Effective rate coefficients

Estimates of k26 and k21K26 have been made89 from measurements of the effective rate coefficients for recombination at low and high inert gas pressures. A more exact expression for the observed second-order rate coefficient is... 

It is interesting to consider the temperature dependence of the reaction rates predicted by these limiting expressions, which are contained in the effective rate coefficients. The true surface reaction rate coefficient has the temperature dependence... 

The effective rate coefficient should be given by the expression... 

The rate therefore becomes reduced by species C (as ), and the effective rate coefficient is k" = kRKA/Kc. 

A reactant of bulk concentration Cao reacts on the external surface of catalyst spheres of radius 7 in a slurry reactor. The first-order surface reaction rate coefficient is k , and the diffiisivity of A in the solution is Da- Find fhe effective rate coefficient in terms of these quantities, assuming that stirring is sufficiently slow that fhe fluid around particles is stagnant. 

This reaction is catalyzed by a hydrophilic spherical Pt-y-Al203 catalyst of 3 mm particle size at 70 °C and 1 atm and is considered to be first order with respect to oxygen and 0.5 order with respect to ethanol (Horowitz et al., 1999). The effective rate coefficient, i.e. the rate coefficient including the effect of the internal diffusion is 1.95 x 10-4 (m3/kg s) (m3/kmol)0,5. 

Evaluate the effective rate coefficient, i.e. the product of internal effectiveness factor and intrinsic rate coefficient for this reaction... 

Hart and Anbar [17] pointed out that effective rate coefficients of solvated electron reactions with many strong oxidants were larger than those implied by the encounter distances for the solvated electron and oxidant by a factor of 1.5—2.0 times. Some of these effective encounter distances are listed in Table 5, together with others from recent work. For... 

Fig. 20. Effect of degree of crosslinking (% DVB) of a standard ion exchanger on the diffusivities, Def (cm2 min-1), and the selectivity ratio, S = efs/ efAc ( ef = effective rate coefficient, S = sucrose, Ac = ethyl acetate). Data were obtained by rate measurements and Wheeler—Thiele analysis of simultaneous sucrose and ethyl acetate hydrolysis at 70°C [508],...

Fig. 4.5. Effective rate coefficients calculated with the present CR-model with (full curve) and without (dashed curve) taking into account the vibrational population...

Typical results of such models are effective rate coefficients which depend not only on Te but also on ne and the vibrational population in the ground state. The importance of the vibrational population on some effective rate coefficients can be seen in Fig. 4.5. Especially for low Te, the enhancement can exceed one order of magnitude. Details of the calculation of vibrational populations are described in Sect. 4.4.1. For the analysis of radiation it is very convenient to apply the aforementioned corona model formula in which the pure excitation rate coefficient is replaced by the effective rate coefficient. 

Fig. 4.7. Compilation of effective rate coefficients which are of importance for MAR and EIR processes. Calculations are based on the present CR-model for H2...

From this relation it can be seen that the free-radical polymerization will be of first order in monomer, M, and the effective rate coefficient, will have a temperature dependence that will depend on the activation energies E, Ep and of the elementary reactions ... 

A reeent re-evaluation of the rate coefficient and the branching ratio has been made by Williams et al. (2001) using the pulsed laser photolysis-pulsed laser induced fluorescence (PLP-PLIF) teehnique. The effective rate coefficient for the reaction of OH -1- DMS and OH + DMS-db was determined as a function of O2 partial pressure at 600 Torr total pressure in N2/O2 mixtures the temperature was 240 K for DMS and 240, 261, and 298 K for DMS-db. This new work shows that at low temperatures the currently recommended expression underestimates both the effective rate coefficient for die reaction and also the branching ratio between addition and abstraction. For example, at 261 K a branching ratio of 3.6 was obtained as opposed to a value of 2.8 based on the work of Hynes et al. (1986). At 240 K the discrepancy increases between a measured value of 7.8 and a value of 3.9 using the extrapolated values from the 1986 work of Hynes et al. (the branching ratio is defined here as (kobs-kia)/kia). In addition, at 240 K the expression for Us in 1 atm air based on the work of Hynes et al. (1986) predicts a value which is a factor of 2 lower then the value measured at... 

It is apparent that two limits exist. At low pressures when fcsn(M) kr, the overall rate law of the reaction will follow a termolecular rate law with an effective rate coefficient k0= kskq/kr, whereas at high pressures, when M(M) kr, the n(M) cancel and the formation of the product C proceeds in accordance with a bimolecular rate law. The effective rate coefficient then is kaD= kq. In the intermediate pressure region neither rate law applies, and the rate coefficient becomes pressure-dependent. Usually, the rate of the reaction depends somewhat on the nature of the third body M as well. 

Fig. 3.1. An illustration of some features of the absorption of A molecules by the sink B. The density field of the A species, n Xi, /), is referred to a coordinate frame centered on B. The dashed circle about B signifies a region about the particle where the diffusion equation no longer applies (a diffusion boundary layer). In the application of the radiation boundary condition, the presence of this boundary layer is approximately taken into account by the effective rate coefficient /c, [(3.2)], and its spatial extent is neglected.

The parameter 5- = k /k shows the detachment ability that compensates for electron losses dne to attachment. If 5- 1, the attachment inflnence is negligible and kinetic equation (4-21) becomes eqnivalent to one for non-electronegative gases. The kinetic equation inclndes the effective rate coefficients of ionization, kf = kj + g, and recombination, k f = kf + gk. Eqnation (4-21) describes electron density evolution to the steady-state magnitnde of the recombination-controlled regime ... 

The first term in (5-44) describes the vibrational excitation of CO2 molecules by electron impact with the effective rate coefficient, ev, calculated with respect to the asymmetric... 

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