1. Tardigrade
  2. Question
  3. Chemistry
  4. For following reactions A xrightarrow700 K Product A xrightarrow[ textcatalyst]500 K Product it was found that the Ea is decreased by 30 k J/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same):

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Q. For following reactions
$A \xrightarrow{700\,K}$ Product
$A \xrightarrow[{\text{catalyst}}]{500\,K}$ Product
it was found that the $E_a$ is decreased by $30 \,k J/mol$ in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same):

JEE MainJEE Main 2020Chemical Kinetics

Solution:

$K_{1}=Ae \frac{E a}{R\times700}$
$K_{2}=A\times e\frac{\left(Ea-30\right)}{R\times500}$
For same rate $K_{1}=K_{2}$
$e\frac{E a}{700 R}_{=e} \frac{\left(E a-30\right)}{R\times500}$
$\frac{E a}{700 R}=\frac{E a-30}{R\times500}$
$5 Ea=7Ea-210$
$210=2E a$
$E_{a}=105 kJ/mole$
$E_{a}-30=75$