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General Chemistry I · Gases

Gay-Lussac'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

Gay-Lussac's law states that the pressure of a fixed amount of gas in a fixed volume is directly proportional to its kelvin temperature: P₁/T₁ = P₂/T₂. Because the volume cannot change, heating the gas forces its faster-moving particles to strike the walls harder and more often, raising the pressure.

Why this matters

Gay-Lussac's law explains why aerosol cans and propane tanks carry "do not incinerate" warnings — heating a sealed container can raise the pressure until it bursts. It also governs pressure cookers (raising the temperature raises the internal pressure, letting food cook hotter) and why tire pressure changes between cold mornings and hot afternoons.

The college version

Key Ideas

  • Direct relationship: as T (K) rises, P rises (constant n and V).
  • Rigid container: the law applies when volume is held constant.
  • Kelvin required: temperature must be absolute.
  • P/T is constant: P₁/T₁ = P₂/T₂.
  • Molecular picture: higher T → faster particles → harder, more frequent wall hits.

Equations and Variables

  • P₁/T₁ = P₂/T₂ — P = pressure, T = absolute temperature (K).
  • Equivalent form: P₂ = P₁ × (T₂/T₁).
  • T(K) = T(°C) + 273.15.
  • Graphically: P vs T (K) is a straight line through the origin (for an ideal gas).

How It Works

  1. Confine a fixed amount of gas (n constant) in a rigid container so volume is fixed.
  2. Heat the gas. The average kinetic energy and speed of the particles increase.
  3. Faster particles collide with the walls more often and with more force each time.
  4. With volume unable to expand, the result is a higher pressure.
  5. Pressure rises in direct proportion to the kelvin temperature.

Worked Example

A sealed metal container holds gas at 1.00 atm and 20.0 °C. What is the pressure if the container is heated to 80.0 °C? Convert: T₁ = 20.0 + 273.15 = 293.15 K; T₂ = 80.0 + 273.15 = 353.15 K. P₂ = P₁ × (T₂/T₁) = 1.00 atm × (353.15 K / 293.15 K) = 1.20 atm. The pressure rises from 1.00 atm to 1.20 atm.

Common Confusions

  • "Gay-Lussac's law is the same as Charles's law" — both are direct proportions with temperature, but Charles's law fixes P (V changes) while Gay-Lussac's law fixes V (P changes).
  • "Volume changes in a rigid container" — no; constant volume is the whole premise.
  • "Use Celsius for the ratio" — always convert to kelvin first.
  • "Pressure and temperature are inversely related" — they are directly related here.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a sealed, unbreakable can of air. Cool it and the particles lazily tap the walls — low pressure. Put the can on a stove and the particles start zooming around like they've had too much coffee, slamming the walls faster and harder. The can's size can't change, so all that extra energy has nowhere to go except into harder pushing — the pressure climbs. The analogy's limit: a real can will burst (or the gas may react) at extreme heat, but the "extra energy has to go somewhere" idea is the whole point.

Key takeaways

  • P₁/T₁ = P₂/T₂ (constant n and V).
  • Pressure is directly proportional to kelvin temperature.
  • Applies to rigid, sealed containers (V fixed).
  • Always use kelvin.
  • Doubling T (K) doubles P.
  • Gay-Lussac's law: P₁/T₁ = P₂/T₂ (constant n and V).
  • Pressure ∝ kelvin temperature.
  • Faster particles → harder, more frequent collisions → higher pressure.
  • Convert °C to K before calculating.
  • Explains warnings on sealed pressurized containers.

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 Gay-Lussac's law in words and as an equation.
  • Identify the variables held constant (amount and volume).
  • Solve for an unknown pressure or temperature.
  • Explain the molecular origin of the pressure–temperature relationship.

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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