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1 J. Chem. Thermodynmics 1998, 30, Mixing properties nd derived mgnitudes of the system { x1ch 3COOCH 3 x 2CH 3OH ( 1 x x ) CH ( CH ) OH} t the temperture K A. Rodrıguez, J. Cnos, B. Orge, M. Iglesis, nd J. Tojo Deprtmento de Ingenierı Quımic, Uni ersidd de Vigo, Aptdo. 874, Vigo, Spin In this pper, the physicl properties of densities nd refrctive indices hve been mesured nd derived excess molr volumes nd chnges of refrctive index on mixing hve been clculted t T K nd tmospheric pressure. xperimentl vlues correspond to the ternry x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH nd binry systems xch COOCH Ž 1 x. CH Ž CH. OH4 nd xch OH Ž 1 x. CH Ž CH. OH Different polynomil functions hve been fitted with the excess properties nd their prmeters determined. Severl estimtion methods re pplied to compre the physicl nd derived properties. For the ternry systems, excess molr volumes nd ternry contributions re compred with previous mixtures. A comprison is mde in terms of excess molr volumes nd ternry contributions to this property by vrition of methylene groups of lknol component Acdemic Press Limited KYWORDS: mixing properties, excess properties, correltion, predictive methods 1. Introduction A knowledge of the physicl nd derived properties of zeotropic liquid mixtures is required for the engineering design of extrctive rectifiction columns, which re relted to industril seprtion processes. We report here new experimentl vlues of density nd refrctive index on mixing for multicomponent mixtures x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH nd their corresponding binry mixtures xch COOCH Ž 1 x. CH Ž CH. OH nd xch OH Ž 1 x. CH Ž CH. OH t T K nd tmospheric pressure. xcess molr volumes nd chnges of refrctive index on mixing for binry mixtures were correlted using the Redlich Kister Ž1. eqution. Once we hve obtined these prmeters, they will be pplied to the Cibulk Ž2. eqution through which ternry excess vlues re correlted. For ternry systems, excess molr volumes nd ternry contributions re compred with other systems in which the third component increses the length of the moleculr chin while the position of Ž. To whom correspondence should be ddressed -mil: jtojo@uvigo.es $ ct Acdemic Press Limited

2 216 A. Rodrıguez et l. TABL 1. Comprison of experimentl with literture densities nd refrctive indices n liquids t T K Ž. Ž K gcm. n Ž K. D Component expt. lit. expt. lit. CH 3COOCH c CH 3OH b Ž. CH 3 CH 2 4OH d b D for pure b Reference 9. b Reference 10. c Reference 11. d Reference 12. the functionl group stys constnt. The experimentl densities, refrctive indices, nd derived excess properties re compred with those predicted by severl equtions nd their results re shown. xcess prtil molr volumes nd those corresponding to the infinite dilution condition re lso clculted for binry nd ternry mixtures. 2. xperimentl The chemicls employed in the smple preprtion hve Lichrosolv chromtogrphic Merck qulity. They were kept under n inert rgon ŽN-55, with. 6 mximum content in wter of 2 10 by volume. tmosphere, degssed in n ultrsound bth nd stored over freshly ctived moleculr sieves Type 4 or 3, for severl dys before using. The purity of the components ws further scertined by compring their densities nd refrctive indices t T K with literture vlues in tble 1. A chromtogrphic g.l.c. test of purity shows tht the mss frctions re better thn for CH 3COOCH 3, CH 3OH, nd 0.99 for Ž CH 3 CH 2 4OH, with mximum wter contents of , , nd mss frction Ž Metrohm 737 KF coulometer., respectively. A PolyScience controller bth model 9010 with temperture stbility of 10 2 K ws used to thermostt the smples, which were prepred by mss using Mettler AT-261 Delt Rnge blnce with precision of 10 5 g, covering the whole composition rnge of the mixtures. The densities of the pure chemicls nd mixtures were mesured with n Anton 5. 3 Pr DMA densimeter with n ccurcy of 10 g cm nd the refrctive indices by the utomtic refrctometer ABBMAT-HP Dr Kernchen with precision of Apprtus clibrtion ws relized by testing substnces periodiclly from known vlues of densities nd refrctive indices. A double liquid reference ws used for the clibrtion ŽMillipore qulity wter, degssed nd dried Fluk qulity heptne.. Accurcy in the clcultion of derived excess properties. 3 4 ws estimted s better thn for excess molr volumes nd 10 for chnges of refrctive index on mixing. The experimentl technique nd mode of opertion hve been described previously. Ž3.

3 Ž. 4 Mixing properties of CH COOCH CH OH CH CH OH TABL 2. Densities, refrctive indices n D, excess molr volumes Vm, nd chnges of refrctive index on mixing mix nd for binry mixtures t T K V m x n n g cm cm mol D mix D xch COOCH Ž 1 x. CH Ž CH. OH xch OH Ž 1 x. CH Ž CH. OH Results nd discussion Densities nd refrctive indices of the binry nd ternry mixtures re shown in tbles 2 nd 3. For every set of dt, binry nd ternry properties hve been fitted with polynomil eqution. Physicl properties of xch 3COOCH 3 Ž. 4 Ž4. 1 x CH 3OH hve been mesured nd correlted in previous work. The excess molr volumes nd chnges of refrctive index on mixing of binry nd ternry systems were computed by pplying equtions Ž. 1 nd Ž. 2, which re shown in the lst two columns inside tbles 2 nd 3 for ech composition point: N 1 1 m Ý i i i i 1 Ž. V xm, Ž 1. N Ý n n xn. Ž 2. mix D D i D i i 1 In these equtions, is the density nd nd is the refrctive index of the mixture; i nd nd i re the properties of its pure components. The vlue of N represents the number of components in the mixture. To clculte the derived excess

4 218 A. Rodrıguez et l. TABL 3. Densities, refrctive indices n D, excess molr volumes Vm, nd chnges of refrctive index on mixing mix nd for ternry mixture t T K V m x x n n g cm cm mol 1 2 D mix D x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH

5 Ž. 4 Mixing properties of CH COOCH CH OH CH CH OH FIGUR 1. Devitions V from eqution Ž. 3 for xch COOCH Ž 1 x. CH Ž CH. OH4 m t T K from vilble source:, Reference 10. The curves enclose devitions flling within V. m properties for binry systems, Redlich Kister type eqution ws pplied: M Ý Q xx BŽ x x., Ž 3. ij i j p i j p 0 where Qij is the excess property, x is the mole frction, Bp is the fitting prmeter nd M is the degree of the polynomic expnsion, which ws Ž5. optimized using the F-test. xcess molr volumes for xch 3COOCH 3 Ž. Ž. 4 Ž6. 1 x CH 3 CH 2 4OH hve been reported previously by Orteg et l. Figure 1 shows the differences between the experimentl excess molr volumes from the literture nd our results fitted with eqution Ž. 3. The high conformity between both experimentl vlues is noted. xcess ternry mgnitudes were correlted with the Cibulk eqution: Q Q Q Q x x Ž 1 x x.ž C C. x C. x., Ž where Q 12, Q13 nd Q23 re the binry contributions expressed by the Redlich Kister expression. Curves of constnt excess molr volumes nd chnges of refrctive index on mixing for the ternry system hve been plotted in figures 2Ž. nd 2Ž. b, respectively. The ternry system exhibits expnsive behviour in excess molr volumes usully from the composition digrm, except close to the binry xch COOCH Ž 1 x. CH OH4 where the opposite tendency is p

6 220 A. Rodrıguez et l. FIGUR 2. Curves of:, excess molr volume nd b, chnges of refrctive index on mixing for x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH4 t T K

7 Ž. 4 Mixing properties of CH COOCH CH OH CH CH OH Ž. Ž. TABL 4. Prmeters of equtions 3 nd 4, nd stndrd devitions xch COOCH Ž 1 x. CH Ž CH. OH Ž 3. 1 V cm mol. m B B B B mix nd B B xch OH Ž 1 x. CH Ž CH. OH Ž 3. 1 V cm mol. m B B B B mixnd B B B x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH Ž 3. 1 V cm mol. m C C C mix nd C C C mnifested. For chnges of refrctive index on mixing, it shows positive vlues over the whole composition rnge. The prmeters from fitting equtions Ž. 3 nd Ž. 4 for derived properties, nd corresponding stndrd devitions of eqution Ž. 5 re given in tble 4: n 1 2 DAT 2 ž Ý exp pred DAT / i Ž z z. n. Ž 5. In this eqution, z is the vlue of the property nd ndat is the number of experimentl points. Figure 3 shows the comprison of excess molr volumes Ž4,7,8. for the ternry systems x CH COOCH x CH OH Ž x1 x. CH Ž CH. OH4 when n is incresed from 1 to 4, with Ž n 0.5xCH 3COOCH xch OH. 3 in the entire composition rnge for the third component. In this figure is observed tht the excess molr volume is higher when the length of chin of the third component is incresed, due to the difficulty in the moleculr pcking. Severl methods to predict densities nd refrctive indices of mixtures were pplied to test their vlidity in mixtures of polr components. The density of binry nd ternry systems ws estimted using Hnkinson Brobst Thompson, Rckett, Spencer, nd Dnner modified Rckett, Brdford Thodos, Riedel, Nrsimhm, nd Yen Woods methods in conjunction with expnsion mixing rules proposed by those uthors or the Ky rule. The refrctive indices were compred with the predicted results from the mixing rules proposed by Lorentz Lorenz, Dle Gldstone, Argo Biot, ykmn, Newton, Oster nd yring John. The excess molr volumes nd chnges of refrctive index on mixing of more thn two components my be estimted from binry results by pplying the eqution Ž. 6 : Ý Ž. Q xx x x Q Ž x, x.. Ž 6. ijk i j i j ij i j i j For ech ternry mixture, the mole frctions x my be obtined from tringulr

8 222 A. Rodrıguez et l. FIGUR 3. Curves of excess molr volume V when x x for: m 1 2 x1ch 3COOCH 3 x2ch 3OH Ž 1 x x. CH Ž CH. OH4 from n Ž 1to4. tt K n digrm by projecting the point representing the ternry mixture onto the corresponding binry xis, using different symmetric or symmetric criteri of binry contribution to the ternry vlue. The predictive methods ŽKohler, Jcob nd Fitzner, Colinet, Tso nd Smith, Troop, nd Sctchrd et l.. were used to determine ternry derived properties by mens of dditive binry contributions. ch eqution used in the estimtion of physicl nd derived excess properties hs been compiled in previous work. Ž3. In ternry density estimtions, the Nrsimhm eqution gives the smllest devition, s well s in xch OH Ž 1 x. CH Ž CH. OH 4. The Brdford

9 Ž. 4 Mixing properties of CH COOCH CH OH CH CH OH FIGUR 4. Curves of constnt r per cent for the best physicl properties estimtion method:, estimtion of density by Nrsimhm; nd b, estimtion of refrctive index by Dle-Gldstone for x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH4 mixture t T K

10 224 A. Rodrıguez et l. TABL 5. Stndrd devitions of excess molr volumes Vm nd chnges of refrctive index on mixing mix nd from the prediction results for different empiricl equtions V cm. mol n Ž Ž. m mix D Kohler Jcob Fitzner Colinet Tso Smith b Tso Smith c Tso Smith Sctchrd b Sctchrd c Sctchrd Toop b Toop c Toop The symmetric component in the eqution is: b methnol; nd c methyl cette. 1-pentnol; Thodos nd Yen Woods equtions yield the best results in xch 3COOCH 3 Ž 1 x. CH Ž CH. OH For chnges of refrctive index on mixing, the lowest devitions occurred for xch COOCH Ž 1 x. CH Ž CH. OH with the Oster rule, for xch OH Ž 1 x. CH Ž CH. OH with the ykmn rule, nd for ternry x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH when the Dle Gldstone rule is pplied. In ll cses, non-dditivity on mixing ws ssumed. Figures 4Ž. nd 4Ž. b show for the ternry system the reltive error r eqution Ž.4 7 determined from the best physicl properties estimtion method bsed on experimentl vlues. In these figures, two zones of different behviour with positive nd negtive vlues re observed. In the cse of refrctive index in figure 4Ž b., the devition exhibits mximum vlue of 0.024: Ž.. 2 z z z 10. Ž 7. r exp pred exp In generl for this ternry system, the estimtion of excess molr volumes exhibits lower devitions with respect to experimentl vlues when type c symmetric equtions re pplied except in the cse of Tso Smith eqution, where the best result is obtined when type symmetric eqution is used. For chnges of refrctive index on mixing, similr vlues re observed by pplying symmetric equtions. However symmetric equtions yield better results when type b is used. In tble 5, excess molr volumes nd chnges of refrctive index on mixing re compred. Figure 5 shows the isolines corresponding to the ternry contribution, Ž V V. m, 123 m, bin, where two zones with positive nd negtive vlues re observed. A sign inversion ppers when the concentrtion of the third component is incresed. Figure 6 exhibits comprison of the ternry contribution to excess molr volumes between the systems x CH COOCH x CH OH Ž x1 x. CH Ž CH. OH4 when n is incresed from 1 to 4, for Ž0.5xCH COOCH n 3 3

11 Ž. 4 Mixing properties of CH COOCH CH OH CH CH OH FIGUR 5. Curves of constnt ternry contribution to excess molr volumes of x1ch 3COOCH 3 x CH OH Ž 1 x x. CH Ž CH. OH4 t T K xCH OH. 3. In this figure, it cn be observed tht the ternry contribution tkes on higher positive vlues when the length of chin of lknols in the mixture is incresed. The prtil excess molr volume of component in binry mixture cn be determined from excess molr volume dt by mens of the following expression: nd in multicomponent mixture: Ž. Ž. Ž. Vi Vm 1 xi Vm x i, 8 ž / ž / i j k Vm Vm Vi Vm Ý x k. Ž 9. x x T, p, x T, p, xj In ccordnce with these equtions, the i-component prtil excess molr volumes were computed s function of the corresponding prtil derivtion, the binry nd the prtil excess molr vlues t infinite dilution being determined by cncelltion of dequte molr frctions. The prmeters corresponding to these

12 226 A. Rodrıguez et l. FIGUR 6. Curves of constnt ternry contribution to excess molr volumes Vm, 123 Vm, bin when x x for x CH COOCH x CH OH Ž 1 x x. CH Ž CH. OH4 from n Ž 1to n tt K. compositions re gthered in tble 6. In generl terms, it is observed tht positive influence follows ddition to the mixture of CH COOCH or CH Ž CH OH, nd contrctive trend occurs when the solvent is CH 3OH. The contribution of the short lcohol chin chnges sign when the mixture contins high concentrtion of CH Ž CH OH nd low CH 3COOCH 3, for lmost ny composition of the former lcohol. Ž The uthors wish to thnk the CACTI Deprtment of Technologicl nd Scientific

13 Ž. 4 Mixing properties of CH COOCH CH OH CH CH OH TABL 6. Prtil excess molr volumes t infinite dilution of the ternry mixture t T K V Ž cm. mol. V Ž cm. mol. V Ž cm. mol., 3 1, 3 1, Support to the Reserch of Vigo University. experimentl development of this pper. for its technicl ssistnce in the RFRNCS 1. Redlich, O.; Kister, A. T. Ind. ng. Chem. 1948, 40, Cibulk, I. Coll. Czech. Commun. 1982, 47, Iglesis, M.; Orge, B.; Tojo, J. Fluid Phse quilib. 1996, 126, Rodrıguez, A.; Cnos, J.; Orge, B.; Iglesis, M.; Tojo, J. J. Chem. ng. Dt 1996, 41, Bevington, P. Dt Reduction nd rror Anlysis for the Physicl Sciences. McGrw-Hill: New York Orteg, J.; Susil, P. Cn. J. Chem. 1989, 67, Cnos, J.; Rodrıguez, A.; Iglesis, M.; Orge, B.; Tojo, J. High Tempertures High Pressures 1997, 29, Cnos, J.; Rodrıguez, A.; Iglesis, M.; Orge, B.; Tojo, J. J. Thermochim. Act. Ž in press.. 9. TRC Thermodynmic Tbles, Thermodynmic Reserch Center. Texs A & M University: College Sttion, TX Riddick, J. A.; Bunger, W. B. Orgnic Sol ents, Techniques of Chemistry: 4th edition, Vol. 2. Wiley-Interscience: New York Lorenzi, L.; Fermegli, M.; Torrino, G. J. Chem. ng. Dt. 1995, 40, Linek, J. LDATA: Int. lectron. J. Phys. Chem. Dt. 1995, 1, W-102 ( ) Recei ed 5 June 1997; in finl form 3 September 1997

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es