426
CARL WAQNER AND PAUL HANTELMANN
T H E FREEZING-POINT DIAGRAM OF T H E SYSTEM SILVER CHLORIDE-CADMIUM CHLORIDE' CARL WAGNER' A N D PAUL HANTELMANN
Eduard Zintl Institut fur Anorganische und Physzkalzsche Chemie der Technischen Hochschule, Darmstadt, Germany Received March 7, 1949 INTRODUCTION
According to measurements of the electrical conductivity of solid mixtures consisting of silver chloride and cadmium chloride (l), solid silver chloride dissolves considerable quantities of cadmium chloride, amounting to a t least 10 mole per cent at 350°C. In figure 1 is shown a model of the lattice involving
0 CI'
Ag'
CI'
CI-
A$
CI'
Ad
Cd" CI-
Ag'
ti-
CI- Ag* CI'
Age
FIG.1. Silver chloride with cadmium chloride cation vacancies, which are indicated by squares. To supplement the conclusions drawn from conductivity measurements, the freezing-point diagram has been investigated with the aid of thermal analysis. EXPERIMENTAL
Each sample amounted to 40 g. Temperatures were determined with a platinum and platinum-rhodium thermocouple, the thermoelectric force of which was measured with the aid of a potentiometer and a reflecting galvanometer. Results are shown in figure 2. Temperatures a t the end of crystallization for mixtures up to 20 mole per cent of cadmium chloride are omitted in figure 2, because the intervals between the beginning and the end of the solidification were very narrow. A constant temperature over a longer period of time, corresponding to eutectic crystallization, was obtained only with mixtures containing 30 mole per cent or more of cadmium chloride. coNcLusIoKs
The maximum of the liquidus curve a t about 10 mole per cent is remarkable. In general, such a maximum indicates the occurrence of a compound. Here, however, the other characteristics' of the occurrence of a compound, such as two different eutectic temperatures at both sides, are missing. According to Konowalow a maximum of the liquidus curve can also occur in the case of equilibrium GS-ORD-FTBliss Texas S o . 68. Present address: Department of Metallurgy, Massachusetts Institute of Technology, Camhridge, Masshachusetts. 1
2
SYSTEM SILVER CHLORIDE-CADMIUM
427
CHLORIDE
between a liquid and a solid solution if the equilibrium composition of the liquid phase is the same as that of the solid phase. Accordingly the solidus curve is drawn in figure 2. From inspection of figure 2 it follows that a t low concentrations of cadmium chloride the partition ratio of cadmium chloride between liquid and solid phases is less than unity, whereas a t higher concentrations this ratio becomes greater than unity. This increase of the partition ratio with increasing concentration of cadmium chloride is a necessary consequence of the logical application of the law
ApCl
-
cd c1*
Nw CI,
FIG.2. Freezing-point diagram of the system silver chloride-cadmium chloride. 0 , beginning of crystallization; X , end of crystallization. I , mixed crystals of silver chloride and cadmium chloride; 11, solid cadmium chloride.
of mass act,ion. The transition of cadmium chloride from the liquid into the solid solution may be described by the stoichiometric equation
+ 2C1-(1)
Cdz+(l)
=
Cd2+(cr)
+ h(Ag+) + 2Cl-(cr)
(1)
where the suffix (1) indicates ions in the liquid phase, h(Ag+) is a cation vacancy in the solid phase, and the suffix (cr) indicates ions in normal lattice positions for cations and anions, respectively. Disregarding the concentrations of chloride ions in either phase, we have the equilibrium condition N C d Z t(1)/[NCd2f(or)
x
Nh(Ap+)l
=
K
(2)
where the symbol A’ represents the concentration of the respective constituent in terms of mole fractions and K is a constant. Under the conditions in question, the concentration of cadmium ions in the solid phase practically equals the concentration of cation vacanies, since one molecule of cadmium chloride contains only one cation for each two anions and interstitial cations can be disregarded. Thus, we obtain the modified form of the partition law N c d 2 + 0 ) / N 6 d 2 + ( ~ r )=
K
(3)
428
CARL WAGiYER AiYD PAUL HANTELMANX
analogous to the relation for the partition of acetic acid between benzene and water according to the reaction (HCzH302)2(benzene)= 2HC2H302(aq)
or the dissolution of hydrogen in palladium: Hp(gas) = 2H(in palladium) The dissociation equilibria of the latter reactions correspond t o the coupled occurrence of one cadmium ion and one cation vacancy in the solid phase. Upon transformation of equation 3, it follows that: NcdZ+(l)/NcdZ+(or)
=
K X
NcdZ+(cr)
(4)
This equation shows that the partition ratio should increase with increasing concentration of cadmium chloride. It must be emphasized that the introduction of the ideal law of mass action does not yield results which are quantitatively correct, for large deviations from the relations for ideal solutions occur, as shown recently by Wagner and Zimens (2). Consequently, it is not possible to draw quantitative conclusions from the concentration corresponding to the maximum of the liquidus curve. The modified form of the partition law given in equation 3 may possibly be confirmed in other systems such as potassium chloride-strontium chloride, where the degree of disorder of the pure solvent is very low and only small concentrations of the solute occur in the solid phase. The inconstancy of the usual partition law is to be borne in mind when mixed crystals are drawn from liquid mixtures of different concentrations. If, however, the concentration of an additive in the solid phase is small in comparison with the degree of disorder of the solvent, the concentration of cation vacancies represents a constant value and then the conventional partition law is valid. SUMMARY
The freezing-point diagram of the system silver chloride-cadmium chloride has been investigated. At about 10 mole per cent of cadmium chloride there is a flat maximum corresponding to equal composition of the liquid and the solid solution of cadmium chloride in silver chloride. I t is shown that, according to the ideal law of mass action, the cadmium chloride concentration in the liquid phase should vary as the square of the cadmium chloride concentration in the solid phase insofar as the number of cadmium ions in the solid phase equals the number of cation vacancies. REFERENCES (1) KOCH,E., A X D WAGNER,C . : Z. physik. Chem. B38,295 (1937). (2) WAGNER,C , W D ZIMEKS, K . E . . Acta Chem. Scand. 1, 539 (104i)
