Question

Explain the temperature dependence of the reaction rate on activation energy basis.

Answer 1

The temperature dependence of the reaction rate can be explained on the basis of activation energy using the Arrhenius equation:

\[\ce{k = Ae^{-E_{a}/RT}}\]

Where:

k = rate constant

A = frequency factor (constant for a given reaction)

E_a​ = activation energy

R = universal gas constant

T = temperature in Kelvin

As temperature increases, the term \[\ce{E_a/RT}\] decreases, making the exponential term \[\ce{k = Ae^{-E_{a}/RT}}\] larger. As a result, the value of k increases, which leads to an increase in the rate of the reaction. This happens because at higher temperatures, a larger fraction of the reacting molecules possess energy equal to or greater than the activation energy required to cross the energy barrier and form products. Therefore, even a small rise in temperature can significantly increase the number of effective collisions. Hence, the rate of a chemical reaction increases with temperature due to the increase in the fraction of molecules having sufficient energy to overcome the activation energy barrier, as explained by the Arrhenius equation.