Lesson Plan

• Describe the key assumptions of the kinetic theory of gases and how they lead to the pressure expression.
• Derive the root‑mean‑square speed formula from the kinetic theory and the ideal‑gas law.
• Calculate the rms speed of a gas using \(c_{\text{rms}} = \sqrt{3RT/M}\).
• Explain how temperature and molecular mass influence the rms speed.

• Projector and screen
• Whiteboard and markers
• Printed worksheet with derivation steps and practice problems
• Scientific calculators (one per pair)
• Table of common gases with molar masses (handout)
• Computer simulation of molecular motion (optional)

Begin with a quick demonstration of a sealed container shaking to illustrate invisible molecular motion. Ask students what they already know about the kinetic theory and how it explains pressure. State that by the end of the lesson they will be able to derive and apply the rms speed formula and interpret its dependence on temperature and mass.

1. Do‑now (5'): Students answer three short questions on the kinetic‑theory assumptions.
2. Mini‑lecture (10'): Derive the pressure‑volume‑temperature relationship and introduce the rms speed formula on the board.
3. Guided derivation (12'): Work through the seven‑step derivation using the projector; students complete the corresponding sections in their worksheets.
4. Example calculation (8'): Calculate the rms speed of N₂ at 300 K together, then have pairs repeat with a different gas.
5. Interactive simulation (10'): Explore a web‑based model showing how rms speed changes with temperature and molar mass; discuss observations.
6. Check for understanding (5'): Exit ticket – write one sentence describing the effect of temperature and one sentence describing the effect of molecular mass on rms speed.

Summarise that the rms speed depends only on temperature and molar mass, linking back to the kinetic‑theory assumptions. Collect exit tickets to gauge understanding. For homework, students complete the worksheet by calculating rms speeds for helium and carbon dioxide at 300 K.