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General Chemistry I · Gases

Boyle's Law

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

Boyle's law describes the inverse relationship between the pressure and volume of a fixed amount of gas at constant temperature: when volume goes up, pressure goes down, and their product stays constant. Mathematically, P₁V₁ = P₂V₂.

Why this matters

Boyle's law explains breathing: when the diaphragm contracts, the chest-cavity volume increases, lung pressure drops below atmospheric, and air flows in. It also governs scuba diving (air in the lungs expands as a diver ascends to lower pressure — the reason divers must never hold their breath), syringes, and any piston/cylinder device.

The college version

Key Ideas

  • Inverse relationship: as V increases, P decreases (at constant n and T).
  • Product is constant: P × V = constant, so P₁V₁ = P₂V₂.
  • Constant n and T are required; temperature must be fixed (any temperature works, but it must not change).
  • Molecular picture: bigger volume → particles hit walls less often → lower pressure.
  • Discovered by Robert Boyle (1662), one of the first quantitative gas laws.

Equations and Variables

  • P₁V₁ = P₂V₂ — P = pressure, V = volume; subscripts 1 and 2 = initial and final states.
  • Equivalent forms: P₁ = P₂V₂/V₁ and V₂ = P₁V₁/P₂.
  • Rearranged for graphing: P = (constant)/V, a hyperbola; a plot of P vs 1/V is a straight line through the origin.

How It Works

  1. Start with a fixed amount of gas in a closed container (n constant) at a set temperature (T constant).
  2. Change the volume (e.g., push or pull a piston).
  3. If volume decreases, particles are confined to less space, so they strike the walls more often per second — pressure rises.
  4. If volume increases, particles hit the walls less often — pressure falls.
  5. Pressure and volume move in opposite directions such that their product P × V is unchanged.

Worked Example

A gas occupies 4.0 L at 2.5 atm. What volume does it occupy at 1.0 atm if temperature and amount are unchanged? P₁V₁ = P₂V₂ → V₂ = P₁V₁/P₂ = (2.5 atm)(4.0 L)/(1.0 atm) = 10 L. The gas expands to 10 L: lowering the pressure by a factor of 2.5 raised the volume by the same factor.

A second quick check: a 1.50 L sample at 750 mmHg is compressed to 0.500 L. New pressure? P₂ = P₁V₁/V₂ = (750 mmHg)(1.50 L)/(0.500 L) = 2250 mmHg.

Common Confusions

  • "Higher volume means higher pressure" — it's the opposite; volume and pressure are inversely related.
  • "Temperature changes during a Boyle's-law problem" — no; T (and n) must be constant or the law doesn't apply.
  • "Any pressure unit works without matching" — units must be consistent on both sides; you can't mix atm and mmHg for P₁ and P₂ without converting.
  • "P₁V₁ = P₂V₂ works even if gas leaks out" — no; the amount of gas must be constant.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of a sealed plastic bag of air. Squeeze it into a smaller space and it pushes back harder — the same amount of air crammed into less room hits the walls more often. Let it puff out into a bigger space and the push weakens. That's all Boyle's law says: squeeze more, push harder; give it room, push less. The analogy's limit: a real bag also changes temperature a bit when you squeeze fast, but Boyle's law assumes the temperature is held perfectly constant.

Key takeaways

  • P₁V₁ = P₂V₂ (constant n and T).
  • Pressure and volume are inversely proportional.
  • Doubling volume halves pressure; halving volume doubles pressure.
  • Any consistent pressure unit works (atm, mmHg, kPa) as long as it is the same on both sides.
  • P vs V is a hyperbola; P vs 1/V is a straight line.
  • Boyle's law: P₁V₁ = P₂V₂ at constant n and T.
  • Inverse proportionality: P ∝ 1/V.
  • Larger volume → fewer wall collisions per time → lower pressure.
  • Solve by isolating the unknown: V₂ = P₁V₁/P₂.
  • Keep n and T fixed and units consistent.

Keep learning

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Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • State Boyle's law in words and as an equation.
  • Identify the variables held constant (amount and temperature).
  • Solve for an unknown pressure or volume.
  • Explain Boyle's law at the molecular level.

Sources & references

  1. OpenStax, "9.2 Relating Pressure, Volume, Amount, and Temperature," Chemistry 2e.
  2. Petrucci et al., "6.2 The Simple Gas Laws," Chemistry LibreTexts.
  3. NIST CODATA, "molar gas constant."

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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