Question

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?

Answer 1

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(t)`, 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 = Ae^(-E_a//RT)`

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

And when `E_a = 0`, we thus have:

`color(blue)(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 uarr`, `k uarr`. But if you do not provide each `A`, this problem cannot be mathematically done.