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

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

1.	A hydrogenation reaction is carrid out at 500 K. If the same reaction is carried out in the presence of a catalyst at the same rate, the termperature required is 400 K. Calculatethe activation energy of the reaction if the catalyst lowers the activation barrier by 20 kj mol^(-1).
Answer» Solution :RATE of hydrogenation at `500^@K` for a REACTION is equal to the rateof reaction in presense of catalyst at `400^@ K` Rate = k `xx` conc of REACTANT If rate of reaction are equal therefore their rate constant will also form Arrhenius equation `k = AE^(-E_a//RT)` `k_500 =Ae^(-(E-a//RT)`...(i)`k_400 = Ae^(-E_a//RT_2)`...(ii) When `k_500 = k_400` `:.((E_0)_1)/(RT_1) = ((E_a)_2)/(RT_2)`(From eqs (i) and (ii))or `((E_a)_1)/((E_a)_2) = T_1/T_2` `E_(a_1)/E_(a_2)=T_1/T_2 = 500/400 = 5/4`... (i) In presence of catalyst`E_a`decreases by 20 kJ `mol^(-1)` So,`E_a_1 = 100kJ//mol^(-1)` `E_a_2 = 80 KJ//mol^(-1)` Hence, `E_a` or reaction OS `100kJ mol^(-1)`