For the redox reaction: `MnO_4 +C_2O_4^(2-) + H^+ rarr Mn^(2+) + CO_2 + H_2O` The number of mole of permanganate ion required per mole of oxalate ion for completion of the reaction is

Options

A. `1/5`
B. `2/5`
C. `5/2`
D. `3/5`

Answer

To determine the number of moles of permanganate ion (MnO₄⁻) required per mole of oxalate ion (C₂O₄²⁻) for the given redox reaction, we need to balance the reaction.

### Step-by-Step Solution:

1. **Identify the Oxidation States:**
- In MnO₄⁻, manganese (Mn) has an oxidation state of +7.
- In C₂O₄²⁻, carbon (C) has an oxidation state of +3.
- In Mn²⁺, manganese has an oxidation state of +2.
- In CO₂, carbon has an oxidation state of +4.

2. **Determine Changes in Oxidation States:**
- Mn changes from +7 to +2, which is a reduction of 5 electrons (7 - 2 = 5).
- Each carbon in C₂O₄²⁻ changes from +3 to +4, which means it is oxidized. Since there are 2 carbons, the total change is 2 electrons (4 - 3 = 1 for each carbon, and 1 x 2 = 2).

3. **Balance the Electrons:**
- To balance the number of electrons transferred, we need to find a common multiple of the electrons lost and gained.
- Mn gains 5 electrons, and C₂O₄²⁻ loses 2 electrons. The least common multiple of 5 and 2 is 10.
- Therefore, we need 2 moles of C₂O₄²⁻ to provide 4 electrons (2 x 2 = 4) and 5 moles of MnO₄⁻ to accept 5 x 5 = 25 electrons.

4. **Set Up the Balanced Reaction:**
- The balanced half-reactions are:
- Reduction: \( 5 \text{MnO}_4^- + 10 \text{H}^+ \rightarrow 5 \text{Mn}^{2+} + 5 \text{H}_2O \)
- Oxidation: \( 2 \text{C}_2O_4^{2-} \rightarrow 4 \text{CO}_2 + 4 \text{H}^+ + 4 \text{e}^- \)

5. **Combine the Half-Reactions:**
- The overall balanced reaction will be:
\[ 5 \text{MnO}_4^- + 2 \text{C}_2O_4^{2-} + 16 \text{H}^+ \rightarrow 5 \text{Mn}^{2+} + 4 \text{CO}_2 + 8 \text{H}_2O \]

6. **Calculate the Moles of Permanganate Ion Required:**
- From the balanced equation, we see that 5 moles of MnO₄⁻ are required for every 2 moles of C₂O₄²⁻.
- Therefore, the number of moles of permanganate ion required per mole of oxalate ion is:
\[ \frac{5 \text{ moles of MnO}_4^-}{2 \text{ moles of C}_2O_4^{2-}} = 2.5 \]

### Final Answer:
The number of moles of permanganate ion required per mole of oxalate ion for completion of the reaction is **2.5**.