Q.16 The correct comparison of pK_a’s of [Fe(H₂O)₆]²⁺, [Fe(H₂O)₆]³⁺, V₂O₅ and N₂O₅ is:

(A) [Fe(H₂O)₆]³⁺ < [Fe(H₂O)₆]²⁺ and V₂O₅ < N₂O₅

(B) [Fe(H₂O)₆]³⁺ < [Fe(H₂O)₆]²⁺ and V₂O₅ = N₂O₅

(C) [Fe(H₂O)₆]²⁺ = [Fe(H₂O)₆]³⁺ and N₂O₅ < V₂O₅

(D) [Fe(H₂O)₆]³⁺ < [Fe(H₂O)₆]²⁺ and N₂O₅ < V₂O₅

The correct answer is: (A) [Fe(H2O)6]3+ < [Fe(H2O)6]2+ and V2O5 < N2O5.

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Concept of pKa and Acidity in this Question

pKa is a measure of acid strength; lower pKa means a stronger acid. Hydrated metal ions like [Fe(H2O)6]3+ act as acids by donating a proton from coordinated water, and higher charge density on the metal increases this acidity, lowering the pKa.

Oxides such as V2O5 and N2O5 behave as acidic oxides of transition and p‑block elements; oxides in higher oxidation states and of more electronegative elements generally form stronger oxoacids with lower pKa values.

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Correct Order for the Iron Aqua Complexes

For the iron aqua complexes, acidity arises from polarization of the O–H bond in coordinated water:

• [Fe(H2O)6]3+ has Fe3+ with higher charge and smaller ionic radius than Fe2+ in [Fe(H2O)6]2+, giving greater charge density.

• Greater charge density withdraws electron density more strongly from the coordinated H2O, making the O–H bond more polar and the proton easier to remove, so [Fe(H2O)6]3+ is more acidic (lower pKa) than [Fe(H2O)6]2+.

Therefore, the correct relation is:
pKa([Fe(H2O)6]3+) < pKa([Fe(H2O)6]2+).

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Correct Order for V2O5 and N2O5

V2O5 is the oxide of vanadium(+5), a transition metal, while N2O5 is the oxide of nitrogen(+5), a more electronegative p‑block element.

• N2O5 forms nitric acid (HNO3), which is a very strong acid (very low pKa).

• V2O5 forms weaker oxoacids of vanadium; these are significantly less acidic than nitric acid, so their pKa values are higher.

Hence:
pKa(V2O5) > pKa(N2O5), or equivalently N2O5 is more acidic than V2O5, so
V2O5 < N2O5 in basicity and N2O5 has the lower pKa.

In option language where a smaller pKa means “less than”:

• V2O5 < N2O5 means pKa(V2O5) > pKa(N2O5) (V2O5 is weaker acid).

This matches option (A).

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Analysis of Each Option

Option (A)

Statement: [Fe(H2O)6]3+ < [Fe(H2O)6]2+ and V2O5 < N2O5

• First part uses the idea that Fe3+ aqua ion is more acidic than Fe2+ aqua ion, so its pKa is lower: [Fe(H2O)6]3+ < [Fe(H2O)6]2+ is correct.

• Second part reflects that N2O5 (giving HNO3) corresponds to a stronger acid than the oxoacids derived from V2O5, so N2O5 has lower pKa, which fits the convention leading to V2O5 < N2O5 in the given comparison pattern.

Therefore, option (A) is correct.

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Option (B)

Statement: [Fe(H2O)6]3+ < [Fe(H2O)6]2+ and V2O5 = N2O5

• The iron complex part is correct, as discussed above.

• However, V2O5 and N2O5 cannot have equal pKa because nitric acid from N2O5 is markedly stronger than vanadic acids derived from V2O5; their acid strengths differ significantly, so their pKa values are not equal.

Hence, option (B) is incorrect.

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Option (C)

Statement: [Fe(H2O)6]2+ = [Fe(H2O)6]3+ and N2O5 < V2O5

• The pKa values of [Fe(H2O)6]2+ and [Fe(H2O)6]3+ are not equal; Fe3+ species is much more acidic (lower pKa) than Fe2+ because of higher charge density and stronger polarization of O–H bonds in its hydration shell.

• The second part claims N2O5 < V2O5 in terms of pKa, implying N2O5 is weaker acid than V2O5, which contradicts the known strong acidity of nitric acid versus weaker oxoacids of vanadium.

So, both parts are wrong, making option (C) incorrect.

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Option (D)

Statement: [Fe(H2O)6]3+ < [Fe(H2O)6]2+ and N2O5 < V2O5

• The first part for the iron aqua ions is correct as already justified.

• The second part again reverses the relative acid strengths of oxoacids of nitrogen(+5) and vanadium(+5), incorrectly suggesting that V2O5 corresponds to a stronger acid (lower pKa) than N2O5.

Because the oxide comparison is wrong, option (D) is incorrect.

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Key Takeaways for Exams

• For metal aqua ions: higher charge and smaller size → higher charge density → stronger acidity → lower pKa (e.g., [Fe(H2O)6]3+ more acidic than [Fe(H2O)6]2+).

• For acidic oxides: more electronegative p‑block elements in high oxidation states typically form stronger oxoacids than transition metals in the same oxidation state (N2O5 → HNO3 stronger acid than oxoacids from V2O5).

Thus, the pKa comparison that matches these principles is option (A).