenone (10.46) and two-thirds is fluorenone (10.45, run 1) copper has no effect (run 2). On the other hand, addition of cuprous oxide (run 3) has a striking effect on product ratio and rate. The reaction occurs practically instantaneously and yields predominantly fluorenone. As shown in Scheme 10-77, the authors propose that, after primary dediazoniation and electron transfer from Cu1 to 10.43 the sigma-complex radical 10.44 yields fluorenone by retro-electron-transfer to Cu11 and deprotonation. In the presence of the external hydrogen atom source dioxane (run 12) the reaction yields benzophenone cleanly (10.47) after hydrogen atom abstraction from dioxane by the radical 10.43. 

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

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

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