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 if the catalyst lowers the activation barrier by $20kJmo{l}^{-1}$.
Report your answer as $\alpha$, where activation energy is $100\alpha kJmo{l}^{-1}$.

• A. 1
• B. 4
• C. 3
• D. 6

Answer 1

Answer: (A)

1

According to arrhenius equation $K=A{e}^{-E_a/RT}$

Let $E_a$ of the reaction in absence of catalyst $=xkJmo{l}^{-1}$

Therefore $E_a$ of the reaction in presence of catalyst $=x-20kJmo{l}^{-1}$

The Arrhenius equations in the two conditions can thus be written as

$K=A{e}^{\frac{x}{R\times 500}}....\left(i\right)$

$K=A{e}^{\frac{x-20}{R\times 400}}....\left(ii\right)$

Dividing equation (i) by (ii), we get

$-e^{\frac{x}{500R}}=e^{\frac{x-20}{400R}}\Rightarrow \frac{x}{500}=\frac{x-20}{400}$

or $x=100kJmo{l}^{-1}$