In the Classroom

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Although students of general chemistry often correctlysolve different kinds of numerical problems (in solubilityequilibrium, for example, Ksp and solubility calculations), thisalone does not guarantee a conceptual understanding of thephenomenon because of misconceptions that persist afterinstruction (1–4). The following problem allows us to evaluateconceptual knowledge about solubility equilibrium and todiagnose difficulties in relation to previous concepts. It involvesthe following topics: dissolution, stoichiometry, chemicalequations, the particulate nature of matter, ionic compounds,chemical equilibrium characteristics, solubility, the commonion effect, and Le Châtelier’s principle.

To achieve an adequate conceptual understandingimplies the ability to offer explanations and descriptions atthe macroscopic level (experiments), the microscopic level(atoms, molecules, ions), and the symbolic level (symbols,formulas, equations), and the ability to establish appropriateconnections among the three. One barrier to understandingchemistry is that instruction operates predominantly on thesymbolic level—that is to say, on the most abstract level ofthe three (5). For this reason the problem below begins witha representation using particles; it is similar to methods usedin assessing students’ conceptual knowledge about the kinetictheory of gases (6 ) and the application of Le Châtelier’sprinciple to homogeneous gaseous equilibria (7 ). The num-bering of the particles (uncommon in this type of diagram)allows us to assess comprehension of the dynamic aspect ofthe equilibrium.

The Problem

Figure 1 shows a system in equilibrium between AgCl (asalt of poor solubility, Ksp = 1.6 × 10�10) and its ions, surrounded

by water molecules. For simplicity, the water molecules are notdrawn; in their place a dotted line suggests a liquid medium.

Macroscopic description1. Describe the phenomenon from the moment the salt

was added to the water, using each of the followingterms at least once: solubility, saturated solution, ioniccompound, solvent, solute, salt, equilibrium, dissolution,precipitation.

Utilization of chemical symbols2. Write down the corresponding chemical equation.

Microscopic representations3. Draw a previous situation, at a moment before equi-

librium was reached but after the addition of the saltcrystal to the water.

4. Numbering the ions, depict another state of equilibriumafter some time has passed at a constant temperature.Explain.

5. Depict a new possible state of equilibrium reached af-ter the addition of AgNO3 to the system at constanttemperature.

This problem is aimed at secondary school students aswell as at those in their first year of university. Although forthese latter the assignment may appear to be a simple one, itis observed that for them, too, it presents a series of difficulties,which are discussed below. For classes that have studied ionicsolutions in greater depth and have more realistically consid-ered nonideal behavior, this evaluation may be amplified withadditional items, such as:

6. Complete the description made in question 1, usingeach of the following terms at least once: ideal behavior,nonideal behavior, ionic strength, activity coefficient,univalent ions, electrostatic forces, incomplete disso-ciation, ionic pairing, complex ions.

7. Depict a new possible final solution reached if KNO3

is added to the system instead of AgNO3.

Discussion

Formulated in this way, the first question forces studentsto provide a deep description of the phenomenon. The sentencesthey construct will permit us to see whether the relationshipsthey establish between the concepts involved are correct.

When the students write the chemical equation inquestion 2, the following difficulties arise. (i) They havetrouble identifying the species involved starting from therepresentation with particles. In other words, they havedifficulty in relating the micro and symbolic levels. (ii) They

Assessing Students’ Conceptual Understandingof Solubility EquilibriumAndrés RavioloUniversidad Nacional del Comahue, Bariloche, 8400, Argentina; araviolo@bariloche.com.ar

Resources for Student Assessmentedited by

John AlexanderUniversity of CincinnatiCincinnati, OH 45221

Figure 1. The larger circles represent Cl� ions and the smaller circlesrepresent Ag+ ions. The ions of each type are numbered at randomfor identification.

1

2

3

34

5

2 1 5 4 6

6 7 8 8 7

11 10 9 9 10

13 12 11 13 12

In the Classroom

630 Journal of Chemical Education • Vol. 78 No. 5 May 2001 • JChemEd.chem.wisc.edu

do not incorporate the corresponding aggregation states. (iii)They omit the double arrow. (iv) They confuse the chemicalequation with the particular experimental situation; for example,they write AgCl(s) →← 3Cl�(aq) + 3Ag+(aq) according to thenumber of ions in solution drawn in the figure.

From the particle representations in question 4, one canevaluate whether the students have assimilated the three maincharacteristics of a system in equilibrium:

1. Reversible aspect: The student must take into consid-eration the coexistence of all the species in the newequilibrium situation. For example, some of themdissolve all the salt or completely precipitate it.

2. Constancy of the concentrations: the students must keepthe number of particles in solution constant.

3. Dynamic aspect: They must maintain the same particlesin each phase and change the numbers of the particles.

Alternative conceptions regarding these three characteris-tics of chemical equilibrium have been investigated in variousstudies with students in their final year of secondary schooland first year of university (8–11). Nevertheless, studies havenot been conducted on how students visualize and interpretsolubility equilibrium, although secondary students’ conceptionsof solubility were identified by Ebenezer and Erickson (12).

The particulate nature of matter is a fundamental conceptin chemistry, and an improper understanding of it can leadto difficulties with other concepts that are built upon it (13).In questions 3–5 that the students must

1. Keep the number of ions in the closed containerconstant (conservation of matter);

2. Correctly represent the ionic solid (Taber applied theterm “molecular framework” to the tendency to per-ceive some ions within an ionic lattice to be bondedto one another as in a molecular solid [14]);

3. Properly represent dissociated reactants and products(some students depict all dissolved species as moleculesof AgCl or HCl–AgOH; this difficulty was alsomentioned by Smith and Metz [15]);

4. Consider the kinetic aspect of the model, the translationmovements (students systematically draw the ions inthe same place as in the original situation); and

5. Take into account the distribution of particles accordingto the corresponding aggregation state of matter.

In applying Le Châtelier’s principle or the common ioneffect in question 5, students fail to maintain the solution’sneutrality, even though most assert that the solubility of AgCldecreases with the addition of AgNO3. Some students for-mulate it in quantitative terms; they calculate Ksp from thenumber of ions per unit of volume and obtain as a resultthat Ksp = [Ag+][Cl�] = 3 × 3 = 9. And in order to keep Kspconstant, they draw a possible final situation with 9 Ag+ ions,1 Cl� ion, and 8 NO3

� ions, supposing that 8 Ag+ and 8 NO3�

ions had been added and 2 Ag+ and 2 Cl� ions precipitated. ThisKsp calculation, made on the basis of nonconventional unitsof concentration, may be considered valid in this simulation.

Questions 6 and 7 bring to the discussion the relationshipbetween solubility and solubility product, which has beendealt with in various articles in this Journal (e.g., refs 16–21).They emphasize the difference between the values of the solu-bility of salts in water obtained using the Ksp algorithm and

the values obtained experimentally. This is due to effects suchas ionic strength, incomplete dissociation, and the formationof complex ions, all of which augment the solubility of thesalts. Question 6 allows us to confirm whether the studentsconsider these effects and differentiate among them.

Dissolved ions exert electrostatic forces among themselvesthat produce deviations from ideal behavior, and this neces-sitates the calculation of activity coefficients with solutionsmore concentrated than 10�3 M. Because of this effect of ionicinteraction, if another salt that does not contain a common ionis added to the saturated solution, the solubility of the saltincreases. For example, the solubility of the AgCl in water at25 °C increases by 12% with the addition of 0.01 mol/L ofKNO3(aq) and by 25% with a concentration of 0.1 mol/L.In question 7 one hopes that the students distinguish twoopposite effects on the solubility of the AgCl: common ionand ionic strength, which respectively reduce and augmentthe solubility of the salt. Therefore, the students would haveto draw a greater number of dissolved ions than in the initialsituation.

The formation of ionic pairs of univalent electrolytes islimited in solvents of high dielectric constant such as water,because the electrostatic attraction between the two dissolvedions depends on the charges and the distance between them.Nevertheless, for a solution saturated with a salt of very lowsolubility such as AgCl, the concentration of undissociatedsalt [Ag+Cl�] is similar to that of the silver ion [Ag+] (17 ).This effect is more significant when both ions are divalent(16, 18, 20), as for example in CaSO4.

The formation of complex ions is common in aqueoussolutions of transition metal halides. For the silver chloridesystem, when chloride is added to the solution, the formationof the complex ion AgCl2� occurs (19). A procedure for calcu-lating the solubility considering also the presence of complexions is shown by Ramette (21) for a solution of silver acetate.On the other hand, it is known that the solubility of the silverchloride increases with the addition of NH3(aq) owing to theformation of the complex ion Ag(NH3)2

+.Finally, a student might suggest the occurrence of hydroly-

sis with the formation of Ag(OH). But this effect is negligible;hydrolysis is only significant with very small ions of high chargessuch as Al3+, Cr3+, Fe3+, Bi3+, and Be2+. The case of CaCO3 isgiven as an example by Hawkes (19), in which the hydrolysisof the carbonate contributes more to the solubility than theequilibrium represented by the solubility product.

In the drawings utilized to evaluate comprehension at themicroscopic level, students must be capable of associating theparticles with models and analogies (5). It is important todiscuss with them what the model is about and, as with allmodels, to present its limitations. For example, the model usedis two dimensional and static, and it represents a reducednumber of particles.

During the resolution of this problem the students provehighly motivated and actively participate in the discussionof both their own answers and those of their peers.

Literature Cited

1. Nurrenbern, S.; Pickering, M. J. Chem. Educ. 1987, 64,508–510.

2. Sawrey, B. J. Chem. Educ. 1990, 67, 253–254.3. Pickering, M. J. Chem. Educ. 1990, 67, 254–255.

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4. Nakhleh, M. J. Chem. Educ. 1993, 70, 52–55.5. Gabel, D. J. Chem. Educ. 1999, 76, 548–554.6. Cornely-Moss, K. J. Chem. Educ. 1995, 72, 715–716.7. Huddle, B. J. Chem. Educ. 1998, 75, 1175.8. Johnstone, A.; MacDonald, J.; Webb, G. Educ. Chem. 1977,

14, 169–171.9. Hackling, M.; Garnett, P. Eur. J. Sci. Educ. 1985, 7, 205–214.

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11. Bergquist, W.; Heikkinen, H. J. Chem. Educ. 1990, 67,1000–1003.

12. Ebenezer, J.; Erickson, G. Sci. Educ. 1996, 80, 181–201.13. Nakhleh, M. J. Chem. Educ. 1992, 69, 191–196.14. Taber, K. Educ. Chem. 1994, 31, 100–103.15. Smith, K.; Metz, P. J. Chem. Educ. 1996, 73, 233–235.16. Meites, L.; Pode, J.; Thomas, H. J. Chem. Educ. 1966, 43,

667–672.17. Haight, G. J. Chem. Educ. 1978, 55, 452–453.18. Russo, S.; Hanania, G. J. Chem. Educ. 1989, 66, 148–153.19. Hawkes, S. J. Chem. Educ. 1998, 75, 1179–1181.20. Koubek, E. J. Chem. Educ. 1976, 53, 254.21. Ramette, R. J. Chem. Educ. 1966, 43, 299–302.