Activation energy kinetic theory

If the fraction of sites occupied is 0, and the fraction of bare sites is 0q (so that 00 + 1 = 0 then the rate of condensation on unit area of surface is OikOo where p is the pressure and k is a constant given by the kinetic theory of gases (k = jL/(MRT) ) a, is the condensation coefficient, i.e. the fraction of incident molecules which actually condense on a surface. The evaporation of an adsorbed molecule from the surface is essentially an activated process in which the energy of activation may be equated to the isosteric heat of adsorption 4,. The rate of evaporation from unit area of surface is therefore equal to... 

Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

FIGURE 13.25 (a) In the collision theory of chemical reactions, reaction may take place only when two molecules collide with a kinetic energy at least equal to a minimum value, /rmn (which later we identify with the activation energy), (b) Otherwise, they simply bounce apart. 

According to the collision theory of gas-phase reactions, a reaction takes place only if the reactant molecules collide with a kinetic energy of at least the activation energy, and they do so in the correct orientation. 

In an earlier note (p. 9) we mentioned the occurrence of overvoltage in an electrolytic cell (and overpotentials at single electrodes), which means that often the breakthrough of current requires an Uappl = Eiecomp r] V higher than Ehack calculated by the Nernst equation as this phenomenon is connected with activation energy and/or sluggishness of diffusion we shall treat the subject under the kinetic treatment of the theory of electrolysis (Section 3.2). 

At the heart of this form of kinetic theory is the activated complex. In this context, the word activated simply means a species brimming with energy, and which will react as soon as possible in order to decrease that energy content. 

In classical kinetic theory the activity of a catalyst is explained by the reduction in the energy barrier of the intermediate, formed on the surface of the catalyst. The rate constant of the formation of that complex is written as k = k0 cxp(-AG/RT). Photocatalysts can also be used in order to selectively promote one of many possible parallel reactions. One example of photocatalysis is the photochemical synthesis in which a semiconductor surface mediates the photoinduced electron transfer. The surface of the semiconductor is restored to the initial state, provided it resists decomposition. Nanoparticles have been successfully used as photocatalysts, and the selectivity of these reactions can be further influenced by the applied electrical potential. Absorption chemistry and the current flow play an important role as well. The kinetics of photocatalysis are dominated by the Langmuir-Hinshelwood adsorption curve [4], where the surface coverage PHY = KC/( 1 + PC) (K is the adsorption coefficient and C the initial reactant concentration). Diffusion and mass transfer to and from the photocatalyst are important and are influenced by the substrate surface preparation. 

Within the temperature range from 10 to 40°C, both PAMAM dendrimers in EDA [5] and PPI dendrimers in water [22] showed a linear relationship between In r and /T, in good agreement with the kinetic rate theory of flow [46]. The apparent activation energies of flow (En) were constant and independent of temperature, and it was shown for PAMAM/EDA systems that the dependence of En on solution concentration was linear for all generations examined [5]. This was considerably different from the typical relationships for the solutions of linear and/or randomly branched chain polymers, where a break in the slope of... 

Considering again Eq. (2.6) and referring to E as an activation energy, attention is focused on the collision rate Zab> which from simple kinetic theory can be represented by... 

The kinetic parameters for the reactions of both methanol and ethanol listed in Tables VIII-XI show some interesting features. First, the frequency factors for the decomposition of the alkoxide intermediates to form the aldehydes were observed to be within an order of magnitude of 10 sec as is expected from simple transition state theory. The activation energy for the transfer of the hydrogen atoms from the alkoxide to the surface was... 

Recently, transition state theory calculations were applied to a class of reactions involving OH radicals and haloalkanes, again to account systematically for the expected curvature in Arrhenius plots for these reactions (Cohen and Benson, 1987a). Subsequently, empirical relationships were also derived for the a priori determination of pre-exponential factors (A) and activation energies ( ) based on an assumed T dependency of the pre-exponential factor (Cohen and Benson, 1987b). This and related studies clearly illustrate the broad utility of transition state theory in the systematic development of detailed chemical kinetic mechanisms. 

Substituting (54) into (55), we obtain a kinetic equation typical of activated adsorption (with an activation energy M x), although in our case there may be no potential barrier near the surface. This is a result of the increase in the number of adsorption centers on heating. In the usual theories of... 

Having described the equilibrium structure and thermodynamics of the vapor condensate we then re-examine homogeneous nucleation theory. This combination of thermodynamics and rate kinetics, in which the free energy of formation is treated as an activation energy in a monomer addition reaction, contains the assumption that equilibrium thermodynamic functions can be applied to a continuum of non-equilibrium states. For the purpose of elucidating the effects of the removal of the usual approximations, we retain this assumption and calculate a radially dependent free energy of formation. Ve find, that by removing the conventional assumptions, the presumed thermodynamic barrier to nucleation is absent. 

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