Distribution Coefficients for 2-MethvlJ
1-Propanol-Water and LPentanolWater Svstems d
KENNETH F. GORDON' Department of Chemical Engineering, Massachusetts I n s t i t u t e of Technology, Cambridge 39, Mass.
I
N ORDER to make a study of extraction rates it is desirable
a
to use systems t h a t have constant distribution coefficients over wide ranges of concentration of individual solutes and give a broad range of distribution coefficients by the choice of a suitable solute. The literature reveals few systems that fulfill these requirements. The alcohol-water systems are ones that the literature indicates have constant distribution coefficients for several solutes. The alcohols for which data are available include l-pentanol, 2-methy1-2-butano1, 1-butanol, and 2-butanol (6). As part of a n extraction study it was necessary t o measure the distribution coefficients of a number of solutes for the l-pentanolwater system and for the 2-methyl-1-propanol-water system. The mutual solubilities of the 2-methyl-1-propanol-water system at 25" C., which are given in the literature, were checked.
phenol blue. The burets used had U. S. Bureau of Staudards certificates and the pipets and volumetric flasks were consistent with them. The analytical solutions were 1 N , 0.1 N , and 0.01 N hydrochloric acid and 1 N , 0.1 N , and 0.01 Ai sodium
TABLEI.
Normality 2-Methyl-lpropanol phase
Water phase
2-Methyl-lpropanol phase Water phase
Acetic -4cid
EXPERIMENTAL
METHOD O F CONTACTING. For a series of determinations of the distribution coefficient for any one solute a number of pairs of glass- or rubber-stoppered flasks were assembled with about 40 ml. of pure water i n one flask and the same volume of pure alcohol i n the other. The appropriate amount of solute was added to the alcohol of one pair and the water of the next pair so the solute was i n alternate solvents in the series of pairs having increasing amounts and hence concentration of solute. I n each pair of flasks the solvent in one flask was added to the other solvent in the second flask which was then stoppered and shaken. I n this manner equilibrium was approached from alternate sides. If the distribution coefficient was in the range 0.1 to 10 the solvents were shaken by hand about once every 2 minutes for 15 minutes. If the distribution coefficients lay outside this range, the solvents were agitated on a mechanical shaker for a half hour. After the initial shaking a t room temperature the bottles were immersed in a constant temperature bath at 25" C. for a t least 12 hours, where they were shaken by hand every hour. Material Distilled water 1-Pentanol 2-Methyl-1-propanol Sodium hydroxide Hydrochloric acid) Solutes
COEFFICIENTS BETWEEN 2-hIETHYL1-PROPANOL AND WATER
DISTRIBUTION
0.00389 0.02675 0.0621 0.0804 0.2688 0.588 0.908 2.068
0.00321 0.02282 0.0517 0.0685 0.2278 0.498 0.776 1.913
1.21 1.17 1.20 1.17 1.18 1.18 1.17 1.08
0.00637 0.00747 0.01340 0.0305 0.0510 0.2140 0.598 1.804
Amriionium Hydroxide 0 0315 0 0316 0 0626 0 1348 0 2241 0 871 2 292 5 76
0.202 0.236 0.214 0.226 0.227 0.246 0.261 0.313
0.0502 0.0853 0.1339 0.430 0.857 1.398 1.765 3.98
1-Butyric Acid 0 00547 0 00936 0 01494 0 0483 0 0980 0 1681 0 220 0 639
9.18 9.12 8.95 8.89 8.74 8.31 8.02 6.24
1-Capioic Acid 0.2217 0.507 0.815 0.906
Source Laboratory J. T. Baker Chemical Co. Eimer & Amend J. T. Baker Chemical Co. J. T. Baker Chemical Co. or Eastman Kodak Co.
ANALYSES. All analyses were made by titration with carbonate-free sodium hydroxide or hydrochloric acid in 50: 50 (volume) distilled water-ethanol solvent. Titration samples were taken either by direct1 pipetting a sample of each phase for titration or by diluting txe pipetted sample in a volumetric flask with a 50: 50 (volume) distilled water-ethanol solvent which had previously been brought t o the indicator end point. An aliquot would then be pipetted from this diluted sample. The indicator used was either phenolphthalein or bromo1 Present address, Department of Chemietry and Chemical Engineering, University of California, Berkeley 4, Calif,
1813
0 0 0 0
00294 00650 01083 01153
75.4 77.9 75.2 78.5
0.00856 0.01758 0.03075 0.1114 0.1876 0.3828 0.660
Citric Acid 0.03710 0.0738 0.1270 0.4350 0.725 1.411 2.355
0.231 0.238 0.242 0.256 0.259 0.272 0.280
0.00785 0.01222 0.01892 0.0659 0.1375 0.2151 0.515
Dimethylamine 0 00607 0 00957 0 01530 0 0518 0 1102 0 1698 0 417
1.29 1.28 1.24 1.27 1.25 1.27 1.24
0.00442 0.01505 0.002861 0.01841 0.0452 0.1732 0.1816 0.763
2,2'-Iminodiethanol 0 02177 0 0730 0 01355 0 0938 0 2328 0 805 0 861 2 36
0.203 0.206 0.211 0.196 0.194 0.215 0.211 0.324
INDUSTRIAL AND ENGINEERING CHEMISTRY
1814
Vol. 45, No. 8
TABLEI. DISTRIBUTIOK COEFFICIENTS BETWEEN 2-hIETHYL PROPANOL AXD W.k,rsR (Continued) Normality 2-Methyl-l-
2-3Iethyl-lpropanol uhase
Kater phase
0.00714 0.01472 0.03185 0,0428 0.0865 0.2518 0.553
Lactic Acid 0,01022 0.02170 0.0457 0.0604 0.1182 0.3408 0.718 1.11
0.698 0.679 0. 698 0.710 0.731 0.739 0.770 0.818
0.01177 0.01529 0.03710 0.1314 0.3322
Methylamine 0.01188 0.01678 0.0463 0.1891 0.520
0.990 0.911 0.802 0.694 0.639
0.00461 0.01024 0.01702 0.0338 0.0902 0.1183 0.1844
Potassium Acid Phthalate 0.01078 0.0269 0.0415 0.0819 0.1940 0.2600 0.423
0.428 0.381 0.410 0.413 0.465 0.455 0.435
0.9oY
0.02035 . 0.0475 0.0836 0.1078 0.2293 0.432 1.121 1.150
propanol phase _____
Propionic Acid 0.00639 0.01443 0.02568 0.03268 0.0706 0.1349 0.3748 0.399
Water phase
GRAM EQUIVALENTS/LITER WATER PHASE
Equilibrium Data for 2-Methyl-1-PropanolWater System
Figure 1.
TABLE 11.
k 3 T R I B U T I O N COEFFICIEKTS BETWEEN 1 - P E N T B N O L A N D WATER
1-Pentanol phase 3.19 3.29 3.26 3.30 3.25 3.20 2.99 2.88
Normality Water phase
1-Pentanol phase Water phase
Acetic Acid 0.0394 0,0432 0,0847 0,0919 0.1122 0.1428
0.919 0.907 0.911 0.922 0.913 0.910
0 00387 0 00919 0 01924 0 0304 0 0710
Tetraethanolammonirini Hydroxide 0.0452 0.1251 0.2975 0.436 0.968
0.0867 0.0734 0.0647 0.0697 0.0734
0.001778 0.003945 0.00840 0.02291 0.573
0 01318 0 03015 0 0624 0 1678 4 04
0.00026 0.00078 0.00139 0.00341
Tetramethylammonium Hydroxide 0.02115 0.0795 0.1390 0.3111
0.0123 o.oG99 0.0100 0.0110
0 0191 0 02921 0 0422 0 1371 0 238 0 386 0 900
Trimethylarriinr 0,00670 0.00916 0.01368 0.0434 0,0786 0.1242 0.345
0 0 0 0 0 0 2 3 4
0521 0917 113.5 339 484 809 28 35 60
1-Butyric Acid 0 00557 0 0098fi 0 01208 0 0361 0 0,511 0 0891 0 2848 0 457 0.679
9.35 9.30 9.39 9.39 9 47 9 07 8.00 7 33 6 78
Propionic Acid 0.00420 0 00620 0 01129 0 0236 0.0460 0,0919 0.2036 0.390 0.701 1.87
3.04 2.97 2.94 3.01 3.09 3.01 2.94 2.81 2.65 2.24
Ammonium Hydroxide
2.85 3.19 3.08 3.16 3.03 3.10 2.61
1-Valerir heir1 1044 191 415 804 1 243 1 438
0 0 0 0
0.00423 0 00788 0 01659 0 0322 0 0512 0.0582
24.7 24.2 25.0 25.0 24.3 24.7
hydrovde. Each solute. except the 0 01 N hydrochloric acid, q-as standardized with either potassium acid phthalate or sodium carbonate which was dried for an hour a t 370" C. The analytical solutions mere checked against each other, and all agreed within 0 15%. RESULTS
Evperimental results for the 2-methyl-I-propanol-water system and the 1-pentanol-water system are given in Tables I and 11. For illustrative purposes some of the data for the 2-methyl-lpropanol-water system are also presented in the form of a plot (Figure I ). Colburn and 'Vl'elsh (3) give the mutual solul)ihties of the 2methyl-1-propanol-water system a t 25" C. as 16.57 weight 7 0 water for water in 2-methyl-1-propanol and for X-methyl-lpropanol in water 8.25 weight % 2-methyl-1-propanol. These values a1 e based on results reported in the International Critical T a h l e ~ . Thrse values were checkrd in the present work by
0.01279 0.01841 0.0332 0.0712 0.1421 0.276.; 0.598 1.096
1.860 4.20 0.0383 0.0595 0.0914 0.0915 0.2106 0.281 0.383 0.412 0.557 0.767 0.986
1.158 1.27 1.948 2.615 4.54
1-Valeric Acid 0.001528 0.002511 0.00358 0.003711 0.00778 0,00989 0.01300 0.01386 0,01942 0.0267 0.03515 0.0414 0.0475 0.0741 0.1051 0.208
0.1348 0.1310 0.1348 0.1368 0.1421
25 0 23 7 25.5 24.6 27.1 28.4 29.4 29.7 28.6 28.7 28.0 27.9 26.7 26.3 24.9 21.8
measuring the refractive indices of the saturated solvents hy means of a Bausch & Lomb immersion refractometer. The concentrations mere determined from plots of refractive index versus concentration which were made by measuring the refractive indices of solutions t h a t were prepared volumetrically. The results obtained gave a concentration of 16.60 weight %
August 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
for water in 2-methyl-1-propanol and 8.29 weight % 2-methyl-lpropanol in water, which are considered satisfactory checks. The mutual solubilities of the 1-pentanol-water system were not determined in the investigation. However, Ginnings and Baum (6) and also Butler ( 2 ) have presented data on the mutual solubilities of the 1-pentanol-water system a t 25' C. A tendency to periodicity can be noticed in the distribution data for some of the solutes such as caproic acid and potassium acid phthalate in the 2-methyl-1-propanol-water system. When plotted on log-log coordinates the data for all the systems, except that of methylamine, lie on straight lines with a slope very close to unity, which is necessary for systems with constant distribution coefficient. Collander ( 4 ) has published one or two values for the distribution coefficient between 2-methyl-1-propanol and water for a number of substances at about 20' C. He states that these might be in error by as much as 10 to 20%. The present data, for 25' C., agree with his within his stated error. The agreement
1815
between the present results and those of Archibald ( 1 ) for the 1-pentanol-water system is not particularly close. ACKNOWLEDGMENT
The author is indebted to the Standard Oil Co. (Ind.) and the Kimberly-Clark Corp. for fellowship support, given during the period of the investigation. LITERATURE CITED (1) Archibald, R C . , J . Am. Chem. Soc., 54, 3178 (1932). (2) Butler, J. A. V., Thomson, D. W., Maclennan, W. H., J . Chem. SOC.,1933, p. 674. ( 3 ) Colburn, A. P., and Welsh, D. G . , Trans. Am. I n s t . Ckem. Engrs., 38, 179 (1942). (4) Collander, Runar, Acta Chem. Scand., 4, 1085 (1950). (5) Ginnings, P. M., and Baum, R . , J. Am. C h a . Soc., 59, 1111 (1937). (6) Landolt-Bornstein Tabellen, including I and I11 Erganzungsband, 5 Auflage, Berlin, Julius Springer, 1923. RECEIVED for review December 8, 1952.
A c c E a E n April 17, 1953.
Composition of Vapors from Boiling Binarv Svstems J
J
NEW METHODS OF REPRESENTING AND PREDICTING EQUILIBRIUM DATA DONALD F. OTHMER, LOUIS G. RICCIARDI', AND MAHESH S. THAKAR2 Polytechnic Znstitute of Brooklyn, Brooklyn 2, N . Y .
N
UMEROUS attempts have been made to present thermody-
namically the vapor-liquid equilibrium relationships of volatile liquids, using as a basis t h e Gibbs-Duhem equation. However, this equation applies strictly t o constant temperature systems, while engineering operations-e.g., distillation columnsare a t constant pressure. In the following, simple thermodynamic derivations are presented to represent constant pressure vapor-liquid equilibrium data. Close interrelationship of boiling points and equilibrium vapor compositions with their latent heats of vaporization is also indirated. A method is shown for representing vapor-liquid equilibrium data as straight lines on a logarithmic paper. These straight-line plots are shown t o be useful in conjunction with the thermodynamic equations for the correlation and prediction of the equilibrium data. PREVIOUS METHODS
In 1885 the Gibbs-Duhem differential equation was derived shoM ing the relation between the composition in moles and the partial pressures of the individual constituents of a multicomponent system. Margules (64) in the same year integrated this equation as an infinite series. I n 1900, Zawidski (62) found a method of determining the coefficients of the equation by the slopes at the ends of the total pressure and composition relation-Le., P ws. x a t constant T. Dolezalek (10) and van Laar (19,20) modified the Margules expressions using molecular association and van der Waals' equation, while Bose ( I ) , Marshall (25),and Krichewskil and Kazarnovskii (18) offered methods for solving the Duhem equation Present address, Colgate-Palmolive-Peet Co., Jersey City, N. J. Present address, The Indian Aluminum Co , Ltd, 31 Chowranghee Road, Calcutta, India. 1
2
directly without the Margules' formula. These methods, however, are very laborious and have had little practical application. I n 1914 Rosanoff et al. (39) proposed a semiempirical formula for calculating these equilibrium relations, which Levy (26) showed tto be inaccurate. I n 1924 Lewis and Murphree (23) derived a thermodynamic equation for constant temperature systems and developed a trial and error method for stepwise integrating the Duhem equation. Leslie and Carr (21)proved in 1925 t h a t the Duhring rule is applicable to some solutions, and using this rule calculated the equilibrium relation from Duhring lines. Othmer (29) showed a simplification with improved accuracy using a refrence substance logarithmic plot. Othmer and Gilmont (SO) showed t h a t vapor composition activities, equilibrium constants, and relative volatilities may be plotted a t constant x (or constant y) as straight lines on a logarithmic sheet against a temperature scale derived from a reference substance. They (SO) also showed t h a t these properties could be plotted directly in many cases on logarithmic paper against total pressures t o give straight lines; and this is a simple and effective correlation when data are available a t different pressures. I n a later paper ( S I ) , they gave improved methods for expressing such P, T, x, and y data based on the critical constants, and with associates ( 1 4 )they used activity coefficients to derive a general equation. Levy in 1941 (85') improved Zawidski's method in determining the slopes of the total pressure curve. Carlson and Colburn ( 5 )in 1942 correlated and predicted vapor-liquid equilibrium values for binaries using a modified form of the van Laar equation. Clark ( 6 ) proposed an empirical method for predicting and presenting x, y relationships for any system by using the equation of two hyperbolas. These two equations do not, of course, present a complete expression of t h e equilibrium relations, as they give no
