Question

Which of the following salts of same concentration will have the same value of van't Hoff factor as that of \( K_4[Fe(CN)_6] \)?

• A. \( \text{Na}_2\text{SO}_4 \)
• B. \( \text{MgSO}_4 \)
• C. \( \text{Al}_2(\text{SO}_4)_3 \)
• D. \( \text{Al(NO}_3\text{)}_3 \)

Hint:

The van't Hoff factor is important when considering the dissociation of salts in solution. It is equal to the number of ions produced by dissociation.

Answer 1

The Correct Option is C

Step 1: Understanding van't Hoff factor.
The van't Hoff factor \( i \) is the number of particles into which a compound dissociates in solution. The dissociation of salts in solution gives the following van't Hoff factors: - \( K_4[Fe(CN)_6] \) dissociates into 5 ions, so its \( i = 5 \). - \( \text{Na}_2\text{SO}_4 \) dissociates into 3 ions, so its \( i = 3 \). - \( \text{MgSO}_4 \) dissociates into 2 ions, so its \( i = 2 \). - \( \text{Al}_2(\text{SO}_4)_3 \) dissociates into 5 ions, so its \( i = 5 \). Thus, \( \text{Al}_2(\text{SO}_4)_3 \) has the same van't Hoff factor as \( K_4[Fe(CN)_6] \).
Step 2: Analyzing the options.
(A) \( \text{Na}_2\text{SO}_4 \): Incorrect. This salt dissociates into 3 ions.
(B) \( \text{MgSO}_4 \): Incorrect. This salt dissociates into 2 ions.
(C) \( \text{Al}_2(\text{SO}_4)_3 \): Correct — This salt dissociates into 5 ions, giving the same van't Hoff factor as \( K_4[Fe(CN)_6] \).
(D) \( \text{Al(NO}_3\text{)_3 \):} Incorrect. This salt dissociates into 4 ions.
Step 3: Conclusion.
The correct answer is (C) \( \text{Al}_2(\text{SO}_4)_3 \), as it has the same van't Hoff factor as \( K_4[Fe(CN)_6] \).