AP Chemistry Kinetic Molecular Theory

Temperature, particle speed, and Maxwell-Boltzmann curves, with three worked examples.

Kinetic molecular theory (KMT) is mostly a reasoning topic: you are given a change in temperature or in the gas, and you explain what happens to particle motion. The ideas are few, but the exam tests them in several different disguises, so the worked examples below cover each one.

The Kinetic Molecular Theory Ideas You Need

Gas particles are in constant, random motion and collide elastically; collisions with the walls create gas pressure, the particle-level picture behind the ideal gas law.
The Kelvin temperature of a sample is proportional to the average kinetic energy of its particles, and kinetic energy relates to speed by KE = ½mv².
At the same temperature, all gases have the same average kinetic energy, so lighter particles move faster on average than heavier ones.
A sample contains a spread of speeds, shown by the Maxwell-Boltzmann distribution, not one single speed.

Worked Example 1: How Temperature Changes Average Kinetic Energy

By what factor does the average kinetic energy of a gas change when it is heated (a) from 300 K to 600 K, and (b) from 27°C to 54°C?

(a) Average kinetic energy is proportional to Kelvin temperature, so 600 K / 300 K = 2: the average kinetic energy doubles.
(b) The temperature is not doubled in kelvins. 27°C = 300 K and 54°C = 327 K, so the factor is 327 / 300 = 1.09, about a 9% increase, not a doubling.

The trap in (b) is applying the proportionality to Celsius values. Always convert to kelvins first.

Worked Example 2: Comparing Hydrogen and Oxygen at the Same Temperature

H₂ (molar mass 2.016 g/mol) and O₂ (32.00 g/mol) are in separate containers at the same temperature. Compare their average kinetic energies and average speeds.

Average kinetic energy: equal, because it depends only on temperature.
Average speed: with equal kinetic energy, ½m_H₂v_H₂² = ½m_O₂v_O₂², so the lighter particle must move faster:
v_H₂ / v_O₂ = √(32.00 / 2.016) = √15.87 = about 4.0. Hydrogen molecules move roughly four times faster on average.

Worked Example 3: Reading a Maxwell-Boltzmann Curve at Two Temperatures

The diagram shows the same gas at a lower and a higher temperature (the higher one is twice the Kelvin temperature). Describe how the curves differ.

Peak: the higher-temperature curve is lower and its peak (most probable speed) sits farther right.
Width: it is wider, a broader spread of speeds.
Area: both curves enclose the same area, since the number of particles is unchanged.
Tail: beyond the dashed line, which marks a speed high enough to react, the hot curve holds far more particles (roughly 12% of the particles against under 1% for the cooler curve in this diagram). That growing high-energy tail is why a temperature rise speeds up reactions, the idea behind the collision model in Unit 5.

Common Kinetic Molecular Theory Mistakes

Using Celsius in a proportionality. Average kinetic energy is proportional to temperature in kelvins only.
Saying a heavier gas has more kinetic energy at the same temperature. Average kinetic energy is the same; the heavier particles are simply slower.
Saying every particle moves at the same speed. A sample has a distribution of speeds at any temperature.
Drawing the hotter curve taller. It is lower and wider, with the same total area, shifted to the right.

This same particle-level reasoning shows up across AP Chemistry too, including why temperature stays constant while a substance changes state on a heating curve -- for every other free tool and guide on this site, start from the AP Chem Score Calculator.

Frequently Asked Questions

What is kinetic molecular theory?

A model that explains the macroscopic properties of a gas through the motion of its particles: gas particles move continuously and randomly, collide elastically, and are far enough apart that, in the ideal model, attractions between them are negligible. Gas pressure comes from those collisions with the container walls.

How are temperature and kinetic energy related?

The Kelvin temperature of a sample is proportional to the average kinetic energy of its particles. Doubling the Kelvin temperature doubles the average kinetic energy. This only works in kelvins, never in degrees Celsius.

Do all gas particles at the same temperature move at the same speed?

No. Particles in a sample have a wide spread of speeds and kinetic energies, described by the Maxwell-Boltzmann distribution. At the same temperature, different gases have the same average kinetic energy, but lighter particles move faster on average than heavier ones.

What happens to a Maxwell-Boltzmann curve when temperature increases?

The curve flattens and shifts to the right: the most probable speed increases, the peak gets lower, and the distribution gets wider. The total area under the curve stays the same, because the number of particles has not changed.

Why does raising the temperature speed up reactions?

A larger fraction of particles sits in the high-energy tail of the Maxwell-Boltzmann curve at the higher temperature, so more collisions have enough energy to overcome the activation energy.

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