HW_wk8_solutions_2006 - 2R03 HW for weeks 8_9 Nov 3 2005...

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2R03 HW for weeks 8_9 Nov 3 2005 STUDENT NAME ______________ _____________ STUDENT NUMBER ___________ Credit: 1.5% if submitted with fully explained solutions on or before the due date of Nov 23, 2005 ( drop boxes ##28-30 , which are located in ABB 1 st floor in the beginning of the hallway behind the blue doors opposite the main office ABB-156). Please attend the assigned tutorials if you have any question on these exercises . Note: All gases are assumed to be ideal and all thermochemical data are for 298.15K unless otherwise specified 1.a The air in the barn of a sheep farm contains methane (molar fraction = 0.015), along with N 2 (molar fraction = 0.775) and O 2 (molar fraction = 0.21). Assuming that far enough from the barn the air is composed only of N 2 and O 2 ( x N2 = 0.78), what is the absolute value of the change in the molar Gibbs energy of air caused by the presence of methane? (Assume that the pressure and the temperature are fixed at 1 bar and 298.15 K, respectively, and remember that: R = 8.31 JK -1 mol -1 ) Solution: The change in the molar Gibbs energy of air caused by the presence of methane can be considered as the difference between two mixing processes. The first mixing process is N 2 and O 2 to form air. The second one is mixing of N 2 , O 2 and methane. So, mol J K mol JK x x x x RT x x x x x x RT G G G O O N N CH CH O O N N / 152 ) 22 . 0 ln 22 . 0 78 . 0 ln 78 . 0 015 . 0 ln 015 . 0 21 . 0 ln 21 . 0 775 . 0 ln 775 . 0 ( 15 . 298 31 . 8 ) ln ln ( ) ln ln ln ( 1 1 1 2 2 2 2 2 4 4 2 2 2 2 - = - - + + × × = + - + + = - = - - 1.b For the previous exercise, what is the sign of the change in the molar Gibbs free energy: (a) positive (b) negative Solution: b . See above. Indeed when we add a new (ideal) gas to a system we increase its entropy with affecting its enthalpy. 1.c
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HW_wk8_solutions_2006 - 2R03 HW for weeks 8_9 Nov 3 2005...

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