A first order reaction is 50% complete in 30 min at `27^(@)C`. Calculate the rate constant of the reaction at `27^(@)C`.

Explanation

To calculate the rate constant of a first-order reaction that is 50% complete in 30 minutes at 27°C, we can follow these steps:

### Step 1: Understand the Concept of Half-Life
For a first-order reaction, the time taken for the concentration of the reactant to decrease to half its initial value is known as the half-life (T_half). In this case, the reaction is 50% complete in 30 minutes, which means T_half = 30 minutes.

### Step 2: Use the Formula for Half-Life of a First-Order Reaction
The relationship between the rate constant (k) and the half-life (T_half) for a first-order reaction is given by the formula:
\[ k = \frac{0.693}{T_{half}} \]
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