## Relationship Between Activation Energy and Temperature of an Ideal Gas

The ignition temperature of an ideal gas is the temperature at which the energy gas molecules is greater than the activation energy.
The energy of gas molecules is
$\frac{1}{2} mv^2 = \frac{3}{2} kT$
where
$m$
is the mass of the gas molecules
$v$
is the speed of the gas molecules
$k=1.38 \times 10^{-23}J/K$
is Boltzmanns constant
$T$
is the temperature
In fact,every gas has a distribution of speeds. Temperature defines an average (actually the root mean square speed). At any temperature, some gas molecules have higher speeds than is needed to supply the activation energy. Foe ignition to occur, a sufficiently high proportion of the molecules must have energy greater than the activation energy for a chain reaction to occur, so the energy released by single reaction is used to initiate the next reaction.