Assuming each salt to be completely dissociated which of the following will have highest osmotic pressure-

Options

A. Decimolar `Al_2(SO_4)_3`
B. Decimolar `BaCl_2`
C. Decimolar `Na_2SO_4`
D. A solution obtained by mixing equal volumes of (B) and (C)

Answer

To determine which solution has the highest osmotic pressure, we will use the formula for osmotic pressure (π):

\[ \pi = iCRT \]

Where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = concentration of the solution (in mol/L)
- \( R \) = universal gas constant (same for all solutions)
- \( T \) = temperature (also assumed to be the same for all solutions)

Since \( R \) and \( T \) are constant for all the solutions, we can focus on the factors \( i \) and \( C \).

### Step 1: Identify the dissociation of each salt

1. **Al₂(SO₄)₃**:
- Dissociates into 2 Al³⁺ and 3 SO₄²⁻ ions.
- Total ions = 2 + 3 = 5
- Thus, \( i = 5 \)

2. **BaCl₂**:
- Dissociates into 1 Ba²⁺ and 2 Cl⁻ ions.
- Total ions = 1 + 2 = 3
- Thus, \( i = 3 \)

3. **Na₂SO₄**:
- Dissociates into 2 Na⁺ and 1 SO₄²⁻ ions.
- Total ions = 2 + 1 = 3
- Thus, \( i = 3 \)

4. **Mixing equal volumes of BaCl₂ and Na₂SO₄**:
- From BaCl₂, \( i = 3 \) and concentration \( C = 0.1 \) M (0.1 mol/L)
- From Na₂SO₄, \( i = 3 \) and concentration \( C = 0.1 \) M (0.1 mol/L)
- When mixed, the total volume doubles, so the concentration of each will be halved (0.1 M becomes 0.05 M).
- Total \( i \) for the mixture = \( 3 + 3 = 6 \)
- Thus, for the mixture, \( i = 6 \) and \( C = 0.05 \) M.

### Step 2: Calculate osmotic pressure for each solution

1. **For Al₂(SO₄)₃**:
\[ \pi_1 = i \cdot C = 5 \cdot 0.1 = 0.5 \, \text{atm} \]

2. **For BaCl₂**:
\[ \pi_2 = i \cdot C = 3 \cdot 0.1 = 0.3 \, \text{atm} \]

3. **For Na₂SO₄**:
\[ \pi_3 = i \cdot C = 3 \cdot 0.1 = 0.3 \, \text{atm} \]

4. **For the mixture of BaCl₂ and Na₂SO₄**:
\[ \pi_4 = i \cdot C = 6 \cdot 0.05 = 0.3 \, \text{atm} \]

### Step 3: Compare the osmotic pressures

- \( \pi_1 = 0.5 \, \text{atm} \) (Al₂(SO₄)₃)
- \( \pi_2 = 0.3 \, \text{atm} \) (BaCl₂)
- \( \pi_3 = 0.3 \, \text{atm} \) (Na₂SO₄)
- \( \pi_4 = 0.3 \, \text{atm} \) (Mixture of BaCl₂ and Na₂SO₄)

### Conclusion

The solution with the highest osmotic pressure is from **Al₂(SO₄)₃**, with an osmotic pressure of **0.5 atm**.