Hindered rotation of ethane

From the heat capacity of ethane to confirm the nature of the restricted internal rotation. 

Measurements of the heat capacity of ethane over the temperature range 94 K to 292 °K have been made by various authors (Eucken and Parts, Z. phj ikal. Chem. B1933,20,184 Hunsmann, Z. physikal. Chem. B 1938, 39, 23 Kistiakowsky and Nazmi, J. Chem. Phj. 1938, 6, 18 Kistiakowsky, Lacher, and Stitt, J. Chem. Phys. 1939, 7, 289). Their values for the heat capacity Cy at constant volume are summarized in table 1 

The vibrational wave-numbers , and characteristic temperatures of ethane are given (Hansen and Dennison, J. Chem. Phys. 1952, 20, 317) in table 2. There are six non-degenerate modes including the internal rotation (mode 4) and six pairs of doubly-degenerate modes. The potential energy u restricting the internal rotation has three equal minima and three equal maxima. It may be represented approximately by the form 

We add the contribution to CfR of the internal rotation to those of the other 17 modes and we further add IJ for the three translational and li for the three rotational degrees of freedom. We thus construct table 4. We plot these calculated values of CjR against T in fig. 2 and on the same diagram we plot the experimental values of CjR. We see that there is good agreement over the whole range of temperature. 

The broken curve in fig. 1 represents the calculated contribution to CjR of a vibrational mode with ta = 275 cm We see that at temperatures between 80 K and 180 °K this contribution is nearly the same as that calculated for the restricted rotation, but at higher temperatures the two curves diverge appreciably. 

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