Ternary Liquid
adipate and dibutyl sebacate showed appreciable increases in weight after 12-hour immersion a t 60” C. The neoprene immersed in dibutyl sebacate increased 80 per cent by weight as compared to a 70 per cent increase for the sample immersed in diiiobutyl adipate. On the basis of these observations and the brittle fracture test results, it appears that increased solvent action may offer a better guide to the selection of materials for lowering the brittle fracture point than the freezing point observations on the plasticizers.
A Method of Tie Line Interpolation
CONCLUSIONS
1. The temperature a t which natural and synthetic elastomers fracture on bending depends on the rate of application and the magnitude of the stress applied. The slower the rate of bending and the less the angle of bend, the lower will be the temperature of fracture. 2. A study of the stresses under varying types of service a t subzero temperatures must be made in order to select intelligently the laboratory test conditions which will best simulate performance in the field. 3. I n the case of synthetic elastomers having high fracture temperatures, the addition of certain types of plasticizers serve to correct this difficulty.
CHARLES E. DRYDEN’
RAPHICAL methods for the design of rectification
G
ACKNOW LEDGiMENT
The authors wish to acknowledge the assistance of W. H. Lockwood who performed a large part of the testing in connection with this paper. LITERATURE CITED
(1) Bekkedahl, N., J . Research Natl. Bur. Standards, 13, 411 (1934). (2) Bekkedahl, N., and Scott, R. B., Ibid., 29, 87 (1942). (3) Davies, J. M., Miller, R. F., and Busse. W. F., J. Am. Cheni. Soc.. 63, 361 (1941) (4) Fraser, D., du Pont Rubber Chemicals Div , Rept. 42-1 (1942). (5) Fuoss, R. M., J . Am. Chem. Soc., 63, 369 (1941). (6) Garvey, B. S., Juve, A. E., and Sauser, D. E., IND. ENG.CHEM., 33, 602 (1941). (7) Gee. G . , and Treloar, L. R. G., Trans. Inst. Rubber Ind., 16, 184 (1940). (8) Gehman, S. D., J . Applied Phys., 13, 402 (1942). (9) Gibbons, W. A., Gerke, R. H., and Tingey, H. C., IND.E N G CHEM.,AKAL.ED., 5, 279 (1933). (10) Gloor, W. E., and Gilbert, C. B., Ibid., 33, 597 (1941). (11) Hock, L., Z . Elektrochem., 31, 404-9 (1925). (12) Houwink, R., “Elasticity, Plasticity and Structure of Matter”, p. 71, Cambridge Univ. Press, 1937. (13) I. G. Farbenindustrie, Kunstofe, 28, 171 (1938). (14) Khvostovrtkaya, S., and Margaritov, V., J . Rubber Ind. (U. S . S. R.), 8, 231 (1933). (15) Koch, E. A., Kautschuk, 16, 151 (1940). (16) Kohman, G. T., and Peek, R. L., IND.ENG.CHIM., 20, 81 (1928). (17) Le Blanc, M . , and Krager, M., Kolloid-Z., 37, 205 (1925). (181 McCortney, W. J., and Hendrick, J. V., IND.ENQ.CHEM.,33, 579 (1941). (19) Mark, H., and Valko, E., Re*. gen. caoutchouc, 7, 11 (1930). (20) Nagai, H., J. SOC.Rubber Ind. Japan, 8, 397 (1935); 9, 147 (1936). (21) Polanyi, M., and Schob, A., Mitt. Materialprfijungsamt, 42, 22 (1924). (22) Ruhemrtnn, M., and Simon. F., Z.physik. Chem., 138A, 1 (1928). ENG.CHIOM., 32, 509 (1940). (23) Russell, J. J., IND. (24) Srtgajllo, M., Bobinska, J.. and Saganowski, H., Proc. Rubber Tech. Conf., London, 1938,749. (25) Selker, M. L., Winspear, G. G., and Kemp. A. R., IND. ENG. CHEM.,34, 137 (1942). (26) Somerville, A. A., Proc. Rubber Tech. C m f . , London, 1938, 773. (27) Yerzley, F. L., and Fraser, D. F., IND.ENG.CHEM.,34, 332 (1942).
equipment have been presented by Ponchon (10) and Savarit (11) and extended t o liquid-liquid extraction by Maloney and Schubert (6); for practical use by these methods, equilibrium data for the distribution of the components between the phases must be on a solvent-free basis. All tie line interpolation methods so far reported (1, I, 4, 6) necessitate the use of the triangular diagram to calculate the distribution relation of the solute between the solvent and diluent layers on a solvent-free basis (also termed “concentration data”, 7) for each successive theoretical stage in an extraction system. A straight-line plot on rectangular coordinates of the solute distribution relations on a solvent-free basis may be obtained from three points on the ternary diagram of the system considered. Tie line data, on a solvent-free basis in the case of extraction, may be obtained from this plot and applied directly to the stepwise calculation of theoretical stages by the Maloney-Schubert method without further use of the ternary diagram. In those cases where it is found applicable, the method thus has the advantage of limiting the use of the triangular diagram to the procurement of the above mentioned straight-line plot. This plot is readily applied to the computation of theoretical stages in solvent extraction by the Maloney-Schubert method; the triangular diagram is used together with any one of the tie line methods previously cited to accomplish the same purpose-i. e., to obtain solvent-free distribution relations for each successive stage in the design of a solvent extraction unit. THEORETICAL ASPECT
Varteressian and Fenske (14) found that for the system methylcyclohexane-aniline-n-heptane the distribution of one component (i. e., the solute) between two liquid phases, the solvent layer and the diluent layer, may be expressed by a hyperbolic equation of the type, Pr
= 1
+ ( P - 1)2
where z = weight fraction of solute in diluent laver on solventfree basis y = weight fraction of solute in solvent layer on solventfree basis p = a constant dependent on the system involved; it is a function of the osmotic pressure ratios of solvent and diluent Equation 1 may be rearranged in the form,
”-(
p--l )
2 f z1
?l
PRESENTED as part of the symposium on Compounding and Properties of Elynthetio Rubbers before the Division of Rubber Chemistry at the 104th CHQMICAL SOCIQTY. Buffslo, N. Y. Meeting of the AMERICAN
1
482
Present address, Sational Oil Products Company. Ilarrison, S J
and Binary Vapor-Liquid Systems for Phase Equilibrium Relations
A method of correlating equilibrium distribution relations of the solute between conjugate phases on a solvent-free basis in liquid-liquid systems and its application to the graphical solution of the MaloneySchubert diagram for theoretical extraction stages is presented, together with the analagous vapor-liquid equilibrium method.
Princeton University, Princeton, N. J.
t
/
Oa6
A straight line results when x/u is plotted against x, if the equation is obeyed and /3 is a constant. Thus, if the ratio of the solute in the diluent layer, x, t o the solute in the solvent layer, y (i. e., x/y), is plotted against the solute in the diluent layer, x, all on a solvent-free basis, a straight line should result when the system approximates Equation 1as set down above. APPLICATION OF THE METHOD
Some of the data reported in the literature for liquid-liquid systems have been tested by the above method. Some systems found to conform to the hyperbolic Equation 1are listed in Table I, and plots of the data for some of them are shown in Figure 1. The resulting curves are straight lines well within the accuracy of experimental measurement. Systems which do not follow the law include methylcyclohexane-acetic acidwater , isophorone-acetic acid-water, furfural-acetone-water, and isoamyl alcohol-acetone-water. TABLE I. SYSTEMS CONFORMING TO HYPERBOLIC EQUATION 1 No. 1 2
3 4 5 6
'
LO
7 8 9
10
I
Reference (6) (18)
(6) (14) (3) (13)
(6) (6) (6)
(6)
That the method does not apply to all systems is t o be expected since it is an idealized relation. It appears to be limited to systems in which the ternary solubility line approaches the sides of the triangle, in which case the solvent and the diluent are substantially immiscible, or to systems in which only one pair of components is completely miscible. I n the first type of system a rule for determining the validity of the method can be derived as follows: If m = (p - 1)/p and k = 1/p, components in solvent layer a,,bg, c1 az, bz, cz = components in diluent layer wherea = solvent b = diluent c = solute
46
0
System
Acetic acid-methyl isobutyl ketone-water Glycol-bromobenzene-acetone Tetrachloroethane-acetone-water Methylcyclohexane-aniline-heptane Acetone-chloroform-water Benrene-ethyl alcohol-water Diin-butyl ether-ethyl alcohol-water Diisopropylcarbinol-acetio acid-water Methyl isobutyl ketone-acetone-water Fenohone-acetic acid-water
I 1 1 I I 0.2 a4 0.6 0.8 LO X'WGT: FRACTfON IN D/LU.€ffT LAYER
(3
Figure 1
(41
493
494
INDUSTRIAL AND ENGINEERING CHEMISTRY
Substituting for (p - l)/@, 1/p, 2,and y the above equivalents in Equation 1, c2
(5) c1
Since a1
+
bl
+ bl + c1 = 1,
Vol. 35, No. 4
above method. The required equilibrium relation (on a solvent-free basis) in each stage can be computed directly from this straight-line plot without further use of a complete ternary diagram for the system and without involving tie line interpolation methods previously cited. The MaloneySchubert method, in conjunction with the tie line correlation presented in this paper, gives a much more rapid and accurate determination of theoretical stages required for a given separation in a system where the binodal curve is pinched close t o the solvent end of the triangular diagram. BINARY VAPOR-LIQUID SYSTEMS
Substituting Equation 6 in Equation 5 ,
(7)
Rearrangement of Equation 7 gives:
I n an analogous manner vapor-liquid equilibrium in binary mixtures may be interpolated if equilibrium compositions are known for two points and if Raoult’s law applies; i. e., the relative volatility is approximately constant over the entire range employed. If y = mole fraction of more volatile component in vapor z = mole fraction of more volatile component in liquid a = rclative volatility then the 2-y relation in terms of relative volatility is:
In every case (cz/cl) > 1, since subscript 2 refers to the diluent layer. For most of the systems plotted by this method, k has a very small value-i. e., high osmotic pressure ratio between the solvent and diluent. This would indicate that, as cz approaches zero, (1 - a l ) / ( c ~ b?) approaches zero more rapidly than cz/cl approaches infinity so that in the limit k would be zero. Equation 5 then reduces to
+
m = (bl or
Substituting m
=
(,8
bl/cl
+
=
C1)iCl
m - 1
(9)
(10)
- 1)/p P
=
-( C d b l )
a x
=
1
+ ( a - 1)s
A rearrangement of Equation 12 results in: y/x = a - ( a - 1)y
(13)
Plots of y/z against y for systems such as nitrogen-oxygen ( B ) , and benzene-toluene (9), as well as others following Raoult’s law, give straight lines on rectangular coordinates. These can be readily used in conjunction with the Ponchon chart t o calculate theoretical plates in rectification. ACKNOWLEDGMENT
(11)
Thus, since Equation 2 can represent a straight line only when j3 is constant, we may make the generalization that the method holds where the diluent increases proportionally to the solute in the solvent layer. In systems where only one pair of components is completely miscible, it is possible for the left-hand side of Equation 8 to be greater than zero in the limit, as in the case of methylcyclohexane-aniline-n-heptane. /3, the osmotic pressure coefficient, will then have positive values which can be computed from the type of extrapolation plot presented in this paper. This suggests the correlation method for testing experimental data to determine whether the value of 6 is constant over wide concentration ranges a t one temperature and whether p can be expressed as a function of temperature so that systems can be represented a t any temperature. Work along this line is being conducted in this laboratory. Another important use of this method of tie line correlation is in solving the Maloney-Schubert diagram for theoretical stages in an extraction system. Gsing three or four points on the ternary diagram of the system, a plot of the solvent distribution relations on a solvent-free basis is made by the
The author wishes to acknowledge with thanks the suggestions of Joseph C. Elgin of Princeton University and Donald F. Othmer of Brooklyn Polytechnic Institute which were valuable in the preparation of this paper for publication. LITERATURE CITED
(1) Bachman, I., IIVD. ENG.CHEM.,ANAL.ED.,12, 38 (1940). (2) Branker, A. V., Hunter, T . G., and Nash, A. W., Ihid., 12,35 (1940). (3) Hand, D. B. J . P h y s . Chem., 34, 1961 (1930). (4) International Critical Tables, Vol. I11 (1928). ( 5 ) Maloney, J. O., and Schubert, A. E., Trans. Am. Inst. Chem. Engrs., 36, 741 (1940). (6) Othmer, D. F., and Tobias, P. E., IND. ENG. CHEM.,34, 693 (1942). (7) Othmer, D . F., White, R. E., and Trueger, E., Ihid., 33, 1240 (1941). ( 8 ) Perry, Chemical Engineering Handbook, 2nd ed., p. 1366, New York, McGraw-Hill Book Co., 1941. (9) Ihzd., p. 1377. (10) Ponchon, Tech. moderne, 13,20 (1921). (11) Savarit, in Robinson and Gilliland’s “Elements of Fractional Distillation”, 3rd ed., p. 107, New York, McGraw-Hill Book Co., 1939. (12) Trumble, H. M.. and Frazer, E. E., IND.EIVG.CHEM.,21, 1063 (1929). (13) Varteressian, K. A., and Fenske, M. R., Ihid., 28,929 (1936). (14) Ihid., 29, 270 (1937).
