For following reactions
`A overset( 400K)( rarr) ` Product
`A underset("catalyst")overset("200K")(rarr)` Product
it was found that the `E_(a)` is decreased by 20 kJ` //` mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is ( Assume per exponential factor is same ) `:`

Options

A. 40 kJ` //` mol
B. `20kJ` /mol
C. `80 kJ //mol`
D. `35 kJ //mol`

Explanation

`k_("uncatalysed") = k _("catalysed")`
`Ae^(-Ea_(1) //RT_(1)) = Ae^(-Ea_(2)//RT_(2))rArr ( Ea_(1))/( T_(1))=(Ea_(2))/( T_(2))rArr Ea_(1) =Ea_(2) + 20 `
`rArr ( Ea_(2)+ 20)/( 400) =( Ea_(2))/( 200) rArr 2Ea_(2) = Ea_(2)+20 rArr Ea_(2) = 20`
Activation energy of the catalysed reaction = 20 `kJ //` mol