A more formal way of arriving at the value of the symmetry number is to note that is the order (the number of elements) of the rotational subgroup of the molecule, the point group of the molecule with all but the identity and the rotations removed. The rotational subgroup of H20 is {E, C2}, so 0= 2. The rotational subgroup ofNH3 is {E, 2C3}, so 0"= 3. This recipe makes it easy to find the symmetry numbers for more complicated molecules. The rotational subgroup of CH4 is obtained from the T character table as {E, 8C3, 3C2}, so 0"= 12. For benzene, the rotational subgroup of D6h is {E, 2C6, 2C3, C2' 3C;, 3C;}, so 0= 12.

(a) Estimate the rotational partition function of ethene at 25°C given that A=4.828 cm", B= 1.0012 cm-I, and C= 0.8282 cm-I.

(b) Evaluate the rotational partition function of pyridine, CsHsN, at room temperature (A = 0.2014 cm-1, B = 0.1936 cm-1, C= 0.0987 cm-1).