1.5.2

# Maxwell-Boltzmann Distribution

Test yourself

## The Maxwell-Boltzmann Distribution of Energies

The Maxwell-Boltzmann distribution of energies is a handy little graph showing the energy distribution of all the molecules in a gas.

### The graph

• The number of molecules is on the y-axis.
• The kinetic energy of the molecules is on the x-axis.

### The origin

• No molecules have zero energy, so the curve passes through the origin at (0,0).

### The peak

• There is a peak in the middle.
• This represents the most likely energy of any molecule.
• There are more molecules with this energy than with any other energy.

### The area under the graph

• The area under the graph gives the total number of molecules.
• You can think of this as like adding up the number of molecules with every particular energy.

### Molecule energies

• The average energy is to the right of the maximum (peak).
• The tail of the graph is asymptotic to the x-axis.
• This means it tends to zero, but never touches the x-axis.
• This reflects that there is a small possibility of having a very high energy molecule.

### Activation energies

• We can mark the activation energy on the Maxwell-Boltzmann distribution. This allows us to view the number of molecules with the energy to react.
• On the left-hand side of the activation energy mark, molecules have less energy than the activation energy and so they can't react.
• On the right-hand side, molecules have more energy than the activation energy and so they can react.