Diatomic molecule, heat capacity table

Table III contains the bond energies of some gaseous diatomic molecules. The heat capacities (Cp) for such molecules all range from near 7 cal./mole-°K. at room temperature to 9 cal./mole-°K. at 3700°K.

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. 

Some actual values of 0, as well as 6, are given in Table 29.1. Except for those diatomic molecules containing hydrogen, the values of 9 are indeed about 1 to 2 K. Thus these molecules have the classical value of the heat capacity at any temperature above about 2.5 K. 

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. 

If we sum the three contributions to calculate the value for the heat capacity at constant volume, as the characteristic temperatures of rotation are often lower than the Einstein temperature (see Table 7.3), the variation in the heat capacity, for example of a diatomic molecule, with temperature takes the form of the curve in Figure 7.12(c). At low temperatures, the only contribution is that of translation, given by 3R/2. Then if the temperature increases, the contribution of rotation, is added according to the curve in Figure 7.12(a) until the limiting value of this contribution is reached, then the vibrational contribution is involved until the molecule dissociates which makes the heat capacity become double that of the translational contribution of monoatomic molecules. The limiting value of the vibrational contribution is sometimes never reached. This explains why the values calculated in Table 7.2 are too low if we do not take into account the vibration and too high in the opposite case. 

The energy barrier for the reactions X2—>2X is simply taken as the dissociation energy of the molecular species. Morse curves use potential energies at 0 K hence we subtract the zero-point energy (ZPE) values from and add j)RT to account for the differences in heat capacities between two atoms and a diatomic molecule. The final result is also given for each reaction in Table 12.2. 

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