Models for the Excess Gibbs Energy

Transcription

1 Models for the Ecess bbs Energy

2 Models for the Ecess bbs Energy E/R s a functon of P and composton E R ln herefore E ln R But for lquds at low to moderate pressures t s a very weak functon of P. herefore the pressure dependence of actvty coeffcents s usually neglected.

3 hus Models for the Ecess bbs Energy E g N R For bnary systems the functon most often represented by a power seres n E R a b c

4 Models for the Ecess bbs Energy Snce = - therefore E A B R hs s know as the Redlch/Kster epanson whch s the most commonly used polynomal n regular and subregular soluton models

5 Regular Soluton Recall d R ln Let RS RS Regular soluton s an non deal soluton wth small devaton from deal soluton Regular soluton s defned as a soluton possesses an enthalpy of mng but no entropy of mng.

6 Regular Soluton hat s RS H RS S RS H RS S d herefore RS d H RS H d H RS

7 Enthalpy of Regular Soluton he word regular mples that the molecules m n a completely random manner whch means that there s no segregaton or preference. onsder two neghbors n a soluton. he probablty that one of the neghbors s A or B s smply P P A B N N A A N N A B N N B B A B

8 Enthalpy of Regular Soluton herefore the probablty that a gven ``bond'' s A B type s N A B P AB PAB PBA N A N B If each atom has z nearest neghbors the number of bonds total s total z total z B N A N B B N A B

9 Enthalpy of Regular Soluton he bond densty of A-B type s: total B AB P AB B zab If the energy per bond s w (AB) then the enthalpy densty (due to the A-B bonds) s: Smlarly H H RS H RS zw AB AB A B AA AA A A AA RS z z w w BB BB B B P A

10 Enthalpy of Regular Soluton herefore Snce herefore H A H mng B H sol B H pure and RS AB AB w AB z z A B w RS w AA A w BB

11 Regular Soluton Accordng to the defnton of Regular soluton entropy of mng equals to deal soluton herefore z RS AB AB AB E RS A H B w z RS A RS B w S d Rln ln RS A A B B

12 Regular Soluton A B A A B A B B A A B A B RS AB A RS AB RS E B H H H bbs-duhem

13 Regular Soluton Snce herefore E RS E R ln ln ln A B RS E B B A RS E A R R R R

14 Otto Redlch AND A.. Kster Epanson Recall For bnary system E R ln E R E d R d ln ln ln

15 Otto Redlch AND A.. Kster Epanson herefore Used n H ERS ln E R E d R d ln E R E d R d Let Q E R

16 Otto Redlch AND A.. Kster Epanson Snce Q = 0 for = 0 and = each term must contan the factor ( ). Introduce the epanson E Q B D R he coeffcents may be determned by Q ln ln ( ) hs s know as the Redlch/Kster epanson

17 Or Otto Redlch AND A.. Kster Epanson dq ln B d ase deal soluton ln 0 6 ase B 0 D =0 a form of regular ase B 0 0 DE =0 subregular

18 rtera for Equlbrum Huang Mn hemstry Department ongj Unversty

19 rtera for Phase Equlbrum Assume at the begnnng that we know nothng about the condtons under whch two phases can be n equlbrum. he only thngs we know from the Second Law are the crtera for equlbrum under certan condtons. hat s ds E V 0 d P hat s: the entropy seeks a mamum bbs free energy seeks a mnmum 0

20 rtera for Phase Equlbrum onsder a multphase multcomponent system. Each phase comprses a dfferent subsystem. Reparttonngs of etensve varables can be accomplshed by shufflng portons of the etensve varables between the dfferent phases E a E Reparttonng of the energy would correspond to changng the E(a) s but keepng the total fed. a

21 rtera for Phase Equlbrum We have where s the number of moles of speces n phase a. a a a a a a n n V V S S a n

22 rtera for Phase Equlbrum Form the defnton of d E as the frst-order varatonal dsplacement of E v r a a a a de ds p dv a v dfferent phases r dfferent speces a a n From the Second Law at the equlbrum E must be t s mnmum therefore any devaton must de 0 S V n d

23 rtera for Phase Equlbrum onsder repartton processes whle keepng the total S V n fed. Whch requres a a a n V S r n V S for a a a a a a d d d

24 rtera for Phase Equlbrum onsder a two-phase system

25 rtera for Phase Equlbrum he consstency of S V n corresponds to ds dv dn dn ds dv dn dn dn r dn r

26 rtera for Phase Equlbrum herefore the frst order dsplacement of E at constant S V n s 0 de S V n ds p p dv r dn Snce these varables are ndependent and ther varatons are uncoupled the only soluton to the de 0 S V n

27 rtera for Phase Equlbrum whch wll guarantees p de 0 S V r For multphase p p v v p p v n s r

28 Further Dscuss Snce () = () guarantees mass equlbrum t s nterestng to study what acton a gradent n produces.

29 Further Dscuss onsder the system s prepared ntally wth () > () Mass flow wll brng t to equlbrum wth fnal fnal. If no work s done on the total system and there s no heat flow nto and out the system S > 0. Assumng dsplacements from equlbrum are small S snce n n n. n S > 0 when () > () mples n () < 0 that s matter flows from hgh to low. n

30 Further Dscuss he gradents n (or more precsely gradents n /) produce mass flow. / s a generalzed force. In the varant statement of the Second Law we see a smlar form / s a generalzed force that causes heat to flow from hgh to low.

31 he Phase Rule Suppose v phases are coestng n equlbrum. he condtons for equlbrum p p a a a r r where a < and I r here are r(-) ndependent equatons whch couple together + (r-) dfferent ntensve varables ( p and the mole fractons for each phase).

32 he Phase Rule Hence the thermodynamc degrees of freedom (the number of ndependent ntensve thermodynamc varables) s f v( r r v ) r( v ) hs s the bbs phase rule.

33 opcs n Phase Equlbra

34 Bnary Sold-lqud Equlbra of n- decanol and n-dodecanol Marcos Serra ómez-ncolau utor: Dr. Huang Mn oordnator: Dr. Hu Zhong-Hua Department of hemstry ongj Unversty January 00

35 Inde Introducton hermodynamcs ALPHAD hermo-alc Possble causes of dscrepancy onclusons Append: Drect ontact Melt rystallzaton

36 Introducton aprc alcohol -decanol decan--ol decyl alochol Laurc alcohol lauryl alcohol -dodecanol dodecan--ol Natural: from fats ols and waes of plant or anmal orgn Synthetc: from petrochemcals H (H ) n H OH n = 4-0

37 Introducton Fatty alcohols from natural sources Plant or anmal orgn Wa esters from the sperm ol of whale decanol dodecanol orander leaf osmanthus absolute (9.0%) corander leaf ol ( %) ambrette seed ol (0.60%) frankncense ol from Somala (0.40%) ctronella ol from Zmbabwe (0.%) kachur ol (0.0%) volet leaf (.60%) cochlospermum planchon ol (0.70%) cochlospermum tnctorum ol (0.70%) ambrette seed ol (0.0%) corander leaf ol ( %) Ambrette seed Volet leaf

38 Introducton Uses of fatty alcohols Surfactants (ca %) Ol addtves osmetcs and pharmaceutcal preparatons Polymer processng Preservatves for food Emulsons and mcroemulsons (cosmetcs creams and lotons) Fragrance Materals = fragrance compound + water + alcohol (creams deodorants lotons ) Decanol Dodecanol Odour type Fatty Way Odour strength Medum Medum Odour descrpton at 00% aste descrpton Fatty way floral orange sweet clean watery Aldehydc way green fatty tart perfumstc Earthy soapy way fatty honey coconut Soapy way aldehydc earthy fatty

39 hermodynamcs Real bnary lqud mture bbs energy For the calculaton of phase equlbra t s necessary to mnmze the total bbs Energy: ) ( ) ( ) ( 0 P m P mnmum F n

40 hermodynamcs P P ) ( ) ( IM R P P ln ) ( ) ( Ideal mture: Real mture: e R P P ln ) ( ) ( Real bnary lqud mture bbs energy

41 hermodynamcs e R P P ln ) ( ) ( 0 B A a n e Redlch-Kster polynomal epanson: emperature-dependent parameters: V V A Varables to be optmzed wth hermo-alc Real bnary lqud mture bbs energy

42 tr tr tr tr d p d p S H S H P * * ) ( hermodynamcs Real bnary lqud mture bbs energy e R P P ln ) ( ) ( 4 * p tr H S tr tr ln ln tr tr tr tr tr tr tr tr H r H tr tr

43 p (J K - mol - ) p (J K - mol - ) hermodynamcs Dependence of heat capactes wth temperature p * (K) (K) Růžčka (004) Zábranský (990) ees (00) Equaton p n 0.04n

44 p (J K - mol - ) p (J K - mol - ) p (J K - mol - ) hermodynamcs Dependence of heat capactes wth temperature y = 5E E E E+0 R = 996E * p DE * p DO (K) y = -55E-06-69E E E+0 R = 9975E-0 y = -55E-06-69E E E+0 R = 9975E (K) Růžčka (004) Zábranský (990) ees (00) [8] Equaton () Polynomal (Růžčka (004))

45 hermodynamcs bbs energy functons ln ln tr tr tr tr tr tr tr tr H r H tr tr 5. * p DE 6 * p DO ln DE ln DO K DE m 80. ) ( 7.66 ) ( mol kj DE H fus K DO m 00. ) ( 40.7 ) ( mol kj DO H fus

46 ALPHAD ( P ) ( P) R ln e Bnary: (A B) e bn assessment ernary: (A B ) Etrapolaton assessment: e bn e ter and e bn e ter Quaternary: (A B D) Etrapolaton assessment: e qua e bn e ter and e e ter bn e qua

47 hermo-alc What s hermo-alc software? hermo-alc s a general and fleble software for all knds of thermodynamc and phase dagram calculatons whch s based upon a powerful bbs Energy Mnmzer. It s especally desgned for systems wth strongly non-deal phases. hermo-alc also provdes a unque tool (the PARRO module) for crtcal assessment based upon vared epermental data such as EOS phase equlbra phase dagrams and so forth.

48 Assessment hermo-alc bbs Energy System Module (ES) Optmzaton Module (PARRO)

49 hermo-alc Varable Value RSD V V V V e Reduced sum of squares: A Lqud phase : Sold phase : A V A V 5 V V 6

50 hermo-alc

51 Possble causes of dscrepancy

52 Possble causes of dscrepancy. Fuson enthalpes H H fus fus ( DE) 8.79 kj mol ( DO) 7.74 kj mol vs H fus H fus ( DE) 7.66 kj mol ( DO) 40.7 kj mol DE DO ln ln Varable Value RSD V V V V Reduced sum of squares:

53 Possble causes of dscrepancy. Fuson enthalpes S fus n j n j j S H roup coeffcents Acyclc hydrocarbon groups roup value tr j S Prmary fus ( DE) 4.9 cal K mol sp carbon atom H [] Secondary sp carbon atom H [ ] S ( DO) 9.4cal K mol fus ertary sp carbon atom H[ ] Quaternary sp carbon atom [ 4 ] j k n k K k tr tr H ( DE) 9.8 kj mol roup coeffcent ( K ) fus roup Functonal group (k) value ( k ) H fus ( DO) kj mol 4 Hydroyl group Alcohol Varable Value RSD V V V V Reduced sum of squares:

54 p (J K - mol - ) p (J K - mol - ) p (J K - mol - ) p (J K - mol - ) Possble causes of dscrepancy. Heat capactes (K) old formula Růžčka (004) (K) (K) y = 86E E+0 R = 9987E-0 Růžčka (004) lnear regresson Růžčka (004) cubc regresson y = E E E E+0 R = 0000E (K)

55 p (J K - mol - ) Possble causes of dscrepancy 60. Heat capactes * p DE * p DO DE ln old formula Růžčka (004) new lnear formula new cubc formula DO ln (K) Varable Value RSD V V V V Reduced sum of squares:

56 p (J K- mol-) Possble causes of dscrepancy. Heat capactes * p DE * p DO y = E E E+0 R = 99660E DE DO 494. ln ln Růž čka (004) quadratc formula (K) Varable Value RSD V V V V Reduced sum of squares:

57 (K) (K) Possble causes of dscrepancy. Epermental data Mass fracton of of dodecanol

58 . Epermental data ponts Possble causes of dscrepancy Varable Value RSD V V V V6 Reduced sum of squares:

59 Possble causes of dscrepancy. Epermental data ponts Varable Value RSD V V V V Reduced sum of squares:

60 4. Subregular Model Subregular Soluton Model 罗婕 Level rule E A B ( ) j j j j c c m j j j j j [ A B ( )] E [ A B ( )] m

61 ontnue Suspenson rystallzaton

62 ontnue Suspenson rystallzaton 王文静 O-M Bnary Sold Lqud Equlbrum usng regular soluton model

63 ontnue Suspenson rystallzaton 郭艳姿 郭思斯 mx-px ox-px ox-mx px-mx-ox ernary