We’re being asked to **determine the activation barrier (activation energy, E _{a})** of a reaction given the rate constant and frequency factor.

We can use the ** two-point form of the Arrhenius Equation** to calculate activation energy:

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{k}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}{\mathbf{}}\left(\frac{\mathbf{1}}{\mathbf{T}}\right){\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{}}{\mathbf{A}}}$

where:

**k** = rate constant

**E _{a}** = activation energy (in J/mol)

**R** = gas constant (8.314 J/mol • K)

**T** = temperature (in K)

**A** = Arrhenius constant or frequency factor

The rate constant of a reaction at 32°C is 0.055/s. If the frequency factor is 1.2 x 10^{13}/s, what is the activation barrier?

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