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.​

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.​

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+).​

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).​

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.​

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.

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.

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.

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).