Brigewe Ungerer,' Raul Jurio, and Raul J. Manuele Universidad Nacional d e La Plata La Plata, Argentina
Potentiometric Determination of the "Operational" K, of Ag(CN),Ag
In a previous report2 we have given the results of the determination of the operational solubility product of silver iodide by means of a potentiometric technique in the way of conventional titrations. Now, we shall consider the determination of the solubility product of silver dicyanoargentate by titration with silver nitrate of a mixture of cyanide and iodide, making use of the well-established technique by Liehig-DenigBs. The experiment will be included in a laboratory course on electroanalytical methods. The potentiometric titration of a mixture of cyanide and iodide in the presence of a silver indicating electrode proceeds stepwise. First, the reaction through which dicyanoargentate is formed takes place; then, iodide precipitates; and finally, d v e r dicyanoargentate separates. When the solutions contain known amounts of iodide, a single titration furnishes necessary data for calculating the titer of the silver nitrate and potassium cyanide solutions. The same titrations gives, besides, information to verify the amount of cyanide through the silver dicyanoargentate precipitation step. The titration has, in consequence, a "triple effect." The potentiometric titration curve exhibits sharply the three steps. The figure is one of the experimental curves. The solubility product of the silver dicyanoargentate is calculated making use of the potentials graphically defined by the two intersection points of the straight segments at the final and initial parts of the successive steps in the titration curve, in addition to the iodide and dicyanoargentate concentration in the solution and the solubility product of silver iodide.
The silver nitrate solution is added by increments of 0.5 ml, waiting for the potential to stabilize. Near the equivalent points titrant is added dropwise. Titrations are made a t room temperature: 20 & 0.5"C.
Titration Curve
Point 1 on the titration curve (see figure) indicates potential El,corresponding to the silver ion activity in equilibrium with the iodide ion activity a t the concentration in the solution for that titration step. Point 2 corresponds to potential E2, representing the silver ion activity in equilibrium with the dicyanoargentate complex ion at the concentration in the solution for that titration stage. Volumes Vl, V2, and Va of silver nitrate solution, correepouding to El, E2, and E3, represent the cum-
Experimental Conditions Titrations are conducted on a solution containing 10.00 ml of 0.1000 M potassium iodide, 10.00 ml of an approximately 0.1 M potassium cyanide solution, 20.0 ml of 0.250 M potassium nitrate and 60.0 ml of recently boiled, cold, bidistilled water. Approximately 0.1000 M silver nitrate solution is used as titrant. Oxygen is swept from the solution with a smooth nitrogen stream and carbonates are eliminated by previously treating the potassium cyanide solution with enough barium nitrate to attain a 0.001 M barium ion concentration. Every reagent is analytical grade. The silver electrode employed, its pretreatment, the cell and titration vessel are those already described by the authors in a previous paperBdealing with the determination of the operational solubility product of silver iodide. Potentials were measured with a, 7041 Leeds & Northrup potentiometer. pH values were established during titrations making use of a. Metrohm combined glass electrode (aell) and an E 396 Metrohm potentiometer. Present address: Institute Central de Quimiea, Universidad de Cancepci6n, Republiea. de Chile. R ,MANUELE 11. J., J. CHEM.EDUC., J u ~ f oR. , L.,U N G ~ R ER., 48,122 (1971).
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Titrotion curve for the potentiometric titrotion of and iodide with silver nitrate.
0
mixture of cyonide
mulative stoichiometries for the successive reactiom of formation of dicyanoargentate, silver iodide, and the silver dicyanoargentate, respectively. Theoretically, V 1 should be equal to Va minus V 2 . Nevertheless, i t has been found that the volume difference between Va and V2is larger than V 1by 0.040.06 ml. Volume defined in the third step (precipitation of silver dicyanoargentate) is used to calculate the concentration of dicyanoargentate. Table 1 shows data from five titrations.
Table 1. Experiment
D a b for Five Titrations
I
~-
11
~
Composition of the solution
111
V
IV
~
10.00 ml OlOOO AI K I 10.00 m l O . 1 M K C N 2 0 . 0 ml 0.250.M KNO, 6 0 . 0 ml bidistilled water
Ternnsrature: 20 =t 05'C
Calculations
The electromotive forces of t h e titration cell are related to thc silver ion activity under the circumstances of El and E2 values. Activity coefficients are calculated with the Debye-Hiickel limit equation, log f = -AZ2dG/l Ba& Thc iodide ion concentration at El is deduced from the composition of the solution being titrated, after correcting bccause of dilution, and the concentration of the dicyanoargentate complcx ion at Ez, from the volumetric stoichiometry. Thc equation to calculate the solubility product of the silver dicyanoargcntate is deduced through the following relations
+
EL E%
=
=
+ +
E ~ C E EA.' E ~ C E EA.'
+ 0.0382 log + Ej, + 0.0582 log a*., + Ej2
by substituting thc activities by their expressions as a function of concentrations, and substracting El from E2, thc final cquation for the ~olubilityproduct constant of silver dicyanoargentate is obtained log K,,Ag(CN)2Ag
=
(EZ)
0.0382
- log 11-If, $
Ionic strength of the solution a t points 1 and 2, and activity corfficients a~sociatedwith iodide and dicyanoargcntatr ions arc ul = 0.0662, log f i = -0.1045, us = 0.0605 andlog f 2 = -0.1008, respectively. Concentrations arc defined by the exp~essions
Table 2 collects valucs for the equation terms from five experiments, data of which may be found under Tablc 1, together with the values calculated for the pK of the silvcr dicyanoargcntate. Discussion
The solubility product value obtained is expressed in terms of the activity concept of the dicyanoargentate and silver ions at ionic strength 0 . 0 6 0 5 , The compo~itionof the prccipitate is expressed as silver dicyanoargentatc according to thc species from which it is derived Ag(CNh-
+ AgC
-
Table 2.
-. Experiment
( E L - %)/0.0582 log I ] / I logI.&~h?-lh lox K d d pKAg(CN)?Ag
I -5.2062 -2.1240 -2.4931 -16.0930 11.26
Calculated Results ~
I1 -5.2062 -2.1240 -24922 -16.0930 11.25
111 -5.1890 -2.1239 -2.4904 -16.0930 11.27
V
IV -5.1890 -2.1240 -2.4912 -16.0930 11.27
-5.1890 -2.1240 -2.4912 -16.0930 11.27
of the dicyanoargentate complex ion is approximately lo2' and, thus, it may be legitimately considered that the concentration of the complex ion is the analytical conccntratiou. The method applied lies on the value of the silver iodide operational product solubility constant determined at ionic strength 0.060 ( 1 ) and on the certitude about the response of the silver electrode according to the Nernst stoichiometry. Potential defined by point 2 in the titration curve is in accord with the theoretical value calculated from the concurrent activity of dicyanoargentate ion for the silver electrode in equilibrium. pH changes during the titrations as shown by the pH-curve in the figure, due to the reaction
Under the conditions of concentrations considered, and using potassium iodide concentrations approximately 0.01 M, reaction is almost complete when silver iodide begins to precipitate and reaches to an end with this precipitation. This may be deduced from the small change in pH observed simultaneously with the pAg jump at the equivalent point corresponding to iodide. The systematic error which this circumstance would i~ltroducein titrations is corrected by computing the difference between V8and V 2as the volume equivalent to cyanide, and 2Vz - Va '3 that equivalent to iodide. Constancy of the operational solubility product might be proved by working with total different cyanide-iodide ratios at the same ionic strength and temperature. Experiments on this line, making use of cyanide solutions twice as concentrated, give the mean value 4.3 X 10-12. Results obtained, gathered in Table 2, for the operational solubility product constant of silver dicyanoargentate, are quite close to those registered in the literature. Gauguin3 gives a value of 3.99 X for that constant. and Assam and Shirni,&5.83 X
Ag(CN)*Ag
Silver dicyanoargentate starts precipitating at pH approximately 9.3. The apparent stability constant
GAUGUIN, R., J . Chimie Phus., 42, 28 (1945). A. M., A N D SHIMI, I. A. W., Z. Anol-g. C h m . , 321,284 AZZAM, (1963). Volume 49, Number 6, June 1972
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