Boyle's Law
What is the Boyle's Law?
Boyle's Law states that at constant temperature, a gas's pressure and volume are inversely proportional — when one increases, the other decreases by the same factor. Compress a gas into half its original volume, and its pressure doubles.
It's one of three laws that combine into the ideal gas law; Boyle's Law is the special case where temperature (and amount of gas) is held fixed.
What Each Variable Means
When to Use It
- Predicting how a gas's volume changes when its pressure changes, at constant temperature
- Predicting how pressure changes when volume changes
- As a foundational law that combines with Charles's Law and Avogadro's Law into the ideal gas law
Step-by-Step Example
Problem: A gas occupies 4 L at 2 atm. What volume does it occupy at 8 atm (same temperature)?
Initial pressure and volume, and the new pressure.
P₁=2 atm, V₁=4 L, P₂=8 atm, V₂=?Set up the equal-products relationship.
P₁V₁ = P₂V₂ → 2×4 = 8×V₂Divide both sides by P₂.
V₂ = (2×4)/8 = 8/8Interactive Calculator
Common Mistakes
Mistake: Applying Boyle's Law when temperature is actually changing.
Fix: Boyle's Law only holds at constant temperature — if temperature also changes, the full ideal gas law (or the combined gas law) is needed instead.
Mistake: Mixing up which subscript is initial and which is final.
Fix: Keep P₁/V₁ consistently as the starting state and P₂/V₂ as the ending state throughout the whole calculation.
Practice Questions
A gas at 3 L and 4 atm is compressed to 1 L. Find the new pressure.
A gas at 6 atm and 2 L expands to 4 atm. Find the new volume.
Frequently Asked Questions
Who discovered Boyle's Law?
Robert Boyle published it in 1662, after observing the relationship by trapping air in a J-shaped tube with mercury.
Does Boyle's Law require any particular units?
No — any consistent pressure and volume units work, as long as the same units are used for P₁ and P₂, and for V₁ and V₂, since the formula is really about the ratio between states, not absolute values.