[youngtreeest]

There is no relationship btw temperature and Arrenhius activation energy for a reaction, right?

Thank you very much!

[curiouscat]

One's an independent variable. Other's a constant (to some extent).

No, there's no non-trivial functional relation between a constant and a variable.

[youngtreeest]

Thank you very much for the confirmation!

[Irlanur]

As a reaction can occurr over several transition states, for large molecules some zillions, and these states don't have all the same energy, there certainly is a dependence between Temperature and the activation energy. After all, this dependence is small and assuming the activation energy is a constant is often reasonable.

[Corribus]

In the traditional Arrhenius formulation, the activation energy is usually assumed to be temperature independent. In transition state theory, however, which use a more rigorous thermodynamical formulation, the activation energy (energy difference between the transition state and the reactants) is shown explicitly to be temperature dependent. If you have a p-chem book handy, you might look up the Eyring Equation. In general the Arrhenius activation energy is approximately equal to the activation enthalpy + RT.  (Because reaction coordinates are expressed on a Gibbs energy scale, it should be obvious that there is a temperature dependence because the Gibbs energy is temperature dependent: G = H - TS.) The effect of temperature is usually weak over small temperature ranges, which is why the Arrhenius equation works well in an overwhelmingly large number of cases.

You might find this paper a relevant example of the temperature dependence of the activation energy, if you have access to JACS.

http://pubs.acs.org/doi/abs/10.1021/j150609a003