The rotational constant for the molecule 1H35Cl is B = 10.60 cm-1. Using Boltzmann statistics, determine the most likely rotational state J that such a molecule would be expected to have at a temperature of 300 K.
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- 5. For carbon monoxide at 298K, determine the fraction of molecules in the rotational levels for J=0, 5, 10, 15, and 20. The rotational constant (B) is 3.83x10^-23 Joules.(c) Consider the following rotational temperatures of diatomic molecules: qr(N2) = 2.9K, qr(HD) = 64.7K Assuming classical behaviour (i.e. continuum approximation): (i) Estimate the number of accessible rotational energy levels at 290 K for both moleculesThe three normal modes of water are the symmetric stretch (3652 cm¹), the antisymmetric stretch (3756 cm¹), and the bend (1595 cm¹). (a) Calculate the molecular vibrational partition function of water at 500 K. (b) At 500 K, what fraction of water molecules have the bend excited to v₂=1. What fraction of water molecules have the symmetric stretch excited to v₁=1? Why do more molecules have the bend excited? (c) At 500 K, what fraction of water molecules have both v2-1 and v₁=1 excited?
- 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 frequency for the first excitation of the stretching mode in the HCl molecule was experimentally determined to be ? = 86.6 THz. calculate the partition function q for the stretching mode of HCL at room temperature (T=298K) assuming that it behaves as a harmonic oscillator. explain the significance of the obtained value.b. The energy difference between consecutive vibrational states is 1.0 x 1020 J for a molecule. (i) Calculate the population ratio, n4/n¡, for this system at 298 K and discuss the significance of this ratio in terms of the distribution of molecules in the higher vibrational energy states. (ii) Estimate the vibrational partition function at 298 K. (iii) Estimate the fundamental vibration wave number for this molecule. h = 6.626 x 10-3ª J s k= 1.38 x 1023 J K' c = 2.998 x 10® m s''
- 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 diatomic molecule N2 has a rotational constant B(~) = 2.0 cm-1 and a vibrational constant v(~) = 2400 cm-1. The symmetry number for the molecule is 2. Sorry that I cannot write the symbols properly here for the wavenumber versions of the spectroscopic constants. (a) Suppose that a high-temperature limit for a partition function gives the value q = 0.34. Comment on the value and whether the high-temperature limit is valid.The ground configuration of carbon gives rise to a triplet with the three levels 3P0, 3P1, and 3P2 at wavenumbers 0, 16.4, and 43.5 cm-1, respectively. (a) Eva luate the electronic partition function of carbon at (i) 10 K, (ii) 298 K, (b) Hence derive an expression for the electronic contribution to the molarinternal energy and plot it as a function of temperature. (c) Evaluate the expression at 25 °C.
- Q 1. Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous CH3COOH. Do this calculation WITH the vibrational contribution to the energy.The rotational constant of 12C16O is 57.65 GHz. Calculate the value of J for the most populated level at (a) 300 K and (b) 1000 K.(4) For a rotational-vibrational spectrum of H8'Br (B = 8.46 cm-1) taken at 520 K, determine the R-branch transition that is expected to be the most intense.
