Question

# 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.

Reaction rate is proportional to the exp(-Ea/RT), where Ea- activation energy in Joules, R-gas constant and T -temperature in K.
So, the ratio of rate constants of catalyzed and uncatalyzed reactions will be equal to exp(-Ea1/RT) / exp(-Ea2/RT) = exp((Ea2-Ea1)/RT), where Ea2 - activation energy of catalyzed reaction - 15.3 * 4184 J = 64015.2 J; and Ea1 - activation energy of uncatalyzed reaction - 8.7 * 4184 J = 36400.8 J
Ratio = exp ( ( 64015.2-36400.8 ) / 8.314 * 298 ) = 69269
Catalyzed reaction will be 69269 times faster than uncatalyzed.

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