The unimolecular rate constant

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

Note that in the low pressure limit of iinimolecular reactions (chapter A3,4). the unimolecular rate constant /fu is entirely dominated by energy transfer processes, even though the relaxation and incubation rates... 

Thus, the unimolecular rate constant k s can be found from a plot of k p vs. (D-1. Expressing to as 3.3 x 107 torr-1 s-1 x pressure (torr) and using the Su-Chesnavich13 capture rate constant of 2.28 x 10-9 cm3 molecule-1 s-1 for k3S, a value of 0.083 ps-1 was determined for k s from experiments in the 3-10 torr range. 

QET delivers the following expression for the unimolecular rate constant... 

Marcus and Rice6 made a more detailed analysis of the recombination from the point of view of the reverse reaction, the unimolecular decomposition of ethane, C2Ha - 2CH3. By the principle of microscopic reversibility the transition states must be the same for forward and reverse paths. Although they reached no definite conclusion they pointed out that a very efficient recombination of CH3 radicals would imply a very high Arrhenius A factor for the unimolecular rate constant of the C2H6 decomposition which in turn would be compatible only with a very "loose transition state. Conversely, a very low recombination efficiency would imply a very tight structure for the transition state and a low A factor for the unimolecular decomposition. 

Lindemann s treatment of unimolecular reactions was introduced in Section 9.4. This early analysis was developed to explain the pressure dependence of the observed unimolecular rate constant fcunj. At sufficiently high pressures, kUni is found to be independent of pressure (although it is typically a very strong function of temperature). However, in the limit of very low total pressure, the unimolecular rate constant is found to depend linearly on the pressure. 

Investigation of this reaction isolated in an N2 matrix at 10-20 K has shown that the apparent activation energy is smaller than 0.11 kcal/mol the unimolecular rate constant for N0-03 reactant complexes prepared in this way is 1.4 x 10-5 s-1 at 12 K. Experiments carried out using ozone enriched with 180 have revealed no observable isotope effect. 

Thus the measured unimolecular radiative lifetime is the reciprocal of the sum of the unimolecular rate constants for all the deactivation processes. The general form of the equation is given by... 

Before we go on, we note that it is easy to interpret the physical significance of the unimolecular rate constant. The integrated rate law takes the form... 

Second, we calculate the unimolecular rate constant at the internal energy E via the RRKM theory. We use Eq. (7.54), where the rotational energy is neglected and where the sum and density of vibrational states are evaluated classically. Thus at E = 184 kJ/mol we get... 

The (high-pressure) pre-exponential factor for the ring-opening of cyclo-butene into butadiene is 1013 4 s 1, and the activation energy is 137.6 kJ/mol. Using the RRK theory calculate the unimolecular rate constant for the reaction at an excitation energy of 200 kJ/mol. 

The unimolecular rate constant k(E) is described within the framework of RRKM theory. In the following, we neglect the rotational energy in HCN as well as in the activated complex. The classical barrier height is Ec = 1.51 eV. 

After the high-pressure limit has been established, the unimolecular rate constants (kum) obtained are plotted versus pressure to generate the experimental falloff curve. The RRKM specific rate constants [703] are calculated from ... 

Both these processes can be considered to occur in several distinct stages as follows (i) formation of precursor state where the reacting centers are geometrically positioned for electron transfer, (ii) activation of nuclear reaction coordinates to form the transition state, (iii) electron tunneling, (iv) nuclear deactivation to form a successor state, and (v) dissociation of successor state to form the eventual products. At least for weak-overlap reactions, step (iii) will occur sufficiently rapidly (< 10 16s) so that the nuclear coordinates remain essentially fixed. The "elementary electron-transfer step associated with the unimolecular rate constant kel [eqn. (10)] comprises stages (ii)—(iv). 

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