Question

3. Acetylene is a linear molecule with the C-C bond length of 120.3 pm and C-H bond legth of 106.0 pm. The fundamental frequencies of the mormal modes are vi = 1975 cm , V2 = 3370 cm , v = 3277 cm , VA = 729 cm", and vg = 600 cm . The normal modes V and vg are doubly degenerate. (a) [7 points) Calculate the moment of intertia, rotational temperature and vibra- tional temperature of each normal mode. (b) (8 points) What is the average energy of 1 mol acetylene at 300K? Ignore the electronic contribution to the total energy.

Answer 1

(a) hou = 2 Iw2 It moment of inentia chau: I (2976)2 (:.6=2Tcw) :. Is alicu Rotational temparature Ors hz 2KBI 81 kg 1 Viborational tempoolatude: Ove heu free. Ccm-1) I (kgm2) Orck) Ouck) 1975 S. 665x10-49 71.215 2844.859 8370 3-320x10-49 1219.566 4854.265 - om s i 3277 3.44X10-49 1186-676 4720.305 1535x1048 262.519 1050.077 364.96.1 1-865 X1048 216.065

(b) average @ energy of a molecule - 912 km = 312 x 1-38 X10*23x300 6.21X10-21.)