Rotation-vibration energy, molecular internal

The equipartition principle is a classic result which implies continuous energy states. Internal vibrations and to a lesser extent molecular rotations can only be understood in terms of quantized energy states. For the present discussion, this complication can be overlooked, since the sort of vibration a molecule experiences in a cage of other molecules is a sufficiently loose one (compared to internal vibrations) to be adequately approximated by the classic result. 

Table A4.1 summarizes the equations needed to calculate the contributions to the thermodynamic functions of an ideal gas arising from the various degrees of freedom, including translation, rotation, and vibration (see Section 10.7). For most monatomic gases, only the translational contribution is used. For molecules, the contributions from rotations and vibrations must be included. If unpaired electrons are present in either the atomic or molecular species, so that degenerate electronic energy levels occur, electronic contributions may also be significant see Example 10.2. In molecules where internal rotation is present, such as those containing a methyl group, the internal rotation contribution replaces a vibrational contribution. The internal rotation contributions to the thermodynamic properties are summarized in Table A4.6.

In the calculation of the thermodynamic properties of the ideal gas, the approximation is made that the energies can be separated into independent contributions from the various degrees of freedom. Translational and electronic energy levels are present in the ideal monatomic gas.ww For the molecular gas, rotational and vibrational energy levels are added. For some molecules, internal rotational energy levels are also present. The equations that relate these energy levels to the mass, moments of inertia, and vibrational frequencies are summarized in Appendix 6. 

Generally in molecular beam studies, both beams have comparable velocities and intersect one another at 90°, and thus the CM velocity vector points at a wide angle intermediate between the two beams. Measurement of the displacement of the laboratory angular distribution of products from the centre-of-mass vector enables an estimate of the velocity of the products to be derived. Reaction products have been velocity analysed (e.g. see refs. 8 and 231) and the results support the view that the product relative translational energy is usually within ca. 1 kcal mole of the reactant relative translational energy. Most of the alkali metal reactions studied to date are exothermic, thus the products must be internally excited. It is believed [8] that, for most reactions, the internal excitation consists mainly of vibrational excitation however, the partition of the vibrational energy between, for example, KI and CH3 is as yet unknown. There are a few exceptions, e.g. the K + HBr reaction where KBr is rotationally excited rather than vibrationally excited [8], and the... 

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