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. 105 kJ/mol
B. 198 kJ/mol
C. 75 kJ/mol
D. 135 kJ/mol

Answer

C

Explanation

`r_(1)=Ae^(-(Ea_(1))/(RT_(1))), r_(2) =Ae ^(-(Ea_(2))/(RT_(2)))`
`r_(1)=r_(2)` [Given]
`therefore Ae ^((-(Ea_(1))/(RT_(1))))=Ae ^((-(Ea_(2))/(RT_(2)))" or "(Ea_(1))/(T_(1))=(Ea_(2))/(T_(2))`
Also, `Ea_(2)=Ea_(1) -30, T_(1)=700 K, " "T_(2) =500 K` (Given)
`therefore " "(Ea_(1))/(700) =(Ea_(1)-30)/(500)" or "5Ea_(1) =7Ea_(1) -210`
`2Ea_(1) =210 rArr Ea_(1) =105" kJ/mol "rArr Ea_(2) =105-30 rArr Ea_(2)=75" kJ/mol"`