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 reaction at 500 K, if the catalyst lowers the activation barrier by $20kJmo{l}^{-1}$.

• A. $80kJmo{l}^{-1}$.
• B. $100kJmo{l}^{-1}$.
• C. $110kJmo{l}^{-1}$.
• D. $95kJmo{l}^{-1}$.

Answer 1

The correct option is B $100kJmo{l}^{-1}$.

Arrhenius equation is given by , $k=A{e}^{-Ea/RT}$
Therefore,$k_{500}=A{e}^{-E_{500}/RT}$
$k_{400}=A{e}^{-E_{400}/RT}$
According to the question, $k_{500}=k_{400}\Rightarrow \frac{E_{500}}{R\times 500}=\frac{E_{400}}{R\times 400}$
⇒$\frac{E_{500}}{5}=\frac{E_{400}}{4}$
$E_{500}=\frac{E_{400}}{4}\times 5$ ....(1)
Given, $E_{500}=E_{400}+20$ ....(2)
Substituting equation (2) in equation (1),
we get,
$E_{400}=80kJmo{l}^{-1}$
From equation (2),$E_{500}=100kJmo{l}^{-1}$