Answer Happy

() 4. Using Table 18.4 (on page 59) and equation (18.59) or (18.62) (on page 63 or 64) in Chapter 18 of the pdf material, estimate the relative contribution of vibrational states of H20 to the heat capacity, explicitly, cywib/c, x100 (%), at a temperature of 310 K and discuss why the vibrational contribution is so small compared to translational or rotational contribution. The goal of this problem is to understand the heat capacity in viewpoint of the thermal excitability of a system in response to heat from an external energy source. (20 points)
ror TABLE 18.4 Values of the characteristic rotational temperatures, the characteristic vibrational temperatures, D, for the ground state, and the symmetry number, o, for some polyatomic molecules. The numbers in parentheses indicate the degeneracy of that mode. Molecule @./K ./K D./kJ mol"! 0 CO, 0.561 3360, 954(2), 1890 1596 2 Н,0 40.1, 20.9, 13.4 5360, 5160, 2290 917.6 2 NH, 13.6, 13.6. 8.92 4800, 1360. 4880(2), 2330(2) 1158 3 CIO 2.50, 0.478, 0.400 1360, 640, 1600 378 2 SO, 2.92, 0.495, 0.422 1660, 750, 1960 1063 2 NO 0.603 3200, 850(2), 1840 1104 1 NO 11.5, 0.624, 0.590 1900, 1080, 2330 928.0 2 CH 7.54, 7.54.7.54 4170,2180(2), 4320(3), 1870(3) 1642 12 CHCI 7.32, 0.637,0.637 4270, 1950, 1050, 4380(2) 1551 3 2140(2), 1460(2) CCI, 0.0823, 0.0823.0.0823 660, 310(2), 1120(3), 450(3) 1292 12
3-5 460,7)-(MT) (12), (18:57) 9(= 2л МkТ h 3/2 T V. σΘ. TOR elkar ) The energy is 2 3- /T vib. D U Nk Why-*+*+£) 3 2 - vib, 27 (18.58) 2 K&T and the heat capacity is 3-5 vih су Nk 2 + +£6) 3 2 + 2 vib, T (18.59) (1 - e/? e vib
1/2 Mk 71/2 13 q(V) = V. o TOLA rot, B rot.c (18.60) 3-6 ««v.n= (2018")"." () 24 , -0.) " +) 4.) -6 U /T vib D 3 2 3 + 2 Σ vib.) 2T + (18.61) Nk,T k.7 B and 31-6 су Vi vib, - 3+*+5G) 3 3 + + 2 w/ (1-e //72 (18.62) Nk vib