Laboratory Experiment pubs.acs.org/jchemeduc
A Simple Determination of the Ag2O Solubility Product by Potentiometric Determinations of Both Ag+1 and OH−1 Frederick C. Sauls*,† Department of Chemistry and Physics, King’s College, Wilkes Barre, Pennsylvania 18711, United States S Supporting Information *
ABSTRACT: A simple determination of the Ag2O solubility product, Ksp, suitable for introductory, analytical, or physical chemistry courses is presented. Two pH meters are required and 10‑4 mol of AgNO3 or AgOAc is consumed. The concentration cell, Ag(s) | Ag+ (0.001 M) || Ag+ (0.001 M) {pH electrode} | Ag(s), is used. The cell potential and pH are monitored as standard 0.1 M NaOH is titrated into the cathode compartment, precipitating Ag2O. The cathode pOH, pAg, and pKsp are computed at each point of the titration. The results illustrate theoretical expectation and are in excellent agreement with the literature.
KEYWORDS: First-Year Undergraduate/General, Second-Year Undergraduate, Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Hands-On Learning Manipulatives, Electrochemistry, Equilibrium, Potentiometry, Solutions/Solvents
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THEORY The solubility of Ag2O can be described by
he most obvious and convincing way to determine a solubility product, Ksp, is to measure the activities of all the ions involved. As far as can be determined, this approach has not been used in undergraduate laboratories. Several undergraduate laboratory experiments determining solubility or a solubility product have been proposed. Most commonly, a saturated solution is prepared and one of its components is determined by gravimetric, volumetric, spectroscopic, spectrophotometric, or radiochemical techniques.1−19 Some experiments use potentiometric cells, but do not yield titration curves and require an assumed Eo value.10,20−22 Two experiments give one of the curves.23,24 Many suffer from toxicity or radioactivity concerns.2−6,8,9,11,15,17,23 None appears to have become a standard undergraduate experiment. A simple determination of the Ag2O pKsp suitable for introductory, analytical, or physical chemistry courses is presented. As Ag1+ is titrated with OH−1, both the pAg and pOH curves are determined and summed to give pKsp. Because the activities of both ions are determined directly, most complications encountered by other experiments are absent. The results are highly robust toward experimental error and in excellent agreement with the literature. The experiment is readily understood and executed, can be applied at levels of sophistication from introductory through analytical and physical chemistry, uses small quantities of reagents and commonly available apparatus, demands modest experimental skill, and requires less than 3 h for completion. It may be done individually or in small groups. It has been favorably received by students. The core concepts illustrated are equilibrium constant, potentiometry, and titration curves. More advanced ideas that may be included are the theory of pH determination, activity corrections, and competing equilibria. © 2013 American Chemical Society and Division of Chemical Education, Inc.
1 Ag O(s) + 1 H O(l) ⇌ Ag +(aq) + OH−(aq) 2 2 2 2
(1)
K sp = {Ag +}{OH−}
(2)
and Ksp may be determined by simultaneous potentiometric measurements of both {OH−} and {Ag+} (braces indicate thermodynamic activity). The cell used is Ag(s)|Ag +(aq) Ag +(aq) {pH electrode}|Ag(s)
The cathode solution is part of two independent concentration cells. One depends on its pAg, the other on its pH. The cell voltage, Ecell, measured across the Ag wires will depend on pAg Ecell = −0.0592 V (pAgcathode − pAganode)
(3)
+
As the initial Ag concentration is the same in each half cell, the initial voltage is zero: the initial pAgcathode is equal to pAganode. The anode is a reference: pAganode remains constant. During the experiment, NaOH solution is titrated into the cathode compartment and the Ag cell voltage and cathode pH are measured. Ag2O precipitates; both pOHcathode and pAgcathode change, causing a corresponding change in Ecell. Ag + + OH− → 1 2 Ag 2O + 1 2 H 2O(l)
(4)
Because the anode remains unchanged and the initial Ecell = 0, as NaOH is added Ecell = −0.0592 V ΔpAgcathode
(5)
Published: August 14, 2013 1212
dx.doi.org/10.1021/ed300586g | J. Chem. Educ. 2013, 90, 1212−1214
Journal of Chemical Education
Laboratory Experiment
At each point in the titration, the glass electrode (the second concentration cell) allows calculation of pOHcathode and the cell voltage gives the ΔpAgcathode. As pAgcathode = pAganode + ΔpAgcathode
(6)
pK sp = pAganode + ΔpAgcathode + pOH cathode
(7) −
At the equivalence point, the moles of added OH equal the initial moles of Ag+ in the cathode. The initial pAgcathode can thus be calculated, which is equal to pAganode.
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Figure 2. Data for the Ag2O solubility product determination.
EXPERIMENTAL OVERVIEW The apparatus is assembled as in Figure 1. Each beaker contains 50 mL of ∼0.001 M AgNO3 or AgOAc and a 1 mm diameter
expectation. The plot of pKsp is remarkably straight and level, as theory predicts. The effects of experimental error are minimal. Changing the assumed equivalence point or the NaOH concentration by 10% changes pKsp < 0.06. Seven runs made over a week with both AgNO3 and AgOAc as the source of silver ion gave an average pKsp of 7.75 (pooled s = 0.04, n = 191 points), in excellent agreement with the accepted value25 of 7.72.
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DISCUSSION For an introductory treatment, data analysis may stop here. For more advanced courses, the experiment provides entry to many concepts. The students’ depth of understanding and the data reduction can be substantially improved. The activity of a single ion is thermodynamically undefined. From an experimental viewpoint, this is because junction potentials (Ej) can neither be measured nor reliably computed. This problem affects both ΔpAgcathode and pH values. For the ΔpAgcathode determinations, the initial net anode−cathode junction potential must be zero. Changes in the junction potential should be minimal given the high concentration of the salt bridge and the minor change in cathode solution composition during the titration.26 The ΔpAgcathode error should be small. The glass electrode gives a conventional and reasonable value for pH.26,27 The difference between the standard calibration buffers and the cathode solution changes Ej for the combination electrode. This will cause a small unavoidable pH error. Because pH < 12 and [Na+] ≪ 0.1 M, the alkaline error is small, as is the acid error.28,29 Each of these errors will vary as the titration proceeds. The constancy of the calculated Ksp suggests that these errors are negligible. As a concentration cell is used, the method is independent of uncertainties in Eo. Because the cell responds to the activity of silver, complications due to changing activity coefficients, ion pairing, competing equilibria, dissolution of the glass, and so forth in the cathode do not affect the results and can be ignored. However, any errors in pAganode will be directly reflected in pKsp. It is important to get that value correct. Competing equilibria may consume Ag+, causing a difference between the concentration determined stoichiometrically and the amount actually available in the solution. However, the Ag(OH)2−1 concentration (Kf = 10−3.72)25 at the initial pH (∼6) is 11.1. The pH electrode is briefly immersed in 7 M NH3 between runs to remove AgCl formed at the salt bridge. Experimental details are available in the Supporting Information.
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HAZARDS NaOH is corrosive. AgNO3 and NaNO3 are oxidants. Silver ion stains skin and clothing, and is slightly toxic. Proper disposal is essential.
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RESULTS The equivalence point is located from the titration curve and pAganode calculated. At each point pAgcathode, pOH, and pKsp are calculated. The results are shown in Figure 2. The plot shows that the pOH and pAg curves cross at the equivalence point and at the steepest part of the curves, in agreement with 1213
dx.doi.org/10.1021/ed300586g | J. Chem. Educ. 2013, 90, 1212−1214
Journal of Chemical Education
Laboratory Experiment
(17) Hwang, J. S.; Oweimreen, G. A. J. Chem. Educ. 2003, 80, 1051− 1052. (18) Willey, J. D. J. Chem. Educ. 2004, 81, 1644−1646. (19) Bonomo, R. P.; Tabbi, G.; Vagliasindi, L. I. J. Chem. Educ. 2012, 89, 545−547. (20) Carmody, W. R. J. Chem. Educ. 1959, 36, 125−127. (21) Chesick, J. P.; Patterson, A., Jr. J. Chem. Educ. 1959, 36, 496− 498. (22) Tackett, S. L. J. Chem. Educ. 1969, 46, 857−858. (23) Ungerer, B.; Jurio, R.; Manuele, R. J. J. Chem. Educ. 1972, 49, 434−435. (24) Berger, M. J. Chem. Educ. 2012, 89, 812−813. (25) Biedermann, G.; Sillen, L. G. Acta Chem. Scand. 1960, 14, 717− 725. (26) Bates, R. G. Determination of pH: Theory and Practice, 2nd ed.; Wiley: New York, 1973; p 27. (27) IUPAC. Compendium of Chemical Technology, 2nd ed. [Online]; Laboratory of Informatics and Chemistry of the Institute of Chemical Technology: Prague, 2006. http://goldbook.iupac.org; created by Nic, M.; Jirat, J.; Kost, B. (accessed Apr 2013). (28) Koryta, J. Ann. Rev. Mat. Sci. 1986, 16, 13−27. (29) Bates, R. G. Determination of pH: Theory and Practice, 2nd ed.; Wiley: New York, 1973; p 38. (30) Biedermann, G.; Hietanen, S. Acta Chem. Scand. 1960, 14, 711− 716. (31) Robinson, R. H. and Stokes, R. H. Electrolyte Solutions, revised 2nd ed.; Butterworths: London, 1968; p 408. (32) Debye, P.; Hückel, E. Phys. Z. 1923, 24, 185. (33) Robinson, R. H.; Stokes, R. H. Electrolyte Solutions, revised 2nd ed.; Butterworths: London, 1968; p 230.
Although dilute, the anode solution is not ideal. The activity coefficient f1 may be estimated from the Debye−Hückel limiting law32 log f1 = − 0.51|Z+Z −|I1/2
(9)
where the ionic strength is defined as I = 1 2 ΣciZi 2
(10)
and c is the molarity, Z is the charge. As
{Ag} = f1 [Ag]
(11)
pAganode = pAganode (uncorrected) − log f1
(12)
Log f1 is −0.016 for 0.001 M AgNO3. This will have the effect of shifting the entire pAg curve upward by 0.016. This changes the equivalence point very slightly, requiring recalculation, and an increase in pKsp by approximately 0.016. Although extensions of the Debye−Hückel law are available,33 at this concentration their predictions of log f1 differ by about 3%. As the activity correction itself is less than the uncertainty in Ksp, a 3% change in the correction is insignificant.
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ASSOCIATED CONTENT
S Supporting Information *
Comments for the instructor; the student handout containing detailed directions; and the spreadsheet used in data reduction. This material is available via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address †
295 Morio Drive, Mountain Top, Pennsylvania 18707, United States. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the King’s College Department of Chemistry and Physics. REFERENCES
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