Translational energies, average product

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3.4.82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for tire energy dependence of the effective reaction cross section. They often fonn the basis for the interpretation of the temperature dependence of thennal cross sections. Figure A3.4.5 illustrates several cross section models. 

Table B2.5.3. Product energy distribution for some IR laser chemical reactions. (E ) is the average relative translational energy of fragments, is the average vibrational and rotational energy of polyatomic fragments, and/ is the fraction of the total product energy appearing as translational energy [109],...

The impact operator corrected in such a way still remains semiclassical though the requirements of detailed balance are satisfied. It is reasonable provided that the change of rotational energy is small on average, relative to translational energy ey — ej < ikT, where the overbar means averaging performed over the distribution of products after collision. 

Thus, we see that overall rate constant that is determined from traditional bulk kinetics experiments for an elementary reaction is an average of microscopic observables, which are dependent on internal states of the reactants and products, the relative translational energy of reactants and the product scattering angle. Their relation may be summarised as follows ... 

With the various experimental techniques, the actual measurement concerns product ions after they have been extracted from the source. That is to say, the decomposition occurs in a source before acceleration, but what is actually measured is translational energy after the product ion has been accelerated. To be still more precise, it is, in most cases, the distribution of the component of velocity along the axis of the mass spectrometer (i.e. in the direction in which the ions were accelerated out of the source) which is, in effect, measured. The measured quantity is, therefore, distinct from the translational energy distribution of the product ion (called the laboratory distribution ) as it was upon its formation in the source (i.e. before acceleration). The measured distribution needs to be analysed to obtain the laboratory distribution. Working with means or averages is much simpler, but there are possible pitfalls (see the discussion of the time-of-flight technique below). 

The translational energy distribution of the product ion in the source (laboratory distribution) is still not what is needed. What is required is the distribution of energy released in the centre-of-mass framework. The conversion of the translational energy distribution in the laboratory framework to the energy release distribution in the centre-of-mass is not a simple exercise [723]. If mean or average energies are considered, however, an expression for conversion from laboratory to centre-of-mass coordinates can be written down [311]. 

To obtain the reaction attributes for a particular set of vibrational, rotational and translational energies, many trajectories were simulated at given values of N2 vibrational and rotational quantum numbers and N2-O relative translational energy. The N2 molecular orientation, vibrational phase and impact parameter were chosen randomly for each trajectory. The reaction attributes were then determined by averaging the outcomes of all collisions. The information obtained is state-specific, so for example, the energy distributions of the reactant and product molecules can be determined. The method used to calculate the vibrational and rotational state of the product molecule is outlined in Ref. 67. With the QCT approach, reaction cross sections were determined solely from the precollision state. The method knows nothing of the fluid flow environment and so... 

Fig. 12. Average final translational energies of hyperthermal OH products as a function of exit angle, corresponding to (E,) = 47 kJ mol" (top panel) and (E,) = 21 kJ mol" (bottom panel) and to three incident angles, 60°, 45°, and 30°. Solid lines connect the data points. Representative error bars are shown.

The use of laser-induced fluorescence as a molecular beam detector for the measurement of internal state distributions of reaction products is presented and applied to the reactions of barium with the hydrogen halides. It is found that most of the reaction exoergicity appears as translational energy of the products and that the total reactive cross section is positively correlated with the average fraction of the exoergicity appearing as vibrational excitation. 

Figure 4- Average fractions of energj- in products as a function of collision energj- for the H elimination reaction channel in the O( P) + methane, ethane and propane reactions. Thick lines show average fractions of product translational energy and thin lines are for average fractions of internal cnergv in the oxyradical molecules.

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