PREDICTION OF VAPOR-LIQUID EQUILIBRIA OF BINARY MIXTURES USING QUANTUM CALCULATIONS AND ACTIVITY COEFFICIENT MODELS

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1 Joural of Chemstry, Vol. 47 (5), P , 9 PREDICTIO OF VAPOR-LIQUID EQUILIBRIA OF BIARY MIXTURES USIG QUATUM CALCULATIOS AD ACTIVITY COEFFICIET MODELS Receved May 8 PHAM VA TAT Departmet of Chemstry, Uversty of Dalat ABSTRACT I ths work, the coductor-lke screeg model COSMO-SAC (segmet actvty coeffcet) obataed from the desty fuctoal theory calculatos DFT-VW-BP wth bass set DP (double umercal bass set augmeted wth polarzato fucto). The molecular-sgle sgma profles were geerated by usg COSMO calculatos. The vapor-lqud equlbra (VLE) for three bary mxtures water() - ethaol(), methaol() - bezee() ad toluee() - chlorobezee() were calculated from these sgma profles. The VLE data of these mxtures tur out to be good agreemet wth expermetal data as far as such data resultg from the actvty coeffcet models Wlso [] ad RTL (o-radom two-lqud) []. RMS error, mea relatve devato of pressure (MRD p ) ad mea devato of vapor composto (MD y ) are less tha.87, 9.5 ad.65, respectvely. Keywords: Vapor-lqud equlbra, coductor-lke screeg model COSMO-SAC. I - ITRODUCTIO Predcto of vapor-lqud equlbra s a mportat goal physcal chemstry ad chemcal egeerg. Relable formato of vapor-lqud equlbra s most decsve for developg the usual lqud fuels. The expermetal measuremet of VLE ca be expesve ad sometmes hghly challegg several dustral applcatos. Recet years, trustworthy theoretcal methods based o ab to quatum calculatos [3, 4] ad Gbbs esemble Mote Carlo smulato techque [5, 6] are thus very desrable. The theoretcal methods coductor-lke screeg model for real solvets COSMO-RS proposed by Klamt et al. [3] ad the coductor-lke screeg model COSMO-SAC (segmet actvty coeffcet) developed by L et al. [4] were used for predcto of vapor-lqud ad lqud-lqud equlbra ad solublty property of bary, terary ad multcompoet systems. Ths work reports the predcto of vaporlqud equlbra for bary mxtures by usg coductor-lke screeg model COSMO-SAC ad actvty coeffcet models Wlso ad RTL. The sgle-molecule sgma profles water, ethaol, methaol, bezee, toluee ad chlorobezee are calculated from quatum computatos DFT-VW-BP wth bass set DP. These tur are used to predct VLE data of bary mxtures water() - ethaol(), methaol() - bezee() ad toluee() - chlorobezee(). The VLE of them are compared wth expermetal data ad those from models Wlso ad RTL. II - COMPUTATIOAL DETAILS. Cosmo-based thermodyamc model The COSMO-based model s the solvet- 547

2 accessble surface of a solute molecule [3, 4]. The actvty coeffcets resultg from Eq. developed by L ad Sadler [4]: *res *res ΔG / S ΔG / SG lγ / s = + lγ / S () RT *res *res Where ΔG / S ad ΔG / free eergy of restorg the charges aroud the solute molecule a soluto ad the charges a pure SG lqud; γ the Staverma-Gugehem term. / S The screeg charge destes are derved from COSMO calculatos. These ew surfacecharge destes (ã) of the sgle molecules are gve by the followg equato [3, 4]: * r rav d m σ exp r r σ = m () r rav d m exp r r Where σ m the average surface-charge desty o segmet m; the summato s over segmets; r the radus of the actual surface segmet; r av the average radus ad d m the dstace betwee the two segmets.. Actvty coeffcet model The model RTL was developed by Reo ad Praustz [] to mprove o the Wlso equato []. The actvty coeffcets of bary mxtures are calculated by the equato: τ G x τ kg k x G = + k l γ τ (3) Gk Gk Gk k k k Where τ = A + B / T + C l( T ) D T; G = exp( α τ ) ad α = α the adustable ad + system-specfc parameters. 3. Calculato of vapor-lqud equlbra The vapor-lqud equlbra of bary mxtures are geerated by usg the molecular actvty coeffcets. The vapor mole fractos y are calculated by usg the relatos [3, 4]: y p = p x γ / p tot tot = p x γ + p ( =,) x γ RMS = ( yexp y cal ) (5) Here the umber of data pots; y cal the calculated vapor fracto from COSMO-SAC. 548 (4) Where p the vapor pressures of pure compoet at gve temperature; x the mole fractos of the compouds the lqud phase; the actvty coeffcet of the compoud. The RMS error calculatos ca be carred out usg the equato: The mea relatve devato of pressure (MRD p ) ad mea devatos of vapor composto (MD y ) are gve the equatos: (,,exp,exp) MRD,% = ( / ) p p p (,,exp ) MD = ( / ) y y p cal y cal III - RESULTS AD DISCUSSIO. Computato of Sgma Profles (6) The molecular structures were carred out to optmze wth the desty fuctoal theory (DFT) at the level of theory GGA/VW-BP wth bass set DP (Double umercal bass wth Polarzato fuctos) [7, 9, ]. The surface screeg charge destes surroudg the molecule are geerated from a eergy

3 calculato DFT VW-BP/DP. The sglemolecule sgma profles were resulted from these surface charge destes, as depcted Fg. Sgma Profle, P(σ)*A (Å ) 5 5 H 6 CH 3 CH 3 OH C OH Cl H O Screeg Charge Desty, σ(e/å ) Fgure : Sgma profles for the sgle molecules. Vapor-lqud equlbra The vapor-lqud equlbra for mxture ethaol() - water() at P =.35 bar was obtaed usg the relatos (4) over a temperature rage 35 K to 37 K as show Fg. 37 T/ K x, y Fgure : VLE dagram T-x-y of mxture ethaol() - water() at P =.35 bar; #: expermetal data []; : COSMO-SAC; : model Wlso; #####: RTL. The VLE data P-x-y of two bary systems methaol() - bezee() ad toluee() - chlorobezee() at T = K ad T = K obtaed over the pressure rages from.4 to.7 bar ad from. to.3 bar, respectvely. For the three bary systems ths work the VLE data resultg from COSMO-SAC calculato were compared wth expermetal data [] as well as those from the models Wlso ad RTL. Ths s llustrated Fgs, 3. The COSMO-SAC VLE data are very close to 549

4 expermetal data. They agree also well wth those from models Wlso ad RTL. The values of RMS error, the mea relatve devato of pressure (MRD p ) ad mea devato of vapor composto (MD y ) table are less tha.87, 9.5 ad.65, respectvely. So the dscrepaces betwee models are sgfcat..3.9 P/ bar.6 P/ bar Fgure 3: VLE dagram P-x-y of mxtures: a) methaol() - bezee() at T = K ad b) toluee() - chlorobezee() at T = K; for a explaato see Fg.. Table : Comparso betwee the values RMS, MRD p ad MD y of the models RTL Wlso COSMO-SAC RMS MRD p, % MD y RMS MRD p, % MD y RMS MRD p, % MD y ethaol() + water() at P =.35 bar methaol() + bezee() at T = K toluee() + chlorobezee() at T = K x, y x, y a) b) 55 IV - COCLUSIOS We coclude that the molecular-sgle sgma profles water, ethaol, methaol, bezee, toluee ad chlorobezee obtaed from quatum calculatos are relable. The actvty coeffcets of them were calculated from accurately the sgma profles. The vaporlqud equlbra of the bary systems water() - ethaol(), methaol() - bezee() ad toluee() - chlorobezee() resultg from model COSMO-SAC tur out to be good agreemet wth expermetal data ad those from models Wlso ad RTL. These are poted out the RMS error, the relatve devatos MRD p ad MD y. Ackowledgmets: We would lke to thak Prof. Dr. Y. A. Lu (Uversty of Delaware, USA) for makg avalable ther programs code FORTRA ad provdg Sgma Profles Databases.

5 REFERECES. G. M. Wlso., J. Am. Chem. Soc. 86, 7-3, (964).. H. Reo, J. M. Praustz., AIChE J. 4, 35-44, (968). 3. A. Klamt, G. Schuurma., COSMO: A ew approach to delectrc screeg solvets wth explct expressos for the screeg eergy ad ts gradet, J. Chem. Soc., Perk Tras., 799, (993). 4. S. T. L, S. I. Sadler., A Pror Phase Equlbrum Predcto from a Segmet Cotrbuto Solvato Model, Id. Eg. Chem. Res, 4, , (). 5. A. Z. Paagotopoulos, Mol. Phys., 6, 83-86, (987). 6. K. Leohard ad U. K. Deters, Mol. Phys.,, , (). 7. S. J. Vosko, L. Wlk, M. usar, A crtcal aalyss, Ca. J. Phys., 58, -, (98). 8. P. Hoheberg, W. Koh., Phys. Rev. B, 36, , (964). 9. J. P. Perdew, Y. Wag., Phys. Rev. B, 45, 344 (99).. A. D. Becke., J. Chem. Phys., 84, 454 (986).. IST Chemstry databases: 55

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

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