Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- All particles of matter are in continuous, random motion. KMT uses this to explain the properties of gases.
- An ideal gas in KMT: particles move in straight lines, have negligible volume, do not attract or repel, and collide elastically.
- Pressure comes from particles hitting the walls. It rises if the hits are more frequent or harder.
- The Kelvin temperature is proportional to the average kinetic energy of the particles.
- A Maxwell–Boltzmann distribution shows the spread of particle speeds or energies at one temperature.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| KE = ½mv² | kinetic energy of one particle (m mass, v speed) | link energy, mass and speed |
| average KE ∝ T (kelvin) | doubling T doubles average KE | predict the effect of heating |
| v₁ / v₂ = √(M₂ / M₁) at equal T | lighter particles are faster | compare average speeds of two gases |
| average speed ∝ √T for one gas | doubling T raises speed by √2 | compare one gas at two temperatures |
Assumptions behind the model
- Particle volume is tiny compared with the container volume.
- There are no forces between particles except during collisions.
- Collisions are elastic: total kinetic energy is conserved.
- Average kinetic energy is proportional to the Kelvin temperature, so always work in kelvin.
Mistakes to avoid
- Same T ≠ same speed. Same average KE, but heavier particles move more slowly.
- Speed ratio is a square root. A particle 4 times heavier is 2 times slower, not 4.
- Squeezing at constant T does not speed particles up. Pressure rises because hits per unit area become more frequent.
- Celsius ratios are meaningless. Convert to kelvin before comparing.
- Hot curve is lower, not taller. Same area, spread wider.
- No bell curve. Start at zero, single peak, long tail to the right.
- Energy axis vs speed axis. At the same T, all gases share one kinetic-energy curve; on a speed axis the heavier gas peaks at lower speed.
Quick self-check
- Krypton (83.80 g mol⁻¹) and neon (20.18 g mol⁻¹) are at the same temperature. Which atoms move faster on average, and by what factor? (Neon, about 2.04 times faster)
- A gas is heated from 200 K to 400 K. What happens to the average KE and the average speed? (KE doubles; speed rises about 1.41 times)
- A sample of gas is cooled. Describe the change in its Maxwell–Boltzmann speed curve. (Peak moves to lower speed and becomes taller and narrower; area unchanged)
Next: practice questions.