A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in presence of a catalyst at the same rate, the temperature required is 400 K. The activation energy of the reaction, if the catalyst lowers the activation energy barrier by 20 kJ `mol^(-1)` is ............ ` xx 10^(2) kJ mol^(-1)`.

Answer

1

Explanation

Let `E_(a)` and `E._(a)` be the energy of activation in presence and absence of catalyst for hydrogenation reaction, then `K = Ae^(-E_(a)//RT)`
In presence of catalyst : `K_(1) = A e^(-E_(a)//(R xx 500))`, In absence of catalyst : `K_(2) = A e^(-E_(a)^(+)//(R xx 400))`
Given , the two rates are same, i.e., `r_(1) =r_(2) , therefore K_(1) = K_(2)`
Therefore, `e^(-E_(a)//(R xx 500)) = e^(-E_(a)//(R xx 400))` or `(E_(a))/(R xx 400) = (E._(a))/(R xx 400)`
`E_(a) - E._(a) =20` or `(E_(a))/(500) = (E_(a) - 20)/(400) because (E_(a).)/(R xx 400) therefore E_(a) = 100 kJ mol^(-1)`