In the Classroom edited by
Applications and Analogies
Ronald DeLorenzo
A Cyclist’s Guide to Ionic Concentration
Middle Georgia College Cochran, GA 31014
Arthur M. Last Department of Chemistry, University College of the Fraser Valley, Abbotsford, BC, Canada V2S 7M9
A number of analogies to assist students with their understanding of stoichiometry, particularly with the concept of limiting reagent, have been published in recent years (1–5). A related concept, and one that seems to be a source of confusion to many of my first-year students, is that of ionic concentration. In past years, when I have asked students to tell me the concentration of chloride ion in a 0.10 mol L᎑1 solution of magnesium chloride, MgCl2, the most frequently given incorrect answer is 0.033 mol L᎑1. A few students usually suggest 0.050 mol L᎑1, but this answer is generally given by those who believe that the chloride ion is Cl2᎑ (or Cl 2᎑ if they haven’t come to terms with the 2+ charge on a magnesium ion). Recently, I became even more concerned over student confusion in this area when I asked a group of students what the chloride ion concentration would be if 0.10 mol of barium chloride dihydrate, BaCl2⭈2H2O, was dissolved in water to give 1.0 L of solution. One student suggested that it would be 0.040 mol L᎑1! When asked to rationalize this answer, the student indicated that the three species present in this compound—barium ions, chloride ions, and water molecules—were in a ratio of 1:2:2; thus, 0.10 mol of barium chloride should consist of 0.020 mol of barium ion, 0.040 mol of chloride ion, and 0.040 mol of water molecules. At this point I decided to use a simple analogy to try to remedy the situation. The analogy is a modification and extension of the bicycle analogy that has been used to explain limiting reagent (6 ). Consider a unicycle to be analogous to sodium chloride. When the unicycle is dismantled we get one wheel and one frame. When 10 unicycles are dismantled we get 10 wheels and 10 frames. Similarly, dismantling 6.0 × 1023 unicycles (i.e., 1.0 mol) gives 6.0 × 10 23 wheels (i.e., 1.0 mol) and 6.0 × 10 23 frames (i.e., 1.0 mol). By analogy, if we “dismantle” 1.0 mol of sodium chloride by dissolving it in 1.0 L of water we get 1.0 mol of sodium ions and 1.0 mol of chloride ions. Consequently, [Na +] = [Cl ᎑] = 1.0 mol L᎑1. The analogy can be extended to include compounds of the type A X 2 by comparing the compound to a bicycle instead of a unicycle (Fig. 1). If we dismantle a bicycle, we obtain one frame and two wheels. Using the same logic as before, I then explain that 10 bicycles would produce 10 frames and 20 wheels, and that 6.0 × 10 23 bicycles would give 6.0 × 1023 frames and 1.2 × 1024 wheels. That is, 1.0 mol of bicycles gives 1.0 mol of frames and 2 .0 mol of wheels. After considering this analogy, students should be much more willing to accept that the “dismantlement” of 1.0 mol of magnesium chloride will produce 1.0 mol of magnesium ions and 2.0 mol of chloride ions (Fig. 2). At this point one could quickly point out the parallel between a child’s tricycle, 1 frame and 3 wheels, and a compound of the type AX 3 in which each formula unit of the compound consists of one cation and three anions. However, our analogies might not even yet have satisfied the student
Figure 1. 1 bicycle → 1 frame + 2 wheels; 6.0 × 1023 bicycles → 6.0 × 1023 frames + 1.2 × 1024 wheels; 1 mol of bicycles → 1 mol of frames + 2 mol of wheels.
Figure 2. 1 formula unit magnesium chloride → 1 magnesium ion + 2 chloride ions; 6.0 × 1023 formula units magnesium chloride → 6.0 × 1023 magnesium ions + 1.2 × 1024 chloride ions; 1 mol magnesium chloride → 1 mol magnesium ion + 2 mol chloride ions.
who was confused by the barium chloride dihydrate example mentioned above. A possible solution here would be to consider the compound BaCl2⭈2H2O as being analogous to a wheelchair consisting of a frame (the Ba2+ ion), two large wheels (the chloride ions), and two smaller wheels (the water molecules). By this stage of the proceedings, students should be ready to deduce that 1.0 mol of wheelchairs would produce 2 mol of large wheels and that the chloride-ion concentration in 1.0 L of solution containing 0.10 mol of barium chloride dihydrate is 0.20 mol L᎑1. Note that students for whom these analogies are intended should not be confused by telling them that, in reality, most ionic substances do not totally conform to the ideal dissociation pattern that we assume for the purposes of calculating simple ionic concentrations (7). Overhead transparencies showing the various cycles and diagrams of some analogous ionic compounds would be useful when presenting these analogies to students. Literature Cited 1. 2. 3. 4.
Bleam, W., Jr. J. Chem. Educ. 1981, 58, 184–185. Last, A. M. J. Chem. Educ. 1983, 60, 748–750. McMinn, D. J. Chem. Educ. 1984, 61, 591. DeLorenzo, R. A. Problem Solving in General Chemistry, 2nd ed.; Wm. C. Brown: Dubuque, IA, 1993. 5. Fortman, J. J. J. Chem. Educ. 1994, 71, 571–572. 6. Rayner-Canham, G.; Last A. Chemistry: A First Course; Addison Wesley: Don Mills, ON, Canada, 1988. 7. Hawkes, S. J. J. Chem. Educ. 1996, 73, 421–423.
JChemEd.chem.wisc.edu • Vol. 75 No. 11 November 1998 • Journal of Chemical Education
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