Question

For following reactions

$A\stackrel{700K}{⟶}$ Product
$A\underset{catalyst}{\overset{500K}{\to }}$ Product

it was found that the $E_a$ is decreased by $30kJ/\text{mol}$ in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same)

• A. $135kJ/\text{mol}$
• B. $105kJ/\text{mol}$
• C. $198kJ/\text{mol}$
• D. $75kJ/\text{mol}$

Answer 1

The correct option is D $75kJ/\text{mol}$

Rate of reaction at $700K$ in the absence of catalyst is equal to rate of reaction at $500K$ in the presence of catalyst
$\left(E_a\right)-(E_a{)}_c=30kJ/\text{mol}$
$\because$ Rate is same
$\therefore$ Rate constant will also be same

(Assuming same value of pre exponential factor)

$k=A{e}^{-E_a/RT}$

$\Rightarrow \frac{-E_a}{R\times 700}=\frac{-(E_a{)}_c}{R\times 500}$

$\Rightarrow -5E_a=-7(E_a{)}_c-5E_a=-7(E_a-30)$

$2E_a=210\Rightarrow E_a=105\text{kJ/mol}$

$\therefore \text{Activation energy in the presence of catalyst}=105-30=75\text{kJ/mol}$