5 Steps to Chemistry Problem Solving

By Stefan Bosworth

“I studied. I knew all the formulas. I did the homework. But you never told me there would be problems like these . . .”

Here’s our list of vital steps for each problem they encounter:

1. Read the question thoroughly.

Of course students think they do this already, but we think that it’s essential to show them what reading “thoroughly” means. We explain that a necessary component of thorough reading is re-phrasing; if you can put the question in your own words, then you begin to establish ownership, and if you now feel the question belongs to you, you’ll invest more energy in solving it.

Example: “Flask A contains 3.75 L of O₂ at a pressure of 658 torr. Flask B contains 5.46 L of H₂ at a pressure of 354 torr. The gases are combined in Flask C, whose volume is 8.44 L, and the gases are ignited. (The temperature is held constant at 109ºC throughout.) Identify the gases that remain after the reaction, and give the partial pressure of each.”

Paraphrase:

“We’re given a container of oxygen gas, and we’re told P, V, and T. Same for a second container of hydrogen. The gases get mixed in a larger container and they react. They don’t give the reaction, but I can figure it out. T stays constant. I have to tell them what gases are left and what their partial pressures are.”

2. In this step, which has three elements, we lay the groundwork for a solution plan.

 a. Classify the problem.

Students who excel on the AP exam, or on exams in honors classes, have worked a great deal of problems and have gathered their problem-solving experiences into categories. They can read a problem that involves a gas-phase reaction and say something like this:

“This problem concerns the reaction of two gases, X and Y. The data we’re given allow us to compute the amounts of each one, so it looks as if we have a limiting reactant problem.”

This student is going beyond re-phrasing the problem—she’s classifying the problem, trying to fit it into categories that she has already worked out. Most students do this to some extent already; we want them to become deliberate and systematic about their use of classification.

b. Determine what principles are at stake.

For some problems, this step is almost all that’s needed. Take this problem:

“Arrange the following atoms in order of increasing ionization energy: F, Li, C.”

By careful reading and classifying, we can determine that these three elements all occur in the second row of the periodic table. But one of the principles that we’ve learned is that ionization energies increase from left to right in a row owing to the dominant influence of increasing nuclear charge. With that insight, the problem’s almost solved.

c. Identify the formulas that could help us.

Many students consider themselves experts at this step—what can be hard about memorizing formulas?—but they can become confused by multiple formulas that resemble each other but apply to different situations. We encourage them to learn the brief stories that breathe life into formulas so that they can make the correct choices. (As it happens, no formulas are necessary for the ionization energy problem.)

3. Make a plan.

Here’s where we lay out a strategy based on the thinking we’ve done so far. We could write it out in numbered steps, draw up a flowchart, or just visualize it (preferably in brilliant color!). For the ionization energy question, the plan is short:

          1. Determine how the three elements are related in the periodic table (i.e., they’re in the same row).

          2. Recall that IE increases from left to right in the table.

          3. Arrange the elements in the order they appear in the table, from farthest left to farthest right.

For the previous example, which required a calculation, the plan could be stated this way:

1. Find the moles of O₂ and H₂ using the ideal gas law.

2. Determine the limiting reactant.

3. Use the LR to calculate the moles of product and of excess reactant.

4. Use the ideal gas law to calculate the partial pressure of each gas that remains.

4. Solve the problem.

Having the plan laid out should help this to go smoothly. We emphasize the usual cautions about showing calculations clearly, including all units, and being consistent with significant figures.

5. Check the answer.

We think qualitative checking is very important—are the units what you’d expect? Is the answer in the ballpark given the value of the inputs and your prior experience? Could you get the same answer a different way, or could you use the answer to work backwards to calculate one of the starting values?

We reinforce these problem-solving steps in our teaching by using them when we solve problems at the board and by asking our students to follow them explicitly on in-class exercises, on homework, and on exams. We’re pleased with the extra maturity our students have gained.