How to Calculate Using Boyle's Law
Boyle's Law describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature. As pressure increases, volume decreases proportionally—and vice versa.
The Formula
P₁V₁ = P₂V₂
Where subscripts 1 and 2 refer to the initial and final states.
Rearrangements:
- V₂ = P₁V₁ / P₂
- P₂ = P₁V₁ / V₂
Step-by-Step Examples
Example 1: Scuba tank A scuba tank holds 11 L of air at 200 bar (compressed). At atmospheric pressure (1 bar), what volume does this gas occupy?
V₂ = P₁V₁ / P₂ = (200 × 11) / 1 = 2,200 liters of breathable air
Example 2: Syringe A syringe contains 60 mL of air at 1 atm. If you push the plunger to halve the volume, what is the new pressure?
P₂ = P₁V₁ / V₂ = (1 × 60) / 30 = 2 atm
The PV = Constant Relationship
The key insight: for a fixed amount of gas at constant temperature, the product P × V is always the same number. If you plot pressure vs. volume, you get a hyperbola.
Limitations
Boyle's Law applies only to ideal gases at constant temperature. Real gases deviate at very high pressures (where molecules interact) and at temperatures close to the boiling point (where gas-to-liquid conversion occurs).
Combined Gas Law
When temperature also changes:
(P₁V₁) / T₁ = (P₂V₂) / T₂
(Temperature must be in Kelvin: K = °C + 273.15)
Use our gas law calculator for Boyle's Law, Charles' Law, and the Combined Gas Law.