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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 permolecule 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).
 Spring '06
 FREED, J
 Chemistry, pH

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