Solution: Two reactions have identical values for Ea. Does this ensure that they will have the same rate constant if run at the same temperature?

We have to determine if two reactions with the same activation energy would have the same rate constants if they are run at the same temperature.

We will use the two-point form of the Arrhenius equation to solve this problem.

$\boxed{\mathbf{ln}\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{-}{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}\mathbf{(}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{ }\mathbf{-}\mathbf{ }\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\mathbf{)}}$

Where,

k₁ = rate constant at T₁

k₂ = rate constant at T₂

E_a = activation energy

R = universal gas constant

T₂ = higher temperature

T₁ = lower temperature