A hydrogenation reaction is carried out at `500 K`. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is `400 K`. Calculate the activation energy of the reaction if the catalyst lowers the activation barrier by `20 kJ mol^(-1)`.

Explanation

`100" kJ/mol"`
`k_(500)=Ae^(-E_(1)//RT_(1))`
`k_(400) =Ae^(-E_(2)//RT_(2))`
`because k_(500)=k_(400) rArr (E_(1))/(RT_(1)) =(E_(2))/(RT_(2)) rArr (E_(2))/(E_(1)) =(T_(2))/(T_(1))=(400)/(500) =(4)/(5)`
Also `E_(1)=E_(2)+20000 J rArr (E_(1)-20,000)/(E_(1))=(4)/(5) rArr E_(1) =100,000 J =100" kJ mol"^(-1)`