PS1 - 27 August 2010 Michael F Brown CHEMISTRY...

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Unformatted text preview: 27 August, 2010 Michael F. Brown CHEMISTRY 480A (Physical Chemistry) Problem Set 01 To be turned in by: Tuesday, 07 September Worked examples for this course are dealt with primarily in the Discussion Section; whereas new concepts are introduced in the Lectures. You can get help with the homework problems in the Discussion Sections (14:00—14:50 Tuesday, Chemistry 209; and 15:30—16:20 Tuesday, Chemistry 134). The problem sets will be graded P+, P, or F and will be used to increase or decrease borderline grades. On all computational problems be sure to use SI units, and indicate your answer to the proper number of significant figures. For maximum credit show clearly how you obtained your answer, i.e. what numbers were combined to yield the final result. Background reading: Atkins & de Paula, Sections F.1—F.7, 1.1, 1.2 Back of Chapter Exercises related to the homework (optional): F5.5(a), F5.7(a), F6.1(a), F6.2(a), F6.3(a), F7.1(a), F7.2(a), F7.3(a), F7.7(a),1.2(a), 1.3(a), 1.4(a) Back of Chapter Problems related to the homework (optional): Problem 1. You are a rocket scientist interested in the spectroscopic properties of a hypothetical gas at room temperature (T = 25 °C). The energy separations between the ground state and the first excited state for the gas molecules are the following: tyge of spectroscopic transition AE / kJ mole—1 electronic 1000 vibrational 25 rotational 0.050 Hint: take the ground state as having zero energy, since only the energy level differences (separations) are important. a) Calculate the fraction of molecules in the first excited electronic state: b) Calculate the fraction of molecules in the first excited vibrational state: 0) Calculate the fraction of molecules in the first excited rotational state: Problem 2. Nitric oxide (NO) is a diatomic gas molecule that is involved in nerve impulse transmission. (The discovery was worth a Nobel prize.) a) What are the numbers of degrees of freedom for the translational, rotational, and vibrational motions of N0? b) For l\_10 calculate the numerical value of the molar heat capacity at constant volume CV: 0) Imagine that you have discovered yet another nerve transmitter molecule, a triatomic gas molecule, YES. For the non-linear molecule YES calculate the numerical value of the molar heat capacity at constant volume CV: Problem 3. imagine that you are a chemical engineer investigating the properties of gaseous carbon dioxide (CO2) in rocket engines at P = 100 atm and T = 800 K. Based on your training in Physical Chemistry at the University of Arizona, you decide to employ the kinetic theory of gases as a start. a) Beginning with the equipartition theorem, derive a mathematical expression in closed form for the root means square velocity of the 002 molecules in the gas: b) Based on the Maxwell distribution of speeds, what is the mean speed of the 002 molecules? 0) What is the mean free path of the gaseous 002 molecules? d) Finally, what is the collision frequency of the 002 molecules? 08-27—10 chem480A\10\prob\001\mw.doc *3» /, :23” 0 fC‘j‘ffl/A 7Z0 C:C?/(::(x:1vr/(Q0~(Z‘ 7177 L 3/}‘4 971;, (:7 I) 0/ [440/9 C (cl/C45 15671117 ,9 ‘ J:[‘”W‘M"'"WMH mim- -«w~__ H-_H‘ €1\01[[:: g/‘G'A 3’23 If“ 64/317 7119/92.. 69/ /’/"6’-H 61/3432”) :1 um: (,I 51:23 I L7,”; [2: i “‘32-" ’V} :2,* "’ at! 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