Concept: The acidic character of oxides depends on:
- Oxidation state of the central atom — higher oxidation state generally → more acidic.
- Electronegativity of the central atom — more electronegative → more acidic.
- Periodic trend:
- Across a period: acidity increases (due to increasing electronegativity).
- Down a group: acidity decreases (due to decreasing electronegativity and increasing size).
Analyzing Given Oxides:
- I. \( \mathrm{N_2O_5} \): Nitrogen in +5 oxidation state, very electronegative → forms strong acid \( \mathrm{HNO_3} \). ✅
- II. \( \mathrm{P_2O_5} \): Phosphorus in +5 oxidation state, less electronegative → forms moderate acid \( \mathrm{H_3PO_4} \).
- III. \( \mathrm{N_2O_3} \): Nitrogen in +3 oxidation state → forms weak acid \( \mathrm{HNO_2} \).
- IV. \( \mathrm{As_2O_3} \): Arsenic in +3 oxidation state, least electronegative → forms very weak acid \( \mathrm{H_3AsO_3} \). 🔽
Stepwise Comparisons:
- \( \mathrm{N_2O_5} > \mathrm{N_2O_3} \) → due to higher oxidation state of nitrogen.
- \( \mathrm{P_2O_5} > \mathrm{N_2O_3} \) → P has higher oxidation state (+5 vs +3), but N is more electronegative. However, acid strength data supports:
\( K_a(\mathrm{H_3PO_4}) \approx 7.5 \times 10^{-3} > K_a(\mathrm{HNO_2}) \approx 7.2 \times 10^{-4} \) ⇒ \( \mathrm{P_2O_5} > \mathrm{N_2O_3} \) - \( \mathrm{N_2O_3} > \mathrm{As_2O_3} \) → N is more electronegative than As.
Correct Order Based on Analysis:
\[ \boxed{\mathrm{N_2O_5} > \mathrm{P_2O_5} > \mathrm{N_2O_3} > \mathrm{As_2O_3}} \quad \text{(I > II > III > IV)} \]
However, Option (a) is: I > III > II > IV
This implies: \( \mathrm{N_2O_5} > \mathrm{N_2O_3} > \mathrm{P_2O_5} > \mathrm{As_2O_3} \), suggesting that the electronegativity of N is more dominant than the higher oxidation state of P.
Conclusion: Based on acid strengths of corresponding oxoacids (real-world data), the more accurate order is:
\[ \boxed{\mathrm{N_2O_5} > \mathrm{P_2O_5} > \mathrm{N_2O_3} > \mathrm{As_2O_3}} \quad \text{(I > II > III > IV)} \]
But the marked answer is: Option (a): I > III > II > IV — which prioritizes electronegativity over oxidation state in II vs III comparison.
Therefore: If we strictly follow acid strength values, option (a) is incorrect. The correct logical order is:
\[ \boxed{\text{I > II > III > IV}} \]
Note: If exam marking indicates (a) as correct, it's likely an oversimplified approach emphasizing electronegativity dominance, which is not supported by acid strength data.