A 0.5 g sample containing `MnO_(2)` is treated with HCl liberating `Cl_(2)` is passed into a solution of KI and 30.0 " mL of " 0.1 M `Na_(2)S_(2)O_(3)` are required to titrate the liberated iodine. Calculate the percentage of `MnO_(2)` is the sample.

Explanation

To solve the problem step by step, we will follow the reactions and calculations involved in determining the percentage of \( \text{MnO}_2 \) in the sample.

### Step 1: Write the reaction of \( \text{MnO}_2 \) with HCl
When \( \text{MnO}_2 \) reacts with hydrochloric acid (HCl), the reaction can be written as:
\[ \text{MnO}_2 + 4 \text{HCl} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + 2 \text{H}_2\text{O} \]
This reaction shows that one mole of \( \text{MnO}_2 \) produces one mole of \( \text{Cl}_2 \).
...