Calculate the relative population of the first two rotational levels for HCl at 300 K given that the value of the rotational constant of the molecule is 10.59 cm-1.
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Calculate realtive population of the two rotational level for HCl at 300K
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- Calculate the relative population of the first two rotational levels for HCI at 300 K given that the value of the rotational constant of the molecule is 10.59 cm-1.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.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?What is the numerical value of the molecular partition function of a heteronuclear diatomic molecule given the following conditions: (i) the characteristic length is 10 nm and the volume in which the molecules are free to move is a cube with sides of 1 mm each. (ii) Only the first four rotational levels are accessible, but for some odd reason [to keep things simple] each state in each of those levels is equally populated. (iii) all molecules are in the ground vibrational state; (iv) the molecule has a triplet electronic ground level, like O2.
- The rotational constant B-for H2 is 60.86 cm-1. Predict the rotational Raman spectrum of H2 and calculate the bond length of the molecule.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 rotational constant for 1H35Cl is 10.6 cm-1 . What are the degeneracies, g, of the J=2, and J=3 rotational states?
- 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.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 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.