Hydrogen peroxide solution was stored in a mild steel vessel. It was found, however, that the hydrogen peroxide decomposed on the walls of the vessel (a first order reaction). An experiment with 100 ml of a solution gave 10.31 ml oxygen (corrected to 1 atm & 273 K) after 5.1 days under similar storage conditions. Find how long the peroxide can be stored before the loss of 20.00 ml oxygen occurs (per 100 ml solution) if complete decomposition of the sample to `H_(2)O_(2)` gave 46.34 ml oxygen.

Explanation

To solve the problem step by step, we will follow the principles of first-order kinetics and the stoichiometry of the decomposition reaction of hydrogen peroxide (H₂O₂).

### Step-by-Step Solution:

1. **Understand the Reaction**:
The decomposition of hydrogen peroxide can be represented as:
\[
2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2
...