Rate limiting step apparent activation energy

In principle this is derived from an Arrhenius plot of In r+ versus 1/T but such a plot may deviate from a straight line. Hence, the apparent activation energy may only be valid for a limited temperature range. As for the orders of reaction, one should be very careful when interpreting the activation energy since it depends on the experimental conditions. Below is an example where the forward rate depends both on an activated process and equilibrium steps, representing a situation that occurs frequently in catalytic reactions. 

Regarding the first problem, the most elemental treatment consists of focusing on a few points on the gas-phase potential energy hypersurface, namely, the reactants, transition state structures and products. As an example, we will mention the work [35,36] that was done on the Meyer-Schuster reaction, an acid catalyzed rearrangement of a-acetylenic secondary and tertiary alcohols to a.p-unsaturatcd carbonyl compounds, in which the solvent plays an active role. This reaction comprises four steps. In the first, a rapid protonation takes place at the hydroxyl group. The second, which is the rate limiting step, is an apparent 1, 3-shift of the protonated hydroxyl group from carbon Ci to carbon C3. The third step is presumably a rapid allenol deprotonation, followed by a keto-enol equilibrium that leads to the final product. 

Usually, the attack of the nucleophile on the bromonium ion is a fast process. On the other hand, kinetic investigations100 on the bromination shown in Scheme 19 indicate that bromonium ion formation (i.e. the ionization of the CT complex 45) cannot be the RDS. The apparent activation energy for the overall bromination (and the experimental reaction order in bromine, which changes by changing the temperature) confirms the neutralization of the bromonium ion to form the product (47) in a step limiting the observed rate of the overall process. 

Rate-Limiting Steps, Rate-Determining Parameters, and Apparent Activation Energy of Simpie Schemes of Chemicai Transformations... 

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,... 

Thus, the apparent activation energy of the catalyzed stepwise reaction is equal to the activation energy of the rate-limiting step 2 plus the standard enthalpy of the preceding (preadsorption) step A,EI° = AfElj AfElj eEIr- The latter enthalpy is equal to the heat of desorption of the initial reactant R (figure 4.3a) from the first reaction intermediate Ki. 

As before, the apparent activation energy is equal to the activation energy Ea lim of the rate-limiting step plus the sum of standard enthalpies A,H°r rate-limiting step. 

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... 

Let us find the apparent activation energy of the stationary process provided that the overall process is kinetically irreversible, step 2 is rate-limiting, and the catalyst surface is covered predominantly by intermediate K3 Under this statement of the problem, step 2 is kinetically irreversible, while the preceding step 1 being considered partially equilibrium that is, R = N2 K Thus,... 

Find the apparent activation energy of the stationary catalytic process when step 1 is rate limiting and the active center coverage by intermediate K2 is high. What are the rate determining process parameters in this case 3. The stepwise catalytic process... 

Essential advantages of the thermodynamics of non equilibrium pro cesses are the possibility of correct quantitative explanation of important concepts of rate limiting and rate determining steps at complex chemical transformations the possibility of the use of one effective transformation instead of a series of the reaction intermediate transformations, without the loss of the correctness when analyzing a specific influence of this trans formation series on the total course of the complex process as weU as the possibility of analyzing the influence of thermodynamic parameters of both external reactants and of reaction intermediates on some important para meters of complex reactions like apparent activation energy, etc. 

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