Gas Laws4 min read

Boyle's Law

P₁V₁ = P₂V₂

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

P₁, V₁
Initial pressure and volumeThe gas's state before the change. (any consistent pressure/volume units)
P₂, V₂
Final pressure and volumeThe gas's state after the change.

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
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Step-by-Step Example

Problem: A gas occupies 4 L at 2 atm. What volume does it occupy at 8 atm (same temperature)?

1
Identify the known values

Initial pressure and volume, and the new pressure.

P₁=2 atm, V₁=4 L, P₂=8 atm, V₂=?
2
Apply Boyle's Law

Set up the equal-products relationship.

P₁V₁ = P₂V₂ → 2×4 = 8×V₂
3
Solve for V₂

Divide both sides by P₂.

V₂ = (2×4)/8 = 8/8
Answer: V₂ = 1 L — as pressure quadrupled, volume quartered

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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

  1. A gas at 3 L and 4 atm is compressed to 1 L. Find the new pressure.

  2. 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.