Gas Laws: Ideal Gas Law Derivation

Overview

Estimated Time: 60-90 minutes Materials: Internet-connected device, Gas Laws Simulation, notebook/data table NGSS Alignment: HS-PS3-2 (Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles and relative position of particles). Performance Expectation: Students will use the gas laws simulation to derive the relationships between pressure, volume, temperature, and number of particles, and develop a model explaining these macroscopic relationships through the motions of particles.

Part 1: Engage (Anchoring Phenomenon)

The “Flat” Tire Phenomenon On a freezing winter morning (-5 °C / 23 °F), you walk out to your car and notice that one of the tires looks visibly “flat.” When you turn the car on, the low tire pressure warning light illuminates on the dashboard. You don’t have time to fill it up, so you carefully drive onto the highway to get to school. After 15 minutes of highway driving, the tire no longer looks flat, and the low pressure warning light turns off—even though you never added any air!

Discussion Questions:

  1. What variable(s) changed inside the tire during the cold night, and what changed during the highway drive?
  2. How could the pressure warning go away if no air molecules were added?
  3. Generate “Need to Know” questions about how temperature, pressure, and volume interact inside a sealed container like a tire.

Part 2: Explore (Simulation Investigation)

You will use the Gas Laws Simulation to determine the mathematical relationships between pressure ($P$), volume ($V$), temperature ($T$), and the number of particles ($n$).

Procedure:

  1. Open the Gas Laws: Ideal Gas Law Derivation simulation.
  2. The simulation allows you to change four variables: Pressure (atm), Volume (L), Temperature (K), and Number of Particles (mol).
  3. Investigate Boyle’s Law ($P$ and $V$):
    • Keep Temperature and Particles constant.
    • Select Pressure as your dependent variable.
    • Adjust the Volume slider to 5 different values (e.g., 20 L, 40 L, 60 L, 80 L, 100 L).
    • Click “Record Data Point” for each.
    • Sketch the graph produced and write down the relationship (direct or inverse).
  4. Investigate Charles’s Law ($V$ and $T$):
    • Click “Clear Data”.
    • Keep Pressure and Particles constant.
    • Select Volume as your dependent variable.
    • Adjust the Temperature slider to 5 different values.
    • Click “Record Data Point” for each.
    • Sketch the graph and note the relationship.
  5. Investigate Gay-Lussac’s Law ($P$ and $T$):
    • Click “Clear Data”.
    • Keep Volume and Particles constant.
    • Select Pressure as your dependent variable.
    • Adjust the Temperature slider to 5 different values.
    • Click “Record Data Point” for each.
    • Sketch the graph and note the relationship.

Example Data Table: | Trial | Volume (L) | Pressure (atm) | Temperature (K) | Particles (mol) | Constant Variables | |——-|————|—————-|—————–|—————–|——————–| | 1 | 20.0 | | 300 | 1.00 | T, n | | 2 | 40.0 | | 300 | 1.00 | T, n |

Part 3: Explain (Sensemaking)

Using the data and graphs from your exploration, answer the following:

  1. Macroscopic Relationships: Based on the shapes of your graphs, describe the mathematical relationship between:
    • Volume and Pressure (Boyle’s Law)
    • Temperature and Volume (Charles’s Law)
    • Temperature and Pressure (Gay-Lussac’s Law)
  2. Microscopic Motion: The simulation shows particles bouncing around the container. How does an increase in Temperature (average kinetic energy of particles) explain the changes you observed in Pressure when Volume was held constant?
  3. Synthesis: Combine the relationships you discovered into a single proportional statement relating $P$, $V$, $T$, and $n$. (Hint: Put directly proportional variables on opposite sides of the equation, and inversely proportional variables on the same side).

Part 4: Elaborate/Evaluate (Argumentation & Modeling)

Modeling the Phenomenon: Draft a scientific explanation for the “flat” tire phenomenon from the Engage section. Your explanation must include:

  1. A clear claim stating why the tire pressure was low in the morning and why it increased after driving.
  2. Evidence from your simulation data (specifically Gay-Lussac’s and Charles’s laws).
  3. Reasoning that connects the macroscopic observations (tire pressure and temperature) to the microscopic motions and collisions of the air particles inside the tire. Use a model (e.g., drawing or written description) showing the particles at -5 °C versus after highway driving.

Extension: If the tire was perfectly rigid (volume could not change at all), how would the graphs you made in Part 2 look different? How does the flexible nature of rubber make a car tire an imperfect closed system for Gay-Lussac’s law?

Teacher Notes & Alignment

SEPs: Developing and Using Models DCIs: PS3.A: Definitions of Energy CCCs: Energy and Matter

Evidence Statements Addressed: