Calculate the fraction of molecules in all excited vibrational states for 3"C³$Cl with fundamental vibrational frequency 554 cm¯' at 300 K, 1000 K and 2000 K.
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- 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.Calculate the relative numbers of Br2 molecules ( ᷉v = 321 cm−1) in the second and first excited vibrational states at (i) 298 K, (ii) 800 K.Calculate the contribution of each normal mode to the molar vibrational heat capacity of H_2O (g) at 600 K.
- Evaluate, by explicit summation, the mean vibrational energy of CI4 and plot its value as a function of temperature. At what temperature is the equipartition value within 5 per cent of the accurate value? Use 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).The vibrational wavenumber of Br2 is 323.2 cm−1. Evaluate the vibrational partition function explicitly (without approximation) and plot its value as a function of temperature. At what temperature is the value within 5 per cent of the value calculated from eqn 13B.16, which is valid at high temperatures?Calculate the rotational constant (B) for the molecule H12C14N, given that the H-C and C-N bond distances are 106.6 pm and 115.3 pm respectively.
- Calculate the relative populations of a linear rotor at 298 K in the levels with J = 0 and J = 5, given that ᷉ B = 2.71 cm−1.What can we predict about fluorescence intensity as a function of temperature from Boltzmann’s distribution?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?
- The NOF molecule is an asymmetric rotor with rotational constants 3.1752 cm−1, 0.3951 cm−1, and 0.3505 cm−1. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C.Calculate the relative populations of the J = 2 and J = 1 rotational levels of HCI at 25 oC. For HCI the rotational constant is B =318.0 GHz.Estimate the ratio of the number of molecules in the firstexcited vibrational state of the molecule N2 to the numberin the ground state, at a temperature of 450 K. The vibrational frequency of N2 is 7.07 × 1013 s-1.