Match the stoichiometric coefficients listed in Column II with the species listed in Column I that are involved in the balanced equation of the reaction :
`{:(,"LIST -I",,"LIST -II"),((P),FeC_(2)O_(4),(1),10),((Q),MnO_(4)^(-),(2),24),((R),H^(+),(3),5),((S),CO_(2),(4),3):}`

Options

A. `{:(P,Q,R,S),(1,2,4,3):}`
B. `{:(P,Q,R,S),(2,1,4,3):}`
C. `{:(P,Q,R,S),(4,1,3,2):}`
D. `{:(P,Q,R,S),(4,3,2,1):}`

Answer

To solve the question, we need to balance the redox reaction between iron oxalate (FeC₂O₄) and permanganate ion (MnO₄⁻) in acidic medium, and then match the stoichiometric coefficients with the species listed in the columns.

### Step-by-Step Solution:

1. **Identify the Oxidation States:**
- In iron oxalate (FeC₂O₄), iron (Fe) is in the +2 oxidation state.
- In the permanganate ion (MnO₄⁻), manganese (Mn) is in the +7 oxidation state.

2. **Determine the Changes in Oxidation States:**
- Iron (Fe) is oxidized from +2 to +3, which is a change of +1.
- Carbon in oxalate (C₂O₄²⁻) is in the +3 oxidation state (total of +6 for two carbons) and is oxidized to CO₂ (where carbon is +4), resulting in a change of +1 for each carbon. Since there are two carbons, the total change for carbon is +2.
- Manganese (Mn) is reduced from +7 to +2, which is a change of -5.

3. **Balance the Half-Reactions:**
- For the oxidation half-reaction (FeC₂O₄ to CO₂ and Fe³⁺):
- 2 FeC₂O₄ → 2 Fe³⁺ + 4 CO₂ + 2 e⁻ (total change of +5)
- For the reduction half-reaction (MnO₄⁻ to Mn²⁺):
- MnO₄⁻ + 8 H⁺ + 5 e⁻ → Mn²⁺ + 4 H₂O (total change of -5)

4. **Combine the Half-Reactions:**
- To balance the electrons, we multiply the oxidation half-reaction by 5:
- 5 (2 FeC₂O₄ → 2 Fe³⁺ + 4 CO₂ + 2 e⁻) → 10 FeC₂O₄ → 10 Fe³⁺ + 20 CO₂ + 10 e⁻
- The reduction half-reaction remains as:
- MnO₄⁻ + 8 H⁺ + 5 e⁻ → Mn²⁺ + 4 H₂O

5. **Final Balanced Equation:**
- Combining both gives us:
- 10 FeC₂O₄ + 2 MnO₄⁻ + 24 H⁺ → 10 Fe³⁺ + 20 CO₂ + 2 Mn²⁺ + 12 H₂O

6. **Identify Stoichiometric Coefficients:**
- From the balanced equation:
- FeC₂O₄ (10)
- MnO₄⁻ (2)
- H⁺ (24)
- CO₂ (20)

7. **Match the Coefficients with the Species:**
- P (FeC₂O₄) matches with 10
- Q (MnO₄⁻) matches with 2
- R (H⁺) matches with 24
- S (CO₂) matches with 20

### Final Matching:
- P (FeC₂O₄) → 10
- Q (MnO₄⁻) → 2
- R (H⁺) → 24
- S (CO₂) → 20