For following reactions
`A overset( 400K)( rarr) ` Product
`A underset("catalyst")overset("200K")(rarr)` Product
it was found that the `E_(a)` is decreased by 20 kJ` //` mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is ( Assume per exponential factor is same ) `:`

Options

A. 40 kJ` //` mol
B. `20kJ` /mol
C. `80 kJ //mol`
D. `35 kJ //mol`

Explanation

To solve the problem, we need to analyze the activation energy (Ea) for both the uncatalyzed and catalyzed reactions, and how they relate to the rate of the reaction.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let \( E_{a1} \) be the activation energy for the uncatalyzed reaction at 400 K.
- Let \( E_{a2} \) be the activation energy for the catalyzed reaction at 200 K.
- It is given that \( E_{a1} - E_{a2} = 20 \, \text{kJ/mol} \).
...