on Calculate the ratio of the rotational partition functions of 35C1 35Cl to that of 35Cl 33 Cl under identical conditions and at high temperature assuming identical bond distances. 1.03 3.22 0.52 1.62
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- A 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? .0024787What 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 rotational partition function for 1271 1271 at the equilibrium bond length is equal to 929. Using the high-temperature limit, what would the rotational partition function be if the bond was stretched by a factor of 1.35? 510 1693 3583 1254 O 215
- 4. What is the form of the total vibrational partition function for a polyatomic molecule?What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?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
- 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.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?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.
- Give an example of 2 isomers of a molecule that have different values of the rotational partition function at the same temperature.What do you mean by the term equilibrium partition coefficient?Calculate 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 5144