1.17 g an impure sample of oxalic acid dihydrate was dissolved and make up of 200 ml with water. 10 ml of this solution in acidic medium required 8.5 ml of a solution of potassium permanganate containing 3.16 g per litre of solution. The percentage purity of oxalic acid will be:

Options

A. 0.1265
B. 0.3578
C. 0.8276
D. 0.9154

Answer

To find the percentage purity of the impure sample of oxalic acid dihydrate, we can follow these steps:

### Step 1: Calculate the number of equivalents of potassium permanganate (KMnO4)

1. **Given data**:
- Concentration of KMnO4 solution = 3.16 g/L
- Volume of KMnO4 used = 8.5 mL

2. **Calculate the mass of KMnO4 used**:
\[ \text{Mass of KMnO4} = \text{Concentration} \times \text{Volume} = 3.16 \, \text{g/L} \times \frac{8.5 \, \text{mL}}{1000 \, \text{mL/L}} = 0.02686 \, \text{g} \]

3. **Calculate the equivalent mass of KMnO4**:
- The molar mass of KMnO4 = 158 g/mol
- The equivalent mass of KMnO4 = Molar mass / n (where n = 5 for KMnO4 in acidic medium)
\[ \text{Equivalent mass of KMnO4} = \frac{158 \, \text{g/mol}}{5} = 31.6 \, \text{g/equiv} \]

4. **Calculate the number of equivalents of KMnO4**:
\[ \text{Number of equivalents of KMnO4} = \frac{\text{Mass of KMnO4}}{\text{Equivalent mass of KMnO4}} = \frac{0.02686 \, \text{g}}{31.6 \, \text{g/equiv}} = 0.00085 \, \text{equiv} \]

### Step 2: Relate the equivalents of KMnO4 to the equivalents of oxalic acid

1. **Using the stoichiometry of the reaction**:
\[ \text{Number of equivalents of oxalic acid} = \text{Number of equivalents of KMnO4} \]
Therefore,
\[ \text{Number of equivalents of oxalic acid} = 0.00085 \, \text{equiv} \]

### Step 3: Calculate the mass of pure oxalic acid

1. **Let the mass of pure oxalic acid be \( X \)**.
2. **Equivalent mass of oxalic acid (C2H2O4·2H2O)**:
- Molar mass of oxalic acid dihydrate = 126 g/mol (C2H2O4) + 36 g/mol (2H2O) = 162 g/mol
- Equivalent mass = Molar mass / 2 = 81 g/equiv

3. **Calculate the number of equivalents of oxalic acid**:
\[ \text{Number of equivalents of oxalic acid} = \frac{X}{81} \]

4. **Set the equivalents equal**:
\[ \frac{X}{81} = 0.00085 \]

5. **Solve for \( X \)**:
\[ X = 0.00085 \times 81 = 0.06885 \, \text{g} \]

### Step 4: Calculate the percentage purity of oxalic acid

1. **Given the mass of the impure sample**:
- Mass of impure sample = 1.17 g

2. **Calculate the percentage purity**:
\[ \text{Percentage purity} = \left( \frac{\text{Mass of pure oxalic acid}}{\text{Mass of impure sample}} \right) \times 100 \]
\[ \text{Percentage purity} = \left( \frac{0.06885}{1.17} \right) \times 100 \approx 5.88\% \]

### Final Answer
The percentage purity of the oxalic acid is approximately **5.88%**.

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