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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?4. What is the form of the total vibrational partition function for a polyatomic molecule?N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?
- Calculate the ratio of the translational partition functions of H2 and He at the same temperature and volume.Evaluate the rotational partition function of pyridine, C5H5N, at 25 °C given that ᷉ A = 0.2014 cm−1, ᷉ B = 0.1936 cm−1, ᷉ C = 0.0987 cm−1. Take the symmetry number into account.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
- 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 ratio between the translational partition function of H2 to that of unknown gas X2 at 400 K is 80. if the thermal de Broglie wavelength of H2 is 61.71 pm, what would be the thermal de Broglie wavelength of the unknown gas in pm assuming that both gases are confined in the same volume.What is J_max in rotational Boltzman distribution, and calculate J_max for HCl at 1000K
- The bond length of O2 is 120.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 K.The H2O molecule is an asymmetric rotor with rotational constants 27.877 cm−1, 14.512 cm−1, and 9.285 cm−1. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C.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).