Consider rotation about the C~C bond in ethane. A crude model for torsion about this bond is the €œfree 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?

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E; for j = 0,1,±2,-.. 21