I Potentiometric Determination Stanford 1. Tackell

Indiana University of Pennsylvania Indiana, Pennsylvania 15701

I of Solubility Product Constants

I 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 potentio- metric 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 be- ginning chemistry student can obtain excellent re- sults. This experiment readily demonstrates activity effects, and allows the student to verify the Debye- Huckel equation.

A silver electrode, a reference electrode, and a po- tentiometer or pH meter comprise the necessary in- strnmentation. The silver electrode may be a com- mercial 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 con- ventional saturated calomel or silver-silver chloride electrode is used, a KN03 bridge must be used to pre- vent 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 Dehye- Hiickel 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 solu- tion. The bheoretical potential of the Ag electrode was cal- culat,ed for 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 cal- culated 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 I solu- tion. The potenbid difference between the indicator and refer- ence 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 equa- tion

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 solu- tions, the results in Table 2 were obtained. Agree- ment 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 ex- periment 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.

In conclusion, this experiment is recommended for beginning chemistry students as well as for advanced

Volume 46, Number 12, December 1969 / 857

Table 1. Potential Data for AgN03 Solutions with Ag Indicator and Saturated Calomel Reference Electrodes

AgNOs Agf Calculated cone. Activity Potential Eobs Erer fM) Coefficient 1V) fTr) (V) , , , . . . , ,

0.100 0.76 0.7330 0.4933 0.2397 0.0100 0.90 0.6782 0.4400 0.2382 0.00100 0.97 0.6210 0.3805 0.2405

Av. = 0.2396

Table 2. K., Values Obtained from Potential Data

&bs Solu- (volts Activity tion versrls of Agt

0 1 A SCE) (M K,, exptl. K,, Lit. (8)

NaCl 0.0484 2.24 X lo-' 1.70 X 10-lo 1 . 8 X 10-'O KBr -0.1035 6.03X10-11 4 . 5 8 X 1 0 - l a 4 . 9 X 1 0 - ' 5 XI -0.3266 1.05 X lo-" 7.98 X lo-" 8 . 3 X lo-''

students of analytical chemistry. Necessary instru- mentation 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-

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 Analy- sis," (3rd ed.) McBraw-Hill Book Co., New York, 1969.

(2) WILLARD, 11. TI., MI:RIIITT, L. L., JR., AND 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 In- strumental Methods," ~McGraw-Hill Book Co., New York, 1961.

(4) MELOAN, C. E., A N D KISICR, Jt. W., "Problems and Experi- 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.

(6) M~~ITIIS , L., AND THOMAS, H. C., "Advanced Analytienl Chemistry," McGraw-Hill Book Co., New York, 1958.

(7) Pacson, R. L., A N D SHIISLDS, L. D., "hZodern Methods oi Chemical Analysis," John Wiley & Sons, Inc., New York, 1968.

(8) FRITZ, J. S., AND SCHI:NR, G. H., Jn., "Quantitative Analyti- cal Chemistry," Allyn and Bacon, Boston, 1966.

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