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- 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.- NO₂ has the following vibrational temperatures: 1900, 1980 and 2330 K. Calculate the vibrational partition function at 300 K. A) 1.0014 B) 1.0018 C) 1.0036 D) 1.0004 E) 1.00006) 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?
- A certain atom has a doubly degenerate ground level, a triply degenerate electronically excited level at 1250 cm-1, and a doubly degenerate level at 1300 cm-1. Calculate the partition function of these electronic states at 2000 KCalculate the molecular rotational partition function for 14N2 at 298"K for both molecules. The internuclear distance for 14N2 is 0.1095 nm. O 13.21 O 24.85 O 579.10 O 1.74 O 5144The following have to do with rotational partition functions. a) What are the symmetry numbers o for the following molecules? i) 35C13"C1 ii) 35C13$CI iii) triangular H3* iv) All isomers of C2H2F2 v) CH;C1 vi) benzene T b) Assume at = 10 the high temperature limit is reached. At what temperature does the high OR temperature limit become valid for: i) DBr (B = 4.24 cm1) ii) F3$CI (B = 0.516 cm') iii) CsI (B = 0.236 cm-') %3D c) Obtain Jmax and J for the temperatures obtained in part b) and at 500 K.
- (c) A table of energies and degeneracies is given below for the lowest energy vibrational states of carbon dioxide. Calculate the partition function at 400 K using the data below. (The states are labeled for completeness, but are not needed for the solution.) state 9 Evib (cm-¹) (0,0,0) 10 (0,1,0) 2 667 (0,2,0) 3 1334 (1,1,0) 2 2000Calculating Partition Functions. Consider the acetylene molecule, which is linear and has the chemical structure H−C≡C−H. Calculate or determine the following: a. Symmetry number (?) and degrees of freedom b. Moment of inertia (I) and rotational temperature (Θr) c. Vibrational temperatures (Θv,i) d. Translational (qt), rotational (qr), vibrational (qv), and electronic (qe) partition functions at 298 K. e. Total partition function, (q/V). Helpful information: mass of H atom = 1.007947 amu mass of C atom = 12.01078 amu C≡C bond length = 1.203 Å C−H bond length = 1.060 Å vibrational frequencies = 1975, 3370, 3277, 729 (2), 600 (2) cm-1 (numbers in parenthesis indicate the degeneracy of that mode) ground state electronic degeneracy = 14. What is the form of the total vibrational partition function for a polyatomic molecule?
- N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?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 1.4167Consider 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]