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- What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?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.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.
- N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?4. What is the form of the total vibrational partition function for a polyatomic molecule?The bond length of N2 is 109.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 K.
- 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 decreasing6) 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?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
- 2. The rotational partition function of an ethene molecule is 661 at 25°C. What is the rotational contribution to its molar entropy?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.Calculate the ratio of the translational partition functions of H2 and He at the same temperature and volume.