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- Calculate the rotational partition function for a non-linear molecule whose σ=5 at 25°C. Given A = 4.828 cm-1 , B = 1.015 cm-1 and C = 0.824 cm-1.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 02.The three normal modes of water are the symmetric stretch (3652 cm¹), the antisymmetric stretch (3756 cm¹), and the bend (1595 cm¹). (a) Calculate the molecular vibrational partition function of water at 500 K. (b) At 500 K, what fraction of water molecules have the bend excited to v₂=1. What fraction of water molecules have the symmetric stretch excited to v₁=1? Why do more molecules have the bend excited? (c) At 500 K, what fraction of water molecules have both v2-1 and v₁=1 excited?
- What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?Give an example of 2 isomers of a molecule that have different values of the rotational partition function at the same temperature.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 vibrational partition function of CCl4 at 500 K given the wavenumbers 459 cm−1 (symmetric stretch, non-degenerate), 217 cm−1 (deformation, doubly degenerate), 776 cm−1 (deformation, triply degenerate), 314 cm−1 (deformation, triply degenerate).Use the Boltzmann formula to calculate the low and high temperature limits of vibrational partition function. Let 0=hv/k. BIU Σ 10 ►¶4. What is the form of the total vibrational partition function for a polyatomic molecule?
- Evaluate the translational partition function of (a) N2, (b) gaseous CS2 in a flask of volume 10.0 cm3. Why is one so much larger than the other?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.The diatomic molecule N2 has a rotational constant B(~) = 2.0 cm-1 and a vibrational constant v(~) = 2400 cm-1. The symmetry number for the molecule is 2. Sorry that I cannot write the symbols properly here for the wavenumber versions of the spectroscopic constants. (a) Suppose that a high-temperature limit for a partition function gives the value q = 0.34. Comment on the value and whether the high-temperature limit is valid.