Rate constant overall

An alternating copolymer of a-methyl styrene and oxygen as an active polymer was recently reported [20]. When a-methyl styrene and AIBN are pressurized with O2, poly-a-methylstyreneperoxide is obtained. Polymerization kinetic studies have shown that the oligoperoxides mentioned above were as reactive as benzoyl peroxide, which is a commercial peroxidic initiator. Table 1 compares the overall rate constants of some oligoperoxides with that of benzoyl peroxide. 

Table 1 Overall Rate Constants, k, of Some Peroxidic Initiators for Styrene Polymerization at 80 C...

The overall rate constant for conversion of the E S complex to products E + P is called the turnover number because it represents the number of substrate molecules the enzyme turns over into product per unit time. A value of about 103 per second is typical. 

It has been proposed that aromatic solvents, carbon disulfide, and sulfur dioxide form a complex with atomic chlorine and that this substantially modifies both its overall reactivity and the specificity of its reactions.126 For example, in reactions of Cl with aliphatic hydrocarbons, there is a dramatic increase in Ihe specificity for abstraction of tertiary or secondary over primary hydrogens in benzene as opposed to aliphatic solvents. At the same time, the overall rate constant for abstraction is reduced by up to two orders of magnitude in the aromatic solvent.1"6 The exact nature of the complex responsible for this effect, whether a ji-coinplex (24) or a chlorocyclohexadienyl radical (25), is not yet resolved.126- 22... 

The overall rate constant for radical-radical termination can be defined in terms of the rate of consumption of propagating radicals. Consider the simplified mechanism for radical polymerization shown in Scheme 5.4. 

Ideally, as long as the rate constants for reinitiation (AjT, AiM) are high with respect to that for propagation (kv), the transfer reactions should not directly affect the rate of polymerization and they need not be considered further in this section. The overall rate constant for radical-radical termination (A,) can be defined in terms of the rate of consumption of propagating radicals as shown in eq. I ... 

The rate of copolymerization often shows a strong dependence on the monomer feed composition. Many theories have been developed to predict the rate of copolymerization based on the terminal model for chain propagation (Section 7.3.1.1), This usually requires an overall rate constant for termination in copolymerization that is substantially different from that observed in homopolymerization of any of the component monomers. 

Note that all the zero-order rate constants are essentially equivalent except those for the poly-hydric alcohols which are exactly half the value of the others. Ingold et al (Ref 49a) interpret this to mean that the rate of attack of nitronium is the same for both OH groups of the glycol molecule. Since there are two such groups the overall rate constant k0 is Vi that for monohydric alcohols. The explanation for the observed k0 for glycerol is more complex. In essence it consists of postulating that the two outside OH s are readily nitrated, ie, the 1-OH is nitrated at the same rate as the 3-OH, but the middle OH is nitrated much more slowly... 

The first step was found to be a fast pre-equilibrium (Scheme 12-8). The dependence of the measured azo coupling rate constants on the acidity function and the effect of electron-withdrawing substituents in the benzenediazo methyl ether resulting in reduced rate constants are consistent with a mechanism in which the slow step is a first-order dissociation of the protonated diazo ether to give the diazonium ion (Scheme 12-9). The azo coupling proper (Scheme 12-10) is faster than the dissociation, since the overall rate constant is found to be independent of the naphthol con-... 

However, an evaluation of the observed (overall) rate constants as a function of the water concentration (5 to 25 % in acetonitrile) does not yield constant values for ki and k2/k i. This result can be tentatively explained as due to changes in the water structure. Arnett et al. (1977) have found that bulk water has an H-bond acceptor capacity towards pyridinium ions about twice that of monomeric water and twice as strong an H-bond donor property towards pyridines. In the present case this should lead to an increase in the N — H stretching frequency in the o-complex (H-acceptor effect) and possibly to increased stabilization of the incipient triazene compound (H-donor effect). Water reduces the ion pairing of the diazonium salt and therefore increases its reactivity (Penton and Zollinger, 1971 Hashida et al., 1974 Juri and Bartsch, 1980), resulting in an increase in the rate of formation of the o-complex (ik ). 

Radical cyclization. Ring closure of hept-6-en-1 -y 1 radical yields two products, methyl-cyclohexyl radical (85 percent) and cycloheptyl radical (15 percent).39 The overall rate constant is 3.5 X 104 s l. What are the rate constants for each pathway ... 

By adding small amounts of H2 to the gas mixture and observing the rate of formation of ArH +, they also estimated the following overall rate constants for charge transfer at thermal ion energies. 

We have also examined the effect of substituents on orientation in the addition of BH3 to the carbon-carbon double bond. Consider the substituted ethylene XCH=CH2. The boron may become bonded either to carbon 1 or to carbon 2. The overall rate constant for the reaction is given by... 

Kemp and Wojclechowskl referred to F(x) as the refractoriness function and it describes the change In the specific overall rate constant (i.e., 62 F(x)) as a function of extent of reaction (11). 

According to Eq. (14.2), the activation energy can be determined from the temperature dependence of the reaction rate constant. Since the overall rate constant of an electrochemical reaction also depends on potential, it must bemeasured at constant values of the electrode s Galvani potential. However, as shown in Section 3.6, the temperature coefficients of Galvani potentials cannot be determined. Hence, the conditions under which such a potential can be kept constant while the temperature is varied are not known, and the true activation energies of electrochemical reactions, and also the true values of factor cannot be measured. 

Also, Higuchi and Senju [7] have proposed that the overall rate constant is composed of three distinct rate constants corresponding to the hydrolysis of the three possible triad configurations, AAA, AAB, and BAB, and have found that the relative reactivity is 1 0.25 0.005. Thus, the overall rate is determined by the relative proportions of these configurations and a relative composite rate constant K can be derived as follows ... 

Partial rate factors may be obtained by separate kinetic measurements of the overall rate constants /cC(H Y and fcC(,H6 under analogous... 

So far we have derived an expression for the overall rate constant k. As with the copper system, we should also like an expression for the first-order rate constant k, describing the passage of particles from the secondary minimum over the barrier. The equilibrium constant describing the population of the secondary minimum is given by the same expression (49) as (36), where, as in Fig. 14, xR describes the width... 

The rate constant for formation of excited-state S02 was measured by Halstead and Thrush to be 1.7 X 10 12 exp(-2100/T) cm3 molec1 s 1 [28-31], while the overall rate constant for the loss of SO is 3.6 x 10 12 exp(-1100/T) cm3 molec-1 s 1 [11], Thus, at room temperature, S02 constitutes —1.6% of the product channels. This figure can only be considered approximate, however, since mixing of states within the singlet manifold affects the interpretation of the rate constant for formation of the excited state [32],... 

The reaction occurs both heterolytically and homolytically, so that the overall rate constant kx = km + ki. For the rate constants, see Table 17.8. 

This hypothesis is satisfactory for nucleophilic reactions of cyanide and bromide ion in cationic micelles (Bunton et al., 1980a Bunton and Romsted, 1982) and of the hydronium ion in anionic micelles (Bunton et al., 1979). As predicted, the overall rate constant follows the uptake of the organic substrate and becomes constant once all the substrate is fully bound. Addition of the ionic reagent also has little effect upon the overall reaction rate, again as predicted. Under these conditions of complete substrate binding the first-order rate constant is given by (8), and, where comparisons have been made for reaction in a reactive-ion micelle and in solutions... 

The situation is different for reactions of very hydrophilic ions, e.g. hydroxide and fluoride, because here overall rate constants increase with increasing concentration of the reactive anion even though the substrate is fully micellar bound (Bunton et al., 1979, 1980b, 1981a). The behavior is similar for equilibria involving OH" (Cipiciani et al., 1983a, 1985 Gan, 1985). In these systems the micellar surface does not appear to be saturated with counterions. The kinetic data can be treated on the assumption that the distribution between water and micelles of reactive anion, e.g. Y, follows a mass-action equation (9) (Bunton et al., 1981a). 

Analysis of the variation of the overall rate constant of reaction with [surfactant] was discussed in Section 3 (p. 222) and the treatment allows calculation of the second-order rate constants of reaction in the micellar pseudophase. These rate constants can be compared with second-order rate constants in water provided that both constants are expressed in the same dimensions and typically the units are M-1 s-1. Inevitably the comparison... 

Bertole et al.u reported experiments on an unsupported Re-promoted cobalt catalyst. The experiments were done in a SSITKA setup, at 210 °C and pressures in the range 3-16.5 bar, using a 4 mm i.d. fixed bed reactor. The partial pressures of H2, CO and H20 in the feed were varied, and the deactivation, effect on activity, selectivity and intrinsic activity (SSITKA) were studied. The direct observation of the kinetic effect of the water on the activity was difficult due to deactivation. However, the authors discuss kinetic effects of water after correcting for deactivation. The results are summarized in Table 1, the table showing the ratio between the results obtained with added water in the feed divided by the same result in a dry experiment. The column headings refer to the actual experiments compared. It is evident that adding water leads to an increase in the overall rate constant kco. The authors also report the intrinsic pseudo first order rate-coefficient kc, where the overall rate of CO conversion rco = kc 6C and 0C is the coverage of active... 

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