The rate constant of a reaction at `500 K` and `700 K` are `0.02s^(-1)`, respectively. Calculate the values of `E_(a)` and `A` at `500 K`.

Explanation

To solve the problem of calculating the activation energy \( E_a \) and the pre-exponential factor \( A \) for the given reaction at \( 500 K \), we will follow these steps:

### Step 1: Use the Arrhenius Equation
The Arrhenius equation relates the rate constants at two different temperatures to the activation energy:
\[ \ln \left( \frac{k_2}{k_1} \right) = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]
Where:
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