Maxwell-Boltzmann Distributions

Gas particles are not all moving at one speed. They constantly collide, and every collision trades energy between particles — one speeds up while the other slows down. Track billions of these collisions and you get a spread: a few particles barely moving, a few flying fast, and most somewhere in the middle. The Maxwell-Boltzmann distribution plots this: number of particles (y-axis) against speed (x-axis), giving a curve that rises, peaks, and tails off to the right.

Heating the gas adds kinetic energy, and the whole curve shifts right and flattens. The particles spread over a wider range of speeds, so the peak drops in height even as it moves toward higher speed — the area under the curve stays constant because the total number of particles hasn't changed. At the same temperature, lighter particles move faster: helium and xenon have the same average kinetic energy at a given temperature, since that energy depends only on temperature, but because KE = (1/2)mv², the much lighter helium atoms need far higher speeds to match xenon's energy. Helium's curve sits lower, wider, and shifted right of xenon's narrow, tall curve centered at low speed.

This distribution connects directly to reaction rates. Only particles colliding with at least the activation energy can react, and those particles live in the high-speed tail of the curve. Raising temperature shifts the curve right, so a larger fraction of particles sits past that activation-energy threshold — which is the molecular reason reaction rates climb sharply with temperature, a link explored further once rates become the focus.