DIFFUSIOK OF WATER INTO BUTYL ALCOHOL
343
REFERENCES (1) ADAMS:J. Am. Chem. SOC.37, 1181 (1915). (2) BERNER:Z. physik. Chem. A141, 91 (1929). (3) BRODSKII AND SHERSHEVER: Z. physik. Cheni. A166, 417 (1931). (4) CRIST,MURPHY, AND UREY:J. Chem. Phys. 2, 112 (1934). (5) RANDALL, LONGTIX, A N D WEBER: J. Phys. Chem. 46, 343 (1941). (6) RANDALL AND WEBER:J. Phys. Chem. 44, 017 (1940).
THE DIFFUSIOS OF WATER ‘INTO KORMAL BUTYL ALCOHOL AT 30°C.1 JIERLE RANDALL
Department of Chemistry, University of California, Berkeley, California BRUCE LOKGTIN
Department of Chemical Enganeering, Section of Chemzstry, Armour Institute Technology, Chicago, Illinois
01
ASD
HEINZ WEBER Department of Chemistry, Cniversity of California, Berkeley, California Received A p r i l 18, 1940
Fick’s (3) law of diffusion considers the driving force of diffusion to be the concentration gradient of the diffusing component. The diffusion equation takes the form
I
=
-D dc/dx
(1)
where c is the concentration (mols per cm.9 a t the position x (cm.) and I is the number of mols of component diffusing across a unit area per unit time a t this point. The diffusion coefficient D has long been known t o vary with the concentration c. At a phase boundary, as between water and butyl alcohol, the concentration gradient of each component may be practically infinite, although the two phases are at equilibrium. Unless D approaches zero rapidly as the concentrations of the two phases approach the saturation values, Fick’s law will require an infinite rate of diffusion.across the phase boundary. From the thermodynamic standpoint it seems preferable to consider the free energy gradient, -d&/dx, as the driving force of diffusion. As 1 The assistance of the Works Progress Administration is gratefully acknowledged (0. P. 65-1-08-113).
344
MERLE RANDALL, BRUCE LONQTIK AND HEINZ WEBER
equilibrium is approached with respect to diffusion, both the free-energy gradient and the diffusion current I must vanish. This suggests that the diffusion law must take the form
I = -(l/R) dbl/dx mols per cm.2 per second
(2)
proposed by Onsager (9), in which R is the diffusional resistance (analogous to electrical resistance). Equation 2 will reduce to the form of Fick’s law (with D constant) in the case of ideal solutions if the diffusion resistance has the form l/kc, k being a constant. The partial molal free energy is expressed in terms of the fugacity, fi, as b~ = RT lnfp
+ B(T)
ergs per mol
where B(T)is constant a t any given temperature. 2 may be written as
I
= -kcRT(d lnfzldx)
(3)
Consequently equation
(4)
In an ideal solution, the fugacity f i (atmospheres) is approximately proportional to the concentration, c, of the solute, so that c d In fe/dx is approximately equal to dc/dx. I n any solution, the diffusion coefficient D must be of the same order of magnitude as IcRT. For electrolytes, equation 4 reduces to the familiar Nernst (8) expression at infinite dilution, k being the ionic mobility. Onsager and Fuoss (10) have tested equation 4 for solutions of sodium and potassium chlorides. Several independent workers (2,4, 7) have since helped to increase our knowledge of this particular subject, using various aqueous solutions of electrolytes. It seemed important to extend the experimental basis for testing the form of the diffusion law to solutions of non-electrolytes, since thermodynamic relationships are much simpler in these cases. The system n-butyl alcohol-water was chosen as one in which the greatest departure should be expected between the two alternative forms, owing to the presence of partial miscibility. EXPERIMENTAL
The method of Thorvert (13), with slight modifications, was used. Wiener (14)showed that when a beam of parallel light enters an optically non-uniform medium it is refracted, the angle cy being equal to the product of the gradient of the refractive index dn/dx and the thickness 1 of the medium a = 1 dn/dx
(5)
DIFFUSION OF WATER INTO BUTYL ALCOHOL
345
From the diagram (figure 1) it can readily be seen that (Y = g/f, f being the focal length of the cylindrical lens, L, and y being the vertical deviation of the ray as measured on the plate P. dn/dx = y / l j
(6)
Distilled water was diffused into n-butyl alcohol prepared from the same stock as was used (11) for the measurement of the fugacity of the constituents in the aqueous solutions. S
D
L
P
FIG.1. Diagram of the optical system OPTICAL SYSTEM
The apparatus (figure 2) was mounted on an optical bench A, 1 meter long, which was bolted to a bench D and cushioned with rubber discs C and B. It consisted of a Zeiss sodium-vapor lamp E, a cell F filled with *butyl alcohol to remove heat radiation, a collimator G, a screen H, a slit I, a diffusion cell J, and a camera K with a shutter L, cylindrical lens M, and plate S . The diffusion cell, shown in detail in figure 3, was equipped with a scale 0 and a slide P for measuring the position of the phase boundary. The *butyl alcohol flowed from the feed tank Q, thermostated a t 30°C. f 0.1",and equipped with gage-glass R, heater S, stirrer T, and toluene regulator U, through the constant-pressure feed regulator V and the diffusion cell J into the sump tank W. The diffusion cell was carefully shielded from radiation by aluminum foil and the whole apparatus was contained in a small room thermostated at 30°C. f 0.1". All materials were tested for their effect on n-butyl alcohol and water. All necessary connections were made of Neoprene tubing and all openings to the air were closed with weighted disks of Garlock gasket material. The body A (figure 3) of the diffusion cell J (figure 2) was brass. The glass plates BB, 5.08 cm. apart, were roughened a t the surfaces of contact for better cohesion, cemented on with vinyl resin dissolved in acetone, clamped, and air dried. It was found necessary to bake the cell in an oven at 150°C. for a day in order to polymerize thc resin to the point where it was not softened by the iz-butyl alcohol. The shutter of the camera was replaced by a diaphragm containing a hole 30 mm. in diameter and a sliding shutter. -4 cylindrical lens, 43 mm. long by 43 mm. wide
346
MERLE RANDALL, BRUCE LOKGTIN AND HEINZ WEBER
with a focal length of 140 mm., was installed in place of the original lens. The collimator was a brass tube 60 mm. in diameter blackened with carbon black on the inside. One end mas closed with a thin copper plate having a pinhole 0.1 mm. in diameter in the center. The parallel slit was formed by two razor blades mounted on a round disc equipped with a protractor. After the apparatus had been assembled without the cell, the cylindrical lens was tested using white light. The image was found to be perfectly straight in the center for a distance of 25 mm.
FIG.2. Opticnl bcnch
T
E
E
c
-
I
I
I
I
-
I
i
FIG.3. Dctnil of diffusion ccll DIFFUSION 3IE iST;IIE\lENTS
After thoroughly cleaning and drying the cell, it was clamped in its place on the optical bcnch and filled about half full of water. Then the remaining space mas filled with pure n-butyl alcohol, taking care not to disturb the mater, after which a flow of alcohol from the feed tank was started and adjusted to a rate of approximately 2 ml. per minute. By means of white light, the position and inclination of the diagonal slit was adjusted until it covered the whole gradient from the meniscus a t the alcohol-water interface a t the bottom to the stream of pure n-butyl alcohol a t the top. The angle of elcvation was 56'12'. Using sodium
DIFFUSION O F WATER INTO BUTYL ALCOHOL
347
light, exposures were made daily to determine when (about one week) the condition of steady state was reached. At first the meniscus gradually dropped because the volume of water decreased by its diffusion into the n-butyl alcohol layer. The meniscus was retained in its original position by introducing water into the lower layer by means of a capillary tube, taking pains not to disturb the alcohol layer. When exposures (4 min., Eastman I11 D plates, Eastman D-72 developer) made on two successive days gave coincident images, it was assumed that the condition of steady state had been reached.
4
FIG.4. Record plate (enlarged 5x1
The record exposure (curved line, figure 4) was made, the position of the meniscus was determined with a cathetometer, a sample of outflowing alcohol was collected for a certain length of time, the cell was removed, and a second exposure - was made on the record plate to obtain the normal reference line (A'B', figure 1; horizontal line, figure 4). The sample of (r outflow was analyzed in the interferometer, using an 80-mm. cell, after making a preliminary calibration. The current of water, I, was found to be 3.77 X 10V mols per cm.? per second. The plate was then developed and dried. The lower end of the curve, as shown in figure 4, corresponds to the end of the gradient containing nearly pure n-butyl alcohol (0.020 per cent water). A reference line Eperpendicular to the normal A'E' was scratched on the plate.
348
MERLE RANDALL, BRUCE LONQTIN AND HEINZ WEBER
To facilitate measurement of the distances z and y needed in equation 6, an image of the plate was projected by means of an enlarging camera onto a sheet of paper, The outlines of the image, together with the reference were then traced on the paper (figure 5). The estimated central line positions of the normal reference line and the displaced curve were then drawn (curves XX and TU). The dotted line locates the position of the phase boundary. The distance z’ was measured on the enlarged image along XX from the The vertical displacement, y’, of the curve was line H?. - above measured a t each of a number of distances z’ from H F . To reduce these values to the scale of the original plate, the value of y along the reference line was measured on the paper as 4.20 cm., and on the plate with a microscope as 0.334 cm. All of the measured values were reduced in this
e,
FIG.5. Working enlargement of record plate, with chosen curves estimated from maximum density of plate.
proportion by multiplying into the factor 0.0795. Owing to the inclination of the diagonal slit, 1 cm. along @ o n the plate corresponds to 1.5 om. (tan. 56’ 12’) in the vertical direction z in the cell. Table 1 summarizes these measurements. The first column gives the distance z’ and the second column the distance y’ measured on the enlargement. The third and fourth columns give the calculated values of the vertical distance, z, from the meniscus to the position of passage of the beam of light through the diffusion cell, and the displacement, y, of the beam from its normal position a t the plate, expressed in centimeters. The fifth column gives the gradient, dnldz, of the refractive index with respect t o vertical distance in the diffusion cell. Table 2 summarizes the calculations for converting the optical data into values of the diffusion coefficient a t various concentrations of water in n-butyl alcohol. The first column gives the vertical distance measured
349
DIFFUSION OF WATER INTO BUTYL ALCOHOL
TABLE 1 Diffusion of wafer into n-butyl alcohol at 30°C. 2'
Y'
0 1.o 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0
10 8.4 7.35 6.35 5.82 5.20 4.60 4.04 3.54 3.04 2.57 2.1s
2
0 0.119 0.238 0.357 0.476 0.595 0.714 0.833 0.952 1.071 1.190 1 .m
Y
dn: dz
0.795 0.665 0.584 0.520 0.463 0.413 0.365 0.321 0.281 0.241 0.204 0.173
0.01120 0.00940 0.00823 0.00732 0.00652 0.00582 0.00514 0.00452 0.00396 0.00339 0,00287 0,00244
TABLE 2 Diffiision of water into n-6ictyl alcohol at 30°C. (1)
-
(10)
-
(11)
-3
2
1.
8
9
z
$
2
-
- An:
g
g
y
-
5
E -
-/-I-
&
x
-__
1-
Q
per
cent
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.o 1.1 1.2 1.3 1.4
).00882( 21 .O! 1,007784 ) .OO687f ).006061 ) ,005322 I. 00465: I.00404: 1.003494 I.00299f I.002554
1.002151 1.001811 1.001507 1.001242 1.001007
18.61 16.8: 15.0t 13.4: 11.91 10.64 9.44 8.3f 7.4( 6.M: 5.6t 4.91 4.x 3.M
3.383 2.963 2.577 2.230 1.905 1.599
0.2470.0323 0.2220.0305 0.1980.0286 0.1750.0262 0,1530.0237 0.131,0.0212
0.528 0.560 0.600 0.562 0.728 0.534 0.910, 0.492 1.040' 0 504 1.100/ 0:569
7.56 2.86 1.413 1.012 0.905 0.860 0.836 0.841 0.811 0.838 0.841 0.800 0.740 0.753 0.851
2.67 3.91 4.37 4.65 5.20 5.60 6.67 7.18 7.82 8.45 9.20 10.2
11.2 12.0 12.4
0.106 0.155 0.173 0.185 0.206 0.238 0.265 0.285 0.310 0.335 0.365 0.405 0.444 0.476 0,492
350
MERLE RANDALL, BRUCE LONGTIN AND HEINZ WEBER
from the phase boundary; the second gives the increment of the index of refraction at the height z found by graphically integrating the values of dn/dz from the phase boundary to .E; the third the weight per cent of water in the n-butyl alcohol-rich phase found by reading from the curve of index of refraction versus weight coniposition (6) ; thr fourth the density of the phase; the fifth the concentration (mols per cn1.3); the sixth the mol fraction of water in the phase; the seventh the fugacity (atmospheres) of the water from the measurements of Randall and Weber (11); the eighth the negative of rate of change of the natural logarithm of the fugacity with the distance found by combining columns 1 and 7; the ninth the the tenth the diffusion constant in value of -l/[c(d In j2)/dz] X the eleventh accordance with equation 4, -[Z/RTc(d In f*)/dz)] X the value of Fick’s diffusion constant, -Z/(dc/dz) X lo4;and the last the 3
.. C I
:20
U
$ 3
0.
0
I
I
I
,
2
4
6
8
Concenlrarron 01 Wafer i n n - B u l y l Alcohol.
I
mots/lifer
FIG. 6. Diffusion constant of water into n-butyl alcohol. Curve A, equation 4 (proportional t o partial mold frec-cnergy gradient); curve B, equation 1, Fick’s law (proportional to conccntration gradient).
value of -I/[RT(dc/dz)] X 10’3 to convert Fick’s constant to the same units as those of equation 4. The results are shown in figure 6,where the values of columns 10 and 11 rcduced to the same scale (column 12) are shown plotted against the concentration. SUMMARY
The “differential” diffusion constant of water diffusing into n-butyl alcohol was measured continuously over the range of concentration of the n-butyl alcohol-rich phase. ks can be seen from the plot in figure 6, the constant IC, as defined by equation 4, is substantially independent of the concentration except for two points very near the phase boundary. The slope of the fugacity versus composition curve is very small in this particular region, giving rise to a large uncertainty in its value. The experi-
351
ACTIVITY COEFFICIEBT O F POTASSIUhI IODATE
mental error is also greatest in this region where t8heconcentration gradient is greatest, because the assumption that the radius of curvature of the beam of light remains constant through the length 1 of the cell becomes invalid near the interface. The results given here depend on a single experiment. The agreement with the predictions of equation 4 is better than with the predictions of the simple Fick’s law, and me feel justified in concluding that the driving force in diffusion is the free-energy gradient, rather than the concentmtion gradient. REFERENCES COHENAND BRUISS:2. physik. Chein. 103, 319 (1923). COLEAND GORDOS: J. Phys. Chem. 40, 733 (1936). Frcs: Ann. Physik Cheni. [Z] 94, 59 (1855). GORDON: J. Cheni. Phys. 6, 522 (1937). LEWISA K D RLHDALL: Thermodynamics, and the Free Energy OJ Chemical Substances. McGrau-Hill Book Company, Inc., New York (1923). (6) LONGTIN, RANDALL) A N D WEBER:J . Pliys. Chem. 46, 340 (1941). (7) MCBAISASD DATSOS:Proc. Roy. SOC. (London) A148, 32 (1935). (8) NERHST:Z. physik. Chem. 2, 613 (1888). Phys. : Rev. 37, 405 (1931). (9) ~ N S A Q E R (10) ONSAGER . ~ N DFuoss: J. Phys. Cheni. 36, 2689 (1932). (11) R ~ N D A L . ~LN D~ Y E B E R :J. Phys. Chem. 44, 917 (1940). (a) Trans. Cambridge Phil. SOC. 9, 8 (1850); (b) Phys. Papers, Uni(12) STOKES: versity Press, Cambridge 3, 1 (1901). (13) THORVERT: .Inn. phys. 2, 369 (1915). (14) WIETER:Ann. Physik Chem. I31 49, 105 (1893). (1) (2) (3) (4) (5)
LIQCID --lAIAIOSIA AS A SOLVEST. 1);
THE AiCTIVITT COEFFICIEST
O F POTASSIChf IODATE AT
VICTOR .J. A S H O R S
ASD
25°C.’
HERSCHEL HUNT
Depcii,tine,it qf Chemist, y, Pirrditc I7niw?.siti/,ll’est LaJnyette, Indiana
Kecrii,ed .Uau 20, 1940 ISTRODUCTIOS
The researches of Elliott mid Yost (3). Garner, Green, and Yost (4), Pleskov and 3Ionosgon (ti), Larsen and Hunt ( 5 ) , and Ritchey and Hunt (7) have opened u p the important field of liquid amnionia from R thernioThis srtirle is based t i p o i l :L thesis submitted by Victor J. Anhorn to the Faculty of Purduc Vniversity i n partial fnlfillmcnt of the rcquirenients for the degree of Doctor of Philosophy, June, 1940.
