SILVERCEILORIDE SOLUBILITY BY ELECTROMETRIC TITRATION
March, 1935
(CONTRIBUTION FROM THE
LABORATORIES OF THE ROCKEFELLER INSTITUTE
FOR
459
MEDICAL RESEARCH]
The Determination of the Solubility of Silver Chloride by an Electrometric Titration Method
BY ALFREDS. BROW"AND D. A. MACINNES There has been a revived interest in the precise determination of the equilibrium concentrations of slightly soluble salts due to the importance of the results of such measurements in connection with the interionic attraction theory of solutions of electrolytes. For instance, Bronsted and La Mer2demonstrated, by means of measurementson slightly soluble complex salts, the substantial correctness of the limiting law of the DebyeHiickeI theory for electrolytes of various valence types. The method used in their research was the direct analysis of the equilibrium solutions. Solubility measurements have also been made by Popoff and Neuman3 and by Neuman4 by a method which consisted in progressively increasing the concentrations of the components until the first trace of a solid phase appeared. Although the potentiometric method for the determination of the solubilities of slightly soluble salts is responsible for a great part of the published data, it has not been much used in recent years. This is probably due to the fact that the galvanic cells that have been used in the method involve uncertain liquid junction potentials, Theoretical and experimental studies have, however, been made on the method by Lange and Swartz,6Hahn and Klockmann,6and by C a ~ a n a g h . ~ It is the purpose of this paper to describe a modification of the potentiometric method in which the uncertainty due to the liquid junction is reduced to a minimum. The procedure adopted, and applied to the determination of the solubility of silver chloride in certain salt soh: tions, was to set up concentration cells of the type
I
Ag, AgC1, AgNOs, KNOs AgNOa, KNOa, AgC1, Ag (A) Cl cs c4
c,
The solution on one side of the liquid junction was kept constant and, together with the electrode, served as a reference half cell, whereas the composition of the solution in the other half cell was progressively changed by the addition of
increments of potassium chloride solution. This was, of course, an electrometric titration. Since the solutions in the two half cells initially had the same composition, and the titration changed this composition but little, the liquid junction started with a zero potential and took a series of low values (which could be readily estimated) as the titration progressed.
Theory During the titration of silver nitrate with potassium chloride under the condition of constant ionic strength we have the relation [Ag+] [el-]= L
(1)
in which the brackets represent concentrations and L the stoichiometric solubility product. The condition of electrical neutrality requires [&+I [K+l = [Cl-I 4- [Nos-] (2) Since [K+ - NOa-] is a measure of the extent of titration we have, using equation (2)
+
[el-] - [Ag+] = (n
- ne)P/'V
(3)
in which n is the number of increments of potassium chloride solution each containing p equivalents, V the constant volume of solution to which they are added, and ne is the value of n at the equivalent point. Since the reference electrode contained the initial solution and the liquid junction potential is negligible (as will be shown later), the potential of a cell of type A is
in which the subscript i refers to the reference electrode, and y = [Ag+]/[Ag+Ii. Since n = 0 at the beginning of the titration [Cl-li
- [Ag+]i = - P+.P/V
(5)
The data obtained during a titration may be expressed as a linear equation by eliminating [CY-]between (1) and (3), expressing [Ag+] by means of y[Ag+Ii, introducing equation (5), and solving for n/(l - y). This yields
(1) National Research Fellow. (2) Br6nsted and La Mor, TAXS JOUXNAL, 46,555 (1924). (3) Popoff and Neuman, J . Phys. Chem., $4, 1853 (1930). (4) Neuman, THISJOURNAL, M, 2195 (1932). (5) Lange aud Schwartz, 2.physik. Chcm., 129, 111 (1927). (6) aahn and Klockmaan, ibid., 146, 873 (1930). (7) Cavanaah. .I Chem Soc., 843.855 (1928)
Thus if the theory of the operation of the cell A is correct, a plot of n / ( l - y) against (1 y)/y should be a straight line with an intercept at ne.
+
460
ALF~ED S. kRoW AND D. A. MACINNES
The value of the solubility,
