Frequency factor

Calculate what the critical supersaturation ratio should be for water if the frequency factor in Eq. IX-10 were indeed too low by a factor of 10 . Alternatively, taking the observed value of the critical supersaturation ratio as 4.2, what value for the surface tension of water would the corrected theory give ... 

One might expect the frequency factor A for desorption to be around 10 sec (note Eq. XVII-2). Much smaller values are sometimes found, as in the case of the desorption of Cs from Ni surfaces [133], for which the adsorption lifetime obeyed the equation r = 1.7x 10 exp(3300// r) sec R in calories per mole per degree Kelvin). A suggested explanation was that surface diffusion must occur to desorption sites for desorption to occur. Conversely, A factors in the range of lO sec have been observed and can be accounted for in terms of strong surface orientational forces [134]. 

The Franck-Condon principle says that the intensities of die various vibrational bands of an electronic transition are proportional to these Franck-Condon factors. (Of course, the frequency factor must be included for accurate treatments.) The idea was first derived qualitatively by Franck through the picture that the rearrangement of the light electrons in die electronic transition would occur quickly relative to the period of motion of the heavy nuclei, so die position and iiioiiientiim of the nuclei would not change much during the transition [9]. The quaiitum mechanical picture was given shortly afterwards by Condon, more or less as outlined above [10]. 

Nitrocellulose is among the least stable of common explosives. At 125°C it decomposes autocatalyticaHy to CO, CO2, H2O, N2, and NO, primarily as a result of hydrolysis of the ester and intermolecular oxidation of the anhydroglucose rings. At 50°C the rate of decomposition of purified nitrocellulose is about 4.5 x 10 %/h, increasing by a factor of about 3.5 for each 10°C rise in temperature. Many values have been reported for the activation energy, E, and Arrhenius frequency factor, Z, of nitrocellulose. Typical values foiE and Z are 205 kj/mol (49 kcal/mol) and 10.21, respectively. The addition of... 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

The prefactor M(T), also called a frequency factor, has units of inverse seconds. It may have a weak dependence on temperature. Some theoretical models predict a variation with, but such variation is frequently ignored and M is taken as constant over limited temperature ranges. The prefactor M is often... 

Ac tivation energies and frequency factors for the various steps of this model were determined as follows ... 

Reaction Rate constant Activation energ)-, kcal/(g-rnol) Frequency factor, rnin ... 

Thermal activation through obstacles is generally described in terms of a frequency factor Vq and an activation energy AG(r, f). The former is a constant and the latter can be a function of the applied shear stress r and the micromechanical state of the material, as represented by the variable f. The time for thermal activation through a single obstacle is then assumed to be of the form... 

The gas phase decomposition A B -r 2C is conducted in a constant volume reactor. Runs 1 through 5 were conducted at 100°C run 6 was performed at 110°C (Table 3-15). Determine (1) the reaction order and the rate constant, and (2) the activation energy and frequency factor for this reaction. 

The activation energy and frequency factor can be determined from the Anhenius equation... 

Figure 12-11. Self-heat rate analysis. ARC data are shown along with a fitted model obtained by assuming the following kinetic parameters reaction order = 1, activation energy = 31.08 kcal/mol, and frequency factor = 2.31 El 2 min ...

The Arrhenius equation relates the rate constant k of an elementary reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If A is a first-order rate constant, A has the units seconds, so it is sometimes called the frequency factor. 

Line No. Pyridine substituents Nucleophile (solvent) Rate constant" (temp. °C) 10 fc liter mole- seo-i Activation energy kcal mole-1 Entropy of activation cal mole i deg-i Frequency factor logioA Ref. 

The Arrhenius frequency factor,47 9 A, is in units of liter mole sec. e Water was added to absolute ethanol to make 99.8% ethanol. f Values of JH were also given. 

Line No. Pyrimidine substituents Nucleophile in 99.8% EtOH Rate constant (temp. °C) 10 k liter mole i sec Activation energy kcal mole i Entropy of activation cal mole deg-i Frequency factor logic A Ref. 

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