Diatomic molecule, heat capacity frequency

Heat capacities of polyatomic molecules can be explained by the same arguments. As discussed in Chapter 3, bond-stretching vibrational frequencies can be over 100 THz. At room temperature k T heat capacity (which explains why most diatomics give cv % 5R/2, the heat capacity from translation and rotation alone). Polyatomic molecules typically have some very low-frequency vibrations, which do contribute to the heat capacity at room temperature, and some high-frequency vibrations which do not. 

K the value of RT is approximately 2.5 kJ mol"1,) However Aevib is usually much greater than kT and under these circumstances vibrations do not contribute significantly to heat capacity (Fig. 9.7). Thus for nitrogen at room temperature the rotational contribution is approximately iiTand the vibrational contribution almost zero. Thus Cv 5/2)1 and y w 7/5 = 1.40 as opposed to the classical prediction of 1,29. For iodine the vibrational spacings are closer (Table 9.1) and we would predict y 1.29 in accord with the classical value. If the temperature is varied the heat capacity of a diatomic or polyatomic gas may show steps as the contributions from rotations and vibrations rise as the energy separations become comparable to kT, The positions of the steps depend on the moments of inertia and the vibrational frequencies of the molecules. 

Qualitatively sketch the heat capacity of an ideal gas of diatomic molecules as a function of temperature. Indicate the characteristic temperatures (in terms of vibrational frequency, moment of inertia, and so on) where various degrees of freedom begin to contribute. 

The quantity , = hcv/k is called the vibrational temperature, wha-e h is Planck s constant, c is the speed of light, k is Boltzmann s constant, and v is the vibrational frequency in wave numbers (cm ). The vibrational frequencies for F2 and I2 are 919 and 214 cm, respectively. Use the formula above, together with the equipartition values for the translational and rotational contributions, to calculate the constant-pressure heat capacity for these two diatomic molecules. Compare your results with the expraimental values given in Table 7.4. 

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