Gibbs-Duhem Equation
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1 Gbbs-Duhem Equtn rvdes reltnshp (cnstrnt) between prtl mlr prpertes es f dfferent speces n mture. V V (,, n, n,... n,... n m ) dv V d V d m V n, n n,,, n j j dn dv At cnstnt nd : m V n,, n j j dn ut: dv V n dv n V V dn m dv V dn n dv Gbbs-Duhem Eqn. t Cnstnt nd.
2 Gbbs-Duhem (Generlze) In generl e ths sme frm hlds fr ny prtl mlr quntty (cnst. & ): n dk dk dk E Lk t bnry (vlume): n dv n d V dv dv Generl Gbbs Duhem Equtn: K, n ll d K, n ll d m n dk G, n ll d G, n ll d m n dg Sd Vd m ndg m Sd Vd n d
3 Gbbs-Duhem (uses,.e., bnry slutn t cnst. & ) V V (A) 3 d dv Vd dv Vd () dv dv (C) d V d Vd (D) d d d V d V d (E) V V d (E) V V V V V (A) d d V d d V (F) d d
4 rtl Mlr Vlume (bnry) 4 cm 3 ml V V V V d d d d
5 Other Ecess Functns 5 ) ( ) ( E ),, ( ),, (,, s m rusntz, 3 rd Ed, p 38, eqn 7-67 E m E g h h Kretsky p 35 eqn 7 48 n m, Kretsky, p 35, eqn 7.48
6 Multcmpnent hse Equlbr (6.4) 6 Equlbrum: u g g he drvng frce fr mss trnsfer s the dfference n the speces chemcl ptentl between (r mre) phses. In Mss rnsfer Clss the dfference between chemcl ptentls wll nrmlly be epressed s cncentrtn dfference, but nt lwys. Fr equlbrum clcultns, we need t knw the ndependent vrbles.
7 Gbbs hse Rule (nn-rectng system) 7 Or number f degrees ees f freedm: F m nry, A nd? wht nterested dn knwng?
8 Lecture 7 Chpter 5 - hermdynmc Web - Deprture Functns - Revew Equtns f stte (chpter 4, brefly) Chpter 6 - Equlbrum (chemcl ptentl) * ure Cmpnent * Mtures Chpter 7 - Fugcty (chemcl ptentl fugcty equlbrum clcultns) * Vpr (vervew), lqud, slds - Actvty Ceffcents [Fugcty Ceffcents (vervew)] Chpter 8 - hse Equlbrum * Dgrms * Vpr Lqud (VLE) * Lqud Lqud (LLE) * Sld Lqud (SLE) Chpter 9 - Rectn Equlbr 8
9 Lecture 7 Chpter 5 - hermdynmc Web - Deprture Functns - Revew Equtns f stte (chpter 4, brefly) Chpter 6 - Equlbrum (chemcl ptentl) * ure Cmpnent * Mtures Chpter 7 - Fugcty (chemcl ptentl fugcty equlbrum clcultns) * Vpr (vervew), lqud, slds - Actvty Ceffcents [Fugcty Ceffcents (vervew)] Chpter 8 - hse Equlbrum * Dgrms * Vpr Lqud (VLE) * Lqud Lqud (LLE) * Sld Lqud (SLE) Chpter 9 - Rectn Equlbr 9
10 Equlbrum (chemcl ptentl fugcty) Equlbrum: u g g G G n,, n j f f G.N. Lews ntrduced Fugcty: & f f Reference stte r stndrd stte t reference pressure t sme s & f R f f
11 R Fr Idel Gs: f f lm Fugcty (Idel Gs Stte) f p f Fugcty unts f [pressure] cn thnk f s crrected pressure r escpng tendency R p p f p
12 R f f Fugcty (Rel Gs) Fr Rel Gs: f p & p Clculted t system nd f (,, y r )
13 f f f Equlbrum Fr VLE bnry ysystem cntnng speces A nd, wht re equlbrum equtns? f V A f L A f V f L 3
14 Fugcty Ceffcent (methds t clculte) 4. Dt. Equtns f Stte 3. Generlzed crreltns. ure Flud 3. Generlzed crreltns b. Multcmpnent system:. ure Flud. Dt d d R CO t 38 C, 3.79 br [br] dt CO. 95 d R
15 Fugcty Ceffcent (methds t clculte). ure Flud. Equtns f Stte 5 See hndut n webste frm Kyle fr eng-rbnsn EOS 3 ( ) ( A 3 ) ( 3 A) ( ) A CO t 38 C, 3.79 br REOS CO.935
16 Fugcty Ceffcent (methds t clculte). ure Flud 3. Generlzed Crreltns 6 lg lg () lg () Lee-Kesler (eqn 7.3, Kretsky) CO t 38 C, 3.79 br GenCrr.9394 CO t 38 C, 3.79 br CO Chrt CO.96
17 Fugcty Ceffcent (methds t clculte) 7. Dt. ure Flud. Equtns f Stte 3. Generlzed crreltns b. Multcmpnent system: vdw EOS R y y b b R b y f b b m m v v c eng Rbnsn EOS (see Kyle hndut n web) A A A j j j A
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