The decomposition of `H_2 O `, is a first order reaction. When 5 mL portions of `H_2 O_2` are titrated with `KMnO_4` solution at the start of the reaction and 5 minutes later, the volumes of KMnO4 solution required are 37.0 mL and 29.5 mL respectively. Calculate the rate constant of the reaction.

Explanation

To solve the problem, we need to calculate the rate constant (k) for the first-order decomposition of hydrogen peroxide (H₂O₂) based on the volumes of KMnO₄ solution used at the start and after 5 minutes.

### Step-by-Step Solution:

1. **Identify Initial and Final Volumes of KMnO₄**:
- At time \( t = 0 \) (start of the reaction), the volume of KMnO₄ used is \( V_0 = 37.0 \, \text{mL} \).
- After 5 minutes, the volume of KMnO₄ used is \( V_t = 29.5 \, \text{mL} \).

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