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.
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- Use the equipartition principle to estimate the value of γ = Cp/CV for carbon dioxide. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C?Consider 1 mol of N2(g) at room temperature. Calculate the number of molecules in the ground rotational energy (J=0). Calculate also the average rotational energy per molecule.For two nondegenerate energy levels separated by an amount of energy ε/k=500.K, at what temperature will the population in the higher-energy state be 1/2 that of the lower-energy state? What temperature is required to make the populations equal?
- Calculate the value of Cp at 298K and 1 atm pressure predicted for CH4(g) and C2H4(g) by the classical equipartition theorem. Compare the predicted results with the experimental results (see OGB Appendix D) and calculate the percent of the measured value that arises from vibrational degrees of freedom.the rotational constant for 1H35Cl is 10.6 cm-1 . What are the degeneracies, g, of the J=2, and J=3 rotational states?The methyl chloride molecule, CH3Cl, has three non-degenerate vibrations with harmonic wavenumbers 3088, 1396 and 751 cm–1 respectively and three doubly-degenerate vibrations with harmonic wavenumbers 3183, 1496 and 1036 cm–1 respectively. Calculate the vibrational partition function for the methyl chloride molecule at 1200 K.
- Discuss the relation between the thermodynamic and statistical definitions of entropy.Use the equipartition principle to estimate the values of γ = Cp/CV 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?A certain molecule has a doubly degenerate excited state lying at 360 cm−1 above the non-degenerate ground state. At what temperature will 15 per cent of the molecules be in the upper state?
- Calculate the vibrational, rotational, and translational contributions to the constant volume heat capacity (Cv) for 14N2 at 298 K. Assume this represents the high temperature limit for rotational energy and low temperature limit for vibrational energy. Given that Cv=20.81 J/K·mol for N2, state which type or types of energy contribute most to Cv for N2 and explain why those types of energy contribute most.Evaluate the rotational partition function at 298 K of (a) 1H35Cl. for which the rotational constant is 318 GHz, (b) 12C16O2, for which the rotational constant is 11.70 GHz.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.