The activation energy of a reaction can be determined from the effect of temperature on reaction rate.

  • The rate constant depends on temperature according to the Arrhenius equation:
    $k\rm (T) = A_e^{–\frac{E_a}{RT}}$  
    A graph of $\ln k$ against $\rm 1/T$ is a straight line with a gradient $\rm –\dfrac{E_a}{R}$ and the intercept ln $\rm A$.
    $\rm R$ is the gas constant.
    $\rm E_a$ is the activation energy of the reaction and does not depend on the temperature.
  • The pre-exponential factor, $\rm A$, takes into account the symmetry and frequency of collisions of reacting particles. The Arhenius expression assumes that $\rm A$ is independent of temperature.
  • The equation can also be expressed for two temperatures, $\rm T_1$ and $\rm T_2$.
    $\rm \ln \dfrac{\mathcal k_1}{\mathcal k_2} = \dfrac{E_a}{R}\left(\dfrac{1}{T_2}-\dfrac{1}{T_1}\right)$
  • Reactions with higher values for $\rm E_a$ have a higher temperature dependency of $k$ than reactions with lower values for $\rm E_a$.
  • The $\rm E_a$ values of many chemical reactions $\rm \approx +50~kJ~mol^{–1}$ so the rates of different reactions show similar temperature dependence. They approximately double when the temperature increases by $\rm 10~K$.