To determine the purity of the hydrogen peroxide (H₂O₂) sample, we will follow these steps:
### Step 1: Calculate the equivalents of KMnO₄ used in the titration.
Given:
- Volume of KMnO₄ = 10 mL = 0.01 L
- Normality of KMnO₄ = 1 N
The number of equivalents of KMnO₄ can be calculated using the formula:
\[
\text{Equivalents} = \text{Normality} \times \text{Volume (L)}
\]
\[
\text{Equivalents of KMnO₄} = 1 \, \text{N} \times 0.01 \, \text{L} = 0.01 \, \text{equivalents}
\]
### Step 2: Determine the equivalents of H₂O₂ that reacted.
In acidic medium, the reaction between KMnO₄ and H₂O₂ can be represented as:
\[
\text{H₂O₂} + \text{KMnO₄} \rightarrow \text{Products}
\]
From the stoichiometry of the reaction, 1 equivalent of KMnO₄ reacts with 1 equivalent of H₂O₂. Therefore, the equivalents of H₂O₂ that reacted are also 0.01 equivalents.
### Step 3: Calculate the mass of H₂O₂ that corresponds to the equivalents.
The equivalent weight of H₂O₂ can be calculated using its molar mass. The molar mass of H₂O₂ is approximately 34 g/mol. Since H₂O₂ is a dibasic acid (it can donate two protons), its equivalent weight is:
\[
\text{Equivalent weight of H₂O₂} = \frac{\text{Molar mass}}{n} = \frac{34 \, \text{g/mol}}{1} = 34 \, \text{g/equiv}
\]
Now, we can calculate the mass of H₂O₂ that corresponds to 0.01 equivalents:
\[
\text{Mass of H₂O₂} = \text{Equivalents} \times \text{Equivalent weight}
\]
\[
\text{Mass of H₂O₂} = 0.01 \, \text{equivalents} \times 34 \, \text{g/equiv} = 0.34 \, \text{g}
\]
### Step 4: Calculate the purity of the H₂O₂ sample.
Given that the sample of H₂O₂ is 0.2 g, the purity can be calculated as:
\[
\text{Purity (\%)} = \left( \frac{\text{Mass of H₂O₂}}{\text{Mass of sample}} \right) \times 100
\]
\[
\text{Purity (\%)} = \left( \frac{0.34 \, \text{g}}{0.2 \, \text{g}} \right) \times 100 = 170\%
\]
### Conclusion:
The calculated purity of H₂O₂ is 170%, which indicates that the sample contains more H₂O₂ than the mass of the sample itself, suggesting that there may be an error in the assumptions or the data provided.
