ACTIVITY COEFFICIENT MEASUREMENTS IN VARIOUS ELECTROLYTES
4479
should be near zero for the formation of CeC2(c),28 ~ o n o v , ~ ~ w reported ho the heat of formation as pertaining and AF102s8 E - 19.5 kcal/mole. to 298°K. Gschneidner2*has reported that the thermodynamic Acknowledgment. We wish to thank S. Langer, J. quantities associated with the reaction H. Norman, and W. Bell of this laboratory, and A. Ce(c) 2C(c) = CeC2(c) (5) Searcy of the University of California a t Berkeley, for their comments concerning this article. We are inare given by debted to ID. D. Jackson of Lawrence Radiation AFO, = 4.32 x 104 - 3 5 . 5 ~ Laboratory, University of California, Livermore, Calif., (6) for permission to use his unpublished data. over the temperature interval of 1853-1893°K. This result appears to be erroneous. If one assumes (28) A. W. Searcy, in “Survey of Progress in Chemistry,” Academic that the AFor value is correct and that the entropy Press Inc., New York, N. Y., 1963. term is near zero,28then a high-temperature heat of (29) K. A. Gschneidner, Jr., “Rare Earth Alloys,” D. Van Nostrand Company, Inc., New York, N. Y., 1961, p 143. formation is obtained that is in agreement with that (30) G. V. Samsonov, “Plenum Press Handbooks of High-Temperafound in this investigation. The apparent error, as ture Materials, No. 2, Properties Index,” Plenum Press, New York, written in eq 6 was unfortunately magnified by SamN. Y., 1964.
+
Activity Coefficient Measurements in Aqueous NaCl-CaCl, and NaCl-MgCl, Electrolytes Using Sodium Amalgam Electrodes
by James N. Butler and Rima H u s h T y w Laboratories, Inc., Waltham, Maasachusetts 09164
(Received June 19, 1967)
The potential of the cell Na(Hg)INa+, M2+,C1-, H201AgC11Ag,where M2+is either Ca2+ or Mg2+, has been measured, and the activity coefficient of NaCl in the mixed electrolyte has been calculated. At ionic strengths from 0.2 to 6 m, Harned’s rule is obeyed within experimental error. The coefficient a12is near zero at high ionic strength, but becomes more negative a t ionic strengths below 2 m; 1x12 is more negative for NaC1-MgC12 than for NaC1-CaC12 at all ionic strengths. The results obtained agree with published activity coefficient measurements made by the isopiestic method and with cation-sensitive glass electrodes.
Introduction Activity coefficients in multicomponent electrolytes containing NaCl and an alkaline earth chloride are of interest in connection with the chemistry Of Sea Water and the chemistry of physiological processes. Recently, a number of investigators have studied the activity coefficients Of NaC1-CaC12 electrolytes by the isopiestic method’ and by the emf method using cation-
sensitive glass electrode^^-^ or stearate membrane electrodes.‘ The NaCl-MgCh system has also been (1) R. A. Robinson and V. E. Bower, J . Res. Natl. Bur. Std., 70A, 313 (lg6@. (2) R. D. Lanier, J . Phys. Chem., 69,3992 (1965). (3) W. F. Fitzgerald and P. C. Mangelsdorf, unpublished data. (4) J. M. T. M. Gieskes, z, phys,&, Chem. (Frankfurt), 50, 78 (1966).
Volume 71, Number 13 December 1967
4480
JAMES N. BUTLERAND RIMAHUSTON
studied using cation-sensitive glass electrodes,2pa and isopiestic studies are in progress.’ Our previous work with sodium amalgam electrodes,sJ’ which has confirmed both isopiestic and glass-electrode measurements in other multicomponent systems, led us to attempt to measure the activity coefficients of NaCl in electrolytes containing CaC12and MgC12by means of the cell Na, Hg/Na+, M2+, C1-, H20/AgCl/Ag where M2+ is either Ca2+ or R4g2+. As we have pointed out before,g the successful thermodynamic operation of an amalgam cell in an electrolyte containing two cations depends on the difference in potentials of the two amalgams and on the relative rates of the electrode reactions, not on the reduction potentials of the pure metals. For the systems discussed in this paper, both the amalgam potentials and reaction rates are favorable for the measurement of Na+ activity using sodium amalgams in the presnece of either Ca2+or Mg2+. The standard potential of the sodium amalgam electrode is - 1.9575 f 0.0005 v at 25” when the reference state is taken to be infinite dilution on the mole fraction scale.9~10 The conditions under which the alkaline earth metal cation will not interfere with the reversible thermodynamic operation of the sodium amalgam electrode can be obtained by an analysis such as that given previously for NaC1-KC1 electrolyte^.^ We can predict in this way that a sodium amalgam electrode will respond reversibly to 0.05 m Na+ in the presence of 1.0 rn IT2+ with an error of less than 0.1 mv, if the exchange currents are of the same magnitude, and the standard potential of the divalent metal amalgam is more negative than -2.025 v. If the exchange current for calcium is smaller, its standard potential need not be so negative. Some measurements have been made of the potential of calcium amalgam electrodes in aqueous so1utions,11112 and from these we have calculated thestandard potential of the amalgam. Representative values are - 1.99211 and 1.996 v.12 The Nernst equation has been tested over the range of 0.0014.1 m Ca2+ concentration, using amalgams containing 0.064.2 mole % ’ Ca. The irreversibility of the calcium amalgam electrode was pointed out by Robinson13 when he showed that the activity coefficients for CaC12obtained by different workers using the amalgam-electrode method disagreed with each other and with those obtained by the isopiestic method and the freezing point depression method. The polarographic half-wave potential of Ca2+ in a tetraalkylammonium-supporting electrolyte is -1.98 v, and the reduction is irre~ersib1e.l~Since The J O U Tof~P h y s h l Chemistry
the calcium-exchange current appears to be much smaller than the sodium-exchange current, the interference of Ca2+ with the sodium amalgam electrode should be much less than we predicted above on the basis of the thermodynamic potentials. No satisfactory measurements have been made of the potential of magnesium amalgams in aqueous solution, because of severe interference from the reduction of water,15 but the polarographic half-wave potential occurs at approximately -2.06 v, and is distinctly irreversible. l4 This implies that the interference of Mg2+with the sodium amalgam electrode would be less than that of Ca2+. Thus, a consideration of the electrochemical properties of the alkaline earth metal amalgams leads to the conclusion that thermodynamic measurements of sodium ion activity can be made with sodium amalgam electrodes in the presence of Ca2+ or Mg2+ provided the Na+/M2+ ratio is not too small. The Mg2+ ion is expected to interfere less than the Ca2+ ion. In this paper we present our experimental results on these systems and show them to be consistent with results obtained by other methods for measuring activity coefficients in these mixed electrolytes.
Experimental Section The experimental method was the same as previously described.8 The difference in emf between two cells, fed from the same amalgam reservoir, was measured. One cell contained the mixed electrolyte; the other contained a reference solution (NaC1-H20) of known activity.l6 Solutions were prepared from reagent grade salts and triple-distilled conductivity water and analyzed for chloride by titration with AgN03. The reproducibility of measurements varied, but under the best conditions, potentials were constant to within (5) E. W.Moore and J. W. Ross, Jr., J . A p p l . Physwl., 20, 1332 (1965). (6) J. Bagg and H. P. Gregor, J . Am. Chem. Soc., 86, 3626 (1964). (7) R. F. Platford, personal communication. (8) J. N. Butler, P. T. Hsu, and J. C. Synnott, J . Phys. Chem., 71, 910 (1967). (9) J. N. Butler, R. Huston, and P. T. Hsu, ibid., 71, 3294 (1967). (10) M. 0.Davies, E. Schwartz, E. Yeager, and F. Hovorka, “The Physical and Chemical Properties of Dilute Alkali Metal Amalgams,” Part 11, Technical Report No. 20, Contract Nonr 2391(00), July 1963,AD 609 294. (11) R.J. Fosbinder, J . Am. Chem. soc., 51, 1345 (1929). (12) C. Drucker and F. Luft, Z . Physik. Chem., 121, 307 (1926). (13) R. A. Robinson, ?‘rune. F u ~ a d a ySOC.,36, 735 (1940). (14) L. Meites, “Polarographic Techniques,” 2nd ed, Interscience Publishers, Inc., New York, N. Y.,1965, pp 618-621. (15) R. P. Beck, Rec. Trav. Chim., 41, 353 (1922). (16) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Buttexworth and Co., Ltd., London, 1959, Chapter 15, Appendixes 8.3 and 8.10.
ACTIVITYCOEFFICIENT MEASUREMENTS IN VARIOUSELECTROLYTES
4481
Table I : Mean Activity Coefficient of NaCl in NaCl-CaC12 Electrolytes at 25" Total ionic strength"
Ionic strength, %N ~ C I ~
0.2392 0.2406 0.2333 0.2282 0.2222
100 78.83 65.67 28.34 6.09
0 8.20 13.81 39.00 74.00
0.1409c 0.1372 0.1368 0.1327 0.1048 (?)
0.1337 0.1334 0.1310 0.1284 0.1015 (?)
0.5822 0.5723 0.5658 0.5637 0.5591 0.5536 0.5556 0.5460
100 78.32 60.62 54.87 42.47 33.60 14.45 6.74
0 7.32 14.90 17.75 24.90 31.30 52.90 70.45
0.1714" 0.1684 0.1670 0.1661 0.1640 0.1624 0.1545 (?) 0.1444 (?)
0.1668 0.1646 0.1635 0 :1627 0.1609 0.1593 0.1517 (?) 0.1420 (?)
1.011 1.033 1.050 1.089 1.103 1.136 1.177 1.224 1.244 1.269
100 93.47 87.26 72.75 68.84 55.29 40.20 22.75 15.14 6.08
0 1.97 3.82 8.54 10.76 16.56 24.86 39.33 50.56 71.52
0.18260 0.1860 0.1842 0.1797 0.1860 0.1818 0.1778 0.1712 (?) 0.1763 (?) 0.1592 (1)
0.1825 0.1857 0.1837 0.1790 0.1852 0.1810 0.1770 0.1706 (?) 0.1759 (?) 0.1590 ( 1 )
3.022 3.026 3.044 3.066 3.067 3.085 3.109 2.988 2.985 2.983
100 95.42 81.46 65.24 64.45 51.17 32.86 19.74 10.24 5.37
0 2.26 7.10 13.54 14.64 21.44 32.96 48.28 65.42 82.32
0.1458c 0.1511 0.1487 0.1434 0.1484 0.1466 0.1346 (?) 0.1342 (?) 0.1264 (?) 0.1233 (?)
0.1465 0.1520 0.1503 0.1458 0.1508 0.1496 0.1383 (?) 0.1338 (?) 0.1259 (?) 0.1226 (?)
6.028 6.128 6.331 6.400 6.450 6.481
100 79.48 36.15 21.83 11.28 5.83
0 8.50 32.18 45.20 63.71 80.80
0.0045c 0.0136 0.0127 0.0028 0.0079 0.0040 (?)
0.0060 0.0058 0.0192 0.0286 0.0220 0.0297 ( 1 )
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