Subjects and lessons to explore.

Law

General Chemistry I · Gases

Avogadro's Law

3 min read
SourcesReport an error
Want it in plain words first? Jump to Eli explains — the same idea, no jargon.
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

Avogadro's law states that, at constant temperature and pressure, the volume of a gas is directly proportional to its amount (number of moles): V₁/n₁ = V₂/n₂. Equal volumes of any gas at the same temperature and pressure contain equal numbers of particles.

Why this matters

Avogadro's law is the bridge between the microscopic world (numbers of molecules) and the macroscopic world (measurable volumes). It underpins the molar-volume concept, gas stoichiometry (relating volumes of reacting gases), and the ideal gas law itself. It is also why chemists can count molecules by measuring a gas's volume.

The college version

Key Ideas

  • Direct relationship: as the number of moles increases, volume increases (constant T and P).
  • V/n is constant: V₁/n₁ = V₂/n₂.
  • Equal volumes, equal particles: at fixed T and P, 1 L of helium and 1 L of argon contain the same number of molecules.
  • Independent of gas identity: the law holds for every gas because gas particles are so far apart that their own size and identity don't matter.
  • Named for Amedeo Avogadro (1811); one mole = 6.022 × 10²³ particles (Avogadro's number).

Equations and Variables

  • V₁/n₁ = V₂/n₂ — V = volume, n = amount (mol).
  • Equivalent form: V₂ = V₁ × (n₂/n₁).
  • Avogadro's number: Nₐ = 6.022 × 10²³ particles/mol.
  • n = mass/molar mass, and n = N/Nₐ (N = number of particles).

How It Works

  1. Fix the temperature and pressure (e.g., an open balloon at constant atmospheric pressure and room temperature).
  2. Add more gas (increase n). More particles are present.
  3. To keep pressure and temperature constant, the extra particles need more room, so the volume grows.
  4. The volume grows in direct proportion to the number of moles: double the moles, double the volume.
  5. Because the size of individual molecules is negligible compared to the space between them, the identity of the gas doesn't matter — only the count does.

Worked Example

A balloon holds 3.0 mol of gas and occupies 66.0 L at constant temperature and pressure. How much volume will it occupy if 1.0 mol more gas is added? n₁ = 3.0 mol, n₂ = 3.0 + 1.0 = 4.0 mol. V₂ = V₁ × (n₂/n₁) = 66.0 L × (4.0 mol / 3.0 mol) = 88.0 L. The balloon expands from 66.0 L to 88.0 L.

Common Confusions

  • "Heavier gases take up more volume" — at fixed T and P, a mole of a heavy gas (e.g., 1 mol argon) occupies the same volume as a mole of a light gas (e.g., 1 mol helium). Volume depends on the count, not the mass.
  • "Avogadro's law is about mass" — it's about the number of moles (particles), not grams.
  • "Volume doubles when temperature doubles" — that's Charles's law; Avogadro's law relates volume to amount, not temperature.
  • "Fewer moles means more volume" — no; volume and moles move together (directly proportional).
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine two identical shipping boxes, one full of tiny marbles and one full of big beach balls. At the same temperature and pressure, both boxes contain the same number of balls — because the big balls, being bigger, just have more empty space around them. A gas is the same: what matters for volume is how many particles you have, not how big each one is. The analogy's limit: it only works because gas particles are extremely far apart; if you crammed the boxes so full the balls were touching, size would start to matter (that's when gases stop behaving ideally).

Key takeaways

  • V₁/n₁ = V₂/n₂ (constant T and P).
  • Volume is directly proportional to amount (moles).
  • Equal volumes of any gas at the same T and P hold equal numbers of molecules.
  • One mole = 6.022 × 10²³ particles.
  • The gas's identity doesn't matter — only the number of moles does.
  • Avogadro's law: V₁/n₁ = V₂/n₂ (constant T and P).
  • Volume ∝ amount (moles).
  • Equal volumes of gases at equal T and P contain equal numbers of molecules.
  • One mole = 6.022 × 10²³ particles.
  • Adding gas to a flexible container (constant T, P) increases its volume proportionally.

Keep learning

Ready to build on this? Continue to the next lesson.

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 Avogadro's law in words and as an equation.
  • Identify the variables held constant (pressure and temperature).
  • Solve for an unknown volume or amount of gas.
  • Relate equal volumes of different gases to equal numbers of particles.

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.

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.