9. The rotational spectrum of HCN is in far-infrared region, one part is 2.96 cm", 5.92 cm", 8.87 cm", 11.83 cm". Calculate the following for HCN molecule (1) The rotation partition function at 300K (2) The contribution of rotation to the molar constant-volume heat capacity
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- 9. The rotational spectrum of HCN is in far-infrared region, one part is 2.96 cm", 5.92 cm", 8.87 cm', 11.83 cm'. Calculate the following for HCN molecule (1) The rotation partition function at 300K (2) The contribution of rotation to the molar constant-volume heat capacity6) Molecular partition function a) Write down the expressions for molecular partition function over states and levels, and explain the terms used in them, and the difference between two forms. b) If a molecule is confined to the non-degenerate energy levels: 0, ɛ, 2ɛ, what will be i) the molecular partition function of this molecule? ii) the fractional populations of each three levels? c) Answer the question b) above for the degeneracies of levels: 1, 2, 4?The rotational partition function for a sample of carbonyl sulfide (OCS) is found to be 25.0. Above roughly what J value do we expect to see the population (the number of molecules per J level) rapidly decreasing
- 2. The rotational partition function of an ethene molecule is 661 at 25°C. What is the rotational contribution to its molar entropy?The contributions to the molar heat capacity of a N2(g) at 273 K are: (A) Cv(translational) < Cv(rotational) < Cv(vibrational) (B) Cv(vibrational) < Cv(rotational) < Cv(translational) (C) Cv(rotational) < Cv(vibrational) < Cp(translational) (D) Cv(rotational) < Cv (translational) < Cv(vibrational)For carbon monoxide, the characteristic vibrational temperature is 3084K and the characteristic rotational temperature is 2.77K. Calculate the partition functions and the rotational and vibrational contributions to the standard molar entropy at 298K.
- N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?Consider a system at 250 K which has an infinite ladder of evenly spaced quantum states with an energy spacing of 0.25 kJ/mol. 1. The energy for level n=1 is kJ/mol. The minimum possible value of the partition function for this system is The average energy of this system in the classical limit is decimal] 2. 3. 4. The number of thermally populated states is kj/mol. [Answer rounded to 1 [Answer should be whole number]4. The following have to do with rotational partition functions. a) What are the symmetry numbers o for the following molecules? i) "Cl'CI ii) "CP"CI iii) triangular H3* iv) All isomers of C:H.F2 v) CH,CI vi) benzene b) Assume at = 10 the high temperature limit is reached. At what temperature does the high OR temperature limit become valid for: i) DBr (B = 4.24 cm') ii) F"CI (B = 0.516 cm') %3D iii) Csl (B = 0.236 cm) %3D e ) Obtain Jmax and / for the temperatures obtained in part b) and at 500 K.
- Calculate the ratio of the rotational partition functions of 3C13 Cl to that of 3$C133C1 under identical conditions and at high temperature assuming identical bond distances. A) 1.03 B) 3.22 C) 0.52 D) 1.62 E) 2.05 The translational partition function for a noble gas confined to a volume of 1.0 L at 298 K is equal to 2.44× 10²9. What is the identity of this gas? A) He (M-4.00 g mol·') B) Ne (M-20.18 g mol) C) Kr (M-83.80 g mol") D) Xe (M=131.30 g mol) E) Ar (M-39.95 g mol")he lowest electronic levels for 14N 160 have the following characteristics: Calculate, for 5000 k, using statistics. A) The fraction of molecules in the 3 electronic levels B) The partition functions for the 3 electronic levels Qti, Qvib, Qrot, and the total partition function. C) The energies Eti, Evib, Etot, for the 3 electronic levels and the total energy and compare with the classical prediction. D) The fraction of molecules in the state J = 2, V = 2 of the second electronic level. Eye /cm-1 Ge wavelength/cm-1 Radius /10-10 0 2 1904.04 1.15077 43845.88 1 2374.31 1.0634 45793.78 2 1037.20 1.4167A certain molecule can exist in either a nondegenerate singlet state or a triplet state (with degeneracy of 3). The energy of the triplet exceeds that of the singlet by ε. When ?=??(where T is a set value, i.e., ? is a constant), calculate the values of the molecular partition function, molar heat capacity, and molar entropy. Assume the molecules are distinguishable and independent