Question

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

Answer 1

Correct Answer: 4

 The problem involves determining the ratio of rate constants for catalyzed and uncatalyzed reactions using the Arrhenius equation. The equation for rate constant \(K\) is:

\(K=Ae^{-\frac{E_a}{RT}}\)

where \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is temperature. Given:

• Reduction in activation energy \(\Delta E_a=10 \, \text{kJ mol}^{-1}\) (converted to Joules: \(10,000 \, \text{J mol}^{-1}\)).
• \(R=8.31 \, \text{J K}^{-1} \text{mol}^{-1}\)
• \(T=300 \, \text{K}\)