Robert C. Goodman
Shaker Heights High
school
ISthe Solubility Product Constant?
Cleveland, Ohio
Ralph H. Petruccil Western Reserve University Cleveland, Ohio
introductory
experiment in solubility equilibrium
There is a need in introductory chemistry courses for a simple, direct experiment which will illustrate the principles of solubility product. At present, methods which employ the analysis of saturated salt solutions such as silver acetate or one of the lead halides are widely used (1-3). The use of silver acetate gives a K,, value of doubtful accuracy because of the formation of silver acetate and silver hydroxide complexes and the hydrolysis of silver acetate. The formation of a brown silver oxide precipitate may serve further to confuse the student (4). Whether silver acetate or lead halides are used in preparing the saturated solution, volumetric analysis is time-consuming and gravimetric techniques are even more tedious. This article describes an experiment which employs the titration of lead nitrate solutions with potassium iodide solutions as a vivid and straightforward method of determining solubility product. Because of the ease of the laboratory manipulations, the student has time to investigate several equilibrium mixtures and discover the effect of ionic environment on the solubility of lead iodide. Carmody has used a titration technique similar to the one described in this article to study variations in the solubility product of cadmium iodate with ionic strength (5). Barrett has emplayed dropwise addition of reagents to demonstrate K,, of cadmium hydroxide (6). Because it does not seem advisable to present the concept of ionic streugth in an introductory course in chemistry, students may analyze the data in this experiment by graphing solubility product against molar concentration of the ionic enviroment. The results of this experiment may be viewed with varying degrees of sophistication. On a qualitative level, the student can discover intuitively a definition of solubility product. He can see that the bright yellow precipitate of lead iodide forms but that it does not persist until a certain critical product of concentrations is achieved-until a true solubility equilibrium is established. On a simple quantitative level, the student can gain facility in working with molar concentrations by calculating the solubility product for each titration mixture. By analyzing his data, the student discovers that the solubility product based on ion concentrations is by no means a constant. He may hypothesize that the wide variations in solubility product are a result of interionic forces. If he does further laboratory work concerning the effects of ionic environment, he may find that although the interionic forces play a part, there are ~
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1 Present address, California. State College, San Bernardino, California.
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Journal o f Chemicol Educofion
other factors affecting the apparent solubility product. This idea can be pursued further with a set of titrations designed to demonstrate the effect of complex ion formation. The Experiment
Twenty-five ml of 0.5 M lead nitrate solution is placed in a small Erlenmeyer flask and titrated with 1 M potassium iodide solution contained in a hypodermic syringe having a capacity of 2.5 n L 2 The potassium iodide titrant is added a drop a t a time with the syringe held vertically to maintain uniform drop size. The flask must be swirled thoroughly after the addition of each drop to promote the dissolving of lead iodide. A black background is helpful in detecting the faint yellow precipitate of lead iodide which persists when the end-point of the titration is reached. The temperature of the equilibrium mixture is measured a t this point. Other titrations are performed in which 0.1 M potassium iodide solution is added to 25-ml samples of 0.25 M, 0.10 M, 0.05 M, 0.02 M, and 0.01 M lead nitrate solutions. Typical results and a sample calculation for this series of titrations are shown in Table 1. A graph can be prepared on semi-logarithmic paper, with solubility product values as ordinates and coucentrations of the solutions titrated as abscissas. The data from Table 1 are plotted as curve A in Figure 1. It can be seen that the solubility product increases as a function of the concentration of lead nitrate in the solution being titrated. The solubility product a t infinite dilution can be estimated by extrapolating the curve to the y-axis. Studies conducted by high school chemistry classes indicate that student results for this experiment are fairly reproducible. (In an average class the majority of student results are within e20% of the class average for K , for each titration and extrapolate into the range of values reported in the literature.) Difficulties are sometimes experienced by students because of insufficient agitation of the mixture during titration. In solutions involving molar concentrations of 0.01 M or less for lead nitrate, it is difficult to detect the first appearance of the lead iodide precipitate. 'The hypodermic syringes used in this experiment were "Hypak" disposable glaaa syringes No. 702 DN with detachable needle 23G, manufactured by Becton, Dickinson and Co., Rutherford, New Jersey, and available through many laboratory supply houses. A pmticularly good feature of this syringe and needle combination is the fact that the volume of one drop of liquid is very nearly 0.01 rnl far the solutions used in this experiment.
Table 1.
Titrations of Lead Nitrate Solutions with Potassium Iodide as Titrant
Titrstion No.
2
1
Liters of KI s o h used Molerity of X I soln Liters of Pb(NOs)*soln used Molarity of Ph(NO& s o h Concentration of I- at equilibrium (moles/l) Concentration of Pbz+a t equilibrium (moles/l) Solubility product [.PbZ,+] [I-!' Temperature of equhhnum mixture
3
1 . 2 x lo-' 1.0M 2.5 X 0.50 M
7 . 4 x lo-' 0.10 M 2 . 5 X lo-' 0.25 M
4.8 X 10-a
2.9 X
5.0 X lo-' 1.1 X 19.5-
2.4 X 2.0 X 20.5'
lo-' lo-' lo-'
4
5.5 x 1 0 ~ 4 . 9 x lo-' 0.lOM 0.10 M 2 . 5 X lo-' 2 . 5 x lo-¶ 0.lOM 0.05 M 2.2
x
1.9 x
9.8 X lo-' 4 . 5 X 10' 20.5'
lo-"
4.9 X 1 . 8 X 10-I 19.7'
Calculation of K , for Titration No. 1: (1.2 X l W 4 liters KI) (1.0 moles I-A) = 1.2 X
(2.5
x
lo-'
10-2 liters Ph(N0.)2)(.50 moles Pb(NO&/liter)
moles K I added.
=
1.25 X 1 0 P moles Pb'+ ion present.
McAlpine has conducted extensive investigations concerning how much precipitate must be formed in order that it may be seen (7). As Butler has pointed out, extrapolation can be a major source of error (8). The values of K,, corrected to zero ionic strength reported in the literature range from 1.05 X 10-0 to 1.6 X 10-8 a t 25" (9). Recent work seems to favor a value of 7.1 x 10-9. This experiment is open-ended in the sense that it raises more questions and suggests further experiments. One question which is likely to grow out of class dicussion is whether all ionic substances have an identical
effect in increasing the values of K,, as the molar concentration of the ionic environment becomes greater. Curve B in Figure 1 shows the results of a series of titrations in which lead nitrate is the titrant and potassium iodide is the major constituent of the ionic environment. It can be seen that at lower concentrations the solubility product of lead iodide is greater in lead nitrate solution than in potassium iodide. This observation fits well with the concept of ionic strength (5). At higher molarities lead iodide is more soluble in potassium iodide solutions than in lead nitrate. Students who are interested in pursuing the reasons for this increased solubility product may delve more deeply and learn about the formation of complex ions such as PbIs-, PbIIZ-, and PbIs3-. Butler describes methods by which the total solubility of lead iodidemay be calculated (10). Acknowledgment
The authors are grateful to Charles W. Hendrickson for his assistance in conducting studies with students at Shaker Heights High School. The authors enjoyed a student-teacherrelationship during the 186344 NSFInService Institute and the 1964 NSF Summer Fellowship Program a t Western Reserve University, and are indebted to the NSF for sponsoring these programs. literature Cited (1) MALM,L. E., Editor, "Laboratory Manual for Chemistry, An Experimental Science," W. H. Freeman and Co., Srtn Francisco, 1963, pp. 46, 47. F. A,, AND BURTT,B. P., "L&bomtor~Experiments (2) KANDA, in General Chemistry," Harper and Brothers, New York, 1962, p. 147. (3) Chemical Bond Approach Project, "Teachers' Guide to Investigating Chemical Systems," McGraw-Hill Book Co., St. Louis, 1964, pp. 33-1 to 33-13. (4) BUTLER,J. N., "Ionic Equilibrium, A Mathematical Approach," Addison-Wesley Co., Reading, Mass., 1964, pp.
.,
241 -" 1 X 10-8
0
.1M
.2M
.3M
.4M
.5M
Concentrations of Solution Figure 1. Variation in rolvbility produd with molar concentration of solution titroted. Curve A shows K1 solution odded to PblNOsh. Curve B show. Pb(NOalx.elution added to Ki.
51 1
CARMODY, W. R., J. CHEM.EDUC.,36, 125, (1959). BARREIT,R. L., J. CHEM.EDUC.,36, A501, (1959). MCALPINE,R. K., J. CHEM.EDUC.,23, pp. 28-34, (1946). BUTLER,J. N., op. cit., p. 57. C H AND , SILLEN,L. G., BSERRUM,J., S C ~ A R Z E N B AG., "Stability Constmta, Part 11," Specid Publication No. 7, Chemical Society of London, 1958, p. 122. pp. 274-8. (10) BUTLER,J. N., op. d., (5) (6) (7) (8) (9)
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