For carbon monoxide, the characteristic vibrational temperature is 3084K and the characteristic rotational temperature is 2.77K. Calculate the partition functions and the rotational and vibrational contributions to the standard molar entropy at 298K.
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- 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.The 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.A certain atom has a doubly degenerate ground level, a triply degenerate electronically excited level at 1250 cm-1, and a doubly degenerate level at 1300 cm-1. Calculate the partition function of these electronic states at 2000 K
- A certain atom has a triply degenerate ground level, a non-degenerate electronically excited level at 850 cm–1, and a fivefold degenerate level at 1100 cm−1. Calculate the partition function of these electronic states at 2000 K. What is the relative population of each level at 2000 K?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.Calculate the rotational partition function of SO2 at 298 K from its rotational constants 2.027 36 cm–1, 0.344 17 cm–1, and 0.293 535 cm–1 and use your result to calculate the rotational contribution to the molar entropy of sulfur dioxide at 25 °C.
- A certain atom has a fourfold degenerate ground level, a non-degenerate electronically excited level at 2500 cm−1, and a twofold degenerate level at 3500 cm−1. Calculate the partition function of these electronic states at 1900 K. What is the relative population of each level at 1900 K?What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?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.
- The bond length of O2 is 120.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 K.Consider a system of distinguishable particles having only two non-degenerate levels separated by an energy that is equal to the value of kT at 10 K. Calculate (a) the ratio of populations in two states at (1) 1.0 K, (2) 10 K, (3) 100 K, (b) the molecular partition function at 10 K, (c) the molar energy at 10 K, (d) the molar heat capacity at 10 K, € the molar entropy at 10 K.N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?