Rate coefficient, for

A completely analogous derivation leads to the rate coefficient for bimolecular reactions, where dare partition fiinctions per unit volume. ... 

Ciary D C, Smith D and Adams N G 1985 Temperature dependence of rate coefficients for reactions of ions with dipolar molecules Chem. Phys. Lett. 119 320-6... 

The rate coefficient for elastic scattering between two species with non-isothennal Maxwellian distributions is then... 

The amount of energy lost in unit time, the energy-loss frequency, is Vgg = kpN (t). The energy-loss rate coefficient for two-temperature Maxwellian distributions is... 

Fig. 2.4, illustrates the variation with the concentration of sulphuric acid of the logarithm of the second-order rate coefficients for the nitration of a series of compounds for which the concentration of effective... 

Rates of nitration in perchloric acid of mesitylene, luphthalene and phenol (57 I-6i-i %), and benzene (57 i-64 4%) have been deter-mined. The activated compounds are considered below ( 2.5). A plot of the logarithms of the second-order rate coefficients for the nitration of benzene against — ( f + log over the range of acidity... 

Second-order rate coefficients for nitration in sulphuric acid at 25 °C fall by a factor of about 10 for every 10 % decrease in the concentration of the sulphuric acid ( 2.4.2). Since in sulphuric acid of about 90% concentration nitric acid is completely ionised to nitronium ions, in 68 % sulphuric acid [NO2+] io [HNO3]. The rate equation can be written in two ways, as follows ... 

The phenomenon was established firmly by determining the rates of reaction in 68-3 % sulphuric acid and 61-05 % perchloric acid of a series of compounds which, from their behaviour in other reactions, and from predictions made using the additivity principle ( 9.2), might be expected to be very reactive in nitration. The second-order rate coefficients for nitration of these compounds, their rates relative to that of benzene and, where possible, an estimate of their expected relative rates are listed in table 2.6. 

Chain transfer to monomer is the main reaction controlling molecular weight and molecular weight distribution. The chain-transfer constant to monomer, C, is the ratio of the rate coefficient for transfer to monomer to that of chain propagation. This constant has a value of 6.25 x lO " at 30°C and 2.38 x 10 at 70°C and a general expression of 5.78 30°C, chain transfer to monomer happens once in every 1600 monomer... 

Investigators of tower packings normally report kcCi values measured at very low inlet-gas concentrations, so that yBM = 1, and at total pressures close to 100 kPa (1 atm). Thus, the correct rate coefficient For use in packed-tower designs involving the use of the driving force y — y /yBM is obtained by multiplying the reported k co values oy the value of pf employed in the actual test unit (e.g., 100 kPa) and not the total pressure of the system to be designed. 

Linear Driving Force Approximation Simplified expressions can also be used for an approximate description of adsorption in terms of rate coefficients for both extrapai ticle and intraparticle mass transfer controlling. As an approximation, the rate of adsorption on a particle can be written as ... 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

Example 8 Estimation of Rate Coejficient Estimate the rate coefficient for flow of a 0.01-M water solution of NaCl through a bed of cation exchange particles in hydrogen form with e = 0.4. The superficial velocity is 0.2 cm/s and the temperature is 25 C. The particles are 600 im in diameter, and the diffusion coefficient of sodium ion is 1.2 X 10 cmVs in solution and 9.4 X 10 cmVs inside the particles (of. Table 16-8). The bulk density is 0.7 g dry resin/cnd of bed, and the capacity of the resin is 4.9 mequiv/g dry resin. The mass action eqiiihbrium constant is 1.5. 

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. 

Center of mass or translational diffusion is believed to be the rate-determining step for small radicals33 and may also be important for larger species. However, other diffusion mechanisms are operative and are required to bring ihe chain ends together and these will often be the major term in the termination rate coefficient for the case of macromolecular species. These include ... 

Most in depth studies of termination deal only with the low conversion regime. Logic dictates that simple center of mass diffusion and overall chain movement by reptation or many other mechanisms will be chain length dependent. At any instant, the overall rate coefficient for termination can be expressed as a weighted average of individual chain length dependent rate coefficients (eq. 20) 39... 

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... 

Linear plots of ln(l — a) against t were obtained [454] for the removal of water from CaC03 6 H20. The slope of the line gives the rate coefficient for the nucleation step. 

Hofer et al. [671] observed that the decompositions of Ni3C and Co2C (the iron compounds melt) obeyed the zero-order equation for 0.3 < a < 0.9 (596-628 K and E = 255 kJ mole-1) and 0.2 < a < 0.75 (573-623 K and E = 227 kJ mole-1), respectively. The magnitudes of the rate coefficients for the two reactions were closely similar but the nickel compound exhibited a long induction period and an acceleratory process which was not characteristic of the reaction of the cobalt compound. Decomposition mechanisms were not discussed. 

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. 

It can be shown2 that the first-order rate coefficient for the A-l mechanism kx... 

A comparison of the second-order rate coefficients for nitration of 2,4,6-tri-methylpyridine and 1,2,4,6-tetramethylpyridinium ion (both at the 3-position) shows similarity of profile in the common acidity region and a rapidly increasing rate with acidity for the trimethyl compound at acidities below 90 wt. % (where the usual maximum is obtained). These two pieces of evidence show reaction to occur on the conjugate acid as also indicated by the large negative entropy of activation. Surprisingly, the tetramethyl compound is less reactive than the trimethyl compound so maybe this is an example of steric hindrance to solvation. Calculation of the encounter rate also showed that reaction on the free base was unlikely. 

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... 

By contrast, the rate-acidity profiles for nitration of 3-nitro-4-pyridone, 3-and 5-methyl-2-pyridone and l,5-dimethyl-2-pyridone resemble each other and differ from the above-indicated reaction upon the free base, and correction of the observed rates to allow for the concentration of free base actually present gave rate-acidity profiles of the expected form the corrected entropies of activation then turned out to be positive. Furthermore, if the logarithms of the corrected rate coefficients obtained in media of low acidity were plotted against +log aHlQ, then slopes of near unity were obtained (see above, p. 18), but not otherwise. A similar result was obtained from the nitration data for 4-pyridone in media of low acidity suggesting that here it reacts as the free base. A further test which was applied was to calculate the concentration of nitronium ions in the various media and to correct the observed rate coefficients for this the logarithms of these coeffi-... 

RATE COEFFICIENTS FOR NITRATION OF ANILINIUM IONS IN H2S04 AND OF THE CORRESPONDING N-DEUTERATED IONS IN D2S04 AT 25 °C4 ... 

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... 

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