Chem288_2005_PS5_solutions - Chemistry 288 Problem Set 5...

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Unformatted text preview: Chemistry 288 Problem Set 5 Solutions Spring 2005, Marohn A USEFUL THERMODYNAMIC RELATION We start with Z = summationdisplay ASN e ( N- ) / (1) where ASN stands for all states and numbers of parti- cles, as discussed in class. Taking partial derivatives, and applying the chain rule of differentiation very care- fully, we find log( Z ) = 1 Z summationdisplay ASN parenleftbigg- 1 2 parenrightbigg ( N- ) e ( N- ) / (2) and log( Z ) = 1 Z summationdisplay ASN parenleftbigg N parenrightbigg e ( N- ) / (3) Adding these together as follows, the terms with the chemical potential cancel, and we get log Z + 2 log Z = 1 Z summationdisplay ASN e ( N- ) / = U (4) The last equality follows be definition of the average en- ergy. DEATH BY CARBON MONOXIDE POISONING Part a Use the ideal gas relation (derived in class) for the activity e / = n n Q (5) where n Q = parenleftbigg m 2 h 2 parenrightbigg 3 / 2 (6) is the quantum concentration for the gas, m is the mass of one gas molecule, h is Plancks constant, is the temperature in fundamental temperature units, and n in the gas per-molecule concentration. Calculate the O 2 and CO quantum concentrations. Work in SI units: h = 1 . 05 10- 34 J/s = 310 K 1 . 38 10- 23 J/K = 4 . 28 10- 21 J m a m (O 2 ) = 32 1 . 67 10- 27 kgr bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright m H = 5 . 34 10- 26 kgr m b m (CO) = 28 1 . 67 10- 27 kgr bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright m H = 4 . 70 10- 26 kgr Compute: n a Q n Q (O 2 ) = 1 . 89 10 32 particle/m 3 = 3 . 14 10 5 mol/ n b Q n Q (CO) = 1 . 55 10 32 particle/m 3 = 2 . 57 10 5 mol/ Let a = 1 . 10- 5 be the O 2 activity, n a the O 2 concentration, and let b = 1 . 10- 7 be the CO activity, n b the CO concentration. Compute the concentrations using eq 5: n a = a n a Q = 10- 5 3 . 14 10 5 mol/ = 10- 5 1 . 89 10 32 particle/m 3 = 1 . 89 10 27 particle/m 3 = 3 . 14 mol/ n b = b n b Q = 10- 7 2 . 57 10 5 mol/ = 10- 7 1 . 55 10 32 particle/m 3 = 1 . 55 10 25 particle/m 3 = 25 . 7 mmol/ Compute partial pressures. Convert concentration to pressure using the ideal gas law: p = n (as derived in class). Compute (use that J = N m): p a = n a = 1 . 89 10 27 m- 3 4 .....
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This note was uploaded on 09/28/2008 for the course CHEM 2880 taught by Professor Freed, j during the Spring '06 term at Cornell University (Engineering School).

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Chem288_2005_PS5_solutions - Chemistry 288 Problem Set 5...

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