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 are used.

### Step-by-Step Solution:

1. **Write the Balanced Reaction:**
The reaction between permanganate ions and thiosulfate ions can be represented as:
\[ \text{MnO}_4^- + \text{S}_2\text{O}_3^{2-} + \text{H}_2\text{O} \rightarrow \text{MnO}_2 + \text{SO}_4^{2-} + \text{OH}^- \]
This equation shows that permanganate ions oxidize thiosulfate ions to produce manganese dioxide (MnO2), sulfate ions (SO4^2-), and hydroxide ions (OH^-).

2. **Balance the Reaction:**
To balance the reaction, we need to ensure that the number of each type of atom is the same on both sides. The balanced equation is:
\[ 8\text{MnO}_4^- + 3\text{S}_2\text{O}_3^{2-} \rightarrow 8\text{MnO}_2 + 6\text{SO}_4^{2-} + 2\text{OH}^- \]
From this balanced equation, we can see that 8 moles of permanganate ions react with 3 moles of thiosulfate ions to produce 6 moles of sulfate ions.

3. **Determine the Ratio:**
From the balanced equation, we can derive the ratio of permanganate ions to sulfate ions:
\[ 8 \text{ moles of } \text{MnO}_4^- \rightarrow 6 \text{ moles of } \text{SO}_4^{2-} \]
This means that for every 8 moles of permanganate ions, 6 moles of sulfate ions are produced.

4. **Calculate the Moles of Sulfate from 4 Moles of Permanganate:**
We need to find out how many moles of sulfate ions are produced from 4 moles of permanganate ions. Using the ratio derived from the balanced equation:
\[ \text{Moles of } \text{SO}_4^{2-} = \left(\frac{6 \text{ moles of } \text{SO}_4^{2-}}{8 \text{ moles of } \text{MnO}_4^-}\right) \times 4 \text{ moles of } \text{MnO}_4^- \]
Simplifying this gives:
\[ \text{Moles of } \text{SO}_4^{2-} = \frac{6}{8} \times 4 = \frac{3}{2} \times 4 = 3 \text{ moles of } \text{SO}_4^{2-} \]

5. **Conclusion:**
Therefore, when 4 moles of permanganate ions are used, 3 moles of sulfate ions are produced. Thus, the value of X is:
\[ X = 3 \]