PREDICTION OF DIFFUSIVITIES IN LIQUID ASSOCIATING SYSTEMS ON THE BASIS OF A MULTICOMPONENT APPROACH

Transcription

1 PREDICTION OF DIFFUSIVITIES IN LIQUID ASSOCIATING SYSTEMS ON THE BASIS OF A MULTICOMPONENT APPROACH Des Bosse ad Has-Jörg Bart Isttute of Thermal Process Egeerg Uversty of Kaserslauter, D Kaserslauter, Germay ABSTRACT A model for the predcto of pseudo-bary Mawell-Stefa dffusvtes bary systems wth assocato ad solvato effects has bee developed. I aalogy to the chemcal theory ths model s based o a multcompoet approach for the Mawell- Stefa dffuso coeffcets. To reduce the umber of multcompoet dffusvtes a correlato factor has bee developed depedg o the mole fractos ad the acetrc factor. The reacto equlbrum costats for the assocato ad solvato reacto have bee computed from the UNIQUAC assocato model. For frst model assessmet the results obtaed from ths approach are compared wth epermetal fdgs for the system ethaol-cycloheae gathered from Taylor dsperso epermets. Ths comparso reveals a accurate descrpto of the dffusvtes the dluted regos whereas larger devatos are to be epected the mddle cocetrato rage. These devatos ca be eplaed wth the shape of the thermodyamc correcto factor computed from g E -models where ther fluece o the predcto accuracy of dffuso coeffcets has bee addtoally eamed. It ca be show that the UNIQUAC assocato model s superor to the Wlso equato descrbg the VLE data of the system vestgated, especally the dluted cocetrato rages. From ths t ca be cocluded that the correcto factor computed wth ths model yelds dffusvtes of hgher accuracy for ths type of system. INTRODUCTION Dffuso plays a mportat role all kds of separato processes, e.g. dstllato or absorpto. Sce the creasg usage of oequlbrum (NEQ) stage modellg [] a deeper sght to mass trasfer has become more mportat order to allow accurate ad relable predctos of e.g. cocetrato profles ay kd of equpmet. Fudametal kowledge o varous physcal ad thermodyamc propertes, e.g. dffuso coeffcets, s requred. Especally hghly o-deal systems, thermodyamc o-dealtes caused by dfferet szes, shapes, ad teracto eerges as well as assocato ad solvato of molecules strogly

2 fluece the dffusoal behavour. Eve for bary systems these effects usually result large devatos betwee epermetal data ad predcted values sce ether the Mawell-Stefa-dffusvty models (MS) or the g E -models commoly used, e.g. UNIQUAC or Wlso, accout for chemcal teractos. Dffuso problems are tackled wth the Fck s law or the Mawell-Stefa equato. The relato betwee the two has bee gve by Taylor ad Krsha [2]. For a bary mture ths yelds: DΓ Ð () As ca be see from ths equato the Fck dffusvty, D, equals the MS dffuso coeffcet, Ð, tmes the thermodyamc correcto factor, Γ. The ma dfferece betwee both models s that the MS-approach separates dffusoal effects from thermodyamc o-dealtes whle the Fck dffuso coeffcets must also accout for the o-dealtes the mture. Several vestgators have attempted to develop models to predct dffusvtes. Satsfactory results ca be obtaed for deal ad slghtly o-deal bary mtures whereas these approaches fal for hghly o-deal systems, e.g. systems wth a alcohol or ketoe as solute. At frst sght, oly two costtuets are preset such mtures, amely the moomer molecules of a solute ( A ), e.g. alcohol, ad a solvet ( B ). I realty these mtures cosst of several compoets due to assocato ad solvato effects betwee the varous speces formed. Therefore, t s straghtforward to model such systems terms of a multcompoet approach. A frst attempt was coducted by Mc Kegue ad Gular [3] who predcted Fck dffusvtes. Later, aother attempt has bee made by Rutte [4] who developed a model to predct MSdffusvtes a assocatg system, where oly solute-solute teracto effects are cosdered. A dfferet model was also derved by hm that descrbes the stuato of a solvatg system whch oly A, B ad the solvated speces AB are preset. The multcompoet models derved are oly of lmted use sce most systems solute-solvet teracto effects do also occur. Therefore, the ma goal of ths work s to preset a model that accouts for both effects smultaeously. Due to the separate treatmet of o-dealtes ad the dffusoal process tself, the MSdffusvty approach s preferred throughout ths work. Based o Rutte s deas hs assocato model has bee further developed to accout also for solvatg effects. Addtoally, the reacto equlbrum costats requred for the assocato ad solvato reactos wll be computed from a eteso of the commoly used UNIQUAC model whch also accouts for these effects. The preset work s outled as follows. Frst, the dervato of the MS-dffusvty model s gve followed by a bref troducto to the UNIQUAC assocato model. I order to valdate the proposed dffusvty model the computed dffuso coeffcets wll be compared wth epermetal data for the bary system ethaol-cycloheae obtaed from a Taylor dsperso ut. Sce the g E -model chose plays a decsve role the predcto of Fck dffusvtes the thermodyamc correcto factor wll also be computed from the Wlso equato ad the results compared wth the oes obtaed from the UNIFAC assocato model.

3 THEORY Theoretcal Dervato of the MS-Dffusvty Model Dffuso processes bary systems wth assocato ad solvato effects ca be treated two ways. From a macroscopc pot of vew the mass trasfer such a system ca be descrbed terms of the moomer speces A (solute) ad B (solvet) whch form ths bary mture. I cotrast, t ca also be charactersed as a multcompoet mture regardg assocates ad solvates formed by H-bodgs as dstct chemcal speces. Sce both pots of vew descrbe the same chemcal system the fdgs obtaed from the two approaches must be equal. Ths s a prerequste for the model dervato below. The theoretcal part s dvded as follows. Frst, the mass trasfer the multcompoet mture wll be derved, afterwards the same mture wll be treated as a pseudo-bary system. Fally, both mass trasfer relatos wll be equated to deduce the pseudo-bary MS-dffusvty as a fucto of the multcompoet MSdffusvtes. Modellg of the system as a multcompoet mture As metoed the troductory part of ths work a mture cosstg of assocated or solvated speces ca be regarded as a multcompoet mture. The reactos takg place to form assocates ad solvates are cosdered as equlbrum reactos whereas assocato ad solvato must be treated separately. Assocato: A+ A A γ A A A (2) K γ AA γ A A Solvato: K S ( )( ) A + B AB γ ABAB ( γ A )( ) A γ BB From these equatos t ca be see that 2 chemcal speces are preset the mture: assocates (cl. moomer A ),.e. AA, 2,..., A solvates,.e. AB, A2B,..., A B moomer B Here, descrbes the umber of assocates formed cludg the two moomer compoets, e.g. 3 A, A2, B. For the model dervato the mole fractos of these compoets are ordered as follows: A, 2 A2,..., A, AB,..., 22 A B, 2 B The same dces apply to other varables, too. (3)

4 Dffusoal flues the multcompoet system The dffuso flues of the varous speces ca be easly wrtte terms of the Mawell-Stefa-equatos. Hece, the flues of 2 2 compoets are gve by: & c Ad c Ad cδ Ad (4) t j j j t j j j t j j j whereas A j s a elemet of the verse matr of [ B ] wth dmeso (2 2) ad d j equals the drvg force of j. The elemets of matr [ B ] are defed accordg to the dervato of the MS-model [2]. B 2 k + (5) Ð k Ðk k Bj (6) Ðj Ð The addtoally troduced varable δ (4) deotes solvato effects. For δ solvato effects occur, f δ 0 oly assocato effects are cosdered ad the equatos ca be smplfed. The flu of the last costtuet ( 2 ) s defed wth respect to the bootstrap relato 2 & 0 to gve: t j j j & & c A d (7) Drvg forces Due to the Gbbs-Duhem restrcto oly 2 2 drvg forces are depedet: d f f 2 f2 δ f (8) The dmesoless drvg force f s defed by: f µ l ( γ) (9) RT RT Combg these equatos wth the equlbrum reactos gves relatos betwee the varous drvg forces of the speces formed ad those of the moomers. Here must also the two cases be dscered. Assocato (... ): The drvg force o the assocated speces ca easly be derved terms of the drvg force o the moomer speces A. From (2) ad (9) the followg equato ca be obtaed or f f+ f f f (0) whch results : d d ()

5 Solvato ( ): The same ca be appled to the secod set of reacto equatos whch fally results : f f + + f2 Together wth (0) the relato ca be rewrtte to gve f ( + ) f+ f2 (2) or: ( + ) d d 2 d + (3) 2 Combg the relatos derved thus far yelds a epresso for the drvg forces of the moomer speces the multcompoet mture,.e. serto of (0) ad (2) (8) gves or: f d 22 + δ ( + ) 2 f δ 22 + δ ( + ) 2 2 d δ α 2 d (4) (5) Modellg of the system as a pseudo -bary mture Now the same amout of mture s cosdered as a pseudo-bary, whch solely the moomer speces A ad B occur. I order to dstgush betwee pseudo-bary ad multcompoet varables, captal letters are used to deote the former case. Dffuso flu the pseudo bary mture Settg up the MS-equato for total A yelds: CTÐD X2 N & XN& 2 (6) The dces used have bee adopted from the dervato of the multcompoet system. Relato betwee both descrptos As aforemetoed the goal s to fd a relato betwee the two dfferet approaches,.e. to epress the pseudo-bary dffusvty terms of the multcompoet MS-dffusvtes whch are hdde the matr [ A ]. I order to relate the two approaches the varables,.e. mole fractos, drvg forces, ad dffusvtes, of the pseudo-bary model must be epressed as fuctos of the multcompoet varables. Mole fractos Frst, the real (multcompoet) mole fractos are related to the overall (pseudobary) mole fractos of A ad B the followg way

6 X N N + N2 wth the pseudo-umber of moles N ad N2 defed by: 22 N + δ ( + ) 22 N + δ 2 2 From these equatos the relato betwee the mole fractos ca be deduced: X X 22 + δ ( + ) ( ( ) ) + + δ δ ( ( ) ) + + δ (7) (8) (9) Drvg forces Compared to the multcompoet mture the umber of moles the pseudo-bary system s larger by a factor r. r 2 2 ( ) + ( ) + δ Wth ths, the drvg forces of the two systems are lked as follows: 22 ( ( ) δ ) (20) rx F + + f Itroducg the defto of r ad (8) (20) yelds the followg epresso for moomer speces A : F f (2) The same s true for compoet B: F f (22) 2 2 Pseudo-bary dffusvty O the bass of the equatos derved the relato betwee the pseudo-bary ad the multcompoet dffusvtes ca be deduced. Startg pot s (6) whose varables are cosecutvely substtuted. I the followg the dervato s gve step by step, startg wth the rght-had sde of ths equato. Combg wth a aalogous defto to (7) for flues ad (7) yelds: 22 2 r( X2 N & XN& 2) r X2 ( ( ) δ ) X + + & & & 22 r X2 ( ( ) + δ + ) + X & & & (23) Wth (4): 22 j j cr t + X + A d + A d ( X2 + X)( Ajd j + δ Ajd j) δ ( ) ( j j ) 2 j j j j (24)

7 Before cotug wth the serto of ew terms, the summato terms over j are derved frst. The drvg forces are related to the drvg forces of the moomer speces by troducg () ad (3) ad afterwards (5): 22 j 22 j + d 2 Ad j j + δ Ad j j ja j d δ A j j d j j + j j + 2 j 22 j + α ja j j d+ δ A j jj d d + d 22 ja ( ) j j j + δ A j j j j + + α d β (25) Wth (25) troduced (24) the rght-had sde ca be wrtte as: d 22 cr t ( X2 ) X β X2 δ ( ) β (26) By defg 22 + δ ( + ) (27) sum ad makg use of (8) ad (9) the followg epresso ca be obtaed for the rght-had sde of (6): ( 2 δ ) d + k + k sum k k cr t β + δ ( + ) β sum δ k k sum + k k (28) The left-had sde of (6) s easer to develop. Frst, the pseudo-bary drvg force D ca be substtuted by the dmesoless oe: rctðd CTÐrXF (29) Usg (20) leads to: 22 ( δ ( ) ) C Ð + + f T CT Ð sum d Wth r CT / ct both sdes ca be lked aga ad the epresso for the pseudobary MS-dffusvty ca fally be wrtte sum + δ k k β 22 sum δ k k Ð (3) 2 sum k k 22 + δ ( ) β 2 + sum + k k whereas β s the defed by: (30)

8 ( ) 22 β ja j j j + δ A j jj j + + α α ca be wrtte a smlar way: sum α δ The model derved here corporates both multcompoet models derved by Rutte. For δ 0 ad > 2 the assocato model s obtaed whle for δ wth 2 the solvato model ca be foud. I respect to a frst model valdato preseted below the dervato of the dffusvtes at fte dluto wll be gve for the case of a assocatg system,.e. δ 0. The, (3) reduces to the followg epressos whch the left had sdes ca be ether determed from epermetal dffusvty data at fte dluto or from a approprate model, e.g. Wlke-Chag [5]: X Ð Ð Ð (32) 0,2 AB 2 0 Ð Ð,2 X (33) Followg Rutte s dervato values for the multcompoet dffusvtes of the assocated ad solvated speces have bee estmated by relatg them to the multcompoet dffusvty of the moomers usg a correlato factor, C. Ð, j C, jð,2 (34) For these costats he chose a rato of the va der Waals rad: RvdW, RvdW,2 Cj (35) R R vdw, vdw, j The va der Waals radus tur s defed by R vdw 3V vdw 4π N A /3 whereas the va der Waals volumes, V vdw, of the assocates are take as multples of the volume of the moomer solute. Values for the va der Waals volumes have bee lsted by Edward [6] ad Bod [7]. As wll be show later ths type of dffusvty relato ca be further mproved to allow predctos wth hgher accuracy. The moomer par dffusvty may ow be computed as follows. (32) yelds the dffusvty at fte dluto pure solvet whch s equal to the bary epermetal value. I order to obta the fte dluto dffusvty pure solute (33)-(35) must be combed whch yelds a value depedg o the mture composto,.e. equlbrum costats. At termedate composto the multcompoet dffuso coeffcet of the moomer par s computed from the fte dluto dffusvtes usg a mg rule, e.g. Vges [8]. Oce these dffusvtes have bee calculated the computato of the bary dffusvty gve (3) s straghtforward. j (36)

9 The UNIQUAC Assocato Model I 999 Aspro has eteded the commoly used UNIFAC model to accout also for assocato effects [9]. I hs work bary ad terary mtures of alcohols both ert ad solvatg solvets were vestgated by spectroscopc aalyss respect to the structure of the assocates ad solvates formed. I addto to the structure aalyss, phase equlbrum measuremets were coducted order to obta ew sets of teracto parameters. I the resultg UNIQUAC assocato model the molecular speces are troduced as groups, smlar to the commoly used UNIQUAC model. I the followg the dervato of ths model wth respect to systems whch oly assocato reactos occur,.e. a alcohol as solute a ert solvet, wll be preseted. I ths model are assocates regarded as separate chemcal speces wth reacto equlbra defed by (2). The requred equlbrum costats were determed from depedet FT-IR measuremets. For correlato purposes the umber of assocates cosdered the model was reduced by assumg that, besdes dmer assocato, oly oe hgher assocated speces had bee formed. Ths hgher olgomer ca be see as a represetatve for all hgher assocates occurrg the mture. For the calculato of the equlbrum costat the followg relato s favoured Ref. Ref. Rhk Rsk l K k + k D, Po (37) RT R whereas the reacto ethalpy ad reacto etropy for the dmer reacto are gve by: R h Ref. D Rh Ref. Po h D Ref. Ref. RsPo RsD sd (39) Here, refers to the umber of solute molecules a assocate. The values for the dmer reacto ethalpy ad etropy for the alcohol ert solvet systems vestgated are as follows: h kj/mol (40) D s D 30.03J/(mol K) (4) Eample values for the reacto ethalpy ad reacto etropy, whch are assumed to be depedet of temperature ad pressure, of hgher olgomers ca be foud Table. (38)

10 Table : Reacto ethalpes ad etropes for solvets -heae ad cycloheae Compoet Ref. RhPo [kj/mol] Ref. RsPo [J/(mol K)] Methaol Ethaol Propaol Sce the UNIQUAC assocato model does ot dstgush betwee the teracto of alcohol groups a moomer ad a olgomer wth a solvet molecule, oly two teracto parameters are eeded per bary system. Table 2: Iteracto parameters for ethaol cycloheae a 2 /K a 2 /K O the bass of ths formato t s possble to compute multcompoet actvty coeffcets ad also the thermodyamc correcto factor. Addtoally, the speces dstrbuto crucal for the dffusvty model s also obtaed. EXPERIMENTS I order to valdate the model dffuso coeffcets have bee epermetally determed a Taylor dsperso ut. The epermetal set-up of ths ut cossts of stadard HPLC-equpmet whch has bee fully automated (see Fgure ). All epermets have bee coducted sothermally at 25 C.

11 The chemcals obtaed from Merck Eurolab GmbH were of aalytcal grade ad used wthout further purfcato. Dosg system Dos Dos 2 Dos 3 He 6-port valve Membrae degasser vacuum Chael A Chael B Chael C Chael D HPLC pump 530,638g Cotrol ut 0,5mL/m Capllary PC Refractometer 25 C error out Thermostat Autosampler Fgure : Epermetal set-up of the Taylor dsperso ut RESULTS I order to valdate the model proposed here epermetal data o dffusvtes have bee acqured from Taylor dsperso epermets. Valdato epermets of the apparatus have bee coducted for the systems methaol-water ad ethaol-water. The devato of the epermetal fdgs from lterature data are wth 2% whch equals the accuracy kow for ths type of apparatus. A ew set of dffusvty data s gve Table 3 for the bary system ethaol-cycloheae measured at 25 C. Table 3: Dffusvty data for the system ethaol () cycloheae (2) 3% 0% 20% 30% 40% 50% 60% 70% 80% 90% 97% D 2 [m 2 /s 0 9 ] The dffusvtes at fte dluto have bee determed from etrapolato of the data by fttg a polyomal of degree fve (correlato factor 99.9%) D.38 0 m / s D m / s 2 2

12 As metoed the troducto a thermodyamc correcto factor terrelates the Fck ad the MS-dffusvtes ad has, therefore, a great mpact o the outcome of the modellg process. Hece, t s worthwhle to compare the predcto of the UNIQUAC assocato model wth the Wlso equato kow to be as oe of the most accurate models predctg VLE data. Recommeded VLE data have bee take from the DECHEMA data seres [0] for the above metoed system together wth the correspodg teracto parameters gve for the Wlso equato. Fgure 2 depcts the actvty coeffcets computed from the epermetal data ad the predctos of both models. It s obvous that both models are capable of descrbg the data the rego researchers are mostly terested,.e. the mddle cocetrato rage, whereas larger dffereces ca be see the hghly dluted cocetrato rages. For ethaol ftely dluted cycloheae the Wlso equato predcts a actvty coeffcet otceably smaller tha the UNIQUAC assocato model does. The reaso for ths ca be see the addtoal cosderato of chemcal teracto effects the UNIQUAC assocato model whch are remarkable ths cocetrato rage. Comparso wth lterature data o actvty coeffcets at fte dluto [, 2] reveals that the predcto of the UNIQUAC assocato model s close to the values reported. The cosequeces become obvous the dfferet predctos of the thermodyamc correcto factor as depcted Fgure 3. Especally the dluted regos devatos betwee the models are apparet whch ultmately result dfferet fdgs for the dffuso coeffcets. Summarsg, t ca be presumed that computg the thermodyamc correcto factor wth the UNIQUAC assocato model yelds dffusvtes of hgher accuracy for ths system tha wth the Wlso equato. Nevertheless, both models have bee used to compute MS-dffusvtes from the epermetal data to reveal the fluece of the g E -model o ths trasport property ep Wlso UNIQUAC-A Fgure 2: Actvty coeffcets for a ethaol-cycloheae mture computed wth the Wlso equato ad the UNIQUAC assocato model

13 Wlso UNIQUAC-A Fgure 3: Thermodyamc correcto factors for Wlso ad the UNIQUAC assocato model As Rutte foud out [3] relatg the varous MS-dffusvtes of the assocates ad solvates to the oe of the moomer speces the multcompoet mture by meas of va der Waals rad yelds a correct volume correcto the dluted solute rego. Therefore, several methods have bee tred to fd a ew epresso for the correlato factors C j whch takes both the cocetrato depedece ad the oroudess,.e. devato from a sphere, to accout. For ths purpose the volume fracto as defed the UNIQUAC equato r φ (42) 2 r j j j ad the acetrc factor computed from the Lee-Kesler method [4] combed wth the Joback method [5] for crtcal propertes have bee related to each other varous ways. The resultg correlato factors are gve by the ratos of the varous combatos, e.g. model b of the followg tables: Table 4: Correlato factors ad sum of least squares wth Wlso φ φ R vdw, (/ φ ) (/ φ ) / RvdW, Model/ac. factor W W2 W3 W4 W5 W6 (a) var. (b) /( var.) (c)

14 C j φ φ2 2 φ φ j j Tables 4 ad 5 show all the combatos used together wth the resultg sums of least squares whe applyg ether of the g E -models. The tables reveal that for both g E -models the model 5a performs best. However, larger devatos are to be epected. I Fgure 4 a comparso s gve for the MSdffusvtes computed from epermetal data ad the predcted values calculated wth the best performg correlato factors ad the Wlso equato. It s obvous that ether method ca adequately represet the source data. By varato of the acetrc factor t s possble to greatly mprove the predcto accuracy the cocetrato rage > 0.3 whch comes at the epese of larger accuraces the dluted alcohol regos (curve s the smlar to W4c). A smlar pcture ca be draw for the UNIQUAC assocato model. The correlato factors used ca pcture oly qualtatvely the curve computed from epermetal data. The fluece of these accuraces o the predcto of the Fck dffuso coeffcets s depcted Fgure 5. Here, the epermetally determed data as well as the predcted values computed wth the correlato factors performg best are preseted. Addtoally, values calculated accordace wth Rutte s model are gve for comparso purposes. Due to the overpredcto of the MS-dffusvtes the dluted rego (Wlso equato) the epermetal data caot be properly reflected, see curve W5a. Comparso of ths curve wth Rutte s model (W3a, ot show) shows that wth the modfed correlato factor predctos of hgher accuracy ca be made. As prevously metoed varato of the acetrc factor yelds hgh resemblace for the predcted values ad the Fck data whereas the devato the dluted rego creases markedly. I cotrast, the values computed from the UNIQUAC assocato model perform better the dluted rego whle defceces the mddle cocetrato rage occur. Aga, varyg the acetrc factor results better agreemet to the epermetal data. Comparg U2a wth U3a (Rutte) shows that the correlato factor used for U2a s superor to the rato of the va der Waals (43) Table 5: Correlato factors ad sum of least squares wth UNIQUAC assocato model φ φ R vdw, (/ φ ) (/ φ ) / RvdW, Model/ac. factor U U2 U3 U4 U5 U6 (a) var. (b) /( var.) (c)

15 0 Ð [m 2 /s 0 9 ] ep W5a W4c Fgure 4: MS-dffusvtes predcted from the Wlso equato rad. I Table 6 the sums of least squares are gve for the models preseted the last Fgure. The results clearly demostrate that the model performg best s U2a. Table 6: Sums of least squares for Fck dffusvtes computed wth both g E -models 2a 3a (Rutte) 5a Wlso 20 6 UNIQUAC assoc CONCLUSIONS I ths work a ew model for the predcto of dffusvtes bary lqud systems whch assocato ad solvato effects ca occur has bee preseted. Ths model whch s based o a prevously developed assocato model by Rutte computes pseudo-bary MS-dffusvtes from a multcompoet approach. The reacto equlbrum costats requred for the computato of the assocato ad solvato reacto equlbra have bee adopted from the UNIQUAC assocato model. Ths g E -model also serves to compute the thermodyamc correcto factor, a proportoalty costat that relates the Fck ad the MS-dffuso coeffcet. Sce ths proportoalty costat plays a decsve role computg dffusvtes the results for the thermodyamc correcto factor obtaed from the UNIQUAC assocato model ad from the Wlso equato (recommeded teracto parameters were used throughout ths work) were compared. It could be show that both models show ecellet agreemet wth epermetally determed VLE data the mddle cocetrato rage whereas the predcto of the Wlso equato fals at fte dluto. I cotrast, the UNIQUAC assocato model predcts ths rego also wth hgh accuracy whch ultmately results dfferetly shaped curves for the thermodyamc correcto factor. Ths tur affects the shape of the computed MSdffusvty curves.

16 2.5 D [m 2 /s 0 9 ] 2.5 ep W5a U2a U3a (Rutte) Fgure 5: Comparso of epermetal data ad predcted values These curves have bee computed o the bass of a ew set of epermetal data determed for the bary system ethaol-cycloheae from Taylor dsperso epermets (T25 C). Valdato of the epermetal set-up showed that a relatve error of 2% ca be epected. O the bass of ths data a frst assessmet of the dffusvty approach proposed here has bee coducted. Sce the orgal correlato factor (a fed rato of va der Waals rad), used to decrease the umber of MS-dffusvtes the multcompoet system, revealed erroeous volume correctos, ths factor has bee modfed to accout for the cocetrato depedece ad the fluece of o-roudess of the molecules. Ths has bee doe by usg the volume rato as defed the UNIQUAC model ad troducg the acetrc factor computed from the Lee-Kesler method cojucto wth the Joback method for crtcal propertes. Etesve testgs revealed that the best performace (at least for ths bary system) has bee 2 acheved wth a modfed correlato factor defed as C 2 / ( j j φ φ φ φj ) combed wth the UNIQUAC assocato model. Ths resulted good agreemet wth the epermetal data the dluted regos whereas larger devatos occurred the mddle cocetrato rage. I cotrast, the Wlso equato strogly overpredcted the dffusvtes the dluted regos whch s caused by erroeous calculato of actvty coeffcets at fte dluto. Ths also demostrates clearly that the same set of teracto parameters applcable to VLE predctos does ot ecessarly yeld accurate formato o the secod dervatve of the g E -model. Further assessmet of the proposed MS-dffusvty model s vtal sce oly a specal case,.e. solely assocato reactos, has bee vestgated. I ths way the modfcato of the correlato factor ca be further tested. Ivestgato of the fluece of g E -models s also crucal order to obta relable formato o MSdffusvtes from epermetal data.

17 ACKNOWLEDGEMENT The authors are grateful to the Deutsche Forschugsgemeschaft for facal support of ths work. REFERENCES. Krshamurthy, R. ad R. Taylor, A Noequlbrum Stage Model of Multcompoet Separato Processes. AIChE, : p Taylor, R. ad R. Krsha, Multcompoet Mass Trasfer. 993, New York: Joh Wley & Sos. 3. Kegue Mc, K. ad E. Gular, Effect of Molecular Assocato o Dffuso Bary Lqud Mtures. AIChE, : p Rutte, P.W.M., Dffuso lquds. 992, Groge. 5. Wlke, C.R. ad P. Chag, Correlato of Dffuso Coeffcets Dlute Solutos. AIChE, 955. (2): p Edward, J.T., J. Chem. Educ., : p Bod, A., J. Phys. Chem., : p Vges, A., Id. Eg. Chem. Fudam., : p Aspro, N., Awedug der Spektroskope thermodyamsche Utersuchuge assozereder Lösuge. 996, Darmstadt: Dssertatos Druck Darmstadt GmbH. 0. Gmehlg, J., U. Oke, ad W. Arlt, Vapour-Lqud Equlbrum data collecto , Frakfurt a. M.: Dechema.. Aspro, N., H. Hasse, ad G. Maurer, Lmtg Actvty Coeffcets Alcohol- Cotag Orgac Solutos from Headspace Gas Chromatography. J. Chem. Eg. Data, : p Wobst, M., G. Hradetzky, ad H.-J. Bttrch, Measuremet of actvty coeffcets hghly dlute solutos. Part II. Flud Phase Equlbra, : p Rutte, P.W.M., Dffuso Lquds. 992, Delft: Delft Uversty Press. 4. Lee, B.I. ad M.G. Kesler, AIChE, : p Joback, K.G. 984, Massachusetts Isttute of Techology: Cambrdge, Mass.