(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 2000
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- Which of the following molecules should have pure rotational spectra? a Deuterium, D2 D is 2H b Carbon monoxide, CO c cis1,2Dichloroethylene d trans1,2Dichloroethylene e Chloroform, CHCl3 f Buckminsterfullerene, C60A system consists of three energy levels: a ground level (0 = 0, go = 1); a first excited level (₁ = 2kBT, 91 = 3); and a second excited level (&2 = 8kBT, 92 = 3). Calculate the partition function of the system. .406005 What is the probability for the third energy level? .0024787he 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 1.4167
- 4. What is the form of the total vibrational partition function for a polyatomic molecule?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.6) 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 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.What is the numerical value of the molecular partition function of a heteronuclear diatomic molecule given the following conditions: (i) the characteristic length is 10 nm and the volume in which the molecules are free to move is a cube with sides of 1 mm each. (ii) Only the first four rotational levels are accessible, but for some odd reason [to keep things simple] each state in each of those levels is equally populated. (iii) all molecules are in the ground vibrational state; (iv) the molecule has a triplet electronic ground level, like O2.For all three of your assigned systems (Ne, Oxygen, Nitrous oxide), calculate the complete partition function (assuming a perfect gas) at T, = 2.00 and e, = 0.0500. Information on the symmetry number for your polyatomic molecules is posted in a table under the Reference section in the Content Library The symmetry number for rotational partition functions. Homonuclear diatomics: o=2 Heteronuclear diatomics: o=1 Polyatomics: Name Nitrous oxide 1
- 1. Show that the partition function for a harmonic oscillator in the x direction only is given by: qx exp(-ẞhv) 1-exp(-ẞhv)Part A Evaluate the translational partition function for H2 confined to a volume of 191 cm³ at 328 K . (Note: the Avogadro's constant NA 6.022 x 1023 mol-1). Express your answer to three significant figures. ΑΣφ ? qT(H2) = 1.89 • 1031 %3D Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remainingThe lowest triplet state in naphthalene (C10H8) is about 11,000 cm-1 below the lowest excited singlet electronic level at 77 K. Calculate the ratio of populations in these two states at equilibrium. [Hint: The Boltzmann equation is given by N2/N1 = (g2/g1)exp(-AE/kBT), where g1 and g2 are the degeneracies for levels 1 and 2.] N2 1.43e-90 N1