Activation energy equation

[VarshiniC]

How is this equation derived from the given equations on the equation list?

k'/k=Ea/R(1/T1-1/T2)

[yushensun 3F]

Do you mean this one?

I'm not sure about the one you asked but there's this one

[Levy Shaked]

For a reaction at a particular temperature, ln(k) = lnA -(Ea/R)(1/T), where Ea represents the activation energy of a reaction and A is correlated with collision frequency of reactants. Compared to the proportion of collisions with sufficient energy to overcome Ea, collision frequency changes little with respect to temperature, and so A is assumed to be relatively constant across temperature changes.

Constant values of A can be taken advantage of by rearranging the above equation to be lnA = ln(k) + (Ea/R)(1/T) at any temperature. Thus, for two temperatures T1 and T2, ln(k1) + (Ea/R)(1/T1) = lnA = ln(k2) + (Ea/R)(1/T2). This equation can then be arranged into the form

ln(k2/k1) = -(Ea/R)(1/T2 - 1/T1).