Mean vibrational energy diatomic molecule

Each of the vibrational degrees of freedom given by Eq. (6.1) would have a mean kinetic and potential energy of kT according to equipartition, and would contribute an amount R to the specific heat. As with diatomic molecules, however, the quantum theory tells us, and wc find... 

The Frank-Condon principle is based on the fact that the time of an electronic transition (of the order of 10 s) is shorter than that of a vibration (of the order of 10 s). This means that during an electronic transition the nuclei do not change their positions. This phenomenon can be illustrated using the Morse potential energy curves for diatomic molecules (Figure 2.17). The series of horizontal lines... 

The transition of a diatomic molecule from one electronic state to another takes place almost instantaneously, in a time that is very short compared with the period of molecular vibration. That is to say, the transition takes place with virtually no change in internuclear distance. For that reason, a transition can be indicated in energy level diagrams by means of a vertical line. 

There are excellent coincidences between vibration rotation transitions of the NO fundamental in the X n and some strong CO-laser lines near 5.2 jim. If we shine a few watts of this co-laser light into an absorption cell containing NO and Ar, those y- and p-bands occur at IR-laser power densities of less than 1 kW/cm. This means that there must be a way for the energy that is put into the fundamental vibration of the diatomic molecule to get up the ladder of vibrational states to the level of electronic excitation or to the dissociation limit [3,2/3,3]. For a diatomic molecule, particularly at these low power densities, multiphoton excitation is not possible. 

The process of vibrational excitation and deexcitation of a diatom in a collision with an atom represents a simplest example from the host of processes which are relevant to gas-phase chemical kinetics. Experimental techniques available now allow one to measure directly state-to-state energy transfer rate coefficients. Theoretically, it is possible to accomplish completely ab initio calculation of these coefficients. One can therefore, regard the existing models of the vibrational relaxation from a new standpoint as a means for helping to understand more clearly the dynamics of the energy transfer provided that all the models are related to a single fundamental principle. This is the Ehrenfest adiabatic principle as formulated by Landau and Teller in the application to the collisional vibrational transitions of diatomic molecules. 

Because molecules are not rigid, the rotational energy levels for diatomic molecules differ slightly from rigid-rotor levels. From (6.52) and (6.55), the two-particle rigid-rotor levels are = BhJ J -l-1). Because of the anharmonicity of molecular vibration (Fig. 4.6), the average internuclear distance increases with increasing vibrational quantum number v, so as v increases, the moment of inertia I increases and the rotational constant B decreases. To allow for the dependence of B on v, one replaces B in E by The mean rotational constant B for vibrational level v is - Ug v + 1/2),... 

The first values for the heat eapacities have been calculated, by taking into account for each mode, the mean energy corresponding to the equipartition of energy (see section 6.8). Using the values given, respectively, by eqnations [6.71] for the translation, [6.74] for the rotation and [6.78] for the vibration, we obtain for a diatomic molecule ... 

Here, 2 mol of the products are formed from the same number of moles of the reactants. Thus the number of translational degrees of freedom available to products and reactants is the same. Furthermore, CH3CI is a tetrahedral molecule like CH4, and HCI is a diatomic molecule like CI2. This means that vibrational and rotational degrees of freedom available to products and reactants should also be approximately the same. The actual entropy change for this reaction is quite small, A.S° = +2.8 J mol Therefore, at room temperature (298 K) the T AS° term is 0.8 kJ mol and thus the enthalpy change for the reaction and the firee-energy change are almost equal A//° = 101 kJ moF and AG° = 102 kJ moF. ... 

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