Yield, instantaneous relative

This expression requires some qualification. It must be made clear that yield , for this example, means yield of C with respect to A. Also, it must be recognised that the concentration of a reaction species may change with time or with location within a reactor. Consequently, the relative yield may also change. The symbol (j> will be used to denote instantaneous relative yield (for a very small element of space or time) and will be used to denote the overall yield for the whole reactor during its operational period. For the reactions (95) and (96) we have... 

Standard organolithium reagents such as butyllithium, ec-butyllithium or tert-butyllithium deprotonate rapidly, if not instantaneously, the relatively acidic hydrocarbons of the 1,4-diene, diaryhnethane, triarylmethane, fluorene, indene and cyclopentadiene families and all terminal acetylenes (1-alkynes) as well. Butyllithium alone is ineffective toward toluene but its coordination complex with A/ ,A/ ,iV, iV-tetramethylethylenediamine does produce benzyllithium in high yield when heated to 80 To introduce metal into less reactive hydrocarbons one has either to rely on neighboring group-assistance or to employ so-called superbases. 

In these equations it is understood that CA may be (a) the concentration of A at a particular time in a batch reactor, (b) the local concentration in a tubular reactor operating in a steady state, or (c) the concentration in a stirred-tank reactor, possibly one of a series, also in a steady state. Let St be an interval of time which is sufficiently short for the concentration of A not to change appreciably in the case of the batch reactor the length of the time interval is not important for the flow reactors because they are each in a steady state. Per unit volume of reaction mixture, the moles of A transformed into P is thus 9LAP6t, and the total amount reacted (9lAP + 3tAQ)St. The relative yield under the circumstances may be called the instantaneous or point yield will change (a) with time in the batch reactor, or (b) with position in the tubular reactor. 

After instantaneous excitation of A, the normalized decay of A is given by R(t) = NA(t)/NA0). According to (3.10), its Laplace transformation, related to the lifetime xA, defines the relative quantum yield of luminescence ... 

The relative stabilities of cycloheptyne and cyclohexyne generated from 1-amino-4,5-cycloalkeno-l,2,3-triazoles (21) and lead tetraacetate were investigated. After the nitrogen evolution, which occurred instantaneously on addition of lead tetraacetate, had ceased, the trapping reagent was added after different time intervals to the reaction mixture, and yields of adduct (23) were determined. The results... 

One consequence of the continuum approximation is the necessity to hypothesize two independent mechanisms for heat or momentum transfer one associated with the transport of heat or momentum by means of the continuum or macroscopic velocity field u, and the other described as a molecular mechanism for heat or momentum transfer that will appear as a surface contribution to the macroscopic momentum and energy conservation equations. This split into two independent transport mechanisms is a direct consequence of the coarse resolution that is inherent in the continuum description of the fluid system. If we revert to a microscopic or molecular point of view for a moment, it is clear that there is only a single class of mechanisms available for transport of any quantity, namely, those mechanisms associated with the motions and forces of interaction between the molecules (and particles in the case of suspensions). When we adopt the continuum or macroscopic point of view, however, we effectively spht the molecular motion of the material into two parts a molecular average velocity u = (w) and local fluctuations relative to this average. Because we define u as an instantaneous spatial average, it is evident that the local net volume flux of fluid across any surface in the fluid will be u n, where n is the unit normal to the surface. In particular, the local fluctuations in molecular velocity relative to the average value (w) yield no net flux of mass across any macroscopic surface in the fluid. However, these local random motions will generally lead to a net flux of heat or momentum across the same surface. 

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