Inactive frequency of ethylene

To estimate the wave-number of the twisting mode of ethylene from measured values of the heat capacity and the known wave-numbers of the remaining eleven modes. 

The normal vibrational modes of ethylene, numbered according to the convention of Herzberg ( Infra-red and Raman spectra , van Nostrand, 1945) are shown in table 1. Since the molecule has a centre of symmetry no mode symmetrical with respect to this centre can be active in the infra-red and no antisymmetrical mode can be active in the Raman spectrum. The twisting mode number 4 is inactive in both. The most recent assignment (Crawford, Lancaster, and Inskeq , J. Chem. Phys. 1953, 21, 678) of wave-numbers for the remaining eleven modes are given. 

Measured values of C the molar heat capacity at constant pressure (Eucken and Parts, Z.physikal. Chem. B 1933, 20,184 Burcik, Ejreter, and Yost, J. Chem. Phys. 1941, 9,118) are given in table 2. There are also given the calculated contributions (compare problem 57) of the eleven known modes to the heat capacity. 

The molar heat capacity at constant pressure is given by the formula 

We shall tentatively use the alternative values 0 = 1400 deg and 04 = 1500 deg for the twisting mode. With these values we calculate the contribution of this mode to the heat capacity and add this to the contribution of the other 11 modes given in table 1. 

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