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 energy by 20 kJ `mol^(-1)` .

Explanation

Suppose activation energy in the absence of catalyst is `E_(a)` and that in the presence of catalyst it is `E_(c)`. Then
`k="A e"^(-E_(a)//500"R")="A e"^(-E_(c)//400" R")("as k is same in both the cases").`
Hence, `(E_(a))/(500" R")=(E_(c))/(400" R")" or "E_(c)=(4)/(5)E_(a)`
But `E_(a)-E_(c)=20" kJ"`
or `E_(a)-(4)/(5)E_(a)=20" or "(1)/(5)E_(a)=20" or "E_(a)=100" kJ mol"^(-1)`