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Thermodynamics of Mixtures

by: Cordie Balistreri

Thermodynamics of Mixtures CBE 311

Cordie Balistreri
GPA 3.59

Regina Murphy

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Regina Murphy
Class Notes
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This 3 page Class Notes was uploaded by Cordie Balistreri on Thursday September 17, 2015. The Class Notes belongs to CBE 311 at University of Wisconsin - Madison taught by Regina Murphy in Fall. Since its upload, it has received 40 views. For similar materials see /class/205199/cbe-311-university-of-wisconsin-madison in Chemical Engineering at University of Wisconsin - Madison.


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Date Created: 09/17/15
Review answers for Chapters 8 7 10 October 14 2010 CBE 311 1 D 2 Find PM of butane at 12 C by setting fV fL 31175 mm Hg or 154 atm or 0157 mPa 4 62 G1 RTlnPzP1 P2 5 02 01 fZRT LP P P1 6 dG VdP Rlen f lirn 1 at constant T P gt0 7 P 1 1398 8 lni G G P RT P 9 1115 f dP P 0 P 10 attractive intermolecular interactions lead to f lt P f gtP if excluded volume interactions or other repulsive interactions are strong enough to overcome attractive interactions 11 025 7 because PM 1 atm andP 4 atm 12 use the equal area rule N 53 MPa mt 13 atter line is liquid fugacity Intersect at P 14 For water a 89 X 105 b 189 for ethanol at 19 X 106 b 523 It makes sense that b is bigger for ethanol because of its size a is a bit bigger possibly due to greater acentricity 15 Units are MPa For water P N 0065 MPa For ethanol Psat N 016 16 For two component mixture containing A and B TLTV PLPV 542 154 The last 2 equations could be replaced by equivalent expressions about the chemical potentials or Gibbs energy 17 1 atm 18 about 86 C Xem N 011 yem N 046 I I PSllt PSllt 19 Just under 92 C from solv1ng yem yw 1 WTM XWTW 20 yiP xiPlmt is Raoult s Law but also ylQJIVP xiplLP For ideal gas 3 1 and this is almost true for any gas at low pressures so we combine these equations to get that A I Plsat I 0 w h z For ethanol at 90 C and 1 atm pressure from Raoult s law and Antome xi A L 1 187 e uation we estimate z 7 156 q eth 7 60 AL L feth xyethfeth 039155 154 AL 21 pm yethP yemP 0101325 1V V vevm MM 09w yemP yemP 0101325 22 At 900C yew 039 and xm 007 From Q 20 of z i 56 Could correct x1 for vapor fugacity assuming lewisrandall for vapor phase So ethanolwater solution is very nonideal 23 It becomes closer to 1 because y x at the azeotrope 25 b x1121 x2122 a x12a1 2x1x2a12 X22d2d12 alaz 12 26 Good guess ofT is to apply Raoult s law We did this already in Q20 T7 917 C yew 7049 37886 11139 27 I et 7X031158 g ye h 09815 yw 09914 need a new 7 lower 7 guess of T I will also adjust the guess of y by normalizing to y 11581945 0595 This is less important than getting the Tright X 07 0786yeth yW 1945 gt1 so I A L A L 28 Ijust calculate yam xem yw xw at a given temperature 7I know at the at Pw bubblepoint xem 03 and xw 07 and I estimated that vaporphase fugacity coefficients are 71 Or I could use the pure component fugacities plus the LewisRandall rule but I m lazy I estimate the bubblepoint temperature somewhere between 75 and 70 7 say around 73 C This would give a vapor composition of about 63 mol ethanol 29 I should have gotten a T of around 82 C a vapor composition just under 60 Ethanolwater form a minimumboiling azeotrope so need kew gt 0 30 0 4221911119 0 RTExl 111x 31 RTExi1n i 32 The work output is equal to the AGmix You can find this result by looking at the energy and entropy balances assuming SIgen 0 This would give the maX work output and would require a heat input The result is 1728 Jmol 33 Essentially this is the same as calculating G 7 GIG For CO2 work output 2563 Jmol For N2 work output 69 Jmol So CO2 is much better


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