Ideal Gas Law Derivation (Scaffolded): Step-by-Step from Boyle and Charles to PV=nRT

Estimated Time: 60-90 minutes Materials: Computer or tablet with internet access, calculator.

Part 1: Engage — What’s Happening Inside a Syringe?

Think about a sealed syringe. When you pull the plunger back quickly, the gas inside cools down. When you push it in, it warms up. These changes tell us that pressure, volume, and temperature are connected.

  1. Predictions (Before the Simulation):
    • If you decrease the volume of a gas (push the plunger in), do you think the pressure will increase, decrease, or stay the same? Why?
    • If you heat a gas at constant pressure, do you think the volume will increase, decrease, or stay the same? Why?

Part 2: Explore — Boyle’s Law (P and V at Constant T)

Open the Ideal Gas Law simulation. Set Temperature = Constant.

  1. Guided Data Collection: Follow the steps to collect pressure and volume data.

Table 1: P vs. V at Constant T | Trial | Volume (L) | Pressure (atm) | P × V (calculate) | |:—|:—|:—|:—| | 1 | Start at the largest volume → | Record P → | | | 2 | Decrease V by ~1.0 L → | Record P → | | | 3 | Decrease V by ~1.0 L more → | Record P → | | | 4 | Decrease V again → | Record P → | | | 5 | Smallest volume → | Record P → | |

  1. Find the Pattern:
    • Look at your P × V column. What do you notice? (Sentence starter: “As volume decreases, P × V…”)
    • Boyle’s Law states: P₁V₁ = P₂V₂ (when T is constant)

Part 3: Explore — Charles’ Law (V and T at Constant P)

Set Pressure = Constant on the simulation.

  1. Guided Data Collection:

Table 2: V vs. T at Constant P | Trial | Temperature (K) | Volume (L) | V ÷ T (calculate) | |:—|:—|:—|:—| | 1 | 200 K → | | | | 2 | 250 K → | | | | 3 | 300 K → | | | | 4 | 350 K → | | | | 5 | 400 K → | | |

  1. Find the Pattern:
    • Look at your V ÷ T column. What do you notice? (Sentence starter: “As temperature increases, V ÷ T…”)
    • Charles’ Law states: V₁/T₁ = V₂/T₂ (when P is constant)

Part 4: Explain — Putting It Together

  1. The Ideal Gas Law:
    • From Boyle: P ∝ 1/V (at constant T)
    • From Charles: V ∝ T (at constant P)
    • Combine them: PV ∝ T
    • Add the amount of gas (n) and the gas constant (R): PV = nRT
  2. Why This Makes Sense at the Particle Level:
    • Complete these sentences:
      • “When I heat a gas, the particles move __, which means they hit the walls __ often.”
      • “When I compress a gas into a smaller space, the particles are __ together, so they hit the walls __ often, which increases the __.”

Part 5: Apply — Using the Ideal Gas Law

  1. Practice Problem 1: A balloon has a volume of 2.0 L at 300 K and 1.0 atm. It is heated to 400 K at constant pressure. What is the new volume?

    Use: V₁/T₁ = V₂/T₂ V₂ = (V₁ × T₂) / T₁ = __

  2. Practice Problem 2: A 3.0 L container of gas at 1.5 atm is compressed to 1.0 L at constant temperature. What is the new pressure?

    Use: P₁V₁ = P₂V₂ P₂ = __

  3. Real-World Connection: Car engines compress air to about 1/10 its original volume. This causes the temperature to rise so high that diesel fuel ignites without a spark plug. Can you explain why extreme compression causes such high temperatures?

Teacher Notes & NGSS Alignment

Performance Expectation: HS-PS3-2

Scaffolding Supports Included: