Question

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 catalysed reaction if the catalyst lowers the activation energy barrier by 20 kJ/mol.

Answer 1

Catalysed reaction:
$k_1=A.e^{\frac{-E_{a}1}{500R}}$

Uncatalysed reaction:
$k_2=A.e^{\frac{-E_{a}2}{400R}}$

But we know that $k_1=k_2$
$⟹\frac{E_{a}1}{500}=\frac{E_{a}2}{400}$
Hence, $\frac{E_{a}1}{E_{a}2}=\frac{5}{4}$
We have also been told that $E_{a}1-E_{a}2=20$
$⟹E_{a}1=100kJ/mol{E}_{a}2=80kJ/mol$
Hence, activation energy of catalysed reaction = 80 kJ/mol