Review for Exam III /01/02 Study Guide Spring 2002 YT

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1 Revew for Exam III /0/0 Study ude Sprng 00 YT xtures ) What s the defnton of partal molar property? Try sayng t n words rather than equaton. ) Why s the partal molar property not the same as the pure property? What can happen when we mx dfferent speces? 3) How s excess property defned? 4) Do deal gases always form deal mxtures when allowed to mx? 5) Pck a property, say. Revew the ways we can calculate the partal molar volume. What about straght dfferentaton? What s the alternatve way that only works for bnary mxture? What about graphcally? 6) What s the bbs-duhem equaton? In what ways s t useful? 7) For deal soluton, what s the molar volume? 8) For deal soluton, what s the molar enthalpy? 9) For deal soluton, what s the molar entropy? 0) For deal soluton, what s the molar bbs free energy? ) What s the defnton of nfnte dluton property? Phase Equlbrum ) How s fugacty defned? What unt does t have? 3) How s the fugacty coeffcent for a pure component defned? 4) For pure vapor, the fugacty coeffcent can be calculated usng several methods. What are these methods and when are they applcable? 5) How s the actvty coeffcent defned? It descrbes non-dealty n What nformaton s usually needed to calculate t? 6) Fugacty coeffcent of a pure gas s related to bbs free energy by ths equaton: 7) Fugacty coeffcent of a gas n a mxture s related to bbs free energy by ths equaton: 8) Actvty coeffcent s related to bbs free energy by ths equaton: 9) How do we calculate the fugacty of the followng: a) Pure vapor: ) deal gas ) non deal gas b) Speces n a vapor mxture: ) deal gas ) non deal gas c) Pure lqud d) Speces n a lqud mxture: ) deal lqud soluton ) non-deal soluton 0) What s the Poyntng correcton factor? When s ths term sgnfcantly dfferent from? ) For a vapor lqud equlbrum, we have the most general expresson: ) Identfy each term n the equaton above. 3) What equaton do we have to estmate the uraton pressure of a common chemcal speces at a gven temperature? 4) What s Henry s law constant? Ths s useful to calculate fugacty of a speces n soluton when ts mole fracton s or when t s very 5) Draw a Pxy dagram for bnary system. Pck an arbtrary mole fracton. Show graphcally the bubble pont and the dew pont. 6) What s azeotrope? Is azeotrope possble for a system of deal gas and deal soluton? 7) How can we check for azeotrope quckly wthout havng to solve the equlbrum equatons. Dsclamer: Not meant to be comprehensve. Not meant to reflect exam s emphass ether. Consult your notes and textbook before takng prescrptons. Followng ths gude blndly nto the test may cause severe pancs, cold sweatngs, and unwarranted anger towards your TA.

2 Revew for Exam III 0.3 ayday 0 Sprng 00 YT Quck Problems ) What s wrong wth ths demand: I want to set up E of a mxture of speces A and speces B at 00 o C and 50 atm, wth lqud composton x A 0.005? ) For a bnary system, we are told that γ exp(x +Ax x ) and γ exp(x +Ax x ) a) What s E /? b) Are the expressons for γ as gven above thermodynamcally sound? Why or why not? 3) Show that an azeotrope s not possble for a system where the gas s deal and the lqud soluton s deal. 4) (Not too short, not too long) For a bnary mxture, the followng nformaton about entropy (S) and enthalpy (H) are gven. E S x S + x S R x(ax + ln x) - Rx (Ax + ln x ) and H 0 A some constant; S entropy of pure component. Fnd an expresson for γ.

3 Revew for Exam III 0.3 Sprng 00 onger Problems ) (from Fall 000 Exam III) The followng xy chart apples to a bnary mxture of ethanol and water. a) What volumes of pure ethanol and pure water must be mxed n order to produce 00 cm 3 mxture contanng 50% ethanol by mass? b) By how much wll the volume of ths mxture change f 0. cm 3 pure ethanol s added to t? ) For a ternary mxture of water() and two unknown speces () and (3), the followng nformaton s gven: ln γ x x 3 (-x ), ln γ x x 3 (-x ), ln γ 3 x x (-x 3 ). The mxture forms E at 00 o C. a) Calculate the fugacty of water n the vapor when the system s at equlbrum at 00 o C and 50 atm, wth water makng up 50 mol% of the lqud soluton. b) What s the mole fracton of water n the vapor when the system s at equlbrum at 00 o C and atm, wth water makng up 50 mol% of the lqud soluton? 3) The followng nformaton s gven for our two favorte speces () and () at 75 o C: E / x x (A x + A x ) where A 0.6 and A.5. P. atm and P.7 atm. Henry s law constants: H.87 atm and H.0 atm. What s y f x 0.99?

4 onger Problems (cont d) 4) A bnary mxture of () and () was shown to have an azeotrope x 0.85 at T5 o C. The uraton pressures can be approxmated as: P /atm (0.0)(T/ o C) and P /atm + (0.005)(T/ o C). If we assume that E / can be approxmated as Ax x, a) Determne A. b) In a separaton process, a mxture of 30 mol% speces flows nto a flash tank, whch s at some T and P. The mxture forms vapor and lqud, whch are drawn as two separate streams. The vapor and lqud streams have the same molar flow rate. The lqud composton s 35 mol% speces. At what temperature and pressure should the tank be kept at? 5) A bnary mxture forms vapor-lqud equlbrum at 00 o C. At that temperature, P atm and P 0.5 atm. The followng chart s gven for E / for temperature and pressure range of nterest: a) Calculate the bubble pont composton and pressure at 00 o C for x 0.5. E / b) erfy that for y 0.63 the dew pont s at P0.98 atm and dew composton x x

5 xtures : U, H, S,, A,, ln φ, ln γ (n) n T,P,n j x x d 0 (bbs-duhem,const T&P) x 0 For bnary only: + x x d dx d dx graphcal method Ideal and Real xtures Ideal mxture: H d Σ x H S d Σ x S - R Σ x lnx d Σ x d Σ x + Σ x lnx Real mxture: g + R (gas) d + E (lq) Note: A pure lqud s an deal lqud soluton, but a pure gas can stll be non-deal. e.g. x γ but y φ Fugacty and Actvty Γ (T) + ln f Γ (T) + ln (pure) (mxture) φ f P ˆ φ y P γ x f E apples to any phase n equlbrum pure mxture R f φp ln φ φ also fromgen.corr. apor ˆ φ y P R ln ˆ φ pure mxture mxture, x 0 mxture, x f qud φ γ x f x H P x P (P P exp E ln γ Henry 's ) law ews-randall rule Applcatons Txy, Pxy, dew, bubble, azeotrope, flash calculaton