The rate constant of a reaction at 500 K , in presence of catalyst is same as that of 800 K in absence of catalyst if use of catalyst lowers down the energy barrier by 60 J then what will be the value

Question

The rate constant of a reaction at 500 K , in presence of catalyst is same as that of 800 K in absence of catalyst if use of catalyst lowers down the energy barrier by 60 J then what will be the value of activation energy of uncatalysed reaction?

TestHub · Accepted Answer

Let in absence of a catalyst activation energy to be $E_{a}$ . Then, in the presence of a catalyst, it will be $E_{a} - 60$ .

∵ $K_{c a t a l ys t} = K_{w i t h o u t c a t a l ys t}$ , we have:

$e^{- \frac{E _{a} - 60}{RT}} = e^{- \frac{E _{a}}{RT}}$

This implies:

$\frac{E _{a} - 60}{RT} = \frac{E _{a}}{RT}$

$\frac{E _{a} - 60}{500} = \frac{E _{a}}{800}$ ,

$E_{a} = 160 J$

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