the Maxwell-Boltzmann distribution
/ MAKS-wel BOLTS-mahn /
Not all gas molecules move at the same speed; there is a spread. This distribution is the bell-shaped-ish curve that tells you what fraction of molecules move at each speed: a few crawl, a few race, and most sit somewhere in the middle.
Precisely, the probability density for a molecule to have speed v is f(v) proportional to v^2 exp(-m v^2 / (2 k_B T)). It is skewed, with a long high-speed tail rather than being symmetric. Its peak marks the most probable speed v_mp = sqrt(2 k_B T / m); the mean speed is a bit larger, and the root-mean-square speed larger still, so that v_mp < v_avg < v_rms.
Temperature effect: heating the gas shifts the whole curve to the right and flattens it, giving a wider spread and higher speeds. That high-speed tail is physically important. It explains evaporation, and why a small fraction of molecules can escape a planet's gravity or clear the energy barrier of a chemical reaction even when the average molecule cannot.
Plot the speed distribution of nitrogen at different temperatures: the hotter it is, the lower and more spread-out the peak, and the further to the right it sits.
The curve of what fraction of molecules move at each speed.
The curve is asymmetric: because there is no upper limit on speed but speeds cannot be negative, it has a long tail toward high speeds, so the mean and rms speeds lie above the peak.