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General Chemistry I · Gases

Kinetic Molecular Theory of Gases

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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

The kinetic molecular theory (KMT) is a microscopic model that explains the behavior of gases in terms of the motion of their particles. It pictures a gas as a huge number of tiny particles in constant, random motion, with negligible volume, no forces between them, and perfectly elastic collisions. The average kinetic energy of the particles is directly proportional to the absolute temperature.

Why this matters

KMT is the reason all the gas laws work, and it gives temperature a physical meaning: temperature is a measure of the average kinetic energy of particles. The same model underlies our understanding of diffusion, effusion, reaction rates, and the difference between ideal and real gases — and it's the conceptual bridge from the macroscopic gas laws to statistical thermodynamics.

The college version

Key Ideas

  • Point particles: gas particles are far apart and have negligible volume compared to the container.
  • Constant, random motion: particles travel in straight lines until they collide.
  • Elastic collisions: collisions with walls or other particles lose no net kinetic energy.
  • No intermolecular forces: particles exert no attraction or repulsion except during collisions.
  • KE ∝ T: the average kinetic energy depends only on temperature, not on the gas's identity.

Equations and Variables

  • Average kinetic energy per mole: KE_avg = (3/2)RT, with R = 8.314 J/(mol·K).
  • Average kinetic energy per molecule: KE_avg = (3/2)k_B·T, with k_B = 1.381 × 10⁻²³ J/K (Boltzmann constant).
  • T = absolute temperature (K).

How It Works

  1. Model a gas as N tiny particles moving at various speeds in all directions.
  2. Pressure arises because particles strike the container walls and bounce back, transferring momentum (a net force over the wall's area).
  3. Heating the gas raises the average kinetic energy; at a fixed volume, faster particles hit harder and more often → higher pressure (Gay-Lussac's law).
  4. At fixed pressure, heating must be accompanied by expansion so the force per area stays constant (Charles's law).
  5. At fixed temperature, shrinking the volume makes collisions more frequent → higher pressure (Boyle's law).
  6. Because particle size and attractions are negligible, one mole of any gas behaves the same way (Avogadro's law).

Worked Example

Find the average kinetic energy per mole and per molecule of a gas at 300 K. Per mole: KE_avg = (3/2)RT = (3/2)(8.314 J/mol·K)(300 K) = 3740 J/mol. Per molecule: KE_avg = (3/2)k_B·T = (3/2)(1.381 × 10⁻²³ J/K)(300 K) = 6.21 × 10⁻²¹ J.

Common Confusions

  • "Temperature is a measure of heat content" — temperature measures average kinetic energy of the particles; heat is energy transferred.
  • "Heavier gases move as fast as light ones at the same T" — at the same temperature they have the same average kinetic energy, but heavier particles move slower (KE depends on both mass and speed).
  • "Collisions are inelastic" — in an ideal gas, collisions are perfectly elastic: total kinetic energy is conserved.
  • "Gas particles have no volume at all" — the assumption is that their volume is negligible compared to the container, which fails at high pressure.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Picture a swarm of tiny, invisible bees inside a jar, all flying in straight lines and bouncing off the walls without slowing down. The buzzing you'd feel as they hit the walls is the pressure. Warm the jar and the bees fly faster and hit harder (higher pressure); cool it and they slow down. And it doesn't matter whether the bees are "helium bees" or "oxygen bees" — only how many there are and how fast they fly. The analogy's limit: real gas particles do attract each other a little and take up a little space, which is why real gases misbehave when you crowd or chill them.

Key takeaways

  • Five postulates: tiny/far-apart particles, constant random motion, elastic collisions, no intermolecular forces, and KE ∝ T.
  • KE_avg per mole = (3/2)RT; per molecule = (3/2)k_B·T.
  • Temperature measures average translational kinetic energy.
  • KMT explains Boyle's, Charles's, Gay-Lussac's, and Avogadro's laws.
  • Ideal-gas assumptions break down at high pressure and low temperature.
  • KMT models a gas as tiny, far-apart particles in constant random motion.
  • Collisions are elastic; no intermolecular forces (ideal gas).
  • KE_avg = (3/2)RT per mole, (3/2)k_B·T per molecule.
  • Temperature ∝ average kinetic energy.
  • KMT is the microscopic explanation of all the gas laws.

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

  • List the postulates of the kinetic molecular theory (KMT).
  • Explain how KMT accounts for the ideal gas laws.
  • Relate average kinetic energy to absolute temperature.
  • Distinguish the assumptions of an ideal gas from real-gas behavior.

Sources & references

  1. OpenStax, "9.5 The Kinetic-Molecular Theory," Chemistry 2e.
  2. Petrucci et al., "6.7 Kinetic-Molecular Theory of Gases," 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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