In faintly alkaline solution, 4 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of sulphate anion. The value of X

Options

A. 8
B. 6
C. 4
D. 3

Answer

To solve the problem, we need to understand the reaction between permanganate ions (MnO4^-) and thiosulfate ions (S2O3^2-) in a faintly alkaline solution. The goal is to determine how many moles of sulfate ions (SO4^2-) are produced when 4 moles of permanganate ions oxidize thiosulfate ions.

### Step-by-Step Solution:

1. **Identify the Oxidation States**:
- In permanganate (MnO4^-), manganese has an oxidation state of +7.
- In sulfate (SO4^2-), sulfur has an oxidation state of +6.
- In thiosulfate (S2O3^2-), we need to calculate the oxidation states of sulfur.

2. **Calculate the Oxidation State of Sulfur in Thiosulfate**:
- The formula for thiosulfate is S2O3^2-. Let the oxidation state of sulfur be x.
- The equation for the oxidation state is:
\[ 2x + 3(-2) = -2 \]
\[ 2x - 6 = -2 \implies 2x = 4 \implies x = +2 \]
- Thus, the oxidation state of sulfur in thiosulfate is +2.

3. **Determine the Change in Oxidation State**:
- The sulfur in thiosulfate (S2O3^2-) is oxidized from +2 to +6 (in sulfate).
- The change in oxidation state for one sulfur atom is:
\[ +6 - (+2) = +4 \]
- Since there are two sulfur atoms in thiosulfate, the total change for thiosulfate is:
\[ 2 \times 4 = 8 \]

4. **Determine the Change in Manganese Oxidation State**:
- The manganese in permanganate (MnO4^-) is reduced from +7 to +4.
- The change in oxidation state for manganese is:
\[ +4 - (+7) = -3 \]

5. **Balance the Reaction**:
- For every 8 moles of electrons lost by thiosulfate, 3 moles of electrons are gained by permanganate.
- Therefore, the stoichiometry of the reaction can be established:
\[ 8 \text{ moles of S2O3^2-} \text{ react with } 2 \text{ moles of MnO4^-} \]
- This means that 4 moles of MnO4^- will react with:
\[ \frac{8}{2} \times 4 = 16 \text{ moles of thiosulfate} \]

6. **Determine the Moles of Sulfate Produced**:
- Each mole of thiosulfate produces 1 mole of sulfate when oxidized.
- From the stoichiometry, if 4 moles of MnO4^- oxidize thiosulfate, we find how many moles of sulfate are produced:
\[ 4 \text{ moles of MnO4^-} \text{ produce } 3 \text{ moles of SO4^2-} \]

7. **Final Calculation**:
- Therefore, the value of X, which represents the moles of sulfate produced, is:
\[ X = 3 \]

### Conclusion:
The value of X is **3 moles of sulfate anion** produced.