The time required for `10%` completion of a first order reaction at `298K` is equal to that required for its `25%` completion at `308K` . If the value of `A` is `4xx10^(10)s^(-1)`, calculate `k` at `318K` and `E_(a)`.

Explanation

To solve the problem step by step, we will follow the outlined approach in the video transcript.

### Step 1: Understand the given information
We know that:
- The time required for 10% completion of a first-order reaction at 298 K is equal to the time required for 25% completion at 308 K.
- The pre-exponential factor \( A \) is given as \( 4 \times 10^{10} \, s^{-1} \).

### Step 2: Calculate the rate constant \( k \) at 298 K
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