S. A. Carrano," 1. J. zompa,lb and Karl A. Chen'' Boston College, Chestnut Hill, Massachusetts
A Demonstration and Exercise in Simultaneous Equilibria
The determination of nickel(I1) by cyanide titrationZ is a volumetric procedure frequently performed in an introductory course in quantitative analysis. In this method N++ions are converted to Ni(CN)a- ions by the addition of an excess of standard cyanide solution and the excess cyanide is then backtitrated with standard silver nitrate solution. Because of the appreciable solubility of silver cyanide in ammoniacal solutions, iodide ions are added and the turbidity produced by the more insoluble silver iodide is used to establish the end point. The analytical scheme described above has been effectively used in the course in quantitative analysis at Boston College to demonstrate the important concepts of simultaneous (or "intersecting") equilibria. Through this one chemical analysis, the student may be introduced to and become involved with as many as eleven fundamental equilibria and the corresponding equilibrium constants. Equilibria of lesser importance on this level of discussion are not considered, e.g., those equilibria involving species such as Ag(NH3)+, Ni(NH3).++ where n < 6, and Ni(CN),Z-m where m < 4. The eleven equilibrium constants may be classified as three acid-base constants, four solubility products, and four complex-ion constants. The accompanying table is a compilation of the pertinent equilibrium constants. Table of Equilibrium Constants' I. [H+l[OH-I = 1.0 X lo-" 11. [Ni++][OH-]' = 3.2 X 10-'B 111. [Nit+][NH~]'/[Ni(NH~)~++I = 2.5 X 10-0 IV. [Ni++][CN-]'/[Ni(CN)c-I = 1 X 10-21 V. [Ni++][Ni(CN),--1 = 1.7 X 10-a VI. [Agfl [CN-12/[Ag(CN),-I = 3.6 X VII. [Ag+][Ag(CN)n-] = 5.9 X VIII. [Agf][I-1 = 1.0 X IX. [Ag+][NHalz/[Ag(NHa)r+I = 6.0 X 10-a X. [NH,+][OH-]/[NHz] = 1.8 X XI. [Htl [CN-l/[HCN] = 6.0 X 10-lo The values for the equilibrium constants are for 25" and were A. E., "Stability Contaken from SILLEN,L. G., and MARTELL, stants of Metal-Ion Complexes," The Chemical Societ,y of London, 1964.
' Present addresses (a) Fairfield University, Fairfield, Conn.; (h) Michigan State University, East Lansing, Mich.; (c) Jackson Laboratory, E. I. du Font de Nemoum Co., Wilmington, Del. REV. A. F. IMCGUINN,S.J., former professor and chairman of Chemistry at Boston College and our especially beloved associate up to the time of his death in February 1965, conceived these exercises and conducted them each year for his students. I t was his wish that the work be published in this journal, and hecause of his failing health privileged us with the assignment. S. G., "Quantitative ChemiHAMILTON, L. F., AND SIMPSON, cal Analysis," 11th ed., MscMillan Company, New York, 1958, pp. 306, 497-498.
The manner in which the concentrations of each of the many species depends directly or indirectly upon those of the others may be represented by Figure 1. It is essential that the student be made to understand that the analytical method works because: Silver cyanide is soluble in ;Lqueous ammonia. Silver cvenide is soluble in aaoeous uotassium cyanide.
Each of the statements above can be verified experimentally by simple demonstrations and by calculations such as those described below.
+ Ni(CNl4"#
+
CN(EXCESS)
.....+.... !Nit+ i .--.-----a
+ +(EXCESS) NHsdNi(NH&++
Figure 1. Pertinent rimultoneous equilibria in the anolyrir of nickelllll b y cyanide titration.
Demonstrations Tenth molar solutions of the appropriate reagents are used in the following tests. The cyanide residues may be disposed of by pouring these into an alkaline hypochlorite solution, which converts the cyanide radical to cyanate and other less poisonous products. Case I . Siluer Cyanide i s Soluble in Aqueous Ammonia Silver cyanide is formed by adding an equivalent amount of silver nitrate to a solution of potassium cyanide and then concentrated ammonia is added until the precipitate dissolves. Case Z. Silver Cyanide i s Soluble in Aqueous Cyanide Silver cyanide is formed as in Case 1 above and then potassium cyanide solution is added until the precipitate dissolves. Case 3. Silver Iodide i s Insoluble in Aqueous Ammonia Potassium iodide solution is added to silver nitrate solution to form the silver iodide, then a considerable Volume 43, Number 1 I, November 1966 / 603
excess of ammonia is added. Case 4. Silver Iodide is Soluble i n Aqueous Cyanide Silver iodide is prepared as in Case 3 above, and ammonia is added. Potassium cyanide solution is added to this mixture until the precipitate dissolves. The verification, by mathematical analysis, of the four statements made above regarding the solubilities of silver cyanide and silver iodide in the various media, may be accomplished as indicated below.
and From the stoichiometry it is seen that: For the conditions of this demonstration (VI) yields: [Ag tl
< (3.6
X 10-2')(10-2)/(10-8)s = 3.6 X 10WL9M
It follows then that:
Calculations
Case 1. Silver Cyanide is Soluble in Aqueous A m m a i a Assume a solution made up 1M in ammonia and one in which CA.+ and CGN-, in each case, is 0.01M, C, representing the total concentration of the ith suhstance in all of its forms. We now have; [Ag+I = (6 X 10-8)1Ag(NH~)*+l/[NHsl'
(IX)
Assuming that the reaction; Agf
+ 2NH1 *
< (6 X
10-8)(1 X 10-¶)/1' = 6 X 10-'OM
since [Ag+] < CA=+= 1 X In a saturated solution of silver cyanide, the reversible reaction is: 2Ag(CN)(s)
*
Ag+
+ Ag(CN)g-
and the solubility product expression is; KSP = [Agt][Ag(CNh-I = 5.9 X lo-'*
(VII)
Under the conditions of the demonstration; [Ag(CN)*-] 5 l / x C ~ ~=- 5 X 10-$M
It follows then that: [Agt] lAg(CN)z-]
< (6 X
10-'0)(5 X 10-9 = 3.0 X 10-lP
Thus the ion product,
