The number of moles of `KMnO_(4)` that will be needed to react with one mole of sulphite ion in acidic solution is

Options

A. 1
B. `(3)/(5)`
C. `(4)/(5)`
D. `(2)/(5)`

Answer

To determine the number of moles of \( KMnO_4 \) needed to react with one mole of sulfite ion (\( SO_3^{2-} \)) in an acidic solution, we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction between potassium permanganate and sulfite ions in acidic solution is:

\[ 2MnO_4^- + 5SO_3^{2-} + 6H^+ \rightarrow 2Mn^{2+} + 5SO_4^{2-} + 3H_2O \]

### Step 2: Analyze the stoichiometry of the reaction
From the balanced equation, we can see that:
- 2 moles of \( MnO_4^- \) react with 5 moles of \( SO_3^{2-} \).

### Step 3: Determine the moles of \( KMnO_4 \) needed for 1 mole of \( SO_3^{2-} \)
To find out how many moles of \( KMnO_4 \) are needed for 1 mole of \( SO_3^{2-} \), we set up a proportion based on the stoichiometry from the balanced equation:

\[ \text{If } 5 \text{ moles of } SO_3^{2-} \text{ require } 2 \text{ moles of } MnO_4^-, \]
\[ \text{Then } 1 \text{ mole of } SO_3^{2-} \text{ will require } x \text{ moles of } MnO_4^-. \]

Using the ratio:
\[ \frac{2 \text{ moles of } MnO_4^-}{5 \text{ moles of } SO_3^{2-}} = \frac{x \text{ moles of } MnO_4^-}{1 \text{ mole of } SO_3^{2-}} \]

### Step 4: Solve for \( x \)
Cross-multiplying gives:
\[ x = \frac{2 \times 1}{5} = \frac{2}{5} \text{ moles of } MnO_4^-. \]

### Step 5: Conclusion
Since \( KMnO_4 \) dissociates to give \( MnO_4^- \), the number of moles of \( KMnO_4 \) needed to react with 1 mole of sulfite ion in acidic solution is also \( \frac{2}{5} \) moles.

### Final Answer
The number of moles of \( KMnO_4 \) needed to react with one mole of sulfite ion in acidic solution is \( \frac{2}{5} \) moles.

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