For the following reaction,
`A overset(500 K)rarr` Products
`A overset(400K//"catalyst")rarr` Product
If `((-d[A])/(dt))_(500 K)=-((d[A])/(dt))_(400 K)`
no catalyst in presence of catalyst Then `E_(a)` is approximately :

Options

A. `200" kJ mol"^(-1)`
B. `100" kJ mol"^(-1)`
C. `20" kJ mol"^(-1)`
D. `120" kJ mol"^(-1)`

Answer

B

Explanation

`k_(500) =Ae^(-E_(a)//500R), k_(400) =Ae^(-(in_(a)-20)//400 R)`
Since `k_(500)=k_(400) (because (d[A])/(dt)|_(500k)=(d[A])/(dt) |_(400 k))`
`therefore e^(-E_(a)//500 R) =e^(-(E_(a)-20)//400 R) rArr (Ea)/(500 R) =(E_(a) -20)/(400 R)`