Critically energized molecule

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. 

When P(E) is not perturbed by the reaction, so that the distribution of critically energized molecules is that characteristic of equilibrium, the RRK model leads to a specific first-order rate constant of the form k = A exp —E /RT) where A is the frequency of internal energy transfer between oscillators. The Slater formulation in these circumstances gives k = V exp —E /RT ), both results being similar in form to the Arrhenius equation. The A factor in the RRK model represents the frequency of energy transfer between oscillators, which Jor weakly coupled oscillators would be of the order of their beat frequencies, or about 10 to 10 sec In the Slater model, V represents a weighted rms frequency of the normal frequencies which describe the decomposition [Eq. (X.6.1)]... 

While the Slater model does not lend itself to a simple solution in terms of the quantum theory, the fact that it agrees in form with the simple quantum model of Rice-Ramsperger and Kassel suggests that we can write the following expression for the mean rate of decomposition of a critically energized molecule of energy E E ... 

N2O5) represents a critically energized molecule of N2O6 with energy Et E, where E = AEJ.2. If we assume that the NO3 and NO2 species reach temperature eciuilibrium and further that NO3 and each (N206)J reach stationary states, then... 

Rate constants for the chemical exchange processes that occur in alkyl nitrites, cyclohexane, substituted cyclohexanes, sulfur tetrafluoride and formamide are pressure dependent. The mechanism for these thermally initiated, unimolecular gas-phase processes, reported by Lindemann in 1922, involves competition between the reaction and collisional deactivation of the critically energized molecule. A (Fqn [3]). 

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. ... 

Presumably the critically energized n-CJIio would be degraded to n-butane by collisional deactivation with various energy transfer molecules, M. 

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. 

By A or B we mean any energized molecule of A or B with energy in excess of the critical energy E for the reaction. A is differentiated from B rather arbitrarily in terms of the operational criterion that A is any form of active species which can be formed by activation of A and on de-... 

These anomalies appear understandable, however, when the decomposition of ozone is looked upon from the point of view of a unimolecular reaction at its low pressure limit. With three internal vibrations and a maximum of two active rotations, the mean lifetime of the average ozone molecule undergoing decomposition is expected to be very short (2) compared to collision times, even at 1-atm. pressure. In consequence, the stationary state concentrations of critically energized O3 molecules, which contribute to the over-all decomposition, are far below the concentrations calculated at equilibrium and the slow step in the reaction becomes the rate of activation of ozone. 

Therefore, in the treatment of Kassel and that of Rice and Ramasperger the only condition for energization is that the molecule must acquire the critical amount of energy E. ... 

A certain fraction of the molecules become energized by collision, i.e. gain energy in excess of a critical quantity Eq. M represents an added inert gas molecule (collision), or a second molecule of reactant. ki is taken to be energy-independent and is calculated from the simple collision theory equation. 

---