Stanford 1. Tackell Indiana University of Pennsylvania Indiana, Pennsylvania 15701
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Potentiometric Determination of Solubility Product Constants A laboratory experiment
W h i l e all textbooks of instrumental analysis prescnt the theory of potentiometry, some of them have no experiments involving direct potentiometric analysis (1-3). Other texts do have direct potentiometric experiments, but these usually involve fairly dilute solutions and generally ignore activity coefficients and activity effects (4-8). Two of the latter texts describe activity effects and suggest that activity coefficients be calculated for comparison purposes (6,6). The present work describes an experiment in which measured potentials and calculated activity coefficients are used to obtain the solubility product constants of silver halides. The instrumentation required for the experiment is readily available, and the laboratory techniques are simple enough so that even the beginning chemistry student can obtain excellent results. This experiment readily demonstrates activity effects, and allows the student to verify the DebyeHuckel equation. A silver electrode, a reference electrode, and a potentiometer or pH meter comprise the necessary instrnmentation. The silver electrode may be a commercial model, or simply a metallic strip or wire. For this work, an 8-in. length of 16 gauge silver wire was used. About half of the wire was coiled in a helix around a pencil. Any reference electrode may be used, but the fiber-type calomel electrode furnished with pH meters is especially convenient. If a conventional saturated calomel or silver-silver chloride electrode is used, a KN03 bridge must be used to prevent contamination of the test solutions with chloride. A Leeds-Northrup students' potentiometer was used here, but any potentiometer or pH meter may be used with equal success. Procedure A stock solution of 0.100 M AgN03 was prepared by dissolving a weighed amount of the dried reagent grade salt and diluting in a volumetric flask. Solutions of 0.0100 M and 0.00100 M were prepared by volumetric dilution of the stock solut,ion. The activit,y coefficient for Ag+ was calculated with the DehyeHiickel equation for each solution, and the Ag+ activity was established by multiplying the concentration times the activity coefficient. The potential difference between the Ag indicator electrode and the reference electrode was measured for each AgN08 solution. The bheoretical potential of the Ag electrode was calculat,edfor each solution using the Nernst equation m follows
E
=
+0.7991
+ 0.0591 log [Ag+]f.~,*
(1)
where E is the potential of the Ag electrode in volts, +0.7991 is E" for t,he Agf, Ag couple, 0.0591 is the value of 2.303 RTIF a t
Eoba= EM - Ere, (2) where Eobr is the measured potential difference, Ei.a is the calculated potential of the Ag electrode, and E,.r is the potential of bhe reference electrode. Three independent values of E,,r were ohtained, one far each AgNOa solution, and they usually agreed within a. few tenths of a millivolt. A few millivolts difference would he expected if the dilutions were not made carefully. Solutions of 0.100 M NaC1, 0.100 M KI, and 0.100 AT KBr were prepared from the reagent g r d e salts by the procedure used for AgNO*. Each solution was saturated with the respective silver halide by the addition of one or two drops of 0.1 M A ~ N O soluI tion. The potenbid difference between the indicator and reference electrodes was measured for each halide solution. Acbivity coefficients were calculated for each halide. Using the average value for E.., determined with the AgNOl solutions and the measured potential, eqn. (2) allowed the calculation of the Ag potential in each hdide solution. Equation (1) then was used to calculate the Ag+ activity, [Ag+]f ~ , +for , each solution. The solubility product constant for AgCl was cdculated by the equation
K.,
=
[Agt]f~.* (0.100)(0.76)
(3)
where [Agf]f*.+ is the activity of Ag+ calculated by the Nernst equation for the NaCl solution, 0.100 M is the concentration of chloride, and 0.76 is the calculat,ed chloride activity coefficient. K,, valuesfor AgBr and AgI were determined in the samemanner. The constants ohtained here are truly activity products. In view of the current trend of calling the constant a solubility product when concentrations are used and activity coefficients are ignored, the term "activity product" should probably have been used. In view of the familiarity and wide use of the term, K.,, however, i t is hoped that no confusion results.
Resulls and Discussion
Typical student results ohtained for the AgNOa solutions are shown in Table 1. Agreement of the reference electrode potentials shown in the last column of Table 1 is a verification of activity theory and the Debye-Hiickel equation. When the same electrodes were used by the student to measure the potentials in the 0.100 M halide solutions, the results in Table 2 were obtained. Agreement of the experimental K.,'s with literature values is evident in the last 2 columns of Table 2. These data represent the experiment of only one student, but practically all students who have performed the experiment so far have ohtained equally good results. Generally, the agreement of the results of students in the laboratory is better than the agreement of values reported in an equal number of textbooks. I n conclusion, this experiment is recommended for beginning chemistry students as well as for advanced Volume 46, Number 12, December 1969
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857
Table 1. Potential Data for AgN03 Solutions with Ag Indicator and Saturated Calomel Reference Electrodes
AgNOs cone. fM) , ,
Agf Calculated Activity Potential Coefficient 1V) , .
0.100 0.0100 0.00100
0.76 0.90 0.97
Table 2.
0.7330 0.6782 0.6210
Eobs fTr) . . 0.4933 0.4400 0.3805
Erer
(V) , ,
0.2397 0.2382 0.2405 Av. = 0.2396
K., Values Obtained from Potential Data
&bs
Solution 0 1A
(volts versrls SCE)
Activity of Agt
(M
0.0484 2.24 X lo-' -0.1035 6.03X10-11 -0.3266 1.05 X lo-"
NaCl KBr XI
K,, exptl.
K,, Lit. (8)
1.70 X 10-lo 4.58X10-la 7.98 X lo-"
1 . 8 X 10-'O 4.9X10-'5 8 . 3 X lo-''
students of analytical chemistry. Necessary instrumentation is readilv available in most chemistrv laboratories, and the procedure is such that all required data can be obtained in only one short laboratory period. The calculatio-ns are straightforward and simple, yet solubility product constants which are in excellent agreement with literature values can be ob-
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Journol o f Chernicol Educotion
tained by all. Any experiment which so ably verifies both activity theory and solubility theory is worthy of consideration. One that does both and is still short and simple is especially appealing. There is nothing like getting good results to reinforce and enhance enthusiasm among chemistry students. Literature Cited
(1) Ewmu, G. W., "Instvumonlal Methods of Chemical Analysis," (3rd ed.) McBraw-Hill Book Co., New York, 1969. (2) WILLARD,11. TI., MI:RIIITT,L. L., JR., A N D UIIIN, J. A,, "Instrumental Methods of Anslysin," (4t,h ed.), D. Van Nostrand Co., Ine., New York, 1965. (3) RMLLICY, C. N., A N D S.\II.YER,1). T.,"Experiments for Instrumental Methods," ~McGraw-HillBook Co., New York, 1961. C. E., A N D KISICR, Jt.W., "Problems and Experi(4) MELOAN, ments in Instromonbal Analysis," Charles E. & k r i l l Books, Inc., Columbus, Ohio, 1963. (.5) DEIIHIY, P., "Instrumentd Analysis," Tho Rlacblillm Co., New York, 1957. I S , AND THOMAS, H. C., "Advanced Analytienl (6) M ~ ~ I T IL., Chemistry," McGraw-Hill Book Co., New York, 1958. L. D., "hZodern Methods oi (7) Pacson, R. L., A N D SHIISLDS, Chemical Analysis," John Wiley & Sons, Inc., New York, 1968. J. S., AND SCHI:NR, G. H., Jn., "Quantitative Analyti(8) FRITZ, cal Chemistry," Allyn and Bacon, Boston, 1966.
