Which of the following salt has the same value of Van’t Hoff factor ‘i’ as that of `K_3 [Fe (CN)_6]` ?

Options

A. `Na_2SO_4`
B. `Al(NO)_3`
C. `Al_2(SO_4)_3`
D. `NaCl`

Answer

To determine which of the given salts has the same Van't Hoff factor (i) as that of \( K_3[Fe(CN)_6] \), we need to first calculate the Van't Hoff factor for \( K_3[Fe(CN)_6] \) and then compare it with the dissociation of the other salts.

### Step-by-Step Solution:

1. **Understanding Van't Hoff Factor (i)**:
The Van't Hoff factor (i) is defined as the number of particles (ions) a compound dissociates into when it dissolves in a solution.

2. **Dissociation of \( K_3[Fe(CN)_6] \)**:
When \( K_3[Fe(CN)_6] \) dissociates in water, it breaks down into:
- 3 potassium ions (\( K^+ \))
- 1 complex ion (\( [Fe(CN)_6]^{3-} \))

Therefore, the total number of ions produced is:
\[ i = 3 + 1 = 4 \]

3. **Analyzing Other Salts**:
We will now analyze the dissociation of the given salts to find which one also gives an i value of 4.

- **\( Na_2SO_4 \)**:
\[ Na_2SO_4 \rightarrow 2Na^+ + SO_4^{2-} \]
Total ions = 2 + 1 = 3 (i = 3)

- **\( Al(NO_3)_3 \)**:
\[ Al(NO_3)_3 \rightarrow Al^{3+} + 3NO_3^- \]
Total ions = 1 + 3 = 4 (i = 4)

- **\( Al_2(SO_4)_3 \)**:
\[ Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-} \]
Total ions = 2 + 3 = 5 (i = 5)

- **\( NaCl \)**:
\[ NaCl \rightarrow Na^+ + Cl^- \]
Total ions = 1 + 1 = 2 (i = 2)

4. **Conclusion**:
The only salt that has the same Van't Hoff factor (i = 4) as \( K_3[Fe(CN)_6] \) is \( Al(NO_3)_3 \).

### Final Answer:
The salt that has the same value of Van't Hoff factor \( i \) as that of \( K_3[Fe(CN)_6] \) is **\( Al(NO_3)_3 \)**.