2.562 [CONTRIBUTIOA’ FROM
AVERV
LABORATORY O F THE VSIVERSITY O F
NEBRASKA]
The Diffusion of Phenylacetic Acid in Water as Measured by Changes of Surface Tension BY
JAhlES
E. KOLLER~
E. ROGERSVASHBURN
RECEIVED MAY14, 1953 Phenylacetic acid has been allowed t o diffuse through a column of water of known dimensions t o the liquid-air interface. T h e surface tensions, measured after different time intervals, have been used t o calculate t h e corresponding concentrations a t the interface. The diffusion coefficient has been calculated from these values b y a different, and we believe better, relationship than has been used before
The diffusion coefficients of the butyl alcohols in dilute aqueous solutions have been determined by the observation of changes of surface tensions USing a manometric ~ a p i l l a r i m e t e r . ~Values ~~ of the diffusion coefficient were calculated from experimental data by use of an integrated expression for Fick’s second law and by a method based on the solution of the analogous problem in heat transfer by Ingersoll and ZobeL4 The latter development results in obtaining the diffusion coefficient as D
=
L%/t
(1)
in which L is twice the observed length of the column, t is the time interval from the beginning of the experiment until the time of observation and z is evaluated from the series
S(z)is determined experimentally as Sb) = (C” - C,)/C”
(2)
where Co is the concentration of the bulk solution and C h is the concentration of solute a t the liquid-air interface in the capillary. If equation 1 is rearranged and differentiated with respect to time, and if i t is assumed that the diffusion coefficient is constant and that the length of the column does not vary during a time interval fl to t z , the resulting expression is D
=
L2=.! tf -
tl
(3)
Equation 3 may be used to calculate diffusion coefficients on the basis of successive observations throughout an experiment. This was not possible for methods previously used. The object of this investigation was to study further the practical and theoretical considerations affecting determinations by this method. Of particular interest were possible variations in the observed rate of diffusion brought about by varying the length of the liquid column in the capillary. Experimental Apparatus.-The manometric capillarimeter uqed in this investigation was essentially that used in previously reported 1 v o r k . ~ ~ 3During studies of diffusion a small hantloperated stirrer in the capillarimcter was ured to stir solu(1) 3Iinnesota >lining and >Ianufacturing C o m p a n y Research Fellow, 1951-1952 a n d 1952~-11i38. ( 2 ) E. R. Washburn and H. K. Dunning, THISJOURSAI,,73, 1111 (1951). (3) H. h-.Dunning a n d R. R . XT’ashliurn, J . PJISF. C ~ P I ~5 I6., ,2%; (1952). (4) L. R. Ingersoll a n d 0. J, Zobel, “IIeat Condiiction,” I l c G r n w Hill Book C o . , N e w York, N. Y., 1948, p. 127, Appendix C;.
tious s l o ~ ~ lfor y approximately five seconds immediately after the column of water had been reduced t o the desired length and again after t h e surface tension began t o change. The purpose of this procedure was t o ensure uniform miring of the solution in the bulb with the excess water forced from the capillary. The stirring process \vas neither accompanied nor followed by any abrupt change in the rate a t Tvhich surface tension was decreasing. 1Vhile solutions were being stirred as well as a t other times during a determination it was possible t o maintain t h e desired position of the meniscus in the capillary t o within =t0.002 cm. During the work two different capillaries mounted in separate bulbs were used. Each capillary was calibrated a t oneniillimeter intervals throughout t h e working distance by observing the pressure necessary t o prevent the rise of purified water. The manometric method is particularly ~ v e l l adapted for such calibrations. Each calibration consisted of four or more determinations with different samples of water and calibrations were repeated after the capillaries had been in use for several months. The effective radii one millimeter from the lower tips of the two capillaries were found a t the time of the final calibration t o be 0.02538 10.00001 cm. and 0.02547 ?C 0.00001 c m . These values lie between the maximum and minimum values for the slightly elliptical capillaries as measured with an optical microscope equipped with an eyepiece micrometer. The capillarimeter was mounted in an air-bath equipped t o maintain automatically the temperature of the solutioii in t h e bulb a t 25.0 -i: 0.1’. Duplicate determinations of the densities of solutious were made using two glass-stoppered pycnometers with capillary stems. The pycnometers were brought t o constant temperature in a water-bath a t 25.00 It 0.05’. Materials.-Eastman Kodak Co. “white label” grxlc phenylacetic acid lras distilled three times a t 140’ and il pressure of 20 mm. of rnercuri-. The product, collected on the outer vvall of a water-cooled glass test-tube, was i l l the form of elongated crystals which melted a t 76.6-76.8”.
Results Density.-The densities of aqueous solutions of phenylacetic acid were required to calculate the concentrations of solutions in the desired terms. The densities measured for seven solutions of concentrations between zero and 0.8440per cent. by weight are described by the empirical equation d = 0.001dSc f 0.99702 to within +0.00001 g.,’cc. Values obtained from duplicate determinations did not normally differ by more than this amount. Surface Tension.-The surface tensions of‘ twelve aqueous solutions of phenylacetic acid were tletermined by use of the nianometric capillarimcter. The values obtained are described by the empirical equation T = 72.0T - 1 3 . 7 1 ~- 1!).73c? a t concentrations lower than 0,300yCand by the equation 7’ = 73.27 - 28.2% 9.61~2a t concentrations between this value and l.00.3yc. The estimated accuracy of these values is *0.05 dyne/cm. a t concentrations below 0.500% and *O. 10 tlync,: cm. a t concentrations above this value. Surface tensions mere calculated from experimental data by
+
DIFFUSION OF PHENYLACETIC ACID IN I ~ A T E R
May 5 , l9.X
the equation of Ferguson and Dowsonj as modified by Debritt and Roper.6 This equation takes the form
TABLEI RESULTSOF A TYPICAL DIFFUSION EXPERIMENT CO = 0.010015 g./cc.; L = 2 X 0.400 = 0.800 cm. 4
-AT, dynes
C h, g./cc.
0 600 1200 1800 2400 3000 3600 4200 4800 5400
0.000 000 097 343 1 252 2 225 3 375 1 ,571 .i 721 6 815 7 780 8 653 9 431
0 000059 000339 000753 ,001245 001749 no2242 002698 003 152 003584 004002 ,004385
sec.
T r g
/I,,,,
= = = =
hCp,, =
surface tension, dynes/cm. radius of t h e capillary, cm. acceleration of gravity, cm /5ec.z vertical distance between levels of the fluid in t h e manometer, cm. vertical distance between the vnall meniscus in the capillary and the large meniscus in the bulb
for dilute aqueous solutions when water is used in the manometer, when h is small, when r is approximately 0.025 cm. and when the small meniscus is located below the large meniscus. A period of approximately ten minutes was required for surface tensions to reach their equilibrium values. During this time they normally increased by one-tenth of a dyne or less from the values which had been observed initially. The value (54.5 dynes’cm.) which we obtained for a 1.003% solution is approximately the same as that observed for a saturated aqueous solution (reported as 0.0091: g. /cc.) of phenylacetic acid by Rose and Sherwin. Solutions used in the present study were prepared bv weight and their concentrations would not be subject to the possible error due to volatilization of the solute that might be incurred when a solution of phenylacetic acid is analyzed by evaporation of the solvent. Diffusion.-Rates of diffusion were measured for phenylacetic acid solutions of four concentrations (0.005840, 0.007040, 0.008426 and 0.010015 g./cc.) a t each of three observed column lengths (0.300, 0.400 and 0.500 cm.). Three or more determinations were made for each solution a t each column length. The change of surface tension with time was recorded for each experiment until the surface tension had changed by approximately ten dynes. The concentration indicated by each recorded surface tension was determined by reference to a graph of surface tension against concentration of such a scale that one millimeter represented a concentration difference of 0.000005 g./cc. or a change of surface tension of 0.02 dyne. Results of several determinations a t a single concentration and column length were averaged by finding the arithmetic mean of the surface tensions a t each recorded time and then determining from the graph a single “mean” c h for each time. The results of a typical single diffusion experiment are tabulated in Table I. Here the change of surface tension - A T is recorded a t ten-minute time intervals. For each value of - A T , CShas been determined graphically, has been calculated by use of equation 2 and the value of z has been obtained4 and tabulated. Then the diffusion coefficients have been calculated by use of equation 3 for ten-minute intervals. Each value of D in Table I is recorded on the same line as the t and z which were used as fz and z2 in calculating that value.
s(,)
( 5 ) A. Ferguson and P. E. Dowson, Trans. Faraday Soc , 17, 388 (1921). ( 6 ) C. C. DeWitt a n d E. E, Roper, THISJOURNAL. 64, 446 (1932). (7) A. R. Rose and C. P. Sherwin, J . Biol Chem , 68, 565 (1926).
256.7
6000 6600 7200
0,01414 . 02190 ,02891 03593 04276 04948 , OR587 06252 . OR922
Oi609 ,08278
8.28 x 7.48 x 7.49 X 7.29 X 7.17 X c, 82 x 7.09 x 7 15 x 7.33 x 7.14 X
10-fl
1V6 10F lorn 10-6 1o-fl 10-6
The results of this experiment are typical in that the relative rate of diffusion is approximately constant during the final portion (one-half or more) of the experiment but somewhat higher during the initial stages. The results of all studies are summarized in T a ble 11. The values of D have been calculated for the final one-half or more of each set of experiments. Each value of z used in the preparation of this table was obtained from the “mean” c h for three or more experiments as previously described and the values of dz/dt used were the slopes of the plots of z against time as obtained by averaging the slopes during ovcrlapping intervals. SUMMARY OF (-0
THE
D = L2dz
I
g.,:cc.
0 0lOOl.i
008426
007040
005840 (Stirred) (Unstirred)
I.;?
0 500
400 300 500 400 300 j00 400 300 500 400 300 300
TABLEI1 RESULTSOF DIFFUSION STUDIES D”
dt
7 7 6 7 7
X X X 1Vfi X x 10-6 X X X X X
DO (mean) X X 10P X 8 6 X l0-O X x 10-8 X 8 4 X 10-0 X X 10-G X 10F 8 5 X X
6 x 6 Fj2 X
8 8 8 8 8 8 8 8 8 8 8 8
6 64 X
8 4 X 10P
6
7 7
6 7
28 16 84 29 08 65 36 21 70 32 98
4 5 6 4 5 4 5 6 4 4 3 x 2 X
8 3 X lo+
Included in the table are the results of three determinations a t CO = 0.005840 g./cc. and L / 2 = 0.300 cm., conducted a t the conclusion of the study, in which the solution in the bulb was not stirred. For these studies z increased a t a more nearly constant rate throughout the experiment. The average change during the first 60 minutes of these experiments was consistent with a diffusion coefficient of 6.8 X 10-6 while that of the corresponding stirred experiments for the same interval For the remainder gave a coefficient of 7.3 X of each experiment, a period of 100 minutes, the behavior in each case gave diffusion coefficients of The recorded value of approximately 6.5 X
2504
JAMES
I’d.7G
E. KOLLERAND E. ROGERITASITBURN
D for the unstirred experiments is based upon the
DO = Lo2dz/dt (5) entire determination rather than the final portion then it can be shown that only. 1 c _L _ Discussion * = L X (6) Variation of the Apparent Diffusion Coefficient de- Equation 6 indicates that a plot of L / f l against L in Different Portions of Experiments.-The crease in the apparent diffusion coefficient with the should give a straight line, the slope and intercept of passage of time as demonstrated by the data in which can be used to calculate the values of D oand Table I may be explained by one or a combination C. of the following three influences. The data in Table I1 were plotted according to 1. When the solution is stirred a t the beginning equation 6 and the slope and intercept were deterof the experiment, mechanical mixing may cause mined by the method of least squares to give the some solution to be introduced to the lower portion equation of the diffusion column. This would cause solute L _djj = 344.3L 25.31 molecules to arrive a t the meniscus more rapidly (6a) during the early portions of the experiments than they do later in the experiments when diffusion From the constants in this equation, DOis found to and C has the value 0 073 through the entire column accounts for all trans- be (8.44 f 0.14) X 0.008 cm. The deviations listed are calculated port. 2. Rapid diffusion into the column during the from the standard deviations of the slope and interearly parts of experiments may cause the depletion cept of the straight-line equation. I n obtaining of some solute from a more or less hemispherical these results, the observed values of D for a column region below the tip of the capillary. This would length of 0.500 cm. were double-weighted because lengthen the actual column during the course of the the results of studies a t greater column lengths niay experiment causing the apparent diffusion coeffi- be expected to be more reliable. The values of C indicate t h a t the true length of cient calculated on the basis of a constant column the column during the later portions of an experilength to decrease. 3. It is possible that solute can be transported ment exceeds the observed length by 0.037 f 0.005 from a region of higher concentration to a region of cm. The observed length is measured as the vertilower concentration in a layer adsorbed on the wall cal distance between the lower tip of the capillary of the capillary and in so doing supplement the and the lowest portion of the meniscus in the capildiffusion process. This possibility has been sug- lary. This constant error may be due to one or gested in connection with the diaphragm cell tech- both of the following conditions. 1. The extension of the region of reduced connique by Gordon8 and by other writers and the process was shown by Stokesg to occur during the centration below the tip of the capillary would prodiffusion of salts in dilute solutions. The influence duce a column of increased length during all except of surface transport would be relatively greater dur- the earliest parts of experiments. 2. Solute molecules probably must diffuse to a ing the earlier portions of an experiment because the rate a t which solute actually arrives a t the men- level somewhat above the lowest part of the menisiscus is lower than that later in the experiment and cus, the point used as the top of the diffusion colbecause the concentrations a t different levels in the umn in measuring its length, in order to influence capillary and, hence, the extents of adsorption differ capillary behavior. It was found by Antonoff l9 that the capillary behavior of a liquid is influenced by more widely during the initial phase. The fact that the apparent diffusion coefficient the extent of the wall of the capillary above the apvaries less during the initial portions of experi- parent top of the meniscus. If the solute molecules ments in which solutions are not stirred than in must reach or pass the apparent top of the meniscus studies with stirring seems to indicate t h a t one or before influencing the observed surface tension, then both of the first two explanations apply. However, a difference between the effective column length and the excess water forced from the capillary remains the observed column length would exist even though visible below the tip of the capillary for a short pe- movement of solute particles in the surface layer riod of time when the solution is not stirred and it may be more rapid than in the interior of the soluis possible that this introduces an initial error which tion. The Diffusion Coefficient of Phenylacetic Acid.counteracts an influence such as that suggested Equation 1, in the differentiated form, and equaabove as the third possible explanation. Influence of Varying the Length of the Diffusion tion 5 show that for each value of D in Table Column.-Examination of Table I1 shows that as 11, Do can be calculated as Do = D(Lo2/L2)= C ) 2 / L 2 ,and calculated values of D O the length of the column is increased, there is an D X ( L Each value of “DO increase in the apparent diffusion coefficient. are given in that table. The regularity and magnitude of this change suggest (mean) )’ represents an integral diffusion coefficient an error in the value of L used in making calcula- of phenylacetic acid between COand a somewhat tions which is independent of the value of L. If it is lower concentration. All of the determined values assumed t h a t the true column length is given by of “Do(niean)” lie within the standard deviation of L0/2 = ( L C)/2 and the actual diffusion coeffi- DO as obtained from equation 6a. The diffusion coefficients of organic solutes in water, normally cient is given by increase slightly as concentration decreases. This
a+x
+
+
+
(8) A. R. Gordon, A n n . N . Y.Acad. Sci., 46, 297 (1945). (9) R. H. Stokes, Txrs JOURNAL, 72, 766 (1950).
(IO) G . Antonoff, Rcc. tioff. chim., 66, 1011 (1949).
THERASCHIG SYNTHESIS OF HYDRAZINE
May 5, 1954
change for phenylacetic acid in the range of concentrations studied appears to be too small to be measured by this method at its present state of development. The mean value Do, (8.44 0.14) X 19-6, is thought to best represent the diffusion coefficient of phenylacetic acid in aqueous mixtures at concentrations below 0.01 g./cc. and a t a temperature of 25'. The value calculated by use of the StokesEinstein equation based upon the viscosity of water and the mean radius of a Fisher-Hirschfelder model of the phenylacetic acid molecule is 7.7 X 10-6. Because their molecules are disk-like rather than spherical in shape, aromatic compounds have
*
[CONTRIBUTION FRVM
THE
2565
usually been observed to diffuse more rapidly than predicted by the S tokesEinstein equation. For example, o-hydroxybenzyl alcohol was found to have a diffusion coefficient of 7.2 X 10-6 in dilute aqueous solutions at 20". l 1 This corresponds approximately with a value of 8.3 X 10-8 at 25") and is in good agreement with the value reported here for phenylacetic acid. Acknowledgment.-The authors arc grateful to Dr. C. E. Vanderzee for valuable suggestions pertaining to the conduct of this study. (11) "International Critical Tables," McGraw-Hill Book Co., New
York, N. Y.,Vol. V, p. 71.
LINCOLN 8, NEBRASKA
COLLEGE OF CHEMISTRY AXD CHEMICAL ENGINEERING, UNIVERSITY OF CALIFORNIA, BERKELEY 1
The Raschig Synthesis of Hydrazine BY JOHN W. CAHN'AND RICHARDE. POWELL RECEIVED KOVEMBER 5, 1953 It has been possible t o fit existing yield d a t a for the Raschig synthesis by assuming simple rate laws. Hydrazine is formed by a bimolecular reaction between ammonia and chloramine and destroyed by a bimolecular reaction between hydrazine and chloramine. The latter reaction rate constant is about 18 times t h a t of the former reaction, and therefore large excesses of ammonia are needed to make the first reaction predominate. The role of copper can be explained by assuming t h a t copper catalyzes the destruction of hydrazine, again as a bimolecular reaction involving copper and hydrazine. I n terms of these mechanisms the role of gelatin in increasing yield is t h a t of complexing copper. This copper complex of gelatin appears t o be unstable below p H 11.
Today the most useful synthesis of hvdrazine is the Raschig synthesis. I t consists of oxidizing excess ammonia with alkaline hypochlorite. Yields based on hypochlorite, are low unless glue or gelatin is added to the reaction mixture and even then large excesses of ammonia have to be used. Much practical work has been done in search of conditions for maximizing yield. The qualitative conclusion reached from these are that the reaction proceeds in three steps
+
+
NH3 OC1- = KHzC1 OH(1) XHzCI NHa O H - = NzH4 C1HzO (2) NzH4 2 0 H - = Nz 2NHa 2C12H20 ZNHiCl (3)
+
+
+
+
+
+
+
+
+
The first reaction is fast and proceeds to completion rapidly. The second and third reactions are of comparable rates and the qualitative conclusions are that anything increasing the rate of the second or decreasing the rate of the third will increase the yield of hydrazine. Hence large excesses of ammonia are necessary. The purpose of this paper is t o show that the above qualitative conclusions can in fact be expressed quantitatively in terms of simple rate laws and that the role of the other variables can then be determined unequivocally. Bodenstein2 has measured the rate of reaction between ammonia and chloramine to give nitrogen and has found i t to be first order in chloramine and ammonia. We can assume therefore that reaction 2 obeys this same rate law and if we assume that reaction 3 also proceeds as a bimolecular reaction, (1) Institute for the S t u d y of Metals, University of Chicago (2) hl Bodenstein, Z physak. Chem., 139A, 397 (1928).
first order in hydrazine and chloramine, then the rate a t which hydrazine is produced will be the difference between the rate of creation by reaction 2 and destruction by reaction 3. dXzHi/dt =
k2( NHa)(SHzCI)
-
k3( SzH4)(SHzCI) (4)
and the rate a t which chloramine is used up is - dSHzCl/dt = kz( r\"3)(NHzCl) 2kj( NzH4)( NHzCI)
+
(5)
Combining these two equations we get dNzH4 = 1 - (k3NZH4/kl"3)_ - dNHzC1 __I f 2 (kaITi2H,/kzNHs)
which can be integrated, assuming the ammonia concentration to remain constant, over the course of the reaction, using as limits 0 and NzH4 ( t = m ) for the hydrazine and NHzCl ( t = 0) and 0 for thc chloramine. This gives the implicit relation
where y is the yield of hydrazine on hypochlorite and r is the ratio of the final3 ammonia concentration t o initial chloramine concentration. Figure 1 (3) I n t h e derivation of eq. 6 the ammonia concentration is assumed constaut during t h e course of the reaction. This assumption is valid except a t low values of yield and 1. T h e equation then reduces t o
y = (kZ/k3)r or (K2H4)(l =
m)
= (kz/K3)(KHs)
This is t h e same result if one assumes t h a t t h e reaction has reached a steady state with respect to hydrazine in eq. 4
d( KzHd)/dt
0 = kz( XHz)( NHzCI)
-
k3(
NzH4)( NHzCI)
or
i\liH, = ( k z / k 3 ) ( X H 3 ) so if one iises the final ammonia concentration in eq. G , a fit is obtained in the low yield range.
