Stepwise kinetics activation energy

The thermodynamic form of kinetic equations aUows us to easily find the apparent activation energy, EaS, for the stationary occurrence of stepwise processes, especiaUy in the case of their kinetic irreversibility. For instance, if stepwise process (1.54) goes from left to right and is kineticaUy irrevers ible in whole—that is, R P—and if Sum is the smaUest quantity of aU 8 in the transformation chain, then... 

In the case under consideration, the rate-determining and rate-limiting steps of the overall catalytic process are identical, since both are steps with minimal ,. Like the case of noncatalytic transformations (see Section 1.4), the apparent activation energy, Eas, of the catalytic stepwise reaction (4.3) is easy to determine when the stepwise process is kinetically irreversible R P. Evidently,... 

Let us determine the apparent activation energy of the stepwise process in this case under additional conditions of the kinetic irreversibility of the catalyzed process at... 

We can find the apparent activation energy, Eas, of the process by considering separately the limiting cases of controlling the concentration of complex K2 by the "external reactants either R or P and, as usual, under the condition of the kinetic irreversibility of the stepwise process at R P. 

Let us find the rate and apparent activation energy of the stationary process in a particular situation of the kinetically irreversible stepwise reaction of the CO oxidation, step 1 being the rate-limiting stage and intermediate K2 being dominant on the surface. The stationary rate of the overall stepwise process (4.60) is... 

Temperature may not always be raised in a linear fashion. In the case of CRT A (Controlled Rate Thermal Analysis), the heating rate is varied in such a manner as to produce a constant rate of mass loss. Alternatively a sinusoidal temperature rise is superimposed on the linear rise this is known as Modulated TG and allows the continuous calculation of activation energy and pre-exponential factor during a run. Sometimes a Temperature Jump (or stepwise isothermal) " is used, where temperature is held constant for a time, then jumped rapidly to a higher constant temperature (usually quite close in temperature). All of these procedures are supposed to help in the determination of kinetics of reaction. Another system accelerates the temperature rise when no mass loss is experienced, i.e. between reactions. The rate is slowed to a low value during mass loss. Some manufacturers call this High Resolution TG and an example follows. 

As shown by Eq. (8), the kineties governing a thermal decomposition event depend on time, temperature, and rate of decomposition. TG experiments performed at a constant heating rate allow temperature and time to be interehanged in the ease of first order kinetics and one-step decompositions. ] Hi-Res TGA allows the determination of kinetic parameters such as activation energy and reaction order for each step in multiple component materials using four different TG approaches I constant heating rate, constant reaction rate, dynamic heating rate, and stepwise isothermal. 

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