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

Explanation

To solve the problem, we need to calculate the rate constant (k) for a first-order reaction that is 50% complete in 30 minutes at 27°C.

### Step-by-Step Solution:

1. **Understand the Concept of Half-Life in First-Order Reactions**:
- For a first-order reaction, the half-life (t₁/₂) is the time taken for the concentration of the reactant to reduce to half its initial value. The relationship between the rate constant (k) and the half-life for a first-order reaction is given by the formula:
\[
k = \frac{\ln(2)}{t_{1/2}}
...