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calculate the vibrational contribution to the entropy of chlorine molecule at 500K given the wave number of thevibration is 560/cm
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- 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.2. The rotational partition function of an ethene molecule is 661 at 25°C. What is the rotational contribution to its molar entropy?2. Calculate the total molar entropy of HF at 298K. The vibrational frequency is 3960 cm-1 and the rotational constant is 20.6 cm-1.
- Derive an expression showing how entropy can be related to thermodynamic probability.At what temperature is the standard molar entropy of helium equal to that of xenon at 298 K?5. The vibrational modes of a particular molecule are listed below. Calculate the vibrational contribution to the molar entropy at 300 K. Mode Degeneracy wavenumber / cm-1 v1 206 v2 305 v3 1083 v4 1367 USEFUL CONSTANTS R = 8.314 J/mol/K = 0.08205 Latm/mol/K kB =1.38 x10-23 J/K h = 6.626×10-34 J s c = 3x108 m/s 1 cm-1 = 1.98x10-23 J STP = 298 K, 1bar (105 N/m²) 12 3
- An NO molecule has a doubly degenerate electronic ground state and a doubly degenerate excited state at 121.1 cm−1. Calculate and plot the electronic contribution to the molar heat capacity of the molecule up to 500 K.A linear molecule may rotate about two axes. If the molecule consists of N atoms, then there are 3N- 5 vibrational modes. Use the equipartition theorem to estimate the total contribution to the molar internal energy from translation, vibration, and rotation for (a) carbon dioxide, CO2, and (b) dibromoethyne, C2Br2, at 2000 K. In contrast, a nonlinear molecule may rotate about three axes and has 3N- 6 vibrational modes. Estimate the total contribution to the molar in ternal energy from translation, vibration, and rotation for (c) nitrogen dioxide, NO2, and (d) tetrabromoethene, C2Br4,at 2000 K. In each case, first assume that all vibrations are active; then assume that none is.Discuss the relation between the thermodynamic and statistical definitions of entropy.
- A certain molecule can exist in either a nondegenerate singlet state or a triplet state (with degeneracy of 3). The energy of the triplet exceeds that of the singlet by ε. When ?=??(where T is a set value, i.e., ? is a constant), calculate the values of the molecular partition function, molar heat capacity, and molar entropy. Assume the molecules are distinguishable and independentcaculate the vibrational contributio to the entropy of Cl2 at 500K given the wave number of the vibration is 560/cmThe 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.