# If the activation energy of a reaction is zero, what does that mean for the reaction rate? What is now the only thing that it depends on that changes with temperature?

Sep 5, 2017

If the activation energy ${E}_{a}$ is zero, it doesn't matter what temperature $T$ you are at. Your rate constant $k$, and consequently your rate $r \left(t\right)$, will be limited only by how often the collisions occur, and not on them being successful (because all of them will be successful when ${E}_{a} = 0$).

The Arrhenius equation quantifies this concept:

$k = A {e}^{- {E}_{a} / R T}$

where $R$ is the universal gas constant and $A$ is the frequency factor.

And when ${E}_{a} = 0$, we thus have:

$\textcolor{b l u e}{k = A}$

However, since $A$ is to some extent implicitly directly proportional to temperature (being collision-based), it will increase with increasing temperature, and consequently, so will $k$.

As a result, we do retain the relationship that as $T \uparrow$, $k \uparrow$. But if you do not provide each $A$, this problem cannot be mathematically done.