INDUSTRIAL A N D ENGINEERING CHEMISTRY
October 1950
average or mean value of the severs1 properties involved in this function. Consequently, the form of the derived equation satisfies the assumption that diffusion is the controlling factor in the low temperature calcination of Florida limestone particles in the diameter size range of 0.02 to 0.08inch.
and from this equation dr
&
-APcorR1fa 1054
Putting Equation 10 into 7:
8
(11)
If diffusion is the controlling factor, the rate of loss in weight must equal the rate of diffusion. The diffusion rate will, in general, be given by a driving force divided by a resistance, or: Rate of diffusion =
KAPcol driving force resistance
(12)
Q
1 ma
(13)
The resistance will be inversely proportional to the cross section of the diffusion path and directly proportional to several properties such as length of diffusion path, number of each type of gas molecule, and total number of molecules in the diffusion path:
Resistance
diffusion function croas-section area
LITERATURE CITED
Aabe, V. J., Rock Products, 47,No.9,68,704,100-2 (1944). Furnas, C.C., IND.ENO.CHEM.,23,634-8 (1931). Gilkey, W. A., Ibid.. 18,727(1926). Haslam, R.T., and Smith, V. C.. Ibid., 20,170 (1928). Htittig, G.F.,and Kappel, H., Angm. Chem., 53,67-9 (1940). Johnson,J., J. A m . Chem. Soc., 32,938(1910). Khomyakov, K. G.,Yavorovskaya, S. F., and Arbuzov, V. A., Sci. Repts. Moscow State Univ., 1936,No.6,7747.
Comparing Equations 11 and 12, the driving force appears aa it should, and the resistance is indicated as being proportional to: Resistance
2121
(14)
I n this case, r4 is a measure of the cross-sectional area of the diffusion path and appears in the correct place in Equation 13. The mean value of the "diffusion function" in Equation 14 is indicated in 13 as R-'Ia, which does not appear illogical as the
Linzell, H. K., Holmes, M. E., and Withrow, J. R., Trans. Am. Inst. Chem. Enws., 18,249-81 (1926). Maskill, W., and Turner, W. E. S., J. SOC.Glaaa Technol., 16, 80-93 - _ _ _ f1932). I Orosco, E :; Ministerio trabalho id. e com. Inst. nucl. tech. (Rio de Janeiro), 1940 (Separate). (11)Perederii, I.A., Stroilel. Materialy, 1937,No. 11,56-61. (12)Smyth, F. E., and Adams, L. H., J . A m . Chem. SOC.,45, 116784 (1923). (13) Southard, J. C.,and Royster, P. H., J . Phys. Chem., 40,436-8 (1936). (14) Splichal, J., Skramovsky, S.,and Goll, J., Collection Czecho8bv. Chem. Oommun., 9,302-14 (1937). (16)Tamsru, S., Siomi, K., and Adati, M., 2. physik. Chem., A157, 447-67 (1931). (16) Whiting, 0.H., and Turner, W. E. Sa, J . SOC.G h s Technol., 14T,409-24 (1930). (17)Zawadski, J., and Bretsznajder, S., Compt. rend., 194, 1160-2 (1932). RECEIVED March 24, 1950. Abstracted from a thesis presented in June 1949 to the Graduate Suhool of the University of Florida in partial fulfillment of the requirementa for the degree of m t e r of science in engineering.
Vapor-Liquid Equilibria at Subatmospheric Pressures TETRADECANE-HEXADECENE SYSTEM R. R. RASMUSSEN' AND MATTHEW VAN WINKLE University of Texas, Austin, Tex. Experimental vapor-liquid equilibrium data for the system tetradecane-1-hexadeceneat absolute pressures of 760, 400, 200, 100,50,20, and 10 mm. of mercury are presented. In addition, activity coefficient-composition relations are included for the components at the various pressures studied. The experimental data were smoothed by use of the modified Duhem equation and are presented in the form of conventionalx y plots.
T
HE separation of higher boiling hydrocarbons from their
d n
mixtures by fractionation requires the uw of subatmospheric pressures, in most instances, to prevent thermal decomposition. Thus it is necessary to have available vapor-liquid equilibrium data at subatmospheric pressures for equipment design and operation considerations. At the present time, few vapor-liquid equilibrium data are available on the higher molecular weight compounds. The difficulty of obtaining the pure higher boiling campounds has been 1 Present addrw, Carbide & Carbon Chemicals Corporation, Texas City, Tex.
the greatest single factor in delaying investigations in this field of study. PURITY OF COMPOUNDS
The tetradecane and hexadecene used were obtained in a relatively purified form. The refractive index of the hexadecene was n$ = 1.4435 compared to 1.4441 for the pure hexadecene (specified by supplier, 1.4425 to 1.4450), and for the tetradecane n2$ = 1.4298compared to 1.42886 for the pure tetradecane (sperified by supplier, 1.4280 to 1.4310). The hexadecene was checked for the degree of unsaturation by use of the io2ine value test, in accordance with a modification of the procedure given by Prescott (9). An average iodine value of 111.5 was obtained for the hexadecene, compared to the theoretical value of 113. Based on pure hexadecene, this indicates 98.7% of theoretical unsaturation. A series of carbon and hydrogen determinations waa made on a micro scale to obtain further checks on the purity of the compounds. The composition of the hexadecene was indicated to be
2122
INDUSTRIAL AND ENGINEERING CHEMISTRY 360
TEMPERATURE *E 400 440
480
85.64% carbon and 14.35% hydrogen. On the basis of a molecule containing 16 carbon atoms, this shows the formula composition to be C d i a j . ~ , The composition of the tetradecane was indicated to be 84.83% carbon and 15.17% hydrogen, giving B formula composition of CLtHPO oI. The molecular weights of the two compounds were determined by cryoscopic methods. The benzene used as the solvent was purified by washing in sulfuric acid, caustic, and water. It was subsequently dried and fractionated to 0.1' C. The benzene was tested and found to be thiophene-free, and to have a cryoscopic constant of 59.2. This value is the same as that given by Rall (4). From the results of several determinations at different concentrations, it was found that the hexadecene had a molecular weight of 222.4 and the tetradecane, 198.2. The analytical results indicated that both compounds were very near their theoretical compositions.
520
3.2
3.0
28
P E
26
Y
2k!
24
0
3
Vol. 42, No. 10
22
20
VAPOR PRESSURWATA
The vapor pressure data determined by Krafft, as reported by Stull (6),for the individual compounds, were used in this study. Check data were determined experimentally in this investigation and plotted in comparison to Krafft's data in Figure 1.
I / 240
280
320 360 T&3ATURE 'F.
400
EXPERIMENTAL METHODS
Fig ure 1. Vapor Pressure Chart for Tetradecane and IIexadcscene
The determinations of the vapor-liquid equilibria for the tetradecane-hexadecene system were made on a Colburn-ty e (8) equilibrium still. This type still was selected because orthe relatively small charge that was necessar , There were three regular heaters used-one on the flash boiyer, one on the residue chamber, and one on the vapor path, The heater on the flash boiler was wound with No. 26 Nichrome resistance wire (resistance, 17 ohms) and the heaters for the residue and vapor were of No. 28 Nichrome wire (resistance 18 and 20 ohms, respectively). The equilibrium still was connected to a 1-liter, 3-necked, round-bottomed flask through the vacuum outlet. The flask was used as a surge chamber to prevent rapid pressure fluctuations. The connection between the flask and still was a 0.25-mm. capillary tube. A mercury manometer was connected between the capillary tube and the still in order to record accurately the operating pressures. From the surge flask, a tube ran directly to the vacuum pump. One two-way stopcock waa aced directly in the line and another two-way stopcock was pPIaced on a branch line. $he latter stopcock could be opened to the atmosphere to aid in pressure regulation. Another tube extendin from the surge flask was provided with a stopcock which coulcfbe opened to the atmosphere through a fine capillary to make final pressure adjustments. The entlre vacuum system was capable of attaining and holding pressures to an absolute pressure of approximately 5 mm. of mercury. A total charge of 20 ml. was used in each run. The temperature was determined by means of a copper-constantan thermocouple connected to Leeds & Northrup potentiometer. The instrument was capable of indicating to 0.01 millivolt (0.5' F.). The thermocouple readings were checked against standard thermometers. In order to determine the approximate settings for the three heaters before the equilibrium runs were made, each of the pure compounds was distilled under equilibrium conditions et each
CALIBRATION DATAFOR ANALYTICAL TABLE I. EXPERIMENTAL ANALYSIS Mole % Tetradecane n
MOLE PER CENT TETRADECANE
Figure 2. Equilibrium Boiling Point Diagrams
li.5 31.9 54.3 76.9 100 .o
Index of Refraction at 25O C. 1,4408 1.4391 1.4368 1.4340 1.4313 1.4283
October 1950
x
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
1.10
90
$"
1.00
g 70
8x
2123
1.10
so IO0
2 ,
ib W
IO5
+
h t 100
I- 40
E0
g
100
G
095
w 5
3 8
20
100
>
t
: 2
IO
090
a
too
MOLE PER CENT TETRADECANE IN LIQUID.,. X
Figure 3. Vapor-Liquid Equilibrium Diagrams for Tetradecane-Hexadecene System a t Subatmospheric Pressures
I
I
l
0.90
I
I
I
I
l
l
I
I
I
I
I
1
7
l
l
I
I
I
i
i
l
l
l
l
l
l
100
y u r e under study. The pressure-temperature curves thus etermined are given in Figure 1. At each pressure studied, the series of runs was started with a low concentration of the more volatile tetradecane, and its concentration was increased for each succeeding run at that presNure. The power input to the heaters was adjusted proportionately to the concentration of tetradecane. From the known power input for each pure compound and by careful adjustment of the in ut for each binary mixture, vaponzation rates were controllegto ive equilibrium conditions. The stilf;was allowed to o erate for a time at conditions known to be near equilibrium. +he flow of the condensed vapor directly into the flash chamber wag re ulated by means of the threeway stopcock. Minor changes in t i e heat input were made until there was no condensation of vapor in the vapor space above the residue chamber, and until on1 a single drop of liquid remained in the lower part of the flash ciamber. Under the conditions of equilibrium, the rate of heating was such that about 1 ml. of li uid entered the flash chamber every minute. All runs were lowed to operate for 30 to 60 minutes to assure equilibrium conditions. Equilibrium was also indicated by a constant temperature and constant liquid levels on both the residue and vapor condensate.
3:
ANALYSIS OF VAPOR AND LIQUID SAMPLES
The equilibrium samples were analyzed by index of refraction methods, utilizing an Abbe refractometer having a scale graduation of O.OOO1 (Table I). A calibration curve was prepared by preparing mixtures of definite compositions and obtaining their indexes of refraction at 25' C. This calibration proved to be a straight line over the entire range and can be expressed as:
Mole % of tetradecane =
-
1.4408 nYa o~ooo125
The equilibrium boiling points for all runs are presented in Table I1 and plotted in Figure 2. VAPOR-LIQUID EQUILIBRIUM DATA
The experimental data are presented in Table I1 and graphically in Figure 3 for the isobaric conditions of 760,400,200,100, M, 20, and 10 mm. absolute pressures. The data are found to
n an 0
20 40 60 eo MOLE PER CENT TETRADECANE IN LIQUID
Figure 4.
100
.... X
Activity Coefficients in TetradecaneHexadecene System
follow the normal trend with respect to variations in pressurei.e., as the pressure is decreased, the relative volatility increases. This is shown by the shifting away from the z = y line as the pressure is decreased (6). ACTIVITY COEFFICIENTS
The experimental data were smoothed by plotting curves of activity coefficients versus the mole per cent tetradecane in the liquid. The activity Ooefficient is actually a Raoult's law deviation factor, ny/Px. The partial pressures of the components were obtained from their vapor pressures taken from Figure 1 at the equilibrium boiling temperature. The values of activity coefficients are presented in Table I1 and the curves for the different pressures are in Figure 4. The activity coefficientswere plotted rather than their logarithms in order to get a wider spread of the calculated values. The calculated data indicate the activity coefficientsto be very close to unity for all pressures investigated. Therefore, the compounds in this binary mixture deviate but slightly from Raoult's law behavior. When the experimental values of z and y are determined accurately and the vapor pressure data are correct, the activity coefficients for one compound must lie on a smooth curve. Because of the difficulty of determining the equilibrium data accurately, activity coefficients calculated from experimental data rarely fall on a smooth curve. Thermodynamic consistency of equilibrium data is commonly checked by the Duhem, Van Lam, Margules, or the Scatchard equations. The Duhem equation was derived from fundamental
INDUSTRIAL AND ENGINEERING CHEMISTRY
2124
Vol. 42, No. 10
TABLE 111. ANALYSISBY SLOPERATIOOF VAPOR-LIQUID EQUILIBRIUM DATA OF THE TETRADECANE-HEXADECENE SYSTEM ACTIVITY COEFFICIENTS FOR TETRADECANE-HEXADECENE SYSTEM Mole % Tetradeaane
VAPOR-LIQUID EQUILIBRIUM DATA TABLE 11. EXPERIMENTAL AND
T, F.
z
P 9.5 20.7 30.3 35.8 54.3 62.2 67.9 75.1 86.3
521.3 515.3 510.3 508.0 500.0 497.0 495.0 492.5 489.0 479.3 475.3 473.0 464.5 458.6 456.6 455.0 451.3 447.0 445.0 443 5
,
6.2 12.7 17.5 33.5 46.3 50.3 54.3 62.9 72.8 80.0 83.9
436.0 432.0 427.0 423.0 419.3 414.3 412.3 407.7 404.0 400.0
7.0 14.3 23.0 30.3 37.4 47.9 51.7 63.9 73.5 84.0
398.0 393.5 389.0 386.0 383.0 380.7 377.3 374.0 371.3 371.0 369.0 365.0 361.3 357.0
7.8 14.3 22.3 27.1 32.6 36.6 42.3 49.5 54.3 56.0 59.1 68.7 77.5 88.7
362.0 361 .O 358.3 353.7 351.0 354.0 342.0 338,4 333.0 328.3 325.3 324.0
7.9 8.6 13.5 21.5 25.5 35.8 41.4 47.9 59.1 69.5 76.7 80.7
316.3 314.8 312.3 306.3 304.4 298.8 293.0 286.4 281.0
11.9 14.3 18.5 28.5 31.8 43.1 64.3 71.0 84.8
290 8 286.0 285.0 282.0 280.3 274.4 273.3 271.6 268.7 262.0 258.7 254.4
7.0 14.3 16.0 20.7 23.9 34.2 35.8 39.9 46.3 58.3 69.5 81.5
-
Yexptl.
yoor.
760 Mm. 15.6 31.8 43.8 50.0 67.9 74.6 78.9 84.2 91.6
15.9 31.8 43.1 49.4 67.9 74.3 79.0 83.9 91.2 P = 400 Xlm. 11.1 11.1 21.5 21.6 28.7 28.8 49.6 49.6 62.9 62.9 67.1 66.6 70.3 70.0 76.7 76.8 84.0 84.0 88.6 88.5 90.9 90.9 P = 200 M m . 13.5 13.4 26.2 26.1 39.0 39.0 47.9 48.6 55.9 56.7 67.1 67.2 70.3 70.5 79.9 79.8 86.3 86.1 91.8 92.2 P = 100 M m . 15.9 16.1 27.9 27.9 40.0 40.1 46.4 46.8 53.5 53.8 58.3 58.5 64.7 64.4 71.1 71.0 75.1 74.9 76.0 76.1 78.4 78.5 84.8 84.9 90.3 89.9 95.1 95.3 P = 50 Mm. 17.5 17.5 19.1 18.9 28.7 28.5 41.4 41.5 47.9 47.3 59.9 59.9 66.3 66.3 71.8 71.8 80.7 80.4 87.2 86.9 91.1 90.8 92.7 92.7 P = 20 M m . 27.7 27.7 32.6 32.4 39.9 39.9 54.3 54.7 59.1 58.7 70.3 70.1 78.9 78.9 88.7 89.0 95.0 95.0 P 10 Mm. 19.1 19.2 35.0 35.3 38.3 38.6 47.0 46.5 51.7 51.5 63.9 64.3 66.3 66.1 69.5 70.0 75.2 75.3 83.2 83.4 89.6 89.3 94.3 94.2
-
71
YP
Pressure,
M m . Hg
0.999
0.996 1.015 1.022 1.024 1.048 1.047 1.034 1.070 1.122
1.022 1.017 1.015 1.024 1,012 1.015 1.011 1.004 1.012 1.015 1,002
1.005 1.000 1.004 1.009 1.015 1.002 1.008 1.029 1.040 1.038 1.058
1.012 1.018 1.021 1.030 0,991 1.ti08 1.020 1.003 1.008 0.098
1.005 1.001 1,002 1.007 1.023 1.010 1.017 1.002 1.000 1 ,063
0.978 0.981 0,972 0,972 0.983 0.983 0.993 0.988 0.992 0.990 0.990 0.988 1.C04 0.999
1.002 0,998 1.000 1.007 1,000 0.999 0,998 0.994 0.993 0,997 0.998 0.993 0.945 1.017
0.951 0.967 0.966 0.963 0,983 0.977 0 982 0.985 0.996 0.998 0.998 0.997
1.002 1.010 0.987 0,992 0.983 1.002 0.983 1.005 0.978 0.968 0.967 0.965
0.940 0.952 0,969 ‘0.952 0.972 0.967 0,981 0,988 1,000
1.000 0.995 0.997 0.999 0.984 0,982 0.972 0.993 0,979
0.968 0.964 0.969 0,988 0.975 0.973 0.978 0.973 0.978 0.984 0.996 1.002
1.010 0.997 0.987 0.969 0,963 0.973 0.948 0.973 0.973 0.963 0.916 0.936
1.047 1.034 1.016 1.021 1.022 1.015 1.020 1.010
I
760 400 200 100 50 20 10
-
20
Theor.
Actual
0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.27 0.28 0.25 0.23 0.25 0.29 0.37
.
50 Slope Ratio Theor. Aatual
Theor.
Actual
1.15 0.90 1.00 1.18 1.00 0.90 1.05
4.00 4.00 4.00 4.00 4.00 4.00 4.00
4.01 4.06 4.00 4.16 4.00 4 00 4.19
1.00
1.00 1.00 1.00 1.00 1.00 1.00
80
This equation indicates that plots of log y1 and log y2 versus zi should have slopes of opposite sign -at a given composition. The ratio of the slopes of the curves, log 71versus z1and log y2 versus 21,must be equal to the ratio, xZ/x1 (I). The curves of Figure 4 were checked in this manner and their slope ratios recorded in Table I11 for the 20, 50, and 80% points, Because of the slight deviation of the activity coefficients from unity, the slopes of y versus x curves were all very close to zero. The ratios were determined as accurately as possible and proved to be in fairly good agreement to the ratio of z&,. This test tends to prove that the data presented are thermodynamically consistent. Figure 4 indicated the values of the activity coefficient to be greater than 1.0 for both components a t absolute pressures of 760, 400, and 200 mm. The activity coefficients of both compounds approach 1.0 a t 200 mm. SUMMARY AND CONCLUSIONS
Vapor-liquid equilibrium data for the binary system of tetradecane-hexadecene are presented at absolute pressures of 760, 400, 200, 100, 50, 20, and 10 mm. The components represent practically pure hexadecene and tctradecane on the basis of iodine value, molecular weight, index of refraction, and carbon and hydrogen analysis. The activity coefficient curves indicate the binary system investigated to be almost ideal in its Raoult’s law behavior a t the pressures studied. The closest approach to Raoult’s law ideality was found to be a 200-mm. absolute pressure. The data have been tested by the use of a modified Duhem equation and found to be thermodynamically consistent. NOMENCLATURE
thermodynamic relations assuming constant temperature and pressure. A modification of the Duhem equat,ion ( 1 ) which can be applied to constant pressure data without appreciable error is as follows: log ~1 -(I - xi) d b g ya -d = 21 dx dx
n = index of refraction P = vapor pressure of pure component a t the equilibrium boiling temperature 2’ = temperature, O F . 21 = mole 7 tetradecane in liquid phase xa = mole hexadecene in liquid phase y = mole % of compound in va or phase y1 = activity coefficient of tetralecane, ryl/plx1 y~ = activity coefficient of hexadecene, ry2/P2xz T = total pressure, mm. Hg LITERATURE CITED
(1) Dodge, B. F., “Chemical Engineering Thermodynamics,” p. 558,
New York, McGraw-Hill Book Co., 1944. (2) Jones, C. A,, Sohoenborn, E. M., and Colburn, A. P., IND.ENG. CHEM.,35, 666 (1943). (3) Presoott, A. B., “Organic Analysis,” p. 258, New York, D. Van Nostrand Co., Inc., 1887. (4) Rsll, H. T., and Smith, H. M., IND. ENQ.CHEM.,ANAL. ED., 8, 324 (1936). (5) Robinson, C. S., and Gilliland, E. R., “Elements of Fractional Distillation,” p. 43, New York, MoGraw-Hill Book Co., 1939. (6) Stull, D. R.,IND. ENG.CHEM.,39.517 (1947). RECEIVED September 30, 1949. Abstracted from thasis preaented by R. R. Rasmussen to the faoulty of the University of Texas in partial fulfillment of the requirements for the degree of maeter of scienae in ohemical engineering.
