Ind. Eng. Chem. Fundam. 1985, 2 4 , 119-120
Nomenclature a = catalyst activity density function C = reactant concentration De = effective diffusion coefficient E = activation energy of reaction rate constant f =-dimensionless reaction rate, defined by eq 7 k , k = local and volume average reaction rate constant K = adsorption equilibrium constant L = characteristic pellet dimension; half-thickness ( n = 0), radius ( n = 1, 2) n = integer characteristicof particle geometry; = 0 for infinite slab, = 1 for infinite cylinder; = 2 for sphere R = gas constant s = x/L s = dimensionless optimal location of the active catalyst, defined in eq 8 T = absolute temperature u = C/Cf V , = pellet volume x = distance from center of pellet
119
A = parameter defined by eq 9 Xe = particle thermal conductivity p = (e - l ) / e 4, r$o = Thiele modulus; 4 = 4,,/(l + c r ) , 402 = R(Tf)L2/De u = K (Tf)Cf Oc = (1 - PrJ/[l + P(r1 + 2Yz)l Subscripts f = bulk value max = value corresponding to the active catalyst optimal
location
Literature Cited Aris, R. "The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts", Voi. 1; Ciarendron Press: Oxford, 1975. Corbett, W. E., Jr.; Luss, D. Chem. Eng. Sei. 1974, 29, 1473. Downing, D. M.; Lee, J. W.; Butt, J. B. AIChEJ. 1979, 25, 461. Lee, J. W.; Butt, J. B.; Downing, D. M. AIChEJ. 1978, 24, 212. Morbidelli, M.; SeNida, A,; Varma A. Ind. Eng. Chem. Fundam. 1982, 21, 278. Morbidelii, M.; Varma, A. Ind. Eng. Chem. Fundam. 1982, 21, 284.
Department of Chemical Engineering University of Notre Dame Notre Dame, Indiana 46556
Greek Letters P = (-WDeCf/ (XeTf) 71 = E/(RTd yz = (-MJ/(RTf) 6 = Dirac delta function AH = heat of reaction
Massimo Morbidelli Albert0 Servidat Sergio Carrat Arvind Varma*
Received f o r review March 26, 1984 Accepted September 7, 1984
AHa = heat of adsorption 7 = effectiveness factor % = T/Tf
Dipartimento di Chimica Fisica Appiicata, Poiitecnico di Miiano, 20133 Milano, Italy.
Estimation of Vapor Pressures for Halogenated Aromatic Hydrocarbons by a Group-Contribution Method The goupcontribution method for predicting vapor pressures of hydrocarbons and hydrocarbons containing nitrogen and sulfur moieties is extended to include halogenated aromatic groups. The derived group parameters, S, and c0,/R, are 2.094 and 553.4 for fluorine, 2.130 and 1335.7 for chlorine, 1.999 and 1689.1 for bromine, and 1.934 and 2235.7 for iodine, respectively. The average error in prediction was less than 20% for compounds used and not used in deriving these parameters.
Many chemicals of environmental concern are in the general class of halogenated aromatic hydrocarbons. In studying the behavior of these chemicals in the environment, physical chemical properties such as vapor pressures and solubilities are necessary. Unfortunately, these properties have not been measured for most compounds. Consequently, methods for estimating these properties are required. In this communication, we have extended the group-contribution method of Macknick and Prausnitz (1979) for predicting pure-component vapor pressures to include aromatic halogen groups. The group parameters for the aromatic halogens and the compounds used to derive these parameters are listed in Table I. The data used for each compound consisted of ten vapor pressures evenly spaced between the experimental low and high temperatures for the data from Boublik et al. (1973) or all vapor pressures for the liquid state from the work of Stull(l947). In general, the vapor pressures ranged from 1.33 to 101.3 kPa in this work. In deriving these group contributions, the nonhalogen group contributions were calculated using the values of Macknick and Prausnitz (1979) and Bondi (1968). The parameters were estimated by performing a least-squares analysis 0 196-43 1318511024-0 119SO 1.5010
using a pseudo-Gauss-Newton algorithm contained in the BMDP-81 statistical software package (Ralston, 1979). To evaluate the predictive ability of the new parameters, vapor pressures were calculated for experimental temperatures where the vapor pressues equal 1.33, 13.3, and 101.3 kPa. For the compounds used in deriving these parameters, the average errors [f standard deviation (number of experimental values)] in percent were 15.0 f 19.5(19),16.2 f 19.6(25),and 14.9 f 18.6(23),respectively. For a group of compounds not used in deriving these parameters, errors in percent of 20.3 f 21.9(25), 17.8 f 10.4(28),and 17.2 f 11.0(28) were observed. The experimental data for the group of compounds not used in deriving the parameters was obtained from Stull(l947) and Boublik et al. (1973) and consisted of halogenated toluenes, ethylbenzenes, xylenes, anilines, and an isopropylbenzene (28 compounds). Errors typical of both groups of compounds are presented in Table 11. The predictive error for both groups of compounds was found to be independent of the degree of halogenation and the magnitude of the predicted vapor pressure. In addition, the predictive ability is slightly worse for the compounds not used in deriving these parameters. However, 0 1985 American Chemical Society
120
Ind. Eng. Chem. Fundam., Vol. 24, No. 1, 1985
Table I. Group Contributions for Vapor Pressure Parameters S and E o / R for Aromatic Halogens halogen Si toi/R, K uwi, cm3/g-mola vapor pressure data used to derive group parameters
-F
2.094
553.4
5.80
-c1
2.130
1335.7
12.00d
-Br
1.999
1689.1
15.12
-I
1.934
2235.7
"Bondi (1968). 'Stull (1947). 'Boublik et al. (1973).
19.64 duwi
fluorobenzene; 1,3,5-trifluorobenzene 1,2,3,4- and 1,2,3,5-tetrafluorobenzene penta- and hexafluorobenzene all chlorobenzene congeners 2- and 4-chlorobiphenyl 1-chloronaphthalene bromobenzene; 1,4-dibromobenzene 4-bromobiphenyl 1-bromonaphthalene iodobenzene
source b, c c, c
c, c
b b, b b b, b b b b
= 12.24 for perchlorinated substances.
Table 11. Comparison of Experimental a n d Predicted Vapor Pressure compound T1.33, K," exptl P, kPa, calcd % error pentachlorobenzene 417.5 1.45 8.7 1.33 0.3 1-chloronaphthalene 391.8 278.7b 2.88' 28.lb hexafluorobenzene 1.51 260.8 13.3 fluorobenzene 1.2 1.35 4-bromobiphenyl 423.8 0.4 337.2 1.34 iodobenzene 34.9b chloropentafluorobenzeneC 307.9' 2.60' 21.1 375.3 1.61 4-chloroanilinec 22.4 1.03 3,4,5,6-tetrachloro- 1,2-xylene' 413.5 1.31 352.0 1.35 2-bromo-1,4-xylenec 1.12 15.9 347.2 1-bromo-4-ethylben~ene~ 1.09 18.3 2-iodotoluene' 353.0
T101.3, K," exptl
P, kPa, calcd
% error
549.2 532.5 353.4 357.9 583.2 461.8 391.2 503.7 546.7 479.9 479.2 484.2
84.5 105.0 86.7 113.6 160.0 100.9 83.5 121.3 77.5 112.1 111.4 96.8
16.6 3.6 14.6 12.1 57.9 0.4 17.6 19.7 23.5 10.7 10.0 4.4
and T101.3 are temperatures (K) where the vapor pressures equal 1.33 and 101.3 kPa, respectively. bData shown are for T,,,,K. Compounds not used in determining the parameters.
the error range shown in Table I1 for all of the halogenated compounds is similar to the range observed by Macknick and Prausnitz (1979), Edwards and Prausnitz (1981), and Ruzicka (1983), a factor of 2 or less. Some of the predictive error observed in this method can be directly attributed to inaccuracies in the experimental data. This method should be used when no experimental data exist for the compounds of interest and then with extreme caution (Macknick and Prausnitz, 1979). Registry No. 1,3,5-Trifluorobenzene, 372-38-3; 1,2,3,4-tetrafluorobenzene, 551-62-2; 1,2,3,5-tetrafluorobenzene,2367-82-0; pentafluorobenzene, 363-72-4; hexafluorobenzene, 392-56-3; 4chlorobiphenyl, 2051-62-9; 1-chloronaphthalene, 90-13-1; bromobenzene, 108-86-1; 1-bromonaphthalene, 90-11-9;fluorobenzene, 462-06-6; 4-bromobiphenyl, 92-66-0; iodobenzene, 591-50-4; chloropentafluorobenzene, 344-07-0; 4-chloroaniline, 106-47-8; 3,4,5,6-tetrachloro-l,2-~ylene, 877-08-7; 2-bromo-l,4-xylene, 553-94-6; l-bromo-4-ethylbenzene, 1585-07-5; 2-iodotoluene, 615-37-2; 1,4-dibromobenzene, 106-37-6.
Literature Cited Bondi, A. "Physical Properties of Molecular Crystals, Liquids and Gases";
Wiley: New York. 1968, Chapter 14.
Boubllk, T.; Fried, V.; Hala, E. "The Vapor Pressures of Pure Substances"; Elsevier: New York, 1973. Edwards, D. R.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1981, 20, 280. Mecknick, A. B.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1979, 18, 348. Ralston. M. "BMDP-79 Biomedical Computer Programs P-Series"; Dixon, W. J.; Brown, M. B., Ed.; University of California Press: Los Angeles, 1979; Chapter 14.2. Ruzicka, V., Jr. Ind. Eng. Chem. Fundam. 1983, 22, 266. Stull, D. R. Ind. Eng. Chem. 1947, 39, 517.
Water Chemistry Program Uniuersity of Wisconsin-Madison Madison. Wisconsin 53706
L a w r e n c e P.B u r k h a r d
Received for reuiew September 2, 1983 Accepted June 4, 1984
This work was funded by the University of Wisconsin Sea Grant College Program under grants from the Office of Sea Grant, National Oceanic and Atmospheric Administration, U.S.Department of Commerce, and from the State of Wisconsin; Federal Grant NA800-AA-D-00086, Project R/MW-21.
