Rate coefficient, defined

In the thennodynamic fomiiilation of TST the pressure dependence of the reaction rate coefficient defines a volume of activation [24, 25 and 26]... 

Return now to the first part of the two-step procedure for characterizing an adsorption column. Our model represented by Equations 1, 2, 3, 4, and 5 shows that the following space and point rate coefficients define the problem ... 

Acidity Measuring rate coefficients at pH = 0 is the best available means of converting pseudo-first-order rate coefficients into second-order rate coefficients (/ ) defined by Eq. (2.2), since the value of [H+] is 1 mol liter-1. Moreover, all the acidity functions merge near pH = 0. 

An alternative standard procedure has been developed, and this is aimed at producing standard rate coefficients for hydrogen exchange, under the same conditions as those selected for nitration (H0 = -6.6, T = 25°C). These alternative standard rate coefficients, defined as k°2, are calculated as follows [78JCS(P2)613]. 

In this model, the rates of adsorption, migration and desorption from the intrinsic precursor are fea[A2], km [A ], and fc A ], respectively, and it follows that the normalised rate coefficients defined earlier are identical with the probabilities fc, fm and fd defined by King and Wells [46] and equation (65) is readily transformed into their rate expression for dissociative adsorption derived by the statistical method. 

Such discussions then, allow deviations of a few orders of magnitude from the normal pre-exponential value of 1013 s 1, but for even greater deviations, the basic postulate of the above argument appears to break down, i.e. equilibrium between the reactants and transition state is not achieved. A rate coefficient defining energy transfer from adsorbent to adsorbate must then be introduced and Kramers [347] has treated this case if this process is rate-limiting, it causes the pre-exponential factor to be drastically reduced. The model can be modified by the inclusion of an additional rate coefficient to account for the relaxation of the surface population from a non-equilibrium to an equilibrium state and so it is to be expected that v is strongly temperature-dependent [348, 349]. The model has been successfully applied to the desorption of neon from xenon at very low temperatures for which v was found to be 10s s-1 [350]. 

Figure 3. Temperature dependencies assumed for the five microscopic rate coefficients defined in Figure I. The microcoefficients c and s have units (ppm elementfr Khr e, u, and w have units Khr K...

Response curves and concentration profiles calculated according to the simple model with an overall effective rate coefficient defined by Eq. (8.42) provide a reasonably good approximation to the exact solutions, calculated from model 46. This is illustrated in Figure 8.10. The dimensionless parameters are defined by... 

Da - Damkohler number, dimensionless [7] - concentration of initiator, mol/1 hi - initiator decomposition rate coefficient, s h - termination rate coefficient, mol/1 s - propagation rate coefficient, 1/mol s k - effective polymerization rate coefficient (defined in Eq. 1.5.4), s km - polymer interdomain distance, cm Mm - molecular weight of monomer, g/mol Mp - molecular weight of polymer, g/mol Ms - molecular weight of solvent, g/mol [M] - concentration of monomer, mol/1 7 p - propagation rate, mol/1 s r - generalized spatial variable, cm - defined in Eq. (1.5.12),... 

In case the reactions in Scheme 10.1 are assumed to be dependent on the chain length, 2 and 3 have to be replaced by population-weighted rate coefficients defined as... 

RT(r - l)lp is a consequence of using a rate coefficient defined in terms of mole fractions. For a rate coefficient defined in terms of concentration it would become RT(r - l)(31nZ/3p)x, where Z is the system compressibility at the reaction temperature [75]. 

Relative rate coefficients define relative product state (product channel and product energy) distributions. These can often be described by statistical theories of unimolecular reactions, such as the statistical adiabatic channel model, described in Statistical Adiabatic Channel Models. 

Therefore, the rate coefficient defined from the partial pressures contains a term that is inversely proportional to the temperature, whose influence is also neghgible. 

Figure IV-B-1 shows the available measurements, along with a nonlinear fit to the data of Atkinson and Ktts (1978), Stief et al. (1980), Temps and Wagner (1984), Niki et al. (1984), Yetter et al. (1989), and Sivakumaran et al. (2003b). We recommend the use of the rate coefficient defined by the equation = 1.26 x 10 r exp(613/r) over the range 200-400 K which gives k(298) = 8.8 X 10 cm molecule this expression is almost identical to that given in the 2006 lUPAC evaluation (Atkinson et al., 2006).

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