In the Arrhenius equation for a centrain, the value of A and `E_a` (activation energy ) are `4 xx 10^(13)s^(-1)` and 98.6 kJ `mol^(51)` respectively. If the reaction is of first order, at what termperature will its half-life preriod be 10 min ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
We have the following information:
- Pre-exponential factor (A) = \(4 \times 10^{13} \, s^{-1}\)
- Activation energy (\(E_a\)) = \(98.6 \, kJ \, mol^{-1}\) (which we will convert to Joules)
- Half-life (\(t_{1/2}\)) = \(10 \, minutes\) (which we will convert to seconds)

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