Question

Which one of the following salt will have the same value of vant Hoff's factor (i) as that of $K_4[Fe(CN)_6]$ ?

• A. $Al_2(SO_4)_3$
• B. NaCl
• C. $Al(NO_3)_3$
• D. $Na_2SO_4.$

Answer 1

The Correct Option is A

To solve this question, we need to find the salt that will dissociate into the same number of ions as K_4[Fe(CN)_6], and thus have the same van't Hoff factor (\(i\)).

The van't Hoff factor (\(i\)) is defined as the number of particles the compound dissociates into in solution. Let's calculate the values for each compound:

1. K_4[Fe(CN)_6]: This compound dissociates fully into 4 K⁺ ions and one [Fe(CN)_6]^4- ion. Thus, the number of ions is 4 + 1 = 5. Therefore, \(i = 5\).
2. Al_2(SO_4)_3: This compound dissociates into 2 Al³⁺ ions and 3 SO₄^2- ions. Thus, the total number of ions is 2 + 3 = 5. Therefore, \(i = 5\).
3. NaCl: This dissociates into Na⁺ and Cl^- ions. The total number of ions is 2. Therefore, \(i = 2\).
4. Al(NO_3)_3: This compound dissociates into 1 Al³⁺ ion and 3 NO₃^- ions. The total number of ions here is 1 + 3 = 4. Therefore, \(i = 4\).
5. Na_2SO_4: This dissociates into 2 Na⁺ ions and 1 SO₄^2- ion. Hence, the total number of ions is 2 + 1 = 3. Therefore, \(i = 3\).

Comparing the values, Al_2(SO_4)_3 has the same van't Hoff factor of 5 as K_4[Fe(CN)_6]. Thus, the correct answer is Al_2(SO_4)_3.

This matches with the provided correct answer.