Essential Gas Law Equations to Know for AP Physics 2 (2025)

Understanding gas laws is crucial in AP Physics 2. These equations describe how pressure, volume, temperature, and the number of gas moles interact. Mastering these concepts helps explain real-world phenomena, from breathing to weather patterns.

1. Ideal Gas Law: PV = nRT

   • Relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T).
   • Applicable to ideal gases, where interactions between molecules are negligible.
   • Useful for calculating one variable when the others are known.

2. Boyle's Law: P₁V₁ = P₂V₂

   • States that pressure and volume are inversely related at constant temperature.
   • If volume increases, pressure decreases, and vice versa.
   • Important for understanding gas compression and expansion.

3. Charles's Law: V₁/T₁ = V₂/T₂

   • Describes the direct relationship between volume and temperature at constant pressure.
   • As temperature increases, volume increases if pressure remains constant.
   • Essential for understanding thermal expansion of gases.

4. Gay-Lussac's Law: P₁/T₁ = P₂/T₂

   • Indicates that pressure and temperature are directly related at constant volume.
   • If temperature increases, pressure increases, and vice versa.
   • Key for understanding gas behavior in closed systems.

5. Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂

   • Combines Boyle's, Charles's, and Gay-Lussac's laws into one equation.
   • Useful for solving problems involving changes in pressure, volume, and temperature.
   • Allows for analysis of gas behavior under varying conditions.

6. Avogadro's Law: V₁/n₁ = V₂/n₂

   • States that volume is directly proportional to the number of moles of gas at constant temperature and pressure.
   • More gas (in moles) means more volume, assuming other conditions are constant.
   • Important for stoichiometry and gas mixtures.

7. Dalton's Law of Partial Pressures: P_total = P₁ + P₂ + P₃ + ...

   • Total pressure of a gas mixture is the sum of the partial pressures of each gas.
   • Useful for calculating the behavior of gas mixtures.
   • Important in applications like respiration and chemical reactions.

8. Kinetic Theory of Gases: PV = (1/3)Nmv²

   • Relates macroscopic properties (P, V) to microscopic behavior (N, m, v).
   • Explains gas pressure as a result of molecular collisions with container walls.
   • Provides insight into the nature of temperature as a measure of average kinetic energy.

9. Root Mean Square Speed: v_rms = √(3RT/M)

   • Calculates the average speed of gas molecules based on temperature and molar mass.
   • Higher temperatures result in higher molecular speeds.
   • Important for understanding diffusion and effusion of gases.

10. Molar Mass from Density: M = (dRT)/P

    • Relates density (d), gas constant (R), temperature (T), and pressure (P) to molar mass (M).
    • Useful for determining the molar mass of unknown gases.
    • Important in applications involving gas mixtures and reactions.