I recently stumbled across a blog about the use of BCA (Before Change After) tables for stoichiometry written by Lowell Thomson. I was thrilled to discover ChemEd Xchange! I wanted to share my journey, spurred on by my students, into the extensive use of the BCA approach in AP and IB chemistry. I have attached some notes and the key for daily practice on how I apply the approach to titration curve calculations. I have also included two videos to demonstrate the teaching method. Note that I use the acronym BSA – Before Shift After – instead of BCA.
I want to admit up front that BCA is a little more challenging on the front end in terms of student learning, especially for limiting reactant problems. However, there is a huge win in terms of the amount of information and understanding obtained in the end. When a colleague of mine (Daniel Haradem) decided to use them as well he came in and exclaimed that once he figured out the limiting and filled in the table all of the questions became trivial! My students find that as well.
A few compelling reasons to consider this method include the following.
(1) There is an improved understanding and determination of excess reactant remaining. Students who are taught an algorithmic method to determine this have to rely on memorization to obtain the correct answer. Sadly, most miss these questions at the AP level.
(2) AP expects students to be able to draw or interpret particle diagrams showing all substances remaining in solution after a reaction has occurred. Completion of a BCA table clearly shows ALL species present, including all products and the excess reactant remaining.
(3) Smooth transition into equilibrium for common ion or acid base type questions. This has been the biggest win for my class. I believe the approach to titration curves has improved my students understanding of not only the quantitative aspects, but more importantly the qualitative aspects of acid base chemistry.
In terms of the difficulty with limiting reactants, I share three approaches with my students. The most accurate, but longest approach is to perform a quick stoichiometry problem from one reactant to another and compare the moles needed to the moles available. For some reason, this is very challenging for some of my students. If the mole ratio is simple, I encourage them to estimate this concept. If students are not readily grasping either of these, I encourage them to guess – yes guess – the limiting reactant. I have them fill in the chart for the reactants and if one of the answers is negative, they clearly guessed wrong. A quick erase and re-calculation and they are back on track. The video below shows an example of a limiting reactant problem that I worked for my 10th grade pre-AP students. Ensuring they have their mole ratio correctly can be a slight problem so I teach that it is to/from or that the limiting reactant coefficient is in the denominator.
If all dilutions are accounted for, molarity can be used in a BCA table instead of moles. For my AP & IB students I call this approach “DSE” for “Doc Saves Everyone”. We use this as a checklist for all equilibrium. The “D” stands for “dilution”. The first question we ask is “did we add volume to volume?” If the answer is yes we perform the appropriate dilutions. I find that performing dilutions right away helps avoid loss of points from failure to divide by the total volume at the end. The “S” stands for “stoichiometry”. Do we have (1) strong acid/base (2) soluble salt or (3) an acid base neutralization? The results of the dilution provide us with initial molarity values for our stoichiometry problem. Finally, the “E” stands for “equilibrium”. The results of the stoichiometry feed into the initial molarity for our equilibrium calculation. The next video shows me working a point on the titration curve for my AP & IB students. Of course there are shorter ways to do this particular point, but I like to show my students that this method will always provide a framework and valuable information along the way. I don’t introduce short-cuts that may by-pass understanding until students grasp the overall concept. I welcome comments and ways to improve my students’ learning!