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