Ideal Gas Laws
Understand how pressure, volume, and temperature are related in gases

Gas Behavior
P, V, and T relationships
The kinetic theory explains gas behavior using particle motion. Gas particles are in constant rapid, random motion, colliding with each other and the container walls. These collisions create pressure.
An ideal gas is a theoretical model where particles occupy negligible volume, have perfectly elastic collisions, and experience no intermolecular forces. Real gases deviate from this at high pressures and low temperatures.
P₁V₁ = P₂V₂
At constant temperature
Boyle's Law states that pressure is inversely proportional to volume when temperature is constant. If you compress a gas (decrease volume), the pressure increases because particles hit the walls more frequently.
V₁/T₁ = V₂/T₂
At constant pressure (temperature in Kelvin)
Charles's Law states that volume is directly proportional to absolute temperature when pressure is constant. Heating a gas makes particles move faster, so the gas expands to maintain constant pressure.
Important: Always use Kelvin for gas calculations! K = °C + 273
P₁V₁/T₁ = P₂V₂/T₂
Combines Boyle's and Charles's Laws
The combined gas law relates pressure, volume, and temperature when all three can change. Applications include understanding why car tire pressure increases on hot days (constant volume, higher temperature = higher pressure) and why weather balloons expand as they rise (lower atmospheric pressure = larger volume).
P₁V₁ = P₂V₂
At constant temperature, pressure is inversely proportional to volume
Final Pressure P₂
200.0 kPa
Smaller volume = Higher pressure
Boyle's Law
Question:
A gas has volume 200 cm³ at 100 kPa and 300 K. What is its volume at 150 kPa and 450 K?
Answer:
Using P₁V₁/T₁ = P₂V₂/T₂:
Rearranging for V₂: V₂ = P₁V₁T₂ / (T₁P₂)
V₂ = (100 × 200 × 450) / (300 × 150)
V₂ = 9,000,000 / 45,000 = 200 cm³
The volume stays the same because the pressure increase (×1.5) exactly cancels the temperature increase (×1.5).
According to Boyle's Law, if you halve the volume of a gas at constant temperature, what happens to the pressure?