Intrinsic activation energy

Reactions catalyzed by hydrogen ion or hydroxide ion, when studied at controlled pH, are often described by pseudo-first-order rate constants that include the catalyst concentration or activity. Activation energies determined from Arrhenius plots using the pseudo-first-order rate constants may include contributions other than the activation energy intrinsic to the reaction of interest. This problem was analyzed for a special case by Higuchi et al. the following treatment is drawn from a more general analysis. ... 

Activation energy Intrinsic viscosity Reduced viscosity Electrostatic Gibbs energy Fluorescence intensity of excimer... 

Even when there is a transport disguise, the reaction order remains one for a first-order reaction. But for reactions that are not intrinsically first order, the transport disguise changes the observed reaction order for an intrinsically zero-order reaction, the observed order becomes 1/2 and for an intrinsically second-order reaction it becomes 3/2 when 0 10. For all reaction orders the apparent activation energy is approximately half the intrinsic... 

Let us define the activation energy for a (possible hypothetical) thermoneutral reaction as the intrinsic activation energy, AEq. As seen from eq. (15.10), a = 4A q. The TS position and activation energy now become... 

The latter is, except for a couple of terms related to solvent reorganization, the Marcus equation. The central idea is that the activation energy can be decomposed into a component characteristic of the reaction type, the intrinsic activation energy, and a correction due to the reaction energy being different from zero. Similar reactions should have similar intrinsic activation energies, and the Marcus equation obeys both the BEP... 

Another approach was used some years ago by Dewar and Storch (1989). They called attention to solvent effects in ion-molecule reactions which do not yield an activation energy in theoretical calculations related to gas-phase conditions, but which are known to proceed with measureable activation energy in solution. Dewar and Storch therefore make a distinction between intrinsic barriers due to chemical processes and desolvation barriers due to chemical processes. 

Thus, the elementary cellular structure could be regarded as an intrinsic characteristic of fhe detonation in a mixture at given initial composition, temperature, and pressure. The dimension of X is of fhe order of magnitude of millimeters or less for gaseous mixfures with oxygen, but several centimeters for less sensitive mixtures (even larger, for methane/air af afmospheric pressure). It decreases when the initial pressure increases. Its variation with the initial temperature is more complicated and depends on the value of fhe reduced activation energy of fhe chemical reactions. The value of... 

Whereas Class 1 and Class 11 behavior are intrinsically related through microscopic reversibility. Class 111-type behavior implies that there is no BEP relation between the changes in activation energy and structure. 

Minimize the effects of transport phenomena If we are interested in the intrinsic kinetic performance of the catalyst it is important to eliminate transport limitations, as these will lead to erroneous data. We will discuss later in this chapter how diffusion limitations in the pores of the catalyst influence the overall activation energy. Determining the turnover frequency for different gas flow velocities and several catalyst particle sizes is a way to establish whether transport limitations are present. A good starting point for testing catalysts is therefore ... 

P = permeability P0 = intrinsic permeability Ep = apparent activation energy R - the gas constant T = absolute temperature... 

In a similar fashion, it is easily shown that the apparent activation energy of the reaction may differ appreciably from the intrinsic activation energy of the chemical reaction. The apparent rate constant is equal to the product of the effectiveness factor and the true rate constant and, in the limit of low effectiveness factors, it can be said that... 

At low temperatures diffusion will be rapid compared to chemical reaction and diffusional limitations on the reaction rate will not be observed. In this temperature regime, one will observe the intrinsic activation energy of the reaction. However, since chemical reaction rates increase much more rapidly with increasing temperature than do diffusional processes, at... 

Under isothermal conditions, we have seen that the apparent activation energy of the reaction is approximately one half the intrinsic value when rj is sufficiently low. When rj exceeds unity, an opposite effect occurs (i.e., the apparent activation energy will exceed the true activation energy). 

For situations where the reaction is very slow relative to diffusion, the effectiveness factor for the poisoned catalyst will be unity, and the apparent activation energy of the reaction will be the true activation energy for the intrinsic chemical reaction. As the temperature increases, however, the reaction rate increases much faster than the diffusion rate and one may enter a regime where hT( 1 — a) is larger than 2, so the apparent activation energy will drop to that given by equation 12.3.85 (approximately half the value for the intrinsic reaction). As the temperature increases further, the Thiele modulus [hT( 1 — a)] continues to increase with a concomitant decrease in the effectiveness with which the catalyst surface area is used and in the depth to which the reactants are capable of... 

Before terminating the discussion of external mass transfer limitations on catalytic reaction rates, we should note that in the regime where external mass transfer processes limit the reaction rate, the apparent activation energy of the reaction will be quite different from the intrinsic activation energy of the catalytic reaction. In the limit of complete external mass transfer control, the apparent activation energy of the reaction becomes equal to that of the mass transfer coefficient, typically a kilocalorie or so per gram mole. This decrease in activation energy is obviously... 

The physical properties of the anhydrate form and two polymorphic monohydrates of niclosamide have been reported [61], The anhydrate form exhibited the highest solubility in water and the fastest intrinsic dissolution rate, while the two monohydrates exhibited significantly lower aqueous solubilities. In a subsequent study, the 1 1 solvates of niclosamide with methanol, diethyl ether, dimethyl sulfoxide, N,/V -dimethyl formamide, and tetrahydrofuran, and the 2 1 solvate with tetraethylene glycol, were studied [62], The relative stability of the different solvatomorphs was established using desolvation activation energies, solution calorimetry, and aqueous solubilities. It was found that although the nonaqueous solvates exhibited higher solubilities and dissolution rates, they were unstable in aqueous media and rapidly transformed to one of the monohydrates. 

Each of these free energy relationships employs the intrinsic barrier AGo+ as the disposable parameter. [The intrinsic barrier represents the activation energy for electron transfer when the driving force is zero, i.e., AG = AGo at AG = 0 or the equili-... 

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