# The Boltzmann Distribution

Elastic Collisions: Molecules in gas move at high speed and collide with each other. Collisions are
elastic as molecules do not slow down as a result of collision so no energy lost.
• Energy of Molecules: In gas, liquid, or solution, some molecules move slowly with low energy and
some move fast with high energy. Most move close to average speed and have average energy.
This spread of molecular energies in gases called Boltzmann Distributions.
• Boltzmann Distribution: Area under curve is equal to total number of molecules- which stays the
same.
– Marked with a line Ea, activation energy.
– The shaded area shows only small proportion of molecules have more energy than Ea in order
to react.
– Y axis is number of molecules. X axis is energy. Remember axis and all labels. Energy on x axis
refers to kinetic energy.
– No molecules have zero energy so draw curve starting at origin.
– No maximum energy for molecules so don’t draw curve meeting x- axis.
• Temperature:
– At higher temperature, greater proportion of molecules have an energy greater than or equal
to activation energy.
– Therefore more effective collisions.

Increasing rate of reaction.
– Collisions will also be more frequent as molecules moving faster, but increased energy of
molecules more important.
• Need both curves for temperature, label the shorter one with higher temperature, label the