The theory behind BCA Tables (Before, Change, After) is to create a table underneath the chemical reaction that focuses exclusively on moles. Mass, volume or any other non-mole unit must first be changed into moles before working within the table. After these changes have been made the BCA table can effectively highlight the mole ratio concept. An introduction to BCA Tables is shown below for those unfamiliar with them.
One of the biggest advantages to using BCA tables over dimensional analysis is the tables produce final amounts for all chemicals and this lends to very simple limiting reagent solutions. This is especially true for calculations where the excess reagent is to be quantitatively determined. By working exclusively in moles it is very simple to determine the final amounts of reagents in moles because the change is restricted by the balanced coefficients. The changes of each chemical must be proportional to their coefficients in the balanced reaction.
Another important advantage to BCA Tables is their connections to more complex stoichiometry analysis. One of these is that BCA tables mirror ICE (or RICE) chart analysis used for equilibrium. In equilibrium calculations you have stoichiometry limitations of the Change portion of the ICE chart and equilibrium constant limitations of the Equilibrium. Students who have learned stoichiometry using BCA tables have considerable advantage in learning equilibrium calculations as they are familiar with these organizational tools. They now just need to understand that the reaction will not go to completion and so the Change will not result in any particular reagent running out. For acid-base chemistry where we often deal with a neutralization reaction that goes to completion and an equilibrium established with the solution after neutralization, this can greatly simplify the calculations.
A strong method of emphasizing the mole ratio in a unique fashion is to complete teaching of stoichiometry with graphical analysis of reagent amounts as a reaction progresses. The slopes of each reagent should reflect their balanced coefficient. The point where a reactant reaches the x-axis is where the reaction stops and at this point the amounts of product and excess reagents should be determined. This unique perspective should pay dividends again in equilibrium as well as thermochemistry that links to stoichiometry.
Disadvantages of BCA tables are that they take up more room to solve and because they are thorough in their analysis they can take longer. I personally did not find either of these to be a substantial issue. While teaching I did feel as though I was doing less and questioned its effectiveness, but seeing such a large percentage of students able to easily do a limiting reagent problem has minimized my pedagogical concerns. Mole conversions I found to require more thinking on behalf of the students. BCA allows you to emphasize the molar mass concept and the ratio concept better than dimensional analysis, although you can also make a routine of dividing by the molar mass to get into the BCA table and multiplying to get out of the table if needed.
I look forward to the connections I plan on making with BCA tables and ideal gas stoichiometry, titrations and enthalpy considerations. In the future I plan on using them for equilibrium ICE charts, Le Chatelier’s Principle and acid-base titrations. I had concerns over not being able to do some of the engaging teaching methods, but this was not the case in practice. We still were able to easily do the fizzy Hawaiian Punch lesson and we were also able to do a lot of particle representations of reactions. Any lesson previously done can be modified without trouble into this new teaching method. Some additional BCA sample problems and solutions are linked below.
Solutions to sample problems
How I used to teach Limiting Reagent
