Solubility Product Constants in a 4-inch by 4-inch by Glenn Baca and Dennis A. Lewis Rose-Hulrnan Institute of Technology. Terre Haute. IN 47803 In light of the continually rising costs of reagents, a 4 X 4 X 1in. Plexiglas@Unit1 with grooves for metal electrodes has
been designed to study electrochemical cells. Only 7 ml of solution in each chamber is needed to determine the solubility product constants of as many as eight sparingly soluble salts. T h e K., values of six2,:'silver salts were determined using this Unit. T h e system in which a sparingly soluble salt is in equilihrium with its ions in aqueous solution is described by the equilibrium constant Kspr or solubility product. For the sparingly soluble salt, M2X(s), the chemical equation for the equilihrium system is
and the mathematical expression for the equilihrium constant is K,,
=
[M+I2[X2-]
We have identified the concepts of solubility product and molar solubility as areas which give our general chemistry students the most difficulty. We contend that there are two major reasons for this difficulty: I) The concept of solubility pmduct is normally introduced dwing an extensive treatment of chemical equilihrium. It is first seen hv the student as vet another "unioue" eauilibrium constant amidst an alreadvbewilderine arraiof eo;ilihrium constants.
Figure 1. Top view of a 4 X 4 X 1 in. Plexiglas Unit Since the most accurate solubilitv product data is obtained .. from galvanic cell voltage measurements, we feel that the ideal d a c e to eive the concept of K., the thorouah treatment neckssary f& maximum bndentanding is during the electrochemistry portion of the general chemistry program. We have formulated an experiment which allows the student to rapidly construct a number of standard precipitation cells and obtain their cell potentials. Using this data, the student can accurately determine the K,,'s and molar solubilities of the corresponding sparingly soluble salts. I t should be pointed out that silver acetate produces a significant concentration of ion pairs, AgCpHoOn(aq),rather than dissociating completely to its ions.' In this case, it is not possible to determine an accurate K,, value directly from its molar s ~ l u b i l i t y . ~ -7
discussed, the only type of laboratory experiment involving K., is one in which semi-quantitative results can be obtained. Usually, stoichiometric amounts of salt solutions of various conceitrations are mixed. Ion-productcalculationsand visual observation of precipitate formation enables the experimentor to estimate the Kapvalue of the sparingly soluble salt. This experimental method has several serious limitations: a) The K,, values obtained are quite inaccurate (+ two powers of ten). b) An accurate comparison of molar solubility trends cannot be made. c) It is limited tosalts with large K., values; e.g., 10W,10-6. W 5 , ete. Treatment of K,, and molar solubility in lecture alone with no reinforcement through a laboratory experiment seems to leave many students with-the misconception that theonlvr of molar solubilit~esof a number ofsaltscan he prrd~cteddirectly from the order of K.,'s.
'
Experimental A too ~.view of the 4 X 4 X 1 in. Plexielasm Unit is shown in the firmre. Drawings of the necessary pieces of l'lexiglas* nrrded to buildthis Unit are available upon r e q u ~ ~These t. pieces arr "glued" together usmg chloroform (Use in a well ventilated areal.Salt bridyrs and metal electrodes are prepared according to procedures described p~eviously.~ The metals and corresponding solutions are introduced into the various chambers shown in the fizure. The oositive terminal to a digital volrrnctrr is always connected t o rhaml,er 5 when recording the \oltageuf each of thesix ~osslhirprrcip~tatirmcells15-1.5 :I. .U. 5 6 . 5-7, 5 91. Since only stx prnlpmrlon wils were exammed. chambers 2 and 8 were not used.
'
Calculations Using the Nernst equation given below
Details of the construction and usage of this Unit were presented at the ACS Chemical Demonstrations Conference, at Western Illinois University in Macomb. IL on May 1. 1981. Washburn, Edward W. (Editor), international Critical Tables of Numerical Data. Physics. Ckmistly, and Technology. M&awHiil E w k Co., New York. 1930, p. 323. Dean, John A. (Editor),"Lange's Handbook of Chemistry." 12th Bd.. McGraw-Hill Book Co.. New York. 1979, p. 5-11. Gasparro, F. P.. J. CHEM. Ewc., 53,98 (1976). Meites, L., Pcde, J. S. F., and Twmas. H., J. CmM. Eouc.. 43,667 (1966). For details of preparation see Baca, G., and Lewis. Dennis. A.. J. C ~ MEouc.. . 55, 804 (1978).
762
Journal of Chemical Education
Table 1.
Table 2.
Measured Cell Potenllals
A& Chambers
5-1 5-3 5-4 5-6 5-7 5-9
Cell
(volts)
Salt
Kw
AgC2H102 4.6 X Ag2S04 1.6 X A%./~glisi.li,.~u1//~9h,1m~A9is, 0.964 1.7 X AgCl 0.283 5.4 X A ~ ~ . I I A ~ ~ c o ~ ~ , , . C O ~ ~ ~ , ~ M I ~ A ~0.333 ~ ~ , ~ U I I A ~Ag2C03 ~S, A ~ ~ I ~ A ~ ~ ~ ~ ~ I . ~ ~ ~ ~ , ~ ~ 0.719 ) ~ ~ A ~ ~ AgBr , I M ~ 6.8 A %X Agl 4.5 X A ~ I S , / A S C ~ ~ I . C I I . ~ , T M / / A ~ ~ I ~ , T M / A ~ ~ , 0.577
A~,,IA~c~H~~~,~.c~H&,,~I~A~Q,.,*I/A~~
0.138
the student is able to calculate the value of K., for each of the six sparingly soluble salts. For each 1:l salt, K,, = S2(where "S"represents the molar soluhility of that salt). For 1:2 salts, Kap= 4S3 (where "S" represents the molar solubility of that salt). Conclusions
From the data in Table 1 it is evident that the K,, of a salt is dependent not only upon the cell voltage but also upon the value of n in the Nernst equation. Upon examination of the data in Table 2, the student finds that the order of decreasing K,, values and decreasing molar solubilities are the same if
K, and Molar Solublllly ( S ) Values at 25% Salt
1 0 P (4.4 X 10@Ie AgC2H3026.8 X (1.4 X 10-5)b Ag2SO4 3.4 X 1.3 X 10-'0(1.8 X 10-'D)" AgCl 10-'2(8.1 X Ag&03 1.1 X X AgBr 6.3 X ~10-'3(5.0 I lo-'? (8.3 X Agl 7.0 X
S
1 0 P (6.6 X 10@ (1.5 X 10-5(1.3 X 10-'(1.3 X iO-'(7.l X lo-' (9.1 X
lo-')' 10-515 10-9' lo-')' lo-')'
Liferatwe Y&H 88 nDied in foomOIs 2. a Literature valuer as noted In footnote 3. Calculated from lltsrafvre K, valuer.
only the four 1:l salts are compared to one another, or if only the two 1:2 salts are compared to each other. However, upon comparison of all six salts, the student notes that the K., value of AgpCOs is less than that of AgC1, hut the molar solubility of AeGO- is neater than that of AeC1. The student ultimatelv conc%des that, although it is generally true that decreasing solubilitv oroduct values are accom~aniedhv a cones~ondinr! decrease in the respective molar soiubilitiesof the saits being examined. one cannot assume that this direct relations hi^ will always exist.
Volume 60 Number 9
Se~tember1983
763
