What is the correct order of osmotic pressure of 0.01 M aqueous solution os
(1) `Al_2(SO_4)_3`
(2) `K_3PO_4`
(3) `BaCl_2`
(4) Urea

Options

A. `pi_4 gt pi_3 gt pi_2 gt pi_1`
B. `pi_1 gt pi_2 gt pi_3 gt pi_4`
C. `pi_1 = pi_2 = pi_3 = pi_4`
D. `pi_2 gt pi_4 gt pi_1 gt pi_3`

Answer

To determine the correct order of osmotic pressure for the given 0.01 M aqueous solutions, we will analyze each compound based on its van 't Hoff factor (i), which indicates the number of particles the solute dissociates into when dissolved in solution. The osmotic pressure (π) is given by the formula:

\[ \pi = iCRT \]

Where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor
- \( C \) = concentration of the solution (0.01 M for all)
- \( R \) = universal gas constant (constant for all)
- \( T \) = temperature (constant for all)

Since \( C \), \( R \), and \( T \) are constants, the osmotic pressure is directly proportional to the van 't Hoff factor \( i \).

### Step-by-Step Solution:

1. **Calculate the van 't Hoff factor (i) for each compound:**
- **For \( Al_2(SO_4)_3 \)**:
- Dissociation: \( Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-} \)
- Total particles = 2 (from \( Al^{3+} \)) + 3 (from \( SO_4^{2-} \)) = 5
- Therefore, \( i = 5 \)

- **For \( K_3PO_4 \)**:
- Dissociation: \( K_3PO_4 \rightarrow 3K^{+} + PO_4^{3-} \)
- Total particles = 3 (from \( K^{+} \)) + 1 (from \( PO_4^{3-} \)) = 4
- Therefore, \( i = 4 \)

- **For \( BaCl_2 \)**:
- Dissociation: \( BaCl_2 \rightarrow Ba^{2+} + 2Cl^{-} \)
- Total particles = 1 (from \( Ba^{2+} \)) + 2 (from \( Cl^{-} \)) = 3
- Therefore, \( i = 3 \)

- **For Urea**:
- Urea does not dissociate in solution.
- Therefore, \( i = 1 \)

2. **List the van 't Hoff factors:**
- \( Al_2(SO_4)_3 \): \( i = 5 \)
- \( K_3PO_4 \): \( i = 4 \)
- \( BaCl_2 \): \( i = 3 \)
- Urea: \( i = 1 \)

3. **Determine the order of osmotic pressure:**
- Since osmotic pressure is directly proportional to \( i \):
- \( \pi_{Al_2(SO_4)_3} > \pi_{K_3PO_4} > \pi_{BaCl_2} > \pi_{Urea} \)

4. **Final Order:**
- The correct order of osmotic pressure is:
\[ \pi_{Al_2(SO_4)_3} > \pi_{K_3PO_4} > \pi_{BaCl_2} > \pi_{Urea} \]

### Conclusion:
The correct order of osmotic pressure for the 0.01 M aqueous solutions is:
1. \( Al_2(SO_4)_3 \) (highest)
2. \( K_3PO_4 \)
3. \( BaCl_2 \)
4. Urea (lowest)