Calculate the standard molar entropy of O2(g) at 298 K from its rotational constant B=1.4457 cm and its vibrational wavenumber =1580 cm. O2 is a linear rotor with a symmetry number of 2 and a molecular weight of 32 g/mol.
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- 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''The 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 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.
- Calculate the CO and CS bond lengths in OCS from the rotational constants B(16O12C32S) = 6081.5MHz, B(16O12C34S) = 5932.8MHz.the rotational constant for 1H35Cl is 10.6 cm-1 . What are the degeneracies, g, of the J=2, and J=3 rotational states?(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 molecules
- 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.The rotational constant for CO is 1.9314 cm−1 and 1.6116 cm−1 in the ground and first excited vibrational states, respectively. By how much does the internuclear distance change as a result of this transition?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.
- 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.Calculate the rotational partition function for a non-linear molecule whose σ=5 at 25°C. Given A = 4.828 cm-1 , B = 1.015 cm-1 and C = 0.824 cm-1.4. Spectroscopic measurements indicate that the rotational constants of SO2, a non-linear molecule, are 2.02736, 0.34417, and 0.29354 cm-1. Note: kg = 0.69503476 cm-1/K. (a) Compute zrot at T= 350 K assuming its symmetry number is o= 2. Hint: Using the rotational temperatures for the molecule might make this easier. (b) At what temperature would the partition function equal 2.0 × 104?