Kinetic rate coefficient , for

Figure 9 shows the temperature dependence of the recovered kinetic rate coefficients for the formation (k bimolecular) and dissociation (k unimolecular) of pyrene excimers in supercritical CO2 at a reduced density of 1.17. Also, shown is the bimolecular rate coefficient expected based on a simple diffusion-controlled argument (11). The value for the theoretical rate constant was obtained through use of the Smoluchowski equation (26). As previously mentioned, the viscosities utilized in the equation were calculated using the Lucas and Reichenberg formulations (16). From these experiments we obtain two key results. First, the reverse rate, k, is very temperature sensitive and increases with temperature. Second, the forward rate, kDM, 1S diffusion controlled. Further discussion will be deferred until further experiments are performed nearer the critical point where we will investigate the rate parameters as a function of density. 

Table 5.6 Kinetic rate coefficients for heterogeneous reactions if not indicated, reaction order...

Table 5.7 Kinetic rate coefficients for homogeneous reactions.

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

Bagdassarian [428] considered the kinetics of steps in which a germ nucleus accommodates p atoms (ions or molecules) of product and, on the attainment of this number, was converted to a growth nucleus. It was assumed that the rate coefficients for addition of individual atoms were equal below p... 

Hajek et al. [173] have reported a detailed kinetic study of the solid phase decomposition of the ammonium salts of terephthalic and iso-phthalic acids in an inert-gas fluidized bed (373—473 K). Simultaneous release of both NH3 molecules occurred in the diammonium salts, without dehydration or amide formation. Reactant crystallites maintained their external shape and size during decomposition, the rate obeying the contracting volume equation [eqn. (7), n = 3]. For reaction at 423 K of material having particle sizes 0.25—0.40 mm, the rate coefficients for decompositions of diammonium terephthalate, monoammonium tere-phthalate and diammonium isophthalate were in the ratio 7.4 1.0 134 and values of E (in the same sequence) were 87,108 and 99 kJ mole-1. 

A kinetic study of the electrophilic substitution of pyridine-N-oxides has also been carried out50b,c. Rate-acidity dependencies were unfortunately given in graphical form only and the rate parameters (determined mostly over a 30 °C range) are given in Table 4b. There is considerable confusion in Tables 3 and 5 of the original paper, where the rate coefficients are labelled as referring to the free base. In fact the rate coefficients for the first three substituted compounds in... 

Nitration by nitric acid in sulphuric acid has also been by Modro and Ridd52 in a kinetic study of the mechanism by which the substituent effects of positive poles are transmitted in electrophilic substitution. The rate coefficients for nitration of the compounds Pl CHi NMej (n = 0-3) given in Table 10 show that insertion of methylene groups causes a substantial decrease in deactivation by the NMej group as expected. Since analysis of this effect is complicated by the superimposed activation by the introduced alkyl group, the reactivities of the... 

The first kinetic study appears to have been that of Martinsen148, who found that the sulphonation of 4-nitrotoluene in 99.4-100.54 wt. % sulphuric acid was first-order in aromatic and apparently zeroth-order in sulphur trioxide, the rate being very susceptible to the water concentration. By contrast, Ioffe149 considered the reaction to be first-order in both aromatic and sulphur trioxide, but the experimental data of both workers was inconclusive. The first-order dependence upon aromatic concentration was confirmed by Pinnow150, who determined the equilibrium concentrations of quinol and quinolsulphonic acid after reacting mixtures of these with 40-70 wt. % sulphuric acid at temperatures between 50 and 100 °C the first-order rate coefficients for sulphonation and desulphonation are given in Tables 34 and 35. The logarithms of the rate coefficients for sulphonation... 

There has been one kinetic study using sulphuric acid in which methanol was employed as a co-solvent571, the rate coefficients for dedeuteration of five-membered heterocyclics being measured (Table 174). Firstly, it should be noted... 

A kinetic study of dedeuteration at 25 °C yield the following rate coefficients for [2H]-C6H4R578> 579 (R = )4-Me, 1,900 2-Me, 530 3-Me, 2.7 4-Ph, 1,400 2-Ph, 260 3-Ph, < 0.2 2,3-benzo(l position of naphthalene) 20,000-30,000 and 3,4-benzo (2 position of naphthalene) 500. Rather surprisingly, the rates of dedeuteration were little different from the rates of deuteration and it should be noted that quoted partial rate factors in this work were obtained by dividing these rates for dedeuteration at 25 °C by the rates of deuteration of benzene at 20 °C and errors of a factor of 2 or more may be introduced by this. 

Kinetic studies of base-catalysed hydrogen exchange of heterocyclic compounds have been carried out. Paudler and Helmick515 measured second-order rate coefficients for deuteration of derivatives of imidazo[l,2-a]pyridine(XXXIII), imidazo[l,2-a]pyrimidine(XXXIV), and 1,2,4-triazolo[1,5-a]pyrimidine(XXXV)... 

The dependence on [HCrO ] is a feature of many other oxidations by chromic acid and is characterised by a falling-off of the apparent first-order rate coefficient for disappearance of Cr(VI) at higher concentrations of oxidant. In more strongly acidic solutions the kinetics are °°- ° ... 

Attempts have been made to trap the intermediate radical with a monomer, particularly in the reduction of benzyl chloride by Cr(II) to benzylchromium ion (and ultimately to toluene and dibenzyl). The results were ambiguous, however, as benzylchromium ion itself reacts with butadiene and acrylonitrile. This reduction shows second-order kinetics with E — 14.6 kcal.mole and = 14.3 eu. The rate coefficients for benzyl chloride, bromide and iodide follow the expected sequence ... 

The component mass balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

ApA < 1. In Fig. 2 the region of curvature is much broader and extends beyond — 4 < ApA < + 4. One explanation for the poor agreement between the predictions in Fig. 3 and the behaviour observed for ionisation of acetic acid is that in the region around ApA = 0, the proton-transfer step in mechanism (8) is kinetically significant. In order to test this hypothesis and attempt to fit (9) and (10) to experimental data, it is necessary to assume values for the rate coefficients for the formation and breakdown of the hydrogen-bonded complexes in mechanism (8) and to propose a suitable relationship between the rate coefficients of the proton-transfer step and the equilibrium constant for the reaction. There are various ways in which the latter can be achieved. Experimental data for proton-transfer reactions are usually fitted quite well by the Bronsted relation (17). In (17), GB is a... 

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