Question

Calculating a vibrational partition xample 15B.2 Table 15B mbers of the three normal modes of H,O are 1594.8 cm-1, and 3755.8 cm. Evaluate the vibra function s of H,O area 3656.7 cm anartition function at 1500 K vibra.H 15B.15 for each mode, and then form ethod Use P2.6m for eqn 1 ean Metho duct of the three contributions. At 1500 K, More va the product ofthe Ve draw up the following table displaying the contri- the pa butions of each mode: expon Mode: lm- 3656.7 3.507 1.031 1594.8 1.530 1.276 3755.8 3.602 1.028 That The overall vibrational partition function is therefore 1.031x1.276x1.028-1.352 The The three normal modes of H,O are at such high wavenum- bers that even at 1500 K most of the molecules are in their ex vibrational ground state. However, there may be so many nor- tu mal modes in a large molecule that their overall contributionat may be significant even though each mode is not appreciably excited. For example, a nonlinear molecule containing 10 atoms has 3N-6 24 normal modes (Topic 12E). If we assume a value of about 1.1 for the vibrational partition function of one normal mode, the overall vibrational partition function is about f (1.1)*-9.8, which indicates significant vibrational excitation relative to a smaller molecule, such as H,0. ab ti 3.7 Repeat the calculation for CO2, where the vibrational wavenumbers are 1388 cm-1, 6674 cm-, and 2349 cm-1, the second being the doubly-degenerate bending Answer: 6.79 p/easシ/make oteble like

Answer 1

αγ e 2KT enea Kf 2 3 49 3 88 Cm 021x to x2 349 x 13 33 = 0.69089 K T 328 o 64087 33238 2-1134 Az KT 4- 602x lOCm

= (.353) (2-1131) ( ri, 구) ニ 3, 2058