Consider rotation about the C~C bond in ethane. A crude model for torsion about this bond is the “free rotor” model where rotation is considered unhindered. In this model the energy levels along the torsional degree of freedom are given by:

In this expression I is the moment of inertia. Using these energies, the summation expression for the corresponding partition function is:

where σ is the symmetry number.

a. Assuming that the torsional degree of freedom is in the high-temperature limit, evaluate the above expression for Q.

b. Determine the contribution of the torsional degree of freedom to the molar constant volume heat capacity.

c. The experimentally determined C_V for the torsional degree of freedom is approximately equal to R at 340. K. Can you rationalize why the experimental value is greater that than predicted using the free rotor model?