21 A Group Contribution Molecular Model for Liquids Phase Equilibria and Fluid Properties in the Chemical Industry Downloaded from pubs.acs.org by NANYANG TECHNOLOGICAL UNIV on 06/10/16. For personal use only.
and Solutions Composed of the Groups and
CH , 3
CH , 2
OH,
CO
T. NITTA, E. A. TUREK, R. A. GREENKORN, and K. C. CHAO Purdue University, West Lafayette, IN 47907 Group i n t e r a c t i o n models have achieved remarkable success i n the d e s c r i p t i o n of a c t i v i t y c o e f f i c i e n t s of n o n e l e c t r o l y t e s o l u t i o n s . Notable i n t h i s development are the p i o n e e r i n g work by P i e r o t t i , Deal and Derr (]L), Wilson and Deal (2), and subsequent c o n t r i b u t i o n s by S c h e l l e r (3), R a t c l i f f and Chao ( 4 ) , Derr and Deal ( 5 ) , and Fredenslund, Jones, and P r a u s n i t z ( 6 ) . N i t t a e t . a l . (7) extended the group i n t e r a c t i o n model to thermodynamic p r o p e r t i e s of pure p o l a r and non-polar l i q u i d s and t h e i r s o l u t i o n s , i n c l u d i n g energy of v a p o r i z a t i o n , pvT r e l a t i o n s , excess p r o p e r t i e s and a c t i v i t y c o e f f i c i e n t s . The model i s based on the c e l l theory w i t h a c e l l p a r t i t i o n f u n c t i o n d e r i v e d from the C a r n a h a n - S t a r l i n g equation of s t a t e f o r hard spheres. The l a t t i c e energy i s made up of group i n t e r a c t i o n c o n t r i b u t i o n s . An important advantage of the model by N i t t a e t . a l . i s i t s a p p l i c a b i l i t y over a wide temperature range. The same group parameters used i n the same equations have been found to g i v e good r e s u l t s at c o n d i t i o n s f o r which the c e l l model i s known to be a p p l i c a b l e — w h e r e the l i q u i d i s not "expanded", the reduced d e n s i t y i s g r e a t e r than two and the temperature i s not much above the normal b o i l i n g p o i n t . I t i s not necessary to have d i f f e r e n t s e t s of group parameter values f o r d i f f e r e n t temperatures. N i t t a e t . a l . (7) presented the p r o p e r t i e s of the groups CH3, CH2, OH, and CO and t h e i r i n t e r a c t i o n s . Comparisons of the model and experimental data were made f o r a number of pure l i q u i d s and their solutions. A d d i t i o n a l comparisons of s o l u t i o n p r o p e r t i e s w i t h the model c a l c u l a t e d values are presented here to cover the gamut of mixtures made up of the given groups from the non-polar/non-polar, through non-polar/polar, to p o l a r / p o l a r . F i g u r e 1 shows the p r e d i c t e d a c t i v i t y c o e f f i c i e n t s of n-hexane i n s o l u t i o n w i t h n-dodecane compared to experimental data by Broensted and Koefoed ( 8 ) . The same agreement i s obtained between our model and experimental data from the same source on the mixtures of other n-alkanes. F i g u r e 2 shows the p r e d i c t e d a c t i v i t y c o e f f i c i e n t s i n the system ethanol/n-octane at 75C i n comparison w i t h experimental 421
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21.
NITTA E T A L .
Group Contribution Molecular Model
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data by Boublikova and Lu ( 9 ) . The agreement i s the same as that p r e v i o u s l y reported by N i t t a e t . a l . (7) f o r the same system a t 45C w i t h data from the same source. There i s a remarkable change i n a c t i v i t y c o e f f i c i e n t s i n t h i s system i n the temperature i n t e r v a l of 30C. Thus the i n f i n i t e d i l u t i o n v a l u e of e t h a n o l i s reduced by a f a c t o r of about two w h i l e that of n-octane i s reduced by only about 10% w i t h t h i s temperature i n c r e a s e . This remarkable change i s q u a n t i t a t i v e l y described by the model. F i g u r e 3 shows the p r e d i c t e d a c t i v i t y c o e f f i c i e n t s i n n-butanol/n-heptane a t 50C i n comparison w i t h the experimental data of A r i s t o v i c h e t . a l . (10). The agreement that i s obtained here f o r the h i g h a l c o h o l i s about the same as the p r e v i o u s l y reported r e s u l t s (_7) f o r the lower a l c o h o l s . F i g u r e 4 shows the p r e d i c t e d excess enthalpy of n-butanol/nheptane a t 15 and 55C i n comparison w i t h experimental data by Nguyen and R a t c l i f f (11). The agreement i s not q u i t e q u a n t i t a t i v e and d e v i a t i o n s up to 30 cal/g-mole are observed f o r some compositions. F i g u r e 5 through 8 show the a c t i v i t y c o e f f i c i e n t s i n the system n-hexane/2-propanone a t four temperatures 45, 20, -5, and -25C. Experimental data are from Schaefer and R a i l (12) a t 45 and - 2 0 C , and from R a i l and Schaefer (JL3) a t 20 and -25C. The v a r i a t i o n of the a c t i v i t y c o e f f i c i e n t s w i t h temperature appears to be quant i t a t i v e l y d e s c r i b e d by our model. The 45C isotherm was used i n the development of the p r o p e r t i e s of the CO group and the model i s t h e r e f o r e i n a sense f i t t e d to t h i s isotherm. But the other isotherms were not used i n the development of the model, and the c a l c u l a t i o n s f o r them are of a p r e d i c t i v e nature. F i g u r e 9 shows the a c t i v i t y c o e f f i c i e n t s i n the system 2-propanal/n-hexanol (14). The molecular i n t e r a c t i o n s i n t h i s p o l a r / p o l a r mixture i s complex l e a d i n g to an apparent maximum i n the f i g u r e . The e x i s t e n c e of the maximum i s c o r r e c t l y p r e d i c t e d by our model, but the c a l c u l a t e d v a l u e s seem to vary too r a p i d l y at s m a l l c o n c e n t r a t i o n s of acetone. There a l s o seems to be c o n s i d e r a b l e u n c e r t a i n t y and s c a t t e r i n g of the experimental data i n the same range. Acknowledgment This work was supported by N a t i o n a l Science Foundation through grants GK-16573 and ENG76-09190. D. W. Arnold a s s i s t e d i n the calculations.
Abstract The group contribution molecular model for liquids and solutions developed by Nitta et.al.is applied to properties of liquid solutions made up of the groups CH , CH , OH, and CO, and the results are compared with experimental data. A wide range of molecular species in mixtures is included over a wide temperature range. 3
2
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Group Contribution Molecular Model 425
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P H A S E EQUILIBRIA
A N D F L U I D PROPERTIES
I N C H E M I C A L INDUSTRY
.2 .4 .6 MOLE FRRCTION N-HEXRNE
Figure 7. Activity coefficients in n-hexane-2-propanone at 5°C
n
r
~i
r
PREDICTED
cr CD
_l
Figure 8. Activity coefficients in n-hexane—2-propanone at 20°C
L_
.2 .4 .6 .8 MOLE FRRCTION N-HEXRNE
KO
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21. NITTA E T AL.
Group Contribution Molecular Model
Figure 9. Activity coefficients in 2-propanone— n-hexanol at 1 atm
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Literature Cited 1. Pierotti, G. J., Deal, C. H., and Derr, E. L., Ind. Eng. Chem. (1959) 51, 95. 2. Wilson, G. M., and Deal, C. H., Ind. Eng. Chem. Fundamen., (1962) 1, 20. 3. Scheller, W. A., Ind. Eng. Chem. Fundamen. (1965)4,459. 4. Ratcliff, G. A., and Chao, K. C., Canad. J. Chem. Eng. (1969) 47, 148. 5. Derr, E. L. and Deal, C. H., Distillation 1969, Sec. 3, p. 37, Brighton, England: Intern. Conf. Distillation, Sept. 1969. 6. Fredenslund, Aa., Jones, R. L., and Prausnitz, J. M., AIChE J. (1975) 21, 1086. 7. Nitta, T., Turek, E. A., Greenkorn, R. A., and Chao, K. C., AIChE J. (1977) 23, 144. 8. Broensted, J. N., and Koefoed, J., Selskab. Mat. Psy. Medd. (1946) 22, No. 17, 1. 9. Boublikova, L., and Lu, B. C. -Y., J. Appl. Chem. (1969) 19, 89. 10. Aristovich, V. Y., Morachevskii, A. G. and Sabylin, I. I., J. Appl. Chem. USSR (1965) 38, 2633. 11. Nguyen, T. H. and Ratcliff, G. A., J. Chem. Eng. Data (1975) 20, 252. 12. Schaefer, K. and Rall, W., Z. Elektrochem. (1958) 62, 1090. 13. Rall, W., and Schaefer, K., Z. Elektrochem. (1959) 63, 1019. 14. Rao, P. R., Chiranjivi, C., and Dasarao, C. J., J. Appl. Chem. (1967) 17, 118.
