Stoichiometry: Sizing an Airbag Charge

• Project an image of a deployed driver-side airbag and write the simplified reaction on the board: 2 NaN3(s) → 2 Na(s) + 3 N2(g).
• Prepare a one-page calculation sheet with the 60.0 L airbag problem, a dimensional-analysis template, and two independent practice problems. Students need calculators only after the unit pathway is approved.
• Use this only as a paper calculation; do not bring sodium azide to class. Confirm any chemical-safety discussion against school procedures.

Project the deployed-airbag image: “This bag can fill with roughly 60.0 L of gas almost instantly. It does not contain a 60-L tank. How could a small solid charge make that much gas, and how much sodium azide would be needed?” Students silently commit to an estimate and a prediction: Would the mass needed be closer to 6 g, 60 g, or 600 g? Require one reason from memory: what does a coefficient in a balanced equation count?

Ask pairs to distinguish observations from inferences. Observation: the inflated bag occupies a large volume. Inference: the airbag must have stored compressed air. Collect two predictions without confirming them. Tell students the calculation will test the common but inaccurate idea that a reaction coefficient is a mass ratio or that the gas was simply stored in the bag.

Frame the reaction as a simplified model of one airbag reaction; actual inflators include additional reactions that safely manage sodium. Read the equation aloud and recall: coefficients give mole ratios. Because the target is gas volume and the starting substance is a solid mass, build the only sensible pathway before calculating: volume N2 → moles N2 → moles NaN3 → grams NaN3.

At room conditions in this class model, use 24.0 L = 1.00 mol gas. State the needed conversion facts on the board: 1 mol N2 / 24.0 L N2; 2 mol NaN3 / 3 mol N2; 65.01 g NaN3 / 1 mol NaN3.

Think aloud through unit cancellation for 60.0 L N2. “I begin with the quantity I am given, 60.0 L N2. I want grams NaN3 at the end, so each fraction must cancel the unit I no longer want. I do not start by multiplying 60.0 by the coefficients; coefficients are not grams.” Write, but do not yet compute: 60.0 L N2 × (1 mol N2/24.0 L N2) × (2 mol NaN3/3 mol N2) × (65.01 g NaN3/1 mol NaN3).

Circle each cancellation. The predictable error is flipping the mole ratio: students may write 3 mol NaN3/2 mol N2 because they see “3” first. Point to the desired unit: the numerator must contain mol NaN3 so mol N2 cancels. Compare the pathway to changing currency while traveling: each exchange must trade the unit currently held for the unit needed next.

Students copy the pathway and, with calculators covered, annotate each factor: “volume to moles,” “equation ratio,” and “moles to mass.” Partners do a units-only check: place a finger over all numbers and explain why the remaining unit must be grams NaN3.

Explicit check for understanding: Display three possible middle factors: 2 mol NaN3/3 mol N2, 3 mol N2/2 mol NaN3, and 2 g NaN3/3 g N2. Students hold up 1, 2, or 3 and write one cancellation statement. Use responses to immediately reteach the direction of the ratio; have students who chose 2 or 3 rebuild the chain from the desired final unit.

Now allow calculators. Complete the calculation together: 60.0/24.0 × 2/3 × 65.01 = 108 g NaN3 (three significant figures). Ask whether this result supports the 6 g, 60 g, or 600 g prediction and why. Emphasize that a comparatively small solid mass can generate a much larger gas volume because gas particles spread far apart; the volume is not evidence that a 60-L tank was hidden in the steering wheel.

Students solve two airbag-design cases, showing a labeled dimensional-analysis chain before calculating.

1. A smaller airbag requires 36.0 L N2 at the same conditions. What mass of NaN3 is needed?
2. A design calculation gives 81.3 g NaN3. What volume of N2 should it produce at the same conditions?

Require a brief CER for one case: Claim: the required mass/volume is . Evidence: cite the balanced-equation mole ratio and molar-volume conversion. Reasoning: explain how the units and ratios connect the solid to the gas.

Exit ticket, collected individually: “An airbag needs 48.0 L N2 at the stated conditions. Set up and calculate the mass of NaN3 required. Then write one sentence explaining why 2 NaN3 : 3 N2 is used as a mole ratio rather than a gram ratio.” Expected calculation: 86.7 g NaN3. Sort tickets by (1) correct pathway and result, (2) correct pathway with arithmetic issue, or (3) incorrect unit/ratio choice to plan the next lesson’s opening.