Fraction of reaction

When N is large, P may be identified as the fraction of reaction, a thus... 

Solar energy, 6, 488 surface modified electrodes, 6, 30 Sol-Gel process fast reactor fuel, 6, 924 Solid state reactions, 1, 463-471 fraction of reaction, 1, 464 geometric, 1, 464 growth, 1, 464 nucleation, 1, 464 rate laws, 1,464 Solochrome black T metallochromic indicators, 1,555 Solubility... 

Although theoretical estimates for neutral branching fractions of reactions such as 10 have been attempted, their reliability is suspect.32 In the absence of measurement, modelers have typically assumed equal branching fractions between channels in which one and two hydrogen atoms are separated from the molecular skeleton (e.g. 0.50 for reactions 10a and 10b). New assumptions based on recent experimental work have also been made.33... 

In this experiment unreacted isoprene was recovered from the reaction mixture at 98.9% of completion and the amounts of deuterium and 13C at the various positions were compared to those in the starting material using nmr. The KIEs for the various atoms were then calculated from these data using equation (71), where / denotes the fraction of reaction, Rf is the ratio of the isotopes in the unreacted starting material and R0 is the corresponding ratio in the original starting material. 

The subscript indicates the beginning concentration (t = 0), k is the rate constant, and t is time. Introducing the fraction of reaction f,... 

Fig. 7.2 Differences in reaction progress of light and heavy isotope as a function of the fraction of reaction (simultaneous non-competitive measurement of isotope effects)...

Frequently, one of the isotopes is present only in trace quantities (usually the heavier isotope) and the overall fraction of reaction, f, reduces to fi, to good approximation. If this is not the case Equations7.17 and 7.18 can be easily rewritten in terms of f or fq instead of fL. By the same token, with one isotopomer present in trace amounts (the commonly occurring case) the probability of reaction between two labeled molecules is very low, and formal second and higher order kinetics can be approximated using the first-order kinetic expressions developed above. 

Two further approximations are of interest. When the fraction of reaction is small (as a practical matter, say f < 0.1, more conservatively f < 0.05) the right-hand-side of Equation 7.17 can be simplified using ... 

In Equation 7.25, a is the standard deviation, Rf the isotope ratio corresponding to the fraction of reaction, /, of either substrate (Rs) or product (Rp). Expressions for A and B are given in Table7.3. Ro is the isotope ratio in the starting material. Obviously, for simple reactions the isotope composition of the product after full conversion (Rip) is equal to the isotope composition of the initial substrate (Ros)-The dependence of A and B on the progress of the reaction is illustrated in Fig. 7.6 ... 

Equations 7.17 and 7.18 have been developed assuming that the fraction of reaction for the light isotopomer (fL) is the one monitored. Frequently, however, the chemical (overall) fraction of reaction ... 

The question considered is a description of the conditions which must be met by a localized initiator if a spherical detonation wave is to be formed. The first problem is a determination of the possibility of the existence of such a wave. Taylor analyzed the dynamics of spherical deton from a point, assuming a wave of zero-reaction zone thickness at which the Chapman-Jouguet condition applies. He inquired into the hydrodynamic conditions which permit the existence of a flow for which u2 +c2 = U at a sphere which expands with radial velocity U (Here U = vel of wave with respect to observer u2 = material velocity in X direction and c -= sound vel subscript 2 signifies state where fraction of reaction completed e = 1). Taylor demonstrated theoretically the existence of a spherical deton wave with constant U and pressure p2equal to the values for the plane wave, but with radial distribution of material velocity and pressure behind the wave different from plane wave... 

The term in square brackets in Eq. 11 determines which fraction of the alkoxyl radicals will actually react with the probe PH. Thus, the increase in [P"] equals the decrease in [RO"], corrected by the fraction of reaction with PH, relative to all other processes in which the alkoxyl radicals participate. 

Energy Addition to Expanding Gas Flows. In connection with the analyses of optimal rocket engine cycles, it is of interest to develop generalized solutions for the equations of motion with heat addition. An efficient technique is to write the fraction of reaction completed (c), at any station, as a function of the square of the local Mach number (M2), in the form... 

Because reactions in solids tend to be heterogeneous, they are generally described by rate laws that are quite different from those encountered in solution chemistry. Concentration has no meaning in a heterogeneous system. Consequently, rate laws for solid-phase reactions are described in terms of a, the fraction of reaction (a = quantity reacted -r- original quantity in sample). The most commonly encountered rate laws are given in Table 1. These rate laws and their application to solid-phase reactions are described elsewhere. 1 4 10-12 Unfortunately, it is often merely assumed that solid-phase reactions are first order. This uncritical analysis of kinetic data produces results that must be accepted only with great caution. 

Excitation of the Cl2 was not studied. The negative results for NO could be due to insufficient sensitivity of the method, but they do indicate that the fraction of reaction energy going into NO is slight. The reaction... 

If tj and t2 be the times for the completion of the same fraction of reaction with different initial concentrations ai and a2 and if n is the order of reaction, then... 

Because the phosphonate-phosphate rearrangement requires P-C bond breakage and formation of the P-O bond kinetic isotope studies by means of 13C NMR were chosen.50 13C KIEs were derived from NMR analysis of substrate-o-nitro-benzaldehyde or product-phosphate. Samples of aldehyde were prepared using the dead-end method. To the solution of phosphite 3 and triethylamine in acetonitrile an excess of aldehyde was added and solution was heated at 65°C to complete conversion of phosphonate 4 to phosphate 5 monitored by 31P NMR. The aldehyde conversions 0.2-0.8 were calculated from the balance of concentrations. The changes of 13C composition were determined for carbonyl carbon atom using signal of meta aryl carbon as an internal standard. KIE 1.0223(14) was calculated from the slope of linear relationship of isotopic ratio R and fraction of reaction,... 

With each type of PS-II membrane we have measured the absorption increase at 820nm induced by a 20-ps laser flash, first under oxidizing conditions the signal then is due to P-680+ in all the reaction centers. The measurement was then effected under the same conditions, except that QA was reduced the signal then is due to (P-680+, I-) or to excited chlorophyll. The results are as follows (n is the number of chlorophylls per P-680 or antenna size is the half-time of the signal obtained when Q, is reduced b is the ratio (P -680+, r/P-680+ under reducing conditions, i.e. the fraction of reaction centers which are in the radical pair state 1-b is thus the fraction of reaction centers where chlorophyll is excited alternatively, a is the same ratio if we suppose that there is no excited chlorophyll detected in our experiments) ... 

In Table IV.4 are listed the initial pressures of ether and the times required to reach 50 per cent pressure increase in the system, which would correspond roughly to 31 per cent of reaction. If the reaction were a first-order reaction, this column would be constant. However it has been shown " that the reaction is more nearly a -order reaction. For a %-order reaction the time for completion of any given fraction of reaction will be inversely proportional to the square root of the initial pressure [Eq. (IV.5B.1)]. Column 3 is obtained by multiplying column 2 by the square root of the initial pressure. Over the 20-fold variation in Po this product is nearly constant, giving excellent evidence for the conclusion that the rate is closely % order in ether. 

---