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- Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.The rotational constant of 12C16O2 (from Raman spectroscopy) is 11.70 GHz. What is the CO bond length in the molecule?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?
- For 16O2, Δ ᷉ G values for the transitions v = 1 ← 0, 2 ← 0, and 3 ← 0 are, respectively, 1556.22, 3088.28, and 4596.21 cm−1. Calculate ᷉v and xe. Assume ye to be zero.Derive an expression for the mean energy of a collection of molecules that have three energy levels at 0, ε, and 3ε with degeneracies 1, 5, and 3, respectively.A diatomic Hydrogen (H2) molecule with a potential between its two Hydrogen atoms can be modelled using the Morse potential: V(x) = V0 e−αx (e−αx - 2), where α = 19.3 nm−1 and V0 = 4.52 eV. Assuming the H2 molecule has no rotational energy. Determine the minimum value of the Morse potential, V . (State in eV, to 3 s.f.)
- Estimate the values of γ = Cp,m/CV,m for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C? Hint: Note that Cp,m − CV,m = R for a perfect gas.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.Estimate the rotational partition function of ethene at 25 °C given that ᷉ A = 4.828 cm−1, ᷉ B =1.0012 cm−1, and ᷉ C = 0.8282 cm−1. Take the symmetry number into account.
- Calculate the vibrational partition function of CI4 at 500 K given the wavenumbers 178 cm−1 (symmetric stretch, non-degenerate), 90 cm−1 (deformation, doubly degenerate), 555 cm−1 (deformation, triply degenerate), 125 cm−1 (deformation, triply degenerate).Consider the rotational temperatures of the following hetero diatomic molecules: θr(CO) = 2.1 K, θr(HF) = 30.2 K. In which case would the classical approximation be accurate? Justify your answer.The four lowest electronic levels of a Ti atom are: J = 2, 3, 4 and 1, at 0, 170, 387 and 6557 cm-1, respectively. There a many other electronic states at higher energies. The boiling point of Ti is 3287 oC. What are the relative populations of these levels at the boiling point if the degeneracy of levels is 2J + 1? Is the ground state most highly populated level?