The activation energy for a reaction is changed from 184 kJ/mol to 59.0 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 6900 years to occur, about how long will the catalyzed reaction take

The catalyzed reaction will take 2.85 seconds to occur.

Explanation:

The activation energy of a reaction is given by:                                                        

For the reaction without catalyst we have:

  (1)

And for the reaction with the catalyst:

  (2)

Assuming that frequency factor (A) and the temperature (T) are constant, by dividing equation (1) with equation (2) we have:                      

Since the reaction rate is related to the time as follow:

And assuming that the initial concentrations ([R]) are the same, we have:

Therefore, the catalyzed reaction will take 2.85 seconds to occur.

I hope it helps you!                            

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