Question

3. The HCN molecule is a linear molecule, and the following constants are determined spectroscopically: moment of inertia, I = 18.816 x 10-47kg.m2, and three vibrational frequencies, 7 = 2096.7 cm ' (HC-N stretch), üz = 713.46 cm (H-C-N bend, two- fold degeneracy), Dz = 3311.47 cm-' (H-CN stretch). (a) Calculate Orot and Ovit. (b) Calculate the molecular partition function of HCN at 300K and 1 atm. The degeneracy of electronic ground state is 1. (c) Compute the constant volume heat capacity (J/mol K) at T = 3000 K. Note that the temperature is very high.

Answer 1

Sol: Given data, - The How molecule is a lineas molecule. I = 18.816x1047 kg. me and three Vibrational foequencies Vi 2096,7 cm! 7. = 713.46 cm! V = 3311.47 cm Calculate Partition Osot and Oub. function for gotation, | Int 2;09/07 § C251) 23620 Jao Where gg is a rotation degeneracy g; = (2J+) and g; - (2x1 +1) =3

I got (axiti) 1 (1+1), ta . 18.816x1097 Kg x 300 90042 3. Exp / -ax(6.63 x1024) 2x2x(3.143 x 18.8166109 1.38 x 18 82300 ) (-ax(6.63)? ( 243.1432x18.81643 ) - 9.85- Loot 2 3. Exp the KBT where Exp: 1 2 3 Expo & &t az cu 2. cv ( samog ). 1.com () Perseus (13.3 is ). 1cop

explota zc (2096.7+ 2713.46 +3311.471 1.38 x103 X300 1-expa Frost Calculate Seperate -34 8e131.63 3x10 X3.0x10x8121.63 exp (- 22 Ehazcu -- exp 1.38 x 10 23 x 300 20.823 Hence. I vin 0.823 x - 0.676 20.823 x 1,479289940828403 2 1.217455 1.92 b) function Calculate the molecular pastion of tw at 3ook and I atom. Molecular pastion-function, 2 2 2007 - 2 uib? - 2.88 x 1.23 2 3.5136 2 3.50

Moleculare degeneracy. gegoot guib ? 3.2 2 60 9 Compute the Constant volume heat capacity at T = 3000 K, At very high Temperature - heat capacity : Cra de que ha cvo pakabos A JA ---- I>> To] Toz 3ook , T 230ook C. l.34 kroz 6.03 xö (9- 34989 10] Cu 1.38 x 10 x 6.02 x 10 2-3x3,899 -X10 CV 21.38 x 102x 602 x lö? x3 = 24.92