A hydrogenation reaction is carried out at 500K. If the same reaction is carried out in presenceof catalyst at the same rate, the temperature required is 400K. Calculate the activation energy of the reaction if the catalyst lowers the activation energy barrier by 20kJ/mol.

A hydrogenation reaction is carried out at 500K. If the same reaction

1.	A hydrogenation reaction is carried out at 500K. If the same reaction is carried out in presenceof catalyst at the same rate, the temperature required is 400K. Calculate the activation energy of the reaction if the catalyst lowers the activation energy barrier by 20kJ/mol.
Answer» SOLUTION :Let `E_(a)` and `E._(a)` be the energy of activation in absence and presence of CATALYST for hydrogenation reaction, as `k=Ae^(-E_(a)//RT)` `k_(1)=Ae^(-E_(a)//Rxx500)` (In absence of catalyst) `k_(2)=Ae^(-E._(a)//Rxx400)` (In presence of catalyst) Given , `r_(1)=r_(2)`, Hence, `k_(1)=k_(2)` `e^(-E_(a)//Rxx500)=e^(-E._(a)//Rxx400)` `IMPLIES(E_(a))/(Rxx500)=(E._(a))/(Rxx400)` or `(E_(a))/(500)=(E_(a)-20)/(400)` (As `E_(a)-E._(a)=20`) `:.E_(a)=100kJ//mol^(-1)`