In the Laboratory
W
The Solubility Product of PbCl2 from Electrochemical Measurements Jimmy S. Hwang* and Ghassan A. Oweimreen Department of Chemistry, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia; *
[email protected] Electrochemical cell measurements have been used to determine the thermodynamic properties of chemical reactions (1, 2). The experiment presented in this article is not found in physical chemistry laboratory textbooks; however, it reinforces material often discussed in lectures. The experiment illustrates how thermodynamic properties such as the change in the standard Gibbs energy, ∆G°, and the equilibrium constant of a reaction are related to the emf, at different temperatures, of electrochemical cells in which the reaction takes place. The experiment is an application of a metal– insoluble salt electrode to determine the solubility of a sparingly soluble salt, PbCl2. PbCl2
1 M KNO3 salt bridge thermometer AgAgCl electrode rubber stopper
AgAgCl sat KCl electrode thermostated water out internal beaker
saturated PbCl2 solution PbCl2 crystals
1 M AgNO3
magnetic stirrer
thermostated water in
Figure 1. Diagram of the cell 1. Cell 2 is very similar to cell 1; the only difference is that the saturated PbCl2 is replaced by 1 m KCl.
Pb2+ + 2Cl−
Ksp = [Pb2+][Cl−]2 It is suited for a second- or third-year physical chemistry laboratory. The students learn to use equipment for temperature control and to freshly prepare a Ag|AgCl electrode. Experiment The following items are needed for the experiment. •
electrode dipped in 1 m KCl. The left side electrode of cell 1 is a Ag|AgCl(s) electrode dipped in a saturated PbCl2 solution. The diagram of cell 1 is shown in Figure 1. The difference between the emf values of these cells measured at the same temperature T permits the calculation of Ksp at T: ∆E = E 2 − E 1 = (RT兾F )ln aCl᎑
Two standard (sat. KCl)|AgCl(s)|Ag(s) electrodes (Corning Glass)
Ksp = a3Cl᎑兾2
•
A high impedance voltmeter (Hewlett-Packard 34420 Nano Volt/Micro Ohm Meter)
•
Magnetic stirrers
•
Two potassium nitrate salt bridges
The metal–insoluble salt electrode is a second-order indicator electrode since it is used to measure the Cl − activity, which is not directly involved in the electrontransfer process (3).
•
An RCS Lauda Temperature Controller/Circulating System
Hazards
•
Specially designed beakers with jackets for circulation of thermostated water to control the temperatures of the solutions in the half-cells (Figure 1)
•
Silver electrode
•
Platinum electrode
•
1.5-V battery
Two cells were used in the emf measurements at identical temperatures and with identical 1 M KNO3 salt bridges. These cells, numbered 1 and 2 respectively are: Ag(s) AgCl(s) Cl − (a = ?) Ag(s) AgCl(s) Cl − (1m KCl)
(sat. KCl) AgCl(s) Ag(s) (sat. KCl) AgCl(s) Ag(s)
The right side electrode is common to both cells. The left side electrode in cell 2 is a standard reference Ag|AgCl(s)
Powdered PbCl2 is harmful if swallowed; avoid breathing the PbCl2 dust. It is toxic if absorbed through the skin. Concentrated nitric acid is toxic and may be fatal if swallowed or inhaled. It is extremely corrosive. Contact with skin or eyes may cause severe burns and permanent damage. Hydrochloric acid (1M) is corrosive. Inhalation of vapor is harmful and ingestion may be fatal. Liquid can cause severe damage to skin and eyes. Potassium nitrate is harmful if swallowed and may cause reproductive disorders. Results Typical values obtained in an experimental run in the physical chemistry laboratory are shown in Table 1. The variation of ln Ksp with the inverse of the temperature is presented linearly in Figure 2 and quadratically in Figure 3. The thermodynamic values calculated from the slope and intercept of the graphs are listed in Table 2.
JChemEd.chem.wisc.edu • Vol. 80 No. 9 September 2003 • Journal of Chemical Education
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In the Laboratory
Table 1. A Typical Set of Student Data for Cells 1 and 2 T/°C
Ecell 1/mV
Ecell 2 /mV
20.6
134.13
64.60
25.3
134.58
65.31
29.8
136.23
66.71
34.8
137.56
68.47
39.7
139.65
70.11
46.0
142.26
72.73
50.3
144.03
74.45
57.0
147.28
77.39
60.1
148.38
78.31
Table 2. Thermodynamic Quantities at 25 °C Obtained from ln Ksp versus T ᎑1 Least-Squares Fits ∆S°/ (J mol᎑1 K᎑1)
∆H°/ (kJ mol᎑1)
Least-Squares Fits
∆G°/ (kJ mol᎑1)
Linear
18.8
᎑10.2
21.8
Quadratic
21.7
᎑0.5
21.8
Discussion To our knowledge this is the first variable-temperature experiment in which simultaneous emf measurements were made on two cells at identical temperatures and using two identical salt bridges. This approach eliminates the need to correct for the temperature dependence of the two standard reference electrodes and minimizes errors arising from junction potentials across the salt bridge. In the last 20 years, a number of solubility product experiments have been published (4–16). None deal with the determination of the solubility products through electrochemical measurements. Some of the articles deal with the effect of ionic strength on solubility, a few deal with the common ion effect, and one deals with the determination of equilibrium constant of some complex silver ions. The experiment was easily carried out within a threehour lab period and the students enjoyed both the practical aspect of the experiment and its relevance to their theory class. It is recommended to freshly prepare the salt bridge a few days prior to the experiment. W
-7.8
The background, relevant theory, and details of the experimental procedure are available in this issue of JCE Online.
-8.0
ln Ksp
8.2
Acknowledgments
-8.4
The authors acknowledge support for this work from the chemistry department at King Fahd University of Petroleum and Minerals. The technical help of Nasrullah Baig in the physical chemistry laboratory is also acknowledged.
-8.6
-8.8
Literature Cited
-9.0
-9.2 2.9
3.0
3.1
3.2
3.3
3.4
3.5
T ⴚ1/ (10ⴚ3 Kⴚ1) Figure 2. A linear least-squares fit of ln Ksp versus T ᎑1. -7.8
-8.0
ln Ksp
-8.2
-8.4
-8.6
-8.8
-9.0
-9.2 2.9
3.0
3.1
3.2
3.3
3.4
3.5
T ⴚ1/ (10ⴚ3 Kⴚ1) Figure 3. A quadratic least-squares fit of ln Ksp versus T ᎑1.
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Supplemental Material
1. Laidler, K. L.; Meiser, J. H. Physical Chemistry, 3rd ed.; Houghton Mifflin Co.: Boston, 1999; pp 344–346. 2. Alberty, R. A.; Silbey, R. J. Physical Chemistry, 1st ed.; J. Wiley & Sons, Inc.: New York, 1992; pp 255–260. 3. Skoog, R. A.; West, D. M. Fundamentals of Analytical Chemistry, 3rd ed.; Holt, Rinehart and Winston: New York, 1976; pp 382–383. 4. Lehman, T.; Everett, W. W. J. Chem. Educ. 1982, 59, 132. 5. Sawyer, A. K. J. Chem. Educ. 1983, 60, 416. 6. Baca, G.; Lewis, D. A. J. Chem. Educ. 1982, 60, 762–763. 7. Edmiston, M. D.; Suter, R. W. J. Chem. Educ. 1988, 65, 278– 280. 8. Wruck, D. B.; Rechstein J. J. Chem. Educ. 1989, 66, 515– 516. 9. Rice, G. W.; Hall, C. D. J. Chem. Educ. 1990, 67, 430–431. 10. Scaife, C. W.; Hall, C. D. J. Chem. Educ. 1990, 67, 605–606. 11. Gotlib, L. J. J. Chem. Educ. 1990, 67, 937–938. 12. Thomsen, M. W. J. Chem. Educ. 1992, 69, 328–329. 13. Silbermann, R. G. J. Chem. Educ. 1996, 73, 426–427. 14. Green, D. B.; Rechsteiner, G.; Honodel, A. J. Chem. Educ. 1996, 73, 789–792. 15. Marzzacco, C. J. J. Chem. Educ. 1998, 75, 1628–1629. 16. Thompson, M. L.; Kateley, L. J. J. Chem. Educ. 1999, 76, 95–96.
Journal of Chemical Education • Vol. 80 No. 9 September 2003 • JChemEd.chem.wisc.edu
