Topic 3.5 Notes – Kinetic Molecular Theory

1. What the Kinetic Molecular Theory Says About Gases

KMT is a particle model for ideal gases. It explains gas behavior by describing how particles move and interact.

Here are the five assumptions. Know all of them.

1. Constant, random, straight-line motion
   Gas particles move nonstop in random directions. They only change direction when they collide.
2. Particles are far apart
   The volume of individual particles is negligible compared to the container. Most of a gas is empty space.
3. No intermolecular attractions or repulsions
   Ideal gas particles do not stick to or repel each other.
4. Elastic collisions
   Collisions with each other or the walls do not lose total kinetic energy.
5. Average kinetic energy depends only on temperature
   At the same Kelvin temperature, all gases have the same average kinetic energy, no matter their identity.

That last idea is huge. It’s what lets us connect temperature directly to particle motion.

2. Kinetic Energy and Temperature

All particles are always moving. Their motion gives them kinetic energy.

The equation is:

$$KE = \frac{1}{2}mv^{2}$$

• $m$ = mass of the particle
• $v$ = speed
• If speed increases, kinetic energy increases (since $v$ is squared)

Temperature and Average Kinetic Energy

Kelvin temperature is directly proportional to average kinetic energy.

If temperature doubles (in Kelvin), average kinetic energy doubles.

Important distinctions:

• Temperature measures average kinetic energy, not total energy.
• At the same temperature:
  • A heavier gas moves slower
  • A lighter gas moves faster
  • Both have the same average KE

Students often forget that mass affects speed but not average KE at the same temperature.

If you’re explaining this on a free response, use the phrase “average kinetic energy increases” when temperature increases. That language earns points.

3. Maxwell-Boltzmann Distributions

This is the graphical representation of particle energies at different temperatures.

Maxwell-Boltzmann distributions at three temperatures

What the graph shows

• x-axis → speed (which corresponds to kinetic energy)
• y-axis → relative number of particles, $P(v)$
• The area under each curve represents all particles in the sample.

At any temperature, particles have a range of energies. Not all particles move at the same speed. Notice how the three curves (100 K, 300 K, and 1000 K) spread out and shift as temperature increases.

Effect of Increasing Temperature

As temperature increases:

• The peak shifts right (higher speeds and higher kinetic energy)
• The curve gets wider
• The peak gets lower
• More particles have high kinetic energy

A common trap: a taller peak does not mean higher energy. It means more particles share similar (usually lower) energies.

Comparing Different Gases at the Same Temperature

At equal temperature:

• Lighter gas → curve shifts right (higher speeds)
• Heavier gas → curve shifts left (lower speeds)
• Both have the same average kinetic energy

On multiple choice questions, they love showing two curves and asking which gas is lighter. The one farther right is lighter.

4. How Particle Motion Explains Pressure

Pressure comes from collisions of gas particles with container walls.

More forceful or more frequent collisions → higher pressure.

Using KMT, you can explain every gas law.

Increase Temperature (constant volume)

1. Temperature increases
2. Average kinetic energy increases
3. Particle speed increases
4. Collisions are more frequent and more forceful
5. Pressure increases

That’s Gay-Lussac’s Law in particle language.

Decrease Volume (constant temperature)

• Same speed (same KE)
• Particles hit walls more often
• Pressure increases

That’s Boyle’s Law explained microscopically.

Add More Gas (constant T and V)

• More particles
• More total collisions
• Pressure increases

When you write explanations, mention frequency of collisions and force of collisions. Those two phrases connect directly to pressure.

5. Real vs Ideal Gas Behavior

KMT perfectly describes ideal gases. Real gases only approximate this behavior.

Real gases act most ideally at:

• Low pressure → particles far apart
• High temperature → motion overcomes attractions

Small, nonpolar gases like $\ce{H2}$ and $\ce{He}$ behave most ideally.

At high pressure or low temperature, assumptions break down because:

• Particle volume matters
• Intermolecular attractions matter

That’s outside this topic’s math, but conceptually it’s tied to assumptions 2 and 3.