The high-temperature limit for the rotational partition function is valid for all molecules above their boiling point except hydrogen; this is because hydrogen has the smallest moment of inertia, hence the largest rotational constant. One might question this conclusion for methane (CH4); it also has a very small moment of inertia (only the hydrogens contribute since the carbon is at the center of mass) and a low boiling point- 111.7 K. The three moments of inertia of methane are equal: la = p = Ic = 5.313 x 10-40 g cm².

a. Calculate the rotational temperature of this molecule.

b. Calculate the rotational partition function of methane at its boiling point (the symmetry number is o = 12)