Which one of the following salts will have the same value of van't hoff factor (i) as that of `K_(4)[Fe(CN)_(6)]`?

Options

A. `Na_(2)SO_(4)`
B. `Al(NO_(3))_(3)`
C. `NaCl`
D. `Al(SO)_(3)`

Explanation

To determine which salt has the same van't Hoff factor (i) as that of \( K_4[Fe(CN)_6] \), we need to analyze how each salt dissociates into ions in solution.

### Step-by-Step Solution:

1. **Identify the dissociation of \( K_4[Fe(CN)_6] \)**:
- \( K_4[Fe(CN)_6] \) dissociates into:
\[ 4K^+ + [Fe(CN)_6]^{4-} \]
- This results in a total of:
\[ 4 + 1 = 5 \text{ ions} \]
- Therefore, the van't Hoff factor \( i \) for \( K_4[Fe(CN)_6] \) is 5.

2. **Analyze the dissociation of \( Na_2SO_4 \)**:
- \( Na_2SO_4 \) dissociates into:
\[ 2Na^+ + SO_4^{2-} \]
- This results in a total of:
\[ 2 + 1 = 3 \text{ ions} \]
- Thus, \( i = 3 \).

3. **Analyze the dissociation of \( Al(NO_3)_3 \)**:
- \( Al(NO_3)_3 \) dissociates into:
\[ Al^{3+} + 3NO_3^{-} \]
- This results in a total of:
\[ 1 + 3 = 4 \text{ ions} \]
- Thus, \( i = 4 \).

4. **Analyze the dissociation of \( NaCl \)**:
- \( NaCl \) dissociates into:
\[ Na^+ + Cl^- \]
- This results in a total of:
\[ 1 + 1 = 2 \text{ ions} \]
- Thus, \( i = 2 \).

5. **Analyze the dissociation of \( Al_2(SO_4)_3 \)**:
- \( Al_2(SO_4)_3 \) dissociates into:
\[ 2Al^{3+} + 3SO_4^{2-} \]
- This results in a total of:
\[ 2 + 3 = 5 \text{ ions} \]
- Thus, \( i = 5 \).

6. **Conclusion**:
- The only salt that has the same van't Hoff factor \( i = 5 \) as \( K_4[Fe(CN)_6] \) is \( Al_2(SO_4)_3 \).

### Final Answer:
The salt that has the same value of van't Hoff factor (i) as that of \( K_4[Fe(CN)_6] \) is \( Al_2(SO_4)_3 \).