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Calculate the contribution of each normal mode to the molar vibrational heat capacity of H_2O (g) at 600 K.
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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''Chemistry The first excited electronic energy level of the helium atom is 3.13 ✕ 10−18 J above the ground level. Estimate the temperature at which the electronic motion will begin to make a significant contribution to the heat capacity. That is, at what temperature will 5.0% of the population be in the first excited 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.
- 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 ground level of Cl is 2P3/2 and a 2P1/2 level lies 881 cm−1 above it. Calculate the electronic contribution to the heat capacity of Cl atoms at (i) 500 K and (ii) 900 K.The rotationa l energy of a linear or spherical molecule with quantum number J is EJ = hBJ(J + 1 ). For a linear molecule. each rotational level has a degeneracy of (2J + 1 ). For a spherical molecule, the degeneracy is (2J + 1 )2 (a) Calculate the ratio of populations of CO2 molecules with J = 4 and J = 2 at 25 °C, given that the rotational constant of CO2 is B = 11.70 GHz. (b) Also calculate the ratio of populations of CH4 molecules with J = 4 and J = 2 at 25 °C, given that the rotational constant of CH4 is 157 GHz.
- 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).Plot the molar heat capacity of a collection of harmonic oscillators as a function of T/θV, and predict the vibrational heat capacity of ethyne at (i) 298 K, (ii) 500 K. The normal modes (and their degeneracies in parentheses) occur at wavenumbers 612(2), 729(2), 1974, 3287, and 3374 cm–1.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?
- Here we calculate the heat capacity of nitrogen gas. The rotational temperature of nitrogen is Ørot = 2.88K. The vibrational temperature is Ovib = 3374K. Assume T=1000K. Part A Calculate the contribution of vibrational motions to the molar heat capacity of nitrogen at T=1000K Cv = Part B Submit Previous Answers Request Answer Cv = μà X Incorrect; Try Again; 4 attempts remaining Submit Value Part C What is the contribution of vibrational motions to the molar heat capacity of nitrogen gas according to the equipartition principle? Cv = μA Value Units Request Answer μà B) ? Value Units Calculate the molar heat capacity of nitrogen gas including contributions from translational, vibrational, and rotational degrees of freedom. Units 図】? ?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.Use the equipartition theorem to estimate the constant-volume molar heat capacity of (i) I2, (ii) CH4, (iii) C6H6 in the gas phase at 25 °C.