In a recent contribution to ChemEd X "Stoichiometry is Easy", the author states that he has "vacillated over the years between using an algorithmic method, and an inquiry-based approach to teaching stoichiometry." I would like to suggest that there is another approach to mastering stoichiometry and that it should precede the algorithmic one: it is the conceptual approach based on a particle model to represent the species involved in chemical reactions.
Most teachers, and I include among them those responsible for writing the items for the high-stakes tests the author describes, have a tendency to equate quantitative fluency with a genuine understanding of the underlying processes. After all, if students can correctly determine the mass of a product to be expected or which is the limiting reactant, then certainly they must know what is going on during the reaction, right? Unfortunately, as researchers such as Craig Bowen and Diane Bunce1 have shown, typical quantitative test items don't probe whether students have persistent naïve conceptions about chemical reactions and processes.
The 5-step algorithm "Stoichiometry is Easy" to the tune of "Hark the Herald Angels Sing" described by the author is catchy and appears to be effective. But l believe that learning any algorithm is most effective when it follows an introduction stressing conceptual understanding. As Dudley Herron2 wrote about algorithms:
For similar reasons, I teach efficient algorithms for such routine tasks as balancing chemical equations (after I am convinced that the student knows what a balanced equation is and why we want one) and encourage students to use them. I emphasize the point that the algorithm should be sensible (i.e., we know what the product of the procedure means) but should not require them to think any more than necessary. Indeed, the purpose of an algorithm is to reduce the load on working memory and save time. [My emphasis]
In the approach advocated by Modeling Instruction in High School Chemistry3, students use particle diagrams depicting the reaction mixture before and after a reaction has occurred to make the point that the balanced chemical equation relates numbers of particles, not mass or volume, the quantities we typically use to measure how much stuff is involved. The use of a BCA (before-change-after) table, similar to the ICE table used in a quantitative treatment of equilibrium mixtures, helps students connect the particle diagrams to a more convenient way of representing the ratio of reacting species. Consider the example below:
| 2 H2S | + | 3 O2 | → | 2 SO2 | + | 2 H2O | |
| Before | 4 | xs | 0 | 0 | |||
| Change | -4 | -6 | +4 | +4 | |||
| After | 0 | xs | 4 | 4 | |||
Note: xs is shorthand for "excess"
The first examples involve calculations that can be done in one's head and easily related to particle diagrams. By this time students have learned that moles are simply weighable amounts of given species, so they readily accept that the ratios of coefficients relate to numbers of particles. What happens if the information about the situation is given in terms of mass? One has to apply techniques learned in an earlier unit to convert the givens to moles, chemists' counting unit. If the desired quantity is mass (or volume), then that calculation is done on the side using the molar mass or molar volume as the required conversion factor.
The particle diagrams are especially useful when dealing with limiting reactant problems. Consider the reaction in which water is produced when hydrogen and oxygen gas react.
2 H2 + O2→ 2 H2O
The reactant mixture might look like the box at left. Students are encouraged to cross out reacting species and draw in product species until the reaction can no longer proceed. They should end up drawing a product mixture as shown in the "after" box.
| Before | After |
|---|---|
 |  |
The corresponding BCA table appears below:
| 2 H2 | + | O2 | → | 2 H2O | |
| Before | 4 | 4 | 0 | ||
| Change | -4 | -2 | +4 | ||
| After | 0 | 2 | 4 | ||
Once students recognize the connection between the numbers in the table and the particle diagrams for these "obvious" examples, it's a straightforward step to examining cases where one might have to guess which reactant is consumed first. Consider the reaction between aluminum and iodine to produce aluminum iodide.
| 2 Al | + | 3 I2 | → | AlI3 | |
| B | 0.50 | 0.72 | 0 | ||
| C | -0.50 | -0.75?? | +0.50 | ||
| A | 0 | ??? | |||
Here, the typical student guess - that the reactant with the fewest number of moles available is limiting - leads to an obvious problem when one multiplies the 0.50 moles of Al by the 3/2 ratio given in the balanced equation. Students reassess and assume that all of the iodine must be consumed in the reaction and complete the table correctly as follows.
| 2 Al | + | 3 I2 | → | AlI3 | |
| B | 0.50 | 0.72 | 0 | ||
| C | -0.48 | -0.72 | +0.48 | ||
| A | 0.02 | 0 | 0.48 | ||
This approach not only shows the correct number of moles of aluminum iodide produced, but also how many moles of the excess reactant remain.
One might argue, "Well, isn't using the table just a different algorithm?" This might be true if it weren't for the fact that the instructor explicitly connects the values that populate the table with particle diagrams when the students first encounter its use. When a serious effort is made to make the "steps" in a procedure sensible to students, they are more likely to understand what they are doing as they are doing it.
References
- Bowen, C. and Bunce, D., "Testing for Conceptual Understanding in General Chemistry" The Chemical Educator, Vol. 2, No 2, 1997
- Herron, J. Dudley. The Chemistry Classroom, The American Chemical Society, 1996
- American Modeling Teachers Association, http://modelinginstruction.org