Question

As the title says, I am wondering what the physical significance of the frequency/pre-exponential factor in the Arrhenius equation. My idea of it is that:

If the units of Eₐ
are energy per molecule, then the Arrhenius equation can be written

kᵣ = Ae ₋Eₐ / kBT

It is my understanding that, if quantum mechanical effects are not significant, the average kinetic energy of a particle in a system will be kBT; this leads me to interpret the exponential factor as the fraction of particles that possess at least Ea. I have confirmed this by showing that, in a system in which the available energy levels are separated by a factor ϵ, so that energy levels are nϵ, with n=1,2,…, the fraction of molecules in states with E at least nminϵ is
e^−iₘᵢₙϵ / kBT

Which is of the same form as

e^−Eₐ / kBT

So: if all of the particles in a system possess sufficient energy to react, then kr=A
. If not all of the particles in a system possess sufficient energy to react, then the rate constant is A
scaled by the fraction of the particles that do have sufficient energy.

Still, the constant itself seems ambiguous to me, and I would like some guidance - and perhaps to be pointed in the direction of some reading. Please correct any erroneous chemistry in this post; I am not doing a chemistry degree yet, I am in my first year of A levels.

Answer 1

The frequency factor in the Arrhenius equation reflects the number of correctly oriented collisions and the probability of product formation.

Step-by-step explanation:

The physical significance of the frequency factor (often denoted as A) in the Arrhenius equation can be understood by considering its role in the reaction kinetics.

It is essentially a proportionality constant related to the number of collisions having an orientation capable of leading to product formation and also incorporates the effects of molecular geometry and energy distribution.

In other words, it reflects the frequency of collisions and the probability that those collisions are effective in forming product hence the term 'frequency factor'.

The exponential term, e-Ea/RT, is particularly significant as it represents the fraction of molecules possessing enough energy to overcome the activation energy (Ea) barrier.

At high temperatures, this fraction increases, leading to a faster reaction rate due to the increased number of molecules that can react.

Collision theory underpins the Arrhenius equation, and the frequency factor A increases slightly with temperature because the molecules move faster and undergo more collisions per unit time.

Moreover, a higher activation energy leads to a smaller fraction of molecules with the necessary energy, which results in a slower reaction rate.