The energy of activation of a first order reaction is `187.06 kJ mol^(-1)` at `750 K` and the value of pre-exponential factor A is `1.97xx10^(12)s^(-1)`. Calculate the rate constant and half life. `(e^(-30)= 9.35xx10^(-14))`

Explanation

To solve the problem, we need to calculate the rate constant (k) and the half-life (t_half) of a first-order reaction given the activation energy (E_a), the pre-exponential factor (A), and the temperature (T).

### Step-by-Step Solution:

**Step 1: Convert Activation Energy to Joules**
Given:
- Activation Energy, E_a = 187.06 kJ/mol

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