Parallel reactions rate constants

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isotliermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

These values of the reaction rate constants differ from those cited by Pannetier and Souchay (6) because these individuals erroneously treated the two reactions as if they were of the simple parallel type instead of as if there were a competition between the acrolein and butadiene molecules for other butadiene molecules. 

The quenching and back reaction rate constants as determined by flash photolysis, are collected in Table 10. Noteworthy here is the quenching by S032-, which proceeds by two parallel routes. The normal dynamic quenching (reaction 54) has a rate constant kq = 3 x 10s mol-1 dm3 s with... 

In order to determine the reaction pathway for 1,2-dichlorobenzene, Schiith fitted kinetic data and found that the primary pathway was direct reaction to benzene with a parallel reaction of sequential dechlorination through chlorobenzene to benzene. (Figure 7) These pathways were further supported by independent determination and verification of the reaction rate constant for the second hydrodechlorination step. (Schiith and Reinhard 1998)... 

For reactions in parallel, the concentration level of reactant is the key to the control of product distribution. A high reactant concentration favors the reaction of higher order or the one with the larger reaction rate constant. 

The cases dealt with below refer to those below the Schwab inversion point Eq. (11.12) is also to be taken into consideration. The reaction rate constants run approximately parallel to the heights of the energy barriers E, where E is the absolute value of E. We shall call the reactions limited by the adsorption stage (E = E ) as the first-stage reactions and those limited by the desorption stage (E = E ) as the second-stage ones. 

The values of the real systems, obtained from experiments at pressures up to 50 bar, may be extrapolated to still higher pressures since E = f(P) and log A = f(F) are continuous functions. The supply of oxygen in the oxidation experiments at 50 bar pressure is sufficient to ensure attainment of the asymptotic limits at least in the first reaction step (LTO). Evaluation of the second reaction step of the oxidation (fuel deposition) is more difficult because an increase of the heating rate provokes the occurrence of additional peaks, which will be flattened as a consequence of a rise of the pressure. For the consecutive and parallel oxidation and pyrolysis reactions in this step, overall values of E and log A have been found, which only give steady functions for the vacuum residue. The data of the last reaction step (fuel combustion) may be evaluated very easily. They also give steady functions for E = f(P) and log A = f(P). All substances tested behave similarly to activated carbon (charcoal). Only the coke residue of -hexylpyrene reacts completely differently and demonstrates different curves in the plots of the reaction rate constant and the half life time versus the pressure. In this reaction step the curves did not reach the asymptote even at pressures of 50 bar, but they may be extrapolated to higher pressures. 

In process engineering this parameter is called the mass transfer constant. It Is denoted by some authors by (a notation which has the advantage of underlining the parallel shown with the reaction rate constants denoted by k). To be precise, this quantity is not based on the diffusion layer thickness as defined in this document, but rather the value calculated from the interfaclal slope of the concentration profile (see section 4.3.1.4). For example. In the case of an experiment involving forced convection, one should use the thickness of the Nernst layer In order to define the mass transport rate constant. 

What is the explanation Stable molecules hardly react, only when they form free radicals, carbenes or complex intermediates, ions, or valences. These very reactive species combine easily with molecules or other intermediate species, reacting in successive or parallel steps. These intermediate mechanisms should be known to determine the reaction kinetics. This proves that the overall reaction rate constant is not always true but includes several other constants relative to different intermediate steps of the mechanism. 

E17.10 The reaction A — R + S takes place in a combined system of two PFRreactors in parallel where one reactor operates isothermally at 200°C and the other adia-batically, both under constant pressure of 2 atm. Pure reactant A is introduced at lOmol/min in each reactor. The reaction rate constant is expressed as ... 

Competitive parallel reactions (Fig. 8a) and competitive consecutive reactions (Fig. 8b) are common in chemistry. Here R1 and R2 are two different reagents, S is the substrate, and ki and k2 are reaction rate constants. 

Process improvement obtained with periodic operation has been shown to depend on the reaction rate constants. In the case of consecutive competing chemical reactions (e.g., /ci, /c2, k ), no yield or selectively improvement occurs if fci /c2 or 2- With parallel reactions, a 20% increase over the steady-state operation has been observed (Dorawala and Douglas, 1971). 

A decrease in the characteristic dimension of the system (see schematic of parallel plate microreactor in Figure 10.4c) increases the rate of mass transport from the bulk gas to the reactor walls and changes Da. When Da <0.1, surface reaction is limiting and when Da > 10, mass transfer is limiting. The pseudo-first-order reaction rate constant is estimated from k, = a S/C, where o is the rate of fuel consumption (coming from a detailed model), a = 2/dis the catalyst area per unit volume and C is the concentration of the fuel. 

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