Kinetic molecular theory
Two gases, one temperature. Same energy, very different speeds.
Scientific learning path
- 01UnderstandLive
- 02ExploreLive
- 03ExperimentLive
- 04ObserveLive
- 05ExplainLive
- 06ApplyLive
- 07TestBuilding
The swarm
Both boxes hold the same number of particles at the same temperature. Only the speed differs.
Description of this simulation
At 298 K, He has a mean speed of 1256 m/s and Xe has 219 m/s. He is moving 5.73 times faster. Both carry exactly the same average kinetic energy, 6.17e-21 joules per molecule, because that depends on temperature alone. He is faster only because it is lighter: speed goes with the square root of temperature divided by molar mass, so Xe at 131 g/mol lags behind. For He, the most probable speed (1113 m/s), the mean (1256 m/s) and the root mean square (1363 m/s) are three different numbers, in that order, because the distribution has a long tail towards high speeds.
Three different speeds
He4.00 g/mol
- Most probable speed
- 1113
- m/s
- Mean speed
- 1256
- m/s
- Root mean square speed
- 1363
- m/s
Xe131.29 g/mol
- Most probable speed
- 194
- m/s
- Mean speed
- 219
- m/s
- Root mean square speed
- 238
- m/s
The peak, the average and the root mean square are not the same number. The distribution has a long tail towards high speeds, so the average sits above the peak, and squaring before averaging pushes the root mean square higher still.
Mean kinetic energy per molecule
6.172e-21
J
Identical for both gases — kinetic energy depends on temperature alone.
Molecules faster than 1000 m/s
Raise the temperature and watch this fraction grow. It is why evaporation and reaction rates both speed up when things get hotter.
What this model shows — and what it simplifies
Educational ModelThe distribution is the exact Maxwell-Boltzmann expression for an ideal gas, evaluated rather than sketched — the peak on screen sits at the analytic most probable speed.
Where do we see this in real life?
Helium leaks out of a balloon and out of the atmosphere altogether because at any temperature it is the fastest thing in the mixture. The first atomic bombs were fuelled by uranium separated on exactly this effect, diffusing a gas through a barrier thousands of times over.