Overview
This lecture explains how gas pressure relates to volume, describes the inverse relationship using a key equation, and demonstrates how to solve typical gas law calculation problems.
Pressure and Volume Relationship in Gases
- Pressure in gases is caused by particles colliding with container walls.
- Increasing temperature, increasing the number of particles, or decreasing volume increases gas pressure.
- Pressure (P) and volume (V) are inversely related: as volume increases, pressure decreases, and vice versa.
- For a fixed amount of gas at constant temperature, the product of pressure and volume is constant (PV = constant).
Using PV = Constant in Calculations
- If the gas changes from one state to another with constant temperature and mass, PV before equals PV after: ( P_1V_1 = P_2V_2 ).
- To solve for unknowns, plug in values you know and rearrange the equation as needed.
Example Problems
- Example 1: 1.5 m³ of gas at 100 Pa is compressed to 0.3 m³. Using PV = constant, the new pressure is 500 Pa.
- Alternative approach: Use ( P_1V_1 = P_2V_2 ) directly to solve for unknown pressures or volumes.
- Example 2: 1800 L of air at 101 kPa is compressed into a 12 L cylinder; the resulting pressure is 15,150 kPa.
Key Terms & Definitions
- Pressure (P) — The force exerted by gas particles colliding with container walls, measured in Pascals (Pa) or kilopascals (kPa).
- Volume (V) — The space occupied by the gas, measured in cubic meters (m³) or liters (L).
- PV = constant — The equation showing that, for constant temperature and mass, pressure and volume multiply to a constant value.
- Inverse Relationship — As one variable increases, the other decreases.
Action Items / Next Steps
- Practice solving gas law problems using ( P_1V_1 = P_2V_2 ).
- Review units for pressure and volume in calculations.