2079
NOTES
Dec., 1959 cised to eliminate all bubbles. The glass plate then was clamped to the flanged surface. The salt is introduced as follows : (1) The cell is turned upside down to position I (Fig. 1) with the salt cup D aligned with the filling tube F. (2) Salt solution is introduced into D through F and all bubbles forced out with a sharpened rod. (3) The salt cup is turned to position 11, the lead wires are attached and the cell in the upright position I11 is placed in the Lucite box which then is submerged in the water-bath. (4) When the system has come t o temperature equilibrium after 48 hours, the salt cup is t,urned to position IV for a suitable time and then turned to position 111. With 0.15 M potassium chloride in D, it took 70 minutes for sufficient salt to diffuse into the cell to yield a final concentration of 0.00255 M.
Following the former procedure with Lucite cells, five conductance measurements were made each day at approximately two hour intervals. The ratio of the cell constants a t the bottom pair ~ , determined and top pair of electrodes, k ~ / k was before the diffusion experiment was made. If then K B and KT are the specific conductances between the bottom and top electrodes, respectively, a t a time, t ( k ~ Ks ~ T K T=) Ae-l/T
and in
(k
GLASS CELL =!===?A
Fillinp Sequence
D@QD
(1)
KB
- xT)
=
-
+ constant
Fig. 1.-A
where (3)
3 is the diffusion coefficient of the salt and a is the ~ evaludepth of the cell. The quantity l / was ated by the usual method as described by Harned and Nuttall.’ Table I contains the results obtained over a five day period. The first column are the values of the diffusion coefficient of potassium chloride from measurements on the first and second days, the second column values obtained for the second to third day and so on.
F
F II
I
111
IV
glass cell for determining diffusion coefficients.
This result proves that a glass cell of the type described can be used t,o determine diffusion coefficients of salts in dilute solutions. However, attempts to determine the diffusion coefficient of the more mobile electrolyte, hydrochloric acid, in this cell were not successful. This contribution was supported in part by The Atomic Energy Commission under Contract AT (30-1) 1375. (2) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd Edition, Reinhold Publ. Corp., New York, N. Y., 1958,pp. 119-122, 143-144.
THE ACTIVITY COEFFICIENT OF HYDRO-
TABLE I CHLORIC ACID I N THORIUM CHLORIDE DETERMINATION OF THE DIFFUSIOKCOEFFICIENT OF SOLUTIONS AT 25’ POTASSIUM CHLORIDE AT 25’ BY THE GLASS CONDUCTANCE BY HERBERT S. HARNED A N D ALANB. GANCY CELL 1-2 Values are determined from measurements inade on first and second days, 2-3 from second to third day conductances, etc.
Contribution N o . 1660 f r o m the Department of Chemistry o f Yale University, New Haven, Conn. Received June 8 5 , 1969
c = 0.00255 mole/l., a = 8.214 cm., k ~ / = k 0.93 ~
From measurements of the electromotive force of the cell
1-2
2-3
D x 105
3-4
1,908 1 948 1,941 1.910 1,942 1,953 1.913 1.944 1.956 1,903 1.955 1.953 1.915 1.939 1.956 a Mean for three day runs from second to B = 1.946 X theoretical = 1.949 X 10-6.
4-50
1.943 1.942 1,934 1.950 1.942 fifth day:
It is apparent from these results that the diffusion was steady after the second day of the run. The mean result of the last three days is 1.946 X a t 0.00255 molar concentration which agrees well with the value of 1.949 X which was obtained by means of the theory of Onsager and F~oss.~
IT2 IHCl(lnl), ThClr(nz,)l AgC1-Ag
a t 25”, the activity coefficient of the acid has been computed by the equation E = EO
- 0.1183 log ~ * Z / n z l ( m i+ 4mz)
(1)
The results were obtained a t constant total ionic strengths p = (ml lornz) of 0.1, 0.5, 1, 3 and 5 . The experimental electromotive forces and the derived activity coefficientsare given in Table I. The solutions were prepared by weight from carefully analyzed thorium chloride and hydrochloric acid solutions. Uncrystallized thorium chloride by “Lindsay, Code 130” was used. Although no difficulty was encountered in reproducing the electromotive forces, the results should
+
NOTEE.
2080 TABLE I
ELECTROMOTIVE FORCES OF THE CELLH2/HC1 ( m J , ThC14 (mz)/AgCl-Ag AND ACTIVITYCOEFFICIENTS OF HYDROCHLORIC ACID I N SOLUTIONS OF VARIOUSTOTALIONIC STRENGTHS p ’
rnl
= 0.1 E
p
‘YECI
mi
0.5 .3 .1 .01
= 0.5 E
YECl
0.1 .07 .05 .03 .01
0.35261 .36707 .38053 .39978 .44039
0.795 ,792
mi
E
YHCl
ml
E
’YHCI
1.0 .7 .5
0.23321 .24989 .26455
0.811 .774 .745
0.3 .1 .01
0.28572 .32909 .41581
0.700 ,586 * 365
E
YRCI
mi
0.15183 .15779 .16440 .17166 .18000 .18956 .20086 .21529 .23370 .26433 .34054
1.318 1.275 1.229 1.182 1.128 1.069 1.003 0.919 .831 ,688 .283
mi
3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9 .6 .3 .1
.781
.761 .672
...
p - 1
p = 3
5.0 4.5 4.0 3.5 3.0 2.5 2 0 1.5 10 0.5 0.2
0.27227 ,29517 .33804 .43319
...
0.759 .720 .655
.365
...
r = 6
E
’YHC I
0.09519 .lo427 .11434 .12469 .13613 .14879 ,16261 .17995 .20202 ,23325 ,30179
2.380 2.167 1.953 I . 769 1.598 1.427 1.266 1.096 0.923 .756 ,328
Vol. 63
temperature dependence of the distribution coefficient (specifically, the slope of a log k os. 1/T plot, where T is the absolute temperature) of the minority component of the solid solutions has been interpreted to give heats of solid solution of the minority component in alloy systems for which the major component is germanium or silicon. I n certain cases emphasis has been placed on the form of the temperature dependence of k near the melting point of the major component. Recently, for example, Weiser6 has suggested that such data near the melting points of Ge or Si could be used to obtain heats and entropies of solution in the very dilute solution range and would constitute a sensitive test of his theory on the magnitude of k. I n interpreting distribution coefficient data in this manner it has been assumed that the effects of nonideal solution behavior in the liquid phase can be neglected. Recently, however, it has been shown’ that in certain systems the non-ideality of the liquid phase appears to play a major role in determining the temperature dependence of the distribution coefficient. In this note we shall consider in greater detail the effects due to non-ideal solution behavior in both solid and liquid phases. From these considerations it will be evident that the interpretation of distribution Coefficient data is complex and that serious errors can be made in calculating heats of solution from such data. General Equation for the Temperature Dependence of k.-From the usual definitions of activity coefficients, namely
be regarded as preliminary until repeated with other preparations of thorium chloride. Plots of log y ” 1 versus ml, the acid concentrap! = RT In -Ad (1) tion at these constant stoichiometrical ionic pi piL RT In rkzt (2) strengths, all tend to decrease rapidly as the acid and the fact that, a t equilibrium between solid and concentration decreases. This behavior indicates liquid phases, pi = p i it follows that the distrithat the “true” ionic concentration product, bution coefficient k can be written ~ H ~ C is I ,reduced.l This behavior is consistent k E z!/zg = (r:/ri) e x p ( A F j / R T ) (3) with recent investigations of thorium chloride solutions.2.’ I n these equations R is the gas constant, T is the This contribution was sumorted in Dart bv the absolute temperature while xi and &, $ and Atomic Energy Commissio;l^ under Cbntraci AT yi, and pi and pf are the atom fractions, activity (30-1) 1375. coefficients and chemical potentials of component (1) See Fig. (14-13-21,p. 631, H.S. Harned and B. B. Owen, “The 2 (the minor component of the solid solution) in Physical Chemistry of Electrolytic Solutions,” 3rd Edition, Reinhold the solidus and liquidus alloys, respectively. The Publ. Corp., New York, N. Y., 1957. quantities pis and pgL are the chemical potentials (2) W. C. Waggener and R. W. Stoughton, THIa JOURNAL, 66, 1 (1952). of pure solid and liquid component 2 while AF: is (3) K. A. Kraus and R. W. Holmberg, ibid., 68, 325 (1954). the free energy of fusion of component 2, equal to (piL - pi:). Equation 3 is a modified form of an equation developed previously by Thurmond and Struthers.2 HEATS OF SOLUTION FROM THE Since we are concerned here with the interpreTEMPERATURE DEPENDENCE OF tation of the slope of a log k us. 1/T plot we may T H E DISTRIBUTION COEFFICIENT1 write the relation i=
BYF. A. TRUMBORE AND C. D. THURMOND Bell Telephone Laboratories, Incorporalrd, Murray H i l l , Now Jersey Recdived June 69, 1969
The temperature dependence of the distribution coefficient k of a given component of a binary alloy system is determined by the relat,ive amounts of that component in the alloys lying along the solidus and liquidus curves. In recent years, a number of papers have appeared2-+in which the (1) Presented at the American Chemical Society Meeting, Boston, Massachusetts, April 7, 1959.
C
1
i l
+ +
d In IC
d
.
T =
(4) _ .
(2) C. D. Thurmond and J. D. Struthers, THISJOURNAL, 67, 831 (1953). (3) F. Van der MaRsen and J. A. Brenkman, Philip8 Research Repls., 9, 225 (1954). (4) R. N. Hall, J . Phue. Chem. Solids 9, 03 (1957).
*
