12.5 A CO₂ molecule has four vibrational modes with wave- numbers 1388 cm¹, 2349 cm¹, and 667 cm¹ (the last being a doubly degenerate bending motion). Calculate the total vi- brational partition function at (a) 500 K, (b) 1000 K.
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- A CO2 molecule has four vibrational modes with wavenumbers 1388 cm-1, 2349 cm-1, and 667 cm-1, (the last being a doubly degenerate bending motion). Calculate the total vibrational partition function at (a) 500 K, (b) 1000 K.N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?Evaluate the rotational partition function of pyridine, C5H5N, at 25 °C given that ᷉ A = 0.2014 cm−1, ᷉ B = 0.1936 cm−1, ᷉ C = 0.0987 cm−1. Take the symmetry number into account.
- Imagine gaseous Kr at 298K confined to move in a two-dimensional plane of area 4.00 cm2. What is the value of the translational partition function?The ratio between the translational partition function of H2 to that of unknown gas X2 at 400 K is 80. if the thermal de Broglie wavelength of H2 is 61.71 pm, what would be the thermal de Broglie wavelength of the unknown gas in pm assuming that both gases are confined in the same volume.What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?
- 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.Estimate the vibrational contribution to the molar entropy of the most common isotopomer of bromine, 79Br2, at 1000 K. The vibrational wavenumber for 79Br2 is 325 cm-1. You may assume that at this temperature, the equipartition theorem and the high temperature approximation for the vibrational partition function are both valid.Evaluate the rotational partition function at 298 K of (a) 1H35Cl. for which the rotational constant is 318 GHz, (b) 12C16O2, for which the rotational constant is 11.70 GHz.
- Calculate the vibrational partition function of CS2 at 500 K given the wavenumbers 658 cm−1 (symmetric stretch), 397 cm−1 (bend; doubly degenerate), 1535 cm−1 (asymmetric stretch).Calculate the translational partition function at (a) 300 K and (b) 600 K of a molecule of molar mass 100 g mol-1 in a container of volume 4.20 cm3.qtr at 300 K qtr at 600 K Note: this is a measure of the vast number of accessible microstates of translation available to a molecule under these conditions.A certain atom has a 4-fold degenerate ground level, a 3-fold degenerate electronically excited level at 4000 cm-1, and a 4-fold degenerate level at 5500 cm-1.Part 1: Calculate the electronic partition function at 1900 K.Ans = __________ Part 2: Now calculate the electronic contribution to the molar internal energy at this same temperature. Ans = ________ kJ/molFor comparison purposes, it is instructive to consider that the translational contribution to the molar internal energy at this same temperature would be (3/2)RT or 23.69 kJ/mol. So it shows that even at these elevated temperatures, the electronic contribution is fairly small because excited electronic states are populated much less than excited translational states.