Question

The following data were obtained for a given reaction at 300 K. \[ \begin{array}{|c|c|} \hline \text{Reaction} & \text{Energy of activation (kJ mol}^{-1}\text{)} \\ \hline \text{(i) Uncatalysed} & 76 \\ \text{(ii) Catalysed} & 57 \\ \hline \end{array} \] The factor by which the rate of catalysed reaction is increased is

• A. 21
• B. 2100
• C. 2000
• D. 1200

Hint:

The rate of a reaction increases with a decrease in activation energy, as shown by the Arrhenius equation.

Answer 1

The Correct Option is C

Step 1: Arrhenius Equation. 
The rate constant \( k \) is related to activation energy \( E_a \) by the Arrhenius equation: \[ k = A e^{-E_a / RT} \] where \( A \) is the pre-exponential factor, \( R \) is the gas constant, and \( T \) is the temperature. The ratio of the rate constants for catalysed and uncatalysed reactions gives the increase in the rate. 

Step 2: Conclusion. 
The correct answer is (C), 2000.