MUTUAL-DIFFVSION COEFFICIENTS IN AgK03-H20
1853
p o u n d ~ it, ~appears ~~ that the electrical properties of organic compounds are amenable to chemical alteration.
the Department of Defense through the Northwestern University Materials Research Center.
Acknowledgment. We wish to thank Dr. D. F, shriver for discussions‘ This work was ported by the Advanced Research Projects Agency of
(7) A. Rembaum, A. M. Hermam, F. E. Stewart, and F. Gutmann, J . Phys. Chem., 73, 513 (1969). (8) J. H. Lupinski, K. D. Kopple, and I. J. Hertz, J . Polym. A!%., 1561 (1967).
Mutual-Diffusion Coefficients at 25” in the System Silver Nitrate-Water1 by John G. Albright and Donald G. Miller” Chemistry Department, Lawrence Livermore Laboratory, Livermore, California 9.4660
(Received June 7, 1971)
Publication costs assisted by Lawrence Livermore Laboratory, U.S.Atom.ic Energy Commission
Volume-fixed mutual diffusion coefficients D, have been determined by the Rayleigh method for aqueous AgN03 at 25’ from 0.05 to 8 mol/l. A laser light source was successfully used to provide sharp fringes at all concentrationseven with bath water in the reference path of the Tiselius cell. Our results are in good agreement with previously reported optical data in the region of overlap (0.1 to 1.5 M)but differ significantly from two discrepant series of diaphragm cell measurements for higher concentrations.
I. Introduction Application2r3 of irreversible thermodynamics to electrolyte solutions has stimulated interest in obtaining activity, conductance, transference number, and diffusion data for electrolyte solutions from which ionic transport coefficients may be calculated. This paper is concerned with diffusion data for the system Agi\‘O3H 2 0 for which t+ has recently become a ~ a i l a b l e . ~ Harned and Hildreth5 obtained good experimental data for this system in the dilute concentration range (0.0030.06 M ) by the restricted-diffusion conductance method, where M is the concentration in moles per liter. Longsworth6n7obtained data in the moderate concentration range (0.1-1.5 M ) by the free-diffusion method with Rayleigh interferometric optics. Data extending to higher concentrations, 4 and 9 M , have been obtained with the diaphragm-cell method by Firth and TyrrelP and by Janz, et aL19respectively. Because of inherent uncertainties in the diaphragm-cell method and substantial inconsiirtencies found in the comparison of the two sets of data, it was decided to measure diffusion coefficientsto near saturation by the free-diffusion method with Rayleigh interferometric optics.
11. Experimental Section Preparation of Solutions. All solutions were prepared gravimetrically. Triply distilled water was used throughout. Baker Analytical reagent grade AgN03 rated at better than 99.9% purity was used without further purification. Sucrose and KC1 were used for
calibration. Sucrose was obtained from the National Bureau of Standards and rated at better than 99.99% pure. The KC1 was from a sample that had been purified by the method of Pinching and Bates. lo Densities for preparation of solutions were taken from the literature.11-16 (1) This work was performed under the auspices of the U. 8. Atomic Energy Commission. (2) D. G. .Miller, J . Phys. Chem., 70, 2639 (1966). (3) D. G. Miller, ibid., 71, 616 (1967). (4) M. J. Pika1 and D. G. Miller, ibid., 74, 1337 (1970). (5) H. S. Harned and C. L. Hildreth, Jr., J . Amer. Chem. Soc., 73, 3292 (1951). (6) L. G. Longsworth in “Structure of Electrolyte Solutions,” W. S. Hamer, Ed., Wiley, New York, N. Y . , 1959, Chapter 12. (7) Data for the concentration range 0.1-1.0 iM are given in ref 6 as part of the results of thermal-diffusion experiments. Further unpublished data for 0.1-1.5 M obtained by Rayleigh free-diffusion method were graciously sent to us in a private communication and are given in the text with Professor Longsworth’s permission. (8) J. G. Firth and H. J. V. Tyrrell, J . Chem. Soc., 2042 (1962). (9) G. J. Janz, G. R. Lakshminarayanan, M. P. Klotzkin, and G. E. Mayer, J . Phys. Chem., 70, 536 (1966). (10) G. D. Pinching and R . G. Bates, J . Res. Nat. Bur. Stand., 37, 311 (1946). (11) G. Jones and J. H. Colvin, J . Amer. Chem. Soc., 6 2 , 338 (1940). (12) A. N. Campbell and R. J. Friesen, Can. J . Chem., 37, 1288 (1959). (13) A. N. Campbell and K . P. Bingh, ibid., 37, 1959 (1959). (14) L. J. Gosting and M . S, Morris, J . Amer. Chem. Soc., 71, 1998 (1949). (15) L. J. Gosting, ibid., 72, 4418 (1950). (16) The densities of the solid reagents used for buoyancy corrections
were from the “Handbook of Chemistry and Physics,” 47th ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1968.
The Journal of Physical Chemistry, Vol. 76, N o . 13, 1972
JOHN G. ALBRIGHT AND DONALD G. MILLER
1854
Apparatus. A Beckman-Spinco Model-H electrophoresis-diff usion apparatus was used. The instrument was set in the diffusion configuration suggested by the operating manual although the modifications suggested by Creeth, et al.,s7 would have been beneficial; other needs of the laboratory restricted modification. A Pyrocell Tiselius electrophoresis cell with bath solution reference path was used. Free-diffusion initial boundaries were formed with a stainless-steel capillary which was plated with gold to prevent reaction with silver nitrate. The bath temperature was measured with a calibratedls mercury in glass calorimeter thermometer. All experiments were performed at 25.00' f 0.01". For the first three AgNOs and first sucrose experiments the standard light source of the instrument, mercury-vapor lamp with filters (A 5461 A), was used. Because of the line width of this source, the fringe patterns became blurred and unreadable for E greater than 0.5 M with water in the reference channel, where E denotes the average concentration in moles per liter. In the third AgN03 experiment at 1.3 M , ethylene glycol was added to the bath water to give fringes of reasonable quality. For the remainder of the experiments the instrument was adapted with a Spectra-Physics Model 115 Neon laser, X 6328 8. The mercury-vapor lamp and condensing lenses were removed, and the laser was placed on the cabinet floor with the beam reflected up and then over to the source slit. To smooth the effect of speckle, the beam was oscillated by passing it through a rotating optical flat. l9 A reasonable intensity distribution in the fringe pattern was obtained by placing a large cylindrical lensz0just behind the source slit to diverge the light passing through the slit. A cylinder lens was placed between the laser and the source slit to narrow the beam and increase the intensity of light at the slit. Although the alignment of the assembly was sensitive to small variations in positions of components, once aligned, it was stable for several days. With this light source, sharp fringes were obtained in all experiments regardless of concentration. The fringe patterns were recorded on Kodak I I a F photographic glass plates. They were read on a Grant microcomparator with card punch output. Fringes obtained with the laser source, however, were more grainy and more difficult to read on the comparator than those from the regular light source. Experimental Procedure. Theories for the study of diffusion processes by the Rayleigh interferometric method are well e s t a b l i ~ h e d . ~ ~In- ~principle ~ the method is absolute where a magnification factor is obtained from a photograph Of a "led placed at the However, because Of position Of the diffusion problems experienced by Creeth, et aZ.,l7it Was decided to calibrate the instrument with systems for which accurately measured diffusion coefficients are available. The Journal of Phusical Chemistry, Vol. 76, N o . IS, lQ72
It was assumed that problems with the optical system for the experiments with silver nitrate in water would be the same for the calibration experiments, and the effect, of these problems on the analysis of data would mostly cancel. All experiments were allowed to equilibrate for 30 min before initiation of the experiment and at least 40 ml of solution was removed during boundary formulation. At the start of each experiment from three to six photographs were taken to obtain the fractional part of a fringe (fpf). After the fringe pattern became resolved, pictures were taken at regular intervals of l / t l until the boundary had broadened to at least one-third of the length of the fringe pattern, where t' is the time starting a t cessation of siphoning. Analysis of Fringe Patterns. The fringe patterns were slightly bowed, a condition that became more pronounced at higher values of e. The early pictures, used for the fpf determination, were aligned on the comparator so that the straight portions of the fringe pattern adjacent to each side of the boundary were parallel to the y axis of the comparator. The fpf was then determined by observing the fractional fringe shift across the boundary. Later pictures, used to determine fringe separations, were placed so that the straight portions of the pattern were parallel to the x axis. The alignment procedure for reading all fringe patterns was such that by starting on a fringe adjacent to the boundary on one side, by shifting the pattern a fpf on they axis and by proceeding to a position on the x axis symmetrically located on the other side of the boundary, the pattern was again aligned on a fringe. With this alignment procedure, displacements in the y direction due to bowing of fringes within the boundary region were nearly the same at equal distances on either side of the starting boundary position. By following the symmetrical pairing procedure outlined by Creethlz4the positions of symmetrical pairs of fringes, X , and XJ+, were measured where J is the total number of fringes and j is an integral fringe number. The value of the quotient of the apparent diffusion co(17) J. M. Creeth, L.
w. Nichol, and P. J. Winzor, J . Phys. Chem.,
62, 1546 (1958).
(18) This thermometer was calibrated against an NBS calibrated platinum resistance thermometer. Two similarly calibrated mercury thermometers were used to check the bath temperature, and good agreement was observed. (19) The significant problem with speckle in the interference pattern is apparently related to the spatial and temporal coherence of the laser source and the narrow aperture of the source slit. Speckle effects are discussed, for example, by B. J. Thompson in "Progress in Optics," Vol. VII, E. Wolf, Ed., North-Holland Publishing CO., Amsterdam, 1969, Chapter I\'. (20) A 2-cm round sample bottle filled with water was used. (21) J. St. L. Philpot and G. H. Cook, Research, 1, 234 (1948). (22) H. Syensson, Acta Chem. Scand., 3, 1170 (1949). (23) L. G . Longsworth, R ~sei. ~ Instrum., . 21, 524 (1950). (24) J. M. Creeth, J. Amer. Chem. SOC.,77, 6428 (1955). I
MUTUAL-DIFFUSION COEFFICIENTS IN AgN03-H20
1855
efficient and the calibration constant p was calculated from the expression24
gible, these diffusion coefficients are relative to the volume fixed frame of reference. Data4 for the activity of AgN03 were numerically differentiated to give 1 m(d In r/dm), and a smooth curve was drawn through the derivatives. Here m is the number of moles per kilogram of solvent. Values a t experimental concentrations were obtained from a least-squares fit of points taken from this smooth curve as a function of c. Values of Dv/(l m(d In r/dm)) have been tabulated in Table I. The previously unpublished data communicated to us by Longsworth' are given in Table I1 with his kind permission.
+
where 2~j-J - erf x j J
+
Here n is the number of fringe pairs in the summation. Every second or every fifth fringe pair was measured and included in the summation subject to the constraints 2x, < 2.0 and X J + - X j > 2.0 mm.25 The values of the terms in the summation were generally within *0.2% of the mean. Except for an early fringe pattern in a few experiments, five or more fringe pairs were included in each summation. The measured time t', the true time t, and the initial time correction At are related by
t
=
t'
+ At
(3)
With eq 3, eq 1 can be written as D'
D'A.t
F + F
=
(;)[! cxJ-?- x,]2 n
3
ZJ-1
- x,
(4)
By fitting the right-hand side of eq 4 linearly to l / t ' by least squares, one obtains D'/P and At from the intercept and slope, respectively. At least five and usually six or more values of D'(F)/@ were included in this evaluation. The initial time corrections were from 10 to 50 sec. To find the value of p, two experiments with sucrose and one experiment with KC1 were performed. In addition, six of the experiments with AgN03 lie within the concentration range where they could be compared with the data of Longsworth. The value for the sucrose diffusion coefficient was taken from ref 14 where a minor temperature adjustment from 24.95 to 25.00' was made by multiplying by the viscosity ratio of water at these two temperatures. The reference value for the diffusion coefficient of KCl was an average of values from ref 26 and 27. The average of KC1 and the two sucrose solutions gave a value of P of 4.175 X with a standard deviation u of 0.006. The average P based on the data of Longsworth alone was 4.186 X with u = 0.012. An overall average value of p = 4.180 X loM5with u = 0.012 was used for the calculation of the diffusion coefficients for all the AgN03-HzO experiments. No significant difference was observed between the P's from the tB.0 different light sources. A calibration table is available in UCRL73183 describing this work.28 Results. In Table I are listed the concentrations and calculated values of the diffusion coefficients for the On the system Agn'03-H20* Since the volume change on mixing may be considered negli-
111. Discussion The consistency of the calibrations indicates an experimental precision of *0.25%. In spite of the bowing of the fringe pattern only small deviations of the values of AX/Ax within each fringe pattern were found experimentally. This is due in part to the alignment procedure. The equal displacement in the y direction at distances along the x axis equally distant from the initial boundary position increased X , and XJ-, so that the difference stayed nearly the same. The calibration data did not reveal a dependence of p on index of refraction and suggest that changes in p at higher concentrations would be small, if even significant. Effects that are first order in Ac will cancel in the analysis procedure used here. 2 4 Consideration of eq 37 and tabulated values of W(x),U(x), and V ( x ) in ref 24 show that error in calculation owing to the secondorder dependence of Ac of the diffusion coefficients will be negligible. Some plots of Ax - Ad" vs. R of the type considered by CreethZ4were made. This type of plot is sensitive to bowing of the fringe pattern since fringes near the center of the pattern are matched with fringes near the outside. The slopes of the curves were small but opposite in sign from that expected in terms of first-order dependence of diffusion coefficients on Ac. A similar probrem was found and discusscd by Creeth, et al. Values of J / A c from experiments with the laser source appeared to lie on a smooth curve with the exception of 5.98 M . The quality of data from that experiment suggested a small error in determination of concentration (
