Which of the following salts would have the same value of the van’t Hoff factor as that of Al(NO3)3 in aqueous solution?
Assume complete dissociation of electrolytes.
(A) K2SO4
(B) KCl
(C) Al2(SO4)3
(D) K3[Fe(CN)6]
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (D) only
The van’t Hoff factor (i) tells how many particles one formula unit gives in solution. For a strong electrolyte that dissociates completely, i equals the total number of ions formed. A complex ion written inside square brackets stays together as one ion.
For the reference salt:
\( \displaystyle \ce{Al(NO3)3 -> Al^3+ + 3NO3^-} \quad i=4 \)
(A) K2SO4 — Incorrect. It gives 2 + 1 = 3 ions, so i = 3.
\( \displaystyle \ce{K2SO4 -> 2K^+ + SO4^2-} \)
(B) KCl — Incorrect. It gives 1 + 1 = 2 ions, so i = 2.
\( \displaystyle \ce{KCl -> K^+ + Cl^-} \)
(C) Al2(SO4)3 — Incorrect. It gives 2 + 3 = 5 ions, so i = 5.
\( \displaystyle \ce{Al2(SO4)3 -> 2Al^3+ + 3SO4^2-} \)
(D) K3[Fe(CN)6] — Correct. The complex ion stays as one ion, so the salt gives 3 + 1 = 4 ions and i = 4, the same as for \( \ce{Al(NO3)3} \).
\( \displaystyle \ce{K3[Fe(CN)6] -> 3K^+ + [Fe(CN)6]^3-} \)