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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.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.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?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?
- What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?Use the Boltzmann formula to calculate the low and high temperature limits of vibrational partition function. Let 0=hv/k. BIU Σ 10 ►¶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.
- 4. What is the form of the total vibrational partition function for a polyatomic molecule?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).It is possible to approximate the rotational partition function for diatomic molecules by replacing the infinite sum over states with an integral. Why might this be less accurate for H₂? OH₂ has a smaller mass so its rotational constant will be very small. OH₂ has a very high vibrational frequency so the spacings between its energy levels will be large. O the moment of inertia for H₂ is OH₂ has a shorter bond length so its rotational constant will be very small. the integral diverges for smaller-sized diatomic molecules.