Rate constant effective

If certain species are present in large excess, their concentration stays approximately constant during the course of a reaction. In this case the dependence of the reaction rate on the concentration of these species can be included in an effective rate constant The dependence on the concentrations of the remaining species then defines the apparent order of the reaction. Take for example equation (A3,4.10) with e. The... 

Experimentally, one finds the same first-order rate law as for monomolecular reactions, but with an effective rate constant /rthat now depends on [M],... 

The correct treatment of the mechanism (equation (A3.4.25), equation (A3.4.26) and equation (A3.4.27), which goes back to Lindemann [18] and Hinshelwood [19], also describes the pressure dependence of the effective rate constant in the low-pressure limit ([M] < [CHoNC], see section A3.4.8.2). 

If the dominant contributions /r,[M.] are approximately constant, this leads to pseudo second-order kinetics with an effective rate constant... 

Figure A3.4.9. Pressure dependence of the effective unimolecular rate constant. Schematic fall-off curve for the Lindemaim-FIinshelwood mechanism. A is the (constant) high-pressure limit of the effective rate constant...

We thus have a pseudo th-order reaction and an effective rate constant k. The methods discussed in Sections 3.3.1 and 3.3.2 may now be... 

Integration leads to 5.1.10. The form of this equation indicates that the reaction may be considered as first order in the departure from equilibrium, where the effective rate constant is the sum of the rate constants for the forward and reverse reactions. 

The formation of radicals from hydrogen peroxide in cyclohexanol was measured by the free radical acceptor method [60] the effective rate constant of initiation was found to be equal to ki = 9.0 x 106 exp(—90.3/RT) s 1. For the first-order decomposition of H2O2 in an alcohol medium, the following reactions were discussed. 

Effective Rate Constants of Hydroperoxide Decomposition in Solution of Subsequent Either [68]... 

In the case of cobalt ions, the inverse reaction of Co111 reduction with hydroperoxide occurs also rather rapidly (see Table 10.3). The efficiency of redox catalysis is especially pronounced if we compare the rates of thermal homolysis of hydroperoxide with the rates of its decomposition in the presence of ions, for example, cobalt decomposes 1,1-dimethylethyl hydroperoxide in a chlorobenzene solution with the rate constant kd = 3.6 x 1012exp(—138.0/ RT) = 9.0 x 10—13 s—1 (293 K). The catalytic decay of hydroperoxide with the concentration [Co2+] = 10 4M occurs with the effective rate constant Vff=VA[Co2+] = 2.2 x 10 6 s— thus, the specific decomposition rates differ by six orders of magnitude, and this difference can be increased by increasing the catalyst concentration. The kinetic difference between the homolysis of the O—O bond and redox decomposition of ROOH is reasoned by the... 

In real systems (hydrocarbon-02-catalyst), various oxidation products, such as alcohols, aldehydes, ketones, bifunctional compounds, are formed in the course of oxidation. Many of them readily react with ion-oxidants in oxidative reactions. Therefore, radicals are generated via several routes in the developed oxidative process, and the ratio of rates of these processes changes with the development of the process [5], The products of hydrocarbon oxidation interact with the catalyst and change the ligand sphere around the transition metal ion. This phenomenon was studied for the decomposition of sec-decyl hydroperoxide to free radicals catalyzed by cupric stearate in the presence of alcohol, ketone, and carbon acid [70-74], The addition of all these compounds was found to lower the effective rate constant of catalytic hydroperoxide decomposition. The experimental data are in agreement with the following scheme of the parallel equilibrium reactions with the formation of Cu-hydroperoxide complexes with a lower activity. 

Depending on the electron affinity of the catalyst, one of these two routes predominates. The dependence of the hydroperoxide decomposition rate on [ROOH] is in agreement with the conception of preliminary equilibrium sorption of hydroperoxide on the catalyst surface (Me2PhCOOH, AgO, 16m2 L 343 K) [263]). The equilibrium constant was estimated to be K 1 mol L and effective rate constant of described ROOH decomposition is /cis = 70s I[263]. 

A series of steady-state fluorescence experiments were performed in mixtures of propanol and glycerol to investigate the effect of viscosity on the effective second order photosensitization rate constant, k2. Figure 3 illustrates that the effective rate constant decreases as the viscosity of the system is increased. For example, as the reaction solvent is changed from pure propanol to pure glycerol, the viscosity of the system rises by three orders of magnitude, while the effective reaction rate coefficient, k2, decreases by approximately one order of magnitude. 

Because the system initially has excess Hej (relative to equilibrium value), the inlet pressure dependence of EF(7,6) is dominated by the left side of reaction (9) whereas the inlet pressure dependence of EF(7,8) is dominated by the right side. Thus, EF(7,8) and EF(7,6) will approach equilibrium with effective rate constants klff and respectively, given approximately by. 

RTD Models. The next class of models relied on the RTD to calculate conversions. But since the rate of catalytic reaction of an element of gas depends on the amount of solid in its vicinity, the effective rate constant is low for bubble gas, high for emulsion gas. Thus any model that simply tries to calculate conver-... 

Contact Time Distribution Models. To overcome this difficulty and still use the information given by the RTD, models were proposed which assumed that faster gas stayed mainly in the bubble phase, the slower in the emulsion. Gilliland and Knudsen (1971) used this approach and proposed that the effective rate constant depends on the length of stay of the element of gas in the bed, thus... 

SO that the reaction rate has an effective rate constant... 

Figure 8-22 Effective rate constants of reproduction 1, and death ki of living organisms.

For a reaction, if the effective rate constant is given by, then. 

For all but the two smallest alkenes, ethene and propene, the rate constants are at their high-pressure limits at 1 atm, and even for these two compounds, the effective rate constant is within 10% of k... 

However, the formation of the dimer in the ter-molecular reaction is sufficiently fast under stratospheric conditions that the bimolecular reactions are not important. For example, using the recommended termolecular values (DeMore et al., 1997) for the low-pressure-limiting rate constant of /c,3()0 = 2.2 X 10-32 cm6 molecule-2 s-1 and the high-pressure-limiting rate constant of k3()0 = 3.5 X 10-12 cm3 molecule-1 s-1 with temperature-dependent coefficients n = 3.1 and m = 1.0 (see Chapter 5), the effective rate constant at 25 Torr pressure and 300 K is 1.6 X 10-14 cm3 molecule-1 s-1, equal to the sum of the bimolecular channels (Nickolaisen et al., 1994). At a more typical stratospheric temperature of 220 K and only 1 Torr pressure, the effective second-order rate constant for the termolecular reaction already exceeds that for the sum of the bimolecular channels, 2.4 X 10-15 versus 1.9 X 10-15 cm3 molecule-1 s-1. 

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