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The activation barrier for an uncatalyzed reaction is estimated to be 15.3 kcal/mol. The activation barrier...

The activation barrier for an uncatalyzed reaction is estimated to be 15.3 kcal/mol. The activation barrier for the catalyzed reaction is estimated to be 8.7 kcal/mol. How many times faster is the catalyzed rate versus the uncatalyzed rate? In other words, by what factor/coefficient do you have to multiply the uncatalyzed rate to equal the catalyzed rate? Assume the temperature is 298 K, and enter your answer to the nearest ones.

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Answer #1

K1 = Ae-Ea1/RT uncatalysed

k2   = Ae-Ea2/RT catalysed

K1/K2    = Ae-Ea1/RT uncatalysed/Ae-Ea2/RT catalysed

K1/K2    = e-Ea1/RT/e-Ea2/RT

            = -Ea1/RT/-Ea2/RT

           = Ea1/Ea2

          = 15.3/8.7 = 1.758

K1/K2 = 1.758

K1   = 1.758K2

K2/K1   = 0.568

K2      = 0.568K1

catalyses rate 0.568 times faster than un catalysed rate

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