The activation energy of a certain uncatalyzed reaction is 64 kJ/mol. In the presence of a catalyst, the E_a is 55 kJ/mol. How many times faster is the catalyzed than the uncatalyzed reaction at 400^$\circ$C Assume that the frequency factor remains the same.

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The rate of a reaction is exponentially related to the activation energy by the Arrhenius equation. The ratio of the rates of the catalyzed to uncatalyzed reactions can be calculated using the formula: rate ratio = exp[(E_a(uncatalyzed) - E_a(catalyzed)) / (R * T)]. Substituting the given values (E_a(uncatalyzed) = 64 kJ/mol, E_a(catalyzed) = 55 kJ/mol, R = 8.314 J/mol·K, T = 673 K), the rate ratio is approximately 5.0 times.

The Activation Energy of a Certain Uncatalyzed Reaction Is 64 ∘\circ∘

The Activation Energy of a Certain Uncatalyzed Reaction Is 64 $\circ$