assignment 3 solution

assignment 3 solution - Chemistry 350 Assignment 3:...

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Chemistry 350 Assignment 3: Solutions November 1 st 2005 Question 1 15.4 Consider the following table of diatomic molecules and associated rotational constants: Molecule B (cm –1 ) ˜ ! (cm –1 ) H 35 Cl 10.59 2886 12 C 16 O 1.93 2170 39 KI 0.061 200 CsI 0.024 120 a) Calculate the rotational temperature for each molecule. b) Assuming that these species remain gaseous at 100 K, for which species is the equipartition theorem prediction for the rotational contribution to the internal energy appropriate? c) Calculate the vibrational temperature for each molecule. d) If these species were to remain gaseous at 1000 K, for which species is the equipartition theorem prediction for the vibrational contribution to the internal energy appropriate? The rotational and vibrational temperatures are given by: RV B kk ## $$ ! The high-temperature approximation will be valid for rotations or vibrations when the temperature is at least 10-fold greater than the rotational or vibrational temperature, respectively. Using the spectroscopic information provided in the table: Molecule # R K %& High-T for R? V K % & High-T for V? H 35 Cl 15.3 no 4153 no 12 C 16 O 2.78 yes 3123 no 39 KI 0.088 yes 288 no CsI 0.035 yes 173 no
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15.5 The lowest four energy levels for atomic vanadium (V) have the following energies and degeneracies: Level ( n ) Energy (cm –1 ) Degeneracy 0 0 4 1 137.38 6 2 323.46 8 3 552.96 10 What is the contribution to the average energy from electronic degrees of freedom for V when T = 298 K? % & % & % & %& % & 1 1 1 1 1 1 1 137.38 cm 323.46 cm 552.96 cm 137.38 cm 323.46 cm 552.96 cm 1 1 1 137.38 cm 32 11 4 6 8 10 824 cm 2588 cm 5530 cm 824 cm 2588 cm n n n V V q g e e e e q e e e ee Nq UN q ’( ’’ ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )) $ $ * * * +, - $) * * ./ - 01 * )- $$ - 2 % & % & % & % & % &% &% & % 1 1 1 1 1 3.46 cm 552.96 cm 1 137.38 cm 323.46 cm 552.96 cm 1 1 1 3 41 0 1 1 5530 cm 4 6 8 10 143 cm converting to J: 143 cm 143 cm 6.626 10 J s 3.00 10 cm s 1.71 kJ mol 1.71 kJ mol A m e e e e N U N hc nN n U ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) * *** $ $ $ 3 3 $ $ & 1 ) Question 2 15.13 The measured molar heat capacities for crystalline KCl are as follows at the indicated temperatures: T (K) 50 100 175 250 C V,m (J/mol K) 21.1 39.0 46.1 48.6 a) Explain why the high-temperature limit for C V is apparently twofold greater than that predicted by the Dulong–Petit law. b) Determine if the Einstein model is applicable to ionic solids. To do this use the value for C V at 50 K to determine then use this temperature to determine C , V 4 V at 175 K.
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a) The Dulong–Petit law is applicable to atomic crystals. KCl is a molecular crystal where vibrational degrees of freedom will also contribute to C V .
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assignment 3 solution - Chemistry 350 Assignment 3:...

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