Ind. Eng. Chem. Res. 1987,26, 336-337
336
7 = dimensionless distance normal to the sheet 8 = constant defined by eq 31 8, = dimensionless sheet temperature
Literature Cited Abramowitz, M.; Stegun, I. A. Handbook of Mathematics Functions; Dover: New York, 1965. Crane, L. 2. Angew. Math. Phys. 1970, 21, 645. Danberg, J. E.; Fansler, K. S. Q. Appl. Math. 1976, 34, 305. Dutta, B. K.; Roy, P.; Gupta, A. S. Int. Commun. Heat Mass Transfer 1985, 12, 89. Erickson, L. E.; Fan, L. T.; Fox. V. G. Ind. Eng. Chem. Fundam. 1966, 5 , 19.
Fisher, E. G. Extrusion of Plastics, 3rd ed.; Newnes-Butterworths: London, 1976. Gupta, P. S.; Gupta, A. S. Can. J. Chem. Eng. 1977, 55, 744. McCormack, P. D.; Crane, L. Physical Fluid Dynamics; Academic: New York, 1973. Middleman, S. Fundamentals of Polymer Processing; McGraw-Hill: New York, 1977. Piskunov, N. Differential and Integral Calculus; Mir: Moscow, 1964. Sakiadis, B. C. AIChE J . 1961, 7, 26. Vleggaar, J. Chem. Eng. Sci. 1977, 32, 1517. Received f o r review May 3, 1985 Accepted June 2, 1986
Solubility of Mercury in Normal Alkanes H. Lawrence Clever* and Marian Iwamoto Solubility Research a n d Information Project, Department of Chemistry, Emory University, Atlanta, Georgia ,70322
The equation In S (molality) = 5.1059 - 4970.90/T reproduces within experimental error the solubility of mercury in normal alkanes of carbon number 5-10 over the 273.15-336.15 K temperature interval. The molal solubility of mercury appears t o be independent of the normal alkane carbon number a t all temperatures. The equation can be used with caution to estimate the solubility of mercury in normal alkanes of other carbon numbers at other temperatures. During a review of the literature of the solubility of mercury in organic liquids, it was observed that the molal solubility (mol kg-l) of mercury is nearly independent of the solvent a t a given temperature for the C5-Cl0 normal alkanes between 273.15 and 336.15 K. The molar solubility (mol L-l) is also nearly independent of the normal alkane solvent but at a slightly larger uncertainty. The mole fraction solubility shows a systematic change with solvent. The relationship does not apply to branched alkanes. The solubility of mercury in the branched chains depends on the chain branching and is smaller than in the normal alkane of the same carbon number. Figure 1shows a plot of the natural logarithm of molal solubility against the inverse of the absolute temperature. There are 58 points from 10 papers. The papers are not completely independent. Several (Moser and Voigt, 1957a,b; Klehr and Voigt, 1960; Spencer, 1967; Spencer and Voigt, 1968) are from the same laboratory. Another (Kuntz and Mains, 1964) reference their values to the mercury in hexane solubility value at 298.15 K of Moser and Voigt (1957). The experimental values from Okouchi and Sasaki (1981,1983), Reichardt and Bonhoeffer (1931),and Vogel and Gjaldbaek (1974) appear to be independent experiments. All of the experimental values will be published in a volume of the Solubility Series under preparation. Table I gives the average molal solubility at each temperature. At four of the temperatures, dropping one value from the average greatly improves the standard deviation of the average. These values are compared with the smoothed values from an equation obtained from a linear regression of 53 of the 58 points shown in Figure 1. The equation is
Table I. Solubility of Mercury in Normal Alkanes. Comparison of the Average Experimental Molal Solubility with the Calculated Molal Solubility and the Calculated Molar Solubility lo6 M solubility, mol L-' lo6 m solubility, mol kg-' T. K exDtl av. f SD" no. calcd ea 1 calcd ea 2 1.45 2.3 f 0.4 4 2.06 273.15 2.1 f 0.1 3 4 2.86 1.99 2.8 f 0.2 278.15 2.70 3.9 f 0.2 3.92 5 283.15 3.63 5.31 4 5.6 f 0.3 288.15 7 7.13 4.83 6.9 f 0.3 293.15 14 9.4 f 0.6 9.48 6.37 298.15 9.6 f 0.1 13 8.32 12.4 f 0.4 8 12.48 303.15 10.78 15.3 f 1.3 4 16.28 308.15 15.9 f 0.4 3 21.06 13.84 6 20.9 f 1.5 313.15 5 21.4 f 0.9 17.6 27.0 1 18.7 318.15 62.4 39.8 82.8 1 336.15
In S (molal) = (5.1059 f 0.1576) - (4970.90 f 46.40)/T
with a standard error about the regression line of 5.7 x lo-'. Smoothed molar solubilities from eq 2 are in Table I. The equations above are considered reliable for the experimental range of 5-10 carbon normal alkanes at 273.15-336.15 K. The equations can be used with caution to estimate the solubility of mercury in normal alkanes and
(1)
with a standard error about the regression line of 4.0 x lo-'. The constants of the equation relate to thermodynamic changes for the transfer of 1mol of mercury from the liquid
(I
SD = standard deviation.
metal to the hypothetical 1 m solution of AHl = 41.3 f 0.4) kJ mol-' and ASl = (42.5 f 1.3) J K-' mol-'. The treatment assumes the same values for all normal alkanes. The molar solubility fits a similar pattern but with a little larger uncertainty. A linear regression of the concentrations gives In S (molar) = (4.2390 f 0.2472) - (4830.90 f 72.78)/T (2)
0888-588518712626-0336$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res. 1987,26,337-343 Mercury + n - A l k a n e s ( C a t o C ~ O ) In (m, mol k g - ' ) In m , = 5 105848
AH =
\
YS
IOOO/(T, K )
- 4 9 70898/(T/IOOK)
41 3 kJ mol-'
! *
\;
.\+ *\
-130
I
I *\
\
337
Vogel and Gjaldbaek (1974) point out that in vigorously agitated systems colloidal mercury may be present, which would give a large apparent solubility. In such systems the equation would give a lower limit to the mercury content of the alkene. There is not complete agreement on how long it takes to saturate a mercury + alkane system. Kuntz and Mains (1964) claimed saturation within 20 min of vigorous agitatioin. Klehr and Voigt (1960) equilibrated for up to 10 days. Vogel and Gjaldbaek (1974) showed they obtained the same solubility with shaking times of 48 h to 1month. We have searched for other solutes that might show this relationship when dissolved in normal alkanes without success. The solubilities of noble and diatomic gases at 1-bar partial pressure and the solubility of sulfur do not show values that are independent of the alkane solvent at a given temperature.
Acknowledgment We thank Prof. A. F. Voigt of Iowa State University and Dr. S. Okouchi of Hosei University for providing us with experimental data not in their published papers and for copies of difficult to obtain documents. Registry No. Hg, 7439-97-6.
Literature Cited 30
31
32
33
34
35
36
37
38
IOOO/(T, K )
Figure 1. Solubility of mercury in normal alkanes. In S (molal, mol kg-') vs. 1000/T (K).Horizontal clusters of points represent the number of independent data points of one value. Vertical clusters are independent values at a given temperature. There is no systematic change in the solubility with carbon number a t the various temperatures.
normal alkane mixtures of other carbon numbers and at other temperatures. There are experimental mercury solubilities in five branched alkanes at 298.15 K. The solubilities range from 4 % (2,3-dimethylbutane)to 38% (2,2,4-trimethylpentane) less than the solubility predicted for normal alkanes at 298.15 K. Thus, the equations may give an upper limit to the mercury solubility in branched alkanes.
Klehr, E. H.; Voigt, A. F. Radioisot. Phys. Sci. Ind., R o c . Conf. 1960, I , 517-529. Kuntz, R. R.;Mains, G. J. J . Phys. Chem. 1964,68,408-410. Moser, H.C.; Voigt, A. F. US AEC ISC-892, 1957a; Chem. Abstr. 1958,52,10691h. Moser, H. C.; Voigt, A. F. J. Am. Chem. SOC.1957b,79,1837-1839. Okouchi, S.;Sasaki, S. Bull. Chem. SOC.Jpn. 1981,54,2513-2541. Okouchi, S.;Sasaki, S. Report of the College of Engineering of Hosei University, 1983; No. 22, 55-106. Reichardt, H.; Bonhoeffer, K. F. 2.Phys. 1931,67, 780-789. Spencer, J. N. Ph.D. Dissertation, Iowa State University, Ames, IA, 1967. Spencer, J. N.; Voigt, A. F. J. Phys. Chem. 1968,72, 464-470. Vogel, A.; Gjaldbaek, J. C. Arch. Pharm. Chem. Sci. Ed. 1974,2, 25-29. Received for review August 5 , 1985 Revised manuscript received July 7, 1986 Accepted September 22, 1986
Experimental Technique for Determining Mixture Compositions and Molar Volumes of Three or More Equilibrium Phases at Elevated Pressures J. R. DiAndreth,+ J. M. Ritter, and M. E. Paulaitis* Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
An experimental technique is described for the accurate measurement of both the composition and molar volume of individual phases in fluid-phase equilibria involving several coexisting phases. The technique enables the equilibrium compositions and molar volumes to be determined from visual measurements of phase volumes only; no sampling is required. Results are presented for liquidliquid-gas equilibrium for trans-decalin-COz mixtures and 2-propanol-water-COz mixtures and liquid-liquid-liquid-gas equilibrium for 2-propanol-water-C02 mixtures. The experimental technique is well-suited for measurements of phase equilibria a t elevated pressures and a t conditions near the critical point of COP. The specific motivation for studying equilibria involving several coexisting -.vhases at elevated vressures arose from + Current address: ExDerimental Station. E. I. d u P o n t d e Nemours & Company In;., Wilmington, DE' 19898.
0888-5885/87/2626-0337$01.50/0
the need to describe such phase behavior for fluid mixtures of interest in suDercriticd-fluid extractions. Three or more coexisting phases are typically encountered in these extractions when highly compressible fluids are present at conditions in the vicinity of the critical region. Multiphase 0 1987 American Chemical Society
