The iron (Fe) atom has several populated electronic levels. Evaluate the Fe atomic electronic partition function at 298 K using the following energy levels: Level Energy Degeneracy (n) (cm-1) 9. 1 415.9 7 2 704.0 O 11.2 O 9.2 O 16.7 O 8.0 O 10.1
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- 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 KNitric oxide, NO, has two low-lying electronic states. The lowest electronic state has a degeneracy of 2. The second state lies the equivalent of 121 cm-1 higher and has a degeneracy of 4. The next electronic state is much higher inenergy. Calculate the electronic partition function at 298 K.Calculating Partition Functions. Consider the acetylene molecule, which is linear and has the chemical structure H−C≡C−H. Calculate or determine the following: a. Symmetry number (?) and degrees of freedom b. Moment of inertia (I) and rotational temperature (Θr) c. Vibrational temperatures (Θv,i) d. Translational (qt), rotational (qr), vibrational (qv), and electronic (qe) partition functions at 298 K. e. Total partition function, (q/V). Helpful information: mass of H atom = 1.007947 amu mass of C atom = 12.01078 amu C≡C bond length = 1.203 Å C−H bond length = 1.060 Å vibrational frequencies = 1975, 3370, 3277, 729 (2), 600 (2) cm-1 (numbers in parenthesis indicate the degeneracy of that mode) ground state electronic degeneracy = 1
- The bond length of N2 is 109.75 pm. Use the high-temperature approximation to calculate the rotational partition function of the molecule at 300 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 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?
- 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 independentThe 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.Show that bimolecular reactions between nonlinear molecules are much slower than between atoms even when the activation energies of both reactions are equal. Use transition-state theory and make the following assumptions. (1) All vibrational partition functions are close to 1; (2) all rotational partition functions are approximately 1 × 101.5; (3) the translational partition function for each species is 1 × 1026. Hint: Equation 18C.9 is a good starting point.
- 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.What is overall molecular partition function Q, and how it is constructed using the partition functions for each energetic degree of freedom?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.