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General Chemistry I · Gases

Graham's Law: Effusion and Diffusion

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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

Effusion is the escape of a gas through a tiny hole into a vacuum; diffusion is the gradual spreading of one gas through another. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass: rate₁/rate₂ = √(M₂/M₁). Lighter gases effuse and diffuse faster.

Why this matters

Graham's law was historically used to separate isotopes of uranium (UF₆ enrichment) and still explains gas-leak detection, how fast a helium balloon deflates, and how perfume spreads through a room. It also underlies the observation that light gases like helium and hydrogen escape Earth's atmosphere far more readily than heavy ones.

The college version

Key Ideas

  • Effusion = gas escapes through a pinhole into a vacuum.
  • Diffusion = gas mixes/spreads through space or another gas.
  • Graham's law: rate₁/rate₂ = √(M₂/M₁).
  • Lighter is faster: rate ∝ 1/√M.
  • Root cause: at a given temperature, lighter molecules move faster (u_rms = √(3RT/M)).

Equations and Variables

  • Graham's law: rate₁/rate₂ = √(M₂/M₁) — rate = effusion (or diffusion) rate, M = molar mass (any consistent unit, since it's a ratio).
  • Equivalent form: rate₁/rate₂ = u_rms(1)/u_rms(2) = √(M₂/M₁).
  • Time-based form: t₂/t₁ = √(M₂/M₁), since rate ∝ 1/time for equal amounts.

How It Works

  1. Effusion rate depends on how often molecules reach the hole and pass through — which depends on their speed.
  2. At a fixed temperature, average molecular speed is u_rms = √(3RT/M), so a lighter gas has faster molecules.
  3. Faster molecules reach and exit the hole more often, so the lighter gas effuses faster.
  4. The ratio of rates therefore goes as the inverse square root of the molar-mass ratio.
  5. Diffusion follows the same trend for the same reason, though real diffusion is also slowed by collisions with other gas molecules.

Worked Example

Compare the effusion rates of H₂ (M = 2.02 g/mol) and O₂ (M = 32.0 g/mol) at the same temperature. rate(H₂)/rate(O₂) = √(M(O₂)/M(H₂)) = √(32.0 / 2.02) = √15.8 = 4.0. Hydrogen effuses about 4 times faster than oxygen.

If a sample of O₂ takes 60 s to effuse through a pinhole, how long does an equal amount of H₂ take? t(H₂)/t(O₂) = √(M(H₂)/M(O₂)) = √(2.02/32.0) = 0.251. t(H₂) = 60 s × 0.251 = 15 s.

Common Confusions

  • "Effusion and diffusion are the same thing" — effusion is passage through a tiny hole into a vacuum; diffusion is spreading through space or mixing with another gas.
  • "Heavier gases effuse faster" — the opposite; heavier gases are slower.
  • "Rate depends on the gas's physical size" — in Graham's law it depends on molar mass, not molecular diameter.
  • "The ratio is √(M₁/M₂) for rate₁/rate₂" — it's the inverse: rate₁/rate₂ = √(M₂/M₁). Check that the lighter gas ends up with the larger rate.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a sieve with holes, and you shake two batches of sand through it — one made of fine grains and one of big pebbles. The fine grains (the light gas) pour through the holes much faster than the pebbles (the heavy gas). Effusion is the same: small, light molecules slip through a pinhole quicker than big, heavy ones. The analogy's limit: gas "size" here is really about mass, not physical diameter — two gases of equal mass effuse at the same rate even if one molecule is physically larger.

Key takeaways

  • Effusion = through a pinhole; diffusion = spreading through space/another gas.
  • Graham's law: rate₁/rate₂ = √(M₂/M₁).
  • Lighter gas effuses faster; rate ∝ 1/√M.
  • At fixed T, faster-moving (lighter) gases effuse more quickly.
  • Time and rate are inversely related: rate ∝ 1/time.
  • Effusion: escape through a pinhole. Diffusion: spreading/mixing.
  • Graham's law: rate₁/rate₂ = √(M₂/M₁).
  • Lighter gases effuse and diffuse faster.
  • rate ∝ 1/√M, so time ∝ √M.
  • Root cause: lighter molecules move faster at a given temperature.

Keep learning

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Practice General Chemistry I

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Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Distinguish effusion from diffusion.
  • State Graham's law of effusion.
  • Compare the rates of two gases from their molar masses.
  • Explain why lighter gases effuse and diffuse faster.

Sources & references

  1. OpenStax, "9.4 Effusion and Diffusion of Gases," Chemistry 2e.
  2. Petrucci et al., "6.8 Gas Properties Relating to the Kinetic-Molecular Theory," 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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