ELECTROMOTIVE FORCE MEASUREMENTS IN AgS0~-KIY03-K&r04
August, 1963
a t the lower concentrations and may curve a t higher additions. However, curvatures were not surely within experimental error, so no use was made of them. The slopes of the straight lines were read from the graph. According to well known thermodynamic reasoning and to the quasi-lattice theory,8 the limiting slope a t infinite dilution and temperature T may be used to calculate both the association constant for Ag-C1 in this solution and the extra coulombic association energy
where Z is the coordination number and /3 = - A A being the association energy. The reagents in this study are far from those for which the quasi-lattice theory was derived-monovaleiit ions, all of the same TABLE I1 ASSOCIATI~OX COXSTAXTS AND ESERGIES Temperature
650 700 O
2.3 slope = K I = Z(B 2
--
- 1)
R.kglso4 = 0.0006 28 0 27 2
-4 A
(kcal.)
3 81 3 97
RAe2sn4 = 0.002
600" 650" '700"
31.9 24 8 IT 4
3.81 3.62 3 24
~
( 8 ) J . Braunstein, RI. Blander, and R. 31, Lindgren, J . Am. Chem. S o c . , 84, 1529 (1962).
1573
size-so that it is interesting that the curves are of the same type as those found for cases where the assumptions of the theory are followed. Applying the equations of the theory will then give corresponding numbers, which may or may not have theoretical significance. Such an application does, however, give constancy in the calculated association energy, which was one of the tests for the theory. The calculated association constants and energies are given iii Table 11. ,4 coordination number of 4 has been assumed in the calculation of association constants and energies. The coordination iii the liquid is unknown, but in the solid alkali sulfates there are four sulfates about each metal ion, and assumiiig the same or less for the liquid is not unreasonable. The data show the importance of the more dilute solutions, which give a more constant association energy, agreeing better with the predictions of theory. As was shown by Braunstein, Blander, and Lindgren,* more concentratioiis should be studied and an extrapolation to infinite dilution performed. In this first study in sulfate melts a less complete treatment seemed worthwhile. More complete data would also permit evaluation of higher association constants. which would be of much interest. We recognize that fitting our data into the framework of the quasi-lattice theory is not proof of the structure of sulfate melts. However, the fact that agreement is obtained is consistent with the hypothesis of a simple structure for melts with large, nearly spherical anions and small cations arranged more or less as in the solid alkali sulfates.
ELECTROMOTIVE FORCE JIEASUREMEKTS I S THE SYSTEM SILT'ER SITRATEPOTASSIUhI SITRATE-POTASSIUM CHRONATE' AND THEIR C'OMPA4RISOX WITH THE QUASI-LATTICE THEORY BY A. R. ALVilREZ-FUBES2 AKD D. G. HILL Department of Chernzstry, Duke Cniversaty, Durham, 'Y.C Received September 10, 1962 The e.m.f. developed in a concentration cell of AgNO3 in molten KKO, is changed by the addition of K2Cr04 in a manner interpretable by the quasi-lattice theory. The association constants and energies are larger than those for the similar system involving sulfate rather than chromate. Only 1-1 type association may be calculated from the measurements in either system, and the energies are smaller than those found for the monovalent halide ions.
The quasi-lattice description of molten salt solutions as developed by Blander3 and co-workers has been shown to hold for silver ion with several anions, giving a constant "specific bond energy" and an association coiistant for ion pair formation. The postulate of spherical ions of the same diameter and charge was adopted for simplicity, and most of the confirmation has come from studies in which only the size equality restriction has been violated. However, Watt and Blander4 showed that the formalism of the theory could be applied to a (1) Some of the experimental data were rechecked b y D G Hill using the facilitiefi of Oak Ridge National Laboratory, Reactor Cht-mistiy Dim81011, for which kindness we are grateful (2) Uniwrsity of 1ucuman, Tucuman, Irgentina. Fellow of the ConseJo National de Inx estigaciones Cientificas y Tecnicas of Argentina. (3) M Blander, J Phljs C h e m , 63, 1262 (1959). (4) W J Watt and M Blander, a b i d , 64, 729 (1960).
study of sulfate-silver ion association with some success. The present work examines the association of chromate and silver ions. The formalism of the theory applies as well to this case as to the sulfate case and seems to demand next-nearest-neighbor interaction for explanation. Experimental In the experiments, the quantity measured was the e.m .f. of a concentration cell represented by
The solution to which X2Cr04was to be added was maintained in a open Pyrex beaker a t the chosen temperature and a reference electrode inserted in the beaker, making contact through an
1-01. 67
157'4 357 O
x
I?.kgKOa = 1 . 1
4 NO
10-4
x 103 0 0.93 2.14 3.12 4.02 (ppt.)
- A15
RK?(:~O,
0
0.0'127 0058
,0088 ,0108
1?.kg508 = 1.1
-l
