Energised molecules

Thermal unimolecular reactions usually exhibit first-order kinetics at high pressures. As pointed out originally by Lindemann [1], such behaviour is found because collisionally energised molecules require a finite time for decomposition at high pressures, collisional excitation and de-excitation are sufficiently rapid to maintain an equilibrium distribution of excited molecules. Rice and Ramsperger [2] and, independently, Kassel [3] (RRK), realised that a detailed theory must take account of the variation of decomposition rate of an excited molecule with its degree of internal excitation. Kassel s theory is still widely used and is valid for the chosen model of a set of coupled, classical, harmonic oscillators. 

A more general discussion of the dependence of the decomposition rate on internal energy was developed by Marcus and Rice [4] and further refined and applied by Marcus [5] (RRKM). Their method is to obtain the reaction rate by summing over each of the accessible quantum states of the transition complex. The first-order rate coefficient for decomposition of an energised molecule is shown to be proportional to the ratio of the total internal quantum states of the transition complex divided by the density of states (states per unit energy) of the excited molecule. It is a great advance over previous theory because it can be applied to real molecules, counting the states from the known vibrational frequencies. 

These general aspects are due originally to Lindemann [1], who first pointed out that a finite time is required for the decomposition of energised molecules. 

In other words, the vibrational energy of A exceeds the threshold energy for the overall reaction A —> Products. It must be borne in mind that A is simply a molecule in a high vibrational energy level and not an activated complex. In the first step, the energised molecule A is produced by collision with another molecule A. 

N2O5J represents a critically energised molecule of N2O5. 

Energised molecule A returns to a stable state by collision with a molecule of A... 

To find the rate of formation of the products from A molecules with specified internal energy Ei one equates the rate of production of such molecules by process (1.22) to their rate of removal by (1.-22) and (1.23), and then writes the rate of reaction as the product of the rate coefficient for reaction of A molecules with internal energy and the steady-state concentration of these critically energised molecules. This procedure yields the following expression for the rate of reaction ... 

The energised molecule may undergo de-energisation by collisions with a normal molecule, or it may undergo a reaction of molecularity equal to one to form products. There are, therefore, three distinct processes in this mechanism with their own rates (i) the rate of energisation is (ii) A can be de-energised at a rate i[A ][A] and (iii) A can be converted into products at a rate 2 [A ]. 

The highly energised molecule A has a metastable nature due to reasons associated with the slowness of the internal energy flow or, with the insight provided by the RRKM theory, to an entropy barrier arising from the improbability of concentrating vibrational... 

When 8 is sufficiently high, every energised molecule A is essentially an activated species A, but this conditions depends on the value of s as shown in Figure 8.4. Figure 8.5 illustrates the apphcation of Lindemann-Christiansen-Hinshelwood, RRK mechanisms to the isomerisation of cyclopropane as a function of pressure [4]. 

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