# Frequency Factor of the Arrhenius Equation

The question came to my mind as to whether the effect of a catalyst on a reaction included the modification of the frequency factor (or pre-exponential factor) of a reaction, shown in Arrhenius' Equation below as "$$A$$":

$$k = A\exp{\left(\frac{-E_\mathrm{a}}{RT}\right)}$$

On the one hand, we know that catalysts reduce the activation energy of a reaction, thus enabling more particles of reactants to acquire the minimum energy needed to break bonds and form products, therefore speeding up the reaction. But, does the frequency factor stay the same? My guess is that it does, and the effect of the catalysis is manifested solely on the change in activation energy. My question is if this intuition is correct and, if so, why.

Maybe it would help if someone could give a little more insight into the actual meaning of the frequency factor. Is it constant a constant specific to each reaction? What does it represent?

Thanks!

• There are a number of websites and books that try to explain this (example), or you could also look in a physical chemistry textbook. Jan 19 at 19:12
• A catalyst changes the mechanism of a reaction so naturally both $E_a$ and $A$ are different. The factor $A$ describes the rate constant when the activation energy is zero or the temperature infinite and is the fastest the reaction can proceed at and this is controlled by how quickly the species can collide with one another. Jan 20 at 9:31
• This, although I knew it already, let me realise that too often (in organic chemistry at least) we ear "catalysts only reduce the activation energy". It can be practically true but not rigorously correct. Jan 20 at 10:54

The short answer is yes, we can imagine effects on the frequency factor. Without going into too much detail, the frequency factor combines two conceptual elements - the frequency of molecular collisions if reactants are present at 1 M or 1 bar (called z in collision theory) and the probability that such a collision occurs with the correct spatial orientation that a reaction is possible (called $$\rho$$ in collision theory).
Let's start with $$\rho$$. A catalyst that binds multiple reactants can do so in such a way that they are optimally spatially oriented to react. Examples can be found in enzymes which are often large enough to bind the reactants in very specific conformations. So in addition to stabilizing the transition state of the reaction (thus lowering the activation energy), they can also increase $$\rho$$.