Part 1:
a.) The vibrational frequencies of F2, Cl2, Br2, and I2 are 917 cm-1, 525 cm-1, 325 cm-1, and 208 cm-1. Which molecule (F2, Cl2, Br2, or I2) has the largest number of thermally accessible states? Make a prediction and explain your reasoning before you perform any calculations, but assume that all molecules are exposed to the same temperature.
b.) Treat the molecular vibrations as harmonic oscillators to calculate the vibrational partition function of the halogens and the population of their first three vibrational energy levels (i = 0,1,2) at 500 K.
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qv
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p0
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p1
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p2
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F2
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Cl2
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Br2
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I2
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c.) At what temperature would the vibrational partition function of fluorine be identical to the vibrational partition function of iodine calculated at 500 K?
Part 2:
Evaluate the rotational temperature ΘR and the rotational partition function qRfor F2, Cl2, Br2, and I2 at 500 K. Is the high-temperature expression (qR=T/(σ ΘR) valid for all your calculations? The rotational constants for F2, Cl2, Br2, and I2 are 0.889 cm-1, 0.244 cm-1, 0.0821 cm-1, and 0.0374 cm-1.
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ΘR (K)
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qR
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High temperature expression valid?
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F2
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Cl2
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Br2
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I2
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Part 3:
a.) Assume that all electronic ground states of the halogens are non-degenerate. Briefly explain why you can set the electronic partition function equal to one (qE = 1) for all halogens at 500 K.
b.) Demonstrate that your simplification (qE = 1) is justified by calculating the electronic partition function for bromine with the data provided below. Show your work!
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Electronic energy level for Br2
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Energy (cm-1)
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Degeneracy
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Ground state
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0
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1
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First excited state
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13905
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6
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Second excited state
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15902
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6
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Third excited state
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24000
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2
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Part 4:
Calculate the thermal de Broglie wavelength Λ and the translational partition function at 500 K and 1 bar for F2, Cl2, Br2, and I2.
Part 5:
Combine the partition functions of all relevant molecular modes and compute Gm (500 k) - Gm (0) for the four halogens. Assume standard pressure (1 bar).
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Total molecular partition function
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F2
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Cl2
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Br2
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I2
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Part 6:
a.) Write a short essay to highlight the most significant trends in the data that you calculated in this assignment. Compare your data by chemical species and also by energy mode.
b.) Energy can be expressed in various units including J or cm-1 among many other energy units. Convert the value of kT for T= 500 K into units of cm-1. Sometimes the term kT is referred to as a scale of energy. Compare the value of kT at 500K to the energy values of the different modes for the halogen molecules. Briefly elaborate why kT can be a very useful energy scale in thermodynamics or spectroscopy.