Reaction product formation rate

Species Reaction Products Formation Rates, (A in nm) Apparent Quantum Yield (A in nm) Estimated Relative Yields (350 nm) ... 

The theoretical approach involved the derivation of a kinetic model based upon the chiral reaction mechanism proposed by Halpem (3), Brown (4) and Landis (3, 5). Major and minor manifolds were included in this reaction model. The minor manifold produces the desired enantiomer while the major manifold produces the undesired enantiomer. Since the EP in our synthesis was over 99%, the major manifold was neglected to reduce the complexity of the kinetic model. In addition, we made three modifications to the original Halpem-Brown-Landis mechanism. First, precatalyst is used instead of active catalyst in om synthesis. The conversion of precatalyst to the active catalyst is assumed to be irreversible, and a complete conversion of precatalyst to active catalyst is assumed in the kinetic model. Second, the coordination step is considered to be irreversible because the ratio of the forward to the reverse reaction rate constant is high (3). Third, the product release step is assumed to be significantly faster than the solvent insertion step hence, the product release step is not considered in our model. With these modifications the product formation rate was predicted by using the Bodenstein approximation. Three possible cases for reaction rate control were derived and experimental data were used for verification of the model. 

Kinetic Model Discrimination. To discriminate between the kinetic models, semibatch reactors were set up for the measurement of reaction rates. The semi-batch terminology is used because hydrogen is fed to a batch reactor to maintain a constant hydrogen pressme. This kind of semi-batch reactor can be treated as a bateh reactor with a constant hydrogen pressme. The governing equations for a bateh reactor, using the product formation rate for three possible scenarios, were derived, as described in reference (12) with the following results ... 

The MS analysis shows that the C02 profile led that of the PO profile (results not shown). The step switch results further confirm that C02 formation is faster than PO formation and that both reactions take place in parallel. GC analysis of the steady state effluent stream from the reactor revealed that propylene conversion was 10.5% at 250 °C product formation rates were determined to be 1.33, 0.12, and 34.3 pmol/min, respectively, for acetone, PO,... 

The reaction rate can be measured by the product formation rate ... 

In a dehydration reaction (Scheme 12.4), the IR band of the formamide carbonyl group at 1684 cm in (7) decreased and eventually converted to the isonitrile band at 2150 cm in (8) (Fig. 12.8). In a separate example (Scheme 12.5), the conversion of the IR band from the carbonate carbonyl group in (9) to the IR band of the carbamide carbonyl group in (10) can be monitored to assure the reaction completion (Fig. 12.9). Based on FTIR analysis, the reaction time course can be analyzed by integrating peak areas of the IR bands from the starting resin and the product. From the point of view of kinetics, the side reaction product formation can be excluded if the pseudo first order rates of the starting material consumption and the product formation are identical. 

The reaction rates in this system are presumably first-order in catalyst concentration, as implied by the scaling of product formation rates proportionately to rhodium concentration (90, 92, 93). Responses to several other reaction variables may be found in both the open and patent literature. Fahey has reported studies of catalyst activity at several pressures in tet-raglyme solvent with 2-hydroxypyridine promoter at 230°C (43). He finds that the rate to total products is proportional to the pressure taken to the 3.3 power. A large pressure dependence is also evident in the results shown in Table VII. Analysis of these results indicates that the rate of ethylene glycol formation is greater than third-order in pressure (exponents of 3.2-3.5), and that for methanol formation somewhat less (exponents of 2.3-2.8). The pressure dependence of the total product formation rate is close to third-order. A possible complicating factor in the above comparisons is the increased loss of soluble rhodium species in the lower-pressure experiments, as seen in Table VII. Experiments similar to those of Fahey have also been... 

The Primary Product Formation Rate for Various Reactions Involving O Atoms... 

Product Formation Rates for Reactions of O Atoms with Unsaturated Hydrocarbons... 

Due to the time-resolution limitation of the method, FPTRMS can be used to determine the kinetics of only those unimolecular reactions that occur on millisecond time scales or longer. However, even if a unimolecular reaction occurs too rapidly for time resolution of the kinetics, the occurrence of a reaction can be shown by mass spectrometric detection of the products. If the unimolecular reaction is rate limited by a preceding slow step so that the product formation rates are time resolved, then a lower limit to the unimolecular rate coefficient can be estimated. In the case of atmospheric reactions this will frequently be enough information to permit reaction mechanisms to be sorted out. 

When Pt/Ti02 powder is coated with NaOH and illuminated in the presence of gas-phase water, H2 and 02 are produced in a stoichiometric ratio of 2 1 even in the dry state.9,13) Rh and Pd loaded Ti02 powders also show photocatalytic activity for gas-phase water photolysis when coated with NaOH.14) The product formation rates decline with time due to the reverse reaction. The yield of gas-phase water photolysis depends on the pressure of gas-phase water, as shown in Fig. 13.4,14) Since the yield is also dependent upon the amount of NaOH coated,... 

Among the several ways of verifying or disproving such a reaction scheme (Chapter 9, Section 9.2), the derivation of a rate law linking a product formation rate or substrate consumption rate with pertinent concentrations of reactants, products, and auxiliary agents such as catalysts probably has the greatest utility, as conversion to product can be predicted. A proper rate law contains only observables, and no intermediates or other unobservable parameters. In enzyme catalysis, the first rate law was written in 1913 by Michaelis and Menten (the corresponding kinetics is therefore aptly named the Michaelis-Menten (MM) mechanism). 

If the initial concentration of the enzyme is [E]0, then at any timet, [E]0= [E] + [ES]. Thus the reaction rate depends on the enzyme concentration, even though the enzyme remains unchanged at the end of the cycle. The product formation rate and the change in concentration of the catalytic intermediate ES are then given by Eq. (2.36). 

This chapter shows practically all kinds of possible reaction interactions, which part may be united in a general idea of interference of chemical reactions. The notion of interference includes mutual intensification or weakening of the reactions for instance, the rate of primary reaction product formation decreases, whereas the rate of secondary, conjugated reaction product formation increases. Currently, the mutual influence of reactions synchronized in time and space will be taken for interfering chemical processes [1-3]. 

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

By gross reaction rate one understands either a product formation rate c/[prod-uct]/df or a starting material consumption rate — [starting materialj/c/f. The following applies unless the stoichiometry requires an additional multiplier ... 

The diffusion coefficients can be assessed studying the product formation rate in diffusion couples, or the diffusion rate from a gas phase or a liquid into a solid material (e.g., metal oxidation rates) [i-iii]. In this case, however, the results may be affected by microstructural and interfacial factors due to transport in pores, surface diffusion, limited contact area between solid phases, formation of multiple reaction products, etc. 

For ethane-1,2-diol the diester C2 is in equilibrium with the reactants, and its decomposition to the reaction products is rate limiting and not subject to acid-base catalysis. When the concentrations employed are such that C2 is present in appreciable concentration, the mixed-order kinetics described in section 1.3.2 are observed. Second-order kinetics (for the overall reaction) can arise in three ways (a) C2 in equilibrium, but its concentration negligible, (b) formation of C2 from Ci rate limiting, and the latter in equilibrium with the reactants but present in very low concentration, and (c) formation of Q rate-limiting. For pinacol in the range pH 2-10 alternative (a) cannot be operative because general acid-base catalysis is observed. The most likely step to be subject to catalysis is the formation of C2 from Cl, i.e. alternative (b), because this is a cyclisation and a base (B) could well facilitate reaction by removal of the C-OH proton, viz. 

The temperature effect on the rate of reaction was studied between 20 and 122 °C. Plot A of Figure 3 shows the formation of the main still unidentified product in three experiments performed at 25, 100 and 122 °C with the same initial pressures of reactants. A decrease in the product formation rate was observed as the temperature increased. It is interesting to notice that at... 

The arrow "r°" indicates the formation rate of "species 1". This is equal (for the steady state of reaction) to the sum of all product formation rates. Normalization of the sum of all product formation rates to the value "one leads to relative rates of product formation which are equal to probabilities of product formation. 

In order to verify this hypothesis and to verify the predicted influence of water on the equilibrium concentration of the imine and, therefore, on the rate of formation of oxime, a new set of catalytic experiments was carried out vaaring the concentration at low ammonia concentration and in the presence of water added to the reaction atmosphere. Figure 5 shows the influence of the concentration of molecular oxygen on the reaction rates at low ammonia content (2.5 mol%). In these conditions no dependence of the product formation rates on P02 is observed. On the other hand, some catalytic tests carried out adding different amounts of water to the reaction atmosphere showed a negative effect on the conversion and on the imine concentration in the outlet gas phase. 

For the influence of the specific surface area of the semiconductor powder on the rate of product formation, two opposite effects are of major importance [81], One is concerned with the rate of electron-hole recombination, which increases linearly with surface area, and accordingly the reaction rate should decrease. The other is a linear increase of the IFET rate due to increasing concentration of adsorbed substrates per unit volume, which should also increase the product formation rate. It is therefore expected that, depending on the nature of semiconductor and substrates, the reaction rate, or p, may be constant, increase, or decrease with increasing surface area. This is nicely reflected by the CdS/Pt catalyzed photoreduction of water by a mixture of sodium sulfide and sulfite. The highest p values are observed at small surface areas and are constant up to 2 m /g. From there a linear decrease to almost zero at a specific surface area of 6 m /g takes... 

The ILT method is based on the fact that the isotopic transient of the product formation rate [r (t)] represents the Laplace transform of Np k f(k). For a pseudo-first order reaction, the transient of the product formation rate can be expressed as... 

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