24
Ind. Eng. Chem. Fundam. 1984, 23, 24-29
of the petroleum Research Fund, administered by the American Chemical Society, under Grant 14230-AC5. This research made use of the University of Illinois, Materials Research Lab, Center for the Microanalysis of Materials, which is supported as a national facility by the National Science Foundation under Grant DMR 80-20250.
Literature Cited Belyaev, V. D.: Slinko, M. M.; Timoshenko, V. I.; Slinko, M. G. Kinet. Katal. ia73. .- . -, 14. . ., B - I. -D. Beiyaev, V. D.; Sllnko, M. M.: Tlmoshenko, V. I.; Slinko, M. G. Dokl. Akad. Nauk SSSR 1974, 274, 1098. Belyaev, V. D.: Slinko, M. M.: Timoshenko, V. I.; Sllnko, M. G. Kinet. Katal. 1975. 16. 555. Hiavacek, V.; Van Rompay, P. Chem. Eng. Sci. 1981, 36, 1587.
Jensen, K. F.; Ray, W. H. Chem. Eng. Sci. 1980, 35. 2439. Kurtanjek, Z.; Shelntuch, M.: Luss, D. Ber. Bunsenges. Phys. Chem. 198Oa. 8 4 , 374. Kurtanjek, 2.; Sheintuch, M.; Luss, D. J . Catal. 1980b, 66, 11. Ray, W. H.; Uppai, A.; Poore, A. E. Chem. Eng. Sci. 1874, 2 9 , 1330. Renola, G. T. Ph.D. Thesis, University of Illinois, 1980a. Renola, G. T.; Ziodas, A.; Schmitz, R. A. Ber. Bunsenges. Phys. Chem. 1980b, 8 4 , 117. Sault, A. G.; Masel, R. I . J . Catal. 1982, 73, 294. Schmitz. A. A.; DNetto, G. 0. AlChE National Meeting, 1982, Paper 59c. Sllnko, M. 0.;Slinko. M. M. Catal. Rev. 1978, 77, 119. Shelntuch, M.; Schmltz, R. A. Catal. Rev. 1977, 75, 107. Wicke, E.; Kumman, P.; Keil, W.; Schlefler, J. Ber. Gunsenges . Wys . Chem, 1980, 8 4 , 315.
Received for review February 7, 1983 Accepted August 4, 1983
Chain-of-Rotators Equation of State. 2. Polar Fluids Hlrokatsu Yasuoka and Kwang-Chu Chao' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
The chain-of-rotators equation of state of Chien et ai. is extended to polar fluids with the addition of a polar contribution term. The fluid pressure of Stockmayer molecules obtained by Yao et el. by Monte Carlo computer simulation is compared with that of LennardJones molecules to generate the polar contribution term. Consideration is also given to second virial coefficient data of Stockmayer molecules and to experimental data on saturated liquid water. The new augmented chain-of-rotators equation is tested with experimental pVT and vapor pressure data on NH, SO,, H,O, ethyl ether, acetone, methanol. and ethanol.
This paper is a sequel to a previous publication by Chien et al. (1983) on the chain-of-rotators (COR) equation of state. Chien et al. have shown that the COR equation of state describes the fluid state from the supercritical gas to subcritical vapor and liquid for small and large molecules. In this paper the COR equation is extended to polar fluids. The description of thermodynamic properties, particularly phase equilibria, of polar fluids is of interest in both science and engineering, and many papers have been published on equation of state of polar fluids. Progress has been made in applying statistical mechanical theory to the description of polar fluids. Stell et al. (1972) developed a perturbation theory of polar fluids. The perturbation theory of Barker and Henderson (1967) was applied to polar fluids by Masuoka et al. (1977a, b). The Lennard-Jones potential with temperature-dependent parameters was used to represent the intermolecular potentials for both nonpolar and polar molecules. Gubbins and Twu (1978) developed a theory for the thermodynamic properties of polyatomic fluid mixtures for polar fluids based on perturbation theory. Gmehling, Liu, and Prausnitz (1979) extended perturbed-hard-chain theory to strongly polar fluids by taking into account chemical dimerization equilibria. Whiting and Prausnitz (1983) extended the perturbed-hard-chain theory to polar fluids by assigning a temperature dependence to the energy parameter. Recently Yao (1981) and Yao et al. (1982a,b) determined thermodynamic properties of Stockmayer molecules by means of Monte Carlo simulation. Yao's reults are used to develop the new equation of state for polar fluids.
Table I. Constants of Eq 4,9, and 11
-___--
a, a1
a3 a4
as ' 6
a7 0 8
a9
__-__
2.39222 0.790740 -2.24304 -1.027 10 1.08610 0.28 5710 0.0147839 - 0.0006 2780 1 -0.0127978
Correlation of Computer Simulated Polar Contribution to Fluid Pressures According to perturbation theory the pressure of a polar fluid can be separated into two terms p = p(nonpo1ar) + p(po1ar) (1) Calculations for Sbkmayer molecules by Yao by means of the Monte Carlo method provide detailed information on fluid pressure at varying dipole strength. The polar contribution to fluid pressure is extracted from the calculations on Stockmayer potential of the dipole strength of interest and zero dipole strength which is the Lennard-Jones potential. p(po1ar) = p(Stockmayer) - p(Lennard-Jones) (2) Yao (1981) prepared a table of interpolated values from his direct simulated data. The ranges of conditions are as follows 1 < p* < 2 (where .r?yc = k T / c )
< 0.9 (where B* = u/(Ra3)) 0 < p < 1 (where p = p/(ta3)'/*)
0 < l/B*
0196-4313/84/1023-0024$01.50/00 1984 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 23, No. 1, 1984 25 IO
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7* Figure 1. Polar contributed second virial coefficients. A
