I
H. WILLIAM PRENGLE, Jr., and GORDON F. PALMI Department of Chemical Engineering, University of Houston, Houston, Tex.
Thermodynamics of Solutions Determination of Bubble Points at Vario'us Pressures for Prediction of Vapor-L iq u id Equilibria Vapor-liquid equilibria can be calculated without. knowing vapor composition, thus eliminating a lengthy, less accurate analytical procedure
D E T E R M I N A T I O N of vapor-liquid equilibria for binary systems by the total pressure method has been developed on a theoretical basis (6, 8, 9 ) . The theory requires measurement of the bubble point temperatures and pressures for known mixtures. From these data, vapor-liquid equilibria can be calculated without the knowledge of the composition of the vapor, thus eliminating a lengthy and usually less accurate analytical procedure. Extension of the theory by Redlich, Kister. and Turnquist ( 9 ) does not require that the vapor behave as a perfect gas. In addition to the bubble point data, accurate vapor pressure data for the pure components are required, and these can be obtained with the same apparatus. This work presents the evaluation and calibration of a Swietoslawski ebulliometer as a device for determining the bubble point temperatures of a given mixture as a function of the pressure (5, 73). Data were obtained for the system 2,2,4-trimethylpentane-toluene and compared with previously published data (3, 4, 72) for this system obtained with a conventional equilibrium still.
Experimental Apparatus
The apparatus shown in the flow diagram was modified from the unit of Wilson and Simons (76) and was designed for subatmospheric, atmospheric, or elevated pressure operation. The equipment was utilized for simultaneous multiple measurements by use of a specially designed portable table requiring external connections to a water supply, drain, and 110-volt, alternating current electrical source for operation. As designed, three ebulliometers (or stills) may be operated concurrently at the same total pressure, thereby speeding the accumulation of the desired data. The ebulliometers are connected Present address, International Minerals and Chemical Corp., 20 North Wacker Drive, Chicago, Ill.
through a common manifold, a Cartesian manostat, and a ballast tank to the vacuum pump. For pressure operation, the ballast tank and vacuum pump are replaced with the nitrogen cylinder by manipulation of the proper valves. A mercury manometer is used for measurements at vacuum and relatively low pressures. Higher pressure measurements are accomplished by use of the high pressure manometer, dead weight tester, and calibrated pressure gage. Temperatures are determined with a platinum resistance thermometer in conjunction with a Mueller bridge, mercury commutator switch, and a high sensitivity galvanometer fitted with a lamp and scale. Auxiliary facilities include variable voltage transformers, a 6-volt storage battery, water manifold, drain manifold, and additional space for future installation of refrigeration facilities for condensation at low temperatures. The ebulliometer is basically a Swietoslawski ebulliometer (73) modified for electrical heating; construction is of borosilicate glass. The cylindrical boiler at the bottom of the apparatus was roughened on the inside by attaching glass particles to the walls to provide adequate surface nuclei for bubble formation and thereby prevent bumping. Heat is supplied to the boiler by a wrapping of 22-gage Nichrome asbestos-insulated wire. The boiler acts as a Cottrell pump by circulating superheated liquid which flashes at the thermometer well top and flows over the well and both sides of the surrounding glass jacket back to the boiler reservoir. Vapor is condensed, and distillate is discharged to a drop counter for measurement of the boiling rate. The outside of the outer jacket surrounding the thermometer well is also wrapped with Nichrome wire for heat loss compensation ; the voltage on the winding is maintained at a relatively low value, compared to the main heater, and is not critical, provided that heating is not
excessive. The entire apparatus, with exception of a section of the condensate return line to the boiler, was insulated with a 0.5-inch layer of asbestos cement. System pressure is controlled through the condenser and regulated by means of a Cartesian manostate (Emil Greiner Co., New York, N. Y., Model 8). Nitrogen from a cylinder serves as the pressure source. Pressure is measured by suitable range manometers or a dead weight gage, after Wilson and Simons (76),depending on the pressure level of operation; appropriate manometric corrections are applied. Recently a 100-inch manometer, fitted with a calibrated aluminum bar and cathetometer, was added to the apparatus. With this device and using Meriam manometer fluid No. 3 (density 2.9610 grams per ml. a t 20' C., Meriam Instrument Co., Cleveland, Ohio) the pressure can be determined within k0.022 mm. of mercury. The temperature is determined by an L & N platinum resistance thermometer in the circuit of a Mueller bridge. The thermometer was triple-point calibrated by comparison with a thermometer certified by the National Bureau of Standards. Several investigators recommend the use of a differential method of measurement in which the vapor pressure of a solution is directly compared with the vapor pressure of a single component boiling at the same temperature. Redlich (7, 8) points out that the use of a single component as a reference substance greatly simplifies the equipment by eliminating the requirement of high accuracy of temperature and pressure measurements; in a difference measurement a number of tedious corrections of the mercury manometer can be disregarded. The direct measurement method was adopted in the interest of being able to make a number of runs with two or three ebulliometers operating simultaneously; accurate temperature and pressure measurements have not been too difficult thus far. VOL. 49, NO. 10
OCTOBER 1957
1769
P
TO EBULLIOMETERS OR STILLS
P
VACUUM PUMP
Operation at subatmospheric, atmospheric, or elevated pressure
Operation. Prior to the determination of bubble point data it was necessary to determine the optimum boiling rate for the ebulliometer. To accomplish this, approximately 160 ml. of toluene were placed in the ebulliometer, and operation was commenced. Temperature determinations were made for various boiling rates at atmospheric pressure. The rate was determined by counting the drops per minute of condensate falling from the drop counter. The procedure was repeated for 2,2,4trimethylpentane. By plotting the difference in experimental temperatures and the accepted literature values (7) against drop rate, the optimum range of operation was determined. For this device the optimum occurred over a range of from 100 to 300 drops per minute with a temperature variation of less than O.0l0 c. Some explanation should be made of the obvious difference between the drop rate for optimum operation observed in this laboratory and that observed by Swietoslawski (14). The criterion for the region of optimum operation is primarily one of “proper functioning” of the device; obviously such items as tube diameters, static liquid heads. rate of heat transfer, and amount of liquid holdup determine this condition. It was not possible to get satisfactory operation of the device at a drop rate of 10 to 25 drops per minute as claimed by Swietoslawski; it is not clear from his monograph whether he also obtained these low drop rates for the larger electrically heated device. The data from this laboratory indicate that proper functioning, that is a condition of satisfactory rate and steadiness of evolution of bubbles, occurred in the range of 100 to 300 drops per minute. Klecka
1770
( 5 ) has observed this same higher boiling rate. This is attributed to the fact that the authors’ device is larger with considerably more liquid holdup than the one used by Swietoslawski in obtaining 10 to 25 drops per minute. A Cottrell boiler, and consequently the ebulliometer, has certain limitations -for a mixture of components of high relative volatility the boiling point becomes sensitive to boiling rate. Obviously this is a matter of degree, and at this time the data necessary to prove or disprove this point are not available for this device on such a system. For experimental measurements on mixtures, operation is begun a t the lowest pressure desired, because progression to higher pressure eliminates possible “flashing” of the liquid mixture if the procedure is reversed. At the outset of the operation all valves are closed, and the vacuum pump is started and allowed to evacuate the ballast tank for several minutes. The valves to the ebulliometer and the low pressure manometer are opened full. The valve from the ballast tank to the manostat is opened, the bypass vaIve on the manostat is slightly opened, and the system pressure is allowed to decrease slowly. When the manometer indicates 1 or 2 mm. above the desired reading, the bypass valve on the manostat is closed. The bleed valve to the right of the manostat is adjusted until the manostat is in its most stable operating position. This is indicated when a small change in the bleed valve causes no change in pressure. Heat is supplied to the ebulliometer, and final adjustment is made so that a drop rate of 100 to 200 drops per minute is obtained. Compensation voltage is adjusted until no vapor condensation occurs on the walls at the top of the
INDUSTRIAL AND ENGINEERING CHEMISTRY
ebulliometer. The ebulliometer is allowed to reach equilibrium, and experimental measurements are made. After all desired experimental measurements, the heat to the ebulliometer is turned off. The valve from the ballast tank to the manostat is closed, and the bypass valve of the latter slightly opened. The bleed valve is adjusted so that the system pressure slowly increases to the next operating pr‘essure. As this pressure is reached, the bleed valve is closed, the bypass valve on the manostat is closed, and the valve to the ballast tank is opened. Adjustments are made on the bleed valve as before to obtain a stable manostat operation. The system is then at the new operating pressure and ready for operation. For atmospheric pressure, the ebulliometer is opened to the atmosphere at the top of the condenser, heat is supplied and adjusted as before, and temperature and pressure are measured. For elevated pressure operation all valves are closed a t the start of the operation. The nitrogen cylinder regulating valve is adjusted to give a pressure of 20 pounds per square inch gage for operation of the ebulliometer at an absolute pressure of approximately 1100 mm. of mercury. This differential was necessary for stable operation. The valves to the ebulliometer and low pressure manometer are opened full. The valve from the cylinder to the manifold is opened slightly, and the pressure in the system allowed to rise. When the manometer indicates a pressure approximately 100 mm. of mercury above the desired operating pressure, the valve connecting the cylinder and manifold is closed, and the bleed valve to the left of the manostat is opened to the atmosphere. Nitrogen flows through the bleed valve until the system reaches an equilibrium pressure. If this pressure is below the desired operating pressure, the bleed valve is closed, the valve from the cylinder to the manifold is opened, and the procedure is repeated. I t is always necessary to repeat the procedure several times, so that enough nitrogen can be forced beneath the diver in the manostat to give the operating pressure desired. when the bleed valve is opened to the atmosphere. After the desired pressure range is reached, the valve from the cylinder to the manifold is adjusted so that a small flow can be heard leaving the bleed valve. Final pressure adjustment is made with the manostat adjustment screw. Heat to the ebulliometer is supplied as previously described. and the system allowed to reach an equilibrium operating condition as before. Experimental pressures and temperatures are determined. After all measurements are made, the main valve on the nitrogen cylinder is closed, and heat to the ebulliometer is discontinued. After 10
THERMODYNAMICS OF S O L U T I O N S tively, which represent a correction to temperature of about O.OOIo and 0.0015’ C., respectively. Readings of thermometer resistance are made with the mercury commutator in the normal position and then in the reverse position. An average of the two readings is taken for calculation of the system temperature. Temperature and pressure readings are made every 20 or 30 minutes until three successive checks of the temperature corrected to some constant pressure are obtained.
Theoretical Basis The theoretical equations which lead to the proper relations between the activity coefficients and the total pressure arise from a consideration of the total free energy of a mixture of n components at constant temperature-that is, n
F,,, =
xiFiO
n
+ AF,
xiii?,
=
i=l
(1)
i=l
where the free energy change on mixing, AF,, can be represented by an “ideal” free energy of mixing term and an “excess” free energy term as defined by Scatchard. Consequently n
AF, =
F,E
-I- RT
xi In xi
(2)
i=l
-8-MM.
substituting Equation 2 in Equation 1 and solving for FSEgive
(3)
t.‘
For the first term on the right-hand side, the appropriate fugacity functions may be substituted. (F$- F,O) = RT In fi = RT ~n x1 y,
f$0
jl
&5”
(4)
substituting Equation 4 in Equation 3 gives n
Ebulliometer
FSE =
n
x,(RTlnx,ri)
- R T Z xzInx, e=1
i =1
and minutes, the bleed valve is adjusted so that the system slowly returns to atmospheric pressure. A sudden decrease in pressure can cause a possible flashing of the liquid in the ebulliometer and displacement of mercury from the manostat. The system pressure is calculated by proper combination of the corrected barometric pressure, the corrected measuring manometer reading, the static
head of nitrogen between the measuring manometer and the ebulliometer condenser, and the static head of boiling vapors between the nitrogen-boiling vapors interface and the thermometer bulb location. By proper arrangement of the equipment the vapor head corrections are minimized, and for the system reported herein they amounted to 0.02 and 0.03 mm. of mercury at 760 and 1200 mm. of mercury, respec-
For a binary system a t constant temperature.
(ST) + = XI
log YI
x z log Y Z ( 6 )
The term on the left-hand side of Equation 6 has been called the “Q function“ VOL. 49, NO. 10
OCTOBER 1957
1771
~~
(9) and produces certain obvious convenient relations with the activity coefficients :
knowns, yl and yz." As one of the equations is an integral equation, Equations 12 and 13 cannot be solved by direct algebraic manipulation; instead the pressure deviation ratio n/(xlPl XZPZ) us. x 1 curve is fitted by a trial and error procedure using the series functions in Equations 9 and 10 and Equation 13. Once a satisfactory fit has been obtained, (yI/yz) can be calculated a t any value of x from Equation 11 and following this can be solved simultaneously with Equation 13 to give the experimental values of 71and 7 2 .
+
Assuming the usual convention that 7%= 1 at xi = 1, Q may be represented by an appropriate power series which satisfies the theoretical limits that Q = 0 at x i = 1 and x2 = 1. Redlich and Kister have chosen the form:
Q = X I X Z [fB C(XI -
XZ)
3- D ( X I -
which produces
+ . . .I
XZ)'
(8)
+ +
D(Xi - Xz) - x2) . . . I (9) log Y z = X 1 2 [ B + C ( X 1 - 3 x 2 ) + D(u1 - 2 2 ) (XI - 5 x 2 ) -!- . . , 1 (10) log (-/I/Yz) B ( x ~- X Z ) + C(-1 + 6 ~ 1 x 2 + ) D(x~ X Z ) ( -1 + 8 ~ 1 x 2 )+ . . . (11 1
log Y i = X z 2 [ B f c ( 3 X i - X z ) (5x1
Equation 11 obviously produces the condition:
which also can be derived by proper manipulation of the Gibbs-Duhem equation. The connecting equations between Q, the coefficients B, C, D ,etc., and the total pressure are Equations 7, 9, 10 and iT
= XlYlPl
+
X2YlPn,
(13
where the adjusted vapor pressures, PI and P?,can be obtained from an equation of the form
which permits calculations a t elevated pressures. The fugacity coefficients of tbe component in the mixture vi, the fugacity coefficient of the pure component at its vapor pressure v? and the molal volume of the pure component can be evaluated from generalized charts (2) or from an appropriate equation of state (70). For the special case of the vapor acting as perfect gas, Equation 13 becomes : 7r
=
XlYlPlO
+
X2Y2PZO
(15)
Using the foregoing sequence of thermodynamic equations for a binary system, the activity coefficients can be obtained from total pressure measurements at constant temperature, for a series of solutions from x1 = 0 1. More specifically, Equations 12 and 13 provide the necessary "two equations in two un-
-
1772
Treatment of a Set of Data
A set of data was obtained for the system, 2, 2,4trimethylpentane-toluene over the entire concentration range and from 70' to 110' C., using the ebulliometer operation as previously described. The vapor pressure determinations were
in satisfactory agreement with accepted literature values (7). The experimental bubble point data for each individual mixture were fitted to an Antoine type of equation
by method of least squares using the procedure proposed by Willingham and others (75), which is basically the same as Scarborough's nonlinear case ( 7 7). The mean deviations of the derived equations from the experimental values, as expressed in terms of temperature, over the pressure range (200 to 1100 mm. of mercury), were 0.016' C. The Antoine equation constants are presented in Table I. Total pressures of the mixtures and pure materials were calculated from the Antoine equations at constant temperatures of 70°, 80', 90°, IOO', and 110' C., and a large scale plot of n us. x 1 for each temperature was made. Using the data from the plot at a selected temperature a second plot of the total pressure deviation ratio nexptl /(XIPI f x2P4 us. x1 was made and used to monitor the trial and error selection of B , C, D, . . , etc., in Equations 9 and 10 by comparison with 7'roalcd / ( x l P 1 x?P2)tis. xi for a given selection of the constants. For the system in question only two constants, B and C, were required to obtain an adequate fit of the data. Figure 1 shows the experimental total pressure deviation ratio points a t various values of x1 and the calculated curve for 100' C. Table I1 presents the experimental data and the activity coefficients calculated therefrom by the procedure outlined previously. For purposes of comparison with other published data on this system it was necessary to derive the value of the
INDUSTRIAL AND ENGINEERING CHEMISTRY
+
~~
Table
I.
Antoine Equation Constants
51
a
b
C
0.0000 0.2512 0.5024 0.7498 1.0000
6.95334 6.91930 6.97998 6.99834 6.81984
1343.943 1324.843 1359.129 1369.677 1262.490
219.377 233.117 229.742 232.347 221.271
"relative volatility, a'' at 760 mm. or mercury pressure, where
The normal boiling point of 2,2,4trimethylpentane is 99.21' C. and that of toluene is 110.60' C. ; therefore, it was necessary to interpolate the 90°, IOO', 110' C. isotherms to find the vapor compositions at 760 mm. of mercury. This was done by a quadratic interpolation formula of the form
where Ay, = ( Y , ~ - y o ) and the index 0, 1, and 2 refer to the three known points, and AT,, has a similar pattern. The temperatures were interpolated in a similar manner. The isobaric data thus obtained for 760 mm. of mercury is presented in Table 111, and a plot of cr us. X I with data from other sources (3, 4,12) is presented as Figure 2. Analysis of Errors
The temperature deviation from the American Petroleum Institute (API) values ( 7 ) for the pure materials was determined over the entire experimmtal pressure range; 2,2,4-trimethylpentane deviated over the range f0.003' to +0.041' C. at 200 mm. of mercury pressure and over the range +0.013" to -0.016' C. at 1100 mm. of mercury pressure. Toluene deviated over the range of +0.020' to -0.025' C. at 200 mm. of mercury pressure and -0.0105 to -0,026' C. a t 1100 mm. of mercury pressure. The fit of Ihe basic data to the Antoine vapor pressure equations showed a n average deviation of 0.016' C. for X I = 0.2512, 0.016' C . for = 0.5024, and 0.014' C. for X I = 0.7498. In fitting the data to equations the expected standard deviations of a single experimental value were taken as 0.005' C. and 0.10 mm. of mercury pressure. Because of change in vapor density in the ebulliometer with temperature and pressure, the Antoine equations were representative of a slightly varying value of x l rather than a constant value. The change in x 1 was estimated to be -0.0002 mole fraction at 200 mm. of mercury pressure and 60' C. and -0.0006 mole fraction at 1100 mm. of mercury pressure and 120' C.; therefore, an average
THERMODYNAMICS O F S O L U T I O N S 1.1 5
1.10
1.05
1.00 3
XI Figure 1.
correction of -0.0004 mole fraction was made for the mixture compositions. A deviation oftemperature of 0.016'C. and pressure of 0.10 mm. of mercury caused a total temperature deviation of 0.030' C. a t 200 mm. of mercury pressure. This resulted in a maximum de-
= MOLEFRACTION 2.2.4-T MP
Total pressure deviation ratio
viation of activity coefficient of 0.0012 and of vapor composition, yl, of 0.0010 mole fraction. At 1100 mm. of mercury pressure, the maximum deviation of activity coefficient was 0.0006 and of vapor composition, yl, of 0.0003 mole fraction. Correcting for the errors in
liquid compositions resulted in maximum deviations of vapor composition of 0.0013 and 0.0006 mole fraction a t pressures of 200 and 1100 mm. of mercury, respectively. Errors due to preparation of the mixtures were considered to be one part in
2.200
2.000
1.800
1.600
1.400
1.200
0
0.10
0.20
0.50
0.40
0.50
0.60
0.70
0.80
0.90
1.000 1.00
X, = MOLEFRACTION 2,2,4 TMP Figure 2.
Comparison of experimental data for 2,2,4-trimethylpentane-toluene VOL. 49, NO. 10
OCTOBER 1957
1773
Table II.
Vapor-Liquid Data for 2,2,4-Trimethylpentane-Toluene r , Mm. H g 71/yzn Y1 Yl
XI
556.3 = ppo 604.3 643.6 676.0 702.0 721.3 736.2 748 4 758.5 769.5 776.6 = pi0
0.0 0.1703 0.2980 0.4022 0.4905 0.5753 0.6559 0.7395 0.8223 0.9092 1.0000
0.0
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
log ( w / ~ z ) = B ( - x l
a
+
XZ)
f C(-1
1.4588 1.3253 1.2129 1.1247 1.0344 0.9705 0.9104 0.8716 0.8284 0.7973 0.7727
(1.4588) 1.3269 1.2324 1.1671 1.1085 1.0687 1.0363 1.0181 1.0039 1.0010 1.0000
+ ~ x I x ~ ) B. = 0.1380;
50,000 and were, therefore, negligible. The effects of material impurities upon the results were discounted in view of the close check of boiling points with accepted literature values.
Yz
1.0000 1.0048 1.0182 1.0390 1.0676 1.0990 1.1389 1.1692 1.2162 1.2564 (1.2942)
C = -0.0260.
fugacity of pure ith component fugacity of ith component in a mixture = free energy of a mixture F, = free energy of pure ith comF,o ponent = partial molal free energy of ith component AF, = free energy change on mixing FzE = excess free energy for a mixture PI,Pz = adjusted vapor pressures for components 1 and 2, respectively Pi = adjusted vapor pressure for ith component p 1 0 , p 2 0 = vapor pressures for components 1 and 2, respectively p,o = vapor pressure for ith component = =
fi0
fi
E Extension of Total Pressure Method
Azeotropic points can be evaluated by the total pressure method by the simple procedure of finding the point a t which ( - , q / y y ) = (Pz/Pl), which can be handled very conveniently by an appropriate plot. Redlich and others ( 9 ) point out that ternary systems can be evaluated by a combination of the three binary systems involved and suitable measurements on the ternary system. The Q-function for a multicomponent system is defined as
Q
=
x i log T i
(19)
and can be represented as the sum of series involving the activity coefficients of all binary systems, plus terms for the interaction of the three different components, determined from the ternary measurements.
. .. B, C, D .. . a,
6, c
=
= universal gas constant = temperature, C.
xl,
= empiricalconstantsin An-
toine equation constants in activity coefficients equations
= empirical
Q-function =
”
t T Vi
absolute temperature, ” K. molal volume of pure iin vapor state = mole fractions of components 1 and 2, respectively, in liquid phase; subscript 1 usually denotes the more volatile component = mole fraction of ith component in liquid phase = mole fraction of ith component in vapor phase = =
x2
xt Vt
Nomenclature
(____ 2 . 3 ; : R T) ’
Q
R
= relative volatility
CY
=
?*)
Xly7
yl, y z := activity coefficients of com-
ponents 1 and 2, respectively
= activity coefficient of ith com-
vi
= fugacity coefficient of ith com-
vi0
= fugacity coefficikni of pure z
?r
= total pressure
ponent =
ponent =
Vapor-Liquid Data for 2,2,4-TrimethyIpentane-Toluene of Mercury Absolute
Acknowledgment
The authors wish to acknowledge the helpful suggestions, made during review of this paper prior to submispion for publication by Otto Redlich, Shell Development Go.; M. E. Klecka, Shell Oil Go.; C. E. Turnquist, Monsanto Chemical Co.; and J. R . Crump, University of Houston. The financial support of a special research grant made by the University of Houston is also gratefully acknowledged. literature Cited
(1 ) American Petroleum Institute, Carnegie Institute of Technology, Pittsburgh, Pa., Research Project 44, “Selected Values of Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pitts~ burgh, 1953. (2) Dodge, B. F., “Chemical Engineering Thermodynamics,” McGraw-Hill, New York, 1944. (3) Drickamer, H. G., Brown, G. G., White, R. R., Trans. Am. Inst. Chem. Engrs. 41, 555 (1945). (4) Gelus, E., Marple, S., Jr., Miller, M. E., IND.ENG.CHEM.41, 1757 (1949). (5) Klecka, M. E., Shell Oil Co., Houston Tex., unpublished data, 194850. ( 6 ) Levy, R . M., IND. ENG. CHEM.33, 928 (1931). (7) Redlich, O., Shell Development Co., Emeryville, Calif., private communication, March 1953. ( 8 ) Redlich, O., Kister, A. T., J. Am. Chem. Soc. 71, 505 (1949). (9) Redlich, O., Kister, A. T., Turnquist, C. E., Chem. Eng. Progr., Symp. Ser. No. 2, “Phase-Equilibria,” 48 110.521. , - - - - I .
(10) Redlich, O., Kwong, J. N. S., Chem. Revs. 44,233 (1 949). (11) Scarborough, J. . B., “Numerical
at 760 Mm.
(13)
-
a = - YiXa 51
1774
2‘2
111
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
0 0.1647 0.2938 0.3996 0,4899 0.5750 0.6554 0.7394 0.8223 0.9092 1 .oooo
1.0000 0.9000 0.8000 0.7000 0.6000 0 5000 0.4000 0.3000 0.2000 0.1000 0 9
Y2
1.0000 0.8353 0.7062 0.6004 0.5101 0.4250 0.3446 0.2606 0.1777 0.0908 0.0000
INDUSTRIAL AND ENGINEERING CHEMISTRY
xi112
...
1.7746 1.6641 1.5529 1.4406 1.3529 1.2702 1.2160 1.1569 1.1126 (1.1111)
T,OC. 110.601 107.90 105.77 104.10 102.72 101.72 101.03 100.41 99.90 99.50 99.210
(k)
at its vapor pressure
(12) Table 111.
(zi)
yI
at 100” C.
(14) (15)
(16)
Mathematical Analysis,” p. 463-9 Johns Hopkins Press, Baltimore, Md., 1955. Sieg, L., FIAT Rept. 1095, USOPB Rept. 67695 (1947); Chem. 2ng.Tech. 22, 322 (1950). Swietoslawski, W., “Ebulliometric Measurements,” Reinhold, New York, 1945. Ibid.,p. 7-10. Willingham, C. B., Taylor, W. J., Pignocco, J. M., Rossini, F. D., J . Research Natl. Bur. Standards 35,269 (1945). Wilson, A , , Simons, E. L., IND. ENG.CHEM. 44,2214 (1952).
RECEIVED for review October 15, 1956. ACCEPTED April 2, 1957 South Texas Section, AIChE, 9th Annual Meeting, Galveston, Tex., Oct. 22, 1954.
