1. Tardigrade
  2. Question
  3. Chemistry
  4. Catalyst A reduces the activation energy for a reaction by 10 kJ mol -1 at 300 K. The ratio of rate constants, ( k text T, Catalysed / k T text , Uncatalysed ) is e x . The value of x is [nearest integer] [Assume theat the pre-exponential factor is same in both the cases. Given R =8.31 J K -1 mol -1 ]

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Q. Catalyst A reduces the activation energy for a reaction by $10 \,kJ\, mol ^{-1}$ at $300 K$. The ratio of rate constants, $\frac{{ }^{ k } \text { T, Catalysed }}{{ }^{ k } T \text {, Uncatalysed }}$ is $e ^{ x } .$ The value of $x$ is ____[nearest integer]
[Assume theat the pre-exponential factor is same in both the cases.
Given $R =8.31 \,J\, K ^{-1} \,mol ^{-1}$ ]

JEE MainJEE Main 2022Chemical Kinetics

Solution:

$K =A e ^{\frac{- Ea }{ RT }}$
$K_{\text{cat}}=A e^{-\frac{E_{a}{ }^{1}}{R T}}, $
$K_{\text {uncat. }}=A e^{-\frac{E a}{R T}}$
$\frac{ K _{\text {cat }}}{ K _{\text {uncat. }}}= e ^{\frac{ E _{ a }- E _{ a }}{ RT }}$
$= e ^{\frac{10 \times 1000}{8.31 \times 300}}= e ^{4.009}= e ^{ x }$
$\therefore x =4$