M. H. LIETZKEAND R. W. STOUGHTON
662
determined only the ratio E H ~ O : E D ~ Otheir , value for E D ~ O depends on their EH,O data. A plot of this ratio, shown in Figure 7 , shows their data for DzO will be in good agreement with our own if our E H ~ Oare used. This ratio, using E D ~ Oof Malmbergg and EH*O of Malmberg and M a r y ~ t t differs ,~ by a small but significant amount (0.1%) from our ratio. There appears to be a consistent difference of about 0.15 unit in E between our data for D2O and H 2 0 and those measured a t the National Bureau of Standards, with a difference in the
temperature coefficient for HzO that is difficult to explain. Acknowledgment. The authors are indebted to Professor R. H. Cole of Brown University for the use of his laboratory for some of these measurements and for his interest and suggestions during the course of the work. This work was supported by the U. S. Atomic Energy Commission under Contract AT-(30-1)2727 and by the Office of Saline Water, U. S. Department of the Interior, under Contract No. 14-01-0001-359.
Electromotive Force Studies in Aqueous Solutions at Elevated Temperatures. VIII. The Thermodynamic Properties of Hydrochloric Acid-Lanthanum Chloride Mixtures1
by M. H.Lietzke and R. W. Stoughton Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
(Received September 19, 1966)
The activity coefficient of HC1 in HC1-LaC13 mixtures has been studied t o 175". At constant temperature and ionic strength, the logarithm of the activity coefficient of HCl in the mixtures varies linearly with the ionic strength fraction of L a c 4 in conformity with Harned's rule. The activity coefficient of L a c 4 in the mixtures was calculated by using the parameters describing the variation of the logarithm of the activity coefficient of HC1 in the mixtures and those for the variation of the activity coefficient of LaC13 with ionic strength in pure L a c 4 solutions at 25".
Previous papers in this series have described our investigations into the thermodynamic properties of HBr-KBr,2 HC1-NaC1, and HC1-BaClZ4mixtures over a wide range of temperature. The present study represents an extension of this work to a mixture containing a salt of the 3-1 valence type. Only a few such mixtures have been previously investigated, and these only at 25". Randall and Breckenridges observed that in mixtures of this type a plot of the logarithm of the activity coefficient of the acid in mixtures a t constant ionic strength was a nearly linear function The Journal of Physical Chemistry
of the ratio of the mean molality of the acid to the molality of pure acid a t the same ionic strength. 1Mason and Kellam6 found that a t a total ionic strength (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) M. H. Lieteke and R. W. Stoughton, J. Phys. Chem., 67, 2573 (1963). (3) M. H. Lietzke and R. W. Stoughton, ibid., 69,2395 (1965). (4) M. H. Lieteke and R. W. Stoughton, ibid., 70, 756 (1966). (5) M. Randall and G. F. Breckenridge, J . Am. Chem. Soc., 49, 1435 (1927).
663
ELECTROMOTIVE FORCE STUDIESIN AQUEOUS SOLUTIONS
of 1.0, a plot of the logarithm of the activity coefficient of HC1 us. the molality of HCl was linear in the system HC1-CeC13. Harned and Gary' observed the same behavior in the HC1-A1C13 system. I n the present study emf measurements of the cell
values13 of the standard potential, Eo, of the Ag, AgCl electrode, except that 0.2223 v was used instead of 0.2220 v a t 25". I n eq 1, m2 and m3 are the
Pt-H2(p)lHCl(m2), LaC13(m3)(AgC1-Ag have been combined with values of the activity coefficient of LaC138 to compute the thermodynamic properties of both HCl and Lac& in HC1-LaC13 mixtures.
Experimental Section The high-temperature, high-pressure experimental apparatus and the preparation of electrodes and solutions were the same as described pre~iously.9~~0 Since this apparatus was built for moderate accuracy over a wide temperature range rather than for maximum accuracy a t low temperatures, the accuracy in the latter range is not as great as that claimed by other investigators." The emf measurements were carried out in the temperature range 2 5 1 7 5 " in solutions of total ionic strength 0.5 and 1.0 in which the ratio of HC1 to L a c 4 was varied. The emf values taken at the same temperature were reproducible to ca. kO.5 mv. No drift of emf with time was observed. Results and Discussion In treating the results, the hydrogen pressure was calculated by subtracting the vapor pressure of the solution from the observed total pressure, while the vapor pressure of the solution was obtained by taking the vapor pressure of water at the temperature of measurement from the steam tables12 and correcting for the presence of LaC13 and HCl in solution by Raoult's law. No correction was made for the amount of HC1 in the vapor phase since it was previously found unnecessary to do SO below 250" in pure HC1 solution.9 Each emf value was corrected to 1.00 atm of hydrogen pressure by subtracting (RT/25) In fH2, where the hydrogen fugacity, fHz,was taken equal to the hydrogen pressure. The solubility of -4gC1 was neglected and the ionic strength was taken to be equal to m H C l 6rn~~~ The corrected emf values, E , at each ionic strength were dotted as a function of temperature and the values corrected to the round values of the temperat u p , 25, 60, 90, 125, 150, and 175". The tempera-
+
from the Of measurement was never more than corresponding- round temperature. These corrected values are given in Table I. The activity coefficient, yhI of HC1 at each temperature and set Of concentrations in the mixtures mas evaluated by using the Nernst equation and previous 'lire
I
molalities of HC1 and LaCl3, respectively, while T is the absolute temperature, R is the gas constant, and 5 is the faraday. A plot of In yi us. ionic strength fraction of LaC13 was made at each temperature and at the total ionic strengths, 0.5 and 1.0. Also included in these plots were the values for pure HCl13 at all temperatures. I n all cases the plots were linear within experimental error in conformity with Harned's rule. Expressions for yrt of HCZ and LaCE3 in the Mixtures. The activity coefficients of HC1 was smoothed as to HC1 and LaCL concentrations and temperature and those of LaC13 were evaluated as follows. I n accordance with the treatment in the previous the excess free energy of the solution Gel i.e., excess over the molality and Debye-Huckel terms, was expressed as
+
_ Ge - 2n2 In yZe 4n3 In y3e = RT
where n represents the numbers of moles of each solute, w is the number of kilograms of water, and the sums are taken over each solute i, j , IC = 2 (for HCl) to 3 (for LaCl3). Bti and C,, are interaction coefficients to be determined from the data. Then for the HC1 2 In
=
E=
b
G"
(E) = 4CB2m i
+ 6CC2,pn,mj
(3)
l(6) ~ C. . M. Mason and D. B. Kellam, J. Phys. Chem., 38, 689 (1934).
(7) H. 8. Harned and R. Gary, J. Am. Chem. Soc., 77, 4696 (1955). (8) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold Publishing Corp., New Yorkt N. Y.1 1958, P 566. (9) R. 5. Greeley, w. T.Smith, Jr., R. W. Stoughton, and A I . H. Lietzke, J . Phys. Chem., 64, 652 (1960). (10) M. B. Towns, R. S. Greeley, and XI. H. Lietzke, ibid., 64, 1861 (1960). (11) H. S. Harned and B. B . Owen, ibid., 64,456 (1960). (12) "VDI-Wasserdampftafeln," 4th ed, E. Schmitt, Ed., SpringerVerlag, Berlin, 1956. (13) M. H. Lietzke and R. W. Stoughton, J . Phys. Chem., 68, 3043 (1964).
Volume 71,Number 8 February 1967
M. H. LIETZKEAND R. W. STOUGHTON
664
Table I: Values of t'he Emf in Volts for the Cell, Pt-H,(p)lHCl(mz), LaC13(ms)lAgC1-Ag, and Deviations" of the Emf Values Calculated from Smoothed Activity Coefficients t,
oc
mz
ma
25
60
90
125
150
175
0.3766
0.0217
0.2818 0
0.2648 0
0.2466 0
0.2213 -25
0.2018 -4
0.1790 +5
0.2520
0.0418
0.2996 -1
0.2830 0
0.2644 0
0.2400 -5
0.2205 -23
0.1995 -6
0.1242
0.0630
0.3243 0
0.3104 0
0.2964 -5
0.2766 22
+
0.2573 17
+
0.2344 -3
0.7661
0.0417
0.2479 0
0.2247 0
0.2038 0
0.1735 0
0.1519 - 18
0.1311 19
0.5056
0.0912
0.2627 -1
0.2441 -1
0.2237 -8
0.1979 $4
0.1779 20
+
+ 0.1543 +16
0.2743 0
0.2549 $4
0.2293 -5
0.2098 -3
0.1865 -22
0.2541
0.1254
0.2890 +2
" The deviations are given below each emf as observed emf values less the values calculated from smoothed activity coefficients. Thus, a positive deviation indicates that the emf reported here is algebraically larger. while for the Lac13
Hence
+
be Sp"'2/lil(l 1 . 5 4 1 ) for the HC1 and 3Sp'".
