In general, the high-temperature limit for the rotational partition function is appropriate for almost all molecules at temperatures above their boiling point. Hydrogen is an exception to this generality because the moment of inertia is small due to the small mass of H. Given this, other molecules with H may also represent exceptions to this general rule. For example, methane (CH₄) has relatively modest moments of inertia (I_A = I_B = I_C = 5.31 × 10^–40 g cm²), and has a relatively low boiling point of T = 112 K.

a. Determine B_A, B_B, and B_C for this molecule.

b. Use the answer from part (a) to determine the rotational partition function. Is the high-temperature limit valid?