Ind. Eng. Chem. Fundam. 1905, 2 4 , 112-1 14
112
R = right product Registry No. Nickel nitrate, 13138-45-9;blue dextran 2000, 9049-32-5; Sephadex G-25, 9041-35-4; Bio-Gel P-2, 60407-73-0.
Literature Cited Cantow, M. J. R.; Porter, R. S.; Johnson, J. F. J . Poly" Sci. Part A-1, 1987, 5 ,987. Chitumbo, K.; Brown, W. J. Chromatogr. 1973, 8 7 , 17. Edwards, V. H.; Helft, J. M. J . Chromatogr. 1970, 4 7 , 490. Flory. P. J. "Principles of Polymer Chemistry"; Cornell University Press: Ithaca and London, 1953; p 579. Morl, S.; Suzuki, T. Anal. Chem. 1980, 52, 1625. Reiland, J. In "Methods in Enzymology", Jakoby, W. E., Ed., Vol. 22; Academic: New York, 1971; p 287.
Rice, R. G. Sep. Purif. Methods 1978, 5 , 139. Yau, W. W.; Kirkland, J. J.; Bly, D. D. "Modern Size Exclusion Liquid Chromatography"; Wiley: New York, 1979. Wankat, P. C. In "Percolation Theory and Apllications", Rodrigues. A. E.; Tondeur, D., Ed.; Sijthoff and Noordhoff: Alphen aan den Rijn, Netherlands, 1981; pp 443-516.
School o f Chemical Engineering P u r d u e University W e s t L a f a y e t t e , Indiana 47907
Yoon-Mo Koo Phillip C. Wankat*
Received f o r review June 15, 1983 Revised manuscript received April 23, 1984 Accepted July 19, 1984
Prediction of Vapor Pressures for Substituted Benzenes by a Group-Contribution Method A new group-contribution method is developed for prediction of vapor pressures of substituted benzenes. Good representation is obtained for vapor pressure data of 48 substituted benzenes in the region 1.33-199.98 kPa. The model may be useful to predict vapor pressures of substituted benzenes for which experimental data are not available.
Introduction Vapor pressures of pure substances are the most important and fundamental physical properties. Recently, the need of vapor pressure data for high-molecular-weight (HMW) hydrocarbons has rapidly increased. However, sufficient experimental data are not available mainly because of experimental difficulties. A method for prediction of vapor pressures for such HMW hydrocarbons is desired. Of the empirical methods, a group-contribution method based on only a limited number of data for such components is chosen as the most suitable approach. This method has wide applicability for predicting the physical properties of pure compounds such as the critical constants (Lydersen, 1955), the standard heat of formation at 25 "C (Verma and Doraiswamy, 1965), the liquid molar volume at 25 "C (Hoshino et al., 1979), the refractive index a t 25 "C (Hoshino et al., 1979), the latent heat of vaporization a t the normal boiling point (Hoshino et al., 1978, 1979), acetric factor of alkanes (Hoshino et al., 1982), and the entropy of vaporization at the normal boiling point (Hoshino et al., 1983). Macknick and Prausnitz (1979) proposed a group-contribution method for determination of two adjustable parameters of the Abrams-Massaldi-Prausnitz (AMP) vapor-pressure equation (Abrams et al., 1974; Macknick et al., 1977) for HMW hydrocarbons such as paraffins, aromatics, and naphthenics. Edwards and Prausnitz (1981) extended it to nitrogen- and sulfur-contaning groups, and Ruzicka (1983) also developed a method for naphthenic 5-membered ring groups and condensed naphthenic groups. In these works, the group contributions were reduced directly from experimental vapor-pressure data in the range 1.33-199.98 kPa. In the present work, the Antoine equation is adopted to predict vapor pressures. It has three adjustable parameters A , B, and C, and they are determined from boiling temperatures at three specified pressures (1.33, 101.32, and 199.98 kPa). The new group-contribution method is developed to calculate the boiling temperatures of substituted benzenes a t specified pressures and, consequently, the parameters of the Antoine equation are determined for each compound. For 48 substituted benzenes (1296 data points), the average error between 0196-4313/85/ 1024-01 12$01.50/0
calculated and experimental vapor pressure is only 3.7%. Proposed Group-Contribution Method The group-contribution method of Macknick and Prausnitz (1979) could not account for the distinction of fine molecular structures such as the position of substituents in substituted benzenes. The present method takes account of such a distinction of substituted benzenes. As pointed out by Macknick and Prausnitz (1979),many kinds of vapor-pressure equations have been derived from the Clapeyron equation coupled with simplifying or semiempirical assumptions. The equations often contain at least three or more adjustable parameters, with no clearly physical significance, and generally it is difficult to analyze these parameters by use of the group-contribution approach. The Antoine equation adopted here also contains three such kinds of parameters, but it has been widely used in vapor pressure predictions in the range of 1.33-199.98 kPa as mentioned by Reid et al. (1977). To resolve its difficulty, a new group-contribution method for the Antoine equation has been developed. Instead of an attempt to calculate Antoine's parameters directly, a new group-contribution method for estimating three boiling temperatures a t three specified pressures has been developed. These pressures are 1.33,101.32, and 199.98 kPa. The pressure of 101.32 kPa is equal to atomospheric pressure and many experimental data of boiling temperatures are available. Pressures of 1.33 kPa and 199.98 kPa are adopted as the applicable limits of the Antoine equation. Substituted benzenes may contain six kinds of functional groups: -CH3, -CH2-, XH-,>CC< =CH=C
C=) + C(correction for substitution) = (36.84X 3) + (16.73)+ (42.90 X 3) + (28.17X 3) + (-0.71) = 339.75 K =
C (-CHJ
1339.75 - 339.751 x 100 = 0.0% 339.75 n -Tetradecylbenzene (478.15 K). (Note: The group increment -CH2- of this compound is identified as -CH,(a) in Table I.) error:
CH3
I
(cH2)13
I
H-C&-H I II H-Ca A-H
C
I
H
T = ZATj
+ C(-CH2-) + C(-C(H)=) + C(-C=)
= C(-CH,)
+
= (36.84)
;1
-[38.94 - 0.7 X (13 - l)]
1+
(42.90X 5) + (28.17) = 478.02 K
error: 0.0%
Nomenclature A , B , C = Antoine constants E = relative error, % N = number of compounds P = vapor pressure, kPa T = temperature, K ATi = group increment of boiling point of substituted benzene, K Subscripts calcd = calculated
exptl = experimental
Literature Cited Abrams, D. S.;Massaldi, H. A.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1074, 13, 259. Dreisbach. R. R. Adv. Chem. Ser. 1955, No. 15, 7. Edwards, D. R.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1081, 20, 280. Hoshino, D.; Nagahama. K.; Hirata, M. J . Jpn. Pet. lost. 1070, 22, 32, 218. Hoshino, D.; Nagahama, K.; Hirata, M. J. Chem. Eng. Jpn. 1078, 1 1 , 403. Hoshino, D.; Nagahama, K.; Hirata, M. J. Chem. Eng. Jpn. 1082, 15, 153. Hoshino, D.;Nagahama, K.; Hirata, M. Ind. Eng. Chem. Fundam. 1083, 22, 430. Lydersen. A. L. "Estimation of Critical Properties of Organic Compounds", Colleges of Engineering, University of Wisconsin, Engineering Experimental Statlon, Report 3, Madison WI. April 1955. Macknick, A. E.; Wlnnick, J.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1077, 18, 392. Macknlck, A. E.; Prausnltz, J. M. Ind. Eng. Chem. F u M I " 1070, 18, 348. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. "The Properties of Gases and Liquids", 3rd ed.; McGraw-Hill: New York, 1977. Rosenbrock, H. H. Comput. J. 1060, 3 , 175. Ruzicka, V., Jr. Ind. Eng. Chem. Fundam. 1083, 22, 266. Verma. K. K.; Doraiswamy, L. K. Ind. Eng. Chem. Fun&m. 1065, 4 , 389. Wilholt. R. C.; Zwolinski, E. J. "Handbook of Vapor Pressure and Heats of Vaporization of Hydrocarbons and Related Compounds"; American Petroleum Institvte Research Project 44, Texas A 8 M University, College Station, TX, 1971.
Department of Industrial Chemistry Faculty of Engineering Tokyo Metropolitan University 2-1 -1 Fukasawa, Setagaya-Ku Tokyo 158, Japan
Daisuke Hoshino* Xu-Rong Zhu Kunio Nagahama Mitsuho Hirata
Received for review October 25, 1983 Accepted April 26, 1984
