Think about the chemistry, not the math

I tell students on the first day in my undergraduate chemistry class — think about the chemistry, not the math.

Almost every chemistry calculation problem can be deconstructed into a math word problem. This makes the problems relatively straightforward to solve but in doing so can miss the point entirely in terms of learning the fundamental concepts of chemistry. In this article I describe where I have encountered this problem the most in 1st year chemistry. 

Students run into this reliance on the math with stoichiometry, which is typically their first encounter with chemical reactions. Take a thermite reaction as a fiery example:

2 Al + Fe2O3--> 2 Fe + Al2O3.

If 3 moles of Al and an excess of Fe2O3 react, how many moles of Al2O3 are produced?  

When faced with a problem like this, students frequently ask: “Do I use or as the stoichiometric conversion factor?” They are looking for a number to plug into an equation instead of looking at the reaction and thinking about what is produced. A careful chemical reading of the equation makes the answer to that question readily apparent. The equation states that 2 moles of Al are consumed to produce 1 mole of Al2O3.

If students translate the reaction using fully descriptive language, it is easier to see the relationship.

mole equation

Yes, stoichiometry looks like a mathematical equation but it also includes all of the important chemistry. Writing the solution out this way allows students to see the quantitative relationship between reactant and products.

This approach can be extended to limiting reactant problems. Looking at the balanced reaction, students can see that you need twice as much Al as Fe2O3. If 3 moles of Al and 3 moles of Fe2O3 react, how much Al2O3 is produced and how much of which reactant remains? The first step is to determine the limiting reactant. Look at the balanced reaction: it states that 2 moles of Al are consumed for each mole of Fe2O3 consumed.

mole ratio

Each mole of Fe2O3 reacts with 2 moles of Al. So the amount of Al required to react with 3 moles of Fe2O3 is 6. Here we have only 3 moles of Al, so Al is the limiting reactant. Another way to think of it is: for each mole of Al that reacts only 0.5 mole of Fe2O3 react. Three moles of Al react with 1.5 moles of Fe2O3. There are 3 moles of Fe2O3 which is more than needed to react with the Al; so, Al is the limiting reactant. This is much less confusing than simply comparing ratios.

Another common occurrence of students looking to math for the solution is general equilibrium. Although it requires many calculations, focusing only on the mathematics can make equilibrium very confusing. Students ask: what equation do I use? Can any simplifying assumptions be made? I direct students to first look at the concentrations of the reactants and products and the value of the equilibrium constant. With this, one can get a good idea of what the answer should be before any calculations are done. If students understand what K is, they would know that if a K is large then there must be more product than reactant at equilibrium. If K is small then the reverse is true. I stress that if one keeps in mind what K is, then one can tell if the answer makes any sense.   

The topic of pH is another area that demonstrates how confusing a strictly “plug numbers into an equation” approach can be. The most striking example I have seen is asking students the pH of a 10-8 mol L-1 solution of a strong acid such as HCl at room temperature. Half the class of 400 students will say that the pH of this solution of a strong acid is 8. They simply take –log[H3O+] without really thinking about what is in the solution. Remind students to think about the chemistry of the solution. Any solution of an acid, even a very dilute solution, should have a pH less than or equal to 7 but never higher than 7 at 25 °C.

The ICE table (initial, change, equilibrium) is a helpful tool for students to track equilibrium calculations, but sometimes students forget what chemistry they are tracking. For example, when students are asked to calculate the pH of a solution of a weak base they can usually set up the correct ICE tables and solve for the variable x. Problems arise when students forget what x is. For an aqueous solution of a weak base, x is the concentration of OH- in solution, not the concentration of H3O+.

I cannot stress enough that if students remember the chemistry and can predict the ballpark answer to a question before they start a calculation, there will be far fewer errors on tests and assignments.