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 10^{th} 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!

Readers can find the Student Document and Teacher Key in the Supporting Information when logged into their ChemEd X account.

## NGSS

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. Use mathematical representations of phenomena to support claims.

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. Use mathematical representations of phenomena to support claims.

Students who demonstrate understanding can construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties.

*More information about all DCI for HS-PS1 can be found at https://www.nextgenscience.org/dci-arrangement/hs-ps1-matter-and-its-interactions and further resources at https://www.nextgenscience.org.

Students who demonstrate understanding can construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties.

Assessment is limited to chemical reactions involving main group elements and combustion reactions.

Examples of chemical reactions could include the reaction of sodium and chlorine, of carbon and oxygen, or of carbon and hydrogen.

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## Comments 3

## Thanks

Hi Dena!

I have a confession- I am just ok at teaching equilibrium, and providing structures for my students to tackle these tougher problems. Thank you so much for sharing this DSE approach - I have bookmarked this in my notes for next time I teach this.

Have a wonderful end of school year!

## Interesting

I love BCA tables, though I've only tried them once, and my students HATED them. Probably my fault though. it was my first time. By the time I was teaching Equilibrium for AP, I was much better. While I would have a hard time telling students to guess at the lim react, I can see its merits for a Gen Chem class. It avoids the difficult and often confusing line of reasoning and side tracks them from the important question.

at any rate, I'll probably restructure to include more BCA next year in Gen Chem. It is a valuable and powerful tool.

mrfiskteach

## Success with BCA

Thanks for this blog post - it has changed my teaching!

I wanted to share a resource that I made to help students (pre-AP) understand limiting reactants through Acid-Base BCA problems. For my students that were struggling with BCA, this resource helped them connect a visual with the math. Like the dimensional analysis method, BCA could also be just a set of random numbers unless students connect it with the molecules reacting. I am hoping that this will help another teacher in their implementation of BCA tables.

I just published my own blog post with a worksheet and teacher key. I hope you will find them valuable.

Using Visible BCA Tables to Teach Limiting Reactants