Energized molecule

Extensive discussions of procedures for energizing molecules are given elsewhere [5],... 

If the stoichiometric equation for unimolecular reaction is A -> B + C, and if the energized molecules are denoted by A, the Lindemann mechanism consists of the following sequence of events. 

The formation of C2H6 must first involve the formation of the energized molecule C2H ... 

In case of Hinshelwood s modification both k2 and (k lk ) have been treated as independent of E, i.e. amount of energy in the energized molecule. In Hishelwood s treatment the critical energy El is involved, not E. ... 

Rice and Ramsperger and independently Kassel proposed the theories to explain unimolecular reaction, in which both (k2) and (kfk[) have been treated as dependent on the energy of an individual energized molecule E. These theories jointly are referred as RRK theory. According to the theory the expression for the first order rate constant given by Lindemann theory i.e. 

In equation (4.68), dk is a canonical rate constant, relating to energized molecule having energy between E and E + dE. The expression can be integrated between the limits from minimum energy ( Eq ) to infinity to get the ordinary rate constant k, i.e. 

The once rather ephemeral transition state construct derived from logic and statistical mechanics, a virtual entity, has emerged as an experimental reality. Structural changes associated with specific nuclear vibrations in energized molecules in the transition region may be correlated with reaction dynamics. 

Energizing collisions are those with sufficient energy that molecule C obtains enough internal energy that it goes on to react. In the limit of sufficiently low pressure, the rate of energizing collisions becomes small relative to the rate of reaction of an energized molecule. As a result, in the low-pressure limit, the rate of reaction becomes bimolecular, that is, proportional to the C-M collision rate. 

The two thermodynamic quantities AS° and A H° are the net difference in standard-state entropy and enthalpy of the energized molecule C and the stabilized reactant molecule C. 

Activated or energized molecules have energy equal to, or greater than, the critical energy. They can be anywhere on the surface, but can only become activated complexes by rearranging the relative positions of the atoms in the reaction unit (X—-Y—-Z) until the critical configuration is reached. 

This model makes a simple distinction between molecules without the critical energy, and those with at least the critical energy, i.e. activated or energized molecules. It takes no account of the fact that activated molecules actually do have vibrational levels of differing energies and that the question is it as easy to activate a molecule to the first vibrational level above the critical as it is to activate the molecule to a high vibrational level could be asked. Intuitively this seems unlikely. As shown in the analysis of Problem 4.20 this assumption is unlikely to be correct. 

A gaseous molecule, A, can undergo a unimolecular decomposition into C, if it is supplied with a critical amount of energy. An energized molecule of A, designated as A, can be formed by a collision between two ordinary A molecules. Competing with the unimolecular decomposition of A into C is the bimolecular deactivation of A by collision with an ordinary A molecule. 

Function (2.2) can be considered as an empirical model used to best fit the experimental concentration-time data. In practice, laws different from (2.2) are also encountered, especially when dependence on the concentration is considered however, a simple theory based on the kinetic theory of gases can only explain the simplest of these empirical rate laws. The general idea of this theory is that reaction occurs as a consequence of a collision between adequately energized molecules of reactants. The frequency of collision of two molecules can explain simple reaction... 

In a true unimolecular reaction, the energized molecules are formed by absorption of electromagnetic radiation see Section 7.2.2. In an apparent unimolecular reaction, the first step is the formation of the energized molecules by collisions with other molecules. We consider in the following subsection the interplay between the formation of energized molecules—by bimolecular collision—and their subsequent reaction. 

Fig. x.4. Schematic representation of the motion in phase space of the internal coordinates of a critically energized molecule with a single possible mode of decomposition. Bounding surface is one of constant potential energy. 

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