8.7gm of pyrolusite (impure `MmO_(2)`) were heated with concentrated HCl. The `Cl_(2)` gas evolved was passed through excess of KI solution. The iodine gas evolved required 80ml of `(N)/(10)` hypo solution.
The precentage of `MnO_(2)` in pyrolusite will be : `[Mn=55]`

Options

A. 0.04
B. 0.4
C. 0.08
D. 0.8

Answer

To find the percentage of MnO2 in pyrolusite, we will follow these steps:

### Step 1: Write the Reaction
When pyrolusite (MnO2) reacts with concentrated HCl, the reaction can be represented as:
\[ \text{MnO}_2 + 4 \text{HCl} \rightarrow \text{MnCl}_2 + \text{Cl}_2 + 2 \text{H}_2\text{O} \]

### Step 2: Determine the Moles of Hypo Used
Given that 80 mL of \( \frac{N}{10} \) hypo solution was used, we can calculate the equivalents of hypo (Na2S2O3):
- Normality (N) = \( \frac{1}{10} \)
- Volume = 80 mL = 0.080 L

Using the formula for equivalents:
\[ \text{Equivalents of hypo} = \text{Normality} \times \text{Volume in L} = \frac{1}{10} \times 0.080 = 0.008 \text{ equivalents} \]

### Step 3: Relate Equivalents of MnO2 to Hypo
From the stoichiometry of the reactions, we know:
\[ \text{Equivalents of MnO}_2 = \text{Equivalents of Cl}_2 = \text{Equivalents of hypo} \]
Thus, the equivalents of MnO2 is also 0.008.

### Step 4: Calculate the Mass of MnO2
The equivalent weight of MnO2 can be calculated as follows:
- Molecular weight of MnO2 = 55 (Mn) + 32 (O2) = 87 g/mol
- N-factor of MnO2 = 2 (since Mn goes from +4 in MnO2 to +2 in MnCl2)

Using the formula for equivalents:
\[ \text{Equivalents} = \frac{\text{mass}}{\text{equivalent weight}} \]
Thus, we can rearrange to find the mass:
\[ \text{mass of MnO}_2 = \text{Equivalents} \times \text{Equivalent weight} = 0.008 \times 87 = 0.696 \text{ g} \]

### Step 5: Calculate the Percentage of MnO2 in Pyrolusite
The total mass of the pyrolusite sample is given as 8.7 g. The percentage of MnO2 can be calculated as:
\[ \text{Percentage of MnO}_2 = \left( \frac{\text{mass of MnO}_2}{\text{mass of pyrolusite}} \right) \times 100 = \left( \frac{0.696}{8.7} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage of MnO}_2 \approx 8\% \]

### Final Answer
The percentage of MnO2 in pyrolusite is approximately **8%**.

---