Rate constants self reactions

The self-exchange rate constant for reaction 14, when M is Ru and when an excited Ru(II) product is formed, has been esti-... 

T Depends on rate constants for radical self-termination reactions. g Rate constants for reaction of Bu3SnD. 

In specifying rate constants in a reaction mechanism, it is common to give the forward rate constants parameterized as in Eq. 9.83 for every reaction, and temperature-dependent fits to the thermochemical properties of each species in the mechanism. Reverse rate constants are not given explicitly but are calculated from the equilibrium constant, as outlined above. This approach has at least two advantages. First, if the forward and reverse rate constants for reaction i were both explicitly specified, their ratio (via the expressions above) would implicitly imply the net thermochemistry of the reaction. Care would need to be taken to ensure that the net thermochemistry implied by all reactions in a complicated mechanism were internally self-consistent, which is necessary but by no means ensured. Second, for large reaction sets it is more concise to specify the rate coefficients for only the forward reactions and the temperature-dependent thermodynamic properties of each species, rather than listing rate coefficients for both the forward and reverse reactions. Nonetheless, both approaches to describing the reverse-reaction kinetics are used by practitioners. 

The sequence of reactions 2,3, and 4 has a chain branching factor of 2, but, the overall chain branching factor for 1, 2, 3, and 4 is 2(1- a) where a is the ratio of the rate constant for reaction 2 to the sum of the rate constants of reactions 1 and 2. Since reaction 1 is faster than 2, a is less than one. This means that for a self sustaining chain reaction to occur another reaction which provides additional chain branching is necessary. It is generally agreed that in the Thermal DeNOx process reaction 5 has that role... 

Marcus has shown (44, 45) that a relatively simple relation exists between the rate constants for reactions accompanied by a net chemical change (A G° 0) and those for the component self-exchange reactions. 

The data in Table III show excellent self-consistency for the three aromatic rate constants, the individual values of which are nevertheless quite different. Comparison with rate constants determined by iodide ion competition kinetics (21) indicates that the absolute values determined in this work are higher for benzene, ethyl alcohol, and methyl alcohol. Comparison with the rate constants determined by thiocyanate ion competition kinetics (1,2) indicates that our absolute values are higher for benzene, benzoate ion, methyl alcohol and ethyl alcohol. This comparison indicates that the actual rate constants for Reactions 3 and 4 may be higher than the values which have been determined (I, 2, 21) from the formation curves of the optically absorbing product by as much as a factor of 1.6 to 2.3 in the former case and 1.7 in the latter case. That is, the true values may be nearer = 2 X 1010 and k4 = 1.2 X 1010 M"1 sec."1 at 25 °C. This same qualitative conclusion for the case of thiocyanate has recently been reached by a different method by Baxendale and Stott (7) whose suggested value for k4 is approximately 2 X 1010M 1 sec."1. The difficulties in the direct absolute determination lie in the complexities of the kinetics and hence in the interpretation of the formation rate curves. 

For either limiting case, ZJq/T and fcdiffusion-controlled reactions of electronically excited molecules (5) and for radical self-termination reactions (6), especially when high-molecular-weight alkanes or alcohols are employed as solvents. But even in such cases, rate constants for reactions considered to be diffusion-controlled mirror the behavior of empirical diffusion coefficients, which, if not known, can be calculated from available empirical or semiempirical formulas (6). 

This has significant implications for the interpretation of the observed peroxy radical decay rate constant. If reaction (44) is very fast (an estimated rate constant of 2.5 x 10 cm s was obtained from modeling the product study), then four, as opposed to two, peroxy radicals are effectively removed for every reactive encounter between two CF3O2 molecules, implying that the actual self-reaction rate constant is half the observed value. A more careful analysis by both studies gives the corrected selfreaction rate constant as A = 1.8 x 10 cm s . ... 

The kinetics of the self-reaction (6) and the cross reactions (7) and (8) were studied by conventional flash photolysis [5, 11] and later by laser flash photolysis [4] combined with UV long path absorption spectroscopy. Rate constants for reaction (6) to (8) were obtained ... 

The rate constant increases with increasing basicity of A. At 15°C and an ionic strength of 0.50 M, the self-catalyzed second-order rate constant for water is 0.16 M s . The calculated rate constants for catalysis by hypochlorite and carbonate are 3.6 X 10 and 2.1 X 10 M s respectively, using 7.633 and 10.431 for their respective pK. The extrapolated rate constant for reaction with hydroxide at 15°C and an ionic strength of 0.50 M is 4.1 X 10 M s . However, hydroxide may react directly with chlorine by the following reaction, which is kinetically indistinguishable from the other two schemes ... 

Most of the propagation-rate constants (/Cp) listed in 8.5.3 have been measured relative to the rate constant for self-reaction, i.e., cdculated from the rate constant ratio kp/(2k,). Very few absolute rate constants estimated from co-oxidation studies have been included. Similarly many of the rate constants for reaction of RO2 with phenols and aromatic amines (kj h) have been estimated from rate constant ratios, kp/kj h- Consequently values of kp and km), depend critically on the accuracy of the measurement of 2k. It should be noted that we have made no attempt to normalize values of kp and k) , to a best value for 2k,. All the rate constants are based on the authors own measurement of 2k, which may differ from the value obtained in another laboratory. The reader should bear this in mind when he is using rate constants for peroxyl radical-molecule reactions. 

Micelles not only can alter rate constants of reactions but they can alter the conformation of molecules and thus affect the outcome of a reaction [8]. Selfassociation of alkyl tyrosines enhances the population of one conformer (Fig. 11.1) (a) over conformer (b) and (c) (Table 11.1). The special aspect of conformer (a) is that it is the only one which has a trans carboxylate co-planar with the hydrocarbon and could expose its ionic group to the water phase while the alkyl group points to the centre of the aggregate, thus it will be preferred. Self-associating solutes are a special class of compounds (so called functional micelles") which are dealt with separately. It is more common to experience solutes which are more simply... 

Alkylperoxy radicals are generated by the reactions of carbon-centered radicals with oxygen and in the induced decomposition of hydroperoxides (Scheme 3.82). Their reactions have been reviewed by Howard452 and rate constants for their self reaction and for their reaction with a variety of substrates including various inhibitors have been tabulated.453... 

Before any chemistry can take place the radical centers of the propagating species must conic into appropriate proximity and it is now generally accepted that the self-reaction of propagating radicals- is a diffusion-controlled process. For this reason there is no single rate constant for termination in radical polymerization. The average rate constant usually quoted is a composite term that depends on the nature of the medium and the chain lengths of the two propagating species. Diffusion mechanisms and other factors that affect the absolute rate constants for termination are discussed in Section 5.2.1.4. 

Data are given in Table 10-7 to illustrate certain facets of the Marcus cross relation. They refer to six reactions in which the cage complex Mn(sar)3+ is reduced or Mn(sar)2+ oxidized.34 These data were used to calculate the EE rate constant for this pair. The results of the calculation, also tabulated, show that there is a reasonably self-consistent value of fcEE for Mn(sar)3+/Mn(sar)2+ lying in the range 3-51 L mol-1 s-1. When values34 for an additional 13 reactions were included the authors found an average value of kEE = 17 L mol 1 s l. 

In summary, the order of reactivity for the most commonly used ruthenium-based metathesis catalysts was found to be 56d>56c>9=7. This order of reactivity is based on IR thermography [39], determination of relative rate constants for the test reaction 58—>59 (Eq. 8) [40], and determination of turnover numbers for the self metathesis of methyl-10-undecenoate [43]. 

Self-Test 13.12A The rate constant for the second-order gas-phase reaction HO(g)... 

Self-Test 13.13A The rate constant for the second-order reaction between CH,CH2Br and OH in water is 0.28 mL-mol -s 1 at 35.0°C. What is the value of the rate constant at 50.0°C See Table 13.4 for data. 

Determine the order of a reaction, its rate law, and its rate constant from experimental data (Examples 13.1 and L3.2 and Self-Tests 13.2 and 13.3). 

A characteristic reaction of free radicals is the bimolecular self-reaction which, in many cases, proceeds at the diffusion-controlled limit or close to it, although the reversible coupling of free radicals in solution to yield diamagnetic dimers has been found to be a common feature of several classes of relatively stable organic radicals. Unfortunatly, only the rate constants for self-termination of (CH3)jCSO (6 x 10 M s at 173 K) and (CH3CH2)2NS0 (1.1 X 10 M s at 163K) have been measured up to date by kinetic ESR spectroscopy and consequently not many mechanistic conclusions can be reached. 

Esr spectroscopy has also been used to study pure solvent dynamics in electron self-exchange reactions (Grampp et al., 1990a Grampp and Jaenicke, 1984a,b). When the systems are not linked by a spacer (i.e. TCNQ- /TCNQ (TCNQ = tetracyanoquinodimethane), the homogeneous bimolecular rate constants /chom are given by (10), with fcA the association constant and kET... 

The autoxidation of ethers occurs with self-acceleration as autoxidation of hydrocarbons. The kinetics of such reactions was discussed earlier (see Chapter 2). The autoacceleration of ether oxidation occurs by the initiating activity of the formed hydroperoxide. The rate constants of initiation formed by hydroperoxides were estimated from the parabolic kinetic... 

The intensive mechanistic studies of phenoxyl self-reactions proved a great variety of mechanisms and rate constants of these reactions [2,3,6], The substituents can dramatically influence the mechanism and kinetics of self-reactions. Due to free valence delocalization the phenoxyl radical possesses an excess of the electron density in the ortho- and para-positions. Mono- and disubstituted phenoxyls recombine with the formation of labile dimers that after enolization form bisphenols [3,6],... 

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