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 p, = 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: Polyatomics: Name o=1 0

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 p, = 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: Polyatomics: Name o=1 0

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter18: More Statistical Thermodynamics

Section: Chapter Questions

Problem 18.4E

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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, C60
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.
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 overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?
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.
You have a diatomic ideal gas at room temperature with a rotational temperature of Orot = 2 K and vibrational temperature of Ovib = 500 K. If you use the model we derived for the partition function, an increase in the mass of the atoms in the diatomic molecule will increase the the molar heat capacity, Cy. In our model, this is due to an increased contribution to Cy from what degree(s) %3D of freedom? O translations rotations vibrations electronic all of the above Onone of the above
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.
4. What is the form of the total vibrational partition function for a polyatomic molecule?
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 remaining