In the Classroom edited by
Resources for Student Assessment
John Alexander
Assessing Students’ Conceptual Understanding of Solubility Equilibrium
University of Cincinnati Cincinnati, OH 45221
Andrés Raviolo Universidad Nacional del Comahue, Bariloche, 8400, Argentina;
[email protected] Although students of general chemistry often correctly solve different kinds of numerical problems (in solubility equilibrium, for example, Ksp and solubility calculations), this alone does not guarantee a conceptual understanding of the phenomenon because of misconceptions that persist after instruction (1–4). The following problem allows us to evaluate conceptual knowledge about solubility equilibrium and to diagnose difficulties in relation to previous concepts. It involves the following topics: dissolution, stoichiometry, chemical equations, the particulate nature of matter, ionic compounds, chemical equilibrium characteristics, solubility, the common ion effect, and Le Châtelier’s principle. To achieve an adequate conceptual understanding implies the ability to offer explanations and descriptions at the macroscopic level (experiments), the microscopic level (atoms, molecules, ions), and the symbolic level (symbols, formulas, equations), and the ability to establish appropriate connections among the three. One barrier to understanding chemistry is that instruction operates predominantly on the symbolic level—that is to say, on the most abstract level of the three (5). For this reason the problem below begins with a representation using particles; it is similar to methods used in assessing students’ conceptual knowledge about the kinetic theory of gases (6 ) and the application of Le Châtelier’s principle to homogeneous gaseous equilibria (7). The numbering of the particles (uncommon in this type of diagram) allows us to assess comprehension of the dynamic aspect of the equilibrium. The Problem Figure 1 shows a system in equilibrium between AgCl (a salt of poor solubility, Ksp = 1.6 × 10᎑10) and its ions, surrounded
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Macroscopic description 1. Describe the phenomenon from the moment the salt was added to the water, using each of the following terms at least once: solubility, saturated solution, ionic compound, solvent, solute, salt, equilibrium, dissolution, precipitation.
Utilization of chemical symbols 2. Write down the corresponding chemical equation.
Microscopic representations 3. Draw a previous situation, at a moment before equilibrium was reached but after the addition of the salt crystal to the water. 4. Numbering the ions, depict another state of equilibrium after some time has passed at a constant temperature. Explain. 5. Depict a new possible state of equilibrium reached after the addition of AgNO3 to the system at constant temperature.
This problem is aimed at secondary school students as well as at those in their first year of university. Although for these latter the assignment may appear to be a simple one, it is observed that for them, too, it presents a series of difficulties, which are discussed below. For classes that have studied ionic solutions in greater depth and have more realistically considered nonideal behavior, this evaluation may be amplified with additional items, such as: 6. Complete the description made in question 1, using each of the following terms at least once: ideal behavior, nonideal behavior, ionic strength, activity coefficient, univalent ions, electrostatic forces, incomplete dissociation, ionic pairing, complex ions. 7. Depict a new possible final solution reached if KNO3 is added to the system instead of AgNO3.
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by water molecules. For simplicity, the water molecules are not drawn; in their place a dotted line suggests a liquid medium.
Discussion
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Figure 1. The larger circles represent Cl᎑ ions and the smaller circles represent Ag+ ions. The ions of each type are numbered at random for identification.
Formulated in this way, the first question forces students to provide a deep description of the phenomenon. The sentences they construct will permit us to see whether the relationships they establish between the concepts involved are correct. When the students write the chemical equation in question 2, the following difficulties arise. (i) They have trouble identifying the species involved starting from the representation with particles. In other words, they have difficulty in relating the micro and symbolic levels. (ii) They
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In the Classroom
do not incorporate the corresponding aggregation states. (iii) They omit the double arrow. (iv) They confuse the chemical equation with the particular experimental situation; for example, ᎑ + they write AgCl(s) → ← 3Cl (aq) + 3Ag (aq) according to the number of ions in solution drawn in the figure. From the particle representations in question 4, one can evaluate whether the students have assimilated the three main characteristics of a system in equilibrium: 1. Reversible aspect: The student must take into consideration the coexistence of all the species in the new equilibrium situation. For example, some of them dissolve all the salt or completely precipitate it. 2. Constancy of the concentrations: the students must keep the number of particles in solution constant. 3. Dynamic aspect: They must maintain the same particles in each phase and change the numbers of the particles.
Alternative conceptions regarding these three characteristics of chemical equilibrium have been investigated in various studies with students in their final year of secondary school and first year of university (8–11). Nevertheless, studies have not been conducted on how students visualize and interpret solubility equilibrium, although secondary students’ conceptions of solubility were identified by Ebenezer and Erickson (12). The particulate nature of matter is a fundamental concept in chemistry, and an improper understanding of it can lead to 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 container constant (conservation of matter); 2. Correctly represent the ionic solid (Taber applied the term “molecular framework” to the tendency to perceive some ions within an ionic lattice to be bonded to one another as in a molecular solid [14]); 3. Properly represent dissociated reactants and products (some students depict all dissolved species as molecules of AgCl or HCl–AgOH; this difficulty was also mentioned by Smith and Metz [15]); 4. Consider the kinetic aspect of the model, the translation movements (students systematically draw the ions in the same place as in the original situation); and 5. Take into account the distribution of particles according to the corresponding aggregation state of matter.
In applying Le Châtelier’s principle or the common ion effect in question 5, students fail to maintain the solution’s neutrality, even though most assert that the solubility of AgCl decreases with the addition of AgNO3. Some students formulate it in quantitative terms; they calculate Ksp from the number of ions per unit of volume and obtain as a result that Ksp = [Ag+][Cl᎑] = 3 × 3 = 9. And in order to keep Ksp constant, 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. This Ksp calculation, made on the basis of nonconventional units of concentration, may be considered valid in this simulation. Questions 6 and 7 bring to the discussion the relationship between solubility and solubility product, which has been dealt with in various articles in this Journal (e.g., refs 16–21). They emphasize the difference between the values of the solubility of salts in water obtained using the Ksp algorithm and 630
the values obtained experimentally. This is due to effects such as ionic strength, incomplete dissociation, and the formation of complex ions, all of which augment the solubility of the salts. Question 6 allows us to confirm whether the students consider these effects and differentiate among them. Dissolved ions exert electrostatic forces among themselves that produce deviations from ideal behavior, and this necessitates the calculation of activity coefficients with solutions more concentrated than 10᎑3 M. Because of this effect of ionic interaction, if another salt that does not contain a common ion is added to the saturated solution, the solubility of the salt increases. For example, the solubility of the AgCl in water at 25 °C increases by 12% with the addition of 0.01 mol/L of KNO3(aq) and by 25% with a concentration of 0.1 mol/L. In question 7 one hopes that the students distinguish two opposite effects on the solubility of the AgCl: common ion and ionic strength, which respectively reduce and augment the solubility of the salt. Therefore, the students would have to draw a greater number of dissolved ions than in the initial situation. The formation of ionic pairs of univalent electrolytes is limited in solvents of high dielectric constant such as water, because the electrostatic attraction between the two dissolved ions depends on the charges and the distance between them. Nevertheless, for a solution saturated with a salt of very low solubility such as AgCl, the concentration of undissociated salt [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 aqueous solutions of transition metal halides. For the silver chloride system, when chloride is added to the solution, the formation of the complex ion AgCl2᎑ occurs (19). A procedure for calculating the solubility considering also the presence of complex ions is shown by Ramette (21) for a solution of silver acetate. On the other hand, it is known that the solubility of the silver chloride increases with the addition of NH3(aq) owing to the formation of the complex ion Ag(NH3)2+. Finally, a student might suggest the occurrence of hydrolysis with the formation of Ag(OH). But this effect is negligible; hydrolysis is only significant with very small ions of high charges such as Al3+, Cr3+, Fe3+, Bi3+, and Be2+. The case of CaCO3 is given as an example by Hawkes (19), in which the hydrolysis of the carbonate contributes more to the solubility than the equilibrium represented by the solubility product. In the drawings utilized to evaluate comprehension at the microscopic level, students must be capable of associating the particles with models and analogies (5). It is important to discuss with them what the model is about and, as with all models, to present its limitations. For example, the model used is two dimensional and static, and it represents a reduced number of particles. During the resolution of this problem the students prove highly motivated and actively participate in the discussion of 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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Nakhleh, M. J. Chem. Educ. 1993, 70, 52–55. Gabel, D. J. Chem. Educ. 1999, 76, 548–554. Cornely-Moss, K. J. Chem. Educ. 1995, 72, 715–716. Huddle, B. J. Chem. Educ. 1998, 75, 1175. 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. 10. Gorodetsky, M.; Gussarskly, E. Eur. J. Sci. Educ. 1986, 8, 427–441. 11. Bergquist, W.; Heikkinen, H. J. Chem. Educ. 1990, 67, 1000–1003.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
Ebenezer, J.; Erickson, G. Sci. Educ. 1996, 80, 181–201. Nakhleh, M. J. Chem. Educ. 1992, 69, 191–196. Taber, K. Educ. Chem. 1994, 31, 100–103. Smith, K.; Metz, P. J. Chem. Educ. 1996, 73, 233–235. Meites, L.; Pode, J.; Thomas, H. J. Chem. Educ. 1966, 43, 667–672. Haight, G. J. Chem. Educ. 1978, 55, 452–453. Russo, S.; Hanania, G. J. Chem. Educ. 1989, 66, 148–153. Hawkes, S. J. Chem. Educ. 1998, 75, 1179–1181. Koubek, E. J. Chem. Educ. 1976, 53, 254. Ramette, R. J. Chem. Educ. 1966, 43, 299–302.
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