of viscosity given by the present correlation and the values computed by Dean and Stiel’s (3)equations. This may be attributed to inherent errors in the method of determination of the pseudocritical constants ( 3 ) . I n Figure 1, a regular trend is noticed between the limits of the two pure components. This clearly brings out the effect of mixture composition on viscosity of the Freon-12-Freon-22 vapor mixture system.
p
pm u
LITERATURE CITED
Brebach, W.J., Thodos, G., lnd. Eng. Chem. 50, 1095 (1958). Buddenberg, J.W., Wilke, C.R., lnd. Eng. Chem. 41, 1345 (1949). Dean, D.E., Stiel, L.I., A.1.Ch.E. J . 11, 526 (1965). Dolan, J.P., Ellington, R.T., Lee, A.L., J. CHEM.ENG. DATA 9 , 484 (1964). Dolan, J.P., Starling, K.E., Lee, A.L., Eakin, B.E., Ellington, R.T., J. CHEM.ENG.DATA8, 396 (1963). Eakin, B.E., Starling, K.E., Dolan, J.P., Ellington, R.T., J. CHEM.ENG.DATA7, 33 (1962). “Freon,” Technical Bulletin B-2, E.I. du Pont de Nemours & Co., 1966. Hirschfelder, J.O., Bird, R.B., Spotz, E.L., Chem. Reu. 44, 205 (1949). Hirschfelder, J.O., Curtiss, C.F., Bird, R.B., “Molecular Theory of Gases and Liquids,” pp. 529-530, Wiley, New York, 1954. Iwasaki, H., Kestin, J., Physica 29, 1345 (1963). Kim, S.K., Ross, J., J . Chem. Phys. 42, 263 (1965). Makita, T., Reu. Phys. Chem. Japan 24, 74 (1954). Peters, Charles C., Van Voorhis, Walter R., “Statistical procedures and Their Mathematical Bases,” p. 67, McGrawHill, New York, 1940. Sharpe, ii.,“Refrigerating Principles and Practices,” pp. 86-116, McGraw-Hill, S e w York, 1949. Shimotake, H., Thodos, G., A.I.Ch.E. J . 4, 257 (1958). Starling, K.E., Eakin, B.E., Ellington, R.T., A.1.Ch.E. J . 6 , 438 (1960). Sutherland, W., Phil. Mag. 40, 421 (1895). Tribus, M., “Thermostatics and Thermodynamics,” p. 416, D. Van Kostrand, Kew York, 1961. Wilke, C.R., J . Chem. Phys. 18, 517 (1950). Witzell, O.W., Johnson, J.W., ASHRAE Trans. 71, Part I, 30 (1965).
CONCLUSION
The present correlation facilitates design of engineering systems, as viscosity information on pure Freon-12 and Freon-22 vapors and their mixtures may be obtained readily. The determination of viscosity, however, requires an accurate knowledge of the temperature-dependence of viscosity a t zero density. For engineering purposes, it may be convenient to use the atmospheric viscosity values. These atmospheric viscosity values may be calculated for pure components by the correlation of Witzell and Johnson (20) and for mixtures by Herning and Zipperer’s ( 4 ) equation or by Wilke’s (19) equation. NOMENCLATURE
a, b A, B A m ,B , , A,, B, M,
= coefficients in Table I = coefficients in Equation I = coefficients defined in Equations 2 & 3 = molecular weight of the pure components
N = number of experimental points P.E. = probable error T = temperature = molar volume of the mixture = molar volume of the pure components x , = molar fractions of the pure components in the mixture viscosity a t a given temperature and density I.1= !-lo = viscosity at the same temperature as p but at zero density w = viscosity as calculated from Equation 1
= density = density of the mixture = standard deviation
v, v,
RECEIVEDfor review June 7, 1968. Accepted February 4, 1969.
Heterogeneous Phase Equilibrium in the Ethane-n-Dodecane System KYU H. LEE and JAMES P. KOHN Chemical Engineering Department a n d Radiation Laboratory, University of Notre Dame, Notre Dame, Ind.
46556
Vapor-liquid equilibrium compositions, pressures, and liquid molar volumes for the binary system of ethane and n-dodecane are presented for five isotherms between 0’ and 100OC. The Flory-Huggins model of liquid solutions gave better results in fitting the experimental data than the Scatchard modification of regular solution theory.
T H I S WORK was done to obtain accurate equilibrium data on the ethane-n-dodecane system and to test some of the simple solution models. The literature through 1967 shows no existing experimental data on this system. The ethane-n-octane system was reported recently by Rodrigues et al. ( 1 6 ) . The pure materials, ethane and n-dodecane, have been studied by many groups. The ethane has been studied extensively (1-3, 13, 15, 1 7 ) and the properties of n-dodecane were reported by several investigations ( 8 , 1 7 ) . EXPERIMENTAL
T h e equipment and experimental techniques were described in detail by Kohn and Kurata (11j and were the same as those used in the previous studies of binary 292
hydrocarbon systems (9-11, 16-18, 20). A complete schematic flow diagram of the- apparatus is shown in Figure 1. The apparatus is mounted on a plywood housing with 1-inch, 90” steel flanges on the outside. The cell ( 0 ) temperatures were measured by a platinum resistance thermometer ( V ) and controlled by a Sargent Thermonitor proportional controller with probable error within r O . 0 2 ” C. The pressures were measured by Heise bourdon tube gages (G, H ) , with an accuracy of 1 0 . 0 7 atm. The bourdon tube gages were checked frequently against an Ashcroft dead weight gage (S). The equilibrium cell (0) used in this study was a 10-ml. borosilicate glass cell and of‘ the same type as those used in the earlier works. The equilibrium cell was initially partially filled with a known amount of liquid n-dodecane. The weight was JOURNAL OF CHEMICAL AND ENGINEERING DATA
60-
50-
40I t
Figure 1. Flow diagram of apparatus 30-
determined to the nearest milligram by use of an analytical balance. The cell was then purged free of air by flushing with ethane gas. The compositions of ethane in the liquid solutions were determined from the stoichiometric analysis of the amount of the pure ethane which was added to the cell from a reservoir ( D ) by a manually operated mercury displacement pump ( E ) . The gas in the reservoir was kept a t a constant pressure of 41.81 atm. during 0" and 25" C. isothermal runs and 62.22 atm. during the higher temperature isothermal runs. I t s temperature was also kept constant during each run a t around 62'C., with probable error =t0.07". The mercury displacement pump has an accuracy of 10.01 ml. The temperature of the delivery line was kept a t 60°C. with probable error of +2', and its volume was calibrated as a function of pressure at that temperature. Its volume was around 0.9 ml. The ethane used in this study was the same grade and was prepurified the same as the ethane used in the previous study (12, 16). I t was thought to be 99.7 mole 5 ethane. The n-dodecane was claimed by the supplier (HumpreyWilkinson, Inc.) to be a t least 99.0 mole 5 pure. I t had a refractive index of 1.4220 a t 20°C., which was in good agreement with the literature value 1.4216 ( 1 7 ) . I t was used as received without further purification. The impurities are believed to be paraffinic hydrocarbons of similar molecular weight.
3
rn v)
w n
a
-
20 -
Figure 2. Pressure vs. mole fraction ethane in the liquid phase
RESULTS
Figure 2 presents equilibrium pressure us. mole fraction ethane in the liquid phase. Five bubble point isotherms were determined in the temperature range from 0" to 100"C. and a t pressures up to 62 atm. Each isotherm was obtained by several experimental runs to get a reasonably good reproducibility. The average deviations of the experimental bubble points were kO.09 atm. and &0.0019 mole fraction of ethane. Since the vapor pressure of the n-dodecane is very low (15.0 mm. of H g a t lOO'C.), the vapor phase was considered as pure ethane, and dew-point isotherms were not measured separately in this work. Figure 3 presents the curves of liquid molar volume us. mole fraction ethane in the saturated liquid phases. The average deviations of the experimental runs were +0.79 ml. per gram mole and k0.0025 mole fraction of ethane. The smoothed values of the equilibrium properties are given in Table I. The fugacities of ethane are also tabulated in Table I. The vapor phase is almost pure ethane in the temperature range of this study. Therefore, the compressibility factors of pure ethane (13) were used in the calculations of the ethane fugacities. Graphical integrations were applied in these calculations. The fugacities of ethane along each isotherm were fitted to both the Scatchard (19) modification of regular solution VOL. 14, No. 3, JULY 1969
1, 0.0
0.2
0.4
0.6
0.0
I
MOLE F R A C T I O N ETHANE IN L I Q U I D
Figure 3. M o l a r volume-composition diagram
293
Table I . Equilibrium Properties of the Liquid Phase of the Ethane-n-dodecane System Pressure, Atrn.
Mole Fraction
4.00 8.00 12.00 16.00 20.00 22.00
0.190 0.365 0.522 0.677 0.843 0.935
Molar Volume, M1.1 Gram Mole
Ethane Fugacity Atm.
Pressure, Atm.
Mole Fraction
4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00 44.00 48.00 52.00 56.00 60.00 62.00
0.068 0.129 0.198 0.259 0.314 0.365 0.414 0.458 0.498 0.536 0.578 0.608 0.644 0.676 0.710 0.72i
Molar Volume, M1.1 Gram Mole 75" c .
0" c. 193.0 165.5 140.8 116.9 92.4 80.9
3.83 7.33 10.52 13.40 15.98 17.14 aF = 0.615 us
=0.659
25" C. 4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00
0.125 0.240 0.345 0.440 0.530 0.614 0.700 0.790 0.882 0.980
208.5 190.3 173.9 158.8 144.8 131.4 117.9 104.0 91.9 86.0
3.88 7.51 10.91 14.07 16.99 19.68 22.13 24.34 26.29 27.94 aF = 0.605 as = 0.795
50' C. 4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00 44.00 48.00 52.00 56.00 60.00 62.00
Ethane Fugacity Atm.
0.088 0.174 0.254 0.327 0.393 0.454 0.512 0.565 0.616 0.666 0.715 0.764 0.813 0.861 0.910 0.936
219.4 205.5 192.5 180.6 170.0 160.0 150.9 142.1 131.6 126.9 119.5 112.5 105.8 100.2 95.4 93.1
3.91 7.64 11.18 14.54 17.71 20.71 23.53 26.15 28.64 30.93 33.03 34.95 36.70 38.24 39.58 40.20 uF = us =
229.0 219.0 207.i 197.7 188.6 180.4 172.4 1652 158.7 152.5 145.4 140.8 135.8 130.3 125.2 122.8
3.93 m -
1.11
11.35 14.85 18.20 21.42 24.50 27.44 30.25 32.92 35.46 37.88 40.16 42.31 44.34 45.31 aF = US =
1.059 1.468
100" c . 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0 44.0 48.0 52.0 56.0 60.0 62.0
0.050 0.101 0.152 0.200 0.247 0.292 0.334 0.373 0.409 0.444 0.475 0.506 0.536 0.565 0.594 0.608
238.4 230.0 221.6 213.7 206.0 198.6 191.6 185.2 179.2 173.5 168.5 163.2 158.2 153.5 148.8 146.4
3.92 7.75 11.46 15.10 18.59 21.97 25.24 28.40 31.45 34.39 37.23 39.98 42.62 45.17 47.62 48.81 aF = 0.839 us
= 0.938
1.047 1.420
theory and the Flory-Huggins (4, 5 , 7) solution model. Each model has a single parameter, i.e., interchange energy parameter. The expressions for the component fugacity for these models are for the Scatchard modification of regular solution theory,
where Pp is the vapor pressure of-component 1 a t the temperature of the system, T, and I4 is the partial molar volume of ethane in a dilute solution a t temperature T . Above the critical temperature of ethane, its vapor pressure was extrapolated using a modification of an equation proposed by Hougen et al. (6): log PP =
-A(1 - T,)
T,
while for the Flory-Huggins model,
(4)
where the constant A = 2.5693 was computed from the normal boiling point of ethane. The fugacity coefficients where
f
-
p
The standard state fugacity (A) is the fugacity of the hypothetically pure incompressible liquid ethane a t the temperature and pressure of the system. I t was computed from the following equation
294
1
(.?.TI
were obtained by the use of Pitzer's three-parameter method ( 1 4 ) . The partial molar volumes of the components used in the above equations were obtained from the molar volume data (Figure 3). The figure shows that the molar volume us. ethane concentration lines are linear in low concentration ranges, but in the concentrated regions deviate considerably from linearity. The partial molar volume of each component was determined by the intercepts of the straight lines which JOURNAL OF CHEMICAL AND ENGINEERING DATA
Table II. Partial Molar Volumes (MI./Gram Mole) Temp., C.
Ethane
n-Dodecane
0.0 25.0 50.0 75.0 100.0
65.8 69.9 74.2 77.7 82.2
222.2 227.4 231.4 239.0 246.8
NOMENCLATURE fl
= fugacity of component
i in atm.; i = 1,2
f? = standard state fugacity of component i in atm.; i
= 1,2 R = universal gas law constant = 1.987 cal. per gram mole “K. T = temperature in K . T , = reduced temperature, T 1 T, AU12 = interchange energy for component 1 and 2 in cal. per gram mole = partial molar volume of component z in the liquid solution in ml./g. mole; i = 1,2 = mole fraction of component i in the liquid; i = 1,2 4t = liquid volume fraction of component i; i = 1,2 a = standard deviation of the calculated ethane fugacities from the experimental values
v,
were drawn by the least square fit of the data in the low concentration ranges (mole fraction of the ethane less than 0.7). The partial molar volumes for each component are tabulated in Table 11. Through the use of the smoothed experimental data in Table I and the standard state fugacities defined by Equation 3, the values of the interchange energy Au12 were computed a t each pressure in every isotherm for both solution models. These energy parameters calculated from the Flory-Huggins model were very approximately constant in all isotherms and through the pressure ranges studied except a t high concentration regions. Large deviations in the high concentration ranges could be expected, since the molar volume us. ethane mole fraction curves deviate considerably from linearity in these regions. The interchange energies computed for the Scatchard model were considerably more scattered than the values from the Flory-Huggins model. But the over-all results showed that the interchange energy parameters for both models could be considered as constants for all practical purposes in the temperature range of 0” to 100°C. The best constants were obtained by a least squares program for all data points except the highconcentration regions. The results were 849 cal. per gram mole with a standard deviation of 70 cal. per gram mole for the Flory-Huggins model, and 414 cal. per gram mole with standard deviation of 102 cal. per gram mole for the Scatchard model. The fugacities of the ethane in the liquid phase were calculated from both models, using the best constants for the interchange energy parameters. The standard deviations of the calculated fugacities from the experimental values are listed in the Table I for each isotherm. The standard deviations calculated from all values were 0.91 atm. for the Flory-Huggins model and 1.20 atm. for the Scatchard model. But if the values in the highpressure regions were excluded, the standard deviations are considerably reduced. The standard deviations of all values up to 44 atm. are 0.54 atm. for the Flory-Huggins model and 0.76 for the Scatchard model. These values are slightly greater than those obtained from the ethanen-octane system in the previous work. However, the FloryHuggins model is accurate enough to represent the deviations of this system from Raoult’s law for most engineering purposes even at the elevated pressures.
VOL. 14, No. 3, JULY 1969
x,
LITERATURE CITED Barkelew, C.H., Valentine, J.L., Hurd, C.O., Chem. Eng. Pmgress 1, No. 1; Trans. A.I.Ch.E. 43, 25 (1947). Beattie, J.A., Hadlock, C., Poffenberper. N., J . Chem. Phys. 3, 93 (1935). Beattie, J.A., Su, G., S h a r d , G.L., J . Am. Chem. Soc. 61, 924 (1939). Flory, P.J., J . Chem. Phys. 9, 660 (1941). Ibid., 10, 51 (1942). Hougen, O.A., Watson, K.M., Ragatz, R.A., “Chemical Process Principles,” Part 11, p. 576, Wiley, Xew York, 1959. Huggins, M.L., Ann. N . Y.Acad. Sei. 43, 1 (1942). “International Critical Tables,” 111, 29 (1928). Kohn, J.P., A.I.Ch.E. J . 7, No. 3, 514 (1961). Kohn, J.P., Bradish, W.F., J . CHEM.ENG. DATA9, 5 (1964). Kohn, J.P., Kurata, F., Petrol. Process. 11, 57 (1956). Ma, Y.H., Kohn, J.P., J . CHEM.ENG.DATA 9, 3 (1964). Michel, A,, Van Straaten, W., Dawson, J., Physica 20, 17 (1954). Pitzer, K.S., Brewer, L., “Thermodynamics,” pp. 605-29, McGraw-Hill, Xew York, 1961. Rodrigues, A.B.J., M.S. thesis, University of Notre Dame, Notre Dame, Ind., 1965. Rodrigues, A.B.J., McCaffrey, D.S., Jr., Kohn, J.P., J. CHEM. ENG.DATA13, No. 2, 164 (1968). Rossini, F.C., Pitzer, K.S., Arnet, R.L., Brown, R.M., Pimental, G.C., “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Carnegie Institute of Technology, Pittsburgh, Pa., 1953. Shim, J., Kohn, J.P., J. CHEM.ENG.DATA7, 3 (1962). Scatchard, G., C h m . Reu. 8, 321 (1931). Shipman, L.M., Kohn, J.P., Ibid., 11, 176 (1966). I
RECEIVED for review July 8, 1968. Accepted March 3, 1969. This work was made possible by support of the Radiation Laboratory of the University of Xotre Dame. The apparatus was constructed under grants of the Esso Education Foundation and the National Science Foundation. The Radiation Laboratory of the University of Notre Dame is operated under contract with the U.S.Atomic Energy Commission. This is A.E.C. Document No. COO-38-619.
295
