Rate coefficient overall

If Other fall-off broadening factors arising m unimolecular rate theory can be neglected, the overall dependence of the rate coefficient on pressure or, equivalently, solvent density may be represented by the expression [1, 2]... 

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... 

Given this evaporation rate, the overall mass transfer coefficient may then be calculated from Equation 4-391,... 

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... 

Various expressions have been proposed for estimating how the overall rate coefficient kt and the individual rate coefficients k vary with the chain lengths of... 

The overall composition of any reactant mixture, i.e. the total quantity of each component present, is of little practical use in kinetic studies since such (concentration-type) terms are not meaningfully related to magnitudes of rate coefficients or shapes of a—time curves. Of greater signifi-... 

Analysis of the first-order rate coefficient in terms of the two consecutive reactions which were occurring, yielded values of 5.3 xlO-4 and 2.64 xlO-4 the latter value was confirmed as arising from reaction on the first reaction product, 3,4-dichlorodiphenylmethane, because separate 3,4-dichlorobenzylation of this gave a rate coefficient of 2.98 x 10-4. The first-order (overall) rate coefficients obtained at 15 °C (0.665 x 10-4) and 35 °C (6.1 x 10-4) yielded Ea = 19.6, and log A = 14.3, the rate ratio for the consecutive reactions being the same (0.5) at both temperatures later studies have tended to confirm this order of activation energy. 

With gallium chloride, ferric chloride and antimony pentachloride the rate coefficients were dependent upon the concentration of chlorobenzene and the square of the concentration of the catalyst, but the third-order coefficients varied with the initial concentration of the catalyst (Table 103)394. The overall kinetic equation was, therefore,... 

The relatively small dependence of the rate on solvent is demonstrated in Table 5. The rate coefficients are a little greater in the more polar solvents but the overall effects are small. This is taken to indicate that there is only little polar character to the transition state. Another probe to determine the polarity of the transition state is the effect of substituents on the rate. The results obtained for the ortho rearrangement by varying the para substituents are shown in Table 6131 for the conversion... 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

Silverman and Dodson made the first detailed isotopic study of this exchange system using the separation afforded by the addition of 2,2 -dipyridyl at pH 5, followed by the precipitation of the ferric iron with either ammonia or 8-hydro-xyquinoline. Dodson , using this separation method, had previously obtained an overall rate coefficient of 16 l.mole" sec at 23 °C for 0.4 M perchloric acid media. The exchange in perchlorate and perchlorate-chloride media was found to conform to a rate law, first order with respect to both total ferrous and ferric ion concentrations, with an observed rate constant (k bs) dependent on the hydrogen-ion concentration, viz. 

Sheppard and Brown have evaluated the rate coefficient k as 4180 l.mole. sec with 0.53 M HCIO4 at 20 °C. The overall activation energy and entropy corresponding to the term /f,7 17, where Ky-, is the equilibrium constant of the reaction... 

Newton and Baker, using wavelengths of 737 m/i or 648 m/i (U(IV) absorption), have obtained similar overall rate coefficients to those obtained by polaro-graphy . However, they have found U(VI) to retard the disproportionation reaction due to the presence of an additional process... 

In the case of Tl(III) the overall rate coefficient has been resolved into a product kK for the two steps The large positive AS is due almost entirely to the initial association, which was also studied spectroscopically. An alternative rate determining step in the Pd(II) oxidation is hydride ion transfer to Pd(II) . 

The detailed model was constructed as described by Carslaw et al. (1999, 2002). Briefly, measurements of NMHCs, CO and CH4 were used to define a reactivity index with OH, in order to determine which NMHCs, along with CO and CH4, to include in the overall mechanism. The product of the concentration of each hydrocarbon (and CO) measured on each day during the campaign and its rate coefficient for the reaction with OH was calculated. All NMHCs that are responsible for at least 0.1% of the OH loss due to total hydrocarbons and CO on any day during the campaign are included in the mechanism (Table 2). Reactions of OH with the secondary species formed in the hydrocarbon oxidation processes, as well as oxidation by the nitrate radical (NO3) and ozone are also included in the... 

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... 

A subsequent reaction is the recombination of the benzyl radicals to form dibenzyl, so that the rate of formation of dibenzyl measures the rate of reaction (1). Szwarc evaluated his results in terms of first-order kinetics for the overall process, since he could not find a systematic variation of his first-order rate coefficients with total pressure (varied from 5 to 15 torr). However, in view of the fact that only one... 

In spite of the complexity of the pyrolysis, a first-order rate law was found to fit the experimental results at least for the greater part of the reaction time. Stokland s first-order rate coefficients were consistently higher than those of Emel6us and Reid76, this can be understood in the light of the relation between decomposition and pressure change. They could be represented formally by an Arrhenius expression for the overall coefficient... 

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