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.

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

**Where,**

k_{1} = rate constant at T_{1}

k_{2} = rate constant at T_{2}

E_{a} = activation energy

R = universal gas constant

T_{2} = higher temperature

T_{1} = lower temperature

Two reactions have identical values for E_{a}. Does this ensure that they will have the same rate constant if run at the same temperature?

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