Reaction rates rate constant compared with

Relative first-order rate constants compared with the uncatalysed reaction. 

Equation (12.21) shows that the influence of the reaction is to make multiplicity less favoured. The higher the value of the reaction rate constant k2 compared with the desorption step k-lt the greater the attractive interaction aH needed. If k2 increases so that K2 exceed e-2, multiple stationary states will not occur for any finite value of a. 

The self-recombination reactions of HOj, CF3CFHO, and CF3O) have been studied using pulse radiolysis/time-resolved UV absorption spectroscopy.215 The addition of the cumylperoxy radical to a range of alkyl-substituted biphenyls has been studied and the rate constants compared with reactions with related monosubstituted benzenes.216... 

During the last two decades, it has been discovered that, using single crystals as electrodes, one can find crystal planes on which reactions occur much more rapidly than on other planes. In some systems, a particular crystal face may give an advantage of an order of magnitude in rate constant compared with the results on a polycrystal. The effects are reaction specific, that is, the positive... 

The expression for ko in Equation (1.6) or (1.7) cannot be more than an approximation, from the nature of its assumptions, which ignore the molecular structure of the liquid and the consequences of solute-solvent and solute-solute interactions, and take no account of the fact that reactant molecules are seldom spherical and commonly have localised reaction sites. None the less, it provides a general guide to the effects of various factors. An observed rate constant comparable with the calculated value of kp is a useful indication of diffusion control. 

Allylic rearrangements with 3,3,6,6-dj-cyclohexene occurred in 20% of the MMO hydroxylation products compared to 33% for cytochrome P-450. These two experiments suggest that, with M. trichospor-ium OB3b, a rebound reaction must occur with a greater rate constant than with cytochrome P-450, in accord with the radical clock substrate work. 

For non-linear chemical reactions that are fast compared with the local micromixing time, the species concentrations in fluid elements located in the same zone cannot be assumed to be identical (Toor 1962 Toor 1969 Toor and Singh 1973 Amerja etal. 1976). The canonical example is a non-premixed acid-base reaction for which the reaction rate constant is essentially infinite. As a result of the infinitely fast reaction, a fluid element can contain either acid or base, but not both. Due to the chemical reaction, the local fluid-element concentrations will therefore be different depending on their stoichiometric excess of acid or base. Micromixing will then determine the rate at which acid and base are transferred between fluid elements, and thus will determine the mean rate of the chemical reaction. 

ScoOiOPorph/RCoooporph-1 The principle of the method is illustrated in Fig. 18 with the example of reaction (142). The rate constants obtained with the investigated nucleophiles (or with single electron donors—that is the question ) are compared to those of the reaction of a series of anion radicals with the same alkyl halide in the same medium. As discussed on p. 59, aromatic anion radicals behave in this reaction as outer sphere electron donors and the alkyl halide undergoes a dissociative electron transfer. For... 

The rate of a reaction involving a high-energy intermediate appears to depend on an observed first-order rate constant associated with the formation of the product (or disappearance of reactant), which can be expressed in a simplified manner in most cases by applying the steady-state approximation as obs = i 2/( -i +k2). The overall forward reaction (that includes steps associated with ki and k2) is significantly suppressed to the extent that k is comparable in magnitude to k2- In the case of decarboxylation, we propose that the reaction can be accelerated by a catalyst that is capable of effectively... 

The proposed reaction mechanism for the destruction of aqueous solutions of TCE or PCE predicts the formation of stable oxidized polar organic compounds. These compounds consist of acids, aldehydes, and possibly halo-acetic acids. Three possible mechanisms have been proposed for the formation of by-products due to the irradiation of aqueous solutions containing TCE and PCE. The first is for the formation of formaldehyde, acetaldehyde, and glyoxal, which are formed at a concentration of approximately two orders of magnitude less than the influent solute concentration. Second, the formation of formic acid decreased with increasing radiation dose. The formic acid concentration was found to be higher for PCE than TCE. These results are most probably due to the slower reaction rate constants of PCE with e and OH, compared to TCE. The third possible reaction is the formation of haloacetic acids when TCE and OH react. The mechanism of decomposition of PCE by OH is shown in Equation (12.30) to Equation... 

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

A detailed examination of the mass transport effects of the HMRDE has been made. At low rotation speeds and for small amplitude modulations (as defined in Section 10.3.6.2) the response of the current is found to agree exactly with that predicted by the steady-state Levich theory (equations (10.15)-(10.17)) [27, 36, 37]. Theoretical and experimental application of the HMRDE, under these conditions, to cases where the electrode reaction rate constant was comparable to the mass-transfer coefficient has also been made [36]. At higher rotation speeds and/or larger amplitude modulations, the observed current response deviated from the expected Levich behaviour. 

The diester persits in solution because it can only be converted into the ion pair by slow bimolec-ular reaction with THF the faster intramolecular ionization is not possible because of the absence of nucleophilic oxygen atoms. The corresponding dicationic trimer reacts with THF with a rate constant comparable to kp. 

Scission is rapid in polar solvents. The ks for alkoxyl radicals in aqueous solution is 10 -10 s (328-330), 10-100 times faster than rates in nonpolar organic solvents (331-333) that have dielectric constants comparable with fatty acid methyl esters. Even though this is somewhat slower than H- abstraction (Table 10), scission usually competes effectively, and under appropriate conditions, scission can dominate. In polar media, scission accounts for at least half of the LO reactions even in early oxidation. For example, Bors (308) found 48% fragmentation, 48% H abstraction, and 4% unreacted t-BuO in aqueous solution on a pulse radiolysis time scale (ms to s). n-6 Fatty acids oxidized in Tris-KCl + FeSO ascorbic acid for up to 24 hrs gave the scission fragment 2-hydroxyheptanal as the sole product (334). Scission accounted for 7-10% of the oxidation products in neat triolein, but... 

Note also that all the preceding discussions immediately transpose when comparing the half-life times ti/2 associated with chemical reactions to 9. In our opinion this is more satisfactory since it avoids the necessity of defining a rate constant associated with mass transfer processes, which are essentially of a physical, not a chemical, nature. 

The conversion could be enhanced for the forward reaction if the reverse reaction involving ethene and 2-butene is minimized. Further, since 2-butene desorption is a controlling factor due to its strong sorptive properties, 2-butene removal, in particular, will allow improved rate of reaction and product separation with the use of a sorbent such as y-Al203. The effect of the PSR operation (cycle time = 40 sec) on the reactor performance was tested through simulations and by conducting experiments. Step inputs in inlet feed composition containing propene with helium carrier were conducted with clean sorbent beds and constant total gas flow rates. The results, compared with theoretical predictions, are shown in Fig. 9. Because ethene has... 

Wecould combine Eqs. (6.2.10) through (6.2.13) and by eliminating d and b calculate r as a function of a and h. This we shall do shortly, but first let us introduce the notion of a rate determining step. It is conceivable that the reaction is rather slow compared with the process of adsorption and desorption, that is, the rate constants k and k are very much smaller, in some sense, than ka.,k(i, k, and However, although these four constants are very large, the ratios and Kh may have any finite value. Now if ka and kd become exceedingly large the only way in which and fa (which are both equal to f can remain finite is for the two expressions in the brackets of Eqs. 

Energy transfer. To model this mechanism of stabilization, a reaction (number 50, Table I) was included to allow for quenching of the excited ketone by an additive (Ql) with a rate constant comparable to the upper limit for diffusion of a small molecule in a polymer matrix. Figure 8 shows that up to 1M concentration (about 8 wt-%) of quencher had minimal effect on the time to failure (5% oxidation). This assumes completely random distribution of both the excited ketones and the stabilizer as in the calculation of Heller and Blattman (34). Such a bi-molecular process is too slow to compete with the fast unimolecular reactions of the excited ketone, and thus stabilization by such transfer is predicted to be ineffective in polyethylene. Allowance must be made, however, for special cases in which the excitation energy can effectively migrate (e.g., in some aromatic polymers), in which case the bimolecu-lar process may become competitive with the other chemical processes from the excited states. 

The reactions of sulfides with atomic oxygen are quite rapid, as Table 10-2 shows, with rate constants comparable to those of OH reactions in many cases. Note, however, that the average number densities of O atoms in the troposphere are in the range 104- 10s atoms/cm3—that is, an order of magnitude lower than those for OH. Accordingly, the latter is the preferred reagent. COS is an exception because it reacts with OH quite slowly. Table 10-2 includes approximate atmospheric lifetimes of sulfides based on their reactions with OH radicals. Values of the order of days indicate a rapid destruction of sulfides in the troposphere. The major exception is again COS, which is more stable. 

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