To understand the powerful effect of temperature on rate, and the way catalysts work, we need a picture of how energy is shared among the particles in a sample. Not all particles move at the same speed. Collisions constantly transfer energy between them, so at any instant there is a wide spread of molecular kinetic energies. The Maxwell–Boltzmann distribution describes this spread.
Plotted as the number of particles against kinetic energy, the distribution is a characteristic curve. It begins at the origin, because no particle has zero energy, rises to a peak at the most probable energy, and then falls away with a long tail stretching to high energies. The area under the whole curve represents the total number of particles and is fixed for a given sample. Importantly, only the particles in